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.     

Cutter workpiece engagement region and surface topography prediction in five-axis ball-end milling

Based on the machining tool path and the true trajectory equation of the cutting edge relative to the workpiece, the engagement region between the cutter and workpiece is analyzed and a new model is developed for the numerical simulation of the machined surface topography in a multiaxis ball-end milling process. The influence of machining parameters such as the feed per tooth, the radial depth of cut, the angle orientation tool, the cutter runout, and the tool deflection upon the topography are taken into account in the model. Based on the cutter workpiece engagement, the cutting force model is established. The tool deflections are extracted and used in the surface topography model for simulation. The predicted force profiles were compared to the measured ones. A reasonable agreement between the experimental and the predicted results was found.     

Improved analytical chip thickness model for milling

In this paper an analytic expression for chip thickness in milling was formulated while considering the cycloidal motion of the teeth, runout, and uneven teeth spacing. In order to generalize the equation, the cutting parameters associated with milling (linear feed, tool rotational speed, and radius) were combined into a single, non-dimensional parameter. The new parameter allowed abstraction of the milling process and enabled selection of the maximum possible chip thickness in milling. Equations for entry and exit angles of a cut were also developed. The chip thickness values given by the new model were compared to prior models and showed lower error levels.     

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.     

Cutting force prediction for ball-end mills with non-horizontal and rotational cutting motions

Accurate cutting force prediction is essential to precision machining operations as cutting force is a process variable that directly relates to machining quality and efficiency. This paper presents an improved mechanistic cutting force model for multi-axis ball-end milling. Multi-axis ball-end milling is mainly used for sculptured surface machining where non-horizontal (upward and downward) and rotational cutting tool motions are common. Unlike the existing research studies, the present work attempts to explicitly consider the effect of the 3D cutting motions of the ball-end mill on the cutting forces. The main feature of the present work is thus the proposed generalized concept of characterizing the undeformed chip thickness for 3D cutter movements. The proposed concept evaluates the undeformed chip thickness of an engaged cutting element in the principal normal direction of its 3D trochoidal trajectory. This concept is unique and it leads to the first cutting force model that specifically applies to non-horizontal and rotational cutting tool motions. The resulting cutting force model has been validated experimentally with extensive verification test cuts consisting of horizontal, non-horizontal, and rotational cutting motions of a ball-end mill.     

Machining strategy in five-axis milling using balance of the transversal cutting force

Several solutions can be considered to resolve the problem of positioning a cutting tool on a free-form surface when five-axis milling. To choose a unique solution, in addition to the cutter–workpiece contact, an additional criterion can be taken into account. This may concern the local geometry of the surface or yet again the width milled to maximise the metal removal rate, but technological criteria relating to the cutting phenomenon and the quality of the surface produced are not considered. The present article introduces a strategy applying positioning combined with balancing of the transversal cutting force. This method involves using the ploughing effect of the milling cutters by simultaneously engaging the teeth located to the front of the cutter in relation to the feed movement and also those to the rear. The positioning obtained stabilises the cutter and contributes to making a net improvement in its dynamic behaviour. This leads in turn to significantly higher quality of the milled surface. The article presents a method to apply balancing of the transversal cutting force to two types of machining passes and elaborates an associated strategy to plan cutter paths enabling an improvement in surface quality to be achieved.     

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.     

Improved calculation of the cutting force in end milling

Determination of the cutting force in end milling on the basis of the Johnson–Cook phenomenological model is described. The numerical results obtained by this method are compared with experimental data.     

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.     

Torus cutter positioning in five-axis milling using balance of the transversal cutting force

This article introduces a new torus cutter positioning strategy for five-axis milling of free-form surfaces. This approach ensures elimination of local interference while also allowing better surface quality to be obtained than with positioning proposed by computer-aided manufacturing (CAM) software. In practice, the cutter axis is inclined to the rear in relation to the feed movement. A first inclination for the cutter axis is calculated to allow local interference to be eliminated. Then, an additional inclination is given to tool axis to achieve balancing of the transversal cutting force component perpendicular to the plane containing the tool axis and the feedrate vector. This particular machining situation considerably enhances the cutter's dynamic behaviour and gives better roughness values than those obtained with positioning by CAM software. A positioning method is adapted to the negative rearward inclination of the cutter axis, and it is then shown how transversal cutting force balancing is integrated in the form of an additional inclination. Finally, a comparison of the results obtained after milling with this new positioning and positioning calculated by a CAM program highlights the new method’s advantages.     

Tool deflection error compensation in five-axis ball-end milling of sculptured surface

Manufacturing of aircraft structural parts have the characteristics of complex process, large variety, small batch, and frequent change of production status. In order to shorten lead time and reduce cost, high-efficiency communication and collaboration among manufacturing departments are required. However, in the existing research literature, tool/fixture design, manufacturing simulation, and online machining process monitoring are not fully taken into account for collaboration. In order to address these challenging issues, this paper proposes a collaborative manufacturing framework based on machining features and intelligent software agents. The components of the proposed framework include a machining process planning agent, a numerical control (NC) programming agent, a simulation and verification agent, a tool/fixture design agent, a cost estimation agent, a production management agent, and an online machining process monitoring agent. Machining features are used as information carrier for communication and collaboration among these agents. This paper particularly focuses on the collaboration between tool/fixture design and NC programming, as well as the collaboration between online machining processes and related departments. The proposed approach has been implemented through a prototype system and tested in a large aircraft manufacturing enterprise with some very promising results.     

Geometric error compensation for five-axis ball-end milling by considering machined surface textures

Arbitrarily adjusting tool poses during error compensation may affect the quality of surface textures. This paper presents one tool center limitation-based geometric error compensation for five-axis ball-end milling to avoid the unexpected machined textures. Firstly, the mechanism of cutter location generation with cuter contact (CC) trajectory is analyzed. Due to zero bottom radius of ball-end cutter, CC points of the surface are only related to the tool center of the cutter. Realizing that, tool center limitation method of ball-end milling is established based on the generation of movements of all axes in order to ensure the machined textures. Then, geometric error compensation of ball-end milling is expressed as optimizing rotation angles of rotary axes by limiting tool centers of cutter locations. Next, particle swarm optimization (PSO) is intergraded into the geometric error compensation to obtain the compensated numerical control (NC) code. The limited region for particles of rotation angles is established, and moving criterion with a mutation operation is presented. With the help of the tool center limitation method, fitnesses of all particles are calculated with the integrated geometric error model. In this way, surface textures are considered and geometric errors of the machine tool are reduced. At last, cutting experiments on five-axis ball-end milling are carried out to testify the effectiveness of the proposed geometric error compensation.     

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 .     

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.     

Geometry simulation and evaluation of the surface topography in five-axis ball-end milling

Limited by the factors such as dynamic vibrations, cutting heat, and the use of coolant, it is difficult to measure or evaluate the surface quality in real time. Geometry simulation of the surface topography became the main method used in engineering to estimate and control the quality of the surface machining. This paper proposed a new method for geometry simulation and evaluation of a milled surface. Allowing for the coherency in geometric variations management process, the proposed method is developed based on the skin model of a workpiece. To make the simulated surface topography more realistic, the effects of locating errors, spindle errors, geometrical errors of the machine tool, and cutting tool deflections are included. And a new method is adopted to evaluate the milled surface, in which the roughness of the surface is characterized by the modal coefficients, instead of the R _a , R _z , and R _q values. At the end of this paper, measurements and cutting tests are carried out to validate the proposed method.     

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.