Analytical Formula for the Ratio of Central to Minimum Film Thickness in a Circular EHL Contact

Petr Sperka,Ivan Krupka,Martin Hartl

doi:10.3390/lubricants6030080

Petr Sperka, Ivan Krupka + Show 1 more

Open Access

https://doi.org/10.3390/lubricants6030080

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Abstract

Prediction of minimum film thickness is often used in practice for calculation of film parameter to design machine operation in full film regime. It was reported several times that majority of prediction formulas cannot match experimental data in terms of minimum film thickness. These standard prediction formulas give almost constant ratio between central and minimum film thickness while numerical calculations show ratio which spans from 1 to more than 3 depending on M and L parameters. In this paper, an analytical formula of this ratio is presented for lubricants with various pressure–viscosity coefficients. The analytical formula is compared with optical interferometry measurements and differences are discussed. It allows better prediction, compared to standard formulas, of minimum film thickness for wide range of M and L parameters.

Highlights

Prediction of film thickness represents an important step necessary for up-to-date design of lubricated concentrated contact
New analytical formula allowing rapid prediction of minimum film thickness in circular point contact is suggested based on numerical simulations
The new formula is compared to ratio that come from Hamrock–Dowson equations and optical interferometry measurements

Summary

Introduction

Prediction of film thickness represents an important step necessary for up-to-date design of lubricated concentrated contact. A common approach is to make full numerical simulations of a contact for some range of conditions and solve regression analysis of film thickness results on operating conditions These regressions were proven to be surprisingly accurate (considering the time of original formulation), if conditions of contact inlet are isothermal Newtonian. This is especially true for central film thickness, but generally not the case of minimum film thickness [10,11,12,13,14]. New analytical formula allowing rapid prediction of minimum film thickness in circular point contact is suggested based on numerical simulations. The new formula is compared to ratio that come from Hamrock–Dowson equations and optical interferometry measurements

Numerical Calculations

Film Thickness Measurement

Results and Discussion

Dependency of hcof

Dependency hcmin

Conclusions