scholarly journals Simple algorithms for solving steady-state frictional rolling contact problems in two and three dimensions

2013 ◽  
Vol 50 (6) ◽  
pp. 843-852 ◽  
Author(s):  
Gérard-Philippe Zéhil ◽  
Henri P. Gavin
Keyword(s):  
Steady State ◽  
Contact Problems ◽  
Rolling Contact ◽  
Three Dimensions

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.

High-Frequency Contact Mechanics: The Derivation of Frequency-Dependent Creep Coefficient

1984 ◽  
Vol 198 (3) ◽  
pp. 167-173 ◽  
Author(s):  
K Knothe ◽  
A Gross-Thebing
Keyword(s):  
Steady State ◽  
Approximate Method ◽  
Contact Mechanics ◽  
High Frequency ◽  
Contact Problems ◽  
Rolling Contact ◽  
High Frequency Range ◽  
Frequency Range ◽  
Creep Coefficient ◽  
State Case

Kalker's creep coefficients for linear rolling contact problems are only valid in the steady state case. An approximate method for the extension of linear contact mechanics into the high-frequency range is presented

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.

scholarly journals The Indentation Rolling Resistance in Belt Conveyors: A Model for the Viscoelastic Friction

Lubricants ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 58 ◽  
Author(s):  
Nicola Menga ◽  
Francesco Bottiglione ◽  
Giuseppe Carbone
Keyword(s):  
Contact Problem ◽  
Finite Thickness ◽  
Numerical Procedure ◽  
Contact Problems ◽  
Accurate Solution ◽  
Rolling Contact ◽  
Viscoelastic Layer ◽  
Force Coefficient ◽  
Belt Conveyors ◽  
Energy Dissipated

In this paper, we study the steady-state rolling contact of a linear viscoelastic layer of finite thickness and a rigid indenter made of a periodic array of equally spaced rigid cylinders. The viscoelastic contact model is derived by means of Green’s function approach, which allows solving the contact problem with the sliding velocity as a control parameter. The contact problem is solved by means of an accurate numerical procedure developed for general two-dimensional contact geometries. The effect of geometrical quantities (layer thickness, cylinders radii, and cylinders spacing), material properties (viscoelastic moduli, relaxation time) and operative conditions (load, velocity) are all investigated. Physical quantities typical of contact problems (contact areas, deformed profiles, etc.) are calculated and discussed. Special emphasis is dedicated to the viscoelastic friction force coefficient and to the energy dissipated per unit time. The discussion is focused on the role played by the deformation localized at the contact spots and the one in the bulk of the thin layer, due to layer bending. The model is proposed as an accurate solution for engineering applications such as belt conveyors, in which the energy dissipated on the rolling contact of idle rollers can, in some cases, be by far the most important contribution to their energy consumption.

Non-symmetric flow in Laval type nozzles

1972 ◽  
Vol 273 (1232) ◽  
pp. 185-235 ◽  
Keyword(s):  
Steady State ◽  
Combustion Chamber ◽  
Method Of Characteristics ◽  
Three Dimensions ◽  
Symmetric Flow ◽  
Gaseous Flow ◽  
The Method Of Characteristics ◽  
Lateral Forces

The equations of the steady state, compressible inviscid gaseous flow are linearized in a form suitable for application to nozzles of the Laval type. The procedure in the supersonic phase is verified by comparing solutions so obtained with those derived by the method of characteristics in two and three dimensions. Likewise, the solutions in the transonic phase are com pared with those obtained by other investigators. The linearized equation is then used to investigate the nat re of non-symmetric flow in rocket nozzles. It is found that if the flow from the combustion chamber into the nozzle is non-symmetric, the magnitude and direction of the turning couple produced by the emergent jet is dependent on the profile of the nozzle and it is possible to design profiles such that the turning couples or lateral forces are zero. The optimum nozzle so designed is independent of the pressure and also of the magnitude of the non-symmetry of the entry flow. The formulae by which they are obtained have been checked by extensive static and projection tests with simulated rocket test vehicles which are described in this paper.

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