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.     

Predicting the dynamic behaviour of torus milling tools when climb milling using the stability lobes theory

This paper investigates stability and dynamic behaviour of torus tool in climb milling on 5 positioned axes. The stability lobes theory is used to enable stable cutting conditions to be chosen. As the adaptation of such a theory to complex milling configurations is a difficult matter, new methods are presented to identify the dynamic parameters. Tool dynamic characteristics (stiffness and natural pulsation) are determined with an original coupled calculations-tests method. Start and exit angles are computed exactly using an original numerical model. A sensitivity analysis highlights the influence of machining parameters on stability of climb milling. This shows that a third region of “potential instability” must be taken into account in plotting stability lobes, due to the uncertainty of prediction due to modelling and identification of parameters. The results were validated experimentally with an innovative approach, especially through the use of high-speed cameras. Analysis of vibrations and the surface roughness allowed the analytical model to be verified so as to optimise the inclination of the tool on the surface.     

基于模糊推理自校正控制的直接驱动进给系统稳定性分析

直线电机直接驱动进给系统是实现数控机床进给高速化的主要形式，但加工过程中切削力甚至运动部件质量的变化都是系统的干扰，易引起系统不稳定和定位精度下降。离线模糊推理、在线对控制系统实现自校正的控制方法能提高系统的抗干扰能力，并具有良好的实时性。为了研究系统的稳定性，本文介绍了这种基于模糊推理自校正控制的直接驱动进给系统稳定性分析方法，为同类系统设计提供理论参考。     

Rounding and stability in centreless grinding

The paper presents a method for selecting grinding conditions and assists researchers to understand the complex dynamics of centreless grinding. It overcomes the problem of deriving dynamic stability charts for particular geometries and difficulty of interpreting such charts to adjust work speed to overcome lobing problems. Classic dynamic stability charts cannot assess stability levels in proximity to integer lobes, a particular problem for centreless grinding. The paper overcomes these problems employing a simply calculated new dynamic stability parameter A_dyn. The new parameter A_dyn simplifies the optimisation of grinding variables including set-up geometry and work speed in relation to resonant frequency. It is difficult to interpret relative dynamic stability of centreless grinding by classical methods for different set-ups, work speeds and numbers of lobes. A new method is employed in this paper based on the well-established Nyquist stability criterion. The dynamic stability parameter A_dyn is based on the real part of the characteristic equation. It is easily computed and presented on a single chart for particular work speed, resonant frequency and for a wide range of numbers of lobes. The method clearly shows the effect on rounding strength both for stable and unstable conditions. Most authors computing dynamic stability charts have ignored positive down boundaries and negative up boundaries showing a lack of a comprehensive treatment for a situation that conflicts with recommendations for conventional positive up boundaries. The new method simplifies this problem.Small differences in set-up geometry and work speed selection can be easily assessed. The new method can be used as a diagnostic tool for adjusting grinding conditions to overcome roundness problems. The user is not constrained by a historic set-up range since there are practical situations where other set-ups are preferred such as small tangent angles for large and heavy work-pieces, and even negative tangent angle for some types of centreless machine.Previous research is reviewed to provide an understanding of the need for a new approach to stability. Practical implications are explained for selection of grinding conditions. The method is supported by reference to experimental results.     

Estimation of machine-tool dynamic parameters during machining operation through operational modal analysis

The stability of high-speed machining operations determines the reliability of machine tools and the quality of machined parts. Chatter-free cutting conditions are difficult to predict as they require accurately estimated dynamic modal parameters. A spectrogram analysis and impact tests for different configurations of the machine tools were conducted to compare the modal parameters at 0 rpm tests and during machining tests. Variations of between 2% and 8% were observed for the natural frequencies and between 2 and 10 times for the damping ratios.The operational modal analysis (OMA) is considered as a powerful tool for dynamic modal parameter estimations during machining operations. A complete methodology for applying this technique for machining operations was detailed. It was demonstrate how the OMA can be industrially exploited. The proposed approach was successfully applied during the high-speed machining of the 7075-T6 aluminum alloy to extract machine-tool parameters. Two different numerical approaches were used: the autoregressive moving average method (ARMA) and the least square complex exponential method (LSCE), both of which generated similar results. The dynamic parameters found using the operational modal analysis were used to predict machine dynamic stability lobes, and through experimental validation, it was shown that some depths of cut that are stable with standard stability lobes become unstable with dynamic stability lobes.     

Providing stability maps for milling operations

This article presents a new stability prediction tool. The method is based on the dynamic behaviour of both milling tool and workpiece, computed using finite element method. Dynamic behaviour is expressed under the form of transfer functions and used to predict stability lobes at each tool position. The unconditionally stable depth of cut is then stored and displayed on a graphic representation of the machined surface under the form of colour axis, named stability map.An application of the method on a Renault cylinder block is presented as an illustration.     

Machining prediction of spindle–self-vibratory drilling head

The drilling of deep holes with small diameters remains an unsatisfactory technology, since its productivity is rather limited. The main limit to an increase in productivity is directly related to the poor chip evacuation, which induces frequent tool breakage and poor surface quality. Retreat cycles and lubrication are common industrial solutions, but they induce productivity and environmental drawbacks. An alternative response to the chip evacuation problem is the use of a vibratory drilling head, which enables the chips to be fragmented thanks to the axial self-excited vibration. Contrary to conventional machining processes, axial drilling instability is sought, thanks to an adjustment of head design parameters and appropriate conditions of use. A dynamic high-speed spindle/drilling head/tool system model is elaborated on the basis of rotor dynamics predictions. In this paper, self-vibratory cutting conditions are established through a specific stability lobes diagram. Investigations are focused on the drill's torsional–axial coupling role on instability predictions. A generic accurate drilling force model is developed by taking into account the drill geometry, cutting parameters and effect of torsion on the thrust force. The model-based tool tip FRF is coupled to the proposed drilling force model into an analytical stability approach. The stability lobes are compared to experimentally determined stability boundaries for validation purposes.     

Creating Stability Lobe Diagrams during Milling

Motorized spindles are in common use in high-speed milling. The dynamic behavior of the spindle depends on the actual number of revolutions and the temperature. The performance of the spindle during milling, particularly, the behavior concerning chatter, is crucially affected by the speed dependent dynamic behavior of the mechanical system. This paper presents the reasons for the speed-sensitive stiffness and the shifting stability lobes. A new method of measuring and calculating the dynamic behavior during milling by means of sub-space-state-space-identification methods is introduced. Finally, the computed stability lobe diagrams are compared with experimentally determined stability lobe diagrams.     

基于小波神经网络的高速铣削刀具磨损识别

刀具磨损一直是制造技术中引人注目的重要问题,对于高速切削来说由于加工成本较高而且刀具价格比较昂贵,因此对高速切削中的刀具状态进行识别和监控具有非常重要的意义.文章通过建立小波神经网络来实现对高速加工中刀具状态的识别,结果与实际情况基本一致,从而表明通过此方法是可以较好的对高速加工刀具状态进行识别的.     

A new method for the identification of stability lobes in machining

This paper introduces a new method for identifying the stability lobes in milling. The method depends on ramping the spindle speed while monitoring the behaviour of a chatter indicator. Based on the pattern of this indicator, the stability lobes are located accurately. The lobes are identified on-line without stopping the machine. It is not necessary to calculate the frequency spectrum of any vibration signal. The method was tested successfully in immersion down-milling and was shown to be applicable to slotting. Experimental results showed that the frequency characteristics of the stability lobes identified using the developed method are the same as those of the lobes established using constant speed cutting.     

Robust chatter stability in micro-milling operations

Micro-milling utilizes miniature end mills to fabricate complex shapes at high rotational speeds. One of the challenges in micro-machining is regenerative chatter, which results in severe tool wear and reduced part quality. The high rotational speeds of micro-milling cause changes in dynamics; and, the elasto-plastic nature of micro-machining operations results in changes to the cutting coefficients. Variations in dynamics and cutting coefficients affect the stability lobes. The tool tip dynamics can be indirectly obtained through mathematical coupling of substructures using the receptance coupling method. The effect of process damping is also considered. The robust chatter stability theorem, which is based on the edge theorem, is employed to provide the robust stability within the minimum and maximum boundaries of changing parameters.     

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).     

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.     

Analytical stability lobes including nonlinear process damping effect on machining chatter

Indentation of the tool edge and flank face into workpiece surface undulations has been recognized in the literature as the main source of process damping. This damping affects the process stability at low cutting speed greatly. Numerical simulations have allowed integrating the nonlinear indentation force into machining chatter models. It is shown in this paper that the indentation force requires very high discretization resolution for accurate numerical simulation. The objective of the current work is to develop the stability lobes analytically taking into account the effect of nonlinear process damping. The developed lobes could be established for different amplitudes of vibration. This is a departure from the traditional notion that the stability lobes represent a single boundary between fully stable and fully unstable cutting conditions. Plunge turning is utilized in the current work to illustrate the procedure of establishing the lobes analytically. Experimental cutting tests were conducted at three feedrates for sharp and worn tools and the results agreed well with the analytically established lobes.     

Prediction of chatter stability in high-speed finishing end milling considering multi-mode dynamics

The strong demand for increasing productivity and workpiece quality in high-speed milling make the machine-tool system has to operate close to the limit of its dynamic stability. This requires that the chatter stability is predicted accurately to determine the optimal milling parameters. An analytical stability prediction method was proposed with multi-degree-of-freedom (MDOF) system modal analysis. This paper describes the development of this new method which allows considering the effects of multi-mode dynamics of system, higher excited frequency (i.e. tooth passing frequency) and wider spindle speed range on stability limits in high-speed milling, and these to help in selection of milling parameters for a maximum material removal rates (MRR) in real operations without chatter. Some tests were carried out to demonstrate the quality of this method used in real machining. Final, the main influencing factors of stability limits in high-speed milling were analyzed.     

High speed servo control of multi-axis machine tools

Advances in high-speed machining technology, including those in spindle speeds and cutters, are out-pacing advances in the servo control performance of machine tools. To close this gap, new machine tools and improved controls must be developed. Improvements to machine tools under development include special-purpose machine tools, the use of advanced materials, the replacement of ball screws and ways with linear motors and roller guides, and the use of parallel link actuators. This paper focuses on the control issues that will become increasingly important as these high-speed machining and high-speed machine tool advances are realized.The main issues in high-speed servo control are feed rate planning, and servo loop control laws. A method is developed in this paper which takes advantage of the full performance envelope of each axis in an arbitrary path. This near-complete usage of the servo capabilities of a machine tool results in reduced cycle time or reduced path error. A servo loop control law is then developed that uses the axis performance envelope as well as instantaneous position, velocity, and acceleration information of the target path and machine axis to improve servo performance in the presence of disturbances.     

Continuous model for analytical prediction of chatter in milling

A novel analytical approach for prediction of chatter in milling process is presented. Existing approaches use lumped-parameter models to define the dynamics of tools/workpieces. In this paper a continuous beam model is employed for prediction of milling operations dynamics. The tool boundary conditions are elastic support at the tool/holder/spindle interface and free support at the other end. Employing the continuous model eliminates the need for tool tip frequency response function (FRF) measurements in tool-tuning practice, especially in micro-milling, where FRF measurement is practically very difficult. Tool/holder/spindle interface parameters, once identified, can be used for other tool lengths. The impact hammer test is used to identify stiffness and damping parameters of the tool/holder/spindle interface. Using the new analytical approach and picking single-frequency solution (SFS), stability lobes are obtained for a slotting operation. The resulting lobes are compared to those obtained by the well-proven lumped-parameter model. In addition to a good general agreement between the two approaches, the continuous model prediction is more conservative for critical depth of cut, which is attributed to its ability to consider all participating modes in the response and so represents a more accurate representation of the system.     

Surface roughness variation of thin wall milling, related to modal interactions

High-speed milling operations of thin walls are often limited by the so-called regenerative effect that causes poor surface finish. The aim of this paper is to examine the link between chatter instability and surface roughness evolution for thin wall milling. Firstly, the linear stability lobes theory for the thin wall milling optimisation was used. Then, in order to consider the modal interactions, an explicit numerical model was developed. The resulting nonlinear system of delay differential equations is solved by numerical integration. The model takes into account the coupling mode, the modal shape, the fact that the tool may leave the cut and the ploughing effect. Dedicated experiments are carried out in order to confirm this modelling. This paper presents surface roughness and chatter frequency measurements. The stability lobes are validated by thin wall milling. Finally, the modal behaviour and the mode coupling give a new interpretation of the complex surface finish deterioration often observed during thin wall milling.     

Modeling the machining stability of a vertical milling machine under the influence of the preloaded linear guide

The prediction of machining stability is of great importance for the design of a machine tool capable of high-precision and high-speed machining. The machining performance is determined by the frequency characteristics of the machine tool structure and the dynamics of the cutting process, and can be expressed in terms of a stability lobe diagram. The aim of this study is to develop a finite element model to evaluate the dynamic characteristics and machining stability of a vertical milling system. Rolling interfaces with a contact stiffness defined by Hertz theory were used to couple the linear components and the machine structures in the finite element model. Using the model, the vibration mode that had a dominant influence on the dynamic stiffness and the machining stability was determined. The results of the finite element simulations reveal that linear guides with different preloads greatly affect the dynamic behavior and milling stability of the vertical column spindle head system. These results were validated by performing vibration and machining tests. We conclude that the proposed model can be used to accurately evaluate the dynamic performance of machine tool systems designed with various configurations and with different linear rolling components.