非局部摩擦在几种塑性成形工艺中的应用

为了考虑金属材料表面微凸结构对模具与工件接触区域上的非局部摩擦效应,在几种金属塑性成形加工问题中,首次采用Oden等提出的非局部摩擦定律代替经典的库仑摩擦定律,利用主应力法或工程法建立了相应问题的积微分形式的力平衡方程．在简化的情况下,采用摄动法求得接触面上接触压力在非局部摩擦下的近似解析解,并分析了影响接触压力非局部效应的相关因素．     

Determination of a Constitutive Friction Law Using an Elastic-Plastic Half-Space Model

Friction influences metal forming processes both in economic and technical terms. A precise understanding of friction is inevitable as friction restricts the potential of the product design. Friction depends on the occurring contact loads which is especially true for sheet-bulk metal forming (SBMF) as the incorporated contact loads appear in a very broad range. Numerical simulations, which are verified experimentally, are carried out to analyse contact interactions which typically appear in SBMF. On the one hand the multi-scale character of rough surfaces requires a very fine resolution of the contact area, on the other hand a large contact area is necessary to be representative. A half-space model is chosen for the contact analysis, because it only depends on the two-dimensional surface boundary which consumes less computing capacity than the finite element method (FEM) with its three-dimensional volume approach for the same surface resolution and area. The outcome is a constitutive friction law (CFL) consisting of two equations. The law is implemented into the framework of FEM to see the impact in a typical SBMF-process which aims to form metal sheet into cups with integrated gearing teeth. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Contact of ropes and orthotropic rough surfaces

Contact between arbitrary curved ropes and arbitrary curved rough orthotropic surfaces has been revised from the geometrical point of view. Variational equations for the equilibrium of ropes on orthotropic rough surfaces are derived, first, using the consistent variational inclusion of frictional contact constraints via Karush-Kuhn-Tucker conditions expressed in Darboux basis. Then, the systems of differential equations are derived for both statics and dynamics of ropes on a rough surface depending on the sticking-sliding condition for orthotropic Coulomb's friction. Three criteria are found to be fulfilled during the static equilibrium of a rope on a rough surface: “no separation”, condition for dragging coefficient of friction and inequality for tangential forces at the end of the rope. The limit tangential loads still preserve the famous “Euler view” T = T₀e^ωs for the curves and surfaces of constant curvature. It is shown that the curve of the maximum tension of a rough orthotropic surface is geodesic. Equations of motion are derived in the case if the sliding criteria is fulfilled and there is “no separation”. Various cases possessing analytical solutions of the derived system, including Euler case and a spiral rope on a cylinder are shown as examples of application of the derived theory. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Frictional contact of elastomer materials on rough rigid surfaces

The frictional behavior of elastomer materials is still unexplored, but very important for many industrial applications. Special attention is turned to rubber friction on rough road tracks. Due to the non‐rigid material characteristics of the rubber it is not sufficient to use a constant friction coefficient like Coulombs law. The frictional qualities depend on many different influences like sliding velocity, applied normal stress, surface roughness, material properties and the temperature in the contact zone. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the formulation and investigation of a spatial contact problem for elastic bodies under mixed friction conditions

A spatial contact problem is formulated and investgated for rough elastic bodies which touch each other under mixed friction conditions: the elastic bodies are separated in one part of the contact domain by a layer of viscous incompressible liquid (lubricant), while in the other they are in direct contact (such conditions are characteristic for roller bearings, gear transmissions, etc.). The problem is reduced to a system of nonlinear integro-differential and integral equations and inequalities in the contact domain, part of the external boundary, and a number of inner boundaries that are unknown in advance, but separate the lubricated and unlubricated zones. Special cases are problems of dry and completely lubricated contact. A formulation is given for the problem for the case when the materials of the bodies are identical. The problem of mixed friction is considered in strongly drawn out contact. Sections of the contact domain in which the interaction between the bodies is direct or by means of the lubrication layer are investigated using asymptotic methods.     

Surface Deformation due to Shear and Ploughing in a Halfspace

Sheet and bulk metal forming are widely used manufacturing methods. The interaction between worktool and workpiece in such a process causes friction which has a remarkable impact on the expended energy of the process. Therefore the influence of friction is important. Friction can be split into shearing and ploughing [1]. Ploughing is the plastic deformation of a soft surface by a hard contact partner. Shear forces are only transferred in the real contact area where material contact occurs. The investigation of the contribution of both ploughing and shearing to the total friction resistance is done with the use of an elasto-plastic halfspace model. The multiscale character of surfaces demands a fine discretization, which results in numerical effort. While a finite element method takes into account both surface and bulk of the contact partners, the halfspace model only regards the contact surfaces and thereby consumes less computing capacity. In order to identify the friction resistance, two rough surfaces get into contact. After full application of the normal load, the surfaces are moved relatively to each other. New asperities of the contact surfaces get into contact and are plastically deformed. These deformations are used to estimate the ploughing effect in dependency on the relative displacement. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micro‐ and nanoscale modelling of dry friction with application to the wheel/rail contact

Friction is a phenomenon involving elastic interactions, plastic deformation and failure processes at different length scales. A model of dry friction is established based on the method of Movable Cellular Automata (MCA). The influence of material and loading parameters has been investigated within a large number of numerical simulations. The new friction law is applied to the calculation of stresses, deformations and tractive forces in wheel/rail contact with rough surfaces. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Homogenization for contact problems with friction on rough interface

We consider a contact problem between a macroscopic solid with a smooth boundary and a technical textile, while the textile has a periodic microscopic structure and microscopically rough surface. Two–scale homogenization approach is applied to the problem. The microscopic solution is approximated in terms of macroscopic solution and some concentration factor, given as a solution of auxiliary boundary value or contact problems of elasticity on the periodicity cell. Local friction condition is represented as a continuous non–linear functional over the stress field. Two–scale convergence is used to prove the convergence of friction functional. The macroscopic initial frictional limit is found. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parameter study of a multi-body friction oscillator

In many technical applications sliding contacts with multiple contact points or engagements exist, like between seals and rough surfaces, between grinding wheel and workpiece, or between granular material and storage box. In a simplified way these contacts can be represented by a friction oscillator with multiple bodies. The behavior of the friction oscillator with one body is already well known. However only few studies exist on the behavior of a friction oscillator with multiple bodies. In this study especially the dynamical behavior depending on the number of bodies, the friction characteristic and the velocity of the belt has been investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On modeling and simulation of tethered systems with sharp,rough contacts

We extend the analysis of a reeled, tethered system in a constant gravitational field by (i) proposing a differential–algebraic representation when the tether is inextensible and (ii) examining the interaction between the tether and a sharp, fixed guide when contact is rough. The governing equations are derived using an approach that clearly illustrates how singular supplies of linear momentum, such as friction at the fixed guide, feature in the equations of motion. After semidiscretization via finite differences, we formulate the system of differential equations and algebraic constraints as a differential–algebraic equation and solve for various motions of the reeled tether. In addition, we show that, by comparison to a rounded contact analysis with arbitrarily small radius, the reaction force acting on the tether at the guide does not converge to the value of this force when the guide is modeled as a sharp point of contact.     

A dynamically consistent model of the contact stresses in the plane motion of a rigid body

The problem of determining dry friction forces in the case of the motion of a rigid body with a plane base over a rough surface is discussed. In view of the dependence of the friction forces on the normal load, the solution of this problem involves constructing a model of the contact stresses. The contact conditions impose three independent constraints on the kinematic characteristics, and the model must therefore include three free parameters, which are determined from these conditions at each instant. When the body is supported at three points, these parameters (for which the normal stresses can be taken) completely determine the model, while indeterminacy arises in the case of a larger number of contact points and, in order to remove this, certain physical hypotheses have to be accepted. It is shown that contact models consistent with the dynamics possess certain new qualitative properties compared with the traditional quasi-static models in which the type of motion of the body is not taken into account. In particular, a dependence of the principal vector and principal moment of the friction forces on the direction of sliding or pivoting of the body, as well as on the magnitude of the angular velocity, is possible.     

A Two Dimensional Model for the Dynamical Contact of Elastic Rough Surfaces

To model the contact behavior including dynamical effects, a two dimensional mechanical model of elastic rough contact is developed. This model can simulate the contact behaviour between two rough surfaces depending on normal pressure, sliding speed and roughness profiles. The contact between two rough surfaces is reduced to a rough rigid and a rough elastic layer. The elastic layer is modeled by point masses connected by spring-damper elements. The total system is described by coupled ODEs. The number of ODEs and thus the degree of freedom of the model depends on the varying contact conditions. The contact conditions are monitored during the simulation and the simulation interrupts, in case the contact conditions change. The equations of motion are then adapted with respect to the contact constraints. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The solution of contact problems using boundary element method

The formulation of contact problems is extended to the case of moving punches and to the case when the state of the systems being investigated depends on the history of the change in the external actions. The quasi-static contact problem for a moving rigid rough punch and a single linearly deformable body is considered. A new iterational process is proposed for solving contact problems, taking friction in the contact area into account, and its convergence is proved. An algorithm of the solution, based on the boundary element method, is developed. Solutions of specific problems are given and analysed. Estimates of the difference of the solutions due to the difference in the impenetrability conditions and the difference in the steps of the loading parameter are obtained.     

Friction properties of highly elastic materials at high contact pressures

A newly designed high-pressure tribometer has been employed to investigate the pressure dependence of the friction force of SKN-40 crosslinked butadiene-nitrile rubber in contact with a steel surface on the pressure range to 1200 kgf/cm² (20°C). Over the entire range of contact pressures the friction process is molecular-kinetic in nature and characterized by a linear dependence of the friction force on the logarithm of the sliding velocity. In the region of normal pressures up to 200 kgf/cm², where the effect of pressure on the friction force reduces to the formation of the actual contact area, the friction constant (proportionality factor relating the friction force and the actual contact area) is practically independent of the pressure. At pressures above 200–300 kgf/cm² the increase in the friction force at fixed actual contact area is attributable to the effect of pressure on the friction constant. The nature of this effect is related not with an increase in the chain-surface interaction energy (the activation energy does not increase), but with an increase in the forces of adhesion owing to the greater number of polymer chain-steel surface contacts on the actual contact area (increase in contact density).Lenin Moscow State Pedagogical Institute, Laboratory for Problems of Polymer Physics. Translated from Mekhanika Polimerov, No. 1, pp. 140–146, January–February, 1971.     

Experimental and theoretical investigation of creep groan of brakes through minimal models

Creep groan of brake systems is a low frequency vibration phenomenon occurring at low speeds which can make passengers feel uncomfortable. This phenomenon is caused by the stick-slip-effect resulting in limit cycle oscillations with frequencies lower than 200 Hz. For the experimental investigation of this problem, an idealized brake test rig is designed concentrating on the investigation of the frictional contact by realizing low damping and small disturbances in the system. Different sensors are utilized in the test rig. Limit cycles and bifurcation effects can be observed in the experimental results. With respect to modeling, a one degree-of-freedom (DOF) model using Coulomb's friction law and a two DOF model using the bristle friction law are considered. In a comparative study of experimental and simulation results, the parameters of both friction laws can be identified from the dynamic experimental results, such as the static and dynamic friction coefficients, contact stiffness and Stribeck velocity. Experimental and theoretical results show a very good concordance. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

On final motions of a Chaplygin ball on a rough plane

A heavy balanced nonhomogeneous ball moving on a rough horizontal plane is considered. The classical model of a “marble” body means a single point of contact, where sliding is impossible. We suggest that the contact forces be described by Coulomb’s law and show that in the final motion there is no sliding. Another, relatively new, contact model is the “rubber” ball: there is no sliding and no spinning. We treat this situation by applying a local Coulomb law within a small contact area. It is proved that the final motion of a ball with such friction is the motion of the “rubber” ball.     

Plastic deformation of rough surfaces

Friction forces are only transferred within the the real area of contact A_real, which is usually smaller than the apparent area of contact A_o. The maximum friction stress τ_fric is therefore determined by the shear limit τ_max in the area of real contact and the fraction of the real area of contact (τ_fric = τ_max (A_real/A_o)). For rough surfaces the size of A_real is governed o by the plastic deformation of the surface roughness. We present a fully elasto-plastic halfspace contact formulation based on the work of Jacq et al. [1]. Linear elastic-plastic material behavior is modeled based on v. Mises plasticity with isotropic hardening. The algorithm gives the residual stress as well as the full plastic deformation field due to a frictionless normal contact. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)