Hysteretic friction coefficient

The expression for the hysteretic friction coefficient also simplifies greatly in this limit, as we shall see in Sect. 3.8. 

An expression for the hysteretic friction coefficient in the small viscoelasticity approximation is derived in the next section. 

IV. Hysteretic Friction. The hysteretic friction coefficient due to a moving inden-tor in lubricated contact with the half-plane is given by (3.8.1) and in the frictional case, by (3.8.9) or alternatively by (3.8.10) or (3.8.11). On an incompressible half-plane, it reduces to (3.8.12) which has the same form as for lubricated contact, apart from a factor (1 + / ). These expressions cannot be evaluated until the implicit equations governing the problem are solved, since the pressure is required. 

We now give expressions for the coefficient of hysteretic friction, introduced in Sect. 2.11, for the problem of a moving, cylindrical punch discussed in the previous two sections. Let us consider the frictionless case first. We will confine the discussion to steady-state problems. Equation (2.11.12), adapted to plane strain conditions, gives that the coefficient of hysteretic friction has the general form... 

Equation (3.8.15) is a convenient general expression for the coefficient of hysteretic friction of a cylindrical indentor on a lubricated, slightly viscoelastic half-plane. 

We consider the moving load problem in this section to the extent of deriving an expression for the coefficient of hysteretic friction in the small viscoelasticity and small velocity approximations, respectively. 

Let us now consider the coefficient of hysteretic friction, given by (5.4.1). This becomes... 

Sect. 5.4 contains approximate formulae for the coefficient of hysteretic friction. The approximations apply in the cases of small viscoelasticity (5.4.4,13) and small velocity (5.4.22, 23, 26). 

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