Ehl Model

EHL is the study of hydrodynamic lubrication in rolling / sliding contacts when the elastic deformation of the solids is significant. EHL is commonly found in many machines components such as gear teeth contacts, cams and rolling element bearings during variations in load etc. EHL problems constitute the following characteristics such as, high pressure, deformation of the contacted surfaces and shear rates. The mathematical model of EHL problem depends on a proper fluid rheology model for the lubricant. Many researchers have used the systematic approaches for the numerical solution of EHL line and point contact problems [1-4]. Most of the roller bearings are lubricated by grease, it is necessary to solve the EHL equations for grease as lubricant

The model is generally written as , where is the shear stress, the yield stress, the shear rate, the rheological index and is the plastic viscosity. The rheological characteristics of grease depend on index and are functions of pressure and temperature. If the Herschel Bulkley model behaves as a fluid, otherwise it behaves as a solid. If and , this model reduces to the Newtonian fluid. For an incompressible, steady and isothermal flow, the modified Reynolds equation governing grease EHL in its dimensionless form is

Many researchers have developed the generalized ideas in various disciplines underlying multigrid method for the solution of EHL problems. Lubrechet et al. [15] discussed the multigrid method to solve the EHL problem for both line and point contacts which is a significant breakthrough. The efficiency and robustness are improved by eliminating, both high and low frequency error components by a series of grid with different mesh levels. Venner [16, 17] and Nurgat et al. [18] have introduced new relaxation methods for which the technique was greatly improved. The concept of Multigrid method has been discussed in detail by Briggs et al. [19]. For the solution of nonlinear system of equations, we use multigrid method with FAS scheme. FAS involve an inner and an outer iteration; the outer iteration is the FAS correction scheme, while the inner iteration is usually a standard relaxation method such as Gauss-Seidel iteration