月球着陆器着陆过程的DEM-FEM耦合分析
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摘要
实现月球着陆器的安全软着陆是宇航员、搭载设备、仪器安全以及着陆器后续正常工作的重要保证.论文采用离散元-有限元方法建立月壤与着陆器相互作用的耦合模型,其中月壤采用具有粘结作用的球体离散元单元,着陆器采用壳单元和梁单元组合的有限元模型,与缓冲垫连接的支撑腿采用可压缩弹簧模型,以实现着陆器自身的缓冲功能;为分析着陆于不同月表的过程,建立平坦、斜坡月球表面;针对不同坡度的斜坡月表,研究不同着陆模式下着陆器与月壤的相互作用,分析冲击力峰值的大小与作用时间的关系,并从能量方面讨论和解释大坡度下冲击力峰值小的原因.以上研究为月球着陆器的安全着陆分析提供有益的参考.
The safe landing of a lunar lander is a major guarantee for the safety of astronauts and the carrying equipment and instrument,as well as the subsequent operation of the lander.Studying the landing process of the lunar lander is important for achieving safe landing.In this study,a model coupling the discrete element method(DEM)and the finite element method(FEM)is set up to analyze the interactions between the lunar soil and the lander.In this coupled model,the lunar soil is modeled by discrete spherical elements with bond capacity.The lander is constructed with a combined finite element model consisting of shell elements and beam elements.Meanwhile,a compressible spring model is used for the supporting legs connected with the cushion to realize the buffer capacity.In order to analyze the landing process on various lunar surfaces,different flat and sloped lunar surfaces are simulated,and the interactions between the lander and the lunar soil in different landing modes are studied.Studies have shown that during landing,the impact strength of the lander structure decreases with an increase in slope.When the lander landed on the lunar surface in a singular posture,the 1-2-1mode was slightly less impacted than the 2-2mode.The above results are explained in detail from the energy point of view.In addition,the relationship between the peak impact force and the impact duration is analyzed,and the reasons for the small peak impact force under the high surface slope are discussed in terms of energy.This work serves as a useful reference for the safe landing of lunar landers.
The safe landing of a lunar lander is a major guarantee for the safety of astronauts and the carrying equipment and instrument,as well as the subsequent operation of the lander.Studying the landing process of the lunar lander is important for achieving safe landing.In this study,a model coupling the discrete element method(DEM)and the finite element method(FEM)is set up to analyze the interactions between the lunar soil and the lander.In this coupled model,the lunar soil is modeled by discrete spherical elements with bond capacity.The lander is constructed with a combined finite element model consisting of shell elements and beam elements.Meanwhile,a compressible spring model is used for the supporting legs connected with the cushion to realize the buffer capacity.In order to analyze the landing process on various lunar surfaces,different flat and sloped lunar surfaces are simulated,and the interactions between the lander and the lunar soil in different landing modes are studied.Studies have shown that during landing,the impact strength of the lander structure decreases with an increase in slope.When the lander landed on the lunar surface in a singular posture,the 1-2-1mode was slightly less impacted than the 2-2mode.The above results are explained in detail from the energy point of view.In addition,the relationship between the peak impact force and the impact duration is analyzed,and the reasons for the small peak impact force under the high surface slope are discussed in terms of energy.This work serves as a useful reference for the safe landing of lunar landers.
引文
[1]Lin C X,Tu F B,Ling D S,et al.FEM-DEM coupled modeling of cone penetration tests in lunar soil[J].Journal of Central South University,2018,25(2):392-405.
[2]吴晓君,钟世英,凌道盛,等.着陆器足垫垂直冲击模型试验研究[J].岩土力学,2012,33(4):1045-1050.(Wu X J,Zhong S Y,Ling D S,et al.Experimental study on vertical impact model of lander footpad[J].Rock and Soil Mechanics,2012,33(4):1045-1050.(in Chinese))
[3]Sutoh M,Wakabayashi S,Hoshino T.Landing behavior analysis of lunar probe based on drop tests and RFT in a vacuum[J].IEEE Robotics&Automation Letters,2017,99:1-1.
[4]沈航.飞机起落架着陆与滑跑性能分析[J].应用力学学报,2001,18(s1):198-202.(Shen H.Analysis of landing and rolling performance of aircraft landing gears[J].Chinese Journal of Applied Mechanics,2001,18(s1):198-202.(in Chinese))
[5]李波,沈航.飞机着陆下沉速度最大值的确定方法[J].应用力学学报,2008,25(1):168-171.(Li B,Shen H.Method for determining maximum sinking speed of aircraft landing[J].Chinese Journal of Applied Mechanics,2008,25(1):168-171.(in Chinese))
[6]朱汪.欧洲航天局月球着陆器概述及启示[J].航天器工程,2016,25(1):124-130.(Zhu W.Overview and enlightenment of the european space agency lunar lander[J].Spacecraft Engineering,2016,25(1):124-130.(in Chinese))
[7]王文选,王安强,白斌.着陆冲击力对起落架摆振的影响[J].应用力学学报,2013,5:647-651.(Wang W X,Wang A Q,Bai B.Impact of landing impact force on landing vibration of landing gear[J].Chinese Journal of Applied Mechanics,2013,5:647-651.(in Chinese))
[8]牟让科,齐丕骞,吴启荣,等.一种自适应双腔缓冲器动力特性研究[J].应用力学学报,2001,18(s1):96-100.(Zang R K,Qi Q,Wu Q R,et al.Study on the dynamic characteristics of an adaptive dual-chamber buffer[J].Journal of Applied Mechanics,2001,18(s1):96-100.(in Chinese))
[9]杨建中,曾福明,满剑锋,等.嫦娥三号着陆器着陆缓冲系统设计与验证[J].中国科学:技术科学,2014,44(5):440-449.(Yang J Z,Zeng F M,Man J F,et al.Design and verification of the landing buffer system of the No.3lander[J].Science in China:Technical Science,2014,44(5):440-449.(in Chinese))
[10] Ma L,Wang K,Shao Z,et al.Trajectory optimization for lunar rover performing vertical takeoff vertical landing maneuvers in the presence of terrain[J].Acta Astronautica,2018,146:289-299.
[11] Metzger P T,Anderson S,Colaprete A.Experiments indicate regolith is looser in the lunar polar regions than at the lunar landing sites[J].Earth&Space Conf,2018,4:126-137.
[12] Arslantas Y E,Theil S.Attainable landing area computation of a lunar lander with uncertainty by reachability analysis[J].Optimization Methods and Software,2017:497-513.
[13] Jeong H J,Lim J H,Kim J W.Evaluation of landing stability of lunar lander considering various landing conditions[J].Journal of the Korean Society for Aeronautical&Space Sciences,2018,46:46-52.
[14] Kariya K,Ishida T,Sawai S,et al.Position estimation using crater-based linear features for pinpoint lunar landing[J].Aerospace Technology Japan,2018,17:79-87.
[15]梁绍敏,王永滨,季顺迎.基于离散元方法的月球着陆器冲击月壤过程分析[J].航天返回与遥感,2017,38(4):55-63.(Liang S M,Wang Y B,Ji S Y.Analysis of impact of lunar lander by lunar lander based on discrete element method[J].Space Return and Remote Sensing,2017,38(4):55-63.(in Chinese))
[16] Berger K J,Anand A,Metzger P T,et al.Role of collisions in erosion of regolith during a lunar landing[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2013,87(2):652-670.
[17]蒋明镜,奚邦禄,申志福,等.月壤水平开挖推剪阻力影响因素离散元数值分析[J].岩土力学,2016,37(1):229-236.(Jiang M J,Xi B L,Shen Z F,et al.Discrete element numerical analysis of factors affecting horizontal pushing resistance in lunar ground excavation[J].Rock&Soil Mechanics,2016,37(1):229-236.(in Chinese))
[18]林呈祥,凌道盛,钟世英.模拟月壤抗剪强度试验研究及离散元分析[J].岩土力学,2017,38(3):893-901.(Lin C X,Ling D S,Zhong S Y.Experimental research and discrete element analysis of shear strength of lunar soil simulants[J].Rock&Soil Mechanics,2017,38(3):893-901.(in Chinese))
[19] Kulchitsky A V,Johnson J B,Reeves D M.Resistance forces during boulder extraction from an asteroid[J].Acta Astronautica,2016,127:424-437.
[20] Knuth M A,Johnson J B,Hopkins M A,et al.Discrete element modeling of a Mars Exploration Rover wheel in granular material[J].Journal of Terramechanics,2012,49(1):27-36.
[21] Smith W,Peng H.Modeling of wheel-soil interaction over rough terrain using the discrete element method[J].Journal of Terramechanics,2013,50(5-6):277-287.
[22] Jiang M J,Yu H S,Harris D.Discrete element modelling of deep penetration in granular soils[J].International Journal for Numerical&Analytical Methods in Geomechanics,2006,30(4):335-361.
[23] Bahrani N,Kaiser P K,Valley B.Distinct element method simulation of an analogue for a highly interlocked,non-persistently jointed rockmass[J].International Journal of Rock Mechanics&Mining Sciences,2014,71:117-130.
[24] Yue S,Nie H,Zhang M,et al.Design and landing dynamic analysis of reusable landing leg for a nearspace manned capsule[J]. Acta Astronautica2018,S0094576517314984.
[25] Li P,Zhang H,Jiang S,et al.Analysis and testing of load characteristics for rotary-percussive drilling of lunar rock simulant with a lunar regolith coring bit[J].Shock and Vibration,2017,1-15.
[26]蒋万松,黄伟,沈祖炜.月球探测器软着陆动力学仿真[J].宇航学报,2011,32(3):462-469.(Jiang W S,Huang W,Shen Z W.Dynamic simulation of lunar probe soft landing[J].Journal of Astronautics,2011,32(3):462-469.(in Chinese))
[27] Chung Y C,Ooi J Y.Linking of discrete element modelling with finite element analysis for analyzing structures in contact with particulate solid[J].Powder Technology,2012,217:107-120.
[28] Zheng Z,Zang M,Chen S,et al.An improved 3D DEM-FEM contact detection algorithm for the interaction simulations between particles and structures[J].Powder Technology,2016,305:308-322.
[29] Ramírez R,P9schel T,Brilliantov N V,et al.Coefficient of restitution of colliding viscoelastic spheres[J].Physical Review E Statistical Physics Plasmas Fluids&Related Interdisciplinary Topics,1999,60(4Pt B):4465.
[30] Park J W,Song J J.Numerical simulation of a direct shear test on a rock joint using a bonded-particle model[J].International Journal of Rock Mechanics&Mining Sciences,2009,46(8):1315-1328.
[31]王帅霖,季顺迎.锥体导管架海洋平台冰激振动的DEM-FEM耦合分析及高性能算法[J].海洋学报,2017,39(12):98-108.(Wang S L,Ji S Y.Ice induced vibration of conical platform based on coupled DEM-FEM model with high efficiency algorithm[J].Acta Oceanologica Sinica,2017,39(12):98-108.(in Chinese))
[32]郑敏,蒋明镜,申志福.简化接触模型的月壤离散元数值分析[J].岩土力学,2011,S1:766-771.(Zheng M,Jiang M J,Shen Z F.Discrete element numerical analysis of lunar soil with a simplified contact model[J].Rock&Soil Mechanics,2011,32:766-771.(in Chinese))
[33] Nitka M,Combe G,Dascalu C,et al.Two-scale modeling of granular materials:a DEM-FEM approach[J].Granular Matter,2011,13(3):277-281.
[34]张锐,唐志平,郑航.离散元与有限元耦合的时空多尺度计算方法[J].吉林大学学报,2009,39(2):409-412.(Zhang R,Tang Z P,Zheng H.Time and space multiscale numerical method by coupling discrete element method and finite element method[J].Journal of Jilin University(Engineering and Technology Edition),2009,39(2):409-412.(in Chinese))
[35]季顺迎,樊利芳,梁绍敏.基于离散元方法的颗粒材料缓冲性能及影响因素分析[J].物理学报,2016,65(10):164-176.(Ji S Y,Fan L F,Liang S M.Buffering properties and influence factors of granular materials based on discrete element method[J].Acta Physica Sinica,2016,65(10):164-176.(in Chinese))
[36] Jeong J,Shin C S.The effect of gender and foot landing type on lower extremity biomechanics during single-leg landing[J].Journal of the Korean Society for Precision Engineering,2018,35(1):33-39.
[37] Nishiura D,Sakaguchi H.Parallel-vector algorithms for particle simulations on shared-memory multiprocessors[J].Journal of Computational Physics,2011,230:1923-1938.
[38]梁东平,柴洪友.着陆冲击仿真月壤本构模型及有限元建模[J].航天器工程,2012,21(1):18-24.(Liang D P,Chai H Y.Landslide impact simulation of the lunar constitutive model and finite element modeling[J].Spacecraft Engineering,2012,21(1):18-24.(in Chinese))
[39] Hou X,Xue P,Wang Y,et al.Theoretical and discrete element simulation studies of aircraft landing impact[J].Journal of the Brazilian Society of Mechanical Sciences&Engineering,2018,40(3):2-16.
[40]朱汪,杨建中.月球着陆器软着陆机构着陆稳定性仿真分析[J].宇航学报,2009,30(5):1792-1796.(Zhu W,Yang J Z.Touchdown stability simulation of landing gear system for lunar lander[J].Journal of Astronautics,2009,30(5):1792-1796.(in Chinese))
[2]吴晓君,钟世英,凌道盛,等.着陆器足垫垂直冲击模型试验研究[J].岩土力学,2012,33(4):1045-1050.(Wu X J,Zhong S Y,Ling D S,et al.Experimental study on vertical impact model of lander footpad[J].Rock and Soil Mechanics,2012,33(4):1045-1050.(in Chinese))
[3]Sutoh M,Wakabayashi S,Hoshino T.Landing behavior analysis of lunar probe based on drop tests and RFT in a vacuum[J].IEEE Robotics&Automation Letters,2017,99:1-1.
[4]沈航.飞机起落架着陆与滑跑性能分析[J].应用力学学报,2001,18(s1):198-202.(Shen H.Analysis of landing and rolling performance of aircraft landing gears[J].Chinese Journal of Applied Mechanics,2001,18(s1):198-202.(in Chinese))
[5]李波,沈航.飞机着陆下沉速度最大值的确定方法[J].应用力学学报,2008,25(1):168-171.(Li B,Shen H.Method for determining maximum sinking speed of aircraft landing[J].Chinese Journal of Applied Mechanics,2008,25(1):168-171.(in Chinese))
[6]朱汪.欧洲航天局月球着陆器概述及启示[J].航天器工程,2016,25(1):124-130.(Zhu W.Overview and enlightenment of the european space agency lunar lander[J].Spacecraft Engineering,2016,25(1):124-130.(in Chinese))
[7]王文选,王安强,白斌.着陆冲击力对起落架摆振的影响[J].应用力学学报,2013,5:647-651.(Wang W X,Wang A Q,Bai B.Impact of landing impact force on landing vibration of landing gear[J].Chinese Journal of Applied Mechanics,2013,5:647-651.(in Chinese))
[8]牟让科,齐丕骞,吴启荣,等.一种自适应双腔缓冲器动力特性研究[J].应用力学学报,2001,18(s1):96-100.(Zang R K,Qi Q,Wu Q R,et al.Study on the dynamic characteristics of an adaptive dual-chamber buffer[J].Journal of Applied Mechanics,2001,18(s1):96-100.(in Chinese))
[9]杨建中,曾福明,满剑锋,等.嫦娥三号着陆器着陆缓冲系统设计与验证[J].中国科学:技术科学,2014,44(5):440-449.(Yang J Z,Zeng F M,Man J F,et al.Design and verification of the landing buffer system of the No.3lander[J].Science in China:Technical Science,2014,44(5):440-449.(in Chinese))
[10] Ma L,Wang K,Shao Z,et al.Trajectory optimization for lunar rover performing vertical takeoff vertical landing maneuvers in the presence of terrain[J].Acta Astronautica,2018,146:289-299.
[11] Metzger P T,Anderson S,Colaprete A.Experiments indicate regolith is looser in the lunar polar regions than at the lunar landing sites[J].Earth&Space Conf,2018,4:126-137.
[12] Arslantas Y E,Theil S.Attainable landing area computation of a lunar lander with uncertainty by reachability analysis[J].Optimization Methods and Software,2017:497-513.
[13] Jeong H J,Lim J H,Kim J W.Evaluation of landing stability of lunar lander considering various landing conditions[J].Journal of the Korean Society for Aeronautical&Space Sciences,2018,46:46-52.
[14] Kariya K,Ishida T,Sawai S,et al.Position estimation using crater-based linear features for pinpoint lunar landing[J].Aerospace Technology Japan,2018,17:79-87.
[15]梁绍敏,王永滨,季顺迎.基于离散元方法的月球着陆器冲击月壤过程分析[J].航天返回与遥感,2017,38(4):55-63.(Liang S M,Wang Y B,Ji S Y.Analysis of impact of lunar lander by lunar lander based on discrete element method[J].Space Return and Remote Sensing,2017,38(4):55-63.(in Chinese))
[16] Berger K J,Anand A,Metzger P T,et al.Role of collisions in erosion of regolith during a lunar landing[J].Physical Review E Statistical Nonlinear&Soft Matter Physics,2013,87(2):652-670.
[17]蒋明镜,奚邦禄,申志福,等.月壤水平开挖推剪阻力影响因素离散元数值分析[J].岩土力学,2016,37(1):229-236.(Jiang M J,Xi B L,Shen Z F,et al.Discrete element numerical analysis of factors affecting horizontal pushing resistance in lunar ground excavation[J].Rock&Soil Mechanics,2016,37(1):229-236.(in Chinese))
[18]林呈祥,凌道盛,钟世英.模拟月壤抗剪强度试验研究及离散元分析[J].岩土力学,2017,38(3):893-901.(Lin C X,Ling D S,Zhong S Y.Experimental research and discrete element analysis of shear strength of lunar soil simulants[J].Rock&Soil Mechanics,2017,38(3):893-901.(in Chinese))
[19] Kulchitsky A V,Johnson J B,Reeves D M.Resistance forces during boulder extraction from an asteroid[J].Acta Astronautica,2016,127:424-437.
[20] Knuth M A,Johnson J B,Hopkins M A,et al.Discrete element modeling of a Mars Exploration Rover wheel in granular material[J].Journal of Terramechanics,2012,49(1):27-36.
[21] Smith W,Peng H.Modeling of wheel-soil interaction over rough terrain using the discrete element method[J].Journal of Terramechanics,2013,50(5-6):277-287.
[22] Jiang M J,Yu H S,Harris D.Discrete element modelling of deep penetration in granular soils[J].International Journal for Numerical&Analytical Methods in Geomechanics,2006,30(4):335-361.
[23] Bahrani N,Kaiser P K,Valley B.Distinct element method simulation of an analogue for a highly interlocked,non-persistently jointed rockmass[J].International Journal of Rock Mechanics&Mining Sciences,2014,71:117-130.
[24] Yue S,Nie H,Zhang M,et al.Design and landing dynamic analysis of reusable landing leg for a nearspace manned capsule[J]. Acta Astronautica2018,S0094576517314984.
[25] Li P,Zhang H,Jiang S,et al.Analysis and testing of load characteristics for rotary-percussive drilling of lunar rock simulant with a lunar regolith coring bit[J].Shock and Vibration,2017,1-15.
[26]蒋万松,黄伟,沈祖炜.月球探测器软着陆动力学仿真[J].宇航学报,2011,32(3):462-469.(Jiang W S,Huang W,Shen Z W.Dynamic simulation of lunar probe soft landing[J].Journal of Astronautics,2011,32(3):462-469.(in Chinese))
[27] Chung Y C,Ooi J Y.Linking of discrete element modelling with finite element analysis for analyzing structures in contact with particulate solid[J].Powder Technology,2012,217:107-120.
[28] Zheng Z,Zang M,Chen S,et al.An improved 3D DEM-FEM contact detection algorithm for the interaction simulations between particles and structures[J].Powder Technology,2016,305:308-322.
[29] Ramírez R,P9schel T,Brilliantov N V,et al.Coefficient of restitution of colliding viscoelastic spheres[J].Physical Review E Statistical Physics Plasmas Fluids&Related Interdisciplinary Topics,1999,60(4Pt B):4465.
[30] Park J W,Song J J.Numerical simulation of a direct shear test on a rock joint using a bonded-particle model[J].International Journal of Rock Mechanics&Mining Sciences,2009,46(8):1315-1328.
[31]王帅霖,季顺迎.锥体导管架海洋平台冰激振动的DEM-FEM耦合分析及高性能算法[J].海洋学报,2017,39(12):98-108.(Wang S L,Ji S Y.Ice induced vibration of conical platform based on coupled DEM-FEM model with high efficiency algorithm[J].Acta Oceanologica Sinica,2017,39(12):98-108.(in Chinese))
[32]郑敏,蒋明镜,申志福.简化接触模型的月壤离散元数值分析[J].岩土力学,2011,S1:766-771.(Zheng M,Jiang M J,Shen Z F.Discrete element numerical analysis of lunar soil with a simplified contact model[J].Rock&Soil Mechanics,2011,32:766-771.(in Chinese))
[33] Nitka M,Combe G,Dascalu C,et al.Two-scale modeling of granular materials:a DEM-FEM approach[J].Granular Matter,2011,13(3):277-281.
[34]张锐,唐志平,郑航.离散元与有限元耦合的时空多尺度计算方法[J].吉林大学学报,2009,39(2):409-412.(Zhang R,Tang Z P,Zheng H.Time and space multiscale numerical method by coupling discrete element method and finite element method[J].Journal of Jilin University(Engineering and Technology Edition),2009,39(2):409-412.(in Chinese))
[35]季顺迎,樊利芳,梁绍敏.基于离散元方法的颗粒材料缓冲性能及影响因素分析[J].物理学报,2016,65(10):164-176.(Ji S Y,Fan L F,Liang S M.Buffering properties and influence factors of granular materials based on discrete element method[J].Acta Physica Sinica,2016,65(10):164-176.(in Chinese))
[36] Jeong J,Shin C S.The effect of gender and foot landing type on lower extremity biomechanics during single-leg landing[J].Journal of the Korean Society for Precision Engineering,2018,35(1):33-39.
[37] Nishiura D,Sakaguchi H.Parallel-vector algorithms for particle simulations on shared-memory multiprocessors[J].Journal of Computational Physics,2011,230:1923-1938.
[38]梁东平,柴洪友.着陆冲击仿真月壤本构模型及有限元建模[J].航天器工程,2012,21(1):18-24.(Liang D P,Chai H Y.Landslide impact simulation of the lunar constitutive model and finite element modeling[J].Spacecraft Engineering,2012,21(1):18-24.(in Chinese))
[39] Hou X,Xue P,Wang Y,et al.Theoretical and discrete element simulation studies of aircraft landing impact[J].Journal of the Brazilian Society of Mechanical Sciences&Engineering,2018,40(3):2-16.
[40]朱汪,杨建中.月球着陆器软着陆机构着陆稳定性仿真分析[J].宇航学报,2009,30(5):1792-1796.(Zhu W,Yang J Z.Touchdown stability simulation of landing gear system for lunar lander[J].Journal of Astronautics,2009,30(5):1792-1796.(in Chinese))