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.     

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.     

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.     

Characteristics of stiffness and contact stress distribution of a spindle–holder taper joint under clamping and centrifugal forces

An understanding of the contact characteristics of a spindle–holder joint in machine tools calls for an in-depth analysis of its performance under machining conditions. This study specifically aims to model a spindle–holder taper joint to predict the stiffness and stress distribution under different clamping and centrifugal forces. A spindle–holder taper joint subjected to clamping and centrifugal forces was modeled using the finite element method. The stress distribution of the interface was revealed and it was found that the von-Mises stress had a non-linear distribution because of the clamping force of the holder. The centrifugal forces were included in the model to analyze the deformation of the joint. At high speed the centrifugal force caused a stress concentration at the large end of the holder. A typical 7/24 taper joint of a BT50 holder was investigated to identify the stiffness using a special experimental platform. The axial and radial stiffnesses, as well as the hysteresis cycles were obtained to predict the contact characteristics with different clamping forces. The experimental results showed that the model presented in this study was efficient in predicting the characteristics of the spindle–holder joint. The method presented is useful in identifying the dynamics of a spindle–holder and can thus be used to optimize the spindle system.     

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.     

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.     

Milling machine spindle analysis using FEM and non-contact spindle excitation and response measurement

In this paper a method for analysing lateral vibrations in a milling machine spindle is presented including finite-element modelling (FEM), magnetic excitation and inductive displacement measurements of the spindle response. The measurements can be conducted repeatedly without compromising safety procedures regarding human interaction with rotating high speed spindles. The measurements were analysed and compared with the FEM simulations which incorporated a spindle speed sensitive bearing stiffness, a separate mass and stiffness radius and a stiffness radius sensitive shear deformation factor. The effect of the gyroscopic moment and the speed dependent bearing stiffness on the system dynamics were studied for different spindle speeds. Simulated mode shapes were experimentally verified by a scanning laser doppler vibrometer. With increased spindle speed, a substantial change of the eigenfrequencies of the bearing-related eigenmodes was detected both in the simulations and in the measurements. The centrifugal force that acted on the bearing balls resulted in a softening of the bearing stiffness. This softening was shown to be more influential on the system dynamics than the gyroscopic moment of the rotor. The study performed indicates that predictions of high speed milling stability based on 0 rpm tap-test can be inadequate.     

An elastic deformation model of high speed spindles built into ball bearings

Kinematic characteristics and elastic deformation properties of ball bearings such as stiffness, axial, and radial deflections of the rings, speeds of balls, contact angles, and loads, all vary strongly with rotational speed, temperature, and axial preload. This paper presents an elastic deformation model of spindle units built into ball bearings, which are running on high rotational speed and axial preload. For this, software for simulation of the high speed spindle units was developed and introduced into a practical use. A computer aided analysis of the model was carried out and experiments were made, which showed a significant effect of high rotational speed, cutting load, bearing axial preload, and a new effect for which the criteria for a choice of bearing preload are given.     

小型立式离心铸机的结构改进

针对小型立式离心铸机存在的振动问题进行了结构改进,采用一对背对背圆锥滚子轴承作为主承载轴承以提高主轴的旋转精度、减小铸机的振动,对轴上零件的紧固方式做了相应的改进以防止零件窜动。冷却套的设置不仅仅增加轴承的散热,同时还起着安装轴承的作用。还对主轴及相关零件进行了设计计算,结果表明,这种结构改进是合理可行的。     

Characterizations and models for the thermal growth of a motorized high speed spindle

In this paper, the characterizing and modeling of the thermal growth of a motorized high speed spindle is reported. A motorized high speed spindle has more complicated dynamic, non-stationary and speed-dependent thermal characteristics than conventional spindles. The centrifugal force and thermal expansion occurring on the bearings and motor rotor change the thermal characteristics of the built-in motor, bearings and assembly joints. It was found that conventional static models using regression analysis and artificial neural network failed to give satisfactory model accuracy and robustness. An auto-regression dynamic thermal error model, that considers the temperature history and spindle-speed information, has been proposed and proved to improve the model accuracy. However, it was found that temperature-based thermal error models, that correlated thermal displacement of the rotating cutting tool to the temperature measurements on the spindle housing, were not robust. Many nonlinear and time-varying thermal sources, such as coolant jacket, motor air gap, motion joints and assembly interfaces influence thermal displacement. The relationship between temperature measurements and thermal displacements is highly nonlinear, time-varying and non-stationary. A new thermal model which correlates the spindle thermal growth to thermal displacements measured at some locations of the rotating spindle shaft has been proposed. It was found that the displacement-based thermal error model has much better accuracy and robustness than the temperature-based model.     

数控龙门镗铣床滑枕热特性分析

滑枕是影响数控龙门镗铣床加工精度的关键部件。针对切削加工中存在的实际问题,确立导致滑枕热变形的热源,对轴承生热率进行计算,建立热变形数学模型;对滑枕进行热性能分析,并对主轴轴系结构进行改进。结果表明:滑枕的最高温度在主轴轴承支承处,为64.13℃;滑枕的最大的热变形在主轴轴承支承端,为38.9μm;采用冷却套结构、后轴承自由支承方式,减小主轴、滑枕热变形,从而提高数控龙门镗铣床加工精度。     

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。     

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.     

Thermo-mechanical model of spindles

This paper presents a Finite-Element-method-based thermo-mechanical model of spindles with rolling bearings. The heat generated in the bearings and the motor is transferred to the ambient air, the motor coolant and the spindle structure, and causes thermal expansion of spindle parts. The experimentally validated thermo-mechanical spindle model predicts temperature distribution and thermal growth, as well as bearing stiffness and contact loads, under specified operating conditions. Transient changes in temperatures, deformations, viscosity of the lubricant, and bearing stiffness are considered in the solution. The predicted bearing properties are used to estimate the changes in the dynamic behavior of spindles.     

Development of automatic variable preload device for spindle bearing by using centrifugal force

Machine tool spindles of late require high stiffness and fast rotation characteristics all at once for high-speed, high-efficient processing, as well as for a wide range of use rotation. As such, many studies are being carried out on automatic 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 automatic variable preload device that can automatically adjust the preload applied to spindles employing a rolling bearing. It proposes an automatic variable preload device with a completely new composition comprising of a main bearing to which the preload is applied, an auxiliary bearing that conveys the force and a centrifugal element that converts the centrifugal force into a force in the axial direction, and a constant pressure preload spring that applies the initial preload to the main bearing. Other changes in the centrifugal force are also presented. The proposed composition was validated through a contact nonlinear analysis, and the design data necessary to create a prototype were obtained. A prototype for the automatic variable preload device using centrifugal force was then created and tested to confirm that the preload device of the proposed structure runs properly and smoothly.     

表面微织构椭圆轴承的热效应分析

目的 提高摩擦副润滑性能,从而研究表面微织构不同参数对椭圆轴承热效应的影响,同时采用试验方法进一步说明微织构的减摩作用机理。方法 建立表面微织构椭圆轴承仿真模型、编写UDF程序定义黏度,同时采用面–面接触形式的摩擦磨损试验,从理论和试验两个方面研究不同微沟槽宽度和微沟槽轴向分布率的椭圆轴承的热效应变化规律。结果 表面微织构能够有效改善摩擦副表面的摩擦学性能,沟槽状微织构椭圆轴承较光滑椭圆轴承温度均有所降低,主要承载区出现轴向呈条状的低温区域,出现位置大致与沟槽分布位置一致。随着微沟槽轴向分布率的增大,微沟槽降温效果增强,轴承承载力先升高后降低,摩擦力先降低后升高,端泄量先减小后增大,沟槽轴向分布率取0.6较为合适。随着微沟槽宽度的增大,轴承承载力呈先升高后降低的变化趋势,摩擦力呈先降低后升高的变化趋势,当宽度在0.6～0.8 mm时,椭圆轴承有较优的润滑性能。结论 理论分析和试验研究均表明,表面微织构椭圆轴承的摩擦力随着微沟槽宽度的增大先降低后升高,合适的微织构参数才能最大程度地发挥其减摩作用,从而实现提升轴承润滑性能,降低轴承温升的目的。     

Bearing induced vibration in precision high speed routing spindles

This paper presents a detailed model of bearing vibration, including the effect of contact spring non-linearity in balls-to-raceways' contacts. The model incorporates the effect of surface waviness of rolling elements and off-sized balls upon the dynamic internal radial clearance of the bearing. The vibration forces and moments generated are formulated and the significant principal and secondary side-band contributions are highlighted. This model is employed successfully in the recognition of complex real-time vibration spectra of a precision routing spindle, obtained by accurate non-contact sensors.     

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.