Analysis of the machining stability of a milling machine considering the effect of machine frame structure and spindle bearings: experimental and finite element approaches

Chatter vibration has been a troublesome problem for a machine tool toward the high precision and high-speed machining. Essentially, the machining performance is determined by the dynamic characteristics of the machine tool structure and dynamics of cutting process of spindle tool. Prediction of the dynamic behavior at spindle tool tip is therefore of importance for assessing the machining stability of a machine tool at design stage. This study was aimed to evaluate the machining stability of a vertical milling system under the interactive influence of the spindle unit and the machine frame structure. To this end, a realistic finite element model of a vertical milling tool was generated by incorporating the spindle-bearing model into the head stock mounted on machine frame. The influences of the dynamics of spindle-bearing system and the machine frame structure were investigated respectively. Current results show that the machine tool spindle system demonstrates different dynamic behaviors at different frequency ranges, which are also characterized as structural modes and spindle modes, respectively. In particular, the maximum compliance of spindle tool tip was found to occur at the bending vibrations of spindle shaft and vary with the preload amount of spindle bearing. The machining stabilities were predicted to different extent, depending on the exciting modes which could be related to the influences of machine frame and spindle unit.     

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.     

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.     

Modal identification of spindle-tool unit in high-speed machining

The accurate knowledge of high-speed motorised spindle dynamic behaviour during machining is important in order to ensure the reliability of machine tools in service and the quality of machined parts. More specifically, the prediction of stable cutting regions, which is a critical requirement for high-speed milling operations, requires the accurate estimation of tool/holder/spindle set dynamic modal parameters. These estimations are generally obtained through Frequency Response Function (FRF) measurements of the non-rotating spindle. However, significant changes in modal parameters are expected to occur during operation, due to high-speed spindle rotation.The spindle's modal variations are highlighted through an integrated finite element model of the dynamic high-speed spindle-bearing system, taking into account rotor dynamics effects. The dependency of dynamic behaviour on speed range is then investigated and determined with accuracy. The objective of the proposed paper is to validate these numerical results through an experiment-based approach. Hence, an experimental setup is elaborated to measure rotating tool vibration during the machining operation in order to determine the spindle's modal frequency variation with respect to spindle speed in an industrial environment. The identification of natural frequencies of the spindle under rotating conditions is challenging, due to the low number of sensors and the presence of many harmonics in the measured signals. In order to overcome these issues and to extract the characteristics of the system, the spindle modes are determined through a 3-step procedure. First, spindle modes are highlighted using the Frequency Domain Decomposition (FDD) technique, with a new formulation at the considered rotating speed. These extracted modes are then analysed through the value of their respective damping ratios in order to separate the harmonics component from structural spindle natural frequencies. Finally, the stochastic properties of the modes are also investigated by considering the probability density of the retained modes. Results show a good correlation between numerical and experiment-based identified frequencies. The identified spindle-tool modal properties during machining allow the numerical model to be considered as representative of the real dynamic properties of the system.     

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.     

An integrated prediction model for the dynamics of machine tool spindles

ABSTRACT

The predictility of dynamics of the machine tool spindles is essential for machining precision. During machining, the machine tool components and the cutting process interact with each other. Accordingly, it is necessary to take the process-machine interaction effects into account in order to predict the spindle's dynamics accurately. This paper presents an integrated model for the prediction of a spindle's dynamics. The model synthesizes the interactive influence between machine dynamics and forces in grinding process. The thermo-mechanical model of the spindle with angular contact ball bearings was built by using the finite-element method. The analytical model was used to calculate the process forces. A coupled simulation was adopted to accomplish the interactive process between the two models. Basing on the integrated model, the bearing stiffness, the natrual frequency, the spindle tip stiffness and deformations of a grinder's spindle were investigated. The prediction of the deformation fluctuations at the spindle tip due to process-machine interaction was also achieved.     

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。     

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.     

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。     

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.     

螺旋铣孔工艺的切削稳定性及工艺参数规划

以螺旋铣孔工艺时域解析切削力建模、时域与频域切削过程动力学建模、切削颤振及切削稳定性建模为基础,研究了螺旋铣孔的切削参数工艺规划模型和方法。切削力模型同时考虑了刀具周向进给和轴向进给,沿刀具螺旋进给方向综合了侧刃和底刃的瞬时受力特性;动力学模型中同时包含了主轴自转和螺旋进给两种周期对系统动力学特性的影响,并分别建立了轴向切削稳定域和径向切削稳定域的预测模型,求解了相关工艺条件下的切削稳定域叶瓣图。在切削力和动力学模型基础之上,研究了包括轴向切削深度、径向切削深度、主轴转速、周向进给率、轴向进给率等切削工艺参数的多目标工艺参数规划方法。最后通过试验对所规划的工艺参数进行了验证,试验过程中未出现颤振现象,表面粗糙度、圆度、圆柱度可以达到镗孔工艺的加工精度。     

一种改进的基于响应耦合子结构法的刀尖点频响函数预测方法

针对现有的基于响应耦合子结构法(RCSA)的刀尖点频响函数预测方法需要辨识主轴-刀柄、刀柄-刀具结合面参数以及需要自制刀柄模型等引起的预测误差和预测过程复杂等问题,提出一种改进的基于RCSA的铣刀刀尖点频响函数预测方法。该方法首先改进已有的子结构划分方法,将机床-主轴-刀柄-刀具系统划分为机床-主轴-刀柄-部分刀杆、剩余刀杆和刀齿三个子结构;然后改进主轴-刀柄处转动频响函数的计算方法,通过铣刀的模态锤击实验采用反向RCSA和有限差分法计算机床-主轴-刀柄-部分刀杆结构的转动频响函数,并基于Euler梁模型计算出剩余刀杆、刀齿子结构的频响函数;最后将三个子结构的频响函数耦合确定刀尖点的预测频响函数。以一立式加工中心为研究对象,应用所提出的方法对铣刀刀尖点的频响函数进行了预测,并与其实测频响函数进行对比。对比结果表明：刀尖点的预测频响函数与实测频响函数符合程度较高,其预测、实测前三阶固有频率之间的误差在6.9%以内,所提出的方法可行有效、简单方便,且可直接基于铣刀的模态实验计算主轴-刀柄的频响函数,避免了相关结合面参数的辨识和刀柄模型的制作。     

Dynamic stiffness deterioration of a machining center based on relative excitation method

The tool point frequency response function(FRF) is commonly obtained by impacting test or semi-analytical techniques.Regardless of the approach,it is assumed that the workpiece system is rigid.The assumption is valid in common machining,but it doesn’t work well in the cutting processes of thin-wall products.In order to solve the problem,a multi-degree-of-freedom dynamic model is employed to obtain the relative dynamic stiffness between the cutting tool and the workpiece system.The relative direct and cross FRFs between the cutting tool and workpiece system are achieved by relative excitation experiment,and compared with the tool point FRFs at x and y axial direction.The comparison results indicate that the relative excitation method could be used to obtain the relative dynamic compliance of machine-tool-workpiece system more actually and precisely.Based on the more precise relative FRFs,four evaluation criterions of dynamic stiffness are proposed,and the variation trend curves of these criterions during the last six months are achieved and analyzed.The analysis results show that the lowest natural frequency,the maximum and the average dynamic compliances at x axial direction deteriorate more quickly than that at y axial direction.Therefore,the main cutting direction and the large-size direction of workpieces should be arranged at y axial direction to slow down the deterioration of the dynamic stiffness of machining centers.The compliance of workpiece system is considered,which can help master the deterioration rules of the dynamic stiffness of machining centers,and enhance the reliability of machine centers and the consistency of machining processes.     

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.     

Robust regenerative chatter stability in machine tools

The expeditious nature of manufacturing markets inspires advancements in the effectiveness, efficiency and precision of machining processes. Often, an unstable machining phenomenon, called regenerative chatter, limits the productivity and accuracies in machining operations. Since the 1950s, a substantial amount of research has been conducted on the prevention of chatter vibration in machining operations. In order to prevent regenerative chatter vibrations, the dynamics between the machine tool and workpiece are critical. Conventional regenerative chatter theories have been established based on the assumption that the system parameters in machining are constant. However, the dynamics and system parameters change due to high spindle speeds, tool geometries, orientation of the tool with respect to the rest of the machine, tool wear and non-uniform workpiece material properties. This paper provides a novel method, based on the robust stability theorem, to predict chatter-free regions for machining processes, by taking in account the unknown uncertainties and changing dynamics for machining. The effects of time-variant parameters on the stability are analyzed using the robust stability theorem. The experimental tests are performed to verify the stability of SDOF and MDOF milling systems. The uncertainties and changing dynamics are taken into account in order to accommodate the optimal selection of machining parameters, and the stability region is determined to achieve high productivity and accuracy through applications of the robust stability theorem.     

基于动力学不确定性的重型切削工艺参数优化

针对数控重型切削加工过程的切削稳定性具有不确定性的特点,提出了在切削稳定性和机床工作能力的约束下,获得最大材料去除率的工艺参数优化方法。根据重型切削加工的工艺特点建立三维动力学模型,以机床的固有频率、阻尼比、刚度和切削力系数作为不确定因素,结合排零定理和边理论对其进行不确定性分析,获得稳健的切削稳定性叶瓣图,结合切削深度、刀具直径和刀具齿数的关系,为加工过程选择能获得最大切削深度的刀具。在此基础上,建立工艺参数优化模型,选择最佳的轴向切削深度、径向切削深度和主轴转速的组合,最后以一台加工中心上某型号发动机缸体表面的粗加工过程为例进行了验证。     

Electromagnetic actuator for determining frequency response functions of dynamic modal testing on milling tool

Machine tools are the main driving forces of industrialization of a country. However, poor machinability because of chatter vibration results in poor surface quality, excessive noise, and reduced material removal rate. Modal testing is a useful method to investigate dynamic properties of a cutting tool system and improve material removal rate. However, at present, modal testing using impact hammer is limited by certain problems. This paper developed a non-contacting electromagnetic actuator (EMA) to determine frequency response functions (FRFs) under amplitude and speed dependencies of cutting milling tools. The geometry was designed using magnetic circuit analysis and generalized machined theory before finite element analysis was conducted using magnetostatic-ansys software. Next, EMA was used as a contacting and non-contacting exciter of a conventional milling machine to determine the FRFs and dynamic properties of milling tool with amplitude and speed dependencies including comparison with static FRFs. Subsequently, dynamic properties and FRFs are used to establish stability lobe diagram. Stability lobe diagram also shows an improvement of up to 5% of depth of cut at lower spindle speed. In conclusion, by generating force that applies to static and dynamic modal testing, an EMA can determine dynamic properties and stability lobe diagram for increasing material removal rate and production rate.     

超高速主轴陶瓷球轴承性能的研究

陶瓷球轴承采用质轻的Ｓｉ３Ｎ４陶瓷材料作滚珠，减小了高速下作用在滚珠上的离心力和陀螺力矩，不仅具有较低的温升，而且还有较高的刚度，特别适用于超高速机床主轴。     

IMPULSIVE CHIP BREAKING IN METAL MACHINING: A PROOF-OF-CONCEPT STUDY

An innovative non-conventional technique, called impulsive chip breaking, is developed in the present study to break difficult-to-break chips that are often generated in machining high toughness or soft gummy materials, such as pure aluminum, pure copper, aluminum alloys, copper alloys, low carbon steels, and stainless steels. These materials have a wide variety of engineering applications. In impulsive chip breaking, the machine tool spindle rotational speed periodically increases to a prescribed higher speed within a set short period of time and then resumes to its normal constant speed to continue machining operations. The experimental investigations covering a range of cutting conditions on a selected work material are preformed to confirm the feasibility of impulsive chip breaking and study its basic mechanism as well as the characteristic variations of machining performances, including the chip morphology, the cutting forces, the machining vibrations, and the surface roughness of the machined workpiece. It is demonstrated that as long as the impulsive rotational speed of the machine tool spindle is appropriately selected or optimized, both requirements of breaking chips and maintaining the machined surface quality can be simultaneously satisfied.     

Time domain coupled simulation of machine tool dynamics and cutting forces considering the influences of nonlinear friction characteristics and process damping

A higher machining ability is always required for NC machine tools to achieve higher productivity. The self-oscillated vibration called “chatter” is a well-known and significant problem that increases the metal removal rate. The generation process of the chatter vibration can be described as a relationship between cutting force and machine tool dynamics. The characteristics of machine tool feed drives are influenced by the nonlinear friction characteristics of the linear guides. Hence, the nonlinear friction characteristics are expected to affect the machining ability of machines. The influence of the contact between the cutting edge and the workpiece (i.e., process damping) on to the machining ability has also been investigated. This study tries to clarify the influence of the nonlinear friction characteristics of linear guides and ball screws and process damping onto milling operations. A vertical-type machining center is modeled by a multi-body dynamics model with nonlinear friction models. The influence of process damping onto the machine tool dynamics is modeled as stiffness and damping between the tool and the workpiece based on the evaluated frequency response during the milling operation. A time domain-coupled simulation approach between the machine tool behavior and the cutting forces is performed by using the machine tool dynamics model. The simulation results confirm that the nonlinear frictions influence the cutting forces with an effect to suppress the chatter vibration. Furthermore, the influence of process damping can be evaluated by the proposed measurement method and estimated by a time domain simulation.