Railway Truck Response to Random Rail Irregularities

1975 ◽  
Vol 97 (3) ◽  
pp. 957-964 ◽  
Author(s):  
Neil K. Cooperrider
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Tangential Force ◽  
Contact Forces ◽  
Guidance Force ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
Rail Irregularities ◽  
Frequency Domain Techniques

This paper discusses the random response of a seven degree of freedom, passenger truck model to lateral rail irregularities. Power spectral densities and root mean square levels of component displacements and contact forces are reported. The truck model used in the study allows lateral and yaw degrees of freedom for each wheelset, and lateral, yaw and roll freedoms for the truck frame. Linear creep relations are utilized for the rail-wheel contact forces. The lateral rail irregularities enter the analysis through the creep expressions. The results described in the paper were obtained using frequency domain techniques to solve the equations of motion. The reported results demonstrate that the guidance force needed when traveling over irregular rail at high speed utilizes a significant portion of the total available tangential force between wheel and rail.

Regular and Irregular Vibrations of a Non-Ideal Autoparametric System

Volume 2 ◽  
2004 ◽  
Author(s):  
Danuta Sado ◽  
Maciej Kot
Keyword(s):  
Energy Source ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Resonance Region ◽  
The Body ◽  
Damping Force ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
Time Histories ◽  
Limited Power

This paper studies the regular and irregular vibrations of two degrees of freedom autoparametrical system, when the excitation is made by an electric motor (with unbalanced mass), which works with limited power supply. The investigated system consists of a pendulum of the length l and mass m, and a body of mass M suspended on the flexible element. It was assumed that the damping force acting on the body of mass M and resistive moment acting on the pedulum are non-linear. In this case, the excitation has to be expressed as an equation describing how the energy source supplies the energy to the system. The non-ideal source of power adds one degree of freedom, and then the system has three degrees of freedom. The system has been researched for known characteristic of the energy source (DC motor). The equations of motion have been solved numerically what permit to enrich the investigations and to examine not only small and steady state oscillations but also large-amplitude oscillations in transient states. The influence of motor’s speed on the phenomenon of energy transfer has been researched. Near the internal and external resonance region, except different kind of periodic vibration, the chaotic vibration has been observed. For characterizing an irregular chaotic response bifurcation diagrams and time histories, power spectral densities, Poincare´ maps and maximal exponents of Lyapunov have been constructed.

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.

Control of Maglev Suspension Systems

1996 ◽  
Vol 2 (3) ◽  
pp. 349-368 ◽  
Author(s):  
Y. Cai ◽  
S.S. Chen
Keyword(s):  
Degrees Of Freedom ◽  
Ride Comfort ◽  
Vehicle Suspension ◽  
Semiactive Control ◽  
One Dimensional ◽  
Suspension Systems ◽  
Maglev Vehicle ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
Control Designs

This study investigates alternate designs for control of maglev vehicle suspension systems. Active and semiactive control-law designs are introduced into primary and secondary suspensions of maglev vehi cles. A one-dimensional vehicle with two degrees of freedom, simulating the German Transrapid Magiev System, is used. The transient and frequency responses of suspension systems and power spectral densities of vehicle accelerations are calculated to evaluate different control designs. The results show that both active and semiactive control designs improve vehicle response and provide acceptable ride comfort for maglev systems.

Rigid Body dynamics and decoupled control architecture for two strongly interacting manipulators

Robotica ◽  
1991 ◽  
Vol 9 (4) ◽  
pp. 421-430 ◽  
Author(s):  
M.A. Unseren
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Position Control ◽  
Equations Of Motion ◽  
Joint Space ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Control Architecture ◽  
Reduced Order ◽  
Closed Chain

SUMMARYA rigid body dynamical model and control architecture are developed for the closed chain motion of two structurally dissimilar manipulators holding a rigid object in a three-dimensional workspace. The model is first developed in the joint space and then transformed to obtain reduced order equations of motion and a separate set of equations describing the behavior of the generalized contact forces. The problem of solving the joint space and reduced order models for the unknown variables is discussed. A new control architecture consisting of the sum of the outputs of a primary and secondary controller is suggested which, according to the model, decouples the force and position-controlled degrees of freedom during motion of the system. The proposed composite controller enables the designer to develop independent, non-interacting control laws for the force and position control of the complex closed chain system.

Computer Simulation of the Response of a Railway Vehicle Carbody

2002 ◽  
Author(s):  
M. Senthil Kumar ◽  
P. M. Jawahar
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Railway Vehicle ◽  
Lateral Stiffness ◽  
Lateral Vibration ◽  
Kutta Method ◽  
Nonlinear Mathematical Model ◽  
Rail Vehicle ◽  
Runge Kutta Method

In this paper, a nonlinear mathematical model has been constructed by deriving the equations of motion of a Rail Vehicle carbody using Newton’s law. The nonlinear formula is used to evaluate the wheel rail contact forces. The nonlinear profile of wheel and rail are taken into account. Also the lateral stiffness of the track is taken into consideration. The equations of motion are derived for (a) Carbody with conventional wheelset (b) Carbody with unconventional wheelset (independently rotating wheels). For lateral vibration, 17 degrees of freedom are considered. The degrees of freedom represent lateral and yaw movements of 4 wheelsets and lateral, yaw and roll movements of the bogie and carbody. These equations of motion are transformed into a form suitable for numerical differential equation by Runge Kutta method. In the interest of computing economy, certain approximations have been introduced for calculating the creep forces. Sample results are given for a model of a typical railway vehicle used by the Indian Railways. The lateral dynamic response of the railway vehicle carbody for both conventional and unconventional wheelset has been analysed.

A New Approach to Modeling Surface Defects in Bearing Dynamics Simulations

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Ankur Ashtekar ◽  
Farshid Sadeghi ◽  
Lars-Erik Stacke
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Surface Defects ◽  
Equations Of Motion ◽  
Infinite Domain ◽  
Step Size ◽  
Deep Groove ◽  
Dynamics Simulations ◽  
Bearing Dynamics

A dynamic model for deep groove and angular contact ball bearings was developed to investigate the influence of race defects on the motions of bearing components (i.e., inner and outer races, cage, and balls). In order to determine the effects of dents on the bearing dynamics, a model was developed to determine the force-deflection relationship between an ellipsoid and a dented semi-infinite domain. The force-deflection relationship for dented surfaces was then incorporated in the bearing dynamic model by replacing the well-known Hertzian force-deflection relationship whenever a ball/dent interaction occurs. In this investigation, all bearing components have six degrees-of-freedom. Newton’s laws are used to determine the motions of all bearing elements, and an explicit fourth-order Runge–Kutta algorithm with a variable or constant step size was used to integrate the equations of motion. A model was used to study the effect of dent size, dent location, and inner race speed on bearing components. The results indicate that surface defects and irregularities like dent have a severe effect on bearing motion and forces. Furthermore, these effects are even more severe for high-speed applications. The results also demonstrate that a single dent can affect the forces and motion throughout the entire bearing and on all bearing components. However, the location of the dent dictates the magnitude of its influence on each bearing component.

High-Speed Vehicle Models Based on a New Concept of Vehicle/Structure Interaction Component: Part II—Algorithmic Treatment and Results for Multispan Guideways

1993 ◽  
Vol 115 (1) ◽  
pp. 148-155 ◽  
Author(s):  
L. Vu-Quoc ◽  
M. Olsson
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Structural Equations ◽  
Component Part ◽  
Vehicle Speed ◽  
Vehicle Structure ◽  
Algorithmic Treatment ◽  
Nonlinear Equations Of Motion ◽  
High Speed Vehicle

The predictor structural equations for the vehicle models developed in Part I are derived here for use with a new class of predictor/corrector algorithms to solve the mildly nonlinear equations of motion of the vehicle/structure models. Having all accelerations of the vehicle component eliminated, and with the aid of further simplifying approximations, the predictor structural equations are linear with respect to the structural degrees of freedom. In the algorithms, the predictor structural equations are different from the corrector structural equations; the proposed algorithmic treatment has been proved (elsewhere) to yield accurate energy balance. Results obtained for both continuous and discontinuous guideways are discussed, and optimal guideway configurations suggested. Effects of high-speed vehicle braking on a flexible guideway are analyzed using the vehicle models and the proposed algorithmic treatment. The influence of the guideway flexibility on the vehicle speed, an important feature of the present formulation, is clearly demonstrated.

A Compliant Double Pin Track Link Model for Multibody Tracked Vehicles

1999 ◽  
Author(s):  
J. H. Choi ◽  
D. S. Bae ◽  
H. S. Ryu
Keyword(s):  
High Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
High Mobility ◽  
Contact Forces ◽  
Integration Step ◽  
Step Size ◽  
Tracked Vehicles ◽  
Accelerated Motion ◽  
Pin Track

Abstract It is the objective of this investigation to develop compliant double pin track link models and investigate the use of these models in the dynamic analysis of high mobility tracked vehicles. There are two major difficulties encountered in developing the compliant track models discussed in this paper. The first is due to the fact that the integration step size must be kept small in order to maintain the numerical stability of the solution. This solution includes high oscillatory signals resulting from the impulsive contact forces and the use of stiff compliant elements to represent the joints between the track links. The characteristics of the compliant, elements used in this investigation to describe the track joints are measured experimentally. The second difficulty encountered in this investigation is due to the large number of the system equations of motion of the three dimensional multibody tracked vehicle model. The dimensionality problem is solved by decoupling the equations of motion of the chassis subsystem and the track subsystems. Recursive methods are used to obtain a minimum set of equations for the chassis subsystem. Several simulation scenarios including an accelerated motion, high speed motion, braking, and turning motion of the high mobility vehicle are tested in order to demonstrate the effectiveness and validity of the methods proposed in this investigation.

The Characteristic Analysis of Vibration for High-Speed Train-Ballastless Track-Bridge System Base on A Hybrid FE-SEA Method

2012 ◽  
Vol 226-228 ◽  
pp. 387-391
Author(s):  
Wen Jun Luo ◽  
Xiao Yan Lei ◽  
Song Liang Lian ◽  
Lin Ya Liu
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Power Input ◽  
Characteristic Analysis ◽  
State Response ◽  
Complex Dynamic Systems ◽  
Ballastless Track ◽  
Track Bridge ◽  
Bridge System

A hybrid method combining FE and SEA was recently presented for predicting the steady-state response of vibro-acoustic systems. The new method is presented for the analysis of complex dynamic systems which is based on partitioning the system degrees of freedom into a ‘‘global’’ set and a ‘‘local’’ set. The global equations of motion are formulated and solved by using the finite element method (FEM).The local equations of motion are formulated and solved by using statistical energy analysis (SEA). The power input from the global degrees of freedom. This paper deduces the theory for the beam element , and Train-Ballastless Track-Bridge System provides an application, and it showed that the method yields very good results .

Dynamic Modeling and Vibration Response Simulation for High Speed Rolling Ball Bearings With Localized Surface Defects in Raceways

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Linkai Niu ◽  
Hongrui Cao ◽  
Zhengjia He ◽  
Yamin Li
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Surface Defects ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Hertzian Contact ◽  
Ball Bearings ◽  
Rolling Ball ◽  
Vibration Responses

A dynamic model is developed to investigate vibrations of high speed rolling ball bearings with localized surface defects on raceways. In this model, each bearing component (i.e., inner raceway, outer raceway and rolling ball) has six degrees of freedom (DOFs) to completely describe its dynamic characteristics in three-dimensional space. Gyroscopic moment, centrifugal force, lubrication traction/slip between bearing component are included owing to high speed effects. Moreover, local defects are modeled accurately and completely with consideration of additional deflection due to material absence, changes of Hertzian contact coefficient and changes of contact force directions due to raceway curvature variations. The obtained equations of motion are solved numerically using the fourth order Runge–Kutta–Fehlberg scheme with step-changing criterion. Vibration responses of a defective bearing with localized surface defects are simulated and analyzed in both time domain and frequency domain, and the effectiveness of fault feature extraction techniques is also discussed. An experiment is carried out on an aerospace bearing test rig. By comparing the simulation results with experiments, it is confirmed that the proposed model is capable of predicting vibration responses of defective high speed rolling ball bearings effectively.

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