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.     

Optimization of the Tuned Mass Damper for Chatter Suppression in Turning

The tuned mass damper(TMD) has been successfully applied to the vibration control in machining,while the most widely adopted tuning is equal peaks,which splits the magnitude of the frequency response function(FRF) into equal peaks.However,chatter is a special self-excited problem and a chatter-free machining is determined by FRF at the cutting zone.A TMD tuning aiming at achieving the maximum chatter stability is studied,and it is formulated as an optimization problem of maximizing the minimum negative real part of FRF.By employing the steepest descend method,the optimum frequency and damping ratio of TMD are obtained,and they are compared against the equal peaks tuning.The advantage of the proposed tuning is demonstrated numerically by comparing the minimum point of the negative real part,and is further verified by damping a flexible mode from the fixture of a turning machine.A TMD is designed and placed on the fixture along the vibration of the target mode after performing modal analysis and mode shape visualization.Both of the above two tunings are applied to modify the tool point FRF by tuning TMD respectively.Chatter stability chart of the turning shows that the proposed tuning can increase the critical depth of cut 37% more than the equal peaks.Cutting tests with an increasing depth of cut are conducted on the turning machine in order to distinguish the stability limit.The tool vibrations during the machining are compared to validate the simulation results.The proposed damping design and optimization routine are able to further increase the chatter suppression effect.     

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.     

Identification of bearing dynamics under operational conditions for chatter stability prediction in high speed machining operations

Chatter is a major problem causing poor surface finish, low material removal rate, machine tool failure, increased tool wear, excessive noise and thus increased cost for machining applications. Chatter vibrations can be avoided using stability diagrams for which tool point frequency response function (FRF) must be determined accurately. During cutting operations, due to gyroscopic moments, centrifugal forces and thermal expansions bearing dynamics change resulting in tool point FRF variations. In addition, gyroscopic moments on spindle–holder–tool assembly cause separation of modes in tool point FRF into backward and forward modes which will lead to variations in tool point FRF. Therefore, for accurate stability predictions of machining operations, effects of operational conditions on machine tool dynamics should be considered in calculations. In this study, spindle bearing dynamics are identified for various spindle rotational speeds and cutting forces. Then, for a real machining center, tool point FRFs under operating conditions are determined using the identified speed dependent bearing dynamics and the mathematical model proposed. Moreover, effects of gyroscopic moments and bearing dynamics variations on tool point FRF are examined separately. Finally, computationally determined tool point FRFs using revised bearing parameters are verified through chatter tests.     

基于四阶矩法车削颤振可靠性研究*

再生颤振是影响加工质量、加速刀具磨损、刀具破坏的主要原因。以车削加工为研究对象,针对具有不确定参数的车削加工颤振预测问题,研究车削加工系统结构动态特性参数具有随机特性的情况下颤振可靠性建模及求解问题。定义车削加工过程不出现颤振的概率为颤振可靠度,建立车削加工系统可靠性模型,研究四阶矩法求解可靠度的问题,提出利用颤振可靠性叶瓣图方法进行颤振预测。通过模态试验对一车床进行频响函数测试,采用四阶矩法计算获得了颤振可靠度,并与蒙特卡洛法获得的可靠度相比较。结果表明四阶矩法计算获得的可靠度与蒙特卡洛仿真结果一致性很好,但是四阶矩法计算精度高而且计算耗时远小于蒙特卡洛法。进行颤振可靠性切削试验,通过观察振纹和分析噪声功率谱识别颤振,对典型参数进行验证,试验结果与分析结果一致。     

Prediction and experimental validation of micro-milling cutting forces of AISI H13 steel at hardness between 35 and 60 HRC

This paper presents prediction and validation of micro-milling cutting forces of AISI H13 steel at hardnesses between 35 and 60 HRC. The cutting forces are predicted based on an approach considering the full kinematics of the cutting tool including the run-out effect, effects of the cutting velocity and tool geometry, ploughing and chip formation phenomena and the hardness of the AISI H13 steel. A plane strain dynamic thermo-mechanical finite element (FE) model of orthogonal cutting is used to predict the cutting forces where the geometry of the cutting tool edge is modelled based on scanning electron microscope measurements. A constitutive elastic–plastic isotropic material model describing the relationship between stresses, strains, strain rates and hardnesses is modelled and implemented into ABAQUS/Explicit FE code by the user-defined subroutine VUMAT. Finite element analyses (FEA) are employed to obtain the relationship between cutting forces, uncut chip thickness, cutting velocity and material hardness. Numerous FEA are performed at different uncut chip thicknesses (0–20?μm), cutting velocities (104.7–4,723?mm/s) and hardnesses (35–60 HRC) using the FE model of orthogonal cutting. The full kinematics of the cutting tool including the run-out effect and the FE-predicted cutting forces are incorporated to predict the micro-milling cutting forces. The predicted micro-milling cutting forces have been experimentally validated at hardness of 43.2 HRC at different feed rates and spindle speeds. The result showed that the cutting forces and cutting temperatures increase by increasing the hardness of the AISI H13 while the stability limits of the process decrease by increasing the hardness.     

基于SVR-GA算法的广义加工空间机床切削稳定性预测与优化研究

针对机床零件加工位置和进给方向不确定造成刀尖频响函数变化,导致切削稳定性叶瓣图与无颤振工艺参数预测具有不确定性问题,提出一种耦合支持向量回归机(SVR)与遗传算法(GA)的切削稳定性预测与优化方法。该方法采用锤击法模态实验和空间坐标变换,获取样本空间不同加工位置与进给方向的刀尖频响函数;进而结合传统切削稳定性预测方法构建以各向运动部件位移、进给角度、主轴转速、切削宽度、每齿进给量为输入的极限切削深度SVR预测模型;采用该SVR模型作为切削稳定性约束建立材料切除率优化模型,通过遗传算法求解各运动轴位移、进给角度与切削参数的最优配置。以某型加工中心展开实例研究,实验结果表明获取的优化配置能实现稳定切削,验证了该方法的有效性。     

用半理论法预测主轴系统刀尖点频响函数

采用半理论法,即理论与试验相结合的方法预测主轴系统刀尖点频响函数。首先,介绍半理论法的预测原理;然后,应用半理论法预测主轴系统刀尖点频响函数的流程,包括利用梁理论计算自由-自由状态刀具两端的阻抗矩阵、搭建主轴-刀柄频响函数测试系统、测试装卡短光滑圆柱的主轴-刀柄系统的频响函数、根据半理论法计算刀尖点频响函数和试验验证;最后,以某立式加工中心主轴系统为研究对象,应用该方法对刀尖点频响函数进行预测,并与试验进行对比以证明该方法的有效性。     

高速主轴系统切削稳定性预测及影响因素分析

高速主轴系统切削稳定性直接影响产品的表面加工精度和切削系统的使用寿命,是评价高速主轴系统性能优劣的重要因素,而研究影响切削稳定性的因素并制定提高稳定性的合理途径同样也受到关注。提出从稳定性评价准则及系统频响函数的不同求解方法入手,分析无条件稳定区和有条件稳定区的影响因素,总结出系统所受激励、主轴转速及系统结构是影响切削稳定性的重要因素。以德国GMN高速主轴系统为例,在采用5自由度轴承受力与变形关系模型模拟角接触球轴承和分布式弹簧模型模拟主轴-刀柄-刀具结合部的基础上,建立完整高速主轴系统通用有限元模型;利用三维稳定性叶瓣图、极限切削深度和叶瓣交点随参数的变化曲线表征切削力幅值、转速及阻尼比等参数对切削稳定性的影响规律,为优化加工工艺、提高系统切削稳定性提供理论依据。     

Automatic selection of spindle speed for suppression of regenerative chatter in turning

The paper presents a new spindle speed regulation method to avoid regenerative chatter in turning operations. It is not necessary to analyse complex cutting dynamics to search for stable spindle speeds to eliminate regenerative chatter. The metal removal rate is also greatly improved by using this method. The stability lobe diagram for the stability limit of chip width and chatter frequency versus spindle speed is derived by using the Nyquist stability criterion. It is shown that stable spindle speeds can be automatically obtained when the chatter frequency is found. Computational simulations and experimental cutting tests are performed to illustrate the proposed method.     

Receptance Coupling for Tool Point Dynamics Prediction on Machine Tools

Chatter has been a primary obstacle to the successful implementation of high speed machining.The frequency response function(FRF) of the tool point is crucial for identification of chatter free cutting conditions.In order to quickly acquire the FRF of the different components combinations of machine tool,the assembly of machine tool was always decomposed into several parts,where the fluted portion of tool,however,was always treated as a uniform beam,and the associated discrepancy was ignored.This paper presents a new method to predict the dynamic response of the machine-spindle-holder-tool assembly using the receptance coupling substructure analysis technique,where the assembly is divided into three parts:machine-spindle,holder and tool shank,and tool’s fluted portion.Impact testing is used to measure the receptance of machine-spindle,the Timoshenko beam model is employed to analyze the dynamics of holder and tool shank,and the finite element method(FEM) is used to calculate the receptance of the tool’s fluted portion.The approximation of the fluted portion cross section using an equivalent diameter is also addressed.All the individual receptances are coupled by using substructure method.The predicted assembly receptance is experimentally verified for three different tool overhang lengths.The results also show that the equivalent diameter beam model reaches an acceptable accuracy.The proposed approach is helpful to predict the tool point dynamics rapidly in industry.     

Model-based operating recommendations for high-speed spindles equipped with a self-vibratory drilling head

The drilling of deep holes requires the chips to be evacuated using retreat cycles and lubrication, which is problematic for both productivity and the environment. An alternative response to the chip evacuation problem is the use of a vibratory drilling head, which enables the chip to be split thanks to the axial self-excited drill, and hence it can easily be evacuated from the hole. The vibratory drilling head is composed of a specific tool holder with adjustable axial stiffness. In this paper, a dynamic high-speed spindle/drilling head/tool system model is elaborated on the basis of rotor dynamics predictions. The dynamic properties of interfaces between system components are identified by the receptance coupling method and integrated into the model. The model is validated by comparing the numerical FRF with experimental results. Then adequate self-vibratory cutting conditions are established by integrating the model-based tool tip FRF into the chatter approach of Budak-Altintas. Spindle rolling bearing lifespan is also investigated in order to guarantee a rational use of the spindle-tool set with respect to industrial lifespan.     

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.     

基于实验模态分析的集中参数法建模

利用集中参数模型的建立,不仅拓展了实验模态分析(EMA)的使用范围,还能大量缩减原有模型的自由度并保持结构的动态特性。在对一立铣床进行模态测试以及振型可视化的基础上,采用集中质量、弹簧阻尼单元建立了该铣床的7自由度集中参数模型,并在该模型基础上合成刀尖频响函数及预测颤振稳定域,揭示出机床颤振与振型的联系。与原有测试频响函数的比较表明,该模型准确度较高。     

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.     

The use of D-optimal design for modeling and analyzing the vibration and surface roughness in the precision turning with a diamond cutting tool

Using a diamond cutting tool in the precision turning process, the vibration of tool-tip has an undesirable effect on the machined surface??s quality. The objective of this paper is to present the mathematical models for modeling and analyzing the vibration and surface roughness in the precision turning with a diamond cutting tool. Machining parameters including the spindle speed, feed rate and cutting depth were chosen as numerical factor, and the status of lubrication was regarded as the categorical factor. An experimental plan of a four-factor??s (three numerical plus one categorical) D-optimal design based on the response surface methodology was employed to carry out the experimental study. A micro-cutting test is conducted to visualize the effect of vibration of tool-tip on the performance of surface roughness. With the experimental values up to a 95% confidence interval, it is fairly well for the experimental results to present the mathematical models of the vibration and surface roughness. Results show that the spindle speed and the feed rate have the greatest influence on the longitudinal vibration amplitude, and the feed rate and the cutting depth play major roles for the transverse vibration amplitude. As the spindle speed increases, the overall vibration of tool-tip tends to more stable condition which leads to the results of the best machined surface. The effects of the feed rate and cutting depth provide the reinforcement on the overall vibration to cause the unstability of cutting process and exhibit the result of the worst machined surface.     

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.     

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.     

再生颤振的稳定性模型研究

在刀具和工件之间产生的自激颤振不仅影响工件的表面粗糙度和加工精度,而且对刀具寿命有不利影响,甚至无法进行切削加工,这就直接影响生产效率的提高。本文对切削颤振的稳定性模型进行了研究,推导出了稳定切削极限条件下,主轴转速和轴向切深的关系表达式,并用Matlab进行了仿真计算。     

Three-dimensional stability prediction and chatter analysis in milling of thin-walled plate

Stability lobe diagram can be used for selecting proper milling parameters to perform chatter-free operations and improve productivity during milling of thin-walled plates. This paper studies the machining stability in milling of thin-walled plates and develops a three-dimensional stability lobe diagram of the spindle speed, tool position, and axial depth of cut. The workpiece-holder system is modeled as a 2-degree-of-freedom system considering that the tool system is much more rigid than the thin-walled plate, and dynamic equations of motion described for the workpiece-holder system are solved numerically in time domain to compute the dynamic displacements of the thin-walled plate. Statistical variances of the dynamic displacements are then employed as a chatter detection criterion to acquire the stability lobe diagram. The experimentally obtained stability limits correspond well with the predicted stability limits. In addition, influence of feed rate on stability limits is also investigated. By performing frequency analysis of the measured cutting forces to judge if chatter occurs, it is found that feed per tooth has little influence on the stability limits. However, feed per tooth impacts the machined surface quality. The results show that the surface quality drops by increasing feed per tooth.