Improved dynamic cutting force model in ball-end milling. Part I: theoretical modelling and experimental calibration

An accurate cutting force model of ball-end milling is essential for precision prediction and compensation of tool deflection that dominantly determines the dimensional accuracy of the machined surface. This paper presents an improved theoretical dynamic cutting force model for ball-end milling. The three-dimensional instantaneous cutting forces acting on a single flute of a helical ball-end mill are integrated from the differential cutting force components on sliced elements of the flute along the cutter-axis direction. The size effect of undeformed chip thickness and the influence of the effective rake angle are considered in the formulation of the differential cutting forces based on the theory of oblique cutting. A set of half immersion slot milling tests is performed with a one-tooth solid carbide helical ball-end mill for the calibration of the cutting force coefficients. The recorded dynamic cutting forces are averaged to fit the theoretical model and yield the cutting force coefficients. The measured and simulated dynamic cutting forces are compared using the experimental calibrated cutting force coefficients, and there is a reasonable agreement. A further experimental verification of the dynamic cutting force model will be presented in a follow-up paper.     

多硬度拼接淬硬钢铣削动力学分析

颤振是金属切削加工过程中由于刀具和工件之间相互作用所产生的一种强烈的自激振动现象,会导致切削力幅值增加且发生剧烈波动,进而降低工件表面质量和刀具使用寿命。针对此问题,基于铣削过程稳定性预测分析方法建立多硬度拼接工件的动态铣削系统,对多硬度拼接模具铣削过程稳定性进行深入研究,实现了对拼接模具铣削加工过程颤振稳定域的仿真,进而研究了模态参数对稳定性叶瓣图形状的影响。最后通过时域分析、表面形貌和刀具磨损的研究,综合验证了稳定性预测曲线的精度。研究结果为多硬度拼接模具铣削加工提供理论基础,并设置合理的加工参数来实现金属最大切除率,为大型汽车覆盖件模具铣削加工提供理论依据及技术指导。     

汽车覆盖件拼接模具硬态铣削过程的动态特性

针对汽车覆盖件拼接模具铣削过程铣削力及振动信号测试失真问题,运用经验模态分解(empirical mode decomposition,简称EMD)结合小波阈值降噪原理,对铣削力及振动信号进行降噪处理。对降噪后的振动信号进行时频域分析,研究了不同切削参数、切削进给方向对铣削拼接模具过程动态特性的影响,得到铣削方向由硬度大材料切向硬度小材料,走刀方向与拼接缝成30°夹角时铣削力突变值较小的结论。发现x,y,z方向的切削分力及振动幅值的突变值与轴向切深及进给速度呈现正相关,与切削速度是非线性关系的特性。该研究结果为汽车覆盖件拼接模具硬态铣削的工艺优化提供了理论支持。     

Speed-varying cutting force coefficient identification in milling

Accurate simulation of the machining process is crucial to improve milling performance, especially in High-Speed Milling, where cutting parameters are pushed to the limit.Various milling critical issues can be analyzed based on accurate prediction of cutting forces, such as chatter stability, dimensional error and surface finish. Cutting force models are based on coefficients that could change with spindle speed. The evaluation of these specific coefficients at higher speed is challenging due to the frequency bandwidth of commercial force sensors. On account of this, coefficients are generally evaluated at low speed and then employed in models for different spindle speeds, possibly reducing accuracy of results.In this paper a deep investigation of cutting force coefficient at different spindle speeds has been carried out, analyzing a wide range of spindle speeds: to overcome transducer dynamics issues, dynamometer signals have been compensated thanks to an improved technique based on Kalman filter estimator. Two different coefficients identification methods have been implemented: the traditional average force method and a proposed instantaneous method based on genetic algorithm and capable of estimating cutting coefficients and tool run-out at the same time.Results show that instantaneous method is more accurate and efficient compared to the average one. On the other hand, the average method does not require compensation since it is based on average signals. Furthermore a significant change of coefficients over spindle speed is highlighted, suggesting that speed-varying coefficient should be useful to improve reliability of simulated forces.     

凸曲面拼接模具球头铣刀的瞬时铣削力预测

在曲面模具拼接区域球头铣刀铣削过程中,刀具载荷变化大,瞬态铣削力有突变现象,影响模具拼接区域的加工精度和表面质量。为了预测拼接区域球头铣刀的瞬态铣削力,首先,建立考虑冲击振动的球头铣刀三维次摆线轨迹方程,得到瞬时未变形切屑厚度模型;然后,基于铣削微元的思想,建立凸曲面双硬度拼接模具球头铣刀的瞬态铣削力模型,该模型能够综合考虑拼接区冲击振动、硬度变化、刀具工件切触角度变化对瞬态铣削力的影响;最后,进行凸曲面拼接区域球头铣刀铣削加工实验。实验结果表明,预报的瞬态铣削力和实验测量结果在幅值上和变化趋势上具有一致性,在平稳切削时最大铣削力预测误差值基本在15%以内,验证了该模型能有效地预报凸曲面模具拼接区域球头铣刀的瞬态铣削力。     

基于铣削力精确建模的工件表面让刀误差预测分析

航空航天制造业结构件的高速铣削加工中,在切削力作用下由整体铣削刀具挠度变形所引起的工件表面让刀误差,严重制约零件的加工精度和效率。针对这一问题,通过建立铣削力精确预测模型,结合刀具刚度特点,对工件让刀误差进行预测分析。将切削速度和刀具前角对切削力的影响规律引入二维直角单位切削力预测模型,并通过试验进行相关系数标定。借助等效前角将直角切削力预测系数应用到斜角切削力的预测,通过矢量叠加构建整体刀具三维切削力模型。分析刀具挠度变形对铣削层厚度及铣削接触中心角范围影响规律。基于离散化的刀具模型和切削力模型,建立铣削载荷条件下刀具等效直径悬臂梁模型弯曲变形计算方法。构建以刀具变形对铣削过程影响作用规律为反馈的刚性工件表面让刀误差及切削力柔性预测模型,通过整体铣刀铣削试验验证所建立理论模型的预测精度。     

Identification of instantaneous cutting force coefficients using surface error

Cutting force coefficients are the key factors for efficient and accurate prediction of instantaneous milling force. To calibrate the coefficients, this paper presents an instantaneous milling force model including runout and cutter deformation. Also, forming of surface error is analyzed, and a surface error model considering runout is proposed. Using surface errors of two experiments completed with the same cutting conditions but different axial depth only, cutter deformation is obtained. Then, a new approach for the determination of instantaneous cutting force coefficients is provided. The method can eliminate influences of the other factors except cutter deformation and runout. A series of experiments are designed, and the results are used to identify the parameters. With the evaluated coefficients and runout parameters, the instantaneous milling force and surface error are predicted. A good agreement between predicted results and experimental results is achieved, which shows that the method is efficient, and effect of runout on surface error is not negligible.     

A prediction method of milling chatter stability for complex surface mold

This paper proposes a kind of milling chatter stability prediction method used for the stability of milling free-form surface based on the time-domain. Firstly, a dynamic equation is established by considering the influence of mold surface curvature and cutting tool lead angle on dynamic chip thickness without deformation. Then, the multi-delay milling system vibration displacement, which is given by the ratio of dynamic chip thickness and the static chip thickness as the threshold, was calculated based on the numerical method. Finally, the chatter stability domain based on the full-discretization method of milling chatter stability domain is compared to analyze the influence of the characteristics of free surface curvature on the chatter stability domain. The results of the experiment show that the time-domain simulation method can reveal the influence of different processing areas of free-form surface mold on the instability mechanism of the system. The change trend of milling chatter stability domain was found to be consistent with the experimental results.     

汽车覆盖件用淬硬钢模具铣削加工的研究进展

作为汽车产销量第一大国,我国的汽车模具加工能力远远不能适应汽车更新换型的需要,中高档轿车关键覆盖件模具铣削加工质量还达不到设计要求。通过汽车大型覆盖件淬硬钢模具的铣削加工特征和难点的分析可知,铣削过程建模与仿真分析、加工工艺系统动力学特性和铣削稳定性分析、汽车覆盖件淬硬钢模具铣削加工用刀具研制、自由曲面数控编程技术及工艺规划是汽车模具高精度铣削加工的研究重点,总结归纳这几个方面的研究现状,同时探讨汽车覆盖件淬硬钢模具铣削加工仍有待于进一步解决的问题,为其后续研究方向提出一些建议。     

Improved dynamic cutting force model in peripheral milling. Part II: experimental verification and prediction

Cutting trials reveal that a measure of cutter run-out is always unavoidable in peripheral milling. This paper improves and extends the dynamic cutting force model of peripheral milling based on the theoretical analytical model presented in Part I [1], by taking into account the influence of the cutter run-out on the undeformed chip thickness. A set of slot milling tests with a single-fluted helical end-mill was carried out at different feed rates, while the 3D cutting force coefficients were calibrated using the averaged cutting forces. The measured and predicted cutting forces were compared using the experimentally identified force coefficients. The results indicate that the model provides a good prediction when the feed rate is limited to a specified interval, and the recorded cutting force curves give a different trend compared to other published results [8]. Subsequently, a series of peripheral milling tests with different helical end-mill were performed at different cutting parameters to validate the proposed dynamic cutting force model, and the cutting conditions were simulated and compared with the experimental results. The result demonstrates that only when the vibration between the cutter and workpiece is faint, the predicted and measured cutting forces are in good agreement.     

Cutting force prediction for ball nose milling of inclined surface

Ball nose milling of complex surfaces is common in the die/mould and aerospace industries. A significant influential factor in complex surface machining by ball nose milling for part accuracy and tool life is the cutting force. There has been little research on cutting force model for ball nose milling on inclined planes. Using such a model ,and by considering the inclination of the tangential plane at the point of contact of the ball nose model, it is possible to predict the cutting force at the particular cutting contact point of the ball nose cutter on a sculptured surface. Hence, this paper presents a cutting force model for ball nose milling on inclined planes for given cutting conditions assuming a fresh or sharp cutter. The development of the cutting force model involves the determination of two associated coefficients: cutting and edge coefficients for a given tool and workpiece combination. A method is proposed for the determination of the coefficients using the inclined plane milling data. The geometry for chip thickness is considered based on inclined surface machining with overlapping of previous pass. The average and maximum cutting forces are considered. These two forces have been observed to be more dominating force-based parameters or features with high correlation with tool wear. The developed cutting force model is verified for various cutting conditions.     

Prediction of dynamic cutting force and regenerative chatter stability in inserted cutters milling

Currently, the modeling of cutting process mainly focuses on two aspects: one is the setup of the universal cutting force model that can be adapted to a broader cutting condition; the other is the setup of the exact cutting force model that can accurately reflect a true cutting process. However, there is little research on the prediction of chatter stablity in milling. Based on the generalized mathematical model of inserted cutters introduced by ENGIN, an improved geometrical, mechanical and dynamic model for the vast variety of inserted cutters widely used in engineering applications is presented, in which the average directional cutting force coefficients are obtained by means of a numerical approach, thus leading to an analytical determination of stability lobes diagram (SLD) on the axial depth of cut. A new kind of SLD on the radial depth of cut is also created to satisfy the special requirement of inserted cutter milling. The corresponding algorithms used for predicting cutting forces, vibrations, dimensional surface finish and stability lobes in inserted cutter milling under different cutting conditions are put forward. Thereafter, a dynamic simulation module of inserted cutter milling is implemented by using hybrid program of Matlab with Visual Basic. Verification tests are conducted on a vertical machine center for Aluminum alloy LC4 by using two different types of inserted cutters, and the effectiveness of the model and the algorithm is verified by the good agreement of simulation result with that of cutting tests under different cutting conditions. The proposed model can predict the cutting process accurately under a variety of cutting conditions, and a high efficient and chatter-free milling operation can be achieved by a cutting condition optimization in industry applications.     

一种新的螺旋刃球头铣刀铣削力模型

为提高铣削加工的安全性和生产效率，有必要在加工实际进行之前准确地预测切削过程的物理信息，如铣削力、刀具振动等。给出了球头铣刀丸线几何模型，采用理论削力分析与实验--系数识别相结合的方法建立了新的螺旋刃球头铣刀的铣削力模型。对不同切削条件下的铣削力进行了仿真，与实验测量数据吻合良好，证明离线仿真可以对铣削力做出较准确的预测。     

基于动力学约束的端面铣削工艺参数优化

工艺参数优化对提高切削过程的加工效率和加工成本具有重要意义。将铣削系统动力学作为主要约束条件,提出端面铣削工艺参数的多目标优化模型。基于铣削系统动力学分析,得到了综合切削稳定性、工件表面粗糙度、主轴转速、切削力、切削功率等约束的工艺参数多目标优化模型。通过调节权重系数实现优化方向的控制,并采用快速粒子群算法对工艺参数进行优化计算。工艺优化实例及试验表明,采用基于动力学约束的工艺参数优化方法可以获得较好的工艺参数优化结果。     

The effect of characteristics of free<Emphasis Type="Bold">-</Emphasis>form surface on the machined surface topography in milling of panel mold

In the milling process of automobile panel mold of hardened steel, the characteristic of free-form surface is one of the dominant factors for surface topography. In this paper, the trajectory of cutting edge is firstly modeled to analyze the residual height of the free-form surface in ball-end milling of hardened steel. Furthermore, the non-uniform rational B-splines (NURBS) surface reconstruction is utilized to generate the surface topography. Subsequently, the influences of surface curvature, lead angle, milling vibrations on the machined surface topography, and residual height are investigated, respectively. Finally, the accuracy of the surface topography and the roughness prediction model are validated by the milling experiments of free-form surface, where two-dimensional contour maps could be obtained. The simulation and experimental results demonstrate that the machined surface topography of hardened steel is fitted by means of NURBS surface reconstruction. In that manner, the effects of surface characteristics on the machined surface topography can be accurately predicted.     

Prediction of tool breakage in face milling using support vector machine

A new approach is proposed using a support vector machine (SVM) to classify the feature of the cutting force signal for the prediction of tool breakage in face milling. The cutting force signal is compressed by averaging the cutting force signals per tooth to extract the feature of the cutting force signal due to tool breakage. With the SVM learning process, the output of SVM’s decision function can be utilized to identify a milling cutter with or without tool breakage. Experimental results are presented to verify the feasibility of this tool breakage prediction system in milling operations.     

Wall thickness error prediction and compensation in end milling of thin-plate parts

End milling has been widely adopted to machine the thin-plate parts that play increasingly important role in the aerospace industry, due to the advantages of high machining accuracy and fine machined surface quality. In this paper, a systematic method is proposed to predict and compensate the wall thickness errors in end milling of thin-plate parts. The errors are caused by the static deflections induced by the varying cutting force imposed on the weakly rigid part. To improve the efficiency of computing the part deformation, a novel FE model is firstly developed by combing the methods of substructure analysis, special mesh generation and structural static stiffness modification. Then, the time- and position-dependent deformations of the part are calculated based on the proposed FE model to predict the wall thickness errors left on the finished part. It reveals for the first time that the surface topography of the finished thin-plate part is formed by the repeated cutting with the bottom edge of the cutter (BEC) in end milling. Owing to the coupling between the axial cutting depth (ACD) and the force-induced deflection, the modified ACDs for compensation of the static wall thickness errors are finally determined by an iterative adjustment method. The proposed method is verified by three-axis end milling experiments. The experiment results show that the predicted wall thickness errors match well with the really measured ones, and the errors are reduced by 77.18% with the help of the proposed compensation method. Moreover, the proposed FE model reduces the computational time elapsed for error prediction by 67.44% as compared with the benchmark FE model.     

A new method for cutting force prediction in peripheral milling of complex curved surface

The instantaneous uncut chip thickness and entry/exit angle of tool/workpiece engagement vary with tool path, workpiece geometry and cutting parameters in peripheral milling of complex curved surface, leading to the strong time-varying characteristic for instantaneous cutting forces. A new method for cutting force prediction in peripheral milling of complex curved surface is proposed in this paper. Considering the tool path, cutter runout, tool type(constant/nonconstant pitch cutter) and tool actual motion, a representation model of instantaneous uncut chip thickness and entry/exit angle of tool/ workpiece engagement is established firstly, which can reach better accuracy than the traditional models. Then, an approach for identifying of cutter runout parameters and calibrating of specific cutting force coefficients is presented. Finally, peripheral milling experiments are carried out with two types of tool, and the results indicate that the predicted cutting forces are highly consistent with the experimental values in the aspect of variation tendency and amplitude.     

虚拟制造中基于刀具变形的复杂曲面加工误差预报

复杂曲面加工过程中刀具的弹性变形是产生曲面加工误差的重要原始误差。着重研究了虚拟制造环境下基于球面铣刀弹性变形的曲面加工误差预报模型。研究并建立了球面铣刀加工复杂曲面的切削力模型和刀具弹性变形模型,在此基础上,分析了曲面生成机理,提出了利用曲面变形敏感系数建立刀具弹性变形对法向加工误差的影响关系。利用该模型可以在实际切削加工前对曲面加工误差进行预报,用以进行误差补偿或切削参数优化。最后,以二维半圆形拉伸曲面为例通过切削实验对本文提出的模型进行了验证。