Infinite stiffness gas bearings for precision spindles

This paper presents the high stiffness gas bearings (HSB) having all the advantages of the externally pressurized gas bearings and stiffness much higher than the oil bearings. The load-displacement characteristics of the HSB show infinite stiffness at zero shaft displacements in a wide range of the loading forces. The grinding spindle equipped with the HSB has been realized, and some results of the investigations are given in this paper. The grinding results are typical for those obtained by good grinding spindles supported on ordinary gas bearings. The main advantage of the HSB grinding spindle is very short sparkling out time.     

小孔节流静压气体轴颈轴承主轴系统的动态特性分析

通过对小孔节流静压气体轴颈轴承的雷诺方程与描述主轴系统的动力学数学模型联立直接进行数值求解,分析了轴承系统的动力学特性,研究了在不平衡质量作用下轴承主轴系统的响应。结果表明,由于精密离心机小孔节流静压气体轴承的支承刚度大,承载能力高,旋转主轴的运动是稳定的。但在一定条件下,旋转主轴有可能出现不稳定现象,这取决于主轴绕固联坐标系各轴之转动惯量间的关系、轴承支承刚度、主轴旋转速度和不平衡质量控制等因素。该方法用于精密离心机静压气体轴承主轴系统动力学的数值计算,提高了计算精度和可靠性。     

空气静压轴系支承的数值分析

采用有限差分技术,对精密轴系中的径向和轴向空气静压轴承进行了数值分析。主要针对有多个供气孔的径向轴承的复杂流场,沿周向展开承载曲面以雷诺方程为气体润滑的控制方程。同时根据质量守恒原理,制定出每个供气孔出口压力边界条件逐轮修正的迭代路线,计算出不同偏心率和供气压力下的压力分布、承载能力及流量。该技术成功地用于轴系支承精确设计并制造出精密模块化主轴轴系。     

A study of slot-entry hydrostatic/hybrid journal bearing using the finite element method

A theoretical study concerning the static and dynamic performance of hydrostatic/hybrid journal bearing compensated by slot restrictor has been presented using the finite element method (FEM). Results have been presented for a double row symmetric as well as asymmetric configurations for different values of slot width ratios (SWR) and external load ( ). In order to have a better understanding of their performance vis-à-vis other non-recessed bearing configurations, the performance characteristics of slot-entry journal bearings have been compared with that of similar hole-entry compensated journal bearings using capillary, orifice and constant flow valve restrictors for the same bearing geometric and operating parameters. The comparative study indicates that asymmetric slot-entry journal bearings provide an improved stability threshold speed margin compared with asymmetric hole entry journal bearings compensated by capillary, orifice and constant flow valve restrictors.     

Transient response of a journal supported on elastic bearings

By considering the inherent flexibility of the bearing liner, the non-linear dynamic response of a journal bearing system is determined in this study. The transient analysis is presented and the journal centre motion trajectories are plotted for rigid and flexible bearings. Effects of the different parameters such as the eccentricity ratio, and the deformation coefficient etc on non-linear trajectories are reported in this paper. The transient response of the system is also obtained for different values of the normalized journal mass which shows that a rotating system supported in a flexible bearing may have a better performance under dynamic conditions than one supported in rigid bearings.     

Dynamic characteristics of spindle with water-lubricated hydrostatic bearings for ultra-precision machine tools

A key component of ultra-precision machine tools is the spindle. The motivation for this study was to improve machining accuracies in precision cutting and grinding by pursuing improvements in the spindle characteristics by designing a sophisticated spindle with water-lubricated hydrostatic bearings. The static bearing stiffness of the developed spindle was investigated in previous studies. In addition to the static bearing stiffness, the dynamic characteristics regarding bearing stiffness also affect significantly on the machining results. In this study, dynamic characteristics of the developed spindle with water-lubricated hydrostatic bearings were investigated via simulations and experiments. Not only bearing dynamics but also rotor dynamics were considered in this study.In the simulation studies, the spindle dynamic characteristics were analysed based on the transfer matrix method. A spindle rotor supported with hydrostatic bearings was represented by discrete sections of the rotor. The mathematical model of transverse linear vibrations of the spindle rotor was derived with distributed parameters for these discretized rotor sections. As a result of the analysis on the amplitude-frequency characteristic, radial displacements of the rotor due to bearing displacement and bending deformation were defined. Then, the frequency characteristics were represented with Nyquist plots. Resonant frequencies and amplitudes formation in the transverse vibration of the rotor were determined. The influence of rotor bending deformations on spindle compliance was assessed. Furthermore, the study examined the influences of the supply pressure of the lubricating fluid, radial clearance and journal diameter of the hydrostatic bearings on the amplitude of the rotor vibration, and the resonance frequency of the system.Furthermore, the dynamic characteristics of the spindle were examined experimentally. The simulation results were in good agreement with the actual spindle dynamics obtained experimentally. The influence of the structural parameters of the rotor and the operating parameters of the bearings on the spindle dynamic characteristics was also determined. It was verified that the amplitude of the vibration of the rotor overhang part was dominantly affected not by bearing stiffness but by bending stiffness of the bearing journal of the front bearing and the length of the rotor overhang.Then it was verified that the resultant displacement of the rotor in the radial direction due to the influence of the bearing characteristics and the structural effect of the rotor is significantly small. Practical recommendations to improve the spindle design in terms of the dynamic characteristics of the spindle with water-lubricated hydrostatic bearings were also derived.     

Robust rotor dynamics for high-speed air bearing spindles

For ultra-precision machining machine tool components need to operate outside critical frequencies of the machining system to avoid insufficient surface finish caused by vibrations. This particularly applies to tooling spindles as those are generally the component of a machine tool with low stiffness and damping values. Surface finish and shape of a machined part rely directly on the overall accuracy in motion of the tooling spindle over the entire machining parameter and speed range. Thus spindle designs for an operation outside critical frequencies combined with high stiffness and damping values are crucial for ultra-precision machining.For sufficient stiffness properties bearing gaps of gas bearings have to have a size of only a few microns and show a distinct sensitivity on temperature and for journal bearings also on speed. This again means that bearing properties change with temperature and speed. Considering a spindle system comprising a rigid shaft rotating in a radial/axial bearing system with changing stiffness and damping properties leads to a resonance speed map with changing rigid mode resonance speeds.This paper treats the influence of shaft speed and temperature on bearing gaps from which rigid mode resonance speeds for a shaft spinning in a bearing system are derived. The quoted influence of centrifugal load and temperature on bearing stiffness, damping and load capacity can be applied to any kind of gas bearing. Therefore the calculation of bearing stiffness, damping or load capacity is not treated in detail. The reader will be shown that there are simple design rules for air bearing systems and shafts of high-speed tooling spindles to avoid critical speeds through the entire speed range. Finally, methods of how to prove the initial design goals and how to verify dynamics of high-speed spindles in production will be presented to the reader. It will also be shown that there are production high-speed spindles available which do not include any critical speed within their speed range and thus show robust rotor dynamics with extremely low errors in motion.Procedures in design, validation and application treated in this paper shall give the reader not only design guidelines for spindles to avoid critical spindle speeds within its speed range, but also recommendations for machine tool builders and end-users for a machine operation taking machine and rotor dynamics into account. As the knowledge for this paper is predominantly based on the experience and work of the author himself only a few references are used. However presented testing results entirely confirm the approach presented in this paper.     

A Study of Non-Recessed Hybrid Flexible Journal Bearing With Different Restrictors

For bearings operating under heavy loads, the elastic deformation of bearing surface induced by fluid film pressures can no longer be neglected as it is comparable to the order of magnitude of fluid film thickness. In the present work a theoretical study describing comparative performance of non-recessed hybrid journal bearing using different flow control devices has been carried out by considering bearing shell flexibility into the analysis. The relevant governing equations have been solved using finite element method. The comparative performance of non-recessed hybrid journal bearings of two separate configurations have been studied for various values of bearing flexibility parameter (([Cbar]_d)). The results have been presented for hole-entry type journal bearings compensated by capillary, orifice and constant flow valve restrictors and for a slot-entry type journal bearing, for the same set of values of operating and geometric parameters. The computed results indicates that in order to get an improved performance of non-recessed journal bearing, a proper selection of bearing flexibility parameter (([Cbar]_d)) along with type of flow control device (i.e., capillary, orifice, constant flow valve, slot etc.) and type of bearing configuration (symmetric/asymmetric) are essential.     

Maximum oil film pressure and temperature of two‐iobe journal bearings with different bush profiles

This paper presents data on the maximum oil film pressure and temperature of two‐lobe journal bearings with different bore profiles. A bearing with a cylindrical non‐continuous bore profile, and another with a pericycloid continuous profile have been evaluated. For an assumed relative length of the bearings, and parallel orientation of the journal and bearing axes, the minimum values of oil film thickness, maximum pressure values, and temperatures of the oil film have been determined. The calculations were carried out on the assumption of an adiabatic oil film and a static equilibrium position of the journal.     

MEMs hydrodynamic bearings: Applications to and implications for machine failure prevention

Microdynamic systems have been studied for a number of years. Only limited work, however, has been completed on integrating microdynamic components into systems that satisfy mechanical tasks on macroscopic scales. In this paper, we describe microdynamic components needed to produce a surface which is actively deformable on local scales. In particular, we consider the design and demonstration of smart journal and thrust bearings capable of using embedded sensors and actuators to change dynamically the surface geometry. The ability actively to deform bearing surfaces allows for the design of bearings which are less prone to failure, the design of bearings with greater load-carrying abilities, and a fundamental study of the effect of surface geometries and fluid conditions on bearing performance, such as start-up and shut-down conditions. Some results of our new bearing designs are presented, focusing on numerical bearing models, sensor and actuator design and fabrication, and physical experimentation.     

Stiffness and damping coefficients for journal bearing using the 3D transient flow calculation

The dynamic coefficients of journal bearing are necessary components in the analysis of linear stability and response of rotating dynamic systems. We propose a new method for the numerical identification of bearing support force coefficients in flexible rotor-bearing systems based on the 3D transient flow calculation. The CFD commercial software FLUENT is mainly used in this simulation, which employs a finite volume method for the discretization of the Navier-Stokes equations. To determine the dynamic coefficients, a new mesh movement approach is presented to update the volume mesh when the journal moves during the 3D transient flow calculation of a journal bearing. Existing dynamic mesh models provided by FLUENT are not suitable for the transient oil flow in journal bearings. Measurements and identification are performed on a test rotor supported on a pair of identical two-lobe fluid film bearings, and the results obtained from the CFD methods agree well with experimental results. The results indicate that the methods proposed in this paper can predict the dynamic coefficients of the journal bearing in a rotor-bearing system effectively, and provide a further tool for stability analysis.     

Effects of design parameters on the noise of rotor-bearing systems

The purpose of the present paper is to investigate the effects of design parameters on the noise produced by rotor-bearing systems supported by oil lubricated journal bearings. To do this, the effects of radial clearance and the width of the bearing, lubricant viscosity, and mass eccentricity of the rotor on the noise of the bearing are investigated, and the numerical results are presented through the graph of the A-weighted sound pressure level of the bearing for various rotational speeds of the rotor. The results show that the A-weighted sound pressure level of the bearing is markedly influenced by the mass eccentricity of the rotor and the radial clearance and the width of the bearing. High viscosity of the lubricant slightly decreases the noise of the bearing, but its effect is relatively low at high speed. The results of the paper could aid in the design of low-noise rotor-bearing systems supported by oil lubricated journal bearings.     

The Performance of Externally Pressurized Bearings Using Simple Orifice Restrictors

The load capacity and vibration characteristics of externally pressurized thrust and journal bearings have been investigated. The bearings used orifices sufficiently recessed back from the bearing surface to ensure that the area of the orifice is the minimum presented to the gas flow. The journal bearings consist of plain cylinders with one or two rows of eight orifices, and the thrust plates of plain discs with six orifices drilled in equispaced circumferential grooves.

The load capacity of the thrust plates agrees with that calculated but the vibrations are greater than predicted. The load capacity of journal bearings is about half that calculated assuming axial flow conditions in the bearing, but circumferential flow can account for the difference. Synchronous and half-speed vibrations of a shaft rotating within these bearings have been measured and found to agree with those calculated on the assumption that the gas films behave as linear springs.     

EMP径向滑动轴承热弹变形对润滑特性的影响

ＥＭＰ径向滑动轴承特殊的轴瓦材料特性使得其热弹变形对轴承的润滑特性,如油膜的最小间隙、油膜压力和温度分布影响较大。为此本文建立了完整的热弹变形模型,采用有限差分的方法,通过在不同载荷的情况下,对ＥＭＰ径向滑动轴承在计入和未计入热弹复合变形的两种情形进行对比,从而揭示了热弹变形影响轴承工作性能参数的内在规律。     

支点弹性、阻尼可倾瓦轴承动力特性数值仿真及试验研究

依据考虑瓦块摆动和沿几何预载荷方向微幅振动的可倾瓦轴承完全动力特性的解析模型及其对应的八参数简化动力模型,设计制备了支点弹性、阻尼特性可倾瓦轴承。该轴承通过在瓦块支点与轴承体之间设置弹性垫片,使瓦块支点支撑在弹性垫片上,弹性垫片与轴承体之间存在微小间隙并与轴颈润滑系统共享油路以实现局部挤压油膜效应。根据不同加工工艺,制备了两种形式的新型支点弹性、阻尼轴承,并通过理论计算模拟与试验分析对两种新型轴承的动力特性进行研究。结果表明,支点弹性、阻尼可倾瓦轴承能够增大转子的一临界阻尼,有效提高转子系统稳定性。     

Controllable high speed journal bearings, lubricated with electro-rheological fluids. An analytical and experimental approach

The problem of journal bearings control is of great importance in mechanical engineering. A very recent method for doing this is the creation of ‘smart' journal bearings using electro-rheological (ER) fluids. If such a fluid is used to lubricate a journal bearing system, it is expected that the imposition of an electric field between the rotor and the stator will cause an alteration in the dynamic properties of the journal bearing. In this paper an experiment in a high speed journal bearing (16 000 to 35 000 s⁻¹), with small radial clearance is presented. The alternation of the attitude locus (eccentricity and attitude angle) and the stiffness coefficients in a loaded journal bearing lubricated with ER fluid is investigated and presented. The Reynolds equation is solved using the finite element method in order to get the dynamic characteristics of the ER bearings vs the electric field and to simulate its dynamic behavior. The Bingham plastic model of non-Newtonian fluid flow behavior is used to described the ER lubricant. The accuracy of the algorithm is obtained by comparing the results published by previous investigators and the experimental data described in this paper. It is concluded that ER fluids can be used to create ‘smart' journal bearings. and vibration controllers can be constructed to control the dynamics and stability of the ER fluid lubricated bearings.     

Variations of instability in a rotating spindle system with various bearings

To drive the speed of spindle faster and faster, especially for micro-via-drilling, the gas bearing–spindle is a must. However, most investigations of the dynamic characteristics of the spindle system are limited to the ball bearing type of spindle. This work examines the dynamic instability of a rotating spindle system with various bearings to elucidate the difference between the ball and gas bearing–spindle systems. A round Euler–Bernoulli beam is used to approximate the spindle. The Hamilton principle is applied to derive the equation of motion for the spindle system, and the multiple scales perturbation method is employed to solve the instability solution of the system. The effects of bearing types and speeds of rotation on the dynamic characteristics and instability of a rotating spindle system are further studied.     

Approximate Solution of Oil Film Load-carrying Capacity of Turbulent Journal Bearing with Couple Stress Flow

The instability of the rotor dynamic system supported by oil journal bearing is encountered frequently, such as the half-speed whirl of the rotor, which is caused by oil film lubricant with nonlinearity. Currently, more attention is paid to the physical characteristics of oil film due to an oil-lubricated journal bearing being the important supporting component of the bearing-rotor systems and its nonlinear nature. In order to analyze the lubrication characteristics of journal bearings efficiently and save computational efforts, an approximate solution of nonlinear oil film forces of a finite length turbulent journal bearing with couple stress flow is proposed based on Sommerfeld and Ocvirk numbers. Reynolds equation in lubrication of a finite length turbulent journal bearing is solved based on multi-parametric principle. Load-carrying capacity of nonlinear oil film is obtained, and the results obtained by different methods are compared. The validation of the proposed method is verified, meanwhile, the relationships of load-carrying capacity versus eccentricity ratio and width-to-diameter ratio under turbulent and couple stress working conditions are analyzed. The numerical results show that both couple stress flow and eccentricity ratio have obvious influence on oil film pressure distribution, and the proposed method approximates the load-carrying capacity of turbulent journal bearings efficiently with various width-to-diameter ratios. This research proposes an approximate solution of oil film load-carrying capacity of turbulent journal bearings with different width-to-diameter ratios, which are suitable for high eccentricity ratios and heavy loads.     

A study of electrical pitting of journal bearings with water‐contaminated lubricant

The investigations reported in this paper concern the effect of the use of a degraded lubricant on bearing life. A diagnosis of the premature failure of the hydrodynamic journal bearings of a synchronous condenser has been carried out. The surface of the failed bearings has been examined and the cause of the failure investigated. A theoretical analysis has also been undertaken to calculate the number of cycles that take place before failure occurs. The number of cycles thus established matched that of the cycles/duration of operation before the premature failure of the bearings. The process leading to the premature failure and the role of the degraded lubricant have been identified. Remedial measures have been successfully implemented to reuse the existing bearings. Measures have been suggested to avoid repeated failures. The theoretical analysis has the potential to ascertain the shaft voltage once the severity of the physical damage on the liner surface of the bearing and the duration of its operation have been established.