基于线性不等式方程组解的存在性及其通解的工件可达/可离性分析算法

doi:10.3901/JME.2017.21.136

机械工程学报 ›› 2017, Vol. 53 ›› Issue (21): 136-148.doi: 10.3901/JME.2017.21.136

基于线性不等式方程组解的存在性及其通解的工件可达/可离性分析算法

秦国华¹, 黄喆¹, 吴竹溪¹, 王华敏¹, 吴铁军², 李凌³

1. 南昌航空大学航空制造工程学院南昌 330063;
2. 东莞职业技术学院机电工程系东莞 523808;
3. 中国科学院深圳先进技术研究院深圳 518055

收稿日期:2016-06-20 修回日期:2017-03-11 出版日期:2017-11-05 发布日期:2017-11-05
作者简介:秦国华,男,1970年出生,教授,博士后。主要研究方向为数控加工过程建模与仿真、工件装夹分析与综合、刀具磨损检测与分析、残余应力预测与控制、制造业信息化技术。E-mail:qghwzx@126.com;黄喆,女,1990年出生。主要研究方向为夹具的自动化设计、数控加工过程建模与仿真。;吴竹溪,女,1969年出生,副教授。主要研究方向为数控加工与数控编程、计算机辅助夹具设计技术。;王华敏,女,1988年出生。主要研究方向为夹具的自动化设计、数控加工过程建模与仿真。;吴铁军,男,1978年出生,讲师。主要研究方向为计算机辅助技术、高效高精加工技术。;李凌,女,1983年出生,讲师。主要研究方向为智能算法、高效高精加工技术。
基金资助:
国家自然科学基金（51465045，51165039）、江西省主要学科学术和技术带头人资助计划、航空科学基金（2016ZE56011）、江西自然科学基金（20161BAB206114）和深圳市科创委基础研究（JCYJ20140509174140668）资助项目。

Analysis Algorithm of Workpiece Attachment/Detachment Based on Solution Existence and General Solution of Inequalities

QIN Guohua¹, WANG Zhe¹, WU Zhuxi¹, WANG Huamin¹, WU Tiejun², LI Ling³

1. School of Aeronautical Manufacturing Engineering, Nanchang Hangkong University, Nanchang 330063;
2. Department of Mechanical and Electrical Engineering, Dongguan Polytechni, Dongguan 523808;
3. Shenzhen Institutes of Advanced Technology, China Academy of Sciences, Shenzhen 518055

Received:2016-06-20 Revised:2017-03-11 Online:2017-11-05 Published:2017-11-05

摘要/Abstract

摘要： 工件的可达/可离性反映了将工件安装到/脱离出夹具装夹布局的可能性，分析可达/可离性有助于在工件上正确选择装夹表面和装夹点。为此依据工件与装夹元件的实际接触或装配情况，利用泰勒定理提出了工件可达/可离性模型。通过将工件安装到/脱离出装夹布局的可能性等价于可达/可离性模型的解的存在性，借助任意数可表达为两个非负数之差这一数学技巧作为桥梁，将工件可达/可离性模型的解的存在性问题转化为线性规划问题，提出了工件可达/可离性的判断方法。尤其是在判断可达/可离性模型有解的情况下，继而考虑了工件安装到/脱离出装夹布局的方向性。在此基础上，进一步将可达/可离的方向性转化为可达/可离性模型的通解，由此构建了求解线性不等式方程组的Γ-算法。这个“先有解-再求解”的算法仅涉及到装夹元件在工件表面处的位置与单位法矢量信息，不仅适用于形状复杂的工件，而且避免了可达/可离性模型无解情况下依旧求解的局限性，同时也拓展和丰富了自动化夹具设计的理论基础。

关键词: 不等式方程组, 对偶锥, 可达/可离方向, 可达/可离性, 凸锥, 线性规划

Abstract: The workpiece attachment/detachment can reflect the possibility of placing a workpiece in contact with the fixture layout or displacing a workpiece from the fixture layout. The objective of attachment/detachment nanlysis is help the correct selection of fixturing surfaces and fixturing points on workpiece. According to the practical contact/assembly of workpiece with the fixture layout, hence, Taylor theorem is used to formulate the attachment/detachment model. After equalizing the possibility of of placing a workpiece in contact with the fixture layout or displacing a workpiece from the fixture layout to the solution existence of attachment/detachment model, a mathmatics trick is created to express an arbitrary number in the attachment/detachment model as a difference of two nonnegative numbers. Only by doing so can the analysis of solution existence of attachment/detachment model be identified as a linear programming problem and in turn, a judgement method is proposed for the workpiece attachment/detachment. Especially under the condition that the attachment/detachment model has solutions, the direction of attachment/detachment of workpiece to/from the fixturing layout is further considered. By equivalently transforming the directionality of attachment/detachment into the general solution of attachment/detachment model, Γ-algorithm is suggested for solving a set of inear inequalities. The presented "seeking solutions if equations are solvable" algorithm only concerns on the coordinates and unit normal vectors of workpiece at fixturing points. It can not only be carried out for a workpiece with complex surfaces, but also avoid the solving process of the attachment/detachment model without solutions. It is more important, it can develop and enrich the theoretical basis of automated fixture design.

Key words: attachment/detachment, convex cone, directionality of attachment/detachment, dual cone, inequalities, linear programming

中图分类号:

TG702

秦国华, 黄喆, 吴竹溪, 王华敏, 吴铁军, 李凌. 基于线性不等式方程组解的存在性及其通解的工件可达/可离性分析算法[J]. 机械工程学报, 2017, 53(21): 136-148.

QIN Guohua, WANG Zhe, WU Zhuxi, WANG Huamin, WU Tiejun, LI Ling. Analysis Algorithm of Workpiece Attachment/Detachment Based on Solution Existence and General Solution of Inequalities[J]. Journal of Mechanical Engineering, 2017, 53(21): 136-148.

参考文献

[1] PEHLIVAN S, SUMMERS J D. A review of computer aided fixture design with respect to information support requirements[J]. Int J Prod Res. 2008, 46(4):929-947.
[2] RONG Y M, ZHU Y X. Computer aided fixture design[M]. New York:Marcel Dekker Inc, 1999.
[3] CHOU Y C, CHANDRU V, BARASH M M. A mathematical approach to automatic configuration of machining fixture:Analysis and synthesis[J]. ASME J. Eng. Ind., 1989, 111(11):299-306.
[4] 张生文, 苏延浩. 计算机辅助夹具设计技术发展综述[J]. 制造技术与机床, 2015, (4):50-55. ZHANG Shengwen, SU Yanhao. Overview of computer aided fixture design[J]. Manufacturing Technology & Machine Tool, 2015, (4):50-55.
[5] 吴玉光. 基于工序要求的夹具定位方案自动规划方法[J]. 机械工程学报, 2010, 46(11):185-192. WU Yuguang. Approach to automated location planning of fixture based on the processing procedure requirements[J]. Journal of Mechanical Engineering, 2010, 46(11):185-192.
[6] 郑联语,谷强,汪叔淳. 装夹规划中确定工件定位基准的神经网络决策机制[J]. 航空学报, 2001, 22(2):130-134. ZHENG Lianyu, GU Qiang, WANG Shuchun. Decision mechanism for workpiece locating datum based on neural network in stepup planning[J]. Acta Aeronautica et Astronautica Sinica, 2001, 22(2):130-134.
[7] 孙习武,褚学宁,张在房,等. 基于多色集理论的定位基准选择推理技术[J]. 计算机集成制造系统, 2007, 13(12):2463-2468. SUN Xiwu, CHU Xuening, ZHANG Zaifang, et al. Location datum of reasoning technology for mechanical part based on polychromatic sets[J]. Computer Integrated Manufacturing Systems, 2007, 13(12):2463-2468.
[8] QIN G H, ZHANG W H, WAN M. A machining dimension-based approach to locating scheme design[J]. ASME J. Manuf. Sci. Eng., 2008, 130(5):0510101-0510108.
[9] SONG H, RONG Y. Locating completeness evaluation and revision in fixture plan[J]. Robot Comput Integr Manuf, 2005, 21(4-5):368-378.
[10] 秦国华,徐九南,邱志敏. 夹具自动化设计中定位方案的生成式逐点设计法[J]. 计算机集成制造系统, 2011, 17(4):695-700. QIN Guohua, XU Jiunan, QIU Zhimin. Generative design approach of locating scheme in automatic fixture design[J]. Computer Integrated Manufacturing Systems, 2011, 17(4):695-700.
[11] 秦国华,叶海潮,崔跃,等. 面向计算机辅助夹具设计的修订式定位方案设计算法[J]. 计算机集成制造系统, 2012, 18(10):2145-2150. QIN Guohua, YE Haichao, CUI Yue, et al. Computer aided fixture design oriented modified design algorithm for fixture locating scheme[J]. Computer Integrated Manufacturing Systems, 2012, 18(10):2145-2150.
[12] MARIN R A, FERREIRA P M. Optimal placement of fixture clamps:Minimizing the maximum clamping forces[J]. ASME J Manuf Sci Eng, 2002, 124(3):686-694.
[13] KAYA N. Machining fixture locating and clamping position optimization using genetic algorithms[J]. Comput. Ind., 2006, 57(2):112-120.
[14] CHEN W F, NI L J, XUE J B. Deformation control through fixture layout design and clamping force optimization[J]. Int. J. Adv. Manuf. Technol., 2008, 38(9-10):860-867.
[15] QIN G H, YE H C, RONG Y M. A unified point-by-point planning algorithm of machining fixture layout for complex workpiece[J]. Int. J. Prod. Res., 2014, 52(5):1351-1362.
[16] 秦国华,赵旭亮,吴竹溪. 基于神经网络与遗传算法的薄壁件多重装夹布局优化设计[J]. 机械工程学报, 2015, 51(1):203-212. QIN Guohua, ZHAO Xuliang, WU Zhuxi. Optimization of multi-fixturing layout for thin-walled workpiece based on neural network and genetic algorithm[J]. Journal of Mechanical Engineering, 2015, 51(1):203-212.
[17] 秦国华,王子琨,吴竹溪,等. 基于表面网格离散化与遗传算法的复杂工件装夹布局规划方法[J]. 机械工程学报, 2016, 52(13):195-203. QIN Guohua, WANG Zikun, WU Zhuxi, et al. A planning method of fixturing layout for comoplex workpieces based on surface discretization and genetic algorithm[J]. Journal of Mechanical Engineering, 2016, 52(13):195-203.
[18] TRAPPEY A J C, LIU C R. An automatic workholding verification system[J]. Robot Comput. Integr. Manuf., 1992, 9(4-5):321-326.
[19] LI B, MELKOTE S N. Fixture clamping force optimisation and its impact on workpiece location accuracy[J]. Int. J. Adv. Manuf. Technol., 2001, 17(2):104-113.
[20] 秦国华,王华敏,叶海潮,等. 基于力的存在性与可行性的夹紧力变向增量递减规划算法[J]. 机械工程学报, 2016, 52(11):72-79. QIN Guohua, WANG Huamin, YE Haichao, et al. A planning algorithm of clamping forces for workpiece fixturing scheme based on existence and feasibility of forces[J]. Journal of Mechanical Engineering, 2016, 52(11):72-79.
[21] XIONG C H, LI Y F, RONG Y M, et al. Qualitative analysis and quantitative evaluation of fixturing[J]. Robot Comput. Integr. Manuf., 2002, 18(5):335-342.
[22] QIN G H, ZHANG W H, WAN M, et al. A novel approach to fixture design based on locating correctness[J]. Int. J. Manuf. Res., 2010, 5(4):429-448.
[23] 秦国华,张卫红,万敏. 基于线性规划的工件稳定性建模及其应用[J]. 机械工程学报, 2005, 41(9):33-37, 41. QIN Guohua, ZHANG Weihong, WAN Min. Modeling and application of workpiece stability based on the linear programming method[J]. Chinese Journal of Mechanical Engineering, 2005, 41(9):33-37, 41.
[24] QIN G H, ZHANG W H. Modeling and analysis of workpiece stability based on the linear programming method[J]. Int. J. Adv. Manuf. Technol., 2007, 32(1-2):78-91.
[25] 秦国华,吴竹溪,张卫红. 薄壁件的装夹变形机理分析与控制技术[J]. 机械工程学报, 2007, 43(4):211-216, 223. QIN Guohua, WU Zhuxi, ZHANG Weihong. Analysis and control technique of fixturing deformation mechanism of thin-walled workpiece[J]. Chinese Journal of Mechanical Engineering, 2007, 43(4):211-216, 223.
[26] QIN G H, ZHANG W H, WU Z X, et al. Systematic modeling of workpiece-fixture geometric default and compliance for the prediction of workpiece machining error[J]. ASME Journal of Manufacturing Science and Engineering, 2007, 129(4):789-801.
[27] 秦国华,周美丹,叶海潮,等. 基于AHP的夹具定位元件选择方法[J]. 计算机集成制造系统, 2014, 20(2):326-332. QIN Guohua, ZHOU Meidan, YE Haichao, et al. AHP-based fixture locator selection[J]. Computer Integrated Manufacturing Systems, 2014, 20(2):326-332.
[28] VUKELIC D, TADIC B, LUZANIN O, et al, A rule-based system for fixture design[J]. Sci. Res. Essays, 2011, 6(27):5787-5802.
[29] 罗晨,王欣,苏春,等. 基于案例推理的夹具设计案例表示与检索[J]. 机械工程学报, 2015, 51(7):136-143. LUO Chen, WANG Xin, SU Chun, et al. Case representation and retrieval under a case-based reasoning system for fixture design[J]. Journal of Mechanical Engineering, 2015, 51(7):136-143.
[30] 秦国华,黄华平,叶海潮,等. 基于运动学与有向尺寸路径的工件定位误差自动分析算法[J]. 计算机集成制造系统, 2014, 20(12):2935-2943. QIN Guohua, HUANG Huaping, YE Haichao, et al. Automatic analysis algorithm of workpiece locating error based on kinematics and directional dimension path[J]. Computer Integrated Manufacturing Systems, 2014, 20(12):2935-2943.
[31] 吴玉光,张根源,李春光. 夹具定位误差分析自动建模方法[J]. 机械工程学报, 2012, 48(5):172-179. WU Yuguang, ZHANG Genyuan, LI Chunguang. Approach to automated modeling of fixture location errors analysis[J]. Journal of Mechanical Engineering, 2012, 48(5):172-179.
[32] WANG M Y. Tolerance analysis for fixture layout design[J]. Assem Automat, 2002, 2(2):153-162.
[33] ASADA H, BY A B. Kinematics of workpart fixturing for flexible assembly with automatically reconfigurable fixtures[J]. IEEE J. Robot Automat, 1985, RA-1(2):86-94.
[34] HONG M, PAYANDEH S, GRUVER W A. Modeling and analysis of flexible fixturing systems for agile manufacturing[C]//Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, 1996, 2:1231-1236.
[35] 熊有伦. 机器人多手指抓取和适应性夹具夹持的封闭性和可达性[J]. 机械工程学报, 1991, 27(4):60-65. XIONG Youlun. The form closure and accessibility of robot multifinger's grasping and adaptable fixturing[J]. Chinese Journal of Mechanical Engineering, 1991, 27(4):60-65.
[36] 熊有伦. 点接触约束理论与机器人抓取的定性分析[J]. 中国科学:数学, 1994, 24(8):874-883. XIONG Youlun. Theory of point contact restraint and qualitative analysisof robot grasping[J]. Scientia Sinica:Mathematica, 1994, 24(8):874-883.
[37] CASTILLO E, JUBETE F, PRUNEDA R E, et al. Obtaining simultaneous solutions of linear subsystems of inequalities and duals[J]. Linear Algebra and its Applications, 2002, 346:131-154.

基于线性不等式方程组解的存在性及其通解的工件可达/可离性分析算法

Analysis Algorithm of Workpiece Attachment/Detachment Based on Solution Existence and General Solution of Inequalities

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