Effect of Bearing Surroundings on the High-Speed Spindle-Bearing Compliance

This paper investigates the effect of bearing assembly tolerance on spindle-bearing compliance. In a high-speed spindle system, the bearing characteristics are influenced significantly by the initial assembly tolerances and the thermal deformation of the bearing surroundings. In the very early stage of spindle operation, spindle bearings could be under hazardous conditions owing to the rapid change of the internal pressure resulting from thermal deformation or centrifugal force-oriented deformation. The bearing’s internal clearance also may be changed by the operating conditions such as external load, rotational speed, and operating cycle time. To determine the initial tolerance and the optimal cooling regimen, a comprehensive dynamic modelling and analysis of a high-speed spindle system in terms of bearing pressure, bearing compliance, and heat generation is required with consideration of those effects. Moreover, in order to predict spindle characteristics in operation, all of these parameters should be monitored and recalculated in real-time. For this purpose, very simple and effective equations are suggested, representing the bearing stiffness in accordance with the thermal deformation. Most former bearing analyses were based on the Hertzian contact model, without considering the radial elastic defor-mation of the races. In this paper, analytical and experimental investigations of the bearing compliance are conducted with consideration of both the elastic deformation of the race and the thermal deformation of the housing in terms of the bearing stiffness. The experimental results show the effectiveness of the proposed equations, which are simple and useful for fast calculation of the bearing stiffness by dynamic simulation.     

螺旋槽气体轴承动态特性及失稳分析

针对高速动静压气体轴承气膜的复杂非线性动力学行为,以球面螺旋槽动静压气体轴承为研究对象,建立润滑分析数学模型;采用有限差分法与导数积分法进行求解,得到动态扰动压力分布及动态特性系数,并研究切向供气条件下螺旋槽参数、径向偏心率、供气压力、转速对气膜刚度阻尼系数的影响规律;建立线性稳定性计算模型,预测气膜涡动失稳转速,分析运行参数对失稳转速的影响。结果表明:气膜阻尼是一种抑制涡动的因素,气膜的稳定性取决于气膜刚度与阻尼的协同作用;气膜刚度阻尼随着槽宽比、槽深比、螺旋角的增大,整体上呈先增大后减小的趋势;刚度随转速的升高而增大,阻尼则随转速的升高而减小;径向偏心率和供气压力越大,气膜刚度和阻尼越大;在一定范围内,提高供气压力、增大径向偏心率能够提高系统失稳转速;合理地选取轴承结构参数和运行参数,能够优化轴承动态特性,保证气体轴承较高的运行稳定性。     

Dynamic characteristics of spiral groove bearing spindles: comparison between rotating‐shaft and fixed‐shaft designs

In this paper, two types of spiral groove bearing (SGB) spindles, a rotating‐shaft spindle and a fixed‐shaft spindle, are analysed, and the dynamic characteristics of these two types of spindles are tested and compared. The effects of lubricants on the dynamic characteristics and power consumption of the spindles are considered. It is found that the dynamic characteristics of the fixed‐shaft spindle are much better in terms of non‐repeatable run out than those of the rotating‐shaft spindle. The lubricants are found to have significant effects on both the dynamic characteristics and power consumption of the spindles. Copyright © 2006 John Wiley & Sons, Ltd.     

超高转速条件下主轴轴承内部油膜阻尼研究

在受力分析的基础上,利用弹性流体动力学润滑理论和多种网格法,计算超高转速条件下主轴轴承内部球滚动体与内、外滚道之间的润滑油膜厚度,以及轴承内部的润滑油膜阻尼。结果表明,超高转速条件下,转速增加,轴承内部弹流润滑油膜阻尼减小,这不利于减小转子系统的动态响应;径向预载荷增加,轴承内部弹流润滑油膜阻尼增加,有利于减小转子系统的动态响应。超高转速条件下,运行速度和径向预载荷对轴承内部润滑油膜阻尼的影响较大,在研究超高速电主轴轴承-转子系统动力学和动态响应时,应充分考虑油膜阻尼的影响。     

基于ROMAX的球轴承转子系统动态性能分析

滚动轴承转子系统在旋转机械系统中得到广泛应用,其动态性能对旋转机械有着重要的影响。基于Romax软件建立球轴承转子系统的动力学分析模型,通过算例分析了工况参数和结构参数对球轴承转子系统动态特性的影响规律,并通过实验结果验证了Romax对轴承性能预测的准确性。研究发现球轴承的接触角、内外圈沟曲率系数与安装位置对轴承的刚度、寿命与转子系统临界转速等动态性能有较大影响。工程中需要选择合适的结构与工况参数以满足转子系统的性能要求。     

Contour mapping of precision ball defects with laser Doppler vibrometry

Laser Doppler vibrometry is presented as an effective inspection technique for contour mapping of defects on precision roller bearing balls. Localized defects are characterized by measuring the Doppler shift of a laser beam incident on a rotating ball. Contour maps are obtained by scanning the ball at equally spaced azimuths with the laser beam as the ball rotates about a vertical axis. A technique for characterizing the repeatable runout of a ferrofluid spindle is discussed. Tests were performed on two different grades of ceramic ball bearings. With the experimental setup, a height resolution of 5.5 nm could be attained. Defects of 22 μm in width could be detected. Use of the contour mapping technique greatly enhances visualization of defects on ball bearing surfaces.     

Centrifugal force induced dynamics of a motorized high-speed spindle

Trend of the high-speed and high efficiency machining has pushed the continuous demand of higher spindle speed and power for the machining center application. Because the extremely high speed produces significant centrifugal force, it creates a need to predict the spindle dynamical characteristics at dynamic states. This work presents analysis results of the spindle dynamic of a motorized high speed spindle with angular ball contact bearings. For a machining center, two major subsystems determining the overall spindle stiffness are the shaft/bearing subsystem and the draw bar mechanism subsystem. Shaft/bearing stiffness as well as the natural frequency decreased at high speeds due to the bearing softening and gyroscopic effect. The bearing softening is the major reason of the reduced spindle stiffness, while the gyroscopic effect plays the secondary effect. Angular contact ball bearing softening at high speed is due to the reduced contact load and increased contact angle at the ball/inner-raceway contact interface caused by the centrifugal force. For the draw bar mechanism, analysis results show that the dynamic draw force at high speeds is significantly increased from that designed at the static state. Because the toolholder/spindle interface stiffness is proportional to the draw force, centrifugal force theoretically contributes a plus to the spindle stiffness at dynamic state. The dynamic draw force, however, is dependent on the friction loss inside the draw bar mechanism. Because of the low friction coefficient, the ball-type mechanism is superior to the wedge type mechanism.     

Nonlinear Dynamic Analysis of a Rigid Rotor Supported By a Spiral-Grooved Opposed-Hemisphere Gas Bearing

The nonlinear dynamic behavior of a rigid rotor supported by a spiral-grooved opposed-hemisphere gas bearing is investigated in this article, focusing particular attention on its whirl motion. The finite element method combined with the finite difference method is employed to solve the time-dependent Reynolds equation that is coupled with the rotor motion considering five degrees of freedom. The rotor responses to the initial disturbance and synchronous and nonsynchronous excitations are investigated. To analyze the complicated dynamic behavior of the rotor–bearing system, the trajectories of the rotor centerline, time responses, phase portraits, power spectra, Poincare maps, and bifurcation diagrams are obtained from the numerical procedure. The results show that the conical whirl instability appears earlier than the cylindrical whirl instability with increasing rotational speed for the rotor–bearing system with no unbalance mass. Moreover, it reveals that the complex dynamic behavior of the system excited by unbalance mass varies with rotational speed and rotor mass. In addition, bifurcation diagrams employing the rotating speed and rotor mass as bifurcation parameters are obtained. Finally, the nonsynchronous excitation responses are presented, which behave in a different way than the synchronous excitation responses. The results of this study offer a further understanding of the nonlinear characteristics of spiral-grooved opposed-hemisphere gas bearings.     

The nonlinear and ball pass effects of a ball bearing on rotor vibration

A ball bearing is generally assumed as a linear spring in rotor dynamic analysis. In real case, the force equilibrium of the bearing is changed as the relative position, of each ball with respect to the direction of radial force. So, the stiffness of the bearing is also changed and is a function of time and position. In this study, the nonlinear characteristics of a ball bearing are considered in analyzing the vibration response of a rotating shaft due to an unbalance force. A finite element method is used to analyze the vibration characteristics of a rotor-bearing system and a direct numerical integration is performed to calculate the transient response of the rotor system. The responses are converted to the frequency domain and the effects of the parametric excitation due to a ball bearing are examined. The test rig for the investigation of the effect of a ball bearing on the rotor vibration is set up and the results are compared with those of numerical calculation. The calculation results show that the amplitudes of the nonlinear model are larger than those of the linear one. The frequencies of the calculations can be matched to the measured frequencies.     

Stability analysis of a rotor bearing system due to surface waviness and number of balls

In the paper, the stability analysis of a rigid rotor supported by ball bearings has been studied. In the analytical formulation, the contacts between balls and races are considered as nonlinear springs, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The implicit type numerical integration technique Newmark-β with Newton–Raphson method is used to solve the nonlinear differential equations iteratively. The effects of surface waviness and the varying number of balls on stability of rotor bearing system are observed. All results presented in form of fast fourier transformations show that the vibration characteristics of the rotor and its bearings change, when the bearings operate in different regions of their nonlinear load deflection characteristics. From the analysis, it is implied that the number of balls and number of waves in the ball bearing are two important governing parameters affecting its dynamic behavior.     

基于ANSYS数控车床静压气体轴承主轴的模态分析

针对气体静压轴承支撑的精密数控车床主轴系统工作高精度的要求,在机床工作过程中,主轴高速旋转,静压气体轴承的支撑刚度随着转速动态变化。为了了解主轴工作过程中的动态特性,应用Pro／E软件对主轴进行三维建模,并用ANSYS对其进行模态分析,得到各阶固有频率和振型。掌握数控车床主轴各阶振动模态的特点,有利于气体轴承支持下的数控车床主轴结构设计,为机床的进一步研究及优化提供理论依据。     

陶瓷球轴承高精密电主轴临界转速分析

主要研究陶瓷球轴承高精密电主轴动态性能。首先简化并建立轴承—转子系统模型,然后根据电主轴高精度要求选择合适的预紧力,并计算出前后轴承的径向刚度;将所建模型导入软件,根据径向刚度值进行模态分析,结果可以看出所设计电主轴在实际运转中不会产生共振;最后分析出电机转子安装位置变化对临界转速的影响不大,并对比跨距和悬伸量两个模态参数对临界转速的影响,跨距影响最大,悬伸量次之,而安装位置影响最小。该研究为电主轴的设计提供良好的理论依据。     

高速主轴离心膨胀及对轴承动态特性的影响

以高速主轴系统为对象,将主轴转子和轴承内圈分别等效为等截面梁和空心圆盘,计算离心力作用下主轴转子和轴承内圈的径向弹性变形,并分析主轴转子与轴承连接状态随转速升高的变化趋势。考虑旋转部件的离心膨胀变形,建立高速主轴轴承动力学模型并进行试验验证。在此基础上,研究离心效应对主轴轴承径向预紧状态的影响,揭示高速主轴轴承动态特性随转速的变化规律。研究结果表明,离心力引起的径向膨胀变形使滚动体与轴承内、外圈之间的接触角减小,接触力增加。主轴轴承的轴向刚度和径向刚度均随转速的升高而降低。轴承内圈的离心膨胀变形对轴承轴向刚度的影响可以忽略不计,而能在一定程度上提高轴承的径向刚度。     

超高速时电主轴轴承的动态支承刚度分析

基于滚动轴承受力分析的拟静力学和拟动力学模型,利用数值计算方法对超高速时电主轴轴承的内部动力学状态进行计算机模拟仿真,在求解每一个球滚动体动力学基本参量的基础上,计算电主轴轴承对转子支承的动态刚度,并结合具体算例,分析转速、轴承预载荷、径向外载荷等工况条件,以及套圈滚道曲率半径、球滚动体的直径和数量等轴承的内部结构尺寸、球材料的物理性能等方面的因素对轴承动态支承刚度的影响。分析结果表明,外部工况条件以及轴承内部的结构尺寸、球材料的物理性能等方面的因素对超高速时电主轴轴承的动态支承刚度影响较大,超高速时电主轴轴承的动刚度较静态和低速情况有着显著的变化。     

Fluid-induced instability elimination of rotor-bearing system with an electromagnetic exciter

This paper describes an experimental investigation of whirl elimination of a hydrodynamic bearing with an electromagnetic exciter (EE) and includes a stability analysis through a root locus plot. The test apparatus incorporates the EE, which provides additional stiffness through a PD algorithm in order to stiffen a rotating machine to resolve fluid-induced instability. The stiffness of the hydrodynamic bearing gives a significant contribution to the occurrence of unstable vibrations as the speed or the load of a rotating machine increases. With regard to the whirl-eliminated investigations, the EE used to raise the stiffness of the rotating machine can cause important changes in the stability of the rotating machine. The threshold of stability derived in this paper that affects stability conditions can be used to define the stability margin of the rotating machine. A simple control scheme is used to calculate the amount of the supplemental stiffness supplied by the EE, and is confirmed through experiments. To offer a faster, more stable and more effective strategy for whirl elimination, the dynamic behavior of a rotor system affected by fluid-induced whirl instability phenomena has been successfully studied.     

柔性间隙影响下涡旋压缩机主轴系统动力学特性研究

考虑到涡旋压缩机主轴系统的高速回转特性,将自由运动和接触变形两状态非连续接触模型应用于间隙运动副动力学建模。以某卧式涡旋压缩机为依据,在不同运动副间隙下构建基于ADAMS/View的主轴系统刚柔耦合模型。通过柔性接触条件下的动力学仿真计算,深入分析了主轴系统核心部件(如动涡盘、曲轴、十字滑环及轴承)的运行状态及承载情况。结果显示：在理想间隙(间隙为0)下,柔性曲轴质心轨迹为一带有波动的非标准圆,而在非理想状态下,曲柄销与滚针轴承存在多处接触碰撞;当轴承内部存在间隙时,Z方向上的支反力更为连续和集中,且其波动幅度随着间隙增大而减小;间隙为0.01 mm时对于动涡盘加速度影响较大,不利于容积腔形成和气体压缩,而选择0.03 mm或0.05 mm间隙值时,可避免轴承系统发生应力集中和疲劳破坏,同时有助于轴承系统维护和十字滑环防自转。     

Acceleration-Dependent Analysis of Vertical Ball Screw Feed System without Counterweight

The distinguishing feature of a vertical ball screw feed system without counterweight is that the spindle system weight directly acts on the kinematic joints.Research into the dynamic characteristics under acceleration and decel-eration is an important step in improving the structural performance of vertical milling machines.The magnitude and direction of the inertial force change significantly when the spindle system accelerates and decelerates.Therefore,the kinematic joint contact stiffness changes under the action of the inertial force and the spindle system weight.Thus,the system transmission stiffness also varies and affects the dynamics.In this study,a variable-coefficient lumped parameter dynamic model that considers the changes in the spindle system weight and the magnitude and direc-tion of the inertial force is established for a ball screw feed system without counterweight.In addition,a calculation method for the system stiffness is provided.Experiments on a vertical ball screw feed system under acceleration and deceleration with different accelerations are also performed to verify the proposed dynamic model.Finally,the influence of the spindle system position,the rated dynamic load of the screw-nut joint,and the screw tension force on the natural frequency of the vertical ball screw feed system under acceleration and deceleration are studied.The results show that the vertical ball screw feed system has obviously different variable dynamics under acceleration and deceleration.The influence of the rated dynamic load and the spindle system position on the natural frequency under acceleration and deceleration is much greater than that of the screw tension force.     

基于球轴承刚度计算的电主轴结构分析与优化

电主轴的结构,动态特性对数控机床的加工效率和精度的影响很大。对角接触球轴承电主轴单元进行了静刚度分析,在有限元软件ANSYS中建立了电主轴球轴承-转子系统的参数化有限元模型,并以提高电主轴的静刚度为优化目标,对电主轴的支承跨距和电机的安装位置进行了优化分析及计算,并对优化前后的电主轴系统进行了模态分析,对比其前三阶频率及振型的变化,得出了相关结论。     

Dynamic stiffness and damping coefficients of aerodynamic tilting-pad journal bearings

The dynamic gas–film forces of aerodynamic bearing often can be characterized by eight linear stiffness and damping coefficients. How to theoretically predict these coefficients is a very difficult issue for tilting-pad gas bearing design because of its structural complexity. The current study presents a novel and universal theoretical analysis method for calculating the dynamic stiffness and damping coefficients of aerodynamic tilting-pad bearing. The gas–film pressure within the bearing is expressed in the form of dimensionless compressible gas-lubricated Reynolds equation, which is solved by means of the finite element method. With the assumption that the journal and the pads are disturbed with the same frequency, the dynamic coefficients of tilting-pad gas bearing are computed by using the partial derivative method and the equivalent coefficient method. Finally, the investigations are conducted about the effects of bearing number, perturbation frequency of the journal and the pads, eccentricity ratios, preload and length-to-diameter ratio of the bearing on the dynamic coefficients of aerodynamic tilting-pad journal bearing. The numerical results indicate that the dynamic stiffness and damping coefficients of tilting-pad gas bearing are closely related with these factors. The proposed analytical method provides a valuable means of predicting dynamic performances of tilting-pad gas bearing. The solution can be used for the purpose of prediction of dynamic behavior of the rotor systems supported by aerodynamic tilting-pad bearings.     

液体静压主轴油膜滑移现象的分析及试验研究

针对液体静压主轴运动过程中动态特性问题,研究微尺度下油膜滑移对轴承承载力,刚度及动态刚度的影响。把微尺度下发生的速度滑移引入到油膜性能方程中,结合液体静压主轴系统平衡方程推导出了主轴系统承载力、刚度及动态刚度表达式,研究了油膜初期主轴静动态性能及油膜动刚度特性。从仿真结果中得到油膜滑移的发生使得承载力及刚度增大,最大刚度对应油膜厚度减小。最后刚度检测试验间接得出了实际主轴系统油膜流动过程中,存在油膜微滑移现象。本项研究为液体静压主轴微尺度下油膜滑移现象及性能的研究探索了一条新途径。