Study of Thermal Effects in Non-Recessed Hybrid Journal Bearing with Non-Newtonian Lubricant

Abstract

The revolutionary changes have taken place in the field of hydrostatic and hybrid journal bearing from very slow speed radar to very high speed turbo machinery. These find application in ultra precision machine tools requiring high stiffness to improve accuracy. The growing demands from industries for higher speed applications and ability of hybrid journal bearing to support heavy loads have necessitated to study the performance of bearings in detail under more realistic conditions. However, the high speed operation of bearings results in higher operating temperature of both lubricant and bearing surface. Increase in bearing temperature poses a danger to bearing liner as well as to lubricant. It not only degrade the performance of a bearing but also of machine itself. Also, an increase in lubricant temperature reduces its viscosity and thereby changes the fluid-film profile. Thus, analysis based on isothermal assumption predicts inaccurate value of minimum fluid-film thickness and increase the risk of bearing failure. The commonly used lubricants for bearing are mineral in nature and additives are added to enhance bearing performance. Generally used additives are high molecular weight polymers and used to control viscosity variation. The behavior of polymer added mineral oil is no longer Newtonian due to non-linear relationship between shear stress and shear strain rate. The most of the studies concerning analysis and design of hydrostatic/ hybrid journal bearings have been carried out assuming the behavior of lubricants to be Newtonian. There is lack of information concerning the non-linear behavior of viscosity of the lubricant on the performance of non-recessed hybrid journal bearings. A thorough scan of the available literature concerning the hydrodynamic and hydrostatic/ hybrid journal bearings indicates that the thermal effects together with non-Newtonian behavior of lubricant due to additives mixed in the lubricants have been ignored in the analysis to obviate the mathematical complexity. To the best of author’s knowledge, no study is available which deals with thermohydrostatic performance of non-recessed hybrid journal bearings operating with non-Newtonian lubricants. Thus, objective of the proposed work is to investigate the influences of viscosity variation due to temperature rise and non-Newtonian behavior of the lubricant on performance characteristics of hole-entry hybrid journal bearing of symmetric and asymmetric configuration compensated with constant flow valve, capillary and orifice restrictors and slot-entry hybrid journal bearing. To obtain thermohydrostatic (THS) performance characteristics of a non-recessed hybrid journal bearing system operating with non-Newtonian lubricant, the solution of relevant governing equations, i.e. Reynold’s equation, Energy and Conduction equations, are required. The generalized Reynold’s equation is solved by taking the flow of lubricant through restrictor as a constraint, along with relevant boundary conditions. This equation is used to determine the pressure distribution in the clearance space between journal and bearing. The non-Newtonian effect is introduced by modifying the viscosity term using cubic shear stress law and power law as constitutive equation. The heat generated due to viscous friction increases the temperature of the lubricant film which changes its viscosity. To predict temperature field in the film and the bush, 3D energy equation together with 3D conduction equation is required to be solved simultaneously to establish the equilibrium of heat flow from lubricant to surrounding through the bearing bush. The conduction equation is solved using appropriate heat transfer boundary conditions along free surface of the bush. The temperature of lubricant at supply hole is assumed constant. The temperature distribution obtained in film and bush changes lubricant viscosity. The change in the viscosity due to temperature rise and non-Newtonian behavior changes the fluid film thickness profile and converged coupled solution is obtained by simultaneously solving Reynold’s, energy and conduction equations. The finite element method is used to compute the pressure and temperature distributions for the coupled thermohydrostatic (THS) problem. The system equations for the discretized solution domains are obtained using relevant governing equations, employing Galerkin’s method and usual assembly procedure. The lubricant flow field is discretized in two-dimension for the solution of Reynold’s equation and in three dimensions for the solution of energy equation. The derived system equation for solution of Reynold’s equation is modified to maintain continuity of the flow between bearing and restrictor. The modified system equations are linear in case of capillary and constant flow valve compensated bearings. For an orifice compensated bearing, modified system equation becomes nonlinear and to solve these nonlinear equations, Newton-Raphson method is used. A computer program developed for this study is general and capable of handing lubrication problems for the rigid journal bearings operating in hybrid mode of operation and considering the variation of viscosity due to rise in temperature and non-Newtonian behavior of the lubricant. The developed program can also be used for computing the performance characteristics of plain hydrodynamic journal bearing by changing the operating and geometric parameters, which is used for establishing the validity of present analysis, solution scheme and the program. The static equilibrium position of the journal center for a given vertical load is obtained using an iterative loop. To obtain the solution of thermohydrostatic (THS) problem, nested iterative loops are used. The performance characteristics of both symmetric and asymmetric non-recessed hole-entry hybrid journal bearings compensated with constant flow valve, capillary and orifice restrictor and slot-entry bearings are presented. The variation in the bearing performance characteristics is studied for a wide range of bearing parameters. The computed results are discussed in graphical as well as in tabular form to draw conclusions. A comparative study of non-recessed hybrid journal bearings compensated with different restrictors and slot-entry hybrid journal bearing is carried out so as to assess the relative changes in bearing performance. It is observed that at a constant external load ( ) for a non-recessed hybrid journal bearing system operates at reduced value of minimum fluid-film thickness ( ) because of reduction in viscosity of lubricant due to temperature rise and non-Newtonian behavior. There is an increase in the oil requirement for a hybrid journal bearing with the specified operating and geometric parameters, when the viscosity of the lubricant decreases due to the rise in temperature and non-Newtonian behavior of the lubricant. In case of capillary, orifice compensated bearings and slot-entry journal bearings, the percentage increase in the value of lubricant flow ( ) is observed to be of the order of 38.5%, 18.4% and 18.1% respectively for symmetric configuration and of the order of 27.8%, 8.8% and 4.6% respectively for asymmetric configuration operating with non-Newtonian lubricant with non-linearity factor =1.0 as compared to Newtonian case ( =0.0). A comparative assessment of non-recessed hybrid journal bearings is carried out for the same bearing operating and geometric parameters. In general, a constant flow valve compensated non-recessed hybrid journal bearing gives superior performance from the point of view of film thickness and stability parameters. The study indicates that bearing performance parameters like minimum fluid-film thickness, stiffness coefficient and stability margin are changed due to variation of viscosity because of temperature rise and non-Newtonian behavior of the lubricant for the chosen bearing configurations. Thus, to generate more realistic bearing characteristics design data, these effects are essential to be considered in the analysis. The results presented in the thesis are expected to be quite useful to the bearing designer.