Page 41 - Tribology in Machine Design

28 Tribology in machine design

represented as

or approximated by

where r.m.s. indicates the root mean square, c.l.a. denotes the centre-line
average, B m is the surface-to-peak mean proportionality factor, and B d is
the surface-to-peak standard deviation factor. To determine the statistical
parameters, B m and B d, cumulative frequency distributions of both
asperities and peaks are required or, alternatively, the values of X p, a s and
0-p. This information is readily available from the standard surface
topography measurements.
Referring to Fig. 2.11, if the distance between the mean lines of asperital
peaks is h, then

and the clearance may be expressed as

where hi and h 2 are random variables and h is the thickness of the lubricant
film. If it is assumed that the probability density function is equal to
<t>(hi+h 2), then the probability that a particular pair of asperities
has a sum height, between h i+h 2 and (hi +h 2) + d(h l +H 2), will be
<t>(hi + h 2)d(hi +h 2). Thus, the probability of interference between any two
asperities is

Thus (— A/i) is a new random variable that has a Gaussian distribution with
a probability density function