串联双附加气室空气弹簧若干问题研究
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摘要
本文根据某大型飞机机载设备的隔振需求,提出并设计了一款串联双附气室约束膜式空气弹簧。借助流体力学和热力学等方面的理论给出了描述空气弹簧振动的微分方程,利用数值计算方法对空气弹簧进行了分析,取得了较为满意的结果。论文从空气弹簧的结构设计入手,由浅入深,详细地给出了空气弹簧动力学模型的建立过程,对影响弹簧性能的相关因素进行了深入剖析,给出了相应结论,对空气弹簧的设计与研究提供了理论上的支持。
结合膜式空气弹簧的特点,设计了一个双附加气室串联的空气弹簧,确定了主要结构尺寸。以空气弹簧橡胶囊母线长度不变与自由段呈圆弧状假设为基础,对串联双附加气室空气弹簧主气室的垂向静刚度公式进行了详细推导,并在静刚度模型的基础上建立了空气弹簧主气室的自由振动微分方程,为空气弹簧的设计提供了理论依据。对空气弹簧的静刚度和自由振动微分方程进行了编程计算,计算结果表明:空气弹簧主气室垂向静刚度在振动中是一个周期非线性变化量;静刚度随着弹簧的压缩而增加,而且在保持平衡位置不变的条件下,弹簧的初始压力越大,刚度越大;空气弹簧的自由振动是周期非线性振动,自振频率随着初始速度的增加而减少,但变化幅度较小;随着初始速度的增加,空气弹簧的振动非线性越发明显。
为了验证空气弹簧静刚度的理论研究中假设的合理性及推导的准确性,在分析空气弹簧的橡胶材料非线性、胶膜中增强帘线层的非线性、胶膜在变形过程中的几何非线性、上盖板和下座与橡胶膜之间的接触非线性基础上,讨论了各种非线性在有限元软件Msc.Marc中的实现方法。研究了空气弹簧初始内压变化对垂向静刚度的影响规律;分析了上盖板处于不同位置时胶膜母线的伸长量。结果表明:在空气弹簧的垂向力与垂向刚度随着空弹簧的初始内压的增加而增大;空气弹簧胶膜母线在不同初始气压下的长度变化百分比小于1.0%,此误差值是可接受的。同时,空气弹簧垂向刚度有限元模型结果与理论推导结果的比较说明了本文建立的约束膜式空气弹簧主气室垂向刚度的表达式的正确性。
以绝热变化的假设为基础,利用流体力学及热力学等理论,结合气体的能量方程及弹簧内气体的连续性方程,参考空气弹簧的运动特点,建立了串联双附加气室空气弹簧的动力学模型,在建模过程中利用状态控制函数的方法,成功地将离散的状态有机联系起来,简化了方程的推导过程,降低了数值求解程序的编写难度。以此为基础,利用数值计算的方法对串联双附加气室空气弹簧的自由振动、节流孔大小及两附加气室容积比对弹簧的影响进行了细致研究。结果表明:串联双附加气室空气弹簧具有比其它类似空气弹簧更好的垂向动力学性能;串联双附加气室空气弹簧阻尼比的极大值首先与节流孔I有关,在节流孔I的半径足够大时,才与节流孔II有关;在节流孔I的半径足够大以及两个节流孔的大小与两附加气室的总容积不变的前提下,第一附加气室的容积越小,阻尼比越大。
以建立的空气弹簧自由振动微分方程为基础,推导了位移激振条件下的弹簧系统动力学模型;研究了空气弹簧的控制方式,并以主气室压力为调节对象,建立了加入控制执行机构的系统动力学方程。对位移激振的空气弹簧模型和引入控制的空气弹簧模型进行了数值仿真分析。结果显示,本文所设计的串联双附加气室空气弹簧对低频和高频位移激励的响应都较单附加气室空气弹簧要小;在加入控制变量后的系统振动响应明显降低,说明本文所设计的空气弹簧在控制系统的作用下具有更好的隔振效果。
In this dissertation, according to the vibration isolation need of airborne calculating unit in large airplane, a new type of restriction diaphragm air spring with series double attaching gas chambers is brought forward and then designed. On basis of the hydromechanics theory and the thermodynamics theory, the differential equation of air spring’s vibration is deduced. And then the air spring is analyzed by the numerical simulation method and the attained result is satisfactory. The structure of air spring is first designed in the dissertation and then the establishment process of air spring’s kinetic model is gradually deduced in detail. Moreover, the relative factors which affect the air spring’s performance is analyzed in depth and the relative conclusions is attained. The design and research on air spring in the dissertation can offer the aid of theory.
Integrating the characteristic of diaphragm air spring, the air spring with double attaching gas chamber is designed and the main structure dimensions are ascertained. On basis of the supposed conditions which are the no stretched-out generatrix of air spring’s diaphragm and the circular arc shape of unconstrained diaphragm part, the vertical static stiffness formula of air spring with the series double attaching gas chambers is deduced in detail. Moreover, on basis of the static stiffness model, the free vibration differential equation of air spring’s main gas chamber is established, which is in favor for the design of air spring. The static stiffness and the free vibration differential equation are programmed and calculated. The results show that the vertical static stiffness of main gas chamber in the vibration is a periodic non-linear variance, the static stiffness increases with the compression of air spring and the stiffness increases with the increase of air spring’s initial pressure. Moreover, the natural vibration frequency of main gas chamber unobviously decreases with the increase of initial velocity and the vibration non-linear of air spring is more and more obvious with the increase of initial velocity.
In order to verify the rightness of the deduced vertical stiffness of air spring’s main gas chamber, the material non-linear of air spring, the non-linear of curtain line in the rubber diaphragm, the geometric non-linear in the process of diaphragm’s deformation and the contact non-linear between the upper sheet and the rubber capsule or between the lower seat and the rubber capsule are discussed. Afterwards, the implement methods of air spring’s different non-linear in the finite element software Msc.Marc are analyzed. The effect of different initial pressure on the vertical stiffness in the air spring’s loading process and the stretched length of diaphragm generatrix under the different initial pressure of different position are researched. The results show that the vertical force and vertical stiffness increase with the increase of air spring’s initial pressure. Moreover, the change percent is less than 1.0% under the different initial pressure and the error can be accepted. The contrast between the results of air spring’s vertical stiffness attained by simulation method and the results attained by theoretical deduction explains the rightness of vertical stiffness formula of air spring’s main gas chamber in the dissertation.
The kinetic model of air spring’s main gas chamber is established, on basis of supposing adiabatic change, using the hydromechanics theory and the thermodynamics theory, integrating the energy equation and the continuity equation of gas in air spring and consulting the moving characteristic of air spring. Moreover, in the process of modeling, the discrete states are related together by the use of state controlled functions, so the deduction procedure of equation is simplified and the programming difficulty of numerical solver decreases. And then the free vibration, the throttle orifice diameter and the volume ratio between the two attaching gas chambers of air spring with series double attaching gas chambers are researched in detail by the numerical simulation method. The results show that the vertical kinetics performance is better than that of other analogous air springs. Moreover, the damping ratio’s maximum value of air spring is first relative to the throttle orifice I and then is only relative to the orifice II when the diameter of throttle orifice I is enough big. The damping ratio increases with the decrease of the first attaching gas chamber’s volume, when the diameter of orifice I is big enough, the diameters of two throttle orifices are invariable and the volume sum of the two attaching gas chambers is invariable.
On basis of establishing the free vibration differential equation of air spring, the kinetics model of air spring system under the condition of displacement excitation is deduced. The control mode of air spring is researched, the pressure of main gas chamber is ascertained as the controlled member and then the system kinetics equation adding the controlled actuating mechanism is set up. The air spring’s model under the displacement excitation and the air spring’s model adding control are analyzed by the numerical simulation method. The results show that the displacement excitation’s response of air spring with series double attaching gas chambers under the low frequency and high frequency is smaller than that of air spring with one attaching gas chamber. Moreover, the system vibration response adding the controlled variable is obviously decreased, which verifies that the air spring designed in the dissertation owns the better effect of vibration isolation under the effect of control system.
结合膜式空气弹簧的特点,设计了一个双附加气室串联的空气弹簧,确定了主要结构尺寸。以空气弹簧橡胶囊母线长度不变与自由段呈圆弧状假设为基础,对串联双附加气室空气弹簧主气室的垂向静刚度公式进行了详细推导,并在静刚度模型的基础上建立了空气弹簧主气室的自由振动微分方程,为空气弹簧的设计提供了理论依据。对空气弹簧的静刚度和自由振动微分方程进行了编程计算,计算结果表明:空气弹簧主气室垂向静刚度在振动中是一个周期非线性变化量;静刚度随着弹簧的压缩而增加,而且在保持平衡位置不变的条件下,弹簧的初始压力越大,刚度越大;空气弹簧的自由振动是周期非线性振动,自振频率随着初始速度的增加而减少,但变化幅度较小;随着初始速度的增加,空气弹簧的振动非线性越发明显。
为了验证空气弹簧静刚度的理论研究中假设的合理性及推导的准确性,在分析空气弹簧的橡胶材料非线性、胶膜中增强帘线层的非线性、胶膜在变形过程中的几何非线性、上盖板和下座与橡胶膜之间的接触非线性基础上,讨论了各种非线性在有限元软件Msc.Marc中的实现方法。研究了空气弹簧初始内压变化对垂向静刚度的影响规律;分析了上盖板处于不同位置时胶膜母线的伸长量。结果表明:在空气弹簧的垂向力与垂向刚度随着空弹簧的初始内压的增加而增大;空气弹簧胶膜母线在不同初始气压下的长度变化百分比小于1.0%,此误差值是可接受的。同时,空气弹簧垂向刚度有限元模型结果与理论推导结果的比较说明了本文建立的约束膜式空气弹簧主气室垂向刚度的表达式的正确性。
以绝热变化的假设为基础,利用流体力学及热力学等理论,结合气体的能量方程及弹簧内气体的连续性方程,参考空气弹簧的运动特点,建立了串联双附加气室空气弹簧的动力学模型,在建模过程中利用状态控制函数的方法,成功地将离散的状态有机联系起来,简化了方程的推导过程,降低了数值求解程序的编写难度。以此为基础,利用数值计算的方法对串联双附加气室空气弹簧的自由振动、节流孔大小及两附加气室容积比对弹簧的影响进行了细致研究。结果表明:串联双附加气室空气弹簧具有比其它类似空气弹簧更好的垂向动力学性能;串联双附加气室空气弹簧阻尼比的极大值首先与节流孔I有关,在节流孔I的半径足够大时,才与节流孔II有关;在节流孔I的半径足够大以及两个节流孔的大小与两附加气室的总容积不变的前提下,第一附加气室的容积越小,阻尼比越大。
以建立的空气弹簧自由振动微分方程为基础,推导了位移激振条件下的弹簧系统动力学模型;研究了空气弹簧的控制方式,并以主气室压力为调节对象,建立了加入控制执行机构的系统动力学方程。对位移激振的空气弹簧模型和引入控制的空气弹簧模型进行了数值仿真分析。结果显示,本文所设计的串联双附加气室空气弹簧对低频和高频位移激励的响应都较单附加气室空气弹簧要小;在加入控制变量后的系统振动响应明显降低,说明本文所设计的空气弹簧在控制系统的作用下具有更好的隔振效果。
In this dissertation, according to the vibration isolation need of airborne calculating unit in large airplane, a new type of restriction diaphragm air spring with series double attaching gas chambers is brought forward and then designed. On basis of the hydromechanics theory and the thermodynamics theory, the differential equation of air spring’s vibration is deduced. And then the air spring is analyzed by the numerical simulation method and the attained result is satisfactory. The structure of air spring is first designed in the dissertation and then the establishment process of air spring’s kinetic model is gradually deduced in detail. Moreover, the relative factors which affect the air spring’s performance is analyzed in depth and the relative conclusions is attained. The design and research on air spring in the dissertation can offer the aid of theory.
Integrating the characteristic of diaphragm air spring, the air spring with double attaching gas chamber is designed and the main structure dimensions are ascertained. On basis of the supposed conditions which are the no stretched-out generatrix of air spring’s diaphragm and the circular arc shape of unconstrained diaphragm part, the vertical static stiffness formula of air spring with the series double attaching gas chambers is deduced in detail. Moreover, on basis of the static stiffness model, the free vibration differential equation of air spring’s main gas chamber is established, which is in favor for the design of air spring. The static stiffness and the free vibration differential equation are programmed and calculated. The results show that the vertical static stiffness of main gas chamber in the vibration is a periodic non-linear variance, the static stiffness increases with the compression of air spring and the stiffness increases with the increase of air spring’s initial pressure. Moreover, the natural vibration frequency of main gas chamber unobviously decreases with the increase of initial velocity and the vibration non-linear of air spring is more and more obvious with the increase of initial velocity.
In order to verify the rightness of the deduced vertical stiffness of air spring’s main gas chamber, the material non-linear of air spring, the non-linear of curtain line in the rubber diaphragm, the geometric non-linear in the process of diaphragm’s deformation and the contact non-linear between the upper sheet and the rubber capsule or between the lower seat and the rubber capsule are discussed. Afterwards, the implement methods of air spring’s different non-linear in the finite element software Msc.Marc are analyzed. The effect of different initial pressure on the vertical stiffness in the air spring’s loading process and the stretched length of diaphragm generatrix under the different initial pressure of different position are researched. The results show that the vertical force and vertical stiffness increase with the increase of air spring’s initial pressure. Moreover, the change percent is less than 1.0% under the different initial pressure and the error can be accepted. The contrast between the results of air spring’s vertical stiffness attained by simulation method and the results attained by theoretical deduction explains the rightness of vertical stiffness formula of air spring’s main gas chamber in the dissertation.
The kinetic model of air spring’s main gas chamber is established, on basis of supposing adiabatic change, using the hydromechanics theory and the thermodynamics theory, integrating the energy equation and the continuity equation of gas in air spring and consulting the moving characteristic of air spring. Moreover, in the process of modeling, the discrete states are related together by the use of state controlled functions, so the deduction procedure of equation is simplified and the programming difficulty of numerical solver decreases. And then the free vibration, the throttle orifice diameter and the volume ratio between the two attaching gas chambers of air spring with series double attaching gas chambers are researched in detail by the numerical simulation method. The results show that the vertical kinetics performance is better than that of other analogous air springs. Moreover, the damping ratio’s maximum value of air spring is first relative to the throttle orifice I and then is only relative to the orifice II when the diameter of throttle orifice I is enough big. The damping ratio increases with the decrease of the first attaching gas chamber’s volume, when the diameter of orifice I is big enough, the diameters of two throttle orifices are invariable and the volume sum of the two attaching gas chambers is invariable.
On basis of establishing the free vibration differential equation of air spring, the kinetics model of air spring system under the condition of displacement excitation is deduced. The control mode of air spring is researched, the pressure of main gas chamber is ascertained as the controlled member and then the system kinetics equation adding the controlled actuating mechanism is set up. The air spring’s model under the displacement excitation and the air spring’s model adding control are analyzed by the numerical simulation method. The results show that the displacement excitation’s response of air spring with series double attaching gas chambers under the low frequency and high frequency is smaller than that of air spring with one attaching gas chamber. Moreover, the system vibration response adding the controlled variable is obviously decreased, which verifies that the air spring designed in the dissertation owns the better effect of vibration isolation under the effect of control system.
引文
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50 Cho J R, Lee H W, Yoo W S. Study on damping characteristics of hydropneumatic suspension unit of tracked vehicle. KSME International Journal. 2004,18(2):262-271
51刘增华,黄运华.半主动空气弹簧悬挂系统控制策略及仿真分析.系统仿真学报. 2007,19(13):3022-3027
52 Hayashi, Itsuro. Pressure pulsations in piping systems excited by a centrifugal compressor (2nd report, effect of operating conditions on damping characteristics). Transactions of the Japan Society of Mechanical Engineers. 2008,74(3):650-657
53 Sugahara Yoshiki. Vertical vibration suppression of railway vehicle by damping control of air springs. Transactions of the Japan Society of Mechanical Engineers. 2006,72(9):2762-2769
54 John Lewis. Car Spring. US Patent: No.4965,1847-02-10
55 William R F. Pneumatic spring. US Patent:No.19764,1858-03-30
56 Alsop G M. Carriage spring. US Patent:No.24184,1859-05-31
57 Hoagland I W. Carriage spring. US Patent:No.32848,1861-07-16
58 Annable W W. Pneumatic spring for vehicle. US Patent:No.673011,1901-04-30
59 George Bancroft. Pneumatic cushion for vehicle. US Patent:No.980138, 1910-12-27
60 Gieck Hack. Ride on air: a history of air suspension. New York:SAE Inc,1999
61 Bell Benjamin. Pneumatic spring. US Patent:No.971583,1910-10-04.
62 Revans J R. Rail vehicle dynamic simulation using VAMPIRE. Vehicle System Dynamic Supplement.1999, (12):278-285
63 Katsuya Toyofuku, Chuuji Yamada. Study on dynamic characteristic analysis of air spring with auxiliary chamber. JSAE Review. 1999,20(3): 349-355
64 Giuseppe Quaglia, Massimo Rorli. Air suspension dimensionless analysis and design procedure. Vehicle System Dynamics. 2001,35(6):443-455
65 Takuya Yuasa. The application of CAE in the development of air suspension beam. SAE paper. New York: SAE Inc. 1997. SAE973232
66 Alf Homeyer(德).采用现代方法设计空气弹簧系统.国外铁道车辆. 1999,(3):35-38
67 Malin Presthus. Derivation of air spring model parameters for train simulation [dissertation]. Lulea University of Technology. 2002
68 R. S. James. Solution verification for explicit transient dynamics problems in the presence of hourglass and contact forces. Computer Methods in Applied Mechanics and Engineering. 2006,(195):1499-1516
69 A. G. Thompson, C. E. M. Pearce. Performance index for a preview active suspension applied to a quarter-car model. Vehicle System Dynamics. 2001,35(1):55-56
70 L. M. Yuan. Research on vertical dynamic character of air spring-variable throttle system for railway vehicle. Journal of the China Railway Society. 2005,27(1):40-44
71 A. N. Gent, A. G. Thomas. Force-deflection relations for a model air spring. Rubber Chemistry and Technology. 1974,47(2):384-395
72原亮明,宫相太,王渊.铁道车辆空气弹簧垂向动态特性分析方法的研究.中国铁道科学. 2004,25(4):37-41
73 G. J. Stein. A drive’s seat with active suspension of electro-pneumatic type. Journal of Vibration and Acoustics. 1997,119(2):230-235
74 E. Augilera-Gomez. Dynamics of a pneumatic system:modeling, simulation and experiments. International Journal of Robotics and Automation. 1999,14(1):39-43
75 Toshihiko Asami, Osamu Nishihara. Analytical and experimental evaluation of an air damp dynamic vibration absorber: design optimization of the three element type model. Journal of Vibration and Acoustics. 1999,121(6):334-342
76 A. Jolly. Study of ride comfort using a nonlinear mathematical model of a vehicle suspension. Int. J. of Vehicle Design. 1983,4(3):233-244
77 A. Murata, Y. Kume. Application of catastrophe theory to forced vibration of a diaphragm air spring. Journal of Sound and Vibration. 1987,112(1): 31-44
78 C. G. Shuai. Study on the sensitivity of controllable parameters in an active vibration isolation system of air spring with rubber below. Proceeding of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. 2005:2259-2262
79 A. M. A. Soliman. Effect of suspension spring stiffness on vehicle dynamics.Int. J. of Vehicle Design. 2001,8(3):316-334
80 G. J. Stein. New result on an electropneumatic active seat suspension system. Journal of Automobile Engineering. 2000,214(5):533-544
81 Chance B K.1984 continental mark 7/Lincoln continental electronically-controlled air suspension system. SAE paper.New York:SAE Inc,1984. SAE 840342
82 Rambacher C., Mantwill F., Ehrt T., Merk J. Fundamentals for a 6dof model of air springs in car axle simulations. VDI Berichte (2031), 2008, pp. 433-445
83 Shimozawa K., Tohtake T. An air spring model with non-linear damping for vertical motion. Quarterly Report of RTRI (Railway Technical Research Institute) (Japan). 2008,49 (4), pp. 209-214
84原亮明,宫相太.铁道车辆空气弹簧—可变节流阀垂向动态特性的研究.铁道学报. 2005,27(1):40-44
85金锋,张先彤,王广宏.空气弹簧隔振技术.应用能源技术. 1997,(12): 12-14
86 Chang F., Lu Z. Dynamic model of an air spring and integration into a vehicle dynamics model. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering.2008, 222 (10), pp. 1813-1825
87刘茹,徐俊起.基于FPGA的碰浮列车空气弹簧控制系统设计.宜春学院学报. 2008,28(6):10-12
88仇龙晶.空气弹簧在电动振动台中的应用和设计改进.环境技术. 2008,(4):35-37
89张俏红.快速客车空气弹簧故障分析与检测技术.上海铁道科技. 2006,(6):14-16
90刘增华.空气弹簧及其在轨道车辆上的应用.电力机车与城轨车辆. 2003,26(6):24-27
91黄志辉.空气弹簧垂向、横向特性的有限元分析.西南交通大学硕士论文. 2006
92 Wang F., Cheng C., Qin M., Liu Z.-W. Rigid-elastic coupling modelling of air suspension and fatigue life prediction of its key part for heavy-duty truck. International Journal of Vehicle Design.2008, 47 (1-4), pp. 305-317
93盛英,赵建文.空气弹簧在光学平台隔振系统中的应用研究.西安电子科技大学硕士论文. 2006
94陆正刚.空气弹簧振动系统阻尼特性及改进措施.铁道车辆. 1999,(6):5-9
95黄卫平,鲍卫宁.汽车用空气弹簧垂向弹性特性分析与计算.机械. 2008,35(8):9-11
96刘天叶,伟何琳.导向附件对空气弹簧垂向刚度的影响.舰船电子工程. 2008,28(5):194-197
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106 Lee C T, Moon B Y. Study on the damping performance characteristics analysis of shock absorber of vehicle by considering fluid force. Journal of Mechanical Science and Technology. 2008,19(2):520-528
107吴善跃,黄映云.空气弹簧刚度的有限元分析方法.海军工程大学学报. 2001,13(6):94-98
108陈燕虹.半主动空气弹簧悬架智能控制算法的仿真及试验研究.吉林大学博士论文. 2005
109王磊,张慧慧,朱恩洪.空气悬架电子控制单元研究.制造业自动化. 2006,28(增刊):230-233
110陆正刚.铁道车辆主动、半主动空气弹簧悬挂系统的研究.铁道学报. 2001,23(1):33-38
111 Choi H S, Hong S W, Kim J H, et al. Study of oscillatory pneumatic damping in the air duct for an OWC type wave energy device. Proceedings of the Sixth(2004) ISOPE Pacific/ASIA Offshore Mechanics Symposium. 2004:209-215
112刘增华.基于半主动控制空气弹簧悬挂系统及其仿真研究.机械与液压. 2007,35(5):197-200
113周英,王晓雷,郑钢铁.空气弹簧隔振器主动控制的鲁棒控制方法研究.振动与冲击. 2007,26(1):125-128
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7张建文,庄德军,林逸,王望予,刘宏伟.汽车用空气弹簧悬架系统综述.公路交通科技. 2002,19(6):151-155
8 H. Kim, H. Lee. Asynchronous and synchronous load leveling compensation algorithm in airspring suspension. 2007 International Conference on Control, Automation and Systems. 2007:2262-2267
9 N. Docquier, H. Jeanmart. Model-based evaluation of railway pneumatic suspensions. Vehicle System Dynamics. 2008,46(1):481-493
10 N. H. Bayoumi. Large deformation analysis of structures enclosing air cavities. Proceeding of 2006 ASME Pressure Vessels and Piping Division Conference. 2006:7
11 B. Sridhara, J. Prince. Some interesting engineering problem with objects of simple geometry and relatively complex mathematical formulation. 2008 ASEE Annual Conference and Exposition. 2008:15
12 H. Porumamilla. Implementation of a modified skyhook control on a purely pneumatic semi-active suspension system. Proceeding of the ASME International Mechanical Engineering Congress and Exposition. 2007: 925-932
13 H. Porumamilla, A. G. Kelkar. Robust control and analysis of active pneumatic suspension. Proceeding of the 2005 American Control Conference. 2005: 2200-2205
14王进,林达文,彭立群.轨道车辆用空气弹簧的刚度特性试验. 2006,33(11):40-43
15韩厚禄,邓楚南.汽车空气弹簧的应用现状及发展趋势.重型汽车. 2008,(3):26-28
16 Jie Xiao. Sliding mode control of active suspension for transit buses based on a novel air spring model. Proceedings of the 2001 American Control Conference. 2001:201-209
17 Shiichiro Sarai, Masao Ikeda, Takahiro Miura. Decentralized position and attitude control of a vibration isolation system. Proceedings of the 2001 IEEE Intemational Conference on Control Applications. 2001:5-7
18 Masashi Yasuda,Takahide Osaka,Masao Ikeda. Feedforward control of a vibration isolation system for disturbance suppression. Proceedings of the 35th Conference on Decision and Control. 1996:312-321
19 Shinji Wakui. Incline compensation control using an air-spring type active isolated apparatus. Precision Engineering. 2003,(27):170–174
20 Yagiz N, Yuksek I, Sivenoglu S. Robust control of active suspensions for a full vehicle model using sliding mode control. JSME International Journal, Series C. 2003,43(2):254-258
21黄良平.空气弹簧的应用与发展趋势.橡胶科技市场. 2006,(15):10-14
22王力,王清国.空气弹簧在汽车上的应用.汽车工艺与材料. 2007,(2): 49-52
23 J. C. David. Fundamental issues in suspension design for heavy road vehicles. Vehicle System Dynamics. 2002,35(4):319-360
24 J. R. Evans. Rail vehicle dynamic simulation using VAMPIRE. Vehicle System Dynamics. 1999, Supplement:31-35
25 Donald Margolis. The stability of trailing arm suspension in heavy trucks. Vehicle Design. 2001,(3):31-36
26张建文.空气弹簧非线性有限元分析与空气悬架大客车隔振性能的研究.吉林大学博士论文. 2003:1-15
27尹万建.汽车空气弹簧悬架系统的非线性动力学行为研究.北京交通大学博士论文. 2007:1-19
28夏仕朝.空气弹簧隔振系统载荷分配优化研究.西安科技大学硕士论文. 2008
29赵建文,盛英,仇原鹰.空气弹簧参数对减振性能的影响.航空精密制造技术. 2006,42(3):17-20
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33 R. Schilling. Flexible or spring medium of suspension. SAE Journal. 1946,54(7):364-375
34 Ouyang Qing, Shi Yin. The non-linear mechanical properties of an air spring. Mechanical Systems and Signal Processing. 2003,17(3):705-711
35 He Liang. Study on vertical stiffness and damping of air spring based on excitation method. Journal of Vibration and Shock. 2008,27(7):167-170
36 Lin W J, Khatait J P. Modelling of an orifice-type aerostatic thrust bearing. 2006 9th International Conference on Control, Automation, Robotics and Vision. 2006:2111-2116
37 Liu Y S, Zhu B H, Zhu Y Q. Flow and cavitation characteristics of a damping orifice in water hydraulics. Journal of Power and Energy. 2006, 220(A8):933-944
38 Nie S L, Huang G H, Li Y P. Tribological study on hydrostatic slipper bearing with annular orifice damper for water hydraulic axial piston motor. Tribology International. 2006,39(11):1342-1354
39 Colwell S, Basu B. Investigations on the performance of a liquid column damper (LCD) with different orifice diameter ratios. Canadian Journal of Civil Engineering. 2006,33(5):588-595
40 Nagaraju T, Sharma S C, Jain S C. Study of orifice compensated hole-entry hybrid journal bearing considering surface roughness and flexibility effects. Tribology International. 2006,39(7):715-725
41 Wang Y B, Xu M L, Qiu Y. The flow behaviors of MR fluids flowing through an orifice for damper designing. Journal of Intelligent Material Systems and Structures. 2005,16(6):511-516
42 Korst H, Van L L. Mitigation of high-frequency pulsations, using multi-hole restriction orifices. 10th European Fluid Machinery Congress. 2008: 79-80
43 Wolfe R W, Yun H B, Masri S. Fidelity of reduced-order models for large-scale nonlinear orifice viscous dampers. Structural Control and Health Monitoring. 2008,15(8):1143-1163
44 Cundumi O, Suarez L E. A new variable damping semiactive device for seismic response reduction of civil structures. Journal of Mechanics of Materials and Structures. 2007,2(8):1639-1656
45 Cline C H O, Fales R. Solenoid damping of the pilot poppet in a forced-feedback metering poppet valve. Proceedings of the ASME International Mechanical Engineering Congress and Exposition. 2008:409-414
46 Yacout A W. The surface roughness effect on the dynamic stiffness anddamping characteristics of the hydrostatic thrust spherical bearings performance. Proceedings of the ASME International Mechanical Engineering Congress and Exposition. 2008: 449-462
47 Kim J H, Lew J M, Hong D C, et al. A study on motion of a BBDB type OWC wave energy device considering pneumatic damping coefficients in the duct. Proceedings of the Seventeenth (2007) International Offshore and Polar Engineering Conference. 2007:483-488
48赵洪伦.高速客车空气弹簧非线性横向刚度特性研究.铁道学报. 1999,21(6):30-33
49 Wang X J, Lambert M F, Simpson A R. Detection and location of a partial blockage in a pipeline using damping of fluid transients. Journal of Water Resources Planning and Management-ASCE. 2005,131(3):244-249
50 Cho J R, Lee H W, Yoo W S. Study on damping characteristics of hydropneumatic suspension unit of tracked vehicle. KSME International Journal. 2004,18(2):262-271
51刘增华,黄运华.半主动空气弹簧悬挂系统控制策略及仿真分析.系统仿真学报. 2007,19(13):3022-3027
52 Hayashi, Itsuro. Pressure pulsations in piping systems excited by a centrifugal compressor (2nd report, effect of operating conditions on damping characteristics). Transactions of the Japan Society of Mechanical Engineers. 2008,74(3):650-657
53 Sugahara Yoshiki. Vertical vibration suppression of railway vehicle by damping control of air springs. Transactions of the Japan Society of Mechanical Engineers. 2006,72(9):2762-2769
54 John Lewis. Car Spring. US Patent: No.4965,1847-02-10
55 William R F. Pneumatic spring. US Patent:No.19764,1858-03-30
56 Alsop G M. Carriage spring. US Patent:No.24184,1859-05-31
57 Hoagland I W. Carriage spring. US Patent:No.32848,1861-07-16
58 Annable W W. Pneumatic spring for vehicle. US Patent:No.673011,1901-04-30
59 George Bancroft. Pneumatic cushion for vehicle. US Patent:No.980138, 1910-12-27
60 Gieck Hack. Ride on air: a history of air suspension. New York:SAE Inc,1999
61 Bell Benjamin. Pneumatic spring. US Patent:No.971583,1910-10-04.
62 Revans J R. Rail vehicle dynamic simulation using VAMPIRE. Vehicle System Dynamic Supplement.1999, (12):278-285
63 Katsuya Toyofuku, Chuuji Yamada. Study on dynamic characteristic analysis of air spring with auxiliary chamber. JSAE Review. 1999,20(3): 349-355
64 Giuseppe Quaglia, Massimo Rorli. Air suspension dimensionless analysis and design procedure. Vehicle System Dynamics. 2001,35(6):443-455
65 Takuya Yuasa. The application of CAE in the development of air suspension beam. SAE paper. New York: SAE Inc. 1997. SAE973232
66 Alf Homeyer(德).采用现代方法设计空气弹簧系统.国外铁道车辆. 1999,(3):35-38
67 Malin Presthus. Derivation of air spring model parameters for train simulation [dissertation]. Lulea University of Technology. 2002
68 R. S. James. Solution verification for explicit transient dynamics problems in the presence of hourglass and contact forces. Computer Methods in Applied Mechanics and Engineering. 2006,(195):1499-1516
69 A. G. Thompson, C. E. M. Pearce. Performance index for a preview active suspension applied to a quarter-car model. Vehicle System Dynamics. 2001,35(1):55-56
70 L. M. Yuan. Research on vertical dynamic character of air spring-variable throttle system for railway vehicle. Journal of the China Railway Society. 2005,27(1):40-44
71 A. N. Gent, A. G. Thomas. Force-deflection relations for a model air spring. Rubber Chemistry and Technology. 1974,47(2):384-395
72原亮明,宫相太,王渊.铁道车辆空气弹簧垂向动态特性分析方法的研究.中国铁道科学. 2004,25(4):37-41
73 G. J. Stein. A drive’s seat with active suspension of electro-pneumatic type. Journal of Vibration and Acoustics. 1997,119(2):230-235
74 E. Augilera-Gomez. Dynamics of a pneumatic system:modeling, simulation and experiments. International Journal of Robotics and Automation. 1999,14(1):39-43
75 Toshihiko Asami, Osamu Nishihara. Analytical and experimental evaluation of an air damp dynamic vibration absorber: design optimization of the three element type model. Journal of Vibration and Acoustics. 1999,121(6):334-342
76 A. Jolly. Study of ride comfort using a nonlinear mathematical model of a vehicle suspension. Int. J. of Vehicle Design. 1983,4(3):233-244
77 A. Murata, Y. Kume. Application of catastrophe theory to forced vibration of a diaphragm air spring. Journal of Sound and Vibration. 1987,112(1): 31-44
78 C. G. Shuai. Study on the sensitivity of controllable parameters in an active vibration isolation system of air spring with rubber below. Proceeding of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. 2005:2259-2262
79 A. M. A. Soliman. Effect of suspension spring stiffness on vehicle dynamics.Int. J. of Vehicle Design. 2001,8(3):316-334
80 G. J. Stein. New result on an electropneumatic active seat suspension system. Journal of Automobile Engineering. 2000,214(5):533-544
81 Chance B K.1984 continental mark 7/Lincoln continental electronically-controlled air suspension system. SAE paper.New York:SAE Inc,1984. SAE 840342
82 Rambacher C., Mantwill F., Ehrt T., Merk J. Fundamentals for a 6dof model of air springs in car axle simulations. VDI Berichte (2031), 2008, pp. 433-445
83 Shimozawa K., Tohtake T. An air spring model with non-linear damping for vertical motion. Quarterly Report of RTRI (Railway Technical Research Institute) (Japan). 2008,49 (4), pp. 209-214
84原亮明,宫相太.铁道车辆空气弹簧—可变节流阀垂向动态特性的研究.铁道学报. 2005,27(1):40-44
85金锋,张先彤,王广宏.空气弹簧隔振技术.应用能源技术. 1997,(12): 12-14
86 Chang F., Lu Z. Dynamic model of an air spring and integration into a vehicle dynamics model. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering.2008, 222 (10), pp. 1813-1825
87刘茹,徐俊起.基于FPGA的碰浮列车空气弹簧控制系统设计.宜春学院学报. 2008,28(6):10-12
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