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A Mixed EHL Analysis Method for Grease and Formulas for Film Thickness and Asperity Load

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Abstract

This paper introduces the grease average flow model considering non-Newtonian characteristics into the grease-mixed elastohydrodynamic lubrication (EHL) numerical analysis. On this basis, a method of grease EHL analysis is established with the roughness coupled indirectly. The effect of the rheological parameter on the variety law of the lubrication state is studied. The results show that the rheological parameter affects the lubrication state versus the dimensionless speed, material, and roughness. Finally, the film thickness and asperity load prediction formulas are derived based on the numerical simulation results, which are suitable for various greases obeying the Ostwald model.

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Data Availability

Source data available by request.

Code Availability

We used custom code developed by our lab.

Abbreviations

\(a\) :

Constant for pressure flow factor

\(b\) :

Constant for pressure flow factor

\(d\) :

Separation based on asperity, m

\(h\) :

Nominal film thickness, m

\(h_{0}\) :

Rigid body displacement, m

\(h_{d}\) :

Vickers hardness of softer material, Pa

\(h_{T}\) :

Local film thickness, m

\(\overline{h}_{T}\) :

Average gap, m

\(k\) :

Constant in prediction formulas

\(K\) :

Hardness coefficient

\(n\) :

Rheological index

\(p\) :

Total pressure, Pa

\(p_{a}\) :

Asperity pressure, Pa

\(p_{A,B}\) :

Hydrodynamic pressure at boundaries of the ‘unit’

\(p_{h}\) :

Hydrodynamic pressure, Pa

\(P_{H}\) :

Maximum Hertzian contact pressure, Pa

\(\overline{p}\) :

Average hydrodynamic pressure, Pa

\(q_{x}\) :

Unit flow along \(x\) direction, m2/s

\(\overline{q}_{x}\) :

Mean unit flow in the \(x\) direction, m2/s

\(r\) :

Asperity curvature radius

\(R\) :

Equivalence contact radius, m

\(u_{0}\) :

Rolling velocity, m/s

\(w\) :

Total load per unit length, N/m

\(y_{s}\) :

Distance from the mean of surface to that of asperity, m/s

\(z_{s}\) :

Asperity height, m

\(\beta\) :

Roughness parameter

\(\varepsilon_{p,w}\) :

Convergence threshold

\(\dot{\gamma }\) :

Shear rate, s−1

\(\delta\) :

Combined roughness, m

\(\eta_{s}\) :

Fluid viscosity, Pa*s

\(\rho\) :

Fluid density, kg/m3

\(\rho_{0}\) :

Ambient density, kg/m3

\(\sigma\) :

Standard deviation of surface height, m

\(\sigma_{s}\) :

Standard deviation of asperity height, m

\(\tau\) :

Shear stress, N

\(\tau_{s}\) :

Yield shear stress, N

\(\phi\) :

Plastic viscosity, Pa·sn

\(\phi_{0}\) :

Ambient plastic viscosity, Pa·sn

\(\phi_{x}\) :

Pressure flow factor in the \(x\) direction

\(\phi_{{\text{g}}}\) :

Grease pressure flow factor

\(\upsilon\) :

Poisson ratio

\(\omega_{c}\) :

Critical interference, m

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Funding

This work was supported by the National Natural Science Foundation of China (Grant Number 52075146) and the Funds for Creative Research Groups of Hebei Province (Grant Number E2020202142).

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Authors and Affiliations

  1. College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, Hunan, China

    Miaojie Wu & Xu Han

  2. State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin, 300401, China

    Xu Han, Yourui Tao & Jiaxing Pei

Authors
  1. Miaojie Wu
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  2. Xu Han
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  3. Yourui Tao
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  4. Jiaxing Pei
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Contributions

MW, XH, YT, and JP contributed to conceptualization, MW provided methodology, MW and JP provided software, MW performed formal analysis, MW assisted in data curation, MW, XH, YT, and JP contributed to writing of the original draft, MW, YT, and JP contributed to writing, reviewing, & editing of the manuscript, XH and YT supervised the study, and YT and XH contributed to funding acquisition.

Corresponding authors

Correspondence to Xu Han or Yourui Tao.

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Appendix

Appendix

See Tables 4, 5 and 6.

Table 4 Simulation and curve fitting results of minimum film thickness
Full size table
Table 5 Simulation and curve fitting results of central film thickness
Full size table
Table 6 Simulation and curve fitting results of asperity load ratio
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Wu, M., Han, X., Tao, Y. et al. A Mixed EHL Analysis Method for Grease and Formulas for Film Thickness and Asperity Load. Tribol Lett 70, 128 (2022). https://doi.org/10.1007/s11249-022-01666-4

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