# EHL Film Thickness Calculator (Central and Minimum): Line (Cylindircal) Contact

10.03.2021

An EHL Film Thickness Calculator allows calculating central and minimum film thicknesses in a full film lubricated line (cylindrical) contact as a function of entrainment speed. The central and minimum film thicknesses are calculated using equations developed by Dowson et al [1,3] and Moes et al [2,4]. The equations used in the calculator are given below the calculator along with the definitions and references. The calculator allows choosing one of the two equations in the calculations.

## Central film thickness formulas

### Dowson et al formula [1]

Dowson and Toyoda developed a following equation for central film thickness calculations [1]:

(1)

where

(2)

Definition of the dimensionless variables are given below.

Moes developed another central film thickness equation [2]:

(3)

where

(4)

with

(5)

## Minimum film thickness formulas

### Dowson et al formulas

For the calculation of minimum film thickness in a cylindrical contact following Dowson [3], the following equations were used:

(6)

With

(7)

### Moes et al formulas

According to Moes, the equations for calculation of the minimum film thickness are as follows[4]:

(8)

where

(9)

with

(10)

## Definitions:

Poisson’s ratio dimensionless,
Young’s modulus of elasticity , [Pa],
Equivalent elastic constant  , [Pa],
Base oil viscosity (dynamic) , [Pa ],
Pressure-viscosity coefficient , [],

Mean entraining velocity , [] in the equations by Dowson et al. For Moes et al equations, the sum velocity is used: , []
Equivalent radii of curvature in X direction  , []
Material parameter [1], , dimensionless
Speed parameter [1], , dimensionless
Modified load parameter [3], , dimensionless
Viscosity parameter [3], ,  dimensionless

## References:

[1] Dowson, D.; Toyoda, S. A central film thickness formula for elastohydrodynamic line contacts. In Proceedings of the 5th Leeds-Lyon Symposium on Tribology, Leeds, UK, September 1978; pp. 60–65.

[2] H. Moes. Lubrication and beyond, University of Twente lecture notes, 2000.

[3] D. Dowson. Elastohydrodynamic and micro-elastohydrodynamic lubrication. WEAR, 190(2), December 1995.

[4] Moes, H. Optimum Similarity Analysis with applications to Elastohydrodynamic Lubrication. Wear 1992, 159, 57–66.