Dynamic analysis of a wheelset using the D'Alembert-Lagrange method and modified embedded technique

In the present work, the kinematics and dynamics of a wheelset was investigated. An idealized profile shapes for both rail and wheels were used. The profile of the rail is knife edge while that of the wheel is a cone. The kinematic analysis is based on a set of contact constraints between the rails and wheels. These constraints are used to simulate transverse sliding motion of the wheelset. The parameters of the contact equations are divided into a set of independent and dependent variables. Then a scheme based on this dichotomy is developed that incorporates a multi-level dependency among the dependent variables.;For dynamic analysis, a specialized embedded D'Alembert-Lagrange formulation that incorporates a multi-level dependency among the dependent parameters was developed. The approach is designated as Modified Embedded D'Alembrt-Lagrange (MEDL) in this work. MEDL is used to model a spinning wheelset and study its dynamics. In the spinning wheelset model, friction forces at contacts are incorporated using the coulomb friction model. To compute the dry friction, normal force is first evaluated by computing the Lagrange multipliers first. Then the generalized forces associated with friction contact forces are computed.;A simulation study for the spinning wheelset model for several forward studies is conducted. The Fast Fourier Transform (FFT) of the output of simulation studies are used to identify the hunting frequencies. These hunting frequencies are compared to those predicted by Klingel's Formulae. A good agreement between the hunting frequencies is observed.