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# Deformation Behavior Numerical Analysis of the Flat Sliding Layer of the Spherical Bearing with the Lubrication Hole

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## Abstract

The numerical simulation problem of the frictional contact interaction of the flat sliding layer periodicity cell of the spherical bearing is performed. The mathematical formulation of contact problems with a previously unknown contact area and all types of contact states (adhesion, sliding, no contact) is done. Three options for the sliding layer thickness of 4, 6 and 8 mm are considered. The deformation of the thin flat sliding layer of the spherical bearing is made on the example of an antifriction layer of modified PTFE. The deformation theory of elastoplasticity for the active loading case is chosen as the antifriction polymer behavior model. The thermomechanical and friction properties of the modified PTFE were obtained experimentally by a scientific group of Alfa-Tech LLC and IMSS of the Ural Branch of the Russian Academy of Sciences. The experiment to determine the frictional properties of the material was performed to a pressure level of 54 MPa. The analysis of the friction coefficient dependence on the level of pressure acting on the stamp is performed: approximating functions and for contact with $$\upmu\left( P \right) = 0.005 + {{0.111} \mathord{\left/ {\vphantom {{0.111} P}} \right. \kern-0pt} P} + {{0.623} \mathord{\left/ {\vphantom {{0.623} {P^{2} }}} \right. \kern-0pt} {P^{2} }} - {{3.57} \mathord{\left/ {\vphantom {{3.57} {P^{3} }}} \right. \kern-0pt} {P^{3} }} + {{3.335} \mathord{\left/ {\vphantom {{3.335} {P^{4} }}} \right. \kern-0pt} {P^{4} }}$$ and $$\upmu\left( P \right) = - 0.002 + {{1.55} \mathord{\left/ {\vphantom {{1.55} P}} \right. \kern-0pt} P} - {{17.166} \mathord{\left/ {\vphantom {{17.166} {P^{2} }}} \right. \kern-0pt} {P^{2} }} + {{64.979} \mathord{\left/ {\vphantom {{64.979} {P^{3} }}} \right. \kern-0pt} {P^{3} }} - {{55.745} \mathord{\left/ {\vphantom {{55.745} {P^{4} }}} \right. \kern-0pt} {P^{4} }}$$ without lubricant on the mating surfaces are selected. The friction coefficient for a pressure level of more than 54 MPa is calculated from the obtained functions with an error of less than 1%. Simulation of the spherical bearing sliding layer deformation behavior is made taking into account the physicomechanical and friction properties of the polymer material using the example of a periodicity cell made of the modified PTFE with a hole for lubrication. Distribution fields of stress intensity and plastic strain intensity, as well as integral stiffness were obtained and analyzed. The relations of the maximum and minimum integral parameters values of the stress-strain state on the pressure level are established as part of the analysis. The influence of frictional properties and layer thickness on the contact zone parameters is considered. It was established that the 8 mm thickness layer enjoy a more favorable deformation behavior case than the other two variants of the layer thickness. The frictional properties have a slight effect on the stress-strain state parameters of the periodicity cell, their influence significantly on the pattern of the contact states zones distribution and contact tangential stress. It is established that the level of contact tangential stress when taking into account lubricant approximately is on lower 3 times than with contact without lubrication.