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.

High-Speed Vehicle Models Based on a New Concept of Vehicle/Structure Interaction Component: Part I—Formulation

1993 ◽  
Vol 115 (1) ◽  
pp. 140-147 ◽  
Author(s):  
L. Vu-Quoc ◽  
M. Olsson
Keyword(s):  
Nonlinear Equations ◽  
Building Block ◽  
High Speed ◽  
Equations Of Motion ◽  
Interaction Model ◽  
Component Part ◽  
Structure Interaction ◽  
Vehicle Structure ◽  
Interaction Component ◽  
High Speed Vehicle

High-speed vehicle/structure models constructed based on a new formulation of dynamic interaction between high-speed vehicles and flexible guideways are presented. A basic vehicle/structure interaction model forms a basic building block of complex vehicle/structure models in which lumped-parameter sub-components of the vehicle component (e.g., suspended masses with springs and dashpots) are assembled onto the basic vehicle/structure interaction component. A vertical and an inclined vehicle models are formulated. These vehicle models can serve as yet more advanced building-block models in the hierarchical construction of complex vehicle/structure models. The inclined vehicle model can be used to study the effects of braking of high-speed vehicles of flexible guideways. Fully nonlinear equations of motion of both models are given. Upon introducing approximations to the nonlinear kinematics, mildly nonlinear equations with an unusual mathematical structure are consistently derived. These equations are appropriate for use under realistic working conditions of the system, and are particularly amenable for numerical treatment using a recently proposed class of predictor/corrector algorithms.

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.

scholarly journals Moving Element Analysis of High-Speed Train-Slab Track System Considering Discrete Rail Pads

2020 ◽  
pp. 2150014
Author(s):  
Tuo Lei ◽  
Jian Dai ◽  
Kok Keng Ang ◽  
Kun Li ◽  
Yi Liu
Keyword(s):  
Coordinate System ◽  
High Speed ◽  
Harmonic Wave ◽  
Equations Of Motion ◽  
Moving Frame ◽  
Iteration Algorithm ◽  
Vehicle Speed ◽  
Element Analysis ◽  
Slab Track ◽  
Track System

This paper presents a study of the dynamic behavior of a coupled train-slab track system considering discrete rail pads. The slab track is modeled as a three-layer Timoshenko beam. The study is carried out using the moving element method (MEM). By introducing a convected coordinate system moving at the same speed as the vehicle, the governing equations of motion of the slab track are formulated in a moving frame-of-reference. By adopting Galerkin’s method, the element stiffness, mass and damping matrices of a truncated slab track in the moving coordinate system are derived. The vehicle is modeled as a multi-body with 10 degrees of freedom. The nonlinear Hertz contact model is used to account for the wheel–rail interaction. The Newmark integration method, in conjunction with a global Newton–Raphson iteration algorithm, is employed to solve the nonlinear dynamic equations of motion of the vehicle–track coupled system. The proposed MEM model of the system is validated through comparison with available results in the literature. Further study is then made to investigate the vehicle–track system accounting for track irregularities modeled as short harmonic wave forms. Results showed that irregularities with short wavelengths have a significant effect on wheel–rail contact force and rail acceleration, and the dynamic response of the track structure does not increase monotonously with the increase of the vehicle speed.

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.

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.

Nonlinear Modeling and Experimental Validation of Tire Nonuniformity Induced Tangential Steering Wheel Vibrations

2006 ◽  
Author(s):  
Virgile Ayglon ◽  
Nader Jalili ◽  
Imtiaz Haque
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Modeling ◽  
Equations Of Motion ◽  
Quantitative Measure ◽  
Steering System ◽  
Steering Wheel ◽  
Vehicle Speed ◽  
Pinion Gear ◽  
Stiffness And Damping ◽  
Vehicle Chassis

This paper describes the model integration and validation that followed the development of nonlinear models of a tire with non-uniformities, a double wishbone suspension and rack-and-pinion power steering. These submodels are integrated to investigate the effects of variation of tire, suspension and steering parameters on the transmission of tire forces acting on the wheel spindle to the steering system and vehicle chassis. The tire model is based on a rigid ring model which includes mass imbalance and balancing mass. The suspension is idealized as rigid links with seven degrees-of-freedom and the bushings are represented by spring-damper elements. The equations of motion are derived using the Lagrange multiplier method in Maple, and solved numerically using Matlab DAE solver. The steering system is idealized as a four degree-of-freedom system and considers motion of the rack, rack housing, pinion gear and steering wheel. Nonlinear compliant friction is considered between the pinion gear / rack, and the steering column / chassis interfaces. The analytical model is used to develop a quantitative measure of the relative importance of the parameters such as mass/inertia, suspension bushing stiffness and damping, torsion bar stiffness and damping, rack friction and damping, to the force transmissibility to the vehicle chassis and the steering system. Experimental results include a modal analysis, a shop-testing and road testing, which are used to cross verify the numerical simulations. The testing shows the variation of forces in the steering system due to tire imbalances, emphasizing the nonlinear variation of the nibble phenomenon with vehicle speed and tire imbalance. Results obtained from simulation matches well with the experimental measurements.

Dynamic Interactions of a High-Speed Vehicle and a Distributed Discretely Supported Guideway

2010 ◽  
Vol 26 (1) ◽  
pp. N9-N16
Author(s):  
C.-Y. Hu ◽  
K.-C. Chen ◽  
J.-S. Chen
Keyword(s):  
High Speed ◽  
Integration Method ◽  
Equations Of Motion ◽  
Dynamic Interactions ◽  
Coupled Equations ◽  
Steady State Responses ◽  
Loading Modes ◽  
Rigid Supports ◽  
State Responses ◽  
High Speed Vehicle

AbstractThis study investigates the dynamic interactions between a vehicle and guideway of a high-speed ground transportation system based on maglev vehicles. The guideway is assumed to be made up of identical simply supported beams with single spans and rigid supports. The vehicle is considered to a two-dimensional vehicle model with primary and secondary suspensions. Three kinds of loading modes acting at each beam of guideway are first developed according to the locations of suspensions of vehicle. Coupled equations of motion of both vehicle and guideway in various loading modes are derived and solved by using numerical integration method. The simulations have been performed to investigate the parameters of vehicle/guideway system which may affect the steady-state responses of the vehicle and guideway.

scholarly journals Speed Oscillations of a Vehicle Rolling on a Wavy Road

2021 ◽  
Vol 11 (21) ◽  
pp. 10431
Author(s):  
Walter V. Wedig
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Travel Speed ◽  
Differential Algebraic Equations ◽  
Polar Coordinates ◽  
Algebraic Equations ◽  
Traffic Lights ◽  
Analytical Approximations ◽  
Vertical Vibrations ◽  
Nonlinear Equations Of Motion

Every driver knows that his car is slowing down or accelerating when driving up or down, respectively. The same happens on uneven roads with plastic wave deformations, e.g., in front of traffic lights or on nonpaved desert roads. This paper investigates the resulting travel speed oscillations of a quarter car model rolling in contact on a sinusoidal and stochastic road surface. The nonlinear equations of motion of the vehicle road system leads to ill-conditioned differential–algebraic equations. They are solved introducing polar coordinates into the sinusoidal road model. Numerical simulations show the Sommerfeld effect, in which the vehicle becomes stuck before the resonance speed, exhibiting limit cycles of oscillating acceleration and speed, which bifurcate from one-periodic limit cycle to one that is double periodic. Analytical approximations are derived by means of nonlinear Fourier expansions. Extensions to more realistic road models by means of noise perturbation show limit flows as bundles of nonperiodic trajectories with periodic side limits. Vehicles with higher degrees of freedom become stuck before the first speed resonance, as well as in between further resonance speeds with strong vertical vibrations and longitudinal speed oscillations. They need more power supply in order to overcome the resonance peak. For small damping, the speeds after resonance are unstable. They migrate to lower or supercritical speeds of operation. Stability in mean is investigated.

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 .

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