Stability Lobe Diagram Research Articles

Chatter prediction of milling process for titanium alloy thin-walled workpiece based on EMD-SVM

Easy cutting vibration of Titanium alloy thin-walled structural components in processing process directly influences the quality of part machining surface. So, the chatter prediction has become a research hotspot. The milling process of Ti-6Al-4V framework parts for hard alloy cutter is researched and chatter prediction methods are proposed to solve the chatter problem generated in milling process. The signals in milling process are comprehensively considered to work out the stability boundary and the chatter prediction model based on Empirical Mode Decomposition (EMD) and Support Vector Machine (SVM). The stability lobe diagram is utilized to select experiment parameter for experiment, in which the 1/3-2/3 position of framework parts chatters easily in processing. The model training in experiment aims to monitor the time of chatter, with the recognition precision of 97.50%.

Chatter suppression in the milling process of the weakly-rigid workpiece through a moving fixture

This article presents a new method to suppress the chatter vibrations in the milling process of the weakly-rigid workpiece through a moving device. The basic idea is to design a moving fixture to instantaneously and continuously provide additional stiffness and damping to the instantaneous contact position between the moving fixture and the workpiece, and as the device moves, the chatter vibrations of the workpiece during the whole process are suppressed without the need of any other additional hardware. Two theoretical means, i.e. the structure split-assembly technology and the fractal contact theory, are combined to mathematically model the underlying dynamic behavior of the workpiece under the support provided by the moving fixture. The workpiece is divided into three parts, i.e. the machined part, the machining part and the part to be machined. The dynamic response of each part is separately analyzed and then theoretically assembled to calculate the whole workpiece’s varying dynamic characteristics, which involve the support influence induced by the moving fixture. The effect of material removal on the workpiece’s dynamic characteristics is also integrated into the analyzing procedure. Based on the above analysis, the dynamic governing equation of the thin-wall milling process with the moving fixture is finally established and solved to predict the stability lobe diagrams (SLDs). The validity and reliability of the proposed method are verified by conducting a series of actual milling tests with and without the support of the designed moving fixture.

Frequency response function simulation and evaluating in boring

Finite element method of simulating frequency response function (FRF) for boring tool in LS-Dyna solver is investigated in this work. Nowadays, computer numerical simulation allows to obtain FRF using different materials model with high precision compared to real experiments with sensors like impact hammer testing. This function is used in construction of stability lobe diagrams that allows operator of machining center to avoid chatter self-excited vibrations. Such vibration is led to decreasing of productivity and quality in cutting of metals and other materials. Amplitude and phase angle for the model is obtained from LS-Dyna result interpreter, that reads binary files, created during simulation by the program. Amplitude and phase angle of frequency response function are depending on dynamic stiffness of machining system. Real and imaginary part of frequency response function have been obtained during simulation. With luck of dynamic stiffness amplitudes of response increases. 

Active control of milling chatter considering the coupling effect of spindle-tool and workpiece systems

Chatter occurred in the machining process can seriously limit the processing efficiency and reduce the surface quality of the machined workpiece, which urgently needs to be controlled. Aiming at milling of flexible workpieces with similar characteristics to the spindle-tool system, two active chatter control strategies are proposed in this work. Firstly, considering the coupling effect of the spindle-tool system and the workpiece system, the milling force is developed based on the regenerative effect. And the 3D stability lobe diagram along the tool path is constructed. Then, an active chatter control structure is designed by integrating piezoelectric actuators and displacement sensors into the spindle-tool-workpiece (STW) system. Next, based on the developed milling force and active control structure, two chatter control strategies with different feedback signals are proposed using the model predictive control method. Finally, numerical simulations and milling experiments are carried out under different cutting conditions. The results show that milling chatter of the STW system can be effectively controlled by the proposed strategies. The maximum material removal rate is also significantly improved.

Investigation of Gyroscopic Effect on the Stability of High Speed Micromilling via Bifurcation Analysis

Catastrophic tool failure due to the low flexural stiffness of the micro-tool is a major concern for micromanufacturing industries. This issue can be addressed using high rotational speed, but the gyroscopic couple becomes prominent at high rotational speeds for micro-tools affecting the dynamic stability of the process. This study uses the multiple degrees of freedom (MDOF) model of the cutting tool to investigate the gyroscopic effect in machining. Hopf bifurcation theory is used to understand the long-term dynamic behavior of the system. A numerical scheme based on the linear multistep method is used to solve the time-periodic delay differential equations. The stability limits have been predicted as a function of the spindle speed. Higher tool deflections occur at higher spindle speeds. Stability lobe diagram shows the conservative limits at high rotational speeds for the MDOF model. The predicted stability limits show good agreement with the experimental limits, especially at high rotational speeds.

RAPID UNCERTAINTY QUANTIFICATION OF THE STABILITY ANALYSIS USING A PROBABILISTIC ESTIMATION OF THE PROCESS FORCE PARAMETERS

In the course of the digitization of modern production systems, a reliable parameterization of the digital twin of machining processes is essential. For example, the digital representation of milling operations enables the process parameter selection without time-consuming and expensive test series by using stability lobe diagrams (SLD). However, the parameterization of the underlying process force model with very few cutting force experiments can prevent a reliable process design, as errors in the parameterization process are propagated to the stability analysis. Therefore, a novel two-step methodology is proposed to provide probabilistic credible intervals for conventional stability lobe diagrams: First, the unknown parameters of the process force model are estimated using a Bayesian regression method. Secondly, the estimated probability distributions of the process force parameters are used to quantify the uncertainty of the stability boundary using a mechanistic process force model. The proposed methodology is particularly characterized by its low computational cost, since time-consuming and computationally expensive Monte Carlo procedures are avoided. Instead, the methodology relies on the analytical derivation of the model parameters’ posterior probability distribution and on polynomial chaos expansion (PCE) algorithms to quantify the uncertainty in the final stability analysis.

Dynamic analysis and stability prediction of nonlinear feed system coupled with flexible workpiece

The workpiece is prone to self-excited vibration when turning a slender shaft and the flexibility cannot be ignored in this condition. In this paper, a new flexible tool-workpiece system is developed to investigate the nonlinear dynamics and chatter stability for in a turning process. The piecewise-nonlinear restoring function of the tool system is derived by calculating axial deformations and forces of the ball screw feed system. With the variation of time delay, the dynamic behaviors of the cutting system are analyzed by numerical method, which manifests as periodic, quasi-periodic, and chaotic motions. Through determining the critical chip width under different spindle speed, the stability lobe diagram (SLD) of nonlinear system is obtained to distinguish stable and unstable states. In addition, the dynamic characteristics and SLD of nonlinear system are compared with linear system. An experiment is carried out to observe the vibration phenomenon under stable and unstable turning conditions and verify the accuracy of stability prediction.

EFFICIENT DETERMINATION OF STABILITY LOBE DIAGRAMS DEPLOYING AN AUTOMATED, DATA-BASED ONLINE NC PROGRAM ADAPTION

Process instabilities due to regenerative chatter pose significant limitations on the achievable material removal rates and thus on the profitability of machining operations. Stability lobe diagrams serve to exploit the maximum yet stable cutting depth and can be determined either analytically or experimentally. While analytical approaches suffer from inaccuracies because of the assumptions made for the specific models, experimental stability lobe diagrams require extensive cutting tests. Therefore, this paper introduces a new automated experimental method for determining stability lobe diagrams in milling with reduced effort regarding time. A closed-loop system is designed, containing a sensor-based online chatter detection along with a strategy to set parameters for subsequent cuts based on the stability boundaries known at each iteration. Both cuts with continuously increasing cutting depth and varied spindle speed are deployed to ensure fast detection of stability limits. The method is tested for a slot milling use case and the results are compared to a conventionally obtained stability lobe diagram yielding a significantly reduction in required time (-90 %) and resources (-67 %) whilst maintaining good accuracy. The reduced effort qualifies the proposed method as a tool to rapidly deliver maximum productive yet stable cutting parameters for optimization of existing or enhanced planning of new manufacturing processes.

Rapid stability analysis of serrated end mills using graphical-frequency domain methods

Serrated tools result in an irregular distribution of chip thickness and varying time delays along their flutes that disturb the regenerative chatter mechanism and maximize productivity in rough machining operations. The chatter stability simulation with such tools is complex due to the delay differential equations with multiple and distributed delays. Although the time domain numerical integration methods and the semi-discretization method are accurate, they are computationally expensive and hence inhibit the optimal design of serrated cutters. Despite the advantages that serrated tools offer, there has been little attention paid to rapidly predict stability lobes diagram for these tools to help instruct their optimal designs. To address this need, new graphical-frequency methods are presented to solve for stability of serrated tools with arbitrary geometry. The graphical method averages the number of teeth in cut to make the system time-invariant and results in a closed-form analytical solution. It reduces the simulation time by up to ∼99% compared to the semi-discretization method. Generalized solutions to the classical zero-order approximation and the multi-frequency methods are also presented by using the Nyquist stability criterion. The use of the zero-order approximation method and the multi-frequency method reduces simulation times by up to ∼97% and ∼79% respectively compared to the semi-discretization method. These are significant improvements over reports in the previous literature. Stability predictions are validated experimentally and benchmarked with high-fidelity time domain methods. The presented methods are general and can be applied to any end mill with non-uniform pitch and helix angles as well.

Chatter suppression and stability analysis of rotary ultrasonic milling titanium alloy thin-walled workpiece

Titanium alloy and its thin-walled structures are widely used in the aerospace field. Aiming at the processing chatter and difficult-to-machine problem of titanium alloy thin-walled workpieces, rotary ultrasonic milling technology (RUM) is employed to restrict machining vibration in this paper. Firstly, for describing its dynamic characteristics, the titanium alloy web with low stiffness is equivalent to a mass-spring-damping system with three degrees of freedom. Then, a novel stability analysis method is proposed for RUM thin-walled workpiece (RUM-tww) through defining an ultrasonic function angle. Furthermore, RUM-tww stability lobe diagrams (SLDs) are achieved based on the semi-discrete method (SDM). The simulation results show that the milling stability of titanium alloy webs is improved effectively under the effect of ultrasonic vibration energy. Compared with conventional milling thin-walled workpiece (CM-tww), the stability region is increased by 80.32% within the spindle speed from 1000 to 5000r/min. Finally, the milling experiments are carried out to verify the validity and rationality of SLDs via analyzing chatter marks, cutter marks, and flatness on the machined surface. The experimental results are in good agreement with the theoretical prediction.

Моделювання амплітудно-фазової частотної функції і її оцінка при розто- чуванні

Finite element method of simulating frequency response function (FRF) for boring tool in LS-Dyna solver is investigated in this work. Nowadays, computer numerical simulation allows to obtain FRF using different materials model with high precision compared to real experiments with sensors like impact hammer testing. This function is used in construction of stability lobe diagrams that allows operator of machining center to avoid chatter self-excited vibrations. Such vibration is led to decreasing of productivity and quality in cutting of metals and other materials. Amplitude and phase angle for the model is obtained from LS-Dyna result interpreter, that reads binary files, created during simulation by the program. Amplitude and phase angle of frequency response function are depending on dynamic stiffness of machining system.

High-order semi-discretization methods for stability analysis in milling based on precise integration

The third-order and fourth-order semi-discretization methods (3rd SDM and 4th SDM) are presented to predict milling stability based on precise integration. Firstly, the milling system is mathematically represented by a delay differential equation (DDE) and re-expressed in the state space. After dividing the tooth passing period into free and forced vibration time intervals, the forced vibration time interval is equally discretized into many small-time intervals. Then, the DDE is integrated on any small-time interval and solved in the framework of the semi-discretization algorithm. Subsequently, the 3rd SDM and 4th SDM are derived for predicting the stability limits in milling. In the 3rd SDM and 4th SDM, the third-order and fourth-order interpolation polynomials are used to approximate the delayed term, respectively. The periodic-coefficient matrix is approximated by linear interpolation polynomial. The convergence rates of the one degree of freedom (one-DOF) milling system and the milling system with multiple modes are conducted. The results indicate the convergence rates of the 3rd SDM and 4th SDM are higher than those of the benchmark methods. Besides, no matter for large or low radial immersion conditions, the stability lobe diagrams (SLDs) obtained by the proposed 3rd SDM and 4thSDM are closer to the reference than those obtained by the benchmark methods. The computational efficiency of the 3rd SDM and 4th SDM is also evaluated. Compared with the benchmark methods, the presented 3rd SDM and 4th SDM are superior in computational efficiency. Generally, the main advantage of the proposed methods is the improvement of computational efficiency. The proposed 3rd SDM and 4th SDM can use a smaller discrete number for achieving the desired accuracy to reduce the size of the state transition matrix and improve the computational efficiency.

과도상태 밀링에서 시간영역 채터 시뮬레이션

Chatter between the end mill and thin aircraft components reduces tool life and surface quality. This paper presents a time-domain chatter analysis that simulates the peripheral milling of thin aluminum plates. Peak forces and tool deformations were predicted in the time domain by simulation software written in C++. The maximum forces at various cutting depths and spindle speeds were predicted, and the stability lobe diagram was drawn in the frequency domain. The software was validated in comparison with the results of Professor Y. C. Shin’s experiments and was used to analyze the relationship between chatter and runout, number of teeth, and feed rate in virtual space. The chatter in transient state was simulated to predict the side effect of feed rate control.

Time Domain Study on the Construction Mechanism of Milling Stability Lobe Diagrams With Multiple Modes

Abstract The stability lobe diagram (SLD) is an important expression way of milling stability prediction result. The SLD obtained by only selecting the most flexible mode fails to predict the chatter if the milling process is dominated by multiple modes. To reveal the relationship between the SLD with multiple modes and the SLDs corresponding to each single mode, this paper studies the construction mechanism of the SLD with multiple modes by using a time domain method. First, the milling dynamic model of the tool with multiple modes is established. Then, the numerical method based on the Newton-Cotes rules is used to solve the milling dynamic model with multiple modes whose solution is in the form of the SLD. It shows that the SLD with multiple modes can be approximated by using the lowest envelope of the SLDs corresponding to each single mode. Finally, two study cases are adopted to verify the construction mechanism of the SLD with multiple modes. To verify the correctness of the SLD with multiple modes, a series of milling tests are carried out. The experimental results agree with the simulation results, which mean the proposed time domain method can reveal the construction mechanism of the SLD with multiple modes.

Multi-condition identification in milling Ti-6Al-4V thin-walled parts based on sensor fusion

Chatter and tool wear always coexist during the milling of Ti-6Al-4V thin-walled parts, while the boundary characteristics, time-varying, modal coupling, and position dependence characteristics in milling thin-walled parts lead to the variable spatial time–frequency distribution of the signal features related to milling conditions. As a result, the existing milling monitoring methods can only identify single chatter or tool wear while ignoring another condition. Therefore, in order to identify the chatter and tool wear simultaneously, a multi-condition identification method based on sensor fusion is proposed by fusing multi-source heterogeneous data with different spatial time–frequency distributions. Multi-sensor features of the milling process are extracted from sound, acceleration, and cutting bending moment signals. To reduce the complexity of the original feature dataset, an upgraded principal component analysis (UPCA) algorithm is proposed by screening sensor features in specific frequency bands. Moreover, a new signal feature considering energy proportion is extracted to improve the identification accuracy of multiple conditions. The process parameters are designed according to the stability lobe diagram (SLD) to improve the experimental efficiency. The experimental results show that the proposed method can identify the multi-milling condition composed of chatter and tool wear failure. With the help of UPCA and energy proportion, the computational efficiency is also improved, and the identification accuracy of the proposed method reaches 93.75%, which is much higher than the accuracy of classifiers with traditional data processing methods.

Semi-supervised graph convolutional network to predict position- and speed-dependent tool tip dynamics with limited labeled data

The tool tip frequency response function (FRF), as one of the essential inputs to calculate the stability lobe diagram (SLD), varies with the position and speed of changes in the moving components within the machine tool work volume. How to predict the position- and speed-dependent tool tip dynamics accurately has become one of the most challenging tasks in obtaining SLDs while avoiding chatter. However, traditional finite element analyses or kinematic modelling-based methods are costly and time consuming. Data-driven machine learning methods require large amounts of labeled data to train a model, but labeled industrial data are limited and extremely valuable in real manufacturing industries.To minimize experimentation, an improved semi-supervised graph convolutional network (GCN) is proposed to predict position- and speed- dependent tool tip dynamics with limited labeled data. First, the inverse stability solution is applied to identify dominant modal parameters under cutting conditions to obtain labeled samples. Subsequently, both the limited labeled samples and large amounts of unlabeled samples are converted into graph data to train a GCN regression model integrated with a multilayer perceptron. To avoid overfitting under limited data conditions, the conventional GCN is extended by stacking a transposed GCN, which is utilized to reconstruct the initial node features. The results demonstrate an improved prediction performance by adding the unsupervised reconstruction error into the loss function. Compared with other machine learning methods, our proposed method has superior performance in predicting tool tip dynamics with only 20% of the labeled samples. Finally, the SLDs were reconstructed with predicted FRFs, and the accuracy of the SLDs was validated through chatter tests.

Physics-informed Bayesian inference for milling stability analysis

The accurate prediction of chatter stability in milling operations is a continuous pursuit of manufacturing engineering. Physical-based stability analysis methods suffer from inaccurate model parameters, while data-driven methods lack generalisability and physical interpretability. This study proposes a physics-informed Bayesian inference framework for milling stability analysis. The framework leverages experimental data to infer the distribution of model parameters for probabilistic stability lobe diagram (SLD) computation, thus maintaining the generalisability and interpretability of the physical model in a hybrid-driven manner. By defining a novel likelihood function based on the Floquet theory, the underlying connection between the model parameters and experimental cutting data is established. The uncertainties and variations of the model parameters can then be represented by the inferred probability density function, which can be used to generate a reliable probabilistic SLD. The experiments indicate that the proposed method has significant potential for improving the accuracy of milling stability prediction.

Validation of variable helix milling instability islands

During machining, it is well-known that unstable self-excited vibrations known as regenerative chatter can limit productivity. There has been a great deal of research that has sought to understand regenerative chatter, and to avoid it through modifications to the machining process. One promising approach is the use of variable helix tools. Here, the time delay between successive tooth passes is intentionally modified, in order to improve the boundary of instability. Previous research has predicted that such tools can offer significant performance improvements whereby islands of instability occur in the stability lobe diagram. By avoiding these islands, it is possible to avoid regenerative chatter, at depths of cut that are orders of magnitude higher than for traditional tools. However, to the authors’ knowledge, these predictions have not been experimentally validated, and there is limited understanding of the parameters that can give rise to these improvements. The present study seeks to address this shortfall. A recent approach to analysing regenerative chatter stability is modified, and its numerical convergence is shown to outperform alternative methods. It is then shown that islands of instability only emerge at relatively high levels of structural damping, and that they are particularly susceptible to model convergence effects. The model predictions are validated against detailed experimental data that uses a specially designed configuration to minimise experimental error. To the authors’ knowledge, this provides the first experimentally validated study of unstable islands in variable helix milling, whilst also demonstrating the importance of structural damping and numerical convergence on the prediction accuracy.

Three dimensional prediction of stability lobes in end milling of thin-walled structures based on tool and workpiece dimensions

Nowadays, researchers are very interested to investigate the dynamic behavior of the thin-walled structures during the machining process due to their broad application in aerospace, automotive industries and etc. One of the main problems in machining of thin-walled structures is unstable chatter vibrations, which causes the poor machined surface quality and decreases the system life span. In this regard, the main aim of this paper is to propose a practical method to solve the chatter instability problem during the milling process of thin-walled components. To this end, first the effects of geometrical parameters like workpiece height, thickness, and tool overhang, diameter and their ratios on the chatter stability are investigated. Then three dimensional stability lobe diagrams (SLDs) base on the mentioned parameters are presented for the first time. In which one can implement the mentioned diagrams to switch the unstable machining process to stable one by changing the value of the system parameters. Finally, the results obtained by the experimental test show that the presented three dimensional diagrams can be utilized to avoid chatter instability in the milling process.

Research on the milling stability of thin-walled parts based on the semi-discretization method of improved Runge-Kutta method

Chatter is a very common phenomenon in the milling process. The occurrence of chatter will cause chatter marks on the processed surface, cause the tool to jump, and even bring sharp and harsh noise, making the processed surface unable to meet the accuracy requirements. Thin-walled parts are more prone to chatter due to their lower stiffness. In order to avoid the occurrence of chatter, this paper adopts the method of combining theoretical analysis with milling experiments to conduct in-depth research on the prediction of chatter. Considering the first-order and second-order modal parameters of the tool and thin-walled part as well as the specific processing parameters, based on the milling dynamics model, a semi-discretization method based on the improved Runge-Kutta method (IRKM-SDM) is used to draw the chatter stability lobe diagram. Through simulation and experiments, it is proved that in terms of simulation accuracy and calculation speed, compared with the zero-order analysis (ZOA), multi-frequency solution (MFS), and the traditional semi-discretization method (SDM), the stability lobe diagram obtained by the IRKM-SDM is more advantageous. This study is of great significance for optimizing cutting parameters and suppressing chatter in the actual machining process.