Lube-Tech
The above equation has been previously reported by Olver and Spikes [10].
The parameter X can be regarded as a useful measure of the amount of mixed/boundary lubrication in a contact, since when there is no fluid film separating the surfaces, λ = 0, and X = 1. On the other hand, for large values of λ, greater than 3, the rough surfaces are assumed to be completely separated, and in that case X = 0. In order to better predict mixed and boundary friction, it would be extremely useful to know how X varies with λ.
There have been many models that have attempted to predict mixed/boundary friction. Most of these models assume that asperities deform elastically, which is not as drastic an assumption as it looks, particularly after “running-in” has occurred, although such an assumption is likely to lead to incorrect results if such models are applied to brand new surfaces. A recent, thorough, review of mixed/boundary friction models is available for the interested reader [11]. The main analytical models worth mentioning are those due to Archard [12], Greenwood and Williamson [13], Greenwood and Tripp [14], Bush [15] and Persson [16]. In recent years, most modelling efforts have been focussed on numerical analysis of real rough surfaces (see for example reference [17]).
These models generally predict the load carried by the asperities as a function of the separation of the centre line average of the rough surfaces, d (m). If the load carried is WA(d), then the parameter X described above can be calculated by dividing WA(d) by WA(0). For example, the Greenwood and Williamson model [13] describes a rough surface, which can have different probability distribution functions, contacting a perfectly flat surface. In the case where there is an exponential probability distribution function, it is found that:
[5]
PUBLISHED BY LUBE: THE EUROPEAN LUBRICANTS INDUSTRY MAGAZINE
No.152 page 4
If the value of X for λ=1 is considered, then the Greenwood and Williamson model [13], with an exponential probability distribution function predicts a value for X of about 0.368 when λ=1. The Bush model [15] predicts a value for X of 0.317 for λ=1. The Greenwood and Tripp model [14], however, which considers two rough surfaces contacting each other, with each surface having a Gaussian probability distribution of roughness, only predicts a value of 0.131 when λ=1. It is clearly of interest to know which of these different models is the right one to use when predicting mixed/boundary friction. Recent, useful, data has become available [18] in which the variation of X with λ has been reported from experimental measurements. Although there is some spread in the reported data, experiments indicate that for λ=1, X lies in the range 0.3 to 0.5, which suggests that the Greenwood and Tripp model [14] substantially underestimates the amount of mixed/boundary lubrication in contacts, and such a finding was also reported by Morris et al [19].
A mathematical fit to the experimental X versus λ data was reported [20], and it was found that a good fit to the data was provided by:
[6] Where k ≈ 3/2 and a ≈ 4/3. [7]
A similar equation (see below) had previously been reported by Olver and Spikes [10]:
Encouragingly, both equations (6) and (7) have the same asymptotic behaviour at high values of λ, such that X 1/λ2
. For equation (6), the value of X when
λ=1 is 0.397, whereas the value of X calculated using equation (7), when λ=1 is 0.25.
34
LUBE MAGAZINE NO.181 JUNE 2024
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68
