Influence of Wheel-Rail Profiles on the Hunting Vibrations of Rail Vehicle Trucks

1985 ◽  
Vol 107 (2) ◽  
pp. 167-174 ◽  
Author(s):  
A. F. D’Souza ◽  
W-J. Tsung
Keyword(s):  
Dynamic Performance ◽  
Equations Of Motion ◽  
Algebraic Equations ◽  
Wheel Wear ◽  
Hunting Behavior ◽  
Describing Functions ◽  
High Acceleration ◽  
Nonlinear Algebraic Equations ◽  
Wheel Profile ◽  
Freight Trucks

The effect of several wheel and rail profiles on the hunting behavior of three-piece North American freight truck is investigated by the method of describing functions. After replacing the nonlinear terms by their equivalent describing functions, the differential equations of motion are converted to a set of coupled nonlinear algebraic equations which are then solved by the Newton-Raphson method. It is shown that the wearing of the rail profile has a significant adverse effect on the dynamic behavior. It greatly lowers the critical speed for the onset of hunting and raises the frequency, thereby causing high acceleration levels. It is also shown that the modified Heumann wheel profile exhibits a superior dynamic performance for freight trucks than the standard new wheel profile used in North America. The effects of wheel wear and loads on hunting are also investigated.

Multi-step wear evolution simulation method for the prediction of rail wheel wear and vehicle dynamic performance

SIMULATION ◽  
2018 ◽  
Vol 95 (5) ◽  
pp. 441-459 ◽  
Author(s):  
Smitirupa Pradhan ◽  
AK Samantaray ◽  
R Bhattacharyya
Keyword(s):  
Vehicle Dynamics ◽  
Ride Comfort ◽  
Dynamic Performance ◽  
Travel Distance ◽  
Rolling Contact ◽  
Dynamics Simulation ◽  
Railway Vehicle ◽  
Wear Depth ◽  
Wheel Wear ◽  
Wheel Profile

This paper presents a complete model to estimate the effects of wheel wear on the dynamic behavior and ride comfort of a railway vehicle. A co-simulation of the vehicle dynamics modeled in ADAMS VI-Rail and wear evolution modeled in MATLAB is performed in a loop. The outputs from the vehicle dynamics simulation are used to compute the wear evolution, which in turn affects the vehicle dynamics. The local contact parameters, such as normal contact force, tangential stresses and slip, etc., and wear distribution for each cell of the contact surface are estimated with the help of Kalker’s simplified theory of rolling contact and Archard’s wear model, respectively. The wear distribution and smoothening of the wheel profile are obtained for a short travel distance and are then scaled up for larger travel distance. The worn wheel profile is updated in the vehicle dynamics model after every 10,000 km of travel for further dynamic analysis and this process is repeated until either the critical dynamic performance or wheel wear limits are reached. Several new results emerge by considering both acceleration and braking on a tangent track with sinusoidal irregularities. Critical speed appears to increase initially and then decrease quickly, whereas worn wheels give better ride comfort in both lateral and vertical directions as compared to new wheels. According to the results in this work, wheels may be recommended for re-profiling or replacement much before the critical wear depth recommended in maintenance guidelines is reached.

scholarly journals Limit Cycle Predictions of a Nonlinear Journal-Bearing System

1990 ◽  
Vol 112 (2) ◽  
pp. 168-171 ◽  
Author(s):  
M. T. M. Crooijmans ◽  
H. J. H. Brouwers ◽  
D. H. van Campen ◽  
A. de Kraker
Keyword(s):  
Journal Bearing ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Time Discretization ◽  
Linear Stability Theory ◽  
Algebraic Equations ◽  
System Parameters ◽  
Nonlinear Algebraic Equations ◽  
System Equations ◽  
Nonlinear Equations Of Motion

An analysis is presented of the self-excited vibrations of a journal carried in a cylindrical fluid film bearing. Using linear stability theory, the values of the system parameters at the point of loss of stability are determined. These values agree well with those of previous investigators. Solutions of the nonlinear system equations are obtained by time discretization and by an arc-continuation method for solving the obtained nonlinear algebraic equations. In this way periodic solutions of the nonlinear equations of motion are calculated as a function of the system parameters. The behavior of the journal can be explained by the results of these calculations.

Effect of Independently Rotating Wheels on the Dynamic Performance of Railroad Vehicles

2007 ◽  
Author(s):  
Khaled E. Zaazaa ◽  
Brian Whitten
Keyword(s):  
Dynamic Performance ◽  
Equations Of Motion ◽  
Lateral Force ◽  
Ride Quality ◽  
Vehicle Dynamic ◽  
Vehicle Performance ◽  
Railroad Vehicles ◽  
Judicious Choice ◽  
Wheel Profile ◽  
Railroad Vehicle

In recent decades, there has been a considerable effort in improving railroad vehicle dynamic performance. This involves high operational speed with stable behavior, better curving performance, better ride quality, and increased life of the wheel and rail profiles. To achieve this goal, the use of independently rotating wheels (IRW) is proposed as one potential option. Using IRW either partially or totally decouples the pitch rotation of the two wheels of the “wheelset”, thereby reducing or eliminating the longitudinal creepage and thus wheelset hunting motion. On the other hand, the longitudinal creepage is no longer available to provide steering assistance in curves, and continuous flange contact during curving is expected. However, by judicious choice of wheel profile and careful truck design, the lateral force between wheel and rail during curving can be reduced, decreasing the wear on both the wheel and rail profiles. Therefore, such solution is assumed to achieve higher stable operational speed and improved curving behavior. In this paper, the effect of using IRW on railroad vehicle performance is examined. The equations of motion of a single wheelset model and a suspended wheelset model that use IRW are presented and compared with those for similar models that use a rigid wheelset. Using a newly developed general multibody code, a complete vehicle model that uses IRW is examined and compared with one that uses rigid wheelsets. The effect of the IRW system on vehicle dynamic performance is quantitatively presented. In addition, the ability of the contact formulations used in this multibody code for modeling the IRW system is confirmed.

A comparative study of elastic motions in trajectory tracking of flexible RPR planar manipulators moving with high speed

Robotica ◽  
2016 ◽  
Vol 35 (7) ◽  
pp. 1523-1540 ◽  
Author(s):  
Amirhossein Eshaghiyeh Firoozabadi ◽  
Saeed Ebrahimi ◽  
Josep M. Font-Llagunes
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Parallel Manipulators ◽  
Differential Algebraic Equations ◽  
Body Motion ◽  
Inertial Forces ◽  
Algebraic Equations ◽  
Assumed Mode Method ◽  
Planar Manipulators

SUMMARYThe study of inertial forces effects at high speeds in flexible parallel manipulators, which generate undesired deviations, is a challenging task due to the coupled and complicated equations of motion. A dynamic model of the Revolute Prismatic Revolute (RPR) planar manipulators (specifically 3-RPR, 2-RPR and 1-RPR) with flexible intermediate links is developed based on the assumed mode method. The flexible intermediate links are modeled as Euler-Bernoulli beams with fixed-free boundary conditions. Using the Lagrange multipliers, a generalized set of differential algebraic equations (DAEs) of motion is developed. In the simulations, the rigid body motion of the end-effector is constrained by some moving constraint equations while the vibrations of the flexible intermediate links cause deviations from the desired trajectory. From this analysis, the dynamic performance of the manipulators when tracking a desired trajectory is evaluated. A comparison of the results indicates that in some cases, adding each extra RPR chain in the n-RPR planar manipulators with flexible intermediate links reduces the stiffness and accuracy due to the inertial forces of the flexible links, which is opposite to what would be expected. The study provides insights to the design, control and suitable selection of the flexible manipulators.

scholarly journals Frequency–Amplitude Relationship of a Nonlinear Symmetric Panel Absorber Mounted on a Flexible Wall

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1188
Author(s):  
Yiu-Yin Lee
Keyword(s):  
Elliptic Integral ◽  
Algebraic Equations ◽  
Cavity Depth ◽  
Nonlinear Algebraic Equations ◽  
Flexible Panel ◽  
Flexible Wall ◽  
Elliptic Integral Method ◽  
Flexible Panels ◽  
Relationship Of ◽  
Panel Absorber

This study addresses the frequency–amplitude relationship of a nonlinear symmetric panel absorber mounted on a flexible wall. In many structural–acoustic works, only one flexible panel is considered in their models with symmetric configuration. There are very limited research investigations that focus on two flexible panels coupled with a cavity, particularly for nonlinear structural–acoustic problems. In practice, panel absorbers with symmetric configurations are common and usually mounted on a flexible wall. Thus, it should not be assumed that the wall is rigid. This study is the first work employing the weighted residual elliptic integral method for solving this problem, which involves the nonlinear multi-mode governing equations of two flexible panels coupled with a cavity. The reason for adopting the proposed solution method is that fewer nonlinear algebraic equations are generated. The results obtained from the proposed method and finite element method agree reasonably well with each other. The effects of some parameters such as vibration amplitude, cavity depth and thickness ratio, etc. are also investigated.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

scholarly journals A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi-Infinite Interval Using Legendre Rational Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
E. H. Doha ◽  
D. Baleanu ◽  
A. H. Bhrawy ◽  
R. M. Hafez
Keyword(s):  
Numerical Solutions ◽  
Rational Functions ◽  
Absolute Error ◽  
Delay Systems ◽  
Infinite Interval ◽  
Algebraic Equations ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
Linear And Nonlinear ◽  
Pseudospectral Scheme

A new Legendre rational pseudospectral scheme is proposed and developed for solving numerically systems of linear and nonlinear multipantograph equations on a semi-infinite interval. A Legendre rational collocation method based on Legendre rational-Gauss quadrature points is utilized to reduce the solution of such systems to systems of linear and nonlinear algebraic equations. In addition, accurate approximations are achieved by selecting few Legendre rational-Gauss collocation points. The numerical results obtained by this method have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively limited nodes used, the absolute error in our numerical solutions is sufficiently small.

scholarly journals Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams

2005 ◽  
Vol 12 (6) ◽  
pp. 425-434 ◽  
Author(s):  
Menglin Lou ◽  
Qiuhua Duan ◽  
Genda Chen
Keyword(s):  
Perturbation Method ◽  
Dynamic Characteristics ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Solution Process ◽  
Equation Of Motion ◽  
Timoshenko Beams ◽  
Algebraic Equations ◽  
Nonlinear Algebraic Equations ◽  
Shear Distortion

Timoshenko beams have been widely used in structural and mechanical systems. Under dynamic loading, the analytical solution of a Timoshenko beam is often difficult to obtain due to the complexity involved in the equation of motion. In this paper, a modal perturbation method is introduced to approximately determine the dynamic characteristics of a Timoshenko beam. In this approach, the differential equation of motion describing the dynamic behavior of the Timoshenko beam can be transformed into a set of nonlinear algebraic equations. Therefore, the solution process can be simplified significantly for the Timoshenko beam with arbitrary boundaries. Several examples are given to illustrate the application of the proposed method. Numerical results have shown that the modal perturbation method is effective in determining the modal characteristics of Timoshenko beams with high accuracy. The effects of shear distortion and moment of inertia on the natural frequencies of Timoshenko beams are discussed in detail.

Periodic Response of a Link Coupling With Clearance

1989 ◽  
Vol 111 (2) ◽  
pp. 253-259 ◽  
Author(s):  
Y. S. Choi ◽  
S. T. Noah
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Solution Procedure ◽  
Contact Forces ◽  
Steady State Response ◽  
Algebraic Equations ◽  
State Response ◽  
Contact Points ◽  
Integration Schemes ◽  
Nonlinear Algebraic Equations

The nonlinear, steady-state response of a displacement-forced link coupling with clearance with finite stiffness is determined. The solution procedure is derived from satisfying the boundary conditions at the contact points and then solving the resulting nonlinear algebraic equations by setting the duration of contact as a parameter. This direct approach to determining periodic solutions for systems with clearances with finite stiffness is substantially more efficient than numerical integration schemes. Results in terms of contact forces and durations of contact are pertinent to fatigue and wear studies. Parametric relations are presented for effects of the variation of damping, stiffness, exciting displacement, and gap length on the dynamic behavior of the link pair.

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