Response-surface selection optimization of FEA parameter for two-dimensional space turntable

Haosu ZHANG; Zhenyu WANG; Yu CAO; Aihong SHANGGUAN; Youjin XIE; Xi WANG; Shengming SU; Yongfan JIANG

doi:10.37188/OPE.20243223.3446

Journals >Optics and Precision Engineering >Volume 32 >Issue 23 >Page 3446 > Article

Optics and Precision Engineering
Vol. 32, Issue 23, 3446 (2024)

Response-surface selection optimization of FEA parameter for two-dimensional space turntable

Haosu ZHANG¹, Zhenyu WANG^2,*, Yu CAO^1,3, Aihong SHANGGUAN¹..., Youjin XIE^1,3, Xi WANG^1,4, Shengming SU^1,4 and Yongfan JIANG^1,4|Show fewer author(s)

Author Affiliations

¹Xi'an Institute of Optics and Precision Mechanics， Chinese Academy of Sciences， Xi'an709， China

²Innovation Academy for Microsatellites of Chinese Academy of Sciences， Shanghai0103， China

³Key Laboratory of Space Precision Measurement Technology， Chinese Academy of Sciences，Xi'an710119， China

⁴University of Chinese Academy of Sciences， Beijing10009， China

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DOI: 10.37188/OPE.20243223.3446 Cite this Article

Haosu ZHANG, Zhenyu WANG, Yu CAO, Aihong SHANGGUAN, Youjin XIE, Xi WANG, Shengming SU, Yongfan JIANG. Response-surface selection optimization of FEA parameter for two-dimensional space turntable[J]. Optics and Precision Engineering, 2024, 32(23): 3446 Copy Citation Text

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Fig. 1. Schematic diagram of two-dimensional space turntable

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Fig. 2. Explosive view of components of pitching shaft system

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Fig. 3. Distribution of acceleration measuring nodes and strain measuring nodes in mechanical test

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Fig. 4. Cloud diagram of mechanical analysis and corresponding acceleration， stress measuring nodes position and measured frequency response curves of mechanical test of two-dimensional turntable

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Fig. 5. Correction process of response surface method for parameter selection and adjustment of kinematic mechanism

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Fig. 6. Grid model of main parts of two-dimensional turntable

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Fig. 7. Comparison between calculation results of some measuring nodes and mechanical test results

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Fig. 8. Schematic diagram of U-frame area division

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分析次数	因素x₃	因素x₄	因素x₅	因素x₆
1	$k_{3}$	$k_{4}$	0.02	0.034
2	$k_{3}$	$k_{4}$	0.04	0.068
3	1/10 $k_{3}$	1/10 $k_{4}$	0.04	0.068
4	10 $k_{3}$	10 $k_{4}$	0.04	0.068
5	100 $k_{3}$	100 $k_{4}$	0.04	0.068
6	100 $k_{3}$	100 $k_{4}$	0.04	0.068
7	$k_{3}$	$k_{4}$	0.04	0.068
8	$k_{3}$	$k_{4}$	0.04	0.068
9	$k_{3}$	$k_{4}$	0.04	0.068
10	$\infty$	$\infty$	0.04	0.068

Table 1. Adjustment parameters of initial analysis model

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分析序数	一阶	二阶	三阶	四阶	五阶	六阶
1	38.4	56.5	60.1	74.3	81.8	96.9
2	38.4	56.5	60.2	74.3	81.8	96.9
3	33.7	54.4	58.2	68.8	78.8	95.3
4	39.5	57.3	60.6	75.2	82.9	97.4
5	39.6	57.4	60.7	75.3	83.1	97.5
6	38.6	56.6	60.3	74.4	81.8	97.0
7	38.1	50.4	56.0	70.3	80.3	94.1
8	36.7	56.3	59.9	74.2	79.1	92.7
9	36.5	50.0	55.5	69.7	75.9	89.9
10	30.1	48.7	54.2	60.6	75.7	90.8

Table 2. Modal frequency response results of initial analysis

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参数	模态一阶m₁	模态二阶m₂	模态三阶m₃	模态四阶m₄	模态五阶m₅	模态六阶m₆
x₁	○	○	○	×	×	×
x₂	○	○	○	×	×	×
x₃	○	○	○	○	○	○
x₄	○	○	○	○	○	○
x₅	×	×	×	×	×	×
x₆	×	×	×	×	×	×

Table 3. Significance analysis of modal frequency

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参数	A₁	A₂	A₃	S₁	S₂	S₃	S₄	S₁₇
x₁	○	○	○	○	○	○	○	○
x₂	○	○	○	○	○	○	○	○
x₃	○	○	○	○	×	○	×	○
x₄	○	○	○	○	×	○	×	○
x₅	×	×	×	×	×	×	×	×
x₆	○	○	○	○	○	○	○	○

Table 4. Significance analysis of sinusoidal vibration acceleration response and random vibration stress response at characteristic points

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分析序数	因素3 x₃	因素4 x₄	因素5 x₅	因素6 x₆
13	$E_{3}$	$E_{4}$	0.04	0.068
14	1/10 $E_{3}$	1/10 $E_{4}$	0.04	0.068
15	1/100 $E_{3}$	1/100 $E_{4}$	0.04	0.068
16	1/200 $E_{3}$	1/200 $E_{4}$	0.04	0.068
17	1/500 $E_{3}$	1/500 $E_{4}$	0.04	0.068
18	1/500 $E_{3}$	1/500 $E_{4}$	0.08	0.136
19	1/1000 $E_{3}$	1/1000 $E_{4}$	0.04	0.068
20	1/1000 $E_{3}$	1/1000 $E_{4}$	0.08	0.136

Table 5. Parameters after model parameter adjustment

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参数	M₁~M₆	A₁	A₂	A₃	S₁	S₂	S₃	S₄	S₁₇
x₁	○	○	○	○	○	○	○	○	○
x₂	○	○	○	○	○	○	○	○	○
x₃	○	○	○	○	○	○	○	○	○
x₄	○	○	○	○	○	○	○	○	○
x₅	×	×	×	×	×	×	×	×	×
x₆	○	○	○	○	○	○	○	○	○

Table 6. Significance analysis of sinusoidal response， acceleration response and random vibration stress response of characteristic points

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项目	a	b	b	b	c	c	c
M₁	36.4	1.3	-5.2	2.3	1.9	2.7	-6.5
M₂	56.1	-12.4	5.1	7	11.9	-7.9	-8.5
M₃	62.1	-18.8	7.9	4.2	15.6	-10.8	-4
M₄	76.7	-6.4	-1.7	6.5	2.9	-1.9	-8.1
M₅	82.9	-3	3.8	2.3	-1.1	-6.3	-1.7
M₆	97.1	1.3	3.4	2.3	-6.4	-5	-1.4
S₃	131.1	-39.3	22.3	-0.3	46.7	-31.3	4.7
S₁₇	123.7	6.3	-11	20.3	-2	-2	-14
A₂	28.2	5.3	1	18.7	1.3	-0.7	-18.7
A₃	24.8	-12.3	4.3	-13.3	8.7	-7.3	18.7

Table 7. Coefficient matrix of quadratic polynomial response surface

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项目	均方根误差/%
M₁	0.14
M₄	0.32
M₂	0.80
M₅	0.28
M₃	0.60
M₆	0.56
S₃	0.7
S₁₇	0.5
A₁	0.4
A₂	0.4

Table 8. RMS error of structural response value

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深沟球轴承连接刚度 $k_{3}$

（等效弹性模量/MPa）

俯仰角接触球轴承连接刚度 $k_{4}$

（等效弹性模量/MPa）

结构阻尼c₂

59.32

73.2

0.053

Table 9. Modified values of model parameters after optimization

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项目	力学实验结果	修正前	修正后	修正前误差/%	修正后误差/%
M₁	33.9	31.2	32.8	8.0	3.0
M₂	55.2	51.8	54.3	6.0	1.6
M₃	59.9	55.3	58.6	7.7	2.2
S₃	141.2	127.1	135.6	10	4.0
S₁₇	132.4	110.2	125.8	17	4.9
A₁	31.4	28.9	31.0	8.0	1.3
A₂	22.4	24.3	22.9	8.5	2.2