Chatter Stability Research Articles

Time-varying reliability and global sensitivity analysis of regenerative chatter stability in turning considering tool wear

Investigating the effect of the uncertainty in the parameters on time-varying chatter stability is critical to refrain from the time-varying regenerative chatter in turning. In this study, the influence of tool wear on the cutting force coefficient (CFC) in turning processing is taken into consideration, and CFC variation during cutting time is described by the Gamma process. The model of the time-varying chatter stability in turning is established based on the motional and mechanical properties of the cutting process in turning. Time-varying reliability (TVR) is estimated based on the uncertain and time-varying characteristics of the turning process parameters. The method of moment-independent time-varying global sensitivity analysis (TV-GSA) based on the cumulative failure probability (CFP) is proposed to measure the effect of parameters on the CFP of the chatter stability in turning. Furthermore, for reducing the computational cost of moment-independent TV-GSA based on CFP, the active learning Kriging model is established to replace the nonlinear and implicit limit state function of the chatter stability in turning. The dynamic model of the turning chatter is validated by an illustrative example. And the results of the proposed method are compared with the results of the Monte Carlo simulation to verify the effectiveness of the proposed method.

A novel harmonic solution for chatter stability of time periodic systems

Chatter vibrations strongly limit productivity in milling. Due to the presence of rotating parts with asymmetric stiffness and stability enhancement strategies which act through a periodic variation of stiffness, there is growing interest in estimating the stability maps of systems with Linear Time Periodic dynamics together with periodic cutting excitation. Applying Exponentially Periodic Modulated test signals to the dynamic cutting force equation and representing the dynamics of the system through the Harmonic Transfer Function, the innovative Harmonic Solution (HS) and its zero-order approximation were derived in this research. HS is a frequency domain representation of a system described by the combination of two independent periodicities. It is possible to take into account these periodicities together in HS or singularly, resulting in the Zero Order HS or in the well-known Multi-Frequency Solution. This novel formulation can deal efficiently with spindle dependent and independent dynamics and is prone to industrial applications due to its flexibility and efficiency. More specifically, in this work the developed methodologies were used to assess the cutting stability of systems with a periodically modulated stiffness. The accuracy and efficiency of HS were validated by comparison with the results achieved by the use of the semi-discretization method. Results are in agreement with those obtained using semi-discretization. Moreover, admitting a slight precision loss, HS and its zero-order approximation are orders of magnitude faster than semi-discretization, giving reliable stability maps from seconds to a few minutes.

General Cutting Dynamics Model for Five-Axis Ball-End Milling Operations

AbstractFive-axis ball-end milling is used extensively to machine parts with sculptured surfaces. This paper presents the general cutting dynamics model of the ball-end milling process for machine tools with different five-axis configurations. The structural dynamics of both the tool and workpiece are considered for the prediction of chatter stability at each tool location along the tool path. The effects of tool–workpiece engagement and tool axis orientation are included in the model. By sweeping the spindle speeds, the chatter-free spindle speeds are selected followed by the prediction of forced vibrations in five-axis milling of thin-walled, flexible parts. The proposed model has been experimentally illustrated to predict the chatter stability and forced vibrations on a table-tilting five-axis computer numerical control machine tool.

Prediction of chatter stability for enhanced productivity in parallel orthogonal turn-milling

To increase productivity and the material removal rate, an increasing number of factories have been employing multiple tools for simultaneous cutting. Among these tools is parallel orthogonal turn-milling, which is an important parallel-processing method. However, a dynamic interaction occurs during the cutting processes due to the waviness induced on the shared cutting surface and the dynamic coupling through the machine structure, creating machining vibrations, or chatter, which affect the quality of the machined surface. Therefore, to reduce or avoid the vibration problem during the cutting process, chatter stability of parallel orthogonal turn-milling was examined in this study. Initially, a chatter mechanism model of parallel orthogonal turn-milling was designed, and the limit-critical axial depth of the cut formula was obtained. Next, the model parameters of the machine tool were obtained based on the hammer test method. A parallel orthogonal turn-milling stability lobe diagram (SLD) with tool tip runout was constructed. Finally, the experimental results were verified on a high-efficiency turn-milling machine tool. The results showed that chatter can be predicted for parallel orthogonal turn-milling and an SLD can provide a reference for the selection of machining parameters. In addition, the SLD can also guide the formulation of processing technology specifications. Our results are extremely significant for ongoing research in the field of machining methods.

Three degrees of freedom chatter stability prediction in the milling process

Chatter in the cutting process has a great influence on workpiece surface quality, machining efficiency, and service life of the machine tool. This work presents three degrees of freedom (DOF) dynamic model applied to tool chatter for thin-walled structures in milling. Combined with dynamic cutting force modelling in the radial, axial and tangential directions, the stability chart was solved by adopting an improved semi-discretization method in time domain. And the stability prediction model considering regenerative effect was validated by cutting tests with specific axial depth of cut and spindle speed. The cutting experimental results performed at different axial depth of cuts were in accordance with predicted stability lobe diagram (SLD). Moreover, the effects of cutting contact angle and radial immersion ratio on SLD were also analyzed. The study results show that the dynamic model could make a good prediction of chatter stability, and the established approach is high efficient in predicting the chatter stability lobe considering the actual situation.

Dynamic Modeling and Cutting Stability of Rotating Tapered Composite Cutter Bar considering Material Damping

Traditional milling cutter bars are generally made up of metals and exhibit poor capacity of chatter suppression. This study proposes an anisotropic composites tapered cutter bar for increasing natural frequency and damping and finally achieves the goal of enhancing chatter stability. Based on Hamilton principle and Euler–Bernoulli beam theory, the partial differential motion equations of the cutting system with a 3D rotating tapered composite cutter bar are established. Next, using the Galerkin method, the equations of motion are discretized so as to derive ordinary differential equations. In the model, damping modeling of the composite cutter bar is achieved theoretically by using damping dissipation constitutive relations for viscoelastic composites. Moreover, by introducing the rotating effect of the 3D cutter bar in the 2-DOF analytical model of stability analysis first proposed for a fixed-type cutter bar, an improved prediction model is developed and used to solve the stability lobes of the cutting system in the frequency domain analytically. Furthermore, the influences of the gyroscopic effect, material, ply angle, stacking sequence, and taper ratio on chatter stability are also discussed.

Stability analysis of 2-DOF milling dynamics for simultaneously varying tooth pitch and spindle speed with helix angle effect

Suppression of self-excited vibrations in their design and incipient stages is vital for assuring surface finish and machining efficiency in the precision machining process. Various cutting vibration suppression methods (e.g., variable tooth pitch and variable spindle speed) have been designed for suppressing regenerative chatter. However, variable parameter-based cutting vibration suppression models have mostly been developed separately with the other parameter assumed to be constant. In addition, these methods failed to provide detailed helix angle information required by a machining practitioner to determine which helix angle degree or group of helix angle degrees would have matched the stability of milling cutters. Moreover, only a single degree of freedom (1-DOF) milling system was adopted; thus, these methods cannot account for two degrees of freedom (2-DOF) and higher milling system. This study proposes a helix angle-based 2-DOF milling model with simultaneous tooth pitch and spindle speed variation to deal with these aforementioned problems. Experimental results showed that the proposed model can be effectively and efficiently applied to the prediction of the regenerative chatter stability for not only 1-DOF but also 2-DOF milling system. Empirical comparisons indicated that the proposed model outperformed the existing methods in stability prediction, while also offering stable area enlargement capability that facilitates cutting vibration suppression. A numerical example is presented to illustrate the usage of the proposed model.

Chatter Stability of Machining Operations

AbstractThis paper reviews the dynamics of machining and chatter stability research since the first stability laws were introduced by Tlusty and Tobias in the 1950s. The paper aims to introduce the fundamentals of dynamic machining and chatter stability, as well as the state of the art and research challenges, to readers who are new to the area. First, the unified dynamic models of mode coupling and regenerative chatter are introduced. The chatter stability laws in both the frequency and time domains are presented. The dynamic models of intermittent cutting, such as milling, are presented and their stability solutions are derived by considering the time-periodic behavior. The complexities contributed by highly intermittent cutting, which leads to additional stability pockets, and the contribution of the tool's flank face to process damping are explained. The stability of parallel machining operations is explained. The design of variable pitch and serrated cutting tools to suppress chatter is presented. The paper concludes with current challenges in chatter stability of machining which remains to be the main obstacle in increasing the productivity and quality of manufactured parts.

Study on the stability for non-uniform helix angle tools in the milling process

ABSTRACT Uniform helix angle tools cannot effectively suppress the chatter in the high machining process. Consequently, cutters with non-uniform helix and pitch angles are more and more common in various milling operations. To suppress the regeneration chatter, it is crucial to study the stable behavior of the tools. Therefore, this paper considers the relationship between the pitch angle and the chatter stability defined by the regeneration factor (RF). Further, the governing equation of the machining system with non-uniform helix angle cutters is formulated. Based on this model, the Enhanced Multistage Homotopy Perturbation Method (EMHPM) is used to compute the stability lobes. To validate the theory in this paper, the stability lobes are predicted and compared with the results in the literature. The results show that the rational helix and pitch angle cutters exhibit increases stability in the milling process.

Stability Analysis of Cutting Process with Internally Damped Rotating Tapered Composite Cutter Bar

Using the cutter bar made with composite rather than metal in high rotating speed milling or boring operations is a new attempt for suppressing chatter of the cutting system. This is because composite material has much higher specific stiffness and damping as well as dynamic stiffness compared to metal. But, for a rotating composite cutter bar, larger internal damping (or rotational damping) occurs, and such damping may cause the rotor instability in the perspective of rotor dynamics. On the other hand, the effect of internal damping of a rotating composite cutter bar on the chatter stability in high speed cutting process is also an important issue worthy of concern. In this paper, a new dynamic model of the cutting system with a rotating composite cutter bar is presented. The cutter bar is modelled as a rotating, cantilever, tapered, composite Euler–Bernoulli shaft, subjected to a regenerative cutting force. Modal damping loss factors are described based on the viscoelastic constitutive relation of composite combined with an energy approach. The governing equations of the system are obtained by employing Hamilton principle. Galerkin method is used to discretize the partial differential equations of motion. The frequency-domain solution of stability proposed by Altintas and Budak [14] is extended and used to predict the chatter stability of the cutting system. The results reveal the inherent relationship between internal damping instability and cutting chatter. The effects of the geometry parameters of the cutter bar, ply angle, stacking sequences, and internal and external damping are examined.

Effect of controllable magnetic field-induced MRF solidification on chatter suppression of thin-walled parts

Aiming at solving the chattering problem of thin-walled parts, magnetorheological fluid (MRF) was used as phase-change clamping material to study the influence of MRF excitation clamping on the modal parameters of thin-walled parts. In this paper, to clamp the cantilever thin-walled parts firmly and stably, a strong and uniform magnetic field was achieved by designing a yoke-type configuration first. Next, to quantify the clamping effect of MRF, its squeeze stress-strain curves were tested and corresponding elastic squeeze parameters in pre-yield stage were applied on the on thin-walled parts. Then, the influence of MRF clamping on the workpiece mode was researched from simulating results and experimental results. After that, to validate the clamping effect of MRF fixture, reasonable cutting parameters on the thin-walled part were chosen according to the milling chatter stability lobes. By comparing surface roughness, surface topography, and chip type, the clamping effect of MRF fixture is validated. The results indicate that MRF flexible fixture can obviously restrain the machining vibration in milling process and contribute to suppress the machining vibration of thin-walled parts.

3D chatter stability of high-speed micromilling by considering nonlinear cutting coefficients, and process damping

High-speed micromilling can be used to fabricate 3D complex miniature components. The regenerative chatter, which is closely related to machining geometric accuracy, surface quality and tool wear, is a very important topic in micromachining research. In order to predict the high-speed micromilling stability more comprehensively, a micromilling force model was developed, which took into account the nonlinear change of cutting coefficients caused by feed rate, and the process damping effect in the shearing-dominant regimes. The relationship between micromilling force coefficients and feed rate were researched by using the least square and regression analysis method which are suitable to fit the relationship between related variables through experimental data, and ignore the complex internal relationships. The dynamic parameters of tool-machine system were obtained by performing FEM simulation on the entire spindle-holder-tool system. The continuous change of feed rate was first considered into micromilling 3D stability model by analyzing the influence of feed rate on milling force coefficients. Finally, micromilling tests were performed on AL7075 to verify the accuracy of the stability prediction model.

Chatter and Stability Analysis of the Slender Composite Boring Bar with Constrained Damping Layer

This study investigates the chattering stability of the composite boring bar with a constrained damping layer during the deep-hole boring process in depth. Based on the Euler-Bernoulli beam theory, the regenerative chattering linear kinetic model of the composite boring bar with a constrained damping layer was established, and the computational formulas of the rotating speed of the spindle and the corresponding limit cutting depth were derived. By analyzing the chattering stability, the cutting stability lobe curves of the composite boring bar with a constrained damping layer were plotted so as to reveal the effects of the materials of both base layer and constrained layer, the ply angle, the damping composite structure (free or constrained damping structure) and the thickness of various layers on the chattering stability of the boring bar. Through the analysis of dynamic stiffness, the chatter stability analysis theory of a composite boring bar with a constrained damping layer is verified.

Analysis of the Vibration and Chatter Stability of a Tapered Composite Boring Bar

As metal boring bars have low dynamic stiffness, chatter is easily induced during the boring process. Therefore, improvement of the chatter stability is an open problem that requires further study. Though researchers proved that the composite materials suitable for making tapered boring bars can further improve the dynamic stiffness to meet the need of high-speed boring, existing research studies did not study the dynamic characteristics of the tapered composite boring bar comprehensively. In particular, no research has been done about the natural frequency and chatter stability of the composite boring bar under various taper ratios. Therefore, in this paper, a model of a tapered composite boring bar is established based on the Adomian modified decomposition method (AMDM). Second, this paper verifies the effectiveness of the AMDM by using the ANSYS software. Moreover, this paper studies the natural frequency of the boring bar model under various situations. Third, we verify the convergence of chatter stability of the boring bar model. Finally, the chatter stability of the tapered composite boring bar is analyzed comprehensively. The results show that the natural frequency and the chatter stability of the tapered model can be improved by choosing appropriate taper ratio, ply angle, stacking sequences, L/D ratio, T/D ratio, and the carbon composite. The results are helpful for the design of high-quality tapered composite boring bars matching the need of high speed cutting. In particular, these results can provide guidelines for adjusting the cutting speed in CNC boring and can further improve the surface finish of the machined workpieces.

Structural vibration control using delayed state feedback via LMI approach: with application to chatter stability problems

This paper considers the problem of active vibration control in machining processes to prevent dynamic instability and chatter. A method for robust delayed-state feedback control is presented based on Lyapunov–Krasovskii functionals (LKFs). For fast computation and realizability, a partial state feedback approach based on a reduced order model of structural vibration is considered that matches available sensors and captures the main vibratory modes that impact on stability limits. Robustness to neglected dynamics and other model errors are accounted for by a frequency domain description of model uncertainty, augmented with the basic LKF stability condition. The controller synthesis problem is formulated as a set of linear matrix inequality equations that can be solved numerically using convex optimization methods. Evaluations on a hardware-in-the-loop flexible structure test-bed show that feedback controllers optimized via the LKF stability condition provide significant improvements in stability regions compared with optimized PD control and quadratic regulation. The results confirm the methodology as a useful approach for robust chatter control based on combined flexible structure and cutting process models.

Забезпечення вібростійкості процесу розточування однолезовим інструментом на токарному верстаті

Heightening of a chatter stability of boring process at turning is an actual problem. The basic circuit of a dominating vibratory system of process is developed for the theoretical analysis of oscillating processes for boring bars at boring process and the mathematical model of dynamic system of the lathe that allows us to define influence of design data of boring bars on a process of chatter stability is constructed. On the basis of mathematical model with use of transmitting function the influence of a direction of principal axises of rigidity of boring bar-slide elastic system on static characteristic of elastic tool system is determined. Experimental researches of boring bars have given the chance to define their frequency characteristics by a method of harmonic perturbation and to use them at boring process simulation. It is displayed, that ensuring of conditions of vibrational stability of internal turning on machine tools by boring bars can be carried out by a rational choice of their design data taking into account rational orientation of principal axises of rigidity of elastic tool system in relation to a direction of cutting force, a choice of a rational ratio of rigidity on these axes and heightening of damping ability of a cantilever part of boring bar.

Experimental and simulation study on chatter stability region of integral impeller with non-uniform allowance.

In order to accurately improve and predict chatter stability region of machining process, an optimization method of machining process with non-uniform allowance of integral impeller was proposed. The modal parameters of the workpiece process system were obtained using the finite element analysis. Based on the regenerative chatter analysis theory, a limit comparison diagram of the stability with uniform allowance and non-uniform allowance was established. The simulation results showed that the non-uniform allowance natural frequency is about 1.43 times as much as the uniform allowance natural frequency, and the machining system stiffness non-uniform allowance is twice as much as the uniform allowance, while the limit of chatter stability region is increased by 3 times. This article studied uniform allowance and non-uniform allowance of milling chatter stability with experimental method. Tool path for five-axis machining and machine tool simulation based on NX CAM were planned. The comparisons of cutting processing uniform allowance and non-uniform allowance were done, and the surface profile detection of the test part with the three-dimensional scanning was carried out. The experimental results showed that the average optimization rate for manufacturing precision of blade suction surface after optimization and pressure surface was 63.8% and 48.84%. The total experiment showed that this process optimization strategy could effectively improve the stiffness of the integral impeller blade and reduce the cutting chatter of the blade during the cutting process.

An Efficient Third-Order Full-Discretization Method for Prediction of Regenerative Chatter Stability in Milling

The prediction of regenerative chatter stability has long been recognized as an important issue of concern in the field of machining community because it limits metal removal rate below the machine’s capacity and hence reduces the productivity of the machine. Various full-discretization methods have been designed for predicting regenerative chatter stability. The main problem of such methods is that they can predict the regenerative chatter stability but do not efficiently determine stability lobe diagrams (SLDs). Using third-order Newton interpolation and third-order Hermite interpolation techniques, this study proposes a straightforward and effective third-order full-discretization method (called NI-HI-3rdFDM) to predict the regenerative chatter stability in milling operations. Experimental results using simulation show that the proposed NI-HI-3rdFDM can not only efficiently predict the regenerative chatter stability but also accurately identify the SLD. The comparison results also indicate that the proposed NI-HI-3rdFDM is very much more accurate than that of other existing methods for predicting the regenerative chatter stability in milling operations. A demonstrative experimental verification is provided to illustrate the usage of the proposed NI-HI-3rdFDM to regenerative chatter stability prediction. The feature of accurate computing makes the proposed NI-HI-3rdFDM more adaptable to a dynamic milling scenario, in which a computationally efficient and accurate chatter stability method is required.

Unique regenerative chatter in wiper-turning operation with burnishing process Part 2: Experimental verification of predicted generation mechanism, critical stability, and characteristics

In this paper, the predicted generation mechanism, chatter stability, and characteristics of the unique regenerative chatter with the burnishing process in wiper-turning operations are verified experimentally. It was found in the first part of the paper that the vibration regenerates in the burnishing process by the wiper part of the insert causing a novel type of chatter. In this second part, this chatter phenomenon is investigated in an experimental manner to verify its mechanism. The specific burnishing force, which is a gain factor characterizing the burnishing process, is determined by the Hertzian contact law. In addition, the specific cutting force is measured by a cutting test, the compliance of the flexible structure is measured by a hammering test, and the residual compliance is measured by a static indentation test. Then, experiments are conducted where the tilt angle and the feed rate are varied to find the critical stability. The conducted chatter experiments prove that the predicted generation mechanism, critical stability, and characteristics are true.

Broadband pneumatic mass damper for the elimination of workpiece vibrations

This paper proposes a simple damper consisting of a cylindrical weight moving freely within a thin-walled shell to eliminate flexible workpiece vibrations during finish milling. Owing to the air viscosity, the appropriate gap between the weight and shell provides intensive energy dissipation. A theoretical model and a rational damper tuning strategy are presented to provide sufficient efficiency for a wide operating range. Impact and cutting tests confirmed the predicted efficiency, which was higher than that of a particle damper. Increase of workpiece chatter stability by 45 times was obtained. A set of dampers with various masses is designed as an end user product. Examples of industrial applications are presented.