基于灵敏度分析的直升机旋翼桨叶模型修正方法

苏子献; 韩东; 崔钊

doi:10.13224/j.cnki.jasp.20220869

基于灵敏度分析的直升机旋翼桨叶模型修正方法

doi: 10.13224/j.cnki.jasp.20220869

苏子献^1,,
韩东^1,*, ,,
崔钊²

1.
南京航空航天大学航空学院直升机动力学全国重点实验室，南京 210016
2.
中国飞行试验研究院飞机所，西安 710089

基金项目: 国家自然科学基金（11972181）；江苏高校优势学科建设工程资助项目（PAPD）

详细信息

作者简介:
苏子献（1998-），男，硕士生，主要从事直升机旋翼动力学方面的研究。E-mail：444028639@qq.com

通讯作者:
韩东（1979-），男，教授，博士，主要从事直升机动力学及其控制、智能旋翼及旋翼飞行器飞行性能等方面的研究。E-mail：donghan@nuaa.edu.cn

中图分类号: V214.1
计量
- 文章访问数: 528
- HTML浏览量: 239
- PDF量: 36
- 被引次数: 0
出版历程
- 收稿日期: 2023-11-14
- 网络出版日期: 2024-04-03

Helicopter rotor blade model updating method based on sensitivity analysis

SU Zixian^1
,,
HAN Dong^{1,*
, ,},
CUI Zhao²

1.
National Key Laboratory of Helicopter Aeromechanics，College of Aerospace Engineering，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，China
2.
Aircraft Flight Test Technology Institute，Chinese Flight Test Establishment，Xi’an 710089，China

摘要

摘要:
为缩减直升机旋翼桨叶结构有限元模型与实际模型之间模态响应结果之间的偏差，采用一种基于灵敏度分析的模型修正方法，由于传统的灵敏度方法未考虑设计参数变化对灵敏度计算结果的影响，以及出现量化不统一等问题，针对直升机旋翼桨叶模型对该方法进行适当的改进。以碳纤维复合材料直升机旋翼模型桨叶为例，通过试验与有限元分析分别得到其实际模型与有限元分析模型的前6阶模态的固有频率，利用灵敏度方法对桨叶有限元模型的主要设计参数进行优化，使旋翼有限元模型与实际模型间固有频率的平均误差由8.15%降低至1%以内，误差有了明显的降低、精度有明显的提升。修正结果表明，基于灵敏度分析的模型修正方法能够有效提升直升机桨叶结构模型的精度。
- 模型修正 /
- 灵敏度分析 /
- 旋翼桨叶 /
- 有限元模型 /
- 实际模型 /
- 固有频率
Abstract:
In order to reduce the deviation between the modal response results of the finite element model and the actual model of the helicopter rotor blade structure, a model updating method based on sensitivity analysis was used. In view of traditional sensitivity method without consideration of the influence of the change of design parameters on the sensitivity calculation results, as well as the problem of non-uniform quantification, the method was appropriately improved for the helicopter rotor blade model. Taking the carbon fiber composite helicopter rotor blade model as an example, the natural frequencies of the first six modes of the actual model and the finite element analysis model were obtained through experiments and finite element analysis, respectively, and the main design parameters of the finite element model of the rotor blade were optimized by using the sensitivity method. The average error between the rotor blade finite element model and the actual model was reduced from 8.15% to less than 1%. The error was significantly reduced and the accuracy was significantly improved. The updating results showed that the model updating method based on sensitivity analysis can effectively improve the accuracy of the helicopter propeller structure model.
- model updating /
- sensitivity analysis /
- rotor blade /
- finite element model /
- actual model /
- natural frequency

HTML

图 1 有限元模型修正流程图

Figure 1. Finite element model updating flow chart

下载: 全尺寸图片幻灯片

图 2 桨叶总体尺寸（单位：m）

Figure 2. Blade overall dimensions （unit: m）

下载: 全尺寸图片幻灯片

图 3 桨叶剖面结构

Figure 3. Blade profile structure

下载: 全尺寸图片幻灯片

图 4 挥舞、扭转方向测量固有频率

Figure 4. Measurement of natural frequency in flapping and twisting directions

下载: 全尺寸图片幻灯片

图 5 摆振方向测量固有频率

Figure 5. Measurement of natural frequency in lagging direction

下载: 全尺寸图片幻灯片

图 6 桨叶有限元模型

Figure 6. Blade finite element model

下载: 全尺寸图片幻灯片

图 7 设计参数灵敏度

Figure 7. Design parameter sensitivity

下载: 全尺寸图片幻灯片

图 8 桨叶固有频率

Figure 8. Blade natural frequencies

下载: 全尺寸图片幻灯片

图 9 固有频率误差

Figure 9. Natural frequencies errors

下载: 全尺寸图片幻灯片

图 10 固有频率的误差率

Figure 10. Error rate of natural frequencies

下载: 全尺寸图片幻灯片

图 11 设计参数的变化量

Figure 11. Amount of variation of design parameters

下载: 全尺寸图片幻灯片

表 1 桨叶外形参数

Table 1. Blade profile parameters

参数	数值及说明
展长/m	1.093
翼尖弦长/m	0.046
尖削比	2∶1
负扭角/（°）	−5
翼型	OA213

下载: 导出CSV

表 2 桨叶结构设计参数

Table 2. Blade structure design parameters

结构件	设计参数	数值
大梁	密度$ {\rho _1} $/（g/cm³）	1.6
	x方向弹性模量$ {E_{1x}} $/GPa	125
	y方向弹性模量$ {E_{1y}} $/GPa	9.65
	z方向弹性模量$ {E_{1{\textit{z}}}} $/GPa	9.65
后缘	密度$ {\rho _2} $/（g/cm³）	1.6
	x方向弹性模量$ {E_{2x}} $/GPa	125
	y方向弹性模量$ {E_{2y}} $/GPa	9.65
	z方向弹性模量$ {E_{2{\textit{z}}}} $/GPa	9.65
蒙皮	密度$ {\rho _3} $/（g/cm³）	1.6
	x方向弹性模量$ {E_{3x}} $/GPa	125
	y方向弹性模量$ {E_{3y}} $/GPa	8.25
配重	密度$ {\rho _4} $/（g/cm³）	11.34
配重	弹性模量$ {E_4} $/GPa	17
泡沫填充物	密度$ {\rho _5} $/GPa	0.052
泡沫填充物	弹性模量$ {E_5} $/MPa	74
连接件	密度$ {\rho _6} $/（g/cm³）	7.8
连接件	弹性模量$ {E_6} $/GPa	200

下载: 导出CSV

表 3 桨叶有限元频率及试验频率

Table 3. Blade finite element frequencies and test frequencies

模态	有限元频率/Hz	试验频率/Hz
1阶挥舞	11.32	12.60
1阶摆振	42.08	44.10
2阶挥舞	45.36	49.13
3阶挥舞	108.20	118.85
4阶挥舞	203.51	220.87
1阶扭转	245.68	271.88

下载: 导出CSV

表 4 修正后桨叶的有限元频率及试验频率

Table 4. Blade finite element frequencies and test frequencies after updating

模态	频率/Hz			误差/%
模态	试验	修正前	修正后	修正前	修正后
1阶挥舞	12.60	11.32	12.33	10.16	2.14
1阶摆振	44.10	42.08	44.56	4.58	1.04
2阶挥舞	49.13	45.36	49.30	7.67	0.26
3阶挥舞	118.85	108.20	117.56	8.96	1.09
4阶挥舞	220.87	203.51	220.96	7.86	0.04
1阶扭转	271.88	245.68	268.32	9.64	1.31

下载: 导出CSV

表 5 修正前后模型桨叶结构设计参数

Table 5. Design parameters of model blade structure before and after updating

结构件	结构参数	修正前参数值	修正后参数值	参数的变化率/%
大梁	密度$ {\rho _1} $/（g/cm³）	1.60	1.43	−10.43
大梁	x方向弹性模量$ {E_{1x}} $/GPa	125	140	−12.23
后缘	密度$ {\rho _2} $/（g/cm³）	1.60	1.58	−1.13
蒙皮	密度$ {\rho _3} $/（g/cm³）	1.60	1.47	−8.40
	x方向弹性模量$ {E_{3x}} $/GPa	125	133	6.23
	y方向弹性模量$ {E_{3y}} $/GPa	8.25	8.64	4.73
配重	密度$ {\rho _4} $/（g/cm³）	11.34	10.77	−5.00
泡沫填充物	密度$ {\rho _5} $/（g/cm³）	0.052	0.050	−4.20

下载: 导出CSV

参考文献(22)

[1]	MOTTERSHEAD J E,FRISWELL M I. Model updating in structural dynamics: a survey[J]. Journal of Sound Vibration,1993,167(2): 347-375. doi: 10.1006/jsvi.1993.1340
[2]	朱安文,曲广吉,高耀南,等. 结构动力模型修正技术的发展[J]. 力学进展,2002,32(3): 337-348. ZHU Anwen,QU Guangji,GAO Yaonan,et al. A survey of the modifying techniques of structure dynamic models[J]. Advances In Mechanics,2002,32(3): 337-348. (in Chinese doi: 10.3321/j.issn:1000-0992.2002.03.002 ZHU Anwen, QU Guangji, GAO Yaonan, et al. A survey of the modifying techniques of structure dynamic models[J]. Advances In Mechanics, 2002, 32(3): 337-348. (in Chinese) doi: 10.3321/j.issn:1000-0992.2002.03.002
[3]	GRAVITZ S I. An analytical procedure for orthogonalization of experimentally measured modes[J]. Journal of the Aerospace Sciences,1958,25(11): 721-722. doi: 10.2514/8.7855
[4]	IMREGUN M,VISSER W J. A review of model updating techniques[J]. Shock and Vibration Digest,1991,23: 141-162.
[5]	PARK W,KIM H K,JONGCHIL P. Finite element model updating for a cable-stayed bridge using manual tuning and sensitivity-based optimization[J]. Structural Engineering International,2012,22(1): 14-19. doi: 10.2749/101686612X13216060212870
[6]	MACHADO M R,ADHIKARI S,DOS SANTOS J M C,et al. Estimation of beam material random field properties via sensitivity-based model updating using experimental frequency response functions[J]. Mechanical Systems and Signal Processing,2018,102: 180-197. doi: 10.1016/j.ymssp.2017.08.039
[7]	陈德成,魏震松,曲广吉,等. 有限元模型修正技术的工程应用[J]. 中国工程科学,2001,3(10): 59-63. CHEN Decheng,WEI Zhensong,QU Guangji,et al. Engineering application of FEM updating technology[J]. Engineering Science,2001,3(10): 59-63. (in Chinese doi: 10.3969/j.issn.1009-1742.2001.10.011 CHEN Decheng, WEI Zhensong, QU Guangji, et al. Engineering application of FEM updating technology[J]. Engineering Science, 2001, 3(10): 59-63. (in Chinese) doi: 10.3969/j.issn.1009-1742.2001.10.011
[8]	魏锦辉,任伟新. 基于响应面方法的桥梁静动力有限元模型修正[J]. 公路交通科技,2015,32(2): 68-73. WEI Jinhui,REN Weixin. Static and dynamic bridge finite element model updating based on response surface method[J]. Journal of Highway and Transportation Research and Development,2015,32(2): 68-73. (in Chinese doi: 10.3969/j.issn.1002-0268.2015.02.011 WEI Jinhui, REN Weixin. Static and dynamic bridge finite element model updating based on response surface method[J]. Journal of Highway and Transportation Research and Development, 2015, 32(2): 68-73. (in Chinese) doi: 10.3969/j.issn.1002-0268.2015.02.011
[9]	翁顺,朱宏平. 基于有限元模型修正的土木结构损伤识别方法[J]. 工程力学,2021,38(3): 1-16. WENG Shun,ZHU Hongping. Damage identification of civil structures based on finite element model updating[J]. Engineering Mechanics,2021,38(3): 1-16. (in Chinese doi: 10.6052/j.issn.1000-4750.2020.06.ST02 WENG Shun, ZHU Hongping. Damage identification of civil structures based on finite element model updating[J]. Engineering Mechanics, 2021, 38(3): 1-16. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.06.ST02
[10]	MOTTERSHEAD J E,LINK M,FRISWELL M I. The sensitivity method in finite element model updating: a tutorial[J]. Mechanical Systems and Signal Processing,2011,25(7): 2275-2296. doi: 10.1016/j.ymssp.2010.10.012
[11]	ESFANDIARI A,BAKHTIARI-NEJAD F,RAHAI A,et al. Structural model updating using frequency response function and quasi-linear sensitivity equation[J]. Journal of Sound Vibration,2009,326(3/4/5): 557-573.
[12]	PETERSEN Ø W,ØISETH O. Sensitivity-based finite element model updating of a pontoon bridge[J]. Engineering Structures,2017,150: 573-584. doi: 10.1016/j.engstruct.2017.07.025
[13]	BARTILSON D T,JANG J,SMYTH A W. Finite element model updating using objective-consistent sensitivity-based parameter clustering and Bayesian regularization[J]. Mechanical Systems and Signal Processing,2019,114: 328-345. doi: 10.1016/j.ymssp.2018.05.024
[14]	BAYBORDI S,ESFANDIARI A. A novel sensitivity-based finite element model updating and damage detection using time domain response[J]. Journal of Sound and Vibration,2022,537: 117187. doi: 10.1016/j.jsv.2022.117187
[15]	ZHU Hongping,LI Jiajing,TIAN Wei,et al. An enhanced substructure-based response sensitivity method for finite element model updating of large-scale structures[J]. Mechanical Systems and Signal Processing,2021,154: 107359. doi: 10.1016/j.ymssp.2020.107359
[16]	ESFANDIARI A,SANAYEI M. More insight on function-weighted frequency response function sensitivity method for analytical model updating[J]. Journal of Sound and Vibration,2021,509: 116143. doi: 10.1016/j.jsv.2021.116143
[17]	IZADI A,ESFANDIARI A. Structural damage identification by a sensitivity-based finite element model updating method using transmissibility function data[J]. Ships and Offshore Structures,2023,18(10): 1415-1428. doi: 10.1080/17445302.2022.2120296
[18]	李效法. 基于灵敏度分析的模型修正研究及其实现[D]. 南京: 南京航空航天大学,2007. LI Xiaofa. Some study of model updating based on sensitivity analysis and its realization[D]. Nanjing: Nanjing University of Aeronautics and Astronautics,2007. (in Chinese LI Xiaofa. Some study of model updating based on sensitivity analysis and its realization[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2007. (in Chinese)
[19]	张淼. 基于模态参数灵敏度的模型修正方法研究[J]. 长春工程学院学报(自然科学版),2019,20(3): 118-125. ZHANG Miao. Research on methods of finite element model updating based on modal parameter sensitivity[J]. Journal of Changchun Institute of Technology (Natural Sciences Edition),2019,20(3): 118-125. (in Chinese ZHANG Miao. Research on methods of finite element model updating based on modal parameter sensitivity[J]. Journal of Changchun Institute of Technology (Natural Sciences Edition), 2019, 20(3): 118-125. (in Chinese)
[20]	张开银,许灿,张斌,等. 基于设计参数灵敏度分析的模型修正方法研究[J]. 武汉理工大学学报(交通科学与工程版),2021,45(6): 1128-1132. ZHANG Kaiyin,XU Can,ZHANG Bin,et al. Research on model correction method based on sensitivity analysis of design parameters[J]. Journal of Wuhan University of Technology (Transportation Science & Engineering),2021,45(6): 1128-1132. (in Chinese ZHANG Kaiyin, XU Can, ZHANG Bin, et al. Research on model correction method based on sensitivity analysis of design parameters[J]. Journal of Wuhan University of Technology (Transportation Science & Engineering), 2021, 45(6): 1128-1132. (in Chinese)
[21]	NELSON R B. Simplified calculation of eigenvector derivatives[J]. AIAA Journal,1976,14(9): 1201-1205. doi: 10.2514/3.7211
[22]	胡斌. 基于灵敏度分析的模型修正方法在隔震桥梁的运用[J]. 华南地震,2014,34(增刊1): 53-56. HU Bin. Application of model updating based on sensitivity analysis in isolated bridge[J]. South China Journal of Seismology,2014,34(Suppl.1): 53-56. (in Chinese HU Bin. Application of model updating based on sensitivity analysis in isolated bridge[J]. South China Journal of Seismology, 2014, 34(Suppl.1): 53-56. (in Chinese)