磁悬浮轴承-转子系统的机电耦合动力学模型

对磁悬浮轴承 -刚性转子系统建立了完整的机电耦合动力学模型 ,其中除了人们通常所考虑的陀螺效应外 ,着重考虑和增加了推力磁轴承对转子横向振动的耦合效应和由于轴颈倾斜所引起的径向磁轴承之间的耦合效应 ,以及控制系统的电学微分方程和传感器与磁轴承非共点安装对系统性能所带来的耦合影响。该模型可用于五自由度磁悬浮轴承 -刚性转子系统的机电耦合动力学性能研究     

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.     

螺旋锥齿轮铣齿机主轴\|轴承系统的动力学分析

螺旋锥齿轮铣齿机的刀具主轴系统在加工中易出现颤振现象,影响工件的加工质量。针对这一问题,依据集总质量法,构建了刀具主轴系统等效动力学模型;采用Timoshenko梁理论分析得到了主轴转子的刚度矩阵;通过对圆锥滚子轴承的力学分析,构建了轴承在轴向预载荷作用下的轴向刚度和径向刚度计算式。利用力锤激励实验对采用数值分析法构建的刀具主轴系统的动力学模型进行了验证,对比结果表明所构建的动力学模型可以有效反映刀具主轴系统的动力学特性。     

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。     

STUDY ON THE COUPLED ELECTROMECHANICAL DYNAMICS OF ROTOR SYSTEM EQUIPPED WITH MAGNETIC BEARINGS

The influences of thrust magnetic bearing and journal tilt on dynamic characteristics of rotor system are studied mainly. The outcome shows that the influences of coupling effects of thrust magnetic bearing and tilt of journal on critical rotational speeds of system are very large, and the stability of system reduces greatly. That shows it is important that the influence of coupling effects of thrust and radial magnetic bearings due to the rotor tilting must be considered in the study of rotor-magnetic bearings system dynamic characteristics, and also shows it is important that the rotor is mounted and debugged in ideal alignment of magnetic bearings.     

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.     

涡轮泵流体静压轴承设计及性能特性分析

针对流体静压轴承在液体火箭发动机涡轮泵中的设计和应用,以现有的滚动轴承支承的涡轮泵转子为应用对象,提出流体静压轴承的参数设计思路,采用粒子群优化算法设计得到支承刚度最大化的轴承结构参数组合,并计算分析所设计轴承的性能以及轴承-转子系统的动力学特性。分析表明：优化设计得到流体静压轴承的承载力和支承刚度可以满足要求,但轴承总流量达泵流量的21%,这会显著降低涡轮泵的总体效率;仅将滚动轴承改为流体静压轴承,而不改变其他结构或布局,转子的稳定性不能满足要求;涡轮泵流体静压轴承转子系统设计时应尽量将轴承布置在转子位移较大的位置,以充分发挥其阻尼作用。     

Severity Estimation of Cracked Shaft Vibrations within Fluid Film Bearings

The equations of motion, with four degrees of freedom, taking into consideration the flexibility, damping and cross coupling of the fluid film bearings are derived for a cracked Jeffcott rotor supported on fluid film bearings.

Dimensionless equations are developed for dynamic radial load, dynamic pressure developed in the fluid film bearings and coefficient of dissipation considering the journal vibrations in two harmonics; bearing fluid film stiffness and damping coefficients. These are applied to a cracked Jeffcott rotor supported on different types of bearings, i.e., cylindrical journal bearings, offset cylindrical bearings, tilting pad journal bearings and three-lobe bearings. Based on the allowable dynamic pressure developed in the fluid bearings, the severity of cracked shaft and allowable crack depths are estimated in this study. Measurement of dynamic pressure and dissipation for monitoring the crack growth is suggested. However, 2x vibration is the best indicator of cracks in the shafts.     

超临界二氧化碳动静压径向可倾瓦轴承实验台设计与实验研究

针对超临界二氧化碳(S-CO₂)动力机组在启动和停止阶段气体轴承产生非常大的摩擦磨损,以及气体轴承承载力低、刚度低、阻尼小、稳定性较差等问题,设计并改进一种新型动静压S-CO₂润滑径向可倾瓦轴承结构。设计并搭建S-CO₂润滑轴承实验台,针对于实验台转子刚启动和极低转速工况,对新型S-CO₂润滑动静压径向轴承在静压状态下的动态特性进行实验研究,得到轴承的动态刚度和动态阻尼,并分析静压对轴承动态性能的影响。实验结果表明,设计的S-CO₂动静压径向可倾瓦轴承在启停阶段,在轴瓦与轴颈之间产生了足够的静压压力,可将二者完全分隔开,从而能减少启停阶段的摩擦磨损;随着静压压力的增大,轴承X、Y方向上的整体刚度、主阻尼都增大,且2个方向的主刚度系数差别不大,而交叉刚度和交叉阻尼都接近于0。研究结果为进一步揭示S-CO₂润滑径向轴承动压状态特性提供参考。     

Unbalance Response of a Super-Critical Rotor Supported by Foil Bearings—Comparison with Test Results©

This article compares theoretical and experimental results on the unbalance response of a super-critical rotor supported by two kinds of gas foil bearings. Analysis of the super-critical rotor is performed with viscoelastic foil bearings (VEFB) and conventional bump foil bearings and compared with early published experimental data. The vibration orbits obtained by theoretical investigation on the viscoelastic foil bearings (VEFB) and the conventional bump foil bearings are compared with the experimental vibration orbits of the super-critical rotor supported by both foil bearings. A numerical analysis program can calculate the static and dynamic characteristics of the elastically supported gas foil bearing using the measured stiffness and damping of the elastic foundation. After the stiffness and damping of both foil bearings are calculated using the perturbation method, vibration orbits of the flexible rotor modeled by the finite element method are calculated. Vibration orbits calculated by numerical analysis agree well with experimental data when the vibration amplitude is small and the rotating speed is below the bending critical speed. The numerical results also show that the enhanced structural damping of the elastic foundation reduces vibration near the bending critical speed.     

动静压轴承支撑高速主轴系统基本性能分析

以高速主轴水润滑动静压轴承为基础,在双动静压轴承支撑主轴系统实验平台上,分析转速、供水压力、载荷等基本运行参数对系统基本性能的影响,并采用不平衡轴承质量法识别了系统支撑轴承的动特性系数。结果表明:轴承-转子系统静态刚度随供水压力和载荷的增大而增大;流量随供水压力升高而增大,而随转速变化较小;利用不平衡轴承质量法识别系统支撑轴承的动特性系数与理论一致性。     

主动电磁轴承失效后转子坠落在备用轴承过程中的非线性动力学

用有限元法建立了任意个由滚动轴承组成的固定间隙备用轴承-主动电磁轴承-多盘多质量转子系统在主动电磁轴承失效前后的动力学方程,以一个多盘转子系统为例分析了主动电磁轴承失效后转子坠落在备用轴承过程中的瞬态非线性动力学特性,讨论了柔性备用轴承的支撑刚度、支撑阻尼和间隙对转子在坠落过程中动力特性的影响。结果表明采用具有较大阻尼柔性结构的备用轴承能够显著地改善转子坠落在备用轴承上的瞬态动力特性,抑制转子在坠落过程中可能出现具有较大振动和冲击力的全间隙区的涡动运动,减小转子坠落对备用轴承寿命和可靠性的影响。柔性结构备用轴承的支撑阻尼越大,支撑刚度越小,间隙越大,转子坠落后出现全间隙区涡动运动的可能性越小。     

一种典型的静压轴承动态特性分析

用有限差分方法求出线性化的四腔静压轴承的8项动特性系数,并由此分析了典型的毛细管节流静压轴承的动态性能.对静压轴承的稳定性进行了讨论,提出了判定静压轴承稳定性的简明方法.该分析方法及所得数据在实际工作中很有意义.     

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。     

小孔节流深浅腔动静压气体轴承承载特性分析

以小孔节流深浅腔动静压气体轴承为研究对象,采用Fluent软件对轴承的承载特性进行分析,研究偏心率、供气压力、主轴转速、气膜厚度、浅腔深度比等因素对轴承承载力和刚度的影响.结果表明:小孔节流深浅腔动静压气体轴承浅腔区的平均压力大于深腔区的平均压力,压力最大区域出现在浅腔末端靠近轴承端面处;随着供气压力的增加,承载力逐渐...     

一种可控滑动轴承-转子系统性能计算方法*

针对可控滑动轴承油膜性能计算困难问题,提出一种考虑基础参振的滑动轴承性能计算的动网格模型,阐述网格更新原理,给出可控滑动轴承所支撑转子系统轴心轨迹的计算方法。在滑动轴承-转子-基础系统的性能计算时,该方法保证油膜径向网格线和轴颈表面垂直,能减小轴承油膜性能计算的累计误差。通过不平衡载荷条件下的转子轴心静平衡位置计算结果与油膜力数据库方法、经典数据进行对比,验证了该模型的正确性,并利用该方法分析受正弦位移激励的滑动轴承-刚性转子系统的工频振动情况。结果表明：选择合适相位和幅值的正弦位移激励来控制轴承座,可减小转子系统的不平衡振动。这为基于超磁致伸缩材料的轴承、基于压电陶瓷材料的轴承、柔性铰链可倾瓦轴承等可控轴承-转子系统的性能计算提供了一种新方法。     

Dynamic behavior of fluid‐structure coupling of hydrostatic spindle under effect of oil film slip

To better understand the dynamic characteristics of a hydrostatic spindle in fluid‐structure coupling, the impact of oil film slip on the 4 dynamic stiffness and damping coefficients of the spindle is studied. On the basis of modified Reynolds equation, which considers the microscale velocity slip effect, rotation error of the spindle is calculated. To solve the rotor axis orbit under the existence of eccentric quality, 4 dynamic stiffness and damping coefficients of the oil film, which describe the dynamics of a rotor axis orbit, are calculated by using load increment method and the pressure perturbation method. The research results show that velocity slip caused a certain impact on dynamics of bearing stiffness and damping performance. The experiment of the measuring path of the shaft verifies the correct and effect of the orbit of shaft center model.     

高精度无心车床主轴系统动力学建模研究

针对无心车床加工时主轴系统的振动导致加工精度不足的问题,该文以无心车床主轴系统为研究对象,考虑了实际加工中存在的棒料s弯问题,建立了主轴系统动力学模型,并在simulink中进行了动力学分析,得到了主轴在径向1(x向),径向2(y向),轴向(z向)振动信号。通过对主轴参数轴承游隙的改变来观察主轴x方向,y方向,z方向振动的变化趋势,以及改变轴套磨损量来观察主轴z方向的振动变化趋势。分析结果表明,主轴在三个方向上的振动z向最大。最后将试验信号与模型信号进行对比分析,振动实验值与理论值的误差均在5%以内,所得实验结果与模型结果基本一致,z向振动最大,可通过调整主轴参数来提高加工精度,验证了所建立模型的准确性。     

柔性转子滚动轴承系统混沌行为研究

研究了滚动轴承支承的柔性转子系统的混沌行为。考虑空间Euler-Bernoulli杆单元、刚性圆盘、圆柱滚子轴承非线性接触力、不平衡力,使用有限单元法建立了柔性转子轴承系统的非线性动力学方程组。根据FPA修正法确定求解周期,采用Runge-Kutta法、Newton-Raphson法求解非线性动力学方程组,用获得的系统最大Lyapunov指数判断系统的混沌行为。以某滚子轴承柔性转子系统为例,研究了该类转子系统在径向间隙、不平衡力、转轴刚度比对柔性转子系统混沌特性的影响规律,发现随着轴承径向间隙的增大,系统的混沌区间逐渐增大、变多。不平衡力的存在使得系统混沌的转速及范围变大。随着刚度比增大,振幅峰值及对应的转速均逐渐增大,系统混沌区间也增多,轴承非线性振动对柔性转子系统非线性行为的影响逐渐增强。     

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。