Prediction of regenerative chatter by modelling and analysis of high-speed milling

High-speed milling is widely used in the manufacturing industry. For the efficiency of the milling process, high demands on the material removal rate and the surface generation rate are posed. The process parameters, determining these two rates, are restricted by the occurrence of regenerative chatter. Chatter is an undesired instability phenomenon, which causes both a reduced product quality and rapid tool wear. In this paper, the milling process is modelled, based on dedicated experiments on both the material behaviour of the workpiece material and the machine dynamics. These experiments show that both the material properties and the machine dynamics are dependent on the spindle speed. Furthermore, a method for the prediction of the chatter boundaries is proposed and applied in order to predict the chatter boundaries as a function of process parameters, such as spindle speed and depth-of-cut, for spindle speed varying material and machine parameters. Finally, experiments are performed to estimate these chatter boundaries in practice. The modelled chatter boundaries are compared to the experimental results in order to validate the model and the stability analysis.     

Modelling and simulation of chatter in milling using a predictive force model

A predictive time domain chatter model is presented for the simulation and analysis of chatter in milling processes. The model is developed using a predictive milling force model, which represents the action of milling cutter by the simultaneous operations of a number of single-point cutting tools and predicts the milling forces from the fundamental workpiece material properties, tool geometry and cutting conditions. The instantaneous undeformed chip thickness is modelled to include the dynamic modulations caused by the tool vibrations so that the dynamic regeneration effect is taken into account. Runge–Kutta method is employed to solve the differential equations governing the dynamics of the milling system for accurate solutions. A Windows-based simulation system for chatter in milling is developed using the predictive model, which predicts chatter vibrations represented by the tool-work displacements and cutting force variations against cutter revolution in both numerical and graphic formats, from input of tool and workpiece material properties, cutter parameters, machine tool characteristics and cutting conditions. The system is verified with experimental results and good agreement is shown.     

On the mechanics of chip formation in Ti–6Al–4V turning with spindle speed variation

Titanium alloys are hard-to-cut materials and need to be machined at relatively low cutting speeds with obvious negative consequences on the profitability of machining.In order to enhance material removal rate (MRR), a strategy that relies on higher depths of cut could be chosen if vibrational issues due to regenerative chatter did not occur.A lot of research was done to suppress regenerative chatter without detrimental effects on productivity. One of the most interesting chatter suppression methods, mainly due to its flexibility and relative ease of implementation, is spindle speed variation (SSV), which consists in a continuous modulation of the nominal cutting speed. Sinusoidal spindle speed variation (SSSV) is a specific technique that exploits a sinusoidal law to modulate the cutting speed.The vast scientific literature on SSV was mainly focused on cutting process stability issues fully neglecting the study of the mechanics of chip formation in SSV machining. The aim of this work is to fill this gap: thus, finite element method (FEM) models of Ti–6Al–4V turning were setup to simulate both SSSV and constant speed machining (CSM). The models consider both the micro-geometry of the insert and the coating. Numerical results were experimentally validated on dry turning tests of titanium tubes exploiting the experimental assessment of cutting forces, cutting temperatures and chip morphology. Tool–chip contact pressure, tool engagement mechanism and the thermal distribution in the insert are some of the analysed numerical outputs because they cannot be easily assessed by experimental procedures. These quantities were useful to compare thermo-mechanical loads of the insert both in CSM and SSSV machining: it was observed that the loads significantly differ. Compared to CSM, the modulation of the cutting speed involves a higher tool–chip contact pressure peak, a higher maximum temperature and higher temperature gradients that could foster the main tool wear mechanisms.     

Maximizing Chatter Free Material Removal Rate in Milling through Optimal Selection of Axial and Radial Depth of Cut Pairs

Chatter vibrations in milling, which develop due to dynamic interactions between the cutting tool and the workpiece, result in reduced productivity and part quality. Several stability models have been considered in previous publications, where mostly the stability limit in terms of axial depth of cut is emphasized for chatter free machining. In this paper, it is shown that, for the maximization of chatter free material removal rate, radial depth of cut is of equal importance. A method is proposed to determine the optimal combination of depths of cut, so that chatter free material removal rate is maximized. The application of the method is demonstrated on a pocketing example where significant reduction in the machining time is obtained using the optimal depths. The procedure can easily be integrated to a CAD/CAM system or a virtual machining environment in order to identify the optimal milling conditions.     

A closed-form approach for identification of dynamical contact parameters in spindle–holder–tool assemblies

Accurate identification of contact dynamics is very crucial in predicting the dynamic behavior and chatter stability of spindle–tool assemblies in machining centers. It is well known that the stability lobe diagrams used for predicting regenerative chatter vibrations can be obtained from the tool point frequency response function (FRF) of the system. As previously shown by the authors, contact dynamics at the spindle–holder and holder–tool interfaces as well as the dynamics of bearings affect the tool point FRF considerably. Contact stiffness and damping values alter the frequencies and peak values of dominant vibration modes, respectively. Fast and accurate identification of contact dynamics in spindle–tool assemblies has become an important issue in the recent years. In this paper, a new method for identifying contact dynamics in spindle–holder–tool assemblies from experimental measurements is presented. The elastic receptance coupling equations are employed in a simple manner and closed-form expressions are obtained for the stiffness and damping parameters of the joint of interest. Although this study focuses on the contact dynamics at the spindle–holder and holder–tool interfaces of the assembly, the identification approach proposed in this paper might as well be used for identifying the dynamical parameters of bearings, spindle–holder interface and as well as other critical joints. After presenting the mathematical theory, an analytical case study is given for demonstration of the identification approach. Experimental verification is provided for identification of the dynamical contact parameters at the holder–tool interface of a spindle–holder–tool assembly.     

On Stability and Dynamics of Milling at Small Radial Immersion

Stability and dynamics of milling at small radial immersion are investigated. Stability charts are predicted by the Semi Discretization method. Two types of instability are predicted corresponding to quasiperiodic and periodic chatter. The quasiperiodic chatter lobes are open and distributed along the spindle speed axis only, while the periodic chatter lobes are closed curves distributed in the plane of spindle speed and depth of cut. Experiments confirm the stability predictions, revealing the two principal types of chatter, the bounded periodic chatter lobes, and some special chatter cases. The recorded tool deflections in these cutting regimes are studied. The experiments also show that the modal properties of a slender tool may depend on spindle speed.     

The effect of tool geometry on regenerative instability in ultrasonic vibration cutting

Ultrasonic vibration cutting as a cutting process has been widely used in the precision machining of difficult-to-cut materials due to an enhanced cutting stability and increased productivity. The authors' previous researches have shown that chatter vibration prediction is made possible by the suggested cutting model. This paper is an attempt to determine cutting parameters based on regenerative chatter prediction in order to facilitate the machining objectives of high accuracy, high efficiency and low cost in ultrasonic vibration cutting. The machinability of SCM440 steel, called typical hardened steel, is investigated theoretically and experimentally. The cutting model is developed by introducing an experimental cutting database of SCM440 steel. The simulation and experimental results show that the workpiece material parameter has a direct influence on the occurrence of regenerative chatter. In order to achieve the chatter-suppressing dynamics in hard ultrasonic vibration cutting, a stability diagram is predicted based on the simulated work displacement for tool geometry changing. The stability diagram indicates that the regions of the chatter-suppressing dynamics expand with increasing tool rake angle and decreasing tool clearance angle. It is also found from the predictive results that regenerative chatter can be suppressed by a change of tool geometry. The determined tool geometry with the aid of the computer simulation is demonstrated through actual data of ultrasonic vibration cutting. By the use of the designed tool geometry, a good experimental result is achieved.     

Generalized modeling of drilling vibrations. Part I: Time domain model of drilling kinematics, dynamics and hole formation

This two part paper presents a comprehensive exercise in modeling dynamics, kinematics and stability in drilling operations. While Part II focuses on the chatter stability of drilling in frequency domain, Part I presents a three-dimensional (3D) dynamic model of drilling which considers rigid body motion, and torsional–axial and lateral vibrations in drilling, and resulting hole formation. The model is used to investigate: (a) the mechanism of whirling vibrations, which occur due to lateral drill deflections; (b) lateral chatter vibrations; and (c) combined lateral and torsional–axial vibrations. Mechanistic cutting force models are used to accurately predict lateral forces, torque and thrust as functions of feedrate, radial depth of cut, drill geometry and vibrations. Grinding errors reflected on the drill geometry are considered in the model. A 3D workpiece, consisting of a cylindrical hole wall and a hole bottom surface, is fed to the rotating drill while the structural vibrations are excited by the cutting forces. The mechanism of whirling vibrations is explained, and the hole wall formation during whirling vibrations is investigated by imposing commonly observed whirling motion on the drill. The time domain model is used to predict the cutting forces and frequency content as well as the shape of the hole wall, and how it depends on the amplitude and frequency of the whirling vibration. The model is also used to predict regenerative, lateral chatter vibrations. The influence of pilot hole size, spindle speed and torsional–axial chatter on lateral vibrations is observed from experimental cutting forces, frequency spectra and shows good similarity with simulation results. The effect of the drill–hole surface contact during drilling is discussed by observing the discrepancies between the numerical model of the drilling process and experimental measurements.     

Chatter suppression in micro end milling with process damping

Micro milling utilizes miniature micro end mills to fabricate complexly sculpted shapes at high rotational speeds. One of the challenges in micro machining is regenerative chatter, which is an unstable vibration that can cause severe tool wear and breakage, especially in the micro scale. In order to predict chatter stability, the tool tip dynamics and cutting coefficients are required. However, in micro milling, the elasto-plastic nature of micro machining operations results in large process damping in the machining process, which affects the chatter. We have used the equivalent volume interface between the tool and the workpiece to determine the process damping parameter. Furthermore, the accurate measurement of the tool tip dynamics is not possible through direct impact hammer testing. The dynamics at the tool tip is indirectly obtained by employing the receptance coupling method, and the mechanistic cutting coefficients are obtained from experimental cutting tests. Chatter stability experiments have been performed to examine the proposed chatter stability model in micro milling.     

A study of cutting process stability of a boring bar with active dynamic absorber

In this paper, the use of an active dynamic absorber to suppress machine tool chatter in a boring bar is studied. The vibrations of the system are reduced by moving an absorber mass using an active device such as an piezoelectric actuator, to generate an inertial force that counteracts the disturbance acting on the main system.An equivalent lumped mass model of a boring bar with active dynamic absorber is considered. A cutting process model that considers the dynamic variation of shear and friction angle, that causes self-excited chatter during the cutting process, is applied to the lumped mass model. The theory of regenerative chatter is also applied to the model. Stability boundaries have been calculated for maximum permissible width of cut as a function of cutting speed. A comparison of the boundaries for chatter-free cutting operation of a plain boring bar, a boring bar with passive tuned dynamic absorber and a boring bar with active dynamic absorber is provided in this paper. The comparison shows that a substantial increase in the maximum permissible width of cut for stable cutting operation, over a range of cutting speeds, is obtained for a boring bar equipped with an active dynamic absorber.     

An active system of reduction of vibrations in a centerless grinding machine using piezoelectric actuators

Centerless grinding has been extensively used in production engineering to produce accurate cylindrical parts together with high productivities. On the other hand, regenerative chatter vibrations are one of the major problems that limit the ability to produce round workpieces. This constraint can be solved selecting proper machine setup conditions, which still largely relies on a trial and error method, and sometimes this approach is not optimum in a productivity sense. This paper shows a novel method to reduce chatter vibrations in a centerless grinding machine using actively controlled piezoelectric actuators. A simplified model of the machine is used to simulate the behavior of several commercially available piezoelectric actuators in two different locations of the machine. Based on these simulations, a selection of proper actuators and their optimal location is obtained and the control system is implemented experimentally. Experimental results show that the control strategy provides a stabilizing effect on chatter. Thus, the viability of using piezoelectric actuators as active components is demonstrated, providing an important advance in the knowledge of chatter control in centerless grinding machines.     

An automatic spindle speed selection strategy to obtain stability in high-speed milling

Chatter vibration problems arise during machining. This paper aims to produce a strategy that can detect the emergence of chatter so that subsequently, in accordance with the lobe on the stability diagram where the process is located, the proper strategy may be determined, either by taking the machine to a stable spindle speed or causing continuous variation in spindle speed. The effectiveness of this strategy is contrasted for a number of different cases, using both simulation and experimental testing. The context targeted by the strategy is a high-speed mill roughing operation for cases of vibration arising on the headstock/cutting tool unit, when high material removal rates (MRR) must be maintained. Industrial implementation of the strategy and the chatter detection and diagnosis algorithm is carried out using a portable digital assistant (PDA).     

Receptance coupling for tool point dynamic prediction by fixed boundaries approach

The material removal capability of machines is partially conditioned by self-excited vibrations, also known as chatter. In order to predict chatter free machining conditions, dynamic transfer function at the tool tip is required. In many applications, such as high-speed machining (HSM), the problematic modes are related to the flexibility of the tool, and experimental calculation of the Frequency Response Function (FRF) should be obtained considering every combination of tool, toolholder and machine. Therefore, it is a time consuming process which disturbs the production. The bibliography proposes the Receptance Coupling Substructure Analysis (RCSA) to reduce the amount of experimental tests. In this paper, a new approach based on the calculation of the fixed boundary dynamic behavior of the tool is proposed. Hence, the number of theoretical modes that have to be considered is low, instead of the high number of modes required for the models presented up today. This way, the Timoshenko beam theory can be used to obtain a fast prediction. The accuracy of this new method has been verified experimentally for different tools, toolholders and machines.     

Theoretical-experimental modeling of milling machines for the prediction of chatter vibration

Productivity of high speed milling operations can be seriously limited by chatter occurrence. Chatter vibrations can imprint a poor surface finish on the workpiece and can damage the cutting tool and the machine. Chatter occurrence is strongly affected by the dynamic response of the whole system, i.e. the milling machine, the tool holder, the tool, the workpiece and the workpiece clamping fixture. Tool changes must be taken into account in order to properly predict chatter occurrence. In this study, a model of the milling machine-tool is proposed: the machine frame and the spindle were modeled by an experimentally evaluated modal model, while the tool was modeled by a discrete modal approach, based on the continuous beam shape analytical eigenfunctions. A chatter identification technique, based on this analytical-experimental model, was implemented. Tool changes can be easily taken into account without requiring any experimental tests. A 4 axis numerically controlled (NC) milling machine was instrumented in order to identify and validate the proposed model. The milling machine model was excited by regenerative, time-varying cutting forces, leading to a set of Delay Differential Equations (DDEs) with periodic coefficients. The stability lobe charts were evaluated using the semi-discretization method that was extended to n>2 degrees of freedom (dof) models. The stability predictions obtained by the analytical model are compared to the results of several cutting tests accomplished on the instrumented NC milling machine.     

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.     

Chatter stability of a slender cutting tool in turning with tool wear effect

An analysis of the chatter behavior for a slender cutting tool in turning in the presence of wear flat on the tool flank is presented in this research. The mechanism of a self-excited vibration development process with tool wear effect is studied. The components contributing to the forcing function in the turning vibration dynamics are analyzed in the context of cutting force and contact force. A comparison of the chatter stability for a fresh cutting tool and a worn cutting tool is provided. Stability plots are presented to relate width of cut to cutting velocity in the determination of chatter stability. Machining experiments at various conditions were conducted to identify the characteristic parameters involved in the vibration system and to identify the analytical stability limits. The theoretical result of chatter stability agrees qualitatively with the experimental result concerning the development of chatter stability model with tool wear effect.     

Dynamic simulation of boring process

This article presents a model to simulate the dynamics of boring process. In boring operations the boring bar should be long and slender; therefore it is easily subjected to vibrations. Tool vibrations result in reduced tool life, poor surface finish and may also introduce chatter. Hence, predicting the vibrational behavior of boring process for certain cutting conditions and tool work-piece properties is of great importance. The proposed method models the cutting tool geometry by B-spline parametric curves. By using B-spline curves it is possible to simulate different tool geometries with a single approach. B-spline curves also enable the modeling of the kinematics of chip formation for different tool work-piece engagement conditions with a single formulation. The boring bar has been modeled by the Euler–Bernoulli beam theory. The simulation process has been implemented with MATLAB. The algorithm consists of different computational modules that are interconnected by a main program. Experimental machining tests have been conducted to verify the validity of the proposed model. Proposed dynamic models have been able to predict the dynamic cutting force components and vibration frequencies with less than 15% deviation. The proposed model has been also able to predict the chatter onset correctly.     

Optimization of multiple tuned mass dampers to suppress machine tool chatter

Chatter is more detrimental to machining due to its instability than forced vibrations. This paper presents design and optimal tuning of multiple tuned mass dampers (TMDs) to increase chatter resistance of machine tool structures. Chatter free critical depth of cut of a machine is inversely proportional to the negative real part of frequency response function (FRF) at the tool–workpiece interface. Instead of targeting reduction of magnitude, the negative real part of FRF of the machine is reduced by designing single and multiple TMD systems. The TMDs are designed to have equal masses, and their damping and stiffness values are optimized to improve chatter resistance using minimax numerical optimization algorithm. It is shown that multiple TMDs need more accurate tuning of stiffness and natural frequency of each TMD, but are more robust to uncertainties in damping and input dynamic parameters in comparison with single TMD applications. The proposed tuned damper design and optimization strategy is experimentally illustrated to increase chatter free depth of cuts.     

Detection of chatter vibration in end milling applying disturbance observer

Suppression of chatter vibration is required to improve the machined surface quality and enhance tool life. For monitoring the chatter vibrations, additional sensors such as acceleration sensors are generally used, which results in high costs and low reliability of the machine tools. In this study, a novel in-process method to detect chatter vibrations in end milling is developed on the basis of a disturbance observer theory. The developed system does not require any external sensors because it uses only the servo information of the spindle control system. Self-excited and forced chatter vibrations are successfully detected.     

The feasibility of eigenstructure assignment for machining chatter control

The eigenstructure assignment algorithm is proposed for controlling machining chatter by changing the response of the machine tool structure to dynamic cutting forces through the change of its modal properties so that the interaction between the tool and workpiece can be altered. The determination of the desired modal shapes is derived from a concept similar to gain scheduling in adaptive control system theory. By using computer simulations, the desired eigenstructure of the machine tool structure for different cutting conditions is determined and used to form the scheduling table. The gain matrix is adjusted according to the scheduling table and cutting conditions. It was found from experimental results that by changing the principal direction of the machine tool structure, the machining system could be stabilized and that the use of the proper eigenstructure to suppress machine tool chatter could significantly increase the material removal rate. Simulations have shown that the responses of the controlled machining system have been altered from unstable to stable, proving the feasibility of the proposed chatter control concept.