Optimization of carbon fiber truss element for primary mirror chamber of large telescope

Bo-zhong GU; Meng CHEN; Zhong-yu YUE

doi:10.37188/OPE.20212909.2116

Optics and Precision Engineering, Volume. 29, Issue 9, 2116(2021)

Optimization of carbon fiber truss element for primary mirror chamber of large telescope

Bo-zhong GU1...2,*, Meng CHEN1,2,3, and Zhong-yu YUE12 |Show fewer author(s)

¹National Astronomical Observatories / Nanjing Institute of Astronomical Optics & Technology， Chinese Academy of Sciences， Nanjing20042， China

²Key Laboratory of Astronomical Optics & Technology， Nanjing Institute of Astronomical Optics & Technology， Chinese Academy of Sciences， Nanjing1004， China

³University of Chinese Academy of Sciences， Beijing100049， China

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Figures & Tables(20)

Fig. 1. Model of telescope primary mirror chamber truss

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Fig. 2. Force of truss

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Fig. 3. Sampling methods

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Fig. 4. Iteration curves of optimization and pareto diagrams

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Fig. 5. Theoretic fitted curves of deformation-force

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Fig. 6. The first order mode of basic unit of four CFRP schemes

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Fig. 7. Load experiments

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Fig. 8. Experimental fitted curves of deformation-force

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Fig. 9. Truss vibration measurement

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Fig. 10. Response curves of vibration measurement

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Table 1. Material performance properties
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Table 1. Material performance properties
弹性模量/GPa 拉伸强度/GPa 弯曲强度/GPa 剪切模量/GPa 剪切强度/GPa 泊松比
密度ρ
/（g· $c m^{- 3})$
115 2.03 1.25 4.8 0.055 0.3 1.7

Table 2. Geometry of truss rod
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Table 2. Geometry of truss rod
参数长度L/mm 外径D/mm 内径d/mm
单层厚度
t/mm
铺层数n
数据 800 30 28 0.2/0.1 10

Table 3. CoP of various schemes

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Table 3. CoP of various schemes

加载方案	变形类型	预测系数CoP
仅施加1 000 N拉力	轴向变形	0.834 204
仅施加1 000 N压力	轴向变形	0.830 575
仅施加50 N径向力	径向变形	0.818 391
轴向力∶径向力=1∶ $\sqrt[]{3}$	轴向变形	0.852 023
轴向力∶径向力=1∶ $\sqrt[]{3}$	径向变形	0.852 392
轴向力∶径向力= $\sqrt[]{3}$ ∶1	轴向变形	0.860 812
轴向力∶径向力= $\sqrt[]{3}$ ∶1	径向变形	0.861 079

Table 4. Optimization results for different loading schemes

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Table 4. Optimization results for different loading schemes

加载方案	优化结果
仅施加轴向拉力	［±45°/90°/0°/90°/90°］s
仅施加轴向压力	［±45°/90°/0°/90°/90°］s
仅施加径向力	［±45°/0°/90°/90°/90°］s
轴向力∶径向力=1∶ $\sqrt[]{3}$	［±45°/90°/90°/90°/90°］s
轴向力∶径向力= $\sqrt[]{3}$ ∶1	［±45°/90°/90°/90°/90°］s

Table 5. Design layer schemes
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Table 5. Design layer schemes
编号铺层方案
1 ［±45°/45°/135°/45°/135°］s
2 ［±45°/90°/0°/45°/135°］s
3 ［±45°/90°/0°/45°/135°/0°/90°/45°/135°/±45°］
4 ［±45°/90°/0°/90°/0°］s

Table 6. Equation of linear regression of simulation results （R²>0.99）

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Table 6. Equation of linear regression of simulation results （R²>0.99）

编号	轴向变形公式	R²	径向变形公式	R²
1	$y_{a 1} = 0.322 7 x$	1.000	$y_{b 1} = 0.671 2 x$	1.000
2	$y_{a 2} = 0.163 1 x$	1.000	$y_{b 2} = 0.341 4 x$	1.000
3	$y_{a 3} = 0.163 4 x$	1.000	$y_{b 3} = 0.339 0 x$	1.000
4	$y_{a 4} = 0.120 4 x$	1.000	$y_{b 4} = 0.252 0 x$	1.000
钢（归一化）	$y_{a 5} = 0.202 2 x$	1.000	$y_{b 5} = 0.414 3 x$	1.000

Table 7. Nature frequencies of basic unit

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Table 7. Nature frequencies of basic unit

阶数	1	2	3	4	5	6
1	67.410	67.945	135.75	177.19	179.79	180.77
2	84.195	84.572	179.20	198.19	223.82	224.20
3	84.316	84.693	179.44	198.38	224.28	224.67
4	93.699	93.996	204.46	206.29	248.49	248.92
钢（归一化）	64.293	64.349	111.10	153.29	174.74	174.83

Table 8. Equations of linear regression of experimental results
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Table 8. Equations of linear regression of experimental results
编号轴向加载 R² 径向加载 R²
1 $y_{a 1} = 0.259 8 x$ 0.999 8 $y_{b 1} = 0.555 0 x$ 0.999 4
2 $y_{a 2} = 0.172 9 x$ 0.993 5 $y_{b 2} = 0.351 2 x$ 0.999 8
3 $y_{a 3} = 0.163 6 x$ 0.996 2 $y_{b 3} = 0.362 3 x$ 0.999 6
4 $y_{a 4} = 0.134 0 x$ 0.999 5 $y_{b 4} = 0.299 0 x$ 0.998 8

Table 9. Result comparison of statics

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Table 9. Result comparison of statics

编号	等效轴向刚度 /（10⁶ N·m^-1）		误差 /%	等效径向刚度 /（N·m^-1）		误差 /%
编号	模拟值	实验值	误差 /%	模拟值	实验值	误差 /%
1	3.100	3.849	19.5	1 489.9	1 801.8	17.3
2	6.131	5.784	6.0	2 929.1	2 847.4	2.9
3	6.120	6.112	0.1	2 949.9	2 760.1	6.9
4	8.306	7.463	11.3	3 968.3	3 344.5	18.7

Table 10. Result comparison of dynamics
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Table 10. Result comparison of dynamics
六杆三棱锥编号实验值/Hz 模拟值/Hz 误差/%
1 65.171 65.410 0.37
2 77.268 84.195 8.97
3 79.415 84.316 6.17
4 84.683 93.699 10.65

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Bo-zhong GU, Meng CHEN, Zhong-yu YUE. Optimization of carbon fiber truss element for primary mirror chamber of large telescope[J]. Optics and Precision Engineering, 2021, 29(9): 2116

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