Exact Solution for the Time‐Dependent Temperature Field in Dry Grinding: Application to Segmental Wheels

Abstract

We present a closed analytical solution for the time evolution of the temperature field in dry grinding for any time-dependent friction profile between the grinding wheel and the workpiece. We base our solution in the framework of the Samara-Valencia model Skuratov et al., 2007, solving the integral equation posed for the case of dry grinding. We apply our solution to segmental wheels that produce an intermittent friction over the workpiece surface. For the same grinding parameters, we plot the temperature fields of up- and downgrinding, showing that they are quite different from each other.

Analytical Formulation for Temperature Evolution in Flat Wheel-Rail Sliding Surfaces

“…The change rate of temperature difference at the beginning of sliding is high and is gradually decreased to zero at steady state. This figure also shows the time evolution of heat partitioning factor using (15). It increases sharply at the beginning of sliding from 0.5 at time zero to more than 0.9 after 0.5 s. It means that, at the beginning of sliding, the frictional heat enters equally into the wheel and rail.…”

“…Ling and Ng [14] used Green's function method to express the temperature rise in the slider and rider. Gonzalez-Santander et al [15] presented an analytical solution for the temperature evolution of the grinding wheel and the workpiece in dry grinding. Gonzalez-Santander and Martin [16] investigated the heat transfer in surface grinding.…”

Integral Involving Bessel Functions Arising in Propagation Phenomena

“…The authors' own interest in the subject arose out of contact [4][5][6][7] with problems in the theory of heat conduction [8] and quantum field theory [9]. Without aspirations to completeness (the subject is too vast to summarise) let us briefly mention one such occurrence of Bessel functions.…”

New Integrals Arising in the Samara-Valencia Heat Transfer Model in Grinding

“…In [5], this boundary-value problem is transformed into an integral equation that is useful for the numerical evaluation of the heat transfer in intermittent wet grinding [6]. However, in the case of dry grinding, this integral equation can be reduced to a two-dimensional integral ( (0) theorem) [7]. New mathematical identities have been proved in this framework.…”