Approximate solution for a rolling contact problem over a relatively general viscoelastic half-space

Vita.An approximate method is developed to predict the coefficient of friction and normal load for the problem of a rigid circular cylinder moving across a relatively general viscoelastic half-space with constant velocity. The method relied on the assumption that by fitting a simple viscoelastic material model to general viscoelastic material data within the range of the elastic dominant frequencies, the friction coefficient determined from exact analytical expressions for the simple viscoelastic material model will be approximately equal to that obtained by solving the problem directly. The problem is formulated by means of moving point load elastic solutions and the correspondence principle of viscoelasticity. The relation between general distributions of normal surface traction and displacement is obtained, and then some exact results for the friction coefficient and normal load are given for a material whose modulus obeys a standard linear solid and power law material mode, respectively. Different ranges of dominant frequencies are determined from Fourier series, a Fourier integral, and an integral expression for friction coefficient. Of all the three methods, the friction coefficient method is shown to be the most convenient to apply. In addition, it is used to verify that only a very limited range of frequencies is needed in order to determine the coefficient of friction. Numerical results are seen to be satisfactory within the usual engineering requirements of accuracy when the viscoelastic material behavior obeys a generalized power law model if the exponent does not exceed 0.3