多轮多支柱起落架飞机滑跑响应分析
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摘要
在一些必要合理的假设下,利用达朗贝尔原理,建立了多轮多支柱式及小车式起落架飞机地面滑跑动态响应分析的全机模型,考虑全机沉浮、机体弹性(前n阶弹性模态)和定常气动力的影响,起落架支柱的弹性变形,小车式起落架的车架的俯仰运动以及弹性变形,对等速滑跑飞机建立了全机运动的微分方程,并以旧金山28-R跑道为地面输入,利用时域积分的方法得到飞机滑跑的各种响应。
对于随机的地面的滑跑响应,在飞机滑行方向跑道路面不平度为平稳随机函数假设下,通过对起落架缓冲系统刚度和阻尼的线化处理,将非线性随机振动问题简化为线性平稳随机振动问题,运用功率谱密度方法,计算滑行时由地面不平度引起的飞机结构动态响应。
通过对多轮单支柱和多轮多支柱式飞机的时域计算分析,得到如下结论:考虑机体弹性运动是很必要的,特别是对于大型飞机,应该考虑其机体弹性运动。起落架空气腔初始压强和初始容积对起落架的刚度影响较大,而多轮多支柱式起落架飞机,不仅是多个输入问题,还存在起落架载荷分配问题,所以起落架的敏感参数对于全机的动载荷有明显的影响,合理的起落架布局和参数选取有利于降低机体动载荷水平。同时本文还针对多轮多支柱式起落架飞机地面滑跑响应开发了相应的软件,该软件具有友好的用户界面,且软件设计立足于起落架布局、属性的可设计性,因此可以将其应用于实际工程当中,而且还可以根据实际情况,进行扩展、丰富分析模型。
通过对多轮单支柱和多轮多支柱式飞机的频域计算的算例分析,得到如下结论:考虑弹性运动对系统的响应有一定影响。
本文建立的全机模型接近飞机匀速滑跑的实际情况,能真实地反映机体的动力学特性,能够同时考虑机体结构弹性、飞机的定常气动力,具有工程应用价值。
To study the taxiing-induced dynamic response of the aircraft with multiple wheels and multiple landing gears due to runway unevenness, base on several reasonable and necessary assumptions, the mathematical model of aircraft in taxiing is established using the d'alembert's principle. It can simulate taxiing inpact properties accurately, it considers in detail the vertical and horizontal motion and pitching about its center of gravity and the significant symmetric elastic modes. Also considered are the nonlinear hydropneumatic landing gear characteristics, the structural flexibility of landing gear, the nonlinear load-deflection characteristics of the tires, the rolling and sliding friction of the tires versus slip ratio, the rolling moments of inertia of the tire and wheel, the pitching motion and the structural flexibility of carriage and the aerodynamic force. The motion equations of the aircraft taxiing in constant velocity are derived. Using the San Francisco Airport 28R runway unevenness as the input, the taxiing-induced response time history can be integrated.The dynamic responses are also obtained by the statistical analysis with PSD method. The significant problem is that the input of runway unevenness is stationary stochastic process and how the oleo-pneumatic shock absorbers could be linearized. These are all presented in details in this paper.With determinate method, the analysis of taxiing-induced response of aircraft with the multiple wheels and multiple landing gears is conducted. The results show that the flexibility of body should be taken into account, especially to the large aircraft. Additionally, the initial parameter of the oleo-pneumatic shock absorbers affects the loads distribution. The reasonable selection of parameters can help to alleviate dynamic response. Based on the above analysis ,a user-oriented computing program is developed, and it's easy to expand the function of the program with landing gear model.Correspondingly, we analyse the taxiing-induced response of the aircraft with PSD method. And get the same conclusion that the flexibility of airframe could affect the
taxiing-induced response of the aircraft.
对于随机的地面的滑跑响应,在飞机滑行方向跑道路面不平度为平稳随机函数假设下,通过对起落架缓冲系统刚度和阻尼的线化处理,将非线性随机振动问题简化为线性平稳随机振动问题,运用功率谱密度方法,计算滑行时由地面不平度引起的飞机结构动态响应。
通过对多轮单支柱和多轮多支柱式飞机的时域计算分析,得到如下结论:考虑机体弹性运动是很必要的,特别是对于大型飞机,应该考虑其机体弹性运动。起落架空气腔初始压强和初始容积对起落架的刚度影响较大,而多轮多支柱式起落架飞机,不仅是多个输入问题,还存在起落架载荷分配问题,所以起落架的敏感参数对于全机的动载荷有明显的影响,合理的起落架布局和参数选取有利于降低机体动载荷水平。同时本文还针对多轮多支柱式起落架飞机地面滑跑响应开发了相应的软件,该软件具有友好的用户界面,且软件设计立足于起落架布局、属性的可设计性,因此可以将其应用于实际工程当中,而且还可以根据实际情况,进行扩展、丰富分析模型。
通过对多轮单支柱和多轮多支柱式飞机的频域计算的算例分析,得到如下结论:考虑弹性运动对系统的响应有一定影响。
本文建立的全机模型接近飞机匀速滑跑的实际情况,能真实地反映机体的动力学特性,能够同时考虑机体结构弹性、飞机的定常气动力,具有工程应用价值。
To study the taxiing-induced dynamic response of the aircraft with multiple wheels and multiple landing gears due to runway unevenness, base on several reasonable and necessary assumptions, the mathematical model of aircraft in taxiing is established using the d'alembert's principle. It can simulate taxiing inpact properties accurately, it considers in detail the vertical and horizontal motion and pitching about its center of gravity and the significant symmetric elastic modes. Also considered are the nonlinear hydropneumatic landing gear characteristics, the structural flexibility of landing gear, the nonlinear load-deflection characteristics of the tires, the rolling and sliding friction of the tires versus slip ratio, the rolling moments of inertia of the tire and wheel, the pitching motion and the structural flexibility of carriage and the aerodynamic force. The motion equations of the aircraft taxiing in constant velocity are derived. Using the San Francisco Airport 28R runway unevenness as the input, the taxiing-induced response time history can be integrated.The dynamic responses are also obtained by the statistical analysis with PSD method. The significant problem is that the input of runway unevenness is stationary stochastic process and how the oleo-pneumatic shock absorbers could be linearized. These are all presented in details in this paper.With determinate method, the analysis of taxiing-induced response of aircraft with the multiple wheels and multiple landing gears is conducted. The results show that the flexibility of body should be taken into account, especially to the large aircraft. Additionally, the initial parameter of the oleo-pneumatic shock absorbers affects the loads distribution. The reasonable selection of parameters can help to alleviate dynamic response. Based on the above analysis ,a user-oriented computing program is developed, and it's easy to expand the function of the program with landing gear model.Correspondingly, we analyse the taxiing-induced response of the aircraft with PSD method. And get the same conclusion that the flexibility of airframe could affect the
taxiing-induced response of the aircraft.
引文
[1] 杨利等,“起落架随机滑跑响应分析”,振动工程学报,Vol.17,SI,2004
[2] 牟让科,“弹性飞机对称着陆滑跑过程中动响应分析方法研究”,应用力学学报,Vol.13,SI,1996
[3] 姜节胜,“飞机结构随机振动基础”,西北工业大学出版社,1984.5
[4] 晋萍,“飞机起落架动态性能分析”,南京航空航天大学硕士学位论文,2003年2月
[5] 方平,“小车式飞机起落架着陆与滑跑动态性能仿真分析”,南京航空航天大学硕士学位论文,2004年2月
[6] 姚起杭,“飞机动强度设计指南”,西北工业大学出版社,1997.12第一版
[7] 牟让科,胡孟权,“飞机非对称着陆和滑跑载荷的分析方法”,机械科学与技术,Vol.19,SI,2000
[8] 牟让科,罗俊杰,“飞机结构弹性对起落架缓冲性能的影响”,航空学报,Vol.16,No.2,1995
[9] 牟让科、齐丕骞等,“一种自适应双腔缓冲器动力特性研究”,应用力学学报,Vol.18 SI,2001
[10] 沈航,“飞机起落架着陆与滑跑性能分析”,应用力学学报,Vol.18,SI,2001
[11] 张曾锠、张江监、王裕昌,“飞机起落架滑行载荷识别”,航空学报,Vol.15,No.1,1994
[12] 刘莉、杨国柱、何庆芝,“起落架缓冲系统参数对飞机滑行动态响应的影响”,航空学报,Vol.13,No.6,1992
[13] 刘莉、杨国柱、何庆芝,“飞机地面滑行随机振动分析”,航空学报,Vol.14,No.4,1993
[14] 刘莉、杨国柱、何庆芝,“起落架缓冲系统参数优化设计”,航空学报,Vol.13,No.10,1992
[15] 聂铁军,“计算方法”,国防工业出版社,1988年12月第2版
[16] 袁东,飞机起落架仿真数学模型建立方法,《飞行力学》,Vol.20 No.4,2002
[17] 张阿舟、诸德超等,“实用振动工程——振动控制与设计”,航空工业出版社,1997
[18] 芮裕亭,“弹性飞机在不平的跑道上起飞和着陆的数字模拟”,航空学报,Vol.7,No.4,1986
[19] 徐冬苓、李玉忍,“飞机起落架数学模型的研究”,系统仿真学报,Vol.17 No.4,2005
[20] 张志林、苏开鑫,“飞机起落架着陆撞击动力分析”,《洪都科技》,2000年6月,No.2
[21] 刘锐琛,“飞机地面滑行动力响应分析”,航空学报,Vol.8 No.12,1987
[22] 齐丕骞、牟让科,“飞机起落架缓冲性能分析、试验、设计—体化技术”,航空学报,Vol.19 No.3,1998
[23] 冯亚昌、陈刚、李佩琼,“飞机纵向起飞着陆动态特性仿真研究”,北京航空航天大学学报,No4,1989
[24] 李霞,“某型飞机主起落架缓冲系统性能分析研究”,航空工程与维修,2000.06
[25] 史友进,“柔性飞机起落架设计探析”,盐城工学院学报,Vol.18 No.1,2005
[26] 王明义、贾玉红,“摇臂式起落架缓冲器参数设计与计算”,首届全国航空航天领域中的力学问题学术研讨会
[27] 隋福成、陆华,“飞机起落架缓冲器数字模型研究”,飞机设计,No2,2001
[28] 晋萍、聂宏,“起落架着陆动态仿真分析模型及参数优化设计”,南京航空航天大学学报,Vol.35 No5,2003
[29] NieHong, Analysis for Aircraft Taxing at Variable Velocity on Unevenness Runway by the Power Spectral Density Method, Transactions of Nanjing University of Aeronautics&Astronautic, Vol. 17, No. 1, 2000
[30] Donald M. Rehder and Lane B. Mosby, "Ground Loads for Aircraft with Multiple Wheels and Multiple Landing Gear and with Requirements for Semi-Improved Airfield Operations", AIAA Paper, No.65-711, Low-Speed Flight Meeting, October 18-19, 1965
[31] Jocelyn I. Pritchard, An Overview of Landing Gear Dynamics, NASA/TM-1999-209143
[32] William E. Krabacher, Aircraft Landing Gear Dynamics Present and Future, SAE Technical Paper Series 931400 (1993)
[33] Kirk CL, Perry P J, Analysis of Taxiing Induced Vibrations in Aircraft by the Power Spectral Density Method. The Aeronautical Journal of the Royal Aeronautical Society, 1971, 75:180～193
[34] Tung C C, Penzien J, Horonjeff R, The Effect of Runway Uneveness on the Dynamic Response of Supersonic Transports, NASA CR-119,1964
[2] 牟让科,“弹性飞机对称着陆滑跑过程中动响应分析方法研究”,应用力学学报,Vol.13,SI,1996
[3] 姜节胜,“飞机结构随机振动基础”,西北工业大学出版社,1984.5
[4] 晋萍,“飞机起落架动态性能分析”,南京航空航天大学硕士学位论文,2003年2月
[5] 方平,“小车式飞机起落架着陆与滑跑动态性能仿真分析”,南京航空航天大学硕士学位论文,2004年2月
[6] 姚起杭,“飞机动强度设计指南”,西北工业大学出版社,1997.12第一版
[7] 牟让科,胡孟权,“飞机非对称着陆和滑跑载荷的分析方法”,机械科学与技术,Vol.19,SI,2000
[8] 牟让科,罗俊杰,“飞机结构弹性对起落架缓冲性能的影响”,航空学报,Vol.16,No.2,1995
[9] 牟让科、齐丕骞等,“一种自适应双腔缓冲器动力特性研究”,应用力学学报,Vol.18 SI,2001
[10] 沈航,“飞机起落架着陆与滑跑性能分析”,应用力学学报,Vol.18,SI,2001
[11] 张曾锠、张江监、王裕昌,“飞机起落架滑行载荷识别”,航空学报,Vol.15,No.1,1994
[12] 刘莉、杨国柱、何庆芝,“起落架缓冲系统参数对飞机滑行动态响应的影响”,航空学报,Vol.13,No.6,1992
[13] 刘莉、杨国柱、何庆芝,“飞机地面滑行随机振动分析”,航空学报,Vol.14,No.4,1993
[14] 刘莉、杨国柱、何庆芝,“起落架缓冲系统参数优化设计”,航空学报,Vol.13,No.10,1992
[15] 聂铁军,“计算方法”,国防工业出版社,1988年12月第2版
[16] 袁东,飞机起落架仿真数学模型建立方法,《飞行力学》,Vol.20 No.4,2002
[17] 张阿舟、诸德超等,“实用振动工程——振动控制与设计”,航空工业出版社,1997
[18] 芮裕亭,“弹性飞机在不平的跑道上起飞和着陆的数字模拟”,航空学报,Vol.7,No.4,1986
[19] 徐冬苓、李玉忍,“飞机起落架数学模型的研究”,系统仿真学报,Vol.17 No.4,2005
[20] 张志林、苏开鑫,“飞机起落架着陆撞击动力分析”,《洪都科技》,2000年6月,No.2
[21] 刘锐琛,“飞机地面滑行动力响应分析”,航空学报,Vol.8 No.12,1987
[22] 齐丕骞、牟让科,“飞机起落架缓冲性能分析、试验、设计—体化技术”,航空学报,Vol.19 No.3,1998
[23] 冯亚昌、陈刚、李佩琼,“飞机纵向起飞着陆动态特性仿真研究”,北京航空航天大学学报,No4,1989
[24] 李霞,“某型飞机主起落架缓冲系统性能分析研究”,航空工程与维修,2000.06
[25] 史友进,“柔性飞机起落架设计探析”,盐城工学院学报,Vol.18 No.1,2005
[26] 王明义、贾玉红,“摇臂式起落架缓冲器参数设计与计算”,首届全国航空航天领域中的力学问题学术研讨会
[27] 隋福成、陆华,“飞机起落架缓冲器数字模型研究”,飞机设计,No2,2001
[28] 晋萍、聂宏,“起落架着陆动态仿真分析模型及参数优化设计”,南京航空航天大学学报,Vol.35 No5,2003
[29] NieHong, Analysis for Aircraft Taxing at Variable Velocity on Unevenness Runway by the Power Spectral Density Method, Transactions of Nanjing University of Aeronautics&Astronautic, Vol. 17, No. 1, 2000
[30] Donald M. Rehder and Lane B. Mosby, "Ground Loads for Aircraft with Multiple Wheels and Multiple Landing Gear and with Requirements for Semi-Improved Airfield Operations", AIAA Paper, No.65-711, Low-Speed Flight Meeting, October 18-19, 1965
[31] Jocelyn I. Pritchard, An Overview of Landing Gear Dynamics, NASA/TM-1999-209143
[32] William E. Krabacher, Aircraft Landing Gear Dynamics Present and Future, SAE Technical Paper Series 931400 (1993)
[33] Kirk CL, Perry P J, Analysis of Taxiing Induced Vibrations in Aircraft by the Power Spectral Density Method. The Aeronautical Journal of the Royal Aeronautical Society, 1971, 75:180～193
[34] Tung C C, Penzien J, Horonjeff R, The Effect of Runway Uneveness on the Dynamic Response of Supersonic Transports, NASA CR-119,1964