Chatter Stability Analysis Research Articles

铣削过程稳定性时域分析方法研究进展

铣削过程稳定性时域分析方法研究进展

Chatter Stability Analysis of Milling Processes

AbstractFull utilization of the available machine tool cutting performance is often inhibited by chatter vibrations which can lead to poor surfaces, reduced tool life, increased noise emissions and even damage to the machine tool. In this contribution, a systematic approach for modelling regenerative chatter based on measured, modal models of the machine tool is presented. Furthermore, three different methods for solving the governing equations and generating stability charts are compared.

Reliability analysis of chatter stability for milling process system with uncertainties based on neural network and fourth moment method

A reliability analysis of the milling system with uncertainties is developed in this paper to predict reliable chatter-free machining parameters. The chatter reliability refers to the probability of no chatter for the dynamic milling system. Then a reliability model is established to predict the chatter vibration, in which the dominant modal parameters of the dynamic milling system are defined as random variables. To solve the reliable model with the second-order fourth-moment (SOFM) method, the limiting axial cutting depth is substituted by an explicit expression obtained using a neural network. Therefore, after distributions of the random parameters are experimentally determined, the reliability of the given machining parameters can be computed with the SOFM method. Furthermore, a reliable stability lobe diagram (RSLD) can be plotted to obtain more reliable and accurate stable region instead of the conventional SLD. A case study is performed to validate the feasibility of the proposed method. The reliability of the milling system was calculated with the SOFM method, the first-order second-moment (FOSM) method and the Monte Carlo simulation (MCS) method. The results from the SOFM method and MCS method were found to be more consistent. Moreover, a RSLD with the reliability level 0.99 was compared with a conventional SLD plotted using the mean values of the random parameters. Chatter tests shown that the RSLD with the higher reliability level was more accurate for predicting the chatter-free machining parameters.

Analytical Modeling of Process Damping in Machining

The machining process induced damping caused by the indentation of the cutting edge into the wavy cut surface greatly affects the process stability in low-speed machining of thermally resistant alloys and hardened steel, which have high-frequency vibration marks packed with short wavelengths. This paper presents an analytical model to predict the process damping forces and chatter stability in low-speed machining operations. The indentation boundaries are evaluated using the cutting edge geometry and the undulated surface waveform. Contact pressure due to the interference of the rounded and straight sections of the rigid cutting edge with the elastic-plastic work material is analytically estimated at discrete positions along the wavy surface. The overall contact pressure is obtained as a function of the cutting edge geometry, vibration frequency and amplitude, and the material properties of the workpiece. The resulting specific indentation force is evaluated by integrating the overall pressure along the contact length. Then, the process damping force is linearized by an equivalent specific viscous damping, which is used in the frequency domain chatter stability analysis. The newly proposed analytical process damping model is experimentally validated by predicting the chatter stability in orthogonal turning, end milling, and five-axis milling of flexible blades. It is shown that the proposed model can replace currently used empirical models, which require extensive experimental calibration approach or computationally prohibitive finite elements based numerical simulation methods.

Design and chatter prediction analysis of a duplex face turning machine for manufacturing disk-like workpieces

Abstract Simultaneous, parallel or double-sided machining can increase the metal-removal-rate (MRR) of hard-to-cut materials. This paper presents a direct-drive duplex-face-turning (DFT) machine for manufacturing thin-walled disk-like components characterized by a very large diameter-to-thick ratio, which allows simultaneous cutting of opposite sides to improve productivity and mitigate workpiece deformations/vibrations during machining. The unique dynamic characteristics on the cutting interface between the thin-walled disk and the two cutters, however, present some challenges in chatter prediction and process parameter optimization. To address these challenges, a multi-dimensional chatter stability analysis method based on a conceptually straightforward modeling approach in terms of the major oblique cutting parameters is presented, where the dynamic effects of both the workpiece and two cutters in addition to the insert geometries are taken into considerations in the formulation of the DFT process. The proposed chatter stability analysis is numerically illustrated and experimentally validated. The relative merit of the direct-drive DFT process has been experimentally evaluated for machining thin-walled hard-to-machine compressor disks by comparing symmetric and non-symmetric DFT operations with single-sided face-turning, along with an example that illustrates a quick guide for nonsymmetrical DFT in the specified speed range.

Designing of milling tool spindle

Analysis of chatter stability in an end milling process is quite cumbersome because of the inaccurate knowledge in the spindle’s geometrical design, position of the bearings and several issues related to the spindle structure. The effective position of bearings of the spindle plays a key role in investigating the self-excited chatter vibrations, which requires an accurate transfer function at the most flexibility region of the spindle tool structure. The present work focuses on the development of a novel method of measuring the spindle vibration responses experimentally using sine sweep tests for a CNC end milling machine tool. Using these model data, an analytical model of the spindle is estimated by considering the bearing span as a design variable. Trial runs are conducted until the convergence between the identified transfer function from the model and that from experiment is achieved. The final model of the spindle system is then applied with time-varying cutting forces so as to obtain the process stability.Bangladesh J. Sci. Ind. Res.53(3), 191-198, 2018

A method to predict the cutting force for end mills with variable-pitch and variable-helix angle

Cutting force is the most fundamental, and essential for machining error control, chatter stability analysis and milling process planning. In this paper, a method to predict the cutting force for the milling with variable-pitch or variable-helix cutter is provided. The method can take into account the piecewise continuous regions of the cutting that is attributed to the helix angle and the pitch variations between two subsequent teeth along the length of the axis. The piecewise character related to cutting force is deeply analysed and the effective depth of cut which seriously influences the maximum cutting force is discussed as well as its expression. Finally, a series of cutting tests and simulations are carried out to validate the present method.

NC milling simulation for prediction and avoidance of chatter vibration

Chatter stability analysis has been mainly studied under the constant cutting depth conditions. It is insufficient for milling complex shape including die and mold. The paper presents NC milling simulation of chatter stability for complex shape with arbitrary cutting depth conditions. It calculates quantitative indicator of chatter stability for each tool path, visualizes it, and modifies NC programs to avoid chatter vibrations. The simulation results are in good agreement with the machined surface in pocket milling and chatter vibrations are avoided.

Multi-dimensional chatter stability for enhanced productivity in different parallel turning strategies

Simultaneous turning with extra cutting edges increases the material removal rate (MRR), and thus the productivity of the process. On one hand, chatter could be a fatal threat to the productivity and part quality in simultaneous turning operations of slender and flexible workpieces. On the other hand, stability of flexible part turning can be increased significantly if the process parameters are selected properly. In practice, however, ensuring a stable parallel turning of a flexible workpiece is approached by the costly process of trial and error. In order to tackle this problem, a multi-dimensional model for chatter stability analysis of parallel turning operation is presented where the effects of components' dynamics, i.e. workpiece and cutters, in addition to insert's geometry are accounted for. The stability model is formulated for two configurations of the parallel turning operation in frequency and time domains, and verified experimentally. Chatter-free and high productivity cutting conditions are determined through optimal parameter selection employing stability maps generated for each configuration.

Dynamic damping of machining vibration: a review

Machining is one of the important manufacturing processes used in industry. Dynamic interaction between the tool and the workpiece may lead to the occurrence of chatter vibrations, which are associated with problems of poor surface finish, reduced workpiece quality, and low productivity. In the past, researchers developed some important methods to investigate the dynamics of machining processes. Dynamic responses of cutting systems were firstly identified by means of sensors, followed by chatter stability analysis using stability lobe diagrams to determine the stable and unstable regions, and finally, chatters were suppressed by either active or passive damping techniques. Previous reviews emphasized on identification of the chatter vibration with less focus on control. This paper mainly reviews the state of the art on the control of machining chatter vibrations, including damping methods related to boring, turning, and milling processes.

Probabilistic analysis of chatter stability in turning

In practical engineering, randomness of the parameters (mass, stiffness, and cutting coefficients) significantly impacts the stability of turning processes. In this study, the method involving the probabilistic analysis of the regenerative chatter stability in turning is comprehensively investigated. Considering the influences of random factors, the probability characteristic of the regenerative chatter stability in turning is studied using the Monte Carlo simulation (MCS) method and advanced first order second moment (FOSM) method. Dynamic model of regenerative chatter in turning is obtained, and the relationship between the limiting width of cut for stable machining and the rotation speed of the spindle is acquired based on the Laplace transform. The MCS and advanced FOSM methods for predicting the reliability of the stability in turning are proposed by identifying whether the actual cutting width is less than the limiting width of cut. Finally, practical applications and a detailed analysis to evaluate the accuracy of the proposed methods are discussed.

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

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

Evaluation of Sensor-less Identification Method for Stable Spindle Rotation against Chatter with Milling Simulation Analysis

Although chatter stability analysis is necessary to enhance cutting accuracy and efficiency, a reliable prediction is difficult to achieve because of the analysis error of frequency response function. Therefore, the investigation proposes an experiment-based identification method for stable spindle rotations in milling by gradually changing the spindle rotation and capturing chatter frequency shift from servo information. In order to evaluate the identification accuracy, this paper presents theoretical approaches to analyze time-dependent variation in chatter and the expected identification error of proposed method by using a time-domain simulator and a frequency-domain model considering amplitude ratio between inner and outer modulations of the chip.

Curvature effects on circular feed end-milling, part 2: stability analysis

The non-periodic delay differential equation (DDE) derived in Ozoegwu et al. (in press) to govern chatter of circular milling is averaged over a single discrete delay to get a periodic DDE that approximates chatter of circular end-milling. Chatter stability analysis of the averaged periodic DDE respectively using both the second order least squares approximated full-discretisation map and the modified full-discretisation map on systems governed by linear force law and nonlinear force law gives that curvature diminishes chatter stability because of its reducing effect on damping. This result is in conformity with the simulation-derived results in Ozoegwu et al. (in press). The destabilising effect of curvature gets stronger with lowering of the spindle speed. It is recommended that experimental validation of effects of curvature on stability of end-milling should be done at low spindle speed range. The observed destabilising effect of curvature on chatter stability increases with fall in natural frequency of the tool thus stiffer tools with more strengthening profiles should be selected for circular milling.

1705 Enhancement of In-process Identification for Stable Spindle Rotation against Chatter Vibration with a Time-domain Milling Simulator

In order to improve cutting accuracy and efficiency in milling, chatter stability analysis should be performed to find a stable cutting condition. However, the stability prediction has a difficulty to ensure high reliability, because modal parameters of a tool have to be identified accurately, which change with the spindle rotation. In this study, a novel approach for identification of stable spindle rotation against chatter is proposed by decreasing spindle rotation during chatter and capturing drastic shifts of chatter frequency with disturbance observer in the spindle control system. Furthermore, identification error is discussed with a time-domain milling simulator, and a theoretical compensation equation for the error is derived.

Modeling and Application of Process Damping in Milling of Thin-Walled Workpiece Made of Titanium Alloy

The modeling as well as application of process damping in milling of thin-walled workpiece made of titanium alloy is investigated. Titanium alloy used commonly in aviation industry is one typical difficult-to-machine material. Chatter usually occurs in cutting of titanium alloy, which results in poor surface quality and damaged tool. Thus, chatter is one important restriction for the quality and efficiency of titanium alloy manufacture, especially for the thin-walled workpiece made of titanium alloy due to poor structural stiffness. Process damping results from interference between flank face and machined surface, which is critical but usually ignored in chatter analysis for difficult-to-machine material. The paper presents one nonlinear dynamic model considering process damping for milling of thin-walled workpiece made of titanium alloy and designs antivibration clearance angle to suppress chatter based on the model. The experimental and computational results indicate that the presented methods for chatter stability analysis are reasonable, and the antivibration clearance angle designed is effective in suppressing chatter and improving machining quality.

Investigation of Boring Bar Dynamics for Chatter Suppression

Chatter is a concern in boring process, due to the low dynamic stiffness of long cantilever boring bars. Chatter suppression in machining permits higher productivity and better surface finishes. In order to improve the performance of boring operations, several researchers have investigated electro- and magneto-rheological fluids and piezoelectric and electromagnetic actuators as vibration absorbers. In this study, we investigated the feasibility of shifting the natural frequency of boring bar based on semi-active fluid control. Mass at the end of a boring bar was modulated to tune its natural frequency by adjusting the level of fluid in a reservoir. At the same time, different damping materials were used to improve dynamics of the boring bar. Experimental modal analysis was used to obtain frequency response functions for different system configurations. A finite element model was proposed and validated with experimental results. A chatter stability analysis examined chatter suppression characteristics of the proposed method.

Regenerative Chatter Stability and Hopf Bifurcation Analysis in Milling System

The shifted Chebyshev polynomials and Floquet theory are both adopted for the prediction regenerative chatter stability and Hopf bifurcation in milling. The influences of the system parameter on the stability of the milling system have been analyzed. The stability lobe diagrams are obtained. The result shows that the shifted Chebyshev polynomials method is more accurate than the semi-discretion scheme for spindle speed lower than 3500 round per minutes. The stability in milling can well be predicted by the cutting depth and feed rate lobes diagrams. Only Hopf bifurcations are detected by the Eigen-value analysis. The stable solution transform from the stable equilibrium point to the quasi-periodic oscillation after Hopf bifurcation.

Stability Analysis of Chatter in Tandem Rolling Mills—Part 1: Single- and Multi-Stand Negative Damping Effect

Many different modes of chatter in rolling and their possible causes have been identified after years of research, yet no clear and definite theory of their mechanics has been fully established and accepted. In this two-part paper, stability of tandem mills is investigated. In Part 1, state-space models of single- and multi-stand chatter are formulated in a rigorous and comprehensive mathematical form. Then, the stability of the rolling system is investigated in the sense of the single- and multi-stand negative damping effects. First, a single-stand chatter model in state-space representation is proposed by coupling a dynamic rolling process model with a structural model for the mill stand. Subsequently, a multi-stand chatter model is developed by incorporating the inter-stand tension variations and the time delay effect of the strip transportation based on the single-stand chatter model. Stability criteria are proposed and stability analyses are performed to create corresponding stability charts in terms of the single- and multi-stand negative damping mechanism through numerical simulations. Particularly, the effect of friction conditions on chatter is examined and an explanation is given for the existence of an optimum friction condition. In Part 2, the regenerative effect and resulting instabilities are examined. Suitable stability criteria for each mechanism are established and stability charts are demonstrated in terms of relevant rolling process parameters.

Chatter Stability Characterization of a Three-Flute End-Miller Using the Method of Full-Discretization

It was noticed in laboratory practice that certain conditions of slotting operation of a plastic end milling computer Nu merical control (CNC) machine became noisy with increasing depth of cut and eventual perforation of workp iece thus objective is to generate stability characterization of the machine in the form of a chart on the plane of cutting parameters on which stable operation is demarcated fro m the unstable operation. Chatter stability analysis is carried out here using a recently developed method called Fu ll-discretization. The resulting chart is partit ioned into portions of secondary Hopf and flip bifurcations through MATLAB eigen-value analysis of resulting monodro my operator. These two types of bifurcation are d iscovered to be visible for high speed range while only secondary Hopf bifurcat ion is visible for the lo w spindle speed range. It is also discovered for the studied slotting operation, that critical characteristic mu ltipliers are almost pure imaginary at the turning points of secondary Hopf bifurcation lobes and get closer to the negative real axis when critical points move away from min imu m points. Equation describing the infinitely many but discrete secondary Hopf bifurcation chatter frequencies at min imu m points is postulated. The parameters of the end milling process are; tool mass m = 0.0431kg, tool natural frequency ���� n = 5700 rad s −1 , damping factor ξ = 0.02 and workpiece cutting coefficient C = 3.5 × 10 7 Nm −7 4 ⁄ . The stability chart generated for the system shows close agreement with both practice and theory.