Frictional Contact Model Research Articles

Modeling of large deformation frictional contact in powder compaction processes

In this paper, the computational aspects of large deformation frictional contact are presented in powder forming processes. The influence of powder–tool friction on the mechanical properties of the final product is investigated in pressing metal powders. A general formulation of continuum model is developed for frictional contact and the computational algorithm is presented for analyzing the phenomena. It is particularly concerned with the numerical modeling of frictional contact between a rigid tool and a deformable material. The finite element approach adopted is characterized by the use of penalty approach in which a plasticity theory of friction is incorporated to simulate sliding resistance at the powder–tool interface. The constitutive relations for friction are derived from a Coulomb friction law. The frictional contact formulation is performed within the framework of large FE deformation in order to predict the non-uniform relative density distribution during large deformation of powder die pressing. A double-surface cap plasticity model is employed together with the nonlinear contact friction behavior in numerical simulation of powder material. Finally, the numerical schemes are examined for efficiency and accuracy in modeling of several powder compaction processes.

A Kinetic Friction Model for Viscoelastic Contact of Nominally Flat Rough Surfaces

Approximate closed-form equations are derived for normal and tangential contact forces of rough surfaces in dry friction. Using an extension of the Greenwood and Tripp (1970, Proc, Inst. Mech. Eng., 185, pp. 625–633) model, in which the derivations permit asperity shoulder-to-shoulder contact and viscoelastic asperity behavior, mathematical formulae are derived for normal and tangential components of the contact force that depend not only on the proximity of the two surfaces but also the rate of approach and relative sliding. A statistical approach is forwarded in which dependence of the asperity tangential contact force on relative tangential velocity of two asperities can be cast as corrective factors in the mathematical description of tangential force. In this regard two corrective coefficients are derived: force directionality corrective coefficient and force–velocity directionality corrective coefficient. The results show that for a moderate to high load ranges the contact force can be analytically described to within 20% accuracy of that from a numerical integration of the contact equations, well below the uncertainties due to surface profile measurement.

Real time force optimization algorithm of multi-fingered grasp

Based on the fact that nonlinear friction force limit constraints are equivalent to the positive definiteness of a certain matrix, the problem of grasping force planning for multi-fingered hand can be formulated as an optimization problem on the smooth manifold of linearly constrained positive definite matrices, and the optimal grasping force can be found by using the linear constraint gradient flow. When the number of fingers is large, high-dimensional description matrix greatly limits the calculation speed of the traditional linear constraint gradient flow. Therefore, in order to solve the problem, a grasping force vector based linear constraint gradient flow algorithm for real time applications is proposed, based on the affine constraint property of the description matrix in the optimization process. Instead of the description matrix, a grasping force vector is used to describe the linear constraint gradient flow, which greatly reduces the dimensional number and the computational cost of the linear constraint gradient flow expression. The proposed algorithm is implemented on a four-fingered dexterous hand with point friction contact model for grasping force computation. The influence of the weight factor and step factor on the computational result and the convergence speed is analyzed, and the correctness and real-time capacity of the proposed algorithm are verified.

Hermite polynomial smoothing in beam-to-beam frictional contact

In this paper a smoothing procedure is suggested for the 3D beam-to-beam contact. A smooth segment is defined basing on current position vectors of three nodes limiting two adjacent finite elements. The approximated fragment of a beam axis as a 3D curve spans between the centre points of these elements. The curve is described parametrically using three Hermite polynomials. The four boundary conditions necessary to determine the coefficients for each of these polynomials involve co-ordinates and slopes at the curve ends. The slopes are defined in terms of the element nodal co-ordinates, too. There is no dependence on nodal rotations so this formulation can be embedded in a beam analysis using any type of beam finite element. This geometric representation of the curve is incorporated into the 3D beam-to-beam frictional contact model with the penalty method used to enforce contact constraints. The residual vector and the corresponding tangent stiffness matrix are determined for the normal part of contact and for the stick or slip state of friction. A few numerical examples are presented to show the performance of the suggested smoothing procedure in the cases featuring large frictional sliding.

Contact Analysis for Solids Based on Linearly Conforming Radial Point Interpolation Method

To simulate the contact nonlinearity in 2D solid problems, a contact analysis approach is formulated using incremental form of the subdomain parametric variational principle (SPVP). The formulation is based on a linearly conforming radial point interpolation method (LC-RPIM) using nodal integration technique. Contact interface equations are also presented using a modified Coulomb frictional contact model and discretized by contact point-pairs. In the present approach, the global discretized system equations are transformed into a standard linear complementarity problem (LCP) that can be solved readily using the Lemke method. The present approach can simulate various contact behaviors including bonding/debonding, contacting/departing, and sticking/slipping. An intensive numerical study is performed to validate the proposed method via comparison with the ABAQUS® and to investigate the effects of the various parameters used in computations. These parameters include normal and tangential adhesions, frictional coefficient, nodal density, the dimension of local nodal support domain, nodal irregularity, shape parameters used in the radial basis function and the external load. The numerical results have demonstrated that the present approach is accurate and stable for contact analysis of 2D solids.

Modelling of static friction in rubber–metal contact

A static friction model for contact between rough rubber and metal surfaces is developed. This model is based on the contact of a viscoelastic–rigid asperity couple. Single asperity contact is modelled in such a way that the asperities stick together in a central region and slip over an annulus at the edge of the contact. The slip area increases with increasing tangential load. Consequently, the static friction force is the force when the slip area is equal to the contact area. Using the model, the traction distributions, contact area, tangential and normal displacement of two contacting asperities are calculated. The single asperity model is then extended to multi-asperity contact, suitable for rough surfaces. This model allows calculation of the above-mentioned parameters for two rough surfaces (a rubber and a metal one) subjected to normal and tangential loads. A parametric study will be presented. The results are qualitatively in good agreement with those found in literature.

One-dimensional dynamic microslip friction model

A one-dimensional dynamic microslip friction model, including the damper inertia, is presented in this paper. An analytical approach is developed to obtain the steady-state solution of the resulting nonlinear partial differential equations when subjected to harmonic excitation. In the proposed approach, according to the excitation frequency, a single mode of the system is considered in the steady-state solution for simplicity; consequently, phase difference among spatially distributed points is neglected. Three types of normal load distributions, resulting in distinct stick–slip transitions along the contact interface, are studied. The resulting hysteresis curves and the associated Fourier coefficients are obtained and compared with each other. An equivalent point contact friction model is established and compared with the proposed microslip model, illustrating the effects of partial slip in the contact interface for low amplitude or high normal load applications.

A spectral scheme for the simulation of dynamic mode 3 delamination of thin films

Motivated by recent developments in laser-induced spallation testing of thin film structures, we develop a spectral scheme for the simulation of dynamic failure of thin films. In this first study, we focus on the anti-plane shear (mode 3) loading case. The scheme relies on an exact spectral representation of the elastodynamic solutions in the substrate and in the film, and their combination through interface conditions that involve general cohesive failure and/or frictional contact models. A detailed modal analysis of the response of a single spectral mode is performed to assess the stability and precision of the resulting numerical scheme. A set of dynamic fracture problems involving non-propagating and propagating cracks are simulated to show the ability of the numerical scheme to capture the effect of wave reflection on the near-tip stress and displacement fields, and on the dynamic motion of a crack along the film/substrate interface.

On the two points of views of plastically deformed asperity contacts with friction loading

This article discusses two very different points of views of the behaviour of plastically deformed asperity contacts with friction loading. A fundamental mechanics study is carried out using the concept of contact hydrostatic pressure. The study reveals various features of the two view-points. Some literature results are subsequently analysed. The analysis suggests that the friction force may significantly reduce the contact hydrostatic pressure thereby reducing asperity load capacity along with other consequences in the tribo-systems. This article may increase the understanding of the behaviour of asperity microcontacts and may be useful for future modelling of frictional contact of rough surfaces.

An Analysis of the Riveting Process as 2-D Frictional Contact Problem

A frictional contact model is adopted for the analysis of conventional solid rivet setting. Material properties for the selected plates and rivets are obtained from analytical method using elastic constants and tensile strengths for each material. Rigid- and elasto-plastic models are selected for process analysis in this paper. Process variables are selected to investigate the effect of variables on the successful rivet setting and servicing in any structure as force transmitting member. Major variables in riveting process are material variables such as material properties and geometrical variables, which are dimensions of head, shank, and blank diameters. Analysis in this study is concentrated on the influence of variety of materials and of shank dimensions on the contact area after rivet setting, i.e. after forming process of rivet head. Soft and hard materials are selected as mother materials to investigate how the selection of material influences on the riveting process in quantitative manner. The geometry of head is closely investigated through simulation in terms of contact status, i.e. contact area between rivet head and mother material, which would affect the snap fit joint by riveting.

A LuGre Tire Friction Model With Exact Aggregate Dynamics

The LuGre dynamic point contact friction model for the two-dimensional translation of a body on a surface has been used in the past to derive a model for the friction forces and moments at the contact patch of a tire. The resulting tire friction model is distributed, described by a set of partial differential equations. Several approximations have been used in the literature to approximate this distributed model using a set of ordinary differential equations, making the model appropriate for control design and on-line estimation. In this paper, the method of moments is used to derive a set of ordinary differential equations to describe the exact average dynamics of the distributed model. Three cases of normal load distribution are considered and compared: uniform, trapezoidal and cubic load distribution. Simulations are also presented to compare with existing approximate steady-state lumped models.

Method for Direct Parametric Analysis of Nonlinear Forced Response of Bladed Disks With Friction Contact Interfaces

An effective method for direct parametric analysis of periodic nonlinear forced response of bladed disks with friction contact interfaces has been developed. The method allows, forced response levels to be calculated directly as a function of contact interface parameters such as the friction coefficient, contact surface stiffness (normal and tangential coefficients), clearances, interferences, and the normal stresses at the contact interfaces. The method is based on exact expressions for sensitivities of the multiharmonic interaction forces with respect to variation of all parameters of the friction contact interfaces. These novel expressions are derived in the paper for a friction contact model, accounting for the normal load variation and the possibility of separation-contact transitions. Numerical analysis of effects of the contact parameters on forced response levels has been performed using large-scale finite element models of a practical bladed turbine disk with underplatform dampers and with shroud contacts.

Tribological periodic processes exhibited by acceleration or braking of a shaft–pad system

A new one-dimensional thermoelastic frictional pair contact model of a shaft–bush system is proposed. The assumed model includes a study of vibration processes and contact characteristics exhibited by a relative velocity between the two mentioned bodies, contact temperature, pressure and wear. Some important conclusions are formulated.

Numerical Simulation of Viscoplastic and Frictional Heating During Finite Deformation of Metal. Part I: Theory

This paper is concerned with the numerical simulation of hot metal forming, especially superplastic forming. In this first part, a complete thermo-viscoplastic formulation at finite strains is derived and a unified stress update algorithm for thermo-elastoplastic and thermo-elasto-viscoplastic constitutive equations is obtained. The resulting unified implicit algorithm is both efficient and very inexpensive. A staggered scheme is used for the global resolution of the thermomechanical problem. We will also describe the basis of our thermomechanical frictional contact model. Discussion of computational aspects and efficiencies will be assessed in the second part of this work.

Three dimensional finite element modeling of thermomechanical frictional contact between finite deformation bodies using R-minimum strategy

An algorithm for analyzing the transient thermal coupling with the frictional contact between the multiple elastic–plastic bodies in finite deformation is presented using the R-minimum strategy. An arbitrarily shaped contact element strategy, named as node-to-point contact element strategy, is proposed to handle the thermomechanical frictional contact between finite deformation bodies. Assuming the material properties to be temperature dependent, the constitutive equations for both the thermomechanical frictional contact and the thermal-elastic–plastic materials are deduced respectively and applied in our finite element code. Finally, two examples are presented to show the efficiency and usefulness of this algorithm.

２本指操作のための６自由度指先装着型力覚提示装置の開発

In this paper, we introduce 6DOF (degree-of-freedom) finger-mounted haptic device which we have developed. When we operate virtual objects with our fingers, it is necessary to use 6DOF finger-mounted haptic device. But such a device is often so large with many actuators equipped, that most of these reserches to operate virtual objects with haptic device have been done using those with only 3DOF. It is clear, however, that we need to use 6DOF haptic device for more detailed operation. Thus, we developed a small-sized, finger-mounted haptic device, with the mechanism of bevel gear, and then confirmed its operational effectivness by operating a virtual object with two fingers. To calculate force and moment at the state of contact in virtual world, we have used“friction contact model”.

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.

Normal and tangential force–displacement relations for frictional elasto-plastic contact of spheres

In this paper, we present the data obtained from numerical experiments that are at the foundation of our successful elasto-plastic force–displacement (FD) models in both the normal direction and tangential direction of spheres in collision. We also present in detail how these data were obtained. Our numerical experiments are in the form of frictional elasto-plastic finite-element analysis of spherical particles in contact. We use the numerical experiments to observe the behavior of various quantities involved in the contact (e.g. contact-area radius, contact curvature, stresses, FD relations, etc.). This observation has helped us to devise an accurate and consistent model for frictional elasto-plastic contact of spherical particles that are used in granular-flow simulations that may involve tens of thousands of these particles.

An Elastodynamic Model of Frictional Contact and Its Influence on the Dynamics of a Workpiece-Fixture System

A model to predict the dynamics of a workpiece-fixture system has been developed based on the equivalency of the dynamic frictional contact problem with a nonlinear friction law to that of a variation inequality problem. Nonlinear finite element method has been employed to solve the problem. A series of experiments under various fixture configurations were conducted on a modular fixture test-bed to determine the dynamic characteristics of the workpiece-fixture system. Model predictions of the dynamic characteristics have been compared to those obtained from the experiments and are found to be in good agreement. It was found that frictional sliding contact at the workpiece-fixture interfaces provides damping to the system and that the nature of this contact and level of damping are highly dependent on contact forces developed through clamping. Clamping sequence was also found to be important in determining dynamic characteristics.

Simulation of cold forging using contact and practical adaptive meshing algorithms

This paper deals with the importance of frictional contact model for curved geometry with adaptive remeshing in the finite element simulation of cold forging process using flow formulation. Several industrial forging problems have been solved using the above capabilities. These include axisymmetric analysis of (a) backward extrusion, (b) forward–backward extrusion, (c) a fastener component and (d) plane strain analysis of the coining process. The meshing and remeshing procedures are automatic and are implemented in a finite element analysis package, through which analysis can be carried out without user intervention.