Calculation for spring constants of folded serpentine micro-cantilevers

LIU Shuang-jie; HAO Yong-ping

doi:10.3788/OPE.20122010.0388

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Calculation for spring constants of folded serpentine micro-cantilevers

Article | 更新时间：2020-08-12

- Calculation for spring constants of folded serpentine micro-cantilevers
- Optics and Precision Engineering Vol. 21, Issue 2, Pages: 388-393(2013)
- 作者机构：
  
  长春理工大学机电工程学院2. 沈阳理工大学装备工程学院
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20122010.0388
  CLC： TH122;TH703
- Received：29 May 2012，
  
  Revised：04 July 2012，
  
  Published Online：23 February 2013，
  
  Published：15 February 2013
- 稿件说明：
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刘双杰郝永平. S型折叠式微悬臂梁刚度计算[J]. 光学精密工程, 2013,21(2): 388-393

LIU Shuang-jie HAO Yong-ping. Calculation for spring constants of folded serpentine micro-cantilevers[J]. Editorial Office of Optics and Precision Engineering, 2013,21(2): 388-393
刘双杰郝永平. S型折叠式微悬臂梁刚度计算[J]. 光学精密工程, 2013,21(2): 388-393 DOI： 10.3788/OPE.20122010.0388.

LIU Shuang-jie HAO Yong-ping. Calculation for spring constants of folded serpentine micro-cantilevers[J]. Editorial Office of Optics and Precision Engineering, 2013,21(2): 388-393 DOI： 10.3788/OPE.20122010.0388.

摘要

针对目前没有成熟的设计计算S型折叠式悬臂梁刚度公式的问题，本文利用能量法和胡克定律推导了S型折叠悬臂梁x向、y向和z向的刚度计算公式。推导过程中发现对于复杂的微悬臂梁结构，其转角处的弯矩对最终结果影响较大，不可忽略。在ANSYS中对S型折叠悬臂梁建模，应用有限元法计算了S型悬臂梁的刚度，并和理论公式进行了对比。与有限元法对比显示，公式计算值的相对误差分别为0.67%、1.09%和2.95%，均小于3%。应用图像测位移法对S型悬臂梁进行了x、y向的拉伸实验，实验显示得到的实验值和理论值吻合，表明本文推导的 S型悬臂梁的刚度计算公式合理，能够为该类型悬臂梁的设计和计算提供理论依据。

Abstract

For lack of calculating formulas to design folded serpentine micro-cantilevers

this paper deduces calculating formulas to compute the deflection of a folded serpentine micro-cantilever and its spring constants in x

y and z directions combining the Hooke's law and the energy method. In deduction

it is found that the bending moment at the out corner will effect on the final results of the complex micro-cantilever seriously

so it can not be ignore in calculation. The spring constant of the folded serpentine micro-cantilever is calculated by finite element analysis using ANSYS software to validate the theoretic calculation. Compared with the finite element simulation

the relative errors of the folded serpentine micro-cantilever is 0.67%

1.09% and 2.95% in the x

y and z directions respectively

and the values are all less than 3%. An image measurement system is established to measure the distortion of the cantilever. Experimental results indicate that the theoretic calculation values coincide with the measured values well. The formulas deduced for the folded serpentine micro-cantilever are logical

and the formula deduction can offer the gists for the computation and design of the folded serpentine micro-cantilevers.

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references

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