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.     

Angle and frequency domain force models for a roughing end mill with a sinusoidal edge profile

This paper presents analytical force models for a cylindrical roughing end mill with a sinusoidal edge profile in both the angle and frequency domains. Starting from a general expression for the chip thickness model, it is shown that under normal feed conditions, there exists only one cutting point at any axial position for an N-flute roughing end mill with its chip thickness N times that of a regular end mill, while the effective axial depth of cut is only 1/Nth that of a regular end mill. Based on the chip load model, the analytical force model is subsequently established through convolution integration of the elemental cutting function with the cutting edge geometry function in the angular domain, followed by Fourier analysis to obtain the frequency domain force model. Distinctive features of the milling forces for a roughing end mill are illustrated and compared with a regular end mill in the frequency as well as in the angular domain. The effects of the geometric parameters of a roughing end mill on the chip load distribution and on the features of milling force are discussed. The force models in both the frequency and angular domains are finally verified through milling experiments.     

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.     

Mechanistic modeling of five-axis machining with a general end mill considering cutter runout

The accurate and fast prediction of cutting forces in five-axis milling of free-form surfaces remains a challenge due to difficulties in determining the varying cutter-workpiece engagement (CWE) boundaries and the instantaneous uncut chip thickness (IUCT) along the tool path. This paper proposes an approach to predict the cutting forces in five-axis milling process with a general end mill considering the cutter runout effect that is inevitable in the practical machining operations. Based on the analytical model of cutting edge combined with runout parameters, the expression of the rotary surface formed by each cutting edge undergoing general spatial motion is firstly derived. Then by extracting the feasible contact arc along the tool axis, a new arc-surface intersection method is developed to determine the CWE boundaries fast and precisely. Next, the circular tooth trajectory (CTT) model is developed for the calculation of the IUCT with a slight sacrifice of accuracy. In comparison with the true IUCT calculated by the trochoidal tooth trajectory model, the approximation error introduced by the circular assumption is negligible while the computational efficiency improves a lot. Finally, combining with the calibrated cutting coefficients and runout parameters, comprehensive formulation of the cutting force system is set up. Simulations and experimental validations of a five-axis flank milling process show that the novel CTT model possesses obvious advantages in computing efficiency and accuracy over the existing approaches. Rough machining of a turbo impeller is further carried out to test the practicability and effectiveness of the proposed mechanistic model.     

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.     

Chatter identification in end milling process based on EEMD and nonlinear dimensionless indicators

Vibration analysis is widely used to reveal the fundamental cutting mechanics in machining condition monitoring. In this work, vibration signals generated in different chatter conditions as well as stable cutting are studied to understand chatter characteristics. Considering the nonlinear and non-stationary properties of chatter vibration in milling process, a self-adaptive analysis method named ensemble empirical mode decomposition (EEMD) is adopted to analyze vibration signals and two nonlinear indices are extracted as chatter indicators. Firstly, the vibration signal is preprocessed with a comb filter to eliminate the interference of rotation frequency, tooth passing frequency and their harmonics. Secondly, EEMD is applied to decompose the filtered signal into a set of intrinsic mode functions (IMFs). Sensitive IMFs containing rich chatter information are selected. With the development of chatter, an accumulation phenomenon appears in the spectrum of sensitive IMFs and chatter frequencies are modulated by the rotation frequency and tooth passing frequency. Finally, two nonlinear dimensionless indices within the range of [0, 1], i.e., C₀ complexity and power spectral entropy, are extracted from the sensitive IMFs in both time domain and frequency domain. The proposed method is verified with well-designed cutting tests. It is found that, the stochastic noise dominates in the sensitive IMFs of stable cutting and both the C₀ complexity value and power spectral entropy are the largest; with the increase of chatter severity level, the periodic chatter components dominate gradually and the proportion of stochastic noise decreases, and thus these two indicators decrease.     

Detection of chatter vibration in end milling applying disturbance observer

Suppression of chatter vibration is required to improve the machined surface quality and enhance tool life. For monitoring the chatter vibrations, additional sensors such as acceleration sensors are generally used, which results in high costs and low reliability of the machine tools. In this study, a novel in-process method to detect chatter vibrations in end milling is developed on the basis of a disturbance observer theory. The developed system does not require any external sensors because it uses only the servo information of the spindle control system. Self-excited and forced chatter vibrations are successfully detected.     

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.     

Analytical prediction of chatter stability in ball end milling with tool inclination

The paper presents an analytical method to predict chatter stability in ball end milling with tool inclination. The chatter stability limits in ball end milling without the tool inclination have been predicted in the previous study by deriving directional milling force coefficients and then solving a simple quadratic equation. However, the tool is generally inclined and not perpendicular to the cut surface in practice. Therefore, a new method is developed to compute the directional milling force coefficients considering the tool inclination. It is confirmed that the chatter stability predicted by the proposed method agrees well with the experiments.     

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.     

NC end milling optimization using evolutionary computation

Typically, NC programmers generate tool paths for end milling using a computer-aided process planner but manually schedule “conservative” cutting conditions. In this paper, a new evolutionary computation technique, particle swarm optimization (PSO), is proposed and implemented to efficiently and robustly optimize multiple machining parameters simultaneously for the case of milling. An artificial neural networks (ANN) predictive model for critical process parameters is used to predict the cutting forces which in turn are used by the PSO developed algorithm to optimize the cutting conditions subject to a comprehensive set of constraints. Next, the algorithm is used to optimize both feed and speed for a typical case found in industry, namely, pocket-milling. Machining time reductions of up to 35% are observed. In addition, the new technique is found to be efficient and robust.     

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.     

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.     

Fuzzy control of spindle power in end milling processes

This paper reports a fuzzy control system for power regulation in end milling processes. This control system is capable of adjusting both feedrate and spindle speed simultaneously. Experiments have been carried out using both steel and aluminum workpieces of various cutting geometries. Different tools (HSS and carbide tools of different diameters and different number of teeth) have been used for aluminum workpieces. Both full immersion slotting and partial immersion cutting were tested. Our test results show that the system was in sensitive to workpiece and tool changes and cutting power was well regulated around the target levels for various types of variations in depth of cut. Our test results also show that as compared to single parameter (feedrate) adjustment, further savings in machining time can be achieved by adjusting both feedrate and spindle speed.     

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.