The coefficient of friction (CoF) is one of the most important parameters for characterizing the contact between the wheel and the rail. The assumption of a constant CoF is still used in most theoretical studies, although experimental work indicates that the CoF depends on material and dynamic parameters. In the real world, accurate estimation of the CoF is not simple due to various uncertainties. In this paper we present a new 3D nonlinear dry CoF model at the wheel-rail contact. In addition, a stochastic analysis using the polynomial chaos theory is performed with the CoF model. The maximum amplitude of rail roughness and the lateral displacement of the wheel are considered as uncertain parameters in this study. One of the novelties in this study is that our CoF model captures the maximum CoF value (an initial peak) when the wheel starts to move. The stochastic analysis results show that the CoF probability density function (PDF) of a combination of two uncertain parameters has wider PDF ranges than the PDF obtained for only one uncertain parameter. The current work demonstrates that the CoF is strongly affected by the stochastic variation of dynamic parameters. In reality, the CoF is critical to rail tractive performance and efficiency. Thus, the PDF distribution of the CoF must be accounted for in the design of the wheel-rail system.

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