Maximizing Chatter Free Material Removal Rate in Milling through Optimal Selection of Axial and Radial Depth of Cut Pairs

Chatter vibrations in milling, which develop due to dynamic interactions between the cutting tool and the workpiece, result in reduced productivity and part quality. Several stability models have been considered in previous publications, where mostly the stability limit in terms of axial depth of cut is emphasized for chatter free machining. In this paper, it is shown that, for the maximization of chatter free material removal rate, radial depth of cut is of equal importance. A method is proposed to determine the optimal combination of depths of cut, so that chatter free material removal rate is maximized. The application of the method is demonstrated on a pocketing example where significant reduction in the machining time is obtained using the optimal depths. The procedure can easily be integrated to a CAD/CAM system or a virtual machining environment in order to identify the optimal milling conditions.     

机床颤振的若干研究和进展

本文根据颤振的发生机理分别阐述了机床颤振的理论模型的研究方法和发展过程，并且着重讨论了近十几年在机床颤振的控制及在线监控领域内的动态和进展。从文中可以看出机床颤振的研究日益深入，并且与其它学科之间不断交叉发展。     

Chatter in machining processes: A review

Chatter is a self-excited vibration that can occur during machining operations and become a common limitation to productivity and part quality. For this reason, it has been a topic of industrial and academic interest in the manufacturing sector for many years. A great deal of research has been carried out since the late 1950s to solve the chatter problem. Researchers have studied how to detect, identify, avoid, prevent, reduce, control, or suppress chatter.This paper reviews the state of research on the chatter problem and classifies the existing methods developed to ensure stable cutting into those that use the lobbing effect, out-of-process or in-process, and those that, passively or actively, modify the system behaviour.     

Modelling of the stability of variable helix end mills

Chatter in milling is still the main obstacle in achieving high-performance machining operations in industry. In this paper, an analytical model is presented to predict the chatter stability of the variable helix end mills. Owing to the lack of accurate and rapid modelling, variable helix tools are used simply on a trial and error basis, in the hope that they will improve the stability of the process. This work provides a comparative study of the performance of variable helix and variable pitch end mills. Time domain chatter recognition techniques and analytical models are explored and tested against experimental results. For the experimental validation, aluminium test pieces were used to enable a broad range of spindle speeds to be covered. The linearity of the machine tool dynamics is explored through validation of standard stability lobes. A comparison of the predicted and observed performance of variable helix against constant helix, variable pitch end mills are presented.The stability lobes are validated for each of the variable helix, variable pitch and standard tools. The analytical model assumes the variable helix tools to behave as variable pitch tools, calculating the average pitch angle for each flute. This approximation is proven to be accurate for some of the cases. For certain combinations of pitch and helix angle greatly enhanced stability is demonstrated empirically with up to a 20-fold increase in depth of cut for the variable helix over the equivalent variable pitch tool. This enhanced stability is neither predicted by the analytical nor time domain solutions. The time domain chatter recognition criterion is investigated and found to have little influence on the predicted stability plots. It is concluded that the enhanced stability is a result of some mechanism not represented in the well-established time domain model. It is possible that this is a result of the disturbance of regeneration in the manner of an alternating spindle speed or due to a non-linear process damping effect.     

Stable islands in the stability chart of milling processes due to unequal tooth pitch

The use of unequal tooth pitch is a known means to influence and to prevent chatter vibrations in milling. While the process dynamics of equally pitched end mills can be modeled by non-autonomous differential equations with a single constant delay, the dynamics of unequally pitched end mills lead to differential equations with multiple constant delays. In this paper the process stability of an unequally pitched end mill is investigated experimentally and theoretically. The numerical approximation of the stability limit relies on two fundamental methods: Ackermann's method to control systems with delay and the method of the piecewise constant subsystems. On the basis of these two methods two ways for the theoretical stability analysis are derived. The first way neglects the time dependency of the system by replacing the time varying system matrices by their means. The second way accounts for the time dependency of the system by combining Ackermann's method to control systems with delay with the method of the piecewise constant subsystems, which results in the semi-discretization method. Besides the exemplary investigation of a specific end mill the two methods are compared for a simple one degree of freedom system for different number of teeth, different alternating and linear tooth pitch variations and different helix angles. It is shown, that unlike equally pitched end mills also at high radial immersions the time dependency of the system leads to significant differences between the stability limits of the unequally pitched end mills, predicted by the two methods. Depending on the time variance of the system and the unequal tooth pitch stable islands can arise, which are largely located within the stable peaks of the stability diagram of the system where the time varying system matrices are replaced by their means. The correctness of the results are backed up for several operating points by time domain simulations, taking into account the trochoidal movement of the cutting edges, the time varying character of the system and teeth jumping out of contact.     

Creating Stability Lobe Diagrams during Milling

Motorized spindles are in common use in high-speed milling. The dynamic behavior of the spindle depends on the actual number of revolutions and the temperature. The performance of the spindle during milling, particularly, the behavior concerning chatter, is crucially affected by the speed dependent dynamic behavior of the mechanical system. This paper presents the reasons for the speed-sensitive stiffness and the shifting stability lobes. A new method of measuring and calculating the dynamic behavior during milling by means of sub-space-state-space-identification methods is introduced. Finally, the computed stability lobe diagrams are compared with experimentally determined stability lobe diagrams.     

Chatter vibration and surface location error prediction for helical end mills

This paper describes a new theoretical model for the cutting forces of a helical end mill. A specific advantage for the presented model is the convenience in implementing the developed expressions for vibration prediction. Specifically, the presented force model is used to predict cutting forces with a Fourier series expansion, to predict surface location error with a Harmonic Balance approach, and to simultaneously predict surface location error and chatter vibration with an updated temporal finite element analysis. The developed analyses are compared and validated through comparisons with prior works.     

Analytical Modeling of Chatter Stability in Turning and Boring Operations: A Multi-Dimensional Approach

In this study, an analytical model for the stability of turning and boring processes is proposed. The proposed model is a step ahead from the previous studies as it includes the dynamics of the system in a multi-dimensional form, uses the true process geometry and models the insert nose radius in a precise manner. Simulations are conducted in order to compare the results with the traditional oriented transfer function stability model, and to show the effects of the insert nose radius on the stability limit. It is shown that very high errors in stability, which limit predictions can be caused when the true process geometry is not considered in the calculations. The proposed stability model predictions are compared with experimental results and an acceptable agreement is observed.     

Stability of milling processes with continuous spindle speed variation: Analysis in the frequency and time domains, and experimental correlation

Up to now, the theory for analysis of continuous spindle speed variation in milling processes was developed for sinusoidal variation only, and for average tooth passing frequency an exact multiple of speed variation frequency. This paper presents the general theory for analysis in the frequency domain and for any speed variation strategy. Results are compared with those obtained by semidiscretization and time integration, as well as with those obtained by experiments. The discrepancies of the results obtained by the different approaches are discussed, and the analysis of the evolution of the stability along the speed variation period is proposed.     

Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams

The milling of thin parts is a high added value operation where the machinist has to face the chatter problem. The study of the stability of these operations is a complex task due to the changing modal parameters as the part loses mass during the machining and the complex shape of the tools that are used. The present work proposes a methodology for chatter avoidance in the milling of flexible thin floors with a bull-nose end mill. First, a stability model for the milling of compliant systems in the tool axis direction with bull-nose end mills is presented. The contribution is the averaging method used to be able to use a linear model to predict the stability of the operation. Then, the procedure for the calculation of stability diagrams for the milling of thin floors is presented. The method is based on the estimation of the modal parameters of the part and the corresponding stability lobes during the machining. As in thin floor milling the depth of cut is already defined by the floor thickness previous to milling, the use of stability diagrams that relate the tool position along the tool-path with the spindle speed is proposed. Hence, the sequence of spindle speeds that the tool must have during the milling can be selected. Finally, this methodology has been validated by means of experimental tests.     

龙门铣床双摆头动力学特性实验研究

结合实验模态分析技术对龙门铣床双摆头的动力学特性进行研究。对双摆头结构进行模态测试,获取频率响应函数,并进行拟合,分析得到结构固有频率、阻尼比与振型等动力学参数;对安装在双摆头上的螺旋立铣刀进行锤击实验,获取机床-主轴-刀具系统的加速度频率响应函数,结合再生颤振理论,预测其铣削颤振稳定域。根据可视化的整机振型,提出改进机床结构的方案,并提供合理的切削参数。     

Chatter suppression based on nonlinear vibration characteristic of electrorheological fluids

Self-excited chatter is a serious problem in machining shops and its frequency is always near the resonant frequency of the machining system. This paper proposes a novel design method for a tunable-stiffness boring bar containing an electrorheological (ER) fluid to suppress chatter in boring. The ER fluid undergoes a phase change when subjected to an external electrical field and serves as a complex spring behaving nonlinearly in the structure. The deformation modes of the ER fluid are dependent on the applied electric field and the strain amplitude. As a result, the global stiffness and energy dissipation properties of the boring bar under an electric field change drastically at different amplitudes of vibration. It is found that the amplitude of chatter can be prevented from increasing by using the nonlinear vibration characteristic of the ER fluid. It is shown experimentally that the chatter can be suppressed under a certain range of the electric field related to the cutting conditions.     

Generalized modeling of drilling vibrations. Part II: Chatter stability in frequency domain

A time domain model of the drilling process and hole formation mechanism is presented in Part I, and the general solution of drilling chatter stability in frequency domain is presented in this paper. The drill's flexibility in torsional, axial and lateral directions are considered in determining the regenerative chip thickness. Stability is modelled as a fourth order eigenvalue problem with a regenerative delay term. The critical radial depth of cut and spindle speed are analytically determined from the eigenvalues of the characteristics equation of the dynamic drilling process in frequency domain. The method is compared against the extensive numerical solutions in time domain which were presented in Part I, cutting experiments and previously published partial stability laws. The time domain model presented in Part I of the paper considers tool geometry dependent mechanics, all vibration directions and the true kinematics of drilling, while allowing for nonlinearities such as tool jumping out of cut and nonlinear cutting force models. It is shown that accurate prediction of drilling stability requires modeling of drill/hole surface contact stiffness and damping which is still a research challenge.     

Extension of Tlusty׳s law for the identification of chatter stability lobes in multi-dimensional cutting processes

Chatter vibrations in cutting processes are studied in the present paper. A unified approach for the calculation of the stability lobes for turning, boring, drilling and milling processes in the frequency domain is presented. The method can be used for a fast and reliable identification of the stability lobes and can take into account nonlinear shearing forces, as well as process damping forces. The applicability of Tlusty׳s law, which is a simple scalar relationship between the real part of the oriented transfer function of the structure and the limiting chip width, is extended to milling and any other multi-dimensional chatter problem without neglecting the coupled dynamics. The given analysis is suitable for getting a deep understanding of the chatter stability dependent on the parameters of the cutting process and the structure. Basic examples based on experimental data of real machine tools include the dependence of the stability behavior on the rotational direction in turning, the effect of axial–torsional structural coupling in drilling, and the dynamics of slot milling.     

基于并联机床的2A12铝合金铣削力的实验研究

利用BJ-042(A)型并联机床,通过多因素回归正交实验,建立了2A12铝合金材料关于切削速度v、每齿进给fz、径向切深ae、轴向切深ap四个切削参数的铣削力经验公式,并进行了单因素试验验证和时域仿真.对其应用条件进行了讨论,为进一步研究铝合金加工变形及振动提供了可靠的边界条件.     

球头铣刀动力学模型及其铣削加工稳定性的研究

根据螺旋刃球头铣刀的几何模型,考虑切削加工时刀齿的有交切削区及再生效应,建立球头铣刀的单刃切削力模型;进行模态实验和参数识别,建立螺旋刃球头铣刀的动力学模型;在Matlab环境下,基于龙格-库塔法对球头铣刀铣削加工过程稳定性进行仿真,结果表明:该模型能很好地描述切削过程中的稳定性及振动等动学特性,对于实际铣削加工过程及实验机的优化设计具有指导意义。     

Uncharted islands of chatter instability in milling

This paper provides conclusive evidence that isolated islands of chatter vibration can exist in milling processes. Investigations show these islands are induced by the tool helix angle and act to separate regions of period-doubling and quasi-periodic behavior. Modeling efforts develop an analytical force model with three piecewise continuous regions of cutting that describe helix angle tools. Theoretical results examine the asymptotic stability trends for several different radial immersions and helix angles. In addition, new results are shown through the implementation of a temporal finite element analysis approach for delay equations written in the form of a state space model. Predictions are validated by a series of experimental tests that confirm the isolated island phenomenon.     

A general approach to simulating workpiece vibrations during five-axis milling of turbine blades

Workpiece vibrations have a significant influence on the machining process and on the quality of the resulting workpiece surface, particularly when milling thin-walled components. In this paper a simulation system, consisting of an FE model of the workpiece coupled with a geometric milling simulation for computing regenerative workpiece vibrations during the five-axis milling process, is presented. Additionally, a modeling method for visualizing the resulting surface is described. In order to validate the simulation model, turbine blades were machined and the experimental results were compared to the simulation results.     

Analysis of the Influence of Mill Helix Angle on Chatter Stability

Current methods for estimating chatter stability limits for milling do not consider the influence of the helix angle and the consequent phase lag between the forces appearing at different sections of the mill. Budak and Altintas' multifrequency solution is extended to include the helix effect, and results are compared with results of semi-discretization and experiments.As a conclusion, the helix has an important influence on the areas of added lobes (flip lobes), while the influence on the traditional lobes is negligible. Flip lobes become closed curves separated by horizontal lines where the depth of cut equals a multiple of the helix pitch.     

A New Method for Chatter Detection in Grinding

A new method for automatic chatter detection in outer-diameter grinding is proposed which exploits significant changes in grinding dynamics caused by the onset of chatter. The method is based on monitoring of a non-linear statistic called the coarse-grained entropy rate. The entropy rate is calculated from the fluctuations of the normal grinding force. Values of the entropy rate close to zero are typical of chatter, whereas larger values are typical of chatter-free grinding. If the entropy rate is normalized, a threshold value can be set which enables automatic distinction between chatter-free grinding and chatter.