Khaled E. Zaazaa

DEVELOPMENT OF ELASTIC FORCE MODEL FOR WHEEL/RAIL CONTACT PROBLEMS

In this investigation, a new formulation for the wheel/rail contact problem based on the elastic force approach is presented. Crucial to the success of any elastic force formulation for the wheel/rail contact problem is the accurate prediction of the location of the contact points. To this end, features of multibody formulations that allow introducing additional differential equations are exploited in this investigation in order to obtain a good estimate of the rail arc length travelled by the wheel set. In the formulation presented in this paper, four parameters are used to describe the wheel and the rail surfaces. In order to determine the location of the points of contact between the wheel and the rail, a first order differential equation for the rail arc length is introduced and is integrated simultaneously with the multibody equations of motion of the wheel/rail system. The method presented in this paper allows for multiple points of contact between the wheel and the rail by using an optimized search for all possible contact points. The normal contact forces are calculated and used with non-linear expressions for the creepages to determine the creep forces. The paper also discusses two different procedures for the analysis of the two-point contact in the wheel/rail interaction. Numerical results obtained using the elastic force model are presented and compared with the results obtained using the constraint approach.

Modeling Two-Point Wheel/Rail Contacts Using Constraint and Elastic-Force Approaches

Two approaches are commonly used for solving the problem of wheel/rail contact in railroad dynamics. The first is the elastic approach in which the wheel is assumed to have six degrees of freedom with respect to the rail. The normal contact forces are defined using Hertz’s contact theory or in terms of assumed stiffness and damping coefficients. The second approach is the constraint approach in which nonlinear kinematic contact constraint equations are introduced, leading to a model in which the wheel has five degrees of freedom with respect to the rail. It is the objective of this investigation to present a new formulation for the wheel/rail contact problem based on the elastic force approach. Crucial to the success of any elastic force formulation for wheel/rail contact problem is the accurate prediction of the location of the contact points. To this end, features of multibody formulations that allow introducing arbitrary differential equations are exploited in this investigation in order to obtain a good estimate of the rail arc length traveled by the wheel set. In the formulation presented in this paper, four surface parameters are used to describe the wheel and the rail surfaces each with arbitrary geometry. In order to determine the location of the points of contact between the wheel and the rail, a first order differential equation for the rail arc length is introduced and is integrated simultaneously with the multibody equations of motion of the wheel/rail system. The method presented in this paper allows for multiple points of contact between the wheel and the rail by using an optimized search for all possible contact points. The normal contact forces are calculated and used with non-linear expressions for the creepages to determine the creep forces. The paper also discusses two different procedures for the analysis of the two-point contact in the wheel/rail interaction. Numerical results obtained using the elastic force model are presented and compared with the results obtained using the constraint approach.Copyright

A technique for validating a multibody wheel/rail contact algorithm

In this paper, a specialized steady state formulation is developed in order to validate the results obtained using multibody wheel/rail two-point contact algorithms developed at the University of Illinois at Chicago. In the specialized formulation, the wheel set is assumed to have three points of contact with the rail. The steady state curving behavior of the wheel set is examined using this specialized formulation. The balanced steady state curving behavior in which the centrifugal force is equal to the lateral component of the gravity force can be obtained as a special case of the specialized steady state formulation developed in this investigation. No derailment analysis or scenarios are considered in this paper in order to validate the results of both the constraint and elastic contact formulations. The results of the simple specialized formulation are compared with the results of the multibody inverse and forward dynamics approaches. In the inverse dynamics, approach it is assumed that the wheel set will maintain three points of contact with the rail. The inverse dynamics formulation model is conceptually different from the specialized steady state formulation since in the inverse dynamics all the degrees of freedom are specified. In the multibody forward dynamics method, no assumptions are made with regard to the existence of the flange contact.Copyright

Effect of the wheel geometric design on the nonlinear dynamics of railroad vehicles

The effect of the geometry of a wheel profile that allows only a single point of contact with the rail is investigated in this study. The local geometric properties of this profile are compared with the local geometric properties of a profile that allows for two-point contacts in order to understand the basic differences between the two profiles. A simple model is first used to examine the effect of the profile geometry on the stability and nonlinear dynamics of a suspended wheel set. The results obtained using this simple model show that the geometry of the wheel profile can significantly alter the critical speed. A computational approach is then used to investigate and quantify the effect of the wheel geometry wheel on the dynamics and stability of railroad vehicles. Two methods, the contact constraint and elastic formulations, are used. The contact constraint method employs nonlinear algebraic kinematic constraint equations to describe the contact between the wheel and the rail. The contact kinematic constraints, which eliminate one degree of freedom and do not allow for wheel/rail separation, are imposed at the position, velocity and acceleration levels. The system equations of motion are expressed in terms of the generalized coordinates and the nongene rallied surface parameters. In the formulations based on the elastic approach, the wheel has six degrees of freedom with respect to the rail, and the normal contact forces are defined as a function of the penetration using Hertzs contact theory or using assumed stiffness and damping coefficients. In the elastic approach that allows for wheel/rail separation, the locations of the contact points are determined by solving a set of algebraic equations. The distribution of the contact forces resulting from the use of the two profiles that have different geometric properties is investigated using the two methods. Numerical results are presented for a full railroad vehicle model and the effect of the wheel profile on the vehicle stability is investigated.

A Study of the Wheel Geometry Effect on the Dynamic Behavior of Railroad Vehicles

The effect of the geometry of a wheel profile that allows only a single point of contact between the wheel and the rail is investigated in this study. The local geometric properties of this profile are compared with the local geometric properties of a profile that allows for two-point contacts in order to understand the basic differences between the two profiles. A simple model is first used to examine the effect of the profile geometry on the stability and nonlinear dynamics of a suspended wheel set. The results obtained in this paper show that the wheel profile can significantly alter the critical speed. Using surface parameters that define the wheel and rail geometry, the global representations of the positions of the points on the wheel and rail surfaces are obtained and used to define the conditions of the contact between the wheel and the rail. Numerical results are presented for a full railroad vehicle model and the effect of the wheel profile on the vehicle stability is investigated. A comparison between the results obtained using the two wheel profiles in the case of wheel climb scenarios is presented.Copyright