Stability Lobe Diagram Research Articles

Surface location error prediction and stability analysis of micro-milling with variation of tool overhang length

The stability of micro-milling has an important influence on the machined surface, and choosing proper machining parameters can effectively avoid machining process instability and dynamic error. The frequency response function (FRF) of micro-milling tool point varies with tool overhang lengths, and it affects stability lobe diagram (SLD) of the machining system. During the micro-milling process, the cutting thickness was divided into the shearing zone and the plowing zone. In the shearing zone, the cutting thickness was calculated with considering cycloidal tool path and dynamic cutting thickness. After the micro-milling force model was established, the receptance coupling substructure analysis (RCSA) and experimental modal analysis (EMA) were used to obtain the FRFs at the micro-milling tool point. The 2 three-dimensional diagrams, SLD and surface location error (SLE), were developed comprehensively by means of frequency domain method, and the flank micro-milling experiments were carried out. The validity of the three-dimensional SLD containing tool overhang length and the prediction model of SLE was verified by the experimental results, and surface topography was characterized to show the actual machining state. The experimental results show that, compared with SLE, the change of tool overhang length had more significant influence on SLD, and the chatter remarks were not very obvious on the bottom of the workpiece no matter whether the machining process was stable or not. In unstable region, chatter caused by cutting tool left marks on the machined surface. Under the condition of stable milling, a machined surface with smaller SLE and better topography was obtained. The 2 three-dimensional diagrams can provide good references for the selection of optimal tool overhang length and machining parameters comprehensively.

Investigation of rotary inertial dynamic effects on chatter boundary in milling process using three-dimensional Timoshenko tool model

Chatter prediction is essential to conduct stable machining. Many of the previous studies made to simulate milling process have not considered gyroscopic and rotary inertial dynamics effects. The aim of this research is to investigate the effects of rotary inertial dynamics on prediction of chatter in the milling operation. For this purpose, a three-dimensional rotating cantilever Timoshenko beam is considered for modeling the cutting tool. In the proposed model, cutting forces are applied at the end of the beam. Imposing spectral finite element model, the governing delay partial differential equations of the system reduce to nondelay ordinary differential equations. The main contributions of the current research are modeling the cutting tool as a continuous model by Timoshenko beam theory, finding and solving nondelay ordinary differential equations of the cutter via spectral finite element model, and studying the effects of gyroscopic and rotary inertial dynamics, completely. For validating, the system stability predictions obtained from the presented model are compared with experimental outcomes from the literature. Besides the common stability lobe diagram which is in terms of depth of cut and the spindle speed, other stability diagrams based on cutter length and diameter are illustrated. Using this model, influences of rotary inertial dynamics on these stability diagrams are investigated. The results show that ignoring the rotary inertial dynamics causes significant errors in prediction of chatter boundaries especially in high angular velocity of the tool. In addition, the effect of number of the cutter teeth on the stability of milling process is studied. The presented stability diagram may help a machinist to choose a better set of parameters, such as tool length and diameter, number of cutter flutes, depth of cut, and spindle velocity, for doing a stable milling process.

Stability of lateral vibration in robotic rotary ultrasonic drilling

Industrial robot is widely used to accomplish the drilling work in aviation industry due to its flexibility and relatively low cost. However, the low stiffness property of robot makes it easy to induce lateral vibration in the drilling process and restricts further improvement of drilling quality and efficiency. It is urgent to propose a new method for robotic drilling which is able to reduce the cutting force and suppress the lateral chatter effectively. In this study, robotic rotary ultrasonic drilling (RRUD) technology is proposed firstly. And the dynamic model to compute the stability lobe for RRUD is developed. The stability problem is simplified as a two degrees of freedom model. After that, the axial chip thickness is achieved on base of kinematic characteristics analysis. Furthermore, exponential method is applied to develop the dynamic cutting force model. Then, the stability lobe diagrams are obtained by frequency domain analysis. It is found that the stability region of RRUD gets a larger extension compared with robotic conventional drilling (RCD). Finally, pilot experiments are conducted and the results indicate that these stability lobe diagrams agree well with the experimental results.

Robust Active Chatter Control in Milling Processes With Variable Pitch Cutters

Milling chatters caused by the regenerative effect is one of the major limitations in increasing the machining efficiency and accuracy of milling operations. This paper studies robust active chatter control for milling processes with variable pitch cutters whose dynamics are governed by multidelay nonlinear differential equations. We propose a state feedback controller based on linear matrix inequality (LMI) approach that can enlarge multiple stability domains in the stability lobe diagram (SLD) while the controller gain is minimized. Numerical simulations of active magnetic bearing systems demonstrate the effectiveness of the proposed method.

Multi-Objective Optimization of Surface Roughness and Cutting Forces in Hard Milling Using Taguchi and Response Surface Methodology

Cutting forces and surface roughness are important output parameters affecting the machining performance and quality of any machined surface in hard milling. In order to obtain the best surface quality and highest productivity, the input-cutting parameters need be considered and chosen properly whenever hard milling is involved. Therefore, in this paper, an attempt is made to conduct the multi-objective optimization of the surface roughness (Ra) and the resultant cutting force (Ft) in hard milling of SKD61 steel by Taguchi method and Response Surface Methodology (RSM). Values of the input parameters for milling tests are chosen through the stability lobe diagram of a machine tool simulated by the use of Cutpro software. The Taguchi method is used for designing all of the milling experiments. The values of Ra and Ft are measured by a Surftest SJ-400 and a dynamometer, respectively, and then analysis of variance is conducted to find out the effect of machining process conditions on Ra and Ft. In order to get the low Ft and Ra, a multi-objective optimization is implemented with the use of the desirability function. The results reveal that the optimized machining conditions for Ra and Ft are a cutting speed of 100 m/min, a feed rate of 0.015 mm/tooth, and a depth of cut of 0.44 mm, with predicted Ra of 0.206 µm and Ft of 66.58 N.

A Free Interface Component Mode Synthesis Approach for Determining the Micro-End Mill Dynamics

The prediction accuracy of the stability boundary in the machining process depends upon accurate estimation of cutting tool-tip dynamics. Note that the experimental modal analysis using direct impact at miniature end mill (typically 50–500 μm in diameter) is not feasible as it can result in tool failure. Consequently, alternative techniques such as experimental modal analysis using reciprocity theory and frequency-based receptance coupling substructure analysis (RCSA) have been used extensively for determining tool-tip dynamics. The experimental approach based on reciprocity theory assumes that the structure is symmetric (cross frequency response functions (FRFs) are same between two points of interest in a structure). RCSA requires a very fine frequency resolution and matrix inversion, which can lead to computational complexities. In addition, RCSA takes into account the FRFs only at the interface and free end, which can induce errors. Owing to these issues with existing approaches, this paper proposes a free-interface component mode synthesis (CMS) approach for estimation of micro-end mill dynamics. The effect of machine tool compliance including the collet–tool interface has been included for estimation of micro-end mill dynamics via a free-interface CMS approach wherein the experimental and analytical mode shapes are coupled. The predicted micro-end mill dynamics have been compared with RCSA and experimental modal analysis using reciprocity theory. Finally, the stability lobe diagrams for high-speed micromilling of Ti6Al4V has been made using the tool-tip dynamics from CMS, RCSA, and experimental technique using reciprocity theory and validated against experimental measurements for onset of instability.

Robust evaluation of chatter stability for milling process with uncertainties based on optimal configuration of machining position and spindle speed

Chatter vibration in milling process is a major obstacle that limits the machining quality and productivity, which may be avoided by using stability lobe diagrams (SLDs). Many traditional models developed to predict chatter stability assume that dynamic parameters of the machine tool remain constant under operational conditions. However, these parameters such as natural frequencies, damping ratios, stiffness, and cutting force coefficients vary depending upon different aspects including spindle speed, tool wear, and machining position, reducing the accuracy of chatter prediction. In this study, a robust chatter prediction method based on conventional analytical milling stability models is presented by employing the Edge theorem and Zero Exclusion condition. In this method, optimal combinations of spindle speeds and machining positions are firstly researched to obtain higher critical depths of cut, based on the conventional stability model, modal fitting technique, Kriging model, and improved particle swarm optimization. At each combination, related nominal modal parameters and cutting force coefficients are identified, and their left and right worst-case deviations are also determined. Critical stable condition for each combination is detected by a graphic approach within the minimum and maximum bounds of uncertainties. Accordingly, a robust stability lobe diagram is obtained with related spindle speeds and critical cutting depths. The proposed method was verified by chatter tests on a real vertical machining center, demonstrating its reliability in chatter prediction compared to the conventional stability lobe diagram.

Mechanism of process damping in milling of thin-walled workpiece

Abstract Existing ploughing mechanism and velocity-dependent mechanism, which were used for explaining the process damping in milling, did not consider the feedback influence of vibrations in normal direction, and thus, they cannot be used to reveal the underlying cause of process damping in milling process of thin-walled workpiece. This paper systematically studies the generation mechanism of process damping in thin-wall milling, and turns out that the relative vibration of cutter-workpiece system rather than the ploughing indentation is the main source of process damping in this kind of process. Theoretically, the actual cutting velocity and the relative vibrations in both feed and normal directions are combined to formulate the expression of instantaneous uncut chip thickness, which is then used to derive the equations of dynamic cutting forces. Taylor series expansions are carried out around harmonic response to linearize the equations of dynamic cutting forces. Derivations show that the dynamic cutting forces are composed of two items, i.e. the vibration displacements-induced force and the vibration velocities-induced force. The latter, which is actually an additional dissipative force being inversely proportional to the cutting velocity, constitutes a source of process damping. It is subsequently integrated into the process's governing equation to estimate the stability lobe diagrams (SLDs). Verification shows that the SLDs predicted by the proposed velocity-dependent mechanism reasonably agree with the experimentally observed results (among 672 sets of detailed comparisons, agreement rate is more than 95%.). Especially, thin-wall milling experiments with various values of spindle speeds show that the SLDs predicted using the proposed velocity-dependent mechanism are much closer to the experimental observations than those obtained by the ploughing mechanism (among 36 sets of detailed comparisons, agreement rate between the predictions and measurements is more than 94% for the proposed velocity-dependent mechanism, while the agreement rate is only 47% for the ploughing mechanism.).

Efficient determination of stability lobe diagrams by in-process varying of spindle speed and cutting depth

The experimental determination of stability lobe diagrams (SLDs) in milling can be realized by either continuously varying the spindle speed or by varying the depth of cut. In this paper, a method for combining both these methods along with an online chatter detection algorithm is proposed for efficient determination of SLDs. To accomplish this, communication between the machine control and chatter detection algorithm is established, and the machine axes are controlled to change the spindle speed or depth of cut. The efficiency of the proposed method is analyzed in this paper.

Chatter detection and stability region acquisition in thin-walled workpiece milling based on CMWT

Milling chatter is one of the biggest obstacles to achieve high performance machining operations of thin-walled workpiece in industry field. In the milling process, the time-varying and position-dependent characteristics of thin-walled components are evident. So, effective identification of modal parameters and chatter monitoring are crucial. Although the advantage of chatter monitoring by sound signals is obvious, the milling sound signals are nonstationary signals which contain more stability information both in time domain and frequency domain, and the common analytical transformation methods are no longer applicable. In this paper, short time Fourier transform (STFT) is taken as an example to compare the processing results with cmor continuous wavelet transform (CMWT). This article concerns the chatter detection and stability region acquisition in thin-walled workpiece milling based on CMWT. CMWT combines the advantages of the cmor wavelet and continuous wavelet transform which has good locality and the optimal time-frequency resolution. Therefore, CMWT can be adaptively adjusted signal by the window, which is very suitable for processing nonstationary milling signals. Firstly, the model and characteristics of thin-walled workpiece during the cutting process are presented. Secondly, the CMWT method for chatter detection based on acoustic signals in thin-walled component milling process is presented. And the chatter detection results and stability region acquisitions are analyzed and discussed through a specific thin-walled part milling process. Finally, the accuracy of the method presented is verified through the traditional stability lobe diagram predicted using the exiting numerical method and the machined surface morphologies at different cutting positions obtained through the confocal laser microscope.

An Integrated Smarter Cutting Parameter Selection System with a Case Study for Pocket Milling

This paper develops an integrated smart cutting parameter selection system for pocket milling. Currently, general CAD/CAM systems generate pocket milling tool paths according to user-designated cutting parameters typically including cutting depth, feed rate, and spindle speed. Pocket milling is often used for rough machining, and shorter cutting times are used to increase productivity. Although shorter machining times can be accomplished with deeper cutting, it may result in unstable cutting (chatter). Stability lobe diagrams (SLD) generated from cutting and tapping tests on selected machine tools describe the relationship between cut depth and spindle speed. However, despite offering useful information for selecting cutting parameters for chatter-free cutting, SLD has not been integrated with existed CAD/CAM systems. Therefore, this study integrates SLD in a CAD/CAM system to effectively determine the optimum cut depth and spindle speed for a theoretically chatter free pocket milling tool path. A case study is used to verify the proposed system integration.

Effects of helix angle and multi-mode on the milling stability prediction using full-discretization method

Regenerative chatter has a negative effect on the quality of machined surfaces in milling and it is thus vital to predict this accurately. The full-discretization method (FDM) is extensively utilized to predict the chatter stability. However, the effects of helix angle and multi-mode usually cause poor prediction by FDM and are often ignored. The existing fourth-order FDM has better computational efficiency and convergence rate than other existing FDMs. In this paper, a fourth-order FDM is optimized to improve prediction accuracy by considering both the helix angle and multi-mode. Based on the numerical stability computation results, it can firstly be observed that the stability lobe diagram (SLD) obtained using the proposed FDM has advantages over the existing SDM in the aspects of both the convergence rate and computational efficiency, and the effect of helix angle on the SLD is determined by both the number of teeth, radial immersion ratio and helix angle of the tool. Furthermore, a detailed investigation on how to detect chatter in milling experiments is made using an integrated method with time-frequency analysis. Finally, comparing the prediction result with the experimental milling results, it can be concluded that the proposed SLD with first three modes excels in prediction accuracy. A quantitative evaluation about the improvement of prediction accuracy is also made. The intention of proposing the updated FDM is to make the chatter prediction more accurate and efficient.

Determination of optimal geometrical parameters of peripheral mills to achieve good process stability

This paper focuses on optimization of the geometrical parameters of peripheral milling tools by taking into account the dynamic effect. A substructure synthesis technique is used to calculate the frequency response function of the tool point, which is adopted to determine the stability lobe diagram. Based on the Taguchi design method, simulations are first conducted for varying combinations of tool overhang length, helix angle, and teeth number. The optimal geometrical parameters of the tool are determined through an orthogonal analysis of the maximum axial depth of cut, which is obtained from the predicted stability lobe diagram. It was found that the sequence of every factor used to determine the optimal tool geometrical parameters is the tool overhang length, teeth number, and helix angle. Finally, a series of experiments were carried out as a parameter study to determine the influence of the tool overhang length, helix angle, and teeth number on the cutting stability of a mill. The same conclusion as that obtained through the simulation was observed.

Milling stability prediction with simultaneously considering the multiple factors coupling effects—regenerative effect, mode coupling, and process damping

Chatter is a kind of self-excited vibrations which is related to regenerative effect, mode coupling effect, and process damping, etc. To predict milling chatter more accurately, a suitable dynamical model of milling process which can reflect the practical chatter mechanism should be obtained firstly. In this paper, a new milling dynamical model which simultaneously considers the regenerative effect, mode coupling effect, and process damping is established. Based on the new dynamical model and the updated full-discretization method (FDM), the coupling influences of regenerative effect, mode coupling effect, and process damping on the accurate of the stability lobe diagrams (SLDs) for up-milling and down-milling operations are investigated. A series of numerical simulation and experiments are carried out to verify the accuracy of the proposed milling dynamical model. The experiment results show that the mode coupling effect and process damping have great influences on the prediction of milling stability. The SLD which obtained by the new milling dynamical equation (considering the regenerative effect, mode coupling, and process damping) is more accurate than that which obtained by only considering the regenerative effect.

An Investigation of Stability Analysis of Face Milling of Cantilever Plates at Low Cutting Speeds

Considering the production requirement of workpiece optimization in order to reduce mass, the dynamic behavior of a workpiece can be affected. This factor can influence the performance of the milling process due to the occurrence of chatter vibrations. On the other hand, when the recommended cutting speed is relatively low, the tool rubs against the workpiece surface causing process damping. Consequently, the process becomes more stable and hence the depth of cut can be increased. In this paper, the stability of face milling of a cantilever plate at low cutting speed is investigated. The stability lobes diagram is determined numerically considering process damping. Cutting tests are conducted in order to verify the simulated results. An accelerometer is attached to the workpiece and its signal is measured and analyzed. Both workpiece surface and roughness are also investigated. The experimental results show a good agreement with the stability lobes diagram to predict the stable region under process damping. Hence, the depth of cut can be considerably increased, keeping the process stable at low cutting speeds.

An improved full-discretization method for chatter stability prediction

An improved full-discretization method (IFDM) based on the golden search is presented in this brief paper to predict stability lobe diagram (SLD). To begin with, the mathematical model of milling dynamics considering the regenerative chatter is expressed as a state space form. With the time delay being separated equally into a limited amount of elements, the time series expression is obtained by interpolating the integral nonhomogeneous term using linear approximation. Then, 2N order algorithm is adopted to resolve the exponential term into a real matrix, which avoids the exponential matrix that has to be calculated each time in scanning the plane comprised of axial cutting depth and spindle speed. Lastly, the golden search instead of traditional sequential search is applied to seek the crucial axial cutting depths corresponding to different spindle speeds, which can improve computational efficiency remarkably. The verifications with two classic benchmark examples demonstrate that the proposed method has higher computational efficiency.

Prediction of chatter considering the effect of axial cutting depth on cutting force coefficients in end milling

The cutting stability of machine tools during operation is dependent on many parameters including the spindle speed and axial cutting depth. Cutting force coefficients may change due to the effect of heat and influence the stability lobe diagram during dry cutting aluminum alloy. Based on the identification of cutting force coefficients, the dependence of cutting force coefficients on the spindle speed and axial cutting depth are investigated. The spindle speed had a slight effect on cutting force coefficients, while the axial cutting depth greatly affected the cutting force coefficients. The cutting force coefficients were expressed as functions of axial cutting depth, and based on varying cutting force coefficients with axial cutting depths, the stability lobe diagram is modified. Then, stability lobe diagrams of varying cutting force coefficients are compared to that of constant cutting force coefficients, and the stability lobe diagram with varying cutting force coefficients was verified through a series of experiments.

Chatter mitigation for the milling of thin-walled workpiece

During the milling process of thin-walled workpiece, chatter is the major obstacle in achieving desired accuracy and productivity of the final part due to its low rigidity. In this paper, a novel method is proposed to mitigate the chatter of the thin-walled workpiece by submerging the milling system in viscous fluid. To evaluate the effectiveness of the presented method, the influence of the viscous fluid on the milling force coefficients is investigated, and the modal parameters of the thin-walled workpiece are identified under dry and viscous conditions respectively. It is found that compared with the dry milling, the milling force coefficients reduce significantly under viscous fluid condition due to the lubrication. Besides, the damping of the milling system increases substantially under viscous fluid condition, and the natural frequencies of the milling system decrease owing to the added mass of the viscous fluid. The milling stability lobe diagrams are predicted based on the numerical integration method by taking multiple modes of the thin-walled workpiece into consideration. A series of milling tests are conducted to verify the stability lobe diagrams and confirm the effectiveness of the proposed approach. The vibration displacement signals are measured and then analyzed in time-frequency domain to demonstrate the state of the milling process. Moreover, the surface finishes of the thin-walled workpieces are compared. The results show that the thin-walled workpiece chatter could be suppressed greatly with the proposed method and higher stability limit can be achieved.

Chatter stability prediction in high-speed micromilling of Ti6Al4V via finite element based microend mill dynamics

High-speed micromilling (spindle speeds 100 000 r/min) can create complex three-dimensional microfeatures in difficult-to-machine materials. The micromachined surface must be of high quality, to meet functional requirements. However, chatter-induced dynamic instability deteriorates the surface quality and can be detrimental to tool life. Chatter-free machining can be accomplished by identifying stable process parameters via stability lobe diagram. To generate accurate stability lobe diagram, it is essential to determine the microend mill dynamics. Frequency response function is required to determine the tool-tip dynamics obtained by experimental impact analysis. Note that application of impact load at the microend mill tip (typically 100 – 500 μm) is not feasible as it would invariably end with tool failure. Consequently, alternative methods need to be developed to identify the microend mill dynamics. In the present work, the frequency response function for the microend mill is obtained by finite element method modal analysis. The frequency response function obtained from modal analysis has been verified from the experimentally obtained frequency response function. The experimental frequency response function was obtained by impacting the microend mill near the taper portion with an impact hammer and measuring the vibration of the tool-tip with a laser displacement sensor. The fundamental frequency obtained from finite element method modal analysis shows a difference of 6.6% from the experimental fundamental frequency. Microend mill dynamics obtained from the finite element method is used for chatter prediction in high-speed micromilling operations. The stability lobe diagram predicts the stability boundary accurately at 60 000 r · min–1 and 80 000 r/min; however, a slight deviation is observed at 100 000 r/min.

Chatter stability prediction for five-axis ball end milling with precise integration method

The differential dynamic equation (DDE) considering regenerative chatter effect is derived from an ideal cutting model. At the same time, the ball end mill-workpiece engagement (BWE) in five-axis milling is efficiently extracted by the semi-analytical method, where the machining residual left on the finished surface is taken into account. The explicit precise integration method (PIM) is adopted to translate the DDE into a time series expression, ensuring stability prediction without any discretization error loss. With the relationship of cutter edge and BWE at different instants, the stability lobe diagram (SLD) is constructed by Floquet theory, which is subsequently testified in the five-axis NC machine tool. The experimental results keep good agreement with estimations, validating the proposed method. Compared with traditional method in dynamic cutting forces modeling, the proposed approach is more close to actual processing. In contrast to Runge-Kutta based complete discretization method, PIM shows higher superiority no matter in convergence rate or calculation accuracy. Lastly, the influences of different inclination angles on stability are revealed, which can give a reference to selection of suitable process parameters for higher productivity.