Squeeze film lubrication of a short porous journal bearing with couple stress fluids

This paper presents the theoretical investigations of the rheological effects of the couple stress fluids on the static and dynamic behaviour of the pure squeeze films in the porous journal bearings. The present study predicts the effects of percolation of the polar additives (microstructures) into the porous matrix on the performance of squeeze films in the porous journal bearings. The most general modified Reynolds-type equation is derived for a porous journal bearing with no journal rotation. The analysis takes into account of the tangential velocity slip at the porous interface by using the BJ-slip condition. The cases of a short porous journal bearing under a constant applied load and that under an alternating load are analyzed. As compared to the Newtonian lubricants, the lubricants which sustain the couple stresses yield an increase in the load carrying capacity. Under a cyclic load the couple stress fluids provide a reduction in the journal velocity and an increase in the minimum permissible height of squeeze films.     

Numerical solution of couplestress finite Reynolds equation for squeeze film lubrication of partial porous journal bearings

Abstract

In this paper, the general Reynolds equation of finite porous journal bearing lubricated with couplestress fluid is solved numerically for the assessment of dynamic characteristics of the bearings. The Reynolds type equation governing the steady performance is obtained and solved numerically by finite difference technique. From the numerical results, it is observed that the effect of couple stresses is to increase the load carrying capacity and to lengthen the squeeze film time as compared to the corresponding solid case. The effect of permeability is to reduce the load capacity and to decrease the squeeze film time as compared to the solid case.     

Micropolar fluid squeeze film lubrication between rough anisotropic poroelastic rectangular plates: special reference to synovial joint lubrication

Abstract

The effect of anisotropic permeability on micropolar squeeze film lubrication between poroelastic rectangular plates is studied. The non-Newtonian synovial fluid is modelled by Eringen’s micropolar fluid, and the poroelastic nature of cartilage is taken in to account. The stochastic modified Reynolds equation, which incorporates the elastic as well as randomised surface roughness structure of cartilage with micropolar fluid as lubricant, is derived. Modified equations for the mean fluid film pressure, mean load carrying capacity and squeeze film time are obtained using the Christensen’s stochastic theory for the study of roughness effects. The effects of surface roughness, micropolar fluid and anisotropic permeability on the squeeze film characteristics of synovial joint are discussed. It is found that the surface roughness effects are more pronounced for micropolar fluids as compared to the Newtonian fluids, and the anisotropic nature of permeability of cartilage off-squares the plate size for optimum performance.     

Squeeze film characteristics of finite journal bearings: couple stress fluid model

A theoretical study of squeeze film behaviour for a finite journal bearing lubricated with couple stress fluids is presented. On the basis of the microcontinuum theory, the modified Reynolds equation is obtained by using the Stokes equations of motion to account for the couple stress effects due to the lubricant blended with various additives. With the Conjugate Gradient Method of iteration the built-up pressure is calculated, and then applied to predict the squeeze film characteristics of the system. According to the results evaluated, the rheological influence of couple stress fluids is physically apparent. Compared with the case of a Newtonian lubricant, the couple stress effects increase the load-carrying capacity significantly and lengthen the response time of the squeeze film behaviour. On the whole, the presence of couple stresses improves the characteristics of finite journal bearings operating under pure squeeze film motion. The rheological effects of couple stress fluids agree with previous works.     

Performance of finite journal bearings in non-laminar lubrication regime

Fluid dynamic lubrication of journal bearings in a superlaminar regime, ie a transition or turbulent regime, is the subject-matter of this study.Results obtained by solving an appropriately modified Reynolds bidimensional equation have been put in the form of operating diagrams which allow the correct design of journal bearings in real conditions of flow     

Squeeze film characteristics of long partial journal bearings lubricated with couple stress fluids

On the basis of microcontinuum theory, a theoretical analysis of hydrodynamic squeeze film behaviour for long partial journal bearings lubricated by fluids with couple stresses is presented. To take into account the couple stress effects due to the lubricant containing additives or suspended particles, the modified Reynolds equation governing the film pressure is derived by using the Stokes constitutive equations. Various bearing characteristics are then calculated. According to the results obtained, the influence of couple stress effects on the performance of the system is physically apparent and not negligible. Compared with the Newtonian lubricant case, the couple stress effects provide an enhancement in the load-carrying capacity and lengthen the response time of the squeeze film action. On the whole, the presence of couple stresses signifies an improvement in the squeeze film characteristics of the system.     

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.     

Effect of roughness on hydromagnetic squeeze films between porous rectangular plates

The theoretical investigations made in this paper are to study the combined effects of unidirectional surface roughness and magnetic effect on the performance characteristics of a porous squeeze film lubrication between two rectangular plates. The stochastic Reynolds equation accounting for the magnetic effect and randomized surface roughness structure is mathematically derived. The expressions for dimensionless pressure, load carrying capacity and squeeze film time are obtained. Results are computed numerically and it is observed that a roughness effect enhances pressure, load carrying capacity and squeeze film time.     

Linear stability analysis of hydrodynamic journal bearings under micropolar lubrication

The dynamic characteristics of hydrodynamic journal bearings lubricated with micropolar fluids are presented. The modified Reynolds equation is obtained using the micropolar lubrication theory. Applying the first order perturbation of the film thickness and steady state film pressure, the dynamic characteristics in terms of the components of stiffness and damping coefficients, critical mass parameter and whirl ratio are obtained with respect to the micropolar property for varying eccentricity ratios and slenderness ratios. The results show that micropolar fluid exhibits better stability in comparison with Newtonian fluid.     

Roughness effects in a narrow porous journal bearing with arbitrary porous wall thickness

The paper uses Christensen's stochastic theory to study the effects of surface roughness in a narrow porous journal bearing. An exact solution, valid for arbitrary wall thickness, is given for the film pressure and pressure in the bearing material. The results are compared with the approximate solutions, and the range of various influencing parameters, for which the approximate analysis is satisfactory from a practical point of view is determined.     

A study of thermohydrodynamic lubrication in a circular journal bearing

An analytical method to determine the film temperature of circular journal bearings was developed, which considers the cavitation of the oil film and also recirculation and mixing of the lubricant. The results were verified experimentally. The theory is in good agreement with experiment over a wide range of operating conditions. The effects of journal speed, clearance ratio, lubricant viscosity and specific load on the bearing temperature were examined, and the following conclusions derived. (1) T_b,max, the maximum temperature on the bearing metal surface, increases considerably with the increase of speed and lubricant viscosity and with the decrease of clearance ratio. (2) With the increase of speed, the angular position of T_b,max varies considerably towards the direction of journal rotation from the upper stream side of the location of minimum film thickness, h_min, to the lower stream side of it. The change of angular position of T_b,max is greater than that of h_min. The contrary happens with decrease of the clearance ratio. (3) These characteristics of T_b,max correspond to those of the maximum temperature, T_f,max, in the oil film.     

Numerical analysis of plain journal bearing under hydrodynamic lubrication by water

The article aims to provide references for designing water-lubricated plain journal bearings. Considering the differences between the physical properties of the water and of the oil, the effects of eccentricity ratio on pressure distribution of water film are analyzed by computational fluid dynamics (CFD). Then numerical analysis of journal bearings with different dimensions is undertaken under different rotational speeds. Based on the analysis, a reference is produced for selecting the initial diameter dimension which is used to design an efficient water-lubricated plain bearing under the given load and rotational speed. At last, the reference is verified by an experimental case.     

Effects of couple stresses in the cyclic squeeze films of finite partial journal bearings

Based upon the microcontinuum theory, the present paper is to theoretically study the pure squeeze-film behavior of a finite partial journal bearing with non-Newtonian couple-stress lubricants operating under a time-dependent cyclic load. To take into account the couple stress effects resulting from the lubricant blended with various additives, the modified Reynolds equation governing the film pressure is obtained from Stokes equations of motion. The film pressure is numerically solved by using the Conjugate Gradient Method. Bearing characteristics are then calculated from the nonlinear motion equation of the journal. According to the results obtained, the effects of couple stresses result in a decrease in the value of eccentricity of the journal center. The finite partial bearing with a couple stress fluid as the lubricant yields an increase in the minimum permissible clearance and provides a longer time to prevent the journal-bearing contact.     

Dynamic characteristics and stability of a journal bearing in a non-laminar lubrication regime

A mathematical model to determine the stiffness and damping coefficients and the stability limit curves of a journal bearing in a non-laminar lubrication regime is described. The results show the flow regime influence on the dynamic characteristics of cylindrical bearings and on the stability of a rigid rotor on rigid supports.     

Analysis of bearing lubrication under dynamic loading considering micropolar and cavitating effects

Numerical computation of the dynamically loaded journal bearings lubricated with micropolar fluids is undertaken based on the improved Elord cavitation algorithm and over-relaxation method. The results show that the average inflow and average outflow based on the mass conservation boundary conditions are almost equal, which is in accordance with the fact. However, under the Reynolds boundary conditions, large difference is shown between the average inflow and outflow. It is also demonstrated that with the micropolar fluids lubrication, the minimum film thickness, bearing capacity and friction power loss are increased while the maximum film pressure is decreased.     

Effect of pressure dependent viscosity on squeeze film characteristics of micropolar fluid in convex curved plates

In this paper, the effect of pressure dependent viscosity on the squeeze film characteristics between convex curved plates of a cosine form is presented. Micropolar fluid theory, which is a possible non-Newtonian model of a suspension of rigid particle additives, is applied to the study of the lubrication of cosine form convex curved plates. The modified Reynolds equation is solved for the fluid film pressure and then the cosine form by considering the exponential relationship in the viscosity variation. For iso-viscous lubricants, the effects of pressure dependent viscosities signify an increase in the values of the squeeze film pressure, the load capacity and the elapsed time. It provides useful information in designing the mechanisms of squeeze film plates for engineering application.     

Lubrication of a narrow porous journal bearing with a couple stress fluid

This paper describes a theoretical investigation of the rheological effects of couple stress fluids on the performance of narrow porous journal bearings. A most general modified Reynolds equation is derived for narrow porous journal bearings using the Stokes constitutive equations for couple stress fluids. The fluid in the film region and in the porous region has been modelled as a couple stress fluid. The analysis takes into account velocity slip at the porous interface using the Beavers‐Joseph criterion. A closed‐form expression for field pressure is obtained for narrow journal bearings. Eigen‐type expressions for field variations are obtained. The dimensionless load‐carrying capacity, attitude angle, and coefficient of friction are presented for different operating parameters. It is observed that narrow porous journal bearings with couple stress fluids as lubricant show a significant increase in load‐carrying capacity with reduced coefficient of friction as compared to the Newtonian case. The present study predicts the effects of the percolation of polar additives (microstructures) into the porous matrix on the bearing performance.     

A study of the lubricating effectiveness of micropolar fluids in a dynamically loaded journal bearing (T1516)

The lubricating effectiveness of micropolar fluids in a dynamically loaded journal bearing is studied. On the basis of the theory of micropolar fluids, the modified Reynolds equation for dynamic loads is derived. Results from the numerical analysis indicated that the effects of micropolar fluids on the performance of a dynamically loaded journal bearing depend on the size of material characteristic length and the coupling number. It is shown, compared with Newtonian lubricants, that under a dynamic loading the micropolar lubricants produce an obvious increase in the oil film pressure and oil film thickness, but a decrease in the side leakage flow. It is also shown that the friction coefficient for a dynamically loaded journal bearing with micropolar fluids is in general higher than that of Newtonian fluids, which is not the same as the results for a steadily loaded journal bearing. Furthermore, a parametric study of flow and friction for different mass parameters keeping micropolar parameters fixed is undertaken. It is indicated that, with the increase of the mass parameters, the crank angles corresponding to the maximum flow are changed and the maximum friction coefficients are obviously decreased either for the Newtonian fluids or for the micropolar fluids.     

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.     

Novel approach to solve the dynamical porous journal bearing problem

Analytical pressure solutions are a simple and robust way to model plain journal bearings in rotordynamics, but cannot be extended to porous journal bearings. Using the method of weighted residuals—viz. Galerkin's method with global shape functions—a novel and fast approach to solve the dynamical porous journal bearing problem is proposed. This approach allows for the influence of rough surfaces on the hydrodynamic pressure implemented through flow-factors, journal misalignment and calculation of stiffness and damping coefficients for finite bearings. The proposed method will be verified using analytical expressions and new results will be shown for porous journal bearings including the influence of rough surfaces.