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Shi Hemu, Zeng Xiaohui, Wu Han. Analytical solution of the hunting motion of a wheelset nonlinear dynamical system. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(7): 1807-1819. DOI: 10.6052/0459-1879-22-003
 Citation: Shi Hemu, Zeng Xiaohui, Wu Han. Analytical solution of the hunting motion of a wheelset nonlinear dynamical system. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(7): 1807-1819. DOI: 10.6052/0459-1879-22-003

# ANALYTICAL SOLUTION OF THE HUNTING MOTION OF A WHEELSET NONLINEAR DYNAMICAL SYSTEM

• Numerical methods are usually used to analyze the amplitude of limit cycle and nonlinear critical speed of railway vehicle system, which is inconvenient to study the rule of variation with vehicle system parameters. The wheelset system retains several critical elements that affect the dynamic performance of the railway vehicle system, such as the geometric nonlinear constraints of the wheel-rail, the wheel-rail contact creep relationship, and the suspension system, which can reflect the essential characteristics of the hunting motion of the railway vehicle system. The wheelset system has fewer degrees of freedom and parameters, which can be analyzed by the analytical method. In this paper, the nonlinear dynamics equations are nondimensionalized by choosing appropriate characteristic parameters, and the two-degree-of-freedom nonlinear differential equations with small parameters are obtained. The method of multiple scales is used to solve the equations analytically. The analytical expressions of the amplitude of the limit cycle of the wheelset system are given and its stability is judged. The analytical expressions of the bifurcation speed of the wheelset system are given, and then the analytical expressions of the nonlinear critical speed of the wheelset system are obtained. After the analytical solutions are verified by the numerical results, the influence of wheelset system parameters is analyzed by using the analytical solutions. The traditional calculation methods of bifurcation diagram (such as speed reduction method, path-following method, etc.) require a large number of numerical integration calculations on the differential equations to solve the nonlinear critical speed of the system. However, the analytical expressions obtained in this paper can directly give the nonlinear critical speed and amplitude of the limit cycle of the wheelset system, which is convenient for studying the rule of variation of the dynamic performance of the wheelset system with parameters and for quick comparison and screening of schemes, and provide a reference for the optimization design of bogie structure.

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