Theoretical analysis and experimental evaluation of vibration isolation system with broadband characteristic for laser tracker

Liu Hai-Ping; Zhang Shi-Cheng; Men Ling-Ling; He Zhen-Qiang

doi:10.7498/aps.71.20220307

Abstract

High-energy synchrotron radiation source, as a large scientific device, is under construction in Beijing, China. This device is one of the fourth-generation synchrotron radiation sources with the highest brightness in the world. It will provide an important support platform for basic science and engineering science. As a kind of high-precision large-scale measurement equipment, laser tracker is used mainly in high-energy particle accelerator equipment installation, precision poses dynamic measurement and antenna feed dynamic motion precision engineering measurement field. At the construction site of high energy synchrotron radiation source, the laser tracker is often used to calibrate and pre-collimate the high energy source magnet equipment and carry on the tunnel measurement . However, the laser tracker is easily affected by the vibration of the surrounding environment, and the adverse vibration seriously affects its measurement accuracy and even causes the equipment to damage. In order to effectively control the influence of environmental vibration and ensure good static bearing capacity, a broadband vibration isolator for laser tracker is proposed. It is installed in the leg position of the triangular bracket of the laser tracker, which ensures the vibration isolation performance and good bearing capacity. For the above system, the equivalent single freedom nonlinear dynamic differential equation is established, and the steady-state response solution of the broadband isolator is obtained by using the complex variable-average method. The numerical finite element method is used to verify the correctness of the theoretical model and corresponding calculation results. On this basis, the stability of a nonlinear system is analyzed by harmonic balance method, and the influence of key designing parameter K₃ on vibration isolation performance is considered. Combined with the complexity of the actual working environment of laser tracker, a variety of typical working conditions are set up for test, including long time static pressure test, vertical impact excitation and lateral displacement excitation tests, to evaluate the static stability and vibration control effect of broadband isolator. The experimental results show that the maximum static displacement of the laser tracker is about 2×10^–5 m under static pressure in a long time, and the maximum static load is within the allowable error range. When the occasional impacting is triggered, the installation of broadband isolator can make the combination quickly restore stability in about 2.95 s, exhibiting better vibration isolation performance. Under different dynamic loads, by comparing the acceleration frequency response curves of the laser tracker with and without the isolator, in the frequency band below the fundamental frequency of the laser tracker, the attenuation rate of the combined system can be up to about 97% with and without the vibration isolator. In the frequency band above the fundamental frequency, the attenuation rate of the combined system with and without the vibration isolation system can reach up to about 88%, and the effective vibration isolation frequency band is extended. The broadband vibration isolator meets all technical requirements.

Keywords:

laser tracker /
vibration isolation system with broadband characteristic /
high energy photon source /
vibration control

Authors and contacts

1.
School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China
2.
Shunde Graduate School, University of Science and Technology Beijing, Foshan 528300, China
3.
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

Corresponding author: Liu Hai-Ping, liuhaiping@ustb.edu.cn

Funds: Project supported by the Guangdong Basic and Applied Basic Research Foundation, China (Grant No. 2021B1515120049), the Foshan Science and Technology Innovation Funds for Industry University Cooperation Project (Grant No. BK22BE021), and the Beijing Science and Technology Project, China (Grant No. Z191100005619011).

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References

[1]	罗涛, 何晓业, 汪昭义, 王巍, 李笑, 黄晴晴, 何振强, 柯志勇, 马娜, 王铜, 梁静, 李波, 门铃鸰, 王小龙, 董岚 2021 武汉大学学报(信息科学版) DOI: 10.13203/j.whugis20200718 Luo T, He X Y, Wang S Y, Wang W, Li X, Huang Q Q, He Z Q, Ke Z Y, Ma N, Wang T, Liang J, Li B, Men L L, Wang X L, Dong L 2021 Geomatics Inf. Sci. Wuhan Univ. DOI: 10.13203/j. whugis20200718 (in Chinese)
[2]	Jiao Y, Duan Z, Guo Y, Ji D, Li X, Peng Y, Qin Q, Qiu J, Tian S, Wang J 2016 Phys. Procedia 84 40 Google Scholar
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Cited By

图 1 宽频隔振器实物照片

Figure 1. Photo of isolator with broadband characteristic.

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图 2 薄片梁的力-位移曲线

Figure 2. Force-displacement curves of thin sheet beam.

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图 3 宽频隔振器的等效力学模型　(a) 未受载状态; (b) 静平衡状态

Figure 3. Equivalent mechanical model of isolator with broadband characteristic: (a) unloaded state; (b) static equilibrium state.

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图 4 宽频隔振器的安装位置

Figure 4. Installation position of isolator with broadband characteristic.

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图 5 宽频隔振器加速度传递率曲线

Figure 5. Acceleration transmissibility curves of isolator with broadband characteristic.

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图 6 宽频隔振器加速度传递率曲线

Figure 6. Acceleration transmissibility curve of isolator with broadband characteristic.

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图 7 不同K₃对应加速度传递率曲线

Figure 7. Acceleration transmissibility curves for different K₃.

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图 8 宽频隔振器长时间静态力学试验照片

Figure 8. Photograph of long time static mechanical test of isolator with broadband characteristic.

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图 9 测试系统照片

Figure 9. Test System Photo.

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图 10 系统模型的理论、仿真及实测结果对比

Figure 10. Comparison of theoretical, simulation and measured results of the overall model.

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图 11 未安装宽频隔振器组合体的频响曲线(工况1)

Figure 11. Frequency response curves of the assembly without broadband isolator (case 1).

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图 12 频响曲线(工况2)

Figure 12. Frequency response curves (case 2).

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图 13 钢块敲击对应频响曲线(工况2)

Figure 13. Frequency response curves under steel-block hit (case 2).

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图 14 安装宽频隔振器, 不同位置加速度频响曲线(工况3)

Figure 14. Acceleration frequency response curves with broadband isolators at different locations (case 3).

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图 15 安装宽频隔振器前后, 激光跟踪仪安装面垂向加速度频响曲线(工况4)

Figure 15. Vertical acceleration frequency response curves of laser tracker’s mounting position with and without broadband isolators (case 4).

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图 16 安装宽频隔振器前后, 激光跟踪仪安装面水平向加速度频响曲线(工况5)

Figure 16. Acceleration frequency response curve of laser tracker’s mounting position with and without broadband isolators along horizontal direction (case 5).

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图 17 高频模态振型

Figure 17. Modal shape in higher frequency region.

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图 18 时域加速度响应曲线

Figure 18. Acceleration response curve in time domain.

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表 1 薄片梁的设计参数

Table 1. Designing parameters of thin sheet beam.

名称	符号	数值
总长度	L	70 mm
初始角度	θ₁	26°
端点角度	θ₂	–25°
弹性模量	E	208 GPa
厚度	d	1 mm
初始宽度	w	24 mm

DownLoad: CSV

表 2 宽频隔振器材料参数表

Table 2. Material parameters of isolator with broadband characteristic.

名称	薄片梁	转接件
材料	60 Si₂CrVA	10 F
密度/(kg·m³)	7850	7990
泊松比	0.3	0.24
弹性模量/Pa	2.1×10¹¹	1.96×10¹¹

DownLoad: CSV

表 3 长时间静压试验实测变形量

Table 3. Deformation measured under long time compression condition.

		实测变形量/m
测试工况		5 h	15 h
方向	X	–1.2×10^–5	1.6×10^–5
	Y	6×10^-6	–2.1×10^–5
	Z	1.2×10^–5	5×10^–5

DownLoad: CSV

表 4 试验工况表

Table 4. Test conditions table.

序号	工况	测点编号及位置
1	未安装隔振器, 钢块敲击地面	#1, #2, #3; 支架支腿位置
2	安装隔振器, 钢块敲击地面前后, 支架处响应	#1, #2, #3; 支架支腿位置
3	安装隔振器, 钢块敲击地面, 地面、支架及激光跟踪仪处响应	#2, #4, #5; 支架支腿、激光跟踪仪及地面垂向
4	安装隔振器, 钢块敲击地面, 激光跟踪仪处响应	#4; 激光跟踪仪安装面垂向
5	安装隔振器, 钢块敲击地面, 激光跟踪仪处响应	#4; 激光跟踪仪安装面水平向
6	安装隔振器, 水平推动激光跟踪仪处响应	#4; 激光跟踪仪安装面水平向

DownLoad: CSV

表 5 模态固有频率对比及振型图

Table 5. Natural frequencies and mode shapes.

模态阶数	固有频率/Hz			模态振型
模态阶数	仿真结果	实测结果	误差	模态振型
1	14.31	14.75	3.0%
2	41.91	42.75	2.0%
3	60.50	47.25	3.3%
4	86.99	50.25	21.9%
5	88.66	57.75	34.9%

DownLoad: CSV

[1]	罗涛, 何晓业, 汪昭义, 王巍, 李笑, 黄晴晴, 何振强, 柯志勇, 马娜, 王铜, 梁静, 李波, 门铃鸰, 王小龙, 董岚 2021 武汉大学学报(信息科学版) DOI: 10.13203/j.whugis20200718 Luo T, He X Y, Wang S Y, Wang W, Li X, Huang Q Q, He Z Q, Ke Z Y, Ma N, Wang T, Liang J, Li B, Men L L, Wang X L, Dong L 2021 Geomatics Inf. Sci. Wuhan Univ. DOI: 10.13203/j. whugis20200718 (in Chinese)
[2]	Jiao Y, Duan Z, Guo Y, Ji D, Li X, Peng Y, Qin Q, Qiu J, Tian S, Wang J 2016 Phys. Procedia 84 40 Google Scholar
[3]	李广云, 范百兴 2017 测绘学报 46 10 Google Scholar Li G Y, Fan B X 2017 Acta Geod. Cartogr. Sin. 46 10 Google Scholar
[4]	Kristiansen P, Horbach J, Döhrmann R, Heuer J 2015 J. Synchrotron Radiat. 22 4 Google Scholar
[5]	Omidalizarandi M, Kargoll B, Paffenholz J A, Paffenholz J A, Neumann I 2018 Adv. Mech. Eng. 10 119 Google Scholar
[6]	徐亚明, 郑琪, 管啸 2020 测绘地理信息 45 812 Google Scholar Xu Y M, Zheng Q, Guan X 2020 J. Geomat. 45 812 Google Scholar
[7]	Bronowicki A J, Abhyankar N S, Griffin S F 1999 Smart Mater. Struct. 8 740 Google Scholar
[8]	Davis L, Hyland D, Yen G, Dask A 1999 Smart Mater. Struct. 8 753 Google Scholar
[9]	Vaillon L, Petitjean B, Frapard B, Lebihan D 1999 Smart Mater. Struct. 8 781 Google Scholar
[10]	Vaillon L, Sanctorum B, Sperandei J, Defendini A, Griseri G, Alberti M V 2002 Proc. 5th ESA Int. Conf. Spacecr. Guid Italy, Frascati, October
[11]	Onoda J, Minesugi K 1996 AIAA J. 34 207 Google Scholar
[12]	Onoda J, Minesugi K 1994 J. Spacecraft Rockets 31 67 Google Scholar
[13]	Onoda J, Minesugi K 1996 AIAA J. 34 355 Google Scholar
[14]	Chen S B, Xuan M, Xin J, Liu Y, Gu S, Li J, Zhang L 2020 Int. J. Mech. Sci. 179 105592 Google Scholar
[15]	姜伟伟, 徐治洲, 任戈 2014 噪声与振动控制 34 186 Google Scholar Jiang W W, Xu Z Z, Ren G 2014 Noise Vibr. Control 34 186 Google Scholar
[16]	杜言鲁, 丁亚林, 许永森, 聂品 2015 中国机械工程 26 2880 Google Scholar Du Y L, Ding Y L, Xu Y S, Nie P 2015 Chin. Mech. Eng. 26 2880 Google Scholar
[17]	郑凤翥, 宁飞, 王培群, 霍丽烨, 赵志草 2018 应用光学 39 453 Google Scholar Zheng F Z, Ning F, Wang P Q, Huo L Y, Zhao Z C 2018 J. Appl. Opt. 39 453 Google Scholar
[18]	Qi Y, Wang H L, Xu Q Q, Du Y L, Shao X Z, Yang H 2021 Optik 242 167016 Google Scholar
[19]	Dong G, Ma C, Y Luo 2020 Int. J. Appl. Electromagnet. Mech. 64 315 Google Scholar
[20]	杜宁, 胡明勇, 毕勇, 朱庆生 2017 振动与冲击 36 184 Du N, Hu M Y, Bi Y, Zhu Q S 2017 J. Vibr. Shock 36 184
[21]	Carrella A, Brennan M J, Waters T P 2007 J. Sound Vibr. 301 678 Google Scholar
[22]	Takamori A 2002 Ph. D. Dissertation (Tokyo: University of Tokyo)
[23]	Stochino A, Abbot B, Aso Y, Barton M, Bertolini A, Boschi V, Coyne D, DeSalvo R, Galli C, Huang Y M 2007 Nucl. Instrum. Methods Phys. Res. , Sect. A 598 737 Google Scholar
[24]	Yao J, Wu K, Guo M, Wang G, Wang L 2019 IEEE Trans. Instrum. Meas. 99 1 Google Scholar
[25]	Xu D L, Yu Q P, Zhou J X, Bishop S R 2013 J. Sound Vibr. 332 3377 Google Scholar
[26]	Xu D L, Zhang Y Y, Zhou J X, Lou J J 2013 J. Vibr. Control 20 2314 Google Scholar
[27]	李强, 徐登峰, 李林, 魏绍炎 2019 振动与冲击 38 100 Google Scholar Li Q, Xu D F, Li L, Wei S Y 2019 J. Vibr. Shock 38 100 Google Scholar
[28]	严博, 马洪业, 韩瑞祥, 王珂, 武传宇 2019 机械工程学报 55 169 Google Scholar Yan B, Ma H X, Han R X, Wang K, Wu C Y 2019 J. Mech. Eng. 55 169 Google Scholar
[29]	Sun M, Chen J 2018 Math Probl Eng. 2018 5693618 Google Scholar
[30]	刘海平, 申大山, 赵鹏鹏 2021 振动工程学报 34 490 Google Scholar Liu H P, Shen D S, Zhao P P 2021 J. Vibr. Eng. 34 490 Google Scholar

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