Wear equation abrasion

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 ). 

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). 

Road wear is force controlled. This is a fundamental difference to slip-controlled laboratory abrasion test machines or wear tests with a trailer as described above. In force-controlled events the abrasion loss is inversely proportional to the stiffness of the tire whilst under slip control the abrasion is proportional to its stiffness (see Equations 26.18a and 26.19a). 

Equation (6.16) indicates that the maximum brittle wear occurs at ct = 90°, i.e., normal collision. The variation of the ratio of Eb to Bm (= B( m, b)) with a as a function of Kb is plotted on the basis of Eq. (6.16) as given in Fig. 6.7. The figure reflects that for a given Kb, the degree of abrasive damage due to brittle erosion may be estimated from the given particle flow pattern. 

As will be discussed in Chapter 5, scuffing is one of the abrasive wear modes that often happens in metals. This equation is known as Blok s critical contact... 

The probability of crack propagation can be calculated for the classic hexagonal cell and can be related to cell dimensions and the applied stress.9 A new constant is involved in the resultant equations it is related to cell size (since crack propagation is a combination of tensile stress and bending moment). For CMP pads, the equivalent areas of concern will be the cell density (related to the relative density) and the cell size distribution (visualized in Figure 6.33). It is the cell proximity or overlap probability that will determine the material s inherent propensity to support crack propagation. Also, since much of the shear stress concentration is at the top frictional surface, the damage done to the inherent cell structure by the CMP process is likely to determine much of the material s wear response. It is probable that the shape, size, and distribution of abrasives play an important role in the material s wear characteristics. 

A model for abrasive wear with variable rate ca be derived from the experimental observation that the effectivity factor for abrasive papers decreases with use as a negative exponential function [57]. Equation 13-54 would then assume the form... 

Elastomers. Ratner and Klitenik(21) obtained a wear rate equation for the abrasion of rubbers and their vulcanizates ... 

In its simplest form, an abrasive wear model can be defined by considering a hard conical asperity with a slope 6 under a normal load W ploughing through a polymer surface, removing material and producing a groove. The amount of material lost by abrasive wear w is (where symbols have the same meaning as the previous equation) ... 

As conditioning is primarily considered as a mechanical process characterized by a two-body abrasive wear mechanism [8], the classical Preston equation [62], originally used to model polishing of glass, has been widely used to describe material removal (polishing) rate in [61]. Considering the similarity between wafer—pad interaction and pad—conditioner interaction, the Preston s equation has been adopted by many to model pad wear caused by conditioning. The Preston equation states that MRR is proportional to the applied pressure P and the relative velocity V between the wafer and the pad and Kp is a constant, called Preston s coefficient. 

Before dwelling on the design of a siurry pump, it is essential to have a basic understanding of the hydraulics invoived. But since the design of slurry pumps must also take in account the wear due to pumping abrasive solids, many other factors enter into the equation, such as the ability to pump large particles and the use of special alloys or polymers for liners or impellers. 

Sometimes wear factor or specific wear rate is the metric in a PV study. Wear factor is essentially the constant in the Aichard equation that is cited for abrasion and adhesive wear in metals. This equation states that wear volume is proportional to the sliding distance and the normal force. 

Abrasive wear can be modeled by equation (17). In equation (17), is a constant associated with the wear properties of the wear surfaces while other parameters in equation (17) share the same meaning as those in equation (16). 

In equation (18), ki,k2 denote the wear velocity decided from adhesive and abrasive wear, respectively. Traditionally, the coupling effects between the two failure mechanisms are omitted in the development of failure mechanism model. Thus, a linear model shown in equation (18) is used as the traditional PoF model for components subjected to wear mechanisms. 

The wear experiment was interrupted periodically to measure the wear scar diameter. The wear scar was measvu ed using an optical microscope. The wear coefficient was determined according to equation 3, assuming that only one abrasive mechanism or one particular combination of mechanisms prevails dming the test [6]. 

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