Three-dimensional process stability prediction of thin-walled workpiece in milling operation

High-speed machining of thin-walled workpiece is widely used in aerospace industry. To optimize the machining parameters in milling operations, the related process stability is required to be predicted. Compared to the existing two-dimensional (2D) milling stability model, a more completed three-dimensional (3D) regenerative process stability prediction model of thin-walled workpiece is presented based on the newly developed dynamic model. The efficiency and accuracy of the regenerative milling stability can be improved in the presented 3D model. The analysis procedure of the stability of flexible dynamic milling is developed in details. The 3D stability lobes are calculated according to the full discretization method and direct integration scheme. To verify the accuracy of presented 3D stability model, the thin-walled workpiece milling sound pressure signal and surface quality are determined in experiments.     

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.     

Three-dimensional chatter stability prediction of milling based on the linear and exponential cutting force model

Stability lobes are widely used to avoid chatter which restricts the machining quality and productivity. A lot of work has been done to predict the stability lobes fast and accurately. However, most of them are based on the linear force model, and the chatter stability limit is formulated as independent on the feed rate, which is inconsistent with the machining practice. By referencing with the zero-order solution, this paper investigates the chatter stability prediction based on the exponential force model. Focusing on the cutters with a lead angle (i.e., inserted face mill, the ball-end mill, and bull-nose end mill) where chatter is likely to be brought up in Z direction, the stability model is extended to three-dimensional. Taylor equation is utilized to linearize the exponential expressions when computing the directional coefficients in order to solve the stability limit analytically as the linear force model. Simulation results show that the exponential force model agrees with the measurements as well as the linear force model in the cutting force prediction, and it is able to demonstrate the feed rate effect on the stability limit. The stability limit is found to be increased as the feed rate increases, which is evidenced by the time domain simulation. Cutting tests are performed in the end to verify the stability model. The proposed model could be reduced to either X/Y dimensional or linear force model-based stability model by further simplifications.     

薄壁零件高速铣削振动试验与分析

切削速会加强振动随针对薄壁零件在高速铣削加工过程中存在的振动问题,为有效抑制加工振动,采用单因素试验,对每齿进给量、度、工彳车径向轴向切深、径向切深等加工参数进行了研究。试验结果显示：每齿进给量并不是越小越好;转速过高过低都振动：切深增随轴向切深增大振动增强;随径向切深增大振动逐渐减弱,较大轴向切深下,径向切深小于1mm时,大而增强。综合数据优选：薄壁零件高速铣削时,每齿进给量在0．1～0．15mm之间;转速在11000—14000r／min之间;较小的轴向切深和较大径向切深会有效抑制加工振动。     

Three degrees of freedom chatter stability prediction in the milling process

Journal of Mechanical Science and Technology - Chatter in the cutting process has a great influence on workpiece surface quality, machining efficiency, and service life of the machine tool. This...     

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.     

微铣削再生颤振动力学建模及稳定性分析

再生颤振是制约微铣削加工效率和加工质量的主要因素.以微铣削加工为研究对象,建立了考虑再生效应的微铣削颤振系统动力学模型和颤振稳定域解析模型,通过模态实验获得机床-刀具系统的频响函数,在此基础上综合使用铣削稳定性判据进行数值分析,获得了颤振稳定域解析解.最后进行了颤振稳定性加工实验,实验结果与仿真结果吻合良好,验证了建立的微铣削颤振系统动力学模型和颤振稳定域解析模型的正确性.     

A time-space discretization method in milling stability prediction of thin-walled component

The stability prediction of thin-walled workpiece milling is an awkward problem due to the time variant of dynamic characteristics during milling process. Integrating the time discretization method for stability prediction mentioned in many articles, a novel time-space discretization method for thin-walled component milling stability prediction is proposed based on thin plate theory and mode superposition principle, which includes the effects of the engagement position between cutter and workpiece and multi-modes of the system. The results show that the method presented is very reliable and efficient, and its accuracy is also in good agreement with experimental results. Additionally, the method can be used to handle various complex boundary conditions by means of the updated Rayleigh-Ritz solutions together with the penalty method. Two case studies are performed to explain the validation of the method as well as milling experiments of a half-clamped thin plate.     

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.     

考虑犁切力的微铣削颤振稳定域建模与分析

以微结构铣削加工为研究对象,建立了微观尺度下考虑犁切效应的铣削动态铣削力模型和颤振稳定域解析模型。在微铣削加工实验的基础上,对应于刀齿的每一个瞬时转角,对微铣削颤振稳定域进行了时域求解,进而研究了犁切-剪切机制对微铣削颤振稳定域的影响。实验结果表明犁切效应对微细铣削过程的加工不稳定现象没有显著的影响。     

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 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.     

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.     

矩形薄板侧铣加工变形预测与补偿技术研究

针对目前薄壁件加工的高精度要求与铣削加工变形之间的矛盾,基于ABAQUS建立了2Al2铝合金薄壁板侧铣加工变形的有限元预测模型,得到2Al2薄壁板的加工变形曲线,并据此提出一种通过在进给方向上刀心位置偏置和刀具轴向方向偏摆来同时进行补偿的方案.最后,用试验验证了有限元预测变形的可靠性和补偿策略的有效性.     

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.     

Prediction of dynamic cutting force and regenerative chatter stability in inserted cutters milling

Currently, the modeling of cutting process mainly focuses on two aspects: one is the setup of the universal cutting force model that can be adapted to a broader cutting condition; the other is the setup of the exact cutting force model that can accurately reflect a true cutting process. However, there is little research on the prediction of chatter stablity in milling. Based on the generalized mathematical model of inserted cutters introduced by ENGIN, an improved geometrical, mechanical and dynamic model for the vast variety of inserted cutters widely used in engineering applications is presented, in which the average directional cutting force coefficients are obtained by means of a numerical approach, thus leading to an analytical determination of stability lobes diagram (SLD) on the axial depth of cut. A new kind of SLD on the radial depth of cut is also created to satisfy the special requirement of inserted cutter milling. The corresponding algorithms used for predicting cutting forces, vibrations, dimensional surface finish and stability lobes in inserted cutter milling under different cutting conditions are put forward. Thereafter, a dynamic simulation module of inserted cutter milling is implemented by using hybrid program of Matlab with Visual Basic. Verification tests are conducted on a vertical machine center for Aluminum alloy LC4 by using two different types of inserted cutters, and the effectiveness of the model and the algorithm is verified by the good agreement of simulation result with that of cutting tests under different cutting conditions. The proposed model can predict the cutting process accurately under a variety of cutting conditions, and a high efficient and chatter-free milling operation can be achieved by a cutting condition optimization in industry applications.     

薄壁零件的高速铣削稳定性研究

薄壁结构零件在加工过程中极易发生变形和切削振动,这对提高加工质量和加工效率十分不利.在考虑刀具和工件两个方向自由度的基础上,分析了薄壁零件的动态铣削模型.针对2A12铝合金薄壁结构零件,利用MIKRON UCPDUR0800 高速加工中心和相关仪器、软件,通过铣削力辨识实验和模态实验,进行了高速铣削薄壁零件的稳定域分析和实验验证.     

Prediction of chatter stability in high speed milling using the numerical differentiation method

A numerical differentiation method is presented to predict the high speed milling stability of a two degrees of freedom (DOF) system based on the finite difference method and extrapolation method. The milling dynamics taking the regenerative effect into account are represented as linear periodic delayed differential equations (DDE) in the state space form. Then, each component of the first derivative of the state function versus time at the discretized sampling grids is approximated as a weighted linear sums of the state function values at its neighboring grid points, where the weight coefficients are calculated based on the extrapolation method. As such, the DDE on the forced vibration duration is approximately discretized as a series of algebraic equations. Thereafter, the Floquet transition matrix can be constructed on one tooth passing period by combining the analytical solution of the free vibration and the algebraic equations of the forced vibration. Finally, the milling stability is determined according to Floquet theory. The stability diagrams and convergence of critical eigenvalues in comparison with the benchmark algorithms (the semi-discretization method and numerical integration method) via experimentally verified examples are utilized to demonstrate the effectiveness and efficiency of the proposed method.