Toolpath dependent chatter suppression in multi-axis milling of hollow fan blades with ball-end cutter

Aiming at the issue of toolpath dependent machining vibration in multi-axis milling of hollow fan blades, this paper presents an optimal selection method of cutting parameters based on single-line toolpath to suppress cutting chatter. Firstly, the impact of hollow structure on the blade structural modal was analyzed by using the modal analysis method. And the unstable regions of hollow blade surface have been predicted, which were prone to induce machining deformation and vibration. Secondly, the relationship between the hollow structure and the dynamic characteristics was revealed by analyzing the dynamic responses to the different cutting positions of blade surface. Thirdly, the optimization of cutting parameters based on single-line toolpath was proposed by establishing the 3D stability lobe diagram. Finally, the feasibility and effectiveness about the analysis of dynamic characteristics and the suppression method of cutting chatter were verified by a milling experiment of hollow blade.     

考虑变时滞效应的弱刚度球头铣刀铣削稳定性研究

弱刚度球头铣刀广泛应用于深腔模具零件的铣削中,加工过程中容易发生颤振,确定加工稳定域是实现稳定铣削的重要手段,但该铣削系统具有变时滞特点,稳定性分析的难度较大,制约着加工质量的提高。为此,提出一种弱刚度球头铣刀铣削稳定性分析方法。首先,建立弱刚度刀具系统的动力学方程;接着,基于Newton-Raphson求解出刀齿选定点的时滞量;最后,基于全离散法提出考虑变时滞再生效应的稳定性分析方法,并利用Floquet定理获得了不同转速所对应的临界切深,构建出铣削稳定性叶瓣图。实验结果表明在叶瓣图的非稳定域铣削时铣削力中含颤振频率成分,所加工表面的S_y和S_a比稳定域内加工表面增大35%和42%,说明该分析方法是可靠的,可为切削参数的选择和优化提供依据。     

实时振动数据驱动的薄壁件平铣工艺参数自适应优化

为减小加工振动对薄壁件平铣（端面盘铣）加工质量及效率的影响，提出一种实时铣削振动数据驱动的平铣工艺参数自适应优化方法。首先根据再生效应原理建立薄壁件平铣颤振稳定性模型。其次将薄壁件平铣过程中前一个工步内的实测振动数据分为若干段，以此模拟其材料去除过程，对各段铣削振动数据进行分析，由有限元单位力法和优化STD法分别识别出薄壁件刚度和各材料去除阶段模态频率及阻尼比，并由此导出薄壁件单模态频响函数，将其代入颤振稳定性模型求解稳定域叶瓣图并做插值处理后即可确定包含材料去除信息的薄壁件三维颤振稳定域叶瓣图。基于此，以避免铣削颤振、共振和满足机床性能要求为约束条件，以材料去除率最大为目标，利用遗传算法计算薄壁件下一个工步较优的工艺参数，如此循环进行，直到完成薄壁件加工。最后，通过某型飞机垂尾薄壁装配界面平铣试验验证该方法的可行性和有效性。由试验结果可看出，采用优化后的加工工艺参数，能使薄壁装配界面粗加工过程表面粗糙度从Ra 3.2提升为Ra 1.6，加工效率提高33%。     

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。     

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.     

Investigation on chatter stability of thin-walled parts considering its flexibility based on finite element analysis

High-speed milling of thin-walled part is a widely used application for aerospace industry. The low rigidity components, large quantities of material removed in machining progress, are in the risk of the instability of the progress. In this paper, the thin-walled parts have the similar characteristics with the tools. Therefore, the dynamic model and the stability critical condition determined by the relative dynamic behavior between tool subsystem and workpiece subsystem are put forward. The thin-walled parts’ dynamic character varies greatly with time when machining. The whole workpiece has been divided into several stages by finite element analysis (FEA) so that its various modal parameters in the milling progress can be obtained gradually; thus, the variation due to metal removal has been accurately taken into account. The stability critical condition is predicted by frequency domain method based on the dynamic behavior of the two subsystems. With the respect to time-varying critical stability condition, a three-dimensional lobe diagram has been developed to show the changing conditions of chatter. Finally, the proposed methods and models were proven by series milling experiments.     

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.     

Chatter reliability prediction of side milling aero-engine blisk

Reliability analysis of a dynamic structural system is applied to predict chatter of side milling system for machining blisk. Chatter reliability is defined as the probability of stability for processing. A reliability model of chatter was developed to forecast chatter vibration of side milling, where structure parameters and spindle speed are regarded as random variables and chatter frequency is considered as intermediate variable. The first-order second-moment method was used to work out the side milling system reliability model. Reliability lobe diagram (RLD) was applied to distinguish reliable regions of chatter instead of stability lobe diagram (SLD). One example is used to validate the effectiveness of the proposed method and compare with the Monte Carlo method. The results of the two approaches were consistent. Chatter reliability and RLD could be used to determine the probability of stability of side milling.

     

Response sensitivity analysis of the dynamic milling process based on the numerical integration method

As one of the bases of gradient-based optimization algorithms, sensitivity analysis is usually required to calculate the derivatives of the system response with respect to the machining parameters. The most widely used approaches for sensitivity analysis are based on time-consuming numerical methods, such as finite difference methods. This paper presents a semi-analytical method for calculation of the sensitivity of the stability boundary in milling. After transforming the delay-differential equation with time-periodic coefficients governing the dynamic milling process into the integral form, the Floquet transition matrix is constructed by using the numerical integration method. Then, the analytical expressions of derivatives of the Floquet transition matrix with respect to the machining parameters are obtained. Thereafter, the classical analytical expression of the sensitivity of matrix eigenvalues is employed to calculate the sensitivity of the stability lobe diagram. The two-degree-of-freedom milling example illustrates the accuracy and efficiency of the proposed method. Compared with the existing methods, the unique merit of the proposed method is that it can be used for analytically computing the sensitivity of the stability boundary in milling, without employing any finite difference methods. Therefore, the high accuracy and high efficiency are both achieved. The proposed method can serve as an effective tool for machining parameter optimization and uncertainty analysis in high-speed milling.     

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.     

考虑模态耦合的球头铣刀颤振稳定域建模方法

球头铣刀广泛应用于曲面加工中,因此构造出针对球头铣刀的颤振稳定域叶瓣图意义重大。利用精细积分法对铣削系统二阶动力学方程进行时域数值求解,由切削刃与切触区域不同时刻的关系,确定出时域数值求解方程中所需要的刀刃瞬时切削部位,通过Floquet定理获得了高精度的颤振稳定域叶瓣图,并在三轴数控机床上进行了正确性试验验证。试验结果与预测结果相一致,表明所提供的方法能够为球头铣刀实现无颤振切削加工提供有力的技术支撑。     

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。     

基于模态柔度和能量分布的机床动态优化设计

使机床切削点动柔度最大值在整个工作频率范围内最小,是机床实现无颤振稳定切削和高精度切削加工的要求,也是对其进行动态优化设计所应达到的目标。基于模态柔度和能量分布的机床结构动态优化设计原理,实现了一种以降低切削点交叉动柔度值为目标的优化方法。该方法利用切削点交叉动柔度与模态柔度的关系,首先寻找薄弱模态,再分析薄弱模态上各部件和环节的能量分布,确定该模态上的薄弱环节,然后在一定的约束条件下,改进这些环节的设计参数,从而实现优化目标。以某型万能工具铣床为例,在整机建模分析计算的基础上,阐述了该优化方法的具体应用。通过模态柔度和能量分布计算,判明该机床的薄弱环节是横梁-水平主轴体系统,针对薄弱环节设计参数的改进实现其质量和刚度的优化,优化后的静柔度和模态柔度都有较大的降低,而固有频率则相应提高,切削点动柔度的最大值降低近18%。并在此基础上进行结构改进设计,改进前后机床的谐响应分析和切削试验对比结果表明优化方法有效地改善了机床的动态性能,再生颤振稳定性得到大幅提高。     

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。     

Development of a novel boring tool with anisotropic dynamic stiffness to avoid chatter vibration in cutting: Part 1: Design of anisotropic structure to attain infinite dynamic stiffness

This paper presents a novel design method of the anisotropic structure to attain infinite dynamic stiffness to avoid chatter vibration in boring operations. Because a long and slender tool is used for boring operations, the stiffness of the tool holder is likely to decrease, resulting in low chatter stability. Although it is difficult to improve the stiffness of the boring holder itself, the nominal dynamic stiffness for the cutting process can be improved by designing an appropriate anisotropy in the dynamic stiffness of the boring tool. In this study, we formulate a theoretical relationship between the mechanical structural dynamics and chatter stability in boring operation and present the basic concept of tool design with anisotropic structure. In the actual tool design, ideal anisotropy may not be realized because of the influence of design error. Therefore, an analytical study was conducted to clarify the influence of the design error on the vibration suppression effect. Analytical investigations verified that the similarity of the frequency response functions in the modal coordinate system and the design of the compliance ratio according to the machining conditions are important. Furthermore, we designed a boring tool with an anisotropic structure which can achieve the proposed anisotropic dynamics. The frequency response function was evaluated utilizing FEM analysis. The estimated anisotropic dynamics of the proposed structure could significantly improve the nominal dynamics for boring operations.     

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 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.     

Hybrid model- and signal-based chatter detection in the milling process

Chatter causes machining instability and reduces productivity in the metal cutting process. It has negative effects on the surface finish, dimensional accuracy, tool life and machine life. Chatter identification is therefore necessary to control, prevent, or eliminate chatter and to determine the stable machining condition. Previous studies of chatter detection used either model-based or signal-based methods, and each of them has its drawback. Model-based methods use cutting dynamics to develop stability lobe diagram to predict the occurrence of chatter, but the off-line stability estimation couldn’t detect chatter in real time. Signal-based methods apply mostly Fourier analysis to the cutting or vibration signals to identify chatter, but they are heuristic methods and do not consider the cutting dynamics. In this study, the model-based and signal-based chatter detection methods were thoroughly investigated. As a result, a hybrid model- and signal-based chatter detection method was proposed. By analyzing the residual between the force measurement and the output of the cutting force model, milling chatter could be detected and identified efficiently during the milling process.

     

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。