Frictional work

In summary, the temperature rises AT,- and the heat partition coefficient f(x, y, t) can be determined through solving Eqs (18) and (19) simultaneously with (22) or (23), if the heat flux qix, y, t) has been given in advance. In the simplest way, an estimation of heat generation can be made by calculating frictional work in terms of experiential friction coefficients. 

The frictional work loss W/ depends on the geometry of the system and the flow conditions and is an empirical function that will be explained later. When it is known, Eq. (6.13) may be used to find a net work effect Wv for otherwise specified conditions. 

It is clear that the collision between two elastic but frictional spheres is inelastic due to the inevitable sliding at contact which yields the kinetic energy loss by frictional work. Furthermore, the preceding analyses of both Hertzian collision and frictional collision can also be applied to the particle-wall collision, where the radius of the wall is simply set to be infinitely large. 

Hence, the rate of energy input owing to the frictional work done by the stresses on the volume element (sum Eqs. (6.26) to (6.29)), is given by... 

By using Equation (99), they found that frictional work obtained was 46% less than that obtained by the calculation method used by DeBlaey and Potderman (122). Jarvinen and Juslin (124) concluded that friction only occurs at the true areas of interparticulate contact between the compact and the die-wall. Thus, only the movement of these particles and not the movement of the upper punch should be used in the calculation of the work of friction. Therefore, the assumption that the frictional force does not completely coincide with the movement of the upper punch appears plausible. In addition, only the particles in the upper layer of the compact adjacent to the punch are capable of moving the same distance as the upper punch. The particles in the middle of the tablet in double side compression or adjacent to the lower punch in single sided compaction remain stationary. 

But the frictional work will reappear as heat, so the total heating per unit mass is now the sum of the externally imposed heating and the frictional heating ... 

The amount of frictional work per unit mass in typical fluid flow problems is generally less than in the examples cited above. I... 

On a logarithmic scale the frictional work increases with the work of adhesion and the experimental data seem to be in a reasonably good correlation with the theoretically calculated values. (An exception perhaps may be the combination of PP sliding against PS). It appears that for the flat-to-flat conformal contact of the polymer combinations studied, the adhesion component at the interface may be the dominant factor governing the initial frictional behaviour of polymer-polymer sliding pairs. 

Figure 20. Correlation between frictional work and work of adhesion.

Polyimide friction. The friction of polymers consists of an adhesion component and a deformation component. The adhesion component arises from the shearing of adhered junctions and is usually modeled as the product of the real area of contact and the shear strength of the polymer. The deformation component arises from the frictional work required to balance the energy dissipated in plastic deformation. Some Investigators have developed friction models in which the adhesive bonds at the junctions Increase the amount of plastic deformation over that which would exist in the absence of these bonds (13). 

Figure 6. Wear rate of unfilled HR plotted against frictional work (A) unsteady state (O-IOPO rev) (B) steady state (data taken from Reference A)(5),...

Figure 7 Steady-state rate of wear plotted against frictional work (A) unfilled NBR (B) filled NBP (H) unfilled PB and (E) filled PB (data, taken from Reference 4)(6).

V j sum of abraded volume of a tongue after N revolutions U frictional work c proportionality constant h width of tongue (testing rubber wheel) i number of revolutions (passes)... 

The wear of fine monofilaments when they slide over one another has important practical consequences in the deformation behaviour and the durability of fibrous assemblies. The frictional forces at the internal micro-contacts provide the local restraints which generate the cohesive response of the assembly. The flexibility of ropes and the tactile properties of fabrics are in many respects governed by these local forces. The frictional work produces surface damage and wear hence the macroscopic response of an assembly is modified by deformation. Ultimately the damage is sufficient to undermine the strength of the fibres and the assembly strength is weakened. 

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