基于径向基函数代理模型的M形杆刚度优化

杨慧; 范硕硕; 王岩; 刘荣强; 肖洪

doi:10.13700/j.bh.1001-5965.2021.0091

基于径向基函数代理模型的M形杆刚度优化

doi: 10.13700/j.bh.1001-5965.2021.0091

杨慧^1, ,,
范硕硕²,
王岩¹,
刘荣强³,
肖洪³

1.
燕山大学机械工程学院, 秦皇岛 066044
2.
安徽大学电气工程与自动化学院, 合肥 230601
3.
哈尔滨工业大学机器人技术与系统国家重点实验室, 哈尔滨 150001

基金项目:

安徽省自然科学基金 2108085QE221

国家自然科学基金 51975001

国家自然科学基金 51835002

国家自然科学基金 52105013

机器人技术与系统国家重点实验室开放基金 SKLRS-2020-KF-16

详细信息

通讯作者:
杨慧, E-mail: huiyang_0431@163.com

中图分类号: V214.2
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- 被引次数: 0
出版历程
- 收稿日期: 2021-02-24
- 录用日期: 2021-06-06
- 网络出版日期: 2021-06-21
- 整期出版日期: 2022-11-20

Stiffness optimization of M-shaped boom based on radial basis function surrogate model

1.
School of Mechanical Engineering, Yanshan University, Qinhuangdao 066044, China
2.
School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China
3.
State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China

Funds:

Anhui Provincial Natural Science Foundation 2108085QE221

National Natural Science Foundation of China 51975001

National Natural Science Foundation of China 51835002

National Natural Science Foundation of China 52105013

Open Fundings of State Key Laboratory of Robotics and System SKLRS-2020-KF-16

More Information

Corresponding author: YANG Hui, E-mail: huiyang_0431@163.com

摘要

摘要:
在航天任务的执行中, 超弹性杆主要用于大型空间可展天线和太阳帆等展开和支撑。为了提高超弹性杆在展开状态下的刚度, 提出了一种新型M形超弹性杆, 并对M形超弹性杆的刚度进行了研究。采用ABAQUS建立M形超弹性杆的弯曲、压缩和扭转的有限元模型, 利用显示动力学法对屈曲过程进行非线性数值模拟。采用全因子法进行实验设计, 利用径向基函数(RBF)建立M形超弹性杆屈曲过程性能参数的代理模型。以弯曲刚度、扭转刚度和压缩刚度为优化目标, 以质量为约束, 选取黏结段长度和内侧带簧片圆心角为自变量建立优化模型。采用粒子群(PSO)算法进行M形超弹性杆参数优化, 得到最优刚度下, 黏结段长度为7.894 5 mm, 圆心角为26°, 并且得到刚度随其变化规律。
- 复合材料 /
- 可展机构 /
- M形杆 /
- 径向基函数 /
- 优化
Abstract:
In the execution of space missions, the hyper-elastic boom is mainly used in the deployment and support of large space deployable antennas and solar sails. In order to improve the supporting effect of the hyper-elastic boom in the state of deployment, the stiffness of the M-shaped hyper-elastic boom (M boom) with different sizes was studied. By using ABAQUS, the M boom's bending, compression, and torsion finite element models were created, and an explicit dynamic method was used to carry out a nonlinear numerical simulation of the M boom's buckling process.The bending stiffness, torsional stiffness and compression stiffness were taken as optimization objectives, the mass as constraint, and the cross-section arc length and radius as independent variables to establish the optimization model. The full factor method was used to design the experiment, the radial basis function (RBF) was used to establish the buckling surrogate model of the M boom, using the particle swarm optimization (PSO) algorithm to perform parameter optimization of the M boom. The ideal values for the length of bonding segment and the central angle were 7.894 5 mm and 26°, and the variation rule of stiffness with the length of bonding segment and the central angle was obtained.
- composite material /
- deployable structure /
- M-shaped boom /
- radial basis function /
- optimization

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图 1 M形杆缠绕几何示意图

Figure 1. Geometric schematic diagram of M boom coiling

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图 2 M形杆各层材料铺设布置图

Figure 2. Material laying layout of each layer of M boom

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图 3 M形杆有限元模型

Figure 3. Finite element model of M boom

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图 4 M形杆绕x轴弯曲的应力云图和力矩曲线

Figure 4. Cloud chart of stress and bending moment curve of M boom around x-axis

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图 5 M形杆绕y轴弯曲的应力云图和力矩曲线

Figure 5. Cloud chart of stress and bending moment curve of M boom around y-axis

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图 6 M形杆绕z轴扭转的应力云图和力矩曲线

Figure 6. Cloud chart of stress and torsion moment curve of M boom around z-axis

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图 7 M形杆沿z轴压缩的应力云图和反作用力曲线

Figure 7. Stress cloud diagram and reaction force curves of M boom compressed along z-axis

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图 8 EI_x(h, θ₂)响应面

Figure 8. Response surface of EI_x(h, θ₂)

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图 9 EI_y(h, θ₂)响应面

Figure 9. Response surface of EI_y(h, θ₂)

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图 10 GJ_z(h, θ₂)响应面

Figure 10. Response surface of GJ_z(h, θ₂)

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图 11 EA_z(h, θ₂)响应面

Figure 11. Response surface of EA_z(h, θ₂)

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表 1 T800材料属性

Table 1. Material properties of T800

材料属性	T800	黏结胶
纵向弹性模量E₁/MPa	150 000
横向弹性模量E₂=E₃/MPa	7 000	60 000
剪切模量G₁₂=G₁₃/MPa	7 000
面内剪切模量G₂₃/MPa	4 500
泊松比υ	0.3	0.3
密度ρ /(kg·m^-3)	2 500	1 600

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表 2 参考点RP₂在不同情况下的边界条件

Table 2. Reference point RP₂ boundary conditions under different conditions

约束	绕x轴弯曲	绕y轴弯曲	绕z轴扭转	沿z轴正向压缩
UX	0	释放约束	释放约束	释放约束
UY	释放约束	0	释放约束	释放约束
UZ	释放约束	释放约束	0	施加位移载荷
RX	施加旋转载荷	0	0	0
RY	0	施加旋转载荷	0	0
RZ	0	0	施加旋转载荷	0

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表 3 样本点

Table 3. Sample points

序号	h/mm	θ₂/(°)	EI_x(h, θ₂)/(N·m²·rad^-1)	EI_y(h, θ₂)/(N·m²·rad^-1)	GJ_z(h, θ₂)/(N·m²·rad^-1)	EA_z(h, θ₂)/(N·mm^-1)
1	5	22	16.525	8.800	0.022	318.836
2	5	23	17.764	10.718	0.026	322.861
3	5	24	19.018	12.579	0.031	314.631
4	5	25	20.672	14.756	0.037	322.566
5	5	26	21.779	17.296	0.044	341.485
6	6	22	20.299	10.467	0.028	342.641
7	6	23	21.683	12.250	0.031	352.375
8	6	24	23.548	13.527	0.036	359.440
9	6	25	24.680	16.322	0.045	354.424
10	6	26	26.529	19.273	0.051	349.309
11	7	22	24.826	11.736	0.030	362.863
12	7	23	26.121	14.097	0.038	336.068
13	7	24	28.263	15.904	0.043	386.556
14	7	25	30.448	18.814	0.049	387.839
15	7	26	31.960	21.919	0.059	417.498
16	8	22	31.014	13.979	0.035	390.809
17	8	23	24.585	16.280	0.039	391.156
18	8	24	25.897	19.031	0.050	389.042
19	8	25	35.451	22.181	0.059	412.499
20	8	26	36.913	25.155	0.068	398.496
21	9	22	34.444	16.144	0.042	418.356
22	9	23	28.561	18.814	0.050	396.581
23	9	24	30.862	21.860	0.057	421.409
24	9	25	39.797	24.364	0.072	404.325
25	9	26	43.121	24.267	0.079	430.254
26	10	22	42.957	18.604	0.051	417.984
27	10	23	42.714	21.545	0.057	426.818
28	10	24	46.798	24.402	0.064	440.339
29	10	25	47.374	28.437	0.081	454.123
30	10	26	51.486	32.035	0.094	470.183

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表 4 径向基函数代理模型核函数中常数c的取值

Table 4. Values of constant c in kernel function of RBFs surrogate model

目标量	c值
EI_x	1
EI_y	0.3
GJ_z	0.3
EA_z	0.3

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表 5 误差测试样本点

Table 5. Sample points of relative errors

序号	h/mm	θ₂/(°)	有限元结果		代理模型结果		相对误差E/%
序号	h/mm	θ₂/(°)	EI_x(h, θ₂)/(N·m²·rad^-1)	EI_y(h, θ₂)/(N·m²·rad^-1)	EI_x(h, θ₂)/(N·m²·rad^-1)	EI_y(h, θ₂)/(N·m²·rad^-1)	EI_x(h, θ₂)	EI_y(h, θ₂)
1	6	26	26.529	19.273	26.120	19.259	-1.542	-0.073
2	7	24	28.263	15.904	27.329	16.169	-3.305	1.666
3	7	26	31.960	21.919	32.612	22.091	2.040	0.785
4	8	22	31.014	13.979	29.105	14.097	-6.155	0.844
5	8	26	36.913	25.155	38.292	25.342	3.736	0.743

序号	h/mm	θ₂/(°)	有限元结果		代理模型结果		相对误差E/%
序号	h/mm	θ₂/(°)	GJ_z(h, θ₂)/(N·m²·rad^-1)	EA_z(h, θ₂)/(N·mm^-1)	GJ_z(h, θ₂)/(N·m²·rad^-1)	EA_z(h, θ₂)/(N·mm^-1)	GJ_z(h, θ₂)	EA_z(h, θ₂)
1	6	26	0.051 4	349.309	0.051 0	367.851	-0.778	5.308
2	7	24	0.043 4	386.556	0.042 9	366.866	-1.152	-5.094
3	7	26	0.059 3	417.498	0.058 4	400.586	-1.518	-4.051
4	8	22	0.034 8	390.809	0.035 2	395.578	1.149	1.220
5	8	26	0.068 2	398.496	0.067 7	420.565	-0.733	5.538

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表 6 目标量和约束量的比例因子和权重

Table 6. Scale factors and weights of objective and constraint quantities

目标量	S_i	W_i
EI_x	1	1.2
EI_y	1	2
GJ_z	1	1 000
EA_z	1	0.1
M₀	1	1.5

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表 7 Pareto设计点

Table 7. Pareto points of design

序号	h/mm	θ₂/(°)	M₀/g	EI_x(h, θ₂)/(N·m²·rad^-1)	EI_y(h, θ₂)/(N·m²·rad^-1)	GJ_z(h, θ₂)/(N·m²·rad^-1)	EA_z(h, θ₂)/(N·mm^-1)
1	7.970 7	25.727 7	24.932 7	37.814 4	24.341 7	0.065 0	415.960 8
2	7.894 5	26	24.911 4	37.794 9	24.994 1	0.066 6	419.362 2

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表 8 最优设计点

Table 8. Optimal point of design

结果	对应刚度	数值
有限元	EI_x(h, θ₂)/(N·m²·rad^-1)	36.286 2
	EI_y(h, θ₂)/(N·m²·rad^-1)	24.828 4
	GJ_z(h, θ₂)/(N·m²·rad^-1)	0.065 1
	EA_z(h, θ₂)/(N·mm^-1)	430.808 6
代理模型	EI_x(h, θ₂)/(N·m²·rad^-1)	37.794 9
	EI_y(h, θ₂)/(N·m²·rad^-1)	24.994 1
	GJ_z(h, θ₂)/(N·m²·rad^-1)	0.066 6
	EA_z(h, θ₂)/(N·mm^-1)	419.362 2
相对误差E/%	EI_x(h, θ₂)	4.16
	EI_y(h, θ₂)	0.67
	GJ_z(h, θ₂)	2.30
	EA_z(h, θ₂)	-2.66

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