Stability Lobe Diagram Research Articles

Reliability Analysis of the Chatter Stability during Milling Using a Neural Network

The parameters of a system have the randomness generally in the process of milling, which influences the stability of the milling. This paper uses the neural network to get a comprehensive analysis of the influences of random factors in milling and proposes a method for reliability analysis of the regenerative chatter stability in milling. Dynamic model of milling regenerative chatter is established, and stability lobe diagram is obtained by the full-discretization method (FDM). The neural network is applied to approximate the functional relationship of the limit axial cutting depth; then the reliability is computed with the Monte Carlo simulation method (MCSM) and the moment method (MM), respectively. Finally, the results of an example are used to demonstrate the efficiency and accuracy of the proposed method.

Influence of Parameter Uncertainties on the Computation of Stability Lobe Diagrams

To predict stability boundaries of cutting operations models of process forces and dynamic machine behavior are required. Uncertainties of model parameters may lead to significant differences between predicted and measured stability boundaries. To run a lot of simulations with random parameters is a possible approach to take these uncertainties into account when analyzing the stability behavior. However, this is a time consuming task. This paper presents a time efficient method to provide confidence levels of computed stability lobe diagrams based on stability analysis in frequency domain. The required computational time is compared to the effort for an explicit calculation with different stability algorithms. The confidence levels are compared to experimentally determined stability lobe diagrams.

Robust Stability of Machining Operations in Case of Uncertain Frequency Response Functions

Prediction of machine tool chatter requires a dynamic characterization of the machine-tool-workpiece system by means of frequency response functions (FRFs). Stability lobe diagrams are sensitive to the uncertainties of the measured FRF, which reduces the reliability of their industrial application. In this paper, a frequency-domain method is presented to determine robust stability boundaries with respect to the uncertainties of the FRF. The method is based on an envelope fitting around the measured FRFs combined with some considerations of the single-frequency method. The application of the method is validated on a turning operation characterized by a series of FRF measurements. It is shown that stability analysis using the averaged FRF may considerably overestimate the region of robust stability.

Chatter stability prediction for CNC machine tool in operating condition through operational modal analysis

The stability of high-speed machining operations is crucial in machining process and presents a key issue for insuring better surface quality, increasing productivity and protecting both machines and safe workpiece. Stability prediction in milling is based on experimental modal analysis by the estimation of frequency response functions using a tap test. One limitation of accurately estimating the stability using such approach is the change in process and the dynamic characteristics of the machine tool under operation. This paper proposes a signal processing procedure applied to vibrations in machining process in order to obtain spindle’s modal variations in operation. The novelty of the proposed approach consists in removing “virtual modes”, caused by harmonic excitations, from the system response before performing operational modal analysis. Thus, the proposed procedure combines two existing techniques that are the Cepstral Editing Procedure and the Least Square Complex Exponential. The importance of the developed methodology is in adjusting the chatter stability criterion for material removal on a dynamic basis. The main work is given as follows: first of all, the Cepstral Editing Procedure (CEP) algorithm is applied on the acceleration signals for removing deterministic vibrations caused by harmonic excitations. The residue signal is the system response to white noise excitation. The frequency response functions (FRF) are then calculated from these signals at different cutting conditions. The outcome is compared to the result of impact test on the spindle under static condition. Similarities in the form of FRFs obtained in static and operational conditions validate the proposed approach while variations of modal properties under different cutting conditions are successfully captured. Secondly, the Least Square Complex Exponential (LSCE) method in operational modal analysis is invoked to find the natural frequencies and damping ratios of the system at different spindle speeds and cutting depths. Then, the dynamic chatter stability lobes diagrams (SLD) are established which account for spindle’s speed-dependent modal variations. A significant change in the stability border is observed which is interesting in machining fields. It will be shown that some depths of cut that are stable with static stability lobes become unstable with dynamic stability lobes and vice versa.

Speed-varying Machine Tool Dynamics Identification Through Chatter Detection and Receptance Coupling

Tool-tip Frequency Response Function (FRF) represents one of the essential inputs to predict chatter vibration and compute the Stability Lobe Diagram (SLD). Tool-tip FRFs are generally obtained for the stationary (non-rotating) condition. However, high speeds influence spindle dynamics, leading to a reduced accuracy of the SLD prediction. This paper presents a comprehensive method to identify speed-varying tool-tip FRFs and improve chatter prediction. First, FRFs for a screening tool is identified by a novel technique based on a dedicated experimental test and analytical stability solution. Then, a tailored receptance coupling technique is used to predict speed-varying tool-tip FRFs of any other tool. Proposed method was experimentally validated: chatter prediction accuracy was demonstrated through chatter tests.

Verification of the stability lobes of Inconel 718 milling by recurrence plot applications and composite multiscale entropy analysis

Correctness verification of the stability lobe diagrams of milling process determined by commercial software CutPro 9 is the aim of this work. The analysis is performed for nickel superalloy Inconel 718 which is widely used in aviation industry. A methodology of stability analysis which bases on advanced nonlinear methods such as recurrence plot, recurrence quantifications analysis and composite multiscale entropy analysis are applied to the experimental data. Additionally, a new criterion for the determination of the unstable areas is proposed.

Estimation of Safe Chatter-free Technological Parameter Regions for Machining Operations

Experimental cutting tests often show different dynamic behavior from the one predicted by means of theoretical mechanical models. One reason behind this observation is that stability lobe diagrams determined by standard linear stability analysis often under- or overestimate the region of chatter-free parameters. Therefore, reliable selection of technological parameters associated with optimal material removal rate is difficult in practice. In this paper, a simple formula is given to estimate the safe parameter region, where the machining operation is globally stable even for large disturbances. The analytical results are confirmed by numerical simulations.

Study on the Milling Stability of Titanium Alloy Thin-walled Parts Considering the Stiffness Characteristics of Tool and Workpiece

In order to eliminate the chatter in the milling process of titanium alloy thin-walled parts, the milling dynamic model was established taking the stiffness characteristics of tool and workpiece into consideration. The modal analysis and milling experiments were carried out respectively to acquire the system dynamic performance parameters and the milling force coefficient. The cutting stability lobe diagrams were drawn under different stiffness conditions. The results show that the model is valid and the accuracy of lobe diagrams was verified by the milling experiments with different depths of cut.

Prediction of chatter stability for milling process using Runge-Kutta-based complete discretization method

On the basis of the classical Runge-Kutta method and the complete discretization method, a Runge-Kutta-based complete discretization method (RKCDM) is proposed in the paper to predict the chatter stability of milling process, in which the regenerative effect is taken into consideration. Firstly, the dynamics model of milling process is simplified as a 2-DOF vibration system in the two orthogonal directions, which can be expressed as coefficient-varying periodic differential equations with a single time delay. Then, all parts of the delay differential equation (DDE), including delay term, time-domain term, parameter matrices, and most of all the differential terms are discretized using the classical fourth-order Runge-Kutta iteration method to replace the direct integration scheme used in the classical semi-discretization method (C-SDM) and the classical complete discretization scheme with the Euler method (C-CDSEM), which can simplify the complexity of the discretization iteration formula greatly. Lastly, the Floquet theory is adopted to predict the stability of milling process by judging the eigenvalues of the state transition matrix corresponding to certain cutting conditions. Comparing RKCDM with C-SDM and C-CDSEM, the numerical simulation results show that RKCDM has the highest convergence rate, computation accuracy, and computation efficiency. As dichotomy search rather than sequential search is used in the algorithm, the calculation time for obtaining the stability lobe diagrams (SLDs) is greatly reduced. As a result, it is practical to determine the optimal chatter-free cutting conditions for milling operation in shop floor applications.

Effects of Machine Tool Spindle Decay on the Stability Lobe Diagram: An Analytical-Experimental Study

An analytical-experimental investigation of machine tool spindle decay and its effects of the system’s stability lobe diagram (SLD) is presented. A dynamic stiffness matrix (DSM) model for the vibration analysis of the OKADA VM500 machine spindle is developed and is validated against Finite Element Analysis (FEA). The model is then refined to incorporate flexibility of the system’s bearings, originally modeled as simply supported boundary conditions, where the bearings are modeled as linear spring elements. The system fundamental frequency obtained from the modal analysis carried on an experimental setup is then used to calibrate the DSM model by tuning the springs’ constants. The resulting natural frequency is also used to determine the 2D stability lobes diagram (SLD) for said spindle. Exploiting the presented approach and calibrated DSM model it is shown that a hypothetical 10% change in the natural frequency would result in a significant shift in the SLD of the spindle system, which should be taken into consideration to ensure chatter-free machining over the spindle’s life cycle.

Stability-based selection of cutting parameters to increase material removal rate in high-speed machining process

The reasonable selection of cutting parameters is of great significance to improve the productivity in high-speed machining process. In this article, a stability-based selection method of cutting parameters is proposed to increase material removal rate in high-speed machining process. First, the coupled dynamics of the high-speed spindle system and machining process is modeled. Then, the interaction mechanism between the spindle-tool system and the cutting process is investigated. Based on the process stability and surface quality of workpiece, a cutting parameter selection method is proposed from the perspective of machining stability. In order to select reasonable spindle speed and depth of cut, the lower bound of chatter stability lobe diagram and surface finish are taken as constraints, and the maximum material removal rate is set as the target. The proposed method is applied to the machining of the front face of a gearbox cover, which is made of Aluminum-7050. The axial depth of cut and spindle speed are chosen reasonably with the increase in machining efficiency by about 133%.

Estimation of stability lobe diagrams in milling with continuous learning algorithms

The productivity of milling processes is limited by the occurrence of chatter vibrations. The correlation of the maximum stable cutting depth and the spindle speed can be shown in a stability lobe diagram (SLD). The stability is different for different width of cut and can change with the axis positions. Today it is already a great effort to estimate the SLD only for one position. Many experiments are necessary to measure the SLD or derive a detailed mathematical model to calculate the SLD. Moreover not only the cutting depth, but also the cutting width should be represented in the SLD. This paper presents a new approach to assess the process stability based on measured acceleration signals. The multidimensional stability lobe diagram (MSLD) are derived during the production using two new continuously learning algorithms. In this paper the application of a continuous learning support vector machine and a continuous neural network is shown. The support vector machine and the neural network are extended to make them capable for continuous learning and time-variant systems. A new trust criterion is introduced, which gives information about the prediction quality of the output for the selected input region. The learned MSLDs are evaluated against analytically calculated MSLDs and the learning algorithms can reproduce the analytical results very well.

Stability analysis of titanium alloy milling by multiscale entropy and Hurst exponent

This paper discusses the problem of stability in a milling process for titanium super-alloy Ti6242. The phenomenon of chatter vibration is analysed by the multiscale entropy method and Hurst exponent. Although this problem is often considered based on stability lobe diagrams, theoretical findings do not always agree with experimental results. First, a stability lobe diagram is created based on parameters determined by impact testing. Next, cutting forces are measured in an experiment where the axial cutting depth is gradually increased. Finally, the obtained experimental signals are investigated with respect to stability using the multiscale entropy method and Hurst exponent.

Prediction of vibration frequencies in milling using modified Nyquist method

Study of the vibration frequencies at different cutting conditions is an alternative to the use of impact hammer test for identification of natural frequencies of the machining structure and calculation of stability lobe diagrams. Vibration frequencies not only depend on the natural frequencies of the structure, but also they are dependent on the spindle speed, damping ratio of the structure and the depth of cut. Ignoring these additional parameters would lead to errors in identification of the natural frequencies of the system and considerable deviation of the calculated stability lobe diagrams from actual cutting tests. In this study modified Nyquist method is used to investigate the effects of spindle speed, depth of cut and damping ratio of the structure on vibration frequencies. The quality of frequency prediction is compared to linear and nonlinear time domain simulations and machining experiments.

Active Control of an Active Magnetic Bearings Supported Spindle for Chatter Suppression in Milling Process

In machining process, chatter is an unstable dynamic phenomenon which causes overcut and quick tool wear, etc. To avoid chatter, traditional methods aim to optimize machining parameters. But they have inherent disadvantage in gaining highly efficient machining. Active magnetic bearing (AMB) is a promising technology for machining on account of low wear and friction, low maintenance cost, and long operating life. The control currents applied to AMBs allow not only to stabilize the supported spindle but also to actively suppress chatter in milling process. This paper, for the first time, studies an integrated control scheme for stability of milling process with a spindle supported by AMBs. First, to eliminate the vibration of an unloaded spindle rotor during acceleration/deceleration, we present an optimal controller with proper compensation for speed variation. Next, the controller is further enhanced by adding an adaptive algorithm based on Fourier series analysis to actively suppress chatter in milling process. Finally, numerical simulations show that the stability lobe diagram (SLD) boundary can be significantly expanded. Also, a practical issue of constraints on controller output is discussed.

Chatter reliability prediction of turning process system with uncertainties

In this paper, reliability analysis of dynamic structural system is introduced into chatter vibration prediction of a turning process system. Chatter reliability is defined to represent the probability of stability (no chatter occurs) for a turning process system. Probability model (reliability model) of chatter vibration is established to predict turning chatter vibration, in which structural parameters m, c, k and spindle speed Ω are considered as random variables. Choosing chatter frequency ωc as an intermediate variable, reliability model is developed from a model impossible to solve to a new model related to chatter frequency, and the new model can be solved. The first-order second-moment, fourth moment method are adopted to solve the turning process system reliability model and obtain the reliability probability of the system. An example is used to demonstrate the feasibility of the proposed method. The reliability probability of turning chatter system was calculated using the FOSM method, fourth moment and compared with that calculated by Monte Carlo simulation method. The results using the three methods were consistent. Reliability lobe diagram (RLD) is proposed to identify the chatter and no chatter regions for chatter prediction instead of stability lobe diagram (SLD). Comparing with the traditional SLD method, chatter reliability and RLD can be used to judge the probability of stability of turning process system. The RLD and the index of chatter reliability have better prospects in workshop application.

3D stability lobe considering the helix angle effect in thin-wall milling

Chatter is a very detrimental phenomenon occurring in milling process especially in thin-wall milling, which has been a limitation to achieve high productivity and good surface quality. The prediction of milling stability for chatter avoidance plays a key role in high performance milling. However, compared with the case of milling a part with a flexible cutter, the stability analysis and experimental validation for thin-wall milling are seldom provided. In this paper, an approach to obtaining the 3D stability lobe in thin-wall milling is proposed considering both the helix angle effect of cutter and the dynamic behavior of thin-walled part. A systematic cutting force model, which is capable of incorporating the helix angle effect and run-out effect of cutter, is first built. After the effective stiffness of the thin-walled part along the entire tool position is acquired by combining FEM with an impact experiment, the model of dynamic milling system with respect to the mode shape of thin-walled part is then developed. Based on the model, an extended high-order time domain method is subsequently utilized to generate the 3D stability lobe diagram considering helix angle effect. Finally, the proposed method is validated by the results of dedicated experiments.

Identification of chatter in milling of Ti-6Al-4V titanium alloy thin-walled workpieces based on cutting force signals and surface topography

In vertical milling process of Ti-6Al-4V titanium alloy thin-walled workpieces, chatter as a thorny problem occurs easily, which can lead to the instability of the machining process, tool wear, and poor surface finish. It has become a focus issue to identify and avoid chatter in machining process. In this paper, the milling force signals in the direction perpendicular to the machined surface were analyzed by fast Fourier transform and wavelet transform for detecting chatter. The combination of the surface topography and the prediction theory of regenerative chatter were put forward to further verify chatter. The results show that fast Fourier transform in some cases, wavelet transform, and the combination of surface topography and the prediction theory of regenerative chatter can obtain better results for the detection and verification of chatter, and the stable cutting zone was obtained using a stability lobe diagram, which can assist in the selection of reasonable cutting parameters to avoid chatter.

Quenching chatter instability in turning process with a vibro-impact nonlinear energy sink

This paper investigates the passive control of chatter instability in turning processes using a vibro-impact nonlinear energy sink (NES). The workpiece is assumed to be rigid and the tool is flexible. A dynamical model including a nonlinear cutting law is presented and the stability lobes diagram is obtained. The behavior of the system with the vibro-impact NES is investigated using an asymptotic analysis. A control mechanism by successive beating is revealed, similarly to the strongly modulated response in the case of NES with cubic stiffness. It is shown that such a response regime may be beneficial for chatter mitigation. An original experimental procedure is proposed to verify the sizing of the vibro-impact NES. An experimental setup is developed with a vibro-impact NES embedded on the lathe tool and the results are analyzed and validated.

A new method for the prediction of chatter stability lobes based on dynamic cutting force simulation model and support vector machine

Currently, chatter has become the critical factor in hindering machining quality and productivity in machining processes. To avoid cutting chatter, a new method based on dynamic cutting force simulation model and support vector machine (SVM) is presented for the prediction of chatter stability lobes. The cutting force is selected as the monitoring signal, and the wavelet energy entropy theory is used to extract the feature vectors. A support vector machine is constructed using the MATLAB LIBSVM toolbox for pattern classification based on the feature vectors derived from the experimental cutting data. Then combining with the dynamic cutting force simulation model, the stability lobes diagram (SLD) can be estimated. Finally, the predicted results are compared with existing methods such as zero-order analytical (ZOA) and semi-discretization (SD) method as well as actual cutting experimental results to confirm the validity of this new method.