Wheel-Rail Dynamic Model and Stochastic Analysis of the Friction in the Contact Patch

Abstract

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.

Prediction of Random Self Friction-Induced Vibrations in Uncertain Dry Friction Systems Using a Multi-Element Generalized Polynomial Chaos Approach

“…In the analysis of uncertain friction systems, the polynomial chaos formalism has also been recently proposed [23,24]. In the Hyun et al study [24], a three-dimensional nonlinear model dry friction at the wheel-rail is proposed and analyzed by the polynomial chaos formalism.…”

“…In the Hyun et al study [24], a three-dimensional nonlinear model dry friction at the wheel-rail is proposed and analyzed by the polynomial chaos formalism. The authors have shown that the PDF of the friction coefficient is affected by the stochastic variation of dynamic parameters as the lateral displacement of the wheel and the rail roughness.…”

“…In more recent studies, the friction coefficient is considered as a random parameter and is modeled by a probability density function (PDF) [23,24]. In this case, the uncertainty propagation can be performed by using the well-known Monte Carlo (MC) method; however, it is very prohibitive since it requires a great number of samples to ensure good convergence and accuracy [25].…”

Wiener–Askey and Wiener–Haar Expansions for the Analysis and Prediction of Limit Cycle Oscillations in Uncertain Nonlinear Dynamic Friction Systems

“…The method used has been shown to be inefficient due to the pessimism phenomenon which induces the divergence of the envelopes of limit cycle amplitudes [27]. The polynomial chaos formalism has been proposed as a more efficient alternative to take account of the random uncertainty of the friction coefficient in the study of the dynamic behavior of friction systems, [28,29]. In the Lee et al study [28], the polynomial chaos formalism is used to analyze a three dimensional nonlinear dry friction model at the wheel-rail contact.…”

“…The polynomial chaos formalism has been proposed as a more efficient alternative to take account of the random uncertainty of the friction coefficient in the study of the dynamic behavior of friction systems, [28,29]. In the Lee et al study [28], the polynomial chaos formalism is used to analyze a three dimensional nonlinear dry friction model at the wheel-rail contact. The authors show that the probability density function (PDF) of the friction coefficient is affected by the stochastic variation of dynamic parameters as the lateral displacement of the wheel and the rail roughness.…”