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.     

Chatter and dynamic cutting force prediction in high-speed ball end milling

Machine tool chatter is a serious problem which deteriorates surface quality of machined parts and increases tool wear, noise, and even causes tool failure. In the present paper, machine tool chatter has been studied and a stability lobe diagram (SLD) has been developed for a two degrees of freedom system to identify stable and unstable zones using zeroth order approximation method. A dynamic cutting force model has been modeled in tangential and radial directions using regenerative uncut chip thickness. Uncut chip thickness has been modeled using trochoidal path traced by the cutting edge of the tool. Dynamic cutting force coefficients have been determined based on the average force method. Several experiments have been performed at different feed rates and axial depths of cut to determine the dynamic cutting force coefficients and have been used for predicting SLD. Several other experiments have been performed to validate the feasibility and effectiveness of the developed SLD. It is found that the proposed method is quite efficient in predicting the SLD. The cutting forces in stable and unstable cutting zone are in well agreement with the experimental cutting forces.     

Calculations of chip thickness and cutting forces in flexible end milling

In the end milling process of a flexible workpiece, it is well recognized that the precise determination of the instantaneous uncut chip thickness (IUCT) is essential for the cutting force calculation. This paper will present a general method that incorporates simultaneously the cutter/workpiece deflections and the immersion angle variation into the calculation of the IUCT and cutting forces. Contributions are twofold. Firstly, considering the regeneration model, a new scheme for the IUCT calculation is determined based on the relative positions between two adjacent tooth path centers. Secondly, a general approach is established to perform numerical validations. On one hand, the engagement/separation of the cutter from the workpiece is instantaneously identified. On the other hand, the calculation of the IUCT is iteratively performed. To demonstrate the validity of the method, several examples are used to show the convergence history of the cutting force and the IUCT during the flexible end milling process. Both theoretical analyses and numerical results show that the regeneration mechanism is short lived and will disappear after several tooth periods in flexible static end milling process .     

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.     

Analysis of cutting force coefficients in high-speed ball end milling at varying rotational speeds

In high-speed ball end milling, cutting forces influence machinability, dimensional accuracy, tool failure, tool deflection, machine tool chatter, vibration, etc. Thus, an accurate prediction of cutting forces before actual machining is essential for a good insight into the process to produce good quality machined parts. In this article, an attempt has been made to determine specific cutting force coefficients in ball end milling based on a linear mechanistic model at a higher range of rotational speeds. The force coefficients have been determined based on average cutting force. Cutting force in one revolution of the cutter was recorded to avoid the cutter run-out condition (radial). Milling experiments have been conducted on aluminum alloy of grade Al2014-T6 at different spindle speeds and feeds. Thus, the dependence of specific cutting force coefficients on cutting speeds has been studied and analyzed. It is found that specific cutting force coefficients change with change in rotational speed while keeping other cutting parameters unchanged. Hence, simulated cutting forces at higher range of rotational speed might have considerable errors if specific cutting force coefficients evaluated at lower rotational speed are used. The specific cutting force coefficients obtained analytically have been validated through experiments.     

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。     

Correlation between different cutting conditions,surface roughness and dimensional accuracy when ball end micro milling material measures with freeform surfaces

Abstract

Material measures are used to calibrate topography measuring instruments. Micro-milling is a suitable process for the manufacturing of areal material measures in particular of material measures featuring freeform surfaces. To improve their surface quality and to minimize their deviations from the target geometry, the cutting parameters feed per tooth respectively feed rate and spindle speed are examined in this study. Dependent on the varied parameters the deviation of the manufactured topography from its target geometry, the deviation to the nominal surface texture parameters and the short-wavelength roughness parameters are evaluated. Two different ball end micro-mills and two different target geometries are chosen to investigate whether the observed dependence on the varied parameters are valid independent from the tool and the target geometry. It is illustrated that the feed rate has a large influence on the dimensional accuracy: the dynamic properties of the axes are identified as reason for the decreasing amplitude with increasing feed rate. The spindle speed only influences the short wavelength roughness and has a minor influence on the surface quality.     

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...     

Application of a variable flow stress machining theory to helical end milling

A methodology of modeling chip geometry of flat helical end milling based on a variable flow stress machining theory is presented in this article. The proposed model is concerned with the variation of the width of cut thickness. The nonuniform chip thickness geometry is discretized into several segments based on the radial depth of cut. The chip geometry for each segment is considered to be constant by taking the average value of the maximum and minimum chip thickness. The maximum chip thickness for each chip segment is computed based on the current width of cut, feed per tooth and the cutter diameter. The subsequent radial depth of cut is subtracted from the discretized size of the width of cut to obtain the minimum chip thicknesses. The forces for each segment are summed to obtain the total forces acting on the system of the workpiece and the tool. The cutting forces can be predicted from input data of work material properties, cutter configuration and the cutting conditions used. The validation of the proposed model is achieved by correlating experimental results with the predicted results obtained.     

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.     

An experimental investigation on the process parameters influencing machining forces during milling of carbon and glass fiber laminates

Milling is the most feasible machining operation for producing slots and keyways with a well defined and high quality surface. Milling of composite materials is a complex task owing to its heterogeneity and the associated problems such as surface delamination, fiber pullout, burning, fuzzing and surface roughness. The machining process is dependent on the material characteristics and the cutting parameters. An attempt is made in this work to investigate the influencing cutting parameters affecting milling of composite laminates. Carbon and glass fibers were used to fabricate laminates for experimentations. The milling operation was performed with different feed rates, cutting velocity and speed. Numerically controlled vertical machining canter was used to mill slots on the laminates with different cutting speed and feed combinations. A milling tool dynamo meter was used to record the three orthogonal components of the machining force. From the experimental investigations, it was noticed that the machining force increases with increase in speed. For the same feed rate the machining force of GFRP laminates was observed to be very minimal, when compared to machining force of CFRP laminates. It is proposed to perform milling operation with lower feed rate at higher speeds for optimal 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.     

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.     

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.