大行程解耦三平动微定位平台的设计与优化

林苗; 孟刚; 居勇健; 徐伟胜; 曹毅

doi:10.13700/j.bh.1001-5965.2021.0007

大行程解耦三平动微定位平台的设计与优化

doi: 10.13700/j.bh.1001-5965.2021.0007

林苗^{1, 2},
孟刚^{1, 2},
居勇健^{1, 2},
徐伟胜^{1, 2},
曹毅^{1, 2, ,}

1.
江南大学机械工程学院, 无锡 214122
2.
江苏省食品先进制造装备技术重点实验室, 无锡 214122

基金项目:

江苏省"六大人才高峰"资助项目 ZBZZ-012

高等学校学科创新引智计划 B18027

江苏省研究生科研与实践创新计划 JSCX20_0760

江南大学研究生科研与实践创新计划 JNSJ19_005

详细信息

通讯作者:
曹毅, E-mail: caoyi@jiangnan.edu.cn

中图分类号: V414.5;TH122
计量
- 文章访问数: 433
- HTML全文浏览量: 145
- PDF下载量: 37
- 被引次数: 0
出版历程
- 收稿日期: 2021-01-07
- 录用日期: 2021-02-10
- 网络出版日期: 2021-03-11
- 整期出版日期: 2022-07-20

Design and optimization of large-stroke decoupled three-translational micro-positioning platform

LIN Miao^{1, 2},
MENG Gang^{1, 2},
JU Yongjian^{1, 2},
XU Weisheng^{1, 2},
CAO Yi^{1, 2
, ,}

1.
School of Mechanical Engineering, Jiangnan University, Wuxi 214122, China
2.
Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology, Wuxi 214122, China

Funds:

The Six Talent Peaks Project in Jiangsu Province ZBZZ-012

111 Project B18027

Postgraduate Research & Practice Innovation Program of Jiangsu Province, China JSCX20_0760

Postgraduate Research & Practice Innovation Program of Jiangnan University, China JNSJ19_005

More Information

Corresponding author: CAO Yi, E-mail: caoyi@jiangnan.edu.cn

摘要

摘要:
为设计具有大行程与良好解耦特性的三平动微定位平台，提出了一种新型2T3R型运动副。基于2T3R型运动副，设计了三平动微定位平台的结构；采用非线性模型法建立了平台力-位移关系与丢失运动的理论模型，并采用拉格朗日方程建立了平台固有频率的理论模型；采用目标规划法对三平动微定位平台进行了参数优化；通过有限元仿真验证了理论模型的正确性。理论计算与仿真研究结果表明：平台一阶固有频率为51.27 Hz，在1 mm运动行程内，x、z轴方向的丢失运动分别小于0.67%、0.20%，输入与输出完全解耦。研究结果证明了运动副、平台结构设计的有效性及优化模型的可行性。
- 柔顺机构 /
- 结构设计 /
- 微定位平台 /
- 参数优化 /
- 柔性运动副
Abstract:
To design large-stroke three-translational micro-positioning platforms with excellent decoupling characteristics, a new 2T3R type motion pair was proposed. The structure of three-translational micro-positioning platform was designed based on the 2T3R type motion pair. The theoretical models of force-displacement relationship and lost motion were established by nonlinear model method, the theoretical models of platform natural frequency were established by Lagrange equation. The goal programming method was used to optimize parameters of the micro-positioning platform. The correctness of the above theoretical model was verified by finite element simulation. According to the theoretical calculation and simulation results, the first-order natural frequency of the platform is 51.27 Hz. the lost motions in x and z directions are less than 0.67% and 0.20% in 1 mm motion stroke, and the input and output motions are completely decoupled. Results show that the structure design of motion pair and platform is effective, and the optimization model is feasible.
- compliant mechanism /
- structural design /
- micro-positioning platform /
- parameter optimization /
- compliant motion pair

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图 1 2T3R型柔性运动副

Figure 1. 2T3R type compliant motion pair

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图 2 2T3R型运动副自由度原理

Figure 2. Freedom principle of 2T3R type motion pair

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图 3 2T3R型运动副运动原理

Figure 3. Motion principle of 2T3R type compliant pair

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图 4 含有3个移动自由度的柔性支链

Figure 4. Compliant limbs with 3 DOF of translation

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图 5 4-PPPRR&PPPR型微定位平台

Figure 5. 4-PPPRR&PPPR type micro-positioning platform

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图 6 微定位平台沿x轴方向驱动示意图

Figure 6. Schematic diagram of micro-positioning platform driving along x axis direction

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图 7 柔性薄板a₁的力-位移关系模型

Figure 7. Force-displacement relationship model of flexible sheet a₁

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图 8 微定位平台沿z轴方向驱动示意图

Figure 8. Schematic diagram of micro-positioning platform driving along z axis direction

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图 9 柔性薄板b₁的力-位移关系模型

Figure 9. Force-displacement relationship model of flexible sheet b₁

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图 10 微定位平台多轴联动示意图

Figure 10. Schematic diagram of multi-axis motion for micro-positioning platform

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图 11 微定位平台等效输入刚度示意图

Figure 11. Schematic diagram of equivalent input stiffness for micro-positioning platform

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图 12 微定位平台x轴方向静态性能有限元仿真

Figure 12. Finite element simulation of static performance for micro-positioning platform in x axis direction

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图 13 微定位平台x轴方向静态性能验证

Figure 13. Static performance verification for micro-positioning platform in x axis direction

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图 14 微定位平台z轴方向静态性能有限元仿真

Figure 14. Finite element simulation of static performance for micro-positioning platform in z axis direction

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图 15 微定位平台z轴方向静态性能验证

Figure 15. Static performance verification for micro-positioning platform in z axis direction

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图 16 微定位平台x轴驱动时耦合位移仿真值

Figure 16. Simulation value of coupling displacement for micro-positioning platform driving along x axis direction

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图 17 微定位平台z轴驱动时耦合位移仿真值

Figure 17. Simulation value of coupling displacement for micro-positioning platform driving along z axis direction

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图 18 微定位平台多轴联动应力云图

Figure 18. Stress contour of multi-axis motion for micro-positioning platform

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图 19 微定位平台的前6阶模态振型

Figure 19. The first 6 modal shapes of micro-positioning platform

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表 1 微定位平台的结构参数

Table 1. Structural parameters of micro-positioning platform mm

参数	数值
l₁	55.00
w₁	18.00
t₁	0.51
l₂	49.96
w₂	19.75
t₂	0.83
l_w	31.62
t_w	1.00

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表 2 优化前后微定位平台的静、动态性能参数

Table 2. Static and dynamic performance parameters of micro-positioning platform before and after optimization

优化前/后	δ_xlost/μm	δ_zlost/μm	f_z/Hz	f_x-f_z/Hz
优化前	9.31	2.62	34.59	23.53
优化后	6.97	2.01	49.74	0.63
优化率/%	-25.1	-23.3	43.8	-97.3

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表 3 微定位平台输入耦合位移仿真值

Table 3. Simulation value of input coupling displacement for micro-positioning platforms

驱动方式	耦合位移方向	输入耦合位移/μm
驱动方式	耦合位移方向	图 5(a)平台	文献[17]平台
z轴单轴驱动	沿x轴输入耦合	0.16	11.92
x轴单轴驱动	沿y轴输入耦合	0.41	11.92

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表 4 微定位平台固有频率的理论值、仿真值及相对误差

Table 4. Theoretical value, simulation value and relative error of natural frequency for micro-positioning platform

阶数	固有频率/Hz		相对误差/%
阶数	理论值	仿真值	相对误差/%
1	49.74	51.27	3.1
2	50.37	52.44	4.1
3	50.37	53.11	5.4
4		208.57
5		220.31
6		221.65

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