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.     

Cutting force prediction of sculptured surface ball-end milling using Z-map

The cutting force in ball-end milling of sculptured surfaces is calculated. In sculptured surface machining, a simple method to determine the cutter contact area is necessary since cutting geometry is complicated and cutter contact area changes continuously. In this study, the cutter contact area is determined from the Z-map of the surface geometry and current cutter location. To determine cutting edge element engagement, the cutting edge elements are projected onto the cutter plane normal to the Z-axis and compared with the cutter contact area obtained from the Z-map. Cutting forces acting on the engaged cutting edge elements are calculated using an empirical method. Empirical cutting mechanism parameters are set as functions of cutting edge element position angle in order to consider the cutting action variation along the cutting edge. The relationship between undeformed chip geometry and the cutter feed inclination angle is also analyzed. The resultant cutting force is calculated by numerical integration of cutting forces acting on the engaged cutting edge elements. A series of experiments were performed to verify the proposed cutting force estimation model. It is shown that the proposed method predicts cutting force effectively for any geometry including sculptured surfaces with cusp marks and a hole.     

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.     

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.     

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.     

Predictive force model for ball-end milling and experimental validation with a wavelike form machining test

This paper presents a predictive force model for ball-end milling based on thermomechanical modelling of oblique cutting. The tool geometry is decomposed into a series of axial elementary cutting edges. At any active tooth element, the chip formation is obtained from an oblique cutting process characterised by local undeformed chip section and local cutting angles. This method predicts accurately the cutting force distribution on the helical ball-end mill flutes from the tool geometry, the pre-form surface, the tool path, the cutting conditions, the material behaviour and the friction at the tool-chip interface. The model is applied for a complex surface which is a wavelike form used as a validation machining test. The results are compared with experimental data obtained from ball-end milling tests performed on a 3-axis CNC equipped with a Kistler dynamometer.     

Static rigid force model for 3-axis ball-end milling of sculptured surfaces

Static rigid force model is used to estimate cutting forces of sculptured surface in a straightforward way, without considering tool deflection, machine tool dynamic behavior and any vibration effects. Two programs were used for calculations, “ACIS” the 3-D geometric modeler and “VISUAL BASIC”. Two programs were edited and used to perform the calculations, the scheme program to model the work piece, tool and cutting edge and to obtain the geometric data and the VISUAL BASIC program design to use ACIS geometric data to calculate the cutting forces. The engaged part of the cutting edge and work piece is divided into small differential oblique cutting edge segments. Friction, shear angles and shear stresses are identified from orthogonal cutting database available in literature. The cutting force components, for each tool rotational position, are calculated by summing up the differential cutting forces. Laboratory tests were conducted to verify the predictions of the model. The work pieces were prepared from CK45 steel using an insert-type ball-end cutter. No coolant was used in any of the experimental works. The cutting forces predicted have shown good agreement with experimental results.     

The form error prediction in side wall machining considering tool deflection

In this research, an effective method for the form error prediction in side wall machining with a flat end mill is suggested. The form error is predicted directly from the tool deflection without surface generation by cutting edge locus with time simulation. The developed model can predict the surface form error accurately about 300 times faster than the previous method. Cutting forces and tool deflection are calculated considering tool geometry, tool setting error and machine tool stiffness. The characteristics and the difference of generated surface shape in up milling and down milling are discussed. The usefulness of the presented method is verified from a set of experiments under various cutting conditions generally used in die and mold manufacturing. This study contributes to real time surface shape estimation and cutting process planning for the improvement of form accuracy.     

On cutter deflection surface errors in peripheral milling

Cutter deflections induce significant amount of surface error on machined components and it is one of the major obstacles towards achieving higher productivity in peripheral milling operation. These surface errors do not take one particular form and their shape and profile measured along axial direction, varies significantly with cutting conditions. The understanding and characterization of all possible surface error types is of immense value to process planners as it forms a basis for controlling and compensating them. This paper presents a methodology to classify surface error profiles and to relate the same with cutting conditions in terms of axial and radial engagement between cutter and workpiece. The proposed characterization scheme has been validated using computational studies and machining experiments. The importance of proposed characterization is further demonstrated in understanding peripheral milling of curved geometries where workpiece curvature influences radial engagement of the cutter that often changes surface error shape both qualitatively and quantitatively. Computational and experimental studies undertaken to study machining of curved geometries underline the importance of proposed characterization scheme in identifying correct cutting conditions for a given machining situation.     

Feed rate optimization for 3-axis ball-end milling of sculptured surfaces

The aim of this research is to improve the productivity of CNC machine tools by optimizing feed rate. To optimize feed rate two programs were used: “ACIS” (with scheme language) and “Visual Basic”. The scheme program for modeling the work piece, tool, cutting edge, and calculating maximum cutting force and the Visual Basic program to control all the activities linked to the ACIS program for estimating optimized feed values. Laboratory tests were conducted to verify the results from the modeling, using an insert-type one-flute ball-end cutter on a CK45 carbon steel work piece. No coolant was used throughout the experimental works. Comparisons were made between the maximum cutting forces, in the “fix” feed rate tests. The results indicate significant increases in productivity, which can be achieved, by using the optimized feed rate method.     

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.     

The form error reduction in side wall machining using successive down and up milling

In this paper, the form error reduction method is presented in side wall machining. Cutting forces and tool deflection are calculated considering surface profile generated by the previous cutting such as roughing and semi-finishing. Using the form error prediction from tool deflection curve, the effects of tool teeth numbers, tool geometry and cutting conditions on the form error are analyzed. The characteristics and the differences of generated surface shape in up and down milling are also discussed and over-cut free condition in up milling is presented. The form error reduction method through successive down and up milling has been suggested. The effectiveness and usefulness of the suggested method are verified from a series of cutting experiments under various cutting conditions. It is confirmed that the form error prediction from tool deflection in side wall machining can be used in proper cutting condition selection and real time surface error simulation for CAD/CAM systems. This research also contributes to cutting process optimization for the improvement of form accuracy in die and mold manufacture.     

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.     

A study of the surface scallop generating mechanism in the ball-end milling process

This paper presents the model, simulation and experimental verification of the scallop formation on the machined surface in the ball-end milling process. In the milling process, the cutting edges of the cutter are in a motion of combined translation and rotation. The periodical variation of the cutting edge orientation during spindle rotation results in two kinds of scallops generated on the machined surface: the pick-interval scallop and the feed-interval scallop. Because of the low feed and comparably large pick used in the conventional ball-end milling process, the emphasis of previous works has been placed on studying the geometric generating mechanism of the pick-interval scallop while the feed-interval scallop has been largely ignored. Trend of the high-speed and high efficiency machining, however, has pushed the feed reaching the same level of the pick. For the high-speed machining where the high feed/pick ratio is used, the feed-interval scallop must be taken into account. This paper presents a new model that describes the path-interval and feed-interval scallops generating mechanism in the ball-end milling processes. Parameters such as the tool radius, feed/pick ratio, initial cutting edge entrance angle, and tool-axis inclination angles have been studied and experimental verified. It was found that the feed-interval scallop height was 3–4 times large than the path-interval scallop height at the high-speed machining case. The scallop height was continuously reduced by increasing the tool-axis inclination angle. An inclination angle up to 10° is, however, good enough for most tool diameters from the surface roughness viewpoint.     

Effect of cutter runout on process geometry and forces in peripheral milling of curved surfaces with variable curvature

This paper presents a novel method for cutting force modeling related to peripheral milling of curved surfaces including the effect of cutter runout, which often changes the rotation radii of cutting points. Emphasis is put on how to efficiently incorporate the continuously changing workpiece geometry along the tool path into the calculation procedure of tool position, feed direction, instantaneous uncut chip thickness (IUCT) and entry/exit angles, which are required in the calculation of cutting force. Mathematical models are derived in detail to calculate these process parameters in occurrence of cutter runout. On the basis of developed models, some key techniques related to the prediction of the instantaneous cutting forces in peripheral milling of curved surfaces are suggested together with a whole simulation procedure. Experiments are performed to verify the predicted cutting forces; meanwhile, the efficiency of the proposed method is highlighted by a comparative study of the existing method taken from the literature.     

Time domain model of plunge milling operation

Plunge milling operations are used to remove excess material rapidly in roughing operations. The cutter is fed in the direction of spindle axis which has the highest structural rigidity. This paper presents time domain modeling of mechanics and dynamics of plunge milling process. The cutter is assumed to be flexible in lateral, axial, and torsional directions. The rigid body feed motion of the cutter and structural vibrations of the tool are combined to evaluate time varying dynamic chip load distribution along the cutting edge. The cutting forces in lateral and axial directions and torque are predicted by considering the feed, radial engagement, tool geometry, spindle speed, and the regeneration of the chip load due to vibrations. The mathematical model is experimentally validated by comparing simulated forces and vibrations against measurements collected from plunge milling tests. The study shows that the lateral forces and vibrations exist only if the inserts are not symmetric, and the primary source of chatter is the torsional–axial vibrations of the plunge mill. The chatter vibrations can be reduced by increasing the torsional stiffness with strengthened flute cavities.     

Process geometry modeling with cutter runout for milling of curved surfaces

Prediction of cutting forces and machined surface error in peripheral milling of curved geometries is non-trivial due to varying workpiece curvature along tool path. The complexity in this case, arises due to continuously changing process geometry as workpiece curvature varies along tool path. In the presence of cutter runout, the situation is further complicated owing to changing radii of cutting points. The present work attempts to model process geometry in machining of curved geometries and in the presence of cutter runout. A mathematical model computing process geometry parameters which include cutter/workpiece engagements and instantaneous uncut chip thickness in the presence of cutter runout is presented. The developed model is more realistic as it accounts for interaction of cutting tooth trajectory with that of preceding teeth trajectories in computing process geometry. Computer simulation studies carried for this purpose has shown that it is essential to account for teeth trajectory interactions for accurate prediction of process geometry parameters. This aspect is further confirmed with machining experiments, which were conducted to validate this aspect. From the outcomes of present work, it is clearly seen that the computation of process geometry during machining of curved geometries and in presence of cutter runout is not straightforward and requires a systematic approach as presented in this paper.     

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.     

Surface topography in ball-end milling processes as a function of feed per tooth and radial depth of cut

A numerical model was developed that predicts topography and surface roughness in ball-end milling processes, based on geometric tool-workpiece intersection. It allows determining surface topography as a function of feed per tooth and revolution, radial depth of cut, axial depth of cut, number of teeth, tool teeth radii, helix angle, eccentricity and phase angle between teeth. It determines profile roughness parameters, as well as areal roughness parameters such as average roughness Sa, maximum peak-to-valley roughness St, volume of summit material V and a proposed new time coefficient Ct. It relates surface roughness to milling time. Moreover, feed per tooth and revolution f and radial depth of cut Rd were calculated that minimise parameters Sa·Ct, St·Ct and V·Ct. Minimum Sa·Ct and St·Ct provide minimum roughness with minimum milling time. Minimum V·Ct means minimum milling time with minimum material removal in manual polishing operation. At low radial depth of cut, roughness is low regardless of feed employed. On the contrary, at high radial depth of cut, roughness depends remarkably on feed: the higher the feed, the higher the roughness. In order to simultaneously minimise roughness and time, high f and low Rd should be used. In that case also volume of summit material is minimised.     

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.