ABSTRACT
It is known that railroad vehicle dynamic models that employ kinematic linearization can predict significantly different dynamic responses compared with models that are based on fully nonlinear kinematic and dynamic equations. This is particularly true for simulations at high speeds. To analytically examine this problem and study the effect of the approximations used in the linearized railroad vehicle models, the fully nonlinear kinematic and dynamic equations of a wheelset — obtained using the methods discussed in preceding chapters — are summarized in this chapter. The linearized kinematic and dynamic equations used in some railroad vehicle models are obtained from the fully nonlinear model to shed light on the assumptions and approximations used in the linearized models. The assumptions of small angles that are often made in developing railroad vehicle models and their effect on the angular velocity, angular acceleration, and the inertia forces are investigated. The velocity creepage expressions that result from the use of the assumptions of small angles are obtained and compared with the fully nonlinear expressions. Newton-Euler equations for the wheelset are presented, and their dependence on Euler angles and their time derivatives is discussed. The effect of the linearization assumptions on the form of Newton-Euler equations is examined. A suspended wheelset model is used as an example to obtain the numerical results required to quantify the effect of the linearization. The results presented in this chapter show that linearization of the creepages can lead to significant errors in the values predicted for the longitudinal and tangential forces as well as the spin moment. There are also significant differences between the nonlinear and the linearized models in the prediction of the lateral and vertical forces used to evaluate the L/V ratios.
