Elastohydrodynamic analysis of a cylindrical journal bearing with a flexible bearing shell

The effect of the elastic deformation of a bearing shell was considered in the determination of the performance characteristics of a hydrodynamic journal bearing. The finite element method with an iteration scheme was employed to solve the Reynolds equation governing flow in the clearance space and the three-dimensional linear elasticity equations representing the displacement vector field in the bearing shell. For design convenience a nondimensional deformation coefficient ψ relating μ, E_m, U₀ , C, R_j and tis defined. The performance characteristics were obtained in terms of load-carrying capacity, fluid flow, power loss and attitude angle for an aspect ratio $\text{L}\text{D = 1}$, eccentricity ? = 0.6 and for a wide range of deformation coefficients. The results are compared for bearing materials having Poisson's ratio v equal to 0.3 and 0.4.     

Elastohydrodynamic effects in elliptical bearings

In this paper the effect of bearing deformation on the static and dynamic performance characteristics of an elliptical bearing is presented. The finite element method has been used to solve the three-dimensional Navier-Stokes and the continuity equations governing the lubricant flow in the clearance space of the journal bearing and the three-dimensional elasticity equations governing the displacement field in the bearing shell. The static and dynamic performance characteristics are presented at various eccentricities for a wide range of deformation coefficient values which take into account the flexibility of the bearing liner.     

An empirical equation including fracture toughness and describing friction of dental restorative materials

An equation was developed from studies of single-pass wear and fracture toughness of filled and unfilled dental restorative resins and dental amalgams relating the sliding frictional force F to the normal load N, fracture toughness, modulus of elasticity, yield strength and slider diameter. This equation was of the same form as that reported for viscoelastic materials (F = KNⁿ). Friction was caused primarily by ploughing or deformation of the material under the conditions tested.     

A study of elastohydrodynamic effects in a three-lobe journal bearing

The effect of flexibility of bearing liner on the static and dynamic performance characteristics of a three-lobe journal bearing was studied. The three-dimensional Navier-Stokes and the continuity equations governing the lubricant flow in the clearance space of the journal bearing, and the three-dimensional e elasticity equations governing the displacement field in the bearing liner, were solved by using the finite element method and an iteration scheme. The static and dynamic performance characteristics were calculated at various eccentricities for a wide range of values of deformation coefficients which take into account the flexibility of the bearing liner.     

Series expansions for the dimensionless load capacity per unit width of a plane infinite slider bearing

Two series expansions are given for W_∞, the dimensionless load capacity per unit width of an infinite plane slider bearing. One series, which is new, is valid for all inclinations of the bearing pad, whereas the other diverges for an inclination parameter greater than unity. Either series can be used to calculate accurate values of W_∞ at low bearing pad inclination. The new series provides an accurate method for calculating W_∞ for use in the calculation of the dimensionless load capacity per unit width of a plane finite slider bearing either in single precision on a computer or by means of a programmable desktop calculator     

Static and dynamic analysis of elastohydrodynamic elliptical journal bearing with micropolar lubricant

In this paper the effect of deformation of the bearing liner on the static and dynamic performance characteristics of an elliptical (two-lobe) journal bearing operating with micropolar lubricant is presented. Lubricating oil containing additives and contaminants is modeled as micropolar fluid. A generalized form of Reynold's equation is derived from the fluid flow and diffusion equations. Finite element technique is used to solve the modified Reynold's equation governing the flow of micropolar lubricant in the clearance space of the journal bearing and the three-dimensional elasticity equations governing the displacement field in the bearing shell. The static and dynamic characteristics of the bearing are computed for a wide range of deformation coefficient which takes into accountant the flexibility of bearing liner by treating operating lubricant as (i) Newtonian and (ii) micropolar. The computed results show that the increasing volume concentration of additives and mass transfer of additives produce significant changes on the performance characteristics.     

Thermoelastohydrodynamic analysis of the static performance of tilting-pad journal bearings with the Newton–Raphson method

Thermoelastohydrodynamic lubrication (TEHD) analysis is presented to investigate the static performance of tilting-pad journal bearings. A completely numerical solution is obtained. The Newton–Raphson method is employed to predict the bearing characteristics of the hydrodynamic pressure, the eccentricity and the pad attitude angles simultaneously. For the temperature calculation, three-dimensional (3D) energy equations for the fluid under each pad and 3D heat transfer equations for the pads are solved using a sequential sweeping method. The elastic deformation and thermal expansion of each pad are calculated with the 20-node isoparametric finite element method. It is found that the Newton–Raphson method is a smart and efficient method. The results show that the elastic deformation due to the hydrodynamic pressure and the influence of the temperature elevation play an important role in the calculated bearing system.     

径向可倾瓦轴承的热弹流润滑分析

用Newton-Raphson法一次性求出了所有瓦块的压力分布和轴心的位置,用步进扫描法对轴承进行了三维温度场分析,用20节点有限元法构造了瓦块的压力变形矩阵和热变形矩阵。     

考虑稀薄气体有效黏度的微轴承弹流润滑研究

气体稀薄效应和轴瓦弹性变形对微流体设备中气体微型轴承润滑特性影响显著.根据Veijola提出的稀薄气体有效黏度模型,采用有限元法建立柔度矩阵计算轴瓦表面弹性变形量,并推导考虑有效黏度与弹性变形影响的修正Reynolds方程.通过联立求解超薄气膜润滑修正Reynolds方程、稀薄气体有效黏度方程和三维轴瓦弹性方程,分析轴...     

基于Timoshenko梁单元的径向波箔轴承箔片变形分析

为实现对径向波箔轴承箔片变形的更准确分析,基于Timoshenko梁单元建立箔片变形模型,在考虑库仑摩擦效应影响的基础上,计算不同载荷下箔片模型的变形,并与文献中的Heshmat公式、Iordanoff公式以及NDOF模型的计算结果进行对比,验证Timoshenko梁模型计算的准确性;改变摩擦系数的大小计算不同情况下的...     

Thermoelastohydrodynamic Analysis of Fixed Geometry Thrust Bearings Including Runner Deformation

A thermoelastohydrodynamic theory for the analysis of sector thrust bearings is presented. The analysis includes the generalized Reynolds equation and a fully elliptic three-dimensional energy equation in the film. In addition, full three-dimensional heat transfer is allowed in the pad while axisymmetric conduction is allowed in the runner. Three-dimensional elastic deformation due to mechanical and thermal loading is allowed in the pad while axisymmetric mechanical elasticity is allowed in the runner. The performance of a parallel tapered-land thrust bearing including runner deformation effects is analyzed as a function of different models. It is seen that mechanical deformation of the pad affects the operating characteristics only slightly while thermal deformation of the pad can cause large increases in operating temperature. The runner deformation effects can include a reduction of the maximum film temperature at slight deformation or a large increase in film temperature at the inner radius of the pad at larger deformations.     

Theoretical investigations on the performance of an externally adjustable fluid-film bearing including misalignment and turbulence effects

An externally adjustable fluid-film bearing has been devised whereby the hydrodynamic conditions can be changed as required in a continuously controlled manner. Principal feature of the externally adjustable pad bearing is the facility to control the bearing clearance and film thickness gradient in circumferential direction, irrespective of the operating conditions. Unlike a tilting pad bearing, this bearing can have both radial and tilt adjustments. A single pad externally adjustable pad bearing will perform as a conventional partial arc bearing when the adjustments are set to zero.The paper deals with the effect of turbulence and misalignment on steady state characteristics of a centrally loaded 120° single pad externally adjustable bearing. The bearing has an aspect ratio of one and operates over a wide range of eccentricity ratios with adjustments and degrees of misalignment. Reynolds equation incorporated with linearized turbulent lubrication model of Ng and Pan is solved using a finite difference method. Static performance characteristics calculated are presented in terms of attitude angle, Sommerfeld number, friction variable, misalignment moment and oil flow. A study with various adjustments predicts that negative radial and negative tilt adjustment configuration results in superior static characteristics as compared to a conventional fluid-film bearing.     

Influence of pad–pivot friction on tilting pad journal bearing

Some experimental studies reported that the performance of tilting pad journal bearing is related with the pad–pivot friction. Only a few researches, however, consider the friction as a factor even though many ones have theoretically analyzed the performance of bearing. Also, there is no mathematical model for the friction to explain the effect of friction on the performance of bearing. Therefore, this study proposes a mathematical model for the pad–pivot friction and analyzes the effect of friction on the tilting pad journal bearing.The results of this analysis show that the friction has a large influence on the attitude angle of the journal. It is found that the eccentricity direction of the journal does not coincide with the load direction when the friction is not zero. According to working conditions, the attitude angle can be up to 25° when friction coefficient is equal to 0.5. It is also found that the tilt angle of the pad is not determined as a fixed value in case of the bearing with non-zero friction, even though working conditions is given for the static analysis. This study represents four different tilt angles under same working conditions.     

Experimental and theoretical evaluation of friction at contacting magnetic storage slider–disk interfaces

To understand better the friction force and wear processes at contacting slider–disk interfaces, we have developed an experimental method for measuring and a theoretical method for calculating the friction force. For this study, a slider with a 1500 μm² contact pad located at the recording head is burnished against a relatively rough disk (～12 Å rms), which ensures smooth sliding. In the experimental method, the friction force is measured as the disk is spun-down to bring the slider–disk interface into an increasing degree of contact. A modified air bearing code is used to determine the experimental normal contact force for each friction measurement. In the theoretical method, the friction force and other relevant interfacial forces are calculated using an improved sub-boundary lubrication (ISBL) rough surface model. The friction force calculation in this model is based on the force needed to induce yielding of the individual disk asperities contacting the flat surface of the contact pad without any assumption of the coefficient of friction. Good agreement is found between the measured and theoretical friction vs. normal contact force curves, indicating that the model is capturing the essential origins of friction at this interface. The model also provides valuable insights into how wear particles may be generated at this contacting slider–disk interface.     

刚性和弹性支撑可倾瓦推力轴承稳态特性分析

建立刚性球头支撑和弹性橡胶垫支撑可倾瓦推力轴承热弹流耦合模型；在弹性橡胶垫支撑可倾瓦推力轴承橡胶垫的弹性变形分析中采用了变形协调矩阵方法，以协调匹配橡胶垫变形和水膜厚度分布，同时在搜索稳态解的过程中引入模拟退火算法；基于变分原理求解Reynolds方程，得到了轴承水膜压力分布，并比较2种推力轴承在转子存在角不对中时的静特性。结果表明：理想工况下，刚、弹支可倾瓦推力轴承稳态特性没有明显区别；当转子存在不对中时，刚性球头支撑可倾瓦轴承在不同瓦块之间受力偏载严重，进而导致瓦面最小水膜厚度过小，瓦块容易出现磨损，而弹性支撑瓦不同瓦块之间水膜力分布更均匀，利于轴承的长期可靠运行。     

对具有可倾瓦块和固定瓦块的混合型径向滑动轴承性能分析

本分析计算了顶部瓦块固定的可倾瓦径向滑动轴承（简称混合型轴承）的性能参数,与相同尺寸的可倾瓦径向滑动轴承相比,该种混合型轴承在承载能力,流量,摩擦功耗,平均温升等方面都发生了变化,具有明显的特点,最后的验测试验证了本所采用的分析计算方法是可行的。     

On the effect of shear coefficients in free vibration analysis of curved beams

We did a comparative study of shear coefficients in free vibration analysis of curved beams having circular and rectangular crosssections. Until recently, the shear coefficient k in Timoshenko beam theory has been studied by many researchers to include transverse shear deformation effect. To obtain more reliable numerical results, a higher-order hybrid-mixed curved beam element is formulated and programmed in MATLAB. The present numerical experiments show that k = 6(1 + v)² / (7 + 12v + 4v ²) is the best expression both for circular and rectangular cross-sections in the flexural vibration of curved beams.     

Step slider bearing with viscoelastic lubricant

The performance of an idealized step slider bearing with a viscoelastic lubricant is investigated theoretically. The elasticity of the lubricant is characterized by a dimensionless number α. The effects of the elasticity of the lubricant on the pressure, load-bearing capacity, frictional resistance, coefficient of friction and maximum film thickness were studied in detail and are presented in several graphs and tables.     

Elastohydrodynamic studies of circular journal bearings with non-Newtonian lubricants

A computer-aided study is presented for the static and dynamic performance characteristics of a hydrodynamic journal bearing with a non-Newtonian lubricant. The Navier-Stokes equations in cylindrical coordinates representing the flow field in the clearance space of a journal bearing using Newtonian fluids have been solved by finite element method using Galerkin's technique; the non-Newtonian effect is introduced by modifying the viscosity term for the model in each iteration. Deformation of the bearing shell is obtained by solving the three-dimensional elasticity equations. Using a suitable iterative solution procedure, the converged solutions for the lubricant flow and elastic deformation fields are obtained.     

Porous inclined stepped composite bearings with micropolar fluid

Abstract

This paper describes the theoretical analysis of the effect of micropolar fluid on the lubrication characteristics of porous inclined stepped composite bearing. The lubricant with additives in the film region and also in the porous region is modelled as Eringen's micropolar fluid, which is characterised by the presence of suspended rigid particles with microstructures. The generalised Reynolds type equation is derived for the most general porous bearing configuration (porous composite bearings) lubricated with micropolar fluid. The closed form expressions are obtained for the fluid film pressure, load carrying capacity, frictional force and coefficient of friction. These expressions can be utilised to obtain the performance characteristics of four different bearing systems, namely, porous plane inclined slider, porous composite tapered land bearing, porous stepped bearing and composite porous tapered concave bearing. It is observed that the micropolar fluid lubricants provide an increased load carrying capacity and decreased coefficient of friction as compared to the corresponding Newtonian case.