| A boundary element formulation is developed to conduct the analysis of sliding contact. Due to the frictional heat input, the behavior within contact zone may involve high thermal gradients that develop during a short time period. On the other hand, the overall component-scale deformations evolve more slowly. Hence, it is unavoidable to face numerical simulations that require a large number of time steps. Although boundary element methods (BEM) are attractive for analyzing these surface-dominated processes, operation counts of order O(N2) arise from a conventional time domain BEM for the discrete time convolution over N time steps. Therefore, the conventional approach becomes time consuming as a larger value of N is needed. Here a new algorithm is developed to evaluate the time convolution integrals that are associated with BEM for time dependent problems. This approach is based upon the multi-level multi-integration concepts that Brandt and Lubrecht proposed. Several two-dimensional transient heat diffusion problems are examined and the numerical results show that the multi-level convolution algorithm successfully reduces the computational complexity to order O(NlnN) for moderate N (e.g., 100 < N < 1000) and to order O(N3/2) for large N (e.g., N > 1000). Memory requirements are also significantly reduced, while maintaining the same level of accuracy as the conventional time convolution approach.; Afterward, we utilize the new BEM with multi-level convolution algorithm to investigate the transient thermoelastic example of the axisymmetric ring-on-ring sliding system. The investigation of numerical analysis is focused on contact stress, temperature distribution and thermal deformation of components with different surface profiles. Consideration is given to both smooth and rough surface idealizations for the ring-on-ring sliding contact problem. The numerical results show that localization phenomena depend on sliding speed and surface profile has a significant effect on the thermomechanical behavior within sliding contact. |
