Effect of lubricant inertia in bearings with a non-Newtonian lubricant

Summary The inertia effects in externally pressurized and squeeze film bearings with lubricants obeying a power law are considered. It is found that the inertia forces decrease the load capacity of the externally pressurized bearing with a given flow rate and the inertia effect increases with the flow behaviour index. At a given feeding pressure, on the other hand, the inertia increases or decreases the load capacity when the flow behaviour index is smaller than or greater than 3, respectively. For squeeze films between circular plates and rectangular plates, the rate of squeeze is slowed down by the inertia and the inertia effect is larger in dilatant lubricants than in pseudoplastic lubricants.Nomenclature 2a diameter of the bearing, width of rectangular plates - 2b diameter of the recess - 2h film thickness - 2h ₀ initial thickness of squeeze films - l length of the rectangular plates - m consistency index - n flow behaviour index - p pressure - p _e external pressure - p _i feeding pressure - q flow rate - r radial distance - t time - u velocity of the lubricant - v squeeze velocity - w load capacity - W dimensionless load capacity - axial distance - viscosity of the lubricant - density of the lubricant     

Inertia effects in hydromagnetic lubrication

Summary A theoretical investigation of inertia effects on the load capacity of an externally pressurized bearing with an electrically conducting lubricant is presented. It is shown that there is a negative contribution to the load capacity of the bearing by inertia forces. In the presence of an axial magnetic field the absolute value of the load due to inertia forces decreases when the strength of the field increases while in the presence of an axial current, the load due to inertia forces is independent of axial current. At large values of axial magnetic fields and axial currents, it is shown that the inertia forces can be neglected. A numerical example is considered to study the relative importance of inertia and viscous terms.     

Performance of hydromagnetic squeeze films between conducting porous rough conical plates

An endeavor has been made to discuss the behavior of hydromagnetic squeeze film between two conducting rough porous conical plates. The plates are considered to be electrically conducting and the clearance space between them is filled by an electrically conducting lubricant. A transverse magnetic field is applied between the plates. Efforts have been made to solve the concerned Reynolds’ equation with the associated boundary conditions to get the pressure distribution. This in turn, is used to obtain the expression for load carrying capacity leading to the calculation of the response time. The results are presented graphically as well as in tabular form. It is suggested by the results that the bearing system records an enhanced performance as compared to that of a bearing system working with a conventional lubricant. It is noticed that the pressure, load carrying capacity and the response time increase steadily with increasing values of the magnetization parameter. In general, the bearing suffers owing to transverse surface roughness. However, the negatively skewed roughness tends to better the performance of the bearing system marginally. This performance gets further improved especially, when the negative variance is involved. It is observed that the semi-vertical angle increases the load carrying capacity. Besides, the conductivity also increases the load carrying capacity significantly. In addition, it is revealed that the negative effect induced by the porosity can be neutralized to a nominal extent by the positive effect of the magnetization parameter in the case of negatively skewed roughness in the presence of negative variance. Thus, this study provides ample scopes for improving the performance of the bearing system considerably by choosing a suitable combination of magnetization parameter, semi-vertical angle and the conductivities of the plates.     

Inertia effects in externally pressurized bearing with viscoelastic lubricant

A theoretical investigation of inertia effects on the load capacity of an externally pressurized bearing with a visco-elastic lubricant is presented. The methods of iteration and averaged inertia have been employed to find an approximate solution of the resulting non linear differential equation. Graphical representation of results together with those for the case without inertia has been shown. It is found that the elasticity of the liquid increases the load bearing capacity and the pressure at a point in the lubricant film. There is a negative contribution to the load capacity by inertia forces.     

The flow of a power-law liquid in a continuous-flow squeeze film

Consideration is given to the flow of an inelastic ‘power-law’ liquid in a continuous flow squeeze film. This simulates the flow in a conventional squeeze film by continuously injecting fluid into the narrow gap between two plates through the lower plate (Oliver et al. [6]). To zero order in the usual lubrication approximation the results are identical with those for the conventional squeeze film. To first order, useful corrections to the normal force due to the effects of inertia are obtained.     

Reverse squeeze film flow in a continous flow system

The continuous-flow squeeze film apparatus has been adapted to permit flow to take place in either direction. This simulates normal and reversed squeezing flow between discs by having liquid moving through the lower plate, with neither plate moving. The liquid exudes from 1580 uniformly-distributed holes in the plate surface. All tests were performed at a temperature of 24.0°C.Water is used in early tests, and it is shown that the contribution to load bearing from the inertia of the fluid is comparable in reverse and normal flows; fluid inertia increases the force which would be required to move the plates in either direction. A novel “mirror image” graphical presentation is used.Tests using a dilute polymer solution show load enhancement effects for both normal and reversed squeeze film flow. The enhancement is roughly equal in both directions of flow, with no transient effects, and fluid elasticity increases the force which would be required to move the plates in either direction. It is suggested that the stress developed in the fluid is independent of the direction of flow.The significance of the tests regarding lubricating problems is mentioned; the important case of rapid load reversal requires further attention.     

Experimental investigation of bubbly lubricated externally pressurized thrust bearings

Experimental results are presented for a bubbly lubricated externally pressurized circular thrust bearing. The data consists of the measured radial pressure distribution together with the lubricant mass flow rate over a wide range of inlet pressure, air mass flow rate ratio, for an either stationary or rotating bearing.It is shown that the air injection always improves the pressure distribution in the bearing and so can completely avoid the negative pressure generated due to rotational inertia. Also it is shown that the bearing load carrying capacity increases as the injected air mass flow increases, especially at high inlet pressure. The lubricant mass flow rate is reduced by the increase of air mass flow rate and by the decrease of bearing rotational speed.Finally the experimental results described in this paper are in good agreement with the mathematical analysis, based on the homogeneous flow model presented previously.     

基于发动机主轴轴承异常油膜噪声特征的模拟试验研究

由发动机主轴轴承油膜空穴造成的不规则打字机敲击噪声一直是汽车领域未解决的难题. 为了探究发动机主轴轴承动态载荷性能耦合作用下产生的异常空穴噪声,本文作者利用自行设计的平行板挤压油膜试验机进行模拟噪声试验并探究空穴噪声的特征. 该试验机可同时采集振动、位移、声压、力和空穴图像等五种信号,通过试验探究了不同激励信号、挤压振幅、挤压频率、润滑油黏度等因素对空穴噪声的影响,结果表明在方波、大振幅、使用高黏度润滑剂以及挤压频率为12 Hz的状况下容易产生空穴噪声.      

Derivation of two-dimensional couple-stress hydromagnetic squeeze film Reynolds equation and application to wide parallel rectangular plates

On the basis of Stokes couple-stress fluid model together with the hydromagnetic flow equations, a two-dimensional curved squeeze-film Reynolds equation has been derived. This equation can be applied to the study of squeeze film characteristics including the non-Newtonian hydromagnetic effects, in which the general film shape is h=h(x,z,t). To guide the application of the equation, an example of one-dimensional parallel rectangular plates lubricated with a non-Newtonian couple-stress, electrically conducting lubricant is illustrated. According to the results, the effects of couple stresses and external magnetic fields provide an increase in the load capacity and the response time as compared to the classical Newtonian hydrodynamic rectangular squeeze-film plates.     

Effect of magnetic field and velocity slip on porous-walled rectangular squeeze films

This is a study of an electrically conducting flow in a squeeze film between two infinite strips where one of the strips has a porous bounding surface backed by a solid wall. The analysis is directed to study the interaction of a transverse magnetic field with the coupled flows in the squeeze film and the porous medium including the slip velocity at the porous bounding surface. Expressions for load capacity and thickness-time are obtained. It is observed that the magnetic field increases the load capacity and response times of squeeze films. This effect is more marked for small values of the permeability K.     

Combined effects of non-Newtonian couple stresses and fluid inertia on the squeeze film characteristics between a long cylinder and an infinite plate

On the basis of the Stokes micro-continuum theory together with the averaged inertia principle, the combined effects of non-Newtonian couple stresses and convective fluid inertia forces on the squeeze film motion between a long cylinder and an infinite plate are presented. A closed-form solution has been derived for squeeze film characteristics including the film pressure, the load capacity and the response time. Comparing with the Newtonian-lubricant non-inertia case, the combined effects of couple stresses and convective inertia forces provide an increase in the film pressure, the load capacity and the response time. In addition, the quantitative effects of couple stresses and convective inertia forces are more pronounced for cylinder–plate system operating at a larger couple stress parameter and film Reynolds number, as well as a smaller squeeze film height. To guide the use of the present study, a numerical example is also illustrated for engineers when considering both the effects of non-Newtonian couple stresses and fluid convective inertia forces.     

挤压油膜阻尼在储能飞轮转子支承系统中应用研究

在飞轮储能系统实验研究中,利用永磁轴承-螺旋槽流体动压锥轴承的混合支承,并采用了挤压油膜阻尼为转子支承系统提供阻尼。基于流体润滑理论的雷诺方程和长轴承近似理论,推导出一端封闭、一端开口边界的挤压油膜的压力分布近似解析解,得到等效油膜刚度和阻尼系数。最后对比分析了飞轮转子支承系统不平衡响应的计算与试验结果。     

Magnetohydrodynamic lubrication theory for a cylindrical bearing

Liquid metal, which is a conductor of electric current, may be used as a lubricant at high temperatures. In recent years considerable attention has been devoted to various problems on the motion of an electrically conducting liquid lubricant in magnetic and electric fields (magnetohydrodynamic theory of lubrication), Thus, for example, references [1–3] study the flow of a conducting lubricating fluid between two plane walls located in a magnetic field. An electrically conducting lubricating layer in a magnetohydrodynamic bearing with cylindrical surfaces is considered in [4–8] and elsewhere.The present work is concerned with the solution of the plane magnetohydrodynamic problem on the pressure distribution of a viscous eletrically conducting liquid in the lubricating layer of a cylindrical bearing along whose axis there is directed a constant magnetic field, while a potential difference from an external source is applied between the journal and the bearing. The radial gap in the bearing is not assumed small, and the problem reduces to two-dimensional system of magnetohydrodynamic equations.An expression is obtained for the additional pressure in the lubricating layer resulting from the electromagnetic forces. In the particular case of a very thin layer the result reported in [4–8] is obtained. SI units are used.     

Lubrication of a rotating circular thrust bearing with a casson lubricant

Lubricants today are subjected to increasing mechanical shearing forces. This has resulted in an increasing interest in materials having variable viscosity. The problem of rotating circular thrust bearing is investigated with Casson fluid as a shear thinning lubricant. The pressure and load capacity of the thrust bearing is calculated when the feeding is done from the centre of the plates to the periphery. Also, moment of friction acting on the plates is calculated for different values of Casson number and for various values of ratio of inside to outside radius. It has been found that there is a decrease in the value of load capacity of the Casson lubricant. Also, it has been observed that there is an appreciable increase in the values of moment of friction for Casson fluid.     

Fluid inertia effects in squeeze films

Summary Fluid inertia effects in squeeze films are analyzed. Experimental results are also presented. The agreement between theory and experiment is very good.     

Compressible gas flow between closely spaced plates

A theoretical analysis is presented to solve numerically the steady state Navier–Stokes equations, continuity equation and energy equation for a compressible ideal gas flow between two closely spaced, in general nonparallel, infinitely wide plates (siider bearing). The analysis includes the gas inertia effect and covers both non-choked and choked flows. The results of the present analysis compare very well with both analytical and experimental results of compressible flow in a slider bearing comprised of two parallel and stationary plates. It was found that for choked flow the gas inertia effect is important, while the consideration of the energy equation does not affect the accuracy of the calculated flow substantially. Finally, the stiffness of a slider bearing is presented for different geometrical characteristics of the bearing.     

Effects of magnetic Reynolds number on swimming of gyrotactic microorganisms between rotating circular plates filled with nanofluids

The three-dimensional(3D) nano?uid ?ow among the rotating circular plates ?lled with nanoparticles and gyrotactic microorganisms is studied. A generalized form of the magnetic Reynolds number is used for the mathematical modeling of the ferro-nano?uid ?ow. The torque e?ects on the lower and upper plates are calculated.A di?erential transform scheme with the Pad′e approximation is used to solve the coupled highly nonlinear ordinary di?erential equations. The results show that the squeeze Reynolds number signi?cantly suppresses the temperature, microorganism, and nanoparticle concentration distribution, and agree well with those obtained by the numerical method.     

Viscous lifting and drainage of a conducting fluid in the presence of a transverse magnetic field

A theoretical investigation of the effects of a transverse magnetic field on the combined problem of viscous lifting and drainage of a conducting fluid on a plate is presented. The effects of inertia and transverse magnetic field on the liquid film thickness is studied for two cases namely a plate withdrawn with a constant velocity and one withdrawn with a constant acceleration. The expressions for the flow rate and the free surface profiles are obtained for the above two cases. It is found that the free surface profiles are convex in nature as in the non-magnetic case thus showing that the inertia does not effect the general pattern of flow, and the effect of the magnetic field is to retard both the lifting and drainage of the fluid.     

Surface roughness effects on squeeze film behavior in porous circular disks with couple stress fluid

The effect of surface roughness on squeeze film behavior between two circular disks with couple stress lubricant is analyzed when the upper disk has porous facing which approaches the lower disk with uniform velocity. The modified Stochastic Reynolds equation is derived on the basis of Stokes micro-continuum theory for couple stress fluid and Christensen Stochastic theory for the rough surface. Closed form solution of the Stochastic Reynolds equation is obtained in terms of Fourier–Bessel series. The importance of roughness and couple stress on bearing characteristics are presented in terms of load carrying capacity, squeeze time, and relative percentage of the load. It is observed that, effect of couple stress fluid, and surface roughness is more pronounced compared to classical case. These predictions enable design engineers to choose suitable parameters.     

Squeeze flow of Bingham fluids under slip with friction boundary condition

This paper develops a theoretical analysis of a Bingham fluid in slipping squeeze flow. The flow field decomposition consists in combining a central extensional flow zone in the plane of symmetry and shear flow zones near the plates. It is also considered that the slipping zone is located around a central sticking zone as previously shown from experiments. It is assumed that the shear stress at the plates is constant in the slipping zone and equals a fixed friction yield value. The squeeze force required to compress a Bingham fluid under the slipping behaviour as well as the radial evolution of the transition point between both sticking and slipping zones are finally determined.