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.     

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.     

Linear analysis of chatter vibration and stability for orthogonal cutting in turning

The productivity of high speed milling operations is limited by the onset of self-excited vibrations known as chatter. Unless avoided, chatter vibrations may cause large dynamic loads damaging the machine spindle, cutting tool, or workpiece and leave behind a poor surface finish. The cutting force magnitude is proportional to the thickness of the chip removed from the workpiece. Many researchers focused on the development of analytical and numerical methods for the prediction of chatter. However, the applicability of these methods in industrial conditions is limited, since they require accurate modelling of machining system dynamics and of cutting forces. In this study, chatter prediction was investigated for orthogonal cutting in turning operations. Therefore, the linear analysis of the single degree of freedom (SDOF) model was performed by applying oriented transfer function (OTF) and \tau decomposition form to Nyquist criteria. Machine chatter frequency predictions obtained from both forms were compared with modal analysis and cutting tests.     

Simulation of turning operations

One of the most important factors affecting the quality and productivity of turning operations is the dynamics of the system. In this study a computer program is developed to simulate turning operations. The program represents turning operations with a tool geometry simulation module, and the discrete transfer functions of machining process and machine tool structure. The discrete transfer functions of the turning operation are determined by dynamic experiments. The developed program is run at different depth of cuts to study the development and finite amplitude vibrations of chatter. The characteristics of the simulated data agree with the results of previous experimental studies. The simulation program is very convenient to study the chatter susceptibility of machine tool, workpiece and tool geometries.     

Generalized dynamic model of metal cutting operations

This paper presents a unified mathematical model which allows the prediction of chatter stability for multiple machining operations with defined cutting edges. The normal and friction forces on the rake face are transformed to edge coordinates of the tool. The dynamic forces that contain vibrations between the tool and workpiece are transformed to machine tool coordinates with parameters that are set differently for each cutting operation and tool geometry. It is shown that the chatter stability can be predicted simultaneously for multiple cutting operations. The application of the model to single-point turning and multi-point milling is demonstrated with experimental results.     

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.     

An active tool holding device

The machine tool industry has to overcome many challenges to produce efficient, high performance and precise machine tools. These requirements are directly from the customers, who want the ability to produce more cost-effective. In order to achieve this, the machine parameters such as the feed rate or the depth of cut of grinding machines are increased. These new parameters affect the dynamic behavior of the machine tool, and in some cases can result in extreme vibrations. These vibrations can generate chatter marks on the workpiece surface or limit the ability to obtain a stable process. This article deals with an active approach to reduce possible vibrations within machine tools. Here the tool holding device of a surface grinding machine has been extended to create an active tool holding device. The active design allows the manipulation of the dynamic behavior of a surface grinding machine, allowing the implementation of a better parameter set.     

Electrohydraulic Active Damping System

A major characteristic of machine tools is the relative dynamic flexibility at the tool centre point. Poorly damped resonance frequencies often cause self-excited vibrations, so called chatter vibrations, which derogate the machined surface and may cause tool breakage. In practice, typically the metal removal rate and therefore the productivity of the machine are reduced, in order to avoid such vibrations. This paper deals with an active damping system for the improvement of the dynamic flexibility of machine tools. The damping system is based on an electrohydraulic actuator, which combines comparatively large forces and a compact design. The control input for the actuator is determined from the acceleration measurement based on the concept of a so-called velocity feedback control. In experimental investigations, the depth of cut could almost be tripled.     

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.     

Suppressing vibration modes of spindle-holder-tool assembly through FRF modification for enhanced chatter stability

Modifying dynamic response of a machine tool is of great importance for chatter mitigation. Tool tip frequency response function (FRF) can be suppressed by capitalizing on the absorber effect due to dynamic interactions among vibration modes of spindle, holder and tool. In this paper, a practical method is presented to modify the system’s FRF by selecting proper dimensions for assembly component without extensive testing. Robustness of the method is demonstrated through simulation and test results. Milling stability tests were also conducted where significant improvements in chatter free Material Removal Rate (MRR) is achieved.     

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.     

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.     

Modeling and identification of tool holder–spindle interface dynamics

The majority of the chatter vibrations in high-speed milling originate due to flexible connections at the tool holder–spindle, and tool–tool holder interfaces. This article presents modeling of contact stiffness and damping at the tool holder and spindle interface. The holder–spindle taper contact is modeled by uniformly distributed translational and rotational springs. The springs are identified by minimizing the error between the experimentally measured and estimated frequency response of the spindle assembly. The paper also presents identification of the spindle's dynamic response with a holder interface, and its receptance coupling with the holder–tool stick out which is modeled by Timoshenko beam elements. The proposed methods allow prediction of frequency-response functions at the tool tip by receptance coupling of tools and holders to the spindle, as well as analyzing the influence of relative wear at the contact by removing discrete contact springs between the holder and spindle. The techniques are experimentally illustrated and their practical use in high speed milling applications is elaborated.     

Dynamics of the arch-type reconfigurable machine tool

Reconfigurable manufacturing systems (RMS) address challenges in modern manufacturing systems arising from product variety and from rapid changes in product demand. This paper considers an arch-type reconfigurable machine tool (RMT) that has been built to demonstrate the basic concepts of RMT design. The arch-type RMT was designed to achieve customized flexibility and includes a passive degree-of-freedom, which allows it to be reconfigured to machine a family of parts. The kinematic and dynamic capabilities of the machine are presented, including the experimental frequency response functions (FRFs) and computed stability lobes of the machine in different configurations. A comparison of FRFs and stability lobes of the arch-type RMT reveals almost similar dynamic characteristics at different reconfiguration positions. These similar characteristics arise because the dominant mode where chatter occurs is due to the spindle–tool–tool holder assembly. Consequently, to ensure consistent dynamic behavior regardless of reconfiguration, a desirable dynamic design feature for RMTs is that the machine's structural frequencies are less dominant than the structural frequencies of the spindle, tool and tool holder.     

A new receptance coupling substructure analysis methodology to improve chatter free cutting conditions prediction

The cutting process stability depends on machine tool dynamics that is strongly influenced by the tool. Receptance coupling substructure analysis (RCSA) can be used to estimate the tool tip dynamic compliance and consequently the chatter free cutting conditions when the machine is equipped with a tool that has not been previously tested. This methodology can be particularly useful on real shop–floors where a lot of different tool–tool holder configurations are generally used. RCSA typically combines experimental dynamic compliance measurements performed on a machine equipped with a selected tool and the finite element (FE) models of both the already tested tool and the new ones. This paper presents a new receptance coupling substructure analysis (RCSA) approach that overcomes the drawbacks in the estimation of the receptances that contain rotational and moment contributes. This indeed often limits the accuracy of the RCSA techniques presented in other scientific works. The proposed formulation allows to better estimate both the matrices of receptances of the spindle–tool holder assembly and the tool–tool holder connection stiffness. Those quantities are used, together with the FE model of the new tool, to predict the unknown tool tip dynamic compliance. Some useful guidelines to implement the proposed RCSA are also defined: they allow to manage the procedure accuracy considering the experimental methodology typically used to measure dynamic compliances. The proposed innovative RCSA is experimentally tested and validated.     

A new perspective on the stability study of centerless grinding process

Regenerative chatter is one of the most complex dynamic processes in machine tools. It is characterized by the presence of self-excited vibrations during machining, limiting the achievable tolerances in the workpieces. In order to predict the set-up conditions that produce these vibrations, it is necessary to model the regenerative mechanism responsible of their appearance accurately, so that the system stability can be studied solving the characteristic equation of the chatter loop. Although the dynamic behavior of machining processes like milling, turning or drilling is governed by a time delayed differential equation with one time delay term, a very particular problem is presented in centerless grinding. In this process, in addition to the dynamic instabilities, geometric instabilities must be analyzed, which are another important factors limiting the workpiece tolerances and lead to three time delay terms in the modeling procedure. This fact complicates its study remarkably, and the resolution of the characteristic roots of the dynamic process of these kinds of machines has not been tackled in the specialized literature as extensively as in other machining processes, being this field a challenging research line. According to this, in this paper an original and efficient method is presented to solve the roots of the characteristic equation of the centerless grinding process, based on the application of the root locus method. The main features of the proposed procedure are its ability to obtain the solutions accurately and that it is capable of determining the origin of the instabilities, so it constitutes a powerful tool to predict machine response for different set-up conditions. These interesting properties are demonstrated through the simulation results presented in this paper.     

Active control of high frequency chatter with machine tool feed drives in turning

This paper presents a new active vibration control strategy to mitigate high frequency regenerative chatter vibrations using machine tool feed drives. Rather than modal damping, proposed approach aims to control regenerative process dynamics to shape the Stability Lobe diagram (SLD) and attain higher material removal rates. The controller is designed as a feedback filter whose parameters are optimized to compensate regeneration. The proposed strategy is applied to actively control orthogonal (plunge) turning dynamics where >2.5 [kHz] chatter vibrations are suppressed by a fast tool servo (FTS) drive system. Stability lobes are shaped locally to reach up to 4x higher material removal rates.     

Prediction of machining chatter based on FEM simulation of chip formation under dynamic conditions

Machining chatter is an inherently nonlinear phenomenon that is affected by many parameters such as cutting conditions, tool geometry e.g., nose radius and clearance angle and frictional conditions at the tool/workpiece interface. Models for chatter prediction often ignore nonlinearities or introduce them through simple models for friction and geometry. In particular, the effect of chip–tool interaction on the occurrence of chatter is not investigated thoroughly. This paper presents a novel approach for prediction of chatter vibration and for investigation of the effects of various conditions on the onset of chatter. This approach uses finite element simulation to investigate the inter-relationship between the chatter vibration and the chip formation process. Simulation of chip formation is combined with dynamic analysis of machine tool to determine the interaction between the two phenomena. Mesh adaptation technique is used to move the tool inside the workpiece to form the chip, while a flexible tool is used to allow the tool to vibrate under variable loading conditions. By repeating the simulations under various widths of cut, it is shown that the onset of chatter can be detected, and the simulation is able to realistically predict various phenomena observed in actual machining process such as variation of shear angle and the increase of stability at lower speeds known as process damping. The stability map obtained from simulations is compared with experimental data attained through orthogonal cutting tests. Reasonable agreement observed between the two sets of results demonstrates the effectiveness of the simulation approach.     

Total ballbar dynamic tests for five-axis CNC machine tools

The linear and rotary axes of a five-axis machine tool are driven simultaneously to generate a specified tool position and orientation in workpiece coordinates. It is crucial that these servo-controlled axes are of balanced dynamics to achieve high tracking accuracy. In this paper, ballbar circular tests for all possible combinations of linear and rotary axes of a five-axis machine tool are investigated and total ballbar dynamic tests are proposed. Through the relational arrangement of the test sequence, the total ballbar dynamic tests can be employed to identify dynamic differences between linear and rotary axes. More importantly, the velocity gains of the position control loops of all servo-controlled linear and rotary axes can be tuned synchronously to eliminate gain mismatch errors. Experimental results have proved the effectiveness of the new methods.     

Modelling vibration transmission in the mechanical and control system of a precision machine

The relative vibration between tool and workpiece factors significantly to the performance of a precision machine. This paper develops a model for predicting the vibration transmission from two major excitation sources, ground vibration and fluid bearing force, to the tool and the workpiece position through the mechanical and control system of a precision machine. We synthesised the frequency response functions obtained from a finite element analysis of the machine to create transmissibility matrices that define the dynamic behaviours of the electromechanical system. The validity of the developed model was checked by comparing the measured relative vibrations to the results calculated from the measured excitations.