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.

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.

Three-Dimensional Wear Prediction of Four-Degrees-of-Freedom Parallel Mechanism With Clearance Spherical Joint and Flexible Moving Platform

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Gengxiang Wang ◽  
Hongzhao Liu
Keyword(s):  
Contact Force ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Contact Forces ◽  
Force Model ◽  
Spherical Joint ◽  
Normal Contact ◽  
Tangential Contact ◽  
Moving Platform

Three-dimensional (3D) wear of the clearance spherical joint in four-degrees-of-freedom (DOF) parallel mechanism is predicted based on Archard's wear model. The flexible moving platform is treated as thin plate element based on absolute nodal coordinate formulation (ANCF). The tangent frame is introduced to formulate the constraint equation of universal joint. One of the spherical joints is treated as clearance joint. The normal and tangential contact forces are calculated based on Flores contact force model and modified Coulomb friction model. In order to predict 3D wear, the normal contact force, tangential contact velocity, and eccentricity vector are decomposed in the global coordinate system. Simulation results show that 3D wear occurred in three directions are not uniform each other.

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.

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.

scholarly journals Chaos phenomenon and stability analysis of RU-RPR parallel mechanism with clearance and friction

2018 ◽  
Vol 10 (1) ◽  
pp. 168781401774625 ◽  
Author(s):  
Yulei Hou ◽  
Yi Wang ◽  
Guoning Jing ◽  
Yunjiao Deng ◽  
Daxing Zeng ◽  
...  
Keyword(s):  
Friction Coefficient ◽  
Contact Force ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Force Model ◽  
Obvious Effect ◽  
Normal Contact ◽  
Rotational Degrees Of Freedom ◽  
The Stability ◽  
Baumgarte Stabilization

The chaos phenomenon often exists in the dynamics system of the mechanism with clearance and friction, which has obvious effect on the stability of the mechanism, then it is worthy of attention for identifying the relationship between the friction coefficient and the stability of the mechanism. Two rotational degrees of freedom decoupled parallel mechanism RU-RPR is taken as the research object. Considering the clearance existing in the revolute pair, Lankarani–Nikravesh contact force model is used to calculate the normal contact force, and the Coulomb friction force model is used to calculate the tangential contact force. The dynamics model is established using Newton–Euler equations, and the Baumgarte stabilization method is used to keep the stability of the numerical analysis. Then, the equations are solved using the fourth adaptive Runge–Kutta method, and the effect of the revolute pair’s clearance on the dynamic behavior is analyzed. Poincare mapping is plotted, and the bifurcation diagrams are analyzed with varying the friction coefficient corresponding to different values of clearance size. The research contents possess a certain theoretical guidance significance and practical application value on the analysis of the chaotic motion and its stability in the dynamics of the parallel mechanism.

Foundation for Virtual Prototyping of Mechanical Power Management Functions in Actuators

2018 ◽  
Author(s):  
Jean-Charles Mare ◽  
Silvio Akitani
Keyword(s):  
Power Management ◽  
Virtual Prototyping ◽  
Contact Forces ◽  
Mechanical Power ◽  
System Level ◽  
Special Focus ◽  
Force Model ◽  
Electromechanical Actuators ◽  
Normal Contact ◽  
Management Functions

Beside the main functions related to the control and transformation of power, safety-critical electromechanical actuators require many additional functions for power routing, protection and limitation. In practice, these functions are implemented mechanically because their realization at motor drive level is not acceptable for performance and reliability reasons. Contact forces play a major role in these mechanical devices (e.g. endstop, lock, brake, torque limiter, etc.), being either functional to serve the need, or parasitic due to their alteration of performance. The virtual prototyping of such mechanical power management functions therefore requires normal and tangent forces to be modelled with the right level of realism and reduced complexity. This communication provides some proposals to be used as foundation for the system-level modelling and simulation of these types of mechanical power elements that can be found in electromechanical actuators. Special focus is given to the model architecting, decomposition and block-diagram implementation, using the example of normal contact forces. The illustrative example concerns an integrated landing gear extension/retraction electromechanical actuator which embeds free-fall and autolock features. It shows how a well implemented single model (e.g. generic normal contact force model) combined with a right model decomposition can meet various modelling needs (e.g. droppable end-stop, lock and shearable axial stop). The proposed models are made compatible for integration in a 2x1D mechanical model architecture (axial and rotational motion) developed by the authors in previous reported work.

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.

scholarly journals Modelling elastic structures with strong nonlinearities with application to stick–slip friction

2014 ◽  
Vol 470 (2161) ◽  
pp. 20130593 ◽  
Author(s):  
Robert Szalai
Keyword(s):  
Point Contact ◽  
Linear Structure ◽  
Transformation Method ◽  
Friction Model ◽  
Contact Forces ◽  
Stick Slip ◽  
Lipschitz Continuous ◽  
Contact Points ◽  
Dimensional Equation ◽  
Low Dimensional

An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low-dimensional equation with memory. The method is general and well suited to problems with isolated discontinuities such as friction and impact at point contact. It is assumed that the structure is composed of two parts: a continuum but linear structure and finitely many discrete but strong nonlinearities acting at various contact points of the elastic structure. The localized nonlinearities include discontinuities, e.g. the Coulomb friction law. Despite the discontinuities in the model, we demonstrate that contact forces are Lipschitz continuous in time at the onset of sticking for certain classes of structures. The general formalism is illustrated for a continuum elastic body coupled to a Coulomb-like friction model.

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.

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