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.

Using a Multibody Dynamic Simulation Code With Neural Network Technology to Predict Railroad Vehicle-Track Interaction Performance in Real Time

2007 ◽  
Author(s):  
Timothy P. Martin ◽  
Khaled E. Zaazaa ◽  
Brian Whitten ◽  
Ali Tajaddini
Keyword(s):  
Neural Network ◽  
Real Time ◽  
Nonlinear Equations ◽  
Equations Of Motion ◽  
Measured Data ◽  
Network Technology ◽  
Simulation Code ◽  
Nonlinear Equations Of Motion ◽  
Railroad Vehicle ◽  
Neural Network Technology

Recently, there has been a large demand for predicting, in real time, the performance of multiple railroad vehicle types traversing existing track as the geometry of the track is being measured. To accurately predict a railroad vehicle’s response over a specified track requires the solution of nonlinear equations of motion and extensive calculations based on the suspension characteristics of the vehicle. To realize the real time goal, codes are being implemented that use linear approximations to the fully nonlinear equations of motion to reduce computation time at the expense of accuracy. Alternatively, 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 training process can be done using measured data or using simulation data. In general, measured data is very expensive to gather due to the instrumentation requirements and is most often not available. In this paper, the use of multibody simulation code as a training tool for a neural network is presented. The example results estimate the vertical and lateral forces at the wheel-to-rail interface as a function of the geometry of the track and the suspension characteristics of the vehicle type by using a multibody code with neural network technique.

A Nonlinear Rail Vehicle Dynamics Computer Program SAMS/Rail: Part 1—Theory and Formulations

2009 ◽  
Author(s):  
Khaled E. Zaazaa ◽  
Brian Whitten ◽  
Brian Marquis ◽  
Erik Curtis ◽  
Magdy El-Sibaie ◽  
...  
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Contact Element ◽  
Contact Forces ◽  
Simulation Code ◽  
Vehicle Performance ◽  
Normal Contact ◽  
Advantages And Disadvantages ◽  
High Speed Trains

Accurate prediction of railroad vehicle performance requires detailed formulations of wheel-rail contact models. In the past, most dynamic simulation tools used an offline wheel-rail contact element based on look-up tables that are used by the main simulation solver. Nowadays, the use of an online nonlinear three-dimensional wheel-rail contact element is necessary in order to accurately predict the dynamic performance of high speed trains. 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 predict the contact forces between wheel and rail. In this paper, several nonlinear wheel-rail contact formulations are presented, each using the online three-dimensional approach. The methods presented are divided into two contact approaches. In the first Constraint Approach, the wheel is assumed to remain in contact with the rail. In this approach, the normal contact forces are determined by using the technique of Lagrange multipliers. In the second Elastic Approach, wheel/rail separation and penetration are allowed, and the normal contact forces are determined by using Hertz’s Theory. The advantages and disadvantages of each method are presented in this paper. In addition, this paper discusses future developments and improvements for the multibody system code. Some of these improvements are currently being implemented by the University of Illinois at Chicago (UIC). In the accompanying “Part 2” and “Part 3” to this paper, numerical examples are presented in order to demonstrate the results obtained from this research.

Consistent Tangent Stiffness of a Three-Dimensional Wheel–Rail Interaction Element

2021 ◽  
Author(s):  
Quan Gu ◽  
Jinghao Pan ◽  
Yongdou Liu
Keyword(s):  
Finite Element ◽  
Quadratic Convergence ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Light Rail ◽  
Software Framework ◽  
Tangent Stiffness ◽  
Rail Vehicle ◽  
Interaction Element ◽  
Nonlinear Equations Of Motion

Consistent tangent stiffness plays a crucial role in delivering a quadratic rate of convergence when using Newton’s method in solving nonlinear equations of motion. In this paper, consistent tangent stiffness is derived for a three-dimensional (3D) wheel–rail interaction element (WRI element for short) originally developed by the authors and co-workers. The algorithm has been implemented in finite element (FE) software framework (OpenSees in this paper) and proven to be effective. Application examples of wheelset and light rail vehicle are provided to validate the consistent tangent stiffness. The quadratic convergence rate is verified. The speeds of calculation are compared between the use of consistent tangent stiffness and the tangent by perturbation method. The results demonstrate the improved computational efficiency of WRI element when consistent tangent stiffness is used.

Nonlinear Dynamics of Rotating Structures and Helicopter Blades

2018 ◽  
Author(s):  
Matteo Filippi ◽  
Alfonso Pagani ◽  
Erasmo Carrera
Keyword(s):  
Numerical Solutions ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Constitutive Law ◽  
Rotating Blades ◽  
Helicopter Blades ◽  
Strain Components ◽  
Theory Approximation ◽  
Nonlinear Equations Of Motion ◽  
Lagrange Strain

This work explores the effects of geometrical nonlinearities in the vibration analysis of rotating structures and helicopter blades. Structures are modelled via higher-order beam theories with variable kinematics. These theories fall in the domain of the Carrera Unified Formulation (CUF), according to which the nonlinear equations of motion of rotating blades can be written in terms of fundamental nuclei, whose formalism is an invariant of the theory approximation. The inherent three-dimensional nature of CUF enables one to include all Green-Lagrange strain components as well as all coupling effects due to the geometrical features and the three-dimensional constitutive law. Numerical solutions are considered and opportunely discussed. Also, linearized and full nonlinear solutions for vibrating rotating blades are compared both in case of small amplitudes and in the large deflections/rotations regime.

Modal Analysis of Ballooning Strings With Small Sag

1999 ◽  
Author(s):  
Rongjun Fan ◽  
Sushil K. Singh ◽  
Christopher D. Rahn
Keyword(s):  
Steady State ◽  
High Speed ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Theoretical Predictions ◽  
Nonlinear Equations Of Motion

Abstract During the manufacture and transport of textile products, yarns are rotated at high speed and form balloons. The dynamic response of the balloon to varying rotation speed, boundary excitation, and disturbance forces governs the quality of the associated process. Resonance, in particular, can cause large tension variations that reduce product quality and may cause yarn breakage. In this paper, the natural frequencies and mode shapes of a single loop balloon are calculated to predict resonance. The three dimensional nonlinear equations of motion are simplified via small steady state displacement (sag) and vibration assumptions. Axial vibration is assumed to propagate instantaneously or in a quasistatic manner. Galerkin’s method is used to calculate the mode shapes and natural frequencies of the linearized equations. Experimental measurements of the steady state balloon shape and the first two natural frequencies and mode shapes are compared with theoretical predictions.

On-Track Measurement of Lateral/Vertical Wheel Loads of Running Railway Vehicles Based on the Neural Network

2008 ◽  
Author(s):  
Davood Younesian ◽  
Fahim Javid ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Neural Network ◽  
Probability Distribution ◽  
Contact Forces ◽  
Strain Gauges ◽  
Network Algorithm ◽  
The Neural Network ◽  
Neural Network System ◽  
Neural Network Algorithm ◽  
Vertical Contact ◽  
Electric Signals

A new approach for on-track measurement of the lateral/vertical contact forces is presented in this paper. The proposed method is based on measurement of the strain at two sides of the wheel web. Electric signals generated by the strain gauges are fed into a neural network algorithm in order to predict the lateral/vertical contact forces. Feed-forward technique is used in the neural network algorithm. A sensitivity analysis has been carried out to find the best position for the strain gauges. A dynamic model of a freight wagon is provided and a variety of numerical simulations are performed to obtain the probability distribution of the lateral and vertical contact forces. The obtained probability distribution function is then utilized to generate lateral/vertical contact forces within the practical range. In order to train the neural network system, the generated contact forces are applied to the wheel flange and the strain signals are obtained. More than 100 configurations are fed into the system in order to train it. Reliability, accuracy and sensitivity of the proposed measurement system are then 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.

Generalized Vector-Network Formulation for the Dynamic Simulation of Multibody Systems

1986 ◽  
Vol 108 (4) ◽  
pp. 322-329 ◽  
Author(s):  
M. J. Richard ◽  
R. Anderson ◽  
G. C. Andrews
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
New Approach ◽  
System Description ◽  
Nonlinear Equations Of Motion ◽  
Systematic Formulation ◽  
Multi Body ◽  
Entire Procedure

This paper describes the vector-network approach which is a comprehensive mathematical model for the systematic formulation of the nonlinear equations of motion of dynamic three-dimensional constrained multi-body systems. The entire procedure is a basic application of concepts of graph theory in which laws of vector dynamics have been combined. The main concepts of the method have been explained in previous publications but the work described herein is an appreciable extension of this relatively new approach. The method casts simultaneously the three-dimensional inertia equations associated with each rigid body and the geometrical expressions corresponding to the kinematic restrictions into a symmetrical format yielding the differential equations governing the motion of the system. The algorithm is eminently well suited for the computer-aided simulation of arbitrary interconnected rigid bodies; it serves as the basis for a “self-formulating” computer program which can simulate the response of a dynamic system, given only the system description.

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.

Multiharmonic Forced Response Analysis of a Turbine Blading Coupled by Nonlinear Contact Forces

2009 ◽  
Author(s):  
Christian Siewert ◽  
Lars Panning ◽  
Jo¨rg Wallaschek ◽  
Christoph Richter
Keyword(s):  
Frequency Domain ◽  
Steam Turbine ◽  
Equations Of Motion ◽  
Forced Vibrations ◽  
Forced Response ◽  
Contact Forces ◽  
Dynamic Loads ◽  
Turbine Stage ◽  
Nonlinear Equations Of Motion ◽  
Turbine Blading

The rotor blades of a low pressure (LP) steam turbine stage are subjected to high static and dynamic loads during operation. The static loads are mainly due to the centrifugal force and thermal strains, whereas the dynamic loads are caused by fluctuating gas forces resulting in forced vibrations of the blades. The forced vibrations can lead to high cycle fatigue (HCF) failures causing substantial damage and high maintenance effort. Thus, one of the main tasks in the design of LP steam turbine blading is the vibration amplitude reduction in order to avoid high dynamic stresses that could damage the blading. The vibration amplitudes of the blades in a LP steam turbine stage can be reduced significantly to a reasonable amount if adjacent blades are coupled by shroud contacts that reinforce the blading, see Fig. 1. Furthermore, in the case of blade vibrations, relative displacements between neighboring blades occur in the contacts and friction forces are generated that provide additional damping to the structure due to the energy dissipation caused by micro- and macroslip effects. Therefore, the coupling of the blades increases the overall mechanical damping. A three-dimensional structural dynamics model including an appropriate spatial contact model is necessary to predict the contact forces generated by the shroud contacts and to describe the vibrational behavior of the blading with sufficient accuracy. To compute the nonlinear forced vibrations of the coupled blading, the nonlinear equations of motion are solved in the frequency domain owing to the high computational efficiency of this approach. The transformation of the nonlinear equations of motion into the frequency domain can be carried out by representing the steady-state displacement in terms of its harmonic components. After that transformation, the nonlinear forced response is computed as a function of the excitation frequency in the frequency domain.

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