Prediction of cutting forces and machining error in ball end milling of curved surfaces -II experimental verification

This paper presents the results of a series of experiments performed to examine the validity of a theoretical model for evaluation of cutting forces and machining error in ball end milling of curved surfaces. The experiments are carried out at various cutting conditions, for both contouring and ramping of convex and concave surfaces. A high precision machining center is used in the cutting tests. In contouring, the machining error is measured with an electric micrometer, while in ramping it is measured on a 3-coordinate measuring machine. The results show that in contouring, the cutting force component that influences the machining error decreases with an increase in milling position angle, while in ramping, the two force components that influence the machining error are hardly affected by the milling position angle. Moreover, in contouring, high machining accuracy is achieved in “Up cross-feed, Up cut” and “Down cross-feed, Down cut” modes, while in ramping, high machining accuracy is achieved in “Left cross-feed, Downward cut” and “Right cross-feed, Upward cut” modes. The theoretical and experimental results show reasonably good agreement.     

Theoretical modelling of cutting forces in helical end milling with cutter runout

A theoretical cutting force model for helical end milling with cutter runout is developed using a predictive machining theory, which predicts cutting forces from the input data of workpiece material properties, tool geometry and cutting conditions. In the model, a helical end milling cutter is discretized into a number of slices along the cutter axis to account for the helix angle effect. The cutting action for a tooth segment in the first slice is modelled as oblique cutting with end cutting edge effect and tool nose radius effect, whereas the cutting actions of other slices are modelled as oblique cutting without end cutting edge effect and tool nose radius effect. The influence of cutter runout on chip load is considered based on the true tooth trajectories. The total cutting force is the sum of the forces at all the cutting slices of the cutter. The model is verified with experimental milling tests.     

球头铣刀数控加工表面形貌几何仿真的研究

几何仿真是建立铣削力预测模型的基础,而传统的几何仿真只考虑刀具的平动而忽略其转动。本文在同时考虑刀具平动和转动的基础上,利用工件Z-Map表示模型和刀刃离散表示法,提出了一种球头铣刀三轴数控铣削的微观几何仿真算法。该算法鲁棒性好、适用范围广,不仅能高效而准确地仿真铣削表面形貌,而且能准确提供切屑的轮廓,为建立精确的切削力预测模型提供了重要的几何参数。     

Effect of tool stiffness upon tool wear in high spindle speed milling using small ball end mill

Longer tool life can be tentatively achieved at a higher feed rate using a small ball end mill in high spindle speed milling (over several tens of thousands of revolutions per minute), although the mechanism by which tool life is improved has not yet been clarified. In the present paper, the mechanism of tool wear is investigated with respect to the deviation in cutting force and the deflection of a ball end mill with two cutting edges. The vector loci of the cutting forces are shown to correlate strongly with wear on both cutting edges of ball end mills having various tool stiffnesses related to the tool length. The results clarified that tool life can be prolonged by reducing tool stiffness, because the cutting forces are balanced, resulting in even tool wear on both cutting edges as tool stiffness is lowered to almost the breakage limit of the end mill. A ball end mill with an optimal tool length showed significant improvement in tool life in the milling of forging die models.     

锥铣刀加工端面螺旋面法及误差计算

介绍了波形弹簧成形模具凸、凹螺旋面参数的计算公式,提出了锥铣刀在铣床上利用挂轮装置铣削端面螺旋面的方法及刀具选择方法,用螺旋面加工理论建立刀具坐标系及工件坐标系,推导了本文所述加工方法的加工误差计算公式及铣刀安装角度的优化计算公式,推证了螺旋面波谷的曲率半径与工件半径成线性关系的公式.用实例进行了系统计算,锥铣刀加工方...     

A study on calibration of coefficients in end milling forces model

This paper presents an improved approach to calibrate the cutting coefficients in an end-milling model. In order to predict end-milling forces, lots of simulative models are established. In order to use them, coefficients in the models, for example, cutting pressure constants etc., must firstly be calibrated experimentally, and simulative precision and applicability of the models are influenced by them. For simplicity, using average forces to calibrate cutting parameters are widely adopted by lots of researchers. However, the existence of an instruments zero-drift, noise, etc., will have effect on the precision of experimental data, so, it is difficult to directly obtain exact average-cutting forces through experimental data. Aiming at the above problem, the paper investigates milling forces in the frequency domain, discusses the impact of experimental data at different frequencies on cutting force coefficients and the influence of sensitivity of error on experimental data at different frequencies on coefficients is studied. Based on the research, an improved method to calibrate the cutting coefficients is provided. Based on a series of experiments and numerical simulations, the validity of the method is confirmed. At the end of the paper, some useful conclusions are drawn.     

高速切削加工中切削力的应用研究

通过采用一种新型的试验装置,可重现在了较大的切削速度范围内(从15～100m/s),正交切削下的切削过程.该试验设备可以记录在正交切削下的切削过程中法线方向上和切线方向上的作用力数值.从而在很大的切削速度范围内,可以对刀具和切屑之间的摩擦力进行分析.给出了切削力的分力变化和摩擦系数变化的情况.此外,通过可以使用一台高速摄影机,记录了高速加工中,切屑的形成过程的图像.     

球头立铣刀铣削加工表面粗糙度仿真技术研究

铣削加工表面粗糙度的形成与铣刀和工件振动、主轴偏心、刀具磨损、刀具变形等物理和几何因素有关。多年来中外学者针对各种影响因素建立了“相对单一”的数学模型。这些数学模型只考虑了一种或两种影响因素,还没有建立起描述物理和几何变化过程的综合数学模型,为此对这些相关因素进行了深入研究,建立了基于球头立铣刀的铣削加工表面粗糙度仿真的整体数学模型。从而为虚拟数控加工仿真提供技术支撑。     

An integrated system development for ball end mill design, creation and evaluation

The purpose of this paper is to provide a reasonable means to approach tool shape optimization of ball end mill for high-speed milling operation. The paper presents a new development of an integrated system for ball end mill design, creation and evaluation that is more flexible and more systematic than the commercially available tool fabrication systems.The study consists of three major contents: (1) 3D-CAD/CAM system development for ball end mill design and creation, (2) fundamental investigations of cutting characteristics with different ball end mills, and (3) improvement of tool life and machining stabilization for high-speed milling by means of new tool shape proposals. These are explained in the following sections, respectively. Through the above developments and investigations, it is evidently found that the developed system shows great validity and possibility to realize tool shape optimization of the ball end mill.     

On modeling of cutting forces in micro-end milling operation

Micro-end milling is used for manufacturing of complex miniaturized components precisely in wide range of materials. It is important to predict cutting forces accurately as it plays vital role in controlling tool and workpiece deflections as well as tool wear and breakage. The present study attempts to incorporate process characteristics such as edge radius of cutting tool, effective rake and clearance angles, minimum chip thickness, and elastic recovery of work material collectively while predicting cutting forces using mechanistic model. To incorporate these process characteristics effectively, it is proposed to divide cutting zone into two regions: shearing- and ploughing-dominant regions. The methodology estimates cutting forces in each partitioned zone separately and then combines the same to obtain total cutting force at a given cutter rotation angle. The results of proposed model are validated by performing machining experiments over a wide range of cutting conditions. The paper also highlights the importance of incorporating elastic recovery of work material and effective rake and clearance angle while predicting cutting forces. It has been observed that the proposed methodology predicts the magnitude and profile of cutting forces accurately for micro-end milling operation.     

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.     

Study on the influence of meso-geometrical features on milling force in precision machining of titanium alloy

Titanium Alloy is a typical material difficult to be processed for its characteristics of low thermal conductivity, and high chemical activity, which result in tool wear and the poor quality of the machined surface. In order to solve the problems existing in the processing of Titanium Alloy, considering the tool edge, micro-texture is implanted into the cemented carbide ball end milling cutter. The article analyzes the influence law of micro-texture and the tool edge radius of ball end milling cutter on mechanical properties of Titanium Alloy, establishes and verifies a mechanical predictive model of milling Titanium Alloy with ball end milling cutter surface based on the effect of micro-texture and the tool edge. Finally, with regard to the minimum cutting force as the target, the article uses genetic algorithm to optimize meso-geometrical features parameters of the cemented carbide ball end milling cutter. The article also provides the foundation for efficient and high-quality processing of Titanium Alloy.     

Development and experimental validation of a mechanistic model of cutting forces in micro- ball end milling of full slots

In the present work, a mechanistic model of cutting forces is developed with a novel approach to arrive at the cutting edge geometry as well as the cutting mechanics. The geometry of cutting elements derived and verified using a virtual tool generated in CAD environment is considered. The cutting and edge force coefficients at every discrete point on the cutting edge of micro-ball end mill are established in a novel way from the basic metal cutting principles and fundamental properties of materials, considering edge radius and material strengthening effects. Further, measured edge radius is used in the model. Full slot micro-ball end milling experiments are conducted on a high-precision high-speed machining center using a 0.4 mm diameter tungsten carbide tool and cutting forces are measured using a high-sensitive piezo-electric dynamometer. It is established that the predicted as well as experimental cutting forces are higher at very low uncut chip thickness in comparison with the cutting edge radius in micro-ball end milling also. Amplitudes of cutting forces and instantaneous values with incremental rotation of the tool are compared with predicted values over two revolutions for validation of proposed model.     

A real time machining error compensation method based on dynamic features for cutting force induced elastic deformation in flank milling

During the machining process, cutting forces cause deformation of thin-walled parts and cutting tools because of their low rigidity. Such deformation can lead to undercut and may result in defective parts. Since there are various unexpected factors that affect cutting forces during the machining process, the error compensation of cutting force induced deformation is deemed to be a very difficult issue. In order to address this challenge, this article proposes a novel real time deformation error compensation method based on dynamic features. A dynamic feature model is established for the evaluation of feature rigidity as well as the association between geometric information and real time cutting force information. Then the deformations are calculated based on the dynamic feature model. Eventually, the machining error compensation for elastic deformation is realized based on Function Blocks. A thin-walled feature is used as an example to validate the proposed approach. Machining experiment results show that the errors of calculated deformation with the monitored deformation is less than 10%, and the thickness errors were between ?0.05 mm and +0.06 mm, which can well satisfy the accuracy requirement of structural parts by NC (Numerical Control) machining.     

超高速铣削及其在高硬度钢加工中的应用

阐述了高硬度钢超高速铣削的特点和应用,并讨论了其刀具系统、切削工艺参数和铣削方式等主要相关技术。     

关于逆向车削加工细长轴误差的力学分析

针对细长轴车削加工，分别在两种不同装夹条件下(一端卡盘夹紧、一端顶尖支承和两端顶尖支承)进行正向切削和逆向切削时的工件变形进行了力学分析，建立了正逆向切削工件在切削力作用下产生弯曲变形的解析模型。具体算例表明：逆向切削时工件的弯曲变形以及由此引起的加工误差远小于同等条件下正向切削的变形和误差。该模型及分析结果可用于细长轴加工的工艺设计。     

Effects of cutting edge geometry, workpiece hardness, feed rate and cutting speed on surface roughness and forces in finish turning of hardened AISI H13 steel

In this study, the effects of cutting edge geometry, workpiece hardness, feed rate and cutting speed on surface roughness and resultant forces in the finish hard turning of AISI H13 steel were experimentally investigated. Cubic boron nitrite inserts with two distinct edge preparations and through-hardened AISI H13 steel bars were used. Four-factor (hardness, edge geometry, feed rate and cutting speed) two-level fractional experiments were conducted and statistical analysis of variance was performed. During hard turning experiments, three components of tool forces and roughness of the machined surface were measured. This study shows that the effects of workpiece hardness, cutting edge geometry, feed rate and cutting speed on surface roughness are statistically significant. The effects of two-factor interactions of the edge geometry and the workpiece hardness, the edge geometry and the feed rate, and the cutting speed and feed rate also appeared to be important. Especially honed edge geometry and lower workpiece surface hardness resulted in better surface roughness. Cutting-edge geometry, workpiece hardness and cutting speed are found to be affecting force components. The lower workpiece surface hardness and honed edge geometry resulted in lower tangential and radial forces.     

整体叶轮五轴侧铣刀位优化新算法与误差分析

为提高整体叶轮数控侧铣加工的精度和效率,分析厂锥形球头铣刀包络面与刀轴轨迹面之间的关系,提出了一种不可展直纹曲面五轴数控侧铣刀位优化的新算法.该算法首先利用两点偏置法确定圆柱刀初始刀位,然后通过刀轴旋转半锥角得到锥刀初始刀位,最后以刀具包络面与设计曲面间的极差最小为优化目标.采用刀轴上三点优化初始刀位.针对锥刀侧铣加工编程误差计算复杂问题,建立了一种编程误差计算新方法,并成功应用于整体叶轮的锥刀编程误差计算.通过数控加工仿真实例、实际加工试验和编程误差综合对比分析证明,所建立的刀位计算优化新算法正确有效,可显著减小编程误差.     

平面铣削刀具前刀面瞬态切削温度的研究

刀具切削温度对刀具寿命、刀具磨损等有重要影响。因此在实际加工之前预测出刀具温度,对合理选择切削参数、优化数控程序等均具有重要意义。平面铣削等断续切削过程的热条件不同于车削等连续切削过程。用数学物理方法建立了平面铣削过程刀具的一维传热学模型,用解析的方法预测平面铣削过程中刀具前刀面的温度分布,考虑了刀具切出时空气强化对流散热对刀具前刀面温度的影响。结果表明,刀具切入时间和切出时间对刀具温度有较大影响。用文献中断续车削刀具温度实验数据对铣削刀具前刀面温度的传热学预测模型进行了验证,结果表明二者趋势一致,但平面铣削预测的刀具温度略低于断续车削的刀具温度。