A comprehensive dynamic cutting force model for chatter prediction in turning

This paper presents a model of the dynamic cutting force process for the three-dimensional or oblique turning operation. To obtain dynamic force predictions, the mechanistic force model is linked to a tool–workpiece vibration model. Particular attention was paid to the inclusion of the cross-coupling between radial and axial vibrations in the force model. The inclusion of this cross-coupling facilitates prediction of the unstable–stable chatter phenomenon which usually occurs in certain cases of finish turning due to process non-linearity. The dynamic force model developed was incorporated into a computer program to obtain time-saving chatter predictions. Experimental tests were performed on AISI 4140 steel workpieces to justify the chatter predictions of the dynamic cutting process model in both the finishing and roughing regimes. Experimental results corroborate the unstable–stable chatter predictions of the model for different cases of finish machining. In addition, experimental results also confirmed the accuracy of chatter predictions for various cases of rough turning.     

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.     

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.     

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.     

Stability analysis of modulated tool path turning

A new periodic sampling-based method for identifying the stability of modulated tool path turning (MTP) is presented. A metric is defined that provides a numerical value to indicate stability; it is nominally zero for forced vibration and large for self-excited vibration. Tests were performed using ASM 6061-T6 aluminum tubes with varying wall thicknesses to control stability, where MTP was applied to create discrete chips by superimposing sinusoidal oscillation in the feed direction. Results are compared for the new periodic sampling metric and the traditional frequency-domain approach, where the frequency spectrum is analyzed to identify the chatter frequency (should it exist).     

A grey prediction fuzzy controller for constant cutting force in turning

Constant force control is gradually becoming an important technique in the modern manufacturing process. Especially, constant cutting force control is a useful approach in increasing the metal removal rate and the tool life for turning systems. However, turning systems generally have non-linear with uncertainty dynamic characteristics. Designing a model-based controller for constant cutting force control is difficult because an accurate mathematical model in the turning system is hard to establish. Hence, this study employed a model-free fuzzy controller to control the turning system in order to achieve constant cutting force control. Nevertheless, the design of the traditional fuzzy controller (TFC) presents difficulties in finding control rules and selecting an appropriate membership function. To solve this problem, a grey-theory algorithm was introduced into the TFC to predict the next output error of the system and the error change, rather than the current output error of the system and the current error change, as input variables of the TFC. This design of the grey prediction fuzzy controller (GPFC) cannot only simplify the TFC design, but also achieves the desired result in TFC implementation. To confirm the applicability of the proposed intelligent controllers, this work retrofitted an old lathe for a turning system to evaluate the feasibility of constant cutting force control. The GPFC has better control performance in constant cutting force control than does the TFC, as verified in experimental results.     

Evaluation of cutting force uncertainty components in turning

A procedure is proposed for the evaluation of those uncertainty components of a single cutting force measurement in turning that are related to the contributions of the dynamometer calibration and the cutting process itself. Based on an empirical model including errors from both sources, the uncertainty for a single measurement of cutting force is presented, and expressions for the expected uncertainty vs. cutting parameters are proposed. This approach gives the possibility of evaluating cutting force uncertainty components in turning, for a defined range of cutting parameters, based on few experiments.     

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.     

Identification of cutting force characteristics based on chatter experiments

Cutting force coefficients exhibit strong nonlinearity as a function of chip loads, cutting speeds and material imperfections. This paper presents the connection between the sensitivity of the dynamics of regenerative cutting and the cutting force characteristic nonlinearity. The nonlinear milling process is mathematically modelled. The transitions of dynamic cutting process between the stable and unstable zones are considered and experimentally illustrated by applying wavelet transformations on the measurement data.     

A stability analysis of turning a tailstock supported flexible work-piece

This paper proposes a new approach to analyze the stability of a cutting process. Previously, most studies have generally assumed the work-piece to be rigid and have, therefore, ignored work-piece deformation. In analyzing, the stability of the cutting process, these studies simply considered the dynamic equation of the tool. However, in practice, the work-piece undergoes deformation as a result of the application of an external force by the cutting tool. This deformation changes the chip thickness and has an effect on the critical chip thickness. Consequently, this study proposes a novel stability analysis method for the turning process in which deformation of the work-piece is considered. The cutting, which takes place in the turning process, is described using partial differential equations, and a set of dynamic equations is developed by considering the interaction between the tool and the work-piece. Having performed Laplace transformation, the stability of the cutting system can be analyzed in terms of the work-piece length, radius, natural frequency, deflection, slenderness ratio, cutting point, and material. The relationship between the critical chip width and the cutter spindle speed is investigated under a range of cutting and work-piece conditions. The analytical results for the current flexible work-piece are compared with those for a rigid work-piece. It is found that the critical chip width of the flexible work-piece is always greater than that of the rigid body.     

Comparison of one-dimensional and multi-dimensional models in stability analysis of turning operations

Chatter is one of the main problems in machining resulting in poor surface quality and low productivity. Chatter can be avoided by applying stability diagrams which are generated using stability models. The stability analysis of turning has mostly been performed using single dimensional, so-called oriented transfer function approach whereas the actual turning processes usually involve multi-dimensional dynamics. In this paper, a comparative analysis between one dimensional (1D) and multi-dimensional stability models is given for turning operations. The multi dimensional model includes the inclination and side edge cutting angles and insert nose radius in order to demonstrate their effect on absolute stable depth of cut predictions. Chatter experiments are conducted in order to compare with both model predictions. It is demonstrated that for higher inclination angles and insert nose radii 1D models result in significant errors, and multi-dimensional solutions are required.     

Programming spindle speed variation for machine tool chatter suppression

This paper presents a novel method for programming spindle speed variation for machine tool chatter suppression. This method is based on varying the spindle speed for minimum energy input by the cutting process. The work done by the cutting force during sinusoidal spindle speed variation S³V is solved numerically over a wide range of spindle speeds to study the effect of S³V on stable and unstable systems and to generate charts by which the optimum S³V amplitude ratio can be selected. For on-line application, a simple criterion for computing the optimal S³V amplitude ratio is presented. Also, a heuristic criterion for selecting the frequency of the forcing speed signal is developed so that the resulting signal ensures fast stabilization of the machining process. The proposed criteria are suitable for on-line chatter suppression, since they only require knowledge of the chatter frequency and spindle speed. The effectiveness of the developed S³V programming method is verified experimentally.     

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.     

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.     

Sliding mode cutting force regulator for turning processes

Continuous sliding mode control is applied to turning processes for cutting force regulation. The motivation of the use of the slide mode control scheme is to solve the nonlinearity problem caused by the feedrate override command element in the commercial CNC machine tool. When the adaptive control algorithm is applied to the commercial CNC machine tool, it is one of the practical methods that the programmed feedrate is overridden after the control algorithm is carried out. However, most CNC lathe manufacturers offer limited number of data bits for feedrate override, thus resulting in nonlinear behavior of the machine tools. Such nonlinearity brings ‘quantized' or discrete effect so that the optimal feedrate is rounded off before being fed into the CNC system. To compensate for this problem, continuous sliding mode control is applied. Simulation and experimental results are presented in comparison with those obtained from applying adaptive control which is a widely used approach in cutting force regulation. Adaptive control loses its effectiveness in the presence of nonlinearity since it generally requires linear parametrization of the control law or the system dynamics. Experiments are conducted under various machining conditions, subject to changes in spindle speed, material of work-piece, and type of machining process. The suggested slide mode controller shows smoother cutting force fluctuation, which cannot be achieved by the conventional adaptive controller. The experimental set-up reflects the emphasis on the practicality of the sliding mode controller. In order to avoid the use of a dynamometer in the course of measuring the cutting force, the indirect cutting force measuring system is used by means of feed drive servo-motor current sensing.     

A chatter free calibration method for determining cutter runout and cutting force coefficients in ball-end milling

The accuracy of cutting force coefficients plays an important role in predicting reliable cutting force, stability lobes as well as surface location error in ball-end milling. In order to avoid chatter risk of the traditional calibration test with an entire-ball-immersed cutting depth, a cylindrical surface milling method is proposed to calibrate the cutting force coefficients with the characteristics of low cutting depth and varying lead angle. A dual-cubic-polynomial function is also presented to describe the non-uniform cutting force coefficients of the ball part cutting edge and the nonlinear chip size effect on cutting force. The variation of the maximum chip thickness versus the lead angle is established with the consideration of cutter runout. According to the dependence of chip thickness on lead angle, a runout identification method is introduced by seeking the critical lead angle at which one of the cutter flutes is just thoroughly out of cut. Then, a lumped equivalent method is adopted for the low cutting depth condition so that the dual-cubic-polynomial model can be calibrated for the chip size effect and the cutting force coefficients respectively. The accuracy of the proposed calibration method has been validated experimentally with a series of milling tests. The stability examinations indicate that the proposed method has an evident chatter-free advantage, compared with that of varying cutting depth method.     

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.     

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.     

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.