Wear equation

The wear, W, of friction materials can best be described by the wear equation (32,33) W = KP° P where K is the wear coefficient, P the normal load, D the sliding speed, t the sliding time, and a,b, and c ate a set of parameters for a given friction matenal—rotor pair at a given temperature. 

Figure 3.2 Theoretical transition probability v = 0 - v = 1, according to Thiele and Weare (equation 33), as a function of total energy E and mass factor m [equation (14)]. is a quantity depending upon the potential range. Curves labeled 1st, 2nd, and 3rd are the first-, second-, and third-order distorted-wave (DW) results. Curves labeled S and J are Secrest and Johnson s exact values [32], Curves labeled E1 and Et in (c) and (d) are additional approximations useful in the one-quantum-exchange case.

In this chapter, we use K as the symbol for a lumped constant in the wear equation Eqn 13-27. 

The importance of fatigue wear was first recognized by Soviet scientists.(23) Some of extended fatigue wear equations were proposed by Kraghelsky and Nepomnyashchi,(2 ) and recently by 3ain and Bahadur.(23,26) For our discussion, we use the simple relation based on Wohler s a-N curve (27)... 

This is the wear equation of rubber abrasion in unsteady state. Assuming that the steady state has been reached when the number of revolution is equal to N, on the basis of Equations(14,a) and (14,b), the sum of volume loss of a tongue after another N revolutions, i.e., from N to 2N revolutions, can be calculated by... 

However, in this equation, the spacing of ridges is S instead of S as it is considered to be unchanged only if the frictional force is kept constant. Obviously, in this case, S = Sjj. Inserting Equations (18), (23), (4), and (21) into the equation above, the wear equation of rubber abrasion in steady state is given by... 

As seen from the wear Equations (25) and (27), in either cases, the wear rate is mainly dependent on the frictional force. This conclusion is in accordance with the results of a number of experimental studies (j -O (Figures 6 and 7) moreover. Southern and Thomas pointed out that the exponent oC is equal to 2 at least for the steady-state rate of wear ) As for the unsteady-state rate of wear, it increases as abrasion proceeds. This result is consistent with the experimental observation (Figure 8) (5 ). 

Inserting Equations (23), (28), (5), and (21) into Equation (24) the modification of the steady-state wear equation will be obtained... 

The wear equation of rubber abrasion in steady state reveals the basic correlation among the material property, running condition and wear characteristic. The wear rate increases with an increase in the frictional force, however, it is inversely proportional to the tensile strength. 

The abrasive wear equation predicts that wear rate should be inversely proportional to hardness. This is not the case for the wear of polymers where the correlation is much worse than for metals. The reason for this lies in the difficulty of measuring the hardness of a polymer and separating it from time-dependent effects and the contribution of elastic and plastic effects. A much better correlation is found according to the Ratner-Lancaster correlation, which relates the inverse of the area under the stress-strain curve of a polymer (to the point of tensile failure) to abrasive wear rate (Hutchings, 1992). 

Not only friction forces but also working life is essential when designing a bearing. The calculation below follows the basic energetic wear equation" as proposed by Fleischer [8]. It is based on the wear-specific friction work" vty. This characteristic is an expression of the friction work input into the friction material with reference to the worn volume. For the material combination examined here the wear volume is calculated only from the wom-off volume of the bearing material. The wear-specific friction work is calculated as follows ... 

This wear mode is shown in Figure 13.13. Of course, fiber wear occurs with concurrent matrix wear. In general, the fiber reinforcement will be the limiting factor on the wear rate. For this situation the following wear equation has been... 

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