锥形可展桁架的设计与分析
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摘要
在太空探索和空间站的建设中,由于受到发射器空间的限制,航天设备不可能都是以展开的状态发射到太空中,所以随着航天科技的进步,可展机构得到前所未有的发展机遇,并且在许多地方得到了实际的应用。可展机构是一类能够从折叠状态变化到展开状态,并能够形成稳定结构而承受一定载荷的机构。相对其它可展机构,空间可展桁架虽然结构比较简单,但在大型空间结构中具有更广泛的应用价值,如用于展开柔性太阳能帆板、支撑太空望远镜及合成孔径雷达等。空间可展桁架要求具有高刚性、高可靠性、大的折叠比和尽量小的质量。目前对于可展桁架的研究都是集中于等截面桁架,本课题提出一种新颖的锥形可展桁架,同等质量情况下具有更好机械性能,对于推动可展桁架的发展具有一定的意义。
由于可展桁架可以转换为连续梁等效模型,本文首先分析比较了锥形梁和等截面梁的强度、刚度性能,提出设计锥形可展桁架的可行性。对锥形可展桁架进行了构型设计和驱动设计,分析了锥形可展桁架的展开折叠机理。
考虑到机构的复杂性,应用螺旋理论分析了单自由度锥形可展桁架的运动度,证明了单自由度可展桁架设计的正确性。利用机构综合理论,提出三自由度可展桁架的机构方案。分析了锥形可展桁架所必须满足的几何条件和折叠率等,并提出多种锥形可展桁架的设计方案。
锥形可展桁架的各个杆件的截面面积、桁架锥度等参数对桁架性能影响很大,且不易直接观察,对其优化分析可以使桁架获得最优性能。首先建立优化数学模型,然后应用有限元分析软件ANSYS参数化设计语言APDL对桁架参数化建模并进行优化分析,得出优化结果。分别比较等刚度和等质量情况下锥形可展桁架可等截面桁架的相关性能,证明了锥形可展桁架可以获得较高的质量刚度比。分析了锥形可展桁架的模态性能,得出桁架的固有频率和对应的振型,航天器的控制频率应当避开桁架的固有频率,以免发生共振。
建立单自由度可展桁架实体模型,应用ADAMS对其进行运动学分析,说明了桁架的展开过程,并得到桁架展开时的位移、速度、加速度曲线。对三自由度锥形可展桁架进行运动学分析,并用MATLAB获得仿真结果。
In the activity of space exploration and space station construction, equipments can not be all launched into aerospace in deployed status as the limit of rocket’s carrying capacity. Deployable structures obtain unprecedented development opportunities and have been widely applied in many areas with the advancement of related space technology. Deployable structure is the broad category of prefabricated structures that can be transformed from a closed compact or folded configuration to a predetermined expanded form of a complete stable structure capable of supporting loads. Space deployable truss is one kind of deployable structures that has simpler mechanical structure relative to other deployable structures and it is always used in large space structures. It is usually used as support structures of solar panels, space telescope and synthetic aperture radar, etc. The main technique requirements of deployable truss are high rigidity, high reliability, large stowage ratio and light weight. Current researches on space trusses are focusing on the kind of identical cross section. In this paper, a kind of truss that has tapering cross section is proposed. Tapered truss performs more excellent mechanical characters compared to normal truss. This issue will promote the development of deployable truss in a certain degree.
As deployable truss can be converted to the equivalent beam model, this paper first analyzes and compares the strength and stiffness performance of tapered beam and normal beam. Then the feasibility of tapered deployable truss is discussed. Configuration and driving mechanism of developable module is devised. The extending or retracting principle of tapered mast is briefly depicted. Taking the complexity of 1-DOF (degree of freedom) tapered deployable truss into account, screw theory is adopted to analyze the degree of freedom, and the mobility is also pointed out. The result proves this design is correct. Using mechanism synthesis theory, a 3-DOF tapered deployable truss is brought out. Geometry conditions this mechanism must satisfy and stowage radio is derived.
The performance of tapered deployable truss is significantly affected by cross sectional area of bars, taper of truss, etc. And it is not intuitive. Optimization analysis can make truss obtain optimum performance. After establishing optimal mathematical model, Parametric Design Language APDL of finite element analysis software ANSYS is used to model and optimize the truss. Comparison of tapered truss and consistent-cross-sectional truss on equal mass or stiffness is then implemented. The result shows that tapered truss can have higher quality truss stiffness ratio. Through modal analysis, natural frequencies and corresponding vibration mode of truss is acquired. The control frequency of spacecraft should avoid the natural frequencies of truss in order to avoid resonance. Solid model of 1-DOF tapered deployment truss is founded and kinematics analysis is analyzed with multi-system dynamic analysis software ADAMS. The simulation result gives the deployment process and displacement, velocity, acceleration curves of truss when extending. Kinematics analysis of 3-DOF tapered deployment truss is executed and the simulation results are acquired with MATLAB.
由于可展桁架可以转换为连续梁等效模型,本文首先分析比较了锥形梁和等截面梁的强度、刚度性能,提出设计锥形可展桁架的可行性。对锥形可展桁架进行了构型设计和驱动设计,分析了锥形可展桁架的展开折叠机理。
考虑到机构的复杂性,应用螺旋理论分析了单自由度锥形可展桁架的运动度,证明了单自由度可展桁架设计的正确性。利用机构综合理论,提出三自由度可展桁架的机构方案。分析了锥形可展桁架所必须满足的几何条件和折叠率等,并提出多种锥形可展桁架的设计方案。
锥形可展桁架的各个杆件的截面面积、桁架锥度等参数对桁架性能影响很大,且不易直接观察,对其优化分析可以使桁架获得最优性能。首先建立优化数学模型,然后应用有限元分析软件ANSYS参数化设计语言APDL对桁架参数化建模并进行优化分析,得出优化结果。分别比较等刚度和等质量情况下锥形可展桁架可等截面桁架的相关性能,证明了锥形可展桁架可以获得较高的质量刚度比。分析了锥形可展桁架的模态性能,得出桁架的固有频率和对应的振型,航天器的控制频率应当避开桁架的固有频率,以免发生共振。
建立单自由度可展桁架实体模型,应用ADAMS对其进行运动学分析,说明了桁架的展开过程,并得到桁架展开时的位移、速度、加速度曲线。对三自由度锥形可展桁架进行运动学分析,并用MATLAB获得仿真结果。
In the activity of space exploration and space station construction, equipments can not be all launched into aerospace in deployed status as the limit of rocket’s carrying capacity. Deployable structures obtain unprecedented development opportunities and have been widely applied in many areas with the advancement of related space technology. Deployable structure is the broad category of prefabricated structures that can be transformed from a closed compact or folded configuration to a predetermined expanded form of a complete stable structure capable of supporting loads. Space deployable truss is one kind of deployable structures that has simpler mechanical structure relative to other deployable structures and it is always used in large space structures. It is usually used as support structures of solar panels, space telescope and synthetic aperture radar, etc. The main technique requirements of deployable truss are high rigidity, high reliability, large stowage ratio and light weight. Current researches on space trusses are focusing on the kind of identical cross section. In this paper, a kind of truss that has tapering cross section is proposed. Tapered truss performs more excellent mechanical characters compared to normal truss. This issue will promote the development of deployable truss in a certain degree.
As deployable truss can be converted to the equivalent beam model, this paper first analyzes and compares the strength and stiffness performance of tapered beam and normal beam. Then the feasibility of tapered deployable truss is discussed. Configuration and driving mechanism of developable module is devised. The extending or retracting principle of tapered mast is briefly depicted. Taking the complexity of 1-DOF (degree of freedom) tapered deployable truss into account, screw theory is adopted to analyze the degree of freedom, and the mobility is also pointed out. The result proves this design is correct. Using mechanism synthesis theory, a 3-DOF tapered deployable truss is brought out. Geometry conditions this mechanism must satisfy and stowage radio is derived.
The performance of tapered deployable truss is significantly affected by cross sectional area of bars, taper of truss, etc. And it is not intuitive. Optimization analysis can make truss obtain optimum performance. After establishing optimal mathematical model, Parametric Design Language APDL of finite element analysis software ANSYS is used to model and optimize the truss. Comparison of tapered truss and consistent-cross-sectional truss on equal mass or stiffness is then implemented. The result shows that tapered truss can have higher quality truss stiffness ratio. Through modal analysis, natural frequencies and corresponding vibration mode of truss is acquired. The control frequency of spacecraft should avoid the natural frequencies of truss in order to avoid resonance. Solid model of 1-DOF tapered deployment truss is founded and kinematics analysis is analyzed with multi-system dynamic analysis software ADAMS. The simulation result gives the deployment process and displacement, velocity, acceleration curves of truss when extending. Kinematics analysis of 3-DOF tapered deployment truss is executed and the simulation results are acquired with MATLAB.
引文
1韦娟芳.空间4~10米可展开天线的动力耦合分析及实验技术研究.浙江大学博士学位论文. 2002:1~15
2 Gunnar Tibert. Deployable Tensegrity Structures for Space Applications. Royal Institute of Technology, Doctoral Dissertation. 2002:1~6
3刘荣强,郭宏伟,邓宗全.空间索杆铰接式伸展臂设计与实验研究.宇航学报. 2009, 30(1):315~320
4陈务军,董石麟.空间展开折叠结构设计分析理论与应用技术研究.上海交通大学博士后论文集粹. 2000:103~116
5关富玲,陈务军.国内外可展天线最新研究进展.浙江大学空间结构研究室. 1996
6 Freeland R E. Survey of Deployable Antenna Concepts—Large Space Antenna Systems Technology. NASA-2269, PartΙ. 1983:381~421
7 John M Hedgepeth. Primary Requirements for Large Space Structures. 2nd AIAA Conf. on Large Space Platforms. 1981
8杨玉龙.空间展开桁架结构设计理论与热控制研究.浙江大学博士学位论文. 2007:1~12
9 Jing-Shan Zhao, Fulei Chu, Zhi-Jing Feng. The Mechanism Theory and Application of Deployable Structures Based on SLE. Mechanism and Machine Theory. 2009, 44(2):324~335
10 G.E.B Tan, S. Pellegrion. Nonlinear Vibration of Cable-stiffened Pantographic Deployable Structures. J. of Sound and Vibration. 2008, 314(3-5):783~802
11 Jin Mitsugi, Kazuhide Ando, Yumi Senbokuya, et al. Deployment Analysis of Large Space Antenna Using Flexible Multibody Dynamics Simulation. Acta Astronautica. 2000, 47(1):19~26
12 (O|¨)mer Soykasap. Deployment Analysis of a Self-deployable Composition boom. J. of Composite Structures. 2009, 89(3):374~381
13 A.V. Lopatin, E.V. Morozov. Modal Analysis of the Thin-walled Composite Spoke of an Umbrella-type Deployable Space antenna. J. of Composite Structures. 2009, 88(1):46~55
14 Johanne C. Heald. Deployment Repeatability in Mechanically Jointed Precision Structures. University of Colorado, Doctoral Dissertation, Report No:CU-CAS-03-06
15 Jennifer A. Dooley, Peter R. Lawson. Technology Plan for the Terrestrial Planet Finder Coronagraph. JPL Publication, Technical Report. 2005:5~8
16 Pellegrino S. Large Retractable Appendages in Spacecraft. J. of Spacecraft and Rockets. 1995, 32(6):1006~1014
17 Miura K, Natori M, et al. Simplex Mast: An Extendible for Space Application. Proc. 14th International Symp. on Space Technology & Science. Tokyo. 1984:357~362
18 Michael E. Mceachen, Thomas A. Trautt and David M. Murphy. SALT: Senond-oder Augmentation of Lattice Trusses. AIAA-2004-1729
19 Thomas W. Murphey. A Material Structural Performance Index for Strain Based Deployable Trusses. AIAA-2004-1656
20 J. Winter, G. Spanjers, D. Cohen. Deployable Structures Mission in Medium Earth Orbit. Proceedings of 2005 IEEE Aerospace Conference. 2005:564~574
21 Thomas W. Murphey, Jason D. Hinkle. Some Performance Trends in Hierarchical Truss Structures. AIAA-2003-1903
22 Eiden M, Brunner O, et al. Deployable Analysis of Olympus Astromast and Comparison with Test Measurements. Journal of Spacecraft & Rocket. 1987, 24(1):63~83
23 Takayuki K, Kakuma Okazaki. Deployment of a "Hingless Mast" and Its Application. Acta Astronautica. 1998, 17(3):341~346
24张淑杰.空间可展桁架结构的设计与热分析.浙江大学博士学位论文. 2001:1~22
25 Kwan, A. S. K. A Pantographic Deployable Mast. PhD Thesis, University of Cambridge, UK, 1991
26 John F. Shaker. Static Stability of a Three-dimensional Space Truss. Proceedings of the XIII Space Photovoltaic Research and Technology Conference. NASA CP-3278, 1994
27 Takayuki Kitamura, Michihiro Natori, et al. Development of a High Stiffness Extendible and Retractable Mast "HIMAT" for Space Application. AIAA-90-1054-CP
28张淑杰.空间实验室半刚性太阳电池阵展开机构设计及热—结构耦合分析.上海航天技术研究院. 2004
29 Takayuki Kitamura. Development of Extendible Beams for Space Application. AIAA-93-0977
30 Dalia A. Mc Watters, George Lutes, Edward R. Caro. Optical Calibration Phase Locked Loop for the Shuttle Radar Topography Mission. IEEE Transactions on Instrumentation and Measurement. 2001, 50(1):40~46
31 Brown Jr., Charles G, Sarabandi Kamal, el at. Validation of the Shuttle Radar Topography Mission Height Data. IEEE Transactions on Geoscience and Remote Sensing. 2005, 43(8):1707~1715
32 AEC-Able Engineering Company. http://www.aec-able.com
33苏斌,关富玲,石卫华,等.索杆式伸展臂的结构设计与分析.工程设计学报. 2003, 10(10):287~294
34 K. Miura, H. Furuya, K. Suzuki. Variable Geometry Truss and Its Application to Deployable Truss and Space Crane Arm. Acta Astronautica. 1985, 12(7-8):599~607
35 Kwan, A. S. K., You Z, Pellegrino S. Active and Passive Cable Elements in Deployable/Retractable Masts. J. of Space Structures. 1993, 8(1-2):29~40
36 Chen Wujun, Guan Fuling, et al. Design and Analysis of a Deployable/Retractable Space Mast. J. of IASS. 1998, 39(2):111~116
37张淑杰,李瑞祥,丁同才.盘绕式杆状展开机构的设计与力学分析.力学季刊. 2006, 27(2):341~347
38陈务军,张淑杰.空间可展结构体系与分析导论.中国宇航出版社. 2006:13~41
39杨治,关富玲,杨大彬.索杆式伸展臂分析与设计.机械. 2005, (1):9~11
40苏斌,关富玲,杨大彬,等.索杆式伸展臂的展开驱动设计与动力学分析.空间科学学报. 2004, 24(4):312~320
41刘荣强,郭宏伟,邓宗全.空间铰接式伸展臂一般设计方法研究.中国空间科学学会空间机电与空间光学专业委员会2008年学术年会. 2008:73~77
42郭宏伟,刘荣强,邓宗全,罗昌杰.空间索杆式伸展臂展开过程动力学分析与仿真.机械设计. 2008, 25(7):31~35
43郭宏伟,刘荣强,邓宗全.空间索杆铰接式伸展臂性能参数分析与设计.北京航空航天大学学报. 2008, 34(10):1186~1190
44陈务军.空间展开桁架结构设计原理与展开动力学分析理论研究.浙江大学博士学位论文. 1998:1~25
45郭宏伟.索杆铰接式伸展臂及动力学特性研究.哈尔滨工业大学博士学位论文. 2009:57~70
46陈务军,董石麟,付功义,关富玲.高刚性同步展开空间伸展臂设计研究. 2000年中国博士后学术大会论文集机械与仪表分册. 2000: 391~39
47 Ball R.S. Theory of Screws. England. Cambridge University Press. 1900
48黄真.基于约束螺旋理论的自由度简易计算方法.全国印刷、包装机械凸轮、连杆机构学术研讨会暨第6届全国凸轮机构学术年会. 2005:36~45
49严云.基于ANSYS参数化设计语言的结构优化设计.华东交通大学学报. 2004, 21(4):52~55
2 Gunnar Tibert. Deployable Tensegrity Structures for Space Applications. Royal Institute of Technology, Doctoral Dissertation. 2002:1~6
3刘荣强,郭宏伟,邓宗全.空间索杆铰接式伸展臂设计与实验研究.宇航学报. 2009, 30(1):315~320
4陈务军,董石麟.空间展开折叠结构设计分析理论与应用技术研究.上海交通大学博士后论文集粹. 2000:103~116
5关富玲,陈务军.国内外可展天线最新研究进展.浙江大学空间结构研究室. 1996
6 Freeland R E. Survey of Deployable Antenna Concepts—Large Space Antenna Systems Technology. NASA-2269, PartΙ. 1983:381~421
7 John M Hedgepeth. Primary Requirements for Large Space Structures. 2nd AIAA Conf. on Large Space Platforms. 1981
8杨玉龙.空间展开桁架结构设计理论与热控制研究.浙江大学博士学位论文. 2007:1~12
9 Jing-Shan Zhao, Fulei Chu, Zhi-Jing Feng. The Mechanism Theory and Application of Deployable Structures Based on SLE. Mechanism and Machine Theory. 2009, 44(2):324~335
10 G.E.B Tan, S. Pellegrion. Nonlinear Vibration of Cable-stiffened Pantographic Deployable Structures. J. of Sound and Vibration. 2008, 314(3-5):783~802
11 Jin Mitsugi, Kazuhide Ando, Yumi Senbokuya, et al. Deployment Analysis of Large Space Antenna Using Flexible Multibody Dynamics Simulation. Acta Astronautica. 2000, 47(1):19~26
12 (O|¨)mer Soykasap. Deployment Analysis of a Self-deployable Composition boom. J. of Composite Structures. 2009, 89(3):374~381
13 A.V. Lopatin, E.V. Morozov. Modal Analysis of the Thin-walled Composite Spoke of an Umbrella-type Deployable Space antenna. J. of Composite Structures. 2009, 88(1):46~55
14 Johanne C. Heald. Deployment Repeatability in Mechanically Jointed Precision Structures. University of Colorado, Doctoral Dissertation, Report No:CU-CAS-03-06
15 Jennifer A. Dooley, Peter R. Lawson. Technology Plan for the Terrestrial Planet Finder Coronagraph. JPL Publication, Technical Report. 2005:5~8
16 Pellegrino S. Large Retractable Appendages in Spacecraft. J. of Spacecraft and Rockets. 1995, 32(6):1006~1014
17 Miura K, Natori M, et al. Simplex Mast: An Extendible for Space Application. Proc. 14th International Symp. on Space Technology & Science. Tokyo. 1984:357~362
18 Michael E. Mceachen, Thomas A. Trautt and David M. Murphy. SALT: Senond-oder Augmentation of Lattice Trusses. AIAA-2004-1729
19 Thomas W. Murphey. A Material Structural Performance Index for Strain Based Deployable Trusses. AIAA-2004-1656
20 J. Winter, G. Spanjers, D. Cohen. Deployable Structures Mission in Medium Earth Orbit. Proceedings of 2005 IEEE Aerospace Conference. 2005:564~574
21 Thomas W. Murphey, Jason D. Hinkle. Some Performance Trends in Hierarchical Truss Structures. AIAA-2003-1903
22 Eiden M, Brunner O, et al. Deployable Analysis of Olympus Astromast and Comparison with Test Measurements. Journal of Spacecraft & Rocket. 1987, 24(1):63~83
23 Takayuki K, Kakuma Okazaki. Deployment of a "Hingless Mast" and Its Application. Acta Astronautica. 1998, 17(3):341~346
24张淑杰.空间可展桁架结构的设计与热分析.浙江大学博士学位论文. 2001:1~22
25 Kwan, A. S. K. A Pantographic Deployable Mast. PhD Thesis, University of Cambridge, UK, 1991
26 John F. Shaker. Static Stability of a Three-dimensional Space Truss. Proceedings of the XIII Space Photovoltaic Research and Technology Conference. NASA CP-3278, 1994
27 Takayuki Kitamura, Michihiro Natori, et al. Development of a High Stiffness Extendible and Retractable Mast "HIMAT" for Space Application. AIAA-90-1054-CP
28张淑杰.空间实验室半刚性太阳电池阵展开机构设计及热—结构耦合分析.上海航天技术研究院. 2004
29 Takayuki Kitamura. Development of Extendible Beams for Space Application. AIAA-93-0977
30 Dalia A. Mc Watters, George Lutes, Edward R. Caro. Optical Calibration Phase Locked Loop for the Shuttle Radar Topography Mission. IEEE Transactions on Instrumentation and Measurement. 2001, 50(1):40~46
31 Brown Jr., Charles G, Sarabandi Kamal, el at. Validation of the Shuttle Radar Topography Mission Height Data. IEEE Transactions on Geoscience and Remote Sensing. 2005, 43(8):1707~1715
32 AEC-Able Engineering Company. http://www.aec-able.com
33苏斌,关富玲,石卫华,等.索杆式伸展臂的结构设计与分析.工程设计学报. 2003, 10(10):287~294
34 K. Miura, H. Furuya, K. Suzuki. Variable Geometry Truss and Its Application to Deployable Truss and Space Crane Arm. Acta Astronautica. 1985, 12(7-8):599~607
35 Kwan, A. S. K., You Z, Pellegrino S. Active and Passive Cable Elements in Deployable/Retractable Masts. J. of Space Structures. 1993, 8(1-2):29~40
36 Chen Wujun, Guan Fuling, et al. Design and Analysis of a Deployable/Retractable Space Mast. J. of IASS. 1998, 39(2):111~116
37张淑杰,李瑞祥,丁同才.盘绕式杆状展开机构的设计与力学分析.力学季刊. 2006, 27(2):341~347
38陈务军,张淑杰.空间可展结构体系与分析导论.中国宇航出版社. 2006:13~41
39杨治,关富玲,杨大彬.索杆式伸展臂分析与设计.机械. 2005, (1):9~11
40苏斌,关富玲,杨大彬,等.索杆式伸展臂的展开驱动设计与动力学分析.空间科学学报. 2004, 24(4):312~320
41刘荣强,郭宏伟,邓宗全.空间铰接式伸展臂一般设计方法研究.中国空间科学学会空间机电与空间光学专业委员会2008年学术年会. 2008:73~77
42郭宏伟,刘荣强,邓宗全,罗昌杰.空间索杆式伸展臂展开过程动力学分析与仿真.机械设计. 2008, 25(7):31~35
43郭宏伟,刘荣强,邓宗全.空间索杆铰接式伸展臂性能参数分析与设计.北京航空航天大学学报. 2008, 34(10):1186~1190
44陈务军.空间展开桁架结构设计原理与展开动力学分析理论研究.浙江大学博士学位论文. 1998:1~25
45郭宏伟.索杆铰接式伸展臂及动力学特性研究.哈尔滨工业大学博士学位论文. 2009:57~70
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