3-PPP型柔性并联微定位平台的设计与分析

王保兴; 孟刚; 林苗; 李巍; 曹毅

doi:10.13700/j.bh.1001-5965.2019.0286

3-PPP型柔性并联微定位平台的设计与分析

doi: 10.13700/j.bh.1001-5965.2019.0286

王保兴¹,
孟刚¹,
林苗¹,
李巍²,
曹毅^{1, 3, ,}

1.
江南大学机械工程学院, 无锡 21412
2.
苏州工业职业技术学院, 苏州 215104
3.
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”计划 ZBZZ-012

高等学校学科创新引智计划 B18027

江苏省研究生创新计划 SJCX18-0630

江苏省研究生创新计划 KYCX18-1846

详细信息

作者简介:
王保兴男, 硕士研究生。主要研究方向:柔性机构学

孟刚男, 硕士研究生。主要研究方向:柔性机构学

林苗男, 硕士研究生。主要研究方向:柔性机构学

李巍男, 博士。主要研究方向:软体机器人

曹毅男, 博士, 教授。主要研究方向:并联机器人、混联机器人、柔性机器人、软体机器人

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

中图分类号: V414.5;TH122
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- 文章访问数: 861
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- 被引次数: 0
出版历程
- 收稿日期: 2019-06-10
- 录用日期: 2019-08-30
- 网络出版日期: 2020-04-20

Design and analysis of a 3-PPP compliant parallel micro-positioning stage

WANG Baoxing¹,
MENG Gang¹,
LIN Miao¹,
LI Wei²,
CAO Yi^{1, 3
, ,}

1.
School of Mechanical Engineering, Jiangnan University, Wuxi 21412
2.
Suzhou Vocational Institute of Industrial Technology, Suzhou 215104, China
3.
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 and Practice Innovation Program of Jiangsu Provence SJCX18-0630

Postgraduate Research and Practice Innovation Program of Jiangsu Provence KYCX18-1846

More Information

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

摘要

摘要:
为解决现有空间平动柔性并联微定位平台（CPMS）结构布局不紧凑，且多轴驱动时各运动副的寄生运动相互累加，导致平台耦合误差增大的问题。首先，设计了一种基于柔性薄板的分布柔度式3-PPP型柔性并联微定位平台。其次，通过结构优化减小了平台的体积，并消除了支链中移动副寄生运动的累加现象。然后，基于柔度矩阵法建立了平台的输入刚度理论模型，并采用有限元仿真验证了理论模型的正确性；同时计算了平台的固有频率，并探究了其与柔性薄板尺寸参数之间的关系。最后，将结构优化前后的平台通过有限元仿真进行了对比分析。结果表明：结构优化后平台的体积减小了67%，且平台在单轴和多轴驱动时均具有更优的运动解耦特性和输入输出一致性。
- 柔性并联微定位平台(CPMS) /
- 柔度矩阵 /
- 耦合误差 /
- 固有频率 /
- 有限元仿真
Abstract:
The structure layouts of the existing spatial translational compliant parallel micro-positioning stages are not compact, and the parasitic motion of each kinematic joint accumulates during multi-axis actuation, which leads to the augment of cross-axis coupling error. In order to solve these problems, first, a distributed-compliance 3-PPP spatial translational compliant parallel micro-positioning stage (CPMS) based on compliant sheet was designed. Secondly, the stage volume was reduced, and the parasitic motion accumulation phenomenon of kinematic joints in each limb was eliminated by the way of structure optimization. Then, the theoretical model of input stiffness was deduced through compliance matrix method. The validity of the theoretical model was proved by finite element simulation. Besides, the natural frequency of the CPMS was calculated, and the relationship between natural frequency of the CPMS and size parameters of compliant sheet was explored. Finally, comparative analysis of the CPMS before and after structure optimization was conducted by finite element simulation. The results show that the volume of the CPMS is reduced by 67% after structure optimization, and the CPMS has better kinematic decoupling characteristic and input output consistency in both single-axis and multi-axis actuation.
- compliant parallel micro-positioning stage (CPMS) /
- compliance matrix /
- coupling error /
- natural frequency /
- finite element simulation

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图 1 3-PPP型柔性并联微定位平台的初始结构

Figure 1. Original structure of a 3-PPP compliant parallel micro-positioning stage

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图 2 支链3中被动副的变形示意图

Figure 2. Schematic diagram of deformation of passive joints in limb 3

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图 3 反向串联方法示意图

Figure 3. Schematic diagram of inversion series method

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图 4 结构优化后的柔性支链

Figure 4. One compliant limb after structure optimization

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图 5 结构优化后的微定位平台

Figure 5. Micro-positioning stage after structure optimization

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图 6 一端固定的等截面梁

Figure 6. A constant section beam with one end fixed

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图 7 z轴方向的柔性支链

Figure 7. Compliant limb in z-axis direction

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图 8 驱动力为50 N时平台的仿真结果

Figure 8. Simulation result of stage with 50 N actuating force

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图 9 驱动力与参考点位移之间的关系

Figure 9. Relationship between actuating force and reference point displacement

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图 10 平台的1~6阶模态振型

Figure 10. 1-6 order mode shapes of stage

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图 11 平台的固有频率与柔性薄板尺寸参数之间的关系

Figure 11. Relationship between natural frequency of stage and compliant sheet size parameters

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图 12 不同输入条件下平台的仿真分析

Figure 12. Simulation analysis of stage under different input conditions

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图 13 单轴驱动条件下的仿真结果

Figure 13. Simulation results with single-axis actuation

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图 14 两轴驱动时平台在z轴方向的耦合位移

Figure 14. Coupling displacement of stage in z-axis direction with two-axis actuation

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图 15 三轴驱动时平台的丢失运动

Figure 15. Lost motion of stage with three-axis actuation

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表 1 平台的尺寸参数

Table 1. Dimension parameters of stage

参数	数值/mm
t	0.5
w	25
l	40
H	59
u1	45.5
u2	28.5
s	44

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表 2 参考点位移的矩阵法计算值、仿真值及相对误差

Table 2. Matrix method calculation values, simulation values and relative error of reference point displacement

驱动力/N	参考点位移/μm		相对误差/%
驱动力/N	理论计算值	仿真值	相对误差/%
10	70.74	73.15	3.41
20	141.47	143.36	1.33
30	212.21	208.78	1.62
40	282.94	268.73	5.02
50	353.68	323.36	8.57

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表 3 参考点位移非线性法计算值、仿真值及相对误差

Table 3. Nonlinear method calculation values, simulation values and relative error of reference point displacement

驱动力/N	参考点位移/μm		相对误差/%
驱动力/N	理论计算值	仿真值	相对误差/%
10	70.1	73.15	4.35
20	136.9	143.36	4.72
30	198.3	208.78	5.28
40	253.8	268.73	5.88
50	303.7	323.36	6.47

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表 4 平台有限元分析的固有频率

Table 4. Natural frequency of stage obtained by finite element analysis

阶数	1阶	2阶	3阶	4阶	5阶	6阶
频率/Hz	94.49	94.49	94.49	694.13	700	700.13

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表 5 单轴驱动时参考点的耦合位移与丢失运动

Table 5. Coupling displacement and lost motion of reference point with single-axis actuation μm

平台结构	y轴方向的最大耦合位移	z轴方向的最大耦合位移	x轴方向的最大丢失运动
初始结构	-1.08	-1.09	0.45
优化后的结构	-1.04	0.85	0.23

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