考虑双重柔性的空间机器人动力学建模与仿真

张青云

doi:10.13433/j.cnki.1003-8728.20230391

考虑双重柔性的空间机器人动力学建模与仿真

doi: 10.13433/j.cnki.1003-8728.20230391

张青云

1.
天津财经大学珠江学院数据工程学院，天津　301811

基金项目: 天津市教委科研计划（2023SK151）

详细信息

作者简介:
张青云，讲师，博士，zqy_pretty@163.com

中图分类号: TP24
计量
- 文章访问数: 41
- HTML全文浏览量: 15
- PDF下载量: 1
- 被引次数: 0
出版历程
- 收稿日期: 2023-10-09
- 刊出日期: 2024-03-25

Dynamic Modeling and Simulation of Spatial Robots Considering Dual Flexibility

ZHANG Qingyun

1.
School of Data Engineering, Tianjin University of Finance and Economics Pearl River College, Tianjin 301811, China

摘要

摘要: 以具有柔性关节和柔性构件的空间机器人作为研究对象，提出了一种双重柔性作用下的空间机器人动力学建模方法。首先，柔性关节简化为具有恒定刚度的线性扭转弹簧；其次，通过有限元法与浮动坐标系法相结合，描述含高阶模态信息的柔性空间构件位移场矢量。然后，将柔性关节和柔性空间构件简化为具有单向弹性约束的两个柔性构件和一个简支梁，再根据边界条件建立两者的约束方程。最后，根据协调矩阵建立含位移变化较小的末端执行器动力学模型。结果表明：新方法考虑了柔性关节和柔性空间构件之间的弹性影响，使得末端执行器运动轨迹在双重柔性变形抵消状态下，绝对变形量减小，轨迹精度提高。其中，z方向的偏差范围为0 ~ 0.31 mm，x方向的偏差范围为0 ~ 2.68 mm，y方向的偏差为0 ~ 3.02 mm。因此，所提出的构建双重柔性空间机器人的动力学方法正确，可为下一步控制策略及振动性能分析提供精确模型。
- 末端执行器 /
- 双重柔性 /
- 空间机器人 /
- 动力学分析
Abstract: A dynamic modeling method for spatial robots with dual flexibility is proposed, taking spatial robots with flexible joints and links as the research object. Firstly, the flexible joint is simplified as a linear torsion spring with constant stiffness; Secondly, the displacement field vector of flexible spatial links containing higher-order modal information is described by combining the finite element method with the floating coordinate system method. Then, the flexible joints and spatial links are simplified as two flexible links with unidirectional elastic constraints and a simply supported beam, and the system constraint equation is established by combining the boundary conditions. Finally, a dynamic model of the end effector with small displacement changes is established based on the coordination matrix. The results indicate that the new method takes into account the elastic influence between the flexible joint and the flexible spatial link, resulting in a decrease in absolute deformation and an improvement trajectory accuracy of the end effector in a dual flexible deformation cancellation state. Among them, the deviation range in the z direction is 0 - 0.31 mm, the deviation range in the x direction is 0 - 2.68 mm, and the deviation in the y direction is 0 - 3.02 mm. Therefore, the proposed dynamic modeling method for dual flexible spatial robots is correct and can provide accurate models for system control and vibration analysis.
- end effector /
- multiple flexibility /
- spatial robots /
- dynamic analysis

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图 1 3-RRRU双重柔性空间机器人

Figure 1. 3-RRRU dual flexible spatial robot

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图 2 柔性空间连杆模型

Figure 2. Flexible spatial link model

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图 3 柔性虎克铰模型

Figure 3. Flexible hooke hinge model

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图 4 双重柔性空间机器人模型

Figure 4. Dual flexible spatial robot model

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图 5 柔性空间连杆坐标系简图

Figure 5. Coordinate system of flexible spatial link

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图 6 双重柔性空间机器人商品化仿真模型

Figure 6. Commercialization simulation model for dual flexible spatial robot

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图 7 末端执行器空间轨迹

Figure 7. End effector spatial trajectory

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图 8 固有频率对比图

Figure 8. Comparison of natural frequencies

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图 9 不同弹性模量下关节接触力

Figure 9. Joint contact force under different elastic moduli

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表 1 双重柔性空间机器人几何参数

Table 1. Geometric parameters of dual flexible spatial robot

参数	质量/kg	长度/m	密度/（kg·m⁻³）	泊松比	弹性模量/Pa
主动杆	2	0.4	7801	0.29	2.07 × 10¹¹
中间杆	0.3	0.1	7801	0.29	2.07 × 10¹¹
柔性连杆	1.5	0.8	2740	0.33	7.17 × 10¹⁰
末端执行器	2.6	0	7801	0.29	2.07 × 10¹¹
柔性虎克铰	0.14	0.04	2740	0.33	7.17 × 10¹⁰

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表 2 运动轨迹偏差

Table 2. Motion trajectory deviation

坐标轴	最大绝对偏差/mm		最大偏差/mm
坐标轴	本文数值模型	商品化仿真模型	最大偏差/mm
x	96.230	93.550	2.680
y	84.100	87.120	3.020
z	0.701	0.390	0.311

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表 3 柔性关节材料对系统固有频率的影响

Table 3. The influence of flexible joint materials on the natural frequency of the system

关节材料	10阶/Hz	11阶/Hz	12阶/Hz
铜	4.2368 × 10⁻⁴	9.3765	20.1237
铝合金	2.0576 × 10⁻⁴	14.9298	23.6968
钢	0.0126	17.4983	42.5228

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