Regenerative Machine Tool Chatter Research Articles

On process damping induced by vibration-dependency of cutting direction in milling

The process damping effect is analyzed for regenerative machine tool chatter in milling via a velocity-dependent cutting force model. This model takes into account that the effective cutting direction depends on the vibrations of the machine tool-workpiece system, which modifies the effective rake angle, the chip thickness, and the cutting force. The model was originally introduced for turning operations where it results in a process damping term that improves the stability of metal cutting at low cutting speeds. Now this model is extended to milling. It is shown that the vibration-dependency of the cutting direction induces a time-periodic process damping term that is negative when the radial immersion is low. This decreases the stability at low cutting speeds, thus the low-speed stability improvement phenomenon in low radial immersion milling can be explained by extended process damping models only.

Spectral element method for stability analysis of milling processes with discontinuous time-periodicity

This paper presents an application of the spectral element method for the stability analysis of regenerative machine tool chatter models in milling operations. An extension of the spectral element method is introduced in order to handle the discontinuities in the cutting force in an efficient way. The efficiency of the method is demonstrated on some well-known machine tool chatter models taken from the literature. Efficiency is characterized by the computational time, the convergence of the stability boundaries, and the convergence of critical characteristic multipliers. Results show that compared to the most widespread methods in machining literature, the spectral element method provides significant improvements in computational time while maintaining high accuracy levels.

Estimation of the Bistable Zone for Machining Operations for the Case of a Distributed Cutting-Force Model

Regenerative machine tool chatter is investigated for a single-degree-of-freedom model of turning processes. The cutting force is modeled as the resultant of a force system distributed along the rake face of the tool, whose magnitude is a nonlinear function of the chip thickness. Thus, the process is described by a nonlinear delay-differential equation, where a short distributed delay is superimposed on the regenerative point delay. The corresponding stability lobe diagrams are computed and are shown numerically that a subcritical Hopf bifurcation occurs along the stability boundaries for realistic cutting-force distributions. Therefore, a bistable region exists near the stability boundaries, where large-amplitude vibrations (chatter) may arise for large perturbations. Analytical formulas are obtained to estimate the size of the bistable region based on center manifold reduction and normal form calculations for the governing distributed-delay equation. The locally and globally stable parameter regions are computed numerically as well using the continuation algorithm implemented in dde-biftool. The results can be considered as an extension of the bifurcation analysis of machining operations with point delay.

State-dependent distributed-delay model of orthogonal cutting

In this paper, we present a model of turning operations with state-dependent distributed time delay. We apply the theory of regenerative machine tool chatter and describe the dynamics of the tool-workpiece system during cutting by delay differential equations. We model the cutting force as the resultant of a force system distributed along the rake face of the tool, which results in a short distributed delay in the governing equation superimposed on the large regenerative delay. According to the literature on stress distribution along the rake face, the length of the chip–tool interface, where the distributed cutting force system is acting, is function of the chip thickness, which depends on the vibrations of the tool-workpiece system due to the regenerative effect. Therefore, the additional short delay is state dependent. It is shown that involving state-dependent delay in the model does not affect linear stability properties, but does affect the nonlinear dynamics of the cutting process. Namely, the sense of the Hopf bifurcation along the stability boundaries may turn from sub- to supercritical at certain spindle speed regions.

On the Effect of Distributed Regenerative Delay on the Stability Lobe Diagrams of Milling Processes

Regenerative machine tool chatter is investigated for milling operations with helical tools. The stability of a two-degrees-of-freedom milling model is analyzed, where the cutting-force is modeled as a force system distributed along the rake face of the tool. Introducing a distributed force system instead of a concentrated cutting-force results in an additional short, periodically varying distributed delay in the governing equations of the system. It is shown that the additional delay significantly affects the stability of the machining operation, especially at low spindle speeds. This phenomenon is referred to as the short regenerative effect, and is studied by computing the stability lobe diagrams of milling operations via the semi-discretization technique. The sensitivity of the stability charts to the shape of the force distribution and the contact length between the chip and tool is investigated.

Numerical Solution of Tuned Mass Dampers for Optimum Milling Chatter Suppression

The most common tunings for the TMD in the field of vibration suppression areH∞andH2. However, regenerative machine tool chatter is a complex problem with many variations, which therefore requires a new tuning for the optimum chatter suppression. The real part based tuning is investigated numerically by employing the minimax numerical approach, which aims to maximize the minimum real part of the primary structure under the harmonic excitation. The performances of multiple TMDs system are discussed. A face milling case is employed to verify the benefits of multiple TMDs in increasing the chatter free depth of cut. It is concluded that multiple TMDs configuration are more effective than single TMD in chatter control.

Delay differential equations via the matrix lambert w function and bifurcation analysis: application to machine tool chatter

In a turning process modeled using delay differential equations (DDEs), we investigate the stability of the regenerative machine tool chatter problem. An approach using the matrix Lambert W function for the analytical solution to systems of delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis. The Lambert W function, known to be useful for solving scalar first-order DDEs, has recently been extended to a matrix Lambert W function approach to solve systems of DDEs. The essential advantages of the matrix Lambert W approach are not only the similarity to the concept of the state transition matrix in lin ear ordinary differential equations, enabling its use for general classes of linear delay differential equations, but also the observation that we need only the principal branch among an infinite number of roots to determine the stability of a system of DDEs. The bifurcation method combined with Sturm sequences provides an algorithm for determining the stability of DDEs without restrictive geometric analysis. With this approach, one can obtain the critical values of delay, which determine the stability of a system and hence the preferred operating spindle speed without chatter. We apply both the matrix Lambert W function and the bifurcation analysis approach to the problem of chatter stability in turning, and compare the results obtained to existing methods. The two new approaches show excellent accuracy and certain other advantages, when compared to traditional graphical, computational and approximate methods.

Model-based chatter stability prediction for high-speed spindles

The prediction of stable cutting regions is a critical requirement for high-speed milling operations. These predictions are generally made using frequency response measurements of the tool/holder/spindle set, obtained from a non-rotating spindle. However, significant changes in system dynamics occur during high-speed rotation. In this paper, a dynamic model of a high-speed spindle-bearing system is elaborated on the basis of rotor dynamics predictions, readjusted with respect to experimental modal identification. Variations in dynamic behaviour according to speed range are then investigated and determined with accuracy. Dedicated experiments are carried out in order to confirm model results. By integrating the proposed speed-dependant transfer function into the chatter vibration stability approach of Budak–Altintas [S. Tobias, W. Fishwick, Theory of regenerative machine tool chatter, The Engineer February (1958)] a dynamic stability lobes diagram is predicted. The proposed method enables a new stability lobes diagram to be established that takes into account the effect of spindle speed on dynamic behaviour. Significant variations are observed and allow the accurate prediction of cutting conditions. Finally, experiments are performed in order to validate chatter boundary predictions in practice. The proposed modelling approach can also be used to qualify a spindle design in a given machining process and can easily be extended to other types of spindle.

Use of finite element structural models in analyzing machine tool chatter

It is widely accepted and well-documented that regenerative machine tool chatter is due to system instability. It is also well-known that machining system stability depends on both structural parameters and cutting process parameters. This paper focuses on the use of structural finite element (FE) models in the stability analysis of turning operations. The method presented allows for inclusion of both cutting tool and workpiece flexibility in the analysis. A structural model representing the machine tool system is created using the commercial FE code, ANSYS. This structural model can include practically any degree of detail desired. The structural model is then imported into a stand-alone FORTRAN program, which incorporates a cutting process model, and calculates the lobed borderline of stability. Numerical examples are provided.

A new perspective and analysis for regenerative machine tool chatter

The paper contains a practical perspective on regenerative machine tool chatter. Chatter is a well known phenomenon, occurrence of which is undesired in manufacturing. Aggressive machining conditions, in the sense of removing more metal rapidly, usually cause chatter. In most cases, these conditions can be determined a priori to the operation. A chatter stability study and its reasoning based on root locus plot analysis of time delayed systems is presented as a new and practical perspective in the field. At the junction of root locus and chatter concepts an area of particular interest to the authors arises: a new method for active vibration suppression, the Delayed Resonator. It is an active vibration absorber tuning of which is achieved utilizing a simple time delayed feedback. The cross linking between the Delayed Resonator study and the subject matter, machine tool chatter, is exciting to share. This is the primary motivation in pursuing this study. One of the highlights of the work appears at the phenomenon called Dual Frequency Delayed Resonator. This feature has been conjectured in the literature using the well known “stability lobes”, but never discussed with detail.

A Graphical Analysis of Regenerative Machine Tool Instability

A graphical method for the investigation of regenerative machine tool chatter is presented. The method is based on the harmonic response locus of the machine tool structure and allows the determination of the stable and unstable cutting speed ranges. The chip thickness variation effect as well as the penetration rate effect are taken into consideration. The method is illustrated by a number of examples relating to drilling or spot facing chatter arising on a radial drilling machine. The effects of mode interaction and of the penetration rate on the stability and on the variation of the chatter frequency are discussed. A critical assessment of the method is presented, in comparison with other methods available.

Ceramic tooling. Use of sintered-oxide tools for heavy-duty metal removal: Developments in production turning methods at Alvis, Ltd. : Aircraft production, v. 20, July 1958, p. 274–282

The prediction of stable cutting regions is a critical requirement for high-speed milling operations. These predictions are generally made using frequency response measurements of the tool/holder/spindle set, obtained from a non-rotating spindle. However, significant changes in system dynamics occur during high-speed rotation. In this paper, a dynamic model of a high-speed spindle-bearing system is elaborated on the basis of rotor dynamics predictions, readjusted with respect to experimental modal identification. Variations in dynamic behaviour according to speed range are then investigated and determined with accuracy. Dedicated experiments are carried out in order to confirm model results. By integrating the proposed speed-dependant transfer function into the chatter vibration stability approach of Budak–Altintas [S. Tobias, W. Fishwick, Theory of regenerative machine tool chatter, The Engineer February (1958)] a dynamic stability lobes diagram is predicted. The proposed method enables a new stability lobes diagram to be established that takes into account the effect of spindle speed on dynamic behaviour. Significant variations are observed and allow the accurate prediction of cutting conditions. Finally, experiments are performed in order to validate chatter boundary predictions in practice. The proposed modelling approach can also be used to qualify a spindle design in a given machining process and can easily be extended to other types of spindle.