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.     

A method of using turning process excitation to determine dynamic cutting coefficients

Identification of the dynamic cutting force coefficients is an essential work in cutting process modeling. The excitation equipment employed to produce dynamic cutting process is usually sophisticated and may lead to potential error. An alternative method of turning process excitation is proposed to simplify the procedure of cutting dynamics measurement. A cantilever workpiece used in cylindrical turning process has been modeled with a double degree-of-freedom system that supports variable dynamic parameters. The structural dynamics of the equivalent system are analyzed with the theoretical derivation and the finite element simulations. The influence of structural dynamic variation on the chatter frequency is investigated, based on which the self-excited chatter is considered as a method of the turning process excitation. This method is applied in the cutting dynamics tests. The dynamic cutting force coefficients could be measured through a single chattering turning process. Stability analysis is conducted for verification of the measured dynamic cutting coefficients.     

Stability lobes for general turning operations with slender tools in the tangential direction

During the turning of large and heavy cases and rings, the tool must be cantilevered over long distances, and chatter due to modes in the tangential direction may occur. This paper proposes a numerical method based on a nonlinear cutting force model, which includes the effects of the cutting parameters to construct precise stability charts for this special machining case. This method has been successfully applied to general cutting geometries in rough and medium longitudinal turning operations, assuming a rigid workpiece and a flexible tool. This study proposes a dynamic model to implement the effects of the tangential mode on chip regeneration in the regenerative plane based on an experimentally obtained dynamic displacement factor. From the simulations and experimental results, the model provides a reliable approach to obtain chatter-free turning conditions.     

Thermal modeling for white layer predictions in finish hard turning

Part thermal damage is a process limitation in finish hard turning and understanding process parameter effects, especially, tool wear, on cutting temperatures is fundamental for process modeling and optimization. This study develops an analytical model for cutting temperature predictions, in particular, at the machined-surfaces, in finish hard turning by either a new or worn tool.A mechanistic model is employed to estimate the chip formation forces. Wear-land forces are modeled using an approach that assumes linear growth of plastic zone on the wear-land and quadratic decay of stresses in elastic contact. Machining forces and geometric characteristics, i.e. shear plane, chip–tool contact, and flank wear-land, approximate the heat intensity and dimensions of the shear plane, rake face, as well as wear-land heat sources. The three heat sources are further discretized into small segments, each treated as an individual rectangular heat source and subsequently used to calculate temperatures using modified moving or stationary heat-source approaches. Temperature rises due to all heat-source segments are superimposed, with proper coordinate transformation, to obtain the final temperature distributions due to the overall heat sources. All heat sources are simultaneously considered to determine heat partition coefficients, both at the rake face and wear-land, and evaluate the final temperature rises due to the combined heat-source effects.Simulation results show that, in new tool cutting, maximum machined-surface temperatures are adversely affected by increasing feed rate and cutting speed, but favorably by increasing depth of cut. In worn tool cutting, flank wear has decisive effects on machined-surface temperatures; the maximum temperature increases 2–3 times from 0 to 0.2 mm wear-land width. White layers (phase-transformed structures) formed at the machined-surfaces have been used to experimentally validate the analytical model by investigating tool nose radius effects on the white layer depth. The experimental results show good agreement with the model predictions.The established model forms a framework for analytical predictions of machined-surface temperatures in finish hard turning that are critical to part surface integrity and can be used to specify a tool life criterion.     

A comprehensive chatter prediction model for face turning operation including tool wear effect

This paper presents a three-dimensional mechanistic frequency domain chatter model for face turning processes, that can account for the effects of tool wear including process damping. New formulations are presented to model the variation in process damping forces along nonlinear tool geometries such as the nose radius. The underlying dynamic force model simulates the variation in the chip cross-sectional area by accounting for the displacements in the axial and radial directions. The model can be used to determine stability boundaries under various cutting conditions and different states of flank wear. Experimental results for different amounts of wear are provided as a validation for the model.     

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.     

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.     

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.     

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.     

Prediction of chatter in NC machining based on a dynamic cutting force model for ball end milling

Ball end milling is one of the most widely used cutting processes in the automotive, aerospace, die/mold, and machine parts industries, and the chatter generated under unsuitable cutting conditions is an extremely serious problem as it causes excessive tool wear, noise, tool breakage, and deterioration of the surface quality. Due to the critical nature of detecting and preventing chatter, we propose a dynamic cutting force model for ball end milling that can precisely predict the cutting force for both stable and unstable cutting states because our uncut chip thickness model considers the back-side cutting effect in unstable cutting states. Furthermore, the dynamic cutting force model considers both tool runout and the penetration effect to improve the accuracy of its predictions. We developed software for calculating the cutting configuration and predicting the dynamic cutting force in general NC machining as well as single-path cutting. The chatter in ball end milling can be detected from the calculated cutting forces and their frequency spectra. A comparison of the predicted and measured cutting forces demonstrated that the proposed method provides accurate results.     

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.     

Analysis of chatter suppression in vibration cutting

The occurrence of chatter is strongly influenced by the tool geometry in conventional cutting. Therefore, the tool geometry is regarded as a very important factor. On the other hand, it is known that vibration cutting is capable of cutting hardened steels. However, the theoretical explanation for finish hard-cutting with vibration cutting is still unknown. In this paper, experimental investigations show that chatter is effectively suppressed without relying on the tool geometry, and the work displacement amplitudes are reduced from a wide range of 10–102 μm to the range of 3–5 μm by applying vibration cutting. In order to study the precision machining mechanism of vibration cutting, a new cutting model which contains a vibration cutting process is proposed. Simulations of the chatter model exhibit the main feature of chatter suppression in vibration cutting. The simulation results are in good agreement with the measurement values and accurately predict the work displacement amplitudes of vibration cutting.     

On-line prediction of surface finish and dimensional deviation in turning using neural network based sensor fusion

This paper examines the feasibility for an intelligent sensor fusion technique to estimate on-line surface finish (Ra) and dimensional deviations (DD) during machining. It first presents a systematic method for sensor selection and fusion using neural networks. Specifically, the turning of free-machining and low carbon steel is considered. The relationships of the readily sensed variables in machining to Ra and DD, and their sensitivity to process conditions are established. Based on this experimental data and using statistical tools, the sensor selection and fusion method assists the experimenter in determining the average effect of each candidate sensor on the performance of the measuring system. In the case studied, it appeared that the cutting feed, depth of cut and two components of the cutting force (the feed and radial force components) provided the best combination to build a fusion model for on-line estimation of Ra and DD in turning. Surface finish was assessed with an error varying from 2 to 25% under different process conditions, while errors ranging between 2 and 20 μm were observed for the prediction of dimensional deviations.     

In-process monitoring and detection of chip formation and chatter for CNC turning

In order to realize the intelligent machine tool, an in-process monitoring and detection of cutting states is developed for CNC turning machine to check and improve the stability of the processes. The method developed utilizes the power spectrum density, or PSD of dynamic cutting force measured during cutting. Experimental results suggested that there are basically three types of patterns of PSD when the cutting states are the continuous chip formation, the broken chip formation, and the chatter. The broken chip formation is desired to realize safe and reliable machining.     

Modeling the mechanics and dynamics of arbitrary edge drills

This paper presents a new approach for modelling the cutting forces and chatter stability limits in drills with arbitrary lip geometry. The oblique cutting geometry at each point on the drill lip is modelled using parametric curve equations. The cutting force and process damping coefficients at different parts of the drill lip are identified empirically; the cutting force coefficients are identified from non-symmetric drilling tests, and the process damping coefficients are identified from chatter-free orthogonal turning tests. The presented approach provides a practical method for modelling the cutting forces and vibration stability without needing the detailed geometry of drill lips. The accuracy of presented model in predicting lateral and torsional-axial chatter stability limits is verified by conducting drilling tests using drills with various edge geometries.     

Identification of dynamic cutting force coefficients and chatter stability with process damping

This paper presents a cutting force model which has three dynamic cutting force coefficients related to regenerative chip thickness, velocity and acceleration terms, respectively. The dynamic cutting force coefficients are identified from controlled orthogonal cutting tests with a fast tool servo oscillated at the desired frequency to vary the phase between inner and outer modulations. It is shown that the process damping coefficient increases as the tool is worn, which increases the chatter stability limit in cutting. The chatter stability of the dynamic cutting process is solved using Nyquist law, and compared favourably against experimental results at low cutting speeds.     

Effectiveness of continuous workpiece speed variation (CWSV) for chatter avoidance in throughfeed centerless grinding

The continuous rotation speed variation is demonstrated to be an efficient method to avoid regenerative chatter in different machining processes. This paper presents a time-domain dynamic model for throughfeed centerless grinding process that can predict chatter by means of part roundness error evolution. Continuous workpiece speed variation (CWSV) has been implemented in this model to analyze the influence of this disturbing method on the dynamic instability. Experimental results have validated the model and verified the effectiveness of CWSV for chatter avoidance and surface finish and dimensional tolerances improvement. It has been demonstrated that the selection of the optimal variation parameters is an important factor not only for chatter avoidance, but also for the stability of surface finish and dimensional tolerances since workpiece speed variation has a direct influence on throughfeed rate and grinding forces.     

Analysis of acoustic emission in chatter vibration with tool wear effect in turning

The progressive wear of cutting tools and occurrence of chatter vibration often pose limiting factors on the achievable productivity in machining processes. An effective in-process monitoring system for tool wear and chatter therefore offers the unique advantage of relaxing the process parameter constraints and optimizing the machining production rate. This research presents a dynamic model of the cutting RMS acoustic emission (AE) signal when chatter occurs in turning, and it determines how this motion is related to the RMS AE signal in the presence of tool flank wear. The tool wear effect on acoustic emission generated in turning is expressed as an explicit function of the cutting parameters and tool/workpiece geometry. The AE generated from the sliding contact on the flank wear flat during chatter is investigated based on the energy dissipation principle. This model offers an explanation of the phenomenon of chatter vibration in the neighborhood of the chatter frequency of the tool. It also sheds light on the variation of the RMS AE signal power in close correlation to the characteristic of the state of wear. Cutting tests were conducted to determine the amplitude relationship between RMS AE and cutting parameters. It is shown that RMS AE is quite sensitive to the dynamic incremental changes in the friction and the wear flat mechanism active in machining processes.     

铣削加工颤振稳定域影响参数研究及优化

建立圆柱形铣刀铣削加工动态切削数学模型,采用一种解析法计算并绘制稳定域图,获取加工稳定性随工艺参数变化的规律。分析系统参数对铣削加工颤振稳定特性的影响,提高固有频率、增大系统刚度和阻尼有助于提高系统加工稳定性。基于动态变化的稳定域图及共振功率半频带频率,提出一种铣削稳定性约束下铣削参数优化模型,获取最大加工效率下的主轴转速、径向进给量及轴向进给量参数的最优值。开发铣削稳定性分析仿真软件,实现铣削颤振稳定域分析、共振区域分析、铣削参数优化等功能。将复杂设计分析过程工程实用化,具有工程应用价值。该方法同样可推广到磨削、车削的颤振分析。