A three-dimensional analytical cutting force model for micro end milling operation

In the present day manufacturing arena one of the most important fields of interest lies in the manufacturing of miniaturized components. End milling with fine-grained carbide micro end mills could be an efficient and economical means for medium and small lot production of micro components. Analysis of the cutting force in micro end milling plays a vital role in characterizing the cutting process, in estimating the tool life and in optimizing the process. A new approach to analytical three-dimensional cutting force modeling has been introduced in this paper. The model determines the theoretical chip area at any specific angular position of the tool cutting edge by considering the geometry of the path of the cutting edge and relates this with tangential cutting force. A greater proportion of the helix face of the cutter participating in the cutting process differs the cutting force profile in micro end milling operations a bit from that in conventional end milling operations. This is because of the reason that the depth-of-cut to tool diameter ratio is much higher in micro end milling than the conventional one. The analytical cutting force expressions developed in this model have been simulated for a set of cutting conditions and are found to be well in harmony with experimental results.     

A cutting force model for face milling operations

A procedure for the simulation of the static and dynamic cutting forces in face milling is described. For the static force model, the initial position errors of the inserts and the eccentricity of the spindle are taken into consideration as the major factors affecting the variation of the chip cross-section. The structural dynamics model for the multi-tooth oblique cutting operation is assumed as a multi-degrees of freedom spatial system. From the relative displacement of this system, based on the double modulation principle, the dynamic cutting forces were derived and simulated. The simulated forces were subsequently compared to measured forces in the time and frequency domains.     

Modelling the cutting edge radius size effect for force prediction in micro milling

This paper presents a theoretical model for cutting force prediction in micro milling, taking into account the cutting edge radius size effect, the tool run out and the deviation of the chip flow angle from the inclination angle. A parameterization according to the uncut chip thickness to cutting edge radius ratio is used for the parameters involved in the force calculation. The model was verified by means of cutting force measurements in micro milling. The results show good agreement between predicted and measured forces. It is also demonstrated that the use of the Stabler's rule is a reasonable approximation and that micro end mill run out is effectively compensated by the deflections induced by the cutting forces.     

Predictive cutting force model in complex-shaped end milling based on minimum cutting energy

A force model is presented to predict the cutting forces and the chip flow directions in cuttings with complex-shaped end mills such as ball end mills and roughing end mills. Three-dimensional chip flow in milling is interpreted as a piling up of the orthogonal cuttings in the planes containing the cutting velocities and the chip flow velocities. Because the cutting thickness changes with the rotation angle of the edge in the milling process, the surface profile machined by the previous edge inclines with respect to the cutting direction. The chip flow model is made using the orthogonal cutting data with taking into account the inclination of the pre-machined surface. The chip flow direction is determined so as to minimize the cutting energy, which is the sum of the shear energy on the shear plane and the friction energy on the rake face. Then, the cutting force is predicted for the chip flow model at the minimum cutting energy. The predicted chip flow direction changes not only with the local edge inclination but also with the cutting energy consumed in the shear plane cutting model. The cutting processes with a ball end mill and a roughing end mill are simulated to verify the predicted cutting forces in comparison with the measured cutting forces.     

Cutting force model for multi-toothed cutting processes and force measuring equipment for face milling

This article presents a mechanical cutting force model for multi-tooth cutting processes, where initial position errors in radial and axial direction, eccentricity and edge wear are taken into account. The cutting forces are presented for each individual cutting edge, and in a system of coordinates where one axis is parallel to the cutting speed vector at any instant. The process parameter cutting resistance, C_r is derived from the measured main cutting force F_M. C_r should be regarded as a parameter since it is always increasing with decreasing values of theoretical chip thickness h₁. A new way of measuring cutting forces in multi-tooth cutting processes is also presented. Eight cutting force components are measured on the tool close to each of the four cutting edges. The aroused signals are filtered, amplified, A/D-converted and put together in a serial stream for transmission through a hollow spindle via a fibre optic cable. The signals are sent from the rotating spindle to the frame of the machine over an air gap with Light Emitting Diodes. They are then demultiplexed, D/A-converted, and stored in a PC-based eight channel oscilloscope. With this measurement equipment it is possible to directly measure the cutting forces acting on each individual cutting edge.     

Development of a reference cutting force model for rough milling feedrate scheduling using FEM analysis

Recently developed feedrate scheduling systems regulate cutting forces at the desired level by changing the feedrate to reduce the machining time and to avoid undesirable situations. For effective scheduling, an optimized criterion is required to adjust the feedrate. In this study, a method to obtain the most appropriate reference cutting force for rough milling was developed. The reference cutting force was determined by considering the transverse rupture strength of the tool material and the area of the rupture surface. A finite element method analysis was performed to accurately calculate the area of the rupture surface. Using the analyzed results, the effect of various cutting parameters on the chipping phenomenon was determined. The calculation method for the reference cutting force considered the area of the rupture surface, the effect of the rake angle, and the axial depth of the cut. The reference cutting force calculated using the developed model was applied to feedrate scheduling for pocket machining. The experimental results clearly show that the reference cutting force obtained from the proposed method met the desired constraints that guarantee higher productivity without tool failure.     

An improved cutting force and surface topography prediction model in end milling

During the milling operation, the cutting forces will induce vibration on the cutting tool, the workpiece, and the fixtures, which will affect the surface integrity of the final part and consequently the product's quality. In this paper, a generic and improved model is introduced to simultaneously predict the conventional cutting forces along with 3D surface topography during side milling operation. The model incorporates the effects of tool runout, tool deflection, system dynamics, flank face wear, and the tool tilting on the surface roughness. An improved technique to calculate the instantaneous chip thickness is also presented. The model predictions on cutting forces and surface roughness and topography agreed well with experimental results.     

Simulation of cutting process in peripheral milling by predictive cutting force model based on minimum cutting energy

The cutting force and the chip flow direction in peripheral milling are predicted by a predictive force model based on the minimum cutting energy. The chip flow model in milling is made by piling up the orthogonal cuttings in the planes containing the cutting velocities and the chip flow velocities. The cutting edges are divided into discrete segments and the shear plane cutting models are made on the segments in the chip flow model. In the peripheral milling, the shear plane in the cutting model cannot be completely made when the cutting point is near the workpiece surface. When the shear plane is restricted by the workpiece surface, the cutting energy is estimated taking into account the restricted length of the shear plane. The chip flow angle is determined so as to minimize the cutting energy. Then, the cutting force is predicted in the determined chip flow model corresponding to the workpiece shape. The cutting processes in the traverse and the contour millings are simulated as practical operations and the predicted cutting forces verified in comparison with the measured ones. Because the presented model determines the chip flow angle based on the cutting energy, the change in the chip flow angle can be predicted with the cutting model.     

Development of micro milling tool made of single crystalline diamond for ceramic cutting

In order to machine micro aspheric ceramic molds precisely and efficiently, micro milling tools made of single crystalline diamond (SCD) are developed. Many cutting edges are fabricated 3-dimensionally on the edge of a cylindrical SCD by a laser beam. Flat binderless tungsten carbide mold was cut with the developed tool to evaluate the tool wear rate and its life. Some micro aspheric molds of tungsten carbide were cut with the tool at a rotational speed of 50,000 min⁻¹. The molds were cut in the ductile mode. The form accuracy obtained was about 100 nm P–V and the surface roughness 12 nm R_z.     

Simplified and efficient calibration of a mechanistic cutting force model for ball-end milling

Accurate evaluation of the empirical coefficients of a mechanistic cutting force model is critical to the reliability of the predicted cutting forces. This paper presents a simplified and efficient method to determine the cutting force coefficients of a ball-end milling model. The unique feature of this new method is that only a single half-slot cut is to be performed to calibrate the empirical force coefficients that are valid over a wide range of cutting conditions. The instantaneous cutting forces are used with the established helical cutting edge profile on the ball-end mill. The half-slot calibration cut enables successive determination of the lumped discrete values of the varying cutting mechanics parameters along the cutter axis whereas the size effect parameters are determined from the known variation of undeformed chip thickness with cutter rotation. The effectiveness of the present method in determining the cutting force coefficients has been demonstrated experimentally with a series of verification test cuts.     

Radial immersion angle estimation using cutting force and predetermined cutting force ratio in face milling

Radial immersion ratio is an important factor to determine the threshold for tool conditioning monitoring and automatic force regulation in face milling. In this paper, a method of on-line estimation of the radial immersion angle using cutting force is presented. When a tooth finishes sweeping, a sudden drop of cutting force occurs. This force drop is equal to the cutting force that acts on a single tooth at the swept angle of cut and can be obtained from the cutting force signal in feed and cross-feed directions. The ratio of cutting forces in feed and cross-feed directions acting on the single tooth at the immersion angle is a function of the immersion angle and the ratio of radial-to-tangential cutting force. In this study, it is found that the ratio of radial-to-tangential cutting force is not affected by cutting conditions and axial rake angle. Therefore, the ratio of radial-to-tangential cutting force determined by just one preliminary experiment can be used regardless of the cutting conditions for a given tool and workpiece material. Using the measured cutting force during machining and a predetermined ratio, the radial immersion ratio is estimated in the process. Various experiments show that the radial immersion ratio and instantaneous ratio of the radial to tangential direction cutting force can be estimated very well by the proposed method.     

Virtual cutting and optimization of three-axis milling processes

This paper presents generalized process simulation and optimization strategies to predict and improve the performance of three-axis milling operations. Cutter-part engagement conditions are extracted from a solid modeling system, which can handle free form part surfaces found in dies and molds. The cutting force distribution along the engaged cutting edge-part surface is evaluated based on the laws of mechanics of milling. By integrating the distributed force along the cutting edge, total forces, torque and power are either predicted analytically using closed-form solutions, or numerically if the cutting tool shape is discontinuous. Simulation results are then used in a constraint-based optimization scheme to maximize the material removal rate (MRR) by calculating acceptable feedrate levels. The proposed virtual milling system is demonstrated experimentally in milling a stamping die with free form surfaces.     

The prediction of cutting force in ball-end milling

Due to the development of CNC machining centers and automatic programming software, the ball-end milling have become the most widely used machining process for sculptured surfaces. In this study, the ball-end milling process has been analysed, and its cutting force model has been developed to predict the instantaneous cutting force on given machining conditions. The development of the model is based on the analysis of cutting geometry of the ball-end mill with plane rake faces. A cutting edge of the ball-end mill was considered as a series of infinitesimal elements, and the geometry of a cutting edge element was analysed to calculate the necessary parameters for its oblique cutting process assuming that each cutting edge was straight. The oblique cutting process in the small cutting edge element has been analysed as an orthogonal cutting process in the plane containing the cutting velocity and chip flow vectors. And with the orthogonal cutting data obtained from end turning tests on thin-walled tubes over wide range of cutting and tooling conditions, the cutting forces of ball-end milling could be predicted using the model. The predicted cutting forces have shown a fairly good agreement with test results in various machining modes.     

Improved modelling of cutting force coefficients in peripheral milling

Titanium is one of the most widely used metals in the aircraft and turbine manufacturing industries. Accurate prediction of cutting forces is important in controlling the dimensional accuracy of thin walled aerospace components. In this paper, a general three-dimensional mechanistic model for peripheral milling processes is presented. The effects of chip thickness, rake angle and cutting geometry on chip flow, rake face friction and pressure, and cutting forces are analyzed. A set of closed form expressions with experimentally estimated cutting force factors are presented for the prediction of cutting forces. The model is verified experimentally in the peripheral milling of a titanium alloy. For a given set of cutting conditions and tool geometry, the model predicts the cutting forces accurately for the chip thickness and rake angle ranges tested.     

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.     

Feedrate scheduling for indexable end milling process based on an improved cutting force model

In CNC machining, an optimal process plan is needed for higher productivity and machining performance. This paper proposes a mechanistic cutting force model to perform feedrate scheduling that is useful in process planning for indexable end milling. Indexable end mills, which consist of inserts and a cutter body, have been widely used in the roughing of parts in the mold industry. The geometry and distribution of inserts compose a discontinuous cutting edge on the cutter body, and tool geometry of indexable end mill varies with axial position due to the geometry and distribution of inserts. Thus, an algorithm that calculates tool geometry data at an arbitrary axial position was developed. The developed cutting force model uses cutting-condition-independent cutting force coefficients and considers run out, cutter deflection, geometry variation and size effect for accurate cutting force prediction. Through feedrate scheduling, NC code is optimized to regulate cutting forces at given reference force. Experiments with general NC codes show the effectiveness of feedrate scheduling in process planning.     

A closed form mechanistic cutting force model for helical peripheral milling of ductile metallic alloys

A closed form mechanistic model is developed for cutting forces in helical peripheral milling (endmilling) of ductile metallic alloys. This paper presents an alternative derivation, using the frontal chip area, to describe two series of cutting force expressions—one using a Heaviside unit step function and the other using a Fourier series expansion. A specific advantage of the present work is highlighted by deriving analytical expressions for sensitivity coefficients required to analytically propagate the uncertainty in the cutting-force model parameters. Another advantage is that even very small radial immersions can be used to derive cutting coefficients reliably, along with their variances. The aforementioned analytical investigations are applied to a series of experimental cutting tests to estimate the force-model cutting coefficients. Experimental investigations include the study of a tool having radial runout. Finally, confidence intervals are placed on predicted forces which experimentally verify the validity of the proposed force model.     

A model for thread milling cutting forces

This paper presents a mechanistic model for prediction of the thread milling forces. The mechanics of cutting for thread milling is analyzed similar to the end milling process but with modified cutting edge geometry. The chip thickness and cutting force models are developed considering the unique geometry of the tool. The model has been calibrated for 6061 Aluminum and validated. The effects of tool and thread geometry have been studied using the model.     

Systematic study on cutting force modelling methods for peripheral milling

This paper systematically studies the cutting force modelling methods in peripheral milling process in the presence of cutter runout. Emphasis is put on how to efficiently calibrate the cutting force coefficients and cutter runout. Mathematical derivations and implementation procedures are carried out based on the measured cutting force or its harmonics from Fourier transformation. Five methods are presented in detail. In the first three methods the cutting force coefficients are assumed to be constants whereas in the last two they are taken as functions of instantaneous uncut chip thickness. The first method and the fifth one are taken from literatures for comparison. The second, the third and the fourth methods are original contributions, which are carried out with optimization ideas. The second method proceeds using the first and Nkth harmonic forces as the source signal while the third and the fourth are derived based on the measured cutting forces and its first harmonics. The engagement of the cutter with the workpiece is considered in these three new calibration procedures without the requirement of a prior knowledge of the actual cutter runout. Comparisons among the calibrated results from different methods are made to study the limitations and consistency of the presented methods. Experiments are also conducted to show the prediction ability of all methods.     

Indirect cutting force measurement in multi-axis simultaneous NC milling processes

There have been many research works for the indirect cutting force measurement in machining process, which deal with the case of one-axis cutting process. In multi-axis cutting process, the main difficulties to estimate the cutting forces occur when the feed direction is reversed. This paper presents the indirect cutting force measurement method in contour NC milling processes by using current signals of servo motors. A Kalman filter disturbance observer and an artificial neural network (ANN) system are suggested. A Kalman filter disturbance observer is implemented by using the dynamic model of the feed drive servo system, and each of the external load torques to the x and y-axis servo motors of a horizontal machining center is estimated. An ANN system is also implemented with a training set of experimental cutting data to measure cutting force indirectly. The input variables of the ANN system are the motor currents and the feedrates of x and y-axis servo motors, and output variable is the cutting force of each axis. A series of experimental works on the circular interpolated contour milling process with the path of a complete circle has been performed. It is concluded that by comparing the Kalman filter disturbance observer and the ANN system with a dynamometer measuring cutting force directly, the ANN system has a better performance.