The estimation of cutting forces and specific force coefficients during finishing ball end milling of inclined surfaces

The majority of cutting force models applied for the ball end milling process includes only the influence of cutting parameters (e.g. feedrate, depth of cut, cutting speed) and estimates forces on the basis of coefficients calibrated during slot milling. Furthermore, the radial run out phenomenon is predominantly not considered in these models. However this approach can induce excessive force estimation errors, especially during finishing ball end milling of sculptured surfaces. In addition, most of cutting force models is formulated for the ball end milling process with axial depths of cut exceeding 0.5 mm and thus, they are not oriented directly to the finishing processes. Therefore, this paper proposes an accurate cutting force model applied for the finishing ball end milling, which includes also the influence of surface inclination and cutter's run out. As part of this work the new method of specific force coefficients calibration has been also developed. This approach is based on the calibration during ball end milling with various surface inclinations and the application of instantaneous force signals as an input data. Furthermore, the analysis of specific force coefficients in function of feed per tooth, cutting speed and surface inclination angle was also presented. In order to determine geometrical elements of cut precisely, the radial run out was considered in equations applied for the calculation of sectional area of cut and active length of cutting edge. Research revealed that cutter's run out and surface inclination angle have significant influence on the cutting forces, both in the quantitative and qualitative aspect. The formulated model enables cutting force estimation in the wide range of cutting parameters, assuring relative error's values below 16%. Furthermore, the consideration of cutter's radial run out phenomenon in the developed model enables the reduction of model's relative error by the 7% in relation to the model excluding radial run out.     

Fuzzy control of feed rate in end milling operations

In order to improve productivity in end milling operations, a new adaptive control system based on fuzzy logics to maintain a constant cutting force is developed. It is shown, by experimental cutting tests, that the cutting tool travels in the air cut with fast feed rate, yet in the varying depths of cut, the tool travels with an adjustable feed rate to prevent the occurrence of tool breakage and maintain a high metal removal rate.     

CAD assisted chatter-free NC tool path generation in milling

A chatter vibration-free NC tool path preparation strategy is presented for CAD/CAM systems. The stability charts, which contain chatter-free axial depth and radial width of cuts at a practical cutting speed range, are identified from time domain simulation of dynamic end milling operations. The time domain simulation system allows multiple modes of the machine tool-end mill structure whose transfer functions are measured. The existing pocketing routines in a CAD/CAM system are corrected by planning chatter-free axial depth and radial width of cuts that are automatically selected from the stability data bank during NC tool path generation. A newly introduced linear tool-path pocketing strategy is shown to be the most productive algorithm for dynamically corrected tool paths. The method is supported by experimental results.     

Prediction of chatter in NC machining based on a dynamic cutting force model for ball end milling

Ball end milling is one of the most widely used cutting processes in the automotive, aerospace, die/mold, and machine parts industries, and the chatter generated under unsuitable cutting conditions is an extremely serious problem as it causes excessive tool wear, noise, tool breakage, and deterioration of the surface quality. Due to the critical nature of detecting and preventing chatter, we propose a dynamic cutting force model for ball end milling that can precisely predict the cutting force for both stable and unstable cutting states because our uncut chip thickness model considers the back-side cutting effect in unstable cutting states. Furthermore, the dynamic cutting force model considers both tool runout and the penetration effect to improve the accuracy of its predictions. We developed software for calculating the cutting configuration and predicting the dynamic cutting force in general NC machining as well as single-path cutting. The chatter in ball end milling can be detected from the calculated cutting forces and their frequency spectra. A comparison of the predicted and measured cutting forces demonstrated that the proposed method provides accurate results.     

An examination of the fundamental mechanics of cutting force coefficients

In metal cutting, the cutting force is the key factor affecting the machined surface, and is also important in determining reasonable cutting parameters. The research and construction of cutting force prediction models therefore has a great practical value. The accuracy of cutting force prediction largely depends on the cutting force coefficients of the material. In the average cutting force model, cutting force coefficients are considered to be constant. This study makes use of experiments to investigate the cutting force coefficients in the average cutting force model, with a view to accurately identifying cutting force coefficients and verifying that they are related only to the tool–workpiece material couple and the tool geometrical parameters, and are not affected by milling parameters. To this end, the paper first examines the theory behind identifying cutting force coefficients in the average cutting force model. Based on this theory, a series of slot-milling experiments are performed to measure the milling forces, fixing spindle speeds and radial/axial depths of cutting, and linearly varying the feed per tooth. The tangential milling force coefficient and the radial milling force coefficient are then calculated by linearly fitting the experimental data. The obtained results show that altering the milling parameters does not change the milling force coefficients for the selected tool/workpiece material combination.     

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.     

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.     

On the dynamics of ball end milling: modeling of cutting forces and stability analysis

This paper presents a dynamic force model and a stability analysis for ball end milling. The concept of the equivalent orthogonal cutting conditions, applied to modeling of the mechanics of ball end milling, is extended to include the dynamics of cutting forces. The tool is divided into very thin slices and the cutting force applied to each slice is calculated and summed for all the teeth engaged. To calculate the instantaneous chip thickness of each tooth slice, the method of regenerative chip load calculation which accounts for the effects of both the surface undulations and the instantaneous deflection is used. To include the effect of the interference of the flank face of the tool with the finished surface of the work, the plowing force is also considered in the developed model. Experimental cutting forces are obtained using a five-axis milling machine with a rotary dynamometer. The developed dynamic model is capable of generating force and torque patterns with very good agreement with the experimental data. Stability of the ball end milling in the semi-finishing operation of die cavities is also studied in this paper. The tangential and radial forces predicted by the method of equivalent orthogonal condition are fitted by the equations F_t = K_t(Z)bh_av and F_r = K_r(Z)F_t, where b is the depth of cut and h_av is the average chip thickness along the cutting edge and Z is the tool axis coordinate. The polynomial functions K_t(Z) and K_r(Z) are the cutting force constants. The interdependency of the axial and radial depths of cut in ball end milling results in an iterative solution of the characteristic equation for the critical width of cut and spindle speed. In addition, due to different cutting characteristics of the cutting edge at different heights of the ball nose, stability lobes are represented by surfaces. Comparison of the time domain simulation for the shoulder removal process in die cavity machining with the analytical predictions shows that the proposed method is capable of accurate prediction of the stability lobes.     

Maximizing Chatter Free Material Removal Rate in Milling through Optimal Selection of Axial and Radial Depth of Cut Pairs

Chatter vibrations in milling, which develop due to dynamic interactions between the cutting tool and the workpiece, result in reduced productivity and part quality. Several stability models have been considered in previous publications, where mostly the stability limit in terms of axial depth of cut is emphasized for chatter free machining. In this paper, it is shown that, for the maximization of chatter free material removal rate, radial depth of cut is of equal importance. A method is proposed to determine the optimal combination of depths of cut, so that chatter free material removal rate is maximized. The application of the method is demonstrated on a pocketing example where significant reduction in the machining time is obtained using the optimal depths. The procedure can easily be integrated to a CAD/CAM system or a virtual machining environment in order to identify the optimal milling conditions.     

A predicted milling force model for high-speed end milling operation

In this study, a predicted milling force model for the end milling operation is proposed. The speed of spindle rotation, feed per tooth, and axial and radial depth of cut are considered as the affecting factors. An orthogonal rotatable central composite design and the response surface methodology are used to construct this model. The milling force per spindle revolution period obtained from each treatment is equally divided into suitable sections. The extreme value of the milling force in each section is selected to build the predicted model so as to predict the extreme force in each section for any cutting conditions within the specified range of the design database, including the speed of spindle rotation, feed per tooth, and axial and radial depth of cut. Moreover, the predicted extreme force in each section is applied to reconstruct the milling force waveform by means of the expansion of the Fourier series. The predicted model presented in this paper is adequate for a 95% confidence interval, and shows good correlation between experimental and predicted results.     

Analytical modeling of acoustic emission for monitoring of peripheral milling process

This paper presents the development of an analytical model relating the acoustic emission (AE) energy content to the cutting process parameters in peripheral milling and the experimental verification of the effects of the cutting parameters on the AE energy measurement to assess the applicability of AE sensing to the monitoring of peripheral milling. The model consists of an oblique cutting component and a rubbing component. It includes the contribution from both the AE attributed to plastic deformation in the primary shear zone and the AE resulting from interfaces between chips and the rake faces of the cutting teeth, between the workpiece and the cutter periphery as well as between the cutter flank and the machined workpiece surface. The adoption of an effective shear angle and a mean fraction angle in the model formulation provides insight into the fundamental mechanism of the cutting process responsible for the generation of the acoustic emission. A numerical example following the model development and a series of peripheral milling tests show that the true mean square voltage of the AE signal from peripheral milling increases with the primary cutting parameters (cutter rotating speed, feedrate, axial and radial depths of cut). The result of this work suggests that the energy measurement of the AE signal can be effectively used for the monitoring of peripheral milling processes.     

铣削加工颤振稳定域影响参数研究及优化

建立圆柱形铣刀铣削加工动态切削数学模型,采用一种解析法计算并绘制稳定域图,获取加工稳定性随工艺参数变化的规律。分析系统参数对铣削加工颤振稳定特性的影响,提高固有频率、增大系统刚度和阻尼有助于提高系统加工稳定性。基于动态变化的稳定域图及共振功率半频带频率,提出一种铣削稳定性约束下铣削参数优化模型,获取最大加工效率下的主轴转速、径向进给量及轴向进给量参数的最优值。开发铣削稳定性分析仿真软件,实现铣削颤振稳定域分析、共振区域分析、铣削参数优化等功能。将复杂设计分析过程工程实用化,具有工程应用价值。该方法同样可推广到磨削、车削的颤振分析。     

针对表面粗糙度和刀具振幅的切削用量优化研究

对进给量、切削速度和轴向切深这3个切削参数对工件表面粗糙度和刀具振动幅度的影响进行试验研究。采用BBD响应面法对6061铝工件进行端铣加工试验,并通过数学建模对试验结果进行分析。提出一种基于遗传算法的多目标优化方法来同时减小工件表面粗糙度和刀具振动幅度。建立能预报表面粗糙度和刀具振动的径向基神经网络模型,并通过试验验证其准确性。     

Grey relational analysis coupled with principal component analysis for optimization design of the cutting parameters in high-speed end milling

This paper investigates optimization design of the cutting parameters for rough cutting processes in high-speed end milling on SKD61 tool steel. The major characteristics indexes for performance selected to evaluate the processes are tool life and metal removal rate, and the corresponding cutting parameters are milling type, spindle speed, feed per tooth, radial depth of cut, and axial depth of cut. In this study, the process is intrinsically with multiple performance indexes so that grey relational analysis that uses grey relational grade as performance index is specially adopted to determine the optimal combination of cutting parameters. Moreover, the principal component analysis is applied to evaluate the weighting values corresponding to various performance characteristics so that their relative importance can be properly and objectively described. The results of confirmation experiments reveal that grey relational analysis coupled with principal component analysis can effectively acquire the optimal combination of cutting parameters. Hence, this confirms that the proposed approach in this study can be an useful tool to improve the cutting performance of rough cutting processes in high-speed end milling process.     

Generating mechanism and formation criteria of kinked surface in peripheral end milling

A kinked surface is commonly generated in a peripheral end milling process. In this paper, the generating mechanism of a kinked surface in end milling is systematically analyzed and revealed under the convolution framework through the establishment of a surface generation and form error model. It is found that the shape and kink positions of a form error profile can be determined by the three angular parameters: the axial and radial immersion angles and the flute spacing angle. From these angular parameters, four types of flute/work engagement conditions are defined to serve as the kink formation criteria with each type generating its own distinctive surface error profile in both down and up milling configurations. These form error profiles are characterized by either a kink-free form or by a single or a combination of three types of kink forms, which are defined based on changes in the flute/work engagement conditions and the resulting slope discontinuity in the force profile. Based on the kink formation criteria, kink charts scaled in normalized axial and radial depths of cut are devised to identify the types of kinked surface generated at any given depths of cut. An algebraic closed-form expression for the positions of kink points is also derived. The proposed kink formation criteria, the kink chart and the kink height prediction are validated through experiments and by comparison with data extracted from previously published results.     

Sensing Cutter Breakage in Milling

The paper describes a system for sensing milling cutter breakage. It is based on recognizing changes in the pattern of the cutting force. The regular periodic variation per tooth is filtered out by synchronized sampling, averaging per tooth and first differencing and the change due to the broken tooth stands out. The threshold for alarm is set with respect to the mean force per revolution (moving average) to make it independent of changes in radial and axial depths of cut and in chip load. Due to practical difficulties with force measurements the use of vibrational signal is explored and found feasible.     

模糊田口法在重切削制程中切削参数最佳化设计

为了快速有效获得重切削时良好的切削性能参数,以田口法与模糊逻辑相结合,对侧面铣削SUS304不锈钢重切削制程时的切削参数进行最佳化设计。由于评估重切削制程的刀具寿命与金属移除率两项主要切削性能,受到主轴转速、每刃进给、轴向切深与径向切深的影响,由此将4个切削参数设置为可控制因子。经过田口法将各品质特性转化为S/N比,通过模糊逻辑运算,采用多重品质特性指标(MPCI)求得切削参数最佳水准组合。试验结果表明:以模糊田口法获得的切削参数最佳水准组合,能够有效改善侧面重切削制程时的切削性能,为刀具制造厂或刀具使用者寻求最佳切削条件提供参考。     

Stability prediction in radial immersion for milling with symmetric structure

In this study, an analytical approach is presented to find stability limits in terms of radial immersion for a given axial depth of cut, and vice versa. Under the assumption of axis-symmetric structure and using the zero order force model, the direction coefficient matrix is decoupled to reduce the 2D milling system to a 1D stability problem. The effect of the radial immersion and radial cutting coefficient on the system stability are explicitly represented through the eigenvalue function of the directional coefficient matrix. The resulting characteristic equation allows the limiting radial immersion be solved for a given axial immersion. A procedure is presented in obtaining the radial stability diagram, in which additional unstable island and secondary lobes are shown to exist besides the traditional lobes. Stability diagrams in both axial and radial immersion are presented to demonstrate the physical insights offered by the presented method. The model is validated by comparing with results from the existing analytical and numerical models.     

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°.     

The optimal cutting-parameter selection of production cost in HSM for SKD61 tool steels

The main purpose of this study was to construct an investigation of optimal cutting parameters for minimizing production cost on the rough machining of high speed milling operation. A machining model is constructed based on a polynomial network. The polynomial network can learn the relationships between cutting parameters (cutting speed, feed per tooth, and axial depth of cut) and tool life through a self-organizing technique. Once the material removal volume for machined parts and various time and cost components of the high speed milling operations are given, an optimization algorithm using a simulated annealing method is then applied to the polynomial network for determining optimal cutting parameters. The optimal cutting parameters are subjected to an objective function of minimum production cost with the feasible range of cutting parameters.