Optimum shape design for surface of a thermohydrodynamic lubrication slider bearing

This paper utilises a thermohydrodynamic model of bearing to optimise the shape of slider bearing. Friction is minimised subject to load and centre of pressure requirements using a sequential quadratic programming algorithm. A generalised Reynolds equation is solved simultaneously with an energy equation using the finite volume method to obtain bearing characteristics, such as friction, load and centre of pressure. Results show that the coefficient of friction is reduced by the optimisation approach. Results also show that larger temperature–viscosity coefficient and inlet viscosity tend to yield smaller optimal friction, whereas larger thermal conductivity tends to yield larger optimal friction. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal film shape for two-dimensional slider bearings lubricated with couple stress fluids

The shape of a slider bearing is one of the major geometric conditions influencing the performance of the bearing. The aim of this study is to design the optimum shapes of the surfaces of sliders to meet the load and center of pressure demands specified by the designers. The design strategy uses COMSOL Multiphysics software package to solve the modified Reynolds equation derived on the basis of stokes microcontinuum theory. The sequential quadratic programming (SQP) is used to optimize the shape of the slider bearing. Results show that designers seeking to effectively reduce friction should consider a reducing the aspect ratio since it is the most significant parameter affecting optimal friction. In addition, slider bearings should be optimized with a polynomial profile of order 6 to reduce the computational effort and yield a solution that is very close to the solution of higher order polynomials.     

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     

Ferrofluid lubrication in porous inclined slider bearing with velocity slip

The effects of slip velocity and the material constant in a porous inclined slider bearing lubricated with a ferrofluid were theoretically studied by using Jenkins model. Expressions were obtained for pressure, load capacity, friction on the slider, coefficient of friction and position of the centre of pressure. The increase in slip parameter caused decrease in load capacity as well as friction and increase in the coefficient of friction without altering the centre of pressure much. As the material constant increased, the load capacity decreased, friction and coefficient of friction increased and the position of the centre of pressure shifted slightly towards the inlet of the bearing.     

Static Performance of Finite Hydrodynamic Journal Bearings Lubricated by Magnetic Fluids with Couple Stresses

Based upon the Stokes micro-continuum theory, the problem of lubrication of finite hydrodynamic journal bearing lubricated by magnetic fluids with couple stresses is investigated. By taking into account the couple stresses due to the microstructure additives and the magnetic effects due to the magnetization of the magnetic fluid, modified Reynolds equation is obtained. The effects of couple stresses are studied by defining the couple stress parameter L that can be considered as a measure of the chain length of the additive molecule. The magnetic effects of the magnetic fluid are investigated by the magnetic coefficient γ. Using the finite-difference technique and for different values of couple stress parameter and magnetic coefficient, the Reynolds equation is solved, and pressure distributions are obtained. The bearing static characteristics namely load carrying capacity, attitude angle, friction coefficient, and side leakage flow are determined. The results indicate that the influence of couple stresses and magnetic effects on the bearing characteristics are significantly apparent. It is concluded that fluids with couple stresses are better than Newtonian fluids. The improvement of the bearing characteristics is enhanced if the magnetic effects are present.     

Optimal design of one-dimensional porous slider bearings using the Brinkman model

On the basis of the Brinkman model, a theoretical study of the optimal load-carrying capacity and friction coefficient for one-dimensional curved porous slider bearings with the gap width varying slowly is presented. The modified Reynolds equation is obtained by applying Brinkman equations to guide oil motion through the porous matrix. By using the technique of calculus of variations, the optimization is performed over a class of step profiles. According to the analysis, the step height ratio and riser location of the optimal geometry are found to depend upon the permeability parameter of the porous matrix. Compared with the inclined-plane bearing case, the stepped porous slider bearing provides an enhancement in the load-carrying capacity as well as a reduction in the friction parameter. An illustrative design example is also included for engineering and industrial applications.     

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.     

Different Magnetic Models in the Design of Hydrodynamic Journal Bearings Lubricated with Non-Newtonian Ferrofluid

This work is concerned with theoretical study of hydrodynamic journal bearings lubricated with ferrofluids exhibiting non-Newtonian behavior. Based on the momentum and continuity equations for ferrofluid under an applied magnetic field, a modified Reynolds equation has been obtained. Assuming linear behavior for the magnetic material of the ferrofluid, the magnetic force was calculated. The Reynolds equation has been derived to be able to apply to any magnetic field distribution model. Using different magnetic field models, the equation has been solved numerically by the finite-difference technique with appropriate iterative technique and pressure distributions have been obtained. The boundary shape of the load-carrying active regions (positive-pressure regions) and cavitation regions (zero-pressure regions) could be then determined. The solution renders the bearing performance characteristics, namely: load-carrying capacity, attitude angle of the journal center, frictional force at the journal surface, friction coefficient and bearing side leakage. The results indicated that the flow-behavior index has a large effect on the bearing performance. When the bearing operates at high eccentricity ratios, the increase of flow-behavior index gives higher load capacity, lower attitude angle, higher frictional force, lower friction coefficient and higher side leakage. At low eccentricity ratios where the magnetic effects are significant, the effect of the flow-behavior index depends mainly on the magnetic field distribution model used.     

Influence of micropolar lubricants on the performance of slot-entry hybrid journal bearing

A theoretical study concerning the slot-entry hybrid journal bearing lubricated with micropolar lubricants is presented. The modified Reynolds equation for micropolar lubricant is solved using finite element method along with equation of lubricant flow through slot-entry restrictors as a constraint together with appropriate boundary conditions. It has been observed that a slot-entry hybrid journal bearing operating with micropolar lubricant shows an increase in the value of minimum fluid film thickness and a reduction in the value of coefficient of friction as compared to a corresponding similar slot-entry hybrid journal bearing operating with Newtonian lubricant.     

Effects of lubricant additives on the performance of hydrodynamically lubricated journal bearings

A non-Newtonian rheological model to investigate theoretically the effects of lubricant additives on the steady state performance of hydrodynamically lubricated finite journal bearings is introduced. In this model, the non-Newtonian behavior resulting from blending the lubricant with polymer additives is simulated by Stokes couple stress fluid model. The formed boundary layer at the bearing surface is described through the use of a hypothetical porous medium layer that adheres to the bearing surface. The Brinkman-extended Darcy equations are utilized to model the flow in the porous region. A stress jump boundary condition is applied at the porous media/fluid film interface. A modified form of the Reynolds equation is derived and solved numerically using a finite difference scheme. The effects of bearing geometry, and non-Newtonian behavior of the lubricant on the steady-state performance characteristics such as pressure distribution, load carrying capacity, side leakage flow, and coefficient of friction are presented and discussed. The results showed that lubricant additives significantly increase the load carrying capacity and reduce both the coefficient of friction and the side leakage as compared to the Newtonian lubricants.     

Misalignment Effect on the Static Characteristics of Magnetized Journal Bearing Lubricated with Ferrofluid

In this paper a generalized Reynolds equation suitable for misaligned hydrodynamic journal bearings lubricated by either Newtonian or non-Newtonian ferrofluid is developed. The equation has been solved numerically by the finite difference technique with an appropriate iterative method and the pressure distributions have been obtained. Design charts for all static characteristics (including load capacity, attitude angle, side flow, friction force and misaligned moments) under different misalignment conditions are presented. The effects of misalignment conditions on all these bearing-performance characteristics are analyzed. The results conclude that magnetic lubrication improves, in general, the bearing performance under misalignment.     

Numerical Calculation of Rotation Effects on Hybrid Air Journal Bearings

Hybrid air journal bearings are of great importance in the precision engineering. Despite much progress, the influence of the aerostatic effect and the aerodynamic effect on the bearings is still not clear. Numerical calculation is a useful technique to evaluate bearing performance. Many theoretical problems related to Reynolds equation have been figured out by numerical simulation. The present study analyzes the effects of rotational speed—that is, the bearing speed number—on the performance of hybrid bearings. The behaviors of the pure aerostatic bearing and the pure aerodynamic bearing are investigated for comparison. The second-order finite difference method (FDM) and an iterative procedure are proposed to solve the Reynolds equation and derive the air film pressure distribution. The bearing characteristics such as load capacity, stiffness, friction coefficient, attitude angle, and mass inflow rate are taken into consideration. The research reveals the very dependence of the hybrid bearing's performance on the journal rotation and eccentricity ratio. The numerical results indicate that at a small bearing speed number of 0.223 and eccentricity ratio of 0.15, about 99.8% of the load capacity and 99.7% of the stiffness are determined by the aerostatic effect, whereas at a large bearing speed number of 2.229 and eccentricity ratio of 0.55, about 63.2% of the load capacity and 83.3% of the stiffness are determined by the aerodynamic effect.     

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.     

Influence of balancing of internal combustion engines on the operating conditions of hydrodynamic bearings

We studied the influence of balancing internal combustion engines on the performance of hydrodynamic plain bearings. A non-linear approach makes it possible to calculate the forces of pressure generated by the lubricant film. This approach is coupled with a dynamic calculation, which determines the inertia forces of the rod. The counterweight to balance the engine is applied to the heads of rods and not to the crankshaft. We chose three models of connecting rod (rod of an engine in series, rod with partial and rod with complete counterweight). To determine the lubricant pressure field in the bearing, the modified Reynolds equation was solved using the finite difference method, taking into account the boundary conditions of Reynolds. Since the bearing is subjected to a variable load, the mobility method was used to facilitate the resolution of the Reynolds equation. The proposed numerical simulation allowed us to analyze the influence of counterweight applied to the connecting rod head on the variation of the lubricant pressure field, the minimum film thickness, the axial flow and the friction torque in the big end bearing during the operating cycle.     

Hydrodynamic lubrication of short porous bearings

A theoretical analysis is presented for the hydrodynamic lubrication of short porous metal bearings that are press-fitted into a solid housing. It is customary with such bearings to neglect the circumferential flow of the lubricant compared to the axial flow and consequently the modified Reynolds equation has a simpler form. However, this device is not resorted to while considering the flow of the lubricant within the bearing material, and consequently the three dimensional Laplace equation describing such flow is solved. The pressure continuity at the bearing-film interface is maintained and the modified Reynolds equation is solved by the Galerkin method. Numerical results obtained on a digital computer indicate a progressive reduction in the load capacity and increment in the friction parameter and attitude angle as the permeability parameter is increased. These results significantly aid the rational design of short porous bearings.     

计入轴瓦弹性的应力偶流体润滑分析

推导了计入轴瓦弹性的应力偶流体润滑轴承的变形雷诺方程。数值分析表明,刚性轴瓦的最大油膜压力值比弹性轴瓦的最大油膜压力值大,且随着应力偶参数的增大,最大油膜压力提高明显;润滑油分别为牛顿流体和应力偶流体时,弹性系数越大轴承的承载力越小,应力偶参数越大轴承的承载力越大,且轴承的偏心率越大,应力偶参数对承载力的影响越明显,应力偶参数对刚性轴瓦材料的影响比对弹性轴瓦材料的影响大。     

An analytical approach for analysis and optimisation of slider bearings with infinite width parallel textures

This paper introduces an analytical approach to study the textured surfaces in hydrodynamic lubrication regime. For this purpose, a method of integrating the Reynolds equation for slider bearings with surface discontinuities is presented. By introducing appropriate dimensionless parameters, analytical relations for various texture profiles in both indented and projected forms are delivered. These relations express the nature of mathematical dependence between textured bearing performance measures and geometrical/operational parameters. An optimisation procedure is employed to achieve the optimum texturing parameters promoting maximum load capacity, load capacity to lubricant flow rate ratio and minimum friction coefficient for asymmetric partially textured slider bearings.     

The squeeze film in an inclined porous slider bearing

The behaviour of a squeeze film in an inclined porous slider bearing is analysed. Expressions for pressure, load capacity, friction, coefficient of friction and the position of the centre of pressure are obtained. Pressure, load capacity and friction are increased as a result of squeeze. The coefficient of friction is decreased and the centre of pressure is unaffected. An expression for the time-height relation is given.     

The squeeze film in a porous composite slider bearing

The squeeze film behaviour in a porous composite slider bearing is analysed. Expressions for the pressure, the load capacity, the friction and the position of the centre of pressure are obtained. The pressure, load capacity and friction are increased owing to the squeeze and the position of the centre of pressure moves slightly towards the inlet face. An expression for the time-height relation is also obtained. The response time for a composite slider bearing is greater than that for an inclined slider bearing.     

Design of annular recess hydrostatic thrust bearing under dynamic loading

Design charts are presented of a dynamically loaded thrust bearing with as annular recess. The effect of non-parallelism between the bearing and the runner surfaces is also considered, since this is a common problem in hydrostatic thrust bearings. Based on pre-assigned dynamic excitations the pressure equation is solved numerically by finite difference methods to render the bearing performance characteristics namely: load capacity; bearing stiffness; damping coefficient; and lubricant flow rate. Results concluded that the bearing performance chareacteristics are dependent on the bearing radii ratios, the squeeze number, the bearing number and the tilt parameter.