Error bounds of variable conductivity temperature estimates in frictionally heated contacts

We analyze the effect of using a linear conductivity-temperature model to solve the nonlinear heat equation for two rubbing solids. We divide errors into two groups, sampling errors and linearization errors. We relate the first to the choice of a reference conductivity in the linear model. Whereas, we relate the second to the modeling of the conductivity values when the k-theta curve of the material includes an inflation point (classC materials). The results suggest that the temperature estimates are sensitive to the choice of the reference conductivity, when the variation in the conductivity of the material with temperature is considerable( e.g., for Sapphire). We show that the errors for class c materials are proportional to the ratio of the inflation, to the melting temperatures of the sliding solid. (C) 1998 Elsevier Science Ltd.