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RESEARCH PAPERS

# Effect of the Wheel Geometric Design on the Nonlinear Dynamics of Railroad Vehicles

[+] Author and Article Information
Ahmed A. Shabana, Mahmoud Tobaa, Khaled E. Zaazaa

Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL 60607-7022

J. Mech. Des 128(5), 1130-1140 (Oct 20, 2005) (11 pages) doi:10.1115/1.2214739 History: Received January 06, 2005; Revised October 20, 2005

## Abstract

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 nongeneralized 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 Hertz’s 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.

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## Figures

Figure 8

The root loci for the suspended wheel set model for the two profiles

Figure 9

Lateral displacement of the suspended wheel set (Profile A)

Figure 10

Lateral displacement of the suspended wheel set (Profile B)

Figure 11

Location of the contact points on the right wheel for Profile A

Figure 12

Location of the contact points on the right wheel for Profile B

Figure 13

Schematic representation of two bodies in contact

Figure 1

Rail profile

Figure 2

Wheel Profile A

Figure 3

Wheel Profile B

Figure 4

The two wheel profiles

Figure 5

Differences between the tangents for the two profiles

Figure 6

Difference in curvature between the two profiles

Figure 7

Top view of the suspended wheel set

Figure 19

Tangent track with two lateral bumps

Figure 20

Lateral displacement of the front wheel set of the leading truck (Profile A)

Figure 21

Lateral displacement of the front wheel set of the leading truck (Profile B)

Figure 22

Normal contact force on the right wheel of the front wheel set of the leading truck (Profile A)

Figure 23

Normal contact force on the right wheel of the front wheel set of the leading truck (Profile B)

Figure 24

Lateral contact force on the right wheel of the front wheel set of the leading truck (Profile A)

Figure 14

Surface parameters

Figure 15

Track geometry

Figure 16

Wheel geometry

Figure 17

Vehicle model

Figure 18

Components of the truck

Figure 25

Lateral contact force on the right wheel of the front wheel set of the leading truck (Profile B)

Figure 26

Lateral displacement of the front wheel set of the leading truck

## Errata

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