Researching | Design technology of the truss support structure of the ultra-low thermal deformation gravitational wave detection telescope

Opto-Electronic Engineering, Volume. 50, Issue 11, 230155-1(2023)

Design technology of the truss support structure of the ultra-low thermal deformation gravitational wave detection telescope

Bohong Li¹, Jian Luo¹, Minyan Qiu¹, Wenduo Chen², and Hongchao Zhao^3、*

Author Affiliations

¹MOE Key Laboratory of TianQin Mission, TianQin Research Center for Gravitational Physics & School of Physics and Astronomy, Frontiers Science Center for TianQin, Gravitational Wave Research Center of CNSA, Sun Yat-sen University (Zhuhai Campus), Zhuhai, Guangdong 519082, China

²School of Materials, Shenzhen Campus of Sun Yat-sen University, Shenzhen, Guangdong 518107, China

³School of Advanced Manufacturing, Shenzhen Campus of Sun Yat-Sen University, Shenzhen, Guangdong 518107, China

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References (22)

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Figures & Tables(22)

Fig. 1. Single-layer CFRP schematic diagram. Direction 1 corresponds to the in-plane fiber direction referred to as the longitudinal direction；Direction 2 is perpendicular to direction 1 within the plane referred to as the transverse direction

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Fig. 2. Laminate composite material schematic diagram

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Fig. 3. Three-stage design of the TianQin telescope: 1) Main load-bearing plate; 2) Three main support rods; 3) Sub-mirror support adjustment backplate

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Fig. 4. Replaceable telescope CFRP support tube joint

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Fig. 5. Geometric model of the support structure

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Fig. 6. Finite element simulation of thermal expansion of CFRP material — taking laying method 6 as an example

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Fig. 7. Main support structure model and coordinate system

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Fig. 8. Solid model (left); truss structure model (middle); theoretical model (right)

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Fig. 9. Solid simulation and truss simulation result — example of thermal deformation in the dz direction

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Fig. 10. Optimization results for structural thermal deformations

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Fig. 11. First mode: oscillation along the Y direction, 122.61 Hz

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Fig. 12. Second mode: oscillation along the X direction, 128.47 Hz

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Fig. 13. Element analysis of thermal deformation of truss support structure — example with layer 1

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Fig. 14. Taking 50 μK temperature noise as an example

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Fig. 15. The relative thermal deformation in the M1-M2 separation direction is 12 pm/ $\sqrt{Hz}$

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Table 1. Candidate materials for truss support structure of telescope prototype

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Table 1. Candidate materials for truss support structure of telescope prototype

材料	密度/(kg/m³)	工程常数	线胀系数/(10⁻⁶/K)
钛合金	$ρ = 4430$	$E$ =114 $GPa, ν$ =0.34	$α = 8.8$
碳化硅	$ρ = 3210$	$E$ =466 $GPa,$ $ν$ =0.21	$α = 2.4$
Zerodur	$ρ = 2530$	$E$ =91 $GPa,$ $ν$ =0.24	$α = 0.05$
常规Invar合金	$ρ = 8110$	$E$ =148 $GPa,$ $ν$ =0.30	$α = 4.30$
定制Invar合金	$ρ = 8150$	$E$ =144 $GPa,$ $ν$ =0.30	$α = 0.63$
CFRP^1* M40J(3k)/wp-s3000单层板^[21]	$ρ = 1596$	$E$ 1=231 $GPa,$ $ν_{12}$ =0.26 $E$ 2=7.76 $GPa$ $G$ 12=4.3 $GPa$ $G$ 23=2.8 $GPa,$	$α_{1} = - 0.481$ $α_{2} = 35.841$
CFRP^2* T800H/M21单层板^[22]	$ρ = 1590$	$E$ 1=134.7 $GPa,$ $ν_{12}$ =0.369 $E$ 2=7.70 $GPa$ G12=4.2 $GPa$ $G$ 23=2.5 $GPa$	$α_{1} = - 0.31$ $α_{2} = 31.8$

Table 2. Alternative CFRP layup methods

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Table 2. Alternative CFRP layup methods

序号	铺层方式	$α_{x - CFRP}$ ${/ (10}^{- 7} / K)$	$α_{y - CFRP}$ ${/ (10}^{- 7} / K)$
1	${[\pm 45 / 0 / 90 / 0 / 90 / 45 / - 45 / 90 / 0]}_{s}$	$9.817$	$9.817$
2	${[\pm 45 / 90 / 0 / - 45 / 0 / 45 / 0 / 90 / 0]}_{s}$	$3.555$	$18.90$
3	${[\pm 45 / 60 / 0 / - 45 / 90 / 45 / 0 / - 60 / 0]}_{s}$	$5.518$	$14.99$
4	${[37.08 / - 59.45 / 31.38 / - 57.01 / - 16.64 / 16.64 / 57.01 / - 31.38 / 59.45 / - 37.08]}_{s}$	$1.205$	$20.87$
5	${[32.61 / - 53.67 / 37.04 / - 56.86 / - 32.65 / 32.65 / 56.86 / - 37.04 / 53.67 / - 32.61]}_{s}$	$0.826$	$20.28$
6	${[- 30.49 / - 51.63 / 36.10 / - 60.38 / - 30.44 / 30.44 / 60.38 / - 36.10 / 51.63 / 30.49]}_{s}$	$0.069$	$21.69$

Table 3. Comparison of theoretical model calculation results with simulation results
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Table 3. Comparison of theoretical model calculation results with simulation results
铺层方案 $α_{x - CFRP} {/ (10}^{- 7} / K)$ (理论结果) $α_{x - CFRP} {/ (10}^{- 7} / K)$ (仿真结果) 相对误差/ $%$
1 $9.817$ $9.817$ 0
2 $5.518$ $5.518$ 0
3 $6.713$ $6.713$ 0
4 $1.205$ $1.199$ $0.42$
5 $0.826$ $0.821$ $0.63$
6 $0.069$ $0.065$ $6.10$

Table 4. Design requirements for main support structure of telescope prototype

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Table 4. Design requirements for main support structure of telescope prototype

指标项目	输入条件	性能要求
1.结构重量	固有性质	$< 7.5 kg$ (仅支架)
2.模态特性	固有性质	$f r e q_{1} > 80 Hz$
3.重力卸载	任意方向	$Δ z_{M1,2} < 10 μ m$ $Δ y_{M1,2} < 10 μ m$ $Δ T_{M1,2}^{x} < 30 μ rad$
4.大尺度热变形	周期内环境温变 $Δ t = 10 K$	$d z_{M1,2} < 10 μ m, d y_{M1,2} < 5 μ m$
5.热变形稳定性(极限)	$S_{Δ t} < 10 μ K / \sqrt{Hz}$ $(10 mHz \sim 0.1 Hz)$	$S_{Δ l_{M 1,2}} < 1.0 pm / \sqrt{Hz}$ 对应 $α_{z} < 1 \times 10^{- 7} / K$
6.热变形稳定性(常规)	$S_{Δ t} < 50 μ K / \sqrt{Hz}$ $(10 mHz \sim 0.1 Hz)$	$S_{Δ l_{M 1,2}} < 0.4 pm / \sqrt{Hz}$ 对应 $α_{z} < 1 \times 10^{- 8} / K$

Table 5. Comparison and verification among the three models
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Table 5. Comparison and verification among the three models
铺层序号理论模型/ $μ m$ 桁架模型/ $μ m$ 实体单元模型/ $μ m$
间隔z $8.224$ $8.224$ $8.646$
偏心y $4.556$ $4.556$ $4.124$

Table 6. Gravity unloading deformation analysis

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Table 6. Gravity unloading deformation analysis

重力卸载方向	设计要求	分析结果
沿Z方向卸载	$Δ z_{M 1 - M 2} < 10 μ m$ $Δ y_{M 1 - M 2} < 10 μ m$ $Δ T_{M 1 - M 2}^{x} < 30 μ rad$	$Δ z_{M 1 - M 2} = 0.38 μ m$ $Δ y_{M 1 - M 2} = - 2.66 μ m$ $Δ T_{M 1 - M 2}^{x} = - 0.16 μ rad$
沿Y方向卸载	$Δ z_{M 1 - M 2} < 10 μ m$ $Δ y_{M 1 - M 2} < 10 μ m$ $Δ T_{M 1 - M 2}^{x} < 30 μ rad$	$Δ z_{M 1 - M 2} = - 2.57 μ m$ $Δ y_{M 1 - M 2} = - 5.47 μ m$ $Δ T_{M 1 - M 2}^{x} = - 2.31 μ rad$
沿X方向卸载	$Δ z_{M 1 - M 2} < 10 μ m$ $Δ y_{M 1 - M 2} < 10 μ m$ $Δ x_{M 1 - M 2} < 10 μ m$ $Δ T_{M 1 - M 2}^{x} < 30 μ rad$	$Δ z_{M 1 - M 2} = 0.02 μ m$ $Δ y_{M 1 - M 2} = - 0.04 μ m$ $Δ x_{M 1 - M 2} = 5.91 μ m$ $Δ T_{M 1 - M 2}^{x} = 0.03 μ rad$

Table 7. Comparison results of structural thermal deformation between different materials

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Table 7. Comparison results of structural thermal deformation between different materials

主支撑结构选材	稳定性结果@ $10mHz \sim 0.1 Hz$ / $(pm / \sqrt{Hz})$	对应结构热膨胀系数 $α_{z}$ /K
CFRP支杆-铺层4-优化铺层方案	$12.0$	$3.31 \times 10^{- 7}$
CFRP支杆-铺层1-各向同性铺层	$44.2$	$12.19 \times 10^{- 7}$
SiC支杆	$104.3$	$28.77 \times 10^{- 7}$
Invar-42支杆	$186.8$	$51.52 \times 10^{- 7}$
钛合金支杆	$373.6$	$103.05 \times 10^{- 7}$

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Bohong Li, Jian Luo, Minyan Qiu, Wenduo Chen, Hongchao Zhao. Design technology of the truss support structure of the ultra-low thermal deformation gravitational wave detection telescope[J]. Opto-Electronic Engineering, 2023, 50(11): 230155-1

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Paper Information

Category: Article

Received: Jun. 29, 2023

Accepted: Oct. 16, 2023

Published Online: Mar. 26, 2024

The Author Email: Hongchao Zhao (赵宏超)

DOI:10.12086/oee.2023.230155

Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology