Thermohydrodynamic Analysis of Misaligned Journal Bearing

Abstract

Hydrodynamic journal bearings are used to support rotating shafts of machines such as compressors, turbogenerators, pumps, etc. under imposed operating conditions which comprises speed and load. These bearings are normally designed using data developed with the assumptions that they operate with isoviscous lubricants and are aligned. Oil viscosity is a strong function of oil temperature and varies throughout the film. This, in turn, influences the prediction of various bearing performance characteristics. The temperature of the lubricant is largely controlled by the speed of the journal. Since there is a tendency to design rotors to operate at high speeds for optimum performance, the assumption of constant temperature (and hence constant viscosity) appears to be doubtful. Further, due to manufacturing tolerances, deflection of journal and bearing support, asymmetric bearing load, etc., journal bearings may quite often operate at the misaligned condition. The geometry of clearance space between the journal and the bush influences the bearing performance significantly. The clearance geometry depends largely on the amount of misalignment present between the axes of bearing and journal. Therefore, for a more accurate prediction of bearing performance, it is essential to perform a complete thermo hydrodynamic (THD) analysis of misaligned journal be~ings. The present study has been planned with these forethoughts. Although the theory of thermohydrodynamic (THD) lubrication developed quite significantly during the last few decades, it remained confined mainly to the problems of aligned journal bearings. The published literature on the THD investigations on misaligned journal bearings is scant. Even the isothermal literature on misaligned journal bearings is generally limited to the computation of static and dynamic performance characteristics of circular bearing geometries (ie plain and two-axial-groove) only. Therefore, there is a need to investigate the THD effects in misaligned circular and non-circular journal bearings with more realistic mathematical models and boundary conditions for the physical problems involved. This work is an attempt to bridge this gap present in the existing literature The work contained in this study is broadly divided into five parts. The first part deals with the validity of the results. In the second part, the static and dynamic performance characteristics, isopressure curves, pressure profiles, isotherms and temperature profiles are studied for different bearing configurations viz. plain journal bearing, two-axial-groove journal bearing, elliptical journal bearing and three-lobe journal bearing respectively. The third part consist of the study of transient motion trajectories followed by the comparative study of vital parameters of journal bearings. The last part deals with the effect of operating parameters on static and dynamic characteristics. The generalised Reynolds equation is used to represent the flow of lubricant in the clearance space of journal bearings. The clearance space geometry between bearing pads/lobes and journal is expressed by including the effect of bi-planar misalignment. In the thermal (THD) analysis, the temperature distributions in the fluid-flow field and the bushhousing assembly are computed using the three-dimensional energy and Fourier heat conduction equation, respectively. A one-dimensional heat conduction equation for journal has been solved. Viscosity of the lubricant has been expressed as function of temperature using conventional exponential form. Heat transfer between bush/journal and oil in supply grooves is considered. Finite element method is employed for solving the Reynolds equation and finite difference method with Successive Over Relaxation is employed for solving the energy and heat conduction equations. The computational procedure used to obtain the performance characteristics is an iterative one. In the global iteration scheme, the viscosity of oil is computed using the previous iteration temperatures. The Reynolds equation is then solved to obtain the converged pressure field. The temperature field for the lubricant, bush-housing and journal is then established for the computed film pressures which, in turn, gives the modified values for lubricant viscosity for tne solution of Reynolds equation in the next iteration. Suitable weighting factors have been used to improve the rates of convergence of various iteration loops. The performance characteristics of misaligned journal bearings are reported as functions of load. These characteristics include eccentricity ratio, attitude angle, maximum fluid-film pressure, minimum fluid-film thickness, side flow, mean journal temperature, maximum bush temperature, sixteen stiffness coefficients, sixteen damping coefficients, threshold speed and whirl frequency ratio The results for aligned and misaligned journal bearings are given for three different values of bi-planar misalignment ratios. To examine the combined effects of mi~~lipnmp.nt and THD, isopressure curves ::mrl m-essure profiles are plotted for the aligned and misaligned journal bearings. Also, the isotherms and temperature profiles are plotted for oil and bush at different locations for all bearing configurations operating with misalignment. The analysis reveals that performance characteristics are highly influenced by the inclusion of thermal effects. The THD results for the performance characteristics of misaligned journal bearings show that these characteristics are significantly altered by misalignment, particularly, when the load is heavy and/or misalignment is large. These studies indicate appreciable reduction in the bearing load capacity by the misalignment. The minimum fluid-film thickness is reduced drastically when the bearings operate with misalignment. The effect of misalignment is to make the distribution of bearing pressure asymmetric and at the same time, it changes the maximum bearing pressure values. At higher load values, misalignment reduces the side flow. The misalignment significantly improves the stability margin of all journal bearing systems. The journal temperature and maximum bush temperature, each, increases with the increase in misalignment. For a misaligned bearing, the journal temperature varies significantly along the axial length of the journal. Hence, the journal cannot be assumed as a lumped thermal element in the analysis of misaligned bearings. The bush-fluid interface temperature at all load values increases with the misalignment in all the journal bearings studied. There is considerable variation in bush-fluid interface temperature along the circumferential and axial direction. This variation further increases with the increase in the value of load. The isotherms indicate that the heat flows into the journal from the hot regions of oil and out of the journal in the cold regions of the oil They also show that due to misalignment, the maximum temperature region does not remain in the central plane but shifts away from the central plane. The maximum bush temperature occurs in the vicinity of hottest region of oil-film. In the high temperature region of the bush, most of the heat transfers directly out of the bush outer surface to the surroundings It is also observed that heat transfer takes place not only in radial direction in the bush but also in the circumferential and axial directions. Hence, a two-dimensional thermal analysis is not sufficient for the study of misaligned journal bearings and a complete three-dimensional analysis is desired. The study of transient motion trajectories of journal-centre show that all bearings are relatively more stable when operating under misaligned condition and the relative stability is even better when the operating load is higher.