Decoupled chip thickness calculation model for cutting force prediction in five-axis ball-end milling

Cutting force prediction plays very critical roles for machining parameters selection in milling process. Chip thickness calculation supplies the basis for cutting force prediction. However, the chip thickness calculation in five-axis ball-end milling is difficult due to complex geometrical engagements between parts and cutters. In this paper, we present a method to calculate the chip thickness in five-axis ball-end milling. The contributions of lead and tilt angles in five-axis ball-end milling on the chip thickness are studied separately in detail. We prove that the actual chip thickness can be decoupled as the sum of the ones derived from the two individual cutting conditions, i.e., lead and tilt angles. In this model, the calculation of engagement boundaries of tool–workpiece engagement is easy; thus, time consumption is low. In order to verify the proposed chip thickness model, the chip volume predicted based on the proposed chip thickness calculation model is compared with the theoretical results. The comparison results show that the desired accuracy is obtained with the proposed chip thickness calculation model. The validation cutting tests, which are in a constant material removal rate and with only ball part engaged in cutting, are carried out. The optimized lead and tilt angles are analyzed with regard to cutting forces. The geometrical as well as the kinematics meaning of the proposed method is obvious comparing with the existing models.     

Cutting force prediction in ball-end milling with inclined feed by means of geometrical analysis

A geometrical model for the analysis of cutting forces in ball-end milling has been presented in a previous work (Tsai CL, Liao YS, J Mater Process Technol 205:24–33, 10), which can be used to analyze cutting forces in vertical or horizontal feed. In this paper, the three-dimensional geometrical analysis is depicted with different interacting relations among cutting edge, undeformed chip and shear zone along nonhorizontal cutting direction, and a general geometrical model of inclined feed in ball-end milling is presented. According to the geometrical analysis, the cutting directions of horizontal, vertical, inclined downward, and inclined upward feed are defined with a feed angle. A general force model is derived, and the three-dimensional cutting forces are predicted. Experiments are conducted to verify the geometric force model. The influences of different feed angle and helix angle on cutting forces in inclined downward and inclined upward feed are discussed and simulated.     

Extended octree for cutting force prediction

Prediction of cutting force plays an essentially important role in the selection of optimum cutting parameters and investigation of cutting mechanisms. In this work, an extended octree is presented to represent the workpiece and tool swept volume to acquire the cutting depth and cutting width with high precision so that the cutting forces can be predicted precisely. The algorithm of acquisition of cutting width and cutting depth in flat-end milling is described. A framework of cutting force prediction based on virtual machining was established and a demonstration system was developed consequently. The simulated values of cutting width and cutting depth show good consistency with the theoretically calculated data.     

球头刀高速铣削铝合金切削力的试验研究

采用切削力理论分析与实验相结合的方法,建立了高速铣削常用的球头铣刀的铣削力数学模型.通过实验数据拟合了高速铣削状态下铝合金LY12的铣削速度与单位铣削力之间的关系.并通过铝合佥材料LY12高速铣削切削力的实验,验证了球头铣刀高速铣削力的数学模型.     

The effects of cutter eccentricity on the cutting force in the ball-end finish milling

Ball-end mill are usually used for finish machining with multi-axis CNC milling centers. Cutter eccentricity (offset magnitude e _c, angular location of the offset vector λ _c) is very important when predicting cutting forces accurately. In the process of cutting force modeling, not only the e _c, but also the λ _c, affects the cutting forces by associating with the rotation angle, the chip thickness, and the entry and exit angles of the cutting forces. The e _c affects the values of the cutting forces, while λ _c causes the delay phenomenon of the cutting forces mainly. Experiment results show that the cutting forces, considering the cutter eccentricity, more especially considering the influence of the λ _c, agree better with the measured cutting forces than the cutting forces without considering the cutter eccentricity.     

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.     

Feedrate optimization for variant milling process based on cutting force prediction

Machining process modeling, simulation and optimization is one of the kernel technologies for virtual manufacturing (VM). Optimization based on physical simulation (in contrast to geometrical simulation) will bring better control of a machining process, especially to a variant cutting process – a cutting process so complex that cutting parameters, such as cutting depth and width, change with cutter positions. In this paper, feedrate optimization based on cutting force prediction for milling process is studied. It is assumed that cutting path segments are divided into micro-segments according to a given computing step. Heuristic methods are developed for feedrate optimization. Various practical constraints of a milling system are considered. Feedrates at several segments or micro-segments are determined together but not individually to make milling force satisfy constraints and approach an optimization objective. After optimization, an optimized cutting location data file is outputted. Some computation examples are given to show the optimization effectiveness. This revised version was published online in October 2004 with a correction to the issue number.     

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.     

数控车削加工切削力的预测研究

应用六西格玛原理对数控车削加工钛合金材料进行正交切削试验,通过采集三向切削力信号,对数据结果进行分析,找出在正交试验范围内切削用量对切削力的影响规律,并通过对数据进行因子刻画,提出了一种在缺乏切削力经验公式和检测条件下进行切削力预测的有效方法,为优化切削加工条件提供了重要依据。     

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.     

Cutting torque and tangential cutting force coefficient identification from spindle motor current

This article presents an enhanced methodology for cutting torque prediction from the spindle motor current, readily available in modern machine tool controllers. This methodology includes the development of the spindle power model which takes into account all mechanical and electrical power losses in a spindle motor for high-speed milling. The predicted cutting torque is further used to identify tangential cutting force coefficients in order to predict accurately the cutting forces and chatter-free regions for milling process planning purposes. The developed model is compared with other studies available in the literature, and it demonstrates significant improvements in terms of the completeness and accuracy achieved. The developed model is also validated experimentally, and the obtained results show good compliance between the predicted and the measured cutting torque. The developed enhanced procedure is very appealing for industrial implementation for cutting torque/force monitoring and tangential cutting force coefficient identification.     

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.     

Investigating the cutting phenomena in free-form milling using a ball-end cutting tool for die and mold manufacturing

This paper presents an investigation of nonplanar tool-workpiece interactions in free-form milling using a ball-end cutting tool, a technique that is widely applied in the manufacturing of dies and molds. The influence of the cutting speed on the cutting forces, surface quality of the workpiece, and chip formation was evaluated by considering the specific alterations of the contact between tool-surface along the cutting time. A trigonometric equation was developed for identifying the tool-workpiece contact along the toolpath and the point where the tool tip leaves the contact with the workpiece. The experimental validation was carried out in a machining center using a carbide ball-end cutting tool and a workpiece of AISI P20 steel. The experimental results demonstrated the negative effect of the engagement of the tool tip into the cut on machining performance. The length of this engagement depends on the tool and workpiece curvature radii and stock material. When the tool tip center is in the cut region, the material is removed by shearing together with plastic deformation. Such conditions increase the cutting force and surface roughness and lead to an unstable machining process, what was also confirmed by the chips collected.     

车削AISI420不锈钢切削力预测模型构建

为了进一步研究AISI420不锈钢的切削机制,在Third Wave Advant Edge中建立车削有限元模型,进行车削加工仿真模拟,并对实验数据进行回归分析,得到三向切削力的预测模型。结果表明:车削力预测模型拟合度较好,回归分析效果显著,有较高的置信度,可为AISI420不锈钢的切削研究提供理论参考。