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。     

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.     

Prediction of cutting forces and machining error in ball end milling of curved surfaces -I theoretical analysis

This paper presents a theoretical model by which cutting forces and machining error in ball end milling of curved surfaces can be predicted. The actual trochoidal paths of the cutting edges are considered in the evaluation of the chip geometry. The cutting forces are evaluated based on the theory of oblique cutting. The machining errors resulting from force induced tool deflections are calculated at various parts of the machined surface. The influences of various cutting conditions, cutting styles and cutting modes on cutting forces and machining error are investigated. The results of this study show that in contouring, the cutting force component which influences the machining error decreases with increase in milling position angle; while in ramping, the two force components which influence machining error are hardly affected by the milling position angle. It is further seen that in contouring, down cross-feed yields higher accuracy than up cross-feed, while in ramping, right cross-feed yields higher accuracy than left cross-feed. The machining error generally decreases with increase in milling position angle.     

高速干式飞刀铣齿切削力模型

利用金属切削理论,采用高速干式飞刀铣齿模拟滚齿切削过程,建立飞刀铣齿切削力模型,推导出飞刀铣削力的计算公式。该模型的建立对进一步分析高速干式滚齿过程中的特征参数、进行切削机理的研究具有重要意义。     

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.     

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.     

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.     

基于MATLAB的高速铣削加工再生型颤振的建模与仿真

针对国内高速铣削加工工艺参数选择存在的问题,基于动态铣削力建模和颤振稳定域分析计算,以MATLAB为开发工具,得到了铣削加工再生型颤振仿真算法.通过模态锤击实验获得频响函数,利用Visio Basic软件设计了圆柱立铣刀动力学仿真系统,对整个加工系统的颤振稳定域图形进行仿真,为铣削加工切削参数选择和优化提供了理论依据.实验验证了该仿真算法的有效性和准确性,并在实际应用中取得了良好的效果.     

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.     

Cutting force model considering tool edge geometry for micro end milling process

The analysis of the cutting force in micro end milling plays an important role in characterizing the cutting process, as the tool wear and surface texture depend on the cutting forces. Because the depth of cut is larger than the tool edge radius in conventional cutting, the effect of the tool edge radius can be ignored. However, in micro cutting, this radius has an influence on the cutting mechanism. In this study, an analytical cutting force model for micro end milling is proposed for predicting the cutting forces. The cutting force model, which considers the edge radius of the micro end mill, is simulated. The validity is investigated through the newly developed tool dynamometer for the micro end milling process. The predicted cutting forces were consistent with the experimental results.     

铣削加工系统三维稳定性理论研究与进展

切削颤振是高速加工过程中经常遇到的一种现象,而判断稳定切削常用的一种方法就是绘制稳定性图。主要针对国内外铣削加工颤振三维稳定性图和三维稳定性理论研究状况进行了综述,重点给出了Thevenot、U.Bravo和S.Herranz、Tony L.Schmitz和Altintas的稳定性理论。研究指出,为了保证材料的最大去除率,必须研究切削参数对于稳定性的影响,也就是需要研究主轴转速、轴向切深和径向切深对切削颤振影响的三维稳定性图。     

Prediction of cutting force for ball end mill in sculptured surface based on analytic model of CWE and ICCE

Abstract

The force prediction is the precondition of improving equipment utilization ratio and optimizing process for CNC machining. Cutter-workpiece engagement (CWE) and in-cut cutting edge (ICCE) are the keys. In this article, a new analytic method of CWE and ICCE is proposed for ball end milling of sculptured surface and the prediction model of milling force is established. The sculptured surface is discretized into a series of infinitesimal inclined planes corresponding to cutter location points. The geometry relationships of cutter axis, feed direction and inclined plane are defined parametrically. The boundary curves and the boundary inflection points of the CWE are obtained by intersecting spatial standard curved surfaces with rotation transformation of coordinate system. The effective intersection points of the CWE and the cutter edge curve in X_c-Y_ctwo-dimensional plane are the upper and lower boundary points of ICCE. Based on the instantaneous chip thickness considering arbitrary feed direction, the force prediction model for ball end mill of three-axis surface milling is established. Simulation and experiment show that CWE and ICCE calculated by analytic method are well consistent with those of solid method. The predicted cutting forces match well with the measurements both in magnitude and variation trend.     

复杂形状工件的端铣切削力模型

以传统的端铣切削力模型为基础，提出了一种新的端铣加工中静态切削力的预报模型。该模型考虑了复杂的工件形状和不同的铣刀进给轨迹。给出了一种新的工件和铣刀接触算法。     

Implementation of analytical boundary simulation method for cutting force prediction model in five-axis milling

A simulation system was developed that deals with cut geometry and machining forces when a toroidal cutter is used during semifinishing in five-axis milling. The cut geometry was calculated using an analytical method called analytical boundary simulation (ABS). ABS was implemented to calculate the cut geometry when the machining used an inclination angle and a screw angle. The effect of tool orientation on the cut geometry was analyzed. The accuracy of the proposed method was verified by comparing the cut lengths calculated using ABS with cuts obtained experimentally. The result indicated that the method was accurate. ABS was subsequently applied to support a cutting force prediction model. A validation test showed that there was a good agreement with the cutting force generated experimentally.     

高速铣削GH3039高温合金的切削用量研究

GH3039是一种镍基高温合金,对其切削加工时会产生很大的切削力,以至于对刀具磨损、加工精度和生产效率等均产生很大的影响。针对上述问题,提出使用硬质合金刀具来加工这种材料,利用线性回归方法,建立GH3039高温合金的铣削力模型,并通过极差分析得到合理的切削用量,为GH3039高温合金的实际铣削加工提供参考依据。     

The prediction of cutting force in milling Inconel-718

Due to the enormous engineering advancement in modern industries, the competition in manufacturing technologies has been increasingly intense, as can be seen in automobile and aerospace industries. Nickel-based superalloys are widely in the manufacture of components for aircraft turbine engines for cryogenic tankage, in liquid rockets, reciprocating engines, space vehicles, heat-treating equipment, chemical and petrochemical industries, because of their ability to retain high-strength at elevated temperatures. But, because of its characteristics of high-strength, poor thermal diffusion and work hardening, the cutting of nickel-based superalloys results in decreased tool life and poor efficiency of works. This is much more prominent than in other materials. AISI4340 are widely used in the manufacture of component parts for gear, pistons, and automobiles.     

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.