Theoretical hydrodynamic load capacity of an axially undefined full porous journal bearing in the turbulent regime considering slip flow and curvature

A mathematical analysis using a new generalized pressure equation is reported for the hydrodynamic lubrication of a 360° long porous metal journal bearing with arbitrary wall thickness which is press fitted in a solid housing and works with a turbulent film of newtonian lubricant. The limiting case of an axially undefined length of the bearing is considered and the axial flow of lubricant in the clearance space is neglected so that the governing differential equation is simpler to solve. Half Sommerfeld boundary conditions are used for the extent of the azimuthal film and film curvature has been included. The curvature effect of the thick porous bearing matrix is taken into account by a new direct approach in which the separation of variables is used for the first time in such a problem. The collocation technique is utilized to determine the hydrodynamic pressure from which the characteristics are evaluated. 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.     

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 The adhesion condition used in earlier porous bearing analysis is no longer valid, due to the presence of the thin layer of fluid moving streamwise just beneath the surface of the porous bearing material, a new modified lubrication equation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.     

Estimation of the performance of a narrow porous journal bearing with hydrodynamic turbulent lubrication considering slip velocity and arbitrary wall thickness

A closed-form mathematical analysis is presented for the hydrodynamic lubrication of a 360° short porous metal journal bearing with arbitrary wall thickness which is press fitted in a solid housing and works with a turbulent film of newtonian lubricant. A new pressure equation is used. The bearing is assumed to be narrow, and therefore circumferential flow of the lubricant in the clearance region is negligible in comparison with that in the axial direction which makes the governing differential equation simpler to solve. However, this simplification is not applicable to darcian flow in the porous matrix so that a three-dimensional Laplace equation is required to describe the continuity of flow in the pores. The film curvature is included by retaining terms containing $\text{C}\text{R}{}_1$ in the expression for film thickness. The curvature of the permeable bearing matrix, which allows it to have an arbitrary wall thickness, is taken into account by a direct approach. Infinite Fourier series and their orthogonal properties are utilized for the determination of the turbulent hydrodynamic pressure distribution from which the load-carrying capacity and attitude angle are calculated. All the results of interest are simple and fully analytical in nature permitting easy and economical calculation of numerical data over a very wide range of parameters.     

Elastic and damping properties of partial porous journal bearings of finite length and arbitrary wall thickness taking film curvature and slip flow into account

A self-acting porous journal bearing of finite length has been analysed in order to obtain the dynamic characteristics when an active film of a homogeneous single-phase liquid lubricant extends over the whole bearing arc span. A new governing lubrication equation which considers slip flow, film curvature and unsteady motion of the journal has been derived and solved analytically to yield results in a closed form for a dynamic load, taking into account the curvature of the porous bearing matrix and thus allowing the porous wall thickness to be arbitrary. Closed form results obtained in this way are valid for any arbitrary clearance ratio C/R₁ and wall thickness ratio H/R₁. The dynamic characteristics are evaluated as for impermeable bearings. The pertinent 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 involved.     

Hydrodynamic lubrication of a porous slider bearing with slip velocity

An inclined porous slider bearing is analysed with slip velocity at the porous boundary considered. The expressions for dimensionless loadcarrying capacity, friction and the centre of pressure are obtained in the form of integrals. Minimization of the slip parameter is essential to increase the load capacity.     

An approximate solution of oil film forces of turbulent finite length journal bearing

An approximate analytical method is proposed for calculating oil film forces of turbulent finite length journal bearings. The dynamic ‘π’ oil film assumption is usually taken to determine oil film forces in the dynamic analysis of hydrodynamic journal bearing-rotor systems. However oil film field is not in the ‘π’ zone, i.e. the start position of the oil film is not 0, and the termination position of the oil film is not ‘π’. Based on the variational principle, separation of variables is employed to obtain the pressure distribution in this paper. The pressure distribution of the infinitely long journal bearing model is taken as a circumferential separable function of the pressure distribution. The start and termination positions of oil film in the circumferential direction are determined by using the continuity condition. The axial separable function of the pressure distribution is obtained by the variational principle and the circumferential separable function. The results calculated by the proposed method are in good agreement with the oil film forces by the finite element method, and the computing cost is reduced greatly. Meanwhile, the influence of the parameters on the oil film forces is analyzed.     

The load capacity of a partial journal bearing with a non-Newtonian film

Lubricating oils with viscosity index improver additives exhibit non-Newtonian behaviour. Starting from the most general type of fluid flow equation, connecting cubic shear stress to rate of shear for non-Newtonian lubricants, a modified form of Reynolds' equation has been derived and solved for the steady state load capacity for finite width full cylindrical journal bearings. The method has been extended to partial journal bearings both for the centrally loaded film and for the film with minimum thickness at the trailing edge. Numerical results are given for bearing arcs of 180° and 120° and length-to-diameter ratios of 1 and $\text{1}\text{2}$.     

考虑进油孔有限长滑动轴承油膜力的近似解析解

针对具有进油孔的有限长滑动轴承油膜力求解问题,采用变分原理和分离变量法,求得了有限长滑动轴承油膜压力分布的近似解析表达式。将油膜压力分布的近似解析表达式在油膜存在区域上进行积分,即得到了油膜力。将提出的计算有限长滑动轴承油膜力方法与无限长轴承模型、有限元方法的计算结果进行了比较,发现了提出的方法与有限元方法的计算结果很接近。最后,研究了进油孔位置和进油压力对油膜存在区域、油膜力等的影响,研究结果表明进油孔位置和进油压力对油膜存在区域和油膜力有较大的影响。     

Calculated load capacity of non-newtonian lubricants in finite width journal bearings

Starting from the most general type of fluid flow equation connecting cubic shear stress to rate of shear for non-Newtonian lubricants, a modified form of Reynolds' equation was derived for steady finite width journal bearings. The finite difference technique with successive over relaxation was used incorporating Reynolds' boundary conditions for pressure to obtain the pressure distribution and hence the load capacity and the attitude angle. It is shown that the flatter pressure profile and higher load capacity at low eccentricity ratios have practical advantages. The apparent viscosity loss at higher rates of shear decreases the load capacity at higher eccentricity ratios but it is expected that the flatter viscosity temperature slope of the polymer thickened non-Newtonian lubricants will compensate for their apparent viscosity decrease.     

Non-linear analysis of finite hydrodynamic journal bearings in laminar and turbulent flow regimes

The Navier-Stokes equations were modified by adopting the non-linear turbulence theory proposed by Constantinescu to take into account the turbulent stresses. The modified equations were solved by the finite element method using Galerkin's technique and a suitable iterative procedure.The performance characteristics of a finite hydrodynamic journal bearing (aspect ratio b = 1) were studied in terms of the load-carrying capacity, non-dimensional stiffness and damping coefficients and critical journal mass at various eccentricities for Reynolds' numbers up to 13 300. The computed results are compared with those obtained using the twodimensional triangular element formulation and the linearized turbulence theory.     

Hydrodynamic lubrication of finite porous journal bearings—Use of the Brinkman-extended Darcy model

This paper applies the Brinkman-extended Darcy model (BEDM) to investigate the hydrodynamic lubrication of finite porous journal bearings. A finite difference technique employing the Preconditioned Conjugate Gradient method (PCGM) of iteration is used to solve the modified Reynolds equation. The results show that the influences of viscous shear stresses on the lubrication performance of porous journal-bearing systems are apparent and not negligible. Comparing with those of the Darcy model (DM), the effects of viscous shear stresses of the BEDM provide an increase in the load capacity, as well as a reduction in the friction parameter; and the quantitative effects of the viscous shear stresses on the static characteristics are more pronounced for the cases of large length-to-diameter ratios.     

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.     

Friction coefficient and oil flow in plain finite partial journal bearings during turbulent operation

Plain partial journal bearings of finite length with a turbulent hydrodynamic film of a newtonian lubricant were analysed to determine the friction coefficient and the total oil flow. The coefficient of friction, which is a performance characteristic, is presented analytically in the closed form. The total oil flow through superlaminar bearings is also treated as a bearing performance characteristic. The results of interest, which are dimensionless and available in the closed form, are simple yet exact over a wide range of the parameters involved.     

Stability of a rigid rotor in turbulent hybrid porous journal bearings

Stability characteristics of hybrid porous journal bearings with a turbulent fluid film have been investigated theoretically following Constantinescu's turbulent lubrication theory. The stability curves have been drawn for different Re, eccentricity ratios, slenderness ratios and bearing speed parameters. In the absence of any experimental data, laminar flow results obtained by this analysis have been compared and found to be in excellent agreement with the previous results. It is observed that turbulence deteriorates the stability of the rotor and for better performance the value of the bearing feeding parameter, β, should be kept small.     

Coefficient of friction and oil flow in plain finite partial journal bearings during turbulent operation

Bearings which have been properly designed with respect to the provision of a hydrodynamic oil film can sometimes fail by overheating. Hence the complete analysis of journal bearings requires the evaluation of friction and oil flow. Plain partial journal bearings of finite length with a turbulent hydrodynamic film of a newtonian lubricant were analysed to obtain the coefficient of friction and the total oil flow. The coefficient of friction, which is a performance characteristic, is presented analytically in the closed form. The total oil flow through superlaminar bearings is also considered as a bearing performance characteristic. All the results of interest are dimensionless and available in a closed form which is simple yet exact over the wide range of parameters involved.     

Load and flow characteristics of a capillary-compensated hydrostatic journal bearing

A theoretical analysis of load and flow characteristics of a capillary compensated oil-lubricated externally pressurized journal bearing having four rectangular recesses is presented. The analysis is based on an exact solution of the pressure distribution over the bearing sill area and has been made for two configurations of loading, through the centre of any recess and through the centre of the circumferential sill between any two recesses. The influence of circumferential sill length and intensity of compensation on the load carrying capacity and the flow requirement is shown. Theoretical analysis and experimental results are compared.     

单排球式回转支承的承载能力分析

回转支承是工程机械行业的重要基础件。通过运用赫兹的弹性接触理论对单排球式回转支承内部的接触问题进行计算,推导出了该类型回转支承承载能力的理论计算公式,进而分析了回转支承的结构及工艺参数对其承载能力的影响,并给出了提高回转支承承载能力的方法,以供工艺人员参考。     

The effect on load-carrying capacity of the lubricating film and lubricant flow caused by radial motion of the journal in a bearing

This paper is a continuation of previous work and deals with the calculation of Sommerfeld's number and lubricant flow from a radial bearing with radial motion of the journal. Bearing discontinuities caused by a lubrication hole and axial grooves have been considered. The results can be applied to the computer calculation of journal motion and increase of temperature in a dynamically loaded bearing.     

Numerical analysis of unstable turbulent flows in a centrifugal pump impeller considering the curvature and rotation effect

Journal of Mechanical Science and Technology - In this study, a modified partially averaged Navier-Stokes model (MSST PANS) is proposed by treating a modified shear stress transport (SST) k-ω...