热和离心位移对球轴承刚度影响的数值分析

针对高速角接触球轴承刚度影响因素多、精确预测困难的特点,基于拟静力学模型考虑了离心力、陀螺力矩、轴承套圈热变形和内套圈离心膨胀等多种因素影响,计算了轴承动态刚度,分析了工况和结构参数对轴承动态刚度的影响。分析结果表明:热和离心效应使轴承轴向刚减小,径向刚度增加,对轴承动刚度影响不容忽视;轴向和径向刚度随轴向载荷增加而增大,随径向载荷增加而减小;不考虑热和离心效应时轴向刚度随内沟曲率系数增加而明显减小,考虑热和离心效应时轴向刚度略有增加;轴向和径向刚度随外沟曲率系数增加而减小;转速和球径对轴承刚度影响较复杂,是转速和球径综合作用结果。     

高速滚动轴承-转子系统时变轴承刚度及振动响应分析

高速滚动轴承广泛应用于机床主轴、航空发动机等转子系统中。在复杂运行工况下,滚动轴承的刚度表现出强烈的时变特性和非线性特性,往往是系统非线性的主要根源。考虑离心力、陀螺力矩、轴承内圈离心膨胀和热变形等因素,建立高速滚动轴承力学模型,计算轴承的时变刚度。将滚动轴承非线性模型与转子有限元模型集成,建立滚动轴承-转子耦合系统动力学模型。以FAG角接触球轴承(HCB7012E)为例,分别计算静载荷作用下的内外圈轴向、径向相对位移,并与舍弗勒轴承分析软件BearinX?的计算结果进行比较,验证了模型对静态位移仿真的精度。在不同轴承预紧状态下,仿真滚动轴承-转子系统在不平衡激励下的振动响应,并与试验结果比较,验证了模型仿真系统动态响应的精度。利用一个背对背安装的角接触球轴承-转子系统,研究在静载荷、不平衡载荷激励作用下滚动轴承刚度的变化规律,并计算时变轴承刚度作用下转子的时域振动响应及频域特征,为高速滚动轴承-转子系统设计、动力学分析与故障诊断提供依据。     

新型离心膨胀动态补偿高速刀柄的静态性能分析

设计了一种新型离心膨胀动态补偿高速刀柄,该刀柄以离心力作为驱动力、液压油作为力传递介质,使膨胀套产生弹性变形对刀柄/主轴接口锥面的离心膨胀进行动态补偿。利用Ansys Workbench分析得到刀柄/主轴接口的接触压力分布规律,确定了刀柄的极限转速;计算了刀柄/主轴接口的径向刚度,确定了接口的名义径向刚度和许用弯矩。结果表明:与HSK-A63高速刀柄相比,新型高速刀柄的极限转速提高了40%、接口名义径向刚度相当、许用弯矩提高约33%。新型高速刀柄适于更高速加工。     

离心力驱动液压膨胀式高速刀柄设计

针对高速刀柄与主轴锥孔离心膨胀不匹配的问题,设计了一种新型高速刀柄。刀柄采用实心短锥、双面定位结构。刀柄上安装有离心力驱动液压弹性膨胀系统,用以补偿刀柄与主轴锥孔的离心膨胀差。阐述了新型高速刀柄的结构原理,对刀柄几何参数和配合过盈量进行了设计;利用ANSYS有限元软件分析了刀柄的极限转速及与主轴的径向连接刚度。研究结果表明,新型刀柄与同规格的HSK高速刀柄相比,极限转速提高了约38%,且径向连接刚度也有所提高,适合用于高速加工。     

高速微孔钻床主轴系统的动态特性分析

依据转子动力学理论,利用Timoshenko粱轴理论,建立了包含旋转惯性力、陀螺力矩、离心力、弯曲变形、扭转变形、钻削轴向力和钻头的三种边界条件在内的高速微孔钻床主轴系统动力学模型。在利用实验和现有文献对所建立的模型进行了检验的基础上,对高速微孔钻床主轴系统的临界转速、临界轴向压力进行了分析。结果表明高速微孔钻床主轴系统的临界转速随钻削轴向压力的增大而减小,并且钻削过程中比刚入钻时能承受更高的转速,更大的轴向力;临界轴向压力随高速微孔钻床主轴系统转速的升高而降低,即随着钻削转速的提高,应适当减小钻削轴向力。     

高速角接触球轴承刚度计算及影响因素分析

在Jones-Harris刚度模型的基础上,建立了一个基于沟道控制理论的五自由度角接触球轴承刚度模型,该模型综合考虑了高转速下球的离心力、陀螺力矩等因素对轴承刚度的影响,应用准静态模型的增量法计算轴承刚度矩阵,并将轴承刚度的计算值与文献中试验值进行对比,验证了该模型的可靠性。在此基础上分析了轴向载荷、径向载荷、轴承转速和安装过盈量等因素对轴承刚度的影响,结果表明:随轴向载荷增大,径向刚度、轴向刚度和角刚度均增大;随径向载荷增大,轴向刚度和角刚度逐渐减小,径向刚度增大;随轴承转速增大,径向刚度减小,轴向刚度和角刚度先减小后趋于稳定;随安装过盈量增大,轴承径向刚度增大,轴向刚度和角刚度先减小后趋于稳定。     

高速主轴-刀柄接口离心膨胀动态补偿系统的研究

为解决高速主轴-刀柄接口因离心膨胀导致极限转速偏低及定位精度下降的问题,设计了一种新型离心膨胀动态补偿系统,并对其性能进行了分析。利用ANSYS有限元软件分析了主轴-刀柄接口的锥面接触应力,确定了主轴-刀柄接口的极限转速,计算了主轴-刀柄接口的径向刚度。通过与常规主轴-刀柄接口进行对比,验证了补偿系统的补偿效果。带补偿系统的主轴-刀柄接口锥面接触应力满足径向定位要求,接口极限转速提高43.8%,接口径向刚度随转速与载荷的变化关系更符合高速加工实际要求。     

高速角接触球轴承热特性和机械特性研究

基于动力学和摩擦生热理论,建立高速角接触球轴承热机完全耦合有限元模型,分析了滚动轴承的高速运动特性、温度分布、动刚度等,并与理论计算结果和试验结果对比.之后分析了轴承在不同转速下的温度和轴向变形,得到轴承在高速运行状态下的机械特性和热特性规律.分析结果表明:轴承内圈转速增大会导致各部件温度升高和轴承动刚度减小.另外,通...     

支承轴承对高速主轴系统特性的影响

结合轴系变形方程,对支承部位轴承与主轴的位移耦合以及对系统轴向力平衡条件进行了分析,提出用迭代法求解高速主轴系统刚度和临界转速的概念。计算结果表明,支承轴承的非线性对系统性能影响明显,当轴承预加轴向载荷增加时,轴承支承刚度增大,导致主轴系统刚度和临界转速随之增大。     

离心力对高速主轴轴承内环过盈配合特性的影响

利用弹性力学,推出了高速离心力作用下厚壁主轴与薄壁轴承内环的变形量及其配合初始过盈量的理论计算公式,给出了主轴转速与过盈量的定量关系;借助接触非线性有限元建立了高速旋转主轴与轴承内圈过盈配合的三维有限元模型,模拟仿真了离心力对过盈配合面间接触应力、过盈量的影响。     

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.     

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.     

多列组合角接触球轴承刚度和位移量

以滚动轴承动力学分析和滚道控制理论为基础,提出了应用Powell优化算法和Newton-Raphson算法相结合的方式计算非线性方程组,给出了预紧力和转速的多列组合角接触球轴承组合刚度相应程序。对7016A5轴承DBD组合的研究结果表明:预紧力和转速与单个轴承和轴承的组合刚度及位移量呈现非线性关系。轴承的组合轴向刚度小于单个轴承的轴向刚度,其径向刚度大于单个轴承的径向刚度。为实现预定的轴承动态性能,单双侧轴承内圈的间隙量须大于两侧轴承位移量之和。     

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。     

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.     

三点接触球轴承打滑动力学分析与验证

三点接触球轴承是航空发动机中的关键基础件。目前对三点接触球轴承的仿真分析多基于拟静力学模型,对于打滑、擦伤等特殊行为缺乏解释,而滚球打滑易引起滚道磨损、蹭伤等故障。在对轴承元件进行受力分析的基础上,引入滚球与左右半内圈的接触状态判断条件,采用动力学方法对三点接触球轴承进行了打滑分析。然后,分析了设计接触角及运行参数对轴承打滑率的影响。最后,通过实验研究了滚球通过内圈频率及滚球公转转速随轴向载荷及内圈转速的变化规律,并与动力学模型仿真值进行对比验证了方法的有效性。研究结果表明：轴向载荷越小或转速越高,打滑率越大;在转速和载荷工况条件相同的情况下,轴承打滑率随着设计接触角的增加而增加;而在不同转速工况下,轴承发生打滑的轴向载荷临界值不同,其数值随转速的升高而增加。     

高速角接触球轴承动力学特性参数分析

根据滚动轴承的分析理论,在100000r/min的转速范围内,对角接触球轴承的接触应力、接触角、旋滚比及刚度的变化特性进行了全面分析。分析结果表明:各性能参数均呈现显著的非线性变化特征;随转速升高,轴承径向刚度及轴向刚度值也是先下降后上升,且变化范围较大;陶瓷球混合轴承几乎在所有的性能参数对比上均明显优于传统的钢球轴承,与传统钢球轴承相比,其接触应力明显降低、接触角变化较小、轴向与径向刚度变化程度相对较低、动态特性相对稳定,从而具有传统钢球轴承无可比拟的优越性。     

高速角接触球轴承动力学特性参数分析

根据滚动轴承的分析理论，在100000r／min的转速范围内，对角接触球轴承的接触应力、接触角、旋滚比及刚度的变化特性进行了全面分析。分析结果表明：各性能参数均呈现显著的非线性变化特征；随转速升高，轴承径向刚度及轴向刚度值也是先下降后上升，且变化范围较大；陶瓷球混合轴承几乎在所有的性能参数对比上均明显优于传统的钢球轴承，与传统钢球轴承相比，其接触应力明显降低、接触角变化较小、轴向与径向刚度变化程度相对较低、动态特性相对稳定，从而具有传统钢球轴承无可比拟的优越性。     

On an isotropic and centrifugal force invariant layout of a conically shaped gas-lubricated high-speed spiral-groove bearing

The following elaboration discusses the analytically complete layout of a self-acting gas-lubricated high-speed conically shaped spiral-groove bearing as well as suggestions for practical realization. The simple conically shaped bearing is separated into two conical main bearings, which are situated at the ends of the cone-stump. Both have an identical angle size, but otherwise differ with regard to their bearing geometries and bearing gap sizes. The isotropic layout of the two bearings in radial direction, i.e. the determination of the bearing geometries for the same load angle, the same load capacity and the same stiffness at the same nominal operating conditions, is determined analytically in an iterative way and has the goal of providing dynamically benign behavior. The radial expansion of the rotor which occurs at the nominal rotation, and therefore the occurrence of distortions of the bearing gaps due to enormous centrifugal forces that affect the rotor masses, is rendered ineffective by means of a centrifugal force invariant inner outline of the rotor. For this purpose, the outer contour of the rotor is designed in such a manner that the conically shaped inner contour expands congruently to itself and therefore causes a parallel increase in the bearing gap. The autonomous regulation of the bearing following the gap increase subject to the decrease in load capacity as a result of the decrease of the expanded rotor to the nominal bearing gap sizes restores the nominal state independent of the rotor speed. The half-frequency whirl which is dependent on natural frequencies and detrimental to self-acting, gas-lubricated bearings requires an investigation of the dynamic behavior of the bearing system. It will be shown that natural frequencies will be reached while passing through the turning frequency range. However, the suspension of the “rotor–stator” system in defined additional stiffnesses will show that the natural frequencies of the original system can be displaced upwards so that the turning frequency will no longer reach a natural frequency at any operating point. This prevents the occurrence of the half-frequency whirl. The realization of the described bearing system is supported by suggestions for a non-self-acting start-up assistance at low rotation speeds as well as by suggestions for actuation, pre-stressing, sensor and measurement devices as well as system regulation. It lays the foundation for high-speed bearings in spindle construction, laser and dental technology as well as for precision gyroscopes.     

A study on the development of a new conceptual automatic variable preload system for a spindle bearing

In machine-tool spindle systems, rolling bearings are generally the most widely used type of bearing, offering high stiffness and a large load capacity. The performance of bearings is greatly affected by the applied preload. This paper suggests a new automatic variable preload system that uses an eccentric mass device applied to the bearings of a spindle system. A spindle sustains centrifugal force when rotating. The eccentric mass device converts the radial direction force caused by the centrifugal force into axial force using an eccentric mass device. The eccentric mass device applies a small amount of force to the bearing when the spindle rotates at a low speed and applies large force to the bearing when the spindle rotates at a high speed. In this design, the device maintains a large preload at low speeds and lowers the preload at high speeds. Depending on the increase in the spindle rpm, the force that the eccentric mass device delivers to the axial direction will also increase. In addition, the preload applied to the bearings will be reduced. A finite element analysis was conducted to predict the shape of the eccentric mass device and changes of the preload. Based on the analysis results, a prototype was fabricated. According to the results of experiments conducted on the prototype, it was confirmed that the automatic variable preload device with the suggested structure operated satisfactorily. Also, vibration and noise of the prototype were measured and analyzed. The approach suggested in this study is expected to allow reduced manufacturing and operating costs, as the complex devices for hydraulic pressure or electricity required in existing variable preload devices can be eliminated.