基于机器动力学指标的最优等截面切削方向：自由曲面加工的微分几何路径方法

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本文主要探讨了"Optimal iso-planar cutting direction based on machine kinematic metric"这一主题，它是计算机辅助设计与应用领域的一项关键研究。文章关注于通过机器运动学指标优化自由曲面加工的等距切削方向，这是一种基于微分几何的方法，旨在提高自由曲面加工的精度和效率。在现代制造工程中，尤其是当涉及到复杂形状零件的加工时，选择正确的切削路径至关重要。机器运动学指标（machine kinematic metric）是衡量和控制切削过程中的关键参数，它们反映了工具相对于工件的运动关系，包括刀具的进给速度、旋转角度以及切削深度等因素。优化的等距切削方向能够减少刀具路径的长度，降低表面粗糙度，从而减少加工时间并提升产品质量。作者Chen-Han Lee和Changya Yan在2016年11月22日提交了这篇论文，他们在文中详细阐述了一种新的方法，即运用微分几何理论来确定这种最优的等距切削方向。微分几何在此处提供了数学工具，使得可以通过分析曲面的局部特性来找到最佳的切削路径，这在处理自由曲面时尤其有用，因为这些表面通常具有复杂的曲率和拓扑结构。他们提出的算法可能包括对刀具路径的局部曲率分析，以及考虑工件材料特性和刀具性能等因素，以确保在满足加工精度的同时，兼顾切削的稳定性和生产效率。论文引用了《Computer-Aided Design and Applications》期刊，该刊的在线网址为http://china.tandfonline.com/loi/tcad20，表明这项研究是在国际上得到认可的学术成果。读者可以通过DOI:10.1080/16864360.2016.1257182链接到原文，或者访问http://dx.doi.org/10.1080/16864360.2016.1257182查看全文。此外，这篇论文也鼓励其他研究人员提交他们的相关研究，显示出该领域仍然保持着活跃的研究氛围。这篇论文为自由曲面加工领域的工程师和研究人员提供了一个重要的理论框架和计算工具，对于提高等距切削的效率和质量，推动制造业向更精密、高效的方向发展具有重要意义。

COMPUTER-AIDED DESIGN & APPLICATIONS 3

more closely related to our work. Optimal cut direction

based on machining width is not the focus of our work

but has similarity in terms of the methodology. We cover

the relevant references in the second subsection. Machine

kinematic capability optimization is our main focus and

the references of previous contributions are listed in the

third subsection. The mathematical instrument of elds,

including scalar, vector, and tensor elds, is used in some

of the previous works in freeform surface machining. The

use of elds is essential to our approach and we present

the eld-based works in the fourth subsection. A sum-

mary and discussion of the listed references is given in

the last subsection.

2.1. Freeform surface machining

Numerous researchers in the last two decades made sig-

nicant contributions to the topic of tool path genera-

tion for free form surface machining. Traditionally iso-

parametric and iso-planar methods have been used for

the tool path generation [7]. Afterwards many methods

were developed to improve the machining quality and

eciency, such as curved curvature matched machin-

ing [3], iso-phote based methods [6], conguration space

methods [20],region based tool path generation [5], etc.

Manyresearchersworkedontoolaxis/orientation

computation in 5-axis machining. The two rotary axes

allow the exibility to avoid collision/gouging and con-

trol the cutting condition during machining. However

the additional freedom from the rotary axes makes the

5-axis machining much more complicated than 3-axis

machining. Interference avoidance and smooth tool ori-

entation transition are the two key subjects in ve-

axis tool path generation. Researchers reported C-space

based tool orientation methods [13], rolling ball method

(RBM) [9], arc intersect method (AIM) techniques [10],

and tool orientation smoothing algorithms [1].

2.2. Machining width optimization

On top of tool path computation strategies and methods,

itisimportanttoimprovetheeciencyofmachining.In

general, the approaches to increase the machining e-

ciency in freeform surface machining could be classied

into tool path length reduction and optimal feed speed

assignment.

Wider machining strip width leads to less machining

passes which also means shorter tool path length. Eec-

tive cutting shape (ECS) and eective cutter radius (ECR)

were used to increase the machining strip width in tool

path optimization [21]. They concluded that the increase

of machining strip width is induced by the matching of

ECR with the surface normal curvature. Other methods

to obtain maximization of machining strip include curva-

ture matched method, adaptive space-lling curve (SFC)

method [22], interference-free tool orientation optimiza-

tion [12],andmachiningpotentialeldmethod[3].

2.3. Kinematic capability optimization

Several previous works considered machine tool kine-

matic capabilities in the CAM stage to achieve opti-

mal feed speed. The tool path generated and optimized

in CAM with only geometrical consideration could not

guarantee a superior machining eciency because the

actual feedrate assigned by the controller must respect the

machine tool’s physical performance constraints.

Kim [14]providedatime-optimaltoolpathgener-

ation method by considering the speed limits of the

machine axes and the surface nish requirements. Beu-

daert [1] provided a tool path smoothing algorithm based

on the maximum reachable feedrate by considering the

velocity, acceleration and jerk limits of each drive. The

proposed algorithm starts from a given tool path and iter-

atively smoothes the joint motions in order to raise the

real feedrate. Hu and Tang [11] proposed a concept called

machine-dependent potential eld (MDPF), which char-

acterized the relationship between the material removal

rate and the feed direction with considering the kine-

matic constraints of the machine’s axes. Based on the

MDPF, the optimal direction is searched which has the

maximal MDPF value and a so-called principal MDPF

curve can thus be traced out along the optimal direction

of each point. With the principle MDPF curve, a region

by region tool path generation method is proposed sim-

ilar to that in [3]. Tool path generation in this way is a

compromise between the machining eciency and the

uniformness of the tool path pattern.

2.4. Field based methods

Several authors used scalar and vector elds to gener-

ate smooth tool paths. The work in [8] issued a patent

to produce spiral tool path for blade milling. The patent

uses an imaginary electrical potential eld to generate

auxiliary lines for constructing a spiral two-dimensional

guild path. Makhanov [19] transformed the formulation

ofatoolpathtoacurvilinearcoordinatesystemonthe

surface with the elastic deformation being minimized.

It involves solving two scalar elds. Bieterman [2]and

Chuang [4] used path scalar elds to represent the tool

path pattern to optimize the smoothness of the tool path,

he optimization is achieved by solving an Elliptic PDE as

a boundary value problem. The formulation of Bieterman

and Sandstrom method lacks of metric tensor and is not

covariant. The Chuang and Yang method is independent

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基于机器动力学指标的最优等截面切削方向：自由曲面加工的微分几何路径方法

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