Restrictor Design Parameter Research Articles

Restrictor-based studies of hybrid hole-entry conical journal bearings

PurposeThis paper aims to describe how successfully a particular restrictor delivers its best in increasing the conical journal bearing performance. The restrictors are used in the hole-entry conical journal bearing subjected to hybrid mode. Thus, the restrictors, like constant flow valve (CFV), orifice and capillary, are studied comparatively.Design/methodology/approachNumerical simulation for the bearing results with the three restrictors are obtained by using finite element method (FEM) under the well-known modified Reynolds equation.FindingsWhen the hole-entry conical journal bearings, with the restrictor design parameter range s2 = 0.03 – 0.09, are operated, the results obtained are quite distinctive and significant. It indicates that the CFV restrictor-based conical bearing gives enhanced performance in comparison to orifice and capillary restrictors. Moreover, it suggests the performance-wise sequence of the restrictors in hybrid bearings as CFV > Orifice > Capillary.Originality/valueThe outcome of the research paper will give insight to help the bearing designer to choose the particular restrictor in hybrid conical bearing depending on the industrial need.

Magnetohydrodynamics of Lubricant in Recessed Conical Hybrid Journal Bearing With Taper Error

Abstract To improve the performance accuracy of a conical journal bearing system, the surface error needs to be considered in the analysis since a tiny difference in dimensional values can alter the performance; the consideration of surface error may degrade the performance behavior of bearing. However, a better way to overcome such degradation may be to make use of magnetohydrodynamics (MHDs) of fluid. Therefore, the present work is planned to investigate the impact of taper error and MHD lubricant in recessed conical hybrid journal bearing. In this article, the Reynolds equation is derived under stated assumptions along with frictional power loss expression and finally solved using the finite element analysis, Newton–Raphson method, and generalized minimum residual method. The conducted research helped in determination of optimum values of recess width, land width ratio, and restrictor design parameter, and also obtaining the results corresponding to distinct performance indices. The outcome of these results may inspire practicing designers for the development of better tribo components.

Effect of non-newtonian lubricants on static and dynamic characteristics of journal bearings

Journal bearings play a significant role to increase overall level of reliability in machines. Advancements in lubrication methodology have a great impact on the performance of journal bearings which operate under multifarious parameters and lubrication conditions. Bearing behaviour is monitored by bringing out changes in various aspects like geometry, misalignment value, restrictor design parameter, restrictor types, eccentricity, roughness, aspect ratio, lubricant feeding conditions and lubricating oil properties. Performance of bearings is tremendously dependent on the variation in lubricant properties. This paper presents the state-of-the-art review on the behaviour of lubricants, namely, micropolar, power-law fluids and couple stress lubricants and their effects on journal bearings efficiency. An effort is made to understand the behaviour of different non-Newtonian lubricants on various journal bearing configurations and their comparison with Newtonian lubricants so as to choose the appropriate lubricant for specific bearing configuration. Non- Newtonian lubricants have shown improvements in journal bearing performance when compared with Newtonian lubricants operating at selected conditions.

Combined influence of couple stress lubricant, recess geometry and method of compensation on the performance of hydrostatic circular thrust pad bearing

This study concerns with the theoretical investigation to show the influence of recess geometry and method of compensation on the performance of recessed hydrostatic circular thrust pad bearing operating with couple stress lubricant. Modified Reynolds equation for couple stress lubricant has been derived using Stokes microcontinuum theory. Stokes theory describes the behavior of fluids consisting of long chain polymer additives having sizes comparable to that of the fluid film thickness. Finite element method technique and commercially available software MATLAB 2013 have been used to solve the modified Reynolds equation and, thus, performance characteristics of bearing have been computed. The performance of capillary- and orifice-compensated hydrostatic thrust pad bearings performance have been compared vis-à-vis to different geometric shapes of recess. Each recess shape has identical ratio of bearing pad area to recess area. It has been observed that the couple stress additives have significant positive influence on the static and dynamic performance of the compensated hydrostatic thrust pad bearing provided that restrictors operates with lower values of the restrictor deign parameter[Formula: see text]. Limiting values of 10 and 5 for restrictor design parameter [Formula: see text] have been noticed for capillary and orifice restrictor; beyond these values of [Formula: see text], use of couple stress lubricant on the performance of hydrostatic thrust pad bearing become insignificant.

On the Stiffness and Damping Coefficients of Constant Flow Valve Compensated Conical Hydrostatic Journal Bearing with Micropolar Lubricant

A theoretical analysis for performance characteristics of a conical multirecess hydrostatic journal bearing compensated with constant flow valve has been carried out considering micropolar lubricant. The numerical solution of the modified Reynolds equation for the conical bearing has been done using finite element method with necessary boundary conditions. The performance characteristics have been presented for various values of the restrictor design parameter, load, micropolar parameters, semi-cone angle and aspect ratio (L/D ratio) of the bearing at zero speed. It has been observed that the bearing develops large stiffness and damping coefficients with increase in restrictor design parameter, micropolar effect and semi-cone angle.

Performance characteristics of constant flow valve compensated conical multirecess hybrid journal bearing under micropolar lubrication

This paper presents the theoretical study on the effect of micropolar parameters of the fluid and the semi-cone angle on the performance characteristics of a conical multirecess hybrid journal bearing under micropolar lubrication compensated with constant flow valve. The numerical solution of the modified Reynolds equation for micropolar fluid flow on the conical surface has been done by using finite element method using Galerkin's technique along with the necessary boundary conditions and iterative scheme. The performance characteristics have been presented for a wide range of the semi-cone angle and the restrictor design parameter of the conical hybrid journal bearing system operating under Newtonian and micropolar lubrication. The study suggests that the semi-cone angle of the bearing, constant flow valve restrictor and micropolar parameters significantly influence the performance characteristics of conical bearing. With increase in semi-cone angle of bearing the direct stiffness, damping coefficients and the stability margin have been observed to increase significantly.

Influence of wear on the performance of hole-entry hybrid misaligned journal bearing in turbulent regime

Purpose – The present work aimed to study analytically the influence of wear on the performance of a capillary-compensated hole-entry hybrid misaligned journal bearing system operating in a turbulent regime. The numerically simulated results are presented for the chosen values of restrictor design parameter, Reynolds numbers, wear depth and misalignment parameters. Design/methodology/approach – The wear caused on the bearing surface due to start/stop operations is modeled using the Dufrane’s abrasive wear model. The modified Reynolds equation based on Constantinescu’s lubrication theory is solved using finite element method together with capillary restrictor flow equation. Findings – It is found that the value of minimum fluid-film thickness increases significantly for a constant value of restrictor design parameter when unworn aligned bearing operates in turbulent regime vis-à-vis laminar regime. Further, it has also been observed that when a worn bearing operates in laminar/turbulent regimes, the reduction in the value of minimum fluid-film thickness is more due to journal misalignment as compared to the aligned bearing operates in laminar regime. Originality/value – The present work is original concerning the performance of worn hole-entry hybrid misaligned journal bearing system operating in turbulent regime. The results are expected to be quite useful for the bearing designer.

Analysis of orifice compensated non-recessed hole-entry hybrid journal bearing operating with micropolar lubricants

A numerical study concerning the performance of non-recessed hole-entry hybrid journal bearing lubricated with micropolar lubricants is presented. The modified Reynolds equation governing the flow of micropolar lubricant in the bearing clearance space is solved using Finite Element Method along with appropriate boundary conditions. Dependence of bearing performance characteristics upon the bearing operating, geometric and micropolar parameters, over a range, has been analyzed. The numerically simulated results are pointed to the choice of restrictor design parameter, for the chosen combination of micropolar parameters of lubricant, in order to obtain optimum values of fluid film stiffness coefficients.

Analysis of capillary compensated hydrostatic journal bearing operating with micropolar lubricant

PurposeThe paper seeks to study, theoretically, the performance characteristics of capillary compensated multi‐recessed hydrostatic journal bearings operating with micropolar lubricant. The finite element method is used to solve the modified Reynolds' equation governing the micropolar lubricant flow in the clearance space of a hydrostatic journal bearing. The performance characteristics of bearing operating with micropolar lubricant are presented and compared with that of Newtonian lubricant, for a wide range of non‐dimensional load, capillary restrictor design parameter and micropolar parameters.Design/methodology/approachThe modified Reynolds' equation governing the flow of the micropolar lubricant is solved along with restrictor flow equation by finite element method so as to obtain fluid‐film pressures. The iterative procedure is repeated until the converged solution for the fluid‐film pressure field is obtained.FindingsA study of four‐pocket hydrostatic journal bearing system capillary compensated and operating with micropolar lubricant is presented. The following conclusions are made from the results presented in this study: at a constant load, pocket pressures and minimum film thickness, stiffness coefficients and, the damping coefficients increase with increase in micropolar effect of lubricant as compared to the Newtonian lubricant; the influence of the micropolar parameters of lubricant is more significant upon the minimum fluid‐film thickness at higher values of load and lower values of restrictor design parameter; the non‐dimensional flow decreases with increase in the micropolar effect of the lubricant a given values of restrictor design parameter and load; and the stiffness coefficient in the direction of load is found to be influenced by the micropolar parameters and more significantly at lower values of restrictor design parameter and load.Originality/valueStudies of capillary compensated multi‐recess hydrostatic journal bearing operating with micropolar fluid/lubricant are not available in the existing literature to the best of authors' knowledge. Although, such bearing has been studied with Newtonian lubricant and available in open literature. Therefore, this paper is an original piece of work in the area of micropolar lubrication and compensated hydrostatic bearings.

Orifice compensated multirecess hydrostatic/hybrid journal bearing system of various geometric shapes of recess operating with micropolar lubricant

The objective of the present paper is to study analytically the performance of four-pocket orifice compensated hydrostatic/hybrid journal bearing system of various geometric shapes of recess operating with micropolar lubricant. The modified Reynolds equation for micropolar lubricant is solved using FEM and the Newton–Raphson method along with appropriate boundary conditions. The results suggest that the influence of micropolar effect of lubricant on bearing performance is predominantly affected by the geometric shape of recess and restrictor design parameter. Therefore, the bearing designer must judiciously choose an appropriate geometric shape of recess in order to get an overall enhanced bearing performance.

A study of misaligned roughened two‐lobe hole‐entry hybrid journal bearing

PurposeThe non‐recessed hybrid journal bearings of cylindrical type, when operating at higher rotational speeds can suffer self‐exited vibrations(oil‐whirl Instability), which can cause excessive rotor motion causing bearing and sometimes total machine failure. The multi‐lobe journal bearing exhibits better stability as well as a superior capability to suppress oil‐whirl. The paper aims to present a theoretical study pertaining to a two‐lobe hole‐entry hybrid journal bearing by considering the combined influence of surface roughness and journal misalignment on the performance of the bearing.Design/methodology/approachThe average Reynolds equation governing the flow of lubricant in the clearance space between the rough bearing surfaces together with the equation of flow through a capillary restrictor has been solved using FEM. The bearing performance characteristics have been simulated for a two‐lobe hole‐entry hybrid journal bearing for the various values of offset factor, restrictor design parameter, surface roughness parameter, surface pattern parameter and journal misalignment parameters.FindingsThe two‐lobe hole‐entry hybrid journal bearing system with an offset factor greater than one indicates significant improvement of the order of 15‐25 percent in the values of direct stiffness and direct damping coefficients compared to a circular hole‐entry hybrid journal bearing system. Also the lubricant flow of a two‐lobe hole‐entry hybrid journal bearing is reduced by 25 percent vis‐à‐vis circular bearing.Originality/valueThe present work is original of its kind, in case of two‐lobe hole‐entry hybrid journal bearing. The results are quite useful for the bearing designer.

Thermohydrostatic analysis of capillary compensated symmetric hole‐entry hybrid journal bearing operating with non‐Newtonian lubricant

PurposeEvery high speed machine, demanding high level of perfection, can operate successfully through a precise design of bearings. Such a design can be formulated after carefully studying both static and dynamic characteristics of the journal bearing. The present paper aims to describe the study of static and dynamic performance of a hole‐entry hybrid journal bearing system compensated with capillary restrictor by considering the combined influence of thermal effects and non‐Newtonian behavior of the lubricant.Design/methodology/approachThe variation of the viscosity due to the non‐Newtonian behavior of the lubricant and temperature rise is considered in the study. The numerical solution of the generalized Reynold's, equation governing the flow of the lubricant having variable viscosity along with the energy and heat conduction equations is obtained using finite element method. The non‐Newtonian lubricant has been assumed to follow the cubic shear stress law. The study includes performance of a double row symmetric hole entry hybrid journal bearing configuration containing 12 holes per row.FindingsThe results indicate that change in viscosity of lubricant affects the bearing design parameters.Originality/valueThe paper shows that accurate theoretical modeling of the bearing is an effective tool for the selection of design parameter such as bearing land width ratio (ab), restrictor design parameter (Cs2), and non‐linearity factor (K).

Performance of an Orifice Compensated Two‐Lobe Hole‐Entry Hybrid Journal Bearing

The work presented in this paper aims to study the performance of a two‐lobe hole‐entry hybrid journal bearing system compensated by orifice restrictors. The Reynolds equation governing the flow of lubricant in the clearance space between the journal and bearing together with the equation of flow through an orifice restrictor has been solved using FEM and Galerkin′s method. The bearing performance characteristics results have been simulated for an orifice compensated nonrecessed two‐lobe hole‐entry hybrid journal bearing symmetric configuration for the various values of offset factor (δ), restrictor design parameter , and the value of external load . Further, a comparative study of the performance of a two‐lobe hole‐entry hybrid journal bearing system with a circular hole‐entry symmetric hybrid journal bearing system has also been carried out so that a designer has a better flexibility in choosing a suitable bearing configuration. The simulated numerical results indicate that for the two‐lobe symmetric hole‐entry hybrid journal bearing system with an offset factor (δ) greater than one provides 30 to 50 percent larger values of direct stiffness and direct damping coefficients as compared to a circular symmetric hole‐entry hybrid journal bearing system.

FEM analysis for different configurations of non‐recessed hole‐entry hybrid journal bearings for non‐Newtonian lubricants

PurposeThe present work aims to predict accurately the bearing design data for non‐recessed hybrid journal bearings, considering the effect of non‐Newtonian behavior of lubricant for different symmetric and non‐symmetric bearing geometric configurations.Design/methodology/approachThe simultaneous solution of generalized Reynold's equation governing the laminar flow of incompressible lubricant and the equation of flow of lubricant through the capillary restrictor, considering variable viscosity of lubricant following the “Power law”, has been carried out using FEM. For a given set of bearing geometric, operating parameters and for given external vertical load, the values of various performance characteristics have been obtained for a range of values of power law index, after establishing the journal center equilibrium position, the analysis for which has been elaborately explained.FindingsThe results obtained have been presented graphically for various bearing performance characteristics. It has been observed that with decrease in power law index “n”(0<n≤1), the value of h¯min and load carrying capacity decreases, while bearing flow rate increases for all configuration. The load‐carrying capacity of asymmetric configurations is better and stable over entire range of restrictor design parameter. Bearing configuration with land width ratio = 0.25 and aspect ratio = 1.0, having two rows of holes and six holes in each row, will be better suited for high‐load support, as it has maximum value of minimum fluid film thickness, moderate value of bearing flow and value of attitude angle is almost constant.Originality/valueThe performance characteristics of journal bearing have been presented for a wide range of values of power law index and for different values of restrictor design parameter for capillary restrictor, after establishing the journal center equilibrium position. The comparison of the different symmetric and non‐symmetric journal‐bearing configurations to find the best geometric configuration at different operating conditions, considering the effect of non‐Newtonian behavior of lubricant, represents the originality of the work.

Analysis of hybrid journal bearing for non-Newtonian lubricants

The performance characteristics of capillary compensated hole-entry hybrid journal bearing systems have been studied theoretically. The analysis considers the generalized Reynolds equation governing the flow field of lubricant, having variable viscosity, taking the equation of lubricant flow through a capillary restrictor as constraint. The non-Newtonian lubricant is assumed to follow the cubic shear stress law. The results obtained from the study suggest that bearing static performance characteristics can be optimized for the particular bearing operating conditions by proper selection of parameters such as bearing land width ratios (āb), the restrictor design parameter (Cs2), and the non-linearity factor (K). Copyright © 2006 John Wiley & Sons, Ltd.

On the restrictor design parameter of hybrid journal bearing for optimum rotordynamic coefficients

The precise design of bearings can be formulated after carefully studying both static and dynamic characteristics of journal bearing. The present paper deals with the investigation of restrictor design parameter of a capillary compensated hole–entry hybrid journal bearing system for optimum stiffness and dynamic coefficients of the bearing. The bearing flexibility and variation of viscosity due to temperature rise of the lubrication has been considered in the study. The numerical solution of governing equations, i.e. Reynold's, energy, heat conduction, and elasticity equations has been obtained using finite element method. The study includes performance of a double row symmetric hole–entry hybrid journal bearing configuration containing 12 holes per row. The results presented herein indicate that change in viscosity of lubricant and bearing flexibility affects the bearing design parameter, so the stability of rigid rotor also gets affected. The results show that theoretical modeling of the bearing presented in this work will certainly prove to be effective tool for the selection of restrictor design parameter, C ¯ s 2 for optimum stability parameters.

Stability Margin of Hybrid Journal Bearing: Influence of Thermal and Elastic Effects

This paper deals with the stability margin of a constant flow valve compensated hole-entry hybrid journal bearing system considering bearing flexibility and variation of viscosity due to temperature rise of the lubricant. The journal temperature is computed on the basis of average fluid-film temperature and axisymmetric isothermal element is assumed. The coupled solution of Reynold’s, energy, conduction, and elasticity equations is obtained using finite element method. The performance of a symmetric and asymmetric hole-entry hybrid journal bearing configurations is studied. The results presented in the study indicate that the bearing flexibility and temperature rise of the lubricant fluid-film affects the performance of the hole-entry hybrid journal bearing system quite significantly and proper selection of restrictor design parameter is quite useful in maintaining the fluid film thickness and threshold speed of the journal.

Influence of surface roughness effects on the performance of non-recessed hybrid journal bearings

The effect of journal and bearing surface roughness on the performance of a capillary compensated hole-entry hybrid journal bearing system has been theoretically studied. The analysis considers the average Reynold’s equation for the solution of lubricant flow field in the clearance space of a rough surface journal bearing system. The finite element method and Galarkin’s technique has been used to derive the system equation for the lubricant flow field. The non-dimensional parameters Λ (surface roughness parameter) and γ (surface pattern parameter) have been defined to represent the magnitude of height distribution of surface irregularities and their orientation, respectively. The influence of surface roughness on the bearing performance has been studied for the transverse, isotropic and longitudinal surface patterns. The bearing performance characteristics have been computed for both symmetric and asymmetric capillary compensated hole-entry journal bearing configurations for the various values of surface roughness parameter (Λ), surface pattern parameter ( γ) and restrictor design parameter ( C ̄ S2 ). The computed results indicate that the inclusion of surface roughness effects in the analysis affects the performance of a bearing quite significantly vis-à-vis smooth surface bearing. The study indicates that for generation of accurate bearing characteristic data, the inclusion of surface roughness effects in the analysis is essential.

Influence of recess shape on the performance of a capillary compensated circular thrust pad hydrostatic bearing

This work describes a theoretical study concerning the static and dynamic performance of a circular thrust pad hydrostatic bearing having recesses of different geometric shapes. The Finite Element Method has been used to compute the performance characteristics of a circular thrust pad hydrostatic bearing with circular, rectangular, elliptical and annular recesses. The performance has been compared on the basis of the same bearing operating and the same geometric parameters, i.e. the same ratio of bearing to pocket area ( A ̄ ) and the same value of restrictor design parameter C ̄ s2 . Further, a comparative study of the various bearing configurations has been carried out vis-à-vis different compensating devices such as capillary, orifice, and constant flow valve restrictors so as to study the combined influence of the geometric shape of recesses and the compensating device on bearing performance. The computed results indicate that to get an improved performance from a hydrostatic circular thrust pad bearing, a proper selection of the geometric shape of the recess in conjunction with the type of restrictor and the value of the restrictor design parameter C ̄ s2 is essential.

A comparative study of flexible thrust pad hydrostatic bearings with different restrictors

The characteristics of flexible thrust pad hydrostatic bearings with different flow control devices, such as capillary, orifice and constant flow valves, have been studied. The results of bearing characteristics of circular thrust pad and single-pocket and multipocket rectangular thrust bearing configurations have been presented for various values of the deformation coefficient C ̄ d and restrictor design parameter C ̄ s2 . These results provide a comparative study of the performance of compensated flexible thrust bearing configurations.