Wear Contact Problem Research Articles

Theory and experiment of tribological test methods

Based on the analysis of the current state of test methods for wear of friction pairs and the need for methods with certain operating conditions, the problem of developing a theory of test methods for wear of friction pairs according to the ball-cylinder scheme was solved, which makes it possible to determine the parameters of wear models and the general characteristics of the wear resistance of materials. It is shown that the type of wear within the range of properties of the friction pair parameters ensures compliance with the basic conditions in contact: materials, lubrication, pressure, speed, temperature, type of movement, and other less significant factors. It has been established that one of the fundamental issues in the development and conduct of wear tests is to take into account the influence of the stationarity of the wear mode at a point. Test methods in steady and unsteady modes (transient mode) are different. The test method should be based on the solution of the contact problem for a friction pair sample-counter-sample. Based on the solution of wear-contact problem for the "ball-cylinder" scheme, a theory has been developed for identifying the parameters of the wear pattern. To solve the inverse problem, a method of approximating function is proposed and implemented. The power approximation of the experimental function after substitution into the resolving equation gives simple expressions for calculating the model parameters. The results obtained make it possible to predict the intensity of wear of tribocouples under given initial operating conditions: according to loads, sliding speed, characteristics of lubricants and structural materials.

A Fractional Time-Derivative Model for Severe Wear: Hypothesis and Implications

Based on the example of wear of polymers, which exhibit a power-law time variation of the wear loss under constant loading conditions, a fractional time-derivative wear equation has been introduced. The wear contact problem with a fixed contact zone is solved using the known method of separation of spatial and time variables. It is shown that during the wear process, the contact pressure approaches a uniform distribution over the contact area, which is termed as a quasi-steady-state solution, since the mean volumetric wear rate does not tend to become constant. It is of interest that the contact pressure variation displays a decaying oscillatory nature in the case of severe wear, when the mean volumetric wear rate increases with time.

FORMULATION OF TOOL WEAR LAW WHEN CUTTING POLYMER COMPOSITES

Numerous experimental studies in the field of mechanical processing of composite materials for individual materials and tools made it possible to formulate particular models for describing tool wear, changing its microgeometry during operation and predicting durability. There are significant difficulties in measuring current wear and recalculation in mathematical models, since they include a large number of parameters. This does not allow for simple technical control of cutting edge wear and predicting tool life. The formulation of the wear-contact problem of the tool tip and the material interaction during turning of reinforced composite plastics is presented. Based on known studies, it is assumed that wear occurs along the flank of the tool, and is accompanied by an asymmetric change in the geometry of its tip. A model of abrasive wear during sliding of a tool tip rear surface with a polymer composite reinforcement material and fracture products is considered. It is assumed that the wear law is hereditary and there is a linear dependence of the wear rate on the rate of contact interaction and pressure. Shear stresses through the contact pressure and the coefficient of friction nonlinearly depend on the operating time of the tool due to the change due to wear in the geometric shape of the tool and the processing parameters of the product over time. The volumetric wear factor is a tool run time function. It reflects the fact that the interaction of the “tool-workpiece” pair with time should, as it were, forget about the running-in stage, which has a high wear rate, and the fact that the dependence of wear on the load (contact pressure) is characterized by the presence of aftereffect. A simplified relationship is obtained for the wear law under the assumption that there is no change in the coefficient of friction, temperature and contact pressure over time. Ultimately, to describe the wear law and predict the tool life, it is necessary to know a number of empirical constants, the values of which are determined by the change in the microgeometry of the tool tip during interaction during cutting.

Prediction of the life time of cylindrical tribosystems of a vehicle

Development and research of methods for calculating the life of friction parts of a vehicle is an actual problem. Ball joints of a car suspension are one of the most responsible for reliability and safety friction unit of transport vehicles. In this paper the approaches to the computational and experimental assessment of the wear and reliability of the ball joint of a vehicle are proposed. The calculation of wear will be carried out based on the solution of the wear contact problem. The equilibrium condition, the wear law, and the geometric condition in the contact are taken as the basic equations. As a result, design formulas for wear and contact pressures have been proposed. A method for calculating the reliability function with determining the coefficients of variation of the wear parameters of ball joints is proposed. To assess the effectiveness of lubricants, a method for calculating wear parameters based on solving the inverse wear-contact problem is considered.

Investigation of slippage and wear in rolling bearings of machines

The purpose of this work was to study the processes of slipping and wear in the sliding bearings of machines. It is determined that slippage in bearings is the main cause of bearing parts failure according to the criterion of wear. Analytical relations for determining the amount of slip and sliding path in the bearing are presented. For experimental research of sliding in rolling bearings the test installation is designed. Experimental tests on the effect on load slip, sliding speed and lubrication conditions in the bearing were performed. The model of wear of rings of the sliding bearing on the basis of a solution of a wear contact problem is offered. The formulas for calculating wear and parameters of the wear model are obtained. The obtained results are recommended to evaluate the influence of design and technological factors on the durability of rolling bearings by the criterion of wear.

On the Calculation of Coating Wear Kinetics: the Use of Refined Deformation Models

A number of deformation models are considered for a wear coating. They are used as a basis to perform the calculations of coating wear kinetics within the two-dimensional formulation of the wear contact problem. It is shown that the use of refined deformation models for a coating with consideration for its shape transformation may have a significant effect on the results of calculating the coating wear kinetics.

A Simple Model for the Wear Accumulation in Partial Slip Hertzian Contact

A two-dimensional wear contact problem with a stick zone is considered for a Hertzian cylindrical contact configuration and Archard’s equation of wear. A one-free-parameter simple model for the wear volume accumulation during the reciprocating wear process, which occurs in two symmetric variable slip zones, is developed and validated against numerical solutions available in the literature. The developed model takes into account the observed effect of non-monotonic evolution of the friction dissipated energy. The presented analytical modeling framework does not make use of any fitting parameters to be evaluated from experiments. The only free dimensionless parameter is suggested to be fixed based on numerical simulations for the maximum of the frictional damage that is proportional to the cumulative wear rate.

Wear contact problem with friction: Steady-state regime and wearing-in period

A two-dimensional contact problem for an elastic layer of a finite thickness is considered with the effects of friction and wear taken into account. It is assumed that the contact zone is constant, but the shape of a wear-resisting punch changes during the sliding wear process. The punch is loaded by constant external normal and tangential loads, the latter of which is equal to the maximum value predicted by Coulomb’s law. The steady-state profile of the punch, which has been reproduced in the steady-state wear regime, is determined in an integral form. In the case of a very thick layer, explicit formulas are given for the initial vertical displacement of the punch and the moment of contact pressures, both of which vary during the wear process. The duration of the wearing-in process is estimated, and it is shown that the effect of friction extends the wearing-in period.

Wear of elastic tube with nonuniform coating by rigid bush

This article is devoted to the statement and construction of analytical solution of the wearcontact problem for a rigid bush and elastic pipe with a coating in the case when the coating is nonuniform. The presence of nonuniformity leads us to the necessity of constructing a solution in a special form over special functions, since standard methods does not allow us to effectively take into account the complex properties of the coating. Analytical representation for contact stresses under the bush is presented in series with separate factor, which connect with complex properties of coating. This allows provide effective calculation even if these properties are described by rapidly changing or discontinuous functions. It is also shown that contact stresses will be negligible over time.

Estimation of the Effect of Temperature and Microgeometry of the Counterbody Surface on Wear Resistance of Tread Rubber

A study has been conducted on the wear resistance of the tread rubber of an all-metal radial truck tire at various temperatures: –25, 23, and 80°C. Sandpaper of various grains is used as a counterbody. The tests were carried out at a constant sliding rate of 2 cm/s and a normal pressure of 0.7 MPa. This paper presents the results of assessing the effect of temperature on the intensity and mechanism of wear for rubber. A contactless 3D gauge was used to study the evolution of the surface microgeometry and changes in the size of wear particles. The rubber wear resistance parameter was determined by processing experimental data on mass wear using a simplified solution of the corresponding wear contact problem.

Прямая износоконтактная задача для радиального подшипника скольжения

The paper presents an approximate solution of the wear-contact problem for a cylindrical sliding bearing. The law of wear is adopted in a dimensionless form, depending on the determining factors: contact pressure and sliding speed. The law of wear also includes: the coefficient of friction, the modulus of elasticity of the material of the bearing, the gap in the bearing and the thermal diffusivity of the material of the bearing. For the calculation, an approximate relationship was used for maximum contact pressures in the bearing. To simplify the geometric dependence of normal wear on the contact angle, the decomposition of trigonometric functions into a power series was used.

Effective wear coefficient and wearing-in period for a functionally graded wear-resisting punch

A two-dimensional wear contact problem for an elastic layer and a wear-resisting punch is considered. The contact area and the contact load are assumed to be fixed, whereas the punch’s shape changes according to Archard’s law of wear with variable wear coefficient. By neglecting the effect of tangential tractions, the problem of determining the normal contact pressure is reduced to a two-dimensional integral equation containing a Fredholm coordinate operator and a Volterra time operator. By the method of separation of variables, the transient contact pressure distribution has been constructed in terms of the solutions of some eigenvalue problem. A special attention is paid to quantities of practical interest, such as the wearing-in period and the transient effective wear coefficient.

A variational formulation of the wear contact problems for coated bodies

Plane wear contact problems for an elastic half-plane with thin coating and a rigid punch are considered. A local (differential) setting of the wear contact problem assumes that actual contact areas are unknown in advance, may be multiple (discrete), and may change through wear. The thin coating is modelled by a Winkler-type layer. An additional normal displacement of a substrate surface is proportional to a local pressure. A variational approach to the problem is used. The variational formulation in the form of a system of an evolutionary variational inequality and an ordinary differential equation of first order is obtained. An explicit Euler scheme is used for the time discretization. A spatial discretization of the problems is made using spaces of integrated fundamental solutions. The boundary element method is applied to construct such spaces, whose elements satisfy homogeneous equilibrium equations and compatibility conditions.

Limiting shape of profiles in fretting wear

Abstract Fretting wear in the displacement- and load-controlled settings is considered. The axisymmetric wear contact problem with stick and slip zones is studied under the assumption that the contacting bodies are elastically similar and their stress-strain states can be modeled by half-space approximations. It is shown that in the presence of a stick zone, the worn shape of profiles in contact tends to some limiting shape which is determined solely by the solution of a certain frictionless normal contact problem. In the both cases, it has been proved that the value of the limiting stick-zone radius corresponds to that of the initial stick zone, and the limiting shape of profiles is obtained in a closed form involving one quadrature. The novelty of this work is in study of the limiting shapes in load controlled fretting wear situations.

Prediction the wear of sliding bearings

The problem of developing a calculation-experimental method for calculating wear of a sliding bearing based on a two-factor wear model (contact pressure - sliding velocity) with identification of wear resistance parameters was considered. On the basis of the proposed wear model, the wear-contact problem for a cylindrical sliding bearing was solved. The equation of equilibrium for medium pressures and the approximating function of linear wear from the arc of contact between the shaft and the bushing were used as the determining equations. To identify parameters of wear resistance in the wear model, a calculation-experimental method for determining calculated dependences of wear resistance parameters was developed on the basis of the wear test by the «cone – three balls» scheme. The results of wear tests of bronze conical specimens with a variable wear spot and two values of sliding velocity were taken as a base. The obtained results were recommended for predicting wear of sliding bearings at the design stage and optimizing their design and operational parameters.

Inverse wear contact problem of the friction unit

In this study, theoretical analysis for defining the function of displacements of a hub’s external contour points and microgeometry of the friction unit providing the absence of initial wear that holds to the end of running-in period, was carried out based on a rough friction surface model. A closed system of algebraic equations admitting to obtain the solution of the problem of optimal design of a friction unit depending on the geometrical and mechanical characteristics of a hub and plunger was constructed. The found function of displacements of the hub’s external contour points and microgeometry of friction surface provide wear resistance increase of friction pair. Calculations for friction units applied to the borehole sucker–rod oil pumps were considered as an example.

Calculation-experimental modeling of wear of cylindrical sliding bearings

The problem of developing a calculation-experimental method for calculating wear of a sliding bearing based on a two-factor wear model (contact pressure - sliding velocity) with identification of wear resistance parameters was considered. Analysis of known studies has shown that existing approaches required solution of complex systems of integral-differential equations or cumbersome numerical methods that are unacceptable in the engineering practice. As a result, a model of the sliding bearing wear in conditions of boundary friction was obtained in a form of dependence of the wear rate on the dimensionless complexes of contact pressure and sliding velocity. On the basis of the proposed wear model, the wear-contact problem for a cylindrical sliding bearing was solved. The equation of equilibrium for medium pressures and the approximating function of linear wear from the arc of contact between the shaft and the bushing were used as the determining equations. The solution was obtained in a closed form as a dependence of wear degree on the friction path. To identify parameters of wear resistance in the wear model, a calculation-experimental method for determining calculated dependences of wear resistance parameters was developed on the basis of the wear test by the «cone – three balls» scheme. The results of wear tests of bronze conical specimens with a variable wear spot and two values of sliding velocity were taken as a base. An example of implementation of the calculation-experimental method for calculating wear of a cylindrical bearing was given. It has shown that the calculated wear values were consistent with the operational data on wear of sliding bearings. Influence of determining factors of sliding velocity and load on bearing wear was studied. The obtained results were recommended for predicting wear of sliding bearings at the design stage and optimizing their design and operational parameters

Implementation of asymptotics of the wear contact problem solution for identifying the wear law based on the results of tribological tests

The parameter of the wear law of bronze coupled with steel under dry friction is identified by comparing the results of mathematical modeling with experimental data. The wear tests were carried out according to the steel-ball–flat-bronze sample scheme under relative reciprocal sliding of the tested samples. The modeling of the wear of the sample was based on asymptotic behavior of the solution of the corresponding wear-contact problem. The effectiveness of using this asymptotic behavior to identify the wear law based on the tribological test results has been demonstrated.

On the durability prediction for an elastic cylinder-elastic layer pair reinforced by thin coating according to the wear criterion

The plane (plane-deformation) wear contact problem of elasticity theory concerning the interaction of a cylinder and a thick layer reinforced by a thin coating along the boundary is considered. The cylinder glides on the coating surface with a low speed (sufficient for neglecting inertia effects of the contacting bodies), which leads to the wear of their surfaces. The problem is traced to the solution of a nonlinear integral equation relative to the unknown contact pressure and size of the contact area depended on the cylinder pressing force. In case of the soft coating in relation to the cylinder and coating layer and the abrasive character of wear, actual solutions of the problem in quadrature are developed. Variants of the low and high wear of the coating are discussed. It is noted that the proposed method may be used for the investigation of the contact problem concerning pressing a smooth indenter into the thin viscoelastic coating on a rigid base.

Wear process for coated bodies with periodic microgeometry at the interface

The model to study the wear kinetics and shape variation of the surfaces of coated bodies with given microgeometry at the interface is presented. The model is based on the wear contact problem solution for the layered elastic body. The microgeometry at the interface between elastic layer and substrate is described by the periodic function. This study makes it possible to analyze the dependence of the worn surface shape and pressure redistribution on parameters of the interface microgeometry, and on the relative coating and substrate mechanical and tribotechnical characteristics.