角接触球轴承组合轴向预紧力分析

在赫兹接触理论和滚动轴承拟静力学分析理论的基础上,建立了角接触球轴承串联组合时计算轴向预紧力的方程.采用Matlab编程求解了动态条件下的轴向预紧力,分析了轴承内外圈宽度尺寸偏差、隔套长度尺寸偏差、滚动体直径尺寸偏差、转速及轴承沟曲率半径系数对轴承组合轴向预紧力的影响规律.结果表明:尺寸偏差越大两个轴承轴向预紧力的差别越大,内外圈沟曲率半径系数越大轴向预紧力的差别越小;外圈沟曲率半径系数比内圈沟曲率半径系数对轴向预紧力分配的影响更明显;转速增大时两个轴承轴向预紧力的差别先减小后增大.     

Bearing load analysis and control of a motorized high speed spindle

Angular contact ball bearings are the most popular bearing type used in the high speed spindle for machining centers. Because the bearing load is increased rapidly with the raised spindle speed due to the centrifugal force and temperature raise, proper initial preload and especially operating-induced load control of the angular ball bearing is important to the rigidity, accuracy and life of the spindle. The bearing layout, preload mechanism an on-line load bearing control are discussed in this paper. The management of the centrifugal force and thermally-induced bearing loads is especially emphasized. An active bearing load monitoring and control mechanism that consists of an integrated strain-gage load cells and piezoelectric actuators has been developed and tested. This active control and monitoring mechanism on-line adjusts the bearing load according the cutting conditions. Experiments were conducted to identify the proper initial bearing preload range. Optimal preload for the lowest bearing temperature raise existed for a specified spindle speed. The optimum preload, however, should be raised when the operational speed is increased.     

空心滚珠丝杠在数控机床伺服进给系统中的应用

针对数控机床主轴和伺服传动系统的热误差阻碍进一步提高机床定位精度的问题,对数控机床伺服进给系统的热变形作了深入研究。结果表明:螺母摩擦和轴承摩擦是滚珠丝杠伺服进给系统的主要热源,其摩擦热量与滚珠丝杠转速及轴向载荷几乎成正比;采用空心丝杠和空心螺母有效抑制了滚珠丝杠在高速进给时的热变形量,减小伺服进给系统的稳态误差。     

Effect of bearing support structure on the high-speed spindle bearing compliance

This paper investigates the effect of bearing assembly tolerance on the spindle–bearing compliance. In a high-speed spindle system, the bearing characteristics are significantly influenced by the initial assembly tolerance and the thermal deformation of the bearing support structure. In particular, in the very early stage of spindle operation, spindle–bearings could be under hazardous conditions due to the rapid change of the internal pressure resulting from the thermal deformation or the centrifugal force-oriented deformation. The bearing's internal clearance may be also changed with 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 modeling and analysis of the high speed spindle system in terms of bearing pressure, bearing compliance and heat generation is required with consideration to those effects. Furthermore, in order to predict spindle characteristics in operation, all of these parameters should be monitored and recalculated in real time. For this purpose, simple and effective equations have been suggested, representing the bearing stiffness in accordance with the thermal deformation. Moreover, contrast to the former bearing analyses which are mostly based on the Hertzian contact model without considering the radial elastic deformation of the races, this paper presents the analytical and experimental investigations on the bearing compliance with additional consideration to 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 will provide a very simplified calculation of the bearing stiffness in dynamic simulation.     

Evaluation of an internally spring preloaded four contact-points bearing for spindle units

In this paper, the concept of an internally spring preloaded four contact-points bearing for the use in high precision and high speed applications is investigated. It is designed as a compact self-contained fixed bearing unit that is free of play, easy to mount and resistant against temperature differences between the inner and outer ring. The concept of the bearing, its functionality and properties are introduced and the results of an experimental analysis of a first prototype are presented. The prototype bearing, which is based on a hybrid 7014 spindle bearing with an additional spring preload unit, was manufactured by hard turning. Its properties are compared to those of similar two and three contact-points spindle bearings. Typical requirements in modern high precision applications, e.g. machine tool spindle units, and limiting characteristics of bearings, such as displacement, stiffness, friction torque and operating temperature, are considered. Finally, the potential of the new bearing concept is discussed.     

联合外载荷作用下角接触球轴承内部载荷分布和变形的数值迭代计算

为了研究联合外载荷作用下球轴承的内部载荷分布和变形特性,提出一种基于赫兹接触理论的数值迭代计算方法.以角接触球轴承为对象,考虑在预紧力、轴向力、径向力等联合外载荷工况条件下内外圈滚道接触角的变化,以及滚珠载荷分布、载荷大小随接触角的变化,利用滚道接触角与滚珠载荷之间的关系式进行数值迭代求解,来寻找轴承受载后内部的平衡状态.通过与典型有限元分析结果的比较可以看出:所提方法不仅详细计算出了轴承内部的载荷情况,而且更为准确地分析了联合载荷对轴承变形的影响机制.搭建了模拟联合外载荷工况的轴承试验台,测量了轴承的变形,验证了该方法的正确性.     

A study of dynamic stresses in micro-drills under high-speed machining

In this paper, a dynamic model of micro-drill-spindle system is developed using the Timoshenko beam element from the rotor dynamics to study dynamic stresses of micro-drills. The model includes effects of eccentricity of the spindle-clamp-drill system, the axial drilling force, the system rotational inertia, the gyroscopic moment, and bearings of micro-hole drilling machines on bending deformation of micro-drills during machining. After the model is verified using the published work, effects of the clamped length of micro-drills, the bearing stiffness and damping, the spindle speed, the system eccentricity, and the axial drilling force on dynamic stresses of micro-drills are analyzed using the model.     

Modeling of spindle-bearing and machine tool systems for virtual simulation of milling operations

This paper presents a general, integrated model of the spindle bearing and machine tool system, consisting of a rotating shaft, tool holder, angular contact ball bearings, housing, and the machine tool mounting. The model allows virtual cutting of a work material with the numerical model of the spindle during the design stage. The proposed model predicts bearing stiffness, mode shapes, frequency response function (FRF), static and dynamic deflections along the cutter and spindle shaft, as well as contact forces on the bearings with simulated cutting forces before physically building and testing the spindles. The proposed models are verified experimentally by conducting comprehensive tests on an instrumented-industrial spindle. The study shows that the accuracy of predicting the performance of the spindles require integrated modeling of all spindle elements and mounting on the machine tool. The operating conditions of the spindle, such as bearing preload, spindle speeds, cutting conditions and work material properties affect the frequency and amplitude of vibrations during machining.     

Modelling of angular contact ball bearings and axial displacements for high-speed spindles

This paper presents modelling of moving sleeve and spindle tip displacements in spindle bearing systems equipped with angular contact ball bearings. The balance of axial forces produced in high-speed bearings is examined, with a particular consideration of centrifugal forces, gyroscopic moments, contact deformations, and contact angles. It has been shown that centrifugal forces acting on bearing balls do not cause sleeve axial shifts. Those sleeve shifts can only result from gyroscopic moments, and changes in spindle dimensions due to centrifugal forces. The proposed model has been verified experimentally, and can be used for compensation of spindle tip displacements.     

An integrated thermo-mechanical-dynamic model to characterize motorized machine tool spindles during very high speed rotation

High speed machining (HSM) is a promising technology for drastically increasing productivity and reducing production costs. Development of high-speed spindle technology is strategically critical to the implementation of HSM. Compared to conventional spindles, motorized spindles are equipped with built-in motors for better power transmission and balancing to achieve high-speed operation. However, the built-in motor introduces a great amount of heat into the spindle system as well as additional mass to the spindle shaft, thus complicating its thermo-mechanical-dynamic behaviors. This paper presents an integrated model with experimental validation and sensitivity analysis for studying various thermo-mechanical-dynamic spindle behaviors at high speeds. Specifically, the following effects are investigated: the bearing preload effects on bearing stiffness, and subsequently on overall spindle dynamics; high-speed rotational effects, including centrifugal forces and gyroscopic moments on the spindle shaft and, subsequently, on overall spindle dynamics; and the spindle dynamics on the cutting point receptance. The proposed integrated model is a useful tool for differentiating quantitatively different effects on the spindle behaviors. The results show that a motorized spindle softens at high speeds mainly due to the centrifugal effect on the spindle shaft.     

Virtual Design and Optimization of Machine Tool Spindles

An integrated digital model of spindle, tool holder, tool and cutting process is presented. The spindle is modeled using an in-house developed Finite Element system. The preload on the bearings and the influence of gyroscopic and centrifugal forces from all rotating parts due to speed are considered. The bearing stiffness, mode shapes, Frequency Response Function at any point on the spindle can be predicted. The static and dynamic deflections along the spindle shaft as well as contact forces on the bearings can be predicted with simulated cutting forces before physically building and testing the spindles. The spacing of the bearings are optimized to achieve either maximum dynamics stiffness or maximum chatter free depth of cut at the desired speed region for a given cutter geometry and work-piece material. It is possible to add constraints to model mounting of the spindle on the machine tool, as well as defining local springs and damping elements at any nodal point on the spindle. The model is verified experimentally.     

3- and 4-Contact Point Spindle Bearings - a new Approach for High Speed Spindle Systems

One important demand on spindle systems in modem machine tools is to realise higher rotational speeds in order to increase the machining efficiency. In conventional spindle bearings the contact angles on inner and outer ring deviate extremely from one another with rising rotational speeds due to centrifugal forces. Axial shift of trie inner ring (elastic mounted bearing) and increasing normal forces in the contact zones on the outer ring are typical consequences leading to high internal bearing loads and a reduced life span. Based on these problems bearings with a new inner geometry are studied. Instead of two contact zones these bearings have three or four contact zones to ensure constant contact angles and reduced normal forces on the outer ring. In this paper analytic operation studies and first experimental tests are presented.     

Effect of preload on running accuracy of spindle

The rotational performance of a machine tool spindle has a direct influence upon both the surface finish and geometric shape of the finished workpiece. The variation of preload affects the stiffness of the spindle and the temperature of the bearing, which are also important factors in spindle motion. Although the large preload and stiffness will probably increase the stability of the spindle, the high temperature of the bearing will decrease the processing accuracy and damage the bearing. Contrarily, if the preload is not large enough, the error in the running spindle will increase, which represents lower precision. Therefore, the preload cannot be too large or too small, resulting in the compromising of these factors. In this study, the effect of the preload on the roundness accuracy has been examined at the different cutting conditions through the developments of measurement system of preload, temperature and roundness accuracy. The step-by-step data analysis procedure has also been developed to get the spindle radial error motions from the measured data. Through measurements of spindle running accuracy, the optimal preload was determined at the different cutting conditions.     

Computational modelling of precision spindles supported by ball bearings

This paper outlines a method for the modelling of a precision spindle supported by ball bearings. The support bearings are represented as piece-wise linear springs with damping provided by concentrated forces external to the bearings at each end of the spindle. The simplified damping model can simulate the squeeze film effect exerted by seals. The main elastic modes of the spindle vibrations are considered and the results corresponding to various machine tool spindle designs under various operating conditions are presented.     

高速电主轴辐射噪声特性分析

研究了3种电主轴的辐射噪声特性。通过实验测量了电主轴辐射噪声,分析了全陶瓷轴承电主轴、钢轴承电主轴和无内圈式陶瓷轴电主轴辐射噪声的时频特性。实验结果表明:提高旋转速度,全陶瓷轴承电主轴与钢轴承电主轴辐射噪声均呈增大趋势,且辐射噪声中含有旋转频率和2倍转频特征,而无内圈式陶瓷轴电主轴的辐射噪声呈现波动式变化,其声压级高于其他2种电主轴,且频谱较为杂乱;在高转速时全陶瓷轴承电主轴声波具有明显的周期性;3种电主轴辐射噪声中均具有较高的摩擦与冲击噪声。     

Development of a newly structured variable preload control device for a spindle rolling bearing by using an electromagnet

For high speed and high efficiency machining, the spindle of modern machine tools simultaneously requires high speed and high stiffness characteristics, and its range of use rotation is becoming wider. Both heavy cutting at low speed and light cutting at high speed must be carried out successively in series with a single machine tool spindle. As such, many studies are being carried out on variable preload control methods that apply a preload to a spindle rolling bearing, as an alternative to the existing fixed position preload and constant pressure preload methods. This paper introduces a newly structured variable preload control device that can arbitrarily adjust the preload applied to spindles employing a rolling bearing. The device controls the coil current on an electromagnet and thereby uses the magnetic force between the electromagnet and a magnetic substance to arbitrarily control the preload applied to the rolling bearing during operation. A prototype for the variable preload control device of the proposed structure was created and a functionality test was then carried out with a test bench prepared using a load cell. The operating principle of the proposed device was verified and the interrelationships between the coil current on the electromagnet and the preload applied to rolling bearing were analyzed through the functionality test. Lastly, the fabricated variable preload control device was applied to a prototype of a spindle system, and a rigidity test was carried out. The test results confirmed that the variable preload control device operates properly and smoothly.     

微型钻头磨床砂轮轴振动的分析与消除

微型钻头磨床砂轮轴振动严重地影响了钻头加工精度。通过对砂轮轴的传递矩阵建模分析，发现砂轮轴轴承刚工和砂轮尺寸是影响其振动的固有频率与振型的两个主要因素。轴承刚度越高，砂轮尺寸越小，基各阶固有频率越高；由于砂轮小对称布置，砂轮尺寸越大，各阶振型的振幅也越大。在调整砂轮轴轴承预紧前，采用Machinery Analyzer model 2130振动分析仪的测试结果也显示该砂轮轴在低频部分的振动较为严重，预紧轴承和精修砂轮后，振动消除。     

高速机床主轴－轴承系统动态性能研究

为研究主轴－轴承系统的动态性能,以某型号精密卧式加工中心主轴系统为研究对象,通过偏心质量激励法测得主轴支承轴承刚度,采用Timoshenko梁单元对主轴进行有限元建模,系统地分析了主轴离心效应、轴承预紧力对于主轴动态性能的影响,并进行了实验验证。结果表明：提高预紧力可有效增加主轴轴承刚度,提高主轴动态性能。同时证明采用有限元法计算主轴轴承的刚度是一种行之有效的方法。     

高速球轴承生热量的理论及试验研究

结合高速球轴承的拟动力学模型,分析轴承各零件在接触点处的切向摩擦力和相对滑动速度。利用局部分析法建立轴承生热量计算模型。研究转速、载荷和轴承几何结构参数对轴承各单元间的局部生热量和总生热量的影响。搭建轴承试验台,监测轴承生热量随工况的变化规律;将相同条件下的理论计算结果和试验结果进行对比,验证理论模型的正确性。结果表明:轴承在稳定运行时,转速和外加轴向载荷是造成轴承总生热量的主要因素;在球径一定的情况下,内、外圈沟曲率半径系数存在一个使轴承生热量最小的最优值;分析轴承生热量变化规律,有利于轴承的温度场计算、润滑油油量的选取等。研究结果为轴承结构的优化设计提供参考。     

Thermal characteristics of the spindle bearing system with a gear located on the bearing span

High cutting speeds and feeds are essential requirements of a machine tool structure to accomplish its basic function which is to produce a workpiece of the required geometric form with an acceptable surface finish at as high a rate of production as is economically possible. Since bearings in high speed spindle units are the main heat source of total cutting system, in this work, the thermal characteristics of the spindle bearing system with a tilting axis were investigated using finite element method to improve the performance of the spindle bearing system. Based on the numerical results, a specially designed prototype spindle bearing system was manufactured. Using the manufactured spindle bearing system, the thermal characteristics were measured and compared to the numerical results. From the comparison of the numerical results with the experimental results, it was found that the finite element method predicted well the thermal characteristics of the spindle bearing system.