Study of fuzzy stochastic limited cutting width on chatter

Fuzzy mathematical theory is applied to drawing the fuzzy stability lobes in which each lobe is characterized by a membership grade of experiential distribution of testing data in the theoretical distribution set of chatter signal. The judgement of limit value of free-chatter cutting width is spread over the fuzzy domain in this paper. The fuzzy combination relationship between the spindle speed and the depth of cut in milling is also addressed. According to the limit width, a safety criterion on which the cutting process is stable is developed. Also, the concept and definition of safety criterion for the cutting process stability operation for fuzzy stochastic meaning are given. Analysis indicates that the fuzzy stability lobes have definite physical significance. First, they can tell us in which status the cutting process is for the drawn lobe. Second, they reflect the probability distribution of the limit value of cut width in the fuzzy domain with respect to the identification of chatter status (fuzzy event). Meanwhile, it indicates that there is a transition between unstable lobes and stable lobes in a stability threshold graph with the influence of both fuzzy stochastic parametric excitation and fuzzy stochastic external excitation. Testing value curves of the fuzzy allowed domain of the limited cutting width are developed via experiment.     

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.     

切削颤振分析与模糊控制实验研究

切削颤振是影响金属切削加工生产率和加工质量的重要因素。建立了金属切削过程的二维颤振数学模型;对颤振的稳定性进行了线性分析和非线性分析;并以颤振位移作为反馈变量,建立了基于二维模糊控制器的颤振控制系统。实验结果表明,该分析与控制对降低加工表面粗糙度具有重要意义。     

切削颤振的动力学模型研究

振动是金属切削加工过程巾经常遇到的一种现象,也是影响零件加工质量和限制生产率提高的主要因素之一。本文在切削颤振机理研究的基础上,对切削颤振的二维稳定性进行了研究,推导出了在稳定性极限条件下,轴向切深和主轴转速的关系,并用Matlab进行了计算仿真。     

颤振征兆早期识别的模糊信息融合法

基于切削试验探讨颤振征兆早期识别的模糊信息融合方法。试验中在同一个测量区内使用了功率传感器和加速度传感器,利用模糊数学与Dempster-Shafer证据论相结合的方法对两种传感器信息进行了分析融合,对切削状态进行了描述。试验证实:利用证据理论与模糊推理相结合的信息融合方法进行颤振征兆的早期模糊识别得出的目标切削状态的隶属度介于单一征兆隶属度之间,对过于敏感的传感器,会考虑其他传感器的信息予以修正,降低其评价隶属度;对于不敏感传感器,会考虑其他传感器的信息予以补偿。这种方法弥补了最大隶属度原则的缺陷,即在模糊推理中,系统对某一状态的隶属程度实际上是由模式特征集中贡献最大的那个特征决定的,而没有用到其他特征提供的信息,这说明证据理论与模糊推理相结合的信息融合方法在进行颤振征兆早期识别时具有更高的可靠度。     

Active suppression of chatter in peripheral milling. Part II. Application of fuzzy control

In this paper, a feasibility study is conducted where fuzzy logic control is investigated to actively vary spindle speed modulation parameters for chatter suppression. A justification for using fuzzy control is given, as well as a brief synopsis of the fuzzy inferencing mechanism. Proportional and proportional-integral fuzzy control algorithms are developed. The set point in these controllers is established from experimental observations and measurements of the machined surfaces. Controller performance is tested by simulating changes in the axial depth of cut from a stable depth to 20% and 50% beyond the stable limit for constant speed cutting. It was found that both controllers were able to regulate the vibration in the milling process, however, the proportional-integral controller generally exhibited more desirable performance characteristics.     

再生型切削颤振稳定性极限的图解法

分析了再生型切削颤振的稳定性极限,并提出一种简单的确定稳定性曲线的图解法,这种图解法对于分析系统的稳定性更具有直观性,并为抑制再生型切削颤提供了理论依据。     

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.

     

Vibration analysis in milling titanium alloy based on signal processing of cutting force

In metal cutting processes, the chatter may cause fast wear of tools and poor surface quality of the processed parts; it can happen on different cutting parameters, but how do we identify the chatter and how do we select suitable cutting parameters to avoid chatter at high material removal rate (MRR). In this paper, the signal processing methods such as time domain, frequency domain, and time–frequency domain analysis are introduced. The signals of cutting force that were collected in milling titanium alloy Ti–6Al–4V at variable cutting speeds varied from 80 to 360 m/min; signal analysis methods such as time domain, frequency domain, and time–frequency domain were put forward. Further analysis results reveal that the chatter occur when cutting speeds are 240 and 360 m/min, when the maximum value of cutting forces increase by 61.9–66.8%, the standard deviation increase by 84.1–86.1%, and the surface roughness increase by 34.2–40.5% compared with that of at 80 m/min. Detail signal d2 is employed to monitor cutting stability state from the result of wavelet analysis.     

ESPRIT- and HMM-based real-time monitoring and suppression of machining chatter in smart CNC milling system

Suppression of machining chatter during milling processes is of great significance for surface finish and tool life. In this paper, a smart CNC milling system integrating the function of signal processing, monitoring, and intelligent control is presented with the aim of real-time chatter monitoring and suppression. The algorithm of estimation of signal parameters via rotational invariance techniques (ESPRIT) is adopted to extract the frequency characteristics of acceleration signals, and then, cutting state is categorized as stable state, chatter germination state, and chatter state based on amplitude-frequency characteristics of identified acceleration signals. The model of chatter identification is acquired by training a hidden Markov model (HMM), which combines acceleration signals and labeled cutting state. To implement real-time chatter suppression, the algorithm of fuzzy control is integrated into a smart CNC kernel to determine the relationship between cutting force and spindle speed. Furthermore, spindle speed of machine tool could be adjusted timely in the presented system once the chatter is identified. Finally, the effectiveness of the proposed real-time chatter monitoring and suppression system is experimentally validated.     

Proposal of novel spindle speed variation profile with constant acceleration rate for improvement of chatter stability

Spindle speed variation (SSV) is one of the effective methods which suppresses regenerative chatter. However, regenerative chatter can grow even if SSV is applied. In the previous work, the chatter growth characteristics in SSV were clarified. The chatter frequency changes proportionally to the varying spindle speed, and it causes the change of the magnitude of the dynamic compliance. Hence, chatter can be suppressed through SSV since the dynamic compliance usually reduces as the chatter frequency changes. A greater compliance reduction can be obtained by a higher rate of spindle speeds in two consecutive revolutions at the same angular position, i.e., acceleration rate. From the investigations in the previous work, limitation of the conventionally utilized SSV profiles is found as follows: the acceleration rate always fluctuates with speed variation and the chatter vibration grows where the acceleration rate is insufficient for suppression, and hence suppressing chatter in all sections of SSV is difficult. In this paper, a new SSV profile with a constant acceleration rate, namely CAR-SSV, is proposed to overcome the limitation of chatter stability improvement by utilizing conventional SSV profiles. The magnitude of the acceleration rate is kept constant to realize the chatter suppression effect throughout the cutting process. Through time-domain simulation and cutting experiments, the chatter stability of CAR-SSV is investigated based on the previously introduced chatter stability evaluation indices. Influence of the parameters of CAR-SSV on the stability is investigated, and an appropriate strategy for setting SSV parameters to achieve higher stability is discussed. In addition, in order to verify the effectiveness of the proposed profile, the stabilities of conventional SSV profiles and CAR-SSV are compared through time-domain simulations and cutting experiments.     

Automatic selection of spindle speed for suppression of regenerative chatter in turning

The paper presents a new spindle speed regulation method to avoid regenerative chatter in turning operations. It is not necessary to analyse complex cutting dynamics to search for stable spindle speeds to eliminate regenerative chatter. The metal removal rate is also greatly improved by using this method. The stability lobe diagram for the stability limit of chip width and chatter frequency versus spindle speed is derived by using the Nyquist stability criterion. It is shown that stable spindle speeds can be automatically obtained when the chatter frequency is found. Computational simulations and experimental cutting tests are performed to illustrate the proposed method.     

高速铣削时颤振的诊断和稳定加工区域的预报

给出一种通过测量加工过程中的噪声来诊断高速铣削时颤振的方法.先测量环境噪声,然后测量加工噪声.理论分析和试验结果表明,如果加工噪声的主谐振频率接近其中一个环境噪声主谐振频率或者是齿频的整数倍,那么系统无颤振,否则有颤振.建立系统结构和铣削过程动力学特征参数的数学模型.根据测出的颤振频率,通过所建模型可解出系统的固有频率、阻尼比和过程参数,并计算出稳定极限曲线.试验证明,该方法能较好地预报高速铣削时的稳定加工区域.     

切削的稳定界与颤振预报

在文献[1]的基础上,本文导出了无再生颤振、再生颤振及特殊情况下再生颤振的切削稳定界及绝对稳定界公式。指了Tobais公式、Tlusty公式不妥文中指出,k的研究是不完备的。目前许多关于k的说法与事实和实验不符。文中提供了切削与磨擦颤振的统一问题。根据本文给出的公式,作者较成功地预报了切削颤振的发生,因而公式对建立CAM数据库有指导意义。     

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.     

Unique regenerative chatter in wiper-turning operation with burnishing process Part 1: Prediction and analytical investigation of generation mechanism,critical stability,and characteristics

The purpose of this paper is to understand the generation mechanism and to propose an analytical model of a unique regenerative chatter with the burnishing process in wiper-turning operations. The authors have found a unique chatter when using wiper inserts, which cannot be explained by the existing chatter theory found in the literature. The authors believe that this occurs because of the burnishing process of the wiper insert, which is the only difference from ordinary turning. At first, the burnishing process, which accompanies wiper inserts, is explained, and the turning operation with this process and the well-known regenerative effect in the cutting process is discussed. Then, the stability of the turning process with the regenerative effects in the cutting and burnishing processes are investigated, and an analytical model is proposed to evaluate the critical stability. Finally, the stability analysis of this unique chatter is conducted, and its generation mechanism and characteristics are examined clearly.     

Proposal of novel chatter stability indices of spindle speed variation based on its chatter growth characteristics

Chatter is one of the most critical problems that causes poor surface quality and restriction of machining efficiency. Spindle speed variation (SSV) is a well-known technique for suppression of regenerative chatter. However, in the authors’ understanding, the chatter suppression effect diminishes when the spindle speed difference between the present and previous cutting moments is small. Furthermore, the stability changes largely according to the spindle speed variation profile which changes with the set condition of SSV parameters, e.g., nominal spindle speed, variation period and variation amplitude. Therefore, SSV parameters should be adequately set to avoid this limitation and to exert its effect throughout the entire duration of cutting. However, there is no clear methodology to determine the optimal condition. This paper presents the characteristics of chatter growth during SSV focusing on the change of chatter frequency, which lead to novel indices to evaluate the chatter stability when cutting with SSV. To verify the validity of the indices, time-domain simulations and the cutting experiments with triangular spindle speed variation (TSSV) are carried out. The influence of SSV parameters on the chatter stability is investigated from the simulation and experimental results. The limitations of widely utilized SSV profiles are discussed.     

Chatter suppression in micro-milling using shank-mounted Two-DOF tuned mass damper

The tuned mass damper (TMD) has been used in machining processes for reducing forced vibration, suppressing chatter, and improving machined surface quality. In micro-milling process, the tiny size of the cutting tool-tip and the high rotating speed bring challenges in implementing the TMD. Besides, the TMD needs to have two degrees-of-freedom (DOFs) for reducing vibrations of micro-mill in two orthogonal directions. This paper presents the chatter suppression for micro-milling by attaching a two-DOF TMD to the tool shank and rotates with the cutting tool. The frequency response function (FRF) at the tip of the micro-mill clamped by an aerostatic spindle is predicted using receptance coupling analysis. A two-DOF TMD is designed via graphical approach based on the FRF result at the tool-tip. The natural frequencies and damping ratio of the TMD are optimized under different spindle speeds in order to enhance the cutting stability. The chatter stability of micro-milling is predicted considering the gyroscopic and centrifugal effects of the TMD structure. Modal tests and micro-milling experiments are conducted to validate the effect of the TMD on chatter stability. The results show that the TMD is able to improve the critical depth of cut by 13 folds, and satisfy the compact design requirement for micro-milling.     

高速切削加工稳定性研究综述

高速切削加工的稳定性是影响加工效率和质量的重要因素,从20世纪初就引起了各国研究者的广泛关注。本文综合介绍了国内外研究者在切削加工稳定性领域的研究成果,在综述切削颤振产生机理和切削稳定性模型建立的基础上,重点论述了切削颤振的检测和控制方法,同时指出了高速切削稳定性研究的发展方向。     

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。