Effect of the Wheel Geometric Design on the Nonlinear Dynamics of Railroad Vehicles

2005 ◽  
Vol 128 (5) ◽  
pp. 1130-1140 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Mahmoud Tobaa ◽  
Khaled E. Zaazaa
Keyword(s):  
Nonlinear Dynamics ◽  
Simple Model ◽  
Single Point ◽  
Contact Forces ◽  
Geometric Properties ◽  
Normal Contact ◽  
Railroad Vehicles ◽  
Contact Points ◽  
Contact Constraint ◽  
Wheel Profile

The effect of the geometry of a wheel profile that allows only a single point of contact with the rail is investigated in this study. The local geometric properties of this profile are compared with the local geometric properties of a profile that allows for two-point contacts in order to understand the basic differences between the two profiles. A simple model is first used to examine the effect of the profile geometry on the stability and nonlinear dynamics of a suspended wheel set. The results obtained using this simple model show that the geometry of the wheel profile can significantly alter the critical speed. A computational approach is then used to investigate and quantify the effect of the wheel geometry wheel on the dynamics and stability of railroad vehicles. Two methods, the contact constraint and elastic formulations, are used. The contact constraint method employs nonlinear algebraic kinematic constraint equations to describe the contact between the wheel and the rail. The contact kinematic constraints, which eliminate one degree of freedom and do not allow for wheel/rail separation, are imposed at the position, velocity and acceleration levels. The system equations of motion are expressed in terms of the generalized coordinates and the nongeneralized surface parameters. In the formulations based on the elastic approach, the wheel has six degrees of freedom with respect to the rail, and the normal contact forces are defined as a function of the penetration using Hertz’s contact theory or using assumed stiffness and damping coefficients. In the elastic approach that allows for wheel/rail separation, the locations of the contact points are determined by solving a set of algebraic equations. The distribution of the contact forces resulting from the use of the two profiles that have different geometric properties is investigated using the two methods. Numerical results are presented for a full railroad vehicle model and the effect of the wheel profile on the vehicle stability is investigated.

A Study of the Wheel Geometry Effect on the Dynamic Behavior of Railroad Vehicles

2005 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Mahmoud Tobaa ◽  
Khaled E. Zaazaa
Keyword(s):  
Critical Speed ◽  
Single Point ◽  
Vehicle Stability ◽  
Point Contacts ◽  
Vehicle Model ◽  
Geometric Properties ◽  
Railroad Vehicles ◽  
Wheel Profile ◽  
The Stability ◽  
Railroad Vehicle

The effect of the geometry of a wheel profile that allows only a single point of contact between the wheel and the rail is investigated in this study. The local geometric properties of this profile are compared with the local geometric properties of a profile that allows for two-point contacts in order to understand the basic differences between the two profiles. A simple model is first used to examine the effect of the profile geometry on the stability and nonlinear dynamics of a suspended wheel set. The results obtained in this paper show that the wheel profile can significantly alter the critical speed. Using surface parameters that define the wheel and rail geometry, the global representations of the positions of the points on the wheel and rail surfaces are obtained and used to define the conditions of the contact between the wheel and the rail. Numerical results are presented for a full railroad vehicle model and the effect of the wheel profile on the vehicle stability is investigated. A comparison between the results obtained using the two wheel profiles in the case of wheel climb scenarios is presented.

Estimation of Graphite Dust Production in a Pebble-Bed Type Nuclear Reflector

2014 ◽  
Author(s):  
Ji-Ho Kang ◽  
Eung Seon Kim ◽  
Seungyon Cho
Keyword(s):  
Adhesive Wear ◽  
Cell Model ◽  
Estimation Method ◽  
Unit Cell ◽  
Contact Forces ◽  
Dust Explosion ◽  
Dust Production ◽  
Pebble Bed ◽  
Normal Contact ◽  
Contact Points

In this study, an estimation method of graphite dust production in the pebble-bed type reflector region of Korean HCSB (Helium-Cooled Solid Breeder) TBM (Test Blanket Module) in the ITER (International Thermonuclear Experimental Reactor) project using FEM (Finite Element Method) was proposed and the amount of dust production was calculated. A unit-cell model of uniformly arranged pebbles was defined with appropriate thermal and mechanical loadings. A commercial FEM program, Abaqus V6.10 was used to model and solve the stress field under multiple contact constraints between pebbles in the unit-cell. Resulting normal contact forces and slip distances on contact points were applied into the Archard adhesive wear equation to calculate the amount of graphite dust. The friction effect on contact points was investigated. The calculation result showed that the amount of graphite dust production was estimated to 2.22∼3.67e−4 g/m3 which was almost linearly proportional to the friction coefficient. The analysis results will be used as the basis data for the consecutive study of dust explosion.

On the Influence of Contact Geometry on Grasp Stability

2008 ◽  
Author(s):  
Gert A. Kragten ◽  
Just L. Herder ◽  
A. L. Schwab
Keyword(s):  
Contact Stiffness ◽  
Contact Geometry ◽  
Contact Forces ◽  
Minor Effect ◽  
Dynamic Simulations ◽  
Normal Contact ◽  
Contact Points ◽  
Grasp Stability ◽  
The Stability ◽  
A Minor

This paper demonstrates that the predicted grasp stability is highly sensitive to only small changes in the character of the contact forces. The contribution of the geometry and stiffness at the contact points to the grasp stability is investigated by a planar grasp with three contact points. Limit cases of zero and infinite contact curvatures, and finite to infinite contact stiffnesses are considered. The stability is predicted based on the approach of Howard and Kumar [1], and verified with multibody dynamic simulations. For rigid objects and fingers with only normal contact stiffness, the grasp stability is dominated by the contact geometry, whereas the local contact stiffness and preload have a minor effect. Furthermore, grasps with pointed finger tips are more likely to be stable than grasps with flat finger tips.

scholarly journals A Study on the Dynamics of Spatial Mechanisms With Frictional Spherical Clearance Joints

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Filipe Marques ◽  
Fernando Isaac ◽  
Nuno Dourado ◽  
António Pedro Souto ◽  
Paulo Flores ◽  
...  
Keyword(s):  
Friction Force ◽  
Contact Process ◽  
Contact Forces ◽  
Force Model ◽  
Spherical Joint ◽  
Normal Contact ◽  
Clearance Joints ◽  
Dissipative Term ◽  
Contact Points ◽  
Spatial Mechanisms

An investigation on the dynamic modeling and analysis of spatial mechanisms with spherical clearance joints including friction is presented. For this purpose, the ball and the socket, which compose a spherical joint, are modeled as two individual colliding components. The normal contact-impact forces that develop at the spherical clearance joint are determined by using a continuous force model. A continuous analysis approach is used here with a Hertzian-based contact force model, which includes a dissipative term representing the energy dissipation during the contact process. The pseudopenetration that occurs between the potential contact points of the ball and the socket surface, as well as the indentation rate play a crucial role in the evaluation of the normal contact forces. In addition, several different friction force models based on the Coulomb's law are revisited in this work. The friction models utilized here can accommodate the various friction regimens and phenomena that take place at the contact interface between the ball and the socket. Both the normal and tangential contact forces are evaluated and included into the systems' dynamics equation of motion, developed under the framework of multibody systems formulations. A spatial four-bar mechanism, which includes a spherical joint with clearance, is used as an application example to examine and quantify the effects of various friction force models, clearance sizes, and the friction coefficients.

A Study on the Dynamics of Spatial Mechanisms With Frictional Spherical Clearance Joints

2016 ◽  
Author(s):  
Filipe Marques ◽  
Fernando Isaac ◽  
Nuno Dourado ◽  
António Pedro Souto ◽  
Paulo Flores ◽  
...  
Keyword(s):  
Friction Force ◽  
Contact Process ◽  
Contact Forces ◽  
Force Model ◽  
Spherical Joint ◽  
Normal Contact ◽  
Clearance Joints ◽  
Dissipative Term ◽  
Contact Points ◽  
Spatial Mechanisms

An investigation on the dynamic modeling and analysis of spatial mechanisms with spherical clearance joints including friction is presented. For this purpose, the ball and the socket which compose a spherical joint are modeled as two individual colliding components. The normal contact-impact forces that develop at the spherical clearance joint are determined by using a continuous force model. A continuous analysis approach is used here with a Hertzian based contact force model, which includes a dissipative term representing the energy dissipation during the contact process. The pseudo-penetration that occurs between the potential contact points of the ball and the socket surface, as well as the indentation rate play a crucial role in the evaluation of the normal contact forces. In addition, several different friction force models based on the Coulomb’s law are revisited in this work. The friction models utilized here can accommodate the various friction regimens and phenomena that take place at the contact interface between the ball and the socket. Both the normal and tangential contact forces are evaluated and included into the systems’ dynamics equation of motion, developed under the framework of multibody systems formulations. A spatial four bar mechanism, which includes a spherical joint with clearance, is used as an application example to examine and quantify the effects of various friction force models, clearance sizes, and the friction coefficients.

Influence of the Wheel and Rail Interpolation Scheme on the Contact Evaluation in Railway Dynamics

2005 ◽  
Author(s):  
J. Pombo ◽  
J. Ambro´sio
Keyword(s):  
Three Dimensional ◽  
Contact Forces ◽  
Railway Vehicle ◽  
Interpolation Scheme ◽  
Normal Contact ◽  
Contact Points ◽  
Rail Vehicles ◽  
Direct Measurements ◽  
Spatial Geometry ◽  
Conventional Rail

The dynamic behavior of the railway vehicles is strongly influenced by the complex interaction between the wheels and rails. In conventional rail vehicles the wheelsets are assembled with two wheels that are not free to rotate independently. Hence, their treads are profiled in order to allow them to negotiate curves without slipping. The dynamics of guidance depends on the wheel-rail contact forces resultant from the vehicle interaction with the track. In this work a methodology for the accurate geometric description of track models is proposed in the framework of multibody dynamics. It includes the representation of the track spatial geometry and its irregularities. The wheel and rail surfaces are parameterized with a formulation that allows using any wheel and rail profiles obtained from direct measurements or design requirements. A methodology is proposed to find online the coordinates of the contact points between wheel and rail surfaces, even for the most general three dimensional motion of the wheelset. A formulation for the description of the normal contact forces, which result from the wheel-rail interaction, is also presented. The tangential creep forces in the wheel-rail contact area are evaluated using: Kalker linear theory; Heuristic force method; Polach formulation. All methodologies proposed here are implemented in a general multibody code. The advantages and drawbacks of the computational tool are discussed with emphasis on the influence of the interpolation scheme used to parameterize the wheel and rail profiles. The discussion is supported through the dynamic analysis of the wheelset of the railway vehicle ML95 on a straight track.

The Direct Contact Problem in a Trochoidal-Type Machine

1993 ◽  
Author(s):  
John B. Shung ◽  
Gordon R. Pennock
Keyword(s):  
Direct Contact ◽  
Contact Point ◽  
Element Model ◽  
Contact Forces ◽  
Combined Model ◽  
Normal Contact ◽  
Contact Points ◽  
Satisfactory Method ◽  
Type Machine ◽  
Static Conditions

Abstract Reducing the contact forces in a trochoidal-type machine is important because the machine can not be adjusted for wear. The main difficulty in calculating the contact forces is to determine the forces that are transmitted through each contact point. Since there are many points of contact, at any instant, the problem is quasi-statically indeterminate and no satisfactory method of analysis is available in the current literature. The first part of this paper presents a simplified analytical model of a trochoidal-type machine when friction and deformation at the contact points are neglected. From this model, closed-form equations are derived for the normal contact forces. Then the second part of the paper presents a combined analytical and finite element model of the same machine. The analysis for the combined model includes the effects of friction and deformation at the contact points. The analysis for both models is for quasi-static conditions. The results from the two models are compared and important conclusions are drawn.

Effect of Disabled Fastening Systems and Ballast on Vehicle Derailment

2006 ◽  
Vol 129 (2) ◽  
pp. 217-229 ◽  
Author(s):  
Xinbiao Xiao ◽  
Xuesong Jin ◽  
Zefeng Wen
Keyword(s):  
Degrees Of Freedom ◽  
Great Influence ◽  
Contact Forces ◽  
Railway Vehicle ◽  
Vertical Force ◽  
Nonlinear Creep ◽  
Wheel Load ◽  
Creep Theory ◽  
Normal Contact ◽  
Contact Points

The effect of disabled fastening systems and ballast on railway vehicle derailment is investigated by developing a nonsymmetrical coupled vehicle/track model. In the model a half passenger car is considered, and modeled with a multi-body system with 18 degrees of freedom, which runs on a tangent track at a constant speed. The tangent track is modeled as two elastic beams by discrete nonsymmetrical supporters modeling fastening systems, sleepers, and ballasts. The normal contact forces between wheels and rails are described by Hertzian elastic contact theory, and the tangential forces by the nonlinear creep theory of Shen et al. (Proceedings of the 8th IAVSD Symposium, Cambridge, MA, pp. 591–605). In the numerical analysis, the disabled rail fastening, rail pad, and ballast, on one and two sides of the track are, respectively, considered. Through a detailed analysis, derailment coefficients and the track state variations are obtained. The derailment coefficients are defined as the ratio of the lateral force to the vertical force of the wheel and rail (indicated by L∕V), duration of L∕V, and rate of the wheel load reduction (indicated by ΔV∕V), respectively. The variations of the contact points on the wheel treads, the track gauge, the track cross-level, and rail turnover angle are present in the paper. The numerical results obtained indicate that the failure of rail supports has a great influence on the vehicle running safety.

Modeling and Simulation of Rotated Dual-Plates Ball-Lapping

2010 ◽  
Vol 37-38 ◽  
pp. 679-683
Author(s):  
Ju Long Yuan ◽  
Yong Liang Hu ◽  
Bing Hai Lv ◽  
Qian Fa Deng ◽  
Xin Ma
Keyword(s):  
Surface Morphology ◽  
Removal Rate ◽  
Spherical Surface ◽  
Single Point ◽  
Spherical Shape ◽  
Contact Forces ◽  
Real Surface ◽  
Contact Points ◽  
Morphology Model ◽  
Shape Errors

Different spherical shape models of precision ball-lapping are presented and discussed in this paper. A selective analysis of spherical surface morphology model of rotated dual-plates (RDP) ball-lapping is presented. With combined shape errors of three contact points, the spherical surface morphology is more close to the real surface of precision ball. Simulations show that the spherical surface morphology model of RDP method can well express the shape errors of precision balls. The wear rate is easily obtainable as an empirical function of the contact forces, velocities and material properties of the surfaces in contact. The expansion of the net material removal rate gives the rate of the spherical harmonics. The modeling method can capture the change of single point in the process of lapping. Then the parameters, such as lapping speed, preload, and entry point orientation can be studied using this model in the subsequent research.

Modeling Two-Point Wheel/Rail Contacts Using Constraint and Elastic-Force Approaches

2002 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Khaled E. Zaazaa ◽  
Jose´ L. Escalona ◽  
Jalil R. Sany
Keyword(s):  
Contact Problem ◽  
Degrees Of Freedom ◽  
Point Contact ◽  
Elastic Force ◽  
Contact Forces ◽  
Force Model ◽  
Arc Length ◽  
Normal Contact ◽  
Contact Points ◽  
Constraint Approach

Two approaches are commonly used for solving the problem of wheel/rail contact in railroad dynamics. The first is the elastic approach in which the wheel is assumed to have six degrees of freedom with respect to the rail. The normal contact forces are defined using Hertz’s contact theory or in terms of assumed stiffness and damping coefficients. The second approach is the constraint approach in which nonlinear kinematic contact constraint equations are introduced, leading to a model in which the wheel has five degrees of freedom with respect to the rail. It is the objective of this investigation to present a new formulation for the wheel/rail contact problem based on the elastic force approach. Crucial to the success of any elastic force formulation for wheel/rail contact problem is the accurate prediction of the location of the contact points. To this end, features of multibody formulations that allow introducing arbitrary differential equations are exploited in this investigation in order to obtain a good estimate of the rail arc length traveled by the wheel set. In the formulation presented in this paper, four surface parameters are used to describe the wheel and the rail surfaces each with arbitrary geometry. In order to determine the location of the points of contact between the wheel and the rail, a first order differential equation for the rail arc length is introduced and is integrated simultaneously with the multibody equations of motion of the wheel/rail system. The method presented in this paper allows for multiple points of contact between the wheel and the rail by using an optimized search for all possible contact points. The normal contact forces are calculated and used with non-linear expressions for the creepages to determine the creep forces. The paper also discusses two different procedures for the analysis of the two-point contact in the wheel/rail interaction. Numerical results obtained using the elastic force model are presented and compared with the results obtained using the constraint approach.

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