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.     

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.     

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.     

A machine tool motorized spindle with hybrid structure of steel and carbon fiber composite

Carbon fiber reinforced plastic (CFRP) is a promising material for enhancing the spindle performance of machine tools because of its high specific stiffness and low thermal expansion. However, when a conventional steel spindle shaft is replaced by a CFRP shaft, the anisotropic property of CFRP makes it difficult to maintain the static stiffness that is equivalent to that of conventional spindles. This study proposes a hybrid structure of steel and CFRP to avoid reduced stiffness of the shaft. Fundamentals of shaft design are described to enable discussion of a favorable steel-CFRP ratio. An experimental evaluation of a developed CFRP spindle is also reported.     

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.     

Creating Stability Lobe Diagrams during Milling

Motorized spindles are in common use in high-speed milling. The dynamic behavior of the spindle depends on the actual number of revolutions and the temperature. The performance of the spindle during milling, particularly, the behavior concerning chatter, is crucially affected by the speed dependent dynamic behavior of the mechanical system. This paper presents the reasons for the speed-sensitive stiffness and the shifting stability lobes. A new method of measuring and calculating the dynamic behavior during milling by means of sub-space-state-space-identification methods is introduced. Finally, the computed stability lobe diagrams are compared with experimentally determined stability lobe diagrams.     

轴芯冷却对电主轴热-机械特性影响的实验研究

电主轴的热特性与机械特性相互作用,采用轴芯冷却在降低电主轴温升的同时也会影响其机械特性。对具有轴芯冷却结构的150SD电主轴进行热特性、静刚度和动态响应测试,研究轴芯冷却对电主轴热-机械特性的影响。结果表明：轴芯冷却减少了电主轴系统热平衡时间和轴向热变形,但会导致不同转速下系统静刚度和1、2阶固有频率降低。在设计阶段需要对轴芯冷却电主轴从悬伸量、跨距和几何尺寸等方面进行综合优化设计,提高其机械特性。     

Expert spindle design system

This paper presents an expert spindle design system strategy which is based on the efficient utilization of past design experience, the laws of machine design, dynamics and metal cutting mechanics. The configuration of the spindle is decided from the specifications of the workpiece material, desired cutting conditions, and most common tools used on the machine tool. The spindle drive mechanism, drive motor, bearing types, and spindle shaft dimensions are selected based on the target applications. The paper provides a set of fuzzy design rules, which lead to an interactive and automatic design of spindle drive configurations. The structural dynamics of the spindle are automatically optimized by distributing the bearings along the spindle shaft. The proposed strategy is to iteratively predict the Frequency Response Function (FRF) of the spindle at the tool tip using the Finite Element Method (FEM) based on the Timoshenko beam theory. The predicted FRF of the spindle is integrated to the chatter vibration stability law, which indicates whether the design would lead to chatter vibration free cutting operation at the desired speed and depth of cut for different flutes of cutters. The arrangement of bearings is optimized using the Sequential Quadratic Programming (SQP) method.     

Rotary-axial spindles for ultra-precision machining

By combining pressurized fluid journal bearings with a novel magnetic thrust bearing, a rotary-axial spindle design is presented to achieve both rotary motion for cutting and mm-range linear motion along the axial direction for feeding. The advantages of such rotary-axial spindles include stiffer structure loops, fewer components, higher accuracy and resolution, and less heat generation. Our first prototype has demonstrated 9000 rpm, 600 N axial load capacity, 100 N/μm dynamic stiffness, 1 mm axial stroke, and 5 nm resolution. These are significant improvements over aerostatic spindles of comparable size.     

机床主轴系统静刚度分析及实验研究

为研究机床主轴系统静刚度特性,建立一种高性能加工中心主轴-轴承系统模型,该模型包括主轴转子和轴承。采用有限元法建立主轴轴系零件模型,并与轴承拟静力学模型集成得到主轴系统有限元模型,通过计算得到主轴系统3个方向的静刚度。对该机床主轴系统进行静刚度测试实验,以验证理论计算结果的正确性。研究表明:理论计算结果和实验结果具有较好一致性,因此可以有效地证明该有限元模型的准确性;此外,由于主轴系统内部存在阻尼效应及摩擦作用,卸载时静刚度大于加载时静刚度;同时其轴向静刚度存在一定非线性。     

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.     

Prediction of thermo-elastic behavior in a spindle–bearing system considering bearing surroundings

This paper presents a simulation method based on system dynamics to establish a comprehensive prediction model for the thermal and mechanical behavior of a spindle–bearing system in consideration of bearing surroundings such as assembly tolerance, geometric dimension, cooling conditions, operating conditions and thermal deformation. By introducing a lumped element into the system, not only mechanical properties but also thermal behaviors can be readily examined and predicted. The most important behavior in the spindle–bearing system is the bearing pressure, which determines the spindle characteristics and friction moment. In this study three different simplified assemblies are investigated. One is the bearing inner race–shaft subassembly that includes a negative assembly clearance, and another is the outer race–housing assembly that includes a positive assembly clearance. The third is the entire system that is composed of a rolling element bearing, an inner race–shaft subassembly and an outer race subassembly. The two subassemblies are coupled by rolling elements in which the frictional moment and heat generation vary with the assembly clearance and thermal deformation of the bearing surroundings. The new method can be applied to spindle cooling as well as the optimal thermal and mechanical design of the spindle–bearing system for various surrounding conditions. Furthermore, on the basis of the proposed model, the effect of steel and ceramic bearing materials on the thermo-elastic behavior of the spindle system was investigated.     

The development of a high-speed spindle measurement system using a laser diode and a quadrants sensor

Reducing the manufacturing time is the trend of precision manufacturing, and the precision of a work-piece is very important for manufacturing industry. High-speed cutting is becoming more widely used and the high-speed spindle is a very important element, whose precision may affect the overall performance of high-speed cutting. Most of the studies on high-speed cutting are focused on the cutting force, the vibration of the spindle and the effects of the spindle's thermal expansion; however, the measurement of the high-speed spindle continues to use the conventional spindle measurement method.As with the measurement of the high-speed spindle, more strict demands are set on the dynamic balance of cutting tools and the bandwidth of the measurement systems when compared with common spindles. The capacitance displacement sensor has been employed for the spindle error test. The precision of the measurement system is limited by the reference (such as a master ball or a master cylinder). Also the capacitance sensor and the reference must be grounded together. This paper presents a simple spindle measurement system using a laser diode and a quadrants sensor, with accuracy up to 1 μm, within 300,000 rpm for various spindles. The system does not need any reference and it is easy to set up. This system can be applied to measure the spindle errors, the spindle speed and the spindle indexing.     

考虑参数不确定性的疲劳断轴可靠性分析方法

主轴是综合传动装置中的核心元件，其可靠性直接影响综合传动装置的正常运行。针对综合传动装置主轴的疲劳失效模式，在有限元仿真的基础上考虑参数不确定性进行可靠性分析。针对疲劳断裂的主轴建立模型进行瞬态动力学仿真，获取承载工况下最大剪切应力。在此基础上考虑参数分散性对主轴强度与所受应力的影响，进行不确定性分析，并基于广义应力-强度干涉理论，运用蒙特卡洛抽样方法进行可靠度计算。在实际使用中，特殊任务下多次发生未预料的断轴故障，主轴的实际使用寿命远低于设计寿命，以该特殊任务为例进行主轴的可靠性分析。研究结果表明：针对疲劳断轴故障，采用考虑不确定性的可靠性分析方法可行。通过案例分析得到了主轴特殊工况下的疲劳寿命。     

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.     

机床主轴的仿生设计

基于对稻麦秸秆空心结构的仿生,提出了主轴的仿生空心结构设计.计算结果表明,当空心轴的壁厚约为其外径的2/7时,其主轴的抗扭、抗弯性能最好,而且使用的材料最少;对于阶梯轴或圆锥轴,可按其当量光轴直径来设计空心轴壁厚.另外,计算分析了滚动轴承的刚度,认为一定预紧力与定压预紧方式有益于提高主轴刚度.     

主动磁悬浮电主轴系统建模与控制参数分析

为实现磁悬浮电主轴的稳定悬浮运行并满足加工精度要求,通过对某型号主动磁悬浮电主轴的结构和控制原理进行研究,在忽略主轴转子磁化和磁漏等非线性因素影响的前提条件下,通过对主轴转子在磁悬浮轴承中的受力分析,建立了磁悬浮轴承的电磁支承力与轴承气隙偏移量及控制电流的表达式,对基于不完全微分PID控制的磁悬浮电主轴系统的临界转速与磁悬浮轴承的电磁刚度进行了定量研究,得到不同PID控制参数下,磁悬浮轴承支承刚度随涡动频率的变化曲线及固有频率随PID控制参数的变化曲线图。研究结果为磁悬浮电主轴控制系统进一步设计使用和分析优化提供了依据。     

Non-contact measurement of spindle stiffness by using magnetic loading device

The radial stiffness of a rotating spindle is investigated in this research. A magnetic loading device (magnet loader) that attracts a dummy tool attached to the spindle is developed for this investigation. The dummy tool is designed so that the eddy current generated at higher rotational speed is suppressed. The spindle stiffness was measured with the developed device and compared with the calculated value. From the measurement results, speed and thermal effects on the stiffness were clarified quantitatively.     

Effect of preload of linear guides on dynamic characteristics of a vertical column–spindle system

Realization on the dynamic characteristics of the column–spindle system is of importance for enhancing the structural performance of a vertical milling machine. Generally, the spindle head is fed under linear guide mechanism through a ball-screw driver. To assess the dynamic characteristics of a vertical column–spindle system under the influence of a linear guide, this study developed a finite element model integrated with the modeling of linear components with the implementation of contact stiffness at the rolling interface. Both the finite element simulations and the vibration tests reveal that the preload of a linear guide greatly affects the vibration behavior associated with a spindle head, and the dynamic stiffness of the spindle head could be enhanced by increasing the preload of the linear guide. Current results clearly indicate that the simulations agree well with the experimental measurements. This also confirms that the proposed model can be successfully applied to evaluate the dynamics characteristics of machine tool systems of various configurations.     

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.