Uncertainty analysis on the wear coefficient of Archard model

This paper proposes a probabilistic model for the wear of surfaces in contact. An initial value problem (IVP) is formulated from the particularization of Archard model for a contact in line. Based on this problem, two mathematical formulations for this model are presented. In the former, the wear coefficient is modeled as a random variable, while in the latter this coefficient is assumed as a stochastic process. The Karhunen–Loeve series is employed to represent the wear coefficient stochastic process. The solution of the IVP is the worn height stochastic process (WHSP). From this result, the functions of expectation and covariance are obtained. The results of mathematical formulations are compared with the simulations made by Monte Carlo and Latin Hypercube methods. The stochastic process presented better results, regarding the expectation and covariance functions. In relation to the propagation of uncertainty of wear coefficient through Archard model it was observed that in both presented problems, the variance of WHSP increased as the sliding time increased.