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.

Stability Analysis of High-Speed Railway Vehicle Based on Multibody Dynamics Analysis

2013 ◽  
Vol 392 ◽  
pp. 156-160
Author(s):  
Ju Seok Kang
Keyword(s):  
Stability Analysis ◽  
Multibody Dynamics ◽  
High Speed ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Design Parameters ◽  
Railway Vehicle ◽  
Dynamics Analysis ◽  
Contact Points ◽  
The Stability

Multibody dynamics analysis is advantageous in that it uses real dimensions and design parameters. In this study, the stability analysis of a railway vehicle based on multibody dynamics analysis is presented. The equations for the contact points and contact forces between the wheel and the rail are derived using a wheelset model. The dynamics equations of the wheelset are combined with the dynamics equations of the other parts of the railway vehicle, which are obtained by general multibody dynamics analysis. The equations of motion of the railway vehicle are linearized by using the perturbation method. The eigenvalues of these linear dynamics equations are calculated and the critical speed is found.

Linear Stability Analysis of a Waveboard Multibody Model With a Minimal Set of Equations

2021 ◽  
Author(s):  
A. G. Agúndez ◽  
D. García-Vallejo ◽  
E. Freire ◽  
A. M. Mikkola
Keyword(s):  
Stability Analysis ◽  
Multibody System ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Design Parameters ◽  
Multibody Model ◽  
Aspect Ratios ◽  
Holonomic And Nonholonomic Constraints ◽  
The Stability ◽  
Nonlinear Equations Of Motion

Abstract In this paper, the stability of a waveboard, the skateboard consisting in two articulated platforms, coupled by a torsion bar and supported of two caster wheels, is analysed. The waveboard presents an interesting propelling mechanism, since the rider can achieve a forward motion by means of an oscillatory lateral motion of the platforms. The system is described using a multibody model with holonomic and nonholonomic constraints. To perform the stability analysis, the nonlinear equations of motion are linearized with respect to the forward upright motion with constant speed. The linearization is carried out resorting to a novel numerical linearization procedure, recently validated with a well-acknowledged bicycle benchmark, which allows the maximum possible reduction of the linearized equations of motion of multibody systems with holonomic and nonholonomic constraints. The approach allows the expression of the Jacobian matrix in terms of the main design parameters of the multibody system under study. This paper illustrates the use of this linearization approach with a complex multibody system as the waveboard. Furthermore, a sensitivity analysis of the eigenvalues considering different scenarios is performed, and the influence of the forward speed, the casters’ inclination angle and the tori aspect ratios of the toroidal wheels on the stability of the system is analysed.

Study on the Role of Geogrid-Reinforced for Fly Ash Retaining Wall Basing on the Analysis of FLAC3D

2011 ◽  
Vol 368-373 ◽  
pp. 599-603
Author(s):  
Wei Shi ◽  
Jin Han ◽  
Yong Bin Li
Keyword(s):  
Fly Ash ◽  
Safety Factor ◽  
Lateral Displacement ◽  
Retaining Wall ◽  
Vertical Displacement ◽  
Design Parameters ◽  
Finite Element Software ◽  
The Stability ◽  
The Impact

Geogrid-reinforced retaining wall is widely used in civil engineering, the role of geogrid reinforcement and the calculations of reinforcement material in the retaining wall design need further refinement.This paper analyzes the fly ash retaining wall with and without reinforcement by using finite element software of FLAC3D,studys the impact of geogrid-reinforced function on the stability of fly ash retaining wall ,gets the design parameters of geogrid-reinforced fly ash retaining wall.The numerical results show that: the fly ash retaining walls' safety factor is lower when its height is greater than 6m,reinforcement is needed for fly ash retaining wall to improve its safety factor to ensure the stability of retaining wall.Simulate and analyze the 8m high geogrid reinforced fly ash retaining wall,the results show that: increasing the reinforcement spacing can increase the lateral and vertical displacement of geogrid reinforced fly ash retaining wall, the maximum vertical displacement of retaining wall is in the upper wall,maximum lateral displacement occurs in the lower parts of the retaining wall;the reasonable distance of 8m high fly ash retaining wall is 0.8m.

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.

Derailment Analysis of High-Speed Railway Vehicle Bogies

2011 ◽  
Vol 110-116 ◽  
pp. 186-195 ◽  
Author(s):  
Yung Chang Cheng ◽  
Chern Hwa Chen ◽  
Che Jung Yang
Keyword(s):  
High Speed ◽  
Lateral Displacement ◽  
Vertical Displacement ◽  
Creep Model ◽  
Railway Vehicle ◽  
Vehicle Speed ◽  
Nonlinear Creep ◽  
Bogie Frame ◽  
Suspension Parameters ◽  
Yaw Angle

Based on the heuristic nonlinear creep model, the nonlinear coupled differential equations of the motion of a 12 degree-of-freedom (12-DOF) bogie system which takes account of the lateral displacement, vertical displacement, the roll angle and the yaw angle of the each wheelset and the bogie frame, moving on curved tracks are derived. The nonlinear creep forces and moments are constructed via the saturation constant of the nonlinear creep model in completeness. The effect of the suspension parameters of a bogie system on the derailment quotient is investigated. Results obtained in this study show that the derailment quotient of a bogie system increases as the vehicle speed increases. In addition, the derailment quotient of a bogie system is generally decreased with the increasing values of suspension parameters.

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.

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.

Running Safety and Comfort Analysis of Railway Vehicles Moving on Curved Tracks

2014 ◽  
Vol 14 (04) ◽  
pp. 1450004 ◽  
Author(s):  
Yung-Chang Cheng ◽  
Chin-Te Hsu
Keyword(s):  
Degrees Of Freedom ◽  
Lateral Displacement ◽  
Equations Of Motion ◽  
Creep Model ◽  
Railway Vehicle ◽  
Nonlinear Creep ◽  
Running Safety ◽  
Comfort Index ◽  
Vertical Displacements ◽  
Index Formulas

Using a heuristic linear creep model, this study derives the governing differential equations of motion for the railway vehicle traveling on curved tracks. The railway vehicle is modeled as a car system with 27 degrees-of-freedom (DOFs), taking into account the lateral and vertical displacements, roll and yaw angles of the wheelsets and truck frames, as well as the lateral displacement, roll and yaw angles of the car body. The effects of railway vehicle speeds on the derailment quotients and offload factors related to running safety are evaluated by both the linear and nonlinear creep models for various radii of curved tracks. Using the Sperling and modified Sperling index formulas, the effects of railway vehicle speeds on lateral riding quality and comfort are illustrated for the two models with various radii of curved tracks. Furthermore, the effects of railway vehicle speeds on the lateral Sperling comfort index of the 27-DOF car model are presented and compared for various suspension parameters. Finally, the acceptable region for riding quality and comfort are drawn.

Dynamic Analysis for Derailment Safety of High-Speed Railway Vehicle Bogies

2011 ◽  
Vol 199-200 ◽  
pp. 239-242
Author(s):  
Chern Hwa Chen ◽  
Yung Chang Cheng ◽  
Shun Chin Yang ◽  
Yuh Yi Lin ◽  
Cheng Hsin Chang ◽  
...  
Keyword(s):  
High Speed ◽  
Lateral Displacement ◽  
Vertical Displacement ◽  
Creep Model ◽  
Railway Vehicle ◽  
Vehicle Speed ◽  
Nonlinear Creep ◽  
Suspension Parameters ◽  
Derailment Safety ◽  
Yaw Angle

Based on the heuristic nonlinear creep model, the nonlinear coupled differential equations of the motion of a 12 degree-of-freedom (12-DOF) bogie system which takes account of the lateral displacement, vertical displacement, the roll angle and the yaw angle of the each wheelset and the bogie frame, moving on curved tracks are derived. The nonlinear creep forces and moments are constructed via the saturation constant of the nonlinear creep model in completeness. The effect of the suspension parameters of a bogie system on the derailment quotient is investigated. Results obtained in this study show that the derailment quotient of a bogie system increases as the vehicle speed increases. In addition, the derailment quotient of a bogie system is generally decreased with the increasing values of suspension parameters.

Parametric Analysis of Ride Comfort for Tilting Railway Vehicles Running on Irregular Curved Tracks

2016 ◽  
Vol 16 (09) ◽  
pp. 1550056 ◽  
Author(s):  
Yung-Chang Cheng ◽  
Chin-Te Hsu
Keyword(s):  
Ride Comfort ◽  
Lateral Displacement ◽  
Equations Of Motion ◽  
Roll Angle ◽  
Creep Model ◽  
Railway Vehicle ◽  
Vehicle Speed ◽  
Nonlinear Creep ◽  
Rail Irregularities ◽  
Yaw Angle

The ride comfort of a tilting railway vehicle moving on curved tracks with rail irregularities is studied. Using the nonlinear creep model and Kalker's linear theory, the governing differential equations of motion for a tilting railway vehicle running on irregular tracks are first derived. The tilting railway vehicle is modeled by a 27 degree-of-freedom (DOF) car system, considering the lateral displacement, vertical displacement, roll angle and yaw angle of both the wheelsets and bogie frames, as well as the lateral displacement, roll angle and yaw angle of the car body. Based on the international standard ISO 2631-1, the effect of vehicle speed on the ride comfort index of the tilting vehicle is investigated for various tilting angles, using both linear and nonlinear creep models, and various radii of curved tracks, as well as for various suspension parameters. Finally, the ride comfort indices computed with rail irregularities are found to be higher than those with no rail irregularities, indicating that the effect of rail irregularities on the ride comfort of a tilting vehicle cannot be disregarded in practice.

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