Prediction of chatter in high speed milling including gyroscopic effects

Dynamic stability of machine tools during operations is dependent on many parameters including the spindle speed. In high and ultra high speed machining, the gyroscopic effect on the spindle dynamics becomes more pronounced and can affect the borders of stability of the rotating system. In this paper, a finite element based model of spindle, tool holder and cutting tool is presented which uses Timoshenko beam theory to obtain the frequency response of the system when gyroscopic terms are included. Using this response, the stability of a high speed spindle system in the presence of gyroscopic effect is investigated. It is shown that the gyroscopic effects lower the critical depth of cut in high speed milling.     

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.     

Analysis of bearing configuration effects on high speed spindles using an integrated dynamic thermo-mechanical spindle model

This work presents the effects of bearing configuration on the thermo-dynamic behavior of high speed spindles using the comprehensive dynamic thermo-mechanical model. The dynamic thermo-mechanical model consists of a comprehensive bearing dynamic model, a shaft dynamic model and a thermal model. The thermal model is coupled with the spindle dynamic model through bearing heat generation and thermal expansion of the whole system based on the bearing configuration. Thus the entire model becomes a comprehensive dynamic thermo-mechanical model. The new thermo-mechanical model also considers a pertinent mapping between bearing stiffness and shaft stiffness matrices based on bearing configurations, so that more general cases of bearing configurations can be modeled. Based on this model, the effects of bearing orientation on the spindle dynamics are systematically described and experimentally validated. It is shown that bearing orientation has a significant effect on spindle stiffness. Finally, the effects of various bearing configurations on spindle thermal and dynamic behavior are illustrated through numerical analysis with three different spindles.     

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.     

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.     

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.     

Stability-based spindle speed control during flexible workpiece high-speed milling

High-speed machining (HSM) is a technology used to increase productivity and reduce production costs. The prediction of stable cutting regions represents an important issue for the machining process, which may otherwise give rise to spindle, cutter and part damage. In this paper, the dynamic interaction of a spindle-tool set and a thin-walled workpiece is analysed by a finite element approach for the purpose of stability prediction.The gyroscopic moment of the spindle rotor and the speed-dependent bearing stiffness are taken into account in the spindle-tool set finite element model and induce speed-dependent dynamic behaviour. A dedicated thin-walled workpiece is designed whose dynamic behaviour interacts with the spindle-tool set. During the machining of this flexible workpiece, chatter vibration occurs at some stages of machining, depending on the cutting conditions and also on the tool position along the machined thin wall.By coupling the dynamic behaviour of the machine and the workpiece, respectively, dependent on the spindle speed and the relative position of both the systems, an accurate stability lobes diagram is elaborated.Finally, the proposed approach indicates that spindle speed regulation is a necessary constraint to guarantee optimum stability during machining of thin-walled structures.     

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.     

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.     

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.     

Modeling and identification of tool holder–spindle interface dynamics

The majority of the chatter vibrations in high-speed milling originate due to flexible connections at the tool holder–spindle, and tool–tool holder interfaces. This article presents modeling of contact stiffness and damping at the tool holder and spindle interface. The holder–spindle taper contact is modeled by uniformly distributed translational and rotational springs. The springs are identified by minimizing the error between the experimentally measured and estimated frequency response of the spindle assembly. The paper also presents identification of the spindle's dynamic response with a holder interface, and its receptance coupling with the holder–tool stick out which is modeled by Timoshenko beam elements. The proposed methods allow prediction of frequency-response functions at the tool tip by receptance coupling of tools and holders to the spindle, as well as analyzing the influence of relative wear at the contact by removing discrete contact springs between the holder and spindle. The techniques are experimentally illustrated and their practical use in high speed milling applications is elaborated.     

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。     

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.     

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.     

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.     

高速电主轴关键技术的研究

高速加工技术能极大地提高生产率和降低生产成线,是２１世纪最有发展前任的先进制造技术之一。电主轴是实现机床高速化的核心部件,本文结合高速铣削用大功率电主轴开发课详细分析了高速主轴技术的现状,存在问题及解决方法。     

A new method to quantify radial error of a motorized end-milling cutter/spindle system at very high speed rotations

The radial error motion of a machine tool cutter/spindle system is critical to the dimensional accuracy of the parts to be machined. The spindle's radial error motions can be measured by mounting a sphere target onto the spindle as a reference. A set of sensors is used to measure displacements of the reference sphere in various directions to determine spindle error motions. This measurement technique can be reliably carried out when the spindle is at rest or at low rotational speeds. However, at very high speeds, the reference sphere must be carefully centered and balanced to avoid introducing additional error motions. In addition, the sensors must be held with very rigid mounts in order to avoid measurement errors caused by vibrations. For high-speed end milling spindles, the spindle is operated with a cutter. The cutter must be removed when mounting a reference sphere. Because the cutter itself can introduce errors due to centering and unbalancing effects, the error motions measured by the reference sphere method do not include the error caused by the cutter. This paper introduces a new and practical method to provide an indicator of the radial error of a motorized end-milling cutter/spindle system at very high speed rotations without the need of a reference sphere. This indicator of the radial error is based on the size of the cutting marks produced by the end mill, which is attached to the spindle. The cutting marks are circular, and their diameters are related to the radial error of the cutter/spindle system. Quantitative precision analysis was carried out to confirm the accuracy and repeatability of this new measurement technique. This technique has been implemented in order to determine the effects of the spindle speed, the level of unbalanced mass, and the spindle stiffness on the cutter/spindle's radial error. The results reveal that the centrifugal force generated by the unbalanced mass is the main factor causing the increase in radial error. One way to compensate for the effect of unbalanced mass is to increase the spindle stiffness. Experimental results confirm that a higher front bearing preload can render the spindle stiffer, thus reducing the radial error of the cutter/spindle system. Finally, it should be pointed out that the proposed cutting mark measurement cannot replace the sphere method because it cannot provide time-resolved or angle-resolved information as those obtained from polar charts. However, the proposed cutting mark measurement can provide the characterization of the spindle with the cutter attached. As a result, both methods can complement each other to provide a more complete picture of the behavior of the cutter/spindle system at high speeds.     

The effects of spindle vibration on surface generation in ultra-precision raster milling

Spindle vibration has a significant influence on surface quality of ultra-precision-machined components. However, relatively few studies on the particular spindle vibration under the excitation of intermittent cutting forces in ultra-precision raster milling (UPRM) have been reported. In this study, a specialized model for an aerostatic bearing spindle under the impulsive excitation from intermittent cutting forces of UPRM is developed and its derived mathematical solutions reveal that the spindle vibration is impulsive response. The theoretical and experimental results signify that the impulsive spindle vibration produces inhomogeneous scallops forming ribbon-stripe patterns and irregular patterns like run-out on a surface of UPRM. The potential benefits for UPRM are the theoretical supports for optimization and prediction of surface generation through the optimal selection of spindle speed.     

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.     

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.