Analysis of Steady-State Rolling Contact Problems in Nonlinear Viscoelastic Materials

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Alaa A. Abdelrahman ◽  
Ahmed G. El-Shafei ◽  
Fatin F. Mahmoud
Keyword(s):  
Steady State ◽  
Contact Problems ◽  
Rolling Contact ◽  
Coulomb’S Friction ◽  
Nonlinear Viscoelastic ◽  
Lagrangian Finite Element ◽  
History Of ◽  
Steady State Rolling ◽  
Incremental Form ◽  
Contact Response

A comprehensive numerical model is developed using Lagrangian finite element (FE) formulation for investigating the steady-state viscoelastic (VE) rolling contact response. Schapery's nonlinear viscoelastic (NVE) model is adopted to simulate the VE behavior. The model accounts for large displacements and rotations. A spatially dependent incremental form of the VE constitutive equations is derived. The dependence on the history of the strain rate is expressed in terms of the spatial variation of the strain. The Lagrange multiplier approach is employed. The classical Coulomb's friction law is used. The developed model is verified and its applicability is demonstrated.

Analysis of steady-state frictional rolling contact problems in Schapery–nonlinear viscoelasticity

2018 ◽  
Vol 233 (6) ◽  
pp. 911-926 ◽  
Author(s):  
Alaa A Abdelrahman ◽  
Ahmed G El-Shafei ◽  
Fatin F Mahmoud
Keyword(s):  
Steady State ◽  
Mechanical Response ◽  
Past History ◽  
Rotational Velocity ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Contact Problems ◽  
Rolling Contact ◽  
Nonlinear Viscoelastic ◽  
Steady State Rolling

In the context of an updated Lagrangian formulation, a computational model is developed for analyzing the steady-state frictional rolling contact problems in nonlinear viscoelastic solids. Schapery's nonlinear viscoelastic model is adopted to simulate the viscoelastic behavior. In addition to the material nonlinearity, the model accounts for geometrical nonlinearities, large displacements, and rotations with small strains. To satisfy the steady-state rolling contact condition, a spatially dependent incremental form of the viscoelastic constitutive equations is derived. Consequently, the dependence on the past history of the strain rate in the stress–strain law is expressed in terms of the spatial variation of the strain. The contact conditions are exactly satisfied by employing the Lagrange multiplier approach to enforce the contact constraints. The classical Coulomb's friction law is used to simulate friction. The developed model is verified and compared and good agreement is obtained. The applicability of the developed model is demonstrated by analyzing the steady-state rolling contact response of viscoelastically walled-wheel over rigid foundation. Moreover, the obtained results show remarkable effects of the rotational velocity and the viscoelastic material parameters on the mechanical response of steady-state frictional rolling contact.

NONLINEAR ANALYSIS OF VISCOELASTICALLY LAYERED ROLLS IN STEADY STATE ROLLING CONTACT

2014 ◽  
Vol 06 (06) ◽  
pp. 1450065 ◽  
Author(s):  
ALAA A. ABDEL RAHMAN ◽  
AHMED G. EL-SHAFEI ◽  
FATIN F. MAHMOUD
Keyword(s):  
Steady State ◽  
Viscoelastic Behavior ◽  
Rolling Contact ◽  
Creep Model ◽  
Viscoelastic Layer ◽  
Element Formulation ◽  
Equilibrium Equations ◽  
Lagrangian Finite Element ◽  
Steady State Rolling ◽  
Updated Lagrangian

The present paper analyzes the steady state rolling contact (SSRC) response of nonlinear viscoelastically layered rigid roll indented by a rigid cylindrical indenter. Both material and geometrical nonlinearities are accounted for in the framework of the updated Lagrangian finite element formulation. The Schapery's viscoelastic creep model is adopted to model the viscoelastic behavior. To accommodate the steady state rolling condition, the constitutive equations are recast into a spatially dependent incremental form. Throughout the contact interface, the Lagrange multiplier method is used to enforce the contact constraints, while the classical Coulomb's law is adopted to simulate friction. The resulting nonlinear equilibrium equations are solved by the Newton–Raphson method. The developed model is applied to analyze a viscoelastically layered rigid roll in steady state rolling and intended by a rigid cylindrical indenter. Results showed the distinct effects of angular velocity, retardation time, indenter radius, and viscoelastic layer thickness on the SSRC configuration.

A Consistent Implementation of Inelastic Material Models into Steady State Rolling

2016 ◽  
Vol 44 (3) ◽  
pp. 174-190 ◽  
Author(s):  
Mario A. Garcia ◽  
Michael Kaliske ◽  
Jin Wang ◽  
Grama Bhashyam
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Viscoelastic Material ◽  
Rolling Contact ◽  
Arbitrary Lagrangian Eulerian ◽  
Ale Formulation ◽  
Inelastic Material ◽  
Material Formulation ◽  
Steady State Rolling ◽  
Efficient Alternative

ABSTRACT Rolling contact is an important aspect in tire design, and reliable numerical simulations are required in order to improve the tire layout, performance, and safety. This includes the consideration of as many significant characteristics of the materials as possible. An example is found in the nonlinear and inelastic properties of the rubber compounds. For numerical simulations of tires, steady state rolling is an efficient alternative to standard transient analyses, and this work makes use of an Arbitrary Lagrangian Eulerian (ALE) formulation for the computation of the inertia contribution. Since the reference configuration is neither attached to the material nor fixed in space, handling history variables of inelastic materials becomes a complex task. A standard viscoelastic material approach is implemented. In the inelastic steady state rolling case, one location in the cross-section depends on all material locations on its circumferential ring. A consistent linearization is formulated taking into account the contribution of all finite elements connected in the hoop direction. As an outcome of this approach, the number of nonzero values in the general stiffness matrix increases, producing a more populated matrix that has to be solved. This implementation is done in the commercial finite element code ANSYS. Numerical results confirm the reliability and capabilities of the linearization for the steady state viscoelastic material formulation. A discussion on the results obtained, important remarks, and an outlook on further research conclude this work.

Prediction of Tire Tread Wear with FEM Steady State Rolling Contact Simulation

2003 ◽  
Vol 31 (3) ◽  
pp. 189-202 ◽  
Author(s):  
D. Zheng
Keyword(s):  
Weight Loss ◽  
Steady State ◽  
Cross Section ◽  
Rolling Contact ◽  
Dynamic Simulations ◽  
Element Analysis ◽  
Vehicle Acceleration ◽  
Steady State Rolling ◽  
Driving Conditions ◽  
Rate Profile

Abstract A procedure based on steady state rolling contact Finite Element Analysis (FEM) has been developed to predict tire cross section tread wear profile under specified vehicle driving conditions. This procedure not only considers the tire construction effects, it also includes the effects of materials, vehicle setup, test course, and driver's driving style. In this algorithm, the vehicle driving conditions are represented by the vehicle acceleration histogram. Vehicle dynamic simulations are done to transform the acceleration histogram into tire loading condition distributions for each tire position. Tire weight loss rates for different vehicle accelerations are generated based on a steady state rolling contact simulation algorithm. Combining the weight loss rate and the vehicle acceleration histogram, nine typical tire loading conditions are chosen with different weight factors to represent tire usage conditions. It is discovered that the tire tread wear rate profile is changing continuously as the tire is worn. Simulation of a new tire alone cannot be used to predict the tire cross-section tread wear profile. For this reason, an incremental tread wear simulation procedure is performed to predict the tire cross section tread wear profile. Compared with actual tire cross-section tread wear profiles, good results are obtained from the simulations.

A Re-Examination of the Proneness to Derailment of a Railway Wheel-Set

1976 ◽  
Vol 18 (3) ◽  
pp. 131-141 ◽  
Author(s):  
A. O. Gilchrist ◽  
B. V. Brickle
Keyword(s):  
Decision Making ◽  
Steady State ◽  
Tangential Force ◽  
Rolling Contact ◽  
Contact Theory ◽  
Classical Formula ◽  
Parameter Region ◽  
Railway Wheel ◽  
Recent Developments ◽  
Steady State Rolling

The circumstances giving rise to the incipient derailment of a railway wheel-set under steady-state rolling conditions are re-examined in the light of recent developments in rolling-contact theory. It is found that the problem can be stated in a form which avoids difficulties inherent in most earlier treatments. However, a quantitative solution requires data relating tangential force to creepage and spin in a parameter region previously unexplored. New experimental results are presented which partially correct this lack of data, but more work, both theoretical and experimental, is required. One outcome of the new study is the establishment of the region of applicability of Nadal's classical formula. It shows it to be highly relevant for practical decision-making.

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