动静压气体轴承的结构参数设计

针对人字槽狭缝节流动静压气体轴承的结构参数对轴承静态特性的影响，采用四因素三水平的正交试验法，以人字槽深度hg、人字槽宽度b、狭缝宽度z以及狭缝深度H为4种因素，以4种参数的3个不同取值为3种水平，组合成正交表。采用Solidworks软件、ICEM 软件以及Fluent软件对正交表中的各种组合的人字槽狭缝节流动静压气体轴承分别进行三维建模，网格划分以及仿真求解。根据仿真结果，利用灰色关联分析法分析与轴承静承载力、静刚度的关系最密切的轴承参数组合，及各个轴承参数对轴承的静承载力以及静刚度的影响程度，为动静压气体轴承的结构参数设计提供理论基础。     

Thermo-hydrodynamic analysis of herringbone grooved journal bearings

Steady-state and stability characteristics of herringbone grooved journal bearings (HGJBs) are found considering thermal effect. The temperature of the fluid film rises significantly due to the frictional heat, thereby the viscosity of the fluid and the load carrying capacity decrease. A thermodynamic analysis requires the simultaneous solution of Reynolds equation along with energy equation of the fluid and heat conduction equations in the bush and the shaft. The linearized first-order perturbation technique is employed for the prediction of stiffness and damping coefficients of the oil film. Thereafter mass parameter and whirl ratio are found from the stability analysis. It is difficult to obtain the solution due to the numerical instability when the bearing is operated at high eccentricity ratios.     

湍流润滑动静压气体径向滑动轴承性能研究

以动静压气体径向滑动轴承为研究对象,考虑湍流润滑,基于有限差分方法求解引入湍流因子改良的可压缩雷诺润滑方程,计算湍流润滑动静压气体径向滑动轴承的压力分布,获得轴承承载力、静态刚度、交叉刚度、主刚度、交叉阻尼和主阻尼等表征动静压轴承静动态特性的基本参数,并分析偏心率、槽深、槽数、长径比等结构参数及轴颈转速和供气压力等工况对轴承静动态性能的影响规律。结果表明：连续性狭缝湍流润滑动静压气体径向滑动轴承的静态特性优于非连续性狭缝;轴承承载力随着偏心率、长期径比的增大而增大,随着槽区长度、槽深的增大而减小,槽数对承载力影响不大;轴承静态刚度随着偏心率的增大先增大后减小,随着长径比、槽深、槽数的增大而增大,随着槽区长度的增大而减小;较大的转速和供气压力有助于提升轴承的承载力和静态刚度;随着偏心率的增大,交叉刚度逐渐增大,主刚度先增大而减小,而交叉阻尼和主阻尼均增大。     

Rolling element bearings absolute life prediction using modal analysis

In this paper, the authors introduce an experimental procedure for predicting the fatigue life of each individual rolling element bearing separately using vibration modal analysis. The experimental procedure was developed based on a statistical analysis. A statistical analysis was performed to find an empirical model that correlates the dynamic load capacity of rolling bearings to their dynamic characteristics (Natural frequencies and damping). These dynamic characteristics are obtained from the frequency response function of each individual bearing that results from vibration modal analysis. A modified formula to the already known Lundberg-Palmgren life formula is proposed for rolling element bearings. Given the modified formula, one can predict the fatigue life of each individual rolling element bearing based on its dynamic characteristics. The paper compares the results from the modified formula with those from Lundberg-Palmgren formula. The modified formula provides an accurate prediction for the fatigue life of each individual bearing based on its dynamic characteristics. The experimental validation of the modified formula is considered for future work. Therefore, it can be used in various applications of rolling element bearings in machinery systems.     

Stability of multilobe hybrid bearing with short sills—part II

A small amplitude perturbation analysis has been carried out to determine the rotordynamic characteristics of multilobe hybrid bearings with short axial and circumferential sills. Unsteady state recess flow continuity equation has been written for orifice compensated bearing in terms of dynamic recess pressures by perturbing steady state flow equation. Dynamic recess pressures are evaluated by solving unsteady recess flow continuity equations to determine the dynamic load capacity of the bearing. Stiffness and damping coefficients of the bearing are determined from the dynamic load capacity of the bearing. Results of dynamic characteristics of three lobe and four lobe hybrid bearings are presented for various offset factors, speed, concentric pressure and eccentricity ratios. Multilobe hybrid bearings with offset factors more than one are found to exhibit better dynamic behaviour than circular hybrid bearings.     

Theoretical and experimental investigations of a variable- impedance hydrodynamic bearing

The aim of the work described in this paper is to develop a hydrodynamic bearing whose oil film dynamic stiffness and damping coefficients could be tuned to take on low values, without upsetting the bearing steady load carrying capacity, in order to obtain an improved dynamic response for machines running in such bearings. It was required that this tuning of the bearing dynamic characteristics could be carried out after assembly of the machine in question, and if necessary while the machine was in operation.A theoretical analysis of the new design of bearing was carried out, based on a finite-difference model of the bearing oil film. This analysis enabled the steady-state load carrying capacity of the bearing to be calculated for any particular running conditions. The oil film stiffness and damping characteristics were then calculated using the finite-displacement technique; these were then used to calculate the unbalance response of a flexible rotor running in such bearings. Experimental measurements of the unbalance response of a model rotor running in the new bearing design were also recorded, and compared with similar measurements obtained when conventional bearings were used.Both theoretical and experimental results show that the proposed new bearing design has a similar steady load carrying capacity to that of conventional hydrodynamic bearings, but that the unbalanced response and force transmissibility of machines running in the new design of bearing are substantially superior to that obtained with conventional bearings.     

基于匀压和阻尼的空气静压轴承静态特性研究*

针对常规空气静压轴承设计时存在的承载能力、刚度与气动锤之间的矛盾,提出一种基于虚拟均压和被动阻尼设计方法。采用该方法设计一种含环布均压槽和阵列阻尼孔的矩形平面空气静压止推轴承,并研究其静态特性。研究结果表明：与常规空气静压轴承结构相比,设计的空气静压止推轴承在供气压力0.5 MPa下的最高承载力提高了43.4%,最高刚度提高了51.3%;减小阻尼孔数量、减小节流孔径、提高供气压力和增设均压槽可获得最佳刚度特性;增加阻尼孔数量、减小节流孔径、提高供气压力和增设均压槽可获得最佳静态特性和动态稳定特性的综合性能。     

Stability of Rotors Under the Combined Influence of Fluid Film Bearing Characteristics and Shaft Material Damping

Fluid film characteristics and shaft material damping form an interesting combination in rotor dynamic applications. Under certain conditions, a rotor which is unstable due to the damping, can be stabilized with the proper choice of fluid film bearings as supports. On the other hand, increasing the material damping in the rotor shaft can attenuate stress fluctuations in the rotors supported by fluid film bearings. The influence of the above combination on the stability of rotor bearing systems is investigated using a Jeff cot rotor with significant material damping and supported by fluid film bearings in the rotor dynamic model. The results indicate that under certain conditions, the interaction of the above two factors can be gainfully utilized in the design of rotor bearing systems.     

The design of partially grooved externally pressurized bearings

Most hydrostatic and aerostatic bearings are designed using external restrictors in order to obtain sufficient bearing stiffness. Alternatives such as the shallow pocket or partially grooved externally pressurized bearing are seldom applied, in spite of their advantageous constructive simplicity. In this article a simple analytical model to analyze journal bearings with partially grooved surfaces is described. The results of the analytical model are compared to the results obtained by numerical analysis. Both incompressible and compressible fluids are considered. The formulas derived are of extreme simplicity and helpful in finding the groove dimensions for optimal load capability and calculating approximate bearing characteristics using a simple calculator.     

Dynamic characteristics of a flexible rotor system supported by a viscoelastic foil bearing (VEFB)

Foil bearings have been considered as an alternative to traditional bearings with the increasing need for high-speed, high-temperature turbomachinery. However, the lack of adequate load capacity and sufficient damping capacity is a key technical hurdle to super-bending-critical operation as well as widespread use of foil bearings in turbomachinery such as turbopumps, turbocompressors and turbochargers. A new foil bearing, ViscoElastic Foil Bearing (VEFB) is suggested in this paper. The super-bending-critical operation of the conventional bump foil bearing and the VEFB is examined, as well as the structural dynamic characteristics. The structural dynamic test results show that the equivalent viscous damping of the VEFB is much larger than that of the bump bearing and that the structural dynamic stiffness of the VEFB is comparable or larger than that of the bump bearing. The results of super-bending-critical operation of the VEFB indicate that the enhanced structural damping of the viscoelastic foil dramatically reduces the vibration near the bending critical speed. With the help of increased damping resulting from the viscoelasticity, suppression of the nonsynchronous orbit is possible beyond the bending critical speed.     

The Static and Dynamic Characteristics of a Two-Lobe Journal Bearing Lubricated with Couple-Stress Fluid

Static and dynamic characteristics of two-lobe journal bearings lubricated with couple-stress fluids are studied. The load-carrying capacity, the stiffness and damping coefficients, the non-dimensional critical mass, and the whirl ratio are determined for various values of the couple stress parameter l. The results obtained are compared with the characteristics of two-lobe bearings lubricated with Newtonian fluids. It is found that the effect of the couple stress parameter is very significant on the performance of the journal bearing. The stability is improved compared to bearings lubricated with Newtonian fluids.     

微极流体对错位轴承的润滑性能研究

错位轴承比普通径向轴承表现出了更好的性能,因此对错位轴承的静态性能和动态性能的研究具有重要意义。推导了微极性润滑时错位圆和错位椭圆轴承的动静特性方程,采用有限差分法计算微极错位圆和错位椭圆的静特性,同时采用偏导数法计算其动特性,研究耦合数和特征长度对轴承性能的影响。结果表明：随耦合数增大,错位圆和错位椭圆轴承承载力和摩擦力增大、摩擦因数减小、刚度系数和阻尼系数绝对值增大,轴承稳定性提高;随特征长度增大,错位圆和错位椭圆轴承承载能力和摩擦力减小、摩擦因数先减小再增大、刚度系数和阻尼系数绝对值减小,轴承稳定性降低;相比于牛顿流体,微极流体的承载力更大,摩擦因数更小;微极流体会加大轴承的阻尼系数和刚度系数的绝对值,并且会提高轴承的稳定性;与错位圆轴承相比,错位椭圆轴承承载力大、摩擦力大但是摩擦因数小、稳定性更好。     

Computation model of composite cylindrical bearing working in steady-state regime for partial filling of gap with lubricant material

In [1–10], devoted to theoretical analysis of finite-length porous bearings working in non-steady-state regime, it is assumed that the gap is completely filled with lubricant material. In addition, bearing structures considered in this work possessing damping properties have low bearing capacity. Therefore it is necessary to make bearing structures so that the bearings have both damping properties and higher bearing capacity. Existing computational models of composite bearings [10] assume complete filling of the gap with lubricant material. Two cases of supplying lubricant material (axial and radial) are considered in turn. This work presents a solution to the problem of partial filling of lubricant material without allowance for its supply.     

Experimental Investigation of Friction and Electrical Characteristics of the Porous Bearings with Axial Grooves for Laser Scanner

The electrical and frictional properties of axially grooved oil-impregnated sintered-metal bearing (porous metal bearing) with varying loads and speeds were measured. The results were compared with the performance of bearings without grooves and conventionally used ball bearings. The test results showed that the frictional values of the porous bearings were lower than those of ungrooved bearings and ball bearings, and that the porous bearings operated in a full-hydrodynamic lubrication regime. The values of rating current, starting time and jitter revealed that the grooved-bearing had better electrical characteristics than the ungrooved bearing as well as the ball bearing. From the endurance tests on start-stop and continuous operating, it was confirmed that this bearing could be mass-produced for use in a laser scanner unit.     

Stability Analysis of Floating Ball Bearing

Conventional disk drive motors supported on ball bearings (BBs) cause nonrepeatable runout (NRRO) due to the surface imperfections on balls and raceways. NRRO is a source of track misregistration between head and disk that inhibits high track density in a hard disk drive. Fluid dynamic bearings with herringbone grooves either on the rotating or stationary surfaces are a suitable replacement for conventional ball bearings. Herringbone grooved bearings have considerably lower noise level than ball bearings and have better stability compared to plain journal bearings at concentric operating position. However, herringbone-grooved patterns are difficult to manufacture because groove depth is of the order of bearing clearance. The major limitation of the BBs is the direct contact between the rotating and stationary parts and also lack of damping effects. This present work attempts to overcome these drawbacks in BBs by eliminating the metal-to-metal contact using a layer of fluid film, and a theoretical analysis of stability characteristics of a floating BB is presented. Results indicate that there is an improvement in the stability of floating BB rotor systems with increase in outer to inner film clearance ratio (β) from 0.7 to 1.3, and with decrease in ratio of outer race radius to inner race radius (δ) from 3.0 to 1.2.     

Relative comparison of stiffness and damping properties of double decker high precision and conventional rolling-element bearings

This paper reports the relative comparison of stiffness and damping properties of Double Decker High Precision Bearing (DDHPB) and conventional rolling-element bearings. It has been determined that under different load and speed conditions, DDHPB and the conventional bearings have identical critical speed, comparable net deflection and stiffness. On the contrary, relative damping of the DDHPB, evaluated by rotating speed component of vibrations, at different operating conditions is approximately three times more than that of the conventional bearing. Excitation tests at different speeds have also indicated better damping characteristics of DDHPB as compared to the conventional bearing. This potential of DDHPB permits its use in typical industrial applications where damping is a significant requirement.     

Design of annular recess hydrostatic thrust bearing under dynamic loading

Design charts are presented of a dynamically loaded thrust bearing with as annular recess. The effect of non-parallelism between the bearing and the runner surfaces is also considered, since this is a common problem in hydrostatic thrust bearings. Based on pre-assigned dynamic excitations the pressure equation is solved numerically by finite difference methods to render the bearing performance characteristics namely: load capacity; bearing stiffness; damping coefficient; and lubricant flow rate. Results concluded that the bearing performance chareacteristics are dependent on the bearing radii ratios, the squeeze number, the bearing number and the tilt parameter.     

Experimental Investigation of Thermal and Hydrodynamic Effects on Radially Grooved Thrust Washer Bearings

In this study, an experimental investigation on the effects of grooves on thrust washer bearings is investigated. Eight equally sized grooves are machined about 100 μ m deep into one side of a flat-faced steel washer. This thrust washer bearing is located between a helical gear and its carrier and is tested on a test rig capable of measuring frictional torque and the temperature of the bearing at different speeds. It is found that the grooved washers had lower bearing temperatures and failed at significantly higher loads than the control washer with no grooves. For a test procedure with varying operating conditions, the coefficient of friction is also significantly lower for the grooved washers. However, the grooved washers had about the same coefficient of friction as the control washers at each step when the speeds are very high. The results from various tests suggest that the increased amount of lubricant passing through the grooved surface of the washer removes heat from the washer bearing by convection. This decrease in stored heat conducted from friction deters thermoelastic instabilities and the reduction of hydrodynamic stiffness due to the decrease in viscosity. Enhanced hydrodynamic load-carrying capacity is also evident in the grooved washers test results.     

Effects of magnetic fields on the dynamic characteristics of wide parallel step slider bearings with electrically conducting fluids

By the use of electrically conducting fluids as lubricants together with the application of externally magnetic fields, the dynamic lubrication problems of parallel step slider bearings lubricated with a nonconducting fluid are extended in this paper. A closed‐form solution has been derived for the magneto‐hydrodynamic characteristics of wide parallel step slider bearings. Comparing with the bearing lubricated with nonconducting fluids, the magneto‐hydrodynamic parallel step slider bearings signify an improvement in the load capacity, as well as the dynamic stiffness and damping coefficients. A numerical example and calculated values are also provided in tables for engineers in bearing selection and designing. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic isolators for petroleum and gas platforms of the “Sakhalin-2” project

Friction pendulum bearings have universal properties satisfying various demands when supporting buildings, bridges, and industrial facilities. The oscillation period of the bearing, vertical carrying capacity, damping, displacement ability, and ability to receive tensile load can be chosen independently. Dynamic oscillation periods from 1 to 5 s, shifts of up to 1.5 m, high carrying capacity and damping can be provided. Bearings can endure vertical loads of up to 13 500 tons and have minimal construction costs. Data are given on the influence of earthquakes and other force effects on the thermal state and characteristics of frictional pendulum bearings used as seismic isolators on petroleum and gas platforms of the “Sakhalin-2” project.