Research ArticlePower Flows and Efficiency of Output Compound e-CVT

Francesco Bottiglione and Giacomo Mantriota

Dipartimento di Meccanica Matematica e Management Politecnico di Bari Viale Japigia 182 70125 Bari Italy

Correspondence should be addressed to Giacomo Mantriota giacomomantriotapolibait

Received 9 April 2015 Revised 15 July 2015 Accepted 20 August 2015

Academic Editor Shankar Subramanian

Copyright copy 2015 F Bottiglione and G Mantriota This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Hybridization is themost promising vehicular technology to get significant improvements of the vehicle efficiency and performancein the short-term Mechanical transmissions for hybrid vehicles are very often multiple modes transmission which permitimproving the performance in different working conditions In this context optimal design and control of these transmissions area key point to improve the performance of the vehicles and mathematical models which supports the design can play an importantrole in this field In this work an approach for evaluating the performance ofOutput Compound Split e-CVT (electric ContinuouslyVariable Transmission) in steady-state is proposed This approach in addition to a kinematic analysis of the device leads to thecalculation of the internal power circulation modes and the efficiency of the device in different working conditions

1 Introduction

Hybrid Electric Vehicles (HEVs) represent one of the mostpromising fuel-saving technologies in the short-term forimproving fuel economy of ground vehicles [1] Due totheir significant potential in reducing fuel consumption andemissions many car companies now actively develop HEVsHybrid vehicles work in several operating conditions fullelectric condition charging of battery condition stationarycondition recovering of the energy from brakes conditionThe operating mode control strategy is of great importanceto take the best from the HEV [2ndash6]

Because of the multiple power sources of the HEVstransmissions with multiple ports are often employed asfor example the Power Split Continuously Variable Trans-missions (PS-CVT) Among these the Input Split type hasgood efficiency in the overall shifting range For this reasonit is the most suitable power split system for single modehybrid powertrains However single mode powertrains ofInput Split type show low efficiency at high vehicle speeds [7ndash9] In dual mode powertrains the power split type is selectedamong the two engaging and disengaging a clutch [10ndash15]The use of two modes overcomes the problems of the singlemode powertrain providing better vehicle performance interms of fuel economy acceleration and motor size In fact

multiple-port multiple-mode transmissions permit reducingthe power through the electrical path of which the typicalefficiency is 75 and increasing the power through the moreefficientmechanical path (95) thus increasing the efficiencyof the overall vehicle powertrain [14 15]

Besides the input power split CVT there are severalmore complex solutions based on the use of at least twoepicyclical gear trains and one ormore locking systemsThesesolutions can be classified as compound type power splitand examples are given by the devices developed by AllisonTimken Renault and Toyota and by the GMDaimlerBMWjoint project calledGlobalHybrid Cooperation [16] A propermodeling and simulation tool is very important in theearly design and analysis stage This is even more criticalfor the Compound Split Power Split Electric CVTs (e-CVTs) since there could be numerous possible configura-tionscomponents and various control strategies [17ndash21]

PS-CVTs have been studied inmanyworks with focus onthe efficiency and the development of original types [22ndash26]It has been demonstrated that a fuel economy improvementcan be obtained through a PS-CVT in vehicles with internalcombustion engine [27] Depending on the location of thePG drive they can be distinguished in Output Split (orinput coupled) and Input Split (or output coupled) devicesFurthermore depending on the ratio range of the PS-CVT

Hindawi Publishing CorporationInternational Journal of Vehicular TechnologyVolume 2015 Article ID 136437 12 pageshttpdxdoiorg1011552015136437

2 International Journal of Vehicular Technology

13

5

2

4

6

Input

Output

PGII

PGI

e-CVT

(a)

13

5

2

4

6

Input

Output

PGII

PGI

e-CVT

(b)

Figure 1 Schematic picture of the Output Compound Split Transmission (a) and Input Compound Split Transmission (b)

and of the Continuously Variable Transmission differentinternal power flows may be established which affects theratio between the power through the CVT branch and thepower transmitted by the device

In hybrid vehicles during the recovery of energy inbraking the transmission works in reverse mode and it hasbeen shown that the efficiency in reverse mode is sometimescritically lower than the efficiency in direct mode [22]

Compound Split Transmission uses two motorgenera-tors as variator (eCVT) as well as one or several planetarygear sets as power split device These architectures can workin two different modes by searching for the best globalefficiency in the different operating conditions

A simple approach would be useful to determine theperformance of compoundElectric CVT in order to optimizethe control strategy and then the performance of hybridvehicles [26]

Following this approach it would be possible to predictthe power flows of the transmission and its efficiency Opti-mal control strategies of hybrid vehicles are very importantSeveral studies were carried out in considering the designefficiency and mathematical models for the control strategyThe focus of these surveys is the fuel consumption and theperformance of the hybrid vehicle

In this work a method to evaluate the power flows andthe efficiency of Output Compound Split Transmission isproposed (Figure 1(a)) The Output Compound architectureis made of a planetary gear (PGI) input shaft and an e-CVTconnected by a second planetary gear (PGII) (Figure 1(a))For the first time the Output Compound architecture is herestudied by separating the system into two subsystems Fol-lowing this approach the Output Compound is made of twonested shunted CVT systems of Input or Output Split typeto be analyzed through a previously developed approach Itfollows that after having imposed the requested ratio rangesthe power circulation modes are easily found and also theefficiency can be easily calculated It can be observed thatthe reverse operation of the Output Compound Split system

is closely related to the Input Compound Split (Figure 1(b))that one of the authors has studied in a previous work Suchoperational conditions are typical of the regenerative brakingwhere the power flows backwards with respect to the normaloperation mode of the transmission As it is shown in aprevious work the efficiency of the Power Split Transmissionis very different in reverse operation in comparison to directoperation For this reason in this work the efficiency ofthe Output Split transmission will be investigated and acomparison between the direct and the reverse operationswill be achieved

2 Kinematics of Output CompoundSplit Transmission

A compound power split is made of a continuously variabledrive which can be of mechanical type (CVT) or with twomotorsgenerators working as electrical CVT (e-CVT) aswell as one or several planetary gear sets They can be clas-sified into three different types Input Split Output Split andCompound Split The Input and Output Split configurationshave only one planetary gear operating as a power splitdevice In the Compound Split Transmission the planetarygears are two ormore Hereafter we will consider CompoundSplit Transmissions with two planetary gear sets (PGI andPGII) Many different combinations can be achieved withdifferent arrangements of the connections between all theelements of the transmission Among all possibilities the twomost diffused are shown in Figure 1 the Output CompoundSplit Transmission (Figure 1(a)) and the Input CompoundSplit Transmission (Figure 1(b)) The Input Compound SplitTransmission was studied in a previous work of one of theauthors (G Mantriota) In the present work the OutputCompound Split Transmission is investigatedThese configu-rations can be considered one the reverse mode operations ofthe other Since the object of our study is a ContinuouslyVari-able Unit (CVU)made with a Compound Split Transmissionhereafter we will refer to this with the acronym CVU

International Journal of Vehicular Technology 3

Derivation of the main kinematic relations for the Out-put Compound Split Transmission (Figure 1(a)) follows Bydefining 119896

1and 119896

2the gear ratios of the planetary gears PG1

and PG2 respectively the following algebraic equations hold

1205965+ 11989611205961minus (1 + 119896

1) 1205963= 0 (1)

120596119900+ 11989621205966minus (1 + 119896

2) 1205962= 0 (2)

where 120596119895is the angular speed of the 119895th path

The speed ratio of the compound transmission 120591CVU andthe speed ratio of the eCVT are

120591CVU =120596119900

120596119894

120591ECVT =1205965

1205964

(3)

where 120596119894 120596119900are the angular velocities of the input and the

output shafts of the CVU From (1)ndash(3) and observing that1205963= 120596119894= 1205966and 120596

1= 1205962= 1205964(Figure 1(a)) the speed ratio

of the CVU is obtained

120591CVU =1 + 1198961+ 1198962(1 minus 120591ECVT)

120591ECVT + 1198961 (4)

Making the derivative of (4) with respect to 120591ECVT

119889120591CVU119889120591ECVT

= minus1198961+ 1198962+ 11989621198961

(120591ECVT + 1198961)2 (5)

then the CVU speed ratio is always a monotonic functionsince the sign of the derivate (5) does not change if 120591ECVTchanges

If one desires specific minimum (120591CVU119898) and maximum(120591CVU119872) values of the global speed ratio with given 120591ECVT119898and 120591ECVT119872 it is possible to calculate 1198961 and 1198962 as the uniquesolution of a system of two equations with two unknownsIn fact if 120591CVU is supposed to be a monotonic increasingfunction of 120591ECVT then the following system of equations canbe written

1198961(120591CVU119872 minus 1) + 1198962 (120591ECVT119872 minus 1) + 120591CVU119872120591ECVT119872

minus 1 = 0

1198961(120591CVU119898 minus 1) + 1198962 (120591ECVT119898 minus 1) + 120591CVU119898120591ECVT119898

minus 1 = 0

(6)

From it it follows that

1198961=(120591CVU119872120591ECVT119872 minus 1) (1 minus 120591ECVT119898) minus (120591CVU119898120591ECVT119898 minus 1) (1 minus 120591ECVT119872)

(120591CVU119872 minus 1) (120591ECVT119898 minus 1) minus (120591CVU119898 minus 1) (120591ECVT119872 minus 1)

1198962=(120591CVU119872120591ECVT119872 minus 1) (1 minus 120591CVU119898) minus (120591CVU119898120591ECVT119898 minus 1) (1 minus 120591CVU119872)

(120591CVU119898 minus 1) (120591ECVT119872 minus 1) minus (120591CVU119872 minus 1) (120591ECVT119898 minus 1)

(7)

Then the values of the parameters 1198961and 1198962of the planetary

gears depend only on the limits imposed of 120591ECVT and 120591CVU1198961and 119896

2can also be obtained in case that 120591CVU is

supposed to be a monotonic decreasing function of 120591ECVT

1198961=(120591CVU119872120591ECVT119898 minus 1) (1 minus 120591ECVT119872) minus (120591CVU119898120591ECVT119872 minus 1) (1 minus 120591ECVT119898)

(120591CVU119872 minus 1) (120591ECVT119872 minus 1) minus (120591CVU119898 minus 1) (120591ECVT119898 minus 1)

1198962=(120591CVU119872120591ECVT119898 minus 1) (1 minus 120591CVU119898) minus (120591CVU119898120591ECVT119872 minus 1) (1 minus 120591CVU119872)

(120591CVU119898 minus 1) (120591ECVT119898 minus 1) minus (120591CVU119872 minus 1) (120591ECVT119872 minus 1)

(8)

In conclusion the values of 120591CVU corresponding to workingconditions with zero power through the eCVT (mechanicalpoints) are obtained from (4) with 120596

5= 0 (corresponding to

120591ECVT = infin) or 1205964 = 0 (which corresponds to 120591ECVT = 0)

120591ICVU = minus1198962

120591IICVU =1 + 1198961+ 1198962

1198961

(9)

3 Power Flow and Efficiency ofOutput Compound e-CVT

In order to investigate the power flows and the efficiency ofthe Output Compound Split (Figure 1(a)) the overall systemis divided into a subcomponent (Equivalent e-CVT) and thesecond planetary gear PGII (Figure 2(a)) The Equivalent e-CVT is made of the e-CVT and the PGI (Figure 2(b))

4 International Journal of Vehicular Technology

3

26

Equivalent

Input

Output

PGII

e-CVT

(a)

1

54

3

2

Equivalent

PGI

e-CVT

e-CVT

(b)

Figure 2 (a) Schematic picture of the Output Compound with the ldquoEquivalent e-CVTrdquo (b) Equivalent e-CVT

The scheme of Figure 2(a) is also an Output Split (OS)where the Continuously Variable Transmission is replacedwith the Equivalent e-CVT

For this architecture we define

120591ECVTeq =1205963

1205962

(10)

From (2)-(3) and (10) and considering 1205963= 1205966= 120596119894

(Figure 2(a)) it follows that

120591ECVTeq =120591ECVT + 11989611 + 1198961

(11)

The transmission ratio in (11) depends only on the values ofthe parameter 119896

1of the PGI and it is a monotonic function

From (2) (3) and (11) the CVU speed ratio is obtained as afunction of the Equivalent e-CVT speed ratio

120591CVU =1 + 1198962(1 minus 120591ECVTeq)

120591ECVTeq (12)

It has been demonstrated that in the case of an OutputSplit (OS) (Figure 2(a)) a Type I power flow is obtainedif |120591CVU| = |120596119900120596119894| is a monotonic increasing function of|120591ECVT| = |12059651205964| whereas Type II power flow is obtainedfor a monotonic decreasing function

In the case of Input Split the power flows are the oppositewith respect to the Output Split This means that a TypeI power flow can be obtained by imposing a monotonicdecreasing trend of |120591CVU| = |120596119900120596119894| in function of |120591ECVT| =|12059651205964| whereas a Type II power flow is achieved if the

function has a monotonic increasing trendNow the power flows in the CVU can be analyzed as

they are obtained as combinations of the power flows in theOutput Split and Equivalent e-CVTThe power circulation inthe compound depends only on whether the speed ratios ofthe CVU and Equivalent e-CVT are increasing or decreasingfunctions of Equivalent e-CVT and e-CVT respectively

If a monotonic increase of 120591CVU as a function of 120591ECVTeqis considered a Type I power flow (Figure 3(b)) is obtainedthat is the power through the PGII is greater than the inputpower In this condition the Equivalent e-CVT is in anOutput Split If 120591ECVTeq is an increasing function of 120591ECVTthen a Type I power flow is obtained also in the Equivalent e-CVT (Figure 3(c)) Therefore this kind of power circulationshown in Figure 3(a) is named Type II power flow In theType II power flow also the overall speed ratio 120591CVU is amonotonic increasing function of 120591ECVT In order to achievethe Type II power flow (7) must be used to calculate the gearratios 119896

1and 1198962of the planetary gear trains

If 120591ECVTeq is a decreasing function of 120591ECVT a power flowof Type II is obtained in the Equivalent e-CVT (Figure 4(c))that is the power through the e-CVT is greater than the inputpower of the Equivalent e-CVT Hence with a monotonicincrease of 120591CVU as a function of 120591ECVTeq (Figure 4(b))a power flow named Type III (Figure 4(a)) is obtainedby imposing that 120591CVU is a decreasing function of 120591ECVTTherefore Type III power flow is obtained solving (8) to findthe parameters 119896

1and 1198962of the planetary gear trains

If 120591CVU is a decreasing function 120591ECVTeq (Figure 5(b))the Equivalent e-CVT is in the Input Split (IS) configuration(Figure 5(c)) and Type I power flow occurs when 120591ECVTeq isan increasing function of 120591ECVT Therefore considering thewhole transmission a Type III power flow occurs if 120591CVU isa decreasing function of 120591ECVT (Figure 5(a)) Hence Type IIIpower flow is achieved when (8) are solved to obtain 119896

1and

1198962If 120591CVU is a decreasing function of 120591ECVTeq and 120591ECVTeq

is a decreasing function of 120591ECVT Type IIII power flowoccurs in the Output Compound Split (Figure 6(a)) Thenthe power flow in Figure 6(a) occurs when 120591CVU increaseswith increasing 120591ECVT

In conclusion with (7) Type II and Type IIII are the twopossible power flows that occur in the transmission On thecontrary Type III andType III power flows are achievedwith(8)

International Journal of Vehicular Technology 5

13

5

2

4

6

Output compoundType II power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type I power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type I power flow

e-CVT

e-CVT

PGI

(c)

Figure 3 Power flows in a Compound Split e-CVT with Type II power flow (a) Output Compound Split e-CVT (b) The Output Split withEquivalent e-CVT and Type I power flow and (c) the Equivalent e-CVT with Type I power flow

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type I power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type II power flow

PGI

e-CVT

e-CVT

(c)

Figure 4 Power flows in a Compound Split e-CVT with Type III power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type I power flow and (c) the Equivalent e-CVT with Type II power flow

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type II power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type I power flow

PGI

e-CVT

e-CVT

(c)

Figure 5 Power flows in a Compound Split e-CVT with Type III power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type II power flow and (c) the Equivalent e-CVT with Type I power flow

6 International Journal of Vehicular Technology

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type II power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type II power flow

PGI

e-CVT

e-CVT

(c)

Figure 6 Power flows in a Compound Split e-CVT with Type IIII power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type II power flow and (c) the Equivalent e-CVT with Type II power flow

Finally in agreement with the considerations suggestedin [21] if the following inequality is verified

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)lt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (13)

the Type II or Type III are the working conditions of thetransmission On the contrary if

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)gt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (14)

the Type III or Type IIII are established in the CVUFor the efficiency of Output Compound Split Transmis-

sion the approach is based upon the assumption that onlythe losses in the e-CVT are considered This assumption isgenerally accepted because the efficiency 120578ECVT of the e-CVT is very low (eg an electric motor-generator) comparedwith the other componentsThis condition is named the ldquorealsystemrdquo

The Output Compound Split Transmission with powerflow of Type II is considered (Figure 3(a)) Both the idealsystem (without losses) and the real system are analyzed andcompared to each other For given kinematic conditions (120596

119894

120591ECVT) and output torque 119879119900 the ratios of the torques of

PGII shaft (branches ldquo2rdquo and ldquo6rdquo) are fixed and so the ratiosbetween powers are also determined This means that thepowers in the branches ldquo2rdquo (119875

2) and ldquo6rdquo (119875

6) have the same

value in the ideal and the real systemOn the other hand the input power and the power of

branch 3 are different in the ideal system and in the realsystem In the real system because of the power loss of thee-CVT the input power 119875in is increased and the power 119875

3is

decreased

It has been demonstrated in [28] that the ratio given bythe power through the e-CVT branch divided by the inputpower of the overall CVU can be easily calculated (underthe assumption of negligible power loss) relying only on thesystem kinematics

10038161003816100381610038161003816100381610038161003816

119875ECVT119875in

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

119889120591CVU119889120591ECVT

120591ECVT120591CVU

10038161003816100381610038161003816100381610038161003816 (15)

Equation (15) is general and therefore it can be applied tothe Compound Split Transmission as well as the Equivalent e-CVTAsmentioned above the input power119875

2(Figure 3(c)) of

the Equivalent e-CVTdoes not changewhen the ideal and thereal cases are compared Hence (15) is suitable for calculatingthe power in the real system The power ratio is simply givenby

100381610038161003816100381610038161003816100381610038161003816

119875ECVTeq

119875in

100381610038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198752

119875out

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198752

119875out

10038161003816100381610038161003816100381610038161003816real

=

100381610038161003816100381610038161003816100381610038161003816

119889120591CVU119889120591ECVTeq

120591ECVTeq

120591CVU

100381610038161003816100381610038161003816100381610038161003816

=

100381610038161003816100381610038161003816100381610038161003816

1 + 1198962+ 1198961+ 11989621198961

1 + 1198961+ 1198962(1 minus 120591ECVT)

100381610038161003816100381610038161003816100381610038161003816

(16)

The power loss in the Equivalent e-CVT of the real systemcan be obtained as follows

119875119908CVU= minus (1 minus 120578ECVTeq)

100381610038161003816100381611987521003816100381610038161003816

= minus (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq10038161003816100381610038161003816

(17)

International Journal of Vehicular Technology 7

Using (16)-(17) and the power at the input shaft of the CVUthe efficiency can be finally calculated

120578CVU = minus119875out119875in=119875out119875out + 119875119908CVU

=1

1 + (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816real

=1

1 + (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816ideal

(18)

The efficiency 120578ECVTeq of Equivalent e-CVT can be derivedusing the same approach

Indeed if the Equivalent e-CVT is considered(Figure 3(c)) with given 120596

2 120591ECVT and 1198793 the angular

velocities and torques at branches ldquo1rdquo and ldquo5rdquo do no differbetween the ideal and real system

The power loss in the e-CVT of the real Equivalent ECVTcan be easily written as a function of the power 119875

5

119875119908ECVT= minus (1 minus 120578ECVT)

100381610038161003816100381611987551003816100381610038161003816 (19)

Therefore it follows that the efficiency in the Equivalent e-CVT is

120578ECVTeq = minus119875out119875in=119875out

119875out + 119875119908ECVT=

1

1 + 119875119908ECVT119875out

=1

1 + (1 minus 120578ECVT)1003816100381610038161003816119875511987531003816100381610038161003816ideal

=1

1 + (1 minus 120578ECVT)1003816100381610038161003816119875ECVT1198753

1003816100381610038161003816ideal

(20)

By considering (11) and (15) the power ratio in the Equivalente-CVT can be obtained as follows (Figure 3(c))

10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

119875ECVT1198753

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198755

1198753

10038161003816100381610038161003816100381610038161003816ideal

=

100381610038161003816100381610038161003816100381610038161003816

120597120591ECVTeq

120597120591ECVT

120591ECVT120591ECVTeq

100381610038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

120591ECVT120591ECVT + 1198961

10038161003816100381610038161003816100381610038161003816

(21)

In conclusion the efficiency can be calculated with (18) inwhich 120578ECVTeq can be obtained by (20) where |119875ECVTeq119875in|ideal and |119875ECVT1198753|ideal are derived from (16) and (21)respectively

For the Output Compound Split Transmission withpower flow of Type III the CVU architecture is the same asthe previous case (Figure 4(b)) Therefore the power loss issimply given by (17) and the efficiency by (18) whereas theformula for 120578ECVTeq is different

The power flow in the Equivalent e-CVT and its efficiency120578ECVTeq change compared with the previous case Also inthis case 119875

5does not change when comparing the ideal

system and the real system (Figure 4(c)) This means thatthe expression for the power loss in the Equivalent e-CVT is

a function of the e-CVT output power 1198755 that is the power

loss is given by

119875119908CVTeq= minus(1 minus 120578ECVT)

120578ECVT

100381610038161003816100381611987551003816100381610038161003816 (22)

From (20) and (22) the efficiency of the Equivalent e-CVT is

120578ECVTeq = minus119875out119875in=119875out

119875out + 119875119908ECVT=

1

1 + 119875119908ECVT119875out

=1

1 + ((1 minus 120578ECVT) 120578ECVT)1003816100381610038161003816119875ECVT1198753

1003816100381610038161003816ideal

(23)

In conclusion the efficiency of Type III power flow can becalculated through (18) where 120578ECVTeq can be obtained by(23)

The efficiency of the CVU working with Type III powerflow is derived using a similar approach

From Figure 5(b) it follows that the power 1198752which has

the same value in the ideal system and in the real system isthe output power of the Equivalent e-CVTThe power loss inthe e-CVT of the real Equivalent e-CVT (Figure 4(c)) is

119875119908CVU= minus(1 minus 120578ECVTeq)

120578ECVTeq

100381610038161003816100381611987521003816100381610038161003816

(24)

Thus the efficiency of the CVU is given by

120578CVU = minus119875out119875in=119875out119875out + 119875119908CVU

=1

1 + ((1 minus 120578ECVTeq) 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816ideal

(25)

It follows that the power loss and efficiency of the Equivalente-CVT are given by

119875119908ECVTeq= minus(1 minus 120578ECVT)

120578ECVT

100381610038161003816100381611987551003816100381610038161003816 (26)

120578ECVTeq = minus119875out119875in=119875in + 119875119908ECVT119875in

= 1 minus(1 minus 120578ECVT)

120578ECVT

10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal

(27)

The power ratio in the Equivalent e-CVT is obtained using(21) hence the efficiency in the Equivalent e-CVT followsfrom (27)

In conclusion the efficiency of Type III can be calculatedthrough (25) where 120578ECVTeq can be obtained by (27)

Finally in theOutput Compound Split Transmissionwithpower flow of Type IIII we obtained (Figure 6)

119875119908ECVTeq= minus (1 minus 120578ECVT)

100381610038161003816100381611987551003816100381610038161003816 (28)

8 International Journal of Vehicular Technology

The power ratio in the Equivalent e-CVT follows from (21)Therefore the efficiency of the Equivalent e-CVT is deducedfrom equation

120578ECVTeq = minus119875out119875in=119875in + 119875119908ECVT119875in

= 1 minus (1 minus 120578ECVT)10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal

(29)

It can be noticed that the power flowof Figure 6(b) is identicalto Figure 5(b) It follows that also in this case the efficiency iscalculated with (25) with 120578ECVTeq calculated as (29)

4 Numerical Example

In this section a numerical example is given which alsoincludes the calculation of the transmission efficiency usingthe simplified approach described in this work The calcula-tions can be performed after the speed ratio of the CVU andthe e-CVT have been imposed It is here assumed that speedratio of the e-CVT varies between the bounds 120591ECVT119898 = 04and 120591ECVT119872 = 2 which is typical of mechanical CVT Theratio range of the CVU is a system requirement so it canbe chosen arbitrarily A CVU is here designed with a speedratio bounded between 120591CVU119898 = minus1 and 120591CVU119872 = 2 inorder to comprise also the neutral gear These CVU boundscan be obtained only by choosing two planetary gear trainscharacterized by 119896

1and 119896

2calculated with (7) in the case

of monotonic increase of the CVU speed ratio for increasingECVT speed ratio It is obtained that

1198961= 029

1198962= minus329

(30)

If the case of a monotonic decreasing CVU speed ratio withincreasing e-CVT speed ratio 119896

1and 119896

2must be calculated

with (8) it follows that

1198961= minus10

1198962= minus17

(31)

The CVU speed ratio as a function of the e-CVT speed ratiogiven by (4) is shown in Figure 7 for the two aforementionedcases

The power ratio |119875ECVT119875CVU| calculated with (15) isshown in Figure 8

Two regions can be distinguished corresponding to twodifferent ranges of 120591CVU the first range 0 le 120591CVU le 2 and thesecond range minus1 lt 120591CVU lt 0

Each region corresponds to a different power circulationConsidering the limits imposed on the speed ratio of thisexample it results in the following

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)gt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (32)

With the help of (13) and (14) one can determine the powerflow type taking also into account the sign change of the

Monotonically increasing Monotonically decreasing

minus10

minus05

00

05

10

15

20

120591CV

U

020 040 060 080 100 120 140 160 180 200000120591ECVT

Figure 7 Speed ratio of the CVU (120591CVU) as a function of the e-CVTspeed ratio (120591ECVT)

Monotonically increasing Monotonically decreasing

0123456789

10

00minus05minus10 10 15 2005120591CVU

PEC

VT

PCV

U

Figure 8 Power ratio |119875ECVT119875CVU| considering no losses plotted asa function of the overall speed ratio 120591CVU

ratio 120591CVU In fact when 120591CVU is an increasing function of120591ECVT the Type IIII power flow occurs for 120591CVU gt 0 as aconsequence of (14) whereas in the other regionwith 120591CVU lt0 the power flow changes from Type IIII to Type III [21]

On the other hand when 120591CVU is a decreasing function of120591ECVT (14) still holds but in this case the Type III power flowoccurs if 120591CVU gt 0 whereas if 120591CVU lt 0 then the power flowis changed from Type III to Type IIII [21]

The ratio given by the power through the e-CVT dividedby the global power is not equal in the two cases (Figure 8)With 120591CVU lt 1 the power ratio is larger when the speed ratioof the transmission is a decreasing function of the speed ratioof the e-CVTOnly with 120591CVU gt 1 the situation is the oppositeone

The efficiency 120578CVU plotted as a function of 120591CVU isshown in Figure 9 considering that 120578ECVT = 09 For 120591CVU gt0 and with a monotonically increasing CVU speed ratio withincreasing e-CVT speed ratio (power flow of Type IIII) (16)(21) (25) and (29) are utilized In this case the efficiencyis larger than in the case of monotonically decreasing speed

International Journal of Vehicular Technology 9

Monotonically increasing Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Figure 9 The efficiency 120578CVU as a function of the overall speed ratio 120591CVU (120578ECVT = 09)

ratio for 120591CVU lt 1 whereas the opposite condition is verifiedfor 120591CVU gt 1This is expected since the device with the lowestandmost critical efficiency is the e-CVT so the configurationthat minimizes the power through the e-CVT is the mostconvenient one in terms of energy efficiency

5 Efficiency of the Output Compound e-CVTin Direct and Reverse Operation

Hybrid vehicles are the main application for CompoundSplit-eCVT transmission One of themost important featuresof hybrid vehicles is the regenerative braking capabilitySuch a function needs the transmission to work in reverseoperation For this reason it is important to evaluate theefficiency of the transmission in both direct and reverseoperation and to understand the differences

In this section the same transmission data are considered(120591ECVT119898 = 04 120591ECVT119872 = 2 120591CVU119898 = minus1 120591CVU119872 = 2) andthe performance in reverse operation are calculated throughthe model developed in a previous work [22] The efficiency120578ECVT of the e-CVT is considered constant and given by120578ECVT = 09 As mentioned in the compound transmissionwith a monotonic increasing speed ratio (119896

1= 029 119896

2=

minus329) if 120591CVU119898 gt 0 a power flow of Type IIII is obtainedGiven the same kinematic parameters when the transmissionworks in reverse operation (Figure 10) the input and outputtorques are reversed and because of the planetary gear trainPG1 also the torques on links 2 and 6 are reversed Further-more the torque and the power on the link 3 are also reversedand as a consequence of the planetary gear train PG2 alsothe torque and power on links 1 4 and 5 are reversed Soin the change from direct operation (Figure 10(a)) to reverseoperation (Figure 10(b)) the power flow is reversed on all thelinks and the power flow is yet of Type IIII

When 120591CVU119898 lt 0 similar arguments leads to concludethat the power flow is of Type III also in reverse operation(Figure 11)

The monotonic increasing speed ratio is investigatedfirst In Figure 12 it is shown that in reverse operation theefficiency of the transmission is always less than in directoperation with the only exception of the high values of thespeed ratio (120591CVU gt 17) It is very interesting to see that whenthe speed ratio is close to zero (minus027 lt 120591CVU lt 022) theefficiency in reverse operation is negative which means thatthe transmission is nonreversible with the speed ratio in theaforementioned range This result is in agreement with theresults shown in [8] in the case of Power Split TransmissionsIt is actually relevant for applications to the hybrid vehiclesbecause it affects negatively the braking recovery capabilitiesIn particular it is not possible to recover energy in brakingwith minus027 lt 120591CVU lt 022

Similar results can be obtained in the case of monotonicdecreasing speed ratio (Figure 7) Given the speed ratioranges of CVT and CVU (which give 119896

1= minus10 and 119896

2=

minus17) also in this case the power flows do not change whenswitching from direct to reverse operation power flow ofType III with 120591CVU gt 0 (Figure 11) and power flow of TypeIIII with 120591CVU lt 0 (Figure 10) The efficiency in direct andreverse operation is shown in Figure 13 Also in this case theefficiency in reverse operation is visibly less than in directmode Furthermore the nonreversibility range of the speedis even larger being minus040 lt 120591CVU lt 028

6 Conclusions

In recent years compound transmissions are attractingincreasing interest for application in hybrid vehicles becausethey are flexible and they permit optimizing the efficiency indifferent operating conditions The goal of this work was toobtain a systematic approach to determine the power flowsand the efficiency in Output Compound Split Transmissionsfor optimal design and control of HEVs The proposedmethodology is suitable for steady-state working conditionsand it follows from the assumption of negligible power lossin all the components except for the e-CVT It is shown how

10 International Journal of Vehicular Technology

Forward power

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 10 Power flows in a Output Compound Split e-CVT with Type IIII power flow (a) forward power (b) reverse power

Forward power

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 11 Power flows in a Output Compound Split e-CVT with Type III power flow (a) forward power (b) reverse power

the power circulation depends only on kinematic conditionsFurthermore a novel approach is shown to study the effi-ciency of the transmission which relies on the separationof the compound transmission in two subsystems so thatit can be studied as an ldquoEquivalent e-CVTrdquo (which is apower split-like transmission of Input-Output Split type)inside an Output Split device Following our approach the

efficiency is calculated easily for each of all the possiblepower flows A numerical example showed the potentialof this tool for power flows and efficiency calculations ofthe Output Compound Split Transmission in direct andreverse operation Experimental validation of the presentedmethodology is in progress and it will be the subject matterof future works

International Journal of Vehicular Technology 11

Forward power Reverse power

Monotonically increasing

0001020304050607080910

120578CV

U

00 10 201505minus10 minus05120591CVU

Figure 12The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically increasing

Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Forward power Reverse power

Figure 13The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically decreasing

Nomenclature

CVU CVTECVT and PG(subscripts)

Continuously Variable Unit ContinuouslyVariable Transmission ElectronicContinuously Variable Transmission andplanetary gear

119872119898 eq(subscripts)

Maximum minimum and equivalentrespectively

1198961 1198962 Kinematic parameter of the PG 1 and 2

respectively119875119895 Power through the 119895th branch119875119908 119875in and119875out

Dissipated power input power and outputpower

120591 Speed ratio120578 Efficiency120596119895 Angular velocity of the 119895th shaft

120596119900 Angular velocity of the output shaftof theCVU120596119894 Angular velocity of the input shaft of the CVU

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M R Cuddy and K B Wipke ldquoAnalysis of the fuel econ-omy benefit of drivetrain hybridizationrdquo SAE Technical Paper970289 1997

[2] S Stockar V Marano M Canova G Rizzoni and L GuzzellaldquoEnergy-optimal control of plug-in hybrid electric vehiclesfor real-world driving cyclesrdquo IEEE Transactions on VehicularTechnology vol 60 no 7 pp 2949ndash2962 2011

[3] L Serrao S Onori and G Rizzoni ldquoA comparative analysisof energy management strategies for hybrid electric vehiclesrdquoJournal of Dynamic Systems Measurement and Control vol 133no 3 Article ID 031012 2011

[4] F R Salmasi ldquoControl strategies for hybrid electric vehiclesevolution classification comparison and future trendsrdquo IEEETransactions on Vehicular Technology vol 56 no 5 pp 2393ndash2404 2007

[5] F Bottiglione T Contursi A Gentile and G Mantriota ldquoThefuel economy of hybrid buses the role of ancillaries in realurban drivingrdquo Energies vol 7 no 7 pp 4202ndash4220 2014

[6] A Taghavipour N L Azad and J McPhee ldquoAn optimal powermanagement strategy for power split plug-in hybrid electricvehiclesrdquo International Journal of Vehicle Design vol 60 no 3-4pp 286ndash304 2012

[7] Z Zhao C Wang T Zhang X Dai and X Yuan ldquoControloptimization of a compound power-split hybrid transmissionfor electric driverdquo SAE Technical Papers 2015

[8] G Mantriota ldquoPerformances of a series infinitely variabletransmission with type I power flowrdquo Mechanism and MachineTheory vol 37 no 6 pp 579ndash597 2002

[9] G Mantriota ldquoPerformances of a parallel infinitely variabletransmissions with a type II power flowrdquo Mechanism andMachine Theory vol 37 no 6 pp 555ndash578 2002

[10] B Si ldquoReconfigurable Hybrid Gear Trainrdquo US Patent 0 070 992A1 2011

[11] B Si ldquoDual mode input split compound split configurationEPPV transmissionrdquo US Patent 8 075 435 B2 2011

[12] F Bottiglione andGMantriota ldquoMG-IVT an infinitely variabletransmission with optimal power flowsrdquo Journal of MechanicalDesign vol 130 no 11 Article ID 112603 2008

[13] K T Chau andW Li ldquoOverview of electricmachines for electricand hybrid vehiclesrdquo International Journal of Vehicle Design vol64 no 1 pp 46ndash71 2014

[14] A G Holmes and M R Schmidt ldquoHybrid Electric PowertrainIncluding a Two-Mode Electrically Variable Transmissionrdquo USPatent 6 478 705 B1 2002

[15] C Brendan ldquoComparative analysis of single and combinedhybrid electrically variable transmission operatingmodesrdquo SAETechnical Paper 2005-01-1165 2005

[16] B Mashadi and S A M Emadi ldquoDual-mode power-splittransmission for hybrid electric vehiclesrdquo IEEE Transactions onVehicular Technology vol 59 no 7 pp 3223ndash3232 2010

12 International Journal of Vehicular Technology

[17] J Kim J Kang Y Kim T Kim B Min and H Kim ldquoDesignof power split transmission design of dual mode power splittransmissionrdquo International Journal of Automotive Technologyvol 11 no 4 pp 565ndash571 2010

[18] Y Zou F-C Sun C-N Zhang and J-Q Li ldquoOptimal energymanagement strategy for hybrid electric tracked vehiclesrdquoInternational Journal of Vehicle Design vol 58 no 2ndash4 pp 307ndash324 2012

[19] N-D Kim J-M Kim and H-S Kim ldquoControl strategy for adual-mode electromechanical infinitely variable transmissionfor hybrid electric vehiclesrdquo Proceedings of the Institution ofMechanical Engineers PartD Journal of Automobile Engineeringvol 222 no 9 pp 1587ndash1601 2008

[20] J Kim T Kim B Min S Hwang and H Kim ldquoModecontrol strategy for a two-mode hybrid electric vehicle usingelectrically variable transmission (EVT) and fixed-gear moderdquoIEEE Transactions on Vehicular Technology vol 60 no 3 pp793ndash803 2011

[21] Z Zhou CMi andG Zhang ldquoIntegrated control of electrome-chanical braking and regenerative braking in plug-in hybridelectric vehiclesrdquo International Journal of Vehicle Design vol 58no 2ndash4 pp 223ndash239 2012

[22] F Bottiglione and G Mantriota ldquoReversibility of power-splittransmissionsrdquo Journal ofMechanicalDesign Transactions of theASME vol 133 no 8 Article ID 084503 2011

[23] F Bottiglione and G Mantriota ldquoEffect of the ratio spread ofCVU in automotive kinetic energy recovery systemsrdquo Journalof Mechanical Design Transactions of the ASME vol 135 no 6Article ID 061001 2013

[24] F Bottiglione G Carbone L De Novellis L Mangialardiand G Mantriota ldquoMechanical hybrid KERS based on toroidaltraction drives an example of smart tribological design toimprove terrestrial vehicle performancerdquoAdvances in Tribologyvol 2013 Article ID 918387 9 pages 2013

[25] S De Pinto F Bottiglione andGMantriota ldquoInfinitely variabletransmissions in neutral gear torque ratio and power re-circulationrdquo Mechanism and Machine Theory vol 74 pp 285ndash298 2014

[26] S de Pinto and G Mantriota ldquoA simple model for compoundsplit transmissionsrdquo Proceedings of the Institution of MechanicalEngineers Part D Journal of Automobile Engineering vol 228no 5 pp 549ndash564 2014

[27] G Mantriota ldquoFuel consumption of a vehicle with power splitCVT systemrdquo International Journal of Vehicle Design vol 37 no4 pp 327ndash342 2005

[28] M Cammalleri ldquoEfficiency of split-way CVTrsquos A simplifiedmodelrdquo SAE Technical Papers 15 2007

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation

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DistributedSensor Networks

International Journal of

2 International Journal of Vehicular Technology

13

5

2

4

6

Input

Output

PGII

PGI

e-CVT

(a)

13

5

2

4

6

Input

Output

PGII

PGI

e-CVT

(b)

Figure 1 Schematic picture of the Output Compound Split Transmission (a) and Input Compound Split Transmission (b)

and of the Continuously Variable Transmission differentinternal power flows may be established which affects theratio between the power through the CVT branch and thepower transmitted by the device

In hybrid vehicles during the recovery of energy inbraking the transmission works in reverse mode and it hasbeen shown that the efficiency in reverse mode is sometimescritically lower than the efficiency in direct mode [22]

Compound Split Transmission uses two motorgenera-tors as variator (eCVT) as well as one or several planetarygear sets as power split device These architectures can workin two different modes by searching for the best globalefficiency in the different operating conditions

A simple approach would be useful to determine theperformance of compoundElectric CVT in order to optimizethe control strategy and then the performance of hybridvehicles [26]

Following this approach it would be possible to predictthe power flows of the transmission and its efficiency Opti-mal control strategies of hybrid vehicles are very importantSeveral studies were carried out in considering the designefficiency and mathematical models for the control strategyThe focus of these surveys is the fuel consumption and theperformance of the hybrid vehicle

In this work a method to evaluate the power flows andthe efficiency of Output Compound Split Transmission isproposed (Figure 1(a)) The Output Compound architectureis made of a planetary gear (PGI) input shaft and an e-CVTconnected by a second planetary gear (PGII) (Figure 1(a))For the first time the Output Compound architecture is herestudied by separating the system into two subsystems Fol-lowing this approach the Output Compound is made of twonested shunted CVT systems of Input or Output Split typeto be analyzed through a previously developed approach Itfollows that after having imposed the requested ratio rangesthe power circulation modes are easily found and also theefficiency can be easily calculated It can be observed thatthe reverse operation of the Output Compound Split system

is closely related to the Input Compound Split (Figure 1(b))that one of the authors has studied in a previous work Suchoperational conditions are typical of the regenerative brakingwhere the power flows backwards with respect to the normaloperation mode of the transmission As it is shown in aprevious work the efficiency of the Power Split Transmissionis very different in reverse operation in comparison to directoperation For this reason in this work the efficiency ofthe Output Split transmission will be investigated and acomparison between the direct and the reverse operationswill be achieved

2 Kinematics of Output CompoundSplit Transmission

A compound power split is made of a continuously variabledrive which can be of mechanical type (CVT) or with twomotorsgenerators working as electrical CVT (e-CVT) aswell as one or several planetary gear sets They can be clas-sified into three different types Input Split Output Split andCompound Split The Input and Output Split configurationshave only one planetary gear operating as a power splitdevice In the Compound Split Transmission the planetarygears are two ormore Hereafter we will consider CompoundSplit Transmissions with two planetary gear sets (PGI andPGII) Many different combinations can be achieved withdifferent arrangements of the connections between all theelements of the transmission Among all possibilities the twomost diffused are shown in Figure 1 the Output CompoundSplit Transmission (Figure 1(a)) and the Input CompoundSplit Transmission (Figure 1(b)) The Input Compound SplitTransmission was studied in a previous work of one of theauthors (G Mantriota) In the present work the OutputCompound Split Transmission is investigatedThese configu-rations can be considered one the reverse mode operations ofthe other Since the object of our study is a ContinuouslyVari-able Unit (CVU)made with a Compound Split Transmissionhereafter we will refer to this with the acronym CVU

International Journal of Vehicular Technology 3

Derivation of the main kinematic relations for the Out-put Compound Split Transmission (Figure 1(a)) follows Bydefining 119896

1and 119896

2the gear ratios of the planetary gears PG1

and PG2 respectively the following algebraic equations hold

1205965+ 11989611205961minus (1 + 119896

1) 1205963= 0 (1)

120596119900+ 11989621205966minus (1 + 119896

2) 1205962= 0 (2)

where 120596119895is the angular speed of the 119895th path

The speed ratio of the compound transmission 120591CVU andthe speed ratio of the eCVT are

120591CVU =120596119900

120596119894

120591ECVT =1205965

1205964

(3)

where 120596119894 120596119900are the angular velocities of the input and the

output shafts of the CVU From (1)ndash(3) and observing that1205963= 120596119894= 1205966and 120596

1= 1205962= 1205964(Figure 1(a)) the speed ratio

of the CVU is obtained

120591CVU =1 + 1198961+ 1198962(1 minus 120591ECVT)

120591ECVT + 1198961 (4)

Making the derivative of (4) with respect to 120591ECVT

119889120591CVU119889120591ECVT

= minus1198961+ 1198962+ 11989621198961

(120591ECVT + 1198961)2 (5)

then the CVU speed ratio is always a monotonic functionsince the sign of the derivate (5) does not change if 120591ECVTchanges

If one desires specific minimum (120591CVU119898) and maximum(120591CVU119872) values of the global speed ratio with given 120591ECVT119898and 120591ECVT119872 it is possible to calculate 1198961 and 1198962 as the uniquesolution of a system of two equations with two unknownsIn fact if 120591CVU is supposed to be a monotonic increasingfunction of 120591ECVT then the following system of equations canbe written

1198961(120591CVU119872 minus 1) + 1198962 (120591ECVT119872 minus 1) + 120591CVU119872120591ECVT119872

minus 1 = 0

1198961(120591CVU119898 minus 1) + 1198962 (120591ECVT119898 minus 1) + 120591CVU119898120591ECVT119898

minus 1 = 0

(6)

From it it follows that

1198961=(120591CVU119872120591ECVT119872 minus 1) (1 minus 120591ECVT119898) minus (120591CVU119898120591ECVT119898 minus 1) (1 minus 120591ECVT119872)

(120591CVU119872 minus 1) (120591ECVT119898 minus 1) minus (120591CVU119898 minus 1) (120591ECVT119872 minus 1)

1198962=(120591CVU119872120591ECVT119872 minus 1) (1 minus 120591CVU119898) minus (120591CVU119898120591ECVT119898 minus 1) (1 minus 120591CVU119872)

(120591CVU119898 minus 1) (120591ECVT119872 minus 1) minus (120591CVU119872 minus 1) (120591ECVT119898 minus 1)

(7)

Then the values of the parameters 1198961and 1198962of the planetary

gears depend only on the limits imposed of 120591ECVT and 120591CVU1198961and 119896

2can also be obtained in case that 120591CVU is

supposed to be a monotonic decreasing function of 120591ECVT

1198961=(120591CVU119872120591ECVT119898 minus 1) (1 minus 120591ECVT119872) minus (120591CVU119898120591ECVT119872 minus 1) (1 minus 120591ECVT119898)

(120591CVU119872 minus 1) (120591ECVT119872 minus 1) minus (120591CVU119898 minus 1) (120591ECVT119898 minus 1)

1198962=(120591CVU119872120591ECVT119898 minus 1) (1 minus 120591CVU119898) minus (120591CVU119898120591ECVT119872 minus 1) (1 minus 120591CVU119872)

(120591CVU119898 minus 1) (120591ECVT119898 minus 1) minus (120591CVU119872 minus 1) (120591ECVT119872 minus 1)

(8)

In conclusion the values of 120591CVU corresponding to workingconditions with zero power through the eCVT (mechanicalpoints) are obtained from (4) with 120596

5= 0 (corresponding to

120591ECVT = infin) or 1205964 = 0 (which corresponds to 120591ECVT = 0)

120591ICVU = minus1198962

120591IICVU =1 + 1198961+ 1198962

1198961

(9)

3 Power Flow and Efficiency ofOutput Compound e-CVT

In order to investigate the power flows and the efficiency ofthe Output Compound Split (Figure 1(a)) the overall systemis divided into a subcomponent (Equivalent e-CVT) and thesecond planetary gear PGII (Figure 2(a)) The Equivalent e-CVT is made of the e-CVT and the PGI (Figure 2(b))

4 International Journal of Vehicular Technology

3

26

Equivalent

Input

Output

PGII

e-CVT

(a)

1

54

3

2

Equivalent

PGI

e-CVT

e-CVT

(b)

Figure 2 (a) Schematic picture of the Output Compound with the ldquoEquivalent e-CVTrdquo (b) Equivalent e-CVT

The scheme of Figure 2(a) is also an Output Split (OS)where the Continuously Variable Transmission is replacedwith the Equivalent e-CVT

For this architecture we define

120591ECVTeq =1205963

1205962

(10)

From (2)-(3) and (10) and considering 1205963= 1205966= 120596119894

(Figure 2(a)) it follows that

120591ECVTeq =120591ECVT + 11989611 + 1198961

(11)

The transmission ratio in (11) depends only on the values ofthe parameter 119896

1of the PGI and it is a monotonic function

From (2) (3) and (11) the CVU speed ratio is obtained as afunction of the Equivalent e-CVT speed ratio

120591CVU =1 + 1198962(1 minus 120591ECVTeq)

120591ECVTeq (12)

It has been demonstrated that in the case of an OutputSplit (OS) (Figure 2(a)) a Type I power flow is obtainedif |120591CVU| = |120596119900120596119894| is a monotonic increasing function of|120591ECVT| = |12059651205964| whereas Type II power flow is obtainedfor a monotonic decreasing function

In the case of Input Split the power flows are the oppositewith respect to the Output Split This means that a TypeI power flow can be obtained by imposing a monotonicdecreasing trend of |120591CVU| = |120596119900120596119894| in function of |120591ECVT| =|12059651205964| whereas a Type II power flow is achieved if the

function has a monotonic increasing trendNow the power flows in the CVU can be analyzed as

they are obtained as combinations of the power flows in theOutput Split and Equivalent e-CVTThe power circulation inthe compound depends only on whether the speed ratios ofthe CVU and Equivalent e-CVT are increasing or decreasingfunctions of Equivalent e-CVT and e-CVT respectively

If a monotonic increase of 120591CVU as a function of 120591ECVTeqis considered a Type I power flow (Figure 3(b)) is obtainedthat is the power through the PGII is greater than the inputpower In this condition the Equivalent e-CVT is in anOutput Split If 120591ECVTeq is an increasing function of 120591ECVTthen a Type I power flow is obtained also in the Equivalent e-CVT (Figure 3(c)) Therefore this kind of power circulationshown in Figure 3(a) is named Type II power flow In theType II power flow also the overall speed ratio 120591CVU is amonotonic increasing function of 120591ECVT In order to achievethe Type II power flow (7) must be used to calculate the gearratios 119896

1and 1198962of the planetary gear trains

If 120591ECVTeq is a decreasing function of 120591ECVT a power flowof Type II is obtained in the Equivalent e-CVT (Figure 4(c))that is the power through the e-CVT is greater than the inputpower of the Equivalent e-CVT Hence with a monotonicincrease of 120591CVU as a function of 120591ECVTeq (Figure 4(b))a power flow named Type III (Figure 4(a)) is obtainedby imposing that 120591CVU is a decreasing function of 120591ECVTTherefore Type III power flow is obtained solving (8) to findthe parameters 119896

1and 1198962of the planetary gear trains

If 120591CVU is a decreasing function 120591ECVTeq (Figure 5(b))the Equivalent e-CVT is in the Input Split (IS) configuration(Figure 5(c)) and Type I power flow occurs when 120591ECVTeq isan increasing function of 120591ECVT Therefore considering thewhole transmission a Type III power flow occurs if 120591CVU isa decreasing function of 120591ECVT (Figure 5(a)) Hence Type IIIpower flow is achieved when (8) are solved to obtain 119896

1and

1198962If 120591CVU is a decreasing function of 120591ECVTeq and 120591ECVTeq

is a decreasing function of 120591ECVT Type IIII power flowoccurs in the Output Compound Split (Figure 6(a)) Thenthe power flow in Figure 6(a) occurs when 120591CVU increaseswith increasing 120591ECVT

In conclusion with (7) Type II and Type IIII are the twopossible power flows that occur in the transmission On thecontrary Type III andType III power flows are achievedwith(8)

International Journal of Vehicular Technology 5

13

5

2

4

6

Output compoundType II power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type I power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type I power flow

e-CVT

e-CVT

PGI

(c)

Figure 3 Power flows in a Compound Split e-CVT with Type II power flow (a) Output Compound Split e-CVT (b) The Output Split withEquivalent e-CVT and Type I power flow and (c) the Equivalent e-CVT with Type I power flow

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type I power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type II power flow

PGI

e-CVT

e-CVT

(c)

Figure 4 Power flows in a Compound Split e-CVT with Type III power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type I power flow and (c) the Equivalent e-CVT with Type II power flow

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type II power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type I power flow

PGI

e-CVT

e-CVT

(c)

Figure 5 Power flows in a Compound Split e-CVT with Type III power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type II power flow and (c) the Equivalent e-CVT with Type I power flow

6 International Journal of Vehicular Technology

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type II power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type II power flow

PGI

e-CVT

e-CVT

(c)

Figure 6 Power flows in a Compound Split e-CVT with Type IIII power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type II power flow and (c) the Equivalent e-CVT with Type II power flow

Finally in agreement with the considerations suggestedin [21] if the following inequality is verified

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)lt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (13)

the Type II or Type III are the working conditions of thetransmission On the contrary if

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)gt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (14)

the Type III or Type IIII are established in the CVUFor the efficiency of Output Compound Split Transmis-

sion the approach is based upon the assumption that onlythe losses in the e-CVT are considered This assumption isgenerally accepted because the efficiency 120578ECVT of the e-CVT is very low (eg an electric motor-generator) comparedwith the other componentsThis condition is named the ldquorealsystemrdquo

The Output Compound Split Transmission with powerflow of Type II is considered (Figure 3(a)) Both the idealsystem (without losses) and the real system are analyzed andcompared to each other For given kinematic conditions (120596

119894

120591ECVT) and output torque 119879119900 the ratios of the torques of

PGII shaft (branches ldquo2rdquo and ldquo6rdquo) are fixed and so the ratiosbetween powers are also determined This means that thepowers in the branches ldquo2rdquo (119875

2) and ldquo6rdquo (119875

6) have the same

value in the ideal and the real systemOn the other hand the input power and the power of

branch 3 are different in the ideal system and in the realsystem In the real system because of the power loss of thee-CVT the input power 119875in is increased and the power 119875

3is

decreased

It has been demonstrated in [28] that the ratio given bythe power through the e-CVT branch divided by the inputpower of the overall CVU can be easily calculated (underthe assumption of negligible power loss) relying only on thesystem kinematics

10038161003816100381610038161003816100381610038161003816

119875ECVT119875in

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

119889120591CVU119889120591ECVT

120591ECVT120591CVU

10038161003816100381610038161003816100381610038161003816 (15)

Equation (15) is general and therefore it can be applied tothe Compound Split Transmission as well as the Equivalent e-CVTAsmentioned above the input power119875

2(Figure 3(c)) of

the Equivalent e-CVTdoes not changewhen the ideal and thereal cases are compared Hence (15) is suitable for calculatingthe power in the real system The power ratio is simply givenby

100381610038161003816100381610038161003816100381610038161003816

119875ECVTeq

119875in

100381610038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198752

119875out

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198752

119875out

10038161003816100381610038161003816100381610038161003816real

=

100381610038161003816100381610038161003816100381610038161003816

119889120591CVU119889120591ECVTeq

120591ECVTeq

120591CVU

100381610038161003816100381610038161003816100381610038161003816

=

100381610038161003816100381610038161003816100381610038161003816

1 + 1198962+ 1198961+ 11989621198961

1 + 1198961+ 1198962(1 minus 120591ECVT)

100381610038161003816100381610038161003816100381610038161003816

(16)

The power loss in the Equivalent e-CVT of the real systemcan be obtained as follows

119875119908CVU= minus (1 minus 120578ECVTeq)

100381610038161003816100381611987521003816100381610038161003816

= minus (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq10038161003816100381610038161003816

(17)

International Journal of Vehicular Technology 7

Using (16)-(17) and the power at the input shaft of the CVUthe efficiency can be finally calculated

120578CVU = minus119875out119875in=119875out119875out + 119875119908CVU

=1

1 + (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816real

=1

1 + (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816ideal

(18)

The efficiency 120578ECVTeq of Equivalent e-CVT can be derivedusing the same approach

Indeed if the Equivalent e-CVT is considered(Figure 3(c)) with given 120596

2 120591ECVT and 1198793 the angular

velocities and torques at branches ldquo1rdquo and ldquo5rdquo do no differbetween the ideal and real system

The power loss in the e-CVT of the real Equivalent ECVTcan be easily written as a function of the power 119875

5

119875119908ECVT= minus (1 minus 120578ECVT)

100381610038161003816100381611987551003816100381610038161003816 (19)

Therefore it follows that the efficiency in the Equivalent e-CVT is

120578ECVTeq = minus119875out119875in=119875out

119875out + 119875119908ECVT=

1

1 + 119875119908ECVT119875out

=1

1 + (1 minus 120578ECVT)1003816100381610038161003816119875511987531003816100381610038161003816ideal

=1

1 + (1 minus 120578ECVT)1003816100381610038161003816119875ECVT1198753

1003816100381610038161003816ideal

(20)

By considering (11) and (15) the power ratio in the Equivalente-CVT can be obtained as follows (Figure 3(c))

10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

119875ECVT1198753

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198755

1198753

10038161003816100381610038161003816100381610038161003816ideal

=

100381610038161003816100381610038161003816100381610038161003816

120597120591ECVTeq

120597120591ECVT

120591ECVT120591ECVTeq

100381610038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

120591ECVT120591ECVT + 1198961

10038161003816100381610038161003816100381610038161003816

(21)

In conclusion the efficiency can be calculated with (18) inwhich 120578ECVTeq can be obtained by (20) where |119875ECVTeq119875in|ideal and |119875ECVT1198753|ideal are derived from (16) and (21)respectively

For the Output Compound Split Transmission withpower flow of Type III the CVU architecture is the same asthe previous case (Figure 4(b)) Therefore the power loss issimply given by (17) and the efficiency by (18) whereas theformula for 120578ECVTeq is different

The power flow in the Equivalent e-CVT and its efficiency120578ECVTeq change compared with the previous case Also inthis case 119875

5does not change when comparing the ideal

system and the real system (Figure 4(c)) This means thatthe expression for the power loss in the Equivalent e-CVT is

a function of the e-CVT output power 1198755 that is the power

loss is given by

119875119908CVTeq= minus(1 minus 120578ECVT)

120578ECVT

100381610038161003816100381611987551003816100381610038161003816 (22)

From (20) and (22) the efficiency of the Equivalent e-CVT is

120578ECVTeq = minus119875out119875in=119875out

119875out + 119875119908ECVT=

1

1 + 119875119908ECVT119875out

=1

1 + ((1 minus 120578ECVT) 120578ECVT)1003816100381610038161003816119875ECVT1198753

1003816100381610038161003816ideal

(23)

In conclusion the efficiency of Type III power flow can becalculated through (18) where 120578ECVTeq can be obtained by(23)

The efficiency of the CVU working with Type III powerflow is derived using a similar approach

From Figure 5(b) it follows that the power 1198752which has

the same value in the ideal system and in the real system isthe output power of the Equivalent e-CVTThe power loss inthe e-CVT of the real Equivalent e-CVT (Figure 4(c)) is

119875119908CVU= minus(1 minus 120578ECVTeq)

120578ECVTeq

100381610038161003816100381611987521003816100381610038161003816

(24)

Thus the efficiency of the CVU is given by

120578CVU = minus119875out119875in=119875out119875out + 119875119908CVU

=1

1 + ((1 minus 120578ECVTeq) 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816ideal

(25)

It follows that the power loss and efficiency of the Equivalente-CVT are given by

119875119908ECVTeq= minus(1 minus 120578ECVT)

120578ECVT

100381610038161003816100381611987551003816100381610038161003816 (26)

120578ECVTeq = minus119875out119875in=119875in + 119875119908ECVT119875in

= 1 minus(1 minus 120578ECVT)

120578ECVT

10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal

(27)

The power ratio in the Equivalent e-CVT is obtained using(21) hence the efficiency in the Equivalent e-CVT followsfrom (27)

In conclusion the efficiency of Type III can be calculatedthrough (25) where 120578ECVTeq can be obtained by (27)

Finally in theOutput Compound Split Transmissionwithpower flow of Type IIII we obtained (Figure 6)

119875119908ECVTeq= minus (1 minus 120578ECVT)

100381610038161003816100381611987551003816100381610038161003816 (28)

8 International Journal of Vehicular Technology

The power ratio in the Equivalent e-CVT follows from (21)Therefore the efficiency of the Equivalent e-CVT is deducedfrom equation

120578ECVTeq = minus119875out119875in=119875in + 119875119908ECVT119875in

= 1 minus (1 minus 120578ECVT)10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal

(29)

It can be noticed that the power flowof Figure 6(b) is identicalto Figure 5(b) It follows that also in this case the efficiency iscalculated with (25) with 120578ECVTeq calculated as (29)

4 Numerical Example

In this section a numerical example is given which alsoincludes the calculation of the transmission efficiency usingthe simplified approach described in this work The calcula-tions can be performed after the speed ratio of the CVU andthe e-CVT have been imposed It is here assumed that speedratio of the e-CVT varies between the bounds 120591ECVT119898 = 04and 120591ECVT119872 = 2 which is typical of mechanical CVT Theratio range of the CVU is a system requirement so it canbe chosen arbitrarily A CVU is here designed with a speedratio bounded between 120591CVU119898 = minus1 and 120591CVU119872 = 2 inorder to comprise also the neutral gear These CVU boundscan be obtained only by choosing two planetary gear trainscharacterized by 119896

1and 119896

2calculated with (7) in the case

of monotonic increase of the CVU speed ratio for increasingECVT speed ratio It is obtained that

1198961= 029

1198962= minus329

(30)

If the case of a monotonic decreasing CVU speed ratio withincreasing e-CVT speed ratio 119896

1and 119896

2must be calculated

with (8) it follows that

1198961= minus10

1198962= minus17

(31)

The CVU speed ratio as a function of the e-CVT speed ratiogiven by (4) is shown in Figure 7 for the two aforementionedcases

The power ratio |119875ECVT119875CVU| calculated with (15) isshown in Figure 8

Two regions can be distinguished corresponding to twodifferent ranges of 120591CVU the first range 0 le 120591CVU le 2 and thesecond range minus1 lt 120591CVU lt 0

Each region corresponds to a different power circulationConsidering the limits imposed on the speed ratio of thisexample it results in the following

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)gt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (32)

With the help of (13) and (14) one can determine the powerflow type taking also into account the sign change of the

Monotonically increasing Monotonically decreasing

minus10

minus05

00

05

10

15

20

120591CV

U

020 040 060 080 100 120 140 160 180 200000120591ECVT

Figure 7 Speed ratio of the CVU (120591CVU) as a function of the e-CVTspeed ratio (120591ECVT)

Monotonically increasing Monotonically decreasing

0123456789

10

00minus05minus10 10 15 2005120591CVU

PEC

VT

PCV

U

Figure 8 Power ratio |119875ECVT119875CVU| considering no losses plotted asa function of the overall speed ratio 120591CVU

ratio 120591CVU In fact when 120591CVU is an increasing function of120591ECVT the Type IIII power flow occurs for 120591CVU gt 0 as aconsequence of (14) whereas in the other regionwith 120591CVU lt0 the power flow changes from Type IIII to Type III [21]

On the other hand when 120591CVU is a decreasing function of120591ECVT (14) still holds but in this case the Type III power flowoccurs if 120591CVU gt 0 whereas if 120591CVU lt 0 then the power flowis changed from Type III to Type IIII [21]

The ratio given by the power through the e-CVT dividedby the global power is not equal in the two cases (Figure 8)With 120591CVU lt 1 the power ratio is larger when the speed ratioof the transmission is a decreasing function of the speed ratioof the e-CVTOnly with 120591CVU gt 1 the situation is the oppositeone

The efficiency 120578CVU plotted as a function of 120591CVU isshown in Figure 9 considering that 120578ECVT = 09 For 120591CVU gt0 and with a monotonically increasing CVU speed ratio withincreasing e-CVT speed ratio (power flow of Type IIII) (16)(21) (25) and (29) are utilized In this case the efficiencyis larger than in the case of monotonically decreasing speed

International Journal of Vehicular Technology 9

Monotonically increasing Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Figure 9 The efficiency 120578CVU as a function of the overall speed ratio 120591CVU (120578ECVT = 09)

ratio for 120591CVU lt 1 whereas the opposite condition is verifiedfor 120591CVU gt 1This is expected since the device with the lowestandmost critical efficiency is the e-CVT so the configurationthat minimizes the power through the e-CVT is the mostconvenient one in terms of energy efficiency

5 Efficiency of the Output Compound e-CVTin Direct and Reverse Operation

Hybrid vehicles are the main application for CompoundSplit-eCVT transmission One of themost important featuresof hybrid vehicles is the regenerative braking capabilitySuch a function needs the transmission to work in reverseoperation For this reason it is important to evaluate theefficiency of the transmission in both direct and reverseoperation and to understand the differences

In this section the same transmission data are considered(120591ECVT119898 = 04 120591ECVT119872 = 2 120591CVU119898 = minus1 120591CVU119872 = 2) andthe performance in reverse operation are calculated throughthe model developed in a previous work [22] The efficiency120578ECVT of the e-CVT is considered constant and given by120578ECVT = 09 As mentioned in the compound transmissionwith a monotonic increasing speed ratio (119896

1= 029 119896

2=

minus329) if 120591CVU119898 gt 0 a power flow of Type IIII is obtainedGiven the same kinematic parameters when the transmissionworks in reverse operation (Figure 10) the input and outputtorques are reversed and because of the planetary gear trainPG1 also the torques on links 2 and 6 are reversed Further-more the torque and the power on the link 3 are also reversedand as a consequence of the planetary gear train PG2 alsothe torque and power on links 1 4 and 5 are reversed Soin the change from direct operation (Figure 10(a)) to reverseoperation (Figure 10(b)) the power flow is reversed on all thelinks and the power flow is yet of Type IIII

When 120591CVU119898 lt 0 similar arguments leads to concludethat the power flow is of Type III also in reverse operation(Figure 11)

The monotonic increasing speed ratio is investigatedfirst In Figure 12 it is shown that in reverse operation theefficiency of the transmission is always less than in directoperation with the only exception of the high values of thespeed ratio (120591CVU gt 17) It is very interesting to see that whenthe speed ratio is close to zero (minus027 lt 120591CVU lt 022) theefficiency in reverse operation is negative which means thatthe transmission is nonreversible with the speed ratio in theaforementioned range This result is in agreement with theresults shown in [8] in the case of Power Split TransmissionsIt is actually relevant for applications to the hybrid vehiclesbecause it affects negatively the braking recovery capabilitiesIn particular it is not possible to recover energy in brakingwith minus027 lt 120591CVU lt 022

Similar results can be obtained in the case of monotonicdecreasing speed ratio (Figure 7) Given the speed ratioranges of CVT and CVU (which give 119896

1= minus10 and 119896

2=

minus17) also in this case the power flows do not change whenswitching from direct to reverse operation power flow ofType III with 120591CVU gt 0 (Figure 11) and power flow of TypeIIII with 120591CVU lt 0 (Figure 10) The efficiency in direct andreverse operation is shown in Figure 13 Also in this case theefficiency in reverse operation is visibly less than in directmode Furthermore the nonreversibility range of the speedis even larger being minus040 lt 120591CVU lt 028

6 Conclusions

In recent years compound transmissions are attractingincreasing interest for application in hybrid vehicles becausethey are flexible and they permit optimizing the efficiency indifferent operating conditions The goal of this work was toobtain a systematic approach to determine the power flowsand the efficiency in Output Compound Split Transmissionsfor optimal design and control of HEVs The proposedmethodology is suitable for steady-state working conditionsand it follows from the assumption of negligible power lossin all the components except for the e-CVT It is shown how

10 International Journal of Vehicular Technology

Forward power

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 10 Power flows in a Output Compound Split e-CVT with Type IIII power flow (a) forward power (b) reverse power

Forward power

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 11 Power flows in a Output Compound Split e-CVT with Type III power flow (a) forward power (b) reverse power

the power circulation depends only on kinematic conditionsFurthermore a novel approach is shown to study the effi-ciency of the transmission which relies on the separationof the compound transmission in two subsystems so thatit can be studied as an ldquoEquivalent e-CVTrdquo (which is apower split-like transmission of Input-Output Split type)inside an Output Split device Following our approach the

efficiency is calculated easily for each of all the possiblepower flows A numerical example showed the potentialof this tool for power flows and efficiency calculations ofthe Output Compound Split Transmission in direct andreverse operation Experimental validation of the presentedmethodology is in progress and it will be the subject matterof future works

International Journal of Vehicular Technology 11

Forward power Reverse power

Monotonically increasing

0001020304050607080910

120578CV

U

00 10 201505minus10 minus05120591CVU

Figure 12The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically increasing

Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Forward power Reverse power

Figure 13The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically decreasing

Nomenclature

CVU CVTECVT and PG(subscripts)

Continuously Variable Unit ContinuouslyVariable Transmission ElectronicContinuously Variable Transmission andplanetary gear

119872119898 eq(subscripts)

Maximum minimum and equivalentrespectively

1198961 1198962 Kinematic parameter of the PG 1 and 2

respectively119875119895 Power through the 119895th branch119875119908 119875in and119875out

Dissipated power input power and outputpower

120591 Speed ratio120578 Efficiency120596119895 Angular velocity of the 119895th shaft

120596119900 Angular velocity of the output shaftof theCVU120596119894 Angular velocity of the input shaft of the CVU

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M R Cuddy and K B Wipke ldquoAnalysis of the fuel econ-omy benefit of drivetrain hybridizationrdquo SAE Technical Paper970289 1997

[2] S Stockar V Marano M Canova G Rizzoni and L GuzzellaldquoEnergy-optimal control of plug-in hybrid electric vehiclesfor real-world driving cyclesrdquo IEEE Transactions on VehicularTechnology vol 60 no 7 pp 2949ndash2962 2011

[3] L Serrao S Onori and G Rizzoni ldquoA comparative analysisof energy management strategies for hybrid electric vehiclesrdquoJournal of Dynamic Systems Measurement and Control vol 133no 3 Article ID 031012 2011

[4] F R Salmasi ldquoControl strategies for hybrid electric vehiclesevolution classification comparison and future trendsrdquo IEEETransactions on Vehicular Technology vol 56 no 5 pp 2393ndash2404 2007

[5] F Bottiglione T Contursi A Gentile and G Mantriota ldquoThefuel economy of hybrid buses the role of ancillaries in realurban drivingrdquo Energies vol 7 no 7 pp 4202ndash4220 2014

[6] A Taghavipour N L Azad and J McPhee ldquoAn optimal powermanagement strategy for power split plug-in hybrid electricvehiclesrdquo International Journal of Vehicle Design vol 60 no 3-4pp 286ndash304 2012

[7] Z Zhao C Wang T Zhang X Dai and X Yuan ldquoControloptimization of a compound power-split hybrid transmissionfor electric driverdquo SAE Technical Papers 2015

[8] G Mantriota ldquoPerformances of a series infinitely variabletransmission with type I power flowrdquo Mechanism and MachineTheory vol 37 no 6 pp 579ndash597 2002

[9] G Mantriota ldquoPerformances of a parallel infinitely variabletransmissions with a type II power flowrdquo Mechanism andMachine Theory vol 37 no 6 pp 555ndash578 2002

[10] B Si ldquoReconfigurable Hybrid Gear Trainrdquo US Patent 0 070 992A1 2011

[11] B Si ldquoDual mode input split compound split configurationEPPV transmissionrdquo US Patent 8 075 435 B2 2011

[12] F Bottiglione andGMantriota ldquoMG-IVT an infinitely variabletransmission with optimal power flowsrdquo Journal of MechanicalDesign vol 130 no 11 Article ID 112603 2008

[13] K T Chau andW Li ldquoOverview of electricmachines for electricand hybrid vehiclesrdquo International Journal of Vehicle Design vol64 no 1 pp 46ndash71 2014

[14] A G Holmes and M R Schmidt ldquoHybrid Electric PowertrainIncluding a Two-Mode Electrically Variable Transmissionrdquo USPatent 6 478 705 B1 2002

[15] C Brendan ldquoComparative analysis of single and combinedhybrid electrically variable transmission operatingmodesrdquo SAETechnical Paper 2005-01-1165 2005

[16] B Mashadi and S A M Emadi ldquoDual-mode power-splittransmission for hybrid electric vehiclesrdquo IEEE Transactions onVehicular Technology vol 59 no 7 pp 3223ndash3232 2010

12 International Journal of Vehicular Technology

[17] J Kim J Kang Y Kim T Kim B Min and H Kim ldquoDesignof power split transmission design of dual mode power splittransmissionrdquo International Journal of Automotive Technologyvol 11 no 4 pp 565ndash571 2010

[18] Y Zou F-C Sun C-N Zhang and J-Q Li ldquoOptimal energymanagement strategy for hybrid electric tracked vehiclesrdquoInternational Journal of Vehicle Design vol 58 no 2ndash4 pp 307ndash324 2012

[19] N-D Kim J-M Kim and H-S Kim ldquoControl strategy for adual-mode electromechanical infinitely variable transmissionfor hybrid electric vehiclesrdquo Proceedings of the Institution ofMechanical Engineers PartD Journal of Automobile Engineeringvol 222 no 9 pp 1587ndash1601 2008

[20] J Kim T Kim B Min S Hwang and H Kim ldquoModecontrol strategy for a two-mode hybrid electric vehicle usingelectrically variable transmission (EVT) and fixed-gear moderdquoIEEE Transactions on Vehicular Technology vol 60 no 3 pp793ndash803 2011

[21] Z Zhou CMi andG Zhang ldquoIntegrated control of electrome-chanical braking and regenerative braking in plug-in hybridelectric vehiclesrdquo International Journal of Vehicle Design vol 58no 2ndash4 pp 223ndash239 2012

[22] F Bottiglione and G Mantriota ldquoReversibility of power-splittransmissionsrdquo Journal ofMechanicalDesign Transactions of theASME vol 133 no 8 Article ID 084503 2011

[23] F Bottiglione and G Mantriota ldquoEffect of the ratio spread ofCVU in automotive kinetic energy recovery systemsrdquo Journalof Mechanical Design Transactions of the ASME vol 135 no 6Article ID 061001 2013

[24] F Bottiglione G Carbone L De Novellis L Mangialardiand G Mantriota ldquoMechanical hybrid KERS based on toroidaltraction drives an example of smart tribological design toimprove terrestrial vehicle performancerdquoAdvances in Tribologyvol 2013 Article ID 918387 9 pages 2013

[25] S De Pinto F Bottiglione andGMantriota ldquoInfinitely variabletransmissions in neutral gear torque ratio and power re-circulationrdquo Mechanism and Machine Theory vol 74 pp 285ndash298 2014

[26] S de Pinto and G Mantriota ldquoA simple model for compoundsplit transmissionsrdquo Proceedings of the Institution of MechanicalEngineers Part D Journal of Automobile Engineering vol 228no 5 pp 549ndash564 2014

[27] G Mantriota ldquoFuel consumption of a vehicle with power splitCVT systemrdquo International Journal of Vehicle Design vol 37 no4 pp 327ndash342 2005

[28] M Cammalleri ldquoEfficiency of split-way CVTrsquos A simplifiedmodelrdquo SAE Technical Papers 15 2007

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International Journal of Vehicular Technology 3

Derivation of the main kinematic relations for the Out-put Compound Split Transmission (Figure 1(a)) follows Bydefining 119896

1and 119896

2the gear ratios of the planetary gears PG1

and PG2 respectively the following algebraic equations hold

1205965+ 11989611205961minus (1 + 119896

1) 1205963= 0 (1)

120596119900+ 11989621205966minus (1 + 119896

2) 1205962= 0 (2)

where 120596119895is the angular speed of the 119895th path

The speed ratio of the compound transmission 120591CVU andthe speed ratio of the eCVT are

120591CVU =120596119900

120596119894

120591ECVT =1205965

1205964

(3)

where 120596119894 120596119900are the angular velocities of the input and the

output shafts of the CVU From (1)ndash(3) and observing that1205963= 120596119894= 1205966and 120596

1= 1205962= 1205964(Figure 1(a)) the speed ratio

of the CVU is obtained

120591CVU =1 + 1198961+ 1198962(1 minus 120591ECVT)

120591ECVT + 1198961 (4)

Making the derivative of (4) with respect to 120591ECVT

119889120591CVU119889120591ECVT

= minus1198961+ 1198962+ 11989621198961

(120591ECVT + 1198961)2 (5)

then the CVU speed ratio is always a monotonic functionsince the sign of the derivate (5) does not change if 120591ECVTchanges

If one desires specific minimum (120591CVU119898) and maximum(120591CVU119872) values of the global speed ratio with given 120591ECVT119898and 120591ECVT119872 it is possible to calculate 1198961 and 1198962 as the uniquesolution of a system of two equations with two unknownsIn fact if 120591CVU is supposed to be a monotonic increasingfunction of 120591ECVT then the following system of equations canbe written

1198961(120591CVU119872 minus 1) + 1198962 (120591ECVT119872 minus 1) + 120591CVU119872120591ECVT119872

minus 1 = 0

1198961(120591CVU119898 minus 1) + 1198962 (120591ECVT119898 minus 1) + 120591CVU119898120591ECVT119898

minus 1 = 0

(6)

From it it follows that

1198961=(120591CVU119872120591ECVT119872 minus 1) (1 minus 120591ECVT119898) minus (120591CVU119898120591ECVT119898 minus 1) (1 minus 120591ECVT119872)

(120591CVU119872 minus 1) (120591ECVT119898 minus 1) minus (120591CVU119898 minus 1) (120591ECVT119872 minus 1)

1198962=(120591CVU119872120591ECVT119872 minus 1) (1 minus 120591CVU119898) minus (120591CVU119898120591ECVT119898 minus 1) (1 minus 120591CVU119872)

(120591CVU119898 minus 1) (120591ECVT119872 minus 1) minus (120591CVU119872 minus 1) (120591ECVT119898 minus 1)

(7)

Then the values of the parameters 1198961and 1198962of the planetary

gears depend only on the limits imposed of 120591ECVT and 120591CVU1198961and 119896

2can also be obtained in case that 120591CVU is

supposed to be a monotonic decreasing function of 120591ECVT

1198961=(120591CVU119872120591ECVT119898 minus 1) (1 minus 120591ECVT119872) minus (120591CVU119898120591ECVT119872 minus 1) (1 minus 120591ECVT119898)

(120591CVU119872 minus 1) (120591ECVT119872 minus 1) minus (120591CVU119898 minus 1) (120591ECVT119898 minus 1)

1198962=(120591CVU119872120591ECVT119898 minus 1) (1 minus 120591CVU119898) minus (120591CVU119898120591ECVT119872 minus 1) (1 minus 120591CVU119872)

(120591CVU119898 minus 1) (120591ECVT119898 minus 1) minus (120591CVU119872 minus 1) (120591ECVT119872 minus 1)

(8)

In conclusion the values of 120591CVU corresponding to workingconditions with zero power through the eCVT (mechanicalpoints) are obtained from (4) with 120596

5= 0 (corresponding to

120591ECVT = infin) or 1205964 = 0 (which corresponds to 120591ECVT = 0)

120591ICVU = minus1198962

120591IICVU =1 + 1198961+ 1198962

1198961

(9)

3 Power Flow and Efficiency ofOutput Compound e-CVT

In order to investigate the power flows and the efficiency ofthe Output Compound Split (Figure 1(a)) the overall systemis divided into a subcomponent (Equivalent e-CVT) and thesecond planetary gear PGII (Figure 2(a)) The Equivalent e-CVT is made of the e-CVT and the PGI (Figure 2(b))

4 International Journal of Vehicular Technology

3

26

Equivalent

Input

Output

PGII

e-CVT

(a)

1

54

3

2

Equivalent

PGI

e-CVT

e-CVT

(b)

Figure 2 (a) Schematic picture of the Output Compound with the ldquoEquivalent e-CVTrdquo (b) Equivalent e-CVT

The scheme of Figure 2(a) is also an Output Split (OS)where the Continuously Variable Transmission is replacedwith the Equivalent e-CVT

For this architecture we define

120591ECVTeq =1205963

1205962

(10)

From (2)-(3) and (10) and considering 1205963= 1205966= 120596119894

(Figure 2(a)) it follows that

120591ECVTeq =120591ECVT + 11989611 + 1198961

(11)

The transmission ratio in (11) depends only on the values ofthe parameter 119896

1of the PGI and it is a monotonic function

From (2) (3) and (11) the CVU speed ratio is obtained as afunction of the Equivalent e-CVT speed ratio

120591CVU =1 + 1198962(1 minus 120591ECVTeq)

120591ECVTeq (12)

It has been demonstrated that in the case of an OutputSplit (OS) (Figure 2(a)) a Type I power flow is obtainedif |120591CVU| = |120596119900120596119894| is a monotonic increasing function of|120591ECVT| = |12059651205964| whereas Type II power flow is obtainedfor a monotonic decreasing function

In the case of Input Split the power flows are the oppositewith respect to the Output Split This means that a TypeI power flow can be obtained by imposing a monotonicdecreasing trend of |120591CVU| = |120596119900120596119894| in function of |120591ECVT| =|12059651205964| whereas a Type II power flow is achieved if the

function has a monotonic increasing trendNow the power flows in the CVU can be analyzed as

they are obtained as combinations of the power flows in theOutput Split and Equivalent e-CVTThe power circulation inthe compound depends only on whether the speed ratios ofthe CVU and Equivalent e-CVT are increasing or decreasingfunctions of Equivalent e-CVT and e-CVT respectively

If a monotonic increase of 120591CVU as a function of 120591ECVTeqis considered a Type I power flow (Figure 3(b)) is obtainedthat is the power through the PGII is greater than the inputpower In this condition the Equivalent e-CVT is in anOutput Split If 120591ECVTeq is an increasing function of 120591ECVTthen a Type I power flow is obtained also in the Equivalent e-CVT (Figure 3(c)) Therefore this kind of power circulationshown in Figure 3(a) is named Type II power flow In theType II power flow also the overall speed ratio 120591CVU is amonotonic increasing function of 120591ECVT In order to achievethe Type II power flow (7) must be used to calculate the gearratios 119896

1and 1198962of the planetary gear trains

If 120591ECVTeq is a decreasing function of 120591ECVT a power flowof Type II is obtained in the Equivalent e-CVT (Figure 4(c))that is the power through the e-CVT is greater than the inputpower of the Equivalent e-CVT Hence with a monotonicincrease of 120591CVU as a function of 120591ECVTeq (Figure 4(b))a power flow named Type III (Figure 4(a)) is obtainedby imposing that 120591CVU is a decreasing function of 120591ECVTTherefore Type III power flow is obtained solving (8) to findthe parameters 119896

1and 1198962of the planetary gear trains

If 120591CVU is a decreasing function 120591ECVTeq (Figure 5(b))the Equivalent e-CVT is in the Input Split (IS) configuration(Figure 5(c)) and Type I power flow occurs when 120591ECVTeq isan increasing function of 120591ECVT Therefore considering thewhole transmission a Type III power flow occurs if 120591CVU isa decreasing function of 120591ECVT (Figure 5(a)) Hence Type IIIpower flow is achieved when (8) are solved to obtain 119896

1and

1198962If 120591CVU is a decreasing function of 120591ECVTeq and 120591ECVTeq

is a decreasing function of 120591ECVT Type IIII power flowoccurs in the Output Compound Split (Figure 6(a)) Thenthe power flow in Figure 6(a) occurs when 120591CVU increaseswith increasing 120591ECVT

In conclusion with (7) Type II and Type IIII are the twopossible power flows that occur in the transmission On thecontrary Type III andType III power flows are achievedwith(8)

International Journal of Vehicular Technology 5

13

5

2

4

6

Output compoundType II power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type I power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type I power flow

e-CVT

e-CVT

PGI

(c)

Figure 3 Power flows in a Compound Split e-CVT with Type II power flow (a) Output Compound Split e-CVT (b) The Output Split withEquivalent e-CVT and Type I power flow and (c) the Equivalent e-CVT with Type I power flow

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type I power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type II power flow

PGI

e-CVT

e-CVT

(c)

Figure 4 Power flows in a Compound Split e-CVT with Type III power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type I power flow and (c) the Equivalent e-CVT with Type II power flow

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type II power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type I power flow

PGI

e-CVT

e-CVT

(c)

Figure 5 Power flows in a Compound Split e-CVT with Type III power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type II power flow and (c) the Equivalent e-CVT with Type I power flow

6 International Journal of Vehicular Technology

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type II power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type II power flow

PGI

e-CVT

e-CVT

(c)

Figure 6 Power flows in a Compound Split e-CVT with Type IIII power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type II power flow and (c) the Equivalent e-CVT with Type II power flow

Finally in agreement with the considerations suggestedin [21] if the following inequality is verified

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)lt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (13)

the Type II or Type III are the working conditions of thetransmission On the contrary if

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)gt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (14)

the Type III or Type IIII are established in the CVUFor the efficiency of Output Compound Split Transmis-

sion the approach is based upon the assumption that onlythe losses in the e-CVT are considered This assumption isgenerally accepted because the efficiency 120578ECVT of the e-CVT is very low (eg an electric motor-generator) comparedwith the other componentsThis condition is named the ldquorealsystemrdquo

The Output Compound Split Transmission with powerflow of Type II is considered (Figure 3(a)) Both the idealsystem (without losses) and the real system are analyzed andcompared to each other For given kinematic conditions (120596

119894

120591ECVT) and output torque 119879119900 the ratios of the torques of

PGII shaft (branches ldquo2rdquo and ldquo6rdquo) are fixed and so the ratiosbetween powers are also determined This means that thepowers in the branches ldquo2rdquo (119875

2) and ldquo6rdquo (119875

6) have the same

value in the ideal and the real systemOn the other hand the input power and the power of

branch 3 are different in the ideal system and in the realsystem In the real system because of the power loss of thee-CVT the input power 119875in is increased and the power 119875

3is

decreased

It has been demonstrated in [28] that the ratio given bythe power through the e-CVT branch divided by the inputpower of the overall CVU can be easily calculated (underthe assumption of negligible power loss) relying only on thesystem kinematics

10038161003816100381610038161003816100381610038161003816

119875ECVT119875in

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

119889120591CVU119889120591ECVT

120591ECVT120591CVU

10038161003816100381610038161003816100381610038161003816 (15)

Equation (15) is general and therefore it can be applied tothe Compound Split Transmission as well as the Equivalent e-CVTAsmentioned above the input power119875

2(Figure 3(c)) of

the Equivalent e-CVTdoes not changewhen the ideal and thereal cases are compared Hence (15) is suitable for calculatingthe power in the real system The power ratio is simply givenby

100381610038161003816100381610038161003816100381610038161003816

119875ECVTeq

119875in

100381610038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198752

119875out

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198752

119875out

10038161003816100381610038161003816100381610038161003816real

=

100381610038161003816100381610038161003816100381610038161003816

119889120591CVU119889120591ECVTeq

120591ECVTeq

120591CVU

100381610038161003816100381610038161003816100381610038161003816

=

100381610038161003816100381610038161003816100381610038161003816

1 + 1198962+ 1198961+ 11989621198961

1 + 1198961+ 1198962(1 minus 120591ECVT)

100381610038161003816100381610038161003816100381610038161003816

(16)

The power loss in the Equivalent e-CVT of the real systemcan be obtained as follows

119875119908CVU= minus (1 minus 120578ECVTeq)

100381610038161003816100381611987521003816100381610038161003816

= minus (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq10038161003816100381610038161003816

(17)

International Journal of Vehicular Technology 7

Using (16)-(17) and the power at the input shaft of the CVUthe efficiency can be finally calculated

120578CVU = minus119875out119875in=119875out119875out + 119875119908CVU

=1

1 + (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816real

=1

1 + (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816ideal

(18)

The efficiency 120578ECVTeq of Equivalent e-CVT can be derivedusing the same approach

Indeed if the Equivalent e-CVT is considered(Figure 3(c)) with given 120596

2 120591ECVT and 1198793 the angular

velocities and torques at branches ldquo1rdquo and ldquo5rdquo do no differbetween the ideal and real system

The power loss in the e-CVT of the real Equivalent ECVTcan be easily written as a function of the power 119875

5

119875119908ECVT= minus (1 minus 120578ECVT)

100381610038161003816100381611987551003816100381610038161003816 (19)

Therefore it follows that the efficiency in the Equivalent e-CVT is

120578ECVTeq = minus119875out119875in=119875out

119875out + 119875119908ECVT=

1

1 + 119875119908ECVT119875out

=1

1 + (1 minus 120578ECVT)1003816100381610038161003816119875511987531003816100381610038161003816ideal

=1

1 + (1 minus 120578ECVT)1003816100381610038161003816119875ECVT1198753

1003816100381610038161003816ideal

(20)

By considering (11) and (15) the power ratio in the Equivalente-CVT can be obtained as follows (Figure 3(c))

10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

119875ECVT1198753

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198755

1198753

10038161003816100381610038161003816100381610038161003816ideal

=

100381610038161003816100381610038161003816100381610038161003816

120597120591ECVTeq

120597120591ECVT

120591ECVT120591ECVTeq

100381610038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

120591ECVT120591ECVT + 1198961

10038161003816100381610038161003816100381610038161003816

(21)

In conclusion the efficiency can be calculated with (18) inwhich 120578ECVTeq can be obtained by (20) where |119875ECVTeq119875in|ideal and |119875ECVT1198753|ideal are derived from (16) and (21)respectively

For the Output Compound Split Transmission withpower flow of Type III the CVU architecture is the same asthe previous case (Figure 4(b)) Therefore the power loss issimply given by (17) and the efficiency by (18) whereas theformula for 120578ECVTeq is different

The power flow in the Equivalent e-CVT and its efficiency120578ECVTeq change compared with the previous case Also inthis case 119875

5does not change when comparing the ideal

system and the real system (Figure 4(c)) This means thatthe expression for the power loss in the Equivalent e-CVT is

a function of the e-CVT output power 1198755 that is the power

loss is given by

119875119908CVTeq= minus(1 minus 120578ECVT)

120578ECVT

100381610038161003816100381611987551003816100381610038161003816 (22)

From (20) and (22) the efficiency of the Equivalent e-CVT is

120578ECVTeq = minus119875out119875in=119875out

119875out + 119875119908ECVT=

1

1 + 119875119908ECVT119875out

=1

1 + ((1 minus 120578ECVT) 120578ECVT)1003816100381610038161003816119875ECVT1198753

1003816100381610038161003816ideal

(23)

In conclusion the efficiency of Type III power flow can becalculated through (18) where 120578ECVTeq can be obtained by(23)

The efficiency of the CVU working with Type III powerflow is derived using a similar approach

From Figure 5(b) it follows that the power 1198752which has

the same value in the ideal system and in the real system isthe output power of the Equivalent e-CVTThe power loss inthe e-CVT of the real Equivalent e-CVT (Figure 4(c)) is

119875119908CVU= minus(1 minus 120578ECVTeq)

120578ECVTeq

100381610038161003816100381611987521003816100381610038161003816

(24)

Thus the efficiency of the CVU is given by

120578CVU = minus119875out119875in=119875out119875out + 119875119908CVU

=1

1 + ((1 minus 120578ECVTeq) 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816ideal

(25)

It follows that the power loss and efficiency of the Equivalente-CVT are given by

119875119908ECVTeq= minus(1 minus 120578ECVT)

120578ECVT

100381610038161003816100381611987551003816100381610038161003816 (26)

120578ECVTeq = minus119875out119875in=119875in + 119875119908ECVT119875in

= 1 minus(1 minus 120578ECVT)

120578ECVT

10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal

(27)

The power ratio in the Equivalent e-CVT is obtained using(21) hence the efficiency in the Equivalent e-CVT followsfrom (27)

In conclusion the efficiency of Type III can be calculatedthrough (25) where 120578ECVTeq can be obtained by (27)

Finally in theOutput Compound Split Transmissionwithpower flow of Type IIII we obtained (Figure 6)

119875119908ECVTeq= minus (1 minus 120578ECVT)

100381610038161003816100381611987551003816100381610038161003816 (28)

8 International Journal of Vehicular Technology

The power ratio in the Equivalent e-CVT follows from (21)Therefore the efficiency of the Equivalent e-CVT is deducedfrom equation

120578ECVTeq = minus119875out119875in=119875in + 119875119908ECVT119875in

= 1 minus (1 minus 120578ECVT)10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal

(29)

It can be noticed that the power flowof Figure 6(b) is identicalto Figure 5(b) It follows that also in this case the efficiency iscalculated with (25) with 120578ECVTeq calculated as (29)

4 Numerical Example

In this section a numerical example is given which alsoincludes the calculation of the transmission efficiency usingthe simplified approach described in this work The calcula-tions can be performed after the speed ratio of the CVU andthe e-CVT have been imposed It is here assumed that speedratio of the e-CVT varies between the bounds 120591ECVT119898 = 04and 120591ECVT119872 = 2 which is typical of mechanical CVT Theratio range of the CVU is a system requirement so it canbe chosen arbitrarily A CVU is here designed with a speedratio bounded between 120591CVU119898 = minus1 and 120591CVU119872 = 2 inorder to comprise also the neutral gear These CVU boundscan be obtained only by choosing two planetary gear trainscharacterized by 119896

1and 119896

2calculated with (7) in the case

of monotonic increase of the CVU speed ratio for increasingECVT speed ratio It is obtained that

1198961= 029

1198962= minus329

(30)

If the case of a monotonic decreasing CVU speed ratio withincreasing e-CVT speed ratio 119896

1and 119896

2must be calculated

with (8) it follows that

1198961= minus10

1198962= minus17

(31)

The CVU speed ratio as a function of the e-CVT speed ratiogiven by (4) is shown in Figure 7 for the two aforementionedcases

The power ratio |119875ECVT119875CVU| calculated with (15) isshown in Figure 8

Two regions can be distinguished corresponding to twodifferent ranges of 120591CVU the first range 0 le 120591CVU le 2 and thesecond range minus1 lt 120591CVU lt 0

Each region corresponds to a different power circulationConsidering the limits imposed on the speed ratio of thisexample it results in the following

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)gt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (32)

With the help of (13) and (14) one can determine the powerflow type taking also into account the sign change of the

Monotonically increasing Monotonically decreasing

minus10

minus05

00

05

10

15

20

120591CV

U

020 040 060 080 100 120 140 160 180 200000120591ECVT

Figure 7 Speed ratio of the CVU (120591CVU) as a function of the e-CVTspeed ratio (120591ECVT)

Monotonically increasing Monotonically decreasing

0123456789

10

00minus05minus10 10 15 2005120591CVU

PEC

VT

PCV

U

Figure 8 Power ratio |119875ECVT119875CVU| considering no losses plotted asa function of the overall speed ratio 120591CVU

ratio 120591CVU In fact when 120591CVU is an increasing function of120591ECVT the Type IIII power flow occurs for 120591CVU gt 0 as aconsequence of (14) whereas in the other regionwith 120591CVU lt0 the power flow changes from Type IIII to Type III [21]

On the other hand when 120591CVU is a decreasing function of120591ECVT (14) still holds but in this case the Type III power flowoccurs if 120591CVU gt 0 whereas if 120591CVU lt 0 then the power flowis changed from Type III to Type IIII [21]

The ratio given by the power through the e-CVT dividedby the global power is not equal in the two cases (Figure 8)With 120591CVU lt 1 the power ratio is larger when the speed ratioof the transmission is a decreasing function of the speed ratioof the e-CVTOnly with 120591CVU gt 1 the situation is the oppositeone

The efficiency 120578CVU plotted as a function of 120591CVU isshown in Figure 9 considering that 120578ECVT = 09 For 120591CVU gt0 and with a monotonically increasing CVU speed ratio withincreasing e-CVT speed ratio (power flow of Type IIII) (16)(21) (25) and (29) are utilized In this case the efficiencyis larger than in the case of monotonically decreasing speed

International Journal of Vehicular Technology 9

Monotonically increasing Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Figure 9 The efficiency 120578CVU as a function of the overall speed ratio 120591CVU (120578ECVT = 09)

ratio for 120591CVU lt 1 whereas the opposite condition is verifiedfor 120591CVU gt 1This is expected since the device with the lowestandmost critical efficiency is the e-CVT so the configurationthat minimizes the power through the e-CVT is the mostconvenient one in terms of energy efficiency

5 Efficiency of the Output Compound e-CVTin Direct and Reverse Operation

Hybrid vehicles are the main application for CompoundSplit-eCVT transmission One of themost important featuresof hybrid vehicles is the regenerative braking capabilitySuch a function needs the transmission to work in reverseoperation For this reason it is important to evaluate theefficiency of the transmission in both direct and reverseoperation and to understand the differences

In this section the same transmission data are considered(120591ECVT119898 = 04 120591ECVT119872 = 2 120591CVU119898 = minus1 120591CVU119872 = 2) andthe performance in reverse operation are calculated throughthe model developed in a previous work [22] The efficiency120578ECVT of the e-CVT is considered constant and given by120578ECVT = 09 As mentioned in the compound transmissionwith a monotonic increasing speed ratio (119896

1= 029 119896

2=

minus329) if 120591CVU119898 gt 0 a power flow of Type IIII is obtainedGiven the same kinematic parameters when the transmissionworks in reverse operation (Figure 10) the input and outputtorques are reversed and because of the planetary gear trainPG1 also the torques on links 2 and 6 are reversed Further-more the torque and the power on the link 3 are also reversedand as a consequence of the planetary gear train PG2 alsothe torque and power on links 1 4 and 5 are reversed Soin the change from direct operation (Figure 10(a)) to reverseoperation (Figure 10(b)) the power flow is reversed on all thelinks and the power flow is yet of Type IIII

When 120591CVU119898 lt 0 similar arguments leads to concludethat the power flow is of Type III also in reverse operation(Figure 11)

The monotonic increasing speed ratio is investigatedfirst In Figure 12 it is shown that in reverse operation theefficiency of the transmission is always less than in directoperation with the only exception of the high values of thespeed ratio (120591CVU gt 17) It is very interesting to see that whenthe speed ratio is close to zero (minus027 lt 120591CVU lt 022) theefficiency in reverse operation is negative which means thatthe transmission is nonreversible with the speed ratio in theaforementioned range This result is in agreement with theresults shown in [8] in the case of Power Split TransmissionsIt is actually relevant for applications to the hybrid vehiclesbecause it affects negatively the braking recovery capabilitiesIn particular it is not possible to recover energy in brakingwith minus027 lt 120591CVU lt 022

Similar results can be obtained in the case of monotonicdecreasing speed ratio (Figure 7) Given the speed ratioranges of CVT and CVU (which give 119896

1= minus10 and 119896

2=

minus17) also in this case the power flows do not change whenswitching from direct to reverse operation power flow ofType III with 120591CVU gt 0 (Figure 11) and power flow of TypeIIII with 120591CVU lt 0 (Figure 10) The efficiency in direct andreverse operation is shown in Figure 13 Also in this case theefficiency in reverse operation is visibly less than in directmode Furthermore the nonreversibility range of the speedis even larger being minus040 lt 120591CVU lt 028

6 Conclusions

In recent years compound transmissions are attractingincreasing interest for application in hybrid vehicles becausethey are flexible and they permit optimizing the efficiency indifferent operating conditions The goal of this work was toobtain a systematic approach to determine the power flowsand the efficiency in Output Compound Split Transmissionsfor optimal design and control of HEVs The proposedmethodology is suitable for steady-state working conditionsand it follows from the assumption of negligible power lossin all the components except for the e-CVT It is shown how

10 International Journal of Vehicular Technology

Forward power

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 10 Power flows in a Output Compound Split e-CVT with Type IIII power flow (a) forward power (b) reverse power

Forward power

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 11 Power flows in a Output Compound Split e-CVT with Type III power flow (a) forward power (b) reverse power

the power circulation depends only on kinematic conditionsFurthermore a novel approach is shown to study the effi-ciency of the transmission which relies on the separationof the compound transmission in two subsystems so thatit can be studied as an ldquoEquivalent e-CVTrdquo (which is apower split-like transmission of Input-Output Split type)inside an Output Split device Following our approach the

efficiency is calculated easily for each of all the possiblepower flows A numerical example showed the potentialof this tool for power flows and efficiency calculations ofthe Output Compound Split Transmission in direct andreverse operation Experimental validation of the presentedmethodology is in progress and it will be the subject matterof future works

International Journal of Vehicular Technology 11

Forward power Reverse power

Monotonically increasing

0001020304050607080910

120578CV

U

00 10 201505minus10 minus05120591CVU

Figure 12The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically increasing

Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Forward power Reverse power

Figure 13The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically decreasing

Nomenclature

CVU CVTECVT and PG(subscripts)

Continuously Variable Unit ContinuouslyVariable Transmission ElectronicContinuously Variable Transmission andplanetary gear

119872119898 eq(subscripts)

Maximum minimum and equivalentrespectively

1198961 1198962 Kinematic parameter of the PG 1 and 2

respectively119875119895 Power through the 119895th branch119875119908 119875in and119875out

Dissipated power input power and outputpower

120591 Speed ratio120578 Efficiency120596119895 Angular velocity of the 119895th shaft

120596119900 Angular velocity of the output shaftof theCVU120596119894 Angular velocity of the input shaft of the CVU

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M R Cuddy and K B Wipke ldquoAnalysis of the fuel econ-omy benefit of drivetrain hybridizationrdquo SAE Technical Paper970289 1997

[2] S Stockar V Marano M Canova G Rizzoni and L GuzzellaldquoEnergy-optimal control of plug-in hybrid electric vehiclesfor real-world driving cyclesrdquo IEEE Transactions on VehicularTechnology vol 60 no 7 pp 2949ndash2962 2011

[3] L Serrao S Onori and G Rizzoni ldquoA comparative analysisof energy management strategies for hybrid electric vehiclesrdquoJournal of Dynamic Systems Measurement and Control vol 133no 3 Article ID 031012 2011

[4] F R Salmasi ldquoControl strategies for hybrid electric vehiclesevolution classification comparison and future trendsrdquo IEEETransactions on Vehicular Technology vol 56 no 5 pp 2393ndash2404 2007

[5] F Bottiglione T Contursi A Gentile and G Mantriota ldquoThefuel economy of hybrid buses the role of ancillaries in realurban drivingrdquo Energies vol 7 no 7 pp 4202ndash4220 2014

[6] A Taghavipour N L Azad and J McPhee ldquoAn optimal powermanagement strategy for power split plug-in hybrid electricvehiclesrdquo International Journal of Vehicle Design vol 60 no 3-4pp 286ndash304 2012

[7] Z Zhao C Wang T Zhang X Dai and X Yuan ldquoControloptimization of a compound power-split hybrid transmissionfor electric driverdquo SAE Technical Papers 2015

[8] G Mantriota ldquoPerformances of a series infinitely variabletransmission with type I power flowrdquo Mechanism and MachineTheory vol 37 no 6 pp 579ndash597 2002

[9] G Mantriota ldquoPerformances of a parallel infinitely variabletransmissions with a type II power flowrdquo Mechanism andMachine Theory vol 37 no 6 pp 555ndash578 2002

[10] B Si ldquoReconfigurable Hybrid Gear Trainrdquo US Patent 0 070 992A1 2011

[11] B Si ldquoDual mode input split compound split configurationEPPV transmissionrdquo US Patent 8 075 435 B2 2011

[12] F Bottiglione andGMantriota ldquoMG-IVT an infinitely variabletransmission with optimal power flowsrdquo Journal of MechanicalDesign vol 130 no 11 Article ID 112603 2008

[13] K T Chau andW Li ldquoOverview of electricmachines for electricand hybrid vehiclesrdquo International Journal of Vehicle Design vol64 no 1 pp 46ndash71 2014

[14] A G Holmes and M R Schmidt ldquoHybrid Electric PowertrainIncluding a Two-Mode Electrically Variable Transmissionrdquo USPatent 6 478 705 B1 2002

[15] C Brendan ldquoComparative analysis of single and combinedhybrid electrically variable transmission operatingmodesrdquo SAETechnical Paper 2005-01-1165 2005

[16] B Mashadi and S A M Emadi ldquoDual-mode power-splittransmission for hybrid electric vehiclesrdquo IEEE Transactions onVehicular Technology vol 59 no 7 pp 3223ndash3232 2010

12 International Journal of Vehicular Technology

[17] J Kim J Kang Y Kim T Kim B Min and H Kim ldquoDesignof power split transmission design of dual mode power splittransmissionrdquo International Journal of Automotive Technologyvol 11 no 4 pp 565ndash571 2010

[18] Y Zou F-C Sun C-N Zhang and J-Q Li ldquoOptimal energymanagement strategy for hybrid electric tracked vehiclesrdquoInternational Journal of Vehicle Design vol 58 no 2ndash4 pp 307ndash324 2012

[19] N-D Kim J-M Kim and H-S Kim ldquoControl strategy for adual-mode electromechanical infinitely variable transmissionfor hybrid electric vehiclesrdquo Proceedings of the Institution ofMechanical Engineers PartD Journal of Automobile Engineeringvol 222 no 9 pp 1587ndash1601 2008

[20] J Kim T Kim B Min S Hwang and H Kim ldquoModecontrol strategy for a two-mode hybrid electric vehicle usingelectrically variable transmission (EVT) and fixed-gear moderdquoIEEE Transactions on Vehicular Technology vol 60 no 3 pp793ndash803 2011

[21] Z Zhou CMi andG Zhang ldquoIntegrated control of electrome-chanical braking and regenerative braking in plug-in hybridelectric vehiclesrdquo International Journal of Vehicle Design vol 58no 2ndash4 pp 223ndash239 2012

[22] F Bottiglione and G Mantriota ldquoReversibility of power-splittransmissionsrdquo Journal ofMechanicalDesign Transactions of theASME vol 133 no 8 Article ID 084503 2011

[23] F Bottiglione and G Mantriota ldquoEffect of the ratio spread ofCVU in automotive kinetic energy recovery systemsrdquo Journalof Mechanical Design Transactions of the ASME vol 135 no 6Article ID 061001 2013

[24] F Bottiglione G Carbone L De Novellis L Mangialardiand G Mantriota ldquoMechanical hybrid KERS based on toroidaltraction drives an example of smart tribological design toimprove terrestrial vehicle performancerdquoAdvances in Tribologyvol 2013 Article ID 918387 9 pages 2013

[25] S De Pinto F Bottiglione andGMantriota ldquoInfinitely variabletransmissions in neutral gear torque ratio and power re-circulationrdquo Mechanism and Machine Theory vol 74 pp 285ndash298 2014

[26] S de Pinto and G Mantriota ldquoA simple model for compoundsplit transmissionsrdquo Proceedings of the Institution of MechanicalEngineers Part D Journal of Automobile Engineering vol 228no 5 pp 549ndash564 2014

[27] G Mantriota ldquoFuel consumption of a vehicle with power splitCVT systemrdquo International Journal of Vehicle Design vol 37 no4 pp 327ndash342 2005

[28] M Cammalleri ldquoEfficiency of split-way CVTrsquos A simplifiedmodelrdquo SAE Technical Papers 15 2007

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

4 International Journal of Vehicular Technology

3

26

Equivalent

Input

Output

PGII

e-CVT

(a)

1

54

3

2

Equivalent

PGI

e-CVT

e-CVT

(b)

Figure 2 (a) Schematic picture of the Output Compound with the ldquoEquivalent e-CVTrdquo (b) Equivalent e-CVT

The scheme of Figure 2(a) is also an Output Split (OS)where the Continuously Variable Transmission is replacedwith the Equivalent e-CVT

For this architecture we define

120591ECVTeq =1205963

1205962

(10)

From (2)-(3) and (10) and considering 1205963= 1205966= 120596119894

(Figure 2(a)) it follows that

120591ECVTeq =120591ECVT + 11989611 + 1198961

(11)

The transmission ratio in (11) depends only on the values ofthe parameter 119896

1of the PGI and it is a monotonic function

From (2) (3) and (11) the CVU speed ratio is obtained as afunction of the Equivalent e-CVT speed ratio

120591CVU =1 + 1198962(1 minus 120591ECVTeq)

120591ECVTeq (12)

It has been demonstrated that in the case of an OutputSplit (OS) (Figure 2(a)) a Type I power flow is obtainedif |120591CVU| = |120596119900120596119894| is a monotonic increasing function of|120591ECVT| = |12059651205964| whereas Type II power flow is obtainedfor a monotonic decreasing function

In the case of Input Split the power flows are the oppositewith respect to the Output Split This means that a TypeI power flow can be obtained by imposing a monotonicdecreasing trend of |120591CVU| = |120596119900120596119894| in function of |120591ECVT| =|12059651205964| whereas a Type II power flow is achieved if the

function has a monotonic increasing trendNow the power flows in the CVU can be analyzed as

they are obtained as combinations of the power flows in theOutput Split and Equivalent e-CVTThe power circulation inthe compound depends only on whether the speed ratios ofthe CVU and Equivalent e-CVT are increasing or decreasingfunctions of Equivalent e-CVT and e-CVT respectively

If a monotonic increase of 120591CVU as a function of 120591ECVTeqis considered a Type I power flow (Figure 3(b)) is obtainedthat is the power through the PGII is greater than the inputpower In this condition the Equivalent e-CVT is in anOutput Split If 120591ECVTeq is an increasing function of 120591ECVTthen a Type I power flow is obtained also in the Equivalent e-CVT (Figure 3(c)) Therefore this kind of power circulationshown in Figure 3(a) is named Type II power flow In theType II power flow also the overall speed ratio 120591CVU is amonotonic increasing function of 120591ECVT In order to achievethe Type II power flow (7) must be used to calculate the gearratios 119896

1and 1198962of the planetary gear trains

If 120591ECVTeq is a decreasing function of 120591ECVT a power flowof Type II is obtained in the Equivalent e-CVT (Figure 4(c))that is the power through the e-CVT is greater than the inputpower of the Equivalent e-CVT Hence with a monotonicincrease of 120591CVU as a function of 120591ECVTeq (Figure 4(b))a power flow named Type III (Figure 4(a)) is obtainedby imposing that 120591CVU is a decreasing function of 120591ECVTTherefore Type III power flow is obtained solving (8) to findthe parameters 119896

1and 1198962of the planetary gear trains

If 120591CVU is a decreasing function 120591ECVTeq (Figure 5(b))the Equivalent e-CVT is in the Input Split (IS) configuration(Figure 5(c)) and Type I power flow occurs when 120591ECVTeq isan increasing function of 120591ECVT Therefore considering thewhole transmission a Type III power flow occurs if 120591CVU isa decreasing function of 120591ECVT (Figure 5(a)) Hence Type IIIpower flow is achieved when (8) are solved to obtain 119896

1and

1198962If 120591CVU is a decreasing function of 120591ECVTeq and 120591ECVTeq

is a decreasing function of 120591ECVT Type IIII power flowoccurs in the Output Compound Split (Figure 6(a)) Thenthe power flow in Figure 6(a) occurs when 120591CVU increaseswith increasing 120591ECVT

In conclusion with (7) Type II and Type IIII are the twopossible power flows that occur in the transmission On thecontrary Type III andType III power flows are achievedwith(8)

International Journal of Vehicular Technology 5

13

5

2

4

6

Output compoundType II power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type I power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type I power flow

e-CVT

e-CVT

PGI

(c)

Figure 3 Power flows in a Compound Split e-CVT with Type II power flow (a) Output Compound Split e-CVT (b) The Output Split withEquivalent e-CVT and Type I power flow and (c) the Equivalent e-CVT with Type I power flow

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type I power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type II power flow

PGI

e-CVT

e-CVT

(c)

Figure 4 Power flows in a Compound Split e-CVT with Type III power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type I power flow and (c) the Equivalent e-CVT with Type II power flow

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type II power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type I power flow

PGI

e-CVT

e-CVT

(c)

Figure 5 Power flows in a Compound Split e-CVT with Type III power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type II power flow and (c) the Equivalent e-CVT with Type I power flow

6 International Journal of Vehicular Technology

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type II power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type II power flow

PGI

e-CVT

e-CVT

(c)

Figure 6 Power flows in a Compound Split e-CVT with Type IIII power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type II power flow and (c) the Equivalent e-CVT with Type II power flow

Finally in agreement with the considerations suggestedin [21] if the following inequality is verified

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)lt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (13)

the Type II or Type III are the working conditions of thetransmission On the contrary if

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)gt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (14)

the Type III or Type IIII are established in the CVUFor the efficiency of Output Compound Split Transmis-

sion the approach is based upon the assumption that onlythe losses in the e-CVT are considered This assumption isgenerally accepted because the efficiency 120578ECVT of the e-CVT is very low (eg an electric motor-generator) comparedwith the other componentsThis condition is named the ldquorealsystemrdquo

The Output Compound Split Transmission with powerflow of Type II is considered (Figure 3(a)) Both the idealsystem (without losses) and the real system are analyzed andcompared to each other For given kinematic conditions (120596

119894

120591ECVT) and output torque 119879119900 the ratios of the torques of

PGII shaft (branches ldquo2rdquo and ldquo6rdquo) are fixed and so the ratiosbetween powers are also determined This means that thepowers in the branches ldquo2rdquo (119875

2) and ldquo6rdquo (119875

6) have the same

value in the ideal and the real systemOn the other hand the input power and the power of

branch 3 are different in the ideal system and in the realsystem In the real system because of the power loss of thee-CVT the input power 119875in is increased and the power 119875

3is

decreased

It has been demonstrated in [28] that the ratio given bythe power through the e-CVT branch divided by the inputpower of the overall CVU can be easily calculated (underthe assumption of negligible power loss) relying only on thesystem kinematics

10038161003816100381610038161003816100381610038161003816

119875ECVT119875in

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

119889120591CVU119889120591ECVT

120591ECVT120591CVU

10038161003816100381610038161003816100381610038161003816 (15)

Equation (15) is general and therefore it can be applied tothe Compound Split Transmission as well as the Equivalent e-CVTAsmentioned above the input power119875

2(Figure 3(c)) of

the Equivalent e-CVTdoes not changewhen the ideal and thereal cases are compared Hence (15) is suitable for calculatingthe power in the real system The power ratio is simply givenby

100381610038161003816100381610038161003816100381610038161003816

119875ECVTeq

119875in

100381610038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198752

119875out

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198752

119875out

10038161003816100381610038161003816100381610038161003816real

=

100381610038161003816100381610038161003816100381610038161003816

119889120591CVU119889120591ECVTeq

120591ECVTeq

120591CVU

100381610038161003816100381610038161003816100381610038161003816

=

100381610038161003816100381610038161003816100381610038161003816

1 + 1198962+ 1198961+ 11989621198961

1 + 1198961+ 1198962(1 minus 120591ECVT)

100381610038161003816100381610038161003816100381610038161003816

(16)

The power loss in the Equivalent e-CVT of the real systemcan be obtained as follows

119875119908CVU= minus (1 minus 120578ECVTeq)

100381610038161003816100381611987521003816100381610038161003816

= minus (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq10038161003816100381610038161003816

(17)

International Journal of Vehicular Technology 7

Using (16)-(17) and the power at the input shaft of the CVUthe efficiency can be finally calculated

120578CVU = minus119875out119875in=119875out119875out + 119875119908CVU

=1

1 + (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816real

=1

1 + (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816ideal

(18)

The efficiency 120578ECVTeq of Equivalent e-CVT can be derivedusing the same approach

Indeed if the Equivalent e-CVT is considered(Figure 3(c)) with given 120596

2 120591ECVT and 1198793 the angular

velocities and torques at branches ldquo1rdquo and ldquo5rdquo do no differbetween the ideal and real system

The power loss in the e-CVT of the real Equivalent ECVTcan be easily written as a function of the power 119875

5

119875119908ECVT= minus (1 minus 120578ECVT)

100381610038161003816100381611987551003816100381610038161003816 (19)

Therefore it follows that the efficiency in the Equivalent e-CVT is

120578ECVTeq = minus119875out119875in=119875out

119875out + 119875119908ECVT=

1

1 + 119875119908ECVT119875out

=1

1 + (1 minus 120578ECVT)1003816100381610038161003816119875511987531003816100381610038161003816ideal

=1

1 + (1 minus 120578ECVT)1003816100381610038161003816119875ECVT1198753

1003816100381610038161003816ideal

(20)

By considering (11) and (15) the power ratio in the Equivalente-CVT can be obtained as follows (Figure 3(c))

10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

119875ECVT1198753

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198755

1198753

10038161003816100381610038161003816100381610038161003816ideal

=

100381610038161003816100381610038161003816100381610038161003816

120597120591ECVTeq

120597120591ECVT

120591ECVT120591ECVTeq

100381610038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

120591ECVT120591ECVT + 1198961

10038161003816100381610038161003816100381610038161003816

(21)

In conclusion the efficiency can be calculated with (18) inwhich 120578ECVTeq can be obtained by (20) where |119875ECVTeq119875in|ideal and |119875ECVT1198753|ideal are derived from (16) and (21)respectively

For the Output Compound Split Transmission withpower flow of Type III the CVU architecture is the same asthe previous case (Figure 4(b)) Therefore the power loss issimply given by (17) and the efficiency by (18) whereas theformula for 120578ECVTeq is different

The power flow in the Equivalent e-CVT and its efficiency120578ECVTeq change compared with the previous case Also inthis case 119875

5does not change when comparing the ideal

system and the real system (Figure 4(c)) This means thatthe expression for the power loss in the Equivalent e-CVT is

a function of the e-CVT output power 1198755 that is the power

loss is given by

119875119908CVTeq= minus(1 minus 120578ECVT)

120578ECVT

100381610038161003816100381611987551003816100381610038161003816 (22)

From (20) and (22) the efficiency of the Equivalent e-CVT is

120578ECVTeq = minus119875out119875in=119875out

119875out + 119875119908ECVT=

1

1 + 119875119908ECVT119875out

=1

1 + ((1 minus 120578ECVT) 120578ECVT)1003816100381610038161003816119875ECVT1198753

1003816100381610038161003816ideal

(23)

In conclusion the efficiency of Type III power flow can becalculated through (18) where 120578ECVTeq can be obtained by(23)

The efficiency of the CVU working with Type III powerflow is derived using a similar approach

From Figure 5(b) it follows that the power 1198752which has

the same value in the ideal system and in the real system isthe output power of the Equivalent e-CVTThe power loss inthe e-CVT of the real Equivalent e-CVT (Figure 4(c)) is

119875119908CVU= minus(1 minus 120578ECVTeq)

120578ECVTeq

100381610038161003816100381611987521003816100381610038161003816

(24)

Thus the efficiency of the CVU is given by

120578CVU = minus119875out119875in=119875out119875out + 119875119908CVU

=1

1 + ((1 minus 120578ECVTeq) 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816ideal

(25)

It follows that the power loss and efficiency of the Equivalente-CVT are given by

119875119908ECVTeq= minus(1 minus 120578ECVT)

120578ECVT

100381610038161003816100381611987551003816100381610038161003816 (26)

120578ECVTeq = minus119875out119875in=119875in + 119875119908ECVT119875in

= 1 minus(1 minus 120578ECVT)

120578ECVT

10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal

(27)

The power ratio in the Equivalent e-CVT is obtained using(21) hence the efficiency in the Equivalent e-CVT followsfrom (27)

In conclusion the efficiency of Type III can be calculatedthrough (25) where 120578ECVTeq can be obtained by (27)

Finally in theOutput Compound Split Transmissionwithpower flow of Type IIII we obtained (Figure 6)

119875119908ECVTeq= minus (1 minus 120578ECVT)

100381610038161003816100381611987551003816100381610038161003816 (28)

8 International Journal of Vehicular Technology

The power ratio in the Equivalent e-CVT follows from (21)Therefore the efficiency of the Equivalent e-CVT is deducedfrom equation

120578ECVTeq = minus119875out119875in=119875in + 119875119908ECVT119875in

= 1 minus (1 minus 120578ECVT)10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal

(29)

It can be noticed that the power flowof Figure 6(b) is identicalto Figure 5(b) It follows that also in this case the efficiency iscalculated with (25) with 120578ECVTeq calculated as (29)

4 Numerical Example

In this section a numerical example is given which alsoincludes the calculation of the transmission efficiency usingthe simplified approach described in this work The calcula-tions can be performed after the speed ratio of the CVU andthe e-CVT have been imposed It is here assumed that speedratio of the e-CVT varies between the bounds 120591ECVT119898 = 04and 120591ECVT119872 = 2 which is typical of mechanical CVT Theratio range of the CVU is a system requirement so it canbe chosen arbitrarily A CVU is here designed with a speedratio bounded between 120591CVU119898 = minus1 and 120591CVU119872 = 2 inorder to comprise also the neutral gear These CVU boundscan be obtained only by choosing two planetary gear trainscharacterized by 119896

1and 119896

2calculated with (7) in the case

of monotonic increase of the CVU speed ratio for increasingECVT speed ratio It is obtained that

1198961= 029

1198962= minus329

(30)

If the case of a monotonic decreasing CVU speed ratio withincreasing e-CVT speed ratio 119896

1and 119896

2must be calculated

with (8) it follows that

1198961= minus10

1198962= minus17

(31)

The CVU speed ratio as a function of the e-CVT speed ratiogiven by (4) is shown in Figure 7 for the two aforementionedcases

The power ratio |119875ECVT119875CVU| calculated with (15) isshown in Figure 8

Two regions can be distinguished corresponding to twodifferent ranges of 120591CVU the first range 0 le 120591CVU le 2 and thesecond range minus1 lt 120591CVU lt 0

Each region corresponds to a different power circulationConsidering the limits imposed on the speed ratio of thisexample it results in the following

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)gt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (32)

With the help of (13) and (14) one can determine the powerflow type taking also into account the sign change of the

Monotonically increasing Monotonically decreasing

minus10

minus05

00

05

10

15

20

120591CV

U

020 040 060 080 100 120 140 160 180 200000120591ECVT

Figure 7 Speed ratio of the CVU (120591CVU) as a function of the e-CVTspeed ratio (120591ECVT)

Monotonically increasing Monotonically decreasing

0123456789

10

00minus05minus10 10 15 2005120591CVU

PEC

VT

PCV

U

Figure 8 Power ratio |119875ECVT119875CVU| considering no losses plotted asa function of the overall speed ratio 120591CVU

ratio 120591CVU In fact when 120591CVU is an increasing function of120591ECVT the Type IIII power flow occurs for 120591CVU gt 0 as aconsequence of (14) whereas in the other regionwith 120591CVU lt0 the power flow changes from Type IIII to Type III [21]

On the other hand when 120591CVU is a decreasing function of120591ECVT (14) still holds but in this case the Type III power flowoccurs if 120591CVU gt 0 whereas if 120591CVU lt 0 then the power flowis changed from Type III to Type IIII [21]

The ratio given by the power through the e-CVT dividedby the global power is not equal in the two cases (Figure 8)With 120591CVU lt 1 the power ratio is larger when the speed ratioof the transmission is a decreasing function of the speed ratioof the e-CVTOnly with 120591CVU gt 1 the situation is the oppositeone

The efficiency 120578CVU plotted as a function of 120591CVU isshown in Figure 9 considering that 120578ECVT = 09 For 120591CVU gt0 and with a monotonically increasing CVU speed ratio withincreasing e-CVT speed ratio (power flow of Type IIII) (16)(21) (25) and (29) are utilized In this case the efficiencyis larger than in the case of monotonically decreasing speed

International Journal of Vehicular Technology 9

Monotonically increasing Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Figure 9 The efficiency 120578CVU as a function of the overall speed ratio 120591CVU (120578ECVT = 09)

ratio for 120591CVU lt 1 whereas the opposite condition is verifiedfor 120591CVU gt 1This is expected since the device with the lowestandmost critical efficiency is the e-CVT so the configurationthat minimizes the power through the e-CVT is the mostconvenient one in terms of energy efficiency

5 Efficiency of the Output Compound e-CVTin Direct and Reverse Operation

Hybrid vehicles are the main application for CompoundSplit-eCVT transmission One of themost important featuresof hybrid vehicles is the regenerative braking capabilitySuch a function needs the transmission to work in reverseoperation For this reason it is important to evaluate theefficiency of the transmission in both direct and reverseoperation and to understand the differences

In this section the same transmission data are considered(120591ECVT119898 = 04 120591ECVT119872 = 2 120591CVU119898 = minus1 120591CVU119872 = 2) andthe performance in reverse operation are calculated throughthe model developed in a previous work [22] The efficiency120578ECVT of the e-CVT is considered constant and given by120578ECVT = 09 As mentioned in the compound transmissionwith a monotonic increasing speed ratio (119896

1= 029 119896

2=

minus329) if 120591CVU119898 gt 0 a power flow of Type IIII is obtainedGiven the same kinematic parameters when the transmissionworks in reverse operation (Figure 10) the input and outputtorques are reversed and because of the planetary gear trainPG1 also the torques on links 2 and 6 are reversed Further-more the torque and the power on the link 3 are also reversedand as a consequence of the planetary gear train PG2 alsothe torque and power on links 1 4 and 5 are reversed Soin the change from direct operation (Figure 10(a)) to reverseoperation (Figure 10(b)) the power flow is reversed on all thelinks and the power flow is yet of Type IIII

When 120591CVU119898 lt 0 similar arguments leads to concludethat the power flow is of Type III also in reverse operation(Figure 11)

The monotonic increasing speed ratio is investigatedfirst In Figure 12 it is shown that in reverse operation theefficiency of the transmission is always less than in directoperation with the only exception of the high values of thespeed ratio (120591CVU gt 17) It is very interesting to see that whenthe speed ratio is close to zero (minus027 lt 120591CVU lt 022) theefficiency in reverse operation is negative which means thatthe transmission is nonreversible with the speed ratio in theaforementioned range This result is in agreement with theresults shown in [8] in the case of Power Split TransmissionsIt is actually relevant for applications to the hybrid vehiclesbecause it affects negatively the braking recovery capabilitiesIn particular it is not possible to recover energy in brakingwith minus027 lt 120591CVU lt 022

Similar results can be obtained in the case of monotonicdecreasing speed ratio (Figure 7) Given the speed ratioranges of CVT and CVU (which give 119896

1= minus10 and 119896

2=

minus17) also in this case the power flows do not change whenswitching from direct to reverse operation power flow ofType III with 120591CVU gt 0 (Figure 11) and power flow of TypeIIII with 120591CVU lt 0 (Figure 10) The efficiency in direct andreverse operation is shown in Figure 13 Also in this case theefficiency in reverse operation is visibly less than in directmode Furthermore the nonreversibility range of the speedis even larger being minus040 lt 120591CVU lt 028

6 Conclusions

In recent years compound transmissions are attractingincreasing interest for application in hybrid vehicles becausethey are flexible and they permit optimizing the efficiency indifferent operating conditions The goal of this work was toobtain a systematic approach to determine the power flowsand the efficiency in Output Compound Split Transmissionsfor optimal design and control of HEVs The proposedmethodology is suitable for steady-state working conditionsand it follows from the assumption of negligible power lossin all the components except for the e-CVT It is shown how

10 International Journal of Vehicular Technology

Forward power

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 10 Power flows in a Output Compound Split e-CVT with Type IIII power flow (a) forward power (b) reverse power

Forward power

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 11 Power flows in a Output Compound Split e-CVT with Type III power flow (a) forward power (b) reverse power

the power circulation depends only on kinematic conditionsFurthermore a novel approach is shown to study the effi-ciency of the transmission which relies on the separationof the compound transmission in two subsystems so thatit can be studied as an ldquoEquivalent e-CVTrdquo (which is apower split-like transmission of Input-Output Split type)inside an Output Split device Following our approach the

efficiency is calculated easily for each of all the possiblepower flows A numerical example showed the potentialof this tool for power flows and efficiency calculations ofthe Output Compound Split Transmission in direct andreverse operation Experimental validation of the presentedmethodology is in progress and it will be the subject matterof future works

International Journal of Vehicular Technology 11

Forward power Reverse power

Monotonically increasing

0001020304050607080910

120578CV

U

00 10 201505minus10 minus05120591CVU

Figure 12The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically increasing

Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Forward power Reverse power

Figure 13The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically decreasing

Nomenclature

CVU CVTECVT and PG(subscripts)

Continuously Variable Unit ContinuouslyVariable Transmission ElectronicContinuously Variable Transmission andplanetary gear

119872119898 eq(subscripts)

Maximum minimum and equivalentrespectively

1198961 1198962 Kinematic parameter of the PG 1 and 2

respectively119875119895 Power through the 119895th branch119875119908 119875in and119875out

Dissipated power input power and outputpower

120591 Speed ratio120578 Efficiency120596119895 Angular velocity of the 119895th shaft

120596119900 Angular velocity of the output shaftof theCVU120596119894 Angular velocity of the input shaft of the CVU

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M R Cuddy and K B Wipke ldquoAnalysis of the fuel econ-omy benefit of drivetrain hybridizationrdquo SAE Technical Paper970289 1997

[2] S Stockar V Marano M Canova G Rizzoni and L GuzzellaldquoEnergy-optimal control of plug-in hybrid electric vehiclesfor real-world driving cyclesrdquo IEEE Transactions on VehicularTechnology vol 60 no 7 pp 2949ndash2962 2011

[3] L Serrao S Onori and G Rizzoni ldquoA comparative analysisof energy management strategies for hybrid electric vehiclesrdquoJournal of Dynamic Systems Measurement and Control vol 133no 3 Article ID 031012 2011

[4] F R Salmasi ldquoControl strategies for hybrid electric vehiclesevolution classification comparison and future trendsrdquo IEEETransactions on Vehicular Technology vol 56 no 5 pp 2393ndash2404 2007

[5] F Bottiglione T Contursi A Gentile and G Mantriota ldquoThefuel economy of hybrid buses the role of ancillaries in realurban drivingrdquo Energies vol 7 no 7 pp 4202ndash4220 2014

[6] A Taghavipour N L Azad and J McPhee ldquoAn optimal powermanagement strategy for power split plug-in hybrid electricvehiclesrdquo International Journal of Vehicle Design vol 60 no 3-4pp 286ndash304 2012

[7] Z Zhao C Wang T Zhang X Dai and X Yuan ldquoControloptimization of a compound power-split hybrid transmissionfor electric driverdquo SAE Technical Papers 2015

[8] G Mantriota ldquoPerformances of a series infinitely variabletransmission with type I power flowrdquo Mechanism and MachineTheory vol 37 no 6 pp 579ndash597 2002

[9] G Mantriota ldquoPerformances of a parallel infinitely variabletransmissions with a type II power flowrdquo Mechanism andMachine Theory vol 37 no 6 pp 555ndash578 2002

[10] B Si ldquoReconfigurable Hybrid Gear Trainrdquo US Patent 0 070 992A1 2011

[11] B Si ldquoDual mode input split compound split configurationEPPV transmissionrdquo US Patent 8 075 435 B2 2011

[12] F Bottiglione andGMantriota ldquoMG-IVT an infinitely variabletransmission with optimal power flowsrdquo Journal of MechanicalDesign vol 130 no 11 Article ID 112603 2008

[13] K T Chau andW Li ldquoOverview of electricmachines for electricand hybrid vehiclesrdquo International Journal of Vehicle Design vol64 no 1 pp 46ndash71 2014

[14] A G Holmes and M R Schmidt ldquoHybrid Electric PowertrainIncluding a Two-Mode Electrically Variable Transmissionrdquo USPatent 6 478 705 B1 2002

[15] C Brendan ldquoComparative analysis of single and combinedhybrid electrically variable transmission operatingmodesrdquo SAETechnical Paper 2005-01-1165 2005

[16] B Mashadi and S A M Emadi ldquoDual-mode power-splittransmission for hybrid electric vehiclesrdquo IEEE Transactions onVehicular Technology vol 59 no 7 pp 3223ndash3232 2010

12 International Journal of Vehicular Technology

[17] J Kim J Kang Y Kim T Kim B Min and H Kim ldquoDesignof power split transmission design of dual mode power splittransmissionrdquo International Journal of Automotive Technologyvol 11 no 4 pp 565ndash571 2010

[18] Y Zou F-C Sun C-N Zhang and J-Q Li ldquoOptimal energymanagement strategy for hybrid electric tracked vehiclesrdquoInternational Journal of Vehicle Design vol 58 no 2ndash4 pp 307ndash324 2012

[19] N-D Kim J-M Kim and H-S Kim ldquoControl strategy for adual-mode electromechanical infinitely variable transmissionfor hybrid electric vehiclesrdquo Proceedings of the Institution ofMechanical Engineers PartD Journal of Automobile Engineeringvol 222 no 9 pp 1587ndash1601 2008

[20] J Kim T Kim B Min S Hwang and H Kim ldquoModecontrol strategy for a two-mode hybrid electric vehicle usingelectrically variable transmission (EVT) and fixed-gear moderdquoIEEE Transactions on Vehicular Technology vol 60 no 3 pp793ndash803 2011

[21] Z Zhou CMi andG Zhang ldquoIntegrated control of electrome-chanical braking and regenerative braking in plug-in hybridelectric vehiclesrdquo International Journal of Vehicle Design vol 58no 2ndash4 pp 223ndash239 2012

[22] F Bottiglione and G Mantriota ldquoReversibility of power-splittransmissionsrdquo Journal ofMechanicalDesign Transactions of theASME vol 133 no 8 Article ID 084503 2011

[23] F Bottiglione and G Mantriota ldquoEffect of the ratio spread ofCVU in automotive kinetic energy recovery systemsrdquo Journalof Mechanical Design Transactions of the ASME vol 135 no 6Article ID 061001 2013

[24] F Bottiglione G Carbone L De Novellis L Mangialardiand G Mantriota ldquoMechanical hybrid KERS based on toroidaltraction drives an example of smart tribological design toimprove terrestrial vehicle performancerdquoAdvances in Tribologyvol 2013 Article ID 918387 9 pages 2013

[25] S De Pinto F Bottiglione andGMantriota ldquoInfinitely variabletransmissions in neutral gear torque ratio and power re-circulationrdquo Mechanism and Machine Theory vol 74 pp 285ndash298 2014

[26] S de Pinto and G Mantriota ldquoA simple model for compoundsplit transmissionsrdquo Proceedings of the Institution of MechanicalEngineers Part D Journal of Automobile Engineering vol 228no 5 pp 549ndash564 2014

[27] G Mantriota ldquoFuel consumption of a vehicle with power splitCVT systemrdquo International Journal of Vehicle Design vol 37 no4 pp 327ndash342 2005

[28] M Cammalleri ldquoEfficiency of split-way CVTrsquos A simplifiedmodelrdquo SAE Technical Papers 15 2007

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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DistributedSensor Networks

International Journal of

International Journal of Vehicular Technology 5

13

5

2

4

6

Output compoundType II power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type I power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type I power flow

e-CVT

e-CVT

PGI

(c)

Figure 3 Power flows in a Compound Split e-CVT with Type II power flow (a) Output Compound Split e-CVT (b) The Output Split withEquivalent e-CVT and Type I power flow and (c) the Equivalent e-CVT with Type I power flow

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type I power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type II power flow

PGI

e-CVT

e-CVT

(c)

Figure 4 Power flows in a Compound Split e-CVT with Type III power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type I power flow and (c) the Equivalent e-CVT with Type II power flow

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type II power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type I power flow

PGI

e-CVT

e-CVT

(c)

Figure 5 Power flows in a Compound Split e-CVT with Type III power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type II power flow and (c) the Equivalent e-CVT with Type I power flow

6 International Journal of Vehicular Technology

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type II power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type II power flow

PGI

e-CVT

e-CVT

(c)

Figure 6 Power flows in a Compound Split e-CVT with Type IIII power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type II power flow and (c) the Equivalent e-CVT with Type II power flow

Finally in agreement with the considerations suggestedin [21] if the following inequality is verified

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)lt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (13)

the Type II or Type III are the working conditions of thetransmission On the contrary if

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)gt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (14)

the Type III or Type IIII are established in the CVUFor the efficiency of Output Compound Split Transmis-

sion the approach is based upon the assumption that onlythe losses in the e-CVT are considered This assumption isgenerally accepted because the efficiency 120578ECVT of the e-CVT is very low (eg an electric motor-generator) comparedwith the other componentsThis condition is named the ldquorealsystemrdquo

The Output Compound Split Transmission with powerflow of Type II is considered (Figure 3(a)) Both the idealsystem (without losses) and the real system are analyzed andcompared to each other For given kinematic conditions (120596

119894

120591ECVT) and output torque 119879119900 the ratios of the torques of

PGII shaft (branches ldquo2rdquo and ldquo6rdquo) are fixed and so the ratiosbetween powers are also determined This means that thepowers in the branches ldquo2rdquo (119875

2) and ldquo6rdquo (119875

6) have the same

value in the ideal and the real systemOn the other hand the input power and the power of

branch 3 are different in the ideal system and in the realsystem In the real system because of the power loss of thee-CVT the input power 119875in is increased and the power 119875

3is

decreased

It has been demonstrated in [28] that the ratio given bythe power through the e-CVT branch divided by the inputpower of the overall CVU can be easily calculated (underthe assumption of negligible power loss) relying only on thesystem kinematics

10038161003816100381610038161003816100381610038161003816

119875ECVT119875in

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

119889120591CVU119889120591ECVT

120591ECVT120591CVU

10038161003816100381610038161003816100381610038161003816 (15)

Equation (15) is general and therefore it can be applied tothe Compound Split Transmission as well as the Equivalent e-CVTAsmentioned above the input power119875

2(Figure 3(c)) of

the Equivalent e-CVTdoes not changewhen the ideal and thereal cases are compared Hence (15) is suitable for calculatingthe power in the real system The power ratio is simply givenby

100381610038161003816100381610038161003816100381610038161003816

119875ECVTeq

119875in

100381610038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198752

119875out

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198752

119875out

10038161003816100381610038161003816100381610038161003816real

=

100381610038161003816100381610038161003816100381610038161003816

119889120591CVU119889120591ECVTeq

120591ECVTeq

120591CVU

100381610038161003816100381610038161003816100381610038161003816

=

100381610038161003816100381610038161003816100381610038161003816

1 + 1198962+ 1198961+ 11989621198961

1 + 1198961+ 1198962(1 minus 120591ECVT)

100381610038161003816100381610038161003816100381610038161003816

(16)

The power loss in the Equivalent e-CVT of the real systemcan be obtained as follows

119875119908CVU= minus (1 minus 120578ECVTeq)

100381610038161003816100381611987521003816100381610038161003816

= minus (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq10038161003816100381610038161003816

(17)

International Journal of Vehicular Technology 7

Using (16)-(17) and the power at the input shaft of the CVUthe efficiency can be finally calculated

120578CVU = minus119875out119875in=119875out119875out + 119875119908CVU

=1

1 + (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816real

=1

1 + (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816ideal

(18)

The efficiency 120578ECVTeq of Equivalent e-CVT can be derivedusing the same approach

Indeed if the Equivalent e-CVT is considered(Figure 3(c)) with given 120596

2 120591ECVT and 1198793 the angular

velocities and torques at branches ldquo1rdquo and ldquo5rdquo do no differbetween the ideal and real system

The power loss in the e-CVT of the real Equivalent ECVTcan be easily written as a function of the power 119875

5

119875119908ECVT= minus (1 minus 120578ECVT)

100381610038161003816100381611987551003816100381610038161003816 (19)

Therefore it follows that the efficiency in the Equivalent e-CVT is

120578ECVTeq = minus119875out119875in=119875out

119875out + 119875119908ECVT=

1

1 + 119875119908ECVT119875out

=1

1 + (1 minus 120578ECVT)1003816100381610038161003816119875511987531003816100381610038161003816ideal

=1

1 + (1 minus 120578ECVT)1003816100381610038161003816119875ECVT1198753

1003816100381610038161003816ideal

(20)

By considering (11) and (15) the power ratio in the Equivalente-CVT can be obtained as follows (Figure 3(c))

10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

119875ECVT1198753

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198755

1198753

10038161003816100381610038161003816100381610038161003816ideal

=

100381610038161003816100381610038161003816100381610038161003816

120597120591ECVTeq

120597120591ECVT

120591ECVT120591ECVTeq

100381610038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

120591ECVT120591ECVT + 1198961

10038161003816100381610038161003816100381610038161003816

(21)

In conclusion the efficiency can be calculated with (18) inwhich 120578ECVTeq can be obtained by (20) where |119875ECVTeq119875in|ideal and |119875ECVT1198753|ideal are derived from (16) and (21)respectively

For the Output Compound Split Transmission withpower flow of Type III the CVU architecture is the same asthe previous case (Figure 4(b)) Therefore the power loss issimply given by (17) and the efficiency by (18) whereas theformula for 120578ECVTeq is different

The power flow in the Equivalent e-CVT and its efficiency120578ECVTeq change compared with the previous case Also inthis case 119875

5does not change when comparing the ideal

system and the real system (Figure 4(c)) This means thatthe expression for the power loss in the Equivalent e-CVT is

a function of the e-CVT output power 1198755 that is the power

loss is given by

119875119908CVTeq= minus(1 minus 120578ECVT)

120578ECVT

100381610038161003816100381611987551003816100381610038161003816 (22)

From (20) and (22) the efficiency of the Equivalent e-CVT is

120578ECVTeq = minus119875out119875in=119875out

119875out + 119875119908ECVT=

1

1 + 119875119908ECVT119875out

=1

1 + ((1 minus 120578ECVT) 120578ECVT)1003816100381610038161003816119875ECVT1198753

1003816100381610038161003816ideal

(23)

In conclusion the efficiency of Type III power flow can becalculated through (18) where 120578ECVTeq can be obtained by(23)

The efficiency of the CVU working with Type III powerflow is derived using a similar approach

From Figure 5(b) it follows that the power 1198752which has

the same value in the ideal system and in the real system isthe output power of the Equivalent e-CVTThe power loss inthe e-CVT of the real Equivalent e-CVT (Figure 4(c)) is

119875119908CVU= minus(1 minus 120578ECVTeq)

120578ECVTeq

100381610038161003816100381611987521003816100381610038161003816

(24)

Thus the efficiency of the CVU is given by

120578CVU = minus119875out119875in=119875out119875out + 119875119908CVU

=1

1 + ((1 minus 120578ECVTeq) 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816ideal

(25)

It follows that the power loss and efficiency of the Equivalente-CVT are given by

119875119908ECVTeq= minus(1 minus 120578ECVT)

120578ECVT

100381610038161003816100381611987551003816100381610038161003816 (26)

120578ECVTeq = minus119875out119875in=119875in + 119875119908ECVT119875in

= 1 minus(1 minus 120578ECVT)

120578ECVT

10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal

(27)

The power ratio in the Equivalent e-CVT is obtained using(21) hence the efficiency in the Equivalent e-CVT followsfrom (27)

In conclusion the efficiency of Type III can be calculatedthrough (25) where 120578ECVTeq can be obtained by (27)

Finally in theOutput Compound Split Transmissionwithpower flow of Type IIII we obtained (Figure 6)

119875119908ECVTeq= minus (1 minus 120578ECVT)

100381610038161003816100381611987551003816100381610038161003816 (28)

8 International Journal of Vehicular Technology

The power ratio in the Equivalent e-CVT follows from (21)Therefore the efficiency of the Equivalent e-CVT is deducedfrom equation

120578ECVTeq = minus119875out119875in=119875in + 119875119908ECVT119875in

= 1 minus (1 minus 120578ECVT)10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal

(29)

It can be noticed that the power flowof Figure 6(b) is identicalto Figure 5(b) It follows that also in this case the efficiency iscalculated with (25) with 120578ECVTeq calculated as (29)

4 Numerical Example

In this section a numerical example is given which alsoincludes the calculation of the transmission efficiency usingthe simplified approach described in this work The calcula-tions can be performed after the speed ratio of the CVU andthe e-CVT have been imposed It is here assumed that speedratio of the e-CVT varies between the bounds 120591ECVT119898 = 04and 120591ECVT119872 = 2 which is typical of mechanical CVT Theratio range of the CVU is a system requirement so it canbe chosen arbitrarily A CVU is here designed with a speedratio bounded between 120591CVU119898 = minus1 and 120591CVU119872 = 2 inorder to comprise also the neutral gear These CVU boundscan be obtained only by choosing two planetary gear trainscharacterized by 119896

1and 119896

2calculated with (7) in the case

of monotonic increase of the CVU speed ratio for increasingECVT speed ratio It is obtained that

1198961= 029

1198962= minus329

(30)

If the case of a monotonic decreasing CVU speed ratio withincreasing e-CVT speed ratio 119896

1and 119896

2must be calculated

with (8) it follows that

1198961= minus10

1198962= minus17

(31)

The CVU speed ratio as a function of the e-CVT speed ratiogiven by (4) is shown in Figure 7 for the two aforementionedcases

The power ratio |119875ECVT119875CVU| calculated with (15) isshown in Figure 8

Two regions can be distinguished corresponding to twodifferent ranges of 120591CVU the first range 0 le 120591CVU le 2 and thesecond range minus1 lt 120591CVU lt 0

Each region corresponds to a different power circulationConsidering the limits imposed on the speed ratio of thisexample it results in the following

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)gt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (32)

With the help of (13) and (14) one can determine the powerflow type taking also into account the sign change of the

Monotonically increasing Monotonically decreasing

minus10

minus05

00

05

10

15

20

120591CV

U

020 040 060 080 100 120 140 160 180 200000120591ECVT

Figure 7 Speed ratio of the CVU (120591CVU) as a function of the e-CVTspeed ratio (120591ECVT)

Monotonically increasing Monotonically decreasing

0123456789

10

00minus05minus10 10 15 2005120591CVU

PEC

VT

PCV

U

Figure 8 Power ratio |119875ECVT119875CVU| considering no losses plotted asa function of the overall speed ratio 120591CVU

ratio 120591CVU In fact when 120591CVU is an increasing function of120591ECVT the Type IIII power flow occurs for 120591CVU gt 0 as aconsequence of (14) whereas in the other regionwith 120591CVU lt0 the power flow changes from Type IIII to Type III [21]

On the other hand when 120591CVU is a decreasing function of120591ECVT (14) still holds but in this case the Type III power flowoccurs if 120591CVU gt 0 whereas if 120591CVU lt 0 then the power flowis changed from Type III to Type IIII [21]

The ratio given by the power through the e-CVT dividedby the global power is not equal in the two cases (Figure 8)With 120591CVU lt 1 the power ratio is larger when the speed ratioof the transmission is a decreasing function of the speed ratioof the e-CVTOnly with 120591CVU gt 1 the situation is the oppositeone

The efficiency 120578CVU plotted as a function of 120591CVU isshown in Figure 9 considering that 120578ECVT = 09 For 120591CVU gt0 and with a monotonically increasing CVU speed ratio withincreasing e-CVT speed ratio (power flow of Type IIII) (16)(21) (25) and (29) are utilized In this case the efficiencyis larger than in the case of monotonically decreasing speed

International Journal of Vehicular Technology 9

Monotonically increasing Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Figure 9 The efficiency 120578CVU as a function of the overall speed ratio 120591CVU (120578ECVT = 09)

ratio for 120591CVU lt 1 whereas the opposite condition is verifiedfor 120591CVU gt 1This is expected since the device with the lowestandmost critical efficiency is the e-CVT so the configurationthat minimizes the power through the e-CVT is the mostconvenient one in terms of energy efficiency

5 Efficiency of the Output Compound e-CVTin Direct and Reverse Operation

Hybrid vehicles are the main application for CompoundSplit-eCVT transmission One of themost important featuresof hybrid vehicles is the regenerative braking capabilitySuch a function needs the transmission to work in reverseoperation For this reason it is important to evaluate theefficiency of the transmission in both direct and reverseoperation and to understand the differences

In this section the same transmission data are considered(120591ECVT119898 = 04 120591ECVT119872 = 2 120591CVU119898 = minus1 120591CVU119872 = 2) andthe performance in reverse operation are calculated throughthe model developed in a previous work [22] The efficiency120578ECVT of the e-CVT is considered constant and given by120578ECVT = 09 As mentioned in the compound transmissionwith a monotonic increasing speed ratio (119896

1= 029 119896

2=

minus329) if 120591CVU119898 gt 0 a power flow of Type IIII is obtainedGiven the same kinematic parameters when the transmissionworks in reverse operation (Figure 10) the input and outputtorques are reversed and because of the planetary gear trainPG1 also the torques on links 2 and 6 are reversed Further-more the torque and the power on the link 3 are also reversedand as a consequence of the planetary gear train PG2 alsothe torque and power on links 1 4 and 5 are reversed Soin the change from direct operation (Figure 10(a)) to reverseoperation (Figure 10(b)) the power flow is reversed on all thelinks and the power flow is yet of Type IIII

When 120591CVU119898 lt 0 similar arguments leads to concludethat the power flow is of Type III also in reverse operation(Figure 11)

The monotonic increasing speed ratio is investigatedfirst In Figure 12 it is shown that in reverse operation theefficiency of the transmission is always less than in directoperation with the only exception of the high values of thespeed ratio (120591CVU gt 17) It is very interesting to see that whenthe speed ratio is close to zero (minus027 lt 120591CVU lt 022) theefficiency in reverse operation is negative which means thatthe transmission is nonreversible with the speed ratio in theaforementioned range This result is in agreement with theresults shown in [8] in the case of Power Split TransmissionsIt is actually relevant for applications to the hybrid vehiclesbecause it affects negatively the braking recovery capabilitiesIn particular it is not possible to recover energy in brakingwith minus027 lt 120591CVU lt 022

Similar results can be obtained in the case of monotonicdecreasing speed ratio (Figure 7) Given the speed ratioranges of CVT and CVU (which give 119896

1= minus10 and 119896

2=

minus17) also in this case the power flows do not change whenswitching from direct to reverse operation power flow ofType III with 120591CVU gt 0 (Figure 11) and power flow of TypeIIII with 120591CVU lt 0 (Figure 10) The efficiency in direct andreverse operation is shown in Figure 13 Also in this case theefficiency in reverse operation is visibly less than in directmode Furthermore the nonreversibility range of the speedis even larger being minus040 lt 120591CVU lt 028

6 Conclusions

In recent years compound transmissions are attractingincreasing interest for application in hybrid vehicles becausethey are flexible and they permit optimizing the efficiency indifferent operating conditions The goal of this work was toobtain a systematic approach to determine the power flowsand the efficiency in Output Compound Split Transmissionsfor optimal design and control of HEVs The proposedmethodology is suitable for steady-state working conditionsand it follows from the assumption of negligible power lossin all the components except for the e-CVT It is shown how

10 International Journal of Vehicular Technology

Forward power

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 10 Power flows in a Output Compound Split e-CVT with Type IIII power flow (a) forward power (b) reverse power

Forward power

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 11 Power flows in a Output Compound Split e-CVT with Type III power flow (a) forward power (b) reverse power

the power circulation depends only on kinematic conditionsFurthermore a novel approach is shown to study the effi-ciency of the transmission which relies on the separationof the compound transmission in two subsystems so thatit can be studied as an ldquoEquivalent e-CVTrdquo (which is apower split-like transmission of Input-Output Split type)inside an Output Split device Following our approach the

efficiency is calculated easily for each of all the possiblepower flows A numerical example showed the potentialof this tool for power flows and efficiency calculations ofthe Output Compound Split Transmission in direct andreverse operation Experimental validation of the presentedmethodology is in progress and it will be the subject matterof future works

International Journal of Vehicular Technology 11

Forward power Reverse power

Monotonically increasing

0001020304050607080910

120578CV

U

00 10 201505minus10 minus05120591CVU

Figure 12The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically increasing

Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Forward power Reverse power

Figure 13The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically decreasing

Nomenclature

CVU CVTECVT and PG(subscripts)

Continuously Variable Unit ContinuouslyVariable Transmission ElectronicContinuously Variable Transmission andplanetary gear

119872119898 eq(subscripts)

Maximum minimum and equivalentrespectively

1198961 1198962 Kinematic parameter of the PG 1 and 2

respectively119875119895 Power through the 119895th branch119875119908 119875in and119875out

Dissipated power input power and outputpower

120591 Speed ratio120578 Efficiency120596119895 Angular velocity of the 119895th shaft

120596119900 Angular velocity of the output shaftof theCVU120596119894 Angular velocity of the input shaft of the CVU

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M R Cuddy and K B Wipke ldquoAnalysis of the fuel econ-omy benefit of drivetrain hybridizationrdquo SAE Technical Paper970289 1997

[2] S Stockar V Marano M Canova G Rizzoni and L GuzzellaldquoEnergy-optimal control of plug-in hybrid electric vehiclesfor real-world driving cyclesrdquo IEEE Transactions on VehicularTechnology vol 60 no 7 pp 2949ndash2962 2011

[3] L Serrao S Onori and G Rizzoni ldquoA comparative analysisof energy management strategies for hybrid electric vehiclesrdquoJournal of Dynamic Systems Measurement and Control vol 133no 3 Article ID 031012 2011

[4] F R Salmasi ldquoControl strategies for hybrid electric vehiclesevolution classification comparison and future trendsrdquo IEEETransactions on Vehicular Technology vol 56 no 5 pp 2393ndash2404 2007

[5] F Bottiglione T Contursi A Gentile and G Mantriota ldquoThefuel economy of hybrid buses the role of ancillaries in realurban drivingrdquo Energies vol 7 no 7 pp 4202ndash4220 2014

[6] A Taghavipour N L Azad and J McPhee ldquoAn optimal powermanagement strategy for power split plug-in hybrid electricvehiclesrdquo International Journal of Vehicle Design vol 60 no 3-4pp 286ndash304 2012

[7] Z Zhao C Wang T Zhang X Dai and X Yuan ldquoControloptimization of a compound power-split hybrid transmissionfor electric driverdquo SAE Technical Papers 2015

[8] G Mantriota ldquoPerformances of a series infinitely variabletransmission with type I power flowrdquo Mechanism and MachineTheory vol 37 no 6 pp 579ndash597 2002

[9] G Mantriota ldquoPerformances of a parallel infinitely variabletransmissions with a type II power flowrdquo Mechanism andMachine Theory vol 37 no 6 pp 555ndash578 2002

[10] B Si ldquoReconfigurable Hybrid Gear Trainrdquo US Patent 0 070 992A1 2011

[11] B Si ldquoDual mode input split compound split configurationEPPV transmissionrdquo US Patent 8 075 435 B2 2011

[12] F Bottiglione andGMantriota ldquoMG-IVT an infinitely variabletransmission with optimal power flowsrdquo Journal of MechanicalDesign vol 130 no 11 Article ID 112603 2008

[13] K T Chau andW Li ldquoOverview of electricmachines for electricand hybrid vehiclesrdquo International Journal of Vehicle Design vol64 no 1 pp 46ndash71 2014

[14] A G Holmes and M R Schmidt ldquoHybrid Electric PowertrainIncluding a Two-Mode Electrically Variable Transmissionrdquo USPatent 6 478 705 B1 2002

[15] C Brendan ldquoComparative analysis of single and combinedhybrid electrically variable transmission operatingmodesrdquo SAETechnical Paper 2005-01-1165 2005

[16] B Mashadi and S A M Emadi ldquoDual-mode power-splittransmission for hybrid electric vehiclesrdquo IEEE Transactions onVehicular Technology vol 59 no 7 pp 3223ndash3232 2010

12 International Journal of Vehicular Technology

[17] J Kim J Kang Y Kim T Kim B Min and H Kim ldquoDesignof power split transmission design of dual mode power splittransmissionrdquo International Journal of Automotive Technologyvol 11 no 4 pp 565ndash571 2010

[18] Y Zou F-C Sun C-N Zhang and J-Q Li ldquoOptimal energymanagement strategy for hybrid electric tracked vehiclesrdquoInternational Journal of Vehicle Design vol 58 no 2ndash4 pp 307ndash324 2012

[19] N-D Kim J-M Kim and H-S Kim ldquoControl strategy for adual-mode electromechanical infinitely variable transmissionfor hybrid electric vehiclesrdquo Proceedings of the Institution ofMechanical Engineers PartD Journal of Automobile Engineeringvol 222 no 9 pp 1587ndash1601 2008

[20] J Kim T Kim B Min S Hwang and H Kim ldquoModecontrol strategy for a two-mode hybrid electric vehicle usingelectrically variable transmission (EVT) and fixed-gear moderdquoIEEE Transactions on Vehicular Technology vol 60 no 3 pp793ndash803 2011

[21] Z Zhou CMi andG Zhang ldquoIntegrated control of electrome-chanical braking and regenerative braking in plug-in hybridelectric vehiclesrdquo International Journal of Vehicle Design vol 58no 2ndash4 pp 223ndash239 2012

[22] F Bottiglione and G Mantriota ldquoReversibility of power-splittransmissionsrdquo Journal ofMechanicalDesign Transactions of theASME vol 133 no 8 Article ID 084503 2011

[23] F Bottiglione and G Mantriota ldquoEffect of the ratio spread ofCVU in automotive kinetic energy recovery systemsrdquo Journalof Mechanical Design Transactions of the ASME vol 135 no 6Article ID 061001 2013

[24] F Bottiglione G Carbone L De Novellis L Mangialardiand G Mantriota ldquoMechanical hybrid KERS based on toroidaltraction drives an example of smart tribological design toimprove terrestrial vehicle performancerdquoAdvances in Tribologyvol 2013 Article ID 918387 9 pages 2013

[25] S De Pinto F Bottiglione andGMantriota ldquoInfinitely variabletransmissions in neutral gear torque ratio and power re-circulationrdquo Mechanism and Machine Theory vol 74 pp 285ndash298 2014

[26] S de Pinto and G Mantriota ldquoA simple model for compoundsplit transmissionsrdquo Proceedings of the Institution of MechanicalEngineers Part D Journal of Automobile Engineering vol 228no 5 pp 549ndash564 2014

[27] G Mantriota ldquoFuel consumption of a vehicle with power splitCVT systemrdquo International Journal of Vehicle Design vol 37 no4 pp 327ndash342 2005

[28] M Cammalleri ldquoEfficiency of split-way CVTrsquos A simplifiedmodelrdquo SAE Technical Papers 15 2007

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DistributedSensor Networks

International Journal of

6 International Journal of Vehicular Technology

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

3

26

Equivalent

Type II power flow

Input

Output

PGII

e-CVT

(b)

1

54

3

2

Equivalent

Type II power flow

PGI

e-CVT

e-CVT

(c)

Figure 6 Power flows in a Compound Split e-CVT with Type IIII power flow (a) Output Compound Split e-CVT (b) the Output Split withEquivalent e-CVT and Type II power flow and (c) the Equivalent e-CVT with Type II power flow

Finally in agreement with the considerations suggestedin [21] if the following inequality is verified

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)lt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (13)

the Type II or Type III are the working conditions of thetransmission On the contrary if

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)gt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (14)

the Type III or Type IIII are established in the CVUFor the efficiency of Output Compound Split Transmis-

sion the approach is based upon the assumption that onlythe losses in the e-CVT are considered This assumption isgenerally accepted because the efficiency 120578ECVT of the e-CVT is very low (eg an electric motor-generator) comparedwith the other componentsThis condition is named the ldquorealsystemrdquo

The Output Compound Split Transmission with powerflow of Type II is considered (Figure 3(a)) Both the idealsystem (without losses) and the real system are analyzed andcompared to each other For given kinematic conditions (120596

119894

120591ECVT) and output torque 119879119900 the ratios of the torques of

PGII shaft (branches ldquo2rdquo and ldquo6rdquo) are fixed and so the ratiosbetween powers are also determined This means that thepowers in the branches ldquo2rdquo (119875

2) and ldquo6rdquo (119875

6) have the same

value in the ideal and the real systemOn the other hand the input power and the power of

branch 3 are different in the ideal system and in the realsystem In the real system because of the power loss of thee-CVT the input power 119875in is increased and the power 119875

3is

decreased

It has been demonstrated in [28] that the ratio given bythe power through the e-CVT branch divided by the inputpower of the overall CVU can be easily calculated (underthe assumption of negligible power loss) relying only on thesystem kinematics

10038161003816100381610038161003816100381610038161003816

119875ECVT119875in

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

119889120591CVU119889120591ECVT

120591ECVT120591CVU

10038161003816100381610038161003816100381610038161003816 (15)

Equation (15) is general and therefore it can be applied tothe Compound Split Transmission as well as the Equivalent e-CVTAsmentioned above the input power119875

2(Figure 3(c)) of

the Equivalent e-CVTdoes not changewhen the ideal and thereal cases are compared Hence (15) is suitable for calculatingthe power in the real system The power ratio is simply givenby

100381610038161003816100381610038161003816100381610038161003816

119875ECVTeq

119875in

100381610038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198752

119875out

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198752

119875out

10038161003816100381610038161003816100381610038161003816real

=

100381610038161003816100381610038161003816100381610038161003816

119889120591CVU119889120591ECVTeq

120591ECVTeq

120591CVU

100381610038161003816100381610038161003816100381610038161003816

=

100381610038161003816100381610038161003816100381610038161003816

1 + 1198962+ 1198961+ 11989621198961

1 + 1198961+ 1198962(1 minus 120591ECVT)

100381610038161003816100381610038161003816100381610038161003816

(16)

The power loss in the Equivalent e-CVT of the real systemcan be obtained as follows

119875119908CVU= minus (1 minus 120578ECVTeq)

100381610038161003816100381611987521003816100381610038161003816

= minus (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq10038161003816100381610038161003816

(17)

International Journal of Vehicular Technology 7

Using (16)-(17) and the power at the input shaft of the CVUthe efficiency can be finally calculated

120578CVU = minus119875out119875in=119875out119875out + 119875119908CVU

=1

1 + (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816real

=1

1 + (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816ideal

(18)

The efficiency 120578ECVTeq of Equivalent e-CVT can be derivedusing the same approach

Indeed if the Equivalent e-CVT is considered(Figure 3(c)) with given 120596

2 120591ECVT and 1198793 the angular

velocities and torques at branches ldquo1rdquo and ldquo5rdquo do no differbetween the ideal and real system

The power loss in the e-CVT of the real Equivalent ECVTcan be easily written as a function of the power 119875

5

119875119908ECVT= minus (1 minus 120578ECVT)

100381610038161003816100381611987551003816100381610038161003816 (19)

Therefore it follows that the efficiency in the Equivalent e-CVT is

120578ECVTeq = minus119875out119875in=119875out

119875out + 119875119908ECVT=

1

1 + 119875119908ECVT119875out

=1

1 + (1 minus 120578ECVT)1003816100381610038161003816119875511987531003816100381610038161003816ideal

=1

1 + (1 minus 120578ECVT)1003816100381610038161003816119875ECVT1198753

1003816100381610038161003816ideal

(20)

By considering (11) and (15) the power ratio in the Equivalente-CVT can be obtained as follows (Figure 3(c))

10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

119875ECVT1198753

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198755

1198753

10038161003816100381610038161003816100381610038161003816ideal

=

100381610038161003816100381610038161003816100381610038161003816

120597120591ECVTeq

120597120591ECVT

120591ECVT120591ECVTeq

100381610038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

120591ECVT120591ECVT + 1198961

10038161003816100381610038161003816100381610038161003816

(21)

In conclusion the efficiency can be calculated with (18) inwhich 120578ECVTeq can be obtained by (20) where |119875ECVTeq119875in|ideal and |119875ECVT1198753|ideal are derived from (16) and (21)respectively

For the Output Compound Split Transmission withpower flow of Type III the CVU architecture is the same asthe previous case (Figure 4(b)) Therefore the power loss issimply given by (17) and the efficiency by (18) whereas theformula for 120578ECVTeq is different

The power flow in the Equivalent e-CVT and its efficiency120578ECVTeq change compared with the previous case Also inthis case 119875

5does not change when comparing the ideal

system and the real system (Figure 4(c)) This means thatthe expression for the power loss in the Equivalent e-CVT is

a function of the e-CVT output power 1198755 that is the power

loss is given by

119875119908CVTeq= minus(1 minus 120578ECVT)

120578ECVT

100381610038161003816100381611987551003816100381610038161003816 (22)

From (20) and (22) the efficiency of the Equivalent e-CVT is

120578ECVTeq = minus119875out119875in=119875out

119875out + 119875119908ECVT=

1

1 + 119875119908ECVT119875out

=1

1 + ((1 minus 120578ECVT) 120578ECVT)1003816100381610038161003816119875ECVT1198753

1003816100381610038161003816ideal

(23)

In conclusion the efficiency of Type III power flow can becalculated through (18) where 120578ECVTeq can be obtained by(23)

The efficiency of the CVU working with Type III powerflow is derived using a similar approach

From Figure 5(b) it follows that the power 1198752which has

the same value in the ideal system and in the real system isthe output power of the Equivalent e-CVTThe power loss inthe e-CVT of the real Equivalent e-CVT (Figure 4(c)) is

119875119908CVU= minus(1 minus 120578ECVTeq)

120578ECVTeq

100381610038161003816100381611987521003816100381610038161003816

(24)

Thus the efficiency of the CVU is given by

120578CVU = minus119875out119875in=119875out119875out + 119875119908CVU

=1

1 + ((1 minus 120578ECVTeq) 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816ideal

(25)

It follows that the power loss and efficiency of the Equivalente-CVT are given by

119875119908ECVTeq= minus(1 minus 120578ECVT)

120578ECVT

100381610038161003816100381611987551003816100381610038161003816 (26)

120578ECVTeq = minus119875out119875in=119875in + 119875119908ECVT119875in

= 1 minus(1 minus 120578ECVT)

120578ECVT

10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal

(27)

The power ratio in the Equivalent e-CVT is obtained using(21) hence the efficiency in the Equivalent e-CVT followsfrom (27)

In conclusion the efficiency of Type III can be calculatedthrough (25) where 120578ECVTeq can be obtained by (27)

Finally in theOutput Compound Split Transmissionwithpower flow of Type IIII we obtained (Figure 6)

119875119908ECVTeq= minus (1 minus 120578ECVT)

100381610038161003816100381611987551003816100381610038161003816 (28)

8 International Journal of Vehicular Technology

The power ratio in the Equivalent e-CVT follows from (21)Therefore the efficiency of the Equivalent e-CVT is deducedfrom equation

120578ECVTeq = minus119875out119875in=119875in + 119875119908ECVT119875in

= 1 minus (1 minus 120578ECVT)10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal

(29)

It can be noticed that the power flowof Figure 6(b) is identicalto Figure 5(b) It follows that also in this case the efficiency iscalculated with (25) with 120578ECVTeq calculated as (29)

4 Numerical Example

In this section a numerical example is given which alsoincludes the calculation of the transmission efficiency usingthe simplified approach described in this work The calcula-tions can be performed after the speed ratio of the CVU andthe e-CVT have been imposed It is here assumed that speedratio of the e-CVT varies between the bounds 120591ECVT119898 = 04and 120591ECVT119872 = 2 which is typical of mechanical CVT Theratio range of the CVU is a system requirement so it canbe chosen arbitrarily A CVU is here designed with a speedratio bounded between 120591CVU119898 = minus1 and 120591CVU119872 = 2 inorder to comprise also the neutral gear These CVU boundscan be obtained only by choosing two planetary gear trainscharacterized by 119896

1and 119896

2calculated with (7) in the case

of monotonic increase of the CVU speed ratio for increasingECVT speed ratio It is obtained that

1198961= 029

1198962= minus329

(30)

If the case of a monotonic decreasing CVU speed ratio withincreasing e-CVT speed ratio 119896

1and 119896

2must be calculated

with (8) it follows that

1198961= minus10

1198962= minus17

(31)

The CVU speed ratio as a function of the e-CVT speed ratiogiven by (4) is shown in Figure 7 for the two aforementionedcases

The power ratio |119875ECVT119875CVU| calculated with (15) isshown in Figure 8

Two regions can be distinguished corresponding to twodifferent ranges of 120591CVU the first range 0 le 120591CVU le 2 and thesecond range minus1 lt 120591CVU lt 0

Each region corresponds to a different power circulationConsidering the limits imposed on the speed ratio of thisexample it results in the following

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)gt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (32)

With the help of (13) and (14) one can determine the powerflow type taking also into account the sign change of the

Monotonically increasing Monotonically decreasing

minus10

minus05

00

05

10

15

20

120591CV

U

020 040 060 080 100 120 140 160 180 200000120591ECVT

Figure 7 Speed ratio of the CVU (120591CVU) as a function of the e-CVTspeed ratio (120591ECVT)

Monotonically increasing Monotonically decreasing

0123456789

10

00minus05minus10 10 15 2005120591CVU

PEC

VT

PCV

U

Figure 8 Power ratio |119875ECVT119875CVU| considering no losses plotted asa function of the overall speed ratio 120591CVU

ratio 120591CVU In fact when 120591CVU is an increasing function of120591ECVT the Type IIII power flow occurs for 120591CVU gt 0 as aconsequence of (14) whereas in the other regionwith 120591CVU lt0 the power flow changes from Type IIII to Type III [21]

On the other hand when 120591CVU is a decreasing function of120591ECVT (14) still holds but in this case the Type III power flowoccurs if 120591CVU gt 0 whereas if 120591CVU lt 0 then the power flowis changed from Type III to Type IIII [21]

The ratio given by the power through the e-CVT dividedby the global power is not equal in the two cases (Figure 8)With 120591CVU lt 1 the power ratio is larger when the speed ratioof the transmission is a decreasing function of the speed ratioof the e-CVTOnly with 120591CVU gt 1 the situation is the oppositeone

The efficiency 120578CVU plotted as a function of 120591CVU isshown in Figure 9 considering that 120578ECVT = 09 For 120591CVU gt0 and with a monotonically increasing CVU speed ratio withincreasing e-CVT speed ratio (power flow of Type IIII) (16)(21) (25) and (29) are utilized In this case the efficiencyis larger than in the case of monotonically decreasing speed

International Journal of Vehicular Technology 9

Monotonically increasing Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Figure 9 The efficiency 120578CVU as a function of the overall speed ratio 120591CVU (120578ECVT = 09)

ratio for 120591CVU lt 1 whereas the opposite condition is verifiedfor 120591CVU gt 1This is expected since the device with the lowestandmost critical efficiency is the e-CVT so the configurationthat minimizes the power through the e-CVT is the mostconvenient one in terms of energy efficiency

5 Efficiency of the Output Compound e-CVTin Direct and Reverse Operation

Hybrid vehicles are the main application for CompoundSplit-eCVT transmission One of themost important featuresof hybrid vehicles is the regenerative braking capabilitySuch a function needs the transmission to work in reverseoperation For this reason it is important to evaluate theefficiency of the transmission in both direct and reverseoperation and to understand the differences

In this section the same transmission data are considered(120591ECVT119898 = 04 120591ECVT119872 = 2 120591CVU119898 = minus1 120591CVU119872 = 2) andthe performance in reverse operation are calculated throughthe model developed in a previous work [22] The efficiency120578ECVT of the e-CVT is considered constant and given by120578ECVT = 09 As mentioned in the compound transmissionwith a monotonic increasing speed ratio (119896

1= 029 119896

2=

minus329) if 120591CVU119898 gt 0 a power flow of Type IIII is obtainedGiven the same kinematic parameters when the transmissionworks in reverse operation (Figure 10) the input and outputtorques are reversed and because of the planetary gear trainPG1 also the torques on links 2 and 6 are reversed Further-more the torque and the power on the link 3 are also reversedand as a consequence of the planetary gear train PG2 alsothe torque and power on links 1 4 and 5 are reversed Soin the change from direct operation (Figure 10(a)) to reverseoperation (Figure 10(b)) the power flow is reversed on all thelinks and the power flow is yet of Type IIII

When 120591CVU119898 lt 0 similar arguments leads to concludethat the power flow is of Type III also in reverse operation(Figure 11)

The monotonic increasing speed ratio is investigatedfirst In Figure 12 it is shown that in reverse operation theefficiency of the transmission is always less than in directoperation with the only exception of the high values of thespeed ratio (120591CVU gt 17) It is very interesting to see that whenthe speed ratio is close to zero (minus027 lt 120591CVU lt 022) theefficiency in reverse operation is negative which means thatthe transmission is nonreversible with the speed ratio in theaforementioned range This result is in agreement with theresults shown in [8] in the case of Power Split TransmissionsIt is actually relevant for applications to the hybrid vehiclesbecause it affects negatively the braking recovery capabilitiesIn particular it is not possible to recover energy in brakingwith minus027 lt 120591CVU lt 022

Similar results can be obtained in the case of monotonicdecreasing speed ratio (Figure 7) Given the speed ratioranges of CVT and CVU (which give 119896

1= minus10 and 119896

2=

minus17) also in this case the power flows do not change whenswitching from direct to reverse operation power flow ofType III with 120591CVU gt 0 (Figure 11) and power flow of TypeIIII with 120591CVU lt 0 (Figure 10) The efficiency in direct andreverse operation is shown in Figure 13 Also in this case theefficiency in reverse operation is visibly less than in directmode Furthermore the nonreversibility range of the speedis even larger being minus040 lt 120591CVU lt 028

6 Conclusions

In recent years compound transmissions are attractingincreasing interest for application in hybrid vehicles becausethey are flexible and they permit optimizing the efficiency indifferent operating conditions The goal of this work was toobtain a systematic approach to determine the power flowsand the efficiency in Output Compound Split Transmissionsfor optimal design and control of HEVs The proposedmethodology is suitable for steady-state working conditionsand it follows from the assumption of negligible power lossin all the components except for the e-CVT It is shown how

10 International Journal of Vehicular Technology

Forward power

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 10 Power flows in a Output Compound Split e-CVT with Type IIII power flow (a) forward power (b) reverse power

Forward power

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 11 Power flows in a Output Compound Split e-CVT with Type III power flow (a) forward power (b) reverse power

the power circulation depends only on kinematic conditionsFurthermore a novel approach is shown to study the effi-ciency of the transmission which relies on the separationof the compound transmission in two subsystems so thatit can be studied as an ldquoEquivalent e-CVTrdquo (which is apower split-like transmission of Input-Output Split type)inside an Output Split device Following our approach the

efficiency is calculated easily for each of all the possiblepower flows A numerical example showed the potentialof this tool for power flows and efficiency calculations ofthe Output Compound Split Transmission in direct andreverse operation Experimental validation of the presentedmethodology is in progress and it will be the subject matterof future works

International Journal of Vehicular Technology 11

Forward power Reverse power

Monotonically increasing

0001020304050607080910

120578CV

U

00 10 201505minus10 minus05120591CVU

Figure 12The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically increasing

Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Forward power Reverse power

Figure 13The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically decreasing

Nomenclature

CVU CVTECVT and PG(subscripts)

Continuously Variable Unit ContinuouslyVariable Transmission ElectronicContinuously Variable Transmission andplanetary gear

119872119898 eq(subscripts)

Maximum minimum and equivalentrespectively

1198961 1198962 Kinematic parameter of the PG 1 and 2

respectively119875119895 Power through the 119895th branch119875119908 119875in and119875out

Dissipated power input power and outputpower

120591 Speed ratio120578 Efficiency120596119895 Angular velocity of the 119895th shaft

120596119900 Angular velocity of the output shaftof theCVU120596119894 Angular velocity of the input shaft of the CVU

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M R Cuddy and K B Wipke ldquoAnalysis of the fuel econ-omy benefit of drivetrain hybridizationrdquo SAE Technical Paper970289 1997

[2] S Stockar V Marano M Canova G Rizzoni and L GuzzellaldquoEnergy-optimal control of plug-in hybrid electric vehiclesfor real-world driving cyclesrdquo IEEE Transactions on VehicularTechnology vol 60 no 7 pp 2949ndash2962 2011

[3] L Serrao S Onori and G Rizzoni ldquoA comparative analysisof energy management strategies for hybrid electric vehiclesrdquoJournal of Dynamic Systems Measurement and Control vol 133no 3 Article ID 031012 2011

[4] F R Salmasi ldquoControl strategies for hybrid electric vehiclesevolution classification comparison and future trendsrdquo IEEETransactions on Vehicular Technology vol 56 no 5 pp 2393ndash2404 2007

[5] F Bottiglione T Contursi A Gentile and G Mantriota ldquoThefuel economy of hybrid buses the role of ancillaries in realurban drivingrdquo Energies vol 7 no 7 pp 4202ndash4220 2014

[6] A Taghavipour N L Azad and J McPhee ldquoAn optimal powermanagement strategy for power split plug-in hybrid electricvehiclesrdquo International Journal of Vehicle Design vol 60 no 3-4pp 286ndash304 2012

[7] Z Zhao C Wang T Zhang X Dai and X Yuan ldquoControloptimization of a compound power-split hybrid transmissionfor electric driverdquo SAE Technical Papers 2015

[8] G Mantriota ldquoPerformances of a series infinitely variabletransmission with type I power flowrdquo Mechanism and MachineTheory vol 37 no 6 pp 579ndash597 2002

[9] G Mantriota ldquoPerformances of a parallel infinitely variabletransmissions with a type II power flowrdquo Mechanism andMachine Theory vol 37 no 6 pp 555ndash578 2002

[10] B Si ldquoReconfigurable Hybrid Gear Trainrdquo US Patent 0 070 992A1 2011

[11] B Si ldquoDual mode input split compound split configurationEPPV transmissionrdquo US Patent 8 075 435 B2 2011

[12] F Bottiglione andGMantriota ldquoMG-IVT an infinitely variabletransmission with optimal power flowsrdquo Journal of MechanicalDesign vol 130 no 11 Article ID 112603 2008

[13] K T Chau andW Li ldquoOverview of electricmachines for electricand hybrid vehiclesrdquo International Journal of Vehicle Design vol64 no 1 pp 46ndash71 2014

[14] A G Holmes and M R Schmidt ldquoHybrid Electric PowertrainIncluding a Two-Mode Electrically Variable Transmissionrdquo USPatent 6 478 705 B1 2002

[15] C Brendan ldquoComparative analysis of single and combinedhybrid electrically variable transmission operatingmodesrdquo SAETechnical Paper 2005-01-1165 2005

[16] B Mashadi and S A M Emadi ldquoDual-mode power-splittransmission for hybrid electric vehiclesrdquo IEEE Transactions onVehicular Technology vol 59 no 7 pp 3223ndash3232 2010

12 International Journal of Vehicular Technology

[17] J Kim J Kang Y Kim T Kim B Min and H Kim ldquoDesignof power split transmission design of dual mode power splittransmissionrdquo International Journal of Automotive Technologyvol 11 no 4 pp 565ndash571 2010

[18] Y Zou F-C Sun C-N Zhang and J-Q Li ldquoOptimal energymanagement strategy for hybrid electric tracked vehiclesrdquoInternational Journal of Vehicle Design vol 58 no 2ndash4 pp 307ndash324 2012

[19] N-D Kim J-M Kim and H-S Kim ldquoControl strategy for adual-mode electromechanical infinitely variable transmissionfor hybrid electric vehiclesrdquo Proceedings of the Institution ofMechanical Engineers PartD Journal of Automobile Engineeringvol 222 no 9 pp 1587ndash1601 2008

[20] J Kim T Kim B Min S Hwang and H Kim ldquoModecontrol strategy for a two-mode hybrid electric vehicle usingelectrically variable transmission (EVT) and fixed-gear moderdquoIEEE Transactions on Vehicular Technology vol 60 no 3 pp793ndash803 2011

[21] Z Zhou CMi andG Zhang ldquoIntegrated control of electrome-chanical braking and regenerative braking in plug-in hybridelectric vehiclesrdquo International Journal of Vehicle Design vol 58no 2ndash4 pp 223ndash239 2012

[22] F Bottiglione and G Mantriota ldquoReversibility of power-splittransmissionsrdquo Journal ofMechanicalDesign Transactions of theASME vol 133 no 8 Article ID 084503 2011

[23] F Bottiglione and G Mantriota ldquoEffect of the ratio spread ofCVU in automotive kinetic energy recovery systemsrdquo Journalof Mechanical Design Transactions of the ASME vol 135 no 6Article ID 061001 2013

[24] F Bottiglione G Carbone L De Novellis L Mangialardiand G Mantriota ldquoMechanical hybrid KERS based on toroidaltraction drives an example of smart tribological design toimprove terrestrial vehicle performancerdquoAdvances in Tribologyvol 2013 Article ID 918387 9 pages 2013

[25] S De Pinto F Bottiglione andGMantriota ldquoInfinitely variabletransmissions in neutral gear torque ratio and power re-circulationrdquo Mechanism and Machine Theory vol 74 pp 285ndash298 2014

[26] S de Pinto and G Mantriota ldquoA simple model for compoundsplit transmissionsrdquo Proceedings of the Institution of MechanicalEngineers Part D Journal of Automobile Engineering vol 228no 5 pp 549ndash564 2014

[27] G Mantriota ldquoFuel consumption of a vehicle with power splitCVT systemrdquo International Journal of Vehicle Design vol 37 no4 pp 327ndash342 2005

[28] M Cammalleri ldquoEfficiency of split-way CVTrsquos A simplifiedmodelrdquo SAE Technical Papers 15 2007

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International Journal of

International Journal of Vehicular Technology 7

Using (16)-(17) and the power at the input shaft of the CVUthe efficiency can be finally calculated

120578CVU = minus119875out119875in=119875out119875out + 119875119908CVU

=1

1 + (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816real

=1

1 + (1 minus 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816ideal

(18)

The efficiency 120578ECVTeq of Equivalent e-CVT can be derivedusing the same approach

Indeed if the Equivalent e-CVT is considered(Figure 3(c)) with given 120596

2 120591ECVT and 1198793 the angular

velocities and torques at branches ldquo1rdquo and ldquo5rdquo do no differbetween the ideal and real system

The power loss in the e-CVT of the real Equivalent ECVTcan be easily written as a function of the power 119875

5

119875119908ECVT= minus (1 minus 120578ECVT)

100381610038161003816100381611987551003816100381610038161003816 (19)

Therefore it follows that the efficiency in the Equivalent e-CVT is

120578ECVTeq = minus119875out119875in=119875out

119875out + 119875119908ECVT=

1

1 + 119875119908ECVT119875out

=1

1 + (1 minus 120578ECVT)1003816100381610038161003816119875511987531003816100381610038161003816ideal

=1

1 + (1 minus 120578ECVT)1003816100381610038161003816119875ECVT1198753

1003816100381610038161003816ideal

(20)

By considering (11) and (15) the power ratio in the Equivalente-CVT can be obtained as follows (Figure 3(c))

10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

119875ECVT1198753

10038161003816100381610038161003816100381610038161003816ideal=

10038161003816100381610038161003816100381610038161003816

1198755

1198753

10038161003816100381610038161003816100381610038161003816ideal

=

100381610038161003816100381610038161003816100381610038161003816

120597120591ECVTeq

120597120591ECVT

120591ECVT120591ECVTeq

100381610038161003816100381610038161003816100381610038161003816

=

10038161003816100381610038161003816100381610038161003816

120591ECVT120591ECVT + 1198961

10038161003816100381610038161003816100381610038161003816

(21)

In conclusion the efficiency can be calculated with (18) inwhich 120578ECVTeq can be obtained by (20) where |119875ECVTeq119875in|ideal and |119875ECVT1198753|ideal are derived from (16) and (21)respectively

For the Output Compound Split Transmission withpower flow of Type III the CVU architecture is the same asthe previous case (Figure 4(b)) Therefore the power loss issimply given by (17) and the efficiency by (18) whereas theformula for 120578ECVTeq is different

The power flow in the Equivalent e-CVT and its efficiency120578ECVTeq change compared with the previous case Also inthis case 119875

5does not change when comparing the ideal

system and the real system (Figure 4(c)) This means thatthe expression for the power loss in the Equivalent e-CVT is

a function of the e-CVT output power 1198755 that is the power

loss is given by

119875119908CVTeq= minus(1 minus 120578ECVT)

120578ECVT

100381610038161003816100381611987551003816100381610038161003816 (22)

From (20) and (22) the efficiency of the Equivalent e-CVT is

120578ECVTeq = minus119875out119875in=119875out

119875out + 119875119908ECVT=

1

1 + 119875119908ECVT119875out

=1

1 + ((1 minus 120578ECVT) 120578ECVT)1003816100381610038161003816119875ECVT1198753

1003816100381610038161003816ideal

(23)

In conclusion the efficiency of Type III power flow can becalculated through (18) where 120578ECVTeq can be obtained by(23)

The efficiency of the CVU working with Type III powerflow is derived using a similar approach

From Figure 5(b) it follows that the power 1198752which has

the same value in the ideal system and in the real system isthe output power of the Equivalent e-CVTThe power loss inthe e-CVT of the real Equivalent e-CVT (Figure 4(c)) is

119875119908CVU= minus(1 minus 120578ECVTeq)

120578ECVTeq

100381610038161003816100381611987521003816100381610038161003816

(24)

Thus the efficiency of the CVU is given by

120578CVU = minus119875out119875in=119875out119875out + 119875119908CVU

=1

1 + ((1 minus 120578ECVTeq) 120578ECVTeq)10038161003816100381610038161003816119875ECVTeq119875in

10038161003816100381610038161003816ideal

(25)

It follows that the power loss and efficiency of the Equivalente-CVT are given by

119875119908ECVTeq= minus(1 minus 120578ECVT)

120578ECVT

100381610038161003816100381611987551003816100381610038161003816 (26)

120578ECVTeq = minus119875out119875in=119875in + 119875119908ECVT119875in

= 1 minus(1 minus 120578ECVT)

120578ECVT

10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal

(27)

The power ratio in the Equivalent e-CVT is obtained using(21) hence the efficiency in the Equivalent e-CVT followsfrom (27)

In conclusion the efficiency of Type III can be calculatedthrough (25) where 120578ECVTeq can be obtained by (27)

Finally in theOutput Compound Split Transmissionwithpower flow of Type IIII we obtained (Figure 6)

119875119908ECVTeq= minus (1 minus 120578ECVT)

100381610038161003816100381611987551003816100381610038161003816 (28)

8 International Journal of Vehicular Technology

The power ratio in the Equivalent e-CVT follows from (21)Therefore the efficiency of the Equivalent e-CVT is deducedfrom equation

120578ECVTeq = minus119875out119875in=119875in + 119875119908ECVT119875in

= 1 minus (1 minus 120578ECVT)10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal

(29)

It can be noticed that the power flowof Figure 6(b) is identicalto Figure 5(b) It follows that also in this case the efficiency iscalculated with (25) with 120578ECVTeq calculated as (29)

4 Numerical Example

In this section a numerical example is given which alsoincludes the calculation of the transmission efficiency usingthe simplified approach described in this work The calcula-tions can be performed after the speed ratio of the CVU andthe e-CVT have been imposed It is here assumed that speedratio of the e-CVT varies between the bounds 120591ECVT119898 = 04and 120591ECVT119872 = 2 which is typical of mechanical CVT Theratio range of the CVU is a system requirement so it canbe chosen arbitrarily A CVU is here designed with a speedratio bounded between 120591CVU119898 = minus1 and 120591CVU119872 = 2 inorder to comprise also the neutral gear These CVU boundscan be obtained only by choosing two planetary gear trainscharacterized by 119896

1and 119896

2calculated with (7) in the case

of monotonic increase of the CVU speed ratio for increasingECVT speed ratio It is obtained that

1198961= 029

1198962= minus329

(30)

If the case of a monotonic decreasing CVU speed ratio withincreasing e-CVT speed ratio 119896

1and 119896

2must be calculated

with (8) it follows that

1198961= minus10

1198962= minus17

(31)

The CVU speed ratio as a function of the e-CVT speed ratiogiven by (4) is shown in Figure 7 for the two aforementionedcases

The power ratio |119875ECVT119875CVU| calculated with (15) isshown in Figure 8

Two regions can be distinguished corresponding to twodifferent ranges of 120591CVU the first range 0 le 120591CVU le 2 and thesecond range minus1 lt 120591CVU lt 0

Each region corresponds to a different power circulationConsidering the limits imposed on the speed ratio of thisexample it results in the following

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)gt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (32)

With the help of (13) and (14) one can determine the powerflow type taking also into account the sign change of the

Monotonically increasing Monotonically decreasing

minus10

minus05

00

05

10

15

20

120591CV

U

020 040 060 080 100 120 140 160 180 200000120591ECVT

Figure 7 Speed ratio of the CVU (120591CVU) as a function of the e-CVTspeed ratio (120591ECVT)

Monotonically increasing Monotonically decreasing

0123456789

10

00minus05minus10 10 15 2005120591CVU

PEC

VT

PCV

U

Figure 8 Power ratio |119875ECVT119875CVU| considering no losses plotted asa function of the overall speed ratio 120591CVU

ratio 120591CVU In fact when 120591CVU is an increasing function of120591ECVT the Type IIII power flow occurs for 120591CVU gt 0 as aconsequence of (14) whereas in the other regionwith 120591CVU lt0 the power flow changes from Type IIII to Type III [21]

On the other hand when 120591CVU is a decreasing function of120591ECVT (14) still holds but in this case the Type III power flowoccurs if 120591CVU gt 0 whereas if 120591CVU lt 0 then the power flowis changed from Type III to Type IIII [21]

The ratio given by the power through the e-CVT dividedby the global power is not equal in the two cases (Figure 8)With 120591CVU lt 1 the power ratio is larger when the speed ratioof the transmission is a decreasing function of the speed ratioof the e-CVTOnly with 120591CVU gt 1 the situation is the oppositeone

The efficiency 120578CVU plotted as a function of 120591CVU isshown in Figure 9 considering that 120578ECVT = 09 For 120591CVU gt0 and with a monotonically increasing CVU speed ratio withincreasing e-CVT speed ratio (power flow of Type IIII) (16)(21) (25) and (29) are utilized In this case the efficiencyis larger than in the case of monotonically decreasing speed

International Journal of Vehicular Technology 9

Monotonically increasing Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Figure 9 The efficiency 120578CVU as a function of the overall speed ratio 120591CVU (120578ECVT = 09)

ratio for 120591CVU lt 1 whereas the opposite condition is verifiedfor 120591CVU gt 1This is expected since the device with the lowestandmost critical efficiency is the e-CVT so the configurationthat minimizes the power through the e-CVT is the mostconvenient one in terms of energy efficiency

5 Efficiency of the Output Compound e-CVTin Direct and Reverse Operation

Hybrid vehicles are the main application for CompoundSplit-eCVT transmission One of themost important featuresof hybrid vehicles is the regenerative braking capabilitySuch a function needs the transmission to work in reverseoperation For this reason it is important to evaluate theefficiency of the transmission in both direct and reverseoperation and to understand the differences

In this section the same transmission data are considered(120591ECVT119898 = 04 120591ECVT119872 = 2 120591CVU119898 = minus1 120591CVU119872 = 2) andthe performance in reverse operation are calculated throughthe model developed in a previous work [22] The efficiency120578ECVT of the e-CVT is considered constant and given by120578ECVT = 09 As mentioned in the compound transmissionwith a monotonic increasing speed ratio (119896

1= 029 119896

2=

minus329) if 120591CVU119898 gt 0 a power flow of Type IIII is obtainedGiven the same kinematic parameters when the transmissionworks in reverse operation (Figure 10) the input and outputtorques are reversed and because of the planetary gear trainPG1 also the torques on links 2 and 6 are reversed Further-more the torque and the power on the link 3 are also reversedand as a consequence of the planetary gear train PG2 alsothe torque and power on links 1 4 and 5 are reversed Soin the change from direct operation (Figure 10(a)) to reverseoperation (Figure 10(b)) the power flow is reversed on all thelinks and the power flow is yet of Type IIII

When 120591CVU119898 lt 0 similar arguments leads to concludethat the power flow is of Type III also in reverse operation(Figure 11)

The monotonic increasing speed ratio is investigatedfirst In Figure 12 it is shown that in reverse operation theefficiency of the transmission is always less than in directoperation with the only exception of the high values of thespeed ratio (120591CVU gt 17) It is very interesting to see that whenthe speed ratio is close to zero (minus027 lt 120591CVU lt 022) theefficiency in reverse operation is negative which means thatthe transmission is nonreversible with the speed ratio in theaforementioned range This result is in agreement with theresults shown in [8] in the case of Power Split TransmissionsIt is actually relevant for applications to the hybrid vehiclesbecause it affects negatively the braking recovery capabilitiesIn particular it is not possible to recover energy in brakingwith minus027 lt 120591CVU lt 022

Similar results can be obtained in the case of monotonicdecreasing speed ratio (Figure 7) Given the speed ratioranges of CVT and CVU (which give 119896

1= minus10 and 119896

2=

minus17) also in this case the power flows do not change whenswitching from direct to reverse operation power flow ofType III with 120591CVU gt 0 (Figure 11) and power flow of TypeIIII with 120591CVU lt 0 (Figure 10) The efficiency in direct andreverse operation is shown in Figure 13 Also in this case theefficiency in reverse operation is visibly less than in directmode Furthermore the nonreversibility range of the speedis even larger being minus040 lt 120591CVU lt 028

6 Conclusions

In recent years compound transmissions are attractingincreasing interest for application in hybrid vehicles becausethey are flexible and they permit optimizing the efficiency indifferent operating conditions The goal of this work was toobtain a systematic approach to determine the power flowsand the efficiency in Output Compound Split Transmissionsfor optimal design and control of HEVs The proposedmethodology is suitable for steady-state working conditionsand it follows from the assumption of negligible power lossin all the components except for the e-CVT It is shown how

10 International Journal of Vehicular Technology

Forward power

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 10 Power flows in a Output Compound Split e-CVT with Type IIII power flow (a) forward power (b) reverse power

Forward power

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 11 Power flows in a Output Compound Split e-CVT with Type III power flow (a) forward power (b) reverse power

the power circulation depends only on kinematic conditionsFurthermore a novel approach is shown to study the effi-ciency of the transmission which relies on the separationof the compound transmission in two subsystems so thatit can be studied as an ldquoEquivalent e-CVTrdquo (which is apower split-like transmission of Input-Output Split type)inside an Output Split device Following our approach the

efficiency is calculated easily for each of all the possiblepower flows A numerical example showed the potentialof this tool for power flows and efficiency calculations ofthe Output Compound Split Transmission in direct andreverse operation Experimental validation of the presentedmethodology is in progress and it will be the subject matterof future works

International Journal of Vehicular Technology 11

Forward power Reverse power

Monotonically increasing

0001020304050607080910

120578CV

U

00 10 201505minus10 minus05120591CVU

Figure 12The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically increasing

Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Forward power Reverse power

Figure 13The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically decreasing

Nomenclature

CVU CVTECVT and PG(subscripts)

Continuously Variable Unit ContinuouslyVariable Transmission ElectronicContinuously Variable Transmission andplanetary gear

119872119898 eq(subscripts)

Maximum minimum and equivalentrespectively

1198961 1198962 Kinematic parameter of the PG 1 and 2

respectively119875119895 Power through the 119895th branch119875119908 119875in and119875out

Dissipated power input power and outputpower

120591 Speed ratio120578 Efficiency120596119895 Angular velocity of the 119895th shaft

120596119900 Angular velocity of the output shaftof theCVU120596119894 Angular velocity of the input shaft of the CVU

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M R Cuddy and K B Wipke ldquoAnalysis of the fuel econ-omy benefit of drivetrain hybridizationrdquo SAE Technical Paper970289 1997

[2] S Stockar V Marano M Canova G Rizzoni and L GuzzellaldquoEnergy-optimal control of plug-in hybrid electric vehiclesfor real-world driving cyclesrdquo IEEE Transactions on VehicularTechnology vol 60 no 7 pp 2949ndash2962 2011

[3] L Serrao S Onori and G Rizzoni ldquoA comparative analysisof energy management strategies for hybrid electric vehiclesrdquoJournal of Dynamic Systems Measurement and Control vol 133no 3 Article ID 031012 2011

[4] F R Salmasi ldquoControl strategies for hybrid electric vehiclesevolution classification comparison and future trendsrdquo IEEETransactions on Vehicular Technology vol 56 no 5 pp 2393ndash2404 2007

[5] F Bottiglione T Contursi A Gentile and G Mantriota ldquoThefuel economy of hybrid buses the role of ancillaries in realurban drivingrdquo Energies vol 7 no 7 pp 4202ndash4220 2014

[6] A Taghavipour N L Azad and J McPhee ldquoAn optimal powermanagement strategy for power split plug-in hybrid electricvehiclesrdquo International Journal of Vehicle Design vol 60 no 3-4pp 286ndash304 2012

[7] Z Zhao C Wang T Zhang X Dai and X Yuan ldquoControloptimization of a compound power-split hybrid transmissionfor electric driverdquo SAE Technical Papers 2015

[8] G Mantriota ldquoPerformances of a series infinitely variabletransmission with type I power flowrdquo Mechanism and MachineTheory vol 37 no 6 pp 579ndash597 2002

[9] G Mantriota ldquoPerformances of a parallel infinitely variabletransmissions with a type II power flowrdquo Mechanism andMachine Theory vol 37 no 6 pp 555ndash578 2002

[10] B Si ldquoReconfigurable Hybrid Gear Trainrdquo US Patent 0 070 992A1 2011

[11] B Si ldquoDual mode input split compound split configurationEPPV transmissionrdquo US Patent 8 075 435 B2 2011

[12] F Bottiglione andGMantriota ldquoMG-IVT an infinitely variabletransmission with optimal power flowsrdquo Journal of MechanicalDesign vol 130 no 11 Article ID 112603 2008

[13] K T Chau andW Li ldquoOverview of electricmachines for electricand hybrid vehiclesrdquo International Journal of Vehicle Design vol64 no 1 pp 46ndash71 2014

[14] A G Holmes and M R Schmidt ldquoHybrid Electric PowertrainIncluding a Two-Mode Electrically Variable Transmissionrdquo USPatent 6 478 705 B1 2002

[15] C Brendan ldquoComparative analysis of single and combinedhybrid electrically variable transmission operatingmodesrdquo SAETechnical Paper 2005-01-1165 2005

[16] B Mashadi and S A M Emadi ldquoDual-mode power-splittransmission for hybrid electric vehiclesrdquo IEEE Transactions onVehicular Technology vol 59 no 7 pp 3223ndash3232 2010

12 International Journal of Vehicular Technology

[17] J Kim J Kang Y Kim T Kim B Min and H Kim ldquoDesignof power split transmission design of dual mode power splittransmissionrdquo International Journal of Automotive Technologyvol 11 no 4 pp 565ndash571 2010

[18] Y Zou F-C Sun C-N Zhang and J-Q Li ldquoOptimal energymanagement strategy for hybrid electric tracked vehiclesrdquoInternational Journal of Vehicle Design vol 58 no 2ndash4 pp 307ndash324 2012

[19] N-D Kim J-M Kim and H-S Kim ldquoControl strategy for adual-mode electromechanical infinitely variable transmissionfor hybrid electric vehiclesrdquo Proceedings of the Institution ofMechanical Engineers PartD Journal of Automobile Engineeringvol 222 no 9 pp 1587ndash1601 2008

[20] J Kim T Kim B Min S Hwang and H Kim ldquoModecontrol strategy for a two-mode hybrid electric vehicle usingelectrically variable transmission (EVT) and fixed-gear moderdquoIEEE Transactions on Vehicular Technology vol 60 no 3 pp793ndash803 2011

[21] Z Zhou CMi andG Zhang ldquoIntegrated control of electrome-chanical braking and regenerative braking in plug-in hybridelectric vehiclesrdquo International Journal of Vehicle Design vol 58no 2ndash4 pp 223ndash239 2012

[22] F Bottiglione and G Mantriota ldquoReversibility of power-splittransmissionsrdquo Journal ofMechanicalDesign Transactions of theASME vol 133 no 8 Article ID 084503 2011

[23] F Bottiglione and G Mantriota ldquoEffect of the ratio spread ofCVU in automotive kinetic energy recovery systemsrdquo Journalof Mechanical Design Transactions of the ASME vol 135 no 6Article ID 061001 2013

[24] F Bottiglione G Carbone L De Novellis L Mangialardiand G Mantriota ldquoMechanical hybrid KERS based on toroidaltraction drives an example of smart tribological design toimprove terrestrial vehicle performancerdquoAdvances in Tribologyvol 2013 Article ID 918387 9 pages 2013

[25] S De Pinto F Bottiglione andGMantriota ldquoInfinitely variabletransmissions in neutral gear torque ratio and power re-circulationrdquo Mechanism and Machine Theory vol 74 pp 285ndash298 2014

[26] S de Pinto and G Mantriota ldquoA simple model for compoundsplit transmissionsrdquo Proceedings of the Institution of MechanicalEngineers Part D Journal of Automobile Engineering vol 228no 5 pp 549ndash564 2014

[27] G Mantriota ldquoFuel consumption of a vehicle with power splitCVT systemrdquo International Journal of Vehicle Design vol 37 no4 pp 327ndash342 2005

[28] M Cammalleri ldquoEfficiency of split-way CVTrsquos A simplifiedmodelrdquo SAE Technical Papers 15 2007

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Control Scienceand Engineering

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

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International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

8 International Journal of Vehicular Technology

The power ratio in the Equivalent e-CVT follows from (21)Therefore the efficiency of the Equivalent e-CVT is deducedfrom equation

120578ECVTeq = minus119875out119875in=119875in + 119875119908ECVT119875in

= 1 minus (1 minus 120578ECVT)10038161003816100381610038161003816100381610038161003816

119875ECVT1198752

10038161003816100381610038161003816100381610038161003816ideal

(29)

It can be noticed that the power flowof Figure 6(b) is identicalto Figure 5(b) It follows that also in this case the efficiency iscalculated with (25) with 120578ECVTeq calculated as (29)

4 Numerical Example

In this section a numerical example is given which alsoincludes the calculation of the transmission efficiency usingthe simplified approach described in this work The calcula-tions can be performed after the speed ratio of the CVU andthe e-CVT have been imposed It is here assumed that speedratio of the e-CVT varies between the bounds 120591ECVT119898 = 04and 120591ECVT119872 = 2 which is typical of mechanical CVT Theratio range of the CVU is a system requirement so it canbe chosen arbitrarily A CVU is here designed with a speedratio bounded between 120591CVU119898 = minus1 and 120591CVU119872 = 2 inorder to comprise also the neutral gear These CVU boundscan be obtained only by choosing two planetary gear trainscharacterized by 119896

1and 119896

2calculated with (7) in the case

of monotonic increase of the CVU speed ratio for increasingECVT speed ratio It is obtained that

1198961= 029

1198962= minus329

(30)

If the case of a monotonic decreasing CVU speed ratio withincreasing e-CVT speed ratio 119896

1and 119896

2must be calculated

with (8) it follows that

1198961= minus10

1198962= minus17

(31)

The CVU speed ratio as a function of the e-CVT speed ratiogiven by (4) is shown in Figure 7 for the two aforementionedcases

The power ratio |119875ECVT119875CVU| calculated with (15) isshown in Figure 8

Two regions can be distinguished corresponding to twodifferent ranges of 120591CVU the first range 0 le 120591CVU le 2 and thesecond range minus1 lt 120591CVU lt 0

Each region corresponds to a different power circulationConsidering the limits imposed on the speed ratio of thisexample it results in the following

(120591CVU119872 minus 1)

(120591CVU119898 minus 1)gt(120591ECVT119872 minus 1)

(120591ECVT119898 minus 1) (32)

With the help of (13) and (14) one can determine the powerflow type taking also into account the sign change of the

Monotonically increasing Monotonically decreasing

minus10

minus05

00

05

10

15

20

120591CV

U

020 040 060 080 100 120 140 160 180 200000120591ECVT

Figure 7 Speed ratio of the CVU (120591CVU) as a function of the e-CVTspeed ratio (120591ECVT)

Monotonically increasing Monotonically decreasing

0123456789

10

00minus05minus10 10 15 2005120591CVU

PEC

VT

PCV

U

Figure 8 Power ratio |119875ECVT119875CVU| considering no losses plotted asa function of the overall speed ratio 120591CVU

ratio 120591CVU In fact when 120591CVU is an increasing function of120591ECVT the Type IIII power flow occurs for 120591CVU gt 0 as aconsequence of (14) whereas in the other regionwith 120591CVU lt0 the power flow changes from Type IIII to Type III [21]

On the other hand when 120591CVU is a decreasing function of120591ECVT (14) still holds but in this case the Type III power flowoccurs if 120591CVU gt 0 whereas if 120591CVU lt 0 then the power flowis changed from Type III to Type IIII [21]

The ratio given by the power through the e-CVT dividedby the global power is not equal in the two cases (Figure 8)With 120591CVU lt 1 the power ratio is larger when the speed ratioof the transmission is a decreasing function of the speed ratioof the e-CVTOnly with 120591CVU gt 1 the situation is the oppositeone

The efficiency 120578CVU plotted as a function of 120591CVU isshown in Figure 9 considering that 120578ECVT = 09 For 120591CVU gt0 and with a monotonically increasing CVU speed ratio withincreasing e-CVT speed ratio (power flow of Type IIII) (16)(21) (25) and (29) are utilized In this case the efficiencyis larger than in the case of monotonically decreasing speed

International Journal of Vehicular Technology 9

Monotonically increasing Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Figure 9 The efficiency 120578CVU as a function of the overall speed ratio 120591CVU (120578ECVT = 09)

ratio for 120591CVU lt 1 whereas the opposite condition is verifiedfor 120591CVU gt 1This is expected since the device with the lowestandmost critical efficiency is the e-CVT so the configurationthat minimizes the power through the e-CVT is the mostconvenient one in terms of energy efficiency

5 Efficiency of the Output Compound e-CVTin Direct and Reverse Operation

Hybrid vehicles are the main application for CompoundSplit-eCVT transmission One of themost important featuresof hybrid vehicles is the regenerative braking capabilitySuch a function needs the transmission to work in reverseoperation For this reason it is important to evaluate theefficiency of the transmission in both direct and reverseoperation and to understand the differences

In this section the same transmission data are considered(120591ECVT119898 = 04 120591ECVT119872 = 2 120591CVU119898 = minus1 120591CVU119872 = 2) andthe performance in reverse operation are calculated throughthe model developed in a previous work [22] The efficiency120578ECVT of the e-CVT is considered constant and given by120578ECVT = 09 As mentioned in the compound transmissionwith a monotonic increasing speed ratio (119896

1= 029 119896

2=

minus329) if 120591CVU119898 gt 0 a power flow of Type IIII is obtainedGiven the same kinematic parameters when the transmissionworks in reverse operation (Figure 10) the input and outputtorques are reversed and because of the planetary gear trainPG1 also the torques on links 2 and 6 are reversed Further-more the torque and the power on the link 3 are also reversedand as a consequence of the planetary gear train PG2 alsothe torque and power on links 1 4 and 5 are reversed Soin the change from direct operation (Figure 10(a)) to reverseoperation (Figure 10(b)) the power flow is reversed on all thelinks and the power flow is yet of Type IIII

When 120591CVU119898 lt 0 similar arguments leads to concludethat the power flow is of Type III also in reverse operation(Figure 11)

The monotonic increasing speed ratio is investigatedfirst In Figure 12 it is shown that in reverse operation theefficiency of the transmission is always less than in directoperation with the only exception of the high values of thespeed ratio (120591CVU gt 17) It is very interesting to see that whenthe speed ratio is close to zero (minus027 lt 120591CVU lt 022) theefficiency in reverse operation is negative which means thatthe transmission is nonreversible with the speed ratio in theaforementioned range This result is in agreement with theresults shown in [8] in the case of Power Split TransmissionsIt is actually relevant for applications to the hybrid vehiclesbecause it affects negatively the braking recovery capabilitiesIn particular it is not possible to recover energy in brakingwith minus027 lt 120591CVU lt 022

Similar results can be obtained in the case of monotonicdecreasing speed ratio (Figure 7) Given the speed ratioranges of CVT and CVU (which give 119896

1= minus10 and 119896

2=

minus17) also in this case the power flows do not change whenswitching from direct to reverse operation power flow ofType III with 120591CVU gt 0 (Figure 11) and power flow of TypeIIII with 120591CVU lt 0 (Figure 10) The efficiency in direct andreverse operation is shown in Figure 13 Also in this case theefficiency in reverse operation is visibly less than in directmode Furthermore the nonreversibility range of the speedis even larger being minus040 lt 120591CVU lt 028

6 Conclusions

In recent years compound transmissions are attractingincreasing interest for application in hybrid vehicles becausethey are flexible and they permit optimizing the efficiency indifferent operating conditions The goal of this work was toobtain a systematic approach to determine the power flowsand the efficiency in Output Compound Split Transmissionsfor optimal design and control of HEVs The proposedmethodology is suitable for steady-state working conditionsand it follows from the assumption of negligible power lossin all the components except for the e-CVT It is shown how

10 International Journal of Vehicular Technology

Forward power

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 10 Power flows in a Output Compound Split e-CVT with Type IIII power flow (a) forward power (b) reverse power

Forward power

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 11 Power flows in a Output Compound Split e-CVT with Type III power flow (a) forward power (b) reverse power

the power circulation depends only on kinematic conditionsFurthermore a novel approach is shown to study the effi-ciency of the transmission which relies on the separationof the compound transmission in two subsystems so thatit can be studied as an ldquoEquivalent e-CVTrdquo (which is apower split-like transmission of Input-Output Split type)inside an Output Split device Following our approach the

efficiency is calculated easily for each of all the possiblepower flows A numerical example showed the potentialof this tool for power flows and efficiency calculations ofthe Output Compound Split Transmission in direct andreverse operation Experimental validation of the presentedmethodology is in progress and it will be the subject matterof future works

International Journal of Vehicular Technology 11

Forward power Reverse power

Monotonically increasing

0001020304050607080910

120578CV

U

00 10 201505minus10 minus05120591CVU

Figure 12The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically increasing

Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Forward power Reverse power

Figure 13The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically decreasing

Nomenclature

CVU CVTECVT and PG(subscripts)

Continuously Variable Unit ContinuouslyVariable Transmission ElectronicContinuously Variable Transmission andplanetary gear

119872119898 eq(subscripts)

Maximum minimum and equivalentrespectively

1198961 1198962 Kinematic parameter of the PG 1 and 2

respectively119875119895 Power through the 119895th branch119875119908 119875in and119875out

Dissipated power input power and outputpower

120591 Speed ratio120578 Efficiency120596119895 Angular velocity of the 119895th shaft

120596119900 Angular velocity of the output shaftof theCVU120596119894 Angular velocity of the input shaft of the CVU

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M R Cuddy and K B Wipke ldquoAnalysis of the fuel econ-omy benefit of drivetrain hybridizationrdquo SAE Technical Paper970289 1997

[2] S Stockar V Marano M Canova G Rizzoni and L GuzzellaldquoEnergy-optimal control of plug-in hybrid electric vehiclesfor real-world driving cyclesrdquo IEEE Transactions on VehicularTechnology vol 60 no 7 pp 2949ndash2962 2011

[3] L Serrao S Onori and G Rizzoni ldquoA comparative analysisof energy management strategies for hybrid electric vehiclesrdquoJournal of Dynamic Systems Measurement and Control vol 133no 3 Article ID 031012 2011

[4] F R Salmasi ldquoControl strategies for hybrid electric vehiclesevolution classification comparison and future trendsrdquo IEEETransactions on Vehicular Technology vol 56 no 5 pp 2393ndash2404 2007

[5] F Bottiglione T Contursi A Gentile and G Mantriota ldquoThefuel economy of hybrid buses the role of ancillaries in realurban drivingrdquo Energies vol 7 no 7 pp 4202ndash4220 2014

[6] A Taghavipour N L Azad and J McPhee ldquoAn optimal powermanagement strategy for power split plug-in hybrid electricvehiclesrdquo International Journal of Vehicle Design vol 60 no 3-4pp 286ndash304 2012

[7] Z Zhao C Wang T Zhang X Dai and X Yuan ldquoControloptimization of a compound power-split hybrid transmissionfor electric driverdquo SAE Technical Papers 2015

[8] G Mantriota ldquoPerformances of a series infinitely variabletransmission with type I power flowrdquo Mechanism and MachineTheory vol 37 no 6 pp 579ndash597 2002

[9] G Mantriota ldquoPerformances of a parallel infinitely variabletransmissions with a type II power flowrdquo Mechanism andMachine Theory vol 37 no 6 pp 555ndash578 2002

[10] B Si ldquoReconfigurable Hybrid Gear Trainrdquo US Patent 0 070 992A1 2011

[11] B Si ldquoDual mode input split compound split configurationEPPV transmissionrdquo US Patent 8 075 435 B2 2011

[12] F Bottiglione andGMantriota ldquoMG-IVT an infinitely variabletransmission with optimal power flowsrdquo Journal of MechanicalDesign vol 130 no 11 Article ID 112603 2008

[13] K T Chau andW Li ldquoOverview of electricmachines for electricand hybrid vehiclesrdquo International Journal of Vehicle Design vol64 no 1 pp 46ndash71 2014

[14] A G Holmes and M R Schmidt ldquoHybrid Electric PowertrainIncluding a Two-Mode Electrically Variable Transmissionrdquo USPatent 6 478 705 B1 2002

[15] C Brendan ldquoComparative analysis of single and combinedhybrid electrically variable transmission operatingmodesrdquo SAETechnical Paper 2005-01-1165 2005

[16] B Mashadi and S A M Emadi ldquoDual-mode power-splittransmission for hybrid electric vehiclesrdquo IEEE Transactions onVehicular Technology vol 59 no 7 pp 3223ndash3232 2010

12 International Journal of Vehicular Technology

[17] J Kim J Kang Y Kim T Kim B Min and H Kim ldquoDesignof power split transmission design of dual mode power splittransmissionrdquo International Journal of Automotive Technologyvol 11 no 4 pp 565ndash571 2010

[18] Y Zou F-C Sun C-N Zhang and J-Q Li ldquoOptimal energymanagement strategy for hybrid electric tracked vehiclesrdquoInternational Journal of Vehicle Design vol 58 no 2ndash4 pp 307ndash324 2012

[19] N-D Kim J-M Kim and H-S Kim ldquoControl strategy for adual-mode electromechanical infinitely variable transmissionfor hybrid electric vehiclesrdquo Proceedings of the Institution ofMechanical Engineers PartD Journal of Automobile Engineeringvol 222 no 9 pp 1587ndash1601 2008

[20] J Kim T Kim B Min S Hwang and H Kim ldquoModecontrol strategy for a two-mode hybrid electric vehicle usingelectrically variable transmission (EVT) and fixed-gear moderdquoIEEE Transactions on Vehicular Technology vol 60 no 3 pp793ndash803 2011

[21] Z Zhou CMi andG Zhang ldquoIntegrated control of electrome-chanical braking and regenerative braking in plug-in hybridelectric vehiclesrdquo International Journal of Vehicle Design vol 58no 2ndash4 pp 223ndash239 2012

[22] F Bottiglione and G Mantriota ldquoReversibility of power-splittransmissionsrdquo Journal ofMechanicalDesign Transactions of theASME vol 133 no 8 Article ID 084503 2011

[23] F Bottiglione and G Mantriota ldquoEffect of the ratio spread ofCVU in automotive kinetic energy recovery systemsrdquo Journalof Mechanical Design Transactions of the ASME vol 135 no 6Article ID 061001 2013

[24] F Bottiglione G Carbone L De Novellis L Mangialardiand G Mantriota ldquoMechanical hybrid KERS based on toroidaltraction drives an example of smart tribological design toimprove terrestrial vehicle performancerdquoAdvances in Tribologyvol 2013 Article ID 918387 9 pages 2013

[25] S De Pinto F Bottiglione andGMantriota ldquoInfinitely variabletransmissions in neutral gear torque ratio and power re-circulationrdquo Mechanism and Machine Theory vol 74 pp 285ndash298 2014

[26] S de Pinto and G Mantriota ldquoA simple model for compoundsplit transmissionsrdquo Proceedings of the Institution of MechanicalEngineers Part D Journal of Automobile Engineering vol 228no 5 pp 549ndash564 2014

[27] G Mantriota ldquoFuel consumption of a vehicle with power splitCVT systemrdquo International Journal of Vehicle Design vol 37 no4 pp 327ndash342 2005

[28] M Cammalleri ldquoEfficiency of split-way CVTrsquos A simplifiedmodelrdquo SAE Technical Papers 15 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Vehicular Technology 9

Monotonically increasing Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Figure 9 The efficiency 120578CVU as a function of the overall speed ratio 120591CVU (120578ECVT = 09)

ratio for 120591CVU lt 1 whereas the opposite condition is verifiedfor 120591CVU gt 1This is expected since the device with the lowestandmost critical efficiency is the e-CVT so the configurationthat minimizes the power through the e-CVT is the mostconvenient one in terms of energy efficiency

5 Efficiency of the Output Compound e-CVTin Direct and Reverse Operation

Hybrid vehicles are the main application for CompoundSplit-eCVT transmission One of themost important featuresof hybrid vehicles is the regenerative braking capabilitySuch a function needs the transmission to work in reverseoperation For this reason it is important to evaluate theefficiency of the transmission in both direct and reverseoperation and to understand the differences

In this section the same transmission data are considered(120591ECVT119898 = 04 120591ECVT119872 = 2 120591CVU119898 = minus1 120591CVU119872 = 2) andthe performance in reverse operation are calculated throughthe model developed in a previous work [22] The efficiency120578ECVT of the e-CVT is considered constant and given by120578ECVT = 09 As mentioned in the compound transmissionwith a monotonic increasing speed ratio (119896

1= 029 119896

2=

minus329) if 120591CVU119898 gt 0 a power flow of Type IIII is obtainedGiven the same kinematic parameters when the transmissionworks in reverse operation (Figure 10) the input and outputtorques are reversed and because of the planetary gear trainPG1 also the torques on links 2 and 6 are reversed Further-more the torque and the power on the link 3 are also reversedand as a consequence of the planetary gear train PG2 alsothe torque and power on links 1 4 and 5 are reversed Soin the change from direct operation (Figure 10(a)) to reverseoperation (Figure 10(b)) the power flow is reversed on all thelinks and the power flow is yet of Type IIII

When 120591CVU119898 lt 0 similar arguments leads to concludethat the power flow is of Type III also in reverse operation(Figure 11)

The monotonic increasing speed ratio is investigatedfirst In Figure 12 it is shown that in reverse operation theefficiency of the transmission is always less than in directoperation with the only exception of the high values of thespeed ratio (120591CVU gt 17) It is very interesting to see that whenthe speed ratio is close to zero (minus027 lt 120591CVU lt 022) theefficiency in reverse operation is negative which means thatthe transmission is nonreversible with the speed ratio in theaforementioned range This result is in agreement with theresults shown in [8] in the case of Power Split TransmissionsIt is actually relevant for applications to the hybrid vehiclesbecause it affects negatively the braking recovery capabilitiesIn particular it is not possible to recover energy in brakingwith minus027 lt 120591CVU lt 022

Similar results can be obtained in the case of monotonicdecreasing speed ratio (Figure 7) Given the speed ratioranges of CVT and CVU (which give 119896

1= minus10 and 119896

2=

minus17) also in this case the power flows do not change whenswitching from direct to reverse operation power flow ofType III with 120591CVU gt 0 (Figure 11) and power flow of TypeIIII with 120591CVU lt 0 (Figure 10) The efficiency in direct andreverse operation is shown in Figure 13 Also in this case theefficiency in reverse operation is visibly less than in directmode Furthermore the nonreversibility range of the speedis even larger being minus040 lt 120591CVU lt 028

6 Conclusions

In recent years compound transmissions are attractingincreasing interest for application in hybrid vehicles becausethey are flexible and they permit optimizing the efficiency indifferent operating conditions The goal of this work was toobtain a systematic approach to determine the power flowsand the efficiency in Output Compound Split Transmissionsfor optimal design and control of HEVs The proposedmethodology is suitable for steady-state working conditionsand it follows from the assumption of negligible power lossin all the components except for the e-CVT It is shown how

10 International Journal of Vehicular Technology

Forward power

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 10 Power flows in a Output Compound Split e-CVT with Type IIII power flow (a) forward power (b) reverse power

Forward power

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 11 Power flows in a Output Compound Split e-CVT with Type III power flow (a) forward power (b) reverse power

the power circulation depends only on kinematic conditionsFurthermore a novel approach is shown to study the effi-ciency of the transmission which relies on the separationof the compound transmission in two subsystems so thatit can be studied as an ldquoEquivalent e-CVTrdquo (which is apower split-like transmission of Input-Output Split type)inside an Output Split device Following our approach the

efficiency is calculated easily for each of all the possiblepower flows A numerical example showed the potentialof this tool for power flows and efficiency calculations ofthe Output Compound Split Transmission in direct andreverse operation Experimental validation of the presentedmethodology is in progress and it will be the subject matterof future works

International Journal of Vehicular Technology 11

Forward power Reverse power

Monotonically increasing

0001020304050607080910

120578CV

U

00 10 201505minus10 minus05120591CVU

Figure 12The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically increasing

Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Forward power Reverse power

Figure 13The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically decreasing

Nomenclature

CVU CVTECVT and PG(subscripts)

Continuously Variable Unit ContinuouslyVariable Transmission ElectronicContinuously Variable Transmission andplanetary gear

119872119898 eq(subscripts)

Maximum minimum and equivalentrespectively

1198961 1198962 Kinematic parameter of the PG 1 and 2

respectively119875119895 Power through the 119895th branch119875119908 119875in and119875out

Dissipated power input power and outputpower

120591 Speed ratio120578 Efficiency120596119895 Angular velocity of the 119895th shaft

120596119900 Angular velocity of the output shaftof theCVU120596119894 Angular velocity of the input shaft of the CVU

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M R Cuddy and K B Wipke ldquoAnalysis of the fuel econ-omy benefit of drivetrain hybridizationrdquo SAE Technical Paper970289 1997

[2] S Stockar V Marano M Canova G Rizzoni and L GuzzellaldquoEnergy-optimal control of plug-in hybrid electric vehiclesfor real-world driving cyclesrdquo IEEE Transactions on VehicularTechnology vol 60 no 7 pp 2949ndash2962 2011

[3] L Serrao S Onori and G Rizzoni ldquoA comparative analysisof energy management strategies for hybrid electric vehiclesrdquoJournal of Dynamic Systems Measurement and Control vol 133no 3 Article ID 031012 2011

[4] F R Salmasi ldquoControl strategies for hybrid electric vehiclesevolution classification comparison and future trendsrdquo IEEETransactions on Vehicular Technology vol 56 no 5 pp 2393ndash2404 2007

[5] F Bottiglione T Contursi A Gentile and G Mantriota ldquoThefuel economy of hybrid buses the role of ancillaries in realurban drivingrdquo Energies vol 7 no 7 pp 4202ndash4220 2014

[6] A Taghavipour N L Azad and J McPhee ldquoAn optimal powermanagement strategy for power split plug-in hybrid electricvehiclesrdquo International Journal of Vehicle Design vol 60 no 3-4pp 286ndash304 2012

[7] Z Zhao C Wang T Zhang X Dai and X Yuan ldquoControloptimization of a compound power-split hybrid transmissionfor electric driverdquo SAE Technical Papers 2015

[8] G Mantriota ldquoPerformances of a series infinitely variabletransmission with type I power flowrdquo Mechanism and MachineTheory vol 37 no 6 pp 579ndash597 2002

[9] G Mantriota ldquoPerformances of a parallel infinitely variabletransmissions with a type II power flowrdquo Mechanism andMachine Theory vol 37 no 6 pp 555ndash578 2002

[10] B Si ldquoReconfigurable Hybrid Gear Trainrdquo US Patent 0 070 992A1 2011

[11] B Si ldquoDual mode input split compound split configurationEPPV transmissionrdquo US Patent 8 075 435 B2 2011

[12] F Bottiglione andGMantriota ldquoMG-IVT an infinitely variabletransmission with optimal power flowsrdquo Journal of MechanicalDesign vol 130 no 11 Article ID 112603 2008

[13] K T Chau andW Li ldquoOverview of electricmachines for electricand hybrid vehiclesrdquo International Journal of Vehicle Design vol64 no 1 pp 46ndash71 2014

[14] A G Holmes and M R Schmidt ldquoHybrid Electric PowertrainIncluding a Two-Mode Electrically Variable Transmissionrdquo USPatent 6 478 705 B1 2002

[15] C Brendan ldquoComparative analysis of single and combinedhybrid electrically variable transmission operatingmodesrdquo SAETechnical Paper 2005-01-1165 2005

[16] B Mashadi and S A M Emadi ldquoDual-mode power-splittransmission for hybrid electric vehiclesrdquo IEEE Transactions onVehicular Technology vol 59 no 7 pp 3223ndash3232 2010

12 International Journal of Vehicular Technology

[17] J Kim J Kang Y Kim T Kim B Min and H Kim ldquoDesignof power split transmission design of dual mode power splittransmissionrdquo International Journal of Automotive Technologyvol 11 no 4 pp 565ndash571 2010

[18] Y Zou F-C Sun C-N Zhang and J-Q Li ldquoOptimal energymanagement strategy for hybrid electric tracked vehiclesrdquoInternational Journal of Vehicle Design vol 58 no 2ndash4 pp 307ndash324 2012

[19] N-D Kim J-M Kim and H-S Kim ldquoControl strategy for adual-mode electromechanical infinitely variable transmissionfor hybrid electric vehiclesrdquo Proceedings of the Institution ofMechanical Engineers PartD Journal of Automobile Engineeringvol 222 no 9 pp 1587ndash1601 2008

[20] J Kim T Kim B Min S Hwang and H Kim ldquoModecontrol strategy for a two-mode hybrid electric vehicle usingelectrically variable transmission (EVT) and fixed-gear moderdquoIEEE Transactions on Vehicular Technology vol 60 no 3 pp793ndash803 2011

[21] Z Zhou CMi andG Zhang ldquoIntegrated control of electrome-chanical braking and regenerative braking in plug-in hybridelectric vehiclesrdquo International Journal of Vehicle Design vol 58no 2ndash4 pp 223ndash239 2012

[22] F Bottiglione and G Mantriota ldquoReversibility of power-splittransmissionsrdquo Journal ofMechanicalDesign Transactions of theASME vol 133 no 8 Article ID 084503 2011

[23] F Bottiglione and G Mantriota ldquoEffect of the ratio spread ofCVU in automotive kinetic energy recovery systemsrdquo Journalof Mechanical Design Transactions of the ASME vol 135 no 6Article ID 061001 2013

[24] F Bottiglione G Carbone L De Novellis L Mangialardiand G Mantriota ldquoMechanical hybrid KERS based on toroidaltraction drives an example of smart tribological design toimprove terrestrial vehicle performancerdquoAdvances in Tribologyvol 2013 Article ID 918387 9 pages 2013

[25] S De Pinto F Bottiglione andGMantriota ldquoInfinitely variabletransmissions in neutral gear torque ratio and power re-circulationrdquo Mechanism and Machine Theory vol 74 pp 285ndash298 2014

[26] S de Pinto and G Mantriota ldquoA simple model for compoundsplit transmissionsrdquo Proceedings of the Institution of MechanicalEngineers Part D Journal of Automobile Engineering vol 228no 5 pp 549ndash564 2014

[27] G Mantriota ldquoFuel consumption of a vehicle with power splitCVT systemrdquo International Journal of Vehicle Design vol 37 no4 pp 327ndash342 2005

[28] M Cammalleri ldquoEfficiency of split-way CVTrsquos A simplifiedmodelrdquo SAE Technical Papers 15 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 International Journal of Vehicular Technology

Forward power

13

5

2

4

6

Output compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType IIII power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 10 Power flows in a Output Compound Split e-CVT with Type IIII power flow (a) forward power (b) reverse power

Forward power

13

5

2

4

6

Output compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(a)

Reverse power

13

5

2

4

6

Input compoundType III power flow

Input

Output

PGII

PGI

e-CVT

(b)

Figure 11 Power flows in a Output Compound Split e-CVT with Type III power flow (a) forward power (b) reverse power

the power circulation depends only on kinematic conditionsFurthermore a novel approach is shown to study the effi-ciency of the transmission which relies on the separationof the compound transmission in two subsystems so thatit can be studied as an ldquoEquivalent e-CVTrdquo (which is apower split-like transmission of Input-Output Split type)inside an Output Split device Following our approach the

efficiency is calculated easily for each of all the possiblepower flows A numerical example showed the potentialof this tool for power flows and efficiency calculations ofthe Output Compound Split Transmission in direct andreverse operation Experimental validation of the presentedmethodology is in progress and it will be the subject matterof future works

International Journal of Vehicular Technology 11

Forward power Reverse power

Monotonically increasing

0001020304050607080910

120578CV

U

00 10 201505minus10 minus05120591CVU

Figure 12The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically increasing

Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Forward power Reverse power

Figure 13The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically decreasing

Nomenclature

CVU CVTECVT and PG(subscripts)

Continuously Variable Unit ContinuouslyVariable Transmission ElectronicContinuously Variable Transmission andplanetary gear

119872119898 eq(subscripts)

Maximum minimum and equivalentrespectively

1198961 1198962 Kinematic parameter of the PG 1 and 2

respectively119875119895 Power through the 119895th branch119875119908 119875in and119875out

Dissipated power input power and outputpower

120591 Speed ratio120578 Efficiency120596119895 Angular velocity of the 119895th shaft

120596119900 Angular velocity of the output shaftof theCVU120596119894 Angular velocity of the input shaft of the CVU

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M R Cuddy and K B Wipke ldquoAnalysis of the fuel econ-omy benefit of drivetrain hybridizationrdquo SAE Technical Paper970289 1997

[2] S Stockar V Marano M Canova G Rizzoni and L GuzzellaldquoEnergy-optimal control of plug-in hybrid electric vehiclesfor real-world driving cyclesrdquo IEEE Transactions on VehicularTechnology vol 60 no 7 pp 2949ndash2962 2011

[3] L Serrao S Onori and G Rizzoni ldquoA comparative analysisof energy management strategies for hybrid electric vehiclesrdquoJournal of Dynamic Systems Measurement and Control vol 133no 3 Article ID 031012 2011

[4] F R Salmasi ldquoControl strategies for hybrid electric vehiclesevolution classification comparison and future trendsrdquo IEEETransactions on Vehicular Technology vol 56 no 5 pp 2393ndash2404 2007

[5] F Bottiglione T Contursi A Gentile and G Mantriota ldquoThefuel economy of hybrid buses the role of ancillaries in realurban drivingrdquo Energies vol 7 no 7 pp 4202ndash4220 2014

[6] A Taghavipour N L Azad and J McPhee ldquoAn optimal powermanagement strategy for power split plug-in hybrid electricvehiclesrdquo International Journal of Vehicle Design vol 60 no 3-4pp 286ndash304 2012

[7] Z Zhao C Wang T Zhang X Dai and X Yuan ldquoControloptimization of a compound power-split hybrid transmissionfor electric driverdquo SAE Technical Papers 2015

[8] G Mantriota ldquoPerformances of a series infinitely variabletransmission with type I power flowrdquo Mechanism and MachineTheory vol 37 no 6 pp 579ndash597 2002

[9] G Mantriota ldquoPerformances of a parallel infinitely variabletransmissions with a type II power flowrdquo Mechanism andMachine Theory vol 37 no 6 pp 555ndash578 2002

[10] B Si ldquoReconfigurable Hybrid Gear Trainrdquo US Patent 0 070 992A1 2011

[11] B Si ldquoDual mode input split compound split configurationEPPV transmissionrdquo US Patent 8 075 435 B2 2011

[12] F Bottiglione andGMantriota ldquoMG-IVT an infinitely variabletransmission with optimal power flowsrdquo Journal of MechanicalDesign vol 130 no 11 Article ID 112603 2008

[13] K T Chau andW Li ldquoOverview of electricmachines for electricand hybrid vehiclesrdquo International Journal of Vehicle Design vol64 no 1 pp 46ndash71 2014

[14] A G Holmes and M R Schmidt ldquoHybrid Electric PowertrainIncluding a Two-Mode Electrically Variable Transmissionrdquo USPatent 6 478 705 B1 2002

[15] C Brendan ldquoComparative analysis of single and combinedhybrid electrically variable transmission operatingmodesrdquo SAETechnical Paper 2005-01-1165 2005

[16] B Mashadi and S A M Emadi ldquoDual-mode power-splittransmission for hybrid electric vehiclesrdquo IEEE Transactions onVehicular Technology vol 59 no 7 pp 3223ndash3232 2010

12 International Journal of Vehicular Technology

[17] J Kim J Kang Y Kim T Kim B Min and H Kim ldquoDesignof power split transmission design of dual mode power splittransmissionrdquo International Journal of Automotive Technologyvol 11 no 4 pp 565ndash571 2010

[18] Y Zou F-C Sun C-N Zhang and J-Q Li ldquoOptimal energymanagement strategy for hybrid electric tracked vehiclesrdquoInternational Journal of Vehicle Design vol 58 no 2ndash4 pp 307ndash324 2012

[19] N-D Kim J-M Kim and H-S Kim ldquoControl strategy for adual-mode electromechanical infinitely variable transmissionfor hybrid electric vehiclesrdquo Proceedings of the Institution ofMechanical Engineers PartD Journal of Automobile Engineeringvol 222 no 9 pp 1587ndash1601 2008

[20] J Kim T Kim B Min S Hwang and H Kim ldquoModecontrol strategy for a two-mode hybrid electric vehicle usingelectrically variable transmission (EVT) and fixed-gear moderdquoIEEE Transactions on Vehicular Technology vol 60 no 3 pp793ndash803 2011

[21] Z Zhou CMi andG Zhang ldquoIntegrated control of electrome-chanical braking and regenerative braking in plug-in hybridelectric vehiclesrdquo International Journal of Vehicle Design vol 58no 2ndash4 pp 223ndash239 2012

[22] F Bottiglione and G Mantriota ldquoReversibility of power-splittransmissionsrdquo Journal ofMechanicalDesign Transactions of theASME vol 133 no 8 Article ID 084503 2011

[23] F Bottiglione and G Mantriota ldquoEffect of the ratio spread ofCVU in automotive kinetic energy recovery systemsrdquo Journalof Mechanical Design Transactions of the ASME vol 135 no 6Article ID 061001 2013

[24] F Bottiglione G Carbone L De Novellis L Mangialardiand G Mantriota ldquoMechanical hybrid KERS based on toroidaltraction drives an example of smart tribological design toimprove terrestrial vehicle performancerdquoAdvances in Tribologyvol 2013 Article ID 918387 9 pages 2013

[25] S De Pinto F Bottiglione andGMantriota ldquoInfinitely variabletransmissions in neutral gear torque ratio and power re-circulationrdquo Mechanism and Machine Theory vol 74 pp 285ndash298 2014

[26] S de Pinto and G Mantriota ldquoA simple model for compoundsplit transmissionsrdquo Proceedings of the Institution of MechanicalEngineers Part D Journal of Automobile Engineering vol 228no 5 pp 549ndash564 2014

[27] G Mantriota ldquoFuel consumption of a vehicle with power splitCVT systemrdquo International Journal of Vehicle Design vol 37 no4 pp 327ndash342 2005

[28] M Cammalleri ldquoEfficiency of split-way CVTrsquos A simplifiedmodelrdquo SAE Technical Papers 15 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Vehicular Technology 11

Forward power Reverse power

Monotonically increasing

0001020304050607080910

120578CV

U

00 10 201505minus10 minus05120591CVU

Figure 12The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically increasing

Monotonically decreasing

00minus05minus10 10 15 2005120591CVU

0001020304050607080910

120578CV

U

Forward power Reverse power

Figure 13The efficiency 120578CVU as a function of the overall speed ratio120591CVU (120578ECVT = 09) in forward and reverse power transmission ratiomonotonically decreasing

Nomenclature

CVU CVTECVT and PG(subscripts)

Continuously Variable Unit ContinuouslyVariable Transmission ElectronicContinuously Variable Transmission andplanetary gear

119872119898 eq(subscripts)

Maximum minimum and equivalentrespectively

1198961 1198962 Kinematic parameter of the PG 1 and 2

respectively119875119895 Power through the 119895th branch119875119908 119875in and119875out

Dissipated power input power and outputpower

120591 Speed ratio120578 Efficiency120596119895 Angular velocity of the 119895th shaft

120596119900 Angular velocity of the output shaftof theCVU120596119894 Angular velocity of the input shaft of the CVU

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] M R Cuddy and K B Wipke ldquoAnalysis of the fuel econ-omy benefit of drivetrain hybridizationrdquo SAE Technical Paper970289 1997

[2] S Stockar V Marano M Canova G Rizzoni and L GuzzellaldquoEnergy-optimal control of plug-in hybrid electric vehiclesfor real-world driving cyclesrdquo IEEE Transactions on VehicularTechnology vol 60 no 7 pp 2949ndash2962 2011

[3] L Serrao S Onori and G Rizzoni ldquoA comparative analysisof energy management strategies for hybrid electric vehiclesrdquoJournal of Dynamic Systems Measurement and Control vol 133no 3 Article ID 031012 2011

[4] F R Salmasi ldquoControl strategies for hybrid electric vehiclesevolution classification comparison and future trendsrdquo IEEETransactions on Vehicular Technology vol 56 no 5 pp 2393ndash2404 2007

[5] F Bottiglione T Contursi A Gentile and G Mantriota ldquoThefuel economy of hybrid buses the role of ancillaries in realurban drivingrdquo Energies vol 7 no 7 pp 4202ndash4220 2014

[6] A Taghavipour N L Azad and J McPhee ldquoAn optimal powermanagement strategy for power split plug-in hybrid electricvehiclesrdquo International Journal of Vehicle Design vol 60 no 3-4pp 286ndash304 2012

[7] Z Zhao C Wang T Zhang X Dai and X Yuan ldquoControloptimization of a compound power-split hybrid transmissionfor electric driverdquo SAE Technical Papers 2015

[8] G Mantriota ldquoPerformances of a series infinitely variabletransmission with type I power flowrdquo Mechanism and MachineTheory vol 37 no 6 pp 579ndash597 2002

[9] G Mantriota ldquoPerformances of a parallel infinitely variabletransmissions with a type II power flowrdquo Mechanism andMachine Theory vol 37 no 6 pp 555ndash578 2002

[10] B Si ldquoReconfigurable Hybrid Gear Trainrdquo US Patent 0 070 992A1 2011

[11] B Si ldquoDual mode input split compound split configurationEPPV transmissionrdquo US Patent 8 075 435 B2 2011

[12] F Bottiglione andGMantriota ldquoMG-IVT an infinitely variabletransmission with optimal power flowsrdquo Journal of MechanicalDesign vol 130 no 11 Article ID 112603 2008

[13] K T Chau andW Li ldquoOverview of electricmachines for electricand hybrid vehiclesrdquo International Journal of Vehicle Design vol64 no 1 pp 46ndash71 2014

[14] A G Holmes and M R Schmidt ldquoHybrid Electric PowertrainIncluding a Two-Mode Electrically Variable Transmissionrdquo USPatent 6 478 705 B1 2002

[15] C Brendan ldquoComparative analysis of single and combinedhybrid electrically variable transmission operatingmodesrdquo SAETechnical Paper 2005-01-1165 2005

[16] B Mashadi and S A M Emadi ldquoDual-mode power-splittransmission for hybrid electric vehiclesrdquo IEEE Transactions onVehicular Technology vol 59 no 7 pp 3223ndash3232 2010

12 International Journal of Vehicular Technology

[17] J Kim J Kang Y Kim T Kim B Min and H Kim ldquoDesignof power split transmission design of dual mode power splittransmissionrdquo International Journal of Automotive Technologyvol 11 no 4 pp 565ndash571 2010

[18] Y Zou F-C Sun C-N Zhang and J-Q Li ldquoOptimal energymanagement strategy for hybrid electric tracked vehiclesrdquoInternational Journal of Vehicle Design vol 58 no 2ndash4 pp 307ndash324 2012

[19] N-D Kim J-M Kim and H-S Kim ldquoControl strategy for adual-mode electromechanical infinitely variable transmissionfor hybrid electric vehiclesrdquo Proceedings of the Institution ofMechanical Engineers PartD Journal of Automobile Engineeringvol 222 no 9 pp 1587ndash1601 2008

[20] J Kim T Kim B Min S Hwang and H Kim ldquoModecontrol strategy for a two-mode hybrid electric vehicle usingelectrically variable transmission (EVT) and fixed-gear moderdquoIEEE Transactions on Vehicular Technology vol 60 no 3 pp793ndash803 2011

[21] Z Zhou CMi andG Zhang ldquoIntegrated control of electrome-chanical braking and regenerative braking in plug-in hybridelectric vehiclesrdquo International Journal of Vehicle Design vol 58no 2ndash4 pp 223ndash239 2012

[22] F Bottiglione and G Mantriota ldquoReversibility of power-splittransmissionsrdquo Journal ofMechanicalDesign Transactions of theASME vol 133 no 8 Article ID 084503 2011

[23] F Bottiglione and G Mantriota ldquoEffect of the ratio spread ofCVU in automotive kinetic energy recovery systemsrdquo Journalof Mechanical Design Transactions of the ASME vol 135 no 6Article ID 061001 2013

[24] F Bottiglione G Carbone L De Novellis L Mangialardiand G Mantriota ldquoMechanical hybrid KERS based on toroidaltraction drives an example of smart tribological design toimprove terrestrial vehicle performancerdquoAdvances in Tribologyvol 2013 Article ID 918387 9 pages 2013

[25] S De Pinto F Bottiglione andGMantriota ldquoInfinitely variabletransmissions in neutral gear torque ratio and power re-circulationrdquo Mechanism and Machine Theory vol 74 pp 285ndash298 2014

[26] S de Pinto and G Mantriota ldquoA simple model for compoundsplit transmissionsrdquo Proceedings of the Institution of MechanicalEngineers Part D Journal of Automobile Engineering vol 228no 5 pp 549ndash564 2014

[27] G Mantriota ldquoFuel consumption of a vehicle with power splitCVT systemrdquo International Journal of Vehicle Design vol 37 no4 pp 327ndash342 2005

[28] M Cammalleri ldquoEfficiency of split-way CVTrsquos A simplifiedmodelrdquo SAE Technical Papers 15 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 International Journal of Vehicular Technology

[17] J Kim J Kang Y Kim T Kim B Min and H Kim ldquoDesignof power split transmission design of dual mode power splittransmissionrdquo International Journal of Automotive Technologyvol 11 no 4 pp 565ndash571 2010

[18] Y Zou F-C Sun C-N Zhang and J-Q Li ldquoOptimal energymanagement strategy for hybrid electric tracked vehiclesrdquoInternational Journal of Vehicle Design vol 58 no 2ndash4 pp 307ndash324 2012

[19] N-D Kim J-M Kim and H-S Kim ldquoControl strategy for adual-mode electromechanical infinitely variable transmissionfor hybrid electric vehiclesrdquo Proceedings of the Institution ofMechanical Engineers PartD Journal of Automobile Engineeringvol 222 no 9 pp 1587ndash1601 2008

[20] J Kim T Kim B Min S Hwang and H Kim ldquoModecontrol strategy for a two-mode hybrid electric vehicle usingelectrically variable transmission (EVT) and fixed-gear moderdquoIEEE Transactions on Vehicular Technology vol 60 no 3 pp793ndash803 2011

[21] Z Zhou CMi andG Zhang ldquoIntegrated control of electrome-chanical braking and regenerative braking in plug-in hybridelectric vehiclesrdquo International Journal of Vehicle Design vol 58no 2ndash4 pp 223ndash239 2012

[22] F Bottiglione and G Mantriota ldquoReversibility of power-splittransmissionsrdquo Journal ofMechanicalDesign Transactions of theASME vol 133 no 8 Article ID 084503 2011

[23] F Bottiglione and G Mantriota ldquoEffect of the ratio spread ofCVU in automotive kinetic energy recovery systemsrdquo Journalof Mechanical Design Transactions of the ASME vol 135 no 6Article ID 061001 2013

[24] F Bottiglione G Carbone L De Novellis L Mangialardiand G Mantriota ldquoMechanical hybrid KERS based on toroidaltraction drives an example of smart tribological design toimprove terrestrial vehicle performancerdquoAdvances in Tribologyvol 2013 Article ID 918387 9 pages 2013

[25] S De Pinto F Bottiglione andGMantriota ldquoInfinitely variabletransmissions in neutral gear torque ratio and power re-circulationrdquo Mechanism and Machine Theory vol 74 pp 285ndash298 2014

[26] S de Pinto and G Mantriota ldquoA simple model for compoundsplit transmissionsrdquo Proceedings of the Institution of MechanicalEngineers Part D Journal of Automobile Engineering vol 228no 5 pp 549ndash564 2014

[27] G Mantriota ldquoFuel consumption of a vehicle with power splitCVT systemrdquo International Journal of Vehicle Design vol 37 no4 pp 327ndash342 2005

[28] M Cammalleri ldquoEfficiency of split-way CVTrsquos A simplifiedmodelrdquo SAE Technical Papers 15 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of