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1 30 9 Vol.30 No Journal of Computer-Aded Desgn & Computer Graphcs Sep 三维零件模型工程尺寸完备性检查算法 * 罗磊, 刘远, 郑国磊 ( 北京航空航天大学机械工程及自动化学院北京 ) (luole188@126.com, zhengguole@buaa.edu.cn) 摘要 : 三维模型定义技术的发展使得设计和制造逐渐走向三维化, 为了确保设计和加工数据的完整性, 实现三维标注尺寸完备性的自动检查, 提出一种基于参数化建模映射关系的尺寸完备性自动检查算法. 首先建立工程尺寸集和建模参数集之间的映射关系, 利用牛顿迭代法求解其映射矩阵 ; 其次对映射矩阵化简, 建立映射矩阵与尺寸完备性之间的关系 ; 最后通过分析化简后的映射矩阵来完成尺寸完备性检查判断. 在 CAITA 系统上进行实例分析测试, 验证了该算法的正确性和有效性. 关键词 : 三维标注 ; 映射矩阵 ; 尺寸约束 ; 尺寸完备性中图法分类号 : TP391.7 DOI: /SP.J Algorthm for Inspecton of Engneerng Dmensonng Completeness on 3D Part s Model Luo Le, Lu Yuan, and Zheng Guole * (School of Mechancal Engneerng & Automaton, Behang Unversty, Bejng ) Abstract: Wth the development of 3D model defnton technology, complete dmensonng plays an mportant role n dgtal product desgn and manufacturng. To ensure the ntegrty of desgn and processng data and acheve the automatc nspecton of dmensonng completeness on 3D part s models, a novel algorthm of dmensonng completeness nspecton s proposed here based on the mappng relaton n the parametrc modelng. Frst the mappng s establshed by analyzng the relaton between sets of modelng parameters and engneerng dmensons, and the mappng matrx s solved by Newton method. Then the mappng matrx s smplfed by the row elementary trans-formatons, and the judge prncple of dmensonng completeness s establshed by mathematc methods n the analyss of the relatonshp between the smplfed mappng matrx and the dmensonng completeness. Fnally, the algorthm for nspecton of dmensonng completeness s developed based on the judge prncple. The correctness and effectveness of the proposed approach s verfed va the tests on some representatve 3D parts based on the CAITA V5 system. Key words: 3D dmenson; mappng matrx; dmenson constrant; dmensonng completeness,.,,., 40%~60% [1],,, [2]., [3], : ; : 罗磊 (1991),,, CAD/CAM; 刘远 (1989),,, CAD/CAM, ; 郑国磊 (1964),,,,,, CAD/CAM.

2 9, : 1749,., [4] [5] [6] [7-8] [9-10] ;,,., [11-12],, ; [13-14],, ; 2,. [15], ; [16-17], ; [18-20] ; [21], ;,,.,.,,,, ; CATIA V5,,. 1 尺寸完备性检查关键技术, Cg { cg 1, 2,, k}, cg. [23] c ( c k, G g, g,, g, v., k c C ), 1 2 n ; G c, G G; v. M, v V, V v1, v2,, vm., Fk( g1, g2,, gn) c, Fk( g1, g2,, gn) v. C { c1, c2,, c m }, c. M, C Fk( g1, g2,, gn) v1 Fk( g1, g2,, gn) v2 (1) Fk( g1, g2,, gn ) vm, G e g, M,., M. 定义 1. M, G, C, M,, M, C M. 1, M,, C, M. 1 2 M. 1.1 尺素表示模型及参数集之间映射关系, [22]. M FGC (, )., F ; G, G ={ g1, g2,, g n } ; C,, C C( C, C )., Ce, e g e { e 1, 2,, C c m}, ce ; Cg 1 2,,,. M,

3 , ;,,., M C P, V P. C D,, C P, V P V D. [23] V D H DP ( V P ). V P, M, V D d V P, Hdp( p 1 1, p2,, pn) d1 Hd ( 2 p p1, p2,, pn ) d2 (2) Hd ( 1, 2,, ) m p p p pn dm, [24].,, [25].,,, V P V D, Hdp H 1 dp H 1 dp 1 p1 p2 pn d1 p1 Hd2p Hd2p H d2p d 2 p 2 p1 p2 p n d p m n Hdmp Hdmp H dmp p p p 1 2 n (3),, A DP., V P d VD p 1, p 2,, pk, d p 1, p 2,, pk, d p 1, p 2,, pk ;, d p 1, p 2,, pk, d p 1, p 2,, pk. 1.2 尺寸完备与映射矩阵的关系 n M, C V p p p P C D P 1, 2,, n, VD d1, d2,, dm. V P V D, (1) 和 Fk( g1, g2,, gn) p Fk( g1, g2,, gn) p Fk( g1, g2,, gn ) p 1 2 n (4) Fk( g1, g2,, gn) d1 Fk( g1, g2,, gn) d2 (5) Fk( g1, g2,, gn ) dm,, (4), g, p 1, p 2,, pn. (4) g 1, g 2,, gn (5), d 1, d 2,, dm p 1, p 2,, pn, g 1, g 2,, gn p 1, p 2,, pn., d1, d2,, dm p 1, p 2,, pn. 1.1 M V P V D (2), p 1, p 2,, pn, V P V D., A DP,,.., C D V D,, (2). [25],, A DP ().., M, C D A DP. 1.3 尺寸不完备与映射矩阵的关系,.

4 9, : 1751 定义 2. { c 1, c 2,, cn} cn ( 1, 2,, k ), { c 1, c 2,, cn} ;,., 2. A DP, A DP :, A DP A DP ; ; A DP. A DP A DP ,,,,., V D,.,, { d1, d2,, dm}, d., d d1, d2,, dk, d d 1, d 2,, dk,, d d1, d2,, dk,, A DP 0., A DP 0,, d d1, d2,, dk, d d 1, d 2,, dk, { d 1, d 2,, dm}, d.,. 0,,, A DP 1 0., A DP k 0 k ,,,,., VD, V D n. (2), n., R A DP n,., A DP n,, { d1, d2,, dm} n,,,., m n, n 3 : 1 0; 2 0; 2. A DP n 3,., (3) 1 2 m DP p1 p2 pn d d d A. (1) A DP 0. A DP 0, d 1, d 2,, d m p.,, d 1, d 2,, dm p,, p, d 1, d 2,, dm, { d 1, d 2,, dm} p. p, VD. p, 0. (2) 2 0. A DP 0,, p1, p2,, pm d 1, d 2,, d m d., (2),,,.

5 , A DP k 0, k 1, k 1. (3) A DP 0, 2 0, 2,. 1.4 完备性判定准则,,,.,, A DP, : (1). A DP, 0,, ;,. (2). A DP 0,, 0. (3). A DP, 0 2 0,, 本文算法映射矩阵求解,., : Step1., VP p1, p2,, pn,, VD d1, d2,, dm. Step2. V P p 1,, p 1,, p 1 p1 p1, p1 0, p p p, p 0, 2,3,, n. Step3. Step2, VD. V D { d 1, d 2,, d m }. 2 Step4. p 1, p 1,,, ' V D V D. Step5. V D : d d d j 1, 2,, m. j j j T Step6. A DP 1 a1 [ a11 a21 a n 1] a 1 d / p 0 ( j 1,2,, m). j j Step7., p 2, p 3,, pn, p 0, p j 0, 1, 2,, n, j, a. Step8. a 1, a 2,, an, A DP, A DP [ a1 a2 an ]. 2.2 映射矩阵化简, A DP.,. : Step1. A DP, Α DP,. j, j, j.

6 9, : 1753 Step2.,. j, j k, j. Α DP k j, Step3. A DP. 2.3 尺寸完备性判断,, : Step1. A DP ( m=n), 0,, ;,,. Step2. A DP 0,. 0. Step3. A DP 0,. A DP 0, ; 2 0, 0. 3 实例分析 CATIA V5,,. : Step1.. Step2.. Step3.., ;,,. 3~ 4,. 3a 4a,, 3a, d 7 d 21 2 p 6., 4a. 3a 4a, 3b 4b ~ 4, 3a,,, ; 4a,,.,,,,. 4 结语,,,.,,.,,.

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34 7 S R θ Z θ Z R A B C D PTP θ t 0 = θ 0 θ t 0 = 0 θ t 0 = 0 θ t = θ θ t = 0 θ t = 0 θ t V max θ t a max 3 θ t A θ t t 0 t / V max a max A = 3 4 S S 7 0 7 No. 7 Modular Machne Tool & Automatc Manufacturng Technque Jul. 0 00-65 0 07-0033 - 06 *. 0040. 04 PTP s TH6 TP4. A The Moton plannng of Handlng Robot Based on Tme Optmal CAO Bo CAO Q-xn TONG Shang-gao