The Hunting Behavior of Conventional Railway Trucks

1972 ◽  
Vol 94 (2) ◽  
pp. 752-761 ◽  
Author(s):  
N. K. Cooperrider
Keyword(s):  
Equations Of Motion ◽  
Linear Equations ◽  
Nonlinear Effects ◽  
Complex Model ◽  
Railway Vehicle ◽  
Hunting Behavior ◽  
Wheel Slip ◽  
Wheel Load ◽  
Hunting Motion ◽  
Nonlinear Equations Of Motion

Railway vehicles under certain conditions experience sustained lateral oscillations during which the wheel flanges bang from one rail to the other. It has been found that this behavior, called hunting, only occurs above certain critical forward velocities. Approximations to these critical velocities have been found from a stability analysis of the linear equations of motion for many different railway vehicle models. Hunting is characterized by violent motions that impose large loads on the vehicle and track, and bring several important nonlinear effects into play. This paper reports results of an analysis of nonlinear equations of motion written for two models of a railway truck. The influence of the nonlinear effects on stability is determined and the character of the hunting motion is investigated. One model represents a truck whose axle bearings are rigidly held in the truck frame while the truck frame is connected through a suspension system to a reference that moves along the track with constant velocity. The more complex model includes additional suspension elements between the axle bearings and truck frame. The effects of flange contact, wheel slip and Coulomb friction are described by nonlinear expressions. These results show the significant influence of flange contact on stability, and illustrate the effects of vehicle and track parameters such as rail adhesion, forward velocity, and wheel load on the forces and power dissipation at the wheel-rail interface.

Analysis of the Nonlinear Dynamics of a Railway Vehicle Wheelset

1973 ◽  
Vol 95 (1) ◽  
pp. 28-35 ◽  
Author(s):  
E. Harry Law ◽  
R. S. Brand
Keyword(s):  
Lateral Displacement ◽  
Equations Of Motion ◽  
Vertical Displacement ◽  
Linear Analysis ◽  
Design Parameters ◽  
Railway Vehicle ◽  
Nonlinear Variation ◽  
Constraint Equations ◽  
The Stability ◽  
Nonlinear Equations Of Motion

The nonlinear equations of motion for a railway vehicle wheelset having curved wheel profiles and wheel-flange/rail contact are presented. The dependence of axle roll and vertical displacement on lateral displacement and yaw is formulated by two holonomic constraint equations. The method of Krylov-Bogoliubov is used to derive expressions for the amplitudes of stationary oscillations. A perturbation analysis is then used to derive conditions for the stability characteristics of the stationary oscillations. The expressions for the amplitude and the stability conditions are shown to have a simple geometrical interpretation which facilitates the evaluation of the effects of design parameters on the motion. It is shown that flange clearance and the nonlinear variation of axle roll with lateral displacement significantly influence the motion of the wheelset. Stationary oscillations may occur at forward speeds both below and above the critical speed at which a linear analysis predicts the onset of instability.

Nonlinear Wheelset Dynamic Response to Random Lateral Rail Irregularities

1974 ◽  
Vol 96 (4) ◽  
pp. 1168-1176 ◽  
Author(s):  
E. H. Law
Keyword(s):  
Dynamic Response ◽  
Nonlinear Equations ◽  
Equations Of Motion ◽  
Power Spectra ◽  
Railway Vehicle ◽  
Lateral Stiffness ◽  
Wheel Wear ◽  
Rail Irregularities ◽  
Nonlinear Equations Of Motion

The nonlinear equations of motion for a railway vehicle wheelset having profiled wheels and contact of the wheel flange with flexible rails are presented. The effects of spin creep and gyroscopic terms are included. The rails are considered to have random lateral irregularities which are described by prescribed power spectra. The equations of motion are integrated numerically and the effects on the dynamic response of quantities such as speed, track roughness, wheel wear, flange clearance, and lateral stiffness of the rails are investigated.

Symbolic Linearized Equations for Nonholonomic Multibody Systems With Closed-Loop Kinematics

2018 ◽  
Author(s):  
Márton Kuslits ◽  
Dieter Bestle
Keyword(s):  
Lagrange Multipliers ◽  
Multibody Systems ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Algebraic Equations ◽  
Computationally Efficient ◽  
Linearized Equations ◽  
Nonlinear Equations Of Motion ◽  
Loop Constraints

Multibody systems and associated equations of motion may be distinguished in many ways: holonomic and nonholonomic, linear and nonlinear, tree-structured and closed-loop kinematics, symbolic and numeric equations of motion. The present paper deals with a symbolic derivation of nonlinear equations of motion for nonholonomic multibody systems with closed-loop kinematics, where any generalized coordinates and velocities may be used for describing their kinematics. Loop constraints are taken into account by algebraic equations and Lagrange multipliers. The paper then focuses on the derivation of the corresponding linear equations of motion by eliminating the Lagrange multipliers and applying a computationally efficient symbolic linearization procedure. As demonstration example, a vehicle model with differential steering is used where validity of the approach is shown by comparing the behavior of the linearized equations with their nonlinear counterpart via simulations.

scholarly journals Dynamic behavior of the nonlinear planetary gear model in nonstationary conditions

2020 ◽  
pp. 095440622094104
Author(s):  
Ahmed Hammami ◽  
Ayoub Mbarek ◽  
Alfonso Fernández ◽  
Fakher Chaari ◽  
Fernando Viadero ◽  
...  
Keyword(s):  
Dynamic Behavior ◽  
Equations Of Motion ◽  
Planetary Gear ◽  
Nonlinear Effects ◽  
Hertzian Contact ◽  
Mesh Stiffness ◽  
Planetary Gearbox ◽  
Time Frequency ◽  
Run Up ◽  
Nonlinear Equations Of Motion

The nonlinear effects in gearboxes are a key concern to describe accurately their dynamic behavior. This task is difficult for complex gear systems such as planetary gearboxes. The main aim of this work is to provide responses to overcome this difficulty especially in nonstationary operating regimes by investigating a back-to-back planetary gearbox in steady conditions and in the run-up regime. The nonlinear Hertzian contact of teeth pair is modeled in stationary and nonstationary run-up regime. Then it is incorporated in to a torsional model of the planetary gearbox through different mesh stiffness functions. In addition, motor torque and external load variation are taken into account. The nonlinear equations of motion of the back-to-back planetary gearbox are computed through the Newmark- β algorithm combined with the method of Newton–Raphson. An experimental validation of the proposed numerical model is done through a test bench for both stationary and run-up regimes. The vibration characteristics are extracted and correlated to speed and torque. Time–frequency analysis is implemented to characterize the transient regime during the run-up.

A Nonlinear Rail Vehicle Dynamics Computer Program SAMS/Rail: Part 3—Applications to Predict Railroad Vehicle-Track Interaction Performance

2009 ◽  
Author(s):  
Khaled E. Zaazaa ◽  
Timothy P. Martin ◽  
Brian Whitten ◽  
Brian Marquis ◽  
Erik Curtis ◽  
...  
Keyword(s):  
Neural Network ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Contact Forces ◽  
Multibody Simulation ◽  
Wheel Load ◽  
Simulation Code ◽  
Neural Network System ◽  
Nonlinear Equations Of Motion ◽  
Railroad Vehicle

The dynamic response of a railroad vehicle traveling at speed over track deviations can be predicted by using multibody simulation codes. In this case, the solution of nonlinear equations of motion and extensive calculations based on the suspension characteristics of the vehicle are required. Recently, the Federal Railroad Administration, Office of Research and Development has sponsored a project to develop a general multibody simulation code that uses an online nonlinear three-dimensional wheel-rail contact element to simulate contact forces between wheel and rail. In this paper, several applications to examine such issues as critical speed, curving performance at varying cant deficiencies, and wheel load equalization are presented to demonstrate the use of the multibody code. In addition, the application of the multibody code can be extended to train a neural network system. Neural network technology has the ability to learn relationships between a mechanical system input and output, and, once learned, give quick outputs for given input. The neural network can be combined with the use of a nonlinear multibody code to predict the performance of multiple railroad vehicle types in real time. In this paper, this system is briefly presented to shed light on the optimum use of the multibody code to prevent derailment.

The centring dynamics of a thin liquid shell in capillary oscillations

1988 ◽  
Vol 188 ◽  
pp. 411-435 ◽  
Author(s):  
Chun P. Lee ◽  
Taylor G. Wang
Keyword(s):  
Physical Mechanism ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Thin Sheet ◽  
Nonlinear Effects ◽  
Experimental Information ◽  
Centre Of Mass ◽  
One Dimensional ◽  
The Core ◽  
Nonlinear Equations Of Motion

The physical mechanism governing the centring of a hollow liquid shell in capillary oscillations, which has been observed in experiments, is investigated theoretically. First, the shell is assumed to be inviscid and to have a thickness that is much less than its spherical radius. A system of one-dimensional nonlinear equations of motion is derived using a thin-sheet model. From a numerical study the nonlinear effects of the wave are found to cause the core to oscillate slowly relative to the shell while the centre of mass of the whole system remains stationary. The effects of small viscosity are then considered in an approximation. Finally the strength of the centring mechanism is compared with that of the decentring effect due to buoyancy. The findings are consistent with the limited experimental information available.

A Reduced and Linearized High Fidelity Waveboard Multibody Model for Stability Analysis

2022 ◽  
Author(s):  
Alfonso García-Agúndez Blanco ◽  
Daniel García Vallejo ◽  
Emilio Freire ◽  
Aki Mikkola
Keyword(s):  
Multibody Systems ◽  
Jacobian Matrix ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Nonholonomic Constraints ◽  
Design Parameters ◽  
Constrained Multibody Systems ◽  
Multibody Model ◽  
The Stability ◽  
Nonlinear Equations Of Motion

Abstract In this paper, the stability of a waveboard, a human propelled two-wheeled vehicle consisting in two rotatable platforms, joined by a torsion bar and supported on two caster wheels, is analysed. A multibody model with holonomic and nonholonomic constraints is used to describe the system. The nonlinear equations of motion, which constitute a Differential-Algebraic system of equations (DAE system), are linearized along the steady forward motion resorting to a recently validated linearization procedure, which allows the maximum possible reduction of the linearized equations of motion of constrained multibody systems. The approach enables the generation of the Jacobian matrix in terms of the geometric and dynamic parameters of the multibody system, and the eigenvalues of the system are parameterized in terms of the design parameters. The resulting minimum set of linear equations leads to the elimination of spurious null eigenvalues, while retaining all the stability information in spite of the reduction of the Jacobian matrix. The linear stability results of the waveboard obtained in previous work are validated with this approach. The procedure shows an excellent computational efficiency with the waveboard, its utilization being highly advisable to linearize the equations of motion of complex constrained multibody systems.

On the Parametric Excitation of Pendulum-Type Vibration Absorber

1961 ◽  
Vol 28 (3) ◽  
pp. 330-334 ◽  
Author(s):  
Eugene Sevin
Keyword(s):  
Energy Transfer ◽  
Numerical Solution ◽  
Parametric Excitation ◽  
Equations Of Motion ◽  
Vibration Absorber ◽  
Single Cycle ◽  
Linearized System ◽  
Nonlinear Equations Of Motion ◽  
Beam Oscillation ◽  
Energy Interchange

The free motion of an undamped pendulum-type vibration absorber is studied on the basis of approximate nonlinear equations of motion. It is shown that this type of mechanical system exhibits the phenomenon of auto parametric excitation; a type of “instability” which cannot be accounted for on the basis of the linearized system. Complete energy transfer between modes is shown to occur when the beam frequency is twice the simple pendulum frequency. On the basis of a numerical solution, approximately 150 cycles of the beam oscillation take place during a single cycle of energy interchange.

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