Identifying bifurcation behavior during machining process for an irregular milling tool geometry

High-productivity machining processes cause tool and material defects and even damages in machine spindles. The onset of self-excited vibration, known as chatter, limits this high material removal rate. This chatter vibration refers to machining instability during cutting processes, which results in bifurcation behavior or nonlinear effect wherein the tool and the workpiece are not engaged with each other. In particular, bifurcation for low-radial immersion conditions can be easily promoted and identified. In this study, an experiment on an irregular milling tool as a variable helix and variable pitch geometry was conducted under a flexible workpiece condition. The bifurcation behavior from regenerative chatter was identified and quantified from displacement sensor and inductive sensor measurements. A series of cutting tests was used to measure the vibration signals, which were then analyzed based on the frequency spectrum, the one-per-revolution effect, and the Poincaré section. According to results, Hopf bifurcation and period-one bifurcation instabilities apparently occurred to validate chatter stability prediction through a semi-discretization method. However, period-doubling bifurcation was only determined during the unstable cutting of a uniform tool that was not in variable helix/pitch or an irregular milling tool. An irregular tool geometry caused the modulation of the regenerative effect to suppress chatter, and period-doubling instability could not be exhibited during cutting as a regular tool behavior. This period-one chatter instability of an irregular milling tool should be identified and avoided by practitioners to achieve high productivity in machining using the aforementioned irregular milling tools.     

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.     

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.     

Optimum tool path generation for 2.5D direction-parallel milling with incomplete mesh model

Many mechanical parts are manufactured by milling machines. Hence, geometrically efficient algorithms for tool path generation, along with physical considerations for better machining productivity with guaranteed machining safety, are the most important issues in milling. In this paper, an optimized path generation algorithm for direction-parallel milling, a process commonly used in the roughing stage as well as the finishing stage and based on an incomplete 2-manifold mesh model, namely, an inexact polyhedron widely used in recent commercialized CAM software systems, is presented. First of all, a geometrically efficient tool path generation algorithm using an intersection points-graph is introduced. Although the tool paths obtained from geometric information have been successful in forming desired shapes, physical process concerns such as cutting forces and chatters have seldom been considered. In order to cope with these problems, an optimized tool path that maintains a constant MRR for constant cutting forces and avoidance of chatter vibrations, is introduced, and verified experimental results are presented. Additional tool path segments are appended to the basic tool path by means of a pixel-based simulation technique. The algorithm was implemented for two-dimensional contiguous end milling operations with flat end mills, and cutting tests measured the spindle current, which reflects machining characteristics, to verify the proposed method.     

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.     

铣削颤振理论在钛合金结构件加工中的应用

针对钛合金结构件的弱刚度及难加工特性,提出了小径向铣削的方法。使用小径向铣削稳定预测理论,绘制出了稳定叶瓣图,最终选择了合理的加工参数,避免加工过程中发生的颤振,为该理论的实际应用提供了范例。     

插铣过程中稳定域研究现状

切削系统稳定性是插铣技术加工领域中的重要研究内容,插铣切削加工中很多优点的体现必须以无振动稳定切削的实现为前提。稳定域预测的准确与否直接关系到能否有效抑制切削颤振,而切削颤振直接影响工件的表面粗糙度和尺寸精度,刀具磨损和破损以及加工效率等。本文通过求解稳定域的一般步骤,综述稳定域研究现状。通过列举稳定性边界的判别的不同算法,分析和对比各种算法的优缺点,并总结插铣切削过程中稳定性研究存在的问题。     

A coupled dynamics,multiple degree of freedom process damping model,Part 2: Milling

Self-excited vibration, or chatter, is an important consideration in machining operations due to its direct influence on part quality, tool life, and machining cost. At low machining speeds, a phenomenon referred to as process damping enables stable cutting at higher depths of cut than predicted with traditional analytical models. This paper describes an analytical stability model for milling operations which includes a process damping force that depends on the surface normal velocity, depth of cut, cutting speed, and an empirical process damping coefficient. Model validation is completed using time domain simulation and milling experiments. The results indicate that the multiple degree of freedom model is able to predict the stability boundary using a single process damping coefficient.     

A novel chatter stability criterion for the modelling and simulation of the dynamic milling process in the time domain

The modelling of the dynamic processes in milling and the determination of chatter-free cutting conditions are becoming increasingly important in order to facilitate the effective planning of machining operations. In this study, a new chatter stability criterion is proposed, which can be used for a time domain milling process simulation and a model-based milling process control. A predictive time domain model is presented for the simulation and analysis of the dynamic cutting process and chatter in milling. The instantaneous undeformed chip thickness is modelled to include the dynamic modulations caused by the tool vibrations so that the dynamic regeneration effect is taken into account. The cutting force is determined by using a predictive machining theory. A numerical method is employed to solve the differential equations governing the dynamics of the milling system. The work proposes that the ratio of the predicted maximum dynamic cutting force to the predicted maximum static cutting force can be used as a criterion for the chatter stability. Comparisons between the simulation and experimental results are given to verify the new model.     

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.     

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.     

基于阻尼减振器的铣削过程稳定性研究

针对薄壁件铣削加工中出现的颤振现象采用外置式阻尼减振器。该减振器与刀杆过盈配合联接为一体,铣削过程中可以吸收刀杆受到的振动,通过安装阻尼减振器和未安装阻尼减振器两个铣削对比试验,以阻尼材料、阻尼减振器安装位置为变量,探究该阻尼减振器对铣削抑振和加工稳定性的影响程度及变化规律。试验结果表明,安装该阻尼减振器后系统铣削稳定性得到提高,切削深度平均提高2.5倍。     

A mapping-based spiral cutting strategy for pocket machining

Almost 80 % of the milling operations to produce mechanical parts are produced by NC pocket milling, especially in aerospace and automobile industry. At present, for 2.5D pocket machining, direction-parallel and contour-parallel machining strategies have gained nearly universal acceptance. However, in such tool path, abrupt change of path direction, frequent acceleration and deceleration, and sharp velocity discontinuous are found to significantly limit the machining efficiency of pockets. To address these problems, this paper introduces a method for generating a spiral tool path that maintains a steady-state cutting process by as smoothly as possible curvature evolution of the tool path for pocket machining. First, the machined region of a layer of a pocket is mapped onto a circular domain by means of mesh mapping, which reduces the task of tool path generation from the geometrically complex pocket region to a topologically simple disk. On this disk, a guide spiral is constructed according to a mathematical function constrained by the calculated path interval map. Using the mapping from the pocket to the disk as a guide, the guide spiral is inversely mapped into the interior of the pocket and then a smooth low-curvature spiral path is derived. The generated tool paths are guaranteed to not inherit any corners in the subsequent interior tool paths and allows cutting of the pocket without tool retractions during the cutting operations. Finally, the proposed method is implemented and tested on several typical sample pockets to demonstrate its validity and significance.     

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.     

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.     

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.

     

曲面铣削过程加工路径对切削力和磨损的影响研究

针对不同走刀路径下的复杂曲面加工过程进行球头铣刀铣削Cr12MoV加工复杂曲面研究,分析不同走刀路径下铣削力和刀具磨损的变化趋势。试验结果表明:通过对比分析直线铣削和曲面铣削过程中的最大未变形切屑厚度,可以得出单周期内曲面铣削的力大于直线铣削过程的力,铣削相同铣削层时环形走刀测得的切削力普遍大于往复走刀测得的切削力;以最小刀具磨损为优化目标,运用方差分析法分析得出不同走刀路径的影响刀具磨损的主次因素,同时利用残差分析方法建立球头铣刀加工复杂曲面刀具磨损预测模型,并通过试验进行验证。     

Stability charts with large curve-flute end-mills for thin-walled workpieces

The development of advanced performance materials by foundrymen allows new designs of components with similar mechanical resistance but lower thicknesses. This accentuates the well-known problems in machining cutting systems (static form errors, forced vibrations, and chatter), which appear increasingly early. These problems are particularly severe in the case of rotating parts in the field of aeronautics. Currently, the machining time for impellers and blisks can be improved so that new cutting tools with innovative features are continually developed. Barrel type or curved end mills will have a significant impact on the manufacturing of aircraft components during incoming years. In this paper, a time domain method is proposed for the first time to predict stability in milling operations when using these tools. The dynamic cutting forces are first obtained and then used to plot stability contour maps. Key aspects, such as tool orientation angles, several dynamic modes, and runout were also considered. Finally, chatter tests were performed for a low-stiffness mechanical system to validate the model. The presented maps indicate chatter severity and may be used for chatter prediction and productivity improvement.     

基于颤振预报和预测的稳定性控制理论及方法研究

针对由颤振预测控制策略指导的稳定切削控制方法实时动态调整能力差的缺点,综合颤振预报、预测理论,进行了稳定性在线寻优控制理论及方法的研究。基于刀具—工件系统铣削再生颤振动力学模型,研究了考虑系统结构参数(刀具、工件装夹刚度)和加工参数(切削加工参数优化选择)的切削稳定性评价方法,提出了以扩大稳定性区域和稳定最大材料切除率为控制目标的机床稳定性控制方法。形成了以"预报—控制—效果评估—再控制"为步骤的在线监测、智能诊断和实时控制的集成一体化策略。设计并实施了稳定性控制理论验证实验,获得了与理论分析一致的结论。     

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.