Static and Dynamic Analysis of Hydrodynamic Flexible Oil Bearings Using Micropolar Lubrication

Abstract

Necessity to make more efficient mechanical system in order to sustain in competitive world there is demand for efficient bearing system which can carry high load at high speeds. Hydrodynamic journal bearings are best suited for rotating machinery applications which require carrying high load when machinery is working at high speeds. Hydrodynamic journal bearings have wide range of application due to their ability to carry high load at high speed of operation. Ever increasing demand to improve the design in order to increase quality and reliability has led to use of liner. In order to enhance performance of bearings additives are added to lubricating oil. These additives are long chained carbons when mixed in lubricating oil and also metal debris during operation fluid no longer behaves as Newtonian fluid. Many theories are presented by researchers for non-Newtonian behavior of fluids. But, theory of micropolar fluids is widely used in tribology to study performance characteristics of bearings. The above stated factors motivated authors to study effect of flexibility of bearing liner on hydrodynamic journal bearings under micropolar lubrication. Steady state performance characteristics in terms of load carrying capacity, attitude angle, friction parameter and end flow are presented in the study. The effect of flexibility of liner on steady state parameters under micropolar lubrication is presented in terms of graphs. Modified Reynolds equation is derived incorporating the effect of micropolar fluids to general equations of lubrication. Modified Reynolds equation is solved using finite difference method and distortion of liner is calculated by applying theory of elasticity. Results are presented in form of graphs. Detailed parametric study is done taking deformation factor as independent variable and others as parameter. Linear dynamic analysis is conducted using perturbation method to study stability of hydrodynamic journal bearings. Small order perturbations are provided to get stability characteristics in terms of critical mass parameter and whirl ratio. Modified Reynolds equation is solved along with equations of motion. Finite difference method along with successive over relaxation scheme is used to get perturbed pressures along line of centers and perpendicular to lines of centers. Results are presented in the form of graphs for detailed parametric study conducted. Detailed effect of flexibility of linear and micropolar parameters on stability characteristics is discussed in analysis. VII Trajectory of journal centre is predicted by non-linear transient analysis. Modified Reynolds equation is solved with equations of motion to get state space variables applying fourth order Runge-Kutta method. Effect of flexibility of liner on non-linear transient characteristics of hydrodynamic journal bearings is studied by applying theory of elasticity. Critical mass parameter is predicted by hit and trial method. Mass parameter for which trajectory of journal bearing centre follows limit cycle gives us measure of critical mass parameter. Results of non-linear transient analysis are compared with results of linear dynamic analysis. Effect of flexibility of liner and micropolar parameters on limit cycle is studied.