## Friction in Mixed Lubrication Regime

This online calculator allows qualitative estimation of the friction coefficient in a mixed lubricated cylindrical (line) contact. The theory behind this tool is given below the calculator.

## Calculating Stribeck Curve

This calculator is based on the load-sharing concept that can be used to calculate friction in mixed lubrication regime approximately, but very fast and in a robust way. The concept, first introduced by Johnson [1], offers advantages of robustness, significantly reduced computational requirements and a relative simplicity. In these models the general problem is split up into two problems: lubrication problem assuming smooth surfaces and a “dry” rough contact problem, for details see [2]. In this case the flow equations are solved assuming that the surfaces in contact are smooth, while the “dry” contact problem assumes that there is no lubricant between the surfaces. These problems are linked via the load carried by the lubricant and by the “dry” contact [3], see figure below.

In the simplest form, the load-sharing concept can use a central film thickness fit to calculate the lubricant film thickness for the lubrication problem and Greenwood-Williamson model (GW) for the “dry” contact problem. This approach can give a good qualitative prediction of the friction evolution, however, it is likely to overestimate friction due to assumptions used in both GW model (assumption of the independent asperity deformation, which overestimates the load carried by asperities) and central film thickness calculations (assumption of a constant film thickness in the contact area, which is true only for “highly” loaded cases), see [3]. Current calculator uses this approach.

Please refer to the following page for the details on the calculation of roughness parameters needed for the input (density of asperities, mean radius of asperities, etc.). You can find the description below the calculator on that page.

## References:

[1] Johnson KL, Greenwood JA, Poon SY. A Simple Theory of Asperity Contact in Elasto-Hydrodynamic Lubrication. Wear. 1972;19:91-108.

[2] Zhu D, Hu Y-Z. A computer program package for the prediction of EHL and mixed lubrication characteristics, friction, subsurface stresses and flash temperatures based on measured 3-D surface roughness. Tribology Transactions. 2008;44:383-90.

[3] Akchurin, A., Bosman, R., Lugt, P.M. *et al.* On a Model for the Prediction of the Friction Coefficient in Mixed Lubrication Based on a Load-Sharing Concept with Measured Surface Roughness. *Tribol Lett* **59, **19 (2015). https://doi.org/10.1007/s11249-015-0536-z