the effects of crankshaft offset on the engine friction

Int. J. of Vehicle Design, Vol. 31, No. 2, 2003 187

The effects of crankshaft offset on the engine friction

M.-R. Cho*, J.-S. Kimy, D.-Y. Ohz andD.-C. Hanx

*Senior Research Engineer, Gasoline Engine Test Team, PowerTrain R&D Centre, Hyundai Motor Co., 772–1, Changduk-dong,Whasung-city, Kyonggi-do, 445–850, Korea.E-mail: [email protected] Research Engineer, Gasoline Engine Test Team, PowerTrain R&D Centre, Hyundai Motor Co., 772–1, Changduk-dong,Whasung-city, Kyonggi-do, 445–850, Korea.E-mail: [email protected] Research Engineer, Gasoline Engine Test Team, PowerTrain R&D Centre, Hyundai Motor Co., 772–1, Changduk-dong,Whasung-city, Kyonggi-do, 445–850, Korea.E-mail: [email protected] School of Aerospace and Mechanical Engineering, SeoulNational University, San 56–1, Shilim-dong, Kwanak-gu, Seoul,151–742, Korea.E-mail: [email protected]

Abstract: This paper reports on the effects of crankshaft offset on theengine friction. The effects of crank offset are investigated through thetheoretical analysis. In this study, the mathematical models are presentedfor evaluating the friction level of each engine parts. From the predictedresults, the crank offset influences on the side force acted on the piston pinand sliding speed of piston. With application of crank offset, the frictionloss of piston skirt is significantly reduced. The optimal crank offset tominimize the friction losses is variable according to the operatingconditions, and the offset effect is reduced as engine speed and loadincrease As can be seen in the presented results, crank offset is very effectiveto reduce the engine friction.

Keywords: crankshaft, engine, friction, offset, piston skirt, side force.

Reference to this paper should be made as follows: Cho, M.-R., Kim, J.-S.,Oh, D.-Y. and Han, D.-C. (2003) ‘The effects of crankshaft offset on theengine friction’, Int. J. Vehicle Design, Vol. 31, No. 2, pp. 187–201.

Nomenclature

A Bearing surface areaAc Real contact areaa Distance from the top of skirt to the pinB Bearing width

Copyright # 2003 Inderscience Enterprises Ltd.

187

b Distance from the top of skirt to the C.G.bp Ring widthC Clearance between skirt and cylinderCg Distance between C.G. and wrist-pinCo Crank offsetCp Distance between wrist-pin and piston centreCR Radial clearance of engine bearingE Young’s Moduluseb Eccentric length of piston bottomet Eccentric length of piston top_eeb Radial velocity of piston bottom_eet Radial velocity of piston topF Total normal force in skirtFbx;y Connecting-rod bearing forceFc Asperity contact normal forceFcon Connecting-rod forceFf Total friction forceFfc Asperity contact friction forceFfh Hydrodynamic friction forceFgas Combustion gas forceFh Hydrodynamic normal force in skirtFoil Hydrodynamic force of ringFpinx Inertia force due to pin mass in x-directionFpiny Inertia force due to pin mass in y-directionFpisx Inertia force due to piston mass in x-directionFpisy Inertia force due to piston mass in y-directionFpr Total ring forceFr;f Reaction force of bearingH Dimensionless oil film thickness, h=sh Nominal film thicknesshm Minimum oil film thicknessIpis Piston moment of inertiaL Piston skirt lengthl Connecting-rod lengthM Total moment about wrist-pinMc Asperity contact momentMf Total friction momentMfc Friction moment due to asperity contactMfh Friction moment due to hydrodynamicMh Hydrodynamic momentMr Rotating mass of crankshaftMpis Inertia moment of piston skirtmj Equivalent mass of crank journal and pinmpin Wrist-pin massmpis Piston skirt massp Hydrodynamic pressurepb Back pressure in ring groovePc Asperity contact pressure

188 M.-R. Cho et al.

pTE Ring tensionR Nominal radius of piston skirtrc Crank radiust TimeU Sliding speedW External force in bearing, W ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

F2bx þ F2

by

q

€YY Piston skirt accelerationa Piston skirt bearing angleb Connecting-rod anglebr Asperity radius of curvaturee Eccentricity in bearingeb Eccentricity of piston bottomet Eccentricity of piston top_eeb Radial velocity of piston bottom_eet Radial velocity of piston topfx;fy Pressure flow factorfs Shear flow factorff ;ffp;ffs Shear stress factorf Attitude angle of bearingj; ~yy Bearing angular coordinateZ Oil viscositym Asperity densitymf Friction coefficienty Crank angles Composite rms roughness, s ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

s21 þ s22

q

t Hydrodynamic component of shear stresso Rotational speed

1 Introduction

The fuel economy is the most important aspects of modern engine design anddevelopment. Therefore new technologies such as EMV (electromechanicalvalvetrain), GDI (gasoline direct injection) and CVVT(continuous variable valvetiming) are developed, and applied to the new engines. In addition to such efforts,much study is actively in progress to reduce the mechanical friction losses in engineaccounted for 15% of total energy input from the fuel. A 10% reduction ofmechanical friction losses would result in a 2.5% decrease in fuel consumption.The most of engine friction losses occur at the engine moving part composedof valvetrain, piston and crankshaft. The efforts to reduce the engine frictionhave resulted in the reduction of size and the usage of low viscosity engine oil.Specially, it is trend to apply small size bearing, low-tension ring and low-stiffnessvalve spring.

In generally, piston assembly contributes 40–45% of total engine friction losses,and of which 40% is attributed to the piston-skirt. In recent years, the crank offsettechnique is presented for reducing the friction loss of piston skirt. However thereare only a few paper investigating the effects of crank offset on the reduction of

The effects of crankshaft offset 189

engine friction. From the results of Shinichi, et al. [1], about 3% improvement of fuelconsumption was confirmed in the low speed part load condition, and there exists anoptimal crank position to minimize fuel consumption. They supposed that theimprovement of fuel economy is caused by improvement of thermal efficiency.Nakayama, et al. [2] confirmed effect of crank offset through a floating linermethod. They concluded that the improvement of engine friction is caused byreduction of piston side force, and sliding velocity during the expansion stroke.However they concluded crank offset cannot simply be applied to a productionengine.

In this study, an analytical model was presented to determine the effects of crankoffset on the friction of engine bearing, ring-pack and piston skirt. From these, thevarious results were derived to evaluate the effects of crank offset on the reduction ofengine friction.

2 Analytical model

2.1 Equations of motion

Figure 1 shows a schematic diagram of engine with crankshaft offset. Crankshaftaxis from the cylinder bore centre moves to the thrust side of piston. The amount ofoffsetting is adjusted within the range that the rotation of crankshaft is not disturbed

Figure 1 Schematic diagram of piston – crankshaft assembly with crank offset.


by cylinder bore. With application of crank offset, connecting-rod length and crankradius are also changed to maintain the cylinder volume.

The sliding velocity and acceleration of piston with crank offset are defined asfollows:

_YY ¼ rco sin yþ rcoM cos yðl2 �M2Þ�1=2 ð1Þ

€YY ¼ rco2 cos yþ ðrcoM cos yÞ2ðl2 �M2Þ�3=2

þ rco cos yð Þ2�ro2M sin yn o

ðl2 �M2Þ�0:5 ð2Þ

where,

M ¼ rc sin yþ Cp � Co ð3Þ

The variation of acceleration according to offset influences on inertia force of piston,and external force acted on piston and crank pin. Thus, the changes of speed andload will affect dynamics and tribologycal characteristics of engine moving parts.Then analytical models to derive the equations of motion in each moving parts areshown in Figure 2.

Piston skirt shows the first and secondary motion within the cylinder bore. Thefirst motion is translation to the radial direction, and the secondary is rotatingmotion about axis of cylinder centre. From the Figure 2(a), the governing equationof piston secondary motion can be expressed as follows [3, 4]:

mpin 1� a

L

� �

þmpis 1� b

L

� �

mpina

Lþmpis

b

L

Ipis

Lþmpisða� bÞ 1� b

L

� �

mpisða� bÞ bL� Ipis

L

2

6

6

6

4

3

7

7

7

5

€eet

€eeb

( )

¼F � ðFf þ Fgas þ Fpisy þ FpinyÞ tanf

M þMf þ FgasCp � FpisyCg

" #

ð4Þ

In Equation 4, the reaction forces, F , Ff , M, Mf , can be obtained by oil film andasperity contact pressure. The detailed definition is expressed following section.

As can be seen in Figure 2(b), the journal motion within the engine bearing isdescribed by the following the non-linear equilibrium equations [5], along the line ofcentres and its perpendicular direction

mjCR €ee� e _ff2h i

¼ Fr þW cosf ð5Þ

mjCR e€ffþ 2e _ffh i

¼ Ff �W sinf ð6Þ

In Equation 5 and 6, Fr, Ff are the resultant fluid film force which are determinedfrom integrating the oil film pressure. The applied force, W, contains connecting-rodand main bearing load. The applied load to connecting-rod bearing can be obtainedfrom the external force through the connecting-rod, and inertia force of rotating


Figure 2 Dynamic modelling of engine moving parts.


mass. However, it is very difficult to calculate the accurate main bearing loadbecause crankshaft system supported by main bearing is statically indeterminatesystem. In this study, the statically determinate method [6] is used to simplify theanalysis.

In a ring-pack, the reaction forces by oil film and asperity contact are inequilibrium to the ring tension and inter-ring pressure. Therefore the forceequilibrium in the piston ring is expressed as follows [7].

Fpr hm;dh

dt

� �

¼ Foil þ FC � 2pRbpð pTE þ pbÞ ¼ 0 ð7Þ

In the above equations of motion, the reaction force related to oil film and asperitycontact can be obtained using the lubrication and friction analysis, which presentedin the following section.

2.2 Lubrication analysis

The average Reynolds equation [8,9] is used as the governing equation forlubrication analysis, which expressed as following form:

d

dx

fxh3

Zdp

dx

� �

þ d

dy

fyh3

Zdp

dy

!

¼ 6 Uj j dht

dyþ 6s

dfs

dy

� �

þ 12dht

dtð8Þ

We make some assumptions to apply above equation to each lubricating parts. Inthe first, it is assumed that engine bearing is operating under fully hydrodynamiclubrication regime. Therefore the flow factor terms related to surface roughness areeliminated. In the ring-pack, ring width is infinitely shorter than circumferentiallength. Therefore pressure gradient along the ring width is considered only. In thepiston skirt, 2-dimensional mixed lubrication is considered.

The classical Reynolds boundary condition is used to solve the Equation 8.Equation 8 is discretized in finite difference forms and pressure distribution in thefluid film is obtained by iterative technique.

From the Greenwood and Tripp’s asperity contact model [10], the averageasperity contact pressure is expressed as follows:

PcðHÞ ¼8ffiffiffi

2p

15p mbrsð Þ2E

ffiffiffiffiffi

sbr

r

F2:5ðHÞ ð9Þ

FnðHÞ ¼1ffiffiffiffiffiffi

2pp

ð?

H

ðs�HÞne�s e=2ds ð10Þ

In Equations 4–7, the reaction forces can be calculated by using the oil film pressureand contact pressure, and they are defined as following form 3–6.


Piston skirt:

F ¼ Fh þ Fc; M ¼Mh þMc ð11Þ

Fh ¼ R

ð ð

A

p cosð~yy� aÞd~yydy ð12Þ

Mh ¼ R

ð ð

A

pða� yÞ cosð~yy� aÞd~yydy ð13Þ

Fc ¼ R

ð ð

A

Pc cosð~yy� aÞd~yydy ð14Þ

Mc ¼ R

ð ð

A

Pcða� yÞ cosð~yy� aÞd~yydy ð15Þ

Engine bearing:

Fr ¼ð ð

A

p cosj dj dz ð16Þ

Ff ¼ð ð

A

p sinj dj dz ð17Þ

Piston ring:

Foil ¼ 2pRð

bp

0

pdx ð18Þ

Fc ¼ 2pRð

bp

0

Pc dx ð19Þ

The total friction force in each lubricating areas consists of hydrodynamic andboundary frictrion. The shear stress, friction force and its moment acting on roughsurface can be defiend as follows [3]:

th ¼ �mU

h½ff þ ffs� þ ffp

h

2

qPh

qyð20Þ

Ff ¼ð ð

th dAþ mf

ð ð

Pc dAc ð21Þ

Mf ¼ð ð

th ~aadAþ mf

ð ð

Pc ~aadAc ð22Þ

The hydrodynamic friction is considered only in engine bearing.


2.3 Numerical procedure

The numerical procedure for obtaining the variation of minimum oil film thicknessor friction force is as follows:

1 The initial values of journal centre, ring and piston skirt are assumed.

2 The oil film thickness is calculated, and then each fluid factor is determined.

3 The pressure distribution is calculated by using the direct integration or ADI(alternating direction implicit) iteration procedure for solving Equation 8, andcontact pressure is determined by using the Equation 9.

4 The integration to determine the fluid film and asperity contact forces (Equations11–22) is performed using the Simpson’s rule.

5 The new positions of journal centre, ring and skirt are determined by using thefourth-order Runge-Kutta (Equations 4–6) and Newton-Raphson (Equation 7)method. The above procedure is repeated, until the convergence for equilibriumposition is achieved during the whole engine cycle.

3 Results and discussion

Figure 3 shows the calculated side forces acted on the piston pin during the wholeengine cycle for various crank offsets. As crank offset increases, the piston side forceat the anti-thrust side increases during the compression stroke while it decreasesduring the expansion stroke at thrust side. Figure 4 shows the calculated results ofmean side forces for the various engine speeds. There is a crank offset to minimizemean side force, but it is variable according to engine speeds. As engine speedincreases, the amount of offset to minimize the mean side force is decreased, andcrank offset has good effect on the side force reduction at low engine speed.

Table 2 gives the maximum and mean bearing load for each bearing. As can beseen in Table 2, crank offset has little effect on acting force on the engine bearing in

Table 1 Specification of test engine.

Engine type L4/1.5L

Connecting-rod length (mm) 131Bore dia. (mm) 75.5Stroke (mm) 83.5

Main bearingdia (mm) 50width (mm) 18

Connecting-rod bearingdia. (mm) 45width (mm) 16

Bore pitch (mm) 82Total ring tension (kgf) 5.09Total ring width (mm) 5.2Piston Assy. mass (kg) 0.305Crankshaft mass (kg) 13.4Connecting-rod mass (kg) 0.450


spite of side force reduction. It is because that the external load on engine bearings ismainly influenced by gas pressure. The friction torque of engine bearing is functionof oil film thickness, which depends on the bearing force. Therefore the effect ofcrank offset on the friction torque of crankshaft system will also be very small, andthat can be confirmed in Figure 5.

Figure 3 Calculated results side force variation under the full load condition.


Figure 4 Effect of crank offset on the mean side force under the full load condition.

Table 2 Calculated results of maximum and mean bearing force under the full load at 2000 rpm.

Offset(mm)

Maximum and mean load (kN)

Connecting-rod Main 1 Main 2 Main 3

0 18.0/2.85 9.12/1.34 9.59/2.56 8.99/2.535 17.9/2.84 9.08/1.33 9.56/2.55 8.94/2.529 17.8/2.83 9.05/1.33 9.54/2.55 8.91/2.5212 17.8/2.83 9.04/1.33 9.53/2.55 8.90/2.5215 17.8/2.83 9.03/1.33 9.52/2.55 8.89/2.5220 17.7/2.84 9.03/1.33 9.52/2.56 8.88/2.5325 17.8/2.84 9.04/1.34 9.54/2.57 8.89/2.53

Figure 5 Effect of crank offset on the mean friction torque in engine bearings under the full load condition.


The application of offset influences on the sliding velocity of piston and sideforce. The variation of sliding speed of piston by crank offset is displayed in Figure6. The sliding speed is decreased by offset during the 0–908 crank angles, whichresulted in lower shearing rate in the oil film, but friction force increases the otherregion due to higher sliding speed. Therefore, the effect of offset on ring-packfriction is negligible which can be confirmed in Figure 7.

Figure 8 gives results for the offset effect on the skirt friction loss for the differentengine speeds and loads. As the engine speed becomes higher, the friction loss is

Figure 6 Effect of crank offset on the sliding speed of piston at 2000 rpm.

Figure 7 Effect of crank offset on the mean power loss of piston ring-pack under the full load condition.


increased because of higher shear rate of fluid film. The friction of piston skirt isusually determined by piston secondary motion influenced by side force. Therefore,the crank offset significantly decreases the friction loss of skirt by reduction of sideforce. Under the full load condition, the minimum power loss occurs near the 15mmoffset at low engine speeds, but the minimum position moves toward 5mm offset at

Figure 8 Effect of crank offset on the mean power loss of piston skirt.


higher engine speed. This tendency is similar to the result of mean side force inFigure 4. Under the part load condition, the minimum power loss occurs near the20mm offset at low engine speed. The reduction rate of skirt friction is summarizedin Table 3. The offset effect is considerably high at low speed and part loadcondition, but that is decreased as speed and load increase. From the above results, itis confirm that the friction of piston skirt is directly affected by side force, and crankoffset is effective to reduce the piston skirt friction under the low engine speed andpart load condition.

4 Conclusion

In this study, an analytical model for the engine moving system was described, andapplied to investigate the effect of crank offset on engine friction. From theanalytical results, the following conclusions are derived.

1 The crank offset is very effective to reduce the skirt friction. This is caused byreduction of side force. The effect of offset on the other parts is very small.

2 The crank offset is very effective under the part load and low engine speedcondition. As engine speed increases, the offset position for minimizing the skirtfriction is decreased independent of load condition.

3 The crank offset could not cover the overall operating conditions, and thereexists an optimal point where offset effect is extremely high.

References

1 Shinichi, S., Eiichi, K. and Tatehito, U. (1996) ‘Improvement of Thermal Efficiency byOffsetting the Crankshaft Centre to the Cylinder Bore Centre’, JSAE paper 9638770.

2 Nakayama, K., Tamaki, S., Miki, H. and Takiguchi, M. (2000) ‘The Effect of CrankshaftOffset on Piston Friction Force in a Gasoline Engine’, SAE paper 2000–02–0922.

3 Zhu, D., Cheng, H.S., Arai, T. and Hamai, K. (1992) ‘A Numerical Analysis for PistonSkirts in Mixed Lubrication-Part I: Basic Modeling’, ASME Trans. Journal of Tribology,Vol. 114, pp. 553–562.

Table 3 The reduction rate of skirt friction by crank offset.

Offset (mm)

Friction reduction rate (%)

Part Load Full Load

1500 2000 3000 4000 1500 2000 3000 4000

5 8.3 9.1 9.7 6.8 5.7 6.1 7.0 3.99 17.1 19.0 11.5 2.2 9.4 9.3 8.3 �11.412 31.6 21.9 11.7 �15.5 11.0 11.1 6.7 �27.215 34.9 24.4 11.5 �38.4 10.6 13.0 �6.2 �38.920 39.6 29.0 �27.1 �74.0 8.4 1.4 �45.5 �59.725 16.6 2.0 �68.5 �97.3 �19.1 �34.0 �62.2 �72.7


4 Han, D.C., Kim, J.Y., Cho, M.R. and Lee, J.S. (2000) ‘A Study on the Dynamic andMixed Lubrication Analysis of Piston Skirt’, International Tribology Conference 2000,Nagasaki.

5 Cho, M.R., Han, D.C. and Choi, J.K. (1999) ‘Oil Film Thickness in Engine Connecting-Rod Bearing with Consideration of Thermal Effects: Comparison between Theory andExperiment’, ASME Trans. Journal of Tribology, Vol. 121, pp. 901–907.

6 Cho, M.R., Shin, H.J. and Han, D.C. (2000) ‘A Study on the Circumferential GrooveEffects on the Minimum Oil Film Thickness in Engine Bearings’, KSME InternationalJournal, Vol. 14, No. 7, pp. 737–743.

7 Rohde, S.M. (1980) ‘A Mixed Friction Model For Dynamically Loaded Contacts withApplication to Piston Ring Lubrication’, Proc. the 7th Leeds-Lyon Symposium onTribology, Butterworths, pp. 262–278.

8 Patir, N. and Cheng, H.S. (1978) ‘An Average Flow Model for Determining Effectsof Three Dimensional Roughness on Partial Hydrodynamic Lubrication’, ASMETrans. Journal of Lubrication Technology, Vol. 100, No. 1, pp. 12–17.

9 Patir, N. and Cheng, H.S. (1979) ‘Application of Average Flow Model to LubricationBetween Rough Sliding Surface’, ASME Trans. Journal of Lubrication Technology,Vol. 121, No. 2, pp. 220–230.

10 Greenwood, J.A. and Tripp, J.H. (1971) ‘The Contact of Two Nominally Flat RoughSurface’, Proc. Instn. Mech. Engrs., Vol. 185, pp. 48/71.


the effects of crankshaft offset on the engine friction

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