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.     

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.     

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.     

自由曲面平头立铣刀五轴数控加工轨迹的计算方法

提出了一种在参数坐标系下自适应步长和行距的计算方法 ,该算法考虑了不同刀具接触点处的曲率差异 ,在满足加工精度和粗糙度的前提下 ,又能有效地提高加工效率。该算法适合加工汽车车身模具等曲率变化大的曲面。文中还给出了刀位计算公式。     

The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 2: Surface generation model and experimental verification

This paper presents a surface generation model for sculptured surface productions using the ball-end milling process. In this model, machining errors caused by tool deflections are studied. As shown in Part 1 of this paper, instantaneous horizontal cutting forces can be evaluated from the cutting geometries using mechanistic force models. In this paper, a tool deflection model is developed to calculate the corresponding horizontal tool deflection at the surface generation points on the cutter. The sensitivity of the machining errors to tool deflections, both in magnitude and direction, has been analyzed via the deflection sensitivity of the surface geometry. Machining errors are then determined from the tool deflection and the deflection sensitivity of the designed surface. The ability of this model in predicting dimensional errors for sculptured surfaces produced by the ball-end milling process has been verified by a machining experiment. In addition to providing a means to predict dimensional accuracy prior to actual cutting, this surface generation model can also be used as a tool for quality control and machining planning.     

The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 1: Chip geometry analysis and cutting force prediction

The study of machining errors caused by tool deflection in the balkend milling process involves four issues, namely the chip geometry, the cutting force, the tool deflection and the deflection sensitivity of the surface geometry. In this paper, chip geometry and cutting force are investigated. The study on chip geometry includes the undeformed radial chip thickness, the chip engagement surface and the relationship between feed boundary and feed angle. For cutting force prediction, a rigid force model and a flexible force model are developed. Instantaneous cutting forces of a machining experiment for two 2D sculptured surfaces produced by the ball-end milling process are simulated using these force models and are verified by force measurements. This information is used in Part 2 of this paper, together with a tool deflection model and the deflection sensitivity of the surface geometry, to predict the machining errors of the machined sculptured surfaces.     

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.     

An expert troubleshooting system for the milling process

Common problems experienced in milling processes include forced and chatter vibrations, tolerance violations, chipping and premature wear of the tools. This paper presents an expert system which attempts to troubleshoot the source of milling problems by utilising dynamics data coupled with the opinion of the operator and acoustic Fourier spectrum data taken from the cutting process. The expert system utilises a fuzzy logic based process to interpret the signals and information, and recommends possible alterations to the process to achieve high-performance milling operations.Specific inference engines were developed to assess the chatter stability, variation in cutting force coefficient, tool run-out and forced vibration characteristics of the system. Lastly, a stability lobe plot interpretation engine to automate the lobe selection process and recommend new, chatter free cutting conditions, was also developed. The chatter stability inference engine was tested with real cutting data, through acoustic measurements taken from various cutting conditions on an aluminium milling process. The chatter inference engine successfully determined the stability of the system for each sampled cutting condition. The robustness of the troubleshooting system depends on the accuracy of acoustic and frequency response measurements.     

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.     

Sculpture surface machining: a generalized model of ball-end milling force system

A new mechanistic model is presented for the prediction of a cutting force system in ball-end milling of sculpture surfaces. The model has the ability to calculate the workpiece/cutter intersection domain automatically for a given cutter location (CL) file, cutter and workpiece geometries. Furthermore, an analytical approach is used to determine the instantaneous chip load (with and without runout) and cutting forces. In addition to predicting the cutting forces, the model also employs a Boolean approach for a given cutter, workpiece geometries, and CL file to determine the surface topography and scallop height variations along the workpiece surface which can be visualized in 3-D. The results of model validation experiments on machining Ti-6A1-4V are also reported. Comparisons of the predicted and measured forces as well as surface topography show good agreement.     

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.     

面向CNC系统的自由曲面模型的建立

在分析现有的曲面模型不利于进行 Ｃ Ｎ Ｃ 加工的基础上,建立了一种面向 Ｃ Ｎ Ｃ 加工的自由曲面模型,介绍了该曲面模型的基本要求并阐明了建立的措施和方法。     

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.     

Enhanced virtual machining for sculptured surfaces by integrating machine tool error models into NC machining simulation

Sculptured surface machining is a time-consuming and costly process. It requires simultaneously controlled motion of the machine axes. However, positioning inaccuracies or errors exist in machine tools. The combination of error motions of the machine axes will result in a complicated pattern of part geometry errors. In order to quantitatively predict these part geometry errors, a new application framework ‘enhanced virtual machining’ is developed. It integrates machine tool error models into NC machining simulation. The ideal cutter path in the NC program for surface machining is discretized into sub-paths. For each interpolated cutter location, the machine geometric errors are predicted from the machine tool error model. Both the solid modeling approach and the surface modeling approach are used to translate machine geometric errors into part geometry errors for sculptured surface machining. The solid modeling approach obtains the final part geometry by subtracting the tool swept volume from the stock geometric model. The surface modeling approach approximates the actual cutter contact points by calculating the cutting tool motion and geometry. The simulation results show that the machine tool error model can be effectively integrated into sculptured surface machining to predict part geometry errors before the real cutting begins.     

Modeling of process geometry in peripheral milling of curved surfaces

This paper presents an approach for modeling of the process geometry in peripheral milling of curved surfaces. The modeled process geometry involves feed direction, equivalent feedrate and cutter entry/exit angle. The equivalent feedrate, which is defined at the centroid of cutting cross-section, is proposed to measure the actual machining feedrate. The milling process of curved surface is discretized at intervals of feed per tooth for describing the variation of process geometry. The mathematical models for calculating the process geometry of each segmented cutting process are presented. Two same curved surfaces are machined. The tool paths are carried out with NURBS interpolation and traditional consecutive small line segments interpolation, respectively. The simulated and measured results are presented for the verification of the proposed method.     

Estimation of cutter deflection and form error in ball-end milling processes

This paper presents a method to analyze the 3-dimensional form error of a ball-end milled surface due to the elastic compliance of the cutting tool. In order to estimate the form error in various cutting modes, the cutting force and the cutter deflection models including the effect of the surface inclination were established. The cutting forces were calculated by using the cutter contact area determined from the Z-map of the surface geometry and the current cutter location. The tool deflection responding to the cutting force was then calculated by considering the cutter and the holder stiffness. The cutter was modeled as a cantilever beam consisting of the shank and the flute. The stiffness of the holder was measured experimentally. Various experimental works have been performed to verify the validity of the proposed model. It is shown that the proposed method is capable of accurate prediction of cutting forces and the surface form error.     

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.     

Modeling and simulation of milling processes including process damping effects

Especially in high speed milling of aluminum alloys in the aviation industry, chamfered milling tools have proven themselves. Due to the chamfer, an extended contact between the tool and the workpiece at the flank face is evoked, which leads to additional process damping forces opposed to tool vibrations. Hence, the cutting process shows improved stability characteristics. This article presents an approach for the identification and modeling of these process damping effects in transient milling simulations. For this purpose, a simulation- and experiment-based procedure for the identification of required simulation parameters depending on the tool chamfer geometry is introduced and evaluated. Finally, the identified parameters are used for transient simulations of milling processes with extended stability due to the tool chamfer. The suitability of the proposed identification method and simulation model for milling with process damping is finally proved by a comparison between simulations and experiments.     

Compensation for form error of end-milled sculptured surfaces using discrete measurement data

In this research, improvement of the form accuracy of parts having end-milled sculptured surfaces is studied. The proposed scheme uses the discrete measurement data from coordinate measuring machines and consists of three steps: optimal match, decomposition, and compensation. The optimal macth is used to best fit the measurement data with the design form so as to determine sampled form errors. The decomposition is developed to characterize the sampled form errors into the deterministic and the random components, which are associated with the waviness and the roughness of the form errors, respectively. Then, in the compensation step, compensation for the waviness is applied to improve the form accuracy of an end-milled sculptured surface. An experiment is conducted to demonstrate the effectiveness of the proposed scheme.     

Penetration–elimination method for five-axis CNC machining of sculptured surfaces

In this paper, a new tool positioning strategy for five-axis machining, called the penetration–elimination method (PEM), is introduced. The PEM gains from two innovative techniques that can considerably improve the computational efficiency during the calculation of the optimal tool orientations.The first technique includes developing a quantitative definition for the gouging concept and using this definition in conjunction with powerful numerical root-finder algorithms to determine the optimized tool orientations. The second technique dynamically detects the ineffective grid points and drops them from calculations and consequently takes a great role in reducing the computational burden. The ability of the PEM in removing various types of gouging has been shown via several examples. The computational efficiency of the PEM has been compared with another recently described method named the arc-intersect method (AIM). This comparison shows that although the two methods reach the same solution for the tool orientation, the PEM is averagely 7.5 times faster than the AIM.