A study of slot-entry hydrostatic/hybrid journal bearing using the finite element method

A theoretical study concerning the static and dynamic performance of hydrostatic/hybrid journal bearing compensated by slot restrictor has been presented using the finite element method (FEM). Results have been presented for a double row symmetric as well as asymmetric configurations for different values of slot width ratios (SWR) and external load ( ). In order to have a better understanding of their performance vis-à-vis other non-recessed bearing configurations, the performance characteristics of slot-entry journal bearings have been compared with that of similar hole-entry compensated journal bearings using capillary, orifice and constant flow valve restrictors for the same bearing geometric and operating parameters. The comparative study indicates that asymmetric slot-entry journal bearings provide an improved stability threshold speed margin compared with asymmetric hole entry journal bearings compensated by capillary, orifice and constant flow valve restrictors.     

Influence of elastic effects on the performance of slot-entry journal bearings

Modern high-performance machines require bearings to operate under stringent conditions. For bearings operating under heavy loads, the bearing deformations can no longer be neglected as they are comparable to the order of magnitude of the fluid film thickness. This paper describes the performance of slot-entry hydrostatic/hybrid journal bearings by considering bearing shell flexibility in the analysis. The relevant governing equations have been solved by the finite element method. Slot-entry journal bearings of two separate configurations have been studied over a wide range of bearing operating and geometric parameters. Elastic effects are found to significantly affect the static and dynamic performance characteristics of the bearing studied. The study indicates that, for given operating conditions, to get optimum performance of a bearing proper selection of the bearing flexibility parameter (), the concentric design pressure ratio () and the type of bearing configuration (symmetric/asymmetric) are essential.     

Performance of worn non-recessed hole-entry hybrid journal bearings

Non-recessed journal bearings have been successfully used in various engineering applications because of their good performance over a wide range of speed and load, besides their relative simplicity in manufacturing. Due to many starts and stops in its lifespan, the bearing bush wears progressively on account of rubbing, which affects bearing performance. The present work is an attempt to analytically study the performance of a worn non-recessed (hole-entry) capillary-compensated hybrid journal-bearing system. FEM has been used to solve the Reynolds equation, governing the flow of lubricant in the bearing clearance space along with the restrictor flow equation using suitable iterative technique. A study is conducted for two configurations, i.e., symmetrical and asymmetrical hole-entry journal-bearing system. The simulated results of bearing characteristics parameters in terms of maximum fluid-film pressure, minimum fluid-film thickness, flow rate, frictional torque, rotor dynamic coefficients, stability threshold speed and whirl frequency ratio, etc. have been presented for the wide range of various values of load and speed. The results indicate that the wear affects the bearing performance considerably; therefore, a due consideration of wear defect should be given for an accurate prediction of the bearing performance over a number of cycles. The computed results further indicate that the influence of wear defect on journal bearing performance may be minimized if a designer selects a suitable bearing configuration.     

Performance analysis of a multirecess capillary compensated conical hydrostatic journal bearing

The present paper is aimed to study theoretically the performance of a 4-pocket hydrostatic conical journal bearing system. The Reynolds equation governing the flow of lubricant in the clearance space of bearing has been solved using FEM. The bearing static and dynamic performance characteristics have been presented for the values of external load W¯_r=0.1-1.0 and for the semi cone angles (γ=10°, 20°, 30° and 40°). The numerically simulated results indicate that the lubricant flow rate is significantly reduced in case of conical journal bearing vis a vis the corresponding similar circular hydrostatic journal bearing.     

Manufacturing of cast monolithic hydrostatic journal bearings

In this work a self-compensating hydrostatic journal bearing design, which eliminates all but one precision-manufacturing step, was manufactured and tested. Novel manufacturing methods for different sizes are introduced. The bearing sensitivity to manufacturing errors was analyzed computationally using statistical methods. These results were used to show that the introduced manufacturing methods are more cost effective than the traditional precision manufacturing methods for hydrostatic bearings, even when the performance variation is taken into account. Manufactured bearings were tested and the experimental results were compared with theoretical results and satisfactory agreement was achieved.     

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 ( ). 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.     

Static characteristics of a water-lubricated hydrostatic thrust bearing with a porous land region and a capillary restrictor

In this paper, a water-lubricated hydrostatic thrust bearing with a porous land region and capillary restrictor is proposed, and the results of theoretical and experimental investigations of its static characteristics are presented. The results showed that the water-lubricated hydrostatic thrust bearing with a porous land region had good operating characteristics; in particular, it had a high load capacity and static stiffness close to that of a porous bearing when operating with a clearance of less than 15 μm, and a high load capacity and static stiffness equivalent to that of a pocket bearing when running with a clearance larger than 15 μm.     

Performance of membrane compensated multirecess hydrostatic/hybrid flexible journal bearing system considering various recess shapes

The paper describes a theoretical study concerning the performance of an externally pressurized multirecess hydrostatic/hybrid flexible journal bearing system by varying the geometric shape of recess and using the membrane flow valve restrictor as a compensating element. The four different recess geometries of the bearing studied in the present study are a square recessed bearing, a circular recessed bearing, an elliptical recessed bearing and a triangular recessed bearing. The equation governing the flow of lubricant in a journal bearing together with 3D elasticity equation and restrictor flow equation are solved by using the Finite Element Method. The study describes the effect of recess shape, bearing flexibility and a method of compensation on the performance characteristics of a hydrostatic/hybrid journal bearing system. A comparative performance of the membrane compensated hydrostatic/hybrid journal bearing system has also been studied vis-à-vis capillary, orifice and constant flow valve restrictors. The results presented in this study amply demonstrate that the shape of recess/pocket of a hydrostatic/hybrid flexible journal bearing system affects the performance of the bearing quite appreciably and a proper selection of recess shape along with a suitable compensating device is needed to get an improved performance from the bearing.     

Effects of superimposed hydrostatic pressure on fracture in sheet metals under tension

The effect of superimposed hydrostatic pressure on fracture in sheet metals under plane strain tension is studied numerically using the finite element method based on the Gurson damage model. It is demonstrated that the superimposed hydrostatic pressure p has no noticeable effect on necking but significantly increases the fracture strain due to the fact that a superimposed pressure delays or completely eliminates the nucleation, growth and coalescence of microvoids or microcracks. The experimentally observed transition of the fracture surface, from P-type mode under atmospheric pressure to C-type mode under high pressure, is numerically reproduced.     

Comparative study of the performance of six-pocket and four-pocket hydrostatic/hybrid flexible journal bearings

This paper compares the performance of a six-pocket capillary compensated hydrostatic/hybrid flexible journal bearing to that of a simi ar four-pocket journal bearing. The comparison is based on theoretically computed results. The finite-element method has been used to obtain simultaneous solutions of the three-dimensional elasticity equations and the Reynolds equation. It is observed that the six-pocket journal bearing may be more efficient from a stability point of view as compared to a similar four-pocket journal system.     

Performance analysis of flexible multirecess hydrostatic journal bearing operating with micropolar lubricant

This paper presents the analytical study of the effect of the bearing shell flexibility on the performance of multirecess hydrostatic journal bearing system operating with micropolar lubricant. The modified Reynolds equation for the flow of micropolar lubricant through constant flow valve‐compensated hydrostatic journal bearing has been solved by finite element technique based on Galerkins method, and the resulting elastic deformation in the bearing shell due to fluid‐film pressure has been determined iteratively, in which the deformation coefficient accounts for the bearing shell flexibility. The computed results suggest that the influence of the micropolar effect on bearing performance characteristics is significantly affected by the bearing shell flexibility. Copyright © 2012 John Wiley & Sons, Ltd.     

A study of friction in worn misaligned journal bearings under severe hydrodynamic lubrication

Friction occurs in all mechanical systems such as transmissions, valves, piston rings, bearings, machines, etc. It is well known that in journal bearings, friction occurs in all lubrication regimes. However, shaft misalignment in rotating systems is one of the most common causes of wear. In this work, the bearing is assumed to operate in the hydrodynamic region, at high eccentricities, wear depths, and angular misalignment. As a result, the minimum film thickness is 5–10 times the surface finish, i.e., near the lower limit of the hydrodynamic lubrication when taking into account that in the latest technology CNC machines the bearing surface finish could be less than 1–2 μm.An analytical model is developed in order to find the relationship among the friction force, the misalignment angles, and wear depth. The Reynolds equation is solved numerically; the friction force is calculated in the equilibrium position. The friction coefficient is presented versus the misalignment angles and wear depths for different Sommerfeld numbers, thus creating friction functions dependent on misalignment and wear of the bearing. The variation in power loss of the rotor bearing system is also investigated and presented as a function of wear depth and misalignment angles.     

On the non-linear stability of self-acting gas journal bearings

The non-linear stability of finite length self-acting gas journal bearings is studied by solving a time-dependent Reynolds equation using finite difference method. Two threshold values are discovered instead of one through which the self-acting gas journal bearings are changed from stable to unstable state. Keeping other parameters unchanged, when the mass of rotor exceeds the upper threshold value of mass, the system gets unstable; when the mass is less than the lower threshold value of mass, the system is stable; when the mass is between these two threshold values, the stability of bearings is determined by the amplitude of disturbance. Similar facts of two threshold values are also found when the stability parameter is chosen as external force or aspect ratio.     

Thermal error of a hydrostatic spindle

This paper proposes a thermo-mechanical error model of a hydrostatic spindle for a high precision machine tool. By predicting the variation of motion error induced by thermal effects on a machine worktable during machining, this model allows deeper insights into the underlying mechanisms that result in evolutions of the spindle accuracy. The heat power generated in the spindle elements and the coefficients of convection heat transfer over its outer surface have been evaluated. Then, the distribution of temperature and deformation of the spindle have been simulated by a finite element coupled thermo-elastic model, from which the influence on notably spindle stiffness variation was deduced. Experimental measurement of the thrust plate axial displacement under thermal expansion is in close agreement with the computed axial thermal expansion.     

Elasto-hydrodynamic lubrication analysis of partial arc journal bearings

Centrally loaded partial arc bearings having deformable bearing surfaces have been analysed. The coupled Reynolds equation satisfying the pressure field in the fluid and the three-dimensional elasticity equations governing the deformations in the bearing lining are solved simultaneously using the finite element method. The steady state solution for the coupled problem is obtained by using a doubly nested iteration scheme which determines the positive pressure field in the fluid film and the orientation of the load line. The influence of bearing deformation on the load capacity, attitude angle, friction coefficient parameter and oil flow are reported for 60° and 120° partial arc bearings. The analysis is extended for lubricants having pressure-dependent viscosity     

Dynamic characteristics of spindle with water-lubricated hydrostatic bearings for ultra-precision machine tools

A key component of ultra-precision machine tools is the spindle. The motivation for this study was to improve machining accuracies in precision cutting and grinding by pursuing improvements in the spindle characteristics by designing a sophisticated spindle with water-lubricated hydrostatic bearings. The static bearing stiffness of the developed spindle was investigated in previous studies. In addition to the static bearing stiffness, the dynamic characteristics regarding bearing stiffness also affect significantly on the machining results. In this study, dynamic characteristics of the developed spindle with water-lubricated hydrostatic bearings were investigated via simulations and experiments. Not only bearing dynamics but also rotor dynamics were considered in this study.In the simulation studies, the spindle dynamic characteristics were analysed based on the transfer matrix method. A spindle rotor supported with hydrostatic bearings was represented by discrete sections of the rotor. The mathematical model of transverse linear vibrations of the spindle rotor was derived with distributed parameters for these discretized rotor sections. As a result of the analysis on the amplitude-frequency characteristic, radial displacements of the rotor due to bearing displacement and bending deformation were defined. Then, the frequency characteristics were represented with Nyquist plots. Resonant frequencies and amplitudes formation in the transverse vibration of the rotor were determined. The influence of rotor bending deformations on spindle compliance was assessed. Furthermore, the study examined the influences of the supply pressure of the lubricating fluid, radial clearance and journal diameter of the hydrostatic bearings on the amplitude of the rotor vibration, and the resonance frequency of the system.Furthermore, the dynamic characteristics of the spindle were examined experimentally. The simulation results were in good agreement with the actual spindle dynamics obtained experimentally. The influence of the structural parameters of the rotor and the operating parameters of the bearings on the spindle dynamic characteristics was also determined. It was verified that the amplitude of the vibration of the rotor overhang part was dominantly affected not by bearing stiffness but by bending stiffness of the bearing journal of the front bearing and the length of the rotor overhang.Then it was verified that the resultant displacement of the rotor in the radial direction due to the influence of the bearing characteristics and the structural effect of the rotor is significantly small. Practical recommendations to improve the spindle design in terms of the dynamic characteristics of the spindle with water-lubricated hydrostatic bearings were also derived.     

The combined effects of the centripetal inertia and the surface roughness on the hydrostatic thrust spherical bearings performance

This paper deals with the surface roughness and the predominant centripetal inertia terms due to the shaft rotation of the externally pressurized thrust spherical bearings. The solutions are presented for the fitted type of bearings, un-recessed and recessed hemispherical and partial hemispherical seats, with capillary tube and orifice restrictors. On the basis of the stochastic theory, Reynolds equation is developed. The bearing surfaces are assumed to have randomly distributed roughness. Expressions for the pressure distribution, load carrying capacity, volume flow rate, frictional torque, friction factor, power factor, power losses and stiffness factor are obtained. The paper shows the combined effects of the centripetal inertia and the surface roughness on the bearing performance. An optimum design based on the minimum power losses, minimum flow rate and optimal restrictor dimensions is theoretically examined.     

Non‐Newtonian and thermal effects in constant flow valve compensated symmetric hole‐entry hybrid journal bearing

Every 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 described the study of static and dynamic performance of a hole‐entry hybrid journal bearing system compensated with constant flow valve restrictor by considering the combined influence of thermal effects and non‐Newtonian behaviour of the lubricant. The variation of the viscosity due to the non‐Newtonian behaviour of the lubricant and temperature rise has been considered in the study. The numerical solution of the generalized Reynolds equation governing the flow of the lubricant, having variable viscosity along with the energy and heat conduction equations, was obtained using finite element method. The non‐Newtonian lubricant has been assumed to follow the cubic shear stress law. The study included the performance of a double row symmetric hole‐entry hybrid journal bearing configuration containing 12 holes per row. The results presented in this paper indicate that change in viscosity of lubricant affects the performance of the hole‐entry hybrid journal bearing system quite significantly. Copyright © 2007 John Wiley & Sons, Ltd.     

Lubrication performance of finite journal bearings considering effects of couple stresses and surface roughness

To inspect the performance characteristics of finite journal-bearing systems, the combined effects of couple stress due to a Newtonian lubricant blended with additives and the presence of roughness on journal-bearing surfaces are studied in this article. Basing on the Stokes theory and Christensen’s stochastic model, the stochastic generalized Reynolds equation is deduced. The film pressure distribution equation is numerically solved by using the conjugate gradient method of iterations. According to the results, the couple stress effects can raise the film pressure of the lubricant fluid, improve the load-carrying capacity and reduce the friction parameter, especially at high eccentricity ratio. The surface roughness effect is dominant in long bearing approximation and the influence of transverse or longitudinal roughness to the journal bearing is in reverse trend. In general, the critical value of length-to-diameter is 1.1.