Investigation of the Validity of the Carslaw and Jaeger Thermal Theory under Different Working Conditions

Abstract

The temperature rise caused by frictional heat generation is of great importance in many tribological problems. However, due to a lack of a reliable and general experimental methods to measure the flash temperature on the contact surface, numerical simulations are widely used to evaluate the flash temperature under different operating conditions. The theoretical solutions developed by Carslaw and Jaegerare among the most commonly used solutions in tribology to calculate surface temperatures. Carslaw and Jaeger utilized mathematical methods to develop an analytical temperature solution under the assumption that the calculation domain is insulated and semi-infinite in size; however, real working conditions may not satisfy these assumptions. Therefore, in this study, a transient three-dimensional numerical thermal model using second-order finite difference methods to solve the transient heat conduction equation was utilized to evaluate the effect of domain size, heat source position, and material properties on the accuracy of the temperature prediction of the Carslaw and Jaeger solution for low Peclet numbers. Results indicate that for very short sliding times, the Carslaw and Jaeger solution is close to the numerical result; the domain size and heat source position have little influence. However, as time increases, the deviation between the Carslaw and Jaeger solution and the numerical results becomes increasingly larger, indicating that the mathematical solution may no longer be utilized without introducing significant errors. The length of time during which the Carslaw and Jaeger solution performs adequately is a function of the domain size, heat source position, and material properties.