Numerical prediction of the frictional losses in sliding bearings during start-stop operation


With the increased use of automotive engine start-stop systems, the numerical prediction and reduction of frictional losses in sliding bearings during starting and stopping procedures has become an important issue. In engineering practice, numerical simulations of sliding bearings in automotive engines are performed with statistical asperity contact models with empirical values for the necessary surface parameters. The aim of this study is to elucidate the applicability of these approaches for the prediction of friction in sliding bearings subjected to start-stop operation. For this purpose, the friction performance of sliding bearings was investigated in experiments on a test rig and in transient mixed elasto-hydrodynamic simulations in a multi-body simulation environment (mixed-EHL/MBS). In mixed-EHL/MBS, the extended Reynold’s equation with flow factors according to Patir and Cheng has been combined on the one hand with the statistical asperity contact model according to Greenwood and Tripp and on the other hand with the deterministic asperity contact model according to Herbst. The detailed comparison of simulation and experimental results clarifies that the application of statistical asperity contact models with empirical values of the necessary inputs leads to large deviations between experiment and simulation. The actual distribution and position of surface roughness, as used in deterministic contact modelling, is necessary for a reliable prediction of the frictional losses in sliding bearings during start-stop operation.


A :

Nominal contact area, m2

A a :

Real contact area, m2

A f :

Contact area of single asperity contact, m2

D :

Bearing diameter, m

F f :

Friction force, N

F R :

Radial force, N

H :

Bearing hardness, Pa

H s :

Nominal gap height

\(\overline h \) :

Average film thickness, m

h :

Nominal film thickness / surface separation, m

h oil :

Minimum nodal oil film thickness, m

K :

Elastic factor in Greenwood/Tripp model

M F :

Friction torque, N

\(\overline p \) :

Projected pressure, Pa

p a :

Asperity contact pressure, Pa

p :

Oil film pressure, Pa

P f :

Single asperity contact force, N

p Asperity :

Maximum nodal asperity contact pressure, Pa

p oil :

Maximum nodal oil film pressure, Pa

u :

Linear velocity, m/s

r :

Bearing radius, m


Mean roughness, m


Root mean square (RMS) roughness, m


Surface roughness, m

t :

Time, s

u :

Sliding velocity, m

W :

Bearing width, m

Y :

Yield stress, Pa

z s :

Summit height, m

β :

Mean summit radius, m

η :

Dynamic viscosity, Pa·s

φ :

Flow/shear/contact factor

ϕ :

Bearing angle, deg

σ s :

Summit height rms, m

σ s :

Mean summit height, m

θ :

Fill ratio

μ :

Boundary friction coefficient

ϕ s :

Density distribution of all summit heights, m

τ a :

Asperity shear stress, Pa

τ h :

Viscous shear stress, Pa

η s :

Asperity density, m2


Coefficient of friction


Elasto-hydrodynamic lubrication


Laser scanning microscopy


Multi-body simulation





x :

Sliding direction

y :

Cross direction


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This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)-GRK 1856.

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Corresponding author

Correspondence to Florian König.

Additional information

Florian KÖNIG. He received his B.S., M.S., and Ph.D. degrees in mechanical engineering from the RWTH Aachen University, Germany, focusing on mechanical engineering and tribology. Currently, he is head of department in the field of tribology at the Institute for Machine Elements and Systems Engineering, Germany. His research interests include the friction and wear behavior of plain bearings, tribolayers, surface texturing, condition monitoring, and machine learning methods.

Christopher Sous. He received his B.S., M.S., and Ph.D. degrees in mechanical engineering from the RWTH Aachen University, Germany, focusing on mechanical engineering and tribology. He currently is head of department in the field of bearing technology at the Institute for Machine Elements and Systems Engineering, Germany. His research areas cover the tribological behavior and failure mechanisms of rolling and plain bearings, condition monitoring as well as material characterization.

Georg Jacobs. He received his diploma and Ph.D. degree in mechanical engineering from RWTH Aachen University, Germany. Subsequently, he worked as a chief engineer at the Institute for Fluid Power Drives and Controls at RWTH Aachen University, Germany. After several years in industry, he joined the Institute for Machine Elements and Systems Engineering at RWTH Aachen University in 2008. His current position is a professor and the director of the institute. Since 2013 he has been director of the Chair for Wind Power Drives and speaker of the board of the Center for Wind Power Drives at RWTH Aachen University. Since 2016 he has been the director of the Chair and Institute for Engineering Design at RWTH Aachen University.

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König, F., Sous, C. & Jacobs, G. Numerical prediction of the frictional losses in sliding bearings during start-stop operation. Friction 9, 583–597 (2021).

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  • sliding bearing
  • friction
  • wearing-in
  • contact model
  • mixed elasto-hydrodynamic simulation