ELASTOHYDRODYNAMIC ANALYSIS OF GROOVED AND PRESSURE DAM, CIRCULAR AND NONCIRCULAR, JOURNAL BEARINGS

Abstract

Rotating machines such as compressors, turbogenerators, pumps, etc., are generally supported in hydrodynamic journal bearings. These bearings are normally designed using data developed with the assumptions that they operate with isoviscous lubricants and are rigid. However, the continual growth of high speed machines having heavy rotors requires bearings to operate at high fluid pressures and temperatures which make these assumptions questionable. Therefore, for a more reliable operation of these machines, the design of their bearings should be based on an analysis which takes the elastic deformation and the variation of fluid viscosity into account. The present study was planned with these forethoughts. Although the theory of elastohydrodynamic (EHD) lubrication deveolped quite significantly during the last four decades, it remained confined mainly to the problems of heavily loaded contacts as in rolling element bearings and gears, in the early stages of its development. Subsequently , with the experimental evidence of significant distortions of the bearing elements due to the hydrodynamic pressures, the use of EHD lubrication theory was enlarged to Include the studies of hydrodynamic bearings. These studies are either based on certain assumptions or are concerned with the analysis of static and dynamic performance characteristics, . mainly for circular bearings. The published literature on the EHD investigations on noncircular and pressure dam bearings is scant. The information available on the thermoelastohydrodynamic (TEHD) studies of journal bearings, too, is generally limited to the computation of static performance characteristics of circular bearings. Further, the transient motion studies made on journal bearings, are available only for the rigid bearing cases. Therefore, there is a need to investigate the EHD and TEHD effects in circular, noncircular and pressure dam journal bearings with more realistic mathematical models and boundary conditions for the physical problems involved. Also the transient motion studies, using the more appropriate nonlinear equations of motion for the disturbed journal, are required to obtain the dynamic response of a flexible journal bearing system. The present work is an attempt to bridge this gap in the existing literature. The work contained in this study is broadly divided in two parts. In the first part, the static and dynamic performance characteristics of journal bearings are studied whereas in the second part, the transient motion trajectories of journal centre-motion for the rigid and flexible journal bearings are considered. The performance characteristics are obtained with three viscosity conditions for the lubricant, i.e., isoviscous, piezoviscous and thermopiezoviscous. In the hydrodynamic analysis, the generalized Reynolds' equation governs the flow of a liquid lubricant in the clearance space of a journal bearing. In the thermal analysis, the temperature" distributions in the fluid flow-field and the bush-housing assembly are computed using the three-dimensional energy and Fourier heat conduction equation, respectively, assuming journal in the thermal equilibrium. For the calculation of bearing deformation field, the bush, in general, is considered a three-dimensional elastic structure. Finite element method is employed for solving the equations for flow-field, energy, heat conduction and elasticity deformation. Based on the normalization of the governing equations, a nondimensional deformation coefficient (d) is defined as a function of runner speed, geometry of the lubricated surfaces, reference viscosity of the lubricant, modulus of elasticity of the material and thickness of the bush, giving a measure of the bearing flexibility. The transient motion trajectories of rigid and flexible journal bearing systems are obtained using linearized as well as the more realistic nonlinear equations of disturbed motion of the journal in free translatory whirl. The points on these trajectories are found by numerically integrating the governing equations of motion for a specified initial disturbance. The computational procedure used to obtain the performance characteristics is an iterative one. For the solution of an EHD problem, nested iterations are needed to establish pressure and deformation fields and the static equilibrium position of the journal centre for a given vertical load. Based on a comparative study of two numerical techniques, the linear complementarity problem approach was adopted to establish the boundaries of the positive pressure region. In the thermal (THD and TEND) vi studies, the converged temperature fields for the lubricant, the bush-housing assembly and the journal are established by solving simultaneously the coupled energy, heat conduction and thermal equlibrium equations. In the global iteration scheme, using the viscosity computed from the previous iteration temperatures, the Reynolds' and elasticity equations are solved to obtain converged pressure and deformation fields. The temperature field for the lubricant is then established for the computed film pressures which, in turn, gives the modified values for lubricant viscosity for the next iteration. The equilibrium position of the journal centre is established using a direct iteration technique which includes the loops for computing the converged TEND pressure field. The performance characteristics of rigid and flexible circular (two-axial-groove), noncircular (two-lobe and three-lobe) and pressure dam (circular and elliptical) bearings are reported as functions of load capacity_ These characteristics include the eccentricity ratio, attitude angle, minimum fluid-film thickness, side flow, friction power loss, four stiffness and four damping coefficients, threshold speed and whirl frequency ratio. The results for the isoviscous lubricant case are given for several values of Cd ranging from 0 to 0.5 and four values of Reynolds' number. The performance characteristics for two-axial-groove, noncircular and circular pressure dam bearings are also presented for piezoviscous lubricant case. To examine the combined effects of temperature-pressure sensitive viscosity vii (thermopiezoviscous lubricant) and elastic deformation, a few results are given from the THD and TEND analysis of circular and noncircular bearing configurations. The linear and nonlinear trajectories are drawn for laminar rigid/flexible circular (plain and two-axial-groove), noncircular (two- and three-lobe) and pressure dam (circular, and elliptical) journal bearings taking several values of journal mass in each case. Few trajectories are also drawn for turbulent rigid and flexible circular (two-axial-groo've) bearing. The EHD results for the performance characteristics of journal bearings presented in this study show that these characteristics are significantly altered by the flexibility, particularly when the load is heavy and/or Ed is large. The studies for the effects of pressure-sensitive viscosity of the lubricating oil show that the values of bearing characteristics, such as minimum fluid-film thickness and threshold speed, are enhanced by the piezoviscous viscosity conditions but are reduced with the increase in bearing flexibility. The thermal investigations also give significantly different performance characteristics for rigid/flexible bearing cases. These studies indicate appreciable reduction in the bearing load capacity with the inclusion of thermal effects in comparison to the corresponding isothermal value, for a fixed minimum fluid-film thickness. The transient motion trajectories constructed for rigid W;i laminar journal bearings using the linearized as well as the nonlinear approaches are, in general, identical. The linear trajectories for the flexible bearings also follow expected trends, i.e., they display the limit cycle characteristics when the journal mass equals the critical mass. These studies further indicate that a rigid/flexible bearing system remains stable for all values of journal mass which are smaller than the critical mass. Alternatively, the nonlinear trajectory constructed for a flexible bearing by taking the journal mass to be equal to the critical mass represents a highly stable dynamic response of the bearing system. A lonlinear flexible bearing system is shown to remain stable.at values of journal mass appreciably higher than the critical mass.