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.     

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.     

Residual stresses and strains in orthogonal metal cutting

The finite element method is used to simulate and analyze the orthogonal metal cutting process under plane strain conditions, with focus on the residual stress and strain fields in the finished workpiece. Various modeling options have been employed. The frictional interaction along the tool-chip interface is modeled with a modified Coulomb friction law. Chip separation is modeled by the nodal release technique based on a critical stress criterion. Temperature-dependent material properties and a range of tool rake angle and friction coefficient values are considered. It is found that while thermal cooling increases the residual stress level, the effects of the rake angle and the friction coefficient are nonlinear and depend on the range of these parameters. The predicted residual stress results compare well with experimental observations available in the literature.     

Automatic chatter detection in grinding

Two methods for automatic chatter detection in outer diameter plunge feed grinding are proposed. The methods employ entropy and coarse-grained information rate (CIR) as indicators of chatter. Entropy is calculated from a power spectrum, while CIR is calculated directly from fluctuations of a recorded signal. The methods are verified using signals of the normal grinding force and RMS acoustic emission. The results show that entropy and CIR perform equally well as chatter indicators. Based on the normal grinding force, they detect chatter in its early stage, while only cases of strong chatter are detected based on RMS acoustic emission.     

A New Method for Chatter Detection in Grinding

A new method for automatic chatter detection in outer-diameter grinding is proposed which exploits significant changes in grinding dynamics caused by the onset of chatter. The method is based on monitoring of a non-linear statistic called the coarse-grained entropy rate. The entropy rate is calculated from the fluctuations of the normal grinding force. Values of the entropy rate close to zero are typical of chatter, whereas larger values are typical of chatter-free grinding. If the entropy rate is normalized, a threshold value can be set which enables automatic distinction between chatter-free grinding and chatter.     

The effect of tool nose radius in ultrasonic vibration cutting of hard metal

A tool edge with a small nose radius can alleviate the regenerative chatter. In general, it is important for conventional cutting to use the smallest possible tool nose radius. However, a sharp tool shape has an adverse effect on tool strength and the instability of machining process still occurs. Previous researches have shown that vibration cutting has a higher cutting stability as compared with conventional cutting. In the present paper, the influence of tool nose radius on cutting characteristics including chatter vibration, cutting force and surface roughness is investigated by theory. It is found from the theoretical investigation that a steady vibration created by motion between the tool and the workpiece is still obtained even using a large nose radius in vibration cutting. This article presents a vibration cutting method using a large nose radius in order to solve chatter vibration and tool strength problem in hard-cutting. With a suitable nose radius size, experimental results show that a stable and a precise surface finish is achieved.     

A numerical model to determine temperature distribution in orthogonal metal cutting

In this study, a thermal analysis model is developed to determine temperature distribution in orthogonal metal cutting using finite elements method. The model calculates the temperature distribution as a function of heat generation. The heat generation was introduced in the primary deformation zone, the secondary deformation zone and along the sliding frictional zone at the tool–chip interface, as well. The location and shapes of these zones was determined based on the literature work done so far and the model results. The temperature dependency of material properties was included in the model. A series of thermal simulations have been performed, and the value and location of maximum temperature have been determined for various cutting conditions. The comparison of the simulations with earlier works gave promising trend for the presented model. The thermal aspects of metal cutting as a result of the model findings were discussed.     

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.     

Analysis of compliance between the cutting tool and the workpiece on the stability of a turning process

Chatter is a common vibration problem that limits productivity of machining processes, since its large amplitude vibrations causes poor surface finishing, premature damage and breakage of cutting tools, as well as mechanical system deterioration. This phenomenon is a condition of instability that has been classified as a self-excited vibration problem, which shows a nonlinear behavior characterized by the presence of limit cycles and jump phenomenon. In addition, subcritical Hopf and flip bifurcations are mathematical interpretations for loss of stability. Regeneration theory and linear time delay models are the most widely accepted explanations for the onset of chatter vibrations. On the other hand, models based on nonlinearities from structure and cutting process have been also proposed and studied under nonlinear dynamics and chaos theory. However, on both linear and nonlinear formulations usually the compliance between the workpiece and cutting tool has been ignored. In this work, a multiple degree of freedom model for chatter prediction in turning, based on compliance between the cutting tool and the workpiece, is presented. Hence, a better approach to the physical phenomenon is expected, since the effect of the dynamic characteristics of the cutting tool is also taken into account. In this study, a linear stability analysis of the model in the frequency domain is performed and a method to construct typical stability charts is obtained. The effect of the dynamics of the cutting tool on the stability of the process is analyzed as well.     

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.     

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 the stabilizing and destabilizing effects of damping in wood cutting machines

In this paper an analytical investigation of the possibility of employing damping elements to prevent chatter instability in wood machining is presented. A simplified model of a two-degree-of-freedom machine for wood cutting is first established. Then, the stabilizing effect of damping on the initially unstable and undamped system is investigated. The influence of damping on flutter and divergence instability is analyzed separately following different approaches. Some simplified assumptions are made to facilitate the analysis and a set of explicit conditions ensuring stability is found. Since the studied system is nonconservative, not only the effect of damping on the initially unstable system is investigated, but also its effect on the initially stable system. In particular, a condition preventing the destabilization of the system is achieved through the eigenvalue sensitivity analysis. The results attained might ensure important productivity improvements in real wood machining applications.     

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.     

From the basic mechanics of orthogonal metal cutting toward the identification of the constitutive equation

This paper proposes a methodology to identify the material coefficients of constitutive equation within the practical range of stress, strain, strain rate, and temperature encountered in metal cutting. This methodology is based on analytical modeling of the orthogonal cutting process in conjunction with orthogonal cutting experiments. The basic mechanics governing the primary shear zone have been re-evaluated for continuous chip formation process. The stress, strain, strain rate and temperature fields have been theoretically derived leading to the expressions of the effective stress, strain, strain rate, and temperature on the main shear plane. Orthogonal cutting experiments with different cutting conditions provide an evaluation of theses physical quantities. Applying the least-square approximation techniques to the resulting values yields an estimation of the material coefficients of the constitutive equation. This methodology has been applied for different materials. The good agreement between the resulting models and those obtained using the compressive split Hopkinson bar (CSHB), where available, demonstrates the effectiveness of this methodology.     

In-process measurement of friction coefficient in orthogonal cutting

In order to represent actual cutting process conditions, an in-process tribometer is examined to measure friction during orthogonal turning process at cutting speeds up to 300 m/min. The tribometer consists of a spring preloaded tungsten carbide pin with spherical tip mounted behind the cutting edge and rubbing on the freshly generated workpiece surface. The pin preload is set according to feed force. A 3D-force measuring device in the fixation of the pin allows evaluating friction coefficient from tangential and normal forces. Experiments show strongly different results when contacting fresh and oxidized surfaces and decreasing friction coefficient with increasing cutting speed.     

The measurement of parasitic forces in orthogonal cutting

Not all the forces measured during a cutting operation contribute to chip formation. Some fraction of the forces are parasitic forces such as ploughing or flank forces, which make no contribution to the chip formation process. It its desirable to measure these forces so that the mechanics of the cutting process can be interpreted correctly. However, a possibly more important reason is that parasitic forces are known to increase with worn tools. Thus if the parasitic force can be measured directly, or extracted from the overall measured forces it may be useful for in-process tool condition monitoring provided appropriate calibration of the relationship between the parasitic force and cutting tool dullness has been performed.A method for measuring the parasitic forces in orthogonal cutting is proposed and shown to permit calculating workpiece material properties which are consistent with those measured using other techniques. Another technique for evaluating parasitic forces which was previously shown to yield inaccurate results for zinc was re-evaluated for Delrin® and again resulted in incorrect results.     

A simplified methodology to determine the cutting stiffness and the contact stiffness in the plunge grinding process

This paper presents a simplified experimental technique to determine approximately the cutting stiffness and the contact stiffness in the plunge grinding process. The experimental methodology consists of a machine static stiffness test and several grinding processes. The cutting stiffness is obtained from the workpiece headstock static stiffness and from its displacement during the grinding processes, measured by a LVDT transducer. The contact stiffness is resolved from the expression that relates it with the grinding process time constant and other grinding parameters. The time constant is obtained from the exponential that characterises the machine deformation during the spark-out, measured as well by the LVDT transducer placed on the workpiece headstock. The variation of the obtained values of the contact stiffness with some of the grinding parameters is also shown.     

Finite difference analysis of the thermal behaviour of coated tools in orthogonal cutting of steels

Temperature measurement and prediction have been a major focus of machining for several decades but now this problem became more important due to the wider use of advanced cutting tool coatings. Practically, there is a lack of simulation programs for prediction of the temperatures in the cutting zone when machining with differently coated cutting tools. In all literature items cited the finite difference methods (finite difference approaches) were used to find the distribution of temperature inside the uncoated tool body or along the tool–chip interface for continuous (turning) and interrupted (milling) machining processes. The algorithm applied overcomes this limit. In this study, a special variant of the finite difference method called the method of elementary balances (MBE), in which difference equations are defined based on balances of energy produced for all discrete elements of the model, is proposed to predict the tool temperature fields in continuous (orthogonal) machining of AISI 1045 steel with uncoated and coated carbide tools. These predictions provide a detailed view of the changes in the two-dimensional thermal field inside the tool body as a function of cutting speed for the defined friction conditions and values of the heat partition coefficient. Special attention was paid to temperature distribution curves at the tool–chip and work–flank interfaces and possible sources of computed errors. The computed results were compared with the selected experimental values to verify the accuracy of the simulation technique used.