Analytical method of nonlinear oil film force of hydrodynamic crankshaft journal bearing

An analytical method was proposed for calculating the nonlinear oil film force of hydrodynamic crankshaft journal bearing based on variables separation method, Sturm-Liouville theory, and Reynolds boundary conditions.The oil film pressure distribution of Reynoldsequation for incompressible fluid hydrodynamic lubrication of the bearing was expressed as an additive form of a particular solution and a homogeneous solution.By using variables separation method, the pressure distributions of particular solution and homogeneous solution were respectively split in an additive and multiplicative forms of circumferential separation function and axial separation function.For convenience, the circumferential separation function of particular solution was solved by using the Sommerfeld transformation, and the termination position angle of oil film was determined by using the continuity condition.Because there was no direct solution for the circumferential separation function of homogeneous solution, the circumferential separation function was transformed as Sturm-Liouville equation by using the approximation function of oil film thickness, and the eigenvalues and eigenfunctions were obtained by using the boundary conditions.The circumferential separation function of homogeneous solution was expanded by using the infinite series of trigonometric functions.The axial separation function of homogeneous solution was obtained by the hyperbolic tangent function with the eigenvalues.In the complete oil film field, the analytical expression of oil film pressure distribution was integrated to obtain the nonlinear oil film force of crankshaft bearing.Analysis result shows that the nonlinear oil film force calculated by the analytical method is good agreement with the value calculated by the finite difference method, and the difference is about 5% when the eccentricity ratio is small. When the eccentricity ratio rises from 0.2 to 0.6, the maximum value of termination position angle of oil film reduces by 13.5%. When the dimensionless speed disturbance rises from 0 to 0.03, a relative variation of 3.3% is obtained for the termination position angle of oil film.When the number of eigenvalues is greater than 20, the variations of homogeneous solutions of dimensionless oil film force in the radial and tangential directions are really small, and their values are about-2.8 and 4.6, respectively.Therefore, the analytical method can calculate the nonlinear oil film force of hydrodynamic crankshaft journal bearing accurately.The eccentricity ratio has a great influence on the rupture of oil film, and the rupture easily takes place when the eccentricity ratio is bigger.Compared with the eccentricity ratio, the speed disturbance has less influence on the rupture of oil film.A high calculation precision can be obtained for the homogeneous solution of dimensionless oil film force when the number of eigenvalues is not less than 20, which meets the requirement of engineering.18 figs, 25 refs.