Prediction of ball-end milling forces from orthogonal cutting data

The mechanics of cutting with helical ball-end mills are presented. The fundamental cutting parameters, the yield shear stress, average friction coefficient on the rake face and shear angle are measured from a set of orthogonal cutting tests at various cutting speeds and feeds. The cutting forces are separated into edge or ploughing forces and shearing forces. The helical flutes are divided into small differential oblique cutting edge segments. The orthogonal cutting parameters are carried to oblique milling edge geometry using the classical oblique transformation method, where the chip flow angle is assumed to be equal to the local helix angle. The cutting force distribution on the helical ball-end mill flutes is accurately predicted by the proposed method, and the model is validated experimentally and statistically by conducting more than 60 ball-end milling experiments.     

Estimation and experimental validation of cutting forces in ball-end milling of sculptured surfaces

Chip thickness calculation has a key important effect on the prediction accuracy of accompanied cutting forces in milling process. This paper presents a mechanistic method for estimating cutting force in ball-end milling of sculptured surfaces for any cases of toolpaths and varying feedrate by incorporation into a new chip thickness model. Based on the given cutter location path and feedrate scheduling strategy, the trace modeling of the cutting edge used to determine the undeformed chip area is resulted from the relative part-tool motion in milling. Issues, such as the selection of the tooth tip and the computation of the preceding cutting path for the tooth tip, are also discussed in detail to ensure the accuracy of chip thickness calculation. Under different chip thicknesses cutting coefficients are regressed with good agreements to calibrated values. Validation tests are carried out on a sculptured surface with curved toolpaths under practical cutting conditions. Comparisons of simulated and experimental results show the effectiveness of the proposed method.     

Numerical simulation and prediction of cutting forces in five-axis milling processes with cutter run-out

Radial cutter runout is a common issue in milling processes and has a direct effect on milling stability due to variations of resulting chip load and forces. This paper presents a new method to effectively model and predict the instantaneous cutting forces in 5-axis milling processes with radial cutter runout based on tool motion analysis. First, the undeformed chip thickness model taking runout effect into account is established under continuous change of cutter axis orientation by means of the sweep traces of cutter edges. Second, the engaged cutting edge is determined and cutting coefficients are subsequently calibrated. Finally, the method of identifying runout parameters from the measured cutting forces is proposed, and mechanistic method is then applied to predict the cutting force. Since this method is completely based on the relative motion analysis of tool-part, it can reduce the prediction errors of cutting forces effectively and is suitable for generic rotation cutters. Several validation examples are given under different cutting conditions to prove its effectiveness and accuracy. The results reveal that the developed method can predict the cutter forces with a high accuracy and has the ability to be used in simulations and optimizations of five-axis machining.     

Identification of shearing and ploughing cutting constants from average forces in ball-end milling

This paper presents an analytical model for the direct identification of global shearing and ploughing cutting constants from measured average cutting forces in ball-end milling. This model is based on the linear decomposition of elemental local cutting forces into a shearing component and a ploughing component. Then, a convolution integral approach is used to obtain the average cutting forces leading to a concise and explicit expression for the global shearing and ploughing cutting constants in terms of axial depth of cut, cutter radius and average milling forces. The model is verified by comparisons with an existing force model of variable cutting coefficients. Cutting constants are identified through milling experiments and the prediction of cutting forces from identified cutting constants coincides with the experimental measurements. A model for identifying the lumped shearing constants is obtained as a subset of the presented dual mechanism model. Experimental results indicate that a model with dual-mechanism cutting constants predicts the ball-end milling forces with better accuracy than the lumped force model.     

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.     

Prediction of cutting forces in milling of circular corner profiles

This paper proposes an approach to predict the cutting forces in peripheral milling of circular corner profiles in which varying radial depth of cut is encountered. The geometric relationship between an end mill and the corner profile is investigated and a mathematical model is presented to describe the different phases of the cutter/workpiece contact. The milling process for circular corner is discretized into a series of steady-state cutting processes, each with different radial depth of cut determined by the instantaneous position of the end mill relative to the workpiece. A time domain analytical model of cutting forces for the steady-state machining conditions is introduced to each segmented process for the cutting force prediction. The predicted cutting forces can be calculated in terms of tool/workpiece geometry, cutting parameters and workpirece material property, as well as the relative position of the tool to workpiece. Experiments are conducted and the measured forces are compared to the predictions for the verification of the proposed method.     

Prediction of cutting forces in helical end milling fiber reinforced polymers

Machining of fiber reinforced composites is an important activity in the integration of these advanced materials into engineering applications. Machining damage due to excessive cutting forces may result in rejecting the composite components at the last stages of their production cycle. Therefore, the ability to predict the cutting forces is essential for selecting process parameters that would result in minimum machining damage. This work utilizes mechanistic modeling techniques for simulating the cutting of carbon fiber-reinforced polymers (CFRP) with a helical end mill. A methodology is developed for predicting the cutting forces by transforming specific cutting energies from orthogonal cutting to oblique cutting. It is shown that the method developed is capable of predicting the cutting forces in helical end milling of unidirectional and multidirectional composites and over the entire range of fiber orientations from 0° to 180°. This is a significant improvement over previous models that were only capable of addressing orthogonal cutting and/or a limited range of fiber orientations. Model predictions were compared with experimental data and were found to be in good agreement in cutting unidirectional laminate, but with lesser agreement in the case of a multidirectional laminate.     

An investigation of cutting forces in machining with worn ball-end mill

Reliable tool wear monitoring technique is one of the important aspects for achieving an integrated and self-adjusting manufacturing system. In this study, an analytical model is proposed to estimate the cutting forces, the tool geometry, and the chip geometry in relation to the flank wear, when milling with a ball-end mill. Modeling is based on thermomechanical modelling of oblique cutting. The worn tool geometry is decomposed into a series of axial elementary cutting edges. At any active tooth element, the flank wear geometry is calculated and the chip formation is obtained from an oblique cutting process characterised by local undeformed chip section and local cutting angles. Coated carbide ball-end tool, and a titanium workpiece material have been considered in this paper. The results found by using developed models have shown good agreement with experimental results.     

High-speed five-axis milling of hardened tool steel

This paper investigates critical issues related to high-speed five-axis milling of hardened D2 tool steel (hardness HRc 63). A forging die cavity was designed to represent the typical features in dies and molds and to simulate several effects resulting from complex tool path generation. Cutting tool materials used were coated carbide for the roughing and semi-finishing processes and polycrystalline cubic boron nitride (PCBN) for the finishing process. The effects of complex tool paths on several critical machining issues such as chip morphology, cutting forces, tool wear mechanisms, tool life and surface integrity were also investigated. The main tool failure mode was chipping due to the machine tool dynamics. A five-axis analytical force model that includes the cutter location (CL) data file for computing the chip load has been developed. The effect of instantaneous tilt angle variation on the forces was also included. Verification of the force model has been performed and adopted as a basis for explaining the difficulties involved with high-speed five-axis milling of D2 tool steel.     

Predicting cutting forces in face milling

It is shown how orthogonal machining theory can be applied to predict the cutting forces in face milling from a knowledge of the work material properties and cutting conditions. Predicted and experimental results are compared.     

The prediction of cutting forces in the ball-end milling process—II. Cut geometry analysis and model verification

This paper presents a model for the prediction of cutting forces in the ball-end milling process. The steps used in developing the force model are based on the mechanistic principles of metal cutting. The cutting forces are calculated on the basis of the engaged cut geometry, the underformed chip thickness distribution along the cutting edges, and the empirical relationships that relate the cutting forces to the undeformed chip geometry. A simplified cutter runout model, which characterizes the effect of cutter axis offset and tilt on the undeformed chip geometry, has been formulated. A model building procedure based on experimentally measured average forces and the associated runout data is developed to identify the numerical values of the empirical model parameters for the particular workpiece/cutter combination.     

CNC machine tool surface interpolator for ball-end milling of free-form surfaces

This paper presents a new type of CNC machine tool interpolator that is capable of generating the cutter path for ball-end milling of a free-form surface. The surface interpolator comprises on-line algorithms for cutter-contact (CC) path scheduling, CC path interpolation, and tool offsetting. The interpolator algorithms for iso-parametric, iso-scallop and iso-planar machining methods are developed, respectively. The proposed surface interpolator method gains the advantages for minimizing the data loaded to the CNC machine tool and maintaining the desired feedrate and position accuracy along the CC path.     

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.     

Feedrate optimization and tool profile modification for the high-efficiency ball-end milling process

Trend in die/mold machining is to produce highly quailed surface using the high-speed hard machining with the ball-end cutter. The ball-end milling is, however, less efficiency than the flat end milling. It is important to optimize the feedrate that gives the maximum material removal rate constrained by an allowable surface roughness. The state-of-art of the CBN ball-end cutter technology allows increasing the tooth feed for high-speed and high-efficiency machining. However, because the spherical shape of the cutter can result in the scallop-liked cusps on the machined surface, the surface roughness consideration makes a feedrate limitation to the CBN cutter. In this paper, the optimization of the feedrate by considering the generated-scallop effect of the ball-end cutter has been studied. It was found that the tooth feed must be kept within one third of the path pick in order to keep the feed-interval scallop height not over the path-interval scallop height. Therefore, the potential capability of the CBN cutter for the larger tooth feed (i.e. high efficient) machining can not be fully exploited. It was found a notch-cut on the center of the ball-end cutter reduced the feed-interval cusp height, thus allowing an increased feedrate of more than 50% compared with the standard ball-end cutter. If the parameters of the notch-cut profile can be optimized, it is believed that the feedrate can be further increased.     

Modeling of cutting forces in near dry machining under tool wear effect

A predictive model for the cutting forces in near dry machining, in which only a small amount of cutting fluid is used, is developed based on considerations of both the lubricating effect and the cooling effect. For the lubricating effect, with the material properties, lubricating parameters, and cutting conditions, the friction coefficient in near dry machining is calculated based on the boundary lubrication model for use in a modified Oxley's approach to determine the cutting forces. For the cooling effect in near dry machining, a moving heat source method is pursued to quantify the primary-zone shear deformation heating, the secondary-zone friction heating, and flank face air–oil mixture cooling. These two effects are considered collectively to estimate cutting forces under the condition of sharp tools. The predicted variables of flow stress, contact length, and shear angle obtained from the model are used to predict the cutting forces due to the tool flank wear effect based on Waldorf's model. Comparisons are made between predicted and experimental cutting forces for sharp tools and worn tools in the cutting of AISI 1045 with uncoated carbide tools. The results show that the proposed model provides average prediction errors of 14% in the tangential cutting force direction, 21% in the axial directions, and 30% in the radial directions within the experimental test condition range (cutting speeds of 45.75–137.25 m/min, feeds 0.0508–0.1016 mm/rev, and depth of cuts 0.508–1.016 mm). It is also found that the cutting forces in near dry machining are generally lower than those under dry machining condition. Under cutting speeds of 91.5 and 137.25 m/min, the deviations of the predicted forces between near dry machining and dry machining range from 5% to 39% for axial cutting forces, 3% to 36% for radial cutting forces, and 1% to 32% for tangential cutting forces. It suggests that the lubricating mechanism has a stronger effect on cutting forces than the cooling mechanism when cutting AISI 1045 with uncoated carbide tools.     

Theoretical modelling and simulation of cutting forces in face milling with cutter runout

A new approach to theoretical modelling and simulation of cutting forces in face milling is presented. Based on a predictive machining theory, the action of a milling cutter is modeled as the simultaneous actions of a number of single-point cutting tools. The milling forces are predicted from the workpiece material properties, cutter parameters, tooth geometry, cutting conditions and types of milling. The properties of the workpiece material are considered as functions of strain, strain-rate and temperature in the cutting region. It takes into account the effect of the intermittent contact between each milling tooth and the workpiece on the temperature in the cutting region. It also takes into account the effect of cutter runout on the undeformed chip thickness. Milling experiments have been conducted to verify the proposed model. Good agreements between the experimental and simulated results are presented.     

Experimental study of friction from cutting forces in orthogonal milling

The present work shows the procedure used for the study of friction in orthogonal milling. The equipment employed to measure cutting forces includes a rotating dynamometer and a multichannel portable data acquisition system. Signal filtering is applied to reduce the dynamic system problems. The analysis of the relation between cutting force (F_c) and radial force (F_r) allows to assess the dependence of friction and chip thickness on cutting speed and feed per revolution. Also, the study of the influence of workpiece material on milling process shows that cutting force (F_c) decreases and friction increases with improving workpiece material machinability. Hence, a significant contribution to knowledge in a research field with a little previous literature, such as the friction in orthogonal milling, is made in the present work through a comparative analysis of cutting forces (F_c and F_r) that allows to study the influence of cutting speed and feed per revolution on friction and to propose a new approach for machinability associated to F_c rather than to friction coefficient.     

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.     

The prediction of cutting forces in end milling with application to cornering cuts

This paper presents the development, verification, and implementation of a mechanistic model for the force system in end milling. This model is based on chip load, cut geometry, and the relationship between cutting forces and chip load. A model building procedure based on experimentally obtained average forces is presented and both instantaneous and average force system characteristics are described as a function of cut geometry and feed rate. A computer program developed to implement the mechanistic model provides tabular and graphical outputs which show force distributions as functions of the axial depth of cut and rotation of the cutter. Force characteristics during concerning cuts are predicted by the model and verified via a set of cornering cut experiments typical of aerospace machining operations. Force characteristics in cornering are examined as a function of axial depth of cut and feedrate.