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For this reason the feature is sometimes referred to as “Petrushevich” spike.
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Obtained in 1951, his solution was first solution of combined elastic distortion, fluid flow and pressure-viscosity dependency equations. It should be emphasized, that the occurrence of the pressure spike is closely related to the variance of viscosity with pressure along with elastic properties of materials and relative speed.
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In 1959 Dowson and Higginson computed series of numerical solutions of EHL line contact problem for a range and obtained a regression formula for a minimum film thickness. Ī classical EHL system of equations consists of the system of Reynolds equation, film thickness and load balance equations: Further information on the development of the EHL theory can be found in. This equation is the analytical solution of the theory of elasticity equations for a semi-infinite body subjected to normal pressure (for the details of the derivation refer to ). The most robust and fast way (in terms of iterations at least) to solve EHL system is to use a fully coupled approach and Newton’s scheme.
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However, since the elastic distortion equation is given in the integral form, the Jacobian of the system is full which increases the demands in memory enormously. In addition, solution of the equations with full Jacobian is computationally significantly more intense compared to diagonally banded cases.Therefore, researchers worked hard to develop alternative solution methods. The two most common methods for solving EHL systems numerically are the Multilevel-Multigrid and Differential Deflection techniques. The former uses multiple grids and specific integration of the film thickness equation to build an iterative solver. The latter solves a fully coupled system of equations, however, instead of using the original integral form of the film thickness equation, it considered the 2-nd derivative of it. It turns out that the use of the derivative equation allows to construct a banded Jacobian and improve the efficiency of coupled approach significantly. Recently, a so called full system approach was proposed.
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