Leaf Coppin

113

Investigation into the Traction

Coefficient in Elastohydrodynamic

Lubrication

Y.S. Wang Harbin Institute of Technology, Harbin, China and Henan University of Science and Technology, Luoyang, China B.Y. Yang Henan University of Science and Technology, Luoyang, China L.Q. Wang Harbin Institute of Technology, Harbin, China

Abstract

The elastohydrodynamic traction coefficients of two Chinese aviation lubricating oils

were investigated for various loads, rolling velocities, and lubricant inlet temperatures

iising a self-made test rig. Traction coefficient versus slide-to-roll ratio curves were gen-

erated. The concept of critical load varying with the lubricant temperature is proposed.

This paper presents a new empirical formula for the dynamic pevforniance design of

high-speed rolling bearings, that relates traction coefficient with normal load, rolling ve-

locity, and lubricant inlet temperature. The coefficients of the formula may be computed

by regression analysis of the experimental data. Two example calculations are presented.

The predicted results from the formula agree well with experimental obserziations.

Keywords

rolling bearings, elastohydrodynamic lubrication, traction coefficient, empirical

formula, rolling velocity, lubricant temperature

INTRODUCTION

When a lubricated rolling bearing is operating at high speed an elastohydro-

dynamic (EHD) film is developed and excessive slip between rolling elements

shears this oil film to generate a traction force. The traction force between the

lubricant and the rolling element interfaces can cause balls and rollers to accel-

erate, decelerate, skid, or skew. Thus cage instabilities and the life of a rolling

bearing are associated with the traction behaviour of the lubricant. Since the

1960s, many researchers14 have presented various rheological models to calcu-

late the traction force. Unfortunately, the limitations of rheological models and

Tribotest journal 11-2, December 2004. (11) 113 lSSN 1354-4063 $35.00 (2630/1204)

Wang, Yung, and Wang 114

the lack of data for rheological parameters along with the complexity of numer-

ical iteration techniques have restricted the practical application of those models

for traction prediction in engineering. Therefore, the authors’ current aim is to

model the traction behaviour with an empirical formula which can be con-

veniently and quickly used to compute the traction coefficient in simulating the

dynamic performance of rolling bearings. Based on a large number of traction

tests on two Chinese aviation lubricants, a new empirical formula for the trac-

tion coefficient is proposed. The method of calculating the traction coefficient

used in this paper can be adapted to other lubricants working under the same operating conditions. This will not only be of significance in the dynamic behav-

iour design of rolling bearings, but will also help lay the foundations of further

research on traction theory.

PREVIOUS METHOD TO CALCULATE TRACTION COEFFICIENT

The method that has been used in many studies5-’ to calculate the traction co-

efficient needs four basic equations that can be summarised as:

1 dT Gdt 7 = -- + F(T, T*, q)

where 7 is the shear rate, T is the shear stress, G and q are the shear modulus

and the viscosity of the lubricant, T* is the reference stress or the limiting shear

stress, p, c, and k are thermal characteristics of the lubricants, u, T, p, and p are

the sliding velocity, absolute temperature, pressure, and lubricant density, x, y,

and z are the coordinates along and perpendicular to the rolling velocity and

across the lubricant film, respectively, and -a is the abscissa of the inlet of the

Hertzian zone.

Eq. (l), which was presented by Johnson and Tevaarwerk2 and by Bair and

Wir~er,~ has been the more widely accepted rheological model that describes the

lubricant behaviour as a non-linear viscous flow superimposed on a linear

elastic strain. Eq. (2) is an energy equation including the convection and heat

Tribotest journal 11-2, December 2004. (12) 114 ISSN 1354-4063 $35.00

lnuestigation into the traction coeflicient in elastohydrodynamic lubrication 115

Figure 1 Construction of the test rig"

Disc soecimen Motor I

Ball specimen

Motor II

dissipation. Eq. (3) is the momentum equation. Boundary conditions on temper-

ature are calculated by Eq. (4)? Given the thickness of the lubricant film and

rolling velocities, the above equations are solved simultaneously to obtain tem-

peratures, velocities, and shear stress distributions over the contact. The traction

force can be obtained by integrating the shear stress distribution. The traction