直圆柔性球铰柔度矩阵的解析计算

姚建涛; 李立建; 杨维; 赵永生

doi:10.3788/OPE.20142207.1857

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直圆柔性球铰柔度矩阵的解析计算

微纳技术与精密机械 | 更新时间：2020-08-13

- 直圆柔性球铰柔度矩阵的解析计算
- Analytical calculation of compliance matrix for right-circular flexure spherical hinge
- 光学精密工程 2014年22卷第7期页码：1857-1863
- 作者机构：
  
  1. 燕山大学河北省并联机器人与机电系统实验室,河北秦皇岛,066004
  2. 燕山大学先进锻压成形技术与科学教育部重点实验室,河北秦皇岛,066004
- 作者简介：
- 基金信息：
  
  国家973重点基础研究发展计划资助项目（No.2013CB733000）();国家自然科学基金资助项目（No.51305383）();教育部高等学校博士学科点专项科研基
- DOI：10.3788/OPE.20142207.1857
  中图分类号： TH132;TH165
- 收稿日期：2014-01-20，
  
  修回日期：2014-02-27，
  
  纸质出版日期：2014-07-25
- 稿件说明：
移动端阅览
姚建涛, 李立建, 杨维等. 直圆柔性球铰柔度矩阵的解析计算[J]. 光学精密工程, 2014,22(7): 1857-1863

YAO Jian-tao, LI Li-jian, YANG Wei etc. Analytical calculation of compliance matrix for right-circular flexure spherical hinge[J]. Editorial Office of Optics and Precision Engineering, 2014,22(7): 1857-1863
姚建涛, 李立建, 杨维等. 直圆柔性球铰柔度矩阵的解析计算[J]. 光学精密工程, 2014,22(7): 1857-1863 DOI： 10.3788/OPE.20142207.1857.

YAO Jian-tao, LI Li-jian, YANG Wei etc. Analytical calculation of compliance matrix for right-circular flexure spherical hinge[J]. Editorial Office of Optics and Precision Engineering, 2014,22(7): 1857-1863 DOI： 10.3788/OPE.20142207.1857.

摘要

基于线弹性和小变形假设理论，通过引入比例系数（直圆柔性球铰槽口间距与切割半径倍数之比）并利用其结构对称的特点，推导得到了形式较为简洁的直圆柔性球铰柔度矩阵各子元素的解析柔度计算公式。利用有限元仿真软件验证了所推公式的正确性，并绘制了相应的误差曲线。结果表明：当比例系数小于0.2时，直圆柔性球铰各柔度计算公式的相对误差限均在11%以内；随着比例系数的增加，除沿

向的拉压柔度

误差较小外，其他柔度计算公式的误差均呈增加的趋势，最大误差为30%。实验结果显示理论分析与仿真结果基本趋于一致，验证了直圆柔性球铰各柔度解析式的正确性。本文的研究内容为直圆柔性球铰在实际应用中的结构设计和参数优化奠定了理论基础。

Abstract

On the basis of hypothesis theories of linear elasticity and small deformation

the analytical compliance calculation formula of each sub-element in the compliance matrix of a right-circular flexure spherical hinge was deduced.The formula is succinct in form by introducing the proportional coefficient (The ratio of right-circular flexure spherical hinge groove spacing and double cutting radius) and utilizing the symmetrical feature of the structure.The correctness of the formula was verified by adopting the finite element simulation software

and its error curves were drawn corresponding to the simulated values.The results show that the relative errors of serial compliance calculation formula for the right-circular flexure spherical hinge are within 11% when the proportional coefficient is less than 0.2.With the increase of the proportional coefficient

the errors of the other compliance calculation formulas have a trend of increasing with maximum of 30% except the error of tension and compression compliance

along the direction

.The experimental results show that the theoretical analysis is in agreement with the simulation results

which verifies the correctness of the proposed formula.These results will lay a key theoretical basis for the structural design and parametric optimization of the right-circular flexure spherical hinges in practical applications.

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references

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