Method of lines in nonlinear frictional heating during braking

The boundary-value heat conduction problem for two semi-infinite bodies compressed by constant pressure and sliding with a constant deceleration has been formulated. Due to friction at the contact surface the heat is generated. It is assumed that the materials of the bodies are thermal sensitive, i.e. their thermophysical properties are temperature dependent. This problem allows determining temperature fields in such elements of brakes, as a pad and a disk. At the first stage, the Kirchhoff transformation has been used for partial linearization of the nonlinear problem. Next, the Kirchhoff functions have been found by the method of lines. The transition has been made from the Kirchhoff functions to temperatures on the basis of formulas obtained for the friction couple aluminum alloy series (a disk) - the metal-ceramic (a pad). For the case of braking with a constant deceleration and at constant pressure the comparison of the results obtained with the proposed approach, and on the basis of an iterative procedure has been executed. The influence of duration of pressure increase on the temperature has been investigated. (C) 2015 Elsevier Ltd. All rights reserved.