航天飞行器折叠翼锁紧机构力学模型

任浩源; 王毅; 王亮; 周剑波; 常汉江; 蔡毅鹏; 雷豹

doi:10.13224/j.cnki.jasp.20220032

航天飞行器折叠翼锁紧机构力学模型

doi: 10.13224/j.cnki.jasp.20220032

中国航天科技集团有限公司中国运载火箭技术研究院，北京 100076

基金项目: 国家自然科学基金（11902363）

详细信息

作者简介:
任浩源（1994-），男，博士生，主要从事非线性结构动力学研究

通讯作者:
王毅（1963-），男，研究员，博士，主要从事飞行器总体设计和多体系统动力学研究。E-mail：ywangcalt@163.com

中图分类号: V416.2
计量
- 文章访问数: 615
- HTML浏览量: 170
- PDF量: 73
- 被引次数: 0
出版历程
- 收稿日期: 2022-01-19
- 网络出版日期: 2023-09-12

Mechanical model of locking mechanisms of folding wing for spacecraft

China Academy of Launch Vehicle Technology，China Aerospace Science and Technology Corporation，Beijing 100076，China

摘要

摘要:
针对折叠翼插-拔式锁紧机构建模问题，采用平面应变假设和叠加原理对模型简化降维，构建了考虑间隙效应的连接刚度解析模型。首先，采用能量法求解接触摩擦引起的非静定问题，获得法向和切向接触力；其次，基于Hertz基本解计算出等效接触刚度，并采用梁模型计算弹性销的弯曲变形；通过将解析解与文献试验值进行对比，对方法的适用性进行验证，并进一步针对不同接触模式开展参数影响分析，最终给出了载荷和间隙对连接刚度的影响规律。结果表明：当载荷由20 N·m变为50 N·m时，锁紧机构的连接刚度增大约3%～5%，存在刚度渐硬非线性效应；而随间隙增大，连接刚度呈现下降趋势，其原因为配合尺寸影响弹性销与孔壁的相对姿态。
- 折叠翼面 /
- 锁紧机构 /
- 力学模型 /
- 接触刚度 /
- 半解析方法
Abstract:
To model the plug-in locking mechanism, the plane strain assumption and superposition principles were used for dimensionality reduction and simplification, and an analytical model of connection stiffness considering the effect of gap was established. Firstly, the energy method was used to solve the indeterminate problem caused by contact friction, and the normal and tangential contact forces were obtained. Then, the equivalent contact stiffness was calculated by using Hertz’s theory, and the bending deformation of elastic pins was calculated through beam model. To validate the applicability of the method, the analytical results were compared with the experimental results from the reference paper. Finally, the parameter influence analysis was carried out, and the effect of load and clearance on connection stiffness was proposed. The results showed that when the load changed from 20 N·m to 50 N·m, the connection stiffness of the locking mechanism increased by about 3%—5%, demonstrating a hardening spring nonlinear effect. With the increase of the clearance, the connection stiffness showed a downward trend, owing to the fact that the fit size affected the relative attitude of the elastic pin and the hole.
- folding wing /
- lock mechanisms /
- mechanical model /
- contact stiffness /
- semi-analytical method

HTML

图 1 折叠翼与铰接/锁紧机构示意图

Figure 1. Schematic diagram of folding wing and hinged-locking mechanisms

下载: 全尺寸图片幻灯片

图 2 有限元模型及Von Mises应力结果

Figure 2. Finite element model and Von Mises stress results

下载: 全尺寸图片幻灯片

图 3 锁销-孔等效接触分析模型

Figure 3. Equivalent model of pin and hole for contact analysis

下载: 全尺寸图片幻灯片

图 4 Hertz接触模型

Figure 4. Hertz contact model

下载: 全尺寸图片幻灯片

图 5 铰接/锁紧机构平面模型

Figure 5. Plane model of hinged-locking mechanism

下载: 全尺寸图片幻灯片

图 6 “梯-墙”接触模型及几何参数

Figure 6. Ladder-wall contact model and geometry parameters

下载: 全尺寸图片幻灯片

图 7 法向力F_R1的理论值与试验值

Figure 7. Theoretical and experimental results of F_R1

下载: 全尺寸图片幻灯片

图 8 切向力F_R2的理论值与试验值

Figure 8. Theoretical and experimental results of F_R2

下载: 全尺寸图片幻灯片

图 9 锁销三点接触模型及几何参数

Figure 9. Three-point contact model and geometric parameters of locking pin

下载: 全尺寸图片幻灯片

图 10 三点接触时不同间隙下的力矩-转角关系曲线

Figure 10. Moment vs. rotation angle curve under different clearances for three-point contact type

下载: 全尺寸图片幻灯片

图 11 三点接触时不同间隙下的力矩-刚度关系曲线

Figure 11. Moment vs. rotation connection stiffness curve under different clearances for three-point contact type

下载: 全尺寸图片幻灯片

图 12 锁销四点接触模型及几何参数

Figure 12. Four-point contact model and geometric parameters of locking pin

下载: 全尺寸图片幻灯片

图 13 四点接触时不同间隙下的力矩-转角关系曲线

Figure 13. Moment vs. rotation angle curve under different clearances for four-point contact type

下载: 全尺寸图片幻灯片

图 14 四点接触时不同间隙下的力矩-刚度关系曲线

Figure 14. Moment vs. rotation connection stiffness curve under different clearances for four-point contact type

下载: 全尺寸图片幻灯片

表 1 不同载荷下的支反力理论值与试验值

Table 1. Theoretical and experimental values of the support reaction force under different loads

η	F_R1 （P_lad=111.13 N）			F_R1 （P_lad=444.52 N）			F_R2 （P_lad=111.13 N）			F_R2 （P_lad=444.52 N）
η	F_R1T/N	F_R1E/N	ε/%	F_R1T/N	F_R1E/N	ε/%	F_R2T/ N	F_R2E/N	ε/%	F_R2T/N	F_R2E/N	ε/%
0.13	190.92	188.01	1.55	528.50	526.04	0.47	21.14	20.19	4.72	40.50	37.00	9.46
0.25	195.08	188.54	3.47	528.48	526.67	0.34	28.34	22.92	23.67	62.57	58.86	6.31
0.38	195.15	193.31	0.95	528.49	522.06	1.23	33.89	32.47	4.38	84.66	80.60	5.04
0.50	184.99	189.95	−2.61	501.04	520.52	−3.74	35.31	37.15	−4.96	95.65	106.12	−9.86
0.62	183.71	187.31	−1.92	528.59	516.84	2.27	40.31	37.50	7.50	128.86	121.87	5.74
0.75	182.24	188.50	−3.32	489.41	508.11	−3.68	45.24	47.62	−5.00	135.11	145.17	−6.93

下载: 导出CSV

表 2 三点接触时不同载荷和间隙下的连接刚度

Table 2. Connection stiffness under different loads and clearances for three-point contact type

N·m/rad
M/（N·m）	间隙d_c/mm
M/（N·m）	0.4	0.8	1.2	1.6	2.0
20	135793	134629	133371	132009	130537
23	136496	135328	134064	132697	131220
26	137119	135946	134677	133306	131825
29	137678	136501	135228	133853	132367
32	138185	137004	135728	134350	132860
35	138650	137466	136187	134805	133312
38	139079	137892	136609	135224	133728
41	139478	138288	137002	135614	134116
44	139850	138657	137369	135979	134477
47	140199	139004	137714	136321	134817
50	140528	139331	138038	136643	135136

下载: 导出CSV

表 3 四点接触时不同载荷和间隙下的连接刚度

Table 3. Connection stiffness under different loads and clearances for four-point contact type

N·m/rad
M/（N·m）	间隙d_c/mm
M/（N·m）	0.4	0.8	1.2	1.6	2.0
20	14027	13320	12493	11479	10171
23	14107	13419	12587	11590	10266
26	14215	13506	12680	11669	10345
29	14299	13580	12756	11750	10419
32	14371	13656	12824	11820	10486
35	14437	13722	12893	11883	10547
38	14498	13783	12954	11942	10603
41	14556	13840	13010	11997	10656
44	14609	13893	13062	12049	10705
47	14659	13943	13111	12097	10752
50	14707	13990	13158	12143	10796

下载: 导出CSV

参考文献(40)

[1]	YARYGINA M V,POPOV Y I. Development of the weight formula for a folding wing[J]. Russian Aeronautics,2012,55(2): 120-126. doi: 10.3103/S106879981202002X
[2]	DI CAPRIO F,SCIGLIANO R,FAUCI R,et al. Design optimization of interfacing attachments for the deployable wing of an unmanned re-entry vehicle[J]. Algorithms,2021,14(5): 141. doi: 10.3390/a14050141
[3]	宋慧心,金磊. 折叠翼飞行器的动力学建模与稳定控制[J]. 力学学报,2020,52(6): 1548-1559. doi: 10.6052/0459-1879-20-115 SONG Huixin,JIN Lei. Dynamic modeling and stability control of folding wing aircraft[J]. Chinese Journal of Theoretical and Applied Mechanics,2020,52(6): 1548-1559. (in Chinese) doi: 10.6052/0459-1879-20-115
[4]	SOFLA A Y N,MEGUID S A,TAN K T,et al. Shape morphing of aircraft wing: status and challenges[J]. Materials & Design,2010,31(3): 1284-1292.
[5]	张立启,岳承宇,赵永辉. 变后掠翼的参变气动弹性建模与分析[J]. 力学学报,2021,53(11): 3134-3146. doi: 10.6052/0459-1879-21-275 ZHANG Liqi,YUE Chengyu,ZHAO Yonghui. Parameter-varying aeroelastic modeling and analysis for a variable-sweep wing[J]. Chinese Journal of Theoretical and Applied Mechanics,2021,53(11): 3134-3146. (in Chinese) doi: 10.6052/0459-1879-21-275
[6]	刘芳,丁千. 含间隙折叠舵面的主共振响应分析[J]. 航空动力学报,2016,31(12): 2965-2971. doi: 10.13224/j.cnki.jasp.2016.12.019 LIU Fang,DING Qian. Primary resonance response analysis on folding rudder with gaps[J]. Journal of Aerospace Power,2016,31(12): 2965-2971. (in Chinese) doi: 10.13224/j.cnki.jasp.2016.12.019
[7]	YANG Ning,WANG Nan,ZHANG Xin,et al. Nonlinear flutter wind tunnel test and numerical analysis of folding fins with freeplay nonlinearities[J]. Chinese Journal of Aeronautics,2016,29(1): 144-159. doi: 10.1016/j.cja.2015.12.011
[8]	王强,马志赛,张欣,等. 基于模态综合法的含间隙折叠舵面动态特性分析[J]. 航空学报,2020,41(5): 223507. WANG Qiang,MA Zhisai,ZHANG Xin,et al. Dynamic characteristic analysis for a folding fin with freeplay nonlinearities based on mode synthesis method[J]. Acta Aeronautica et Astronautica Sinica,2020,41(5): 223507. (in Chinese)
[9]	MENGA E, HERNANDEZ S, MOLEDO S, et al. Nonlinear dynamic analysis of assembled aircraft structures with concentrated nonlinearities[R]. Saint Petersburg, Russia: 16th International Forum on Aeroelasticity and Structural Dynamics, 2015.
[10]	赵广,王永泉,赵向阳,等. 盘鼓螺栓连接结构接触刚度建模与应用检验[J]. 航空动力学报,2022,37(1): 76-86. doi: 10.13224/j.cnki.jasp.20210065 ZHAO Guang,WANG Yongquan,ZHAO Xiangyang,et al. Modeling and application test of contact stiffness of bolt connection structure of disk and drum[J]. Journal of Aerospace Power,2022,37(1): 76-86. (in Chinese) doi: 10.13224/j.cnki.jasp.20210065
[11]	黄俊,宋保江,宫钇成,等. 锁销位置对折叠翼固有振动特性的影响分析[J]. 导弹与航天运载技术,2018(6): 14-18. HUANG Jun,SONG Baojiang,GONG Yicheng,et al. Impacts of the pin position on inherent vibration characteristics of a folding wing[J]. Missiles and Space Vehicles,2018(6): 14-18. (in Chinese)
[12]	AHLQUIST J R, CARREÑO J M, CLIMENT H, et al. Assessment of nonlinear structural response in A400M GVT[C]//Structural Dynamics: Volume 3. New York, US: Springer, 2011: 1147-1155.
[13]	LAXALDE D,THOUVEREZ F. Complex non-linear modal analysis for mechanical systems: application to turbomachinery bladings with friction interfaces[J]. Journal of Sound and Vibration,2009,322(4/5): 1009-1025.
[14]	BOGRAD S,REUSS P,SCHMIDT A,et al. Modeling the dynamics of mechanical joints[J]. Mechanical Systems and Signal Processing,2011,25(8): 2801-2826. doi: 10.1016/j.ymssp.2011.01.010
[15]	MOUSAKHANI M,THOENI K,FITYUS S,et al. A novel and robust contact detection algorithm for arbitrarily shaped blocks[J]. Computers and Geotechnics,2021,140: 104430. doi: 10.1016/j.compgeo.2021.104430
[16]	MAYER M H,GAUL L. Segment-to-segment contact elements for modelling joint interfaces in finite element analysis[J]. Mechanical Systems and Signal Processing,2007,21(2): 724-734. doi: 10.1016/j.ymssp.2005.10.006
[17]	缪辉,臧朝平,罗欣洋,等. 基于薄层单元的拉杆转子接触界面动力学建模及修正[J]. 航空动力学报,2019,34(9): 1927-1935. doi: 10.13224/j.cnki.jasp.2019.09.009 MIAO Hui,ZANG Chaoping,LUO Xinyang,et al. Dynamic modeling and updating for contact interface of rod fastening rotor based on thin-layer element[J]. Journal of Aerospace Power,2019,34(9): 1927-1935. (in Chinese) doi: 10.13224/j.cnki.jasp.2019.09.009
[18]	LACAYO R M,ALLEN M S. Updating structural models containing nonlinear Iwan joints using quasi-static modal analysis[J]. Mechanical Systems and Signal Processing,2019,118: 133-157. doi: 10.1016/j.ymssp.2018.08.034
[19]	HU Wei,YANG Zhichun,GU Yingsong. Aeroelastic study for folding wing during the morphing process[J]. Journal of Sound and Vibration,2016,365: 216-229. doi: 10.1016/j.jsv.2015.11.043
[20]	CASTRICHINI A,HODIGERE SIDDARAMAIAH V,CALDERON D E,et al. Nonlinear folding wing tips for gust loads alleviation[J]. Journal of Aircraft,2016,53(5): 1391-1399. doi: 10.2514/1.C033474
[21]	ATTAR P J,TANG Deman,DOWELL E H. Nonlinear aeroelastic study for folding wing structures[J]. AIAA Journal,2010,48(10): 2187-2195. doi: 10.2514/1.44868
[22]	LEE B H K,TRON A. Effects of structural nonlinearities on flutter characteristics of the CF-18 aircraft[J]. Journal of Aircraft,1989,26(8): 781-786. doi: 10.2514/3.45839
[23]	王博,马志赛,丁千,等. 基础激励下含间隙折叠舵面非线性系统辨识[J]. 振动与冲击,2020,39(4): 122-128, 135. doi: 10.13465/j.cnki.jvs.2020.04.015 WANG Bo,MA Zhisai,DING Qian,et al. System identification of folding rudders with freeplay nonlinearity under base excitation[J]. Journal of Vibration and Shock,2020,39(4): 122-128, 135. (in Chinese) doi: 10.13465/j.cnki.jvs.2020.04.015
[24]	何昊南,于开平,唐宏,等. 有间隙折叠舵面的振动实验与非线性建模研究[J]. 力学学报,2019,51(5): 1476-1488. doi: 10.6052/0459-1879-19-119 HE Haonan,YU Kaiping,TANG Hong,et al. Vibration experiment and nonlinear modelling research on the folding fin with freeplay[J]. Chinese Journal of Theoretical and Applied Mechanics,2019,51(5): 1476-1488. (in Chinese) doi: 10.6052/0459-1879-19-119
[25]	HE Haonan,TANG Hong,YU Kaiping,et al. Nonlinear aeroelastic analysis of the folding fin with freeplay under thermal environment[J]. Chinese Journal of Aeronautics,2020,33(9): 2357-2371. doi: 10.1016/j.cja.2020.05.005
[26]	NOËL J P,KERSCHEN G. Nonlinear system identification in structural dynamics: 10 more years of progress[J]. Mechanical Systems and Signal Processing,2017,83: 2-35. doi: 10.1016/j.ymssp.2016.07.020
[27]	张静,郭宏伟,刘荣强,等. 铰链对含铰结构非线性动力学特性影响分析[J]. 航空学报,2014,35(5): 1433-1445. ZHANG Jing,GUO Hongwei,LIU Rongqiang,et al. Influence analysis of joints on nonlinear dynamic characteristics of articulated structures[J]. Acta Aeronautica et Astronautica Sinica,2014,35(5): 1433-1445. (in Chinese)
[28]	GUO J,RANDALL R B,BORGHESANI P,et al. A study on the effects of piston secondary motion in conjunction with clearance joints[J]. Mechanism and Machine Theory,2020,149: 103824. doi: 10.1016/j.mechmachtheory.2020.103824
[29]	XIANG W,YAN Shaoze,WU Jianing. Dynamic analysis of planar mechanical systems considering stick-slip and Stribeck effect in revolute clearance joints[J]. Nonlinear Dynamics,2019,95(1): 321-341. doi: 10.1007/s11071-018-4566-6
[30]	PI Ting,ZHANG Yunqing. Simulation of planar mechanisms with revolute clearance joints using the multipatch based isogeometric analysis[J]. Computer Methods in Applied Mechanics and Engineering,2019,343: 453-489. doi: 10.1016/j.cma.2018.08.039
[31]	ZHUANG Fangfang,WANG Qi. Modeling and analysis of rigid multibody systems with driving constraints and frictional translation joints[J]. Acta Mechanica Sinica,2014,30(3): 437-446. doi: 10.1007/s10409-014-0021-1
[32]	ZHANG Jie,WANG Qi. Modeling and simulation of a frictional translational joint with a flexible slider and clearance[J]. Multibody System Dynamics,2016,38(4): 367-389. doi: 10.1007/s11044-015-9474-7
[33]	LIU Cheng,TIAN Qiang,HU Haiyan. Dynamics and control of a spatial rigid-flexible multibody system with multiple cylindrical clearance joints[J]. Mechanism and Machine Theory,2012,52: 106-129. doi: 10.1016/j.mechmachtheory.2012.01.016
[34]	CIRELLI M,VALENTINI P P,PENNESTRÌ E. A study of the non-linear dynamic response of spur gear using a multibody contact based model with flexible teeth[J]. Journal of Sound and Vibration,2019,445: 148-167. doi: 10.1016/j.jsv.2019.01.019
[35]	ROARK R J, YOUNG W C. Formulas for stress and strain[M]. New York, US: McGraw-Hill, 1975.
[36]	SINHA P R. A contact stress model for determining forces in an equilibrium grasp[D]. Philadelphia, US: University of Pennsylvania, 1989: 1-59.
[37]	UGRAY Z,LASDON L,PLUMMER J,et al. Scatter search and local NLP solvers: a multistart framework for global optimization[J]. INFORMS Journal on Computing,2007,19(3): 328-340. doi: 10.1287/ijoc.1060.0175
[38]	GILAT A. MATLAB: an introduction with applications[M]. 4th ed. Hoboken, NJ: John Wiley & Sons, 2011.
[39]	单辉祖. 材料力学: Ⅱ[M]. 3版. 北京: 高等教育出版社, 2010
[40]	SILVERMAN M P. Reaction forces on a fixed ladder in static equilibrium: analysis and definitive experimental test of the ladder problem[J]. World Journal of Mechanics,2018,8(9): 311-342. doi: 10.4236/wjm.2018.89024