Viscoelastic fluid film lubrication with reference to human joints

Squeeze film lubrication between two approaching surfaces is considered with reference to normally loaded human joints. One surface is a rigid sphere and the other is a porous rectangular plate. The fluid between the surfaces is viscoelastic. Analytical closed-form solutions are obtained for the pressure distribution and the load-carrying capacity. The effects of the porosity of the cartilage and the effects of the viscoelastic behaviour of the synovial fluid are presented graphically and are discussed.     

Squeeze film characteristics between a sphere and a rough porous flat plate with micropolar fluids

The effects of surface roughness on the squeeze film characteristics between a sphere and flat plate covered with a thin porous layer are investigated in this paper. The sphere and the plate are separated with a non‐Newtonian lubricant of a micropolar fluid. The well‐established Christensen stochastic theory of hydrodynamic lubrication of rough surfaces is used to incorporate the effects of surface roughness into the Reynolds equation. The film pressure distribution is solved and other squeeze film characteristics, such as the load‐carrying capacity,and time–height relationship, are obtained. The results indicate that lubrication by a micropolar fluid will increase the load‐carrying capacity and lengthen the squeeze film time, regardless to the surface rough and porosity of the flat plate. It is also found that excessive permeability of the porous layer causes a significant drop in the squeeze film characteristics and minimises the effect of surface roughness. For the case of limited or no permeability, the azimuthal roughness is found to increase the load‐carrying capacity and squeeze time, whereas the reverse results are obtained for the case of radial roughness.     

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.     

FORCED VIBRATION AND SOUND RADIATION OF A RECTANGULAR PLATE WITH VISCOELASTIC BOUNDARY SUPPORTS

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Effect of surface roughness on the couple-stress squeeze film between a sphere and a flat plate

In this paper, a theoretical study of the effect of surface roughness on the hydrodynamic lubrication of couple-stress squeeze film between a sphere and a flat plate is presented on the basis of Christensen's stochastic theory for hydrodynamic lubrication of rough surfaces. The modified Reynolds equation accounting for the couple stresses and the surface roughness is mathematically derived. The modified Reynolds equation is solved for the fluid film pressure and the bearing characteristics, such as the load carrying capacity and the time–height relationship, are obtained. It is found that the surface roughness considerably influences the squeeze film characteristics. The load carrying capacity and squeeze film time are found to increase for an azimuthal roughness pattern as compared to the corresponding smooth case, whereas the reverse trend is observed for a radial roughness pattern.     

Dynamic Behaviors of Axially Moving Viscoelastic Plate with Varying Thicknessn

Structural components of varying thickness draw increasing attention these days due to economy and light-weight considerations. In view of the absence of research in vibration analysis of viscoelastic plate with varying thickness, this study devotes to investigate the dynamic behaviors of axially moving viscoelastic plate with varying thickness. Based on the thin plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equation of motion of the axially moving viscoelastic rectangular plate is derived, the plate constituted by Kelvin-Voigt model has linearly varying thickness in the y-direction. The dimensionless complex frequencies of axially moving viscoelastic plate with four edges simply supported are calculated by the differential quadrature method, curves of real parts and imaginary parts of the first three-order dimensionless complex frequencies versus dimensionless moving speed are obtained, the effects of the aspect ratio, thickness ratio, the dimensionless moving speed and delay time on the dynamic behaviors of the axially moving viscoelastic rectangular plate with varying thickness are analyzed. When other parameters keep constant, with the decrease of thickness ratio, the real parts of the first three-order natural frequencies decrease, and the critical divergence speeds of various modes decrease too, moreover, whether the delay time is large or small, the frequencies are all complex numbers.     

Investigation of effects of viscoelastic boundary supports on transient sound radiated from a rectangular plate by modal strain energy method

This work considers analysis of transient sound radiation from an impact-excited rectangular plate with viscoelastic boundary supports based on the Modal Strain Energy (MSE) method. Vibration of the plate is approximated by double infinite series in the spatial coordinates. Each term of the series is constructed with vibration modes of beams having the same boundary conditions as the considered plate, multiplied by a time dependent function. Modal loss factor of each mode is obtained by the MSE method. The sound pressure for impact excitations is obtained in the time and frequency domain by numerical integration of the Rayleigh integral. Then effects of width of the viscoclastic boundary supports on the vibration response and the radiated sound pressure are investigated. It is shown that there is an optimum width of the support.     

Laminar Heat and Fluid Flow Characteristic with a Modified Temperature-Dependent Viscosity Model in a Rectangular Duct

The present study proposes a modified temperature-dependent non-Newtonian viscosity model and investigates the flow characteristics and heat transfer enhancement of the viscoelastic non-Newtonian fluid in a 2:1 rectangular duct. The combined effects of temperature dependent viscosity, buoyancy, and secondary flow caused by the second normal stress difference are considered. Calculated Nusselt numbers by the modified temperature-dependent viscosity model give good agreement with the experimental results. The heat transfer enhancement of viscoelastic fluid in a rectangular duct is highly dependent on the secondary flow caused by the magnitude of second normal stress difference.     

The effect of fluid inertia on the film pressure between two axially oscillating parallel circular plates with a viscoelastic lubricant

A viscoelastic incompressible fluid between two parallel circular plates separated by a small distance with sinusoidal axial vibration of the top plate including fluid inertia terms was considered. Flow phenomena were characterized by non-dimensional parameters such as the Reynolds number Re and the elastic number S. An iteration method was used to solve the non-linear equations. The effects of Re and S on the fluid pressure were studied.     

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.     

平行滑块表面矩形-半球型复合织构润滑性能研究*

研究仿生硅藻的多级孔结构——矩形与半球型结合的复合型织构对平行滑块润滑性能的影响。通过建立矩形-半球型的复合型织构单个单元模型,采用双向流固耦合的方法,分析两滑动表面在不同面积率和织构深度条件下的摩擦润滑性能。结果表明:织构表面摩擦因数随着面积率的增大而减小,承载力随着面积率的增大先增大后减小,在考虑摩擦性能与承载力的条件下,矩形-半球型复合型织构的面积率应控制在25%～36%之间;在确定合适的面积率的条件下,还应考虑不同的织构深度所产生的旋涡的影响。     

An experimental investigation into the performance of externally pressurized rectangular air bearings

An experimental programme which was designed to investigate the performance characteristics of externally pressurized rectangular air bearings considering the effects of pad geometry and inlet gas conditions is presented. Three forms of rectangular bearings were considered: one arrangement consisted of continuous plane surfaces, the second had a recessed pad and a plane bed and the third had a plane bed and a recessed pad with a step in the bearing area following the recess.

The results revealed that the recess length has a dominant effect on the pressure distribution in the air film. The effect of pressure depression is obvious at extremely small clearances and supply pressures. Such an effect is exaggerated when a step is introduced in the pad surface. The introduction of the step improves the load-carrying capacity of the bearing as long as the bearing is free from shock-wave formation.     

The influence of couple stresses on the flow of fluid through a channel with injection

A theoretical study of non-newtonian flow effects is carried out for the flow of a couple stress fluid between two parallel horizontal stationary plates due to fluid injection through the lower porous plate. The governing equations are solved to determine the velocity field and pressure. It is found that the presence of couple stresses in the fluid will enhance the load-bearing capacity of the fluid to a great extent which in turn helps to determine the couple stress parameter of the fluid experimentally.     

Effect of surface roughness on the static characteristics of inclined plane slider bearing: Rabinowitsch fluid model

In this paper, a theoretical study of the effect of surface roughness on the static characteristics of inclined plane slider-bearing lubricated with Rabinowitsch fluid is analysed. Christensen’s stochastic theory for the lubrication of rough surfaces has been used for the derivation of generalised stochastic Reynolds-type equation. The two types of one-dimensional roughness patterns (Longitudinal and Transverse) are considered. Expressions for pressure, load carrying capacity, frictional force and coefficient of friction are obtained. It is found that the presence of transverse roughness pattern on the bearing surface increases pressure and load carrying capacity. Results are well agreement with smooth case.     

Analysis of squeeze film performance between rough porous infinitely long parallel plates with porous matrix of non-uniform thickness under presence of magnetic fluid lubricant

Abstract

The performance of a magnetic fluid based squeeze film between infinitely long porous rough parallel plates with porous matrix of non-uniform thickness has been investigated. The bearing surfaces are considered to be transversely rough. The stochastic film thickness characterising the random roughness is assumed to be asymmetric with non-zero mean and variance. A magnetic fluid is used as a lubricant and the external magnetic field is oblique to the lower plate. With usual assumptions of hydrodynamic lubrication the associated Reynolds' equation is solved with suitable boundary conditions. Then expressions for pressure distribution, load carrying capacity and response time are obtained. It is observed that the load carrying capacity increases nominally due to magnetic fluid lubricant resulting in improved performance. But it is also seen that the composite roughness of the bearing surfaces introduces an adverse effect which gets more compounded due to the thickness ratio. However, the negative effect can be compensated to certain extent by the magnetic fluid lubricant in the case of negatively skewed roughness. This compensation further enhances when negative variance is involved. This study tends to suggest that the thickness ratio may play a crucial role for a better performance of the magnetic fluid based bearing system besides providing an additional degree of freedom.     

Inertia effect of micropolar fluid in squeeze bearings and thrust bearings

A theoretical study is made of squeeze films between two infinitely long rectangular plates and between circular plates, and of a thrust bearing, assuming the lubricant to be a micropolar fluid. The effect of inertia is considered and the effects of the material constants of the fluid on the bearing characteristics are discussed. The effect of inertia is to increase the time of approach for squeeze bearings and to diminish the load capacity for thrust bearings. For squeeze bearings, the time of approach is greater with a micropolar fluid than with a Newtonian fluid and, for thrust bearings, the load capacity is greater with a micropolar fluid than with a Newtonian fluid.     

Analysis of Externally Pressurized Rectangular Pads with Multiple Supply Holes

The externally pressurized rectangular pad with multiple supply holes are analyzed theoretically by use of complex potential theory. An appropriate potential function, which satisfies the boundary conditions, is found by using infinite arrays of infinite sources and sinks. Then, the pressure distribution can be obtained theoretically, which leads to the determination of load capacity and flow. Results are given for both incompressible and compressible fluids. Experimental results coincide very well with theory concerning pressure distribution and load capacity if secondary effects owing to the compressibility of the fluid and pressure loss at supply holes is accounted for.     

燃料电池仿生密封结构的设计与仿真

针对目前质子交换膜燃料电池密封不严导致的电化学性能低和泄漏等问题,从仿生学角度出发,以自然界的鲨鱼牙齿和扇贝壳作为仿生原型,对燃料电池的密封双极板结构进行仿生结构设计,提出4种仿生密封双极板结构,并建立密封双极板的接触力学模型,最后在有限元分析软件ABAQUS和ANSYS Fluent中开展仿生密封双极板与常规密封双极板的仿真对比试验。结果表明：仿生密封双极板接触面上的应力更大,两接触面的结合更加紧密;仿生密封双极板一凸一凹的镶嵌结合方式,减小了泄漏通道的有效高度,增大了泄漏阻力,可有效防止泄漏的发生;仿生密封双极板具有流固耦合密封效应,在双极板之间存在多个阻断面和空腔,可对流体造成明显的压差损失,能有效避免流体的泄漏。     

Inertia effects due to lubricant compressibility in a sliding externally pressurized gas bearing

The sliding externally pressurized gas bearing with parallel surfaces was theoretically investigated taking inertia effects due to lubricant compressibility into account. The ratio of film thickness to bearing width was assumed to be small. An approximate solution of the Navier-Stokes equation for a compressible viscous fluid obeying the barotropic relation was analytically sought to first order in the ratio of film thickness to bearing width. It was found that fluid motion in the directions both perpendicular and parallel to the bearing surface are important in the inertia terms of the equation of motion. The characteristics of the bearing are elucidated by determinations of the load capacity, the mass flow rate, the pressure profile and the stream line. In most cases inertia effects due to compressibility enhance the load capacity irrespective of the direction and the magnitude of the relative velocity.     

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.