Stability Lobe Research Articles

Predicting Milling Stability Based on Composite Cotes-Based and Simpson's 3/8-Based Methods.

Avoiding chatter in milling processes is critical for obtaining machined parts with high surface quality. In this paper, we propose two methods for predicting the milling stability based on the composite Cotes and Simpson’s 3/8 formulas. First, a time-delay differential equation is established, wherein the regenerative effects are considered. Subsequently, it is discretized into a series of integral equations. Based on these integral equations, a transition matrix is determined using the composite Cotes formula. Finally, the system stability is analyzed according to the Floquet theory to obtain the milling stability lobe diagrams. The simulation results demonstrate that for the single degree of freedom (single-DOF) model, the convergence speed of the composite Cotes-based method is higher than that of the semi-discrete method and the Simpson’s equation method. In addition, the composite Cotes-based method demonstrates high computational efficiency. Moreover, to further improve the convergence speed, a second method based on the Simpson’s 3/8 formula is proposed. The simulation results show that the Simpson’s 3/8-based method has the fastest convergence speed when the radial immersion ratio is large; for the two degrees of freedom (two-DOF) model, it performs better in terms of calculation accuracy and efficiency.

Analysis of 3-DOF Cutting Stability of Titanium Alloy Helical Milling Based on PKM and Machining Quality Optimization

Aiming at the requirements of titanium alloy holes in aircraft industry, the 3-DOF cutting stability and surface quality optimization of parallel kinematic manipulator (PKM) are studied. The variation of natural frequencies with the end-effector position of the PKM is analyzed. The cutting force model of titanium alloy helical milling based PKM is developed, and the cutting force coefficients are identified. The prediction model for 3-DOF the stability of helical milling based on the PKM is established through a Semi-Discrete method, and the stability lobes are obtained. The correctness of the stability lobes is verified by subjecting the cutting force signal to time-frequency transformation and roughness detection. The step-cutter is used for machining process improvement to enhance the stability domain. The method proposed in this paper can provide a reference for further optimization of the prediction and optimization of the milling process of difficult-to-process materials based on PKM in the future.

Investigation on dynamic tool deflection and runout-dependent analysis of the micro-milling process

Micro-milling is essential for manufacturing miniature precision components. The process involves free/restricted tool overhang length, runout, deflection, force and stability. In comparison to a macro-milling process, it is very difficult to determine the micro-milling force and stability in such a small machining scale due to higher spindle speeds, runout and deflection of the tool point. In this paper, we have proposed a complete and practical model for micro-milling process, which includes dynamic tool deflection and establishment of a stability lobe diagram (SLD) with runout-dependent effect. First, a multi-sections discretization method combined with dynamic tests was employed to the tool holder and tool dummy so that the frequency response function (FRF) at tool point was identified. Two runout models were introduced with the corresponding parameters, and the instantaneous uncut chip thickness (IUCT) was obtained by numerical solution. Then the dynamic tool deflection was developed by the product of force decomposition and FRF at tool point. Finally, the interaction between feed per tooth, runout and dynamic tool deflection was studied, which led to the proposed SLD. The experiments demonstrated that tool deflection as well as runout affected the IUCT, and runout enabled the cutter pitch angle acting on the workpiece to change, which enhanced stability limits despite reducing machining accuracy. In addition, the increase of feed per tooth also contributed to the improvement of stability boundary.

Milling chatter detection with WPD and power entropy for Ti-6Al-4V thin-walled parts based on multi-source signals fusion

Unstable cutting has a relatively large negative impact on the machining quality and efficiency of thin-walled parts. It can easily cause severe vibration of milling systems, resulting in poor surface roughness of workpieces. Although some promising signal processing methods, such as wavelet packet decomposition (WPD), have been applied to process nonlinear signals, few studies have paid attention to determining a wavelet basis and the number of decomposition layers in WPD. Parameters of WPD play a crucial role and they are often empirically determined. In this paper, an adaptive denoising model based on WPD and recursive least squares with a variable forgetting factor (RLSVFF) is firstly established, and the influence of the forgetting factor in the model on signal denoising are investigated. Then, a novel chatter detection method based on multi-source signals fusion using WPD and power entropy is presented. On this basis, an automated selection method based on a margin indicator and power is proposed for applications to WPD. And the influence of different parameters of WPD on a margin indicator and power are investigated. In order to improve the efficiency of different levels of signal acquisition, a method based on a stability lobe diagram (SLD) is used to design experimental parameters. Compared with traditional denoising models and chatter detection methods based on a single signal, simulation and experimental results show that the adaptive denoising model and chatter detection method based on multi-source signals fusion proposed in this paper can more reliably detect the occurrence of early chatter and different levels of chatter.

Robotically assisted active vibration control in milling: A feasibility study

The role of robots has been increasing in machining applications, with new concepts such as robotic-assisted machining where a robot supports the workpiece while it is machined by a machine tool. This method improves chatter stability to a certain extent. However, forced vibrations or unstable vibrations such as chatter can still be a limiting factor for the productivity and quality of the machining process. In this paper, the robotically assisted milling approach is extended to consider an actively controlled robot arm, to suppress the chatter vibrations for milling operation. To assess the feasibility of the method, a proof-mass actuator is assembled on a beam structure that is representative of the robot system. The beam structure is designed to exhibit two degrees of freedom in its structural dynamics, thereby emulating the robots’ dynamic response. The effect of active control is evaluated. Frequency domain results show that the actively controlled robot arm increases the chatter stability and critical limiting depth of cut. A range of active control methods are evaluated, namely direct velocity feedback (DVF), virtual passive absorber (VPA), proportional integrated derivative (PID), linear quadratic regulator (LQR), H infinity (H∞) and μ synthesis control. To validate the simulated frequency response function (FRF) results, several experimental tests are carried out for each control method. Furthermore, a time domain model is used to validate the stability lobe diagrams by detecting the chatter boundaries with/without actuator force saturation. It is shown that the critical limiting depth of cut can be increased by a factor of 2.6, compared to the scenario where the robot has no active control applied.

Cutting force and nonlinear chatter stability of ball-end milling cutter

Ball-end milling cutters are one of the most widely used cutters in the automotive, aerospace, die, and machine parts industries. Milling chatter reduced the surface quality and production efficiency, resulting in noise. It is particularly important to model the cutting force and analyze the flutter stability of ball-end milling cutters. In this study, a simplified milling force model of ball-end milling cutter with three degrees of freedom was established based on Merchant bevel cutting theory. The model simplified the milling force coefficient. The expressions of instantaneous milling area considering the vibration displacements in X, Y, and Z directions were derived. The nonlinear dynamic cutting force model of ball-end milling cutter with three degrees of freedom was proposed. The nonlinear chatter vibration mechanical model of ball-end milling cutter with three degrees of freedom was developed by introducing the time delay term, and the stability analysis is carried out by the stability lobe diagram. The proposed models were experimentally verified.

Investigation of chatter prediction in end milling using morphological studies on aluminum alloy (Al6061)

Future machine tools have to be highly powerful systems to maintain the needed intellectual performance and stability. The machine tool systems such as Spindle/Tool-holder/Tool assembly are necessary to be optimized for their functionality or cutting performance to meet the productivity and accessibility requirements of the user. Prediction of the dynamic behavior at the spindle tool-tip is, therefore, an important criterion for assessing the machining stability of a machine tool at the design stage. In commercial practice, the machine tool system is extensively influenced by the dynamic rigidity of the spindle system. In this work, a realistic dynamic high-speed spindle/milling tool holder/tool system model is elaborated based on rotor dynamics predictions. Using the finite element modeling with the Timoshenko beam theory, the frequency response at the tool-tip has arrived initially. Further, the numerical model is validated with 3D ANSYS and experimental modal testing. The theoretical stability lobe diagram (SLD) depends on the stiffness and damping properties of the cutting tool and distinguishes the stable and unstable cutting conditions. The mechanism of chatter formation is investigated experimentally during the end milling of Aluminum alloy (Al6061) by two different techniques. Experimental cutting tests are conducted at different depths of cuts, the corresponding vibration signals and cutting samples are examined using the Scanning electronic microscope (SEM) and optical microscope. These studies provide a detailed investigation to predict the stable and unstable cutting zones at different machining conditions.

Optimal cutting condition selection for high quality receptance measurements by sweep milling force excitation

In large machine tool applications, where machine's productivity is limited by structural chatter vibrations, an accurate dynamic characterization is vital for predicting reliable stability lobes. Motivated by the fact that the sweep milling force excitation method shows a great potential, this paper conducts a numerical stability analysis for optimizing the tool radial engagement employed during the characterization cutting tests. Additionally, an alternative spectra computation technique is proposed which considerably improves the signal to noise ratio over the existing technique. The receptance measurement is demonstrated using time domain simulations and applied in a large-scale three axis machining centre obtaining more accurate stability boundary predictions. The source code of the temporal milling simulation and the sweep milling signal processing is freely available to reproduce the simulation and experimental results. https://github.com/OierFranco/SMFE.

Dynamic stability of a paralle kinematic machine

Machine tool chatter causes machining instability, surface roughness, and tool wear in metal cutting processes. A stability lobe diagram based on the theory of regenerative vibration is an effective tool to predict and control the chatter. This paper presents the advances in the mechanical design of a parallel kinematic machine tool. The features that make it ideal for machining tasks, and that make unique in its own way, are highlighted. In addition, the description of the progress of this work will be focused on the analysis of the stability limitation for machining systems to derive the stability lobe diagram with modal analysis of the spindle. A vibratory model is developed by adding cutting forces and including analytical equations for the depth of cut and for the cutting speeds, both depending on the frequency of vibration. A step-by-step procedure provides a stability lobe diagram. The results show that it is relatively easy to provide a relationship between depth of cut and spindle speed. In turn, it makes it easy to compare machining processes under different cutting parameters and conditions.

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.

An improved algorithm to predict the pose-dependent cutting stability in robot milling

Chattering is one of the most important factors affecting productivity of robot machining. This paper investigates the pose-dependent cutting stability of a 5-DOF hybrid robot. By merging the complete robot structural dynamics with the cutting force at TCP, an effective approach for stability analysis of the robot milling process is proposed using the full-discretization technique. The proposed method enables the computational efficiency to be significantly improved because the system transition matrix can be simply generated using a sparse matrix multiplication. Both simulation and experimental results on a full size prototype machine show that the stability lobes are highly pose-dependent and primarily dominated by the lower-order structural modes.

Stability analysis and experimental research on ultrasonic cutting of wave-absorbing honeycomb material with disc cutter

To address the problem of the poor stability of ultrasonic machining of wave-absorbing honeycomb material, this study takes ultrasonic cutting of wave-absorbing honeycomb material with a disc cutter as the research object and establishes a multi-degree-of-freedom mathematical model of the cutting system based on the relative positions of the tool, the wave-absorbing honeycomb material, and the motion characteristics of the tool. On this basis, modal analysis of the disc cutter and the honeycomb cell wall plate is carried out to draw the Lobe diagram of ultrasonic cutting stability, the process experimental parameters are determined to accord to the solved stability Lobe diagram, and machining stability verification experiments are carried out. The experimental results show that the machining parameters in the stable zone of the Lobe diagram result in a neat and clean surface, less fibre pullout, a complete outer substrate, and less tool wear than those in the critical and unstable zones, thus verifying the correctness of the theoretical model and the stability Lobe diagram.

A Novel Updated Full-Discretization Method for Prediction of Milling Stability

This paper presents an updated full-discretization method for milling stability prediction based on cubic spline interpolation. First, the mathematical model of the time-delay milling system considering regenerative chatter is represented by a dynamic delay differential equation. Then, in a single tooth passing period, the time is divided into a finite time intervals, the state item and the time-delay item are approximated in each time interval by cubic spline interpolation and third-order Newton interpolation, respectively. Afterward, a transition matrix is constructed to represent the transfer relationship of the teeth in a period. Finally, based on Floquet theory, the milling stability lobes can be obtained. Meanwhile, in order to improve computational efficiency, an optimized method is proposed based on the traditional algorithm and the proposed method has high precision without losing high efficiency. Finally, several milling experiments are conducted to verify the accuracy of the proposed method, and the results show that the predicted results agree well with the experimental results.

Influence of Axial Depth of Cut and Tool Position on Surface Quality and Chatter Appearance in Locally Supported Thin Floor Milling.

Thin floor machining is a challenging and demanding issue, due to vibrations that create poor surface quality. Several technologies have been developed to overcome this problem. Ad hoc fixtures for a given part geometry lead to meeting quality tolerances, but since they lack flexibility, they are expensive and not suitable for low manufacturing batches. On the contrary, flexible fixtures consisting of vacuum cups adaptable to a diversity of part geometries may not totally avoid vibrations, which greatly limits its use. The present study analyses the feasibility of thin floor milling in terms of vibration and roughness, in the cases where milling is conducted without back support, a usual situation when flexible fixtures are employed, so as to define the conditions for a stable milling in them and thus avoid the use of ad hoc fixtures. For that purpose, the change of modal parameters due to material removal and its influence on chatter appearance have been studied, by means of stability lobe diagrams and Fourier Transform analysis. Additionally, the relationship between surface roughness and chatter frequency, tooth passing frequency, and spindle frequency have been studied. Ploughing effect has also been observed during milling, and the factors that lead to the appearance of this undesirable effect have been analyzed, in order to avoid it. It has been proven that finish milling of thin floors without support in the axial direction of the mill can meet aeronautic tolerances and requirements, providing that proper cutting conditions and machining zones are selected.

Chatter stability analysis in Micro-milling with aerostatic spindle considering speed effect

The regenerative chatter is one of the fundamental obstacles in high-speed micro-milling process, which causes tool wear and poor surface quality. In order to predict the chatter stability of micro-milling with aerostatic spindle more accurately, the effects of rotating speed on the dynamic stiffness and damping coefficients of aerostatic journal bearing are investigated firstly. The frequency response functions (FRFs) of aerostatic spindle under different rotating speeds are calculated considering the speed effect of aerostatic bearing, centrifugal force and gyroscopic moment. A method for calculating the stability lobe diagram (SLD) of micro-milling considering the speed effect is proposed in this paper. The speed-dependent SLD is simulated based on tool tip FRFs under different rotating speeds and is verified by micro-milling of aluminum 7075. In addition, the effects of supply air pressure and air film thickness on the SLD are investigated comprehensively. The results provide guidance to improve the chatter stability and cutting efficiency in micro-milling with aerostatic spindle.

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.

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%.

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.