Research Of Numerical Methods For Solving The Contact And Wear Problem

Contact and wear problems are widely existed in engineering applications.The failure of equipments and components caused by wear leads to enormous e-conomic losses.It is difficult to detect the wear process of materials in real time,because of its complexity.With the help of numerical simulation,the wear gap and stress distribution of materials can be quantificationally analyzed under dif-ferent wear degree.It can also study the failure mechanism of structures,predict service life,optimize design the wear process,reduce the time and experimental costs of product design,so as to assist the engineering application.It is of great significance.Based on the bipotential contact algorithm of our research team,algorithms for wear problem are numerically derived and solved,including:elastic wear,elastic-plastic wear,wear with pressure-dependent friction coefficients,wear with debris.The main research works and conclusions are as follows:(1)The bipotential contact algorithm is extended to solve the elastic wear problems.The wear gap of contact surface of objects is considered as an inter-nal variable.The accumulation of wear gap is stored by this internal variable.The normal contact law of wear problems is obtained by considering the wear depth into the initial contact distance.Combined the normal contact law with the Coulomb friction law,the complete contact law for the wear problem is ob-tained.The trial contact forces are calculated via the augmented Lagrangian Method.Then the corrected contact forces are computed through the bipoten-tial projection.The contact pressure and relative displacements of each contact node are extracted to calculate the corresponding wear gap through the Archard wear law when the iteration of contact is converged.The wear gap is updated to the internal variable of wear which is the initial condition of the normal contact gap in next step.Compared with Hertz solution and commercial finite element software ANSYS,the accuracy of bipotentia contact algorithm is proved.Com-pared with the wear example of Stromberg,the precision of the proposed wear algorithm is verified.The evolution of wear process of two chosen points consists with the complete contact law and the Archard wear law,which certifies the validity and precision of the proposed algorithm.(2)The wear algorithm of elastic-plastic materials is derived and numer-ically implemented.With the base of elastic-plastic constitutive algorithm of our team,the wear algorithm of elastic-plastic materials is derived.The contact iteration need to be implemented inside each Newton iteration.The wear gap,which is assumed to be constant during the Newton iteration,is computed and updated after the convergence of the Newton equilibrium loop.The influence of increment and plasticity is investigated via numerical examples,respectively.Appropriated choice of increments could satisfy the accuracy and obtain a good calculation speed at the same time.In gross slip conditions,the plastic defor-mation could mitigate the normal contact pressure of solution.It is observed that the maximum contact pressure decreased and the contact area increased.The influence of plastic deformation to wear shape is the same that the wear width increased and the maximum wear depth decreased.When the wear depth is larger,the influence of plastic deformation decreases gradually.In partial s-lip conditions,the elastic materials exist peak values of contact pressure in the mixed regions between stick and slip.For elastic-plastic materials,the plastic deformations alleviate the pressure distribution in these mixed regions so that no obvious peak values appear.(3)The wear algorithm with pressure-dependent friction coefficients is de-rived and numerically implemented.The friction coefficients in most engineering material are not constant.The friction coefficients are considered as the function of normal contact pressure.Then the friction coefficients are coupled with the normal contact pressure and wear.The Uzawa algorithm and Newton algorithm are developed to solve the contact and wear problems with pressure-dependent friction coefficients.The piecewise continuous contact tangent matrices of New-ton algorithm contain the derivation of the friction coefficient with respect to the normal contact pressure,in the reason of the variable friction coefficients.The Uzawa algorithm and Newton algorithm are compared through numerical examples.The results show that the global Gauss-Seidel iterations in Newton algorithm is less than that in Uzawa algorithm.But the Newton algorithm needs the local iterations for each contact node.Different friction models are used to study the influence of variable friction coefficients to contact and wear process Through the simulation of different friction models of 3D elastic block example,it is found that the friction coefficients will affect the stress distribution and con-tact states,and thus impact the wear morphology of the objects.In the case of 2D cylinder-flat,two wear states of gross slip and partial slip are even obtained with different friction models(4)The algorithm of wear problem with debris layers is derived and numer-ically implemented.If the debris generated in the wear process between objects can not be ejected in time,it may generate the debris layer on the contact surface.The debris layer between objects will change the contact state and the normal contact gap.The debris layer is stored by another internal variable and connect-ed to the contact surface of an object during numerical simulation.The thickness of new generated debris layer is controlled by a transfer coefficient.When the contact iteration is converged,the wear gap and the corresponding debris layer are calculated and updated.Two debris layer models are established according to the evolution of the debris layer.The effect of thickness and transfer rate of the debris layer on contact pressure distribution and wear process is investigated.When applying the wear debris layer,the maximum normal contact pressure and wear gap increase,but the width of contact pressure distribution and wear shape decrease.When applying the linear transfer rate model of the debris layer,the higher the transfer rate is,the sharper the contact pressure distribution and the wear morphology will be.When considering the variable transfer rate model of debris layer,under the condition of the same transfer rate,the larger the allow-able maximum debris layer thickness is,the sharper the wear morphology will be;Under the condition of the same allowable maximum debris layer thickness,the higher the transfer rate is,the sharper the wear morphology will be.In the same condition of the same debris layer model,the wear morphology of elastic materials is sharper than that of elastic-plastic materials.