A STUDY OF HYDROSTATIC/HYBRID THRUST PAD BEARINGS CONSIDERING NON-LINEAR BEHAVIOUR OF LUBRICANTS

Abstract

Bearings are extensively used in power transmission system of machines, to support external load while simultaneously allowing relative motion along the desired direction. Use of bearings can be traced from common house-hold appliances/equipment’s to supporting moving/stationary parts in power plants, hydraulic pumps, automobiles, telescopes etc. The reliability of machines/systems depends upon proper and smooth functioning of bearing elements. From beginning of twentieth century, rapid technological advancements have taken place to improve the productivity of machines. Nowadays, machines are made to operate in stringent (heavy load and high speed) operating conditions. The performance of bearing is of paramount importance as a loss of energy by friction/material loss due to wear, account for huge economic and environmental burden. Over the years, greater attention has been paid to design and develop energy efficient high load sustaining bearings. Hydrostatic/hybrid thrust pad bearing are generally used for supporting axial load in machines. These bearings are of extreme importance to machines, which often operates under heavy load and relatively low sliding speed. These bearings require many ancillary components namely hydraulic valves restrictors, hydraulic pumps etc., which make lubrication system rather complex and more involved. Nevertheless, unique advantages such as high load carrying capacity, low friction and wear (almost zero), high fluid film stiffness and damping coefficient etc., offered by these bearing substantially expands their range of industrial applications. Hydrostatic/hybrid thrust bearing found usage in application ranging from small precision machines/equipment’s to supporting enormous turbomachines/structures such as rotors of hydraulic pumps and turbines, lock-gates, machine tools, observatory domes etc. Owing to abovementioned advantages/features, researchers around the globe have focused their attention to analyze, enhance and predict performance of hydrostatic/hybrid thrust bearing operating under stringent, exact and precise operating conditions. In the analysis of hydrostatic/hybrid thrust bearing, bearing surfaces are assumed to remain parallel during normal operation of machines. However, in industrial/commercial bearings same amount of tilt is always present between the bearing surfaces because of non-parallelism induced by errors in manufacturing/assembly of bearings. Neglecting tilt in analysis of thrust bearing can lead to generation of inaccurate design data. Presence of even small amount tilt between bearing surfaces can severely deteriorates load sustaining capability and fluid film stiffness characteristics of vi bearings. Therefore, it become imperative to include influence of tilt while numerically simulating hydrostatic thrust bearing. The performance of hydrostatic thrust bearing is also influence by geometric shape of the recess. Rectangular shape is mostly preferred in hydrostatic/hybrid bearing due to their ease in manufacturing. However, with recent advancement in manufacturing, intricate recess shape such as sectorial, elliptical, triangular etc. can be produced relatively with ease. The geometric shape of recess significantly affects pressure distribution in the land area of bearing. Steady-state and dynamic response from bearing can be altered suitably by changing geometric shape of recess. Numerical simulations of bearing employing different recess shapes would enable a bearing designer to select an appropriate recess shape, so as to get desired steady-state and dynamic response from bearing system. Commercially available lubricants are often blended with long chain additives to improve tribological performance of bearing system. Selection of base oil and additives are careful carried out by tribologists/lubrication engineers, in accordance to operating conditions i.e. speed, load, temperature etc. Blending of additives in base oil, induces non-Newtonian character in lubricant behavior. Behavior of non-Newtonian lubricant namely polymer thickened oil, synthetic oils, biofluids etc., considerably deviates from linear behavior as described by classical Newtonian theory. The size of additives in polymer thickened oils could be million times the diameter of water molecules and is comparable to dimensions of fluid film thickness. The additives are assumed to be rigid and undergoes micro-translation motion in the bulk lubricant. Stokes couple stress theory is generally used to describe flow behavior of such lubricants. Similarly, flow behavior of lubricants in which additives undergoes micro-rotation in conjunction with micro-translation are better explained using Eringen Micropolar theory. Nowadays, tribologists/lubrication engineer are formulating and experimenting new class of lubricants, through which better control can be exercised on rotor-dynamic response from the bearings. These lubricants undergo micro-structural transformation upon application of electric/magnetic fields. Electrically conducting and electrorheological lubricants are examples of such type of lubricants. In present work, influence of presence of additives and electric/magnetic field is investigated on performance of hydrostatic/hybrid thrust bearing. The non-Newtonian behavior of lubricant is theoretically described using couple stress, micropolar, Magneohydrodynamic and Electro-Rheological fluid model. Topographical surface of bearings always possesses micro-irregularities in the form of peaks and valleys, even after machining/finishing process such as grinding, polishing, lapping etc. Microtopographical features are random in nature and are inherent to machining/shaping process. These vii micro-features changes local film thickness as well as local film pressure over the surface of bearing, to some extent. Furthermore, bionic-textures over the surface of aquatic life-forms is reported to be beneficial in reducing frictional drag acting on their body. Inspired by these findings, researchers have investigated the performance of hydrodynamic fluid film bearing by applying welldefined/ characterized micro-texture of various forms/patterns over the surface of bearings. Using textured surfaces is reported to substantially enhancing load and frictional behavior of fluid film bearings operating under hydrodynamic and mixed/boundary lubrication regimes. In mixed/boundary lubrication regimes, the micro-features act as lubricant reservoir and trap wear debris. In present work, micro-texture over the surface of thrust pad have been applied in the form of regular arrays of micro-dimple/micro-grooves of various cross-sectional shapes/configurations. Applying micro-texture of optimum geometric shape/configuration substantially enhance load carrying capacity and reduces frictional power loss of hybrid thrust bearing. A thorough review of available literature, revealed that use of non-Newtonian lubricants and textured surface are mostly confined to hydrodynamic thrust bearing. Coupling of lubricant flow equation through restrictor with Reynolds equation provide more complete and accurate analysis of thrust bearing operating in industrial applications. To the best of authors knowledge, no comprehensive study is available which investigates combined influence of non-linear behavior of lubricant, recess geometry, tilt and restrictor on the performance characteristics of hydrostatic/hybrid thrust bearing. Few studies are available dealing with use of micro-dimple textured surface in hybrid thrust bearing, but they too are limited to spherical/conical shape of micro-dimples. In present work, influence of geometric shape/configuration of micro-dimples/grooves have been comprehensively investigated on steady-state and dynamic characteristics of hybrid thrust bearing. In view of above, the following objectives have been formulated in this work:  To study combined effect of recess shapes, compensating element and tilt on steady-state and dynamic performance of hydrostatic thrust bearing operating with various non-Newtonian lubricants.  To study influence of geometric shape/configuration of micro-dimples/micro-grooves on static and dynamic performance of capillary and orifice compensated textured surface hybrid thrust bearing operating with various non-Newtonian lubricants. A source code based on Finite Element Method (FEM), Gauss–Seidel Method and Newton–Raphson method has been developed, to numerically solve modified Reynolds equations for various non- Newtonian lubricants. The developed source code would provide coupled-solution of restrictor viii equation and Reynolds equation, to compute fluid film pressure distribution over the surface of thrust pad. The bearing performance characteristics have been computed in terms of fluid film pressure, lubricant flow rate, fluid film frictional power loss, fluid film stiffness and damping coefficients. The developed source is versatile enough to compute above-mentioned performance parameters for thrust bearing operating in hydrostatic, hydrodynamic and hybrid mode. The numerical results are separately compiled for smooth surface hydrostatic thrust bearing and textured-surface hybrid thrust bearing. Initially, numerical simulations of hydrostatic thrust bearing have been performed to investigate the influence of non-Newtonian lubricant, recess geometry, restrictor and tilt on performance parameters of bearings. These numerical simulations are helpful in generating more accurate and realistic bearing design data. Later, numerical simulations have been performed for textured surface hybrid thrust bearing operating with various non-Newtonian lubricant. In numerical simulations, a mass conserving (JFO based) algorithm has been used to obtain numerical solution of modified Reynolds equation. The texture over the surface of thrust pad surface is produced in the form of well-defined/characterized array of micro-dimples/micro-grooves. Different geometric shape of micro-dimples (spherical, conical, cylindrical and rectangular) and micro-groove (circular, rectangular, triangular and trapezoidal) have been investigated to maximize load carrying capacity of bearing. Additionally, an optimization study has been carried out to determine optimum attributes (i.e. radius, depth, textured length etc.) and configuration (full/half-section) of micro-features to maximize the load carrying capacity of bearing. It has been found that use of half-section microdimple and full-section micro-groove of various geometric shapes, significantly enhance the load carrying capacity of bearing. A substantial reduction in frictional power loss is also reported by use of textured surface in hybrid thrust bearing. Specifically, square micro-dimples and rectangular micro-groove have been found to be best micro-feature shape in terms of load carrying capacity of hybrid thrust bearing operating with electrically conducting couple stress lubricant. Thus, use of textured surfaces in hybrid thrust bearing is quite beneficial in improving the efficiency of bearing, by enhancing load carrying capacity (+122.3% to +402.6%) and reducing frictional power loss (- 46.2% to -53.1%). The bearing design data generated herein is expected to be useful in design of hydrostatic/hybrid thrust bearings.