Chatter Prediction Research Articles

Operational Modal Analysis of Self-excited Vibrations in Milling Considering Periodic Dynamics

Abstract A new method is presented to identify the dynamics of regenerative chatter from measured process vibrations in milling. This method combines the synchronous once-per-revolution sampling of process vibrations with Operational Modal Analysis to estimate the Floquet multipliers of the delayed linear time-periodic dynamics in milling, all from the natural process vibrations without external excitation. The identified multipliers quantify vibration stability, enabling chatter prediction before it occurs. In addition to this, they can be used to calibrate physics-based chatter models based on vibration measurements solely within the stable region. The method's accuracy in identifying Floquet multipliers is validated through extensive numerical simulations and two experimental case studies. The results show that chatter due to both Hopf and period-doubling bifurcations can be predicted from the process vibrations during stable cuts. Moreover, the experimental case studies demonstrate a vibration measurement system for implementing the presented method in standard milling operations and confirm its effectiveness in practice.

Physics-supported Bayesian machine learning for chatter prediction with process damping in milling

Chatter stability of milling operations is a complicated phenomenon causing serious productivity issues in the manufacturing industry, yet a shop-floor implementable solution is lacking. This paper follows a physics-supported Bayesian machine learning approach and incorporates the potential effect of process damping on the stability of the process. Using a likelihood function based on the Nyquist stability criterion, the learning system monitors the actual stability state of the process during arbitrary cuts and refines the underlying model parameter uncertainties in the structural dynamics, cutting force coefficients, as well as the process damping. The framework can operate with limited training data and display the remaining uncertainties in stability predictions to the machine operator. Experimental case studies show the effectiveness of the proposed method and highlight the importance of considering process damping for certain endmills.

Online real-time machining chatter sound detection using convolutional neural network by adopting expert knowledge

In machining processes, chatter detection remains a pivotal challenge, impacting both the quality and efficiency of manufacturing operations. This study introduces an approach that synergizes expert knowledge with the capabilities of advanced convolutional neural networks (CNNs) to enhance chatter detection. A comprehensive monitoring framework is proposed to adopt expert knowledge that digitizes machine tool and sound data, effectively labeling chatter events. This study merges human expertise in identifying milling tool chatter sounds with CNN architecture, marking a notable advancement in blending machining insights of experts with modern artificial intelligence (AI) technologies. The proposed chatter prediction architecture is distinguished by its incorporation of an attention block, fusing outputs from the AlexNet model with cutting parameters. This model outshines baseline models in both in-distribution (ID) and out-of-distribution (OOD) testing datasets. In OOD testing, the proposed model achieved an impressive accuracy of 94.51%, markedly surpassing the standalone CNN model’s accuracy of 88.66%. Real-time 3D visualization of machining operations is demonstrated through the successful implementation of the trained model on a Raspberry Pi.

An effective investigation of chatter prediction system on Al6061 alloy in an end milling process

Visual examination of the surface topography, in conjunction with the other sensors, may confirm the existence of chatter. Online chatter detection during real machining operations is possible with the use of sensors, and the presence of noise in their output and restricted bandwidth are the major drawbacks of these sensors. Productivity drops and manufacturing costs go up when there is a lot of chatter in the machining process. In the present paper, an integrated spindle tool system is modeled using finite element method with Timoshenko beam theory including rotational and shear deformation effects. To maximize the average stable depth of cut in an end milling process while simultaneously minimizing the chatter vibration levels, real time and offline strategies have been investigated. Machining experiments performed on Al6061-alloy specimens provide an empirical confirmation of the stability boundaries. The surface topography methods such as scanning electron microscope (SEM) and optical microscope images along with vibration levels are considered, to identify chatter marks under various machining conditions, which helps to assure cutting process stability. Stability lobe diagrams are plotted with these derived conditions and observed at an incremental level in the axial depths of the cut. The methodology shown in this paper improves the machining stability of the end milling with the reduction in the tool tip vibrations.

Stability of Micro-Milling Tool Considering Tool Breakage

Micro-milling, widely employed across various fields, faces significant challenges due to the small diameter and limited stiffness of its tools, making the process highly susceptible to cutting chatter and premature tool breakage. Ensuring stable and safe cutting processes necessitates the prediction of chatter by considering the tool breakage. Crucially, the modal parameters of the spindle–holder–tool system are important prerequisites for such stability prediction. In this paper, the FRFs of the micro-milling tool are calculated by direct frequency response functions (FRFs) of the micro-milling cutter and cross-FRFs between a point on the shank and one on the tool tip. Additionally, by utilizing a cutting force model specific to micro-milling, the bending stress experienced by the tool is computed, and the tool breakage curve is subsequently determined based on the material’s permissible maximum allowable stress. The FRFs of the micro-milling tool, alongside the tool breakage curve, are then integrated to generate the final stability lobe diagrams (SLDs). The effectiveness and reliability of the proposed methodology are confirmed through a comprehensive series of numerical and experimental validations.

Stability lobe and chatter prediction based on modified zeroth-order approximation in high-speed ball end milling process

Stability lobe and chatter prediction based on modified zeroth-order approximation in high-speed ball end milling process

Stability prediction for robotic milling based on tool tip frequency response prediction by considering the interface stiffness of spindle-tool system

The change of tool tip frequency response caused by the posture dependence of robot dynamic is one of the key problems that make it difficult to accurately predict the milling stability of robot. In this paper, a tool tip frequency response prediction method considering the interface stiffness characteristics of spindle-tool system is proposed for stability prediction of robotic milling under the condition of posture variation. Firstly, the interface stiffness models of spindle-toolholder, toolholder-spring clip and spring clip-tool are established based on Yoshimura's unit area method. Then, The dynamics model for the robot body and the interface stiffness models for spindle-tool system are imported into the finite element analysis model of the spindle system, so that the prediction of the tool tip frequency response is realized by harmonic response analysis. Compared with the experimental results, the maximum error of the natural frequency was not more than 2 %, and the maximum error of the amplitude was not more than 12 %. Finally, the 2 DOF robot milling stability prediction model is established. Then the robot milling chatter is predicted considering redundant degrees of freedom from the perspective of regenerative chatter prediction theory, and the accuracy of prediction results is verified by milling experiment.

Chatter prediction for parallel mirror milling of thin-walled parts by dual-robot collaborative machining system

Thin-walled parts with double-sided features are widely used in the aerospace industry, but the machining of such parts still faces great challenges due to their weak rigid structure and the positioning errors caused by turning/re-clamping of the workpiece. For this purpose, a novel machining approach for parallel mirror robotic milling of thin-walled parts is proposed. Different from conventional single-sided milling, it can simultaneously machine both sides of the workpiece while avoiding the above problems and improving machining efficiency. However, the introduction of multiple cutting excitations makes the vibration behavior of the workpiece more complicated, thus making it difficult for the dynamic modeling of the dual-robot machining system. This paper aims to uncover the dynamic mechanism of chatter phenomenon in parallel mirror robotic milling process in consideration of the interaction of tool-workpiece-tool system. A dual-robot collaborative machining system is first developed for the milling of thin-walled workpiece, and the method of synchronous motion planning for dual robots is described. The slave robot synchronously follows the master robot and the two milling cutters mounted on tool flange of the robot are kept in mirror position. Over a tooth passing period, the engagement state of the cutters and the workpiece is analyzed considering the effect of rotation phase lag (RPL) between the twin cutters. After that, the vibration state and the corresponding instantaneous displacement of the workpiece can be expressed explicitly, then the dynamic resultant cutting force acting on the workpiece is calculated according to the mechanistic force model. Comprehensively considering the dynamic interaction of the tool-workpiece-tool system, multi-mode and position-dependent modal characteristics of thin-walled part, a time-varying delay differential equation is constructed and solved to explore the dynamical behavior of parallel mirror milling process. The predicted stability lobe diagram is validated by a series of parallel mirror milling tests on thin-walled PMMA plates. Comparisons of numerical and experimental results show that the dynamic model successfully predicts the chatter stability for the parallel mirror milling of thin-walled parts.

Chatter failure comparison for high-speed milling of aerospace GH4099 with silicon nitride ceramic end mills: A laboratory scale investigation

Chatter generated in the high-speed cutting process can seriously limit the machining efficiency and affect the surface machining quality, which urgently needs to be controlled. Aiming at brittle ceramic end mills that are very sensitive to vibration, a strategy based on the modal experimental method is proposed to construct effective and accurate stability lobe diagram (SLD) for chatter prediction and failure analysis in this work. Firstly, the tool tip frequency response function (FRF) of four kinds of self-developed ceramic end mills and commercial cemented carbide end mills with the same structure are established by means of hammering modal experiments, and the modal parameters are solved and identified. Then, based on our established high-speed milling chatter prediction model, the milling force coefficients are obtained by linear regression analysis and calculation, thereby the milling SLDs of five end milling tools are developed. Finally, a series of high-speed side milling experiments are carried out using consistent cutting conditions. The results show that the constructed SLDs can effectively predict the chatter failure region and milling stability for five kinds of end mills, and four ceramic milling tools exhibit more excellent chatter suppression performance according to frequency domain analysis of vibration signals and the observation of workpiece surface vibration marks, in which the S4 ceramic milling tool presents the most significant high-speed milling stability.

Generalized model for dynamics and stability of milling of titanium alloys by integrating process damping, multiple modes and multiple delays

Machining dynamics modelling and chatter stability prediction are important for milling of titanium alloys to improve machining productivity and surface quality. Since titanium alloys are typically machined at low spindle speeds, process damping plays an important role in dynamics and stability of milling of titanium alloys. What is more, multiple modes and multiple delays, resulting from the complexity of milling systems and processes, significantly affect chatter stability of milling. However, there is a lack of comprehensive dynamical models capable of studying how these three factors influence chatter stability. To address this gap, this paper proposes a generalized dynamic model for milling of titanium alloys considering process damping, multiple modes and multiple delays. A time-domain chatter prediction method related to the generalized dynamic model is proposed by extending the Gaussian quadrature-based method. Experiments are conducted on multi-mode cutting systems using both uniform and variable pitch cutters to validate the proposed dynamic model and chatter prediction method. The impacts of multiple modes and multiple delays on chatter stability are investigated considering the presence of process damping. Experimental validation and simulation show that in order to accurately predict chatter stability of milling of titanium alloys at low spindle speed, all dynamic modes should be taken into account whether the modes are well separated or not. Even if the low-frequency modes are much more rigid than the high-frequency modes, low-frequency modes may be dominant in milling of titanium alloys and should be considered in the prediction procedure of chatter stability. In addition, it is observed in both simulations and experiments that variable pitch angles can improve the chatter stability limit in the process damping zone.

Multi-Dimensional Bisection Method in HIL Environment: Stability and Chatter Prediction in Turning

In turning operations, the harmful small-amplitude but high-frequency chatter vibrations are identified in hardware-in-the-loop (HIL) experimental environment by means of the application of a multi-dimensional bisection method. The dummy workpiece clamped to the real main spindle is excited by contactless electromagnetic actuators and the response of the workpiece is detected by laser-based sensors. According to the present and the stored previous positions of the rotating workpiece, the desired cutting force characteristic along with the surface regeneration effect can be emulated by means of a high-performance real target computer. While the conventional experimental results in the HIL environment identify the stability limits of the cutting operation accurately only in a high-resolution grid of the technological parameters, the embedded bisection method reduces significantly both the size of the required grid and the time duration of the measurement by path following the boundaries of the linear loss of stability. Based on this technique, the experimental stability boundary of the emulated turning process is presented in a wide range of spindle speeds.

Stability Analysis and Nonlinear Chatter Prediction for Grinding a Slender Cylindrical Part

A cylindrical plunge grinding process was modeled to investigate nonlinear regenerative chatter vibration. The rotating workpiece was a slender Euler–Bernoulli beam, and the grinding wheel was a rigid body moving towards the workpiece at a very low feed speed. A numerical method was proposed to provide the critical boundaries for chatter-free grinding. It was demonstrated that the intersection set surrounded by these critical boundaries was the chatter-free region for the considered parameters. When these parameters were outside of the chatter-free region, the stable grinding process underwent a supercritical Hopf bifurcation, resulting in the loss of the chatter-free behavior and the emergence of periodic chatter motions. Then, the periodic motions of both the grinding wheel and the workpiece were predicted analytically using the method of multiple scales, showing the effect of the regenerative force on the grinding process. We demonstrated that the analytical prediction was valid since it agreed with the numerical simulation. The results showed that there exist three kinds of nonlinear chatter motion, with different amplitudes and mode frequencies.

Multi-step-ahead prediction of cold rolling chatter state based on the combination of Functional Data Analysis and General Autoregression Model

Mill chatter seriously restricts the improvement of production efficiency and the development of new products. Thus, a method of cold rolling chatter monitoring and early warning is proposed based on the combination of Functional Data Analysis (FDA) and General Autoregression Model (GAM). Firstly, the multi-source cold rolling data are preprocessed by FDA to realize the smooth fitting of the unequally sampled data and the sample space is constructed based on chatter mechanism. Then, the multi-step-ahead prediction of cold rolling chatter is executed through different machine learning algorithms based on GAM, and the prediction effects of different algorithms are compared and evaluated. Finally, the maximum prediction step is defined to select the optimal algorithm, and the conclusion is drawn that Extra Tree Regression (ETR) has the best prediction effect. Therefore, the proposed method for cold rolling chatter monitoring can effectively solve the problems of delay, false alarm and distortion in prediction.

Effects of nonlinear behaviour of linear ball guideway on chatter frequency of lathe machine tool

Linear ball guideways (LBGs) have several advantages for the precise positioning control of machine tools. However, the ball-groove contact behaviour leads to poor dynamic compliance, which induces a significant nonlinear behaviour of the guideway and a poor chatter stability. The nonlinearity complicates the chatter prediction due to the dependence of the contact stiffness. This approach aims to offer an industrially orientated method of estimation of chatter stability for structures based on LBG. Consequently, the present study first employs Hertzian contact theory to describe the ball-groove contact behaviour in the LBG of a lathe machine. Two static models are presented, both predict the LBG stiffness under different cutting loads. The first model describes is simplified, ignores the effects of the contact force on the deformation of the guideway components, even with that limitation depicts the main behaviour of the system. The second model is more precise and adopts a dynamic substructuring cosimulation method to incorporate the effects of structural deformation into the analysis. For both models, a linearisation approach is employed to analyse the dynamic behaviour of the system under static loading and define the dynamic compliance. The chatter frequencies of the LBG are estimated using the second model and are shown to be in good agreement with the experimental results. In general, the results of the analysis show that fundamental shifts in the frequency response of the LBG occur under specific values of the cutting force and gravity load. In other words, the results confirm that this method provides sufficient estimation of nonlinear behaviour of machine tool based on the LBG.

A Parameter Optimization Method for Chatter Stability in Five-Axis Milling

Chatter is a dynamic instability caused by the regeneration of waviness on the workpiece surface and damages the machining efficiency and product quality. For five-axis milling, the chatter stability analysis is more complicated because the cutter-workpiece engagement and the direction of the dynamic cutting force vary along the tool path. This paper presents a parameter optimization method to avoid chatter in the five-axis milling process. The dynamic milling system is modeled in each tool-path segment, and the stability is analyzed by introducing the semi-discretization method to solve the delay differential equation. In addition, the multi-frequency solution to the stability prediction for the multiple degrees of freedom spindle-cutter system and workpiece system is presented. Considering the speed and acceleration constraints of the spindle system and the feeding system, the spindle speed optimization iterative method is applied based on the chatter prediction. The verification experiment is conducted on the five-axis milling of the S-curve part to show the predictive accuracy of the chatter model and the validity of the proposed optimization method.

Simulation tool for chatter prediction of varying tool–machine configurations based on dynamic substructuring

Cutting tools of different type, shape and size are used in milling processes. Every individual tool changes the dynamic behavior of the system and results in varying occurrences of chatter vibrations. This paper presents a simulation tool using a frequency based substructuring method for predicting the process stability without separate measurements of the tool-machine configuration. In particular, frequency response functions of any combined tool-machine configuration is synthesized by the receptance coupling substructure analysis. It enables the calculation of critical machining parameters and maximizing material removal rates by avoiding unstable cutting conditions. Verification is done via finite element analysis of exemplary tool and machine structures.

Prediction, detection, and suppression of regenerative chatter in milling

In metal cutting processing, especially in the processing of low-rigidity workpieces, chatter is a key factor affecting many aspects such as surface quality, processing efficiency and tool life. The academic research on chatter mainly focuses on three directions: chatter prediction, real-time detecting, and chatter suppression. With the continuous development of machining toward intelligence, the hot spots and trends of chatter research are also constantly changing. Therefore, an in-depth and systematic summary of the current situation of chatter research is urgently needed. On this basis, it is of great significance to realize the prediction of the hot spots and trends of chatter research. This article summarizes the research status from three aspects of chatter prediction, detecting and suppression, and points out the advantages and limitations of current chatter research. After in-depth discussion, this article also looks forward to the trend of chatter research. The hot spots of chatter research will focus on the following points: (1) Chatter research methods and means based on data-driven. (2) Integrated data collection, processing and decision-making methods. (3) Chatter detecting unit and chatter suppression unit are integrated in the smart spindle. (4) The chatter mechanism and detecting research of robot milling.

An efficient and accurate chatter prediction method of milling processes with a transition matrix reduction scheme

Efficient and accurate chatter prediction is essential for selection of chatter-free process parameters in order to improve machining productivity and surface quality of the workpiece. This paper proposes a five-point Gaussian quadrature-based chatter prediction method of milling processes together with a transition matrix reduction scheme to improve the computational accuracy and efficiency. The five-point Gauss–Legendre quadrature rule is utilized to approximate the equations of motion of milling systems represented in the form of integral equation. By this means, the convergence rate of the chatter prediction method can be improved. Since the transition matrix describing the relation between the states of current and previous tooth or spindle period is used to evaluate chatter stability, its dimension has a significant effect on the computational efficiency. In this paper, it is theoretically proved that the dimension of the transition matrix constructed by numerical integration-based methods can be reduced by half. Based on this, an efficient scheme is firstly proposed to further decrease the computational time. Typical benchmark examples are employed to verify the proposed method. The results demonstrate that the proposed method with the transition matrix reduction scheme is more efficient and accurate than the existing methods. Meanwhile, experimental validation shows the proposed method can predict the milling chatter accurately.

Research on reliability of mode coupling chatter of orthopedic surgery robot

In this paper, the reliability probability method is introduced into the prediction of mode coupling chatter of the orthopedic surgical robot milling to avoid the influence of the randomness of the input parameters on the chatter prediction results. The reliability of mode coupling chatter is defined to represent the probability of the stability (no mode coupling chatter occurs) of milling system. Probability model (reliability model) of mode coupling chatter is established to predict robotic milling chatter, in which the modal stiffness K x, K y and cutting force coefficient Ks involved in the prediction of chatter vibration during robotic milling are considered as random variables. The fourth moment method is adopted to solve the reliability model of milling system to obtain the reliability level. The mode coupling chatter reliability circle diagram (MCCRCD), which is a contour line with a specified reliability level as a function of the angle between the main stiffness direction and the cutting force and the depth of cut, is presented to identify the mode coupling chatter reliable and unreliable regions. An example studies the influence of random variables on the reliability of milling processing, and the time-domain simulation method and experiment method are used to verify the possibility and effectiveness of using MCCRCD to predict the stability of the robotic milling. It can be concluded that MCCRCD can be effectively used to predict the stability of robotic milling.

A Gaussian process regression‐based surrogate model of the varying workpiece dynamics for chatter prediction in milling of thin‐walled structures

AbstractSince the dynamics of thin‐walled structures instantaneously varies during the milling process, accurate and efficient prediction of the in‐process workpiece (IPW) dynamics is critical for the prediction of chatter stability of milling of thin‐walled structures. This article presents a surrogate model of the IPW dynamics of thin‐walled structures by combining Gaussian process regression (GPR) with proper orthogonal decomposition (POD) when IPW dynamics at a large number of cutting positions has to be predicted. The GPR method is used to learn the mapping between a set of the known IPW dynamics and the corresponding cutting positions. POD is used to reduce the order of the matrix assembled by the mode shape vectors at different cutting positions, before the GPR model of the IPW mode shape is established. The computation time of the proposed model is mainly composed of the time taken for predicting a known set of IPW dynamics and the time taken for training GPR models. Simulation shows that the proposed model requires less computation time. Moreover, the accuracy of the proposed model is comparable to that of the existing methods. Comparison between the predicted stability lobe diagram and the experimental results shows that IPW dynamics predicted by the proposed model is accurate enough for predicting the stability of milling of thin‐walled structures.