A neural network approach for force and contour error control in multi-dimensional end milling operations

The problem of controlling the average resultant cutting force together with the contour error in multi-dimensional end milling operations is considered in this study. Two sets of neural networks are used in the control system. The first set is used to specify the feed rate to maintain a desired cutting force. This feed rate is resolved along the feed axes using a parametric interpolation algorithm so that the desired part shape is obtained. The second set is used to make corrections to the feed rate components specified by the parametric interpolation algorithm to minimize the contour error caused by the dynamic lag of the closed-loop servo systems controlling the feed drives. In addition, the control system includes a feedforward input to compensate for static friction effects. Experimental results are presented for machining two-dimensional circular slots and a three-dimensional spherical surface to show the validity of the proposed approach.     

Identification of cutter offset in end milling without a prior knowledge of cutting coefficients

This paper presents a method for the identification of cutter offset through milling force without requiring the specific cutting coefficients to be known as priori. The total milling force in the presence of cutter offset is first obtained on the basis of dual cutting mechanisms, where the local force is comprised of a constant plowing force and a linear shearing force proportional to the chip load under the cutter offset. The total milling force is synthesized through convolution and is shown to be the sum of three force components: the nominal chip shearing force component, the plowing force components and the offset related shearing force component. Fourier analysis of these force components reveals the effects of offset geometry and yields formulas for the identification of offset geometry. The identification process requires only two cutting tests and the evaluation of two algebraic expressions; the shearing constants are found from the average forces of cutting tests and the offset geometry is identified from the force component at the spindle frequency. Through numerical simulation and experimental results, the efficacy of the identification method is demonstrated; the effects of feed per tooth and cutting depths on the accuracy of the model are investigated and criteria for the appropriate selection of these parameters are suggested.     

An analytical force model with shearing and ploughing mechanisms for end milling

An analytical force model with both shearing and ploughing mechanisms is established for the end milling processes. The elemental forces are defined as the linear combination of shearing and ploughing forces in six cutting constants. The analytical model for the total milling forces in the angular and frequency domain are derived by convolution approach and Fourier transform respectively and are expressed as the superposition of the shearing force component and ploughing force component. This dual-mechanism model is analyzed and discussed in the frequency domain and compared with the lumped shear model. An expression is derived for identifying the cutting constants of the dual-mechanism model from the average milling forces. Explicit inclusion of ploughing force in the model is shown to result in better predictive accuracy and yields a linear force model with constant cutting coefficients. Experiments verify the accuracy and the frequency analysis of the dual-mechanism model and show that cutting constants for the dual-mechanism model are fairly independent of chip thickness.     

The estimation of cutting forces and specific force coefficients during finishing ball end milling of inclined surfaces

The majority of cutting force models applied for the ball end milling process includes only the influence of cutting parameters (e.g. feedrate, depth of cut, cutting speed) and estimates forces on the basis of coefficients calibrated during slot milling. Furthermore, the radial run out phenomenon is predominantly not considered in these models. However this approach can induce excessive force estimation errors, especially during finishing ball end milling of sculptured surfaces. In addition, most of cutting force models is formulated for the ball end milling process with axial depths of cut exceeding 0.5 mm and thus, they are not oriented directly to the finishing processes. Therefore, this paper proposes an accurate cutting force model applied for the finishing ball end milling, which includes also the influence of surface inclination and cutter's run out. As part of this work the new method of specific force coefficients calibration has been also developed. This approach is based on the calibration during ball end milling with various surface inclinations and the application of instantaneous force signals as an input data. Furthermore, the analysis of specific force coefficients in function of feed per tooth, cutting speed and surface inclination angle was also presented. In order to determine geometrical elements of cut precisely, the radial run out was considered in equations applied for the calculation of sectional area of cut and active length of cutting edge. Research revealed that cutter's run out and surface inclination angle have significant influence on the cutting forces, both in the quantitative and qualitative aspect. The formulated model enables cutting force estimation in the wide range of cutting parameters, assuring relative error's values below 16%. Furthermore, the consideration of cutter's radial run out phenomenon in the developed model enables the reduction of model's relative error by the 7% in relation to the model excluding radial run out.     

Investigation of surface integrity in high speed end milling of a low alloyed steel

Understanding the effects of cutting speed, feed rate and cutting depth on surface integrity is very important for the control of workpiece quality. This paper presents a global experimental study of surface integrity in the case of high speed end milling. In the global term, we include measurements of residual stresses, surface roughness and cutting forces. Our observations and conclusions are mainly concentrated on the effect of depth of cut with a set of constant parameters, such as cutting speed, feed rate, and tool/material couple. This set of constants has been determined using the theory of stability lobes. All experiments have been performed with an electro-spindle equipped with magnetic bearings. The results lead to a good understanding of the influence of cutting conditions on surface integrity in high speed milling of a low alloyed steel. The discussion examines a specific point where the residual stress and residual stress gradient are lowest and also the origin of the residual stress value.     

Mechanistic modeling and accurate measurement of micro end milling forces

Micro milling operations can fabricate miniaturized components with high relative accuracy. Since micro machining operations are different than conventional macro machining processes, due to the large negative rake angle and elasto-plastic effects, it is important that the modeling of micro end milling forces incorporates the dynamics of the tool, ploughing and elastic recovery. This study examines the mechanistic modeling of shearing and ploughing domain cutting regimes to accurately predict micro milling forces. The tool dynamics are indirectly identified by performing receptance coupling analysis. Furthermore, the Kalman filter compensation method is used to precisely measure the forces to obtain the cutting constants.     

Efficient calibration of instantaneous cutting force coefficients and runout parameters for general end mills

This paper aims at developing a unified approach to identify the cutting force coefficients together with the cutter runout parameters for general end mills such as cylindrical, ball, bull nose ones, etc. The cutting forces that are modeled using the instantaneous cutting force coefficients are analyzed and separated into two terms: a nominal component independent of the runout and a perturbation component induced by the runout. The nominal component enables the calibration of the instantaneous cutting force coefficients whereas the runout parameters are determined from the perturbation component. The validity of the present method is demonstrated with simulation and experimented data.     

A method for the identification of the specific force coefficients for mechanistic milling simulation

This paper presents a new method to obtain the specific cutting coefficients needed to predict the milling forces using a mechanistic model of the process. The specific coefficients depend on the tool–material couple, the cutting conditions and the geometry of the tool, being usually calculated applying the force model in an inverse way. The most used inverse method is based on the calculation of the average cutting force per revolution values measured in a series of slot machining tests at different feed rates. In this research work, the inverse method is applied using the instantaneous cutting force values, solving the equations system by a constrained least squares fitting method. Furthermore, the cutting force and specific cutting coefficients relation with rake angle and chip thickness is analysed. The results are validated by the comparison of the simulations and experiments in orthogonal cutting test, showing the advantages of using the new method.     

An experimental technique for the measurement of temperature on CBN tool face in end milling

An infrared radiation pyrometer with two optical fibers connected by a fiber coupler was developed and applied to the measurement of tool–chip interface temperature in end milling with a binderless CBN tool. The infrared rays radiated from the tool–chip interface and transmitted through the binderless CBN are accepted by the optical fiber inserted in the tool and are then sent to the pyrometer. A combination of the two fibers and the fiber coupler makes it possible to transmit the accepted rays to the pyrometer, which is set up outside of the machine tool. This method is very practical in end milling for measuring the temperature history at tool–chip interface during chip formation. The maximum tool–chip interface temperature in up milling of a 0.55% carbon steel is 480 °C when the cutting speed is 2.2 m/s and 560 °C at 4.4 m/s, and in the down milling, 500 °C at 2.2 m/s and 600 °C at 4.4 m/s.     

On the geometric and stress modeling of taper ball end mills

Taper ball end mills (TBEM) are widely used in 5-axis machining of complex parts such as impellers. Structural models are needed for calculating cutter load capacity and deflection and optimizing tool designs. Developing analytical structural models is difficult due to the geometric complexity. This paper establishes a novel 3D parametric model for as-ground TBEMs. Using this parameterized geometric model, the structure is analyzed to calculate bending stress and cutter deflection. The analytical model results were found to be in good agreement with Finite Element simulation results and experimental data from the literature.     

Monitoring of tool fracture in end milling using induction motor current

This paper describes the use of induction motor current to monitor tool fracture in end milling operations. The principles of induction motors are studied in this paper to establish the relationship between the motor current and the motor torque. It is shown that the square of the stator current of induction motors is approximately proportional to the motor torque. Since the occurrence of tool fracture will cause variations in the motor torque, measurement of the stator current appears to be an indirect technique for monitoring tool fracture. A sensitivity analysis of the stator current to the occurrence of tool fracture is also reported. Finally, experimental results under varying cutting conditions have been presented to demonstrate the effectiveness of this approach for the detection of tool fracture in end milling operations.     

Experimental study of surface roughness in slot end milling AL2014-T6

The aim of this work was to analyze the influence of cutting condition and tool geometry on surface roughness when slot end milling AL2014-T6. The parameters considered were the cutting speed, feed, depth of cut, concavity and axial relief angles of the end cutting edge of the end mill. Surface roughness models for both dry cutting and coolant conditions were built using the response surface methodology (RSM) and the experimental results. The results showed that the dry-cut roughness was reduced by applying cutting fluid. The significant factors affecting the dry-cut model were the cutting speed, feed, concavity and axial relief angles; while for the coolant model, they were the feed and concavity angle. Surface roughness generally increases with the increase of feed, concavity and axial relief angles, while concavity angle is more than 2.5°.     

An experimental study of tool wear and cutting force variation in the end milling of Inconel 718 with coated carbide inserts

Inconel 718 is a difficult-to-cut nickel-based superalloy commonly used in aerospace industry. This paper presents an experimental study of the tool wear propagation and cutting force variations in the end milling of Inconel 718 with coated carbide inserts. The experimental results showed that significant flank wear was the predominant failure mode affecting the tool life. The tool flank wear propagation in the up milling operations was more rapid than that in the down milling operations. The cutting force variation along with the tool wear propagation was also analysed. While the thermal effects could be a significant cause for the peak force variation within a single cutting pass, the tool wear propagation was believed to be responsible for the gradual increase of the mean peak force in successive cutting passes.     

In-process prediction of cutting depths in end milling

In geometric adaptive control systems for the end milling process, the surface error is usually predicted from the cutting force owing to the close relationship between them, and the easiness of its measurement. Knowledge of the cutting depth improves the effectiveness of this approach, since different cutting depths result in different surface errors even if the measured cutting forces are the same. This work suggests an algorithm for estimating the cutting depth based on the pattern of cutting force. The cutting force pattern, rather than its magnitude, better reflects the change of the cutting depth, because while the magnitude is influenced by several cutting parameters, the pattern is affected mainly by the cutting depth. The proposed algorithm can be applied to extensive cutting circumstances, such as presence of tool wear, change of work material hardness, etc.     

Cutting process of glass with inclined ball end mill

Cutting processes with ball end mills are discussed for machining microgrooves on glasses. A surface is finished in undeformed chip thickness less than 1 μm at the beginning and at the end of the cut during the cutter rotation. The milling process is applied to glass machining. A crack-free surface can be finished in a large axial depth of cut more than 10 μm. Because glass undergoes almost no elastic deformation, roughness on a cutting edge in glass machining has a larger influence on surface finish than that of metal machining. The rotational axis of the tool is inclined to improve the surface finish. The cutting processes are modeled to show the effect of the tool inclination on the machined surface with considering the edge roughness. The tool inclination compensates for deterioration of the surface finish induced by the edge roughness in the presented model. The improvement of the surface finish is verified in the cutting experiments with the tool inclination. The orthogonal grooves 15–20 μm deep and 150–175 μm wide, then, are machined with the crack-free surfaces to prove efficiency and surface quality in the milling process.     

An in-process surface recognition system based on neural networks in end milling cutting operations

An in-process based surface recognition system to predict the surface roughness of machined parts in the end milling process was developed in this research to assure product quality and increase production rate by predicting the surface finish parameters in real time. In this system, an accelerometer and a proximity sensor are employed as in-process surface recognition sensors during cutting to collect the vibration and rotation data, respectively. Using spindle speed, feed rate, depth of cut, and the vibration average per revolution (VAPR) as four input neurons, an artificial neural networks (ANN) model based on backpropagation was developed to predict the output neuron-surface roughness R_a values. The experimental results show that the proposed ANN surface recognition model has a high accuracy rate (96–99%) for predicting surface roughness under a variety of combinations of cutting conditions. This system is also economical, efficient, and able to be implemented to achieve the goal of in-process surface recognition by retrieving the weightings (which were generated from training and testing by the artificial neural networks), predicting the surface roughness R_a values while the part is being machined, and giving feedback to the operators when the necessary action has to be taken.     

A study on the development of the laser-assisted milling process and a related constitutive equation for silicon nitride

Laser-assisted machining (LAM) has recently been evaluated as an effective process for machining of difficult-to-cut materials, such as ceramics. It is more difficult to reach a sufficient preheating temperature in laser-assisted milling than in turning. A newly developed back-and-forth preheating method is proposed to obtain proper temperature at the laser spot, which is preceding a cutting tool. Experiments were successfully performed using the calculated laser power and feed, as determined by using finite element analyses. In addition, a constitutive equation of the LAM is proposed. The proposed method and constitutive equation can be applied to the laser-assisted milling of ceramics.     

Simulation and experimental investigation of the end milling process considering the cutter flexibility

In this paper, a new type of model for the end milling process is presented considering cutter flexibility, which includes not only the static but also the dynamic deflection of the cutter. According to the basic assumption for a linear elastic body, the force acting on the cutter and its deflection in the milling process are both divided into two parts: the static and the dynamic. By considering the regenerative feedback in the practical milling process, the dynamic milling force acting on a unit length of the cutter is derived. Furthermore, a new kind of dynamic deflection model of the cutter is established. Based on this model, a new set of efficient numerical simulation algorithms are presented. In the mean time, the static deflection of the cutter is also formulated. Finally, the simulation and measurement of the milled surface topography for the end milling process show the feasibility of this model.     

Experimental studies of cutting force variation in face milling

The purpose of this paper is to present a developed cutting force model for multi-toothed cutting processes, including a complete set of parameters influencing the cutting force variation that has been shown to occur in face milling, and to analyse to what extent these parameters influence the total cutting force variation for a selected tool geometry. The scope is to model and analyse the cutting forces for each individual tooth on the tool, to be able to draw conclusions about how the cutting action for an individual tooth is affected by its neighbours.A previously developed cutting force model for multi-toothed cutting processes is supplemented with three new parameters; eccentricity of the spindle, continuous cutting edge deterioration and load inflicted tool deflection influencing the cutting force variation. A previously developed milling force sensor is used to experimentally analyse the cutting force variation, and to give input to the cutting force simulation performed with the developed cutting force model.The experimental results from the case studied in this paper show that there are mainly three factors influencing the cutting force variation for a tool with new inserts. Radial and axial cutting edge position causes approximately 50% of the force variation for the case studied in this paper. Approximately 40% arises from eccentricity and the remaining 10% is the result of spindle deflection during machining. The experimental results presented in this paper show a new type of cutting force diagrams where the force variation for each individual tooth when two cutting edges are engaged in the workpiece at the same time. The wear studies performed shows a redistribution of the individual main cutting forces dependent on the wear propagation for each tooth.     

Complexity measure of motor current signals for tool flute breakage detection in end milling

Automated tool condition monitoring is an important issue in the advanced machining process. Permutation entropy of a time series is a simple, robust and extremely fast complexity measure method for distinguishing the different conditions of a physical system. In this study, the permutation entropy of feed-motor current signals in end milling was applied to detect tool breakage. The detection method is composed of the estimation of permutation entropy and wavelet-based de-noising. To confirm the effectiveness and robustness of the method, typical experiments have been performed from the cutter runout and entry/exit cuts to cutting parameters variation. Results showed that the new method could successfully extract significant signature from the feed-motor current signals to effectively detect tool flute breakage during end milling. Whilst, this detection method was based on current sensors, so it possesses excellent potential for practical and real-time application at a low cost by comparison with the alternative sensors.