SUPPRESSION OF PERIOD DOUBLING CHATTER IN HIGH-SPEED MILLING BY SPINDLE SPEED VARIATION

Spindle speed variation is a well known technique to suppress regenerative machine tool vibrations, but it is usually considered to be effective only for low spindle speeds. In the current paper, spindle speed variation is applied to the high speed milling process, at the spindle speeds where the constant speed cutting results in period doubling chatter. The stability analysis of triangular and sinusoidal shape variations is made numerically with the semi-discretization method. It is shown that the milling process can be stabilized by increasing the amplitude of the spindle speed variation, while the frequency of the variation has no significant effect on the dynamic behaviour. The results are validated by experiments. Based on the analysis of the machined workpieces, it is shown that the surface roughness can also be decreased by the spindle speed variation technique.     

Proposal of novel spindle speed variation profile with constant acceleration rate for improvement of chatter stability

Spindle speed variation (SSV) is one of the effective methods which suppresses regenerative chatter. However, regenerative chatter can grow even if SSV is applied. In the previous work, the chatter growth characteristics in SSV were clarified. The chatter frequency changes proportionally to the varying spindle speed, and it causes the change of the magnitude of the dynamic compliance. Hence, chatter can be suppressed through SSV since the dynamic compliance usually reduces as the chatter frequency changes. A greater compliance reduction can be obtained by a higher rate of spindle speeds in two consecutive revolutions at the same angular position, i.e., acceleration rate. From the investigations in the previous work, limitation of the conventionally utilized SSV profiles is found as follows: the acceleration rate always fluctuates with speed variation and the chatter vibration grows where the acceleration rate is insufficient for suppression, and hence suppressing chatter in all sections of SSV is difficult. In this paper, a new SSV profile with a constant acceleration rate, namely CAR-SSV, is proposed to overcome the limitation of chatter stability improvement by utilizing conventional SSV profiles. The magnitude of the acceleration rate is kept constant to realize the chatter suppression effect throughout the cutting process. Through time-domain simulation and cutting experiments, the chatter stability of CAR-SSV is investigated based on the previously introduced chatter stability evaluation indices. Influence of the parameters of CAR-SSV on the stability is investigated, and an appropriate strategy for setting SSV parameters to achieve higher stability is discussed. In addition, in order to verify the effectiveness of the proposed profile, the stabilities of conventional SSV profiles and CAR-SSV are compared through time-domain simulations and cutting experiments.     

The role of tool geometry in process damped milling

Spindle speed variation is a well-known technique to suppress regenerative machine tool vibrations, but it is usually considered to be effective only for low spindle speeds. In this paper, the effect of spindle speed variation is analyzed in the high-speed domain for spindle speeds corresponding to the first flip (period doubling) and to the first Hopf lobes. The optimal amplitudes and frequencies of the speed modulations are computed using the semidiscretization method. It is shown that period doubling chatter can effectively be suppressed by spindle speed variation, although, the technique is not effective for the quasiperiodic chatter above the Hopf lobe. The results are verified by cutting tests. Some special cases are also discussed where the practical behavior of the system differs from the predicted one in some ways. For these cases, it is pointed out that the concept of stability is understood on the scale of the principal period of the system—that is, the speed modulation period for variable spindle speed machining and the tooth passing period for constant spindle speed machining.     

Improved experimental-analytical approach to compute speed-varying tool-tip FRF

Chatter stability prediction is crucial to improve the performances of modern milling process, and it gets even more important at high speeds, for which very productive cutting parameters can be achieved if the suitable spindle speed is selected. Unfortunately, the available chatter predictive models suffer from reduced accuracy at high speed due to inaccuracies in the input data, especially the machine tool dynamics that is acquired in stationary configurations but could sensibly change with spindle speed. In this paper, an efficient method to identify the speed-varying Frequency Response Functions (FRFs) under operational conditions is presented. The proposed approach is based on the definition of some experimental chatter limits (i.e., chatter frequency and related depth of cut), obtained by a dedicated test, called Spindle Speed Ramp-up. The experimental results are then combined with the analytical stability solution. By minimizing the differences between the experimental and predicted chatter conditions, a dedicated algorithm computes the speed-varying FRFs. Few tests and simple equipment (i.e., microphone) are enough to calculate the FRFs in a wide range of spindle speeds. The proposed technique was validated in real machining applications, the identified tool-tip FRFs are in accordance with expected trend reported in scientific literature. Speed-varying stability lobe diagram reconstructed with the computed FRFs is proven to be accurate in predicting stable cutting parameters.     

Proposal of novel chatter stability indices of spindle speed variation based on its chatter growth characteristics

Chatter is one of the most critical problems that causes poor surface quality and restriction of machining efficiency. Spindle speed variation (SSV) is a well-known technique for suppression of regenerative chatter. However, in the authors’ understanding, the chatter suppression effect diminishes when the spindle speed difference between the present and previous cutting moments is small. Furthermore, the stability changes largely according to the spindle speed variation profile which changes with the set condition of SSV parameters, e.g., nominal spindle speed, variation period and variation amplitude. Therefore, SSV parameters should be adequately set to avoid this limitation and to exert its effect throughout the entire duration of cutting. However, there is no clear methodology to determine the optimal condition. This paper presents the characteristics of chatter growth during SSV focusing on the change of chatter frequency, which lead to novel indices to evaluate the chatter stability when cutting with SSV. To verify the validity of the indices, time-domain simulations and the cutting experiments with triangular spindle speed variation (TSSV) are carried out. The influence of SSV parameters on the chatter stability is investigated from the simulation and experimental results. The limitations of widely utilized SSV profiles are discussed.     

Parameter optimization of time-varying stiffness method for chatter suppression based on magnetorheological fluid-controlled boring bar

An innovative chatter suppression method based on a magnetorheological (MR) fluid-controlled boring bar for chatter suppression is developed. The MR fluid, which can change stiffness consecutively by varying the strength of the applied magnetic field, was applied to adjust the stiffness of the boring bar and suppress chatter. The cutting dynamic stability under different natural frequencies of the structure was analyzed by an energy method, which shows that cutting dynamic stability depends on both the natural frequency of the structure and the spindle speed. The chatter suppression mechanism with varying natural frequency is analyzed for further parameter optimization. Furthermore, both theoretical analyses and numerical simulations indicate that a square wave exciting current with a large amplitude and a moderate frequency has a better effect on regenerative chatter suppression. Experiments utilizing a MR fluid-controlled boring bar under an exciting current with different waveforms and frequencies were conducted. The experimental results show that the chatter can be significantly suppressed using MR fluid-controlled boring bar under a square wave exciting current with a frequency of 4–6 Hz and an amplitude of 0–2 A.     

Modeling dynamics and stability of variable pitch and helix milling tools for development of a design method to maximize chatter stability

Chatter is one of the major limitations in milling operations causing poor quality and reduced productivity. Stability diagrams can be used to identify deep stable pockets which usually occur at high spindle speeds. However, the required high cutting speeds may not be applied in some cases due to machinability or machine tool limitations. It is known that variable pitch and helix tools help suppressing chatter even at low cutting speeds. These tools may offer high productivity if they are properly designed. The literature on variable geometry milling tools is mainly limited to modelling and simulation whereas for industrial applications design guidelines are needed for selection of variation pattern and amount which is the focus of this paper. Dynamics and stability of variable pitch and helix tools are modelled and solved in frequency domain as well as using Semi-Discretization Method employing multiple delays. A practical but accurate design method is presented for selection of the best variation combination to maximize chatter free material removal rate without using time consuming computer simulations. Increased stability with the tools designed using the proposed method is demonstrated by several examples which are verified experimentally.     

Chatter suppression in micro-milling using shank-mounted Two-DOF tuned mass damper

The tuned mass damper (TMD) has been used in machining processes for reducing forced vibration, suppressing chatter, and improving machined surface quality. In micro-milling process, the tiny size of the cutting tool-tip and the high rotating speed bring challenges in implementing the TMD. Besides, the TMD needs to have two degrees-of-freedom (DOFs) for reducing vibrations of micro-mill in two orthogonal directions. This paper presents the chatter suppression for micro-milling by attaching a two-DOF TMD to the tool shank and rotates with the cutting tool. The frequency response function (FRF) at the tip of the micro-mill clamped by an aerostatic spindle is predicted using receptance coupling analysis. A two-DOF TMD is designed via graphical approach based on the FRF result at the tool-tip. The natural frequencies and damping ratio of the TMD are optimized under different spindle speeds in order to enhance the cutting stability. The chatter stability of micro-milling is predicted considering the gyroscopic and centrifugal effects of the TMD structure. Modal tests and micro-milling experiments are conducted to validate the effect of the TMD on chatter stability. The results show that the TMD is able to improve the critical depth of cut by 13 folds, and satisfy the compact design requirement for micro-milling.     

Prediction of regenerative chatter in the high-speed vertical milling of thin-walled workpiece made of titanium alloy

With the wide application of high-speed cutting technology, high-speed machining approach of titanium alloy has become one of the most effective ways to improve processing efficiency and to reduce the processing cost, but the cutting chatter which often occurs in the cutting process not only affects the machining surface quality but also reduces the production efficiency. Regenerative chatter is a typical phenomenon during actual cutting, and it has the greatest impact on the cutting process. With the purpose of avoiding regenerative chatter and selecting appropriate cutting parameters to achieve a steady cutting process and a high surface quality, it is necessary to determine the critical boundary conditions where chatter occurs. Built on the work of previous theoretical researches of regenerative chatter, this paper utilized Visual C++ software to calculate the chatter stability domain during the finish machining of titanium alloy. It was shown that the border between a stable cut and an unstable cut can be visualized in terms of the axial depth of cut as a function of the spindle speed. Using the result, it can find the specific combination of machining parameters, which lead to the maximum chatter-free material removal rate. In order to verify the result, the high-speed milling experiment of an I-shaped thin-walled workpiece made of titanium alloy was conducted. It revealed that the actual machining result was consistent with the calculation prediction. This study will offer a useful guide for effective parameter selection in future CNC machining applications.     

变速切削抑制颤振的控制系统及实验研究

为解决切削颤振给加工过程带来的不利影响,设计了基于DSP的适用于变速切削的电动机控制系统,编制了控制程序,并应用改造后的铣床进行了变速切削抑振试验。根据检测所得的加速度信号和声音信号,分析了变速幅值和变速频率对切削振动的抑制效果,对变速铣削进行了较为深入的分析和研究。     

Chatter stability prediction for high-speed milling through a novel experimental-analytical approach

Chatter prediction is crucial in high-speed milling, since at high speed, a significant increase of productivity can be achieved by selecting optimal set of chatter-free cutting parameters. However, chatter predictive models show reduced accuracy at high speed due to machine dynamics, acquired in stationary condition (i.e., without spindle rotating), but changing with spindle speed. This paper proposes a hybrid experimental-analytical approach to identify tool-tip frequency response functions during cutting operations, with the aim of improving chatter prediction at high speed. The method is composed of an efficient test and an analytical identification technique based on the inversion of chatter predictive model. The proposed technique requires few cutting tests and a microphone to calculate speed-dependent chatter stability in a wide range of spindle speed, without the need of stationary frequency response function (FRF) identification. Numerical and experimental validations are presented to show the method implementation and assess its accuracy. As proven in the paper, computed speed-dependent tool-tip FRF in a specific configuration (i.e., slotting) can be used to predict chatter occurrence in any other conditions with the same tool.     

Chatter stability prediction in milling using time-varying uncertainties

The chatter stability in milling severely affects productivity and quality of machining. Tool wear causes both the cutting coefficient and the process damping coefficient, but also other parameters to change with cutting time. This variation greatly reduces the accuracy of chatter prediction using conventional methods. To solve this problem, we consider the cutting coefficients of the milling system to be both random and time-varying variables and we use the gamma process to predict cutting coefficients for different cutting times. In this paper, a time-varying reliability analysis is introduced to predict chatter stability and chatter reliability in milling. The relationship between stability and reliability is investigated for given depths and spindle speeds in the milling process. We also study the time-varying chatter stability and time-varying chatter reliability methods theoretically and with experiments. The results of this study show that the proposed method can be used to predict chatter with high accuracy for different cutting times.     

Chatter prediction based on frequency domain solution in CNC pocket milling

Chatter has been a problem in CNC machining process especially during pocket milling process using an end mill with low stiffness. Since an iterative time-domain chatter solution consumes a computing time along tool paths, a fast chatter prediction algorithm for pocket milling process is required by machine shop-floor for detecting chatter prior to real machining process. This paper proposes the systematic solution based on integration of a stability law in frequency domain with geometric information of material removal for a given set of tool paths. The change of immersion angle and spindle speed determines the variation of the stable cutting depth along cornering cut path. This proposed solution transforms the milling stability theory toward the practical methodology for the stability prediction over the NC pocket milling.     

Spindle speed variation in turning: technological effectiveness and applicability to real industrial cases

Spindle speed variation is a well-known technique to suppress regenerative machine tool vibrations especially for low spindle speeds. Although a lot of research effort was made over the years the technique is not widespread in real turning applications. In this paper, the reasons that can limit the diffusion of the spindle speed variation were investigated. Therefore, the analysis of spindle speed variation strategy was not only focused on its chatter suppression properties but also on some more general technological aspects: the surface quality of the machined components, the cutting edge-spindle bearings load and the thermal overload the electrical spindle motor is subjected to when the speed modulation is used. A time-domain numerical model of the turning process was developed and exploited to support the analysis. A lot of cutting tests were also performed both to validate the numerical model and to evaluate the effect of variable spindle speed on surface quality. Finally, some real industrial applications were analyzed focusing on thermal overload issue of the spindle motor.     

变速切削方法的减振原理

在深入研究机床加工系统在变频激励力作用下振动响应规律的基础上,系统地论述了变速切削方法的减振原理。理论分析和试验结果表明,变速切削过程的振动响应是机床加工系统在变频激励力作用下的振动响应,它远比在恒频激励力作用下的振动响应小,这是变速切削方法之所以具有显著减振效果的最为本质的减振机理。     

基于自抗扰控制的变速非圆车削技术研究

为了抑制非圆截面工件加工时的颤振,将变速加工应用于非圆截面车削中,设计了变速车削系统结构,分析了变速车削抑制颤振、提高稳定性的机理,设计了适于变速非圆车削的直线伺服单元,单元控制采用自抗扰控制技术.车床控制系统采用PMAC(Programmable multi-axis controller)时基控制法,实现刀具驱动进给和工件变速旋转的协调控制,完成非圆截面的变速车削.结果表明,直线伺服单元能很好地跟踪刀具目标值,非圆截面车削加工精度和稳定性得到了提高.     

微小型无偏正交车铣加工系统稳定性研究

以微小型车铣复合加工系统为对象,通过对微小型车铣加工工艺系统进行分析将其简化为进行端铣研究。针对加工系统中刚度最低的工件系统利用再生型颤振理论进行分析,得到加工稳定性叶瓣图,并且通过实验验证了该叶瓣图的准确性。得到的微小型车铣稳定性叶瓣图可以指导微小型车铣的加工参数选择,提高微小型车铣加工效率。     

Speed-varying cutting force coefficient identification in milling

Accurate simulation of the machining process is crucial to improve milling performance, especially in High-Speed Milling, where cutting parameters are pushed to the limit.Various milling critical issues can be analyzed based on accurate prediction of cutting forces, such as chatter stability, dimensional error and surface finish. Cutting force models are based on coefficients that could change with spindle speed. The evaluation of these specific coefficients at higher speed is challenging due to the frequency bandwidth of commercial force sensors. On account of this, coefficients are generally evaluated at low speed and then employed in models for different spindle speeds, possibly reducing accuracy of results.In this paper a deep investigation of cutting force coefficient at different spindle speeds has been carried out, analyzing a wide range of spindle speeds: to overcome transducer dynamics issues, dynamometer signals have been compensated thanks to an improved technique based on Kalman filter estimator. Two different coefficients identification methods have been implemented: the traditional average force method and a proposed instantaneous method based on genetic algorithm and capable of estimating cutting coefficients and tool run-out at the same time.Results show that instantaneous method is more accurate and efficient compared to the average one. On the other hand, the average method does not require compensation since it is based on average signals. Furthermore a significant change of coefficients over spindle speed is highlighted, suggesting that speed-varying coefficient should be useful to improve reliability of simulated forces.     

Chatter detection in milling processes using frequency-domain Rényi entropy

Chatter is a kind of self-excited vibration and causes negative effects in machining processes. This paper presents a practical method to identify the chatter with cutting force signals in milling processes. Since the spectrum of the chatter signal exhibits discrete spectral lines around the chatter frequencies and the Rényi entropy is an effective index to characterize the randomness of data series, the frequency-domain Rényi entropy is proposed as a chatter indicator. As the chatter severity level grows, the signal components at the chatter frequencies become more and more significant, which means a reduction of the randomness of the spectral series. As a result, the value of the Rényi entropy-based indicator decreases rapidly at the onset of the chatter. In order to eliminate the interference of the normal signal components, i.e., the spindle speed-related frequency components, the spectrum is preprocessed to filter out those components first. Various milling experiments are conducted. The results show that the value of the proposed indicator changes sharply at the onset of chatter in various milling conditions with different spindle speeds and cutting depths. Also, the proposed indicator is compared with the commonly used Shannon entropy-based indicator and verified to have a larger difference between the stable and chatter statuses and is higher sensitivity to the chatter.     

Gyroscopic and mode interaction effects on micro-end mill dynamics and chatter stability

This paper investigates the gyroscopic and mode interaction effects on the micro-end mill dynamics and the stability behavior due to regenerative chatter. A high-speed spindle system for micro-milling is modeled using finite elements. The transfer functions and the mode shapes are studied to gain a deep insight into the dynamic characteristics. The experimentally identified chatter states and operational vibration modes are given to verify the analytical results. It is shown that, due to the small rotary inertia of the micro-end mill, the gyroscopic effect considered in the inertial frame is less significant despite high rotational speeds. The mode interaction strongly affects the dynamics and the chatter stability. Moreover, piezoelectric elements are applied to in-process excitation in order to identify the transfer behavior of the micro-end mill in the operating state.