doi: 10.1177/0954407013491896 pump for engine lubrication

Original Article

Proc IMechE Part D:J Automobile Engineering227(10) 1414–1430� IMechE 2013Reprints and permissions:sagepub.co.uk/journalsPermissions.navDOI: 10.1177/0954407013491896pid.sagepub.com

Performance analysis of avariable-displacement vane-type oilpump for engine lubrication using acomplete mathematical model

Dinh Quang Truong1, Kyoung Kwan Ahn1, Nguyen Thanh Trung1 andJae Shin Lee2

AbstractVariable-displacement vane-type oil pumps represent one of the most innovative pump types for industrial applications,especially for engine lubrication systems. The aim of this paper is to develop a complete and accurate mathematicalmodel for a typical variable-displacement vane-type oil pump to investigate its working performance. First, the detailedtheoretical model was built on the basis of pump geometric design and dynamic analyses. Next, numerical simulationswith the constructed model and experiments on the actual pump system were carried out to analyse the main powerloss factors in order to develop the complete model for high modelling accuracy. The estimated pump performanceusing the complete pump model was finally verified by numerical simulations in comparison with practical tests.

KeywordsLubrication, vane pump, variable displacement, flow rate, modelling

Date received: 6 September 2012; accepted: 18 March 2013

Introduction

Nowadays, the design requirements for engine lubrica-tion systems, especially for vehicle applications, havebeen oriented towards a general performance improve-ment, coupled with simultaneous reductions in thepower losses, the weights and the volumes. A fixed-displacement lubricating pump driven by a rotatingcomponent of the mechanical system is generallydesigned to operate effectively at a target speed and amaximum operating lubricant temperature. However,the lubrication requirements of the machine do notdirectly correspond to its operating speed. This results inan oversupply of lubricating oil to most machines. Tosecure operational safety in hot idling, these pumps areoversized. Consequently, a low efficiency is obtained atmost operating speeds. A pressure relief valve is thenprovided to return the surplus lubricating oil back intothe pump inlet or a reservoir to avoid over-pressure con-ditions in the mechanical system. As a result, a signifi-cant amount of the energy used to pressurize thelubricating oil is exhausted through the relief valve.1,2

Subsequently, a potential trend for machine lubrica-tion is the employment of variable-displacement vanepumps as lubrication oil pumps. To vary the

displacement, there are two common approaches,namely the use of a linear translating cam ring3–5 andthe use of a pivoting cam ring.6–9 In both cases, eachpump generally includes a ring, the movement of whichis controlled by a mechanism including a return spring.The pump displacement control mechanism is normallysupplied with pressurized lubricating oil from the pumpoutput through an orifice. As the pressure increases,the ring movement changes its eccentricity with respectto the rotor centre-line, which in turn changes the pumpdisplacement. The return spring, which acts to resist thehydraulic force acting on the ring, can be calibrated toachieve the desired pressure regulation characteristicsof the pump. By employing this mechanism, over-pressure situations in the engine throughout the

1School of Mechanical and Automotive Engineering, University of Ulsan,

Ulsan, Republic of Korea2Material Science and Engineering, University of Ulsan, Ulsan, Republic of

Korea

Corresponding author:

Kyoung Kwan Ahn, School of Mechanical Engineering, University of Ulsan,

Daehakro 93, Namgu, Ulsan, 680-749, Korea.

Email: [email protected]

at PENNSYLVANIA STATE UNIV on April 8, 2016pid.sagepub.comDownloaded from

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expected operating range of the system can be avoided.Although this series of pumps provides improvementsin the energy efficiency over those of fixed-displacementpumps, it still results in an energy loss. The reason isthat the displacement control decision is, directly orindirectly, affected by the pressurized oil rather than bythe changing requirements of the lubricating system.

Therefore, development of a variable-displacementvane-type oil pump model is indispensable and can beconsidered a priority in order to investigate a pump’sworking performance as well as to optimize the pump’sdesign structure. Some studies related to this field havebeen made to investigate the pump performances.Giuffrida and Lanzafame10 derived a mathematicalmodel for a fixed-displacement balanced-vane pump toanalyse the theoretical flow rate through the cam shapedesign and the vane thickness. Staley et al.1 carried out astudy on a variable-displacement vane pump for enginelubrication. Loganathan et al.2 also developed avariable-displacement vane pump for automotive appli-cations by simulations and experiments. In anotherstudy, Kim et al.11 investigated an electronic controlvariable-displacement lubrication oil pump through asimple mathematical model. To investigate the dynamiccharacteristics of vane pumps, Karmel12,13 carried outboth a theoretical analysis and a parametric study of thepressure distribution inside the variable-displacementvane pump as well as the forces and torques applied tothe mechanism and the pump shaft. In another study,Rundo and Nervegna14 pointed out that the stator ringgeometry of variable-displacement radial pumps influ-ences the performance characteristics of these units. Thetype of stator ring motion (linear or rotational), the loca-tion of the rotation centre and the porting plate integralwith the casing or with the stator ring all have markedeffects on the steady-state and dynamic performances ofthe pump. Geist and Resh15 developed a detaileddynamic model of a variable-displacement vane pump toobtain a better understanding of how to improve theengine and the circuit efficiency of the engine oil as wellas to assess the pump stability. This pump modelemployed differential equations based on four possiblepressure distribution regions to enable detailed predic-tions to be made of the pump’s dynamic behaviour asthe oil conditions and the circuit pressures vary. The sys-tem phenomena such as the internal leakages from thepump chamber’s volumes, the variable oil conditionssuch as aeration and viscosity, as well as variations inselecting the load spring were also analysed for theireffects on the behaviour and performance of the oilpump. Numerical simulations were performed to investi-gate the simulated pump performance. Although thesestudies provided interesting results, a detailed analysis ofthe theoretical performance as well as a careful investiga-tion of the power losses of a variable-displacement vane-type oil pump in order to derive an accurate model basedon practical experiments were not considered.

From the above analysis, this paper develops an accu-rate and complete mathematical model of a typical

variable-displacement vane-type oil pump. First, the the-oretical model is meticulously constructed using a gen-eral method based on geometric and dynamic analysesof the pump (see the second section). It can then be eas-ily used to model any pump design. By using this model,the ideal pump characteristics can be readily investigatedthrough numerical simulations (see the third section).Second, the complete model including the main powerloss factors is performed on the basis of the theoreticalmodel and experimental data (see the fourth section). Asa result, the actual pump performance can be estimatedwell by using this model. It can be considered as anindispensable step towards a deeper understanding ofpump operation as well as for effectively implementing apump displacement control mechanism to satisfy theurgent lubrication demands. It is, therefore, very usefulfor achieving industry’s time-to-market goals.

A typical variable-displacement vane-typeoil pump and model design

A variable-displacement vane-type oil pump

In this study, a variable-displacement vane-type oilpump made by MyungHwa Co. Ltd11 as displayed inFigure 1 was used for the investigation. Tor vary the

Figure 1. Research vane-type oil pump: (a) outside view of thepump; (b) internal structure of the pump.

Truong et al. 1415



pump displacement, rotation of the main ring aroundthe pivot pin is controlled by the pressurized oil itself inthe control chamber through the orifice, the pumpingchambers, the centrifugal force effects and the returnspring.

A variable-displacement vane-type oil pump model

Vane movement analysis. The analysis of an ith genericvane is carried out for the cross-section of the pumpshown in Figure 2. Points Or and Os are the centre ofthe rotor and the centre of the inner contour of themain ring respectively. The eccentricity between therotor and the ring inner surface is ec. There are N vanesof thickness tv and radius Rv at their tip curves (centrepoint Ovi). In the initial state, each vane stays at theend of the corresponding slot defined by the radius Rrv.Point Bi is the intersection point between the tip arcand the centre-line of the vane.

The rotor rotates with a constant velocity v. At thecurrent angular position a of the rotor, the position ofthe ith vane can be defined as

ai =a� 2p

Ni� 1ð Þ, i=1, . . . ,N ð1Þ

Figure 2 shows that, because of the centrifugal effect,the vane contacts the inner surface of the main ring atpoint Ai at the current time. Point Ai is far from pointBi, which is presented by the angle gi. To determine thecontact point Ai, it is necessary to find the distanceOrAi [ ri and the corresponding angle bi. Consideringthe small triangles OrOviAi and OrOviOs, the relations

ri =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2

v +OrOvi2+2RvOrOvi cosgi

q, i=1, . . . ,N

ð2Þ

bi =arccosr2i + e2c � R2

s

2riec

� �ð3Þ

gi =arcsinec sinai

Rs � Rv

� �ð4Þ

OrOvi =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffie2c + Rs � Rvð Þ2 +2ec Rs � Rvð Þ cos ai+ gið Þ

qð5Þ

can be obtained.Subsequently, the vane lift lv can be obtained as

lvi=OrBi � Rr

= OrOvi+Rv � Rr

ð6Þ

Theoretical pump flow rate analysis. Generally, a pumpwith N vanes is rigorously characterized by N pumpingchambers between the consecutive vanes and N pump-ing chambers under the vanes; thus, the total numberof pumping chambers is 2N. Figure 3 displays a volumevariation analysis for the chamber under the ith consid-ered vane corresponding to a small rotational angle da

of the rotor. The volume derivative dVuv aið Þ=da of thechamber under the ith vane is computed as

dVuv aið Þda

= btvdlv aið Þda

[ btvdlvida

ð7Þ

Figure 2. Geometric analysis of a generic vane.

1416 Proc IMechE Part D: J Automobile Engineering 227(10)



Next, the volume variation for a chamber betweentwo consecutive vanes (namely the ith and the (i+ 1)thvanes) occupying the angular positions ai and

ai+1 [ ai +2p=N respectively is analysed in Figure 4.This volume variation can be computed as

dVbv ai,ai+1ð Þ=dVbv in ai,ai+1ð Þ � dVbv out ai,ai+1ð Þ ð8Þ

As depicted in Figure 4(a), at the current time whenthe rotor is considered at the angle a, the two ith and(i+ 1)th vanes contact the ring inner surface at pointsAi0 and A(i+1)0 respectively. After the small rotationda of the rotor, the two ith and (i+ 1)th vanes contactthe ring surface at the two points Ai1 and A(i+1)1

respectively, which are different from the previouspoints Ai0 and A(i+1)0. Consequently, this causes boththe input volume and the output volume to be reducedby small amounts as indicated by Si2 in Figure 4(b).Based on this figure and from a simple calculation, thevolume of oil entering into the chamber and the volumeof oil being pumped out of the chamber between twoconsecutive vanes can be derived as (represented as Si1in Figure 4(b))

dVbv in ai,ai+1ð Þ=12b r2

i+1 dbi+1 � r2i+1 dui+1

� �ð9Þ

and

Figure 4. Analysis of the volume variation for a chamber between two consecutive vanes: (a) rotational analysis of two consecutivevanes; (b) volume in–volume out analysis of a chamber between two consecutive vanes.

Figure 3. Analysis of the volume variation for a chamber undera generic vane.

Truong et al. 1417



dVbv out ai,ai+1ð Þ=12b r2

i dbi � r2i dui

� �ð10Þ

respectively,where the factors r and db can be obtainedfrom the section on the vane movement analysis; thefactor du can be derived as

dui =dbi � da ð11Þ

From equations (8) to (11), the volume derivative ofthe chamber between the vanes is finally obtained as

dVbv ai,ai+1ð Þda

=b

2r2i+1 � r2

i

� �ð12Þ

Finally, the ideal theoretical flow rate of the vane pumpcan be computed on the basis of equations (7) and (12) as

Qth að Þ= 1

2vXNi=1

dVuv aið Þda

sgn dVuv aið Þ½ � � 1f g

+1

2vXN�1i=1

dVbv ai,ai+1ð Þda

sgn dVbv ai,ai+1ð Þ½ � � 1f g

+1

2vdVbv

daaN,a1ð Þ sgn dVbv aN,a1ð Þ½ � � 1f g

ð13Þ

Analysis of the rotation of the main ring

Force due to the pressurized oil inside the main ring. Inthis research pump, the eccentricity between the rotorand the ring is a maximum (ec_max = Rs–Rr) in the ini-tial state of the main ring. In this case, the rotor con-tacts the inner contour of the ring at point C10 and thecentre point of the ring inner contour is at point Os0.Two coordinate systems have been used, namely aCartesian coordinate system positioned at the rotorcentre (OrXrYr), and a polar coordinate system, thepole of which is located at the centre point of the innercontour of the ring and the axis points to a point on thering at which the ring contour is closest to the rotor.

During the operation, the eccentricity makes thering’s inner contour similar to a cam contour if Or isconsidered as the centre point. Based on the pump’sworking principle at the initial position of the ring, theprofile of the pressure distribution on the ring’s innersurface within one rotation of the pump (Figure 5(a))can be divided into three regions.

1. The first region within the arc C10C20 (where thearc radius presents a positive gradient (with theminimum value Rr at C10)) relates to the suctionzone. Consequently, the pressure is almost thesame as the minimum pressure Pmin (the tank pres-sure) during the rotation angle ar 2 0,ar10½ �ar =a+pð Þ of the rotor. The effect of this pres-sure region on the ring is represented by the anglerange as 2 0,as10½ �[ 0,aC20½ �.

2. The second region within the arc C20C30 (where thearc radius increases or decreases very slowly (nearthe maximum value Rs+ ec_max) gives the pre-compression for the oil chambers. The pressure

increases from Pmin (the tank pressure) to Pmax (theoutlet pressure), corresponding to the rotation anglear 2 ar10,ar10 +ar20½ � of the rotor. The effect ofthis pressure region on the ring is represented by theangle range as 2 as10,as10 +as20½ �[ aC20,aC30½ �.

3. The third region within the arc C30C10 (where thearc radius decreases with the same gradient as inthe first region) relates to the delivery zone. Thepressure is then almost the same as the maximumpressure Pmax (the outlet pressure), correspondingto the rotation angle ar 2 ar10 +ar20,ar10 +½ar20 +ar30�[ ar10 +ar20, 2p½ � of the rotor. Theeffect of this pressure region on the ring is repre-sented by the angle range as 2 as10 +as20, 2p½ �[ aC30, 2p½ �.

For a small rotation du of the ring around the pivotpin Op, the centre point of the ring’s inner contour ismoved from point Os0 to point Os1. The three regionsof pressurized oil are then repositioned so that pointsC10, C20 and C30 are moved to points C11, C21 and C31

respectively (Figure 5(b)). The initial coordinate Os0 ofpoint Os is easily determined as

OpOs0 =Rrot

\HOpOs0=uOs0

ð14Þ

Consequently, the trajectory Ost of the centre point Os

when the ring is rotated around the pivot point Op isdetermined as a rotating vector, the length of which isRrot and the angle is uOs0

� du. Therefore, the three pres-sure regions can be completely determined. Let us definethe angle difference between the pole axis and the centre-line OpOst as cst. Then the total moment acting on thering caused by the pressurized oil inside the ring to makeit rotate around the pivot pin can be computed as

XMOp oil inside

=

ðaC2t

0

Rrot sin (cst +as) PminbRs das

+

ðaC3t

aC2t

Rrot sin (cst+as)

Pmax � Pminð Þ as � aC2t

aC3t � aC2t+Pmin

� �bRs das

+

ð2p

aC3t

Rrot sin (cst+as) PmaxbRs das

ð15Þ

Force due to the pressurized oil outside the main ring(through the control orifice). Considering the oil chamberoutside the ring through the control orifice (seeFigure 1), the relationship between the input flow rateand the output flow rate during a small rotation du ofthe ring can be expressed as

Qinflow �Qoutflow =Vout

boil

dPout

dtð16Þ

where Qinflow and Qoutflow are the input flow rate and theoutput flow rate computed from




Qinflow =CorAor

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2

roil

Pmax � Poutð Þs

ð17Þ

and

Qoutflow = �ðm1b

m1a

OpO1 du sinm� �

bR1 dm

�ðm3b

m3a

OpO3 du sinm� �

bR3 dm

+

ðm2b

m2a

OpO2 du sinm� �

bR2 dm

+

ðm4b

m4a

OpO4 du sinm� �

bR4 dm

ð18Þ

respectively, and where Vout is the outside chamber vol-ume and dPout is the pressure derivative.

The total moment acting on the ring’s outer surfacecaused by the pressurized oil to make it rotate aroundthe pivot pin can be obtained as (Figure 6)

XMOp oil outside

=

ðm1b

m1a

OpO1 sinm PoutbR1 dm

+

ðm3b

m3a


�ðm2b

m2a


�ðm4b

m4a

OpO4 sinm PoutbR4 dm ð19Þ

Force due to the centrifugal effects of the vanes and the oilvolumes between the vanes. The centrifugal force gener-ated by an oil chamber between each two consecutive

vanes is first analysed in Figure 7. As shown in this fig-ure, the boundary of the oil chamber is the polygonAitA(i+t)tMN. The centrifugal force of this chamber ispresented by a vector Fcen positioned at the chamber’smass centre Gi. Let us divide the chamber volumeAitA(i+t)tMN into a rectangular block AitA

�itMN and

a triangular block AitA�itA i+1ð Þt, and consider that the

oil density is distributed uniformly in all the chambervolume. Therefore, the centre mass of this oil chambercan be represented by

j =GiW1

GiQ

=SAitA

�itA i+1ð Þt

SAitA�itMN

ð20Þ

where Wl and Q are the mass centre of the AitA�itMN

block and the mass centre of the AitA�itA i+1ð Þt block

respectively and

SAitA�itA i+1ð Þt =

123AitA

�it3A i+1ð ÞtA

�it

=12 bi � bi+1ð Þ ri+1 � rið Þ

SAitA�itMN=MN3AitN

= bi � bi+1ð Þ ri � Rrð Þ

ð21Þ

By using a simple calculation, the relations

GiU=j

1+ j

ri + ri+1 � 2Rr

3+

3+2j

3+3j

ri � Rr

2

UM =3+2j

3+3j

bi � bi+1

2

ð22Þ

can be obtained.From equation (22), the coordinates of Gi are finally

calculated as

Figure 5. Analysis of the pressure distribution inside the main ring: (a) the pressure distribution at the initial position of the mainring; (b) the pressure distribution after a small rotation of the main ring.

Truong et al. 1419



OrGi =Rr +GiU

\ OrXs!

, OrGi! �

[ ar Gið Þ

[ ar AiAi+1MNð Þ

=bi+1 +3+2j

3+3j

bi � bi+1

2+p

ð23Þ

The centrifugal force of an object of mass mi travel-ling in a circle of radius R(mi) around the rotor centrecan be computed as (Figure 8)

Fcen mið Þ=miv2R mið Þ ð24Þ

where mi and R(mi) are defined as follows: for an oilchamber between two consecutive vanes,

mi = SAitA�itA i+1ð Þt +SAitA

�itMN

�broil

R mið Þ=OrGi

ð25Þ

for an oil chamber under each vane,

Figure 6. Analysis of the pressure distribution outside the main ring: (a) motion analysis of the main ring; (b) pressure analysis inthe outside chamber.

Figure 8. Analysis of the effect of the centrifugal force on therotation of the ring.

Figure 7. Analysis of the centrifugal force generated by thevolume of an oil chamber between two consecutive vanes.




mi = tv Rr � Rrv + lvi � hvð Þbroil

R mið Þ=Rrv+Rr � Rrv + lvi � hv

2

ð26Þ

and, for a vane,

mi = tvhvbrsteel

R mið Þ= lvi+Rr �hv2

ð27Þ

The total moment acting on the ring caused by thecentrifugal forces of N vanes and N oil chambers isderived as

XMOp cen

= �XNi=1

Fcen mið Þ cos d mið Þ½ � OpMi

ð28Þ

where Fcen mið Þ is obtained from equations (24) to (27)and where OpMi and d mið Þare obtained from

OpMi =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiOpOr

2+R2 mið Þ � 2OpOr R mið Þ cos ar mið Þ+cr½ �

qð29Þ

and from

d mið Þ=p

2+arcsin

OpOr

OpMi

sin ar mið Þ+cr½ �( )

ð30Þ

respectively.

Force of the compression spring. From Figure 5, themoment generated by the spring force can be computedas

MOspr= � Fspr OpH cos uCð Þ ð31Þ

where OpH is a constant obtained on the basis of thedistance OpC0 and the angle uC0

defined when the ringis at the initial position, i.e. uC =uC0

� du; Fspr isderived as

Fspr=Fspr0 + ksprxspr ð32Þ

where

xspr=OpH tan uCð Þ � tan uC0

� �� ð33Þ

Finally, the rotation of the ring is defined by sum-ming all the moments acting on the ring around thepivot point according to

Iring €u=X

MOp oil inside+X

MOp oil outside

+X

MOp cen+MOspr

ð34Þ

Numerical simulations and theoreticalpump performance analysis

For the simulations, the pump was operated by theengine, the speed of which was tested up to 4000 r/min.

The sampling time was set to 0.1 ms for all the simula-tions. The parameter settings for the pump model wereobtained from the designed pump geometrics, as shownin Table 1.11

First, the pump model was tested in the free-loadcondition. In this condition, the suction port was con-nected from the oil sump, and the delivery port wasalso linked again to the oil sump without any restrictorto return the pump’s output flow directly to the oilsump. The pump speed and the discharge pressure werekept at constant values of 500 r/min and 1 bar respec-tively. Figure 9 then displays an analysis of the firstfour consecutive vanes as well as the volume derivativesgenerated by these vanes in this case. With the counter-clockwise rotation of the rotor shaft, the vane move-ments were obtained as shown in Figure 9(a).Consequently, the volume derivatives of the chambersunder these vanes and of the chambers between thesevanes generated by the vane lifts were analysed inFigure 9(b) and (c) respectively.

Second, an analysis of the flow ripple was carriedout on the theoretical pump model in the free-load con-dition. In this case, the eccentricity was kept at a maxi-mum value and the working speed was set to aconstant speed of 1000 r/min. The flow ripple result isthen plotted in Figure 10. This figure shows that thepump’s output flow rate contained approximately a61.5% flow ripple. This ripple was due to the variationin the oil chambers between the vanes and under the

Table 1. Parameter settings for the pump model.

Component Factor Units Value

Pumpgeometricdesign

Rr mm 24Rrv mm 13Rs mm 27.5b mm 28N — 9tv mm 2.5hv mm 10dor mm 4Cor (ISO 5167) mm 0.599kspr kgf/mm 4.544Fspr0 kgf 30.8992OpH mm 80.06HC0 mm 29.7OpO1 mm 24OpO2 mm 38.75OpO3 mm 38.15OpO4 mm 48.15R1 mm 15R2 mm 33.25R3 mm 5R4 mm 5

Lubrication oil,SAE 5W-20

boil N/m2 1.5 3 109

roil at 15 �C kg/m3 852loil 1/�C 6.4 3 10–4

noil at –30 �C,40 �C, 100 �C,120 �C

mm2/s 4200, 47,8.9, 5.91

Truong et al. 1421



vanes, as analysed in Figure 9. In other working condi-tions where the ring position is adjusted, the rippleproblem is also caused by the pressure ripple as well asby the forces generated during the pump operation.Furthermore, in the actual vane pump system, the

ripple problem is also caused by some power loss fac-tors such as leakages, friction and incomplete fillingeffects.

Third, the pump model was investigated at differentpressure settings and different pump speeds in the free-load condition. The theoretical steady-state flow–pressure characteristic was then obtained as depicted inFigure 11. The flow–pressure characteristic shows thata higher working pressure causes a smaller pump dis-placement, or a smaller pump flow rate. The reason isthat the significant increase in the force acting on thering due to the pressurized oil outside the ring (see thesection on the force due to pressurized oil outsidethe main ring (through the control orifice)) subse-quently causes the eccentricity of the rotor and theinner contour of the ring to decrease. As a result, thepump flow rate is decreased and becomes zero whenthe centre of the inner contour of the ring coincideswith the centre of the rotor.

Finally, the pump model was tested in the case whenthe pump delivery port is connected to a load compo-nent before returning to the oil sump. In this case, theload was simulated by employing a variable-flowrestrictor (an orifice valve) which could allow a flow

Figure 9. Theoretical performance of four consecutive vanes: (a) analysis of the vane lifts; (b) analysis of the volume derivativeunder the vanes; (c) analysis of the volume derivative between the vanes.

Figure 10. Theoretical analysis of the pump flow ripple atmaximum eccentricity and a speed of 1000 r/min.




rate of 135 l/min corresponding to a pressure drop of10 bar over this valve. The simulations were performedwith three different pump speeds while the valve areaopened was set to 80%. The results were then obtainedas plotted in Figure 12. It can be seen that, at lowspeeds such as 1000 r/min and 2000 r/min, the eccentri-city between the rotor and the ring was constant in theinitial state (maximum eccentricity) (the lowest plots inFigure 12). This is because the low speeds gave corre-spondingly low delivery flow rates, which were allowedto pass fully through the orifice valve. The deliverypressures in these cases were then quite low (the middleplots in Figure 12). However, the sum of the generatedmoments around the pivot pin was not sufficiently highto make the ring rotate. Only when the speed wasincreased as in the cases of 3000 r/min and 4000 r/min,

did the pump deliver a flow that was over the capacityof the restrictor, which consequently caused a large risein the delivery pressure. This high pressure level createda moment around the pivot pin sufficiently large torotate the ring. As a result, the eccentricity was auto-matically changed to the new steady-state position toadjust to an appropriate delivery flow. The pump per-formance in these cases can be seen clearly in Figure 12with the dash-dotted blue and solid black curves. Tomake clear how the main ring operated, the momentcomponents acting on the main ring when the pumpwas operated at 4000 r/min are analysed as shown inFigure 13. The results prove that the pump has suffi-cient ability to adjust automatically the displacementwith respect to each working condition.

Experimental analysis and completemodel development

When designing a hydraulic pump in general and avane-type oil pump in particular, the volumetric effi-ciency is one of the most important factors in evaluat-ing the pump performance. Therefore, an accurateestimation of actual pump responses in comparisonwith the theoretical values is indispensable for carryingout pump performance analyses before manufacturing.

Experimental analysis

Experiments were made with the researched vane pumpto investigate the actual performance of the pump. Thelubrication oil used for these experiments was the SAE5W-20 series. To represent real lubrication conditions,the fixed-flow restriction valve presented in the thirdsection was employed. For the experiments, the pump

Figure 12. Theoretical pump performance in the fixed-loadcondition.

Figure 13. Theoretical analysis of the moments acting on themain ring at a speed of 4000 r/min.

Figure 11. Theoretical steady-state flow–pressurecharacteristic.

Truong et al. 1423



speed was varied from 0 r/min to 4000 r/min in steps of500 r/min while the valve area opened was set to 60%.The working temperature during these experiments wascontrolled to be constant at 120 �C by using a thermo-regulating system. The experimental results were thenobtained as shown in Figure 14. From this figure, it canbe seen that the actual pump flow rate is greatly differ-ent from the theoretical flow rate, as investigated in theprevious section. The reason for this is the loss of powerduring operation of the system.

Complete model development based on power lossanalysis

In fact, the pump performance is affected by many fac-tors; the main factors are as follows:

(a) leakage flows due to the pump design;(b) variation in the flow due to changes in the tem-

perature and pressure;(c) power loss due to friction;(d) power loss due to the incomplete filling effect.

Leakage flow due to the pump design. Internal leakage isgenerally caused by the pressure distribution within thepump and the clearances associated with the pumpingchambers. This leakage is proportional to the pressuredifference and is inversely proportional to the viscosityof the fluid in the regions where internal leakagedominates.

Because the volumes of the chambers under thevanes are extremely small in comparison with those ofthe chambers between the vanes, the leakage flows areinvestigated for only the chambers between the vanes.Figure 15 then displays this analysis with a generic

chamber between two consecutive vanes represented bythe angles ai and ai+ 1. There are eight leakage flowsas follows (the detailed definitions of the leakage flowsare presented in Appendix 1):

(a) Ql1, which is the leakage between the inner area ofthe rotor and the oil chamber due to a clearancezl1 and which is given by

Ql1 ai,ai+1ð Þ= bz3l1 P ai,ai+1ð Þ � Pmin½ �12hoil Rr � Rrið Þ ð35Þ

where hoil is the dynamic viscosity of oil;

(b) Ql2, which is the leakage between the inner area ofthe rotor (defined by the radius Rri\ Rr) and theoil chamber due to a clearance zl2 and which isgiven by

Ql2 ai,ai+1ð Þ

=ai � ai+1j jRri � tv � zl1ð Þz3l2 P ai,ai+1ð Þ � Pmin½ �

12hoil Rr � Rrið Þð36Þ

(c) Ql3, which is the leakage between the inner area ofthe rotor and the oil chamber due to a clearance zl3and which is given by

Ql3 ai,ai+1ð Þ= tvz3l3 P ai,ai+1ð Þ � Pmin½ �12hoil Rr � Rrið Þ ð37Þ

(d) Ql4, which is the leakage between the oil chamberand its previous chamber due to a clearancezl4 [ zl3 and which is given by

Figure 14. Actual performance of the researched vane pump.

Figure 15. Analysis of the leakage flow in a generic chamberbetween two consecutive vanes.




Ql4 ai,ai+1ð Þ=lv i+1ð Þz

3l4 P ai+1,ai+2ð Þ � P ai,ai+1ð Þ½ �

12hoiltv

ð38Þ

(e) Ql5, which is the leakage between the oil chamberand its next chamber due to a clearance zl5 [ zl3and which is given by

Ql5 ai,ai+1ð Þ= lviz3l5 P ai,ai+1ð Þ � P ai�1,aið Þ½ �

12hoiltvð39Þ

(f) Ql6, which is the leakage between the oil chamberand the area outside the ring (defined by the radiusRse . Rs) due to a clearance zl6 and which is givenby

Ql6 ai,ai+1ð Þ

=ai � ai+1j j ri + ri+1ð Þ=2½ �z3l6 P ai,ai+1ð Þ � Pmin½ �

12hoil Rse � Rsð Þð40Þ

(g) Ql7, which is the leakage between the oil chamberand its previous chamber due to a clearancebetween the front side of the vane (the vane tip)and the inner contour of the ring;

(h) Ql8, which is the leakage between the oil chamberand its next chamber due to a clearance betweenthe vane tip and the inner contour of the ring.

During the operation, the edges of the vane tip contactthe inner contour of the ring in most cases owing to thepressurized oil in the chambers under the vanes and thecentrifugal forces. Since the leakages Ql7 and Ql8 areneglected, hence the total leakage flow of an oil cham-ber between two consecutive vanes is obtained as

DQleak ai,ai+1ð Þ=DQleak in ai,ai+1ð Þ� DQleak out ai,ai+1ð Þ

=2Ql4 ai,ai+1ð Þ �X6i=1

Qli ai,ai+1ð Þ

ð41Þ

Variation in the flow due to the changes in the temperatureand pressure. It is clear that the flow rate of oil through apassage increases with increasing oil temperature anddecreasing oil pressure due to the reduction in the oil visc-osity.16 To evaluate the effects of the temperature and thepressure on the pump flow rate, an equivalent laminarflow rate Qeq of oil through a long cylindrical pipe, ofradius Req and length Leq, is used. The equivalent flowrate can be computed using Poiseuille’s equation

Qeq tð Þ= p

8

R4eq

hoil tð ÞPmax tð Þ � Pmin

Leqð42Þ

with

hoil tð Þ= noil tð Þroil tð Þ ð43Þ

where noil tð Þ is the kinematic viscosity of oil, and the oildensity is derived from its defined value at time t= 0 as

roil tð Þ= roilt

=roil0

1+ loil T1 � T0ð Þ½ � 1� Pmax1 � Pmax0ð Þ=boil½ �ð44Þ

where loil is the volumetric temperature expansion coef-ficient, T0–Pmax0 is the initial temperature minus the ini-tial maximum pressure and T1–Pmax1 is the final workingtemperature minus the final maximum pressure.

An approximation is necessary when obtaining theequivalent flow rate for the pump flow rate. Hence, toeliminate the error in evaluating the flow variation dueto the changes in the temperature and the pressure, onlythe derivative of the flow rate caused by these factors isused according to

DQTP tð Þ[Qeq tð Þ �Qeq t� 1ð Þ

=p

8

R4eq

Leq

DP tð Þhoil tð Þ

� DP t� 1ð Þhoil t� 1ð Þ

� � ð45Þ

to evaluate the flow rate loss.

Power loss due to friction. In the ideal pump, the drivingtorque tth without energy loss is derived from

tth =Dth

2pPmax � Pminð Þ ð46Þ

where Dth is the theoretical displacement of the pump,which is given by

Dth =Qth

nð47Þ

Because of the friction problem, the actual drivingtorque of the pump is larger than the ideal torque by anamount called the frictional torque Dt according to

tact= tth +Dt ð48Þ

or

Dt = tact �Qth

nPmax � Pminð Þ ð49Þ

In the researched vane pump, the friction factors areknown to be the following:

(a) friction between the vane tips and the inner con-tour of the ring;

(b) friction between the pump shaft and the oil seals;(c) friction between the pump shaft and the bearings;(d) friction between the ring, rotor and vanes and the

pump cover.

Among the friction factors mentioned above, onlythe friction between the vane tips and the inner contour

Truong et al. 1425



of the ring is varied corresponding to the variations inthe the working pressure and the pump speed while theother friction factors can be considered to be constantvalues during pump operation (Figure 16). The fric-tional force Ffrv between a generic vane (defined by theangle ai =ari � p) and the inner contour of the ring iscomputed as

Ffrv aið Þ= x Fv cen aið Þ+Foil cen aið Þ½f+Fuv oil aið Þ� cos Dar=s aið Þ

� g ð50Þ

In this equation, x is the kinetic frictional coefficientbetween the vane and the ring in the lubrication condi-tion. In this study, the values of this coefficient weredetermined from the work by Inaguma17 and by thecubic spline interpolation method. Fv cen aið Þ andFoil cen aið Þare the centrifugal force of the ith vane andthe centrifugal force of the oil chamber under this vanerespectively. These factors are derived using equations(24) and (27) and equations (24) and (26) respectively.Fuv oil aið Þis caused by the pressurized oil in the chamberunder the considered vane and is given by

Fuv oil aið Þ=P aið Þbtv ð51Þ

where Dar=s aið Þis the angle difference between the direc-tion of the forces Fv cen aið Þ, Foil cen aið Þ and Fuv oil aið Þand the direction perpendicular to the tangent of thering at its contact point with the vane tip and is givenby

Dar=s aið Þ=ar aið Þ � as aið Þ ð52Þ

From equation (50), the frictional torque between ageneric vane and the inner contour of the ring can becalculated as

tfrv aið Þ=Ffrv aið Þ cos Dar=s aið Þ�

ri ð53Þ

Hence, the total frictional torque between the vanesand inner contour of the ring is given by

tfrv=XNi=1

tfrv aið Þ ð54Þ

In other words, the pump flow rate lost owing to thisfriction factor can be evaluated as

DQfrv tð Þ= n2ptfrv

Pmax � Pminð55Þ

Finally, the frictional torque added to the drivingtorque of the pump is derived as

Dt = tfrv+ tfr0 ð56Þ

where tfr0 is the constant frictional torque, which is thesum of frictional torques due to friction between thepump shaft and the oil seals and bearings and due tothe friction between the ring, rotor and vanes and thepump cover. This factor is determined from the actualperformance of the pump.

The total pump flow rate lost owing to all the fric-tion factors is computed as

DQfric tð Þ=DQfrv tð Þ+DQfr0 ð57Þ

where DQfr0 is the lost flow corresponding to the con-stant frictional torque tfr0.

Power loss due to the incomplete filling effect. The final fac-tor that reduces the actual pump flow rate can be con-sidered as the incomplete filling effect of the pumpingchambers with oil. It is normally a function of excessiveflow restriction in the flow path to the pump at a spe-cific shaft speed of the pump. The major causes of theincomplete filling of the working chambers which occurwhen it is communicating with the suction port are asfollows.

1. The pressure existing at the pump intake port istoo low.

2. The resistance of fluid flow through the suctionducts of the pump at the operating speed is toohigh.

3. There is an undesired presence of an excessiveamount of air entering the suction fluid, known ascavitation and aeration problems.

It is probable that this incomplete filling effectincreases at higher rotational speeds of the pump. Inthe ideal working condition, the pumping chambershave sufficient time to fill their volumes before connect-ing to the delivering port, subsequently generating thepressurized oil as described in the section on the forcedue to the pressurized oil inside the main ring. On thecontrary, in the defective filling condition at high work-ing speeds, a large amount of fluid is proportionallypassed through the feed ducts and the distribution ofthe intake valves of the system. Subsequently, the flow

Figure 16. Analysis of the frictional force between a genericvane and the inner contour of the ring.




resistance (the suction head losses) increases corre-spondingly. For a constant fluid pressure at the pumpintake, a certain critical speed exists where the amountof fluid required to fill the working chambers cannotenter the pump at the intake. Therefore, by furtherincreasing the speed above this critical value, no pro-portional increase in pump delivery will occur, or thepump flow rate may even decrease. This problem ispronounced when the pump works in the high-speedregion.

In addition, when the working chambers connect tothe delivering port, amounts of oil from this port enterthe chamber vacancies. This undesirable amount of oilentering the chamber is called the backflow of oil. Itcauses the pressure within each chamber not to increaseuntil the chamber becomes filled after an additionalrotation of the rotor. The additional rotation angle isrepresented by Daadd. The pressure distribution ana-lysed in the section on the force due to the pressurizedoil inside the main ring and in Figure 5 was thenadjusted as presented in Figure 17. As a result, the totalmoment acting on the ring caused by the pressurizedoil inside the ring to make it rotate around the pivotpin in equation (15) becomes

XMOp oil inside

=

ðaC2t

0

Rrot sin (cst+as) PminbRs das

+

ðaC3t +Daadd

aC2t

Rrot sin (cst +as)

Pmax � Pminð Þ as � aC2t

aC3t � aC2t+Pmin

� �bRs das

+

ð2p

aC3t�Daadd

Rrot sin (cst+as) PmaxbRs da

ð58Þ

The pressure redistribution presented in equation (58)makes it easier for the ring to rotate around the pivotin the direction which reduces the eccentricity betweenthe rotor and the ring. In other words, the pump dis-placement is also reduced in this situation. However, asthe pump moves to lower eccentricities with increasingspeed, the pump’s compression ratio also decreases.Consequently, the cavitation and aeration levels areproperly controlled to lower values. Therefore, thispump type operates with a higher efficiency than doesthe fixed-displacement pump type.

It should be pointed out that the incomplete fillingeffect causes a reduction DQfill in the pump flow ratewhich may be proportional to the rotational speed. Thehigher the working speed, the larger is the value of theadditional angle Daadd and the larger is the amount offlow lost. In this study, only how much the pump flowrate is affected by the incomplete filling problem is con-sidered. Hence, to determine this pump flow reduction,the tendency of the additional angle Daadd is determinedby using a comparison between the theoretical flow rateand the actual flow rate and the iterative method.

From all the above analyses, an estimation of theactual pump flow rate can be established from

Qest =Qth +DQleak +DQTP � DQfric � DQfill ð59Þ

Estimation of the actual pump flow rate using thedeveloped complete pump model

In order to estimate the actual pump flow rate, simula-tions with the complete pump model including powerloss analysis were performed with the same testing con-ditions as for the experiments (see the section on experi-mental analysis). The parameters set for the completemodel are displayed in Table 2.

The process to estimate the actual pump flow rateusing the complete pump model can be described asfollows.

Step 1. Run the complete pump model at the lowestspeed. At this operating point, the incomplete fillingproblem does not happen. Then proceed as follows.

Figure 17. Pressure redistribution due to the incomplete fillingeffect.

Table 2. Parameter settings for the complete pump model.

Component Factor Units Value

Pump designclearances

zl1 mm 0.3zl2 mm 0.14zl3[zl4[zl5 mm 0.17zl6 mm 0.1

Lubrication oil,SAE 5W-20

boil N/m2 1.5 3 109

roil at 15 �C kg/m3 852loil 1/�C 6.4 3 10–4

noil at –30 �C,40 �C, 100 �C,120 �C

mm2/s 4200, 47,8.9, 5.91

Vanes and ring x at 1000 r/mina — 0.1064

aFrom the paper by Inaguma.17

Truong et al. 1427



1. Compute the theoretical pump flow rate Qth, theleakage flow DQleak, the variation DQTP in the flowrate and the flow loss DQfrv.

2. By employing equation (59), in which the compo-nent DQfill is zero, to estimate the final output flowrate in the comparison with the actual flow rate atthis speed, derive the flow loss DQfr0 due to theconstant friction factors.

Step 2. Run the complete pump model at higherspeeds. At these operating points, the incomplete fillingproblem has already happened. Then proceed asfollows.

1. Process in the same way as in Step 1 with the flowloss DQfr0 that was determined.

2. By employing equation (59), find the differencebetween the actual flow rate and the estimated flowrate, which is the flow loss caused by the incom-plete filling problem.

3. By using the iterative method, determine the addi-tional angle generated by the incomplete fillingwhich caused the flow loss obtained above and,consequently, derive a set of these angles.

Step 3. Verify the complete model as follows.

1. Consider that the change in the additional angle in theincomplete filling is proportional to the working speed.Then, by using the linear interpolation, derive a set ofadditional angles with respect to the pump speed.

2. Carry out simulations with the complete pumpmodel at other different speeds within the range [0;4000] r/min.

3. Perform an analysis between the actual flow ratesand the estimated flow rates at the same workingconditions.

By employing the process mentioned above, thefitted curve of the additional angles caused by theincomplete filling effect was found as shown in Figure18 by comparison with the set of these angles approxi-mated using linear interpolation. It can be seen that thisangle mostly varied proportionally to the pump speed.As the result, the estimated and actual pump perfor-mances were obtained and compared as plotted inFigure 19 while the power loss was analysed in Figure20. As seen in Figure 20, the power losses were large,especially at high working speeds of the pump. Most ofthe lost energy was due to the friction and leakageproblems. The results demonstrate that the completemodel not only could show the theoretical pump flowrate but also could analyse well most of the power lossfactors and thus, consequently, provide an accurateestimation of the actual pump flow rate.

However, the results in Figure 18 also show that theslope of the additional-angle trajectory actually tendedto be smaller at higher pump speeds. This was due tothe reduction in the pump eccentricity which,

consequently, reduces the pump compression ratio aswell as the cavitation and aeration levels. In addition,other small power loss factors such as the leakagescaused by clearance variations due to temperature and/or surface finish condition changes were not consideredin this study. As a result, the predicted pump perfor-mance did not fit the actual performance well in someworking conditions (Figures 19 and 20). Hence, a bet-ter representation of the additional-angle trajectory aswell as further investigations on other loss factors couldresult in a higher accuracy in estimating the actualpump performance.

Conclusions

The advanced technology for a lubrication system usingthe variable-displacement vane-type oil pump is

Figure 19. Comparison of the actual and the estimated pumpperformances.

Figure 18. Comparison of the fitted and the approximatedcurves of the additional angles in the incomplete filling.




introduced in this paper. By employing the displace-ment control mechanism based on the working pressureand the balance spring, the lubricating oil can be easilyand continuously adjusted with respect to the desiredperformance to obtain the highest lubricatingefficiency.

A variable-displacement vane-type oil pump madeby MyungHwa Co. Ltd was investigated in this study.First, the theoretical model of this pump was fullydeveloped and analysed on the basis of its design anddynamic analyses. The modelling results show that thepump could adapt well to any engine lubricationrequirement. Second, the complete model was derivedon the basis of the theoretical model, the actual tests onthe real pump and the power loss analysis. Finally,numerical simulations were carried out in comparisonwith the experiments to investigate and verify the work-ing performance of the complete pump model. Thecomparison results prove that the complete pumpmodel could estimate the power loss factors well. As aresult, the actual pump performance could be predictedwith high accuracy by using this model. This variable-displacement vane-type oil pump and the developedmodel may become an advanced solution for industrialmachines with lubrication purposes in the near future.

The results also indicate that there still remained dif-ferences between the actual pump performance and theestimated performance. As the next research stage, adeeper investigation into the power loss factors as wellas the common failures of this lubrication system, suchas leakages through clearance variations due to tem-perature and/or surface finish changes, detailed cavita-tion and aeration sources and their impacts on thepump performance, should be carried out in order toimprove the modelling accuracy of the developedmodel.

Declaration of conflicting interest

The authors declare that there is no conflict of interest.

Funding

This work was supported by the Ministry ofEducation, Science Technology and National ResearchFoundation of Korea through the Human ResourceTraining Project for Regional Innovation.

References

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Figure 20. Power loss analysis for the researched pump usingthe complete model.

Truong et al. 1429



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Appendix 1Notation

Aor area of the orificeb depth of the ringCor orifice flow coefficientdor diameter of the orificeDth theoretical displacement of the pumpec eccentricity of the pumpFcen(mi) centrifugal force of a mass mi

Ffrv frictional force between a generic vaneand the inner contour of the ring

Fspr force of the spring at presentFspr0 preloading force of the spring at the

initial conditionhv length of the vaneIring moment of inertia of the ringkspr stiffness of the springlv lift of a vanemi, R(mi) an object of mass mi travelling with

radius R(mi) around the rotor centreMOp cen

moment acting on the ring caused bythe centrifugal forces of N vanes and2N oil chambers

MOp oil insidemoment acting on the ring caused bythe pressurized oil inside the ring

MOp oil outsidemoment acting on the ring caused bythe pressurized oil outside the ring

MOsprmoment acting on the ring caused bythe spring force

n rotational speed of the pumpN number of vanesPmax pressure at the delivering portPmin pressure at the suction portPout pressure in the outside chamberQest estimated value of the actual pump

flow rateQinflow flow rate entering the outside ring of

the chamberQl leakage flows due to clearancesQoutflow flow rate going out of the outside ring

of the chamberQth theoretical pump flow rate

Rr radius of the rotorRrv radius of the curve of the slot-end pointRs radius of the inner contour of the ringRv radius at the tip curve of the vanetv thickness of the vaneT working temperatureVbv volume of a chamber between two

consecutive vanesVout volume of the outside chamberVuv volume of a chamber under the vane

a angular position of the rotorboil bulk modulus of the lubrication oilDQfill total pump flow rate lost owing to the

incomplete filling effectDQfric total pump flow rate lost owing to

friction factorsDQleak total leakage flow of an oil chamber

between two consecutive vanesDQTP variation in the flow due to the changes

in the temperature and pressureDaadd additional rotation angle of the rotor

due to the incomplete filling effectzl1 clearance between a vane and the

corresponding vane slot on rotorzl2 clearance between the top surface of

the rotor and the pump cover (housing)zl3 [ zl4 [ zl5 clearance between the top side of the

vane and the pump coverzl6 clearance between the front side of the

vane (the vane tip) and the innercontour of the ring

hoil dynamic viscosity of the lubrication oilloil volumetric temperature expansion

coefficientnoil kinematic viscosity of the lubrication

oilroil density of the lubrication oilrsteel mass density of the vane material (steel)tfrv total frictional torque between the

vanes and the inner contour of the ringtfr0 sum of the constant frictional torquestth driving torque of the pumpu angular position of the ringx kinetic frictional coefficient between

the vane and the ring in the lubricationcondition

v angular velocity of the rotor




doi: 10.1177/0954407013491896 pump for engine lubrication

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