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.     

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 closed-form approach for identification of dynamical contact parameters in spindle–holder–tool assemblies

Accurate identification of contact dynamics is very crucial in predicting the dynamic behavior and chatter stability of spindle–tool assemblies in machining centers. It is well known that the stability lobe diagrams used for predicting regenerative chatter vibrations can be obtained from the tool point frequency response function (FRF) of the system. As previously shown by the authors, contact dynamics at the spindle–holder and holder–tool interfaces as well as the dynamics of bearings affect the tool point FRF considerably. Contact stiffness and damping values alter the frequencies and peak values of dominant vibration modes, respectively. Fast and accurate identification of contact dynamics in spindle–tool assemblies has become an important issue in the recent years. In this paper, a new method for identifying contact dynamics in spindle–holder–tool assemblies from experimental measurements is presented. The elastic receptance coupling equations are employed in a simple manner and closed-form expressions are obtained for the stiffness and damping parameters of the joint of interest. Although this study focuses on the contact dynamics at the spindle–holder and holder–tool interfaces of the assembly, the identification approach proposed in this paper might as well be used for identifying the dynamical parameters of bearings, spindle–holder interface and as well as other critical joints. After presenting the mathematical theory, an analytical case study is given for demonstration of the identification approach. Experimental verification is provided for identification of the dynamical contact parameters at the holder–tool interface of a spindle–holder–tool assembly.     

Analytical modeling of spindle–tool dynamics on machine tools using Timoshenko beam model and receptance coupling for the prediction of tool point FRF

Regenerative chatter is a well-known machining problem that results in unstable cutting process, poor surface quality and reduced material removal rate. This undesired self-excited vibration problem is one of the main obstacles in utilizing the total capacity of a machine tool in production. In order to obtain a chatter-free process on a machining center, stability diagrams can be used. Numerically or analytically, constructing the stability lobe diagram for a certain spindle–holder–tool combination implies knowing the system dynamics at the tool tip; i.e., the point frequency response function (FRF) that relates the dynamic displacement and force at that point. This study presents an analytical method that uses Timoshenko beam theory for calculating the tool point FRF of a given combination by using the receptance coupling and structural modification methods. The objective of the study is two fold. Firstly, it is aimed to develop a reliable mathematical model to predict tool point FRF in a machining center so that chatter stability analysis can be done, and secondly to make use of this model in studying the effects of individual bearing and contact parameters on tool point FRF so that better approaches can be found in predicting contact parameters from experimental measurements. The model can also be used to study the effects of several spindle, holder and tool parameters on chatter stability. In this paper, the mathematical model, as well as the details of obtaining the system component (spindle, holder and tool) dynamics and coupling them to obtain the tool point FRF are given. The model suggested is verified by comparing the natural frequencies of an example spindle–holder–tool assembly obtained from the model with those obtained from a finite element software.     

Receptance coupling for end mills

Identification of chatter free cutting conditions, the chatter stability lobes, requires a measurement of the frequency response function (FRF) of each tool mounted on the spindle. This paper presents a method of assembling known dynamics of the spindle–tool holder with an analytically modeled end mill using the receptance coupling technique. The classical receptance technique is enhanced by proposing a method of identifying the end mill–spindle/tool holder joint dynamics, which include both translational and rotational degrees of freedom. The method requires measurement of FRFs with impact tests applied on the spindle–tool holder assembly and blank calibration cylinders attached to the spindle. The spindle and tool holder characteristics are completely identified from the two experiments, and used for the mathematical prediction of FRF for end mills with arbitrary dimensions. The proposed method is experimentally proven and verified in cutting tests.     

Dynamic analysis of a motor-integrated method for a higher milling stability

The productivity in High Speed Cutting is often limited by undesirable vibration effects in the main spindle (chatter). In many cases these limits are far below the technically possible cutting parameters provided by the machine technology. This paper presents a new approach to a motor-integrated milling spindle with an embedded electromagnetic actuator to actively reduce chatter vibrations and increase productivity. It is based on the non-contact application of highly-dynamic damping forces on the spindle shaft. That way the process stability can be increased significantly. By measurement and simulation-based analysis of spindle dynamics and transient and analytical approaches to process stability, the efficiency of the damping method is demonstrated in theory. Finally, a new, soft magnetic composite based motor-integrated electromagnetic actuator is introduced in this article.     

Suppressing vibration modes of spindle-holder-tool assembly through FRF modification for enhanced chatter stability

Modifying dynamic response of a machine tool is of great importance for chatter mitigation. Tool tip frequency response function (FRF) can be suppressed by capitalizing on the absorber effect due to dynamic interactions among vibration modes of spindle, holder and tool. In this paper, a practical method is presented to modify the system’s FRF by selecting proper dimensions for assembly component without extensive testing. Robustness of the method is demonstrated through simulation and test results. Milling stability tests were also conducted where significant improvements in chatter free Material Removal Rate (MRR) is achieved.     

Method for chatter detection with standard PLC systems

The aim of growing productivity together with increasing quality demands in machining leads to milling processes that are near their stability limits. The remaining stability reserves become smaller and the risk of unstable processing conditions like chatter increases. Unstable processes cause unwanted vibrations with high amplitudes in bearing loads. As a result, the lifetime of the bearings of the main spindle is reduced. Besides this, the surfaces of unstable processed work-pieces have unwanted chatter marks and do not fulfill the quality demands. To basically avoid unstable processing,a continuous monitoring of the process state is necessary. In this paper, a method for monitoring cutting processes using a standard programmable logic controller which is integrated in the drive controller of the machine tool spindle unit is presented. The method is real time-capable and based on the hypothesis that unstable process conditions result in a modulation of the amplitudes of the cutting forces. To detect this, an order tracking method is implemented, which uses a recursive parameter estimation algorithm together with inherently given signals of the drive controller. It is shown that the characteristic property of the used estimation algorithm and allowed aliasing lead to a reliable chatter detection even at sub-sampling. Finally some results of the first experimental investigation of the method are given.     

立式铣床刀尖频响函数预测方法研究

由于对机械加工精度和效率影响较大,切削颤振一直是制造领域的研究热点之一。为了避免颤振的发生,通常利用稳定性Lobe图确定合适的加工参数,而机床刀尖频响函数是绘制稳定性Lobe图的先决条件。基于模态叠加法、激振实验和响应耦合子结构耦合方法 (Receptance Coupling Substructure Analysis,RCSA),提出了一种新的机床刀尖频响函数计算方法。首先通过模态叠加法计算刀柄和刀具的各个端点频响函数,通过锤击法得到机床主轴的端点频响函数,最后利用RCSA耦合各个子结构,获取机床刀尖频响函数。对比实验结果,本文作者提出的方法能够得到精确的立式铣床刀尖频响函数。     

Optimization of multiple tuned mass dampers to suppress machine tool chatter

Chatter is more detrimental to machining due to its instability than forced vibrations. This paper presents design and optimal tuning of multiple tuned mass dampers (TMDs) to increase chatter resistance of machine tool structures. Chatter free critical depth of cut of a machine is inversely proportional to the negative real part of frequency response function (FRF) at the tool–workpiece interface. Instead of targeting reduction of magnitude, the negative real part of FRF of the machine is reduced by designing single and multiple TMD systems. The TMDs are designed to have equal masses, and their damping and stiffness values are optimized to improve chatter resistance using minimax numerical optimization algorithm. It is shown that multiple TMDs need more accurate tuning of stiffness and natural frequency of each TMD, but are more robust to uncertainties in damping and input dynamic parameters in comparison with single TMD applications. The proposed tuned damper design and optimization strategy is experimentally illustrated to increase chatter free depth of cuts.     

Model-based chatter stability prediction for high-speed spindles

The prediction of stable cutting regions is a critical requirement for high-speed milling operations. These predictions are generally made using frequency response measurements of the tool/holder/spindle set, obtained from a non-rotating spindle. However, significant changes in system dynamics occur during high-speed rotation. In this paper, a dynamic model of a high-speed spindle-bearing system is elaborated on the basis of rotor dynamics predictions, readjusted with respect to experimental modal identification. Variations in dynamic behaviour according to speed range are then investigated and determined with accuracy. Dedicated experiments are carried out in order to confirm model results. By integrating the proposed speed-dependant transfer function into the chatter vibration stability approach of Budak–Altintas [S. Tobias, W. Fishwick, Theory of regenerative machine tool chatter, The Engineer February (1958)] a dynamic stability lobes diagram is predicted. The proposed method enables a new stability lobes diagram to be established that takes into account the effect of spindle speed on dynamic behaviour. Significant variations are observed and allow the accurate prediction of cutting conditions. Finally, experiments are performed in order to validate chatter boundary predictions in practice. The proposed modelling approach can also be used to qualify a spindle design in a given machining process and can easily be extended to other types of spindle.     

Active control of high frequency chatter with machine tool feed drives in turning

This paper presents a new active vibration control strategy to mitigate high frequency regenerative chatter vibrations using machine tool feed drives. Rather than modal damping, proposed approach aims to control regenerative process dynamics to shape the Stability Lobe diagram (SLD) and attain higher material removal rates. The controller is designed as a feedback filter whose parameters are optimized to compensate regeneration. The proposed strategy is applied to actively control orthogonal (plunge) turning dynamics where >2.5 [kHz] chatter vibrations are suppressed by a fast tool servo (FTS) drive system. Stability lobes are shaped locally to reach up to 4x higher material removal rates.     

A new on-line spindle speed regulation strategy for chatter control

A new on-line control method to suppress regenerative chatter vibration during the machining process by regulating spindle speed is proposed. The dynamic cutting force signal collected from a dynamometer is passed through a low pass filter, and then digitized. The fast Fourier transform is carried out to obtain the corresponding power spectrum. The chatter frequency is identified when the intensity at a certain frequency other than the spindle speed and tooth passing frequency exceeds a critical value. Based on the identified chatter frequency, a new spindle speed is computed by applying the principle of keeping the phase between the present and previous undulations to 90°. The new speed command is executed while the cutting proceeds. It is found from simulation that the chatter vibration can be suppressed by this approach in the shortest time. This method is also verified by experiments through actual cutting of various materials by a computer numerically controlled milling machine. The main feature of this approach is that the feed of the machine tool does not need to be halted during the change of spindle speed. Hence, tool wear can be reduced. Furthermore, no system identification of the machine tool structure is needed, and therefore it has great potential in actual applications.     

An automatic spindle speed selection strategy to obtain stability in high-speed milling

Chatter vibration problems arise during machining. This paper aims to produce a strategy that can detect the emergence of chatter so that subsequently, in accordance with the lobe on the stability diagram where the process is located, the proper strategy may be determined, either by taking the machine to a stable spindle speed or causing continuous variation in spindle speed. The effectiveness of this strategy is contrasted for a number of different cases, using both simulation and experimental testing. The context targeted by the strategy is a high-speed mill roughing operation for cases of vibration arising on the headstock/cutting tool unit, when high material removal rates (MRR) must be maintained. Industrial implementation of the strategy and the chatter detection and diagnosis algorithm is carried out using a portable digital assistant (PDA).     

Why is it hard to identify the onset of chatter? A stochastic resonance perspective

A stochastic dynamical model is presented to identify the difficulties in chatter detection during cutting processes. The theoretical implications are based on measurements related to the stochastic character of the cutting force. The stochastic model is validated in a Hardware-In-the-Loop (HIL) environment where the multiplicative component of the stochastic cutting force is varied parametrically. In case of an industrial machine tool, the stochastic resonance effect is also demonstrated quantitatively by means of high-resolution vibration measurements for various spindle speeds in full immersion milling. The proposed method predicts the noise induced peaks in the spectrum of the vibration signals, which occur already within the chatter-free parameter domains and might be misjudged as chatter.     

Feed drive control tuning considering machine dynamics and chatter stability

In large machine tools, where structural dynamics significantly influences the cutting stability, judicious selection of the servo control parameters can increase the damping, thereby improving the chatter stability. This paper presents a new strategy for feed drive controller tuning, which takes this effect into consideration. The proposed strategy generalizes successfully to machine tool structures with high order dynamics, and integrates model-free frequency domain estimation and analysis techniques with model-based root locus design, the latter which is achieved through an efficient and accurate identification approach. The proposed strategy has been tested in machining stability tests, demonstrating up to 30% increase in productivity.     

A unified system model of cutting chatter and its transformation function

Based on the hypothesis of linearity of non-linear machine tool chatter, a new system model of cutting dynamics is presented in this paper, which unifies the existing linear chatter theory, the non-linear chatter theory and the mechanism of the restraint of ultrasonic vibration assisted cutting on chatter.

After introducing the boundary modulation N(s), the transformation function of the new system model is deduced. Then the system model is modified according to the workpiece surface outline. The characteristic equation is deduced from the modified model.

The difference between the boundary modulation frequency and the close-loop mode frequency is analyzed according to the characteristic equation, and our experimental research verifies the analysis.

Ultrasonic vibration assisted cutting is an efficient technology to restrain machine tool chatter. The mechanism of this is that, in ultrasonic vibration assisted cutting, the modulus of the non-linear modulation N(s) is less than 1.00, so that the real cutting stiffness decreases to |N(s)| times that in traditional cutting with the same cutting condition.     

Hybrid modelling of machine tool axis drives

The x-axis dynamics of a milling machine where the workpiece and saddle are mounted on supporting slides is considered. A permanent magnet motor, lead screw, ball nut and bearings are employed as the machine, traverse actuator mechanism. Hybrid, distributed–lumped parameter methods are used to model the machine tool x-axis drive system. Inclusion of the spatial configuration of the drive generates the incident, travelling and reflected vibration signature of the system. Lead screw interactive torsion and tension loading, which is excited by cutting and input disturbance conditions, is incorporated in the modelling process. Measured and results from simulation exercises are presented in comparative studies enabling the dynamic characteristics of the machine to be identified under, no load and with the application of cyclic, cutting force disturbances. The effect of the lead screw length, cutting speed and hence the load disturbance frequency are examined and the resulting performance accuracy is commented upon.     

High frequency bandwidth cutting force measurement in milling using capacitance displacement sensors

This article presents a method of measuring cutting forces from the displacements of rotating spindle shafts. A capacitance displacement sensor is integrated into the spindle and measures static and dynamic variations of the gap between the sensor head and the rotating spindle shaft under cutting load. To calibrate the sensing system, the tool is loaded statically while the deflection of the tool is measured with the capacitance probe. With this calibration, the displacement sensor can be used as an indirect force sensor. However, the measurement bandwidth is limited by the natural modes of the spindle structure. If cutting force frequency contents are within the range of the natural modes of the spindle structure or higher, the measurements are distorted due to the dynamic characteristics of the spindle system. In order to increase the bandwidth of the indirect force sensor by compensating for the spindle dynamics, the design of a Kalman filter scheme, which is based on the frequency response function (FRF) of the displacement sensor system to the cutting force, is presented in this paper. With the suggested sensing and signal processing method, the frequency bandwidth of the sensor system is increased significantly, from 350 to approximately 1000 Hz. The proposed indirect force sensor system is tested experimentally by conducting cutting tests up to 12,000 rpm with a five-fluted end mill. Besides cutting forces, the measured displacements can also be affected by factors such as roundness errors, unbalance at different speeds, or dilatation of the spindle shaft due to temperature variations. Methods to compensate for these disturbing effects are also described in the paper.     

The effect of tool geometry on regenerative instability in ultrasonic vibration cutting

Ultrasonic vibration cutting as a cutting process has been widely used in the precision machining of difficult-to-cut materials due to an enhanced cutting stability and increased productivity. The authors' previous researches have shown that chatter vibration prediction is made possible by the suggested cutting model. This paper is an attempt to determine cutting parameters based on regenerative chatter prediction in order to facilitate the machining objectives of high accuracy, high efficiency and low cost in ultrasonic vibration cutting. The machinability of SCM440 steel, called typical hardened steel, is investigated theoretically and experimentally. The cutting model is developed by introducing an experimental cutting database of SCM440 steel. The simulation and experimental results show that the workpiece material parameter has a direct influence on the occurrence of regenerative chatter. In order to achieve the chatter-suppressing dynamics in hard ultrasonic vibration cutting, a stability diagram is predicted based on the simulated work displacement for tool geometry changing. The stability diagram indicates that the regions of the chatter-suppressing dynamics expand with increasing tool rake angle and decreasing tool clearance angle. It is also found from the predictive results that regenerative chatter can be suppressed by a change of tool geometry. The determined tool geometry with the aid of the computer simulation is demonstrated through actual data of ultrasonic vibration cutting. By the use of the designed tool geometry, a good experimental result is achieved.