Статті в журналах: "Frictional contact model"

1

Chang, L., and H. Zhang. "A Mathematical Model for Frictional Elastic-Plastic Sphere-on-Flat Contacts at Sliding Incipient." Journal of Applied Mechanics 74, no. 1 (December 9, 2005): 100–106. http://dx.doi.org/10.1115/1.2178838.

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This paper presents a mathematical model for frictional elastic-plastic sphere-on-flat contacts at sliding incipient. The model is developed based on theoretical work on contact mechanics in conjunction with finite-element results. It incorporates the effects of friction loading on the contact pressure, the mode of deformation, and the area of contact. The shear strength of the contact interface is, in this paper, assumed to be proportional to the contact pressure with a limiting value that is below the bulk shear strength of the sphere. Other plausible interfacial-shear-strength characteristics may also be implemented into the contact model in a similar manner. The model is used to analyze the frictional behavior of a sphere-on-flat contact where the experimental data suggest that the interfacial shear strength is similar in nature to the one implemented in the model. The theoretical results are consistent with the experimental data in all key aspects. This sphere-on-flat contact model may be used as a building block to develop an asperity-based contact model of rough surfaces with friction loading. It may also serve in the modeling of boundary-lubricated sliding contacts where the interfacial shear strength in each micro-contact is coupled with its flash temperature and related to the lubricant/surface physical-chemical behavior.

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2

Yu, Chunxiao, Dinghui Jing, Chang Fu, and Yanfang Yang. "A Kind of FM-BEM Penalty Function Method for a 3D Elastic Frictional Contact Nonlinear System." Journal of Mathematics 2021 (January 13, 2021): 1–11. http://dx.doi.org/10.1155/2021/6626647.

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In this paper, a kind of node_face frictional contact FM-BEM penalty function method is presented for 3D elastic frictional contact nonlinear problems. According to the principle of minimum potential energy, nonpenetrating constraints are introduced into the elastic frictional contact system as a penalty term. By using the least square method and penalty function method, an optimization mathematical model and a mathematical programming model with a penalty factor are established for the node_face frictional contact nonlinear system. For the two models, a penalty optimization IGMRES (m) algorithm is proposed, and the influences of different penalty factors on the solution of the whole system are analyzed. Finally, a numerical simulation is carried out for two elastic frictional contact objects, and some important results including displacements, pressures, friction forces, and friction slips in the contact area are presented. Theoretical analysis and numerical experiment show that the newly presented FM-BEM penalty function method not only is efficient and practical but also has much superiority. It is easy to implement, and it is fast convergent with good stability.

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3

Li, Zheng, and Ken Mao. "Frictional Effects on Gear Tooth Contact Analysis." Advances in Tribology 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/181048.

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The present paper concentrates on the investigations regarding the situations of frictional shear stress of gear teeth and the relevant frictional effects on bending stresses and transmission error in gear meshing. Sliding friction is one of the major reasons causing gear failure and vibration; the adequate consideration of frictional effects is essential for understanding gear contact behavior accurately. An analysis of tooth frictional effect on gear performance in spur gear is presented using finite element method. Nonlinear finite element model for gear tooth contact with rolling/sliding is then developed. The contact zones for multiple tooth pairs are identified and the associated integration situation is derived. The illustrated bending stress and transmission error results with static and dynamic boundary conditions indicate the significant effects due to the sliding friction between the surfaces of contacted gear teeth, and the friction effect can not be ignored. To understand the particular static and dynamic frictional effects on gear tooth contact analysis, some significant phenomena of gained results will also be discussed. The potentially significant contribution of tooth frictional shear stress is presented, particularly in the case of gear tooth contact analysis with both static and dynamic boundary conditions.

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4

Wingertszahn, Patrick, Oliver Koch, Lorenzo Maccioni, Franco Concli, and Bernd Sauer. "Predicting Friction of Tapered Roller Bearings with Detailed Multi-Body Simulation Models." Lubricants 11, no. 9 (September 1, 2023): 369. http://dx.doi.org/10.3390/lubricants11090369.

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In the presented work, a parametric multibody simulation model is presented that is capable of predicting the friction torque and kinematics of tapered roller bearings. For a highly accurate prediction of bearing friction, consideration of solid and lubricant friction is mandatory. For tapered roller bearings in particular, the friction in the contact between the rolling element and raceway is of importance. Friction forces in the contact between the rolling element end face and inner ring rib as well as roller cage pocket contacts are also considered in the model. A large number of tests were carried out to validate the model in terms of the simulated frictional torque. Influencing variables such as speed, axial load, radial load, and temperature were investigated. The simulation results show good agreement with the measured friction torque, which confirms that the model is well suited to predict frictional torques and therefore the kinematics of tapered roller bearings.

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5

BAJKOWSKI, J., J. R. FERNÁNDEZW, K. L. KUTTLER, and M. SHILLOR. "A thermoviscoelastic beam model for brakes." European Journal of Applied Mathematics 15, no. 2 (April 2004): 181–202. http://dx.doi.org/10.1017/s0956792503005370.

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A model for the dynamic thermomechanical behavior of a viscoelastic beam which is in frictional contact with a rigid rotating wheel is presented. It describes a simple braking system in which the wheel comes to a stop as a result of the frictional traction generated by the beam. Friction is modelled with a temperature and slip rate dependent coefficient of friction. Frictional heat generation is taken into account as well as the wheel temperature evolution, and the wear of the beam's contacting end. The model is formulated as a variational inequality. A FEM numerical scheme for the model is described, implemented, and the results of numerical simulations are shown.

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6

ABDALLA, W. S., S. S. ALI-ELDIN, and M. R. GHAZY. "ADAPTIVE INCREMENTAL FINITE ELEMENT PROCEDURE FOR SOLVING ELASTOPLASTIC FRICTIONAL CONTACT PROBLEMS SUBJECTED TO NORMAL AND TANGENTIAL LOADS." International Journal of Applied Mechanics 06, no. 03 (May 6, 2014): 1450031. http://dx.doi.org/10.1142/s1758825114500318.

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This paper presents a numerical model for analyzing the stresses and displacements of deformable bodies in contact with the presence of friction and material nonlinearity. Based on the finite element method (FEM), the elastoplastic frictional contact problem is formulated as an incremental convex programming model (ICPM) under inequality contact constraints and friction conditions. The classical Coulomb's friction law and the Prandtl–Reuss flow rule with the von Mises yield criterion are used to simulate the interface friction conditions and the elastoplastic behavior of the contacting bodies, respectively. The Lagrange multiplier approach is adopted for imposing the contact constraints. Furthermore, an effective adaptive incremental procedure is developed for solving the elastoplastic frictional contact problems. Examples for the frictional contact having advancing and receding nature are analyzed. The obtained results prove the ability of the developed procedure to investigate the sequence of different events during monotonic application of external loads. In addition, the results elucidate the effect of external side force on the friction behavior in the presence of plastic deformation. Good agreement has been found with published results.

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7

Dickrell, P. L., W. G. Sawyer, and A. Erdemir. "Fractional Coverage Model for the Adsorption and Removal of Gas Species and Application to Superlow Friction Diamond-Like Carbon." Journal of Tribology 126, no. 3 (June 28, 2004): 615–19. http://dx.doi.org/10.1115/1.1739408.

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The frictional behavior of diamond-like carbon (DLC) films varies with environmental condition. One theory asserts that the cause of variations in the frictional performance is environmental contaminants adsorbing onto the DLC film surface. Testing of the frictional performance of DLC films in a pin-on-disk contact has mapped the transient behavior of the friction coefficient. A model for fractional coverage, based on the adsorption of environmental contaminants and their removal through the pin contact, is developed. The rate of adsorption is taken from Langmuir’s model [17], which is combined with the removal ratio from Blanchet and Sawyer [18]. The coefficient of friction is based on the average fractional coverage under the pin contact. The model also gives a closed-form expression for the steady-state fractional coverage. Model calculations compared favorably to the time progression of the friction coefficient for a series of earlier experiments on a superlow friction DLC coating [7], when the fractional removal term was allowed to increase with increasing sliding speed.

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8

Murphey, Todd D. "Kinematic reductions for uncertain mechanical contact." Robotica 25, no. 6 (November 2007): 751–64. http://dx.doi.org/10.1017/s0263574707003827.

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SUMMARYThis paper describes the methods applicable to the modeling and control of mechanical contact, particularly those systems that experience uncertain stick/slip phenomena. Geometric kinematic reductions are used to reduce a system's description from a second-order dynamic model with frictional disturbances coming from a function space to a first-order model with frictional disturbances coming from a space of finite automata over a finite set. As a result, modeling for purposes of control is made more straight-forward by getting rid of some dependencies on low-level mechanics (in particular, the details of friction modeling). Moreover, the online estimation of the uncertain, discrete-valued variables has reduced sensing requirements. The primary contributions of this paper are the introduction of a simplifying representation of friction and formal tests for kinematic reducibility. Results are illustrated using a slip-steered vehicle model and an actuator array model.

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9

Chang, L., Yongwu Zhao, P. B. Hall, R. Thom, and C. Moore. "On Heat Generation in Rolling Contacts Under Boundary and Mixed Lubrication." Journal of Tribology 123, no. 1 (August 17, 2000): 61–66. http://dx.doi.org/10.1115/1.1330733.

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This paper reports on experiments and theoretical analyses of heat generation and scuffing failure in rolling contacts. The experiments were conducted with dry contacts, and the theoretical analyses were carried out using a deterministic thermal contact model. The research reveals that heat generated by asperity plastic deformation in the direction normal to the contact can be significant in high-load, high-speed contacts under boundary and mixed lubrication conditions. Under near rolling conditions, heat generated by the plastic deformation largely dominates that by the friction and is the main source leading to contact scuffing. This heat generation is shown to be significant compared to frictional heating even at relatively large slide-to-roll ratios. Parametric studies show that the ratio of asperity-plastic-deformation heating to frictional heating is sensitive to slide-to-roll ratio, hardness and surface finish but insensitive to contact load, rolling velocity and fluid/asperity load sharing.

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10

Heß, Markus, and Valentin L. Popov. "Voltage-Induced Friction with Application to Electrovibration." Lubricants 7, no. 12 (November 20, 2019): 102. http://dx.doi.org/10.3390/lubricants7120102.

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Due to the growing interest in robotic and haptic applications, voltage-induced friction has rapidly gained in importance in recent years. However, despite extensive experimental investigations, the underlying principles are still not sufficiently understood, which complicates reliable modeling. We present a macroscopic model for solving electroadhesive frictional contacts which exploits the close analogy to classical adhesion theories, like Johnson-Kendall-Roberts (JKR) and Maugis, valid for electrically neutral bodies. For this purpose, we recalculate the adhesion force per unit area and the relative surface energy from electrostatics. Under the assumption of Coulomb friction in the contact interface, a closed form equation for the friction force is derived. As an application, we consider the frictional contact between the fingertip and touchscreen under electrovibration in more detail. The results obtained with the new model agree well with available experimental data of the recent literature. The strengths and limitations of the model are clearly discussed.

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11

Du, Jian Hua, Gui Min Liu, and Wen Zheng Han. "Mathematical Model of the Part Surface Temperature Field." Key Engineering Materials 373-374 (March 2008): 539–42. http://dx.doi.org/10.4028/www.scientific.net/kem.373-374.539.

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Research on the simulation and calculation of the temperature field of friction plate in brake is one of the main references for constructing a frictional material couple. The friction heat generates on the real contact area, so the distribution of the friction heat is asymmetry and localized. In this study, the effects of real contact area on the surface temperature were investigated. Then the mathematical model of the two-dimensional unsteady temperature field of local contact area is presented. The simulation of the model for Cu-based wet friction plate indicates that the local contact has an essential influence on the surface temperature and the maximal contact temperature; the mathematic model of local contact temperature field can be used to predict the critical sliding velocity and allowable rate of energy absorbed.

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12

Shariati, Hossein, Mahdi Saadati, Kenneth Weddfelt, Per-Lennart Larsson, and Francois Hild. "Study of Frictional Effects of Granite Subjected to Quasi-Static Contact Loading." Lubricants 8, no. 12 (December 16, 2020): 106. http://dx.doi.org/10.3390/lubricants8120106.

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The rock fragmentation response to drilling, in particular percussive drilling, is important in order to improve the efficiency of such an operation. The resulting problem includes spherical contact between the drill bit and the material and therefore, a numerical analysis of frictional effects in quasi-static spherical indentation of Bohus granite is presented. The frictional coefficient between the indenter and the granite surface is accounted for in numerical simulations. A previously determined constitutive law is used for the purpose of numerical analyses. The latter consists of a Drucker-Prager plasticity model with variable dilation angle coupled with an anisotropic damage model. Since the tensile strength is random, Weibull statistics was considered. Using a frictionless contact model, the stress state of Bohus granite corresponding to the first material failure occurrence, observed in indentation experiments, was numerically determined. However, the frictional effects, which are of interest in this study, may lead to changes in the numerically established stress state and consequently the Weibull parameters should be recalibrated. The so-called Weibull stress decreases from 120 MPa for a frictionless contact to 75 MPa for frictional contact, and the Weibull modulus from 24 to 12. It is numerically observed that the predicted force-penetration response, using the new set of Weibull parameters, is not influenced by friction. Conversely, the predicted fracture pattern, in the case of frictional contact, is similar to the case of frictionless contact, but its size is somewhat larger. Last, a parametric study analyzing the dependence of the friction coefficient is carried out and no significant changes are detected. The novelty of the present findings concerns the fact that both an advanced damage description in combination with an advanced plasticity model, both implemented for finite element analyses, is used to analyze frictional effects at granite indentation.

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13

Duffaut, Kenneth, Martin Landrø, and Roger Sollie. "Using Mindlin theory to model friction-dependent shear modulus in granular media." GEOPHYSICS 75, no. 3 (May 2010): E143—E152. http://dx.doi.org/10.1190/1.3429998.

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An explicit expression for the effective shear modulus of a random packing of identical spheres is derived as a function of Mindlin’s tangential stiffness with interparticle contact friction. The motivation behind the approach is to incorporate the effect of intergrain friction to predict velocities in unconsolidated sands. The Mindlin friction term, allowing partial slip across the contact area between pairs of spheres, can be viewed as a parameter accounting for the growing macroscopic intergrain friction in sands as burial progresses. Hence, both moduli and velocities will gradually increase as the compressional- to shear-wave velocity ratio [Formula: see text] or Poisson’s ratio [Formula: see text] decreases. An estimate of effective elastic constants in particular shear modulus can be obtained for a spherical grain pack with an arbitrary frictional behavior ranging between two special contact boundary conditions representing infinite friction and zero friction. The proposedmodel predicts a nonlinear transition between the two special grain-contact conditions when compared to previously published linear relationships. Comparison of elastic properties, i.e., dynamic shear-modulus predictions assuming zero contact friction with experimental data on loose glass bead and sand samples undergoing hydrostatic compression, appears to match reasonably well at low confining stress (less than [Formula: see text]) but deviates gradually as stress increases. It is advocated that the increasing effective internal frictional resistance of the experimental core samples control both the frictional attenuation mechanism in loose grain packs under low confining stress for strain amplitudes typical of seismic waves (less than [Formula: see text]) and the higher stress-velocity sensitivity. Circumstantial evidence of this is found in publications describing both laboratory attenuation analysis and consolidation experiments on granular materials with different degrees of competence or static shear strength.

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14

Wang, Wei Zu, Liu Yi Wang, Zeng Xue Zhang, and Hai Bo Chen. "Boundary Lubrication Model under Square Surface Contact Condition." Applied Mechanics and Materials 29-32 (August 2010): 1396–401. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.1396.

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The contact temperature of the frictional surfaces under boundary lubrication in square surface contact is calculated according to classic heat conduction theories. The friction coefficient of boundary lubrication is expressed with the friction coefficient of boundary film and direct contact. Then, a model is developed based on the relationship of adsorption heat, friction coefficient and contact temperature. The model is used to solve a sample question. The results illuminate that when the applied load is relatively small, the friction coefficient keeps at a stable small value with the variation of the sliding speed and the load. However, when the load reaches a certain value, the increase of the sliding speed or the normal load both leads to the increase of the friction coefficient. The friction coefficient is also increases with the increase of the contact temperature. The relative deficiency of oil, which indicates the proportion of the true contact area to mean contact area, has almost the same variation trend of the friction coefficient.

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15

Yamada, Takayoshi, Sushanta Kumar Saha, Nobuharu Mimura, and Yasuyuki Funahashi. "Stability Analysis of Planar Grasp with 2D-Virtual Spring Model." Journal of Robotics and Mechatronics 11, no. 4 (August 20, 1999): 274–82. http://dx.doi.org/10.20965/jrm.1999.p0274.

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We analyze stability of planar grasp using a 2D virtual spring model. A 2D virtual spring model is widely used to explore frictionless grasp, but the direction of contact force has not been studied for a grasped object displaced by external disturbance. Finger displacement is restricted to the normal at initial contact. We introduce a 2D spring model for a frictionless case. The direction of contact force is explicitly formulated. Using potential energy, we analyze stability of frictionless grasp and show that the 1D-spring model is a special case of our proposed 2D-spring model. Frictional grasp stability is also studied using rolling contact. Numerical examples of 2-fingered grasp demonstrate the effects of parameters such as spring stiffness and contact force. It is shown that an optimum force exists for stabilizing frictionless grasp. It is proved that friction enhances grasp stability from the relationship between frictionless and frictional stiffness matrices. Stiffness conditions for stabilizing 3-fingered grasp is clarified.

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16

Amassad, Amina, and Caroline Fabre. "Existence for viscoplastic contact with Coulomb friction problems." International Journal of Mathematics and Mathematical Sciences 32, no. 7 (2002): 411–37. http://dx.doi.org/10.1155/s0161171202110179.

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We present existence results in the study of nonlinear problem of frictional contact between an elastic-viscoplastic body and a rigid obstacle. We model the frictional contact both by a Tresca's friction law and a regularized Coulomb's law. We assume, in a first part, that the contact is bilateral and that no separation takes place. In a second part, we consider the Signorini unilateral contact conditions. Proofs are based on a time-discretization method, Banach and Schauder fixed point theorems.

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17

MIGORSKI, S., A. OCHAL, M. SHILLOR, and M. SOFONEA. "A model of a spring-mass-damper system with temperature-dependent friction." European Journal of Applied Mathematics 25, no. 1 (September 10, 2013): 45–64. http://dx.doi.org/10.1017/s0956792513000272.

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This work models and analyses the dynamics of a general spring-mass-damper system that is in frictional contact with its support, taking into account frictional heat generation and a reactive obstacle. Friction, heat generation and contact are modelled with subdifferentials of, possibly non-convex, potential functions. The model consists of a non-linear system of first-order differential inclusions for the position, velocity and temperature of the mass. The existence of a global solution is established and additional assumptions yield its uniqueness. Nine examples of conditions arising in applications, for which the analysis results are valid, are presented.

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18

Li, Zhi, Jian Chen, Jiazhu Li, and Kun Liu. "Effect of textured surface on the frictional noise under line contact and sliding–rolling conditions." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 9 (April 29, 2017): 1679–89. http://dx.doi.org/10.1177/0954406217706721.

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Line contact and sliding–rolling movements exist widely in gears and bearings. In order to investigate the influence of surface microstructure on the frictional noise, a numerical study on the frictional noise generated by textured surfaces under line contact and sliding–rolling conditions by the use of finite element method is presented. The finite element model is established based on real surface topography. To improve the analysis reliability, friction coefficients used in the simulation are measured for different textured surfaces under various loads and speeds. The relationship between the 3D surface topography parameters and the frictional noise are analyzed. Results show that the frictional noise under line contact sliding–rolling conditions increases with load and speed, which can be explained from an energy dissipation perspective. Moreover, the 3D surface topography parameters of mean peak curvature and peak density influence the frictional noise during sliding–rolling under line contact significantly.

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19

ATTIA, MOHAMED A., AHMED G. EL-SHAFEI, and FATIN F. MAHMOUD. "NONLINEAR ANALYSIS OF FRICTIONAL THERMO-VISCOELASTIC CONTACT PROBLEMS USING FEM." International Journal of Applied Mechanics 06, no. 03 (May 6, 2014): 1450028. http://dx.doi.org/10.1142/s1758825114500288.

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This study presents a numerical finite element model to analyze the response of frictional thermo-viscoelastic contact systems, which experience material and geometrical nonlinearities. Thermo-rheologically complex behavior of the contacting bodies is assumed. The nonlinear viscoelastic constitutive model is expressed by an integral form of a creep function, whose elastic and time-dependent properties vary with stresses and temperatures. Adopting the assumption that the hydrostatic and deviatoric responses are uncoupled, the constitutive equation is expressed in an incremental form, with the hereditary integral updated at the end of each time increment by recursive computation. The Lagrange multiplier approach is applied to incorporate the inequality contact constraints, while friction effect along the contact interface is modeled using a local nonlinear friction law. The material and geometrical nonlinearities are modeled in the framework of the total Lagrangian formulation. The developed nonlinear viscoelastic model is verified using the available benchmarks. The applicability of the developed model is demonstrated by solving two thermo-viscoelastic frictional contact problems with different contact natures. Results show a distinct effect of the thermo-rheological behavior on viscoelastic contact status.

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20

Spinu, Sergiu. ""A NUMERICAL SOLUTION FOR THE ELASTIC SLIDING CONTACT WITH FRICTIONAL HEATING "." International Journal of Modern Manufacturing Technologies 14, no. 2 (December 20, 2022): 302–8. http://dx.doi.org/10.54684/ijmmt.2022.14.2.302.

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A thermoelastic contact model for non-conforming smooth or rough surfaces is proposed in this paper, based on a method for thermoelastic displacement computation. A classical contact model for the contact of rough surfaces is enhanced by integrating the thermal component of displacement. In the sliding contact model, heat is generated by friction at the contact surface, at a rate proportional to the sliding velocity, the frictional coefficient and the contact pressure. The latter, in its turn, is influenced by the initial clearance, the rigid body approach and the normal displacement, which comprises contributions from (1) the elastic displacement due to pressure, (2) the elastic displacement due to the shear tractions, assumed proportional to pressure according to Coulomb law of friction, and (3) the thermoelastic displacement due to the liberated heat, also proportional to pressure. These dependencies suggest that the geometric contact equation can be reduced to an equation in pressure, whose solution is obtained numerically based on an iterative search of the contact area and of the pressure distribution as in the case of isothermal contacts. A spherical contact is simulated with the newly advanced computer program, by including the thermoelastic effects. It is found that the contact area predicted by the isothermal contact model is larger than for the thermoelastic contact, and the pressure in the central contact region is underestimated when the thermal distortion is neglected. The advanced method is expected to provide base for the study of transient contact processes with consideration of thermal parameters.

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21

Zolnoun, Denniz, and Yasser Ashraf Gandomi. "Biomechanical Model of Human Index Finger During Examination." Journal of Science and Medicine 3, no. 1 (February 15, 2021): 1–14. http://dx.doi.org/10.37714/josam.v2i4.51.

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We have developed a mathematical model based on the Hunt-Crossley’s viscoelastic contact formulation for predicting the contact forces in the upper-body. The simulations were carried out in OpenSim software package and the simulations results were compared to experimentally recorded contact forces measured using a pressure algometer for assessing pressure pain sensitivity in the pelvic region 1. We observed a very good agreement between the model prediction and algometer data. Our simulation revealed that by pressing down on the tissue both normal and frictional contact forces increase up to a point- ceiling effect. Moreover, viscoelastic properties of the examinee’s tissue were associated with force; specifically, as the stiffness of the tissue declined both normal and frictional contact forces similarly declined albeit in a different way. Once the contact force reaches a peak point (irrespective of the baseline stiffness of the tissue) additional pressure application by the examiner was associated with incremental decrease in both normal and frictional (wasted) contact force.

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22

Li, Qunyang, and Kyung-Suk Kim. "Micromechanics of friction: effects of nanometre-scale roughness." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2093 (February 19, 2008): 1319–43. http://dx.doi.org/10.1098/rspa.2007.0364.

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Nanometre-scale roughness on a solid surface has significant effects on friction, since intersurface forces operate predominantly within a nanometre-scale gap distance in frictional contact. To study the effects of nanometre-scale roughness, two novel atomic force microscope friction experiments were conducted, each using a gold surface sliding against a flat mica surface as the representative friction system. In one of the experiments, a pillar-shaped single nano-asperity of gold was used to measure the molecular-level frictional behaviour. The adhesive friction stress was measured to be 264 MPa and the molecular friction factor 0.0108 for a direct gold–mica contact. The nano-asperity was flattened in contact, although its hardness at this length scale is estimated to be 3.68 GPa. It was found that such a high pressure could be reached with the help of condensed water capillary forces. In the second experiment, a micrometre-scale asperity with nanometre-scale roughness exhibited a single-asperity-like response of friction. However, the apparent frictional stress, 40.5 MPa, fell well below the Hurtado–Kim model prediction of 208–245 MPa. In addition, the multiple nano-asperities were flattened during the frictional process, exhibiting load- and slip-history-dependent frictional behaviour.

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23

Gao, Hai Tao, Ya Li Han, Fei Hao, and Song Qing Zhu. "Numerical Simulation for Non-Smooth Contact Problem in Mechanical Systems." Applied Mechanics and Materials 341-342 (July 2013): 491–95. http://dx.doi.org/10.4028/www.scientific.net/amm.341-342.491.

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Friction and contact phenomenon widely exist in mechanical systems. In order to tackle the frictional contact problem of mechanical systems, efficient numerical resolution methods and simulation methods are put forward. A mixed nonlinear complementary model describing frictional contact problem is built based on time-stepping method and complementarity theories. In order to solve the model effectively, the block matrix method and linearization method are used to change the mixed nonlinear complementary problem into a linear complementary problem which can be easily solved. At last, the validity of the numerical resolution methods are verified through a numerical example.

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24

Han, Feng, Hao Wei, and Yang Liu. "Thermal–Mechanical Coupling Analysis of Wheel–Rail Sliding Friction under Two-Point Contact Conditions." Lubricants 11, no. 5 (May 22, 2023): 232. http://dx.doi.org/10.3390/lubricants11050232.

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The generation of wheel–rail-sliding frictional heat is often accompanied by transverse displacement of a wheel. To study the thermal problem of wheel–rail sliding friction at two-point contact, this paper uses an LM tread wheel and a 60 kg·m−1 rail as examples. A thermal–mechanical-coupled finite-element model of equal proportion wheel–rail sliding is established. A direct-coupling method is used to analyze the thermal–mechanical coupling of the wheel–rail interface under sliding contact. This model considers the temperature-dependent material properties and boundary conditions, such as thermal convection and thermal dissipation, in the process of nonstationary frictional-heat conduction. Firstly, the effects of different sliding speeds, axle loads, and contact modes on the temperature and stress fields of the contact area are analyzed. Then, the lubrication and cooling effects of friction modifiers on the rail top and rail gauge angle are compared. The results show that, at a sliding speed of 2 m/s and an axle load of 30 t under a sliding condition of 200 mm, on the top and side of the rail, the temperatures at the contact patch centers are 813 °C and 547.7 °C, respectively. Under different operating conditions, the rail-side temperature is 55–75% of that of the temperature at the rail top, and the rail-side contact and friction stress values are 76–96% of those at the rail top. This indicates that frictional thermal damage on the rail side cannot be ignored. With a lower sliding speed, the thermal response of the two contact patches is closer. The impact of axle load on the frictional temperature and stress on the rail side is more critical than the sliding speed. The optimal lubrication choice is overall lubrication, which can decrease the rail top temperature by 47.2% and frictional stress by 56.2%, as well as decreasing the rail side temperature by 70.3% and frictional stress by 77.4%.

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25

Xiong, Cai-Hua, Michael Yu Wang, Yong Tang, and You-Lun Xiong. "On the prediction of passive contact forces of workpiece-fixture systems." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 219, no. 3 (March 1, 2005): 309–24. http://dx.doi.org/10.1243/095440505x30159.

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The prediction of passive forces in a frictional workpiece-fixture system is an important problem, since the contact forces have a strong influence on clamp design and on workpiece accuracy during machining. This paper presents a general method for the computation of passive contact forces. Firstly, an indeterminate system of static equilibrium is defined, in which the passive, frictional contact forces cannot be determined arbitrarily as in an actively controlled robotic multifinger grasp. Then, a locally elastic contact model is used to describe the non-linear coupling between the contact forces and elastic deformations at the contact point. This model captures the essence of the passive contact. Further, a set of ‘compatibility’ equations is given so that the relationship can be developed between the elastic deformations at all contacts and the displacement of the workpiece. Finally, combining the force equilibrium, the locally elastic contact model and the ‘compatibility’ conditions, the passive force computation problem is transformed into a determinate system of non-linear equations governing all of the elastic deformations at all of the passive contacts. By solving the resulting non-linear equations, all passive contact forces can be accurately predicted in the frictional workpiece-fixture system. This method is illustrated with example cases. The method presented here may also have an application to other passive, indeterminate problems such as power grasps in robotics.

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26

Ozaki, Shingo. "Finite Element Analysis of Rate- and State-Dependent Frictional Contact Behavior." Key Engineering Materials 462-463 (January 2011): 547–52. http://dx.doi.org/10.4028/www.scientific.net/kem.462-463.547.

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In the present study, the rate- and state-dependent friction model [Hashiguchi and Ozaki, 2008] is implemented in the dynamic finite element method. The typical rate- and state-dependent frictional contact problems, which are consisted by elastic and rigid bodies having simple shapes, are then analyzed by the present method. The validity of the present method for the microscopic sliding and stick-slip instability is examined under various dynamic characteristics of the system, such as contact load, elastic stiffness, driving velocity and frictional properties. It is shown that the present method can solve simultaneously not only rate- and state-dependent frictional behavior on the contact boundary but also coupling effects with internal deformations, whereas it cannot predicted by the conventional finite element analysis with the Coulomb’s friction law.

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27

Yu, Ming, Di Wu, Jian Zhao, Sinan Liu, Kun Gong, and Ziyi Qu. "Vibration characteristics analysis of a type of turbine disk-blade assembly system in the civil aero-engine." Advances in Mechanical Engineering 14, no. 11 (November 2022): 168781322211369. http://dx.doi.org/10.1177/16878132221136945.

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The coupled vibration in the turbine disk-blade system (TDS) is one of the main bottlenecks that hinder the further development of high-performance engines. To analyze the vibration of the TDS, three types of contact conditions, involving bonded, frictionless, or frictional were used to simulate the contact between the turbine disk and the blades. Three finite element analysis (FEA) models of a typical TDS based on the tenon structure were developed. The experimental system was developed and experimental modal analysis (EMA) was performed. According to the comparison between FEA and EMA results, the most accurate model is the frictional contact FEA model. The average error of the frictional contact FEA model is 1.42%, and the root mean square error is 0.75%. The working modes of the TDS at different speeds were calculated using the frictional contact FEA model. Meanwhile, based on the newly developed FEA model, it is found that the weak links in the TDS are the blades. This work can provide a theoretical basis for the TDS structure optimization and promote the development of high-quality aero-engines.

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28

Wang, Jiawei, Xinlu Yu, Yingqian Fu, and Gangyi Zhou. "A 3D Meso-Scale Model and Numerical Uniaxial Compression Tests on Concrete with the Consideration of the Friction Effect." Materials 17, no. 5 (March 5, 2024): 1204. http://dx.doi.org/10.3390/ma17051204.

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Achieving the real mechanical performance of construction materials is significantly important for the design and engineering of structures. However, previous researchers have shown that contact friction performs an important role in the results of uniaxial compression tests. Strong discreteness generally appears in concrete-like construction materials due to the random distribution of the components. A numerical meso-scale finite-element (FE) method provides the possibility of generating an ideal material with the same component percentages and distribution. Thus, a well-designed meso-FE model was employed to investigate the effect of friction on the mechanical behavior and failure characteristics of concrete under uniaxial compression loading. The results showed that the mechanical behavior and failure profiles of the simulation matched well with the experimental results. Based on this model, the effect of friction was determined by changing the contact friction coefficient from 0.0 to 0.7. It was found that frictional contact had a slight influence on the elastic compressive mechanical behavior of concrete. However, the nonlinear hardening behavior of the stress–strain curves showed a fairly strong relationship with the frictional contact. The final failure profiles of the experiments showed a “sand-glass” shape that might be expected to result from the contact friction. Thus, the numerical meso-scale FE model showed that contact friction had a significant influence on both the mechanical performance and the failure profiles of concrete.

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29

Liu, Chuan-Ping, Chuan-Yu Wu, Chao Zheng, and Li Wang. "Effects of friction on stress on a plate penetrating into granular media." Physics of Fluids 33, no. 5 (May 2021): 053315. http://dx.doi.org/10.1063/5.0049262.

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The penetration of a plate into granular media was analyzed, and the effects of particle–plate and particle–particle frictions, penetration direction, and initial plate orientation were examined. Results showed that stress was directly proportional to immersion depth for frictionless particles but jumped at the bed surface and then increased linearly for frictional particles. Moreover, stress was mostly independent of the penetration direction when the plate was frictionless. However, initial orientation always had an effect regardless of whether the plate was frictional or frictionless. Furthermore, a theoretical model was developed for stress analysis. This model revealed that friction on the plate essentially affected stress via changing the push angle of the particles that were in contact with the plate.

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30

Abdelrahman, Alaa A., Ahmed G. El-Shafei, and Fatin F. Mahmoud. "Analysis of steady-state frictional rolling contact problems in Schapery–nonlinear viscoelasticity." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 233, no. 6 (October 26, 2018): 911–26. http://dx.doi.org/10.1177/1350650118806675.

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In the context of an updated Lagrangian formulation, a computational model is developed for analyzing the steady-state frictional rolling contact problems in nonlinear viscoelastic solids. Schapery's nonlinear viscoelastic model is adopted to simulate the viscoelastic behavior. In addition to the material nonlinearity, the model accounts for geometrical nonlinearities, large displacements, and rotations with small strains. To satisfy the steady-state rolling contact condition, a spatially dependent incremental form of the viscoelastic constitutive equations is derived. Consequently, the dependence on the past history of the strain rate in the stress–strain law is expressed in terms of the spatial variation of the strain. The contact conditions are exactly satisfied by employing the Lagrange multiplier approach to enforce the contact constraints. The classical Coulomb's friction law is used to simulate friction. The developed model is verified and compared and good agreement is obtained. The applicability of the developed model is demonstrated by analyzing the steady-state rolling contact response of viscoelastically walled-wheel over rigid foundation. Moreover, the obtained results show remarkable effects of the rotational velocity and the viscoelastic material parameters on the mechanical response of steady-state frictional rolling contact.

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31

Fang, Shanglong, Wei Xiao, Kewen Chen, and Xuding Song. "Research on the Model for the Friction Coefficient of Resin-Based Friction Material and Its Experimental Verification." Materials 16, no. 13 (July 3, 2023): 4791. http://dx.doi.org/10.3390/ma16134791.

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Resin-based friction materials have been widely used in the friction braking of automobiles and power machinery. Based on experiments for the variation law of friction and wear morphology, a new model for the friction coefficient of resin-based friction materials was proposed, which includes the effects of both the micro convex body on the surface of the friction material and the frictional film generated during the friction process. This quantitative model of friction coefficient materials was established for the modelling of shear strength, compressive strength, shear strength of the frictional film, contact load and wear morphology. The shear strength, compressive strength and wear morphology of the friction material were adjusted by changing the content of basalt fibers and flaky potassium magnesium titanate. Finally, the accuracy of this quantitative model of friction coefficient was verified through experiments on friction samples with different formulations and by changing the frictional contact load. The results show that the predicted friction coefficient of the model is in good agreement with the experimental friction coefficient, the difference between the upper and lower limits of the forecast is only 5.03% and 2.30%, respectively. Meanwhile, the influence of the ratio of shear strength to compressive strength on the friction coefficient is greater than the proportion of wear morphology. The proposed friction model provides a reference value for the study of new resin-based friction materials.

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32

Ahmadian, Hamid, Hassan Jalali, and Fatemeh Pourahmadian. "Nonlinear model identification of a frictional contact support." Mechanical Systems and Signal Processing 24, no. 8 (November 2010): 2844–54. http://dx.doi.org/10.1016/j.ymssp.2010.06.007.

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33

Afferrante, L. "The thermoelastic Aldo contact model with frictional heating." Journal of the Mechanics and Physics of Solids 52, no. 3 (March 2004): 617–40. http://dx.doi.org/10.1016/s0022-5096(03)00116-9.

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34

Nezamabadi, Saeid, Farhang Radjai, Julien Averseng, and Jean-Yves Delenne. "Implicit frictional-contact model for soft particle systems." Journal of the Mechanics and Physics of Solids 83 (October 2015): 72–87. http://dx.doi.org/10.1016/j.jmps.2015.06.007.

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35

Rademacher, Andreas. "Mesh and model adaptivity for frictional contact problems." Numerische Mathematik 142, no. 3 (May 15, 2019): 465–523. http://dx.doi.org/10.1007/s00211-019-01044-8.

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36

Lai, Zhengshou, Qiushi Chen, and Linchong Huang. "A semianalytical Hertzian frictional contact model in 2D." Applied Mathematical Modelling 92 (April 2021): 546–64. http://dx.doi.org/10.1016/j.apm.2020.11.016.

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37

MIGÓRSKI, STANISŁAW, ANNA OCHAL, and MIRCEA SOFONEA. "MODELING AND ANALYSIS OF AN ANTIPLANE PIEZOELECTRIC CONTACT PROBLEM." Mathematical Models and Methods in Applied Sciences 19, no. 08 (August 2009): 1295–324. http://dx.doi.org/10.1142/s0218202509003796.

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We study a mathematical model which describes the antiplane shear deformations of a piezoelectric cylinder in frictional contact with a foundation. The process is static, the material behavior is described with a linearly electro-elastic constitutive law, the contact is frictional and the foundation is assumed to be electrically conductive. Both the friction and the electrical conductivity condition on the contact surface are described with subdifferential boundary conditions. We derive a variational formulation of the problem which is in the form of a system of two coupled hemivariational inequalities for the displacement and the electric potential fields, respectively. Then we prove the existence of a weak solution to the model and, under additional assumptions, its uniqueness. The proofs are based on an abstract result on operator inclusions in Banach spaces. Finally, we present concrete examples of friction laws and electrical conductivity conditions for which our results are valid.

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38

Breki, Alexander. "Generalized law of contact gliding friction of solids." Science intensive technologies in mechanical engineering 2023, no. 2 (February 24, 2023): 32–39. http://dx.doi.org/10.30987/2223-4608-2023-2-32-39.

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Анотація:

A mathematical model describing the law of contact gliding friction, taking into account changes in the sliding contact states, is proposed for consideration. The generalization of classical linear models of contact friction is carried out by putting in more additive components allowing for new state transitions of frictional interaction. The developed mathematical model makes it possible to give analytic description of the schematic diagram of classical slip coefficient change depending on the load of B.I. Kostetsky and allows adding to

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39

Fang, B., R. E. DeVor, and S. G. Kapoor. "An Elastodynamic Model of Frictional Contact and Its Influence on the Dynamics of a Workpiece-Fixture System." Journal of Manufacturing Science and Engineering 123, no. 3 (October 1, 2000): 481–89. http://dx.doi.org/10.1115/1.1381006.

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Анотація:

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.

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40

Gao, Cheng Hui, Jian Meng Huang, and Lei Dai. "Influence of Different Sliding Velocity on the Thermo-Mechanical Coupling of the Rough Surface Contact." Applied Mechanics and Materials 29-32 (August 2010): 332–36. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.332.

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Sliding velocity has a direct impact on friction heat and contact situation. Frictional heating and associated temperature seriously affects the material chemical and physical - mechanical properties, and is one of the direct factors on the wear mechanism. To analyze the influence of the sliding speed on the maximum contact temperature, contact pressure, stress, etc, a 3D thermo-mechanical coupling model for the rough surface frictional sliding is established. The rough surface is characterized based on fractal theory. The model considers friction contact between an elastic flat plane and an elasto-plastic rough surface. Also, the model integrates the heat flux coupling between the sliding surfaces and allows the analysis of the effects of elastic-plastic deformation of rough body and the interplay among asperities. The numerical results from the analysis and simulation show that the maximum contact temperature increases with the increasing of the sliding velocity. But the maximum VonMises equivalent stress and the maximum contact pressure have few relationships with sliding speed. They may increase or reduce with the sliding velocity increasing. Some results are validated by research’s results available in the literature.

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41

Beyer, Florian, Heribert Blum, Dustin Kumor, Andreas Rademacher, Kai Willner, and Thomas Schneider. "Experimental and Simulative Investigations of Tribology in Sheet-Bulk Metal Forming." Key Engineering Materials 639 (March 2015): 283–90. http://dx.doi.org/10.4028/www.scientific.net/kem.639.283.

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Анотація:

Friction has a considerable influence in metal forming both in economic and technical terms. This is especially true for sheet-bulk metal forming (SBMF). The contact pressure that occurs here can be low making Coulomb’s friction law advisable, but also very high so that Tresca’s friction law is preferable. By means of an elasto-plastic half-space model rough surfaces have been investigated, which are deformed in such contact states. The elasto-plastic half-space model has been verified and calibrated experimentally. The result is the development of a constitutive friction law, which can reproduce the frictional interactions for both low and high contact pressures. In addition, the law gives conclusion regarding plastic smoothening of rough surfaces. The law is implemented in the framework of the Finite-Element-Method. However, compared to usual friction relations the tribological interplay presented here comes with the disadvantage of rising numerical effort. In order to minimise this drawback, a model adaptive finite-element-simulation is performed additionally. In this approach, contact regions are identified, where a conventional friction law is applicable, where the newly developed constitutive friction law should be used, or where frictional effects are negligible. The corresponding goal-oriented indicators are derived based on the “dual-weighted-residual” (DWR) method taking into account both the model and the discretisation error. This leads to an efficient simulation that applies the necessary friction law in dependence of contact complexity.

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42

OZAKI, Shingo, Koichi HASHIGUCHI, Takashi OKAYASU, and Naoki HOTTA. "Finite Element Analyses of Frictional Contact Problems by the Subloading-Friction Model." Transactions of the Japan Society of Mechanical Engineers Series A 70, no. 695 (2004): 995–1002. http://dx.doi.org/10.1299/kikaia.70.995.

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43

Yevtushenko, A. A., and E. G. Ivanyk. "Stochastic contact model of rough frictional heating surfaces in mixed friction conditions." Wear 188, no. 1-2 (September 1995): 49–55. http://dx.doi.org/10.1016/0043-1648(95)06596-2.

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44

Faiz, Z., O. Baiz, H. Benaissa, and D. El Moutawakil. "Hemivariational inverse problem for contact problem with locking materials." Mathematical Modeling and Computing 8, no. 4 (2021): 665–77. http://dx.doi.org/10.23939/mmc2021.04.665.

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The aim of this work is to study an inverse problem for a frictional contact model for locking material. The deformable body consists of electro-elastic-locking materials. Here, the locking character makes the solution belong to a convex set, the contact is presented in the form of multivalued normal compliance, and frictions are described with a sub-gradient of a locally Lipschitz mapping. We develop the variational formulation of the model by combining two hemivariational inequalities in a linked system. The existence and uniqueness of the solution are demonstrated utilizing recent conclusions from hemivariational inequalities theory and a fixed point argument. Finally, we provided a continuous dependence result and then we established the existence of a solution to an inverse problem for piezoelectric-locking material frictional contact problem.

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45

Carr, W. W., J. E. Posey, and W. C. Tincher. "Frictional Characteristics of Apparel Fabrics." Textile Research Journal 58, no. 3 (March 1988): 129–36. http://dx.doi.org/10.1177/004051758805800302.

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A study has been conducted to determine the frictional characteristics of several fabrics used in apparel. The objective was to generate fabric frictional data to help in developing automated assemblies for fabrics. The results revealed that the coefficients of static and dynamic friction between fabrics decreased as the normal force per unit area increased. Wilson's model relating frictional force to normal force and the apparent area of contact closely correlated the data.

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46

Xia, Yichun, and Yonggang Meng. "Physics-Informed Neural Network (PINN) for Solving Frictional Contact Temperature and Inversely Evaluating Relevant Input Parameters." Lubricants 12, no. 2 (February 17, 2024): 62. http://dx.doi.org/10.3390/lubricants12020062.

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Ensuring precise prediction, monitoring, and control of frictional contact temperature is imperative for the design and operation of advanced equipment. Currently, the measurement of frictional contact temperature remains a formidable challenge, while the accuracy of simulation results from conventional numerical methods remains uncertain. In this study, a PINN model that incorporates physical information, such as partial differential equation (PDE) and boundary conditions, into neural networks is proposed to solve forward and inverse problems of frictional contact temperature. Compared to the traditional numerical calculation method, the preprocessing of the PINN is more convenient. Another noteworthy characteristic of the PINN is that it can combine data to obtain a more accurate temperature field and solve inverse problems to identify some unknown parameters. The experimental results substantiate that the PINN effectively resolves the forward problems of frictional contact temperature when provided with known input conditions. Additionally, the PINN demonstrates its ability to accurately predict the friction temperature field with an unknown input parameter, which is achieved by incorporating a limited quantity of easily measurable actual temperature data. The PINN can also be employed for the inverse identification of unknown parameters. Finally, the PINN exhibits potential in solving inverse problems associated with frictional contact temperature, even when multiple input parameters are unknown.

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47

Ozaki, Shingo, Takeru Matsuura, and Satoru Maegawa. "Rate-, state-, and pressure-dependent friction model based on the elastoplastic theory." Friction 8, no. 4 (January 4, 2020): 768–83. http://dx.doi.org/10.1007/s40544-019-0321-3.

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AbstractAdhesion is one of essences with respect to rubber friction because the magnitude of the friction force is closely related to the magnitude of adhesion on a real contact area. However, the real contact area during sliding depends on the state and history of the contact surface. Therefore, the friction force occasionally exhibits rate-, state-, and pressure dependency. In this study, to rationally describe friction and simulate boundary value problems, a rate-, state-, and pressure-dependent friction model based on the elastoplastic theory was formulated. First, the evolution law for the friction coefficient was prescribed. Next, a nonlinear sliding surface (frictional criterion) was adopted, and several other evolution laws for internal state variables were prescribed. Subsequently, the typical response characteristics of the proposed friction model were demonstrated, and its validity was verified by comparing the obtained results with those of experiments conducted considering the contact surface between a rough rubber hemisphere and smooth acrylic plate.

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48

Liu, Shuangbiao, and Qian Wang. "A Three-Dimensional Thermomechanical Model of Contact Between Non-Conforming Rough Surfaces." Journal of Tribology 123, no. 1 (August 1, 2000): 17–26. http://dx.doi.org/10.1115/1.1327585.

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A necessary step in understanding failure problems of tribological elements is to investigate the contact performance of rough surfaces subjected to frictional heating. It is essential that the interfacial variables are obtained through solving the interactive thermomechanical contact problem. This paper studies the three dimensional thermomechanical contact of non-conforming rough surfaces, the model of which includes the normal surface displacements caused by the contact pressure, frictional shear, and frictional heating. Influence coefficients and frequency response functions for elastic and thermoelastic displacements, as well as those for temperature rises, are investigated for model construction. In order to develop an accurate and efficient solver, the numerical algorithms with the discrete convolution and fast Fourier transform techniques and the single-loop conjugated gradient method are used. The model modules are numerically verified and the thermomechanical performance of the rough surfaces in a point contact is studied.

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49

Baek, Sumin, and Seunghun Baek. "Influence of contact curvature on frictional energy dissipation under varying tangential loads." Friction 12, no. 2 (November 29, 2023): 363–74. http://dx.doi.org/10.1007/s40544-023-0788-9.

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AbstractThis study investigates the effect of contact surface curvatures on the friction response under varying tangential loadings using a finite element (FE) model. The results showed that the geometry of the surface influences the contact force at the interface and reduces the friction effect through an unsteady distribution of the contact force. The relationship between the friction effect, excitation, and contact surface shape was also examined, revealing a linear inverse relationship between the friction and curvature. The findings provide a comprehensive understanding of the frictional interactions between elastic bodies and highlight the role of curvature as a design parameter for regulating the friction effect.

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50

Torskaya, Elena, and Fedor Stepanov. "Friction Reduction Due to Heating in the Sliding Contact of Smart Coating: Modeling of Mutual Effect." Lubricants 10, no. 7 (July 20, 2022): 165. http://dx.doi.org/10.3390/lubricants10070165.

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Анотація:

In smart coatings designed for friction units operating in wide temperature ranges, the material reacts to heating by changing its frictional properties. Appropriate experimental studies are available. In this paper, a model is proposed for studying the mutual effect of frictional heating, which is inhomogeneous in the contact area, and shear stresses. The distribution of the latter differs from the Amonton–Coulomb law according to local temperatures, from which the local friction coefficient depends. Two problems are independently solved in the model: the problem of elastic contact between a smooth slider and a two-layer elastic half-space, and the thermal problem. The solution methods are numerical–analytical and are based on Hankel integral transforms and iterative procedures. The problem has been solved for two types of sliders simulating pin-on-disk and ball-on-disk test schemes. For the selected dependences of the local friction coefficient on temperature, an analysis was made to study the influence of sliding velocity and coating thickness on the distribution of temperatures, tangential stresses in the contact zone, as well as integral friction force. Relatively rigid and relatively compliant coatings were considered. It was found that for such smart coatings, which implement the mechanism of self-lubrication during frictional heating, there is a decrease in the friction force with increasing velocity, especially for relatively thick coatings with low thermal conductivity.

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