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

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

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

Haosu ZHANG1... Zhenyu WANG2,*, Yu CAO1,3, Aihong SHANGGUAN1, Youjin XIE1,3, Xi WANG1,4, Shengming SU1,4, and Yongfan JIANG14 |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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Figures & Tables(19)

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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Table 1. Adjustment parameters of initial analysis model

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Table 1. Adjustment parameters of initial analysis model

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 2. Modal frequency response results of initial analysis

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Table 2. Modal frequency response results of initial analysis

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 3. Significance analysis of modal frequency
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Table 3. Significance analysis of modal frequency
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 4. Significance analysis of sinusoidal vibration acceleration response and random vibration stress response at characteristic points
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Table 4. Significance analysis of sinusoidal vibration acceleration response and random vibration stress response at characteristic points
参数 A₁ A₂ A₃ S₁ S₂ S₃ S₄ S₁₇
x₁ ○ ○ ○ ○ ○ ○ ○ ○
x₂ ○ ○ ○ ○ ○ ○ ○ ○
x₃ ○ ○ ○ ○ × ○ × ○
x₄ ○ ○ ○ ○ × ○ × ○
x₅ × × × × × × × ×
x₆ ○ ○ ○ ○ ○ ○ ○ ○

Table 5. Parameters after model parameter adjustment

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Table 5. Parameters after model parameter adjustment

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 6. Significance analysis of sinusoidal response， acceleration response and random vibration stress response of characteristic points
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Table 6. Significance analysis of sinusoidal response， acceleration response and random vibration stress response of characteristic points
参数 M₁~M₆ A₁ A₂ A₃ S₁ S₂ S₃ S₄ S₁₇
x₁ ○ ○ ○ ○ ○ ○ ○ ○ ○
x₂ ○ ○ ○ ○ ○ ○ ○ ○ ○
x₃ ○ ○ ○ ○ ○ ○ ○ ○ ○
x₄ ○ ○ ○ ○ ○ ○ ○ ○ ○
x₅ × × × × × × × × ×
x₆ ○ ○ ○ ○ ○ ○ ○ ○ ○

Table 7. Coefficient matrix of quadratic polynomial response surface

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Table 7. Coefficient matrix of quadratic polynomial response surface

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 8. RMS error of structural response value
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Table 8. RMS error of structural response value
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 9. Modified values of model parameters after optimization
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Table 9. Modified values of model parameters after optimization
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 10. Comparison of response results before and after correction of response surface method

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Table 10. Comparison of response results before and after correction of response surface method

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

Table 11. Thickness changes in different areas of U-frame
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Table 11. Thickness changes in different areas of U-frame
区域代号优化后厚度/mm 优化前厚度/mm
1，2 3.5 4
3 3.5 5
4，5 3 3.5
6 3 4
7，8 3.5 4
9 3.5 5

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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

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