Stability analysis of double porous and surface porous layer journal bearing

The linear stability analysis of double porous and surface porous layer journal bearing based on long and short bearing approximations is presented. The Brinkman model is employed in the porous region and the infinite permeability porous layer is simulated as surface layer. The coefficients of load, threshold speed and critical whirl frequency ratio are computed for double porous and surface porous layer configurations. The coefficients obtained using long and short bearing approximations yield same results. Higher threshold speed is obtained for double layer configurations of (i) high permeability bearing adsorbent porous layer topped with low permeability porous layer, and (ii) surface porous layer lubricant film.     

Analysis of Journal Bearing with Double-Layer Porous Lubricant Film: Influence of Surface Porous Layer Configuration

This article presents an analysis of a long journal bearing with a double-layer porous lubricant film using couple stress and Newtonian fluids. The porous layer with infinite permeability analyzed in this study simulates the surface layer. The Brinkman model was utilized to model the flow in the porous region. The effects of couple stresses were analyzed based on Stokes microcontinuum theory. A double-layer porous lubricant film configuration, with a low-permeability porous layer on top of a high-permeability bearing adherent porous layer, improved the journal bearing performance characteristics. A surface porous layered lubricant film configuration increased the load-carrying capacity and reduced the coefficient of friction in a journal bearing.     

Boundary and thermal non-equilibrium effects on convective instability in an anisotropic porous layer

The effects of boundary and local thermal non-equilibrium on the criterion for the onset of convection in a sparsely packed horizontal anisotropic porous layer are investigated. A two-field temperature model each representing the solid and fluid phases separately is used and the flow in the porous medium is described by the Brinkman extended-Darcy model. The lower boundary is rigid, while the upper boundary is considered to be either rigid or free with fixed temperature conditions at the boundaries. The stability equations are solved numerically using the Galerkin method to extract the critical stability parameters. The influence of local thermal non-equilibrium, mechanical and thermal anisotropy parameters representing the fluid and solid phases is assessed on the stability characteristics of the system. The existing results are obtained as limiting cases from the present study.     

Conical whirl instability of turbulent flow hybrid porous journal bearings

An analysis of conical whirl instability of an unloaded rigid rotor supported in a turbulent flow hybrid porous journal bearing has been presented, following Constantinescu's turbulent lubrication theory. The effect of bearing feeding parameter (β), Reynolds number (Re), ratio of wall thickness to journal radius (H/R) and anisotropy of porous material on the stability of rotor-bearing system has been investigated. It is observed that higher values of β gives better stability and higher stability is predicted if the porous bush is considered to be isotropic.     

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.     

Rigid Rotor Stability Analysis on Finite Hydrostatic Double-Layer Porous Oil Journal Bearing with Velocity Slip

A theoretical investigation has been carried out for stability characteristics of a finite hydrostatic double-layer porous oil journal bearing considering the effect of Beavers-Joseph velocity slip at the porous film interface. A linearized perturbation method has been used to obtain the threshold of stability in terms of critical mass parameter. The effect of slip parameters, eccentricity ratios, bearing feeding parameter, and slenderness ratio on the stability is investigated. Furthermore, nonlinear transient analysis is carried out to determine the system stability by tracing the journal center locus. Several trajectories of the journal center locus have been obtained for different operating conditions and are depicted with the help of graphics.     

Characteristics of partial porous journal bearings of finite length considering curvature and slip velocity

A self acting, finite length, partial porous journal bearing with arbitrary load angle has been analysed to obtain the characteristics assuming the active film of a homogeneous single phase liquid lubricant extends over the whole bearing arc span. The adhesion condition used in earlier porous bearing analysis is no longer valid, due to the presence of the thin layer of fluid moving streamwise just beneath the surface of the porous bearing material, a new modified lubrication equation is used for the present analysis. Film curvature has been considered. The curvature effect of the thick porous bearing matrix is taken into account by a direct but new approach which makes possible the use of the separation of variables for the first time in such a problem. Collocation technique is utilised to determine the hydrodynamic pressure from which characteristics are evaluated as usual. The results are fully analytical in nature, simple, yet exact and accurate, permitting easy and economical calculation of numerical data over a very wide range of parameters.     

Brinkman ferromagnetic convection in a porous layer: Effect of MFD viscosity and magnetic boundaries

In the present study, the effect of magnetic field dependent (MFD) viscosity and different types of magnetic boundaries on the onset of ferromagnetic convection in a horizontal layer of Brinkman porous medium is investigated numerically using the Galerkin method. The simultaneous and isolation presence of buoyancy and magnetic forces on the stability characteristics of the system are emphasized. The study reveals that the linear stability of the system depends significantly on the types of magnetic boundaries. The rigid-paramagnetic boundaries are found to be preferred to the ferromagnetic ones in suppressing ferromagnetic convection. Besides, the system is more stable when the magnetic forces alone are present. In addition, increasing MFD viscosity parameter λ and decreasing magnetic number M ₁ and nonlinearity of fluid magnetization parameter M ₃ is to inhibit the onset of ferromagnetic convection in a porous medium. The critical wave number is found to be independent of λ, but increasing M ₁ and χ as well as decreasing M ₃ is to reduce the size of convection cells. At higher values of M ₃ , the critical Rayleigh number and the corresponding wave number coincide for different magnetic boundaries.     

Study of conical whirl instability of hydrodynamic porous oil journal bearings with tangential velocity slip

A theoretical analysis is presented for the stability characteristics of the conical whirling of an unloaded rigid rotor supported in hydrodynamic porous oil journal bearings with tangential velocity slip on the bearing film interface. The rotor has a two degree of freedom motion in self-excited conical whirling. In the stability analysis, the effect of various parameters on stability has also been investigated.     

Linear stability of double-diffusive convection in a micropolar ferromagnetic fluid saturating a porous medium

This paper deals with the theoretical investigation of the double-diffusive convection in a micropolar ferromagnetic fluid layer heated and soluted from below saturating a porous medium subjected to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained. A linear stability analysis theory and normal mode analysis method have been carried out to study the onset of convection. The influence of various parameters like medium permeability, solute gradient, non-buoyancy magnetization and micropolar parameters (i.e. coupling parameter, spin diffusion parameter and micropolar heat conduction parameter) has been analyzed on the onset of stationary convection. The critical magnetic thermal Rayleigh number for the onset of instability is also determined numerically for sufficiently large values of buoyancy magnetization parameter M₁ and results are depicted graphically. The principle of exchange of stabilities is found to hold true for the micropolar ferromagnetic fluid saturating a porous medium heated from below in the absence of micropolar viscous effect, microinertia and solute gradient. The oscillatory modes are introduced due to the presence of the micropolar viscous effect, microinertia and solute gradient, which were non-existent in their absence. In this paper, an attempt is also made to obtain the sufficient conditions for the non-existence of overstability.     

多孔质径向气体静压轴承运动稳定性分析

多孔质轴承在高速运转条件下会出现涡动失稳现象，使轴承的动态稳定性下降。利用线性扰动法对多孔质静压轴承中气体润滑的连续方程求解，得到动态下轴承稳定的临界质量——系统保持稳定的最小质量，并以此为稳定性判据得出轴承参数对稳定性的影响，即轴承的供气压力、渗透数、长径比越大，稳定区域越小，为今后的多孔质轴承设计提供了参数的优化范围。     

Lubricant additives effects on the hydrodynamic lubrication of misaligned conical–cylindrical bearings

Conical–cylindrical bearings are used in electrohydraulic servo systems to improve the control accuracy, eliminate the static friction and increase the normal load‐carrying capacity. A non‐Newtonian rheological model to investigate theoretically the effects of lubricant additives on the performance of misaligned conical–cylindrical bearings is proposed in this study. In this model, the non‐Newtonian behaviour 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 utilised to model the flow in the porous region. A stress jump boundary condition is applied at the porous media/fluid film interface. The misalignment of the cylinder rod is also considered. 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 behaviour of the lubricant on the steady‐state performance characteristics such as pressure distribution, load‐carrying capacity and coefficient of friction are presented and discussed. The results showed that lubricant additives significantly increase the load‐carrying capacity and reduce the coefficient of friction as compared to the Newtonian lubricants. Furthermore, the misalignment of the piston rod has significant effects on the performance of conical–cylindrical bearings. Copyright © 2007 John Wiley & Sons, Ltd.     

气体静压多孔质球面轴承静态性能分析

与传统的小孔节流气体静压轴承相比,气体静压多孔质轴承具有高承载能力、高阻尼和很好的稳定性等。气体静压多孔质球面轴承具有合力始终对准球心,轴承运转平稳等优点,既具有轴向限制同时具有径向限制,在工业当中应用相当普遍。给出了球面轴承的理论分析、有限元推导过程,基于有限元推导过程给出了球面轴承的理论计算静态性能。在自行研制的试验台上进行气体静压试验,由此得到轴承的静态性能。试验结果和理论计算结果之间的吻合良好,从而说明理论计算的正确性和可行性。     

Linear stability performance analysis of finite hydrostatic porous journal bearings under the coupled stress lubrication with the additives effects into pores

A theoretical investigation into the stability performance characteristics of a finite externally pressurized porous journal bearing has been undertaken with the slip flow of coupled stress fluid. The analysis deals with the modified Darcy-type equation incorporating the additive effect in the porous bush. A modified form of Reynolds equation is obtained using Stokes micro-continuum theory of coupled stress fluids as lubricant. Applying the first-order perturbation of the film thickness and steady-state film pressure, the stability parameters are obtained under various parametric conditions. The results reveal that stability deteriorates with increase in coupled stress parameter for a value of percolation factor under full slip condition.     

Integral characteristics of a porous gas axial bearing

A flat axial bearing with pressurized gas supply through an annular flow valve made from anisotropic porous material is considered. The differential equation for the pressure in the lubricant layer adjacent to the porous wall is numerically solved using the Runge-Kutta method, with two boundary conditions taken into account. One of these, which is integral, has remained out of sight in the porous support analysis until recently. An algorithm for calculating the lifting force and rigidity of support as well as mass rate of gas flow through this support is presented. The optimization of support is performed, and conclusions are drawn as to its influence on different factors.     

On Performance Characteristics of Three-Lobe Porous Hydrodynamic Journal Bearings

This paper presents an analysis of a three-lobe porous hydrodynamic journal bearing for its static and dynamic performance characteristics. The performance characteristics of the bearing have been computed and presented in graphical form for a wide range of permeability parameter to investigate the effect of porosity on bearing performance. The stability margin of the three-lobe journal bearing system, in terms of crtical mass of journal, has been established using Routh's criteria. The nature of transient motion of the journal has been analyzed using the complex eigen values of characteristic equation and motion trajectories obtained by numerical integration of equations of motion.     

Optimizing parameters of complexly loaded friction bearings

Crankshaft rod bearings of a combustion engine are used as an example to show the technique and results of optimization of the design parameters of friction bearing under a complex load. The field of hydrodynamic pressures in a lubricating layer, which separates the crank pin and the bearing lining, is determined by integrating the equation for filling of the gap. This approach ensures observance of the condition of lubricant continuity at the boundaries of discontinuity and restoration of the lubricating layer. The lubricant viscosity, which is assumed to be an effective function of the temperature of the lubricating layer, is adjusted at each step of the calculation of the crank pin’s motion trajectory.     

Magnetic-fluid-based porous inclined slider bearing

A porous inclined slider bearing, lubricated with a magnetic fluid, in the presence of an externally applied magnetic field which is oblique to the lower surface of the bearing is discussed. The load capacity of the magnetic-fluid-based porous inclined slider bearing is found to be greater than that of a viscous porous inclined slider bearing. It is shown that the magnetic-fluid-based porous inclined slider bearing has a performance superior to that of the viscous porous inclined slider bearing.     

Calculation of a Safety Margin for Hydrogenerator Thrust Bearings

The purpose of this paper is to present the two-dimensional linear stability analysis considering the fluid flow in both full film and cavitation regions for a plain cylindrical journal bearing. The Lund's infinitesimal perturbation procedure is applied to Elrod's universal equation for evaluation of unsteady pressure gradients. Based on JFO theory, the pressure distribution, film rupture, and reformation boundaries can be obtained using Elrod's universal equation, for a given operating position of the journal. In this work, it is assumed that for infinitesimal perturbation of a journal about the equilibrium position, the film rupture and film reformation boundaries are the same as those obtained for steady state. However, the unsteady pressure gradients in the full film region are evaluated taking into consideration the perturbed flow parameters in the cavitation region, i.e., at both rupture and reformation boundaries. The linearized stiffness and damping coefficients, whirl frequency ratio, and threshold speed for various values of eccentricity and L/D ratios are obtained for a plain cylindrical journal bearing with an axial groove along the load line. Measured data of dynamic coefficients for a 120° partial arc bearing are chosen for comparison with this work. Results show good agreement between the theoretical and experimental results.     

空间轴承多孔聚酰亚胺保持架尺寸稳定性研究*

空间轴承常用的多孔聚酰亚胺含油保持架机械强度低、吸附性强,在制备和使用过程中易受各种内外应力和温湿环境的影响,导致尺寸不稳定。通过测量各种工况下保持架尺寸的变化值,实验研究溶剂清洗、含油状态以及温度循环变化和环境湿度变化等对保持架尺寸稳定性的影响。结果表明:多孔聚酰亚胺保持架溶剂清洗时会因材料孔隙吸附溶剂而使内外径尺寸增大,因此清洗后应充分干燥处理;多孔聚酰亚胺保持架含油状态与不含油状态尺寸基本一致;多孔聚酰亚胺保持架热稳定性好,内外径尺寸不会随着频繁的高低温热循环而发生改变;多孔聚酰亚胺保持架对湿度敏感,环境湿度越大保持架尺寸变化越大。