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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

林苗, 孟刚, 居勇健, 等 . 大行程解耦三平动微定位平台的设计与优化[J]. 北京航空航天大学学报, 2022, 48(7): 1252-1262. doi: 10.13700/j.bh.1001-5965.2021.0007
引用本文: 林苗, 孟刚, 居勇健, 等 . 大行程解耦三平动微定位平台的设计与优化[J]. 北京航空航天大学学报, 2022, 48(7): 1252-1262. doi: 10.13700/j.bh.1001-5965.2021.0007
LIN Miao, MENG Gang, JU Yongjian, et al. Design and optimization of large-stroke decoupled three-translational micro-positioning platform[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(7): 1252-1262. doi: 10.13700/j.bh.1001-5965.2021.0007(in Chinese)
Citation: LIN Miao, MENG Gang, JU Yongjian, et al. Design and optimization of large-stroke decoupled three-translational micro-positioning platform[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(7): 1252-1262. doi: 10.13700/j.bh.1001-5965.2021.0007(in Chinese)

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
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

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

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
  • 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,xz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。

     

  • 图 1  2T3R型柔性运动副

    Figure 1.  2T3R type compliant motion pair

    图 2  2T3R型运动副自由度原理

    Figure 2.  Freedom principle of 2T3R type motion pair

    图 3  2T3R型运动副运动原理

    Figure 3.  Motion principle of 2T3R type compliant pair

    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

    图 5  4-PPPRR&PPPR型微定位平台

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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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
    lw 31.62
    tw 1.00
    下载: 导出CSV

    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 δxlost/μm δzlost/μm fz/Hz fx-fz/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
    下载: 导出CSV

    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
    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
    下载: 导出CSV

    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/%
    理论值 仿真值
    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
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-01-07
  • 录用日期:  2021-02-10
  • 刊出日期:  2021-03-11

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