Three-dimensional stability lobe and maximum material removal rate in end milling of thin-walled plate

Chatter phenomenon often occurs during end milling of thin-walled plate and becomes a common limitation to achieve high productivity and part quality. For the purpose of chatter avoidance, the optimal selection of the axial and radial depth of cut, which are decisive primary parameters in the maximum material removal rate, is required. This paper studies the machining stability in milling of the thin-walled plate and develops a three-dimensional lobe diagram of the spindle speed, axial, and radial depth of cut. Through the three-dimensional lobe, it is possible to choose the appropriate cutting parameters according to the dynamic behavior of the chatter system. Moreover, this paper studies the maximum material removal rate at the condition of optimal pairs of the axial and radial depth of cutting.     

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。     

Prediction of simultaneous dynamic stability limit of time�Cvariable parameters system in thin-walled workpiece high-speed milling processes

A method for predicting simultaneous dynamic stability limit of thin-walled workpiece high-speed milling process is described. The proposed approach takes into account the variations of dynamic characteristics of workpiece with the tool position. A dedicated thin-walled workpiece representative of a typical industrial application is designed and modeled by finite element method. The curvilinear equation of modal characteristics changing with tool position is regressed. A specific dynamic stability lobe diagram is then elaborated by scanning the dynamic properties of workpiece along the machined direction throughout the machining process. The results show that, during thin-walled workpiece milling process, material removing plays an important part on the change of dynamic characteristics of system, and the stability limit curves are dynamic curves with time?Cvariable. In practical machining, some suggestion is interpreted in order to avoid the vibrations and increase the chatter free material removal rate and surface finish. Then investigations are compared and verified by high-speed milling experiments with thin-walled workpiece.     

GRADE OF STABILITY IN FUZZY CHATTER STABILITY LOBE MODEL IN MILLING

The machining productivity and part quality are typically limited by the regenerative chatter induced by the dynamic interactions of spindle-holder-tool combination system. The conventional chatter stability model predicts the permissible stable axial depth of cut versus spindle speed by plotting the stability lobe diagram which represents two independent regions as absolutely stable zone and instable zone divided by the critical lobe curve. In fact, it is more reasonable to be a transition stage between the stable and instable zone. This paper introduced the grade of stability (GOS) to improve the conventional chatter stability model and study the transition zone in the stability lobe diagram. The variation of transition zone width with the stability sensibilities for different order lobe curve in milling system was analyzed. Sigmoid function was used as the membership function to develop the fuzzy stability lobe model. Then, the fuzzy stability lobe diagram with an adjustable slope coefficient was implemented to improve the mould steel milling process. The improved fuzzy stability model enhances the reliability of stability lobe diagram and guarantees the chatter-free milling process.     

Investigation on chatter stability of thin-walled parts in milling based on process damping with relative transfer functions

Chatter usually occurs in cutting of thin-walled workpiece due to poor structural stiffness, which results in poor surface quality and damaged tool. Aiming at process damping caused by interference between a tool flank face and a machined surface of thin-walled part, the dynamic model and critical condition of stability are proposed by the relative transfer functions, when both the tool structure and the machined workpiece have similar dynamic behaviors in this paper. Using the frequency method to solve the stability of the cutting chatter, it can be seen that the process damping can significantly improve the stability of the low speed region. Moreover, the stability domain is different and more exact than the one that derives from the simple superposition of the tool and the workpiece lobe diagrams. The correctness of the model is validated by experiments. These conclusions provide a theoretical foundation and reference for the milling mechanism research.     

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.     

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%。     

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.     

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.

     

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。     

A prediction method of milling chatter stability for complex surface mold

This paper proposes a kind of milling chatter stability prediction method used for the stability of milling free-form surface based on the time-domain. Firstly, a dynamic equation is established by considering the influence of mold surface curvature and cutting tool lead angle on dynamic chip thickness without deformation. Then, the multi-delay milling system vibration displacement, which is given by the ratio of dynamic chip thickness and the static chip thickness as the threshold, was calculated based on the numerical method. Finally, the chatter stability domain based on the full-discretization method of milling chatter stability domain is compared to analyze the influence of the characteristics of free surface curvature on the chatter stability domain. The results of the experiment show that the time-domain simulation method can reveal the influence of different processing areas of free-form surface mold on the instability mechanism of the system. The change trend of milling chatter stability domain was found to be consistent with the experimental results.     

多硬度拼接淬硬钢铣削动力学分析

颤振是金属切削加工过程中由于刀具和工件之间相互作用所产生的一种强烈的自激振动现象,会导致切削力幅值增加且发生剧烈波动,进而降低工件表面质量和刀具使用寿命。针对此问题,基于铣削过程稳定性预测分析方法建立多硬度拼接工件的动态铣削系统,对多硬度拼接模具铣削过程稳定性进行深入研究,实现了对拼接模具铣削加工过程颤振稳定域的仿真,进而研究了模态参数对稳定性叶瓣图形状的影响。最后通过时域分析、表面形貌和刀具磨损的研究,综合验证了稳定性预测曲线的精度。研究结果为多硬度拼接模具铣削加工提供理论基础,并设置合理的加工参数来实现金属最大切除率,为大型汽车覆盖件模具铣削加工提供理论依据及技术指导。     

高速铣削铝合金时切削力和表面质量影响因素的试验研究

对高速铣削典型铝合金框架结构工件时的切削力和加工表面质量进行了试验研究。在高速进给铣削时 ,当进给方向发生改变 ,机床的加减速特性将导致在拐角处进给量减小、铣刀切入角增大 ,从而引起切削力增大和加工振动。在恒切削效率条件下高速铣削铝合金的试验结果表明 ,高速铣削时宜采用较小的轴向切深和较大的径向切深 ,以减小铣削力、提高加工表面质量 ;刀具动平衡偏心量是高速铣削时引起轴向振纹的主要原因     

Fast prediction of chatter stability lobe diagram for milling process using frequency response function or modal parameters

Prediction of chatter stability is important for planning and optimization of machining process in order to improve machining efficiency and reduce machining damage. Based on the classical analytical solution of chatter stability for milling process and in-depth analysis of the impact of modal parameters on the stability lobe diagram, a straight forward procedure for fast predicting stability lobe diagram directly using modal parameters of machining system was put forward. In consideration of the fact that the modal parameters of milling system can be estimated directly from the frequency response function using single DOF modal parameter estimation method, stability lobe diagram can be plotted directly using the tool tip’s frequency response function. The machining performances of a machining center with three different cutting tools were evaluated and the corresponding optimized cutting conditions were determined. The correctness of the proposed method was validated by good agreement of the predicted stability lobe diagram with that using the classical analytical method, and simulation results show that its calculation speed had been improved by 2–3 orders of magnitude. As a result, the proposed method of plotting stability lobe diagram using frequency response function can be utilized as an effective tool to select chatter-free cutting conditions in shop floor applications.     

Precision surface characterization for finish cylindrical milling with dynamic tool displacements model

In this work a new approach to surface roughness parameters estimation during finish cylindrical end milling is presented. The proposed model includes the influence of cutting parameters, the tool’s static run out and dynamic phenomena related to instantaneous tool deflections. The modeling procedure consists of two parts. In the first stage, tool working part instantaneous displacements are estimated using an analytical model which considers tool dynamic deflections and static errors of the machine – tool-holder – tool system. The obtained height of the tool’s displacement envelope is then applied in the second stage to the calculation of surface roughness parameters. These calculations assume that in the cylindrical milling process, two different mechanisms of surface profile formation exist. Which mechanism is present is dependent on the feed per tooth and the maximum height of the tool’s displacement envelope. The developed model is validated during cylindrical milling of hardened hot-work tool steel 55NiCrMoV6 using a stylus profiler and scanning laser vibrometer over a range of cutting parameters. The surface roughness values predicted by the developed model are in good agreement with measured values. It is found that the employment of a model which includes only the effect of static displacements gives an inferior estimation of surface roughness compared to the model incorporating dynamic tool deflections.     

Design for variable pitch end mills with high milling stability

The strong demand for increasing productivity and workpiece quality in milling process makes the machine?Ctool system operate close to the limit of its dynamic stability. Besides predicting accurately chatter stability, it is required that some optimizations should be conducted, e.g., cutter structure, for improving the dynamic stability limits. Milling cutters with variable pitch angles can be very effective in improving stability against chatter for certain speed ranges, which will be predicted by the model presented here. The present paper deals with the design of structural geometry of variable pitch end mills in detail. Based on the analysis of tooth engagement factor, which is expressed and extended in the paper, an approach is proposed to design variable pitch end mill with high milling stability. The certain speed ranges with high milling stability are given. An example of the design of variable pitch end mills is illustrated to demonstrate the validity of this method.     

Chatter and dynamic cutting force prediction in high-speed ball end milling

Machine tool chatter is a serious problem which deteriorates surface quality of machined parts and increases tool wear, noise, and even causes tool failure. In the present paper, machine tool chatter has been studied and a stability lobe diagram (SLD) has been developed for a two degrees of freedom system to identify stable and unstable zones using zeroth order approximation method. A dynamic cutting force model has been modeled in tangential and radial directions using regenerative uncut chip thickness. Uncut chip thickness has been modeled using trochoidal path traced by the cutting edge of the tool. Dynamic cutting force coefficients have been determined based on the average force method. Several experiments have been performed at different feed rates and axial depths of cut to determine the dynamic cutting force coefficients and have been used for predicting SLD. Several other experiments have been performed to validate the feasibility and effectiveness of the developed SLD. It is found that the proposed method is quite efficient in predicting the SLD. The cutting forces in stable and unstable cutting zone are in well agreement with the experimental cutting forces.     

Chatter prediction utilizing stability lobes with process damping in finish milling of titanium alloy thin-walled workpiece

Machining chatter often becomes a big hindrance to high productivity and surface quality in actual milling process, especially for the thin-walled workpiece made of titanium alloy due to poor structural stiffness. Aiming at this issue, the stability lobes are usually employed to predict if chatter may occur in advance. For obtaining the stability lobes in milling to avoid chatter, this article introduces an extended dynamic model of milling system considering regeneration, helix angle, and process damping into the high-order time domain algorithm which can guarantee both high computational efficiency and accuracy. Via stability lobes, the reasonability and accuracy of the proposed method are verified globally utilizing specific examples in literature. More convincingly, the time-domain numerical simulation is also implemented to predict vibration displacement for partial stability verification. In this extended model, process damping is well-known as an effective approach to improve the stability at low spindle speeds, and particularly, titanium alloy as typical difficult-to-machine material is generally machined at low spindle speeds as well due to its poor machinability. Therefore, the proposed method can be employed to obtain the 3D stability lobes in finish milling of the thin-walled workpiece made of titanium alloy, Ti-6Al-4V. Verification experiments are also conducted and the results show a close agreement between the stability lobes and experiments.     

Chatter stability of micro end milling by considering process nonlinearities and process damping

The micro end milling uses the miniature tools to fabricate complexity microstructures at high rotational speeds. The regenerative chatter, which causes tool wear and poor machining quality, is one of the challenges needed to be solved in the micro end milling process. In order to predict the chatter stability of micro end milling, this paper proposes a cutting forces model taking into account the process nonlinearities caused by tool run-out, trajectory of tool tip and intermittency of chip formation, and the process damping effect in the ploughing-dominant and shearing-dominant regimes. Since the elasto-plastic deformation of micro end milling leads to large process damping which will affect the process stability, the process damping is also included in the cutting forces model. The micro end milling process is modeled as a two degrees of freedom system with the dynamic parameters of tool-machine system obtained by the receptance coupling method. According to the calculated cutting forces, the time-domain simulation method is extended to predict the chatter stability lobes diagrams. Finally, the micro end milling experiments of cutting forces and machined surface quality have been investigated to validate the accuracy of the proposed model.