基于传递矩阵法的柔性杠杆放大机构刚度分析

郑洋洋; 宫金良; 张彦斐

doi:10.13700/j.bh.1001-5965.2016.0245

基于传递矩阵法的柔性杠杆放大机构刚度分析

doi: 10.13700/j.bh.1001-5965.2016.0245

山东理工大学机械工程学院, 淄博 255049

基金项目:

国家自然科学基金 61303006

山东省优秀中青年科学家科研奖励基金 BS2012ZZ009

山东理工大学青年教师发展支持计划 2013-02

详细信息

作者简介:
郑洋洋, 女, 硕士研究生。主要研究方向:并联机器人分析与设计理论研究

宫金良，男, 博士, 副教授。主要研究方向:并联机器人分析与设计理论研究

张彦斐, 女, 博士, 副教授。主要研究方向:并联机器人分析与设计理论研究

通讯作者:
宫金良, E-mail:84374294@qq.com

中图分类号: TH112.5
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出版历程
- 收稿日期: 2016-03-29
- 录用日期: 2016-06-03
- 网络出版日期: 2017-04-20

Stiffness analysis of a flexible lever magnifying mechanism based on transfer matrix method

School of Mechanical Engineering, Shandong University of Technology, Zibo 255049, China

Funds:

National Natural Science Foundation of China 61303006

Foundation for Outstanding Young Scientist in Shandong Province BS2012ZZ009

Young Teachers Development Support Plan of Shandong University of Technology 2013-02

More Information

Corresponding author: GONG Jinliang, E-mail: 84374294@qq.com

摘要

摘要:
刚度是影响柔性微动机构动态性能和定位精度的重要指标。将工程中的传递矩阵概念引入到刚度分析中，首先根据结构特点将柔性微动机构模块化并将各子单元视为柔性体，全面考虑其轴向、剪切和弯曲等变形，求解各子单元柔性体的传递矩阵，然后通过传递矩阵将各子单元组合，最后根据力平衡建立柔性微动机构输入力和输出位移之间的关系模型。研究结果表明，传递矩阵法由于考虑了各单元的多维度真实变形，因此保证了结果的高精度。同时分析过程不需要求解刚柔单元变形协调方程，而且避免了微动机构全局坐标系的转换，减少了分析计算量。最后应用该方法建立了一种柔性杠杆放大微动机构的刚度模型，与有限元分析结果的对比误差小于6.4%，有效提高了分析精度，为参数设计提供了重要理论依据。
- 柔性微动机构 /
- 传递矩阵 /
- 柔性杠杆放大机构 /
- 刚度 /
- 有限元
Abstract:
Stiffness is an important performance index for the dynamic performance and positioning precision of compliant micromanipulator. Concept of transfer matrix in engineering was applied to the stiffness analysis here. First, according to its structure characteristics, the compliant micromanipulator was modularized and each unit was treated as flexible body. Taking axial, shear and bending deformation into consideration, we solved transfer matrix of the subunit. Then each unit was assembled through the transfer matrix. Finally, relational model between input force and output displacement of compliant micromanipulator was established according to the force balance. The research result indicates that because multi-dimensional real deformation of each unit was taken into consideration, high-precision result was guaranteed. At the same time, the deformation compatibility equations between flexible and rigid units did not need to be solved during the analysis, and conversion of compliant micromanipulator global coordinate system was avoided. The analysis and computation time was also reduced. A kind of flexible lever magnifying mechanism stiffness model was established with this method. The error is less than 6.4% compared with the result of finite element analysis. The accuracy of analysis is improved effectively, and important theoretical basis is provided for parameter design.
- compliant micromanipulator /
- transfer matrix /
- flexible lever magnifying mechanism /
- stiffness /
- finite element

HTML全文

图 1 梁单元结点力与位移

Figure 1. Beam element node force and displacement

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图 2 梁单元旋转变换

Figure 2. Rotation transform of beam element

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图 3 柔性杠杆放大机构示意图

Figure 3. Schematic diagram of flexible lever magnifying mechanism

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图 4 柔性杠杆放大机构单元划分

Figure 4. Element partition of flexible lever magnifying mechanism

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图 5 柔性杠杆放大机构参数模型

Figure 5. Parameter model of flexible lever magnifying mechanism

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图 6 弹性移动副

Figure 6. Flexible prismatic pair

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图 7 柔性梁单元

Figure 7. Flexible beam element

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图 8 柔性铰链

Figure 8. Flexible hinge

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图 9 子单元2、3、4、5受力分析

Figure 9. Force analysis of subunit 2, 3, 4, 5

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图 10 柔性杠杆放大机构ANSYS网格划分

Figure 10. ANSYS mesh generation of flexible lever magnifying mechanism

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图 11 有限元法与传递矩阵法关系曲线

Figure 11. Relation curves of finite element method and transfer matrix method

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图 12 刚度k与l₅的关系曲线

Figure 12. Relation curve of stiffness k and l₅

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表 1 有限元法与传递矩阵法刚度对比

Table 1. Comparison of stiffness between finite element method and transfer matrix method

l₅/mm	刚度/(MN·m^-1)		误差/%
l₅/mm	有限元法	传递矩阵法	误差/%
50.5	10.931 9	11.618 2	6.278 28
60.5	11.326 9	12.034 7	6.248 46
70.5	12.008 9	12.768 9	6.329 08
80.5	12.903 9	13.273 1	6.348 12

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