Existence and numerical approximation of a solution to frictional contact problem for electro-elastic materials

In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is studied.The contact is modeled by normal compliance with finite penetration and a version of Coulomb’s law of dry friction in which the coefficient of friction depends on the slip.In addition,the effects of the electrical conductivity of the foundation are taken into account.This model leads to a coupled system of the quasi-variational inequality of the elliptic type for the displacement and the nonlinear variational equation for the electric potential.The existence of a weak solution is proved by using an abstract result for elliptic variational inequalities and a fixed point argument.Then,a finite element approximation of the problem is presented.Under some regularity conditions,an optimal order error estimate of the approximate solution is derived.Finally,a successive iteration technique is used to solve the problem numerically and a convergence result is established.

A smoothed assumed enhanced strain method for frictional contact with constant strain elements

This paper presents a finite element framework for imposing frictional contact conditions on embedded fracture faces,implemented by the constant-strain assumed enhanced strain(AES)method,where penalty method is used to impose both non-penetration constraint and Coulomb’s law of friction.The proposed constant-strain AES method for modeling embedded frictional contact can be cast into an integration algorithm similar to those used in the classical plasticity theory,where displacement jump is calculated from the local traction equilibrium at Gauss point,so the method does not introduce any additional global degrees of freedom.Moreover,constant-strain elements are often desirable in practice because they can be easily created automatically for large-scale engineering applications with complicated geometries.As encountered in other enriched finite element methods for frictional contact,the problem of normal contact pressure oscillations is also observed in the constant-strain AES method.Therefore,we developed a strain-smoothing procedure to effectively mitigate the oscillations.We investigated and verified the proposed AES framework through several numerical examples,and illustrated the capability of this method in solving challenging nonlinear frictional contact problems.

Modeling and Calculation of Impact Friction Caused by Corner Contact in Gear Transmission

Corner contact in gear pair causes vibration and noise,which has attracted many attentions.However,teeth errors and deformation make it difficulty to determine the point situated at corner contact and study the mechanism of teeth impact friction in the current researches.Based on the mechanism of corner contact,the process of corner contact is divided into two stages of impact and scratch,and the calculation model including gear equivalent error-combined deformation is established along the line of action.According to the distributive law,gear equivalent error is synthesized by base pitch error,normal backlash and tooth profile modification on the line of action.The combined tooth compliance of the first point lying in corner contact before the normal path is inversed along the line of action,on basis of the theory of engagement and the curve of tooth synthetic complianceload-history.Combined secondarily the equivalent error with the combined deflection,the position standard of the point situated at corner contact is probed.Then the impact positions and forces,from the beginning to the end during corner contact before the normal path,are calculated accurately.Due to the above results,the lash model during corner contact is founded,and the impact force and frictional coefficient are quantified.A numerical example is performed and the averaged impact friction coefficient based on the presented calculation method is validated.This research obtains the results which could be referenced to understand the complex mechanism of teeth impact friction and quantitative calculation of the friction force and coefficient,and to gear exact design for tribology.

FRICTIONAL CONTACT MULTIPOLE-BEM AND 3-D ANALYSIS OF SCREWPAIRS

The 3-D traction field in the pressure screw-pair of a 3 500 heavy and mediumplate mill press down system is successfully calculated by applying the 3-D frictional contactmultipole-BEM and the corresponding program that has been developed. The computing results show themedium diameter orientation is unreliable, especially under the interference of an outer forcecouple. Under such working conditions, the circumferential traction distribution on the screw teethis extremely uneven, which is the main reason for the destruction and short life time ofscrew-pairs. When utilizing the same precision (the relative tolerance is 10X10^(-5)), themultipole-BEM uses almost the same CPU time as used by the FEM, but the needed computer memory sizeis only one eightieth of that needed by the FEM (10 MB vs. 800 MB). The multipole-BEM is well suitedfor computing large-scale engineering problems.

Friction Characteristics of Nanoscale Sliding Contacts between Multi-Asperity Tips and Textured Surfaces

Nanoscale sliding contacts of smooth surfaces or between a single asperity and a smooth surface have been widely investigated by molecular dynamics simulations, while there are few studies on the sliding contacts between two rough surfaces. Actually, the friction of two rough surfaces considering interactions between more asperities should be more realistic. By using multiscale method, friction characteristics of two dimensional nanoscale sliding contacts between rigid multi-asperity tips and elastic textured surfaces are investigated. Four nanoscale textured surfaces with different texture shapes are designed, and six multi-asperity tips composed of cylindrical asperities with different radii are used to slide on the textured surfaces. Friction forces are compared for different tips, and effects of the asperity radii on the friction characteristics are investigated. Average friction forces for all the cases are listed and compared, and effects of texture shapes of the textured surfaces are discussed. The results show that textured surface II has a better structure to reduce friction forces. The multi-asperity tips composed of asperities with R=20r0 （r0=0.227 7 nm） or R=30r0 get higher friction forces compared with other cases, and more atoms of the textured surfaces are taken away by these two tips, which are harmful to reduce friction or wear. For the case of R=10ro, friction forces are also high due to large contact areas, but the sliding processes are stable and few atoms are taken away by the tip. The proposed research considers interactions between more asperities to make the model approach to the real sliding contact problems. The results will help to vary or even control friction characteristics by textured surfaces, or provide references to the design of textured surfaces.

Analysis of sliding electric contact characteristics in augmented railgun based on the combination of contact resistance and sliding friction coefficient

The contact resistance between the armature and rails is an important indicator of the contact characteristics in electromagnetic launches.As the contact resistance depends not only on the contact state but also on the contact stress and temperature,there are some limitations in analyzing the contact characteristics using only the contact resistance.In this paper,the contact characteristics of the augmented railgun are analyzed by the combination of contact resistance and sliding friction coefficient.Firstly,the theoretical calculation model of the contact resistance and friction coefficient of the augmented electromagnetic railgun is established.Then the contact resistance and friction coefficient are calculated by the measured values of the muzzle voltage,rail current and armature displacement.Finally,the contact characteristics are analyzed according to the features of the waveforms of the contact resistance and the friction coefficient,and the analysis conclusions are verified by experimental rail images.The results showed that:the aluminum melt film gradually formed on the contact surface reduces the contact resistance and the friction coefficient;the wear and erosion of the armature cause deterioration of the contact state;after the transition,the reliability of the sliding contact between the armature and rails decreases,resulting in an increase in contact resistance.

Numerical Analysis of Rolling-sliding Contact with the Frictional Heat in Rail

Thermal damage caused by frictional heat of rolling-sliding contact is one of the most important failure forms of wheel and rail. Many studies of wheel-rail frictional heating have been devoted to the temperature field, but few literatures focus on wheel-rail thermal stress caused by frictional heating. However, the wheel-rail creepage is one of important influencing factors of the thermal stress In this paper, a thermo-mechanical coupling model of wheel-rail rolling-sliding contact is developed using thermo-elasto-plastic finite element method. The effect of the wheel-rail elastic creepage on the distribution of heat flux is investigated using the numerical model in which the temperature-dependent material properties are taken into consideration. The moving wheel-rail contact force and the frictional heating are used to simulate the wheel rolling on the rail. The effect of the creepage on the temperature rise, thermal strain, residual stress and residual strain under wheel-rail sliding-rolling contact are investigated. The investigation results show that the thermally affected zone exists mainly in a very thin layer of material near the rail contact surface during the rolling-sliding contact. Both the temperature and thermal strain of rail increase with increasing creepage. The residual stresses induced by the frictional heat in the surface layer of rail appear to be tensile. When the creepage is large, the frictional heat has a significant influence on the residual stresses and residual strains of rail. This paper develops a thermo-meehanical coupling model of wheel-rail rolling-sliding contact, and the obtained results can help to understand the mechanism of wheel/rail frictional thermal fatigue.

Predictions of friction and flash temperature in marine gears based on a 3D line contact mixed lubrication model considering measured surface roughness

Wear and scuffing failures often occur in marine transmission gears due to high friction and flash temperature at the interface between the meshing-teeth.In this paper,a numerical solution procedure was developed for the predictions of transient friction and flash temperature in the marine timing gears during one meshing circle based on the 3D line contact mixed lubrication simulation,which had been verified by comparing the flash temperature with those from Blok’s theory.The effect of machined surface roughness on the mixed lubrication characteristics is studied.The obtained results for several typical gear pairs indicate that gear pair 4-6 exhibits the largest friction and the highest interfacial temperature increase due to severe rough surface asperity contacts,while the polished gear surfaces yield the smallest friction and the lowest interfacial temperature.In addition,the influences of the operating conditions and the gear design parameters on the friction-temperature behaviors are discussed.It is observed that the conditions of heavy load and low rotational velocity usually lead to significantly increased friction and temperature.In the meantime,by optimizing the gear design parameters,such as the modulus and the pressure angle,the performance of interfacial friction and temperature can be significantly improved.

Frictional contact algorithm study on the numerical simulation of large deformations in deep soft rock tunnels

There exist three types of nonlinear problems in large deformation processes of deep softrock engineering, i.e., nonlin- earity caused by material, geometrical and contact boundary. In this paper, the numerical method to tackle the nonlinear eontact and large deformation problem in A Software on Large Deformation Analysis for Soft Rock Engineering at Great Depth was presented. In the software, based on Lagrange multiplier method and Coulomb friction law, kinematic constraints on contact boundaries were introduced in functional function, and the finite element equations was established for two incremental large deformation analyses models, polar decomposition model and additive decomposition model. For every incremental loading step, by searching for the contact points in the potential contact interfaces （the excavation boundaries）, the Lagrange multipliers, i.e., contact forces are cal- culated iteratively by Gauss-Seidel method, and justified through satisfy the inequalities of static constraint on contact boundaries. With the software, large deformation and frictional contact of a transport roadway were analyzed numerically by the two models. The numerical examples demonstrated the efficiency of the method used in the software.

Nonlinear Dynamics Seismic Response of Container Crane Based on Contact Friction Theory

To evaluate the dynamic behavior of a container crane under seismic loads accurately,the contact state between the wheels and the rails or the ground that significantly affect the seismic response of the structure must be considered elaborately.This paper has proposed a modeling method based on the theory of contact and friction for simulating the nonlinear seismic response of large and flexible structure of a jumbo movable container crane,including the contact problem regarding the wheels attached to the bottom of its legs and the rails on which they ride.These models are used to perform extensive dynamic time-history analysis in order to find out their nonlinear dynamic behavior under various excitation modes.It is found that the presented numerical modeling method simulates the nonlinear seismic response of a container crane quite well.Notably,it can verify and expand our understanding of the seismic behaviors by evaluating response performance for the large seaport cranes.

Theoretical analysis of thermoviscoelastic contact between friction lining and wire rope in mine friction hoists

Serious accidents of mine hoists caused by high-speed sliding between friction lining and wire rope are often seen in coal mines.In order to solve this problem,we analyzed the contact characteristics between friction lining and wire rope.Then we carried out a dynamic mechanical analysis(DMA) to explain the change in mechanical properties of the friction lining as function of temperature and load frequency and found that temperature has a stronger effect on the mechanical properties than the frequency.We used multiple regression analysis to obtain the thermoviscoelastic constitutive relations of the friction lining.As well we derived the analytic solution for the thermoviscoelastic contact radius and pressure by combining the theory of viscoelastic contact mechanics with thermoviscoelastic constitutive relations.

NON-INTERIOR SMOOTHING ALGORITHM FOR FRICTIONAL CONTACT PROBLEMS

A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.

Effects of Inter-Particle Frictional Coefficients on Evolution of Contact Networks in Landslide Process

During the process of landslide, its dynamic mechanism is important to understand and predict these kinds of natural hazard. In this paper, a new method, based on concepts of complex networks, has been proposed to investigate the evolution of contact networks in mesoscale during the sliding process of slope. A slope model was established using the discrete element method (DEM), and influences of inter-particle frictional coefficients with four different values on?dynamic landslides were studied. Both macroscopic analysis on slope?landslide?and mesoanalysis on structure evolution of contact networks, including the?average degree, clustering coefficient?and N-cycle, were done during the process?of landslide. The analysis results demonstrate that: 1) with increasing inter-particle?frictional coefficients, the displacement of slope decreases and the stable angle of slope post-failure increases, which is smaller than the peak internal frictional angle;2) the average degree decreases with the increase of inter-particle frictional coefficient. When the displacement at the toe of the slope is smaller,?the average degree there changes more greatly with increasing inter-particle?frictional coefficient;3) during the initial stage of landslide, the clustering coefficient?reduces sharply, which may leads to easily slide of slope. As the landslide?going?on, however, the clustering coefficient?increases denoting increasing stability?with?increasing inter-particle frictional coefficients. When the inter-particle?frictional coefficient is smaller than 0.3, its variation can affect the clustering coefficient?and stable inclination of slope post-failure greatly;and 4) the number of?3-cycle increases, but 4-cycle and 5-cycle decrease with increasing inter-particle frictional coefficients.

Friction Characteristics of Space Lubricating Oil No.4129 in Rolling and Sliding Contact

The friction coefficients between the surfaces of a ball and a disc lubricated by a space lubricating oil No.4129 were measured at various operating conditions on a ball-disc friction test rig. Friction characteristic curves were obtained under sliding and rolling movements at point contact. A new model for calculation of the friction coefficient was presented. The results show that the bigger the load is, the larger the friction coefficient becomes. The rolling speed ranging from 1 m/s to10 m/s has an important effect on the friction coefficient. The friction coefficient increases with the increase in sliding speed and the decrease in rolling speed. The linear variation region of the friction coefficient versus the sliding speed at high rolling speed is wider than that at low rolling speed. The model for calculation of the friction coefficient is accurate for engineering use.

A new visco-elastic contact model of traveling wave ultrasonic motor with stator frictional layer

A new contact model of traveling wave ultrasonic motor （TWUSM） with a visco-elastic stator frictional layer was presented. In this model, the initial boundaries were revised, and the rotor revolution speed could he calculated iteratively. This model was compared with compliant slider and rigid stator model. The results of motor characteristics simulations showed that the motors based on this model would gain bigger stall torque. Then the friction and wear characteristics of two models were analyzed. The motors based on this model had lower coefficient of friction and better wear resistance.

Friction contact mechanisms of layered surface

In this paper,we firstly review the carbon layered surface prepared with electron cyclotron resonance (ECR) plasma sputtering. Secondly,the friction behavior of carbon layered surface under pin-on-disk testing is described. Furthermore,the contact stress evolution processes of layered surface with and without transfer layer during wear are given for understanding the contact mechanisms. Finally,a three-dimension (3D) local yield map of layered surface is introduced,which is useful to predict the possible contact mechanisms.

BOUNDARY ELEMENT-COMPLIANCE MATRIX METHOD FOR 3D ELASTIC FRICTIONAL CONTACT ANALYSIS

Boundary element compliance matrix (BEM) method to deal with 3D elastic frictional contact problem was presented, and its calculation method and convergence criteria were discussed. It has the advantages of both boundary element method and compliance matrix methods: small number of inputting data, simple and convenient model, precise solution, short calculating time and requirements for a small quantity of computer memory. In comparison to the other BEM with friction problems, we obtain more precise solution and less iteration times. The effect of friction coefficient on contact area. contace state, and relative displacement, normal and tangential stress was analyzed by two examples. And because of the quickness of calculation of program and efficient method, we visualize the result in virtual reality (VR) environment. We grant the real time of VR and provide more immersion to users who ware the VR device.

The Effects of Contact Interface on the Friction Characteristics of Self-assembly Monolayers

The effects of different contact interfaces on the friction characteristics of OTS self-assembled monolayers were investigated by a universal micro-tribometer in different sliding velocities. The results indicate that there exist lower friction coefficients between OTS SAMs and Ti, Ni and Cu films deposited on GCr15 steel balls than those between OTS SAMs and GCr15 steel ball. The friction coefficient between OTS SAMs and Ti film is the largest, and the friction coefficient between OTS SAMs and Cu film is the least in these three films, which depends on the intrinsic characteristics of the materials. The friction coefficients between OTS SAMs and GCr15 steel ball and three nanometer films increase with the sliding velocity increasing, which can be explained by the relaxation characteristics of OTS molecules.

A Study on Law of Change of Real Contact Area of Friction during Transition Process

Mechanism of frictional vibration and the difference of kinctic-static friction is an open question. Research shows that the change of real area of contact during transition process of friction results in the phenomena mentioned above. In substance, the F-Vr, descent and F-T ascent characters are caused by A-Vr, and A-T characters respectively. Based on ultrasonic experiment the mechanism of the phenomena is explained and the frictional formulas using the parameter-real area of contact are given in this article.

Influence of Friction Interface Contact on Ultrasonic Motor Efficiency Under Static Conditions

The friction interface matching plays a deterministic role in the motor efficiency,and the microcosmic contact status of friction interface should be investigated to improve the ultrasonic motor performance.The main purpose is to improve the effective output power of ultrasonic motor.Hence,one studies the contact condition of the friction interface of the ultrasonic motor,analyzes the micro condition of contact interface through finite element analysis,optimizes unreasonable structures,and compares the two different-structure ultrasonic motors through experiments.The results reflect the necessity of optimization.After optimization,the stator and rotor deform after pre-pressure and the contact interface of them full contact theoretically.When reaching heat balance the effective output of the motor is 37%,and the average effective output efficiency is 2.384 times higher than that of the unoptimized.It can be seen that the total consumption of the ultrasonic motor system decreases significantly.Therefore,when using in certain system the consumption taken from the system will decreases largely,especially in the system with a strict consumption control.