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`Mathematical Problems in EngineeringVolume 2018, Article ID 7910753, 13 pageshttps://doi.org/10.1155/2018/7910753`
Research Article

## Theoretical 3D Model for Quasistatic Critical Derailment Coefficient of Railway Vehicles and a Simplified Formula

1MOE Key Laboratory of High-Speed Railway Engineering, Southwest Jiaotong University, Chengdu 610031, China
2School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China

Correspondence should be addressed to Daolin Ma; nc.ude.utjws@niloadam

Received 2 October 2017; Accepted 21 December 2017; Published 17 January 2018

Academic Editor: Stefan Balint

Copyright © 2018 Ping Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The formula for the critical derailment coefficient concerning wheelset yaw angles and wheel-rail creep forces is deduced based on the three-dimensional (3D) force equilibrium relationship in the critical wheel derailment state under quasistatic assumption. The change of critical derailment coefficient and wheel-rail contact patch normal force/creep force as wheelset yaw angles change under the influence of the friction coefficient, maximum flange angle, and net wheel weight is analyzed according to the Kalker linear creep theory and Shen-Hedrick-Elkins creep theory. Analysis shows that the wheel-rail friction coefficient and maximum wheel flange contact angle can significantly influence the critical wheel derailment coefficient, further proving the conservative results when the critical Nadal derailment coefficient is adopted in analyzing wheel derailment under small wheelset yaw angles. To realize easy calculation and application of critical 3D derailment coefficients, the ratio of lateral creep force to longitudinal creep force of wheel-rail contact patches under critical quasistatic wheel derailment conditions is deduced. A simplified calculation method of critical derailment coefficients is presented based on this. The calculation accuracy is verified, proving that it can satisfy engineering application.