机械工程学报 >

2018 , Vol. 54 >Issue 21: 156 - 165

DOI: https://doi.org/10.3901/JME.2018.21.156

数字化设计与制造

多环闭链机构偏差传递分析及几何精度建模

  • 赵强强 ,
  • 洪军 ,
  • 郭俊康 ,
  • 刘志刚
展开
  • 1. 西安交通大学机械工程学院 西安 710049;
    2. 西安交通大学机械制造系统工程国家重点实验室 西安 710054
赵强强,男,1992年出生,博士研究生。主要研究方向为串并联结构精密机电产品几何精度建模和装配工艺规划。E-mail:zhaoqiangqiang@stu.xjtu.edu.cn

收稿日期: 2017-11-14

  修回日期: 2018-04-19

  网络出版日期: 2018-11-05

基金资助

国家自然科学基金重点资助项目（51635010）。

收起

Deviation Propagation Analysis and Accuracy Modeling for Multi-closed-loop Mechanism

  • ZHAO Qiangqiang ,
  • HONG Jun ,
  • GUO Junkang ,
  • LIU Zhigang
Expand
  • 1. School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049;
    2. State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an 710054

Received date: 2017-11-14

  Revised date: 2018-04-19

  Online published: 2018-11-05

Fold

摘要

要实现对多环闭链机构的精度预测和反演设计，建立其几何精度模型至关重要。由于存在闭环耦合、结构复杂等不利因素，多环闭链机构精度建模相比开链机构更加困难。为了解决上述问题，提出一种适应于任意多环闭链机构的几何精度建模方法。首先对多环闭链机构中的误差源进行分析和建模，利用提出的两个新概念——独立环和耦合环来描述机构中存在的所有闭环类型。然后通过首次定义的新算子——低层环算子和新序列——低层环序列来表征多环闭链机构中的环与环邻接关系，并以此获得多环闭链机构误差传递规律。在此基础上，利用多环闭链几何位置方程建立精度计算模型，并基于该精度模型和误差源概率分布函数实现多环闭链误差空间分析。最后以平面SAR天线可展支撑机构作为算例，验证了上述方法和理论的有效性。

关键词： 多环闭链机构; 环类型; 低层环序列; 偏差传递; 精度建模

本文引用格式

赵强强 , 洪军 , 郭俊康 , 刘志刚 . 多环闭链机构偏差传递分析及几何精度建模[J]. 机械工程学报, 2018 , 54(21) : 156 -165 . DOI: 10.3901/JME.2018.21.156

Abstract

Establishing geometric accuracy model is essential to conduct the accuracy prediction and inverse design of multi-closed-loop mechanism. Compared with the open-loop mechanism, accuracy modeling for multi-closed-loop mechanism is much more difficult due to the existence of negative factors like coupling and complex structure. In order to solve the above problems, a novel method of accuracy modeling is developed. First of all, the error sources are analyzed and modeled, and then two new concepts of independent loop and coupled loop are proposed to describe the loop types involved in multi-closed-loop mechanisms. Then, the relationship between loops is illustrated by the new low-layer-loop operator and sequence. Additionally, the deviation propagation principle is obtained according to the relationship. Based on the deviation propagation principle, the geometric accuracy model is built by the positional equation of the multi-closed-loop mechanism and the error space is calculated accordingly by combining the above model with the probability distribution of error sources. Eventually, the method is verified by the extendible support structure of planar SAR antenna.

Key words： multi-closed-loop mechanism; loop type; low-layer-loop sequence; deviation propagation; accuracy modeling

参考文献

[1] CEGLAREK D,JIN J. Introduction:Modeling and analysis for complex production systems. position statement[J]. Flexible Services and Manufacturing Journal,2004,16(1):5-9.
[2] 张武翔,杨毅,罗均,等. 多环闭链可展机构尺寸调整方法[J]. 机械工程学报,2015,51(19):11-20. ZHANG Wuxiang,YANG Yi,LUO Jun,et al. Size adjustment of multi-closed-loop deployable mechanisms[J]. Journal of Mechanical Engineering,2015,51(19):11-20.
[3] AGHABEIGI M,MOVAHHEDY M R. An algorithm for geometrical uncertainty analysis in planar truss structures[J]. Structural & Multidisciplinary Optimization,2014,49(2):225-238.
[4] 何博侠,张志胜,戴敏,等. 机械装配过程的偏差传递建模理论[J]. 机械工程学报,2008,44(12):62-68. HE Boxia,ZHANG Zhisheng,DAI Min,et al. Theory of modeling variation propagation of mechanical assembly processes[J]. Journal of Mechanical Engineering,2008,44(12):62-68.
[5] 刘伟东,宁汝新,刘检华,等. 机械装配偏差源及其偏差传递机理分析[J]. 机械工程学报,2012,48(1):156-168. LIU Weidong,NING Ruxin,LIU Jianhua,et al. Mechanism analysis of deviation sourcing and propagation for mechanical assembly[J]. Journal of Mechanical Engineering,2012,48(1):156-168.
[6] 刘又午,吴洪涛. 多体系统理论在机构运动分析中的应用[J]. 机械工程学报,1993,29(3):104-112. LIU Youwu,WU Hongtao. Multi-body system theory applied to the kinematics analysis of mechanisms[J]. Journal of Mechanical Engineering,1993,29(3):104-112.
[7] HARTENBURG R S,DENAVIT J,FREUDENSTEIN F. Kinematic synthesis of linkages[M]. New York:McGrawHill,1964.
[8] HAFTKA R T. Limits on static shape control for space structures[J]. AIAA Journal,1991,29(11):1945-1950.
[9] FURUYA H. Statistical sensitivity analysis of lattice space structures[J]. Journal of Aerospace Engineering,1993,6(3):236-248.
[10] KHODAYGAN S,MOVAHHEDY M R,FOUMANI M S. Fuzzy-small degrees of freedom representation of linear and angular variations in mechanical assemblies for tolerance analysis and allocation[J]. Mechanism & Machine Theory,2011,46(4):558-573.
[11] 常鹏,李铁民,刘辛军. 基于集合理论的并联机构精度分析方法[J]. 清华大学学报,2007,47(11):1984-1988. CHANG Peng,LI Tiemin,LIU Xinjun. Accuracy analysis of parallel mechanisms based on set theory[J]. Journal of Tsinghua University,2007,47(11):1984-1988.
[12] LI X,DING X,CHIRIKJIAN G S. Analysis of angular-error uncertainty in planar multiple-loop structures with joint clearances[J]. Mechanism & Machine Theory,2015,91:69-85.
[13] YANG Y,LUO J,ZHANG W,et al. Accuracy analysis of a multi-closed-loop deployable mechanism[J]. ARCHIVE Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering,2016,230(4):1989-1996.
[14] YANG Y,XIE S,ZHANG W,et al. Accuracy model,analysis,and adjustment in the context of multi-closed-loop planar deployable mechanisms[J]. Advances in Mechanical Engineering,2016,8(3):1-15.
[15] KUMARASWAMY U,SHUNMUGAM M S,SUJATHA S. A unified framework for tolerance analysis of planar and spatial mechanisms using screw theory[J]. Mechanism & Machine Theory,2013,69(6):168-184.
[16] SCHULLER M. A new screw theory method for the estimation of position accuracy in spatial parallel manipulators with revolute joint clearances[J]. Mechanism & Machine Theory,2011,46(12):1929-1949.
[17] 杨玉龙,关富玲. 可展桁架天线形面精度理论分析[J]. 空间科学学报,2009,29(5):529-533. YANG Yulong,GUAN Fuling. Production intelligent assembly modeling based on ports automatic matching[J]. Chinese Journal of Space Science,2009,29(5):529-533.
[18] GREENE W H. Effects of random member length errors on the accuracy and internal loads of truss antennas[J]. Journal of Spacecraft & Rockets,1985,22(5):554-559.
[19] AVILÉS R,AJURIA G. A finite element approach to the position problems in open-loop variable geometry trusses[J]. Finite Elements in Analysis & Design,2000,34(3-4):233-255.
[20] 武清玺. 结构可靠性分析及随机有限元法[M]. 北京:机械工业出版社,2005. WU Qingxi. Structural reliability analysis and stochastic finite element method[J]. Beijing:China Machine Press,2005.
[21] HEDGEPETH J M. Influence of fabrication tolerances on the surface accuracy of large antenna structures[J]. AIAA Journal,1982,20(5):680-686.
[22] VENANZI S,PARENTI-CASTELLI V. A new technique for clearance influence analysis in spatial mechanisms[J]. Journal of Mechanical Design,2005,127(3):446-455.
[23] 宋月娥,吴林,戴明. 机器人关节间隙误差分析[J]. 机械工程学报,2003,39(4):11-14. SONG Yuee,WU Lin,DAI Ming. Error analysis of robot[J]. Chinese Journal of Mechanical Engineering,2003,39(4):11-14.
[24] ZHU J,TING K L. Uncertainty analysis of planar and spatial robots with joint clearances[J]. Mechanism & Machine Theory,2000,35(9):1239-1256.
[25] PARENTI-CASTELLI V,VENANZI S. Clearance influence analysis on mechanisms[J]. Mechanism & Machine Theory,2005,40(12):1316-1329.
[26] TSAI M J,LAI T H. Accuracy analysis of a multi-loop linkage with joint clearances[J]. Mechanism & Machine Theory,2008,43(9):1141-1157.
[27] 孙中超,喻天翔,崔卫民,等. 铰链间隙对连杆机构运动精度的重要性测度分析[J]. 中国机械工程,2014,25(21):2874-2879. SUN Zhongchao,YU Tianxiang,CUI Weimin,et al. Importance Measure of Revolute Joint Clearance about Motion Accuracy of Linkage Mechanism[J]. China Mechanical Engineering,2014,25(21):2874-2879.
[28] 汪劲松,白杰文,高猛,等. Stewart平台铰链间隙的精度分析[J]. 清华大学学报,2002,42(6):758-761. WANG Jinsong,BAI Jiewen,GAO Meng,et al. Accuracy analysis of joint-clearances in a Stewart platform[J]. Journal of Tsinghua University,2002,42(6):758-761.
[29] LEE S J,GILMORE B J. The determination of the probabilistic properties of velocities and accelerations in kinematic chains with uncertainty[J]. Journal of Mechanical Design,1991,113(1):9-13.
Options
文章导航

/

〈 〉

版权所有 © 《机械工程学报》编辑部

技术支持：北京玛格泰克科技发展有限公司