Abstract
Many calculating methods have been already developed for solving contact problems of parts such as gears, cams, and followers under fluid film lubrication conditions considering the temperature and pressure dependence. Similarly, the determination of the elasto-hydrodynamic pressure distribution the processes taking place in the lubricant and the contacting bodies, as well as in their environment, have to be dealt with simultaneously for the determination of the temperature field. A system of equation for the modelling of thermo-elastohydrodynamic lubrication between two contacting bodies containing hydrodynamic, thermodynamic, and strength problems is a highly non-linear system which becomes even more so if the temperature and pressure dependence of the material properties are considered. To solve this system, scientists started to use the finite element formulation in the 1960s and it was found to be a promising and reliable method. Earlier, the lubrication analysts used only the h-version finite element method (h-FEM) till 1991, when the first usage of the p-version finite element method (p-FEM) was published in the literature. In order to reduce the problem, in case of point or line contact, the contact bodies can be handled as semi-infinite ones. Following this simplification that had been successfully applied for the gap size determination, a substructure model was defined using analytical solution of the moving heat source. Instead of an iterative way between the solid and fluid problem, in this paper we present an efficient solution when thermal model for lubricant and surfaces were coupled and solved by a direct numerical method in one step.
Highlights
For rolling sliding parts such as cams and followers, gears, and bearings often operate under high loads, high speed, and high slip; the local or global temperature rise caused by the heat dissipation generated by the pressure distribution acting on the surfaces and the tangential stresses developing in the lubricant, respectively, may reach a level resulting in a non-negligible deformation of the surfaces as well as influencing the lubricant properties
The least square method can be used to obtain the coefficients of discretized form in order to approximate the analytical solution of deformation for half-space. Following this simplification that was successfully applied for the gap size determination, a substructure model was defined using an analytical solution of the moving heat source where the input temperature data were obtained from p-version finite element method (p-FEM) calculation (Carslaw and Jaeger (1959) [13])
The generalized Reynolds equation of Dowson (1961) [14] is highly non-linear partial differential equation with variable viscosity and density extents through the film thickness which is used to calculate the contact pressure generated by fluid film lubrication
Summary
For rolling sliding parts such as cams and followers, gears, and bearings often operate under high loads, high speed, and high slip; the local or global temperature rise caused by the heat dissipation generated by the pressure distribution acting on the surfaces and the tangential stresses developing in the lubricant, respectively, may reach a level resulting in a non-negligible deformation of the surfaces as well as influencing the lubricant properties. The scientists used finite difference method to obtain the solution of the generalized Reynolds equation In case of these solving systems, a very high number of points of grid is needed. A simulation procedure was developed based on a finite element method to model thermo-hydrodynamic processes This method is based on our EHD (elasto-hydrodynamic) simulation procedure, which was supplemented by the incorporation of discretized equations describing the thermal conditions. The least square method can be used to obtain the coefficients of discretized form in order to approximate the analytical solution of deformation for half-space Following this simplification that was successfully applied for the gap size determination, a substructure model was defined using an analytical solution of the moving heat source where the input temperature data were obtained from p-FEM calculation (Carslaw and Jaeger (1959) [13]). Unlike previous penalty parameter methods, continuity can be ensured here, so this method can be incorporated into the p-FEM model of TEHD
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