1

04CVT-39

Improving Push Belt CVT Efficiency by ControlStrategies Based on New Variator Wear Insight

Maaike van der Laan, Mark van Drogen and Arjen BrandsmaVan Doorne’s Transmissie b.v. / Bosch Group

Copyright © 2004 SAE International

ABSTRACT

Developments in clamping force control for the push beltContinuously Variable Transmission (CVT) aim atincreased efficiency in combination with improvedrobustness. Current control strategies attempt to preventmacro slip between elements and pulleys at all times formaximum robustness.

In order to search for the limiting factors in developing anew control strategy, situations where macro slip occurshave been investigated. An important failure mechanismproves to be the occurrence of adhesive wear in thecontact leading to a loss in torque transfer. As acombination of normal load and slip speed, respectivelyclamping force and slip rate in a variator, a transition canbe found from a safe wear region to anexcessive/adhesive wear region. The occurrence of thistransition has been verified with experiments on CVTvariator level. It turns out that macro slip is acceptable toa certain extent.

The new wear insight allows fundamental differentcontrol strategies. In particular strategies based on CVTslip measurement and control are of interest. Thesecontrol strategies enable lower clamping forces whileretaining robustness. Consequently, CVT efficiencyincreases which will lead to an improvement in fuelconsumption of approximately 5%.

1. INTRODUCTION

The market for belt type Continuously VariableTransmissions (CVTs) is rapidly growing. Since beltproduction start up at Van Doorne’s Transmissie (VDT)in 1985, more than 5 million vehicles have beenequipped with a push belt CVT. At this moment, 1.2million push belt CVTs per year are used in theJapanese, North American, European, Korean and

Chinese markets. About 50 different vehicle models arecurrently available with push belt CVT.

Figure 1.1 shows the Van Doorne push belt, Figure 1.2illustrates the working principle of the push belt variator.

To further extend the application range of its push belt,VDT is examining more severe requirements regardingtransmittable power, transmission size (centre distance),ratio coverage and durability. To meet thoserequirements, the power density of belt and pulley needsto be increased [1]. The current push belt status is nicelyshown by the Nissan Murano with push belt CVT that hasa ratio coverage of 5.4 and can cope with a 3.5 liter V6180 kW/350 Nm engine with torque converter, applyingdrive side torque levels on the belt that lie above 500 Nm[2].

Figure 1.1 Example of a partly disassembled Van Doornepush belt with approximately 400 elements and 2 sets of9 rings.

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Figure 1.2 Example of a push belt variator and itsworking principle. In the variator, power is transmittedfrom the primary to the secondary pulley by means offriction between the push belt elements and the pulleysheaves. Stepless shifting between the extreme ratiosLOW and OverDrive (OD) is realised by changing theaxial position of the moveable pulley sheaves throughchanging the pulley clamping forces.

Besides increasing power density, VDT developmentsaim at improving the vehicle fuel consumption byimproving CVT-efficiency [3]. Figure 1.3 shows the fuelconsumption of manual transmissions (MTs) comparedto their CVT counterpart. Among these the recentlyintroduced Mercedes-Benz A-class CVT, applicable forengine torque levels up to 280[Nm] with a ratio coverageof 6.4 [4]. For these applications, the fuel consumption ofthe CVT is comparable to the MT level. In general,possibilities for further improvement of the fuelconsumption of state-of-the-art-CVTs are: increasing theratio coverage [5], reducing actuation losses [6][7] anddecreasing variator clamping forces [8], for instance byapplication of torque fuse [3]. In [3] it is shown that adecrease in variator clamping forces (compared to thestate-of-the-art control strategy) can lead to a decreasein fuel consumption of 5%. The investigation presentedin this paper is aimed at realising this.

Lowering the variator clamping forces is beneficial forboth fuel consumption, because of the decrease inpower consumed by the CVT hydraulic pump, and powerdensity, because of the decrease in push belt stresses.By lowering the clamping forces, the risk of belt slipincreases, for instance in case of torque peaks, or slowor delayed hydraulic responses. One of the

consequences of excessive belt slip can be severe wearin the element/pulley contact. For future improvements ofthe clamping force control strategy it is important todetermine the failure limits for the variator system. Theresults of this investigation are described in this paper.

0

1

2

3

4

5

6

7

8

9

10

fuel

con

sum

ptio

n[l/1

00km

]

5MTCVT

5MTCVT

6MTCVT

5MTCVT

5MTCVT

Honda HR-V 1.6i 4WD

Honda Jazz 1.4i

Nissan Primera 2.0

Subaru R2 660R

MB A-class A150

Figure 1.3 Comparison Manual Transmission (MT)versus CVT for a drive cycle. Source: vehicledocumentation.

In Chapter 2 macro slip and the variator failure mode arediscussed. In Chapter 3 the measurement setup fordetermining the variator failure behaviour is described. InChapter 4 the measurement results are presented.Chapter 5 discusses the consequences of themeasurement results for future variator controlstrategies. Finally the conclusions of this investigationare summarised.

2. MACRO SLIP AND VARIATOR FAILUREMODE

2.1. INTRODUCTION

Current clamping force control strategies for CVTs aredesigned in a way that macro slip is prevented at alltimes. Macro slip will occur if the applied torque is largerthan the maximum transmittable torque. In a CVTdesign, higher clamping forces are applied in order toaccomplish a certain safety margin in order to preventthe occurrence of macro slip [9].

The reasons to prevent macro slip are that, firstly, sliplosses have a negative influence on the efficiency and,secondly, macro slip is often directly associated withsevere belt element and pulley sheave wear.

secondary

primary

LOW OD

3

Severe wear in the belt-pulley interface can lead to aconsiderably lower torque capacity and may be regardedas a failure mode of the variator. Lower torque capacitymay cause macro slip events to occur at even lowertorque levels and this means a deterioration of thefunctional behaviour of the CVT.

Micro and macro slip are defined and explained inSection 2.2. In Section 2.3 the variator failure mode isinvestigated on an experimental level. Wearmechanisms and wear in relation to the contact of beltelement and pulley sheave are presented in Section 2.4.In Section 2.5 failure diagrams available in literature aredescribed.

2.2. BELT-PULLEY MICRO/MACRO SLIP

In the push belt CVT system, torque is transmitted bymeans of friction between the belt elements and thepulley sheaves. Therefore, the maximum transmittabletorque is determined by the normal force and thecoefficient of friction. This situation can be explained bymeans of a so-called slip curve [9] as is shown in Figure2.1.

On the horizontal axis of the slip curve, the primary orinput torque Tp is denoted and on the vertical axis the sliprate. The slip rate sr [%] is defined as

%1000

0 ⋅−

=i

iis s

r , (1)

where the speed ratio is = np/ns and i0 equals the initial isat the no-load condition (spin loss). At the variator test rigthe secondary or output torque Ts will be adjusted andthe input torque Tp is automatically adjusted by keepingthe primary rotational speed at a constant value. It iscustomary at VDT that Tp is labelled instead of Ts.

As can be seen in Figure 2.1, higher torque levels willresult in an increase in slip rate which is indicative of theslip speed between belt elements and pulley sheaves.The maximum transmittable torque Tp,max is reachedwhen all elements in the pulley with the lowest clampingforce are needed for torque transfer. Higher torquescannot be transmitted and the result is a sharp increasein the slip rate and the slip speed between belt elementsand pulley sheaves [10].

The slip rate is defined as micro slip when the slip ratelevel is below the slip rate level at T = Tp,max. Along thesame lines, macro slip is defined as the slip rate whenthe slip rate level is above the slip rate level at T = Tp,max,as shown in Figure 2.1. Excessive slip may lead toexcessive wear in the contact between element and

pulley. This may result in reduced torque capacity and/ormodified element and pulley geometry. At the moment,the control strategy is designed to prevent the macro slipregion at all times (by means of the above-mentionedsafety margin) and thus the objective is that excessiveslip may not occur.

0 20 40 60 80 100 120 140 160 180 200 2200

1

2

3

4

5

6

7

8

torque Tp [Nm]

slip

rat

e s r [%

]

mic

ro s

lip

mac

ro s

lip

Tp,max

Figure 2.1 Slip curve measurement in TOP ratio.

From experience it is known that the belt does notalways show excessive wear marks when it runs for ashort period of time in the macro slip regime. In the testrig configuration used for the standard slip curvemeasurements, it is not possible to let the variator rununder macro slip conditions (e.g. exactly 7% slip rate) fora longer period of time in a controlled way. When Tp,max isexceeded, the slip rate increases quickly in a shortperiod of time. In the next section nevertheless, theeffect of applying very short torque peaks/overshoots isinvestigated at this test rig configuration in order todetermine the failure mode of the belt-pulley contact.

An increase of the clamping forces leads to an extensionof the micro slip region. The transition to the macro slipregion now occurs at higher values for Tp. In other words,the system then has a higher torque capacity. Whenchanges in (output) torque take place at short notice (forinstance torque peaks), the clamping forces need to beat such a level that Tp stays below its critical value Tp <Tp,max. In order to take into account the possibilities ofoccurrence of those torque changes/peaks, a safetyfactor is applied to the clamping force control strategy.Unfortunately, at a certain constant applied torque anincrease of the clamping forces, and thus a safety factor,leads to a lower efficiency and a higher belt load.

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In the macro slip regime it is possible to determine thecoefficient of friction µ in the contact between beltelement and pulley sheave based on the measuredtorque. In the macro slip regime, all elements aretransferring torque and are slipping. Hence the kineticcoefficient of friction µ can be determined by

saxp

p

Fr

T

,2

cosλµ = (2)

where Tp is the primary torque, λ is the cone angle and rp

represents the primary running radius. The coefficient offriction at Tp,max is used to characterise the torquecapacity of the system [9].

2.3. BELT-PULLEY FAILURE MODE INVESTIGATION

In this section measurements to determine the variatorfailure mode are presented. It is important to know whatkind of wear will be introduced during macro slip and howthis will substantially affect the functionality of thevariator.

Factors that may play a role in the occurrence of wear inthe contact between belt element and pulley sheave arenormal force, frictional force and relative motion/slip.Bearing these factors in mind, it is interesting to see if itis possible to map a region of critical parameters that willresult in a condition of1. decreased functionality and/or total failure of the belt-

pulley contact due to wear,2. no decreased functionality and/or failure of the belt-

pulley contact due to wear.

A large number of subsequent slip curve measurementshave been performed to investigate the wear andfunctional behaviour under macro slip conditions. Thefirst measurements were aimed at as small as possiblemacro slip rate values, then the slip rates were stepwiseincreased to find the possible critical behaviour. Themeasurement sequence is presented in Figure 2.2.

The measurements were performed in TOP ratio after 40hours of running-in in this ratio at a nominal primarytorque of 140 Nm, for more information about themeasurement procedure and settings see [9]. Thespecifications of the used variator are presented in Table2.1

For measurements no.1 to 10 at a slip rate of 2% (just inthe macro slip regime as shown in Figure 2.1) theapplied torque was quickly lowered to zero. Due to asmall inertia delay, the slip rate had some overshoot tovalues larger than 2%. No severe (adhesive) wear was

observed and the torque capacity did not significantlydiffer i.e. ten times about 177 Nm with a correspondingmaximum coefficient of friction of 0.090 (i.e. µ at Tp,max).From this result, it may be concluded that thesesuccessive slip curve measurement conditions do notlead to severe wear and a decreased torque capacity.

Table 2.1 Variator specifications (P811).Variator parametersCenter distance [mm] 155Belt length [mm] 649.7Element width [mm] 24Number of rings per set 9Ratio coverage [-] 5.55Lubrication fluid type ESSO EZL799LOW ratio [-] 2.47primary running radius in LOW [mm] 30.0secondary running radius in LOW [mm] 74.1TOP ratio [-] 0.6primary running radius in TOP [mm] 66.7secondary running radius in TOP [mm] 40.0OD ratio [-] 0.445primary running radius in OD [mm] 72.5secondary running radius in OD [mm] 32.3

0 5 10 15 20 25 30 35 40 450

5

10

15

20

25

measurement number

slip

rat

e s r [%

]

Figure 2.2 Overview diagram of slip rate sr values permeasurement.

For the next measurements the maximum slip rate pertest was increased. No severe wear (slip marks) wasobserved during these tests up to no.22. The nextmeasurement no.23 showed adhesive slip marks on theelements (see Figure 2.3). From this we may concludethat at these operating conditions (in TOP ratio) thetransition from a mild wear regime to a severe, adhesive

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wear regime lies at a value for the slip rate between13.1% (no.22) and 16.9% (no.23).

This under the assumption that failure started at themaximum value for the slip rate. The correspondingfriction curve, where the coefficient of friction ispresented as a function of the slip rate, (see Figure 2.5)shows unstable behaviour after reaching the maximumslip rate value. This is not the case for measurementno.22, as is shown in Figure 2.4. Hence it can beconcluded that adhesive wear may occur at thesemeasurement settings between 13.1% and 16.9%.

Figure 2.3 Belt elements - after 23 slip measurements.

0 50 100 150 2000

2

4

6

8

10

12

14

16

18Measurement no. 22

torque Tp [Nm]

slip

rat

e s r [%

]

Tp,max = 180.4 [Nm]

sr,max = 13.1 [%]

i0 = 0.61 [-]

0 5 10 150

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

slip rate sr [%]

µ [-

]

µmax = 0.091 [-]

Figure 2.4 Slip curve and friction curve for measurementno.22 - no severe wear was observed after thismeasurement.

0 50 100 150 2000

2

4

6

8

10

12

14

16

18Measurement no. 23

torque Tp [Nm]

slip

rat

e s r [%

]

Tp,max = 180.2 [Nm]

sr,max = 16.9 [%]

i0 = 0.61 [-]

0 5 10 150

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

slip rate sr [%]

µ [-

]

µmax = 0.091 [-]

Figure 2.5 Slip curve and friction curve for measurementno.23 - severe wear was observed after thismeasurement.

However, no significant change in torque capacity andcoefficient of friction was observed looking at themeasurements no.24 and 25, where small macro slipvalues were applied again. From measurement no.26 onthe maximum slip rate has been increased moreseverely in order to be sure of reaching the 16% slip ormore. Slightly more adhesive wear (slip marks) on theleft side of the flank was observed after measurementsno.36 and 37. Up to measurement no.40, the coefficientof friction decreases from 0.091 (first measurements) to0.085. After 45 slip curve measurements in total thesystem endured several heavy slip events and finallylowered the maximum coefficient of friction to 0.080. Thecorresponding maximum torque capacity ranges from180 Nm in the beginning (measurement no.1) to 160 Nmduring test no.45 (11% lower). An overview of the resultsfor the corresponding coefficient of friction µ (calculatedbased on Tp,max) are shown in Figure 2.7.

It may be concluded from these results that the torquecapacity and hence coefficient of friction is considerablydecreased after reaching the severe, adhesive wearregime with its characteristic slip marks (see Figure 2.6).The number of times and the total amount of time ofeach adhesive slip event determines the overall wearand also the resulting torque capacity level. Therefore, itmay be concluded that the occurrence of severe,adhesive wear in a slip event must be prevented. Thetransition from mild to severe, adhesive wear must beregarded as a failure mode. Furthermore it can be saidthat under the current test conditions, the system allowsquite some macro slip until this transition is reached.

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Figure 2.6 Belt elements after 45 slip measurementsshowing severe wear.

0 5 10 15 20 25 30 35 40 45

0.075

0.08

0.085

0.09

0.095

0.1

measurement number

µ [-

]

Figure 2.7 Overview diagram of coefficient of friction µper measurement.

In the next two sections, a more fundamental approachto wear and transitions/failure is taken in order tounderstand the phenomena described above.

2.4. WEAR

2.4.1. Wear Theory

In general it is possible to distinguish severalmechanisms that lead to wear of an engineeringcomponent in a lubricated contact. These wearmechanisms are [9, 19]:1. tribochemical wear2. abrasive wear3. fatigue4. adhesive wear

In lubricated contacts, such as the element/pulleycontact, lubrication regimes (according to the Stribeckcurve) have to be taken into account. Depending on thelevel of separation of the contacting surfaces by the fluid,it is possible to distinguish the well-known areas:boundary, mixed and (elasto) hydrodynamic lubrication,denoted as BL, ML and EHL respectively [10, 11].

In EHL the only possible wear mechanism is fatigue. InBL (all of) and ML (part of) the load is carried by theroughness asperities of the contacting bodies. Theasperities make contact but there is no metal-metalcontact due to boundary layers formed at the interface byadditives in the lubricant. Now shearing takes place inthose boundary layers. If the hardness of both materialsare of the same order of magnitude, thus excluding twobody abrasive wear, three body abrasive, fatigue andmild chemical wear may take place.

Starting from a condition characterised by one or acombination of the first three wear mechanisms,transition to adhesive wear may take place under certainoperating conditions. If boundary layers will not hold upby thermal and/or mechanical means metal-metalcontact will occur. First (at increasing normal forceand/or sliding velocity) material transfer will take place ata microscopic scale. This condition is called incipientscuffing. At even more extreme conditions (even highernormal force and/or higher velocity) very severe adhesivewear will occur. This condition is commonly referred toas scuffing.

2.4.2. Wear and Failure in the Belt-Pulley Contact

Under operating conditions in the micro slip regime, mildtribochemical wear, abrasive wear and wear due tofatigue play a role in the element-pulley contact of thepush belt. This situation may be regarded as a “relativelymild wear” operating region. Then when in the macro slipregion excessive slip occurs, a transition may take placeand this may lead to severe wear according to theadhesive wear mechanism. The severe wear may lead tomalfunction of the variator (decreased torque capacity asfailure mode), as is explained in Section 2.3. Note againthat the transition from micro to macro slip does not haveto coincide with the transition from mild to adhesive wear.

The elements in the push belt are of the same order ofhardness as the pulleys and therefore this will not lead toabrasive wear. However, it is possible that particlesgenerated due to fatigue, running-in or foreign particlescause abrasive wear in the belt-pulley contact.

Fatigue/pitting may occur in the belt-pulley contact, buttogether with abrasive and tribochemical wear it is not

7

directly related to phenomena that play a role during thetransition described above. In other words when thetransition is about to happen the initial state of thesurface may be affected by one of the milder wearmechanisms and may be worn, but they do not directlylead to a departure from the safe operating region.

At the moment the consensus is that the transition tosevere/adhesive wear must be prevented at all times.Very short slip events in the adhesive wear region willcause a deterioration of the torque capacity whereasexperience shows that the torque capacity does notchange under the assumed safe operating conditions inthe micro slip regime. An indication that this also holdsfor the safe region in the macro slip regime is given inSection 5.2.1.

Diagrams dealing with the transitions in wear regimesand especially diagrams that cover the transition frommild to severe wear are described in the next section.

2.5. FAILURE DIAGRAMS

The Stribeck curve usually maps (lubrication) regimes bymeans of the coefficient of friction as a function ofoperating conditions under mild wear conditions.

To map failure modes (e.g. transition to adhesive wear)as a function of operating conditions, another diagram isneeded. In literature these are known as transition, wearor failure diagrams. For example, see the diagrams byAshby and Lim [13], PV diagrams [12] and IRG diagrams[11,13-16]. All these diagrams have in common that wearmechanisms, characterised by several criteria, aremapped as a function of a set of operational parameters.

The transitions in dominant wear mechanisms occur assliding loads and velocities are changed. In some cases,changes also occur as a function of sliding time (ordistance). The dominant wear mechanisms are based onmechanical strength and interfacial adhesion. Increase innormal load results in an increase in mechanical damagedue to high surface stresses. Increase in both normalload and sliding velocity results in an increase ininterface temperature. High interface temperature resultsin formation or breakdown of chemical films (boundarylayers) at the contact interface. Furthermore hightemperatures may result in a decrease in mechanicalstrength and in some cases structural changes. At veryhigh temperatures very severe adhesive wear will takeplace.

Possible criteria for determining failure diagrams:• Change in friction level

• Critical contact/flash temperature• Failure analysis; wear measurement

In this paper, the IRG-OECD1 transition diagram will beadopted. Failure is mapped with regard to normal forceFN and sliding velocity v and therefore this diagram isalso called the F/v-failure diagram. This correspondsclosely to the variator situation: clamping force and slip.The F/v-failure diagram distinguishes between regions ofefficient (mild wear) and inefficient (adhesive wear)performance in non-conforming lubricated slidingcontacts [11,13-16]. The failure criterion used is basedon the change of friction level in a certain lubricatedconcentrated contact

For the element-pulley contact this is a useful criterion(cf. Figures 2.3, 2.4 and 4.1), whereas criteria only basedon direct wear measurements (e.g. wear volume and/orwear rate k values [17]) are difficult to derive because ofthe complex nature of the contacting bodies especiallythe geometry of the element flank, and in-situ wearevaluation is even more difficult to perform.

An example of the F/v-failure diagram is shown in Figure2.8. In this diagram, where the so-called load-carryingcapacity FN is presented as a function of the slidingvelocity v, three regions, separated by two transitioncurves, can be distinguished. These regions aregoverned by the measured friction time characteristicsseen in Figure 2.9.

FN [N]

v [m/s]

I/II

III*

III

Figure 2.8 Transition diagram or F/v-failure diagram(reproduced from [11]).

1 International Research Group on Wear of EngineeringMaterials

8

µ [-]

t [s]

I/II0.3

0.2

0.1

0.4

µ [-]

t [s]

III*0.3

0.2

0.1

0.4

µ [-]

t [s]

III

0.3

0.2

0.1

0.4

Figure 2.9 Coefficient of friction-time curves (reproducedfrom [11].

Region I/II is considered to be a mild wear or ‘safe’region, where friction is relatively low (µ = 0.15 or less)and wear is virtually negligible (wear rate k ≈ 10-8

mm3/Nm). The lubricating conditions in this region areBL, ML and EHL. In region III* there is incipient scuffing:material transfer takes place at a microscopic scale andthe average contact pressure (pav) decreases. In thisregion, initial values of µ ≈ 0.35 and k ≈ 5·10-6 mm3/Nmoccur, both decreasing with time. If the contact is tooperate in region III, it fails almost immediately byscuffing, with µ ≈ 0.4 and k ≈ 10-3 mm3/Nm. In this regionvery severe adhesive wear (material transfer) will takeplace.

In the next chapters the F/v-failure diagram for thevariator is determined based on measurements.

3. DETERMINATION OF VARIATOR F/V-FAILURE DIAGRAM

To determine the variator F/v-failure diagram, it isnecessary to be able to calculate the slip speed andnormal force levels in the contact of belt element andpulley sheave. A method is described in Section 3.1.Furthermore, a procedure needs to be developed tocontrol the variator slip speed and normal force in apredetermined manner. This procedure is described inSection 3.2. In Section 3.3 the measurement program ispresented.

3.1. DETERMINATION OF SLIP SPEED AND NORMALFORCE

3.1.1. Determination of Slip Speed v

In the micro slip regime, it is very common to express thevariator slip by comparing the variator speed ratio to theno-load or geometrical ratio io (see Eq.(1)). For theoccurrence of adhesive wear, however, the absolute slipspeed in m/s is of importance.

The absolute element/pulley slip speed v is calculatedfrom the primary and secondary running radii (rp and rs)and primary and secondary rotational speeds (ωp and ωs)according to

sspp rrv ωω −= (3)

Since the measurements were performed with thevariator running against its LOW or OD stop, for theprimary and secondary running radii (rp and rs) thetheoretical running radii from the geometrical calculationsare used (see Table 2.1). Note that this means that allthe differences between the no-load ratio and the speedratio are translated into slip speed. This also includesratio change caused by pulley defection and beltelongation. In the macro slip regime this causes an offsetto the actual slip speed of around 0.1-0.2 m/s (1-2% inslip rate).

The relation between relative slip rate sr and absolute slipspeed v depends on rotational speed and geometricalratio and is expressed by

%100⋅=ss

rrv

sω

(4)

3.1.2. Determination of Normal Force FN

The normal force in the element/pulley contact dependsdirectly on the pulley clamping force applied by hydraulicpressure. This force is distributed over all the elements inthe wrapped angle of the pulley. For the determination ofthe F/v-failure diagram of the variator, in principle theelement that carries the maximum load is most critical.

For reasons of simplicity it is decided to assume that theapplied clamping force is distributed equally over allelements in the wrapped angle. As a result, FN can beexpressed as a function of geometrical ratio andsecondary clamping force only.

saxN FicF ,0 )(= (5)

The constant c is determined by the number of elementsin the wrapped angle of the pulley with the highest slipand (in LOW) the pulley clamping force ratio (Fax,p/Fax,s).Table 3.1 shows the value of c for geometrical ratioLOW, TOP and OD.

Table 3.1 Part of the secondary clamping force carriedby a single element in the wrapped angle.i0 [-] LOW TOP OD

c [-] 0.0174 0.0134 0.0176

9

3.2. CONTROL OF SLIP SPEED AND NORMALFORCE

The measurements were performed on a variator test-rig. For the construction of the F/v-failure diagram it wasdecided to control FN at a constant level and to vary slipspeed v according to a predetermined trajectory. InFigure 3.1 a schematical view of the test-rig is shown.

drive/load motorprimarytorque meter

belt box

drive/load motor

push belt

primary pulley

secondary pulleysecondarytorque meter

Figure 3.1 Schematic view of the test-rig.

3.2.1. Control of Normal Force FN

Since FN only depends on the secondary clamping forceand the geometrical ratio (see Eq.(5)), FN was controlledby controlling the secondary and primary pressure at aconstant level. The secondary pressure level was chosenbased on the desired FN level for the desired geometricalratio. The primary pressure level was chosen in a waythat the pulley clamping force ratio (Fax,p/Fax,s)guaranteed that the variator remained at the OD or LOWstop.

3.2.2. Control of Slip Speed v

The variator slip speed depends on no-load ratio andprimary and secondary rotational speed (see Eq.(3)). Inorder to be able to accurately control the variator slipspeed, the variator was driven by an engine on bothsides. This means that instead of the standard setting,which is primary speed and secondary torque control(used for slip curve measurement, see Section 2.2), theprimary speed and secondary speed were controlled.Since the clamping pressures were chosen in a way thatthe geometrical ratio remained constant, the variator slipcould be accurately controlled.

All belts were exposed to one or more macro slip events.Figure 3.2 shows the slip profile that was used.

Three phases can be distinguished:1. Speed up: 0 to 5 s. The variator starts at very low

speed, both the primary and the secondary speedare increased until the target primary speed isreached. During this period, the secondary speed ischosen such that a small positive macro slip iscreated, causing the torque to be at its maximumpositive level corresponding to the applied clampingforce and actual coefficient of friction.

2. Large macro slip: 5 to 9 s. When the target primaryspeed is reached, the secondary speed is decreasedfor 2 s linear in time until the target maximum slipspeed is reached. After that, the secondary speed isincreased in 2 s to the level corresponding to smallpositive macro slip.

3. Slow down: 9 to 13 s. Both the primary andsecondary speed is decreased to zero. Again a smallpositive macro slip is maintained.

0 5 10 150

1000

2000

3000

4000

5000

time[s]

rota

tiona

l spe

ed[rp

m] np

nsn

p/i

0

0 5 10 150

200

400

slip

rat

e[%

]

sr

0 5 10 150

5

10

time[s]

slip

spe

ed[m

/s]

v

0 5 10 150

2

4

6

8

10

time[s]

pulle

y pr

essu

re[b

ar] pp

ps

0 5 10 150

0.5

1

1.5

2

time[s]

ratio

[-]

isi0

Figure 3.2 Example macro slip event in OD in course oftime: setpoints of rotational speeds and setpoints forpulley pressures, the resulting speed ratio and slip level.

3.2.3. Measurement Example

Figure 3.3 shows an example of the measurementaccording to the setpoints shown in Figure 3.2. It is clearthat the desired macro slip profile with slip speed levelsup to 8 m/s, corresponding to a slip rate of 300% can beaccurately controlled with the proposed measurementmethod.

Note that the variator torque levels are now a result ofthe combination of applied clamping force and slipspeed. If the slip changes size or direction (positive tonegative), the torque will do the same. Since positivemacro slip is controlled, the torque is at its positive slip

10

limit all the time. When the macro slip level increases(between 5 and 7 s), the torque decreases, indicating adecrease in coefficient of friction µ with increased slipspeed.

0 5 10 150

1000

2000

3000

4000

5000

time[s]

rota

tiona

l spe

ed[rp

m] np

nsn

p/i

0

0 5 10 150

200

400

slip

rat

e[%

]

sr

0 5 10 150

5

10

time[s]

slip

spe

ed[m

/s]

v

0 5 10 150

2

4

6

8

10

time[s]

pulle

y pr

essu

re[b

ar] pp

ps

0 5 10 150

50

100

150

time[s]

torq

ue[-]

TpTs

Figure 3.3 Measured macro slip event.

3.3. MEASUREMENT PROGRAM

The specification of the variator that was used for themeasurements is described in Table 2.1. Since thepurpose of the tests was determining the occurrence ofadhesive wear, new hardware was used for each test.For each point in the failure diagram a new belt andpulley were used. A running-in procedure at micro sliplevel was used prior to the macro slip events.

The parameters that were varied were:• geometrical ratio• primary rotational speed• clamping force level

Table 3.2 shows the parameter settings for each beltnumber.

Table 3.2 Measurement program.belt number i0[-] np[rpm] ps[bar] FN[N]1 LOW 1500 9.4 1702 OD 1500 8.6 1653 LOW 1500 37.4 6104 OD 1500 17.1 3105 LOW 2200 2.3 606 OD 1500 2.1 557 LOW 4000 9.4 1708 LOW 4000 37.4 6009 OD 1800 8.6 16510 LOW 1500 18.7 33011 OD 1500 4.3 90

4. VARIATOR F/V-DIAGRAM MEASUREMENTRESULTS

4.1. DETERMINATION OF THE ADHESIVE WEARFAILURE LIMIT.

Similar to the theory described in Section 2.5, theadhesive wear transition is primarily detected by lookingat the torque signals (or coefficient of friction) over thecourse of time. Since the clamping force levels areapproximately constant during the test, a suddenincrease in torque is associated with increased torquetransmittance caused by adhesive wear. This isespecially clear when looking at the calculated coefficientof friction during the test.

Figure 4.1 shows the torque signal and calculatedcoefficient of friction during two different tests. The topshows the torque, slip speed and coefficient of friction fora slip event in OD that did not cause adhesive wear. Thebottom shows the same signals for a measurement thatdid cause adhesive wear. The arrow indicates the start ofthe adhesive wear. The measurements are from thesame belt and were performed right after each other. Forthe second measurement the maximum slip speed levelwas increased as compared to the first one (8.3 vs. 9.7m/s).

4.2. THE VARIATOR F/V-FAILURE DIAGRAM

For each parameter setting the slip speed at the point offailure was determined (the slip speed corresponding tothe arrow in Figure 4.1) and displayed in an F/v-failurediagram.

Figure 4.2 shows the variator failure diagram for aselection of measurements:• all at a primary speed of 1500 rpm except test no.5,

which was at a primary speed of 2200 rpm,• in two different ratios (LOW and OD),• and at different normal force levels.

For test no.5 a higher failure limit than the indicated slipspeed is valid, because the belt did not fail at this slipspeed, but the slip speed could not be increasedbecause the secondary pulley speed had reached zero.

Note that the F/v-failure diagrams presented in this paperare valid for the used hardware, lubrication fluid type andrunning-in procedure.

4.2.1. The Influence of the Variator Ratio

When the measurements at the same element normalforce level and in different ratios are compared (LOW vs.OD), the LOW measurement always fails earlier in terms

11

of slip speed level compared to OD. The differencebetween the failure point in LOW and OD are 2 to 5 m/sdepending on the normal force level.

0 5 10 15-50

0

50

100

150

200

250

time[s]

v[0.1m/s]T

p[Nm]

0 5 100

0.1

0.2

0.3

slip speed v[m/s]

coef

ficie

nt o

f fric

tion[

-] µ

0 5 10 15-50

0

50

100

150

200

250

time[s]

v[0.1m/s]T

p[Nm]

0 5 100

0.1

0.2

0.3

slip speed v[m/s]

coef

ficie

nt o

f fric

tion[

-] µ

Figure 4.1 Above, the torque, slip speed and coefficientof friction for a slip event in OD that did not causeadhesive wear. Below, the same signals for ameasurement that did cause adhesive wear.

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800

1 2

3

4

5 no failure 6

10

11

slip speed v[m/s]

elem

ent n

orm

al fo

rce

F N[N

]

F/v-failure diagram np=1500[rpm]

LOW failureLOW no failureLOW failure lineOD failureOD failure line

Figure 4.2 F/v-failure diagram measured at a primaryspeed of 1500 rpm.

4.2.2. The Influence of the Clamping Force Level

As is expected based on theory (see Section 2.5) thehigher the normal force the smaller the failure limit slipspeed. In LOW the adhesive wear starts at a slip speedof 1.2 m/s at 610 N maximum element normal force(corresponding to ps=37 bar, no.3) whereas at 170 N, 4.1

m/s is the failure limit (corresponding to ps=9.4 bar, no.1)and at 60 N the belt did not even fail at 6.9 m/s(corresponding to ps=2.3 bar, no.5). In OD this is lessclear because the failures of belt no.2 and no.4 areinconsistent.

4.2.3. The Influence of the Primary Rotational Speed

Figure 4.3 shows in LOW at 170 and 600 N thedifferences between the adhesive wear limit for a primaryspeed of 1500 and 4000 rpm and in OD at 165 N thedifferences between the adhesive wear limit for a primaryspeed of 1500 and 1800 rpm. In all cases, increasing theprimary speed increases the slip speed at whichadhesive wear occurs.

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800

1 2

3

6

7

8

9

104

slip speed v[m/s]

elem

ent n

orm

al fo

rce

F N[N

]

F/v-failure diagram influence np

LOW failure np=1500[rpm]LOW failure np=4000[rpm]LOW failure line n

p=1500[rpm]

OD failure np=1500[rpm]

OD failure np=1800[rpm]OD failure line np=1500[rpm]

Figure 4.3 F/v-failure diagram. The influence of theprimary rotational speed.

See [18] for a comparison of the F/v-failure diagram thatresulted from the variator measurements with that fromliterature. In the next chapter the consequences of theF/v-diagram investigation for the clamping force controlstrategy will be discussed.

5. CONTROL STRATEGY DISCUSSION

The current control strategy is described in Section 5.1.Section 5.2 discusses control strategy improvementsbased on the F/v-failure diagram.

5.1. CURRENT CONTROL STRATEGY

Because until now it was not possible to predict whatlevel of macro slip was allowed with respect to adhesivewear, current control strategies are aimed at preventing

12

macro slip at all times. From Eq.(2) it can be derived thatthis is realised when the secondary clamping force iscontrolled according to

max

, 2

cos

µ

λ

p

psax r

TF ≥ (6)

The most important problem of this strategy whenapplied in a vehicle, is the determination of Tp. In manysituations Tp can be estimated based on enginecharacteristics and dynamical effects. But disturbancesencountered at the wheels of the vehicle will result intorque disturbances in Tp that cannot be predictedwithout the use of extra sensors at the wheel side of thedrive line. In practice this problem is solved by estimatingthe primary torque level (Tp,est) based on enginecharacteristics and dynamics and applying an extraclamping force based on an estimation of the maximumoccurring torque disturbance Tdist

max

,, 2

cos)(

µ

λ

p

distestpsax r

TTF

+= (7)

Experience with vehicles with CVTs show that adhesivewear is avoided when Tdist is 30% of the maximumengine torque [3].

The amount of overclamping relative to the minimumnecessary force of Eq.(6) is called safety and expressedaccording to

λ

µ

cos

2 max,

p

psaxf T

rFS = (8)

Figure 5.1 shows the controlled safety as a function ofthe actual primary torque relative to the maximum enginetorque. A conclusion is that low torque levels correspondto high safety levels. Especially stationary, part loadconditions (driving constant speed) lead to highoverclamping in order to prevent macro slip.

0 20 40 60 80 100 1200

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Tp/Teng,max[%]

Sf[-]

Figure 5.1 Controlled safety with the current controlstrategy as a function of primary torque relative tomaximum engine torque.

The high safety in part load causes a drawback onefficiency. Figure 5.2 shows an example of measuredvariator efficiency in LOW and OD. Slip losses increaseand the torque losses decrease with decreasing safety.Therefore the variator efficiency shows an optimum. ForLOW this optimum is reached at a safety around 1.3, forOD this optimum is reached for a safety around 1.1. Theextra loss in the variator in part load caused by the highsafety strategy is around 2% in OD at safety 2 and morethan 6% at safety 4 and higher. In LOW the extra loss isaround 1% at safety 2 and more than 4% at safety 4 andhigher.

When besides the losses in the variator, the other lossesin the CVT are also considered the extra loss inefficiency will be even more, because actuation lossesalso decrease with decreasing safety. This implies thatthe safety corresponding to optimal CVT efficiency islower than 1.3 in LOW and lower than 1.1 in OD.

In [3] it is shown that the increase in variator clampingforces of the current control strategy compared to theclamping force levels corresponding to safety 1.3 leadsto an increase in fuel consumption over the NEDC cycleof more than of 5%.

13

0 1 2 3 4 5 60

2

4

6

8

10LOW

safety[-]

loss

[%]

total lossesslip losstorque loss

0 1 2 3 4 5 60

2

4

6

8

10OD

safety[-]

loss

[%]

total lossesslip losstorque loss

0 1 2 3 4 5 690

92

94

96

98

100

safety[-]

effic

ienc

y[%

]

ηmax

η

0 1 2 3 4 5 690

92

94

96

98

100

safety[-]

effic

ienc

y[%

] ηmax

η

Figure 5.2 Variator losses and efficiency as a function ofsafety in LOW and OD.

5.2. CONTROL STRATEGY IMPROVEMENTS BASEDON THE F/V-FAILURE DIAGRAM

By determining the origin of adhesive wear, anddisplaying the failure lines in the F/v-failure diagram, it ispossible to change the basics of the clamping forcecontrol strategy from preventing macro slip at all times toallowing limited macro slip but preventing crossing thefailure lines in the F/v-failure diagram. This will result in adecrease in overclamping and therefore an increase inefficiency. In the next section a simple variator slipbehaviour model is presented in order to understandwhat determines the trajectory in the F/v-failure diagram.

5.2.1. Variator Slip Behaviour Model

Figure 5.3 shows the schematical setup of a drive linesimulation model in a simple form: two masses coupledby the variator.

Js, ωsTp Ts

Teng

Tload

Jp, ωp

Figure 5.3 Variator slip behaviour model.

The variator slip speed is determined by the running radiior geometrical ratio in combination with the rotationalspeeds of the variator (see Eq.(3))

sspp rrv ωω −=

The rotational speeds of the variator are described by

pengp

p TTdt

dJ −=

ω (9)

and

loadss

s TTdt

dJ −=

ω (10)

The primary and secondary torque are coupled to eachother by means of the geometrical ratio (torque lossesare not taken into account)

ps TiT 0= (11)

The primary torque is a function of the secondaryclamping force, the primary running radius and thecoefficient of friction determined by the slip speed andgeometrical ratio

)if(vrF

T psaxp 0

, ,with cos

2== µ

λ

µ (12)

The coefficient of friction can be determined by themeasurements described in Chapter 3 and 4.

Summarising the equations above, the conclusion is thatthe trajectory in the F/v-failure diagram is determined by:• Slip speed v in course of time. The variator slip

speed depends on running radii rp and rs and thepulley speeds (ωp and ωs). These speeds depend on:1. the torque input from engine and wheel side

(Teng and Tload)2. the variator torque levels (Tp and Ts) which

depend on variator clamping force level (Fax,s),running radius rp and coefficient of friction µ(depending on slip speed v and geometrical ratioi0).

• Normal force FN in course of time, this force isdetermined by clamping force Fax,s and geometricalratio i0 (Eq.(5)).

14

5.2.2. Control Strategy Options

As already stated in the introduction, it is possible tochange the basics of the clamping force control strategyfrom preventing macro slip at all times to allowing limitedmacro slip but preventing crossing the failure lines in theF/v-failure diagram. A way to realise this is CVT slipcontrol: clamping force control based on a measured slipsignal instead of estimated torque levels. An example ofa slip controller design is presented in [19]. Figure 5.4shows a control scheme of the current control strategycompared to CVT slip control.

v

Fax,sFax,s,setTp,est setpointgeneration

clampingforce

controller

variatorhydraulics

variator

+-

Fax,svsetη setpointgeneration

clampingforce

controller

variatorhydraulics

variator

+-

Figure 5.4 The current control strategy (above) versusCVT slip control (below).

For the current control strategy, measurement of Fax,s isnecessary, so this requires secondary pressuremeasurement. For slip control instead of secondarypressure measurement, measurement of variator slip isnecessary. To determine v, both rotational speeds (ωp

and ωs) and geometrical ratio i0 need to be determined.Measurement of the geometrical ratio can be realised bymeasuring one of the running radii of the variator or theposition of one of the moveable pulley sheaves. Whenthe variator is against the LOW or OD stop, thegeometrical ratio is also known.

By directly controlling the desired slip level it is possibleto control the optimum efficiency in stationary situations.This point of optimum efficiency will always be in themicro slip regime. Controlling macro slip in stationarysituations (constant vehicle speed) is not desiredbecause of the fact that the optimum efficiency isreached under micro slip conditions. Figure 5.2 showsthat with increasing slip CVT efficiency decreasessharply.

A torque disturbance at the wheels of the vehicle will leadto a disturbance in the measured slip. Short time macroslip is no problem as long as the controller guaranteesthat the failure limits in the F/v-diagram are not reached.From the F/v-failure diagram the necessary controlaccuracy in case of disturbances that cause short timemacro slip can be derived. The position of the failurelines in the F/v-diagram will serve as a basis for thespecification for the requirements the clamping force

control system (delay, clamping force increase/decreaserate).

Besides slip control, there are other relative simplerealisable possibilities to avoid adhesive wear. One is tolimit pulley clamping force Fax,s based on a measured oreven a maximum possible slip speed v. For instance inLOW with positive torque, the maximum slip speed isreached when the secondary pulley speed is reduced tozero. For the P811 variator (see Table 2.1) for a primarypulley speed of 1000 rpm in LOW, the slip speed cannotbe higher than about 3.1 m/s. The clamping force can becontrolled to a maximum limit in this case in order toavoid crossing the failure lines in the failure diagram.

Other way around, it is also possible to limit the slipspeed v depending on the applied clamping force Fax,s.This can be realised by limiting the controlled speed ratioor primary rotational speed.

5.2.3. Control Strategy Example in the F/v-failureDiagram

Figure 5.5 shows an example of adaptation of thesecondary clamping force to an unknown, constanttorque level at a test rig. The test rig controls take carethat both the primary speed and the secondary torqueare controlled at a constant level. The variator is againstthe stop in geometrical ratio LOW. By lowering thesecondary clamping pressure, the transition from microto macro slip is detected. As soon as macro slip arises,the secondary clamping force is increased 1.3 times.This causes the slip to stabilise at small micro slip. Fromthe efficiency plot it can be concluded that aboutoptimum efficiency is controlled in this way without usingany knowledge of the torque level or coefficient offriction, but with the use of slip measurement.

This type of measurement can also be used forcalibration of the maximum level of the coefficient offriction µmax or the estimated engine torque Tp,est in thecurrent control strategy.

15

0 1 2 3 4 5950

1000

1050

spee

d[rp

m]

i0=Low, np=1000[rpm], Ts=82[Nm]

np

0 1 2 3 4 5350

400

450

500

spee

d[rp

m]

ns

0 1 2 3 4 55

10

15

20

pres

sure

[bar

]

ps setpointps

0 1 2 3 4 50

50

100

torq

ue[N

m]

Tp

0 1 2 3 4 50

100

200

time [s]

torq

ue[N

m]

Ts

0 1 2 3 4 5-5

0

5

10

slip

rate

[%]

sr

0 1 2 3 4 5

1

2

3

safe

ty[-] S

f

0 1 2 3 4 50.9

0.95

1

time [s]

effic

ienc

y[%

]

η

Figure 5.5 Variator control strategy example.

Figure 5.6 shows the same measurement in the F/v-diagram. The clamping force/slip speed combination isfar from the failure line, so there is no risk of adhesivewear and also no adhesive wear was observed.

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800

900

slip speed v[m/s]

elem

ent n

orm

al fo

rce

F N[N

]

F/v-failure diagram

Low failure line np=1500[rpm]Low measurement

Figure 5.6 Trajectory of the variator control strategyexample of Figure 5.5 in the F/v-failure diagram.

CONCLUSION

The main conclusion of this paper is that the presentedF/v-failure diagram can be used to optimise the variatorcontrol strategy by applying lower clamping forces inorder to realise improved fuel consumption (ofapproximately 5%) and power density withoutcompromising robustness for adhesive wear.

Furthermore it can be concluded that:• The occurrence of adhesive wear leads to a

decrease in variator torque capacity and musttherefore be regarded as a variator failure mode.

• Adhesive wear in the belt/pulley contact is caused bya combination of a too high slip speed and clampingforce level.

• By controlling both primary and secondary speed at aknown geometrical ratio, it is possible to control adesired macro slip profile in time.

• With respect to adhesive wear, macro slip isacceptable to a certain extent. The allowed macroslip rate depends on the operating conditions.Examples shown in this paper are:1. In TOP at a primary speed of 6000 rpm and a

secondary pressure of 9.9 bar a slip rate of 13%is allowed.

2. In OD at a primary speed of 1000 rpm and asecondary pressure of 3.3 bar, a slip rate of386% is allowed.

• A first estimation of the failure limit for the variator isdetermined by measurements and displayed by afailure line in the F/v-failure diagram.

• In general the relation between normal force and slipspeed that describes the adhesive wear failure limitof the variator is similar to the theory.

• Besides slip speed and clamping force, themeasurements show that the occurrence of wearalso depends on the geometrical ratio (LOW morecritical than OD) and the primary speed (the lowerthe more critical).

• New possible control strategies are based on CVTslip measurement and control.

• A control strategy application example shows that itis possible to change the basics of the clampingforce control strategy from preventing macro slip atall times to allowing limited macro slip but preventingcrossing the failure lines in the F/v-failure diagram.

REFERENCES

1. Brandsma, A., van Lith, J., Hendriks, E., “Push beltCVT developments for high power applications”,Proc. of CVT99, Eindhoven University of Technology1999, pp.142-147.

2. Van der Sluis, F., Brandsma, A., van Lith, J., van derMeer, K., van der Velde, A., Pennings, B., “Stressreduction in push belt rings using residual stresses”,Proc. of CVT2002 Congress, VDI-Berichte 1709,Munich, October 2002, pp.383-402.

3. Van Spijk, G., Veenhuizen, B., "An upshift in CVT-efficiency", Proc. of Getriebe in Fahrzeugen '98. VDI-

16

Berichte 1393, Friedrichshafen, June 1998, pp.659-671.

4. Front-CVT Automatikgetriebe (WFC280) vonMercedes-Benz, New front wheel drive CVT(WFC280) from Mercedes Benz, Greiner, J., Kiesel,J., Lorch, Veil, A., Strenkert, J. Proc. of Getriebe inFahrzeugen '04. VDI-Berichte 1827, Friedrichshafen,June 2004, pp.421-445.

5. Van der Sluis, F., et al., The two-stage push beltCVT, IIR symposium Offenbach Germany 2002

6. Van der Sluis, F, "A New Pump for CVTApplications", SAE 2003-01-3207, Proc. of the 2003Powertrain & Fluid Systems Conference, Pittsburgh,October 2003.

7. Veenhuizen, P.A., Bonsen, B., Klaassen, T.W.G.L.,Albers, P.H.W.M., Changenet, C., Poncy, S.,"Pushbelt CVT efficiency improvement potential byservo-electromechanical actuation and slip control",2004 International Continuously Variable and HybridTransmission Congress, San Fransisco, September2004.

8. Laan, M. van der, Luh, J., "Model-Based VariatorControl Applied to a Belt Type CVT", Proc. ofCVT99, Eindhoven University of Technology 1999,pp.105-116.

9. Pennings, B., Drogen, M. van, Brandsma, A., Ginkel,E. van, Lemmens, M., “Van Doorne CVT Fluid Test –A Test Method on Belt-Pulley Level to Select Fluidsfor Push Belt CVT Application”, SAE 2003-01-3253,Proc. of the 2003 Powertrain & Fluid SystemsConference, Pittsburgh, October 2003.

10. Kobayashi, D., Mabuchi, Y. and Katoh, Y., “A Studyon the Torque Capacity of a Metal Pushing V-belt forCVTs”, SAE Paper 980822, 1998.

11. Schipper, D.J. and Gee, A.W.J. de, “LubricationModes and the IRG Transition Diagram”, LubricationScience 8-1, 1995, pp. 27-35.

12. Bhushan, B., “Principles and Applications ofTribology”, Wiley, New York, 1999.

13. Czichos, H., “Presentation of Friction and WearData”, ASM Handbook, Vol. 18, 1992, pp. 489-492.

14. Begelinger, A. and Gee, A.W.J. de, “Failure of ThinFilm Lubrication – The Effect of Running-In on theLoad Carrying Capacity of Thin Film LubricatedConcentrated Contacts”, Journal of LubricationTechnology, Vol. 103, 1981, pp. 203-210.

15. Gee, A.W.J. de and Begelinger, A., “Failuremechanisms in sliding lubricated concentratedcontacts”, Proceedings of the 11th Leeds-LyonSymposium on Mixed Lubrication and LubricatedWear, 1984.

16. Schipper, D.J., Steenmeijer, R.C. and Gee, A.W.J.de, “The Effects of Variations in the Procedure ofLoading on the Load Carrying Capacity of Thin FilmLubricated Concentrated Contacts”, Proceedings ofthe 4th International Tribology Conference, Austrib94,Vol. I, 1994, pp. 105-112, ISBN 0 646 21097

17. DIN 50321: Verschleißmeßgrößen, Beuth Verlag,Berlin, 1979.

18. Drogen, M. van and Laan, M. van der,“Determination of Variator Robustness under MacroSlip Conditions for a Pushbelt CVT”, SAE 2004-01-0480, SAE 2004 World Congress, Detroit, March2004.

19. Bonsen, B., Klaassen, T.W.G.L., Meerakker, K.G.O.van de, M. Steinbuch, P.A. Veenhuizen,"Measurement and control of slip in a continuouslyvariable transmission", IFAC Mechatronics 2004Sydney, September 2004.

DEFINITIONS

c: element normal force constant [-]i0: no-load speed ratio [-]is: speed ratio [-]k: wear rate [mm3/Nm]np: primary rotational speed [rpm]ns: secondary rotational speed [rpm]pp: primary pressure [bar]ps: secondary pressure [bar]rp: primary running radius [m]rs: secondary running radius [m]sr: slip rate [%]v: slip speed [m/s]Fax,p: primary clamping force [N]Fax,s: secondary clamping force [N]Jp: primary inertia [kg m2]Js: secondary inertia [kg m2]Sf: safety [-]Tdist: disturbance torque [Nm]Teng: engine torque [Nm]Tload: roadload torque [Nm]FN: normal force [N]Tp: primary torque [Nm]Ts: secondary torque [Nm]η: efficiency [%]λ: pulley angle [rad]µ: coefficient of friction [-]ωp: primary rotational speed [rad/s]ωs: secondary rotational speed [rad/s]