Analytical Models for the Deformation and Adhesion Components of Rubber Friction

1978 ◽  
Vol 6 (1) ◽  
pp. 3-47 ◽  
Author(s):  
R. A. Schapery
Keyword(s):  
Friction Coefficient ◽  
Solution Method ◽  
Complex Modulus ◽  
Contact Problems ◽  
Analytical Models ◽  
Exact Results ◽  
Fourier Methods ◽  
Rubber Friction ◽  
Linear Viscoelastic ◽  
Deformation Component

Abstract Fourier methods of analysis are employed to develop linear viscoelastic stress and displacement solutions for use in contact problems, and then some exact results for contact area and the deformation component of the friction coefficient are derived for materials whose complex modulus obeys a power law in frequency. A model for predicting waves of detachment resulting from adhesion is proposed, and it is shown that an analogy exists whereby the solution method for sliding without adhesion can be used to predict these waves and the resulting frictional force.

Estimation of Contact Stiffness and its Role in the Design of a Friction Damper

2001 ◽  
Author(s):  
J. Szwedowicz ◽  
M. Kissel ◽  
B. Ravindra ◽  
R. Kellerer
Keyword(s):  
Finite Element ◽  
Friction Coefficient ◽  
Contact Stiffness ◽  
Contact Problems ◽  
Analytical Models ◽  
Rational Approach ◽  
Friction Damper ◽  
Friction Dampers ◽  
Performance Curves ◽  
Damper Design

The use of under-platform friction dampers is a common practice for the elimination of high cycle fatigue failures of turbomachinery blading. Damper performance curves and damper optimization curves are used for the design of friction dampers. It is establishedAAfrom the previous work that apart from damper mass, the contact stiffness between damper and the blade platform is an important parameter in achieving a good damper design. Several methods for the estimation of damper stiffness have been proposed in the literature. Some of them include: 1. Curve fitting approach to a measured frequency response function, 2. Compliance measurement, 3. Measurement of hysteresis loop etc. However, it is not possible to carry out extensive sets of experiments to observe the influence of various parameters on the contact stiffness. Numerical and/or analytical models for contact stiffness evaluation are the present needs for a damper designer. This paper addresses a detailed investigation of the contact stiffness computation. Finite element modeling of the damper and the platform is carried out to study the effect of various parameters such as friction coefficient, centrifugal load, material properties etc. on the contact stiffness. The role of surface roughness and wear are neglected in the present analysis. The reliability of the applied finite element meshes is verified by simulating Hertz’s contact problems. The parametric study indicates that the contact stiffness builds up with increase in friction coefficient, centrifugal force and elastic modulus of the damper material. The results received from a pilot experiment are also presented for further evaluation of the computed results. Finally, a very good agreement between the numerical and experimental performance curves (resonance response amplitude of the blade versus excitation amplitude for the constant damper mass; Cameron et. al, 1987) of the blade with the damper is found for the tangential contact stiffness obtained from the finite element calculation. The present work extends the quest for a rational approach to damper design.

A Quantitative Theory for the Computation of Tire Friction Under Severe Conditions of Sliding

1986 ◽  
Vol 14 (1) ◽  
pp. 44-72 ◽  
Author(s):  
C. M. Mc C. Ettles
Keyword(s):  
Friction Coefficient ◽  
Flash Temperature ◽  
Contact Conditions ◽  
Quantitative Form ◽  
Heating Effects ◽  
Rubber Friction ◽  
Viscoelastic Effects ◽  
Tire Friction ◽  
Pavement Friction ◽  
Metal Polymer

Abstract It is proposed that tire-pavement friction is controlled by thermal rather than by hysteresis and viscoelastic effects. A numerical model of heating effects in sliding is described in which the friction coefficient emerges as a dependent variable. The overall results of the model can be expressed in a closed form using Blok's flash temperature theory. This allows the factors controlling rubber friction to be recognized directly. The model can be applied in quantitative form to metal-polymer-ice contacts. Several examples of correlation are given. The difficulties of characterizing the contact conditions in tire-pavement friction reduce the model to qualitative form. Each of the governing parameters is examined in detail. The attainment of higher friction by small, discrete particles of aluminum filler is discussed.

scholarly journals Solution of Contact Problems for Nonlinear Gao Beam and Obstacle

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
J. Machalová ◽  
H. Netuka
Keyword(s):  
Solution Method ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Contact Problems ◽  
Beam Model ◽  
Contact Conditions ◽  
Beam Elements ◽  
Solution Methods ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model

Contact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler’s type in some distance under the beam. The problem is static without a friction and modeled either using Signorini conditions or by means of normal compliance contact conditions. The problems are then reformulated as optimal control problems which is useful both for theoretical aspects and for solution methods. Discretization is based on using the mixed finite element method with independent discretization and interpolations for foundation and beam elements. Numerical examples demonstrate usefulness of the presented solution method. Results for the nonlinear Gao beam are compared with results for the classical Euler-Bernoulli beam model.

scholarly journals Rheological and tribological approaches as a tool for the development of sustainable lubricating greases based on nano-montmorillonite and castor oil

Friction ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 415-428
Author(s):  
José Enrique Martín-Alfonso ◽  
María José Martín-Alfonso ◽  
Concepción Valencia ◽  
María Teresa Cuberes
Keyword(s):  
Atomic Force Microscopy ◽  
Friction Coefficient ◽  
Tribological Properties ◽  
Castor Oil ◽  
Force Microscopy ◽  
Oil Blends ◽  
Atomic Force ◽  
Linear Viscoelastic ◽  
Nanoclay Content ◽  
Petrochemicals Industry

AbstractThis study investigates the development of novel montmorillonite/castor oil blends to formulate sustainable lubricating greases to promote the replacement of petrochemicals industry-derived materials by substances obtained from renewable sources. Specifically, the effect of the thickener concentration on the rheological, chemical, thermal, tribological properties, and atomic force microscopy (AFM) microstructure of these systems were studied. The results showed that the C20A nanoclay content could be used to modulate the viscosity values, the linear viscoelastic functions, and tribological properties of these montmorillonite dispersions. In general, these gel-like dispersions exhibited remarkable lubricant properties; the samples showed values of the friction coefficient and wear scars similar or lower than those obtained with model bentonite grease.

Transverse Vibration of a Viscoelastic Column With Initial Curvature Under Periodic Axial Load

1969 ◽  
Vol 36 (4) ◽  
pp. 814-818 ◽  
Author(s):  
K. K. Stevens
Keyword(s):  
Polymethyl Methacrylate ◽  
Transverse Vibration ◽  
Axial Load ◽  
Dynamic Instability ◽  
Complex Modulus ◽  
Lateral Vibrations ◽  
Lateral Response ◽  
Viscoelastic Column ◽  
Linear Viscoelastic ◽  
Frequency Curves

The lateral response of a slightly curved viscoelastic column subjected to a periodic axial load P0 + P1 cos ωt is investigated. The analysis makes use of the complex modulus representation for linear viscoelastic materials. It is shown that the lateral vibrations stemming from imperfections can be of significant amplitude. Experimentally determined amplitude-frequency curves for a polymethyl methacrylate (Plexiglas) column are presented, and are found to be in excellent agreement with the theory. It is shown that there is an analogy between the dynamic instability and the static buckling of imperfect columns.

SET-VALUED PSEUDOMONOTONE MAPS AND DEGENERATE EVOLUTION INCLUSIONS

1999 ◽  
Vol 01 (01) ◽  
pp. 87-123 ◽  
Author(s):  
KENNETH L. KUTTLER ◽  
MEIR SHILLOR
Keyword(s):  
Weak Solution ◽  
Friction Coefficient ◽  
Frictional Contact ◽  
Contact Problems ◽  
Pseudomonotone Operator ◽  
Unique Weak Solution ◽  
Dynamical Models ◽  
Evolution Inclusions ◽  
Theory Of Evolution ◽  
Pseudomonotone Maps

We develop the theory of evolution inclusions for set-valued pseudomonotone maps. The problems we investigate are [Formula: see text] where B=B(t) is a linear operator that may vanish and A is a set-valued pseudomonotone operator. We prove the existence of unique solutions of such, possibly degenerate, problems.We apply the theory to the problem of dynamic frictional contact with a slip dependent friction coefficient and prove the existence of its unique weak solution.This theory opens the way for the investigation of sophisticated dynamical models in mechanics and frictional contact problems.

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