留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于传递矩阵法的柔性杠杆放大机构刚度分析

郑洋洋 宫金良 张彦斐

郑洋洋, 宫金良, 张彦斐等 . 基于传递矩阵法的柔性杠杆放大机构刚度分析[J]. 北京航空航天大学学报, 2017, 43(4): 849-856. doi: 10.13700/j.bh.1001-5965.2016.0245
引用本文: 郑洋洋, 宫金良, 张彦斐等 . 基于传递矩阵法的柔性杠杆放大机构刚度分析[J]. 北京航空航天大学学报, 2017, 43(4): 849-856. doi: 10.13700/j.bh.1001-5965.2016.0245
ZHENG Yangyang, GONG Jinliang, ZHANG Yanfeiet al. Stiffness analysis of a flexible lever magnifying mechanism based on transfer matrix method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(4): 849-856. doi: 10.13700/j.bh.1001-5965.2016.0245(in Chinese)
Citation: ZHENG Yangyang, GONG Jinliang, ZHANG Yanfeiet al. Stiffness analysis of a flexible lever magnifying mechanism based on transfer matrix method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(4): 849-856. doi: 10.13700/j.bh.1001-5965.2016.0245(in Chinese)

基于传递矩阵法的柔性杠杆放大机构刚度分析

doi: 10.13700/j.bh.1001-5965.2016.0245
基金项目: 

国家自然科学基金 61303006

山东省优秀中青年科学家科研奖励基金 BS2012ZZ009

山东理工大学青年教师发展支持计划 2013-02

详细信息
    作者简介:

    郑洋洋, 女, 硕士研究生。主要研究方向:并联机器人分析与设计理论研究

    宫金良,男, 博士, 副教授。主要研究方向:并联机器人分析与设计理论研究

    张彦斐, 女, 博士, 副教授。主要研究方向:并联机器人分析与设计理论研究

    通讯作者:

    宫金良, E-mail:84374294@qq.com

  • 中图分类号: TH112.5

Stiffness analysis of a flexible lever magnifying mechanism based on transfer matrix method

Funds: 

National Natural Science Foundation of China 61303006

Foundation for Outstanding Young Scientist in Shandong Province BS2012ZZ009

Young Teachers Development Support Plan of Shandong University of Technology 2013-02

More Information
  • 摘要:

    刚度是影响柔性微动机构动态性能和定位精度的重要指标。将工程中的传递矩阵概念引入到刚度分析中,首先根据结构特点将柔性微动机构模块化并将各子单元视为柔性体,全面考虑其轴向、剪切和弯曲等变形,求解各子单元柔性体的传递矩阵,然后通过传递矩阵将各子单元组合,最后根据力平衡建立柔性微动机构输入力和输出位移之间的关系模型。研究结果表明,传递矩阵法由于考虑了各单元的多维度真实变形,因此保证了结果的高精度。同时分析过程不需要求解刚柔单元变形协调方程,而且避免了微动机构全局坐标系的转换,减少了分析计算量。最后应用该方法建立了一种柔性杠杆放大微动机构的刚度模型,与有限元分析结果的对比误差小于6.4%,有效提高了分析精度,为参数设计提供了重要理论依据。

     

  • 图 1  梁单元结点力与位移

    Figure 1.  Beam element node force and displacement

    图 2  梁单元旋转变换

    Figure 2.  Rotation transform of beam element

    图 3  柔性杠杆放大机构示意图

    Figure 3.  Schematic diagram of flexible lever magnifying mechanism

    图 4  柔性杠杆放大机构单元划分

    Figure 4.  Element partition of flexible lever magnifying mechanism

    图 5  柔性杠杆放大机构参数模型

    Figure 5.  Parameter model of flexible lever magnifying mechanism

    图 6  弹性移动副

    Figure 6.  Flexible prismatic pair

    图 7  柔性梁单元

    Figure 7.  Flexible beam element

    图 8  柔性铰链

    Figure 8.  Flexible hinge

    图 9  子单元2、3、4、5受力分析

    Figure 9.  Force analysis of subunit 2, 3, 4, 5

    图 10  柔性杠杆放大机构ANSYS网格划分

    Figure 10.  ANSYS mesh generation of flexible lever magnifying mechanism

    图 11  有限元法与传递矩阵法关系曲线

    Figure 11.  Relation curves of finite element method and transfer matrix method

    图 12  刚度kl5的关系曲线

    Figure 12.  Relation curve of stiffness k and l5

    表  1  有限元法与传递矩阵法刚度对比

    Table  1.   Comparison of stiffness between finite element method and transfer matrix method

    l5/mm 刚度/(MN·m-1) 误差/%
    有限元法 传递矩阵法
    50.5 10.931 9 11.618 2 6.278 28
    60.5 11.326 9 12.034 7 6.248 46
    70.5 12.008 9 12.768 9 6.329 08
    80.5 12.903 9 13.273 1 6.348 12
    下载: 导出CSV
  • [1] 于靖军, 郝广波, 陈贵敏, 等.柔性机构及其应用研究进展[J].机械工程学报, 2015, 51(13):53-68. http://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201513006.htm

    YU J J, HAO G B, CHEN G M, et al.State-of-art of compliant mechanisms and their applications[J].Journal of Mechanical Engineering, 2015, 51(13):53-68(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201513006.htm
    [2] 宫金良, 裴童, 张彦斐.面向高精度放大比的微动机构设计与实现[J].北京理工大学学报, 2015, 35(7):691-696. http://www.cnki.com.cn/Article/CJFDTOTAL-BJLG201507007.htm

    GONG J L, PEI T, ZHANG Y F.Parameter design method of micro-motion mechanism targeting for precise displacement amplification ratio[J].Transactions of Beijing Institute of Technology, 2015, 35(7):691-696(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-BJLG201507007.htm
    [3] 赵荣丽, 陈新, 李克天.双柔性平行六连杆微动平台结构的设计及测试[J].光学精密工程, 2015, 23(10):2860-2869. http://www.cnki.com.cn/Article/CJFDTOTAL-GXJM201510017.htm

    ZHAO R L, CHEN X, LI K T.Design and experiments of micro motion platform based on a pair of flexible parallel six-bar linkages[J].Optics and Precision Engineering, 2015, 23(10):2860-2869(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-GXJM201510017.htm
    [4] HAO G B, KONG X W.A novel large-range XY compliant parallel manipulator with enhanced out-of-plane stiffness[J].Journal of Mechanical Design, 2012, 134(6):061009. doi: 10.1115/1.4006653
    [5] SARAJILIC E, YAMAHATA C, CORDERO M, et al.Three-phase electrostatic rotary stepper micromotor with a flexural pivot bearing[J].Journal of Microelectromechanical System, 2012, 19(2):338-349. https://www.researchgate.net/publication/224116279_Three-Phase_Electrostatic_Rotary_Stepper_Micromotor_With_a_Flexural_Pivot_Bearing
    [6] 陈兴林, 刘川, 刘杨, 等.精密运动平台宏微控制系统的设计[J].中南大学学报 (自然科学版), 2013, 44(6):2318-2323. http://www.cnki.com.cn/Article/CJFDTOTAL-ZDHJ201506002.htm

    CHEN X L, LIU C, LIU Y, et al.Dual-stage actuator control system design for precision motion platform[J]. Journal of Central South University (Science and Technology), 2013, 44(6):2318-2323(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-ZDHJ201506002.htm
    [7] 胡俊峰, 徐贵阳, 郝亚州.一种新型空间微操作平台的设计和性能[J].机械设计与研究, 2014, 30(1):42-46. http://www.cnki.com.cn/Article/CJFDTOTAL-JSYY201401017.htm

    HU J F, XU G Y, HAO Y Z.Design and characteristics of a novel spatial micro-manipulation stage[J].Machine Design and Research, 2014, 30(1):42-46(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-JSYY201401017.htm
    [8] YU J J, HU Y D, BI S S, et al.Kinematics feature analysis of a 3 DOF in-parallel compliant mechanism for micro manipulation[J].Chinese Journal of Mechanical Engineering, 2004, 17(1):127-131. doi: 10.3901/CJME.2004.01.127
    [9] YU Y Q, FENG Z L, XU Q P.A pseudo-rigid-body 2R model of flexural beam in compliant mechanisms[J].Mechanism and Machine Theory, 2012, 55(9):19-33. http://www.sciencedirect.com/science/article/pii/S0094114X12000948
    [10] 邱丽芳, 霍明磊, 李威.六杆柔顺机构的伪刚体模型[J].北京科技大学学报, 2013, 35(5):682-686. http://www.cnki.com.cn/Article/CJFDTOTAL-BJKD201305020.htm

    QIU L F, HUO M L, LI W.Pseudo-rigid-body model of a six-bar full-compliant mechanism[J].Journal of University of Science and Technology Beijing, 2013, 35(5):682-686(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-BJKD201305020.htm
    [11] 李茜, 余跃庆, 常星.基于2R伪刚体模型的柔顺机构动力学建模及特性分析[J].机械工程学报, 2012, 48(13):40-48. http://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201213008.htm

    LI Q, YU Y Q, CHANG X.Dynamic modeling and analysis of compliant mechanisms based on 2R pseudo-rigid-body model[J].Journal of Mechanical Engineering, 2012, 48(13):40-48(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201213008.htm
    [12] 于靖军, 毕树生, 宗光华.空间全柔性机构位置分析的刚度矩阵法[J].北京航空航天大学学报, 2002, 28(3):323-326. http://bhxb.buaa.edu.cn/CN/abstract/abstract10852.shtml

    YU J J, BI S S, ZONG G H.Stiffness matrix method for displacement analysis of fully spatial compliant mechanisms[J].Journal of Beijing University of Aeronautics and Astronautics, 2002, 28(3):323-326(in Chinese). http://bhxb.buaa.edu.cn/CN/abstract/abstract10852.shtml
    [13] 艾青林, 黄伟锋, 张洪涛, 等.并联机器人刚度与静力学研究现状与进展[J].力学进展, 2012, 42(5):583-592. doi: 10.6052/1000-0992-11-073

    AI Q L, HUANG W F, ZHANG H T.Review of stiffness and statics analysis of parallel robot[J]. Advances in Mechanics, 2012, 42(5):583-592(in Chinese). doi: 10.6052/1000-0992-11-073
    [14] HOWELL L L, MIDHA A.A method for the design of compliant mechanisms with small-length flexural pivots[J].Transactions of the ASME, Journal of Mechanical Design, 1994, 116(1):280-290. doi: 10.1115/1.2919359
    [15] 李青宁.变截面杆元传递矩阵法[J].西安建筑科技大学学报, 2001, 33(1):18-23. http://www.cnki.com.cn/Article/CJFDTOTAL-XAJZ200101004.htm

    LI Q N.The transfer matrix method of bar elements with variable cross-section[J].Journal of Xi'an University of Architecture & Technology, 2001, 33(1):18-23(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-XAJZ200101004.htm
    [16] 杨春辉.平行板型柔性移动副的刚度计算及分析[J].现代制造工程, 2013(12):30-33. doi: 10.3969/j.issn.1671-3133.2013.12.008

    YANG C H.The stiffness design calculation and analysis of parallel plate flexible prismatic pair[J].Modern Manufacturing Engineering, 2013(12):30-33(in Chinese). doi: 10.3969/j.issn.1671-3133.2013.12.008
    [17] 吴鹰飞, 周兆英.柔性铰链的设计计算[J].工程力学, 2002, 19(6):136-140. http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX200206026.htm

    WU Y F, ZHOU Z Y.Design of flexure hinges[J]. Engineering Mechanics, 2002, 19(6):136-140(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX200206026.htm
  • 加载中
图(12) / 表(1)
计量
  • 文章访问数:  828
  • HTML全文浏览量:  111
  • PDF下载量:  753
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-03-29
  • 录用日期:  2016-06-03
  • 网络出版日期:  2017-04-20

目录

    /

    返回文章
    返回
    常见问答