Development of the Finite Segment Method for Modeling Railroad Track Structures

2011 ◽  
Author(s):  
Martin B. Hamper ◽  
Khaled E. Zaazaa ◽  
Ahmed A. Shabana
Keyword(s):  
Sparse Matrix ◽  
Deformable Body ◽  
Contact Point ◽  
Equations Of Motion ◽  
Variable Step Size ◽  
Variable Order ◽  
Step Size ◽  
Finite Segment ◽  
Finite Segment Method ◽  
Railroad Vehicle

In the finite segment method, the dynamics of a deformable body is described using a set of rigid bodies that are connected by elastic force elements. This approach can be used, as demonstrated in this investigation, in the simulation of some rail movement scenarios. The purpose of this investigation is to develop a new track model that combines the absolute nodal coordinate formulation (ANCF) geometry and the finite segment method. The ANCF finite elements define the track geometry in the reference configuration as well as the change in the geometry due to the movement of the finite segments of the track. Using ANCF geometry and the finite segment kinematics, the location of the wheel/rail contact point is predicted online and used to update the creepage expressions due to the finite segment displacements and rotations. The location of the wheel/rail contact point and the updated creepage expressions are used to evaluate the creep forces. A three-dimensional elastic contact formulation (ECF-A), that allows for wheel/rail separation, is used in this investigation. The rail displacement due to the applied loads is modeled by a set of rigid finite segments that are connected by set of spring-damper elements. Each rail finite segment is assumed to have six rigid body degrees of freedom. The equations of motion of the finite segments are integrated with the railroad vehicle system equations of motion in a sparse matrix formulation. The resulting dynamic equations are solved using a predictor-corrector numerical integration method that has a variable order and variable step size. As shown in this paper, the finite segments may be used to model specific phenomena that occur in railroad vehicle applications, including rail rotations and gage widening. The procedure used in this investigation to implement the finite segment method in a general purpose multibody system (MBS) computer program is described. Four simple models are presented in order to demonstrate the implementation of the finite segment method in MBS algorithms. The limitations of using the finite segments approach for modeling the track structure and rail flexibility are also discussed.

Variable-step-size second-order-derivative multistep method for solving first-order ordinary differential equations in system simulation

2020 ◽  
Vol 11 (01) ◽  
pp. 2050001
Author(s):  
Lei Zhang ◽  
Chaofeng Zhang ◽  
Mengya Liu
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Multistep Method ◽  
Second Order ◽  
Order Derivative ◽  
Variable Step Size ◽  
Variable Order ◽  
Step Size ◽  
Variable Step ◽  
The Stability

According to the relationship between truncation error and step size of two implicit second-order-derivative multistep formulas based on Hermite interpolation polynomial, a variable-order and variable-step-size numerical method for solving differential equations is designed. The stability properties of the formulas are discussed and the stability regions are analyzed. The deduced methods are applied to a simulation problem. The results show that the numerical method can satisfy calculation accuracy, reduce the number of calculation steps and accelerate calculation speed.

Use of Finite Element and Finite Segment Methods in Modeling Rail Flexibility: A Comparative Study

2012 ◽  
Vol 7 (4) ◽  
Author(s):  
Martin B. Hamper ◽  
Antonio M. Recuero ◽  
José L. Escalona ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Element Mesh ◽  
Finite Segment ◽  
Safety Requirements ◽  
Contact Points ◽  
Rigid Finite Element Method ◽  
Contact Formulation ◽  
Finite Segment Method ◽  
Railroad Vehicle

Safety requirements and optimal performance of railroad vehicle systems require the use of multibody system (MBS) dynamics formulations that allow for modeling flexible bodies. This investigation will present three methods suited for the study of flexible track models while conclusions about their implementations and features are made. The first method is based on the floating frame of reference (FFR) formulation which allows for the use of a detailed finite element mesh with the component mode synthesis technique in order to obtain a reduced order model. In the second method, the flexible body is modeled as a finite number of rigid elements that are connected by springs and dampers. This method, called finite segment method (FSM) or rigid finite element method, requires the use of rigid MBS formulations only. In the third method, the FFR formulation is used to obtain a model that is equivalent to the FSM model by assuming that the rail segments are very stiff, thereby allowing the exclusion of the high frequency modes associated with the rail deformations. This FFR/FS model demonstrates that some rail movement scenarios such as gauge widening can be captured using the finite element FFR formulation. The three procedures FFR, FSM, and FFR/FS will be compared in order to establish differences among them and analyze the specific application of the FSM to modeling track flexibility. Convergence of the methods is analyzed. The three methods proposed in this investigation for modeling the movement of three-dimensional tracks are used with a three-dimensional elastic wheel/rail contact formulation that predicts contact points online and allows for updating the creepages to account for the rail deformations. Several conclusions will be drawn in view of the results obtained in this investigation.

Power System Stability Computer Simulation Using a Differential-Algebraic Equation Solver

2005 ◽  
Vol 4 (2) ◽  
Author(s):  
Jose Eduardo Onoda Pessanha ◽  
Osvaldo Saavedra ◽  
Alex Paz ◽  
Carlos Portugal
Keyword(s):  
Computer Simulation ◽  
Power System ◽  
Time Domain ◽  
Differential Algebraic Equations ◽  
System Stability ◽  
Variable Step Size ◽  
Variable Order ◽  
Differential Algebraic Equation ◽  
Step Size ◽  
Variable Step

The preset work tested a freely domain software for solving index zero and one systems of differential-algebraic equations, named as DASSL. The code encompasses an efficient variable step size and variable order based on BDF methods to solve a system of DAEs or ODEs. The code was applied in power systems time domain studies, i.e., synchronous machine angular transient stability and long-term voltage stability, using the Brazilian South-Southeast Equivalent Power System. Using this real power system model including fast and slow response control devices, it was possible to investigate the code capability in simulating different stability phenomena in the same run. The variable step size and variable order algorithm implemented in DASSL results in a very powerful tool for power system time domain computer simulation.

Load Sharing of Parallel Shaft Split Torque Transmission System

2012 ◽  
Vol 490-495 ◽  
pp. 2231-2235 ◽  
Author(s):  
Ning Zhao ◽  
Rui Feng Wang ◽  
Li Tao ◽  
Qing Jian Jia
Keyword(s):  
Equations Of Motion ◽  
Load Sharing ◽  
Transmission System ◽  
Variable Step Size ◽  
Step Size ◽  
Runge Kutta Method ◽  
Torque Transmission ◽  
Torque Load ◽  
Fifth Order ◽  
Split Torque

Parallel shaft split torque Transmission system Split torque Load sharing Abstract: The Newton method was applied to develop a system of equations of motion, the mathematical model includes stiffness of shaft supporting, position of gears, backlashes, time-varying stiffness, composite transmission errors, damping. The model was solved by variable step size forth/fifth-order Runge-Kutta method. The load sharing was affected obviously by asymmetry of gear backlashes, stiffness of shaft supporting and gear position

Modeling Flexibility in Myosin V Using a Multiscale Articulated Multi-Rigid Body Approach

2014 ◽  
Vol 10 (1) ◽  
Author(s):  
Mahdi Haghshenas-Jaryani ◽  
Alan Bowling
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Multiscale Model ◽  
Physical Parameters ◽  
Myosin V ◽  
Step Size ◽  
Finite Segment ◽  
Proposed Model ◽  
Run Time ◽  
Physical Laws

This paper presents a multiscale dynamic model for the simulation and analysis of flexibility in myosin V. A 3D finite segment model, a multirigid body model connected with torsional springs, is developed to mechanically model the biological structure of myosin V. The long simulation run time is one of the most important issues in the dynamic modeling of biomolecules and proteins due to the disproportionality between the physical parameters involved in their dynamics. In order to address this issue, the most-used models, based on the famous overdamped Langevin equation, omit the inertial terms in the equations of motion; that leads to a first order model that is inconsistent with Newton's second law. However, the proposed model uses the concept of the method of multiple scales (MMS) that brings all of the terms of the equations of motion into proportion with each other; that helps to retain the inertia terms. This keeps the consistency of the model with the physical laws and experimental observations. In addition, the numerical integration's step size can be increased from commonly used subfemtoseconds to submilliseconds. Therefore, the simulation run time is significantly reduced in comparison with other approaches. The simulation results obtained by the proposed multiscale model show a dynamic behavior of myosin V which is more consistent with experimental observations in comparison with other overdamped models.

scholarly journals Nonlinear dynamics of rotor system supported by bearing with waviness

2020 ◽  
Vol 103 (3) ◽  
pp. 003685042094409
Author(s):  
Guofang Nan ◽  
Yang Zhang ◽  
Yujie Zhu ◽  
Wei Guo
Keyword(s):  
Equations Of Motion ◽  
Rolling Bearing ◽  
Rotor System ◽  
Variable Step Size ◽  
Nonlinear Stiffness ◽  
Step Size ◽  
Mass Eccentricity ◽  
The Stability ◽  
Shape Characteristics ◽  
The Impact

A new nonlinear rotor model supported by the rolling bearing is established under the consideration of the bearing with waviness fault, the unbalanced excitation, the nonlinear Hertz contact force, the varying compliance vibration, and, especially, the physical nonlinear stiffness of the shaft material. The expression with cubic nonlinear terms is adopted to characterize the physical nonlinear stiffness of the shaft material, and the sinusoidal wave is applied to describe the shape characteristics of the waviness fault. The dynamic equations of motion for the new model are developed, and the calculation example of the rotor system supported by the bearing JIS6306 is solved by the variable step-size Runge–Kutta methods to study the effect of the waviness, the clearance, the mass eccentricity on the dynamic behavior. The research results show that growth of the amplitude for the waviness changes the energy distribution of the vibration process; the enlargement of bearing clearance will reduce the stability of the system; the increase in the number of the waviness will make the order of the frequency components changed; for the nonlinear stiffness bearing-rotor system with waviness fault, the augment of mass eccentricity will enhance the impact of the nonlinear stiffness on the system.

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