Approximation and numerical realization of 3D contact problems with given friction and a coefficient of friction depending on the solution

The paper presents the analysis, approximation and numerical realization of 3D contact problems for an elastic body unilaterally supported by a rigid half space taking into account friction on the common surface. Friction obeys the simplest Tresca model (a slip bound is given a priori) but with a coefficient of friction $ \mathcal{F} $ \mathcal{F} which depends on a solution. It is shown that a solution exists for a large class of $ \mathcal{F} $ \mathcal{F} and is unique provided that $ \mathcal{F} $ \mathcal{F} is Lipschitz continuous with a sufficiently small modulus of the Lipschitz continuity. The problem is discretized by finite elements, and convergence of discrete solutions is established. Finally, methods for numerical realization are described and several model examples illustrate the efficiency of the proposed approach.     

Experimental and numerical analysis of self-excited friction oscillator

A self-excited friction oscillator has been designed and manufactured to carry out experimental analysis of dry friction phenomenon. A mathematical model of this oscillator has been formulated. The influence of the different types of classical friction characteristics on the dynamical behaviour of the model is investigated by way of numerical analysis. A comparison with dynamics of real oscillator is presented and some reasons of observed differences are explained. A particular analysis of experimental data leads to the confirmation of non-reversible friction characteristics and allows to formulate a hypothesis that a course of such characteristics also depends on value (not only on the sign) of acceleration.     

Signorini problem with a solution dependent coefficient of friction (model with given friction): approximation and numerical realization

Contact problems with given friction and the coefficient of friction depending on their solutions are studied. We prove the existence of at least one solution; uniqueness is obtained under additional assumptions on the coefficient of friction. The method of successive approximations combined with the dual formulation of each iterative step is used for numerical realization. Numerical results of model examples are shown.This research was supported under the grant No. 101/01/0538 of the Grant Agency of the Czech Republic, by the projects CEZ:J17/98:272401 and MSM 113200007 of the Ministry of Education od the Czech Republic.This revised version was published online in April 2005 with a corrected missing date string.     

Plastic mechanical analysis of drawing force based on a twin elliptical die

According to the stream function requirement, a twin elliptical die for rod or wire drawing is designed, and the subsequent plastic mechanical analysis is carried out. In terms of the volume constant condition, a kinematically admissible velocity field describing the drawing process is constructed. Based on the velocity field, the analytical expression of internal plastic deformation energy rate accounting for the non-zero shear strain rate is obtained by using the mean value theorem of integral. Then, the analytical expression of friction energy rate is also derived by the mean value theorem of integral. Ultimately, the analytical expression of the drawing force is obtained based on the upper bound method. It is found that there exists the optimal die semi-angle which depends on the relative reduction and friction factor. The analytical drawing force based on the twin elliptical die is validated by the corresponding simulated results, and a very agreement is found since the relative errors between them are less than 9.2%.     

The influence of coriolis force on MHD waves

The influence of coriolis force on the propagation of MHD waves in compressible medium is investigated by using linear stability analysis. In a combined effect we find that, while compressibility gives rise to an acoustic wave, coriolis force results in a modified Alfvén wave.     

Temperature dependence of the coefficient of friction of Ftorlon-graphite fiber

The reduced friction of Ftorlon (fluoroplastic) — graphite fiber against steel on the temperature interval 120–190°C is examined.Khmel'nitskii Technological Institute of Maintenance and Repairs. Translated from Mekhanika Polimerov, No. 6, pp. 1120–1121, November–December, 1973.     

The influence of friction forces on the dynamics of a two-link mobile robot

Controlled periodic motions of a planar two-link robot in a horizontal plane when there is dry friction are considered. The two-link is controlled by means of an internal torque applied to the joint connecting the links. The dynamics of the two-link, taking into account the influence of friction forces and the constrained nature of the control torque, is analysed assuming that the angle between the links is small. The conventional locomotion algorithm of a two-link is modified to ensure rectilinear displacement of the two-link. The influence of various geometrical and mechanical parameters of the system on the average rate of locomotion and on the power consumption during the motion of the two-link robot in a plane is investigated.     

Method of determining the coefficient of friction of polymer monofilaments

An instrument for determining the coefficient of friction of technical polymer monofilaments (100 µ or more in diameter) under various conditions is described and the experimental procedure is explained.Gubkin Moscow Institute of the Petrochemical and Gas Industry. Translated from Mekhanika Polimerov, No. 4, pp. 729–731, July–August, 1971.     

Variational and numerical analysis of a quasistatic viscoelastic contact problem with normal compliance and friction

In this paper, a class of generalized evolution variational inequalities arising in quasistatic friction contact problem for viscoelastic materials is introduced and studied. Under some suitable assumptions, we obtain an existence and uniqueness theorem of the solution for the generalized evolution variational inequalities by using Banach’s fixed point theorem. Moreover, we study two numerical approximation schemes of the problem: semidiscrete scheme and fully discrete scheme. For both schemes, we prove the existence of the solution and derive the error estimations.     

The influence of the externaldc magnetic field on the amplitude dependence of ferromagnetic internal friction

Zusammenfassung Messungen der inneren Reibung eines Drahtes, durch Elektrolyse mit einer dünnen Nickelschicht bedeckt, ziegen, dass die Abhängigkeit des ferromagnetischen Anteils der inneren Reibung ein Maximum besitzt. Das Anwachsen der Intensität des direkten longitudinalen magnetischen Feldes bewirkt zuerst ein. Anwachsen und dann eine Abnahme dieses Maximums. Die Schlussfolgerungen, die wir durch statische Betrachtung der Bloch-Wände erhielten, stimmen mit den Versuchsergebnissen überein.     

A numerical analysis of two point boundary value problem algorithms

The mathematical modeling of optimal control system problems is a method applied in industry to obtain correct electrical and mechanical design parameters once the system equations have been derived. The algorithms required to implement the control loop for these applications must provide stable, relatively accurate, efficient solutions.The purpose of this paper is to address the computational characteristics which would concern a system designer in the consideration of the selection of an effective algorithm to implement a two-point boundary value problem solution. Three Invariant Imbedding Algorithms are evaluated for a worst case and a best case problem by an adaptation of four methods of analysis. The areas of computer science, numerical analysis and Turing Machine Theory are drawn upon in these methods to implement and compare the computational form of the algorithms. The four analysis techniques indicated consistent results for the three two-point boundary value problem algorithms considered. Applications of two-point boundary value problem algorithms occur in problems of nuclear reactor heat transfer, pollution control, fluidics, vibration and magnetics.     

Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance,friction and damage

We consider a model for quasistatic frictional contact between a viscoelastic body and a foundation. The material constitutive relation is assumed to be nonlinear. The mechanical damage of the material, caused by excessive stress or strain, is described by the damage function, the evolution of which is determined by a parabolic inclusion. The contact is modeled with the normal compliance condition and the associated version of Coulomb's law of dry friction. We derive a variational formulation for the problem and prove the existence of its unique weak solution. We then study a fully discrete scheme for the numerical solutions of the problem and obtain error estimates on the approximate solutions.     

The numerical analysis and experimental researches of influence of triangular asperity's outline deviations after turning on the burnished product's technological quality

The paper concerns determination dependence of preparing inaccuracy surface after previous treatment on the state and properties of burnished article's surface layer (SL). The researches were realized in two stages. In the first one numerical analysis were made, and in the second one experimental verification of receiving results. The application in ANSYS was elaborated. It makes possible to analyze the influence of outline deviations of triangular asperity after turning on the surface roughness and the state of strains and stresses in SL after burnishing rolling. The variables in calculations are: height deviation of triangular asperity after turning Δh_t = 0.01 ÷ 0.04 [mm], and its distance deviation Δs_t = 0.05 ÷ 0.2 [mm] as well as the depth of burnishing a = 0.03 ÷ 0.39 [mm]. The results of experimental researches and numerical analysis cover in 5% confidence interval. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The influence of isolated largest eigenvalues on the numerical convergence of the CG method

This paper considers the dependence of the convergence history of the CG method on the largest eigenvalues of a symmetric positive-definite matrix. It is demonstrated that, in solving ill-conditioned linear systems, the reproduction of largest eigenvalues can be so intensive that they cannot be treated as isolated. On the other hand, from the moment the smallest isolated eigenvalues start to govern the numerical convergence of the CG method, the convergence is mainly influenced by the smallest Ritz values. Bibliography: 2 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 248, 1998, pp. 5–16. Translated by A. Yu. Yeremin.     

Mathematical modelling,analysis and numerical simulations for the influence of heat shock proteins on tumour invasion

Invasion is a key property of tumour cells for building metastasis. A class of functionally related proteins called heat shock proteins (HSPs), the expression of which is increased when cells are exposed to elevated temperatures or other stress, play an important role in the invasion. In this paper we develop a mathematical model focusing on the effect of HSPs on the tumour cell migration. The resulting multiscale setting accounts both for the microscopic, intracellular level on which these proteins are acting and for the macroscopic level of the cell population. We prove the local existence of a unique positive solution and perform numerical simulations in order to illustrate the behaviour of cancer cells w.r.t. the fibre density of the tissue and the matrix degrading enzymes, along with the effect of HSPs.     

Determination of a stochastic friction coefficient depending on a randomly rough surface

The goal of this contribution is to calculate the the friction coefficient for a scanned surface of a worn brake pad. The data shows that the asperities can be approximated by paraboloids which allows to calculate the contact force and area with the Hertz contact model if the deformation is elastic. The friction force is calculated with the Bowden-Tabor approach which suggests that the friction force is the force to shear apart contacting asperities. This is considered to be the dominant friction cause in dry contact. To generate many surfaces with similar peak statistics the spectral decomposition is used. The friction coefficient and it's stochastic properties is calculated for these surfaces. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)