A PIEZOELECTRIC CONTACT PROBLEM WITH SLIP DEPENDENT COEFFICIENT OF FRICTION

2004 ◽  
Vol 9 (3) ◽  
pp. 229-242 ◽  
Author(s):  
M. Sofonea
Keyword(s):  
Mathematical Model ◽  
Weak Solution ◽  
Contact Problem ◽  
Coefficient Of Friction ◽  
Dry Friction ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Coupled System ◽  
Piezoelectric Body ◽  
The Coefficient Of Friction

We consider a mathematical model which describes the static frictional contact between a piezoelectric body and an obstacle. The constitutive relation of the material is assumed to be electroelastic and involves a nonlinear elasticity operator. The contact is modelled with a version of Coulomb's law of dry friction in which the coefficient of friction depends on the slip. We derive a variational formulation for the model which is in form of a coupled system involving as unknowns the displacement field and the electric potential. Then we provide the existence of a weak solution to the model and, under a smallness assumption, we provide its uniqueness. The proof is based on a result obtained in [14] in the study of elliptic quasi‐variational inequalities.

A piezoelectric contact problem with slip dependent friction and damage

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Abderrezak Kasri
Keyword(s):  
Weak Solution ◽  
Contact Problem ◽  
Dry Friction ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Normal Compliance ◽  
Electrically Conductive ◽  
Coulomb’S Law ◽  
Electrical Condition ◽  
Coulomb's Law

Abstract The aim of this paper is to study a quasistatic contact problem between an electro-elastic viscoplastic body with damage and an electrically conductive foundation. The contact is modelled with an electrical condition, normal compliance and the associated version of Coulomb’s law of dry friction in which slip dependent friction is included. We derive a variational formulation for the model and, under a smallness assumption, we prove the existence and uniqueness of a weak solution.

A quasistatic frictional contact problem for viscoelastic materials with long memory

2020 ◽  
Vol 27 (2) ◽  
pp. 249-264
Author(s):  
Abderrezak Kasri ◽  
Arezki Touzaline
Keyword(s):  
Contact Problem ◽  
Coefficient Of Friction ◽  
Frictional Contact ◽  
Time Discretization ◽  
Contact Boundary ◽  
Long Term Memory ◽  
Viscoelastic Materials ◽  
Existence Of A Solution ◽  
Frictional Contact Problem ◽  
The Coefficient Of Friction

AbstractThe aim of this paper is to study a quasistatic frictional contact problem for viscoelastic materials with long-term memory. The contact boundary conditions are governed by Tresca’s law, involving a slip dependent coefficient of friction. We focus our attention on the weak solvability of the problem within the framework of variational inequalities. The existence of a solution is obtained under a smallness assumption on a normal stress prescribed on the contact surface and on the coefficient of friction. The proof is based on a time discretization method, compactness and lower semicontinuity arguments.

Weak solvability of a piezoelectric contact problem

2009 ◽  
Vol 20 (2) ◽  
pp. 145-167 ◽  
Author(s):  
STANISŁAW MIGÓRSKI ◽  
ANNA OCHAL ◽  
MIRCEA SOFONEA
Keyword(s):  
Mathematical Model ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Constitutive Law ◽  
Potential Fields ◽  
Material Behaviour ◽  
Abstract Result ◽  
Electrically Conductive ◽  
Piezoelectric Body ◽  
Weak Solvability

We consider a mathematical model which describes the frictional contact between a piezoelectric body and a foundation. The material behaviour is modelled with a non-linear electro-elastic constitutive law, the contact is bilateral, the process is static and the foundation is assumed to be electrically conductive. Both the friction law and the electrical conductivity condition on the contact surface are described with subdifferential boundary conditions. We derive a variational formulation of the problem which is of the form of a system of two coupled hemi-variational inequalities for the displacement and the electric potential fields, respectively. Then we prove the existence of a weak solution to the model and, under additional assumptions, its uniqueness. The proof is based on an abstract result on operator inclusions in Banach spaces.

scholarly journals Variational analysis for some frictional contact problems

2019 ◽  
Vol 38 (7) ◽  
pp. 21-36
Author(s):  
Leila Ait Kaki ◽  
M. Denche
Keyword(s):  
Weak Solution ◽  
Variational Inequalities ◽  
Variational Analysis ◽  
Frictional Contact ◽  
Coupled System ◽  
Contact Problems ◽  
Variational Problems ◽  
Unique Weak Solution ◽  
Piezoelectric Body ◽  
Evolutionary Variational Inequalities

We consider a class of evolutionary variational problems which describes the static frictional contact between a piezoelectric body and a conductive obstacle. The formulation is in a form of coupled system involving the displacement and electric potentiel fieelds. We provide the existence of unique weak solution of the problems. The proof is based on the evolutionary variational inequalities and Banach's xed point theorem.

Analysis of a sliding frictional contact problem with unilateral constraint

2016 ◽  
Vol 22 (3) ◽  
pp. 324-342 ◽  
Author(s):  
Mircea Sofonea ◽  
Yahyeh Souleiman
Keyword(s):  
Contact Problem ◽  
Dry Friction ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Convergence Result ◽  
Uniqueness Result ◽  
Unilateral Constraint ◽  
Penalization Method ◽  
Result Theorem ◽  
Equivalence Result

We consider a mathematical model that describes the equilibrium of an elastic body in frictional contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with unilateral constraint, associated with a sliding version of Coulomb’s law of dry friction. We present a description of the model, list the assumptions on the data and derive its primal variational formulation, in terms of displacement. Then we prove an existence and uniqueness result, Theorem 3.1. We proceed with a penalization method in the study of the contact problem for which we present a convergence result, Theorem 4.1. Finally, under additional hypotheses, we consider a variational formulation of the problem in terms of the stress, the so-called dual variational formulation, and prove an equivalence result, Theorem 5.3. The proofs of the theorems are based on arguments of monotonicity, compactness, convexity and lower semicontinuity.

Tribometer for Dry Friction Measurement

1999 ◽  
Author(s):  
Marc Brandl ◽  
Friedrich Pfeiffer
Keyword(s):  
Coefficient Of Friction ◽  
Dry Friction ◽  
Stribeck Curve ◽  
Body System ◽  
Friction Measurement ◽  
Detailed Model ◽  
The Coefficient Of Friction ◽  
Simulation Results ◽  
Multi Body

Abstract This paper deals with the measurement of dry friction. A tribometer was developed in order to identify both the sticking and the sliding coefficient of friction. The aim was to determine the so called Stribeck-curve of any material in contact. The design of the plant is presented. Avoiding errors in recalculating the coefficient of friction, a detailed model of the plant as a multi body system with motor feedback was generated. Advantages of the tribometer are shown in simulations. Some results of measurements in comparison with simulation results are presented.

The Influence of Surface Roughness on the Mechanism of Friction

1970 ◽  
Vol 92 (2) ◽  
pp. 264-272 ◽  
Author(s):  
T. Tsukizoe ◽  
T. Hisakado
Keyword(s):  
Surface Roughness ◽  
Metal Surface ◽  
Coefficient Of Friction ◽  
Dry Friction ◽  
Metal Surfaces ◽  
Roughness Effects ◽  
Real Area Of Contact ◽  
The Coefficient Of Friction ◽  
Tangential Forces ◽  
Soft Metal

A study was made of surface roughness effects on dry friction between two metals, assuming that the asperities are cones of the slopes which depend on the surface roughness. The theoretical explanations were offered for coefficients of friction of the hard cones and spheres ploughing along the soft metal surface. A comparison of calculated values based on these with experimental data shows good agreement. Moreover, theoretical discussion was carried out of surface roughness effects on dry friction between two metal surfaces on the basis of the analyses of the frictional mechanism for a hard slider on the metal surface. The theoretical estimation of the coefficient of friction between two metal surfaces can be carried out by using the relations between the surface roughness and the slopes of the asperities, and the coefficient of friction due to the adhesion at the interface. The experiments also showed that when two metal surfaces are first loaded normally and then subjected to gradually increasing tangential forces, real area of contact between them increases and the maximum tangential microslip of them increases with the increase of the surface roughness.

scholarly journals A Contact Characteristic of Roller Bearing with Palm Oil-based Grease Lubrication

2021 ◽  
Vol 89 (2) ◽  
pp. 139-149
Author(s):  
Yap Jun Heng ◽  
Nurul Farhana Mohd Yusof ◽  
Lee Ann Yen ◽  
Shazlina Abd Hamid ◽  
Nurul Nadzirah Mohd Yusof
Keyword(s):  
Finite Element ◽  
Coefficient Of Friction ◽  
Palm Oil ◽  
Frictional Contact ◽  
Roller Bearing ◽  
Rolling Contact ◽  
Von Mises Stress ◽  
The Coefficient Of Friction ◽  
Contact Characteristic ◽  
Von Mises

Grease lubricants are widely used in rolling contact applications to reduce friction between two rolling surfaces. Improper lubrication may cause high contact stress and deformation to the bearings and lead to machine failure The purpose of this study is to investigate the coefficient of friction produced by newly developed palm oil-based grease and to investigate the contact characteristics in lubricated roller bearings. In this work, the coefficient of friction of new greases was evaluated experimentally and the values were compared with the conventional mineral oil-based grease to investigate the friction performance. The friction test was performed using a four-ball tester. The finite element model was developed based on the roller bearing geometry and the simulation was carried out the evaluate the contact characteristic. The experimental result shows that the palm oil grease formulation A had the least coefficient of friction, followed by palm oil grease formulation B, mineral grease and food grade grease. This indicates that palm oil-based grease has the potential to be applied in rolling contact applications due to low friction characteristics. Finite element analysis shows that the maximum von Mises stress and total deformation for frictional contact are higher than the frictionless contact. For the frictional contact analysis with various lubricant COF, similar values were obtained with von Mises stress at 400.69 MPa and 3.4033×10-4 mm deformation. The finding shows that the small difference in grease COF did not affect the rolling contact. The finding also shows that the newly developed biodegradable grease has a similar performance in terms of rolling contact friction and contact characteristic in a condition that the bearing is operating in normal condition.

An Empirical Approach to Modeling the Friction Coefficient for Wheel-Rail Contact

2009 ◽  
Author(s):  
HyunWook Lee ◽  
Corina Sandu ◽  
Carvel Holton ◽  
Mehdi Ahmadian
Keyword(s):  
Friction Coefficient ◽  
Coefficient Of Friction ◽  
Dry Friction ◽  
Damping Ratio ◽  
Contact Dynamics ◽  
Nonlinear Dependence ◽  
Accurate Estimation ◽  
Highly Nonlinear ◽  
The Coefficient Of Friction ◽  
Wheel Vibration

The coefficient of friction (CoF) is one of the most important parameters for the contact between the wheel and the rail. Accurate estimation or measurement of the CoF has a very important role, both in terms of modeling the train dynamics and in terms of reducing operational costs in the long-term. For ease of implementation, since the nature of the wheel-rail contact dynamics is very complex, the assumption of a constant CoF is still used in most theoretical studies. Nevertheless, experimental work indicates that the CoF depends on dynamic changes in various wheel-rail conditions, like sliding velocity, contact patch shape and size for stick and sliding region, wheel and rail geometry, wheel vibration, rail surface roughness and/or lubrication, etc. In this paper we present the proposed equation to model the nonlinear dry friction coefficient at the wheel-rail contact. The friction coefficient is calculated at the three different values for change in the damping ratio while maintaining all the other conditions the same. As expected, the analysis performed to estimate the dry friction coefficient based on the proposed equation and using NUCARS® simulation results shows that the coefficient of friction has a highly nonlinear dependence on its parameters.

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