機械加工外文翻譯--五軸曲面加工的刀具路徑（原文）

1、ORIGINAL ARTICLEGenerating tool-path with smooth posture change for five-axis sculptured surface machining based on cutter’s accessibility mapL. L. Li & Y. F. Zhang & H. Y. Li & L. GengReceived: 26 May 2009 /

2、Accepted: 16 July 2010 /Published online: 4 August 2010 # Springer-Verlag London Limited 2010Abstract In five-axis high speed milling, one of the key requirements to ensure the quality of the machined surface is that the

3、 tool-path must be smooth, i.e., the cutter posture change from one cutter contact point to the next needs to be minimized. This paper presents a new method for generat- ing five-axis tool-paths with smooth tool motion a

4、nd high efficiency based on the accessibility map (A-map) of the cutter at a point on the part surface. The cutter’s A-map at a point refers to its posture range in terms of the two rotational angles, within which the cu

5、tter does not have any interference with the part and the surrounding objects. By using the A-map at a point, the posture change rates along the possible cutting directions (called the smoothness map or S-map) at the poi

6、nt are estimated. Based on the A- maps and S-maps of all the sampled points of the part surface, the initial tool-path with the smoothest posture change is generated first. Subsequently, the adjacent tool- paths are gene

7、rated one at a time by considering both path smoothness and machining efficiency. Compared with traditional tool-path generation methods, e.g., iso-planar, the proposed method can generate tool-paths with smaller posture

8、 change rate and yet shorter overall path length. The developed techniques can be used to automate five-axis tool-path generation, in particular for high speed machining (finish cut).Keywords Five-axis milling . Tool-pat

9、h generation . Cutter posture change . Machining strip width1 IntroductionAs the need for complex components such as three- dimensional (3D) moulds and dies has risen, sculptured surface machining has assumed a more and

10、more important role in manufacturing for the last few decades. The employment of five-axis numerical control (NC) machines in sculptured surface machining offers numerous advan- tages over three-axis mode such as setup r

11、eduction, fast material removal rates, and improved surface quality. To make the best use of five-axis machining, however, problems related to complication and complexity caused by the two additional rotary axes have to

12、be solved. One of the challenging tasks is to automatically generate error-free tool-path without user interaction for machining sculptured surfaces. In the process planning of five-axis finish cut, the tool- path genera

13、tion task is to select a tool-path pattern, generate the cutter contact (CC) points that satisfy the accuracy requirement, and determine the cutter’s posture (orienta- tion) at every CC point without causing any interfer

14、ence. During this process, to ensure the quality of the machined surface, the smooth dynamics of cutter motion is a must, i.e., the posture change from one point to the next must be minimized. Extreme change in cutter po

15、sture, which is necessary for interference avoidance, is a major cause for the unnatural movement of the cutter and will lead to over and under cutting in five-axis finish and undesirable irregularity of the surface appe

16、arance [1, 2]. So far, there is limited reported work on obtaining the cutter location (CL) data with smooth continuous change in cutter postures along a pre-set path and cutting direction [1–3], and there is no reported

17、 method that can generate CL data with global optimization of cutter motion dynamics with respect to a cutting direction in five-axis finish cut.L. L. Li: Y. F. Zhang (*): H. Y. Li: L. Geng Department of Mechanical Engin

18、eering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore e-mail: mpezyf@nus.edu.sgInt J Adv Manuf Technol (2011) 53:699–709DOI 10.1007/s00170-010-2849-2efficiency, and in particular,

19、smooth posture changes. Using the A-maps and S-maps at all the sampled points on the surface, the optimal tool-paths are generated such that the change in cutter posture is minimized when passing through the generated CC

20、 points. Besides, machining strip width between adjacent paths is also considered to achieve high machining efficiency.3 The accessibility map of a cutter at a pointThe accessibility map (A-map) is defined in respect to

21、a cutter positioned at a point on the part surface. It refers to the posture range in terms of the two rotational angles, and within this range, the cutter does not have any interference with the part and the surrounding

22、 objects. The A-map effectively characterizes the accessibility of a cutter to a point, which provides important geometric information for cutter selection and interference-free tool-path generation. A brief introduction

23、 of A-map is given here. As shown in Fig. 1a, the local frame (XL ? YL ? ZL) originates at the point of interest Pc with ZL-axis along the surface normal vector, XL-axis along the surface maximum principal direction, and

24、 YL-axis along the surface minimum principal direction [21]. A cutter posture (l, θ) means that the cutter’s axis inclines counter-clockwise with l about YL-axis and rotates a θ about ZL-axis. The A-map of the cutter at

25、this point is represented in [l, θ] domain in the local frame. In order to find the A-map at the point, the four accessible posture ranges based on their respective interference-free attributes, i.e., machine axis limits

26、 (ML), local-gouging (LG), rear-gouging (RG), and global- collision (GC), are found first. For implementation, the part surface (to be machined) is firstly sampled into m points. At a specific point, the feasible range o

27、f θ–l based on ML is first calculated. θ is then uniformly sampled into k angles. At each discrete θ, the minimum l needed to eliminate LG is found. For RG and GC, the range of l ateach discrete θ that is interference-fr

28、ee from all the remaining (m?1) points is identified. The A-map at this point is simply the intersection of these four accessible posture ranges (see Fig. 1b). The overall algorithm for finding the A-map for a cutter at

29、a point on the part surface is called the cutter accessibility (CA) algorithm. Obviously, the CA algorithm is numerical in nature with a computa- tional complexity of Ο(km). For more details about the evaluation of the A

30、-map, readers can refer to [22]. A direct application of this A-map concept is for the optimal cutter selection to finish a given sculptured surface [22]. By applying the CA algorithm to all the sampled points on a part

31、surface, one can judge whether a cutter can traverse the whole surface without any interference. The optimal cutter can therefore be the largest available cutter with non-empty A-maps at all sampled surface points.4 The

32、smoothness map of a cutter at a pointSince the A-map only characterizes the geometric property of the cutter’s potential configuration at a point, it is necessary to add the dynamic property of the cutter at the point to

33、 complete the information set. The dynamic property of cutter is a complex issue involving many factors, e.g., feed-rate, cutting load, and path smoothness. Since this work focuses on finishing tool-path planning, only p

34、ath smoothness is considered, which is measured by the posture change rate (PCR) of the cutter at the point. Given a CC point Pi and next CC point Pi+1 on a path, PCRi is defined as:PCRi ¼ jViþ1 ? VijjPiþ1

35、 ? Pij ð1ÞWhere Vi is the unit vector of cutter axis along its posture (θi, li) at Pi in the global frame. Before a cutting direction is selected, it is necessary to obtain the PCRs along all possible cutting d

36、irections, which is called the smoothness(a) The cutter in the local frame (b) The A-map at PcXLYLPcZLλ θFig. 1 The cutter A-map at a point on the part surface. a The cutter in the local frame. b The A-map at PcInt J Adv