Institute of Fundamental Technological Research

For a structure under service loads, there is a need to induce precise control of a local displacement by additional punch loading. Such problem exists in design of robot grippers or agricultural tools used in mechanical processing. The punch interaction is assumed to be executed by a discrete set of pins or by a continuously distributed contact pressure. The optimal contact force or pressure distribution and contact shape are specified for both discrete and continuous punch action. Several boundary support conditions are discussed, and their effects on punch action are presented.

contact problem, displacement control, optimal pressure distribution, optimal contact shape

The present study is related to analysis of coupled friction and wear process in sliding along the rough surface with an anisotropic asperity pattern characterized by single or mutually orthogonal striations. Due to wear process the initial anisotropic response evolves with the variation of asperity distribution, tending to a steadystate pattern. The orthotropic friction sliding model and the related wear rule are analytically formulated assuming evolution of contact anisotropy to its steady state. The orthotropic frictional sliding model and the related wear rule are analytically formulated assuming evolution of contact anisotropy to its steady state. The experimental study is next presented for orthotropic asperity patterns induced on steel plate surface. The transient and steady states are characterized and the respective evolution parameters calibrated. The numerical finite element wear analysis aimed at validation of model-predictions and wear parameter calibration is presented at the end of paper

Anisotropic contact, Friction sliding and wear rules, Evolution of contact anisotropy, Experimental study, Numerical wear analysis

In the paper a class of wear problems is considered, for which the contact zone is fixed on one of contacting bodies and translates on the surface of another body, like in the case of punch in relative translation on a substrate. In the case of constant normal loads interacting with the induced monotonic sliding, the steady state wear process is reached. In the case of fixed normal load and the reciprocal sliding condition the wear process tends to its steady periodic state. Similarly, for periodically varying normal load, a steady periodic state is reached for the case of monotonic sliding. A most general case occurs for in-phase or out-of-phase periodic variation of normal load interacting with the reciprocal sliding. The paper is aimed to provide further study of steady wear states by considering periodically varying normal load combined with monotonic or alternating sliding conditions. The illustrative examples demonstrate the contact pressure and wear distribution in steady states with application to brake wear analysis.

Contact Problems, Periodic Loading, Periodic Steady-States, p-Version of Finite Elements, Sliding Wear

The relative sliding motion of two elastic bodies in contact induces wear process and contact shape evolution. In the case of a punch sliding on a substrate the transient process tends to a steady state for which the fixed contact stress and strain distribution develops in the contact zone. This state usually corresponds to a minimum of the wear dissipation power. The optimality conditions of the wear dissipation functional provide the contact stress distribution and the wear rate compatible with the rigid body punch motion. The present paper is aimed to extend the previous analyses [1], [2], [3], [4] and [5] of steady state conditions to cases of periodic sliding of punch, assuming cyclic steady state conditions for both mechanical and thermal fields.

Contact optimization problems, Monotonic and periodic sliding wear, Heat generation, Steady wear state, Shape evolution, p-version of the finite element method

The relative sliding motion of two elastic bodies in contact induces the wear process and contact shape evolution. The transient process at the constant relative velocity between the bodies tends to a steady state occurring at fixed contact stress and strain distribution. This state corresponds to a minimum of the wear dissipation power. The optimality conditions of the functional provide a contact stress distribution and a wear rate compatible with the rigid body punch motion. The present paper is devoted to the analysis of wear processes occurring for periodic sliding of contacting bodies, assuming cyclic steady state conditions for mechanical fields. From the condition of the rigid body wear velocity a formula for summarized contact pressure in the periodic steady state is derived. The optimization problem is formulated for calculation of the contact surface shape induced by wear in the steady periodic state.

steady wear process, periodic sliding, unilateral contact, p-version of finite element method, shape optimization

The paper presents a synthetic review of recent research carried out by the writers [1-6, 7-9] on contact shape optimization coupled with wear and on the steady wear regimes reached in the transient wear process. It was shown that these regimes can also be specified from the optimality conditions. In the analysis several classes of shape optimization problems were considered, namely minimization of wear volume rate, friction dissipation power or wear dissipation power. It was demonstrated that the contact shape evolution tends to steady or quasi-steady states satisfying the minimum principle of the wear dissipation power, resulting in the coaxiality rule requiring the wear rate vector to be collinear with the rigid body wear velocity vector. The application of steady state wear rules in specification of contact states for selected problems is discussed in the paper. The extension of method is presented for the case of multi-zone contact problems for which both transient and steady states have been analyzed.

Contact Optimization, P-Version of Finite Element Method, Steady Wear State, Variational Principles

The relative sliding motion of two elastic bodies in contact under compressive tractions induces wear process and contact shape evolution. The transient process tends to a steady state at fixed contact stress and strain distribution. This state was assumed to correspond to the minimum of the wear dissipation power. The stationary condition of the response functional then provides the contact pressure distribution. The present paper is aimed at extending to results of previous analyses [1], [2], [3], [4] and [5] of steady state conditions to cases of periodic sliding of contacting bodies, assuming the existence of cyclic steady state conditions. The wear dissipation in the steady cyclic period is then minimized with respect to the contact pressure distribution. The solutions of several cases of wear processes induced by translational and rotational sliding illustrate the applicability of the proposed variational method.

Contact problems, Sliding wear, Steady-state, Periodic sliding, Optimal contact surface, p-Version of finite elements

The wear process on a frictional interface in a relative sliding motion of a punch on a substrate induces shape evolution of contact interface. For fixed contact zone the process tends to a steady state with fixed contact stress and strain distribution. Such steady state wear regimes were analyzed in the previous papers [1], [2], [3], [4] and [5] by applying the principle of minimum wear dissipation rate. However, when the contact zone evolves in time due to wear process, as in the case of sliding spherical indenter, a quasi-steady state is reached with stress intensity dependent on the contact size parameter. On the other hand, the contact pressure distribution satisfies the condition of steady state. The simplified numerical analysis of wear process is presented by applying the quasi-steady conditions. The numerical predictions are confronted with experimental test results for two specific cases of soft and hard substrates. The quantitative specification of wear parameters is provided, first assuming constant values throughout the whole wear process, next assuming linearly or exponentially varying during the initial period and tending to constant values.

Spherical indenter, Sliding wear, Contact zone evolution, Wear parameters, Experimental data, Numerical simulation

The present work provides the analysis of coupled thermo-elastic steady wear regimes: wear analysis of a punch translating on an elastic strip and wear induced by a rotating punch on a toroidal surface. The contact pressure and temperature are specified from the stationary conditions of the wear dissipation power or from the contact-conformity-condition. The wear and friction parameters are assumed as fixed or temperature dependent. Three transverse friction models are discussed for wear debris motion. The analysis and results presented can be used in design of optimal contact shapes assuring the steady wear regimes throughout the whole contact operation period.

Contact problems, Sliding wear, Steady state, Thermal distortion, Optimal contact surface

In the relative sliding motion of two elastic bodies on contact interfaces both frictional dissipation and wear process occur. The wear process induces shape evolution of contact surface and growth of contact zone. The temperature field is generated by external heat flow and by frictional dissipation on the contact surface. The wear and heat conduction processes are coupled and tend to their steady or quasi-steady states for which the stress and temperature fields are fixed on the translating contact zone and depend only on its size and shape parameters. The steady-state is characterized by the minimum of wear dissipation power for which the stationary conditions generate the contact pressure distribution. The related steady-state temperature field is next specified and the thermal distortion effect is analyzed. The contact shape attained in the steady wear state is optimal as it corresponds to minimal wear rate, and its form depends on both mechanical loading and temeperature field. Several specific examples are presented for translating and rotating punches.

Contact optimization, Heat generation, Minimum principle,p-version of finite element method, Sliding wear, Steady wear state, Thermo-elastic problem, Upwinding Petrov-Galerkin scheme

A transient wear process on frictional interface of two thermo-elastic bodies in a relative steady sliding motion induces shape evolution of contact interface and tends to a steady state for which the wear process occurs at fixed contact stress and strain distribution. The temperature field generated by frictional and wear dissipation on the contact surface is assumed to reach a steady state. This state is assumed to correspond to minimum of the wear dissipation power and the temperature field corresponds to maximum of the heat entropy production. The stationarity conditions of the response functionals provide the contact pressure distribution and the corresponding temperature field. The present approach extends the authors previous analyses of optimal or steady-state contact shapes by accounting for coupled wear and thermal distortion effects.

The wear rule is assumed as a non-linear relation of wear rate to shear stress and relative sliding velocity. The analysis of disk and drum brakes is presented with account for thermal distortion effect. It is shown that the contact shape in a steady thermo-elastic state essentially differs from that specified for mechanical loading with neglect of thermal effects. The thermal instability regimes are not considered in the paper.

The transient wear process on the frictional interface of two elastic bodies in relative steady sliding motion induces shape evolution of the contact interface and tends to a steady state in which the wear develops at constant contact stress and strain distribution. Such a steady state may be attained experimentally or in numerical analysis by integrating the wear rate in the transient wear period. An alternative method of analysis was proposed in previous papers [Páczelt I, Mróz Z. On optimal contact shapes generated by wear. Int J Numer Methods Eng 2005;63:1310–47; Páczelt I, Mróz Z. Optimal shapes of contact interfaces due to sliding wear in the steady relative motion. Int J Solids Struct 2007;44:895–925] by applying a variational procedure and minimizing a response functional corresponding to the wear-dissipation power. The present paper provides an extension of this approach and new applications to the analysis of steady states in disk and drum brakes. The wear rule is assumed as a non-linear relation of wear rate to shear stress and relative sliding velocity. The specification of steady wear states is of engineering importance as it allows for optimal shape design of contacting interfaces in order to avoid the transient run-in periods. The extension to cyclic translation cases can be generated by considering steady cyclic states of wear processes.

Contact problems, Sliding wear, Steady-state, Variational principle, Optimal contact surface

The transient wear process at contact frictional interface of two elastic bodies in relative steady motion induces evolution of shape of the interface. A steady wear state may be reached with uniform wear rate and fixed contact surface shape. In this paper, the optimal contact shape is studied by formulating several classes of shape optimization problems, namely minimization of generalized wear volume rate, friction dissipation power and wear dissipation rate occurring in two bodies. The wear rule was assumed as a nonlinear dependence of wear rate on friction traction and relative sliding velocity, similar to the Archard rule. The wear parameters of two bodies may be different. It was demonstrated that different optimal contact shapes are generated depending on objective functional and wear parameters. When the uniform wear rate is generated at contact sliding surfaces, the steady state is reached. It was shown that in the steady state the wear parameters of two bodies cannot be independent of each other. The solution of nonlinear programming problem was provided by the iterative numerical procedure. It was assumed that the relative sliding velocity between contacting bodies results from translation and rotation of two bodies. In general, both regular and singular regimes of wear rate and pressure distribution may occur. The illustrative examples of drum brake, translating punch and rotating annular punch (disc brake) provide the distribution of contact pressure and wear rate for regular and singular cases associated with the optimality conditions. It is shown that minimization of the generalized wear dissipation rate provides solutions assuring existence of steady wear states.

Sliding wear, Contact optimization, Steady wear state, p-Version of finite element method

The optimal shape design of contacting surfaces has usually been aimed at controlling the contact pressure distribution. However, a much wider class of contact optimization problems can be formulated by maximizing contact force or displacement, torsional moment, or minimizing the friction dissipation. The special classes of optimization problems are considered, namely, minimization of generalized wear volume rate, minimization of generalized friction dissipation power and minimization of the generalized wear dissipation power depending on both normal pressure and slip velocity.

The specific wear rule was assumed and the optimality conditions are derived. They generate optimal contact pressure distribution and the corresponding optimal wear rate. The optimization problems are reduced to non-linear programming problems and for their solution a special iteration process is used. The wear process is analysed in two specific cases. First, when the relative sliding velocity between bodies is constant and the second case, when one of bodies rotates with respect to another body. For rotational motion the problem of minimization of friction dissipation power is considered by applying the technique of control of contact pressure distribution and minimization of the generalized friction dissipation power with a new control parameter q. It is demonstrated that the wear dissipation power at the contact surface is minimal in the steady state of wear process and in many cases corresponds to the uniform wear rate. The illustrative examples for rotating bodies demonstrate the evolution of wear process toward a steady state. The minimization of the generalized wear volume rate and of generalized friction dissipation power does not induce the steady state of wear process in the rotation motion.

The relative sliding motion of two elastic bodies in contact induces wear process and contact shape evolution. The transient process tends to a steady state occuring at fixed contact stress and strain distribution. This state corresponds to the minimum of the wear dissipation power. The optimality conditions of the functional provide the contact stress distribution and the wear rate compatible with the rigid body punch motion. This paper extends the previous analyses [1,2,3,4,5] of the steady state conditions to cases of periodic sliding of contacting bodies, assuming cyclic steady state conditions for both mechanical and thermal fields.

This technique for solution of the coupled thermo-elastic-wear problem provides reasonable results for engineering applications The coupled thermo-mechanical problem is solved by an operator split technique. The mechanical and thermal fields discretized by the finite element approximation are specified separately in consecutive time steps.

The wear effect is calculated incrementally by applying the Archard type wear rule. The wear is accumulated at the end of half period of motion, so the contact pressure is fixed (at the iteration level), and the transient heat conduction problem is next solved for the given temperature field at the beginning of half period. The iterative process for one half period is terminated when the convergence criterion satisfies the error constraint for gap modification.

Numerical examples for different geometrical support conditions confirm the validity of prediction of the maximum value of temperature in the contact zone for the periodical motion of the strip. The results for the monotonic punch motion in the steady state wear state can be used to generate periodic solution.

contact problems, sliding wear, heat generation, steady-state, periodic sliding, optimal contact surface, p-version of finite elements