Solution and Analysis of Chatter Stability for End Milling in the Time-domain

In this paper, the instantaneous undeformed chip thickness is modeled to include the dynamic modulation caused by the tool vibration while the dynamic regenerative effects are taken into account. The numerical method is used to solve the differential equations goveming the dynamics of the milling system. Several chatter detection criteria are applied synthetically to the simulated signals and the stability diagram is obtained in time-domain. The simulation results in time-domain show a good agreement with the analytical prediction, which is validated by the cutting experiments. By simulating the chatter stability lobes in the time-domain and analyzing the influences of different spindle speeds on the vibration amplitudes of the tool under a Fixed chip-load condition, conclusions could be drawn as follows： In rough milling, higher machining efficiency can be achieved by selecting a spindle speed corresponding to the axial depth of cut in accordance with the simulated chatter stability lobes, and in Fmish milling, lower surface roughness can be achieved by selecting a spindle speed well beyond the resonant frequency of machining system.

Influences of electric-hydraulic chattering on backward extrusion process of 6061 aluminum alloy

The possibility of the electric-hydraulic chattering technology and its application in the cold extrusion were presented.The conventional and electric-hydraulic chattering assisted backward extrusion processes were performed on 6061 aluminum alloy billets at room temperature.The experimental results showed that 5.65% reduction in the extrusion load was attained if the die and ejector were vibrated at a frequency of 100 Hz and amplitude of 0.013 mm in the longitudinal direction.The friction coefficient at the billet and tool system interface determined from the finite element analysis（FEA） decreased from 0.2 without chattering to 0.1 with application of electric-hydraulic chattering.The higher values of instantaneous velocity and direction change of material flow were achieved during the chattering assisted backward extrusion process.The strain distribution of the chattering assisted backward extrusion billet revealed lower maximum strain and smoother strain distribution in comparison with that produced by the conventional extrusion method.

Modelling and simulation of high-speed milling chatter regeneration based on MATLAB

Considering the deficiency in milling process parameters selection, based on the modelling of dynamic milling force and the deduction of chatter stability limits, the chatter stability lobes simulation program for milling is developed with MAT- LAB. The simulation optimization application software of dynamics was designed using engineering simulation software Visio Basic. The chatter stability lobes for milling, which can be used as an instruction guide for the selection of process parameters, are simulated with frequency response functions （FRFs） gained by hammer test. The validation and accuracy of the simulation algorithm are verified by experiments. The simulation method has been used in a factory with an excellent application effect.

METHOD FOR SUPPRESSING CUTTING CHATTER IN NUMERICAL CONTROL MACHINE TOOLS

A new method for suppressing cutting chatter is studied by adjusting servo parameters of the numerical control （NC） machine tool and controlling the limited cutting width. A model of the cutting system of the NC machine tool is established. It includes the mechanical system, the servo system and the cutting chatter system. Interactions between every two systems are shown in the model. The cutting system stability is simulated and relation curves between the limited cutting width and servo system parameters are described in the experiment. Simulation and experimental results show that there is a mapping relation between the limited cutting width and servo parameters of the NC machine tool, and the method is applicable and credible to suppress chatter.

AUTOMATIC CONTROL OF REGENERATIVE CUTTING CHATTER BASED ON OPTIMAL REGULATION OF SPINDLE SPEED

An applicable method to control regenerative cutting chatter automatically based on the optimal regulation of spindle speed is introduced. The optimal value of the phase shift angle of the regenerative chatter signal between the two successive cuts is 270°. The cutting process can be adjusted from the unstable region to stable one whenever regenerative chatter occurs if the phase shift angle is kept 270° by the optimal regulation of spindle speed. The theoretical analysis and the experimental results prove that the optimal regulation of spindle speed can effectively control regenerative cutting chatter. In addition, a reliablelly optimal control system of reliable spindle speed is presented. There is no need for system identification of the machine tool, and it is easy to put this regenerative chatter control method into practice, so the method has excellent application prospect.

Grinding Chatter Detection and Identication Based on BEMD and LSSVM

Grinding chatter is a self?induced vibration which is unfavorable to precision machining processes. This paper proposes a forecasting method for grinding state identification based on bivarition empirical mode decomposition(BEMD) and least squares support vector machine(LSSVM), which allows the monitoring of grinding chatter over time. BEMD is a promising technique in signal processing research which involves the decomposition of two?dimen?sional signals into a series of bivarition intrinsic mode functions(BIMFs). BEMD and the extraction criterion of its true BIMFs are investigated by processing a complex?value simulation chatter signal. Then the feature vectors which are employed as an amplification for the chatter premonition are discussed. Furthermore, the methodology is tested and validated by experimental data collected from a CNC guideway grinder KD4020 X16 in Hangzhou Hangji Machine Tool Co., Ltd. The results illustrate that the BEMD is a superior method in terms of processing non?stationary and nonlinear signals. Meanwhile, the peak to peak, real?time standard deviation and instantaneous energy are proven to be e ec?tive feature vectors which reflect the di erent grinding states. Finally, a LSSVM model is established for grinding status classification based on feature vectors, giving a prediction accuracy rate of 96%.

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.

Impact of Modal Parameters on Milling Process Chatter Stability Lobes

Modals of the machine/tool and machine/part system are the principal factors affecting the stability of a milling process. Based on the modeling of chatter stability of milling process,the influence of modal parameters on chatter stability lobes independently or jointly has been analyzed by simulation. Peak-to-valley specific value,lobe coefficient and the corresponding calculation formula have been put forward. General laws and steps of modal simplification for multimodality system have been summarized.

Modeling and Analytical Solution of Chatter Stability for T-slot Milling

T-slot milling is one of the most common milling processes in industry. Despite recent advances in machining technology, productivity of T-slot milling is usually limited due to the process limitations such as high cutting forces and stability. If cutting conditions are not selected properly the process may result in the poor surface finish of the workpiece and the potential damage to the machine tool. Currently, the predication of chatter stability and determination of optimal cutting conditions based on the modeling of T-slot milling process is an effective way to improve the material removal rate（MRR） of a T-slot milling operation. Based on the geometrical model of the T-slot cutter, the dynamic cutting force model was presented in which the average directional cutting force coefficients were obtained by means of numerical approach, and leads 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 was also created to satisfy the special requirement of T-slot milling. Thereafter, a dynamic simulation model of T-slot milling was implemented using Matlab software. In order to verify the effectiveness of the approach, the transfer functions of a typical cutting system in a vertical CNC machining center were measured in both feed and normal directions by an instrumented hammer and accelerators. Dynamic simulations were conducted to obtain the predicated SLD under specified cutting conditions with both the proposed model and CutPro~. Meanwhile, a set of cutting trials were conducted to reveal whether the cutting process under specified cutting conditions is stable or not. Both the simulation comparison and experimental verification demonstrated that the satisfactory coincidence between the simulated, the predicted and the experimental results. The chatter-free T-slot milling with higher MRR can be achieved under the cutting conditions determined according to the SLD simulation.

APPLICATION OF WAVELET TRANSFORM ON DIAGNOSIS AND PREDICTION OF MILLING CHATTER

In order to avoid the accuracy deterioration or tool damage caused by milling chatter, it is necessary to have an efficient and reliable diagnosis system that can on-line predict/detect the occur-rence of chatter. The diagnosis/predicting system proposed is to on-line process and analysis the vi-bration signals of the milling machine measured by accelerometers. According to the analysis results, the system will be able to detect/predict the occurrence of the chatter. The diagnosis algorithm is, first, collecting both the normal signals and chatter signals from milling processes, and then, converting the signals through wavelet transform and fast Fourier transform （FFT）. Since the converted chatter sig-nals exhibit different characteristics from the normal signals, through defining the characteristic val-ues, such as root-mean-square value, max value, and ratio of peak value to root-mean-square value, etc, a diagnosis reference library that contains the distribution of these characteristic values is built for diagnosis. When a diagnosis is executing, the characteristic value of the measured signals is con-trasted with the diagnosis reference. The approach index which shows the possibility of occurrence of milling chatter will, then, be calculated through the diagnosis system. Cutting experiments are con-ducted to verify the proposed diagnosis system. The results show the success of early chatter detecting for the system.

Optimization of the Tuned Mass Damper for Chatter Suppression in Turning

The tuned mass damper（TMD） has been successfully applied to the vibration control in machining, while the most widely adopted tuning is equal peaks, which splits the magnitude of the frequency response function（FRF） into equal peaks. However, chatter is a special self-excited problem and a chatter-flee machining is determined by FRF at the cutting zone. A TMD tuning aiming at achieving the maximum chatter stability is studied, and it is formulated as an optimization problem of maximizing the minimum negative real part of FRF. By employing the steepest descend method, the optimum frequency and damping ratio of TMD are obtained, and they are compared against the equal peaks tuning. The advantage of the proposed tuning is demonstrated numerically by comparing the minimum point of the negative real part, and is further verified by damping a flexible mode from the fixture of a turning machine. A TMD is designed and placed on the fixture along the vibration of the target mode after performing modal analysis and mode shape visualization. Both of the above two ttmings are applied to modify the tool point FRF by tuning TMD respectively. Chatter stability chart of the turning shows that the proposed tuning can increase the critical depth of cut 37% more than the equal peaks. Cutting tests with an increasing depth of cut are conducted on the turning machine in order to distinguish the stability limit. The tool vibrations during the machining are compared to validate the simulation results. The proposed damping design and optimization routine are able to further increase the chatter suppression effect.

Chatter Suppression with Ultrasonic Elliptical Vibration Based on Energy Principle

A new method is proposed to suppress chatter, in which the ultrasonic elliptical vibration is added on the cutting tool edge. It results in the fact that the rake face of tool is separated from the chip and the direction of the frictional force between the rake face and the chip is reversed in each cycle of elliptical vibration cutting. The experimental investigations show that the chatter can be suppressed effectively by adding ultrasonic elliptical vibration on the cutting tool edge. In order to make clear the reason of chatter suppression, the mechanism of chatter suppression is analyzed theoretically from the viewpoint of energy.

Chattering analysis for discrete sliding mode control ofdistributed control systems

The chattering characteristic of sliding mode control isanalyzed when it is applied in distributed control systems （DCSs）.For a DCS with random time delay and packet dropout, a discreteswitching system model with time varying sampling period isconstructed based on the time delay system method. The reachinglaw based sliding mode controller is applied in the proposedsystem. The exponential stability condition in the form of linearmatrix inequality is figured out based on the multi-Lyaponov functionmethod. Then, the chattering characteristic is analyzed for theswitching system, and a chattering region related with time varyingsampling period and external disturbance is proposed. Finally, numericalexamples are given to illustrate the validity of the analysisresult.

CONTINUITY AND BREAK OF CHATTER VIBRATION STATUS

By turning a specifically designed conical part, complete process of metal cutting, in which the chatter occurs and expands, is recorded and analyzed. This process exposes that chatter vibration has two characters called continuity and break. The continuity character means that vibration extent enlarges continuously while chatter frequency is almost changeless as the cutting depth extends downwards continuously. The break one is that chatter frequency moves rapidly downwards to a lower level while chatter remains after the cutting depth reach another given value. It is confirmed through an exciting test that the two chatter frequencies obtained in chatter test belong to the natural frequencies of workpiece system and cutting tool system respectively. From the viewpoints of chatter energy supplying and chatter mass effect, the. chatter should occur on one of the two final executive components in its natural frequency. On this basis, a new chatter model with two chatter active bodies is proposed. This new model can better explain the above phenomenon, and adapt to chatter monitoring and improvement of component structure well.

Limiting Factors for Active Suppression of Structural Chatter Vibrations Using Machine′s Drives

Chatter vibrations are a major limitation for rough milling operations,leading to productivity reduction,low tool life and poor surface finish.It has been shown recently that the machine tool′s own drives can be used to increase the stability limit related to structural modes of the machine.To damp the low frequency modes,a new feedback loop is added to the classical position,velocity and current cascaded control.The objective of this study is to analyse the limitations of this new chatter suppression technique.Constraints related to the non-collocated control are first studied on a simplified three-mass model and then experimentally demonstrated on a three-axis horizontal milling centre.The industrial integration of the new control loop with sampling time constraints and limited drive′s bandwidth is analysed.After determining the appropriate conditions to use this chatter suppression technique,a cutting test demonstrates that the stability limit can be doubled in the low regions of the stability lobes.

Experimental study on chatter of micro-miniature turn-milling

A chatter experiment of micro-miniature turn-milling was carried out in this paper. In or- der to reduce the effect that the natural frequencies of workpieces brought to the chatter experiments of micro-miniature turn-milling, both positive and negative cone-shape workpieces were used . The chatter frequency of micro-miniature turn-milling process was obtained by the sampling and analyzing systems. Then by applying excitation experiments to the workpiece system and tool system respec- tively, the natural frequencies of these two systems were obtained. By comparing chatter frequency of micro-miniature turn-milling process with the natural frequencies of workpiece system and tool system, we found that chatter frequency of micro-miniature turn-milUng was close to the natural fre- quency of the low stiffness vibration body in the machine tool system. The funding could be useful for optimizing the structure of machine-tool and designing the machining process.

On-line Chatter Detection Using an Improved Support Vector Machine

On-line chatter detection can avoid unstable cutting through monitoring the machining process.In order to identify chatter in a timely manner,an improved Support Vector Machine(SVM)is developed in this paper,based on extracted features.In the SVM model,the penalty factor(e)and the core parameter(g)have important influence on the classification,more than from Kernel Functions(KFs).Hence,first the classification results are conducted using different KFs.Then two methods are presented for exploring the best parameters.The chatter identification results show that the Genetic Algorithm(GA)approach is more suitable for deciding the parameters than the Grid Explore(GE)approach.

Countermeasure Against Regenerative and Forced Chatter of Flexible Workpieces in Milling Processs Using Bi-directional Excitation

A novel extended methodology for chatter suppression in milling process by applying external forced vibrations to the workpiece in two orthogonal directions which are the feed and cross-feed directions.Both the regenerative and forced chatter suppression during the milling process of flexible workpieces are investigated.Here,the workpiece is subject to a sinusoidal periodic force in the feed direction to disrupt the regenerative effect.Additionally,to minimize the forced chatter,the workpiece is subject to the periodic excitation force in cross-feed direction.This force is proportional to the magnitude of the estimated cutting force in cross-feed direction and has a phase opposite to the cutting force to minimize the vibration amplitudes.The effectiveness of the proposed method is evaluated numerically and experimentally,for the spindle speed located in both the local minima and local maxima of the stability lobe diagram.The numerical simulations indicate significant suppression effect in terms of vibration amplitudes,resulting in suppression of both the regenerative chatter and the forced chatter.Experiments were conducted by using a workpiece-mounted active stage composed of flexure hinges and driven by piezoelectric actuators.The experimental results agree qualitatively with the numerical simulations.The proposed method indicates a remarkable vibration reduction effect for both regenerative and forced chatters.

Frequency Modulation of High-Speed Mill Chatter

Mill chatter is a common phenomenon in the metal strip rolling process. Product defects caused by mill vibration were reported worldwide during last two decades, which is usually classified as torque vibration of the driving system with low frequencies and vertical vibration of the mill stand with comparative higher frequencies. The frequency range of the vertical vibration is wide (in general from more than 100 Hz to more than 1 000 Hz), and the vibration phenomena are very complex, even it is very difficult to determine the vibration causes, which is followed the name "ghost vibration". During a fieldwork to measure the vibration in high-speed rolling mills, a frequency modulation phenomenon was identified, which had not been reported in strip rolling community. This article makes a theoretical investigation to the newly encountered phenomenon in strip rolling process. According to an analysis of the mill roller bearings, the periodic change of stiffness of roller bearings at the fixed load orientation, together with the periodic change of the effective errors of the bearings, may cause amplitude and frequency modulation,based on the theories of Fourier series and Bessel function. The comparison between test results and theoretical analysis implies that the frequency modulation is caused by the effective errors of the mill roller bearings that have 12 ripples on the internal ring of the bearings.

Extraction and assessment of chatter feature

Presents feature wavelet packets (FWP) a new method of chatter feature extraction in milling process based on wavelet packets transform (WPT) and using vibration signal. Studies the procedure of automatic feature selection for a given process. Establishes an exponential autoregressive (EAR) model to extract limit cycle behavior of chatter since chatter is a nonlinear oscillation with limit cycle. And gives a way to determine FWT’s number, and experimental data to assess the effectiveness of the WPT feature extraction by unforced response of EAR model of reconstructed signal.