Friction and Lubrication in Mechanical Design Episode 2 Part 2 docx

Rolling/ Sliding Contacts 255

which suggests that the elasticity of the rollers causes the minimum film

thickness to increase by approximately 100 times.

Dowson and coworkers [4, 61 approached the problem from first prin￾ciples and simultaneously solved the elasticity and the Reynolds equations.

Their formula for the minimum film thickness is given in a dimensionless

form as:

where

tlo U U = speed parameters = -

Ee Re

-

G = material parameter = aEe

W = load parameter = -

PY

EeR

Using the same dimensionless groups suggested by Dowson and Higginson

[4], the Grubin solution can be given as:

H = 1.95 7 ( Gu)0.73 (7.6)

What is particularly significant in the EHD theory is the very low depen￾dency of the minimum film thickness on load. The important parameters

influencing the generation of the fdm are the rolling speed, the effective

radius of curvature and the oil viscosity. Consequently, Dowson and

Higginson suggested the following simplified formula for practical use:

where

ho = minimum film thickness (in.)

qo = inlet oil viscosity (poise)

Re = effective radius (in.)

U = rolling speed (in./sec)

256 Chapter 7

7.4 FRICTION IN THE ELASTOHYDRODYNAMIC REGIME

The EHD lubrication theory developed over the last 50 years has been

remarkably successful in explaining the many features of the behavior of

heavily loaded lubricated contacts. However, the prediction of the coeffi￾cient of friction is still one of the most difficult problems in this field. Much

experimental work has been done [7-211, and many empirical formulas have

also been proposed based on the conducted experimental results.

Plint investigated the traction in EHD contacts by using three two-roller

machines and a hydrocarbon-based lubricant [14]. He found that roller sur￾face temperature has a considerable effect on the coefficient of friction in the

high-slip region (thermal regime). As the roller temperature increases the

coefficient of friction falls linearly until a knee is reached. With further

increase in temperature the coefficient of friction rises abruptly and errati￾cally and scuffing of the roller surface occurs. He also gave the following

equation to correlate all the experimental results, which was obtained from

28 distinct series of tests:

21 300 f = 0.0335 log (0, - + 40) - 44sb3 (7.8)

where 0,. is the temperature on the central plane of the contact zone ("C) and

h is the radius of the contact zone (inches).

Dyson [15] considered a Newtonian liquid and derived the expression

for maximum coefficient of friction as:

where

a = pressureviscosity coefficient

K = heat conductivity

P = pressure

qo = dynamic viscosity

ho = minimum oil film thickness

y = temperature-viscosity coefficient

(7.9)

If aP >> I, the coefficient of friction increases rapidly with pressure.