Keywords: stability, critical speed, Hopf bifurcation, non-linear dynamics.

The wheelset stability problem is the basis of railway vehicle stability assessment. This paper proposes the Ahmadian-Yang wheel model [1] with non-linear creep theory for wheelsets. Vermeulen and Johnson non-linear creep theory [2] is considered in the equations to correct the linear creep force and compared with the linear models. Specific details are as follows:

1. Four kinds of models of wheelset lateral motion are solved using numerical methods and compared. The models are non-linear conicity and non-linear creep theory, linear conicity and non-linear creep theory, non-linear conicity and linear creep theory, linear conicity and linear creep theory.
2. A bifurcation diagram for the China Railway High-speed 3 (CRH3) on a roller rig test is compared with the four models.
3. Hopf bifurcation points of the models which are defined as vehicle's linear speed are solved using an analytical method. The diagrams of linear critical speed versus parameters diagrams are given..

The conclusions and outlook are:

1. Both non-linear and linear wheelset models have the same linear critical speed as long as the first order approximations are the same, which is the basis of non-linear parameters used for design.
2. Non-linear conicity may alter the amplitude of the limit cycle.
3. Linear creep theory can result in a jumping phenomenon when the speed crossover bifurcation point is reached. On the other hand, non-linear creep theory does not cause a jump and it fits the vehicle application well.
4. Moderately increasing lateral or longtitudinal stiffness of the primary suspension in the range of low stiffness can increase the critical speed. But increasing in the large stiffness range can reduce it rapidly.
5. The conicity and primary yaw spring arm both have an optimum value. As the primary yaw spring arm or conicity increase, initially the critical speed increases. Beyond a certain level, however, it starts to decrease. This behavior indicates that in practice the two parameters must be selected appropriately such that the critical speed is maximum.
6. The models in the paper are simplified. For example the flange force is considered as a piecewise linear function. This is an easy method to express its function and find an analytical solution. In fact, many non-linear terms cannot be written as an expression.

1

M. Ahmadian, S. Yang, "Hopf Bifurcation and Hunting Behavior in a Rail Wheelset with Flange Contact", Nonlinear Dynamics, 15, 15-30, 1998.

2

Y.S. Hu, "Modern railway vehicle system dynamics", China Railway Press, Beijing, 68, 2009.

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