Combined effect of viscosity variation and non-Newtonian Rabinowitsch fluid in wide parallel rectangular-porous plate with squeeze-film characteristics

The present article carries out the study of viscosity variation of non-Newtonian fluid with the homogeneous porous wall on wide parallel rectangular-plate based on the Rabinowitsch fluid model. The non-linear modified Reynolds equation is derived for the lubrication of rectangular squeeze film bearing with viscosity variation and porous parameter. Using the Morgan–Cameron approximation, the nonlinear Reynolds-type equation for squeeze-film which governs the film pressure is solved within the fundamentals of small perturbation technique. The characteristic of the wide parallel rectangular-porous plate is numerically computed for different physical quantities such as film pressure, load carrying capacity and response time. Moreover, as limiting cases some of the results from the available literature are recovered also. Further, the findings reveal that the viscosity variation of non-Newtonian fluid and the presence of porous wall lead to reduction in the load capacity and the response time respectively. Here, the porous matrix consists of a system of capillaries of very small radii with the homogeneous porous wall. The impact of porosity is incorporated as a result it acts as self-lubrication on bearing surface. Also, the effect of viscosity variation is one of the most important characteristics of fluid which helps in the design of bearings for lubrication in engineering and industrial applications.

     

Influence of dimple geometry and micro-roughness orientation on performance of textured hybrid thrust pad bearing

The present study deals with numerical simulation of textured hybrid thrust pad bearing. Influence of providing micro-dimples of different cross-sectional shapes on the bearing surface has been theoretically investigated on the performance of thrust pad bearing. Reynolds equation has been solved using mass-conserving algorithm based on Jakobsson–Floberg–Olsson cavitation boundary conditions. A parametric study is carried out to optimize dimple shapes from the viewpoint of load carrying capacity of bearings. The textured bearing surface is noticed to be beneficial in reducing the frictional power losses. Providing half-section dimples (second half in the direction of runner rotation) towards the leading edge of thrust pad, enhance the load carrying capacity and fluid film stiffness coefficient of bearings. Micro-roughness in a textured surface having transverse orientation is seen to improve the dynamic characteristics of hybrid thrust pad bearings.     

等深度螺旋槽止推轴承的边界元法计算

本文以分析等深度螺旋槽止推轴承为例,介绍了边界元法在润滑力学研究领域中的应用。以及相应的边界条件的处理方法,并且讨论了轴承尺寸参数对性能参数的影响。     

A Frictional Heat Model of Planetary Roller Screw Mechanism Considering Load Distribution

Planetary roller screw (PRS), with higher thrust, higher load capacity, and higher speed, is the best choice of the transmission component of the servo system. However, spinning sliding of rollers and support bearings can cause frictional moments and frictional heat, which is an undesirable phenomenon. Besides, frictional heat will further result in high temperature that causes deterioration of lubrication and eventually lead to destruction of the mechanism. Therefore, it is important to predict frictional moments which result in frictional heat. In order to predict the magnitude of frictional heat of PRS mechanism and study the influence of structural parameters of thread and operating conditions on frictional heat, first, a frictional moment model of bearings is built, and frictional moments models of PRS considering the elastic hysteresis of material, the spinning sliding of the rollers, the viscosity of lubricating oil and the differential sliding of thread raceways are established in this paper, respectively. Second, heat generation models of bearing and PRS are presented, respectively. Finally, relationships between frictional heat in terms of operating conditions of PRS, contact angle, and helix angle of roller thread are investigated. The achievements of this project will provide theoretical basis for the design of PRS with lower frictional moments and higher transmission efficiency.     

变深度螺旋槽止推轴承的边界元法计算

本文以分析变深度螺旋槽止推轴承为例介绍了边界元法在润滑力学研究领域中的应用,以及相应的边界条件的处理方法,同时还讨论了轴承的尺寸参数对其性能参数的影响。     

Validation of the Local Thermal Equilibrium Assumption in Forced Convection of Non-Newtonian Fluids through Porous Channels

In this paper, we assess the validity of the local thermal equilibrium assumption in the non-Newtonian forced convection flow through channels filled with porous media. For this purpose, the problem is solved numerically using local thermal non-equilibrium and non-Darcian models. Numerical solutions obtained over broad ranges of representative dimensionless parameters are utilized to map conditions at which the local thermal equilibrium assumption can or cannot be employed. The circumstances of a higher modified Peclet number, a lower modified Biot number, a lower fluid-to-solid thermal conductivity ratio, a lower power-law fluid index, and a lower microscopic and macroscopic frictional flow resistance coefficients, are identified as unfavorable circumstances for the local thermal equilibrium (LTE) condition to hold. Quantitative LTE validity maps that reflect the proportional effect of each parameter as related to others are presented.     

轴向扩散下简支饱和多孔弹性梁的大挠度分析

基于多孔介质理论和弹性梁的大挠度理论,并考虑轴向变形,在孔隙流体仅沿轴向扩散的假设下,建立了微观不可压饱和多孔弹性梁大挠度弯曲变形的一维非线性数学模型.在此基础上,忽略饱和多孔弹性梁的轴向应变,并利用Galerkin截断法,研究了两端可渗透的简支饱和多孔弹性梁在突加横向均布载荷作用下的拟静态弯曲,给出了饱和多孔梁弯曲时挠度、弯矩和轴力以及孔隙流体压力等效力偶等沿轴线的分布曲线.揭示了大挠度非线性和小挠度线性模型的结果差异,指出大挠度非线性模型的结果小于相应小挠度线性模型的结果,并且这种差异随着载荷的增大而增大.计算表明:当无量纲载荷参数q>5时,应该采用大挠度非线性数学模型进行研究.     

Numerical investigation of variable viscosities and thermal stratification effects on MHD mixed convective heat and mass transfer past a porous wedge in the presence of a chemical reaction

An analysis is presented to investigate the effects of variable viscosities and thermal stratification on the MHD mixed convective heat and mass transfer of a viscous, incompressible, and electrically conducting fluid past a porous wedge in the presence of a chemical reaction. The wall of the wedge is embedded in a uniform nonDarcian porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically with finite difference methods. Numerical calculations up to the thirdorder level of truncation are carried out for different values of dimensionless parameters. The results are presented graphically, and show that the flow field and other quantities of physical interest are significantly influenced by these parameters. The results are compared with those available in literature, and show excellent agreement.     

An approach for calculating the dynamic load of deep groove ball bearing joints in planar multibody systems

This study is focused on dynamic modeling of planar multibody systems with multiple deep groove ball bearing joints, in which the radial clearance, contact deformation, and bearing kinematics are included. By using the approach presented, the variation of the joint reaction force and the dynamic load on each ball element in bearings can be simulated. The deep groove ball bearing joints are modeled by introducing a nonlinear force system, which takes into account the contact elastic deformations between the ball elements and the raceways. The contact force is calculated by the Hertzian contact deformation theory that accounts for the geometrical and material properties of the contacting bodies. A planar slider-crank mechanism with two deep groove ball bearing joints is chosen as an example to demonstrate the application of the methodologies presented in this paper. In this model, one bearing locates at the joint between the ground and crank, while the other one locates at the joint between the crank and connecting rod. By numerical calculation, the dynamic load distribution characteristics of bearings under real mechanism movement conditions are simulated. From the results, it can be concluded that the dynamic load on each rolling element varies differently and belongs to a variable load with the change of mechanism configuration. Load characteristic analysis is the foundation of developing research on the fatigue life and reliability of bearings. This study will provide a key mechanical support for the performance evaluation, dynamic design, and geometrical parameter optimization of the joint rolling element bearings.     

NONLINEAR NUMERICAL ANALYSIS OF A FLEXIBLE ROTOR EQUIPPED WITH SQUEEZE COUPLE STRESS FLUID FILM JOURNAL BEARINGS

This study performs a dynamic analysis of a rotor supported by two squeeze couple stress fluid film journal bearings with nonlinear suspension.The numerical results show that the stability of the system varies with the non-dimensional speed ratios and the dimensionless parameter l*.It is found that the system is more stable with higher dimensionless parameter l*. Thus it can conclude that the rotor-bearing system lubricated with the couple stress fluid is more stable than that with the conventional Newtonian fluid.The modeling results thus obtained by using the method proposed in this paper can be used to predict the stability of the rotor-bearing system and the undesirable behavior of the rotor and bearing center can be avoided.     

Slow Motion of a Porous Cylindrical Shell in a concentric cylindrical cavity

This paper concerns the Slow Motion of a Porous Cylindrical Shell in a concentric cylindrical cavity using particle-in-cell method. The Brinkman’s equation in the porous region and the Stokes equation for clear fluid in their stream function formulations are used. The hydrodynamic drag force acting on each porous cylindrical particle in a cell and permeability of membrane built up by cylindrical particles with a porous shell are evaluated. Four known boundary conditions on the hypothetical surface are considered and compared: Happel’s, Kuwabara’s, Kvashnin’s and Cunningham’s (Mehta-Morse’s condition). Some previous results for hydrodynamic drag force and dimensionless hydrodynamic permeability have been verified. Variation of the drag coefficient and dimensionless hydrodynamic permeability with permeability parameter σ, particle volume fraction γ has been studied and some new results are reported. The flow patterns through the regions have been analyzed by stream lines. Effect of particle volume fraction γ and permeability parameter σ on flow pattern is also discussed. In our opinion, these results will have significant contributions in studying, Stokes flow through cylindrical swarms.     

Thermophoresis and variable viscosity effects on MHD mixed convective heat and mass transfer past a porous wedge in the presence of chemical reaction

An analysis is presented to investigate the effects of thermophoresis and variable viscosity on MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by using the R.K. Gill and shooting methods. Favorable comparison with previously published work is performed. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.     

Voronoi Cell Finite Element Method for Fluid-Filled Materials

A modified Voronoi cell finite element method is proposed to allow for fluid pressure within porous materials. Traction on the hole boundary can equal the force generated by the pressure, and multiplying the Lagrange multiplier by the constraints, we derive a new function. The stiffness matrix and load vector were derived from the modified element energy functional. Numerical examples with various boundary problems were evaluated using the proposed model and compared with a conventional displacement-based finite element model. The results show that the proposed method can measure the irregular local stress on porous materials that contain randomly distributed and sized holes with specifics pressures. The proposed method significantly reduces the number of elements and nodes of the calculated porous structure.     

弹性地基上多孔功能梯度材料矩形板的自由振动与临界屈曲载荷分析

多孔功能梯度材料(FGM)构件的特性与孔隙率和孔隙分布形式有密切关系。本文基于经典板理论,考虑不同孔隙分布形式时修正的混合率模型,研究Winkler弹性地基上四边受压多孔FGM矩形板的自由振动与临界屈曲载荷特性。首先利用Hamilton原理和物理中面的定义推导Winkler弹性地基上四边受压多孔FGM矩形板自由振动的控制微分方程并进行无量纲化,然后应用微分变换法(DTM)对无量纲控制微分方程和边界条件进行变换,得到计算无量纲固有频率和临界屈曲载荷的代数特征方程。将问题退化为孔隙率为零时的FGM矩形板并与已有文献进行对比以验证其有效性。最后计算并分析了梯度指数、孔隙率、地基刚度系数、长宽比、四边受压载荷及边界条件对多孔FGM矩形板无量纲固有频率的影响以及各参数对无量纲临界屈曲载荷的影响。     

Non-linear dynamic analysis of the ultra-short micro gas journal bearing-rotor systems considering viscous friction effects

Due to the micro-fabrication limitations and the low thickness of the silicon wafer, the length-to-diameter ratio (L/D) of the gas journal bearings in Power MEMS is about one order lower than that of the conventional bearings, which suggests that the viscous friction force in the micro-bearing is comparable to the load capacity. The effects of viscous friction force on non-linear dynamic characteristics of the ultra-short micro-bearing-rotor system are studied in this paper. The molecular gas-film lubrication model, which valid for arbitrary Knudsen numbers, is systematically coupled with the rotor kinetic equations and solved simultaneously to investigate the non-linear dynamic behavior of the system. The center orbits, phase portraits, Poincaré maps, and FFT spectra of the system response at different L/D ratio, rotor mass, and bearing number, and the corresponding bifurcation diagrams for cases of ignoring and considering viscous friction force are inspected and compared. The results indicate that, if the viscous friction force is not taken into account in the case of low L/D ratio, the low-frequency large-amplitude self-excited whirl motion will be predicted as the increase of the rotor mass and the bearing number. However, when the viscous friction force is included in the non-linear dynamic model, the rotor motion becomes more stable under the same conditions, as the synchronous motion with smaller amplitude prevails.     

微载荷含油轴承摩擦性能研究Ⅰ.摩擦试验机设计

研制了1种针对径向轴承的微载荷摩擦试验机,介绍了其工作原理及结构,即利用外加载荷抵消浮动测试架重量以施加微小载荷,并利用激光位置传感器(PSD传感器)实现无接触位移测量;同时测量了摩擦副的转动角度并计算出摩擦系数;采用摩擦转角测量法和外加力矩平衡摩擦法测量微载荷下的摩擦性能,以测量时间末端位置作为位置基准,通过极限偏载平衡进行载荷标定.结果表明:微载荷摩擦试验机可应用于径向轴承在微小载荷下的摩擦力测量;可以通过在较大范围内设置结构参数来研究径向轴承的摩擦特性;并可利用数据采集技术研究速度和载荷连续变化条件下的摩擦性能.     

Smoothed Particle Hydrodynamics Modeling of Transverse Flow in Randomly Aligned Fibrous Porous Media

The Lagrangian smoothed particle hydrodynamics (SPH) method is employed to obtain a meso-/micro-scopic pore-scale insight into the transverse flow across the randomly aligned fibrous porous media in a 2D domain. Fluid is driven by an external body force, and a square domain with periodic boundary conditions imposed at both the streamwise and transverse flow direction is assumed. The porous matrix is established by randomly embedding a certain number of fibers in the square domain. Fibers are represented by position-fixed SPH particles, which exert viscous forces upon, and contribute to the density variations of, the nearby fluid particles. An additional repulsive force, similar in form to the 12-6 Lennard-Jones potential between atoms, is introduced to consider the no-penetrating restraint prescribed by the solid pore structure. This force is initiated from the fixed solid material particle and may act on its neighboring moving fluid particles. Fluid flow is visualized by plotting the local velocity vector field; the meandering fluid flow around the porous microstructures always follow the paths of least resistance. The simulated steady-state flow field is further used to calculate the macroscopic permeability. The dimensionless permeability (normalized by the squared characteristic dimension of the fiber cross section) exhibits an exponential dependence on the porosity within the intermediate porosity range, and the derived dimensionless permeability—porosity relation is found to have only minor dependence on either the relative arrangement condition among fibers or the fiber cross section (shape or area).     

Magnetohydrodynamic laminar boundary-layer flow over a porous wedge with thermophoresis particle deposition in the presence of variable stream conditions

An analysis is presented to investigate the effects of thermophoresis variable viscosity on MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by local non-similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by using the R.K. Gill and shooting methods. Favorable comparison with previously published work is performed. Numerical results for the dimensionless velocity, temperature and concentration profiles are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.