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.     

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.     

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 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.     

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.     

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.     

Model development for the prediction of surface topography generated by ball-end mills taking into account the tool parallel axis offset. Experimental validation

This paper presents a model for the topography prediction of ball-end milled surfaces, considering the tool parallel axis offset. First, the equations of cutting edge trajectories and the envelope equation of the material swept by the tool are derived. Later, the trajectories are cut by planes perpendicular to the feed direction obtaining a set of transcendental equations that are solved by transforming them to polynomial equations through Chebyshev expansions. This procedure presents the advantage on previous models in literature of not requiring any starting point to achieve the solution. Finally, experimental results are presented and compared to the model predictions.     

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.     

Experimental study of surface roughness in slot end milling AL2014-T6

The aim of this work was to analyze the influence of cutting condition and tool geometry on surface roughness when slot end milling AL2014-T6. The parameters considered were the cutting speed, feed, depth of cut, concavity and axial relief angles of the end cutting edge of the end mill. Surface roughness models for both dry cutting and coolant conditions were built using the response surface methodology (RSM) and the experimental results. The results showed that the dry-cut roughness was reduced by applying cutting fluid. The significant factors affecting the dry-cut model were the cutting speed, feed, concavity and axial relief angles; while for the coolant model, they were the feed and concavity angle. Surface roughness generally increases with the increase of feed, concavity and axial relief angles, while concavity angle is more than 2.5°.     

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.     

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.     

A study of back cutting surface finish from tool errors and machine tool deviations during face milling

The surface finish of mechanical components produced by face milling is given by factors such as cutting conditions, workpiece material, cutting geometry, tool errors and machine tool deviations. The contribution of the different tool teeth to imperfections in the machined surface is strongly influenced by tool errors such as radial and axial runouts. The surface profile of milled parts is not only affected by chip removal due to front cutting, but also by back cutting, which must be taken into account when predicting surface roughness. In the present work, the influence of back cutting on the surface finish obtained by face milling operations is studied. Final part surface roughness is modelled from tool runouts and height deviations that affect the surface marks provoked by back cutting. Round insert cutting tools and surface positions defined by cutter axis trajectory are considered, and milling experiments are developed for a spindle speed of 750 rpm, depth of cut of 0.5 mm and feeds from 0.4 to 1.0 mm/rev. Experimental observations are compared with the theoretical predictions provided by the surface roughness model, and good agreement is found between both results. Surface imperfections caused by front and back cutting are analysed, and discrepancies between experiments and numerical predictions are explained by undeformed chip thickness variations along the tool tooth cutting edge, the tearing of the workpiece material, and fluctuations in the feedrate and height deviation during machine tool axis displacement.     

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 review of surface roughness generation in ultra-precision machining

Ultra-precision machining (UPM) is capable of manufacturing a high quality surface at a nanometric surface roughness. For such high quality surface in a UPM process, due to the machining complexity any variable would be possible to deteriorate surface quality, consequently receiving much attention and interest. The general factors are summarized as machine tool, cutting conditions, tool geometry, environmental conditions, material property, chip formation, tool wear, vibration etc. This paper aims to review the current state of the art in studying the surface roughness formation and the factors influencing surface roughness in UPM. Firstly, the surface roughness characteristics in UPM is introduced. Then in UPM, a wide variety of factors for surface roughness are then reviewed in detail and the mechanism of surface roughness formation is concluded thoroughly. Finally, the challenges and opportunities faced by industry and academia are discussed and several principle conclusions are drawn.     

An in-process surface recognition system based on neural networks in end milling cutting operations

An in-process based surface recognition system to predict the surface roughness of machined parts in the end milling process was developed in this research to assure product quality and increase production rate by predicting the surface finish parameters in real time. In this system, an accelerometer and a proximity sensor are employed as in-process surface recognition sensors during cutting to collect the vibration and rotation data, respectively. Using spindle speed, feed rate, depth of cut, and the vibration average per revolution (VAPR) as four input neurons, an artificial neural networks (ANN) model based on backpropagation was developed to predict the output neuron-surface roughness R_a values. The experimental results show that the proposed ANN surface recognition model has a high accuracy rate (96–99%) for predicting surface roughness under a variety of combinations of cutting conditions. This system is also economical, efficient, and able to be implemented to achieve the goal of in-process surface recognition by retrieving the weightings (which were generated from training and testing by the artificial neural networks), predicting the surface roughness R_a values while the part is being machined, and giving feedback to the operators when the necessary action has to be taken.     

An improved method for scheduling the tool paths for three-axis surface machining

This paper presents a new tool-path scheduling method to improve the accuracy and efficiency of three-axis surface machining. The features of the proposed method include: (1) surface-error-based segmentation in the feed-forward direction; (2) consideration for the coupled effect of the segmentation in the feed-forward and the path-interval directions; and (3) compensation for the tool location to control the surface error and the segmentation efficiency. In this paper, we consider a ball-end mill for surface machining.     

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.     

Impact of the cutting dynamics of small radial immersion milling operations on machined surface roughness

This paper deals with a numerical and experimental study of the dynamics of flank milling operations at low cutting rates. It focuses on both properties of the cutting vibratory phenomena and their impacts on the roughness of the machined surface. The study is based on a one degree of freedom model of the mechanical machining system. The system is of the rigid cutter–flexible workpiece type. The cutting force model is based on the regenerative mechanism. The roughness of the surface machined at high speed revolutions has been studied for both forced vibrations occurring during stable cutting and self-excited vibrations occurring during unstable cutting. It is shown that forced vibrations have only a very slight impact (roughness remains quite similar to that obtained with a fully rigid mechanical system), while unstable cutting mainly impacts roughness. The stable milling zones can be shown on a roughness map. The study of the roughness shows that the boundary between stable and unstable cutting conditions, in the case of interrupted cutting, is a wide zone characterised by a doubling of the tooth passing period. In this zone, only one tooth over two is removing material due to the vibratory motion. A discussion explains the phenomenon.     

A study on surface roughness in abrasive waterjet machining process using artificial neural networks and regression analysis method

In the present study, artificial neural network (ANN) and regression model were developed to predict surface roughness in abrasive waterjet machining (AWJ) process. In the development of predictive models, machining parameters of traverse speed, waterjet pressure, standoff distance, abrasive grit size and abrasive flow rate were considered as model variables. For this purpose, Taguchi's design of experiments was carried out in order to collect surface roughness values. A feed forward neural network based on back propagation was made up of 13 input neurons, 22 hidden neurons and one output neuron. The 13 sets of data were randomly selected from orthogonal array for training and residuals were used to check the performance. Analysis of variance (ANOVA) and F-test were used to check the validity of regression model and to determine the significant parameter affecting the surface roughness. The statistical analysis showed that the waterjet pressure was an utmost parameter on surface roughness. The microstructures of machined surfaces were also studied by scanning electron microscopy (SEM). The SEM investigations revealed that AWJ machining produced three distinct zones along the cut surface of AA 7075 aluminium alloy and surface striations and waviness were increased significantly with jet pressure.     

高速铣削加工表面位置误差的频域分析

在高速铣削加工过程中,提高轴向切削深度和主轴转速可以获得较高的材料去除率,然而限制轴向切削深度提高的一个因素是加工颤振.高速铣削系统动态失稳可能导致加工零件的表面几何精度偏差.分析高速铣削的表面位置误差对表征切削过程、刀具寿命估算和加工优化都起着重要作用.因此,在不考虑再生颤振影响的前提下,提出了一种数值分析和加工实验相结合的方法来研究表面位置误差.首先,构建了高速铣削加工过程模型,然后建立了动态铣削力模型,并推导了表面位置误差的分析方法.通过数值分析和铣削实验相结合,得到了高速铣削加工的稳定性叶瓣图.接下来,研究了逆铣削加工过程的表面位置误差,并详细分析了主轴转速和轴向切削位置对表面位置误差的影响规律.最后,把稳定性叶瓣和表面位置误差数据组合在同一个图里得到了高速铣削加工的综合分析图.借助综合分析图,能预测表面位置误差和优化高速铣削的工艺条件.