基于键合图理论的多体系统耦合动力学建模方法的研究
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摘要
对于复杂的多体机械系统,许多学者相继提出了不同形式的以分析力学原理为基础的计算机辅助建模与仿真方法。但是,这些方法及软件多数仅限于单一能量形式的系统(例如,机械系统)的局部动力学,对于多种能量形式耦合的多体机械系统(例如:机、电、液、气及刚柔性耦合的系统),无法以统一的方式在计算机上自动地建立系统正、逆动力学方程及运动副约束反力方程,并进行有效的全局动态性能分析,使得分析结果与实际工况差别较大。另外,其仿真效率也有待于进一步地提高。上述问题已成为多种能量形式集成的多体机械系统的分析、研究及开发应用的根本障碍,使键合图理论在多能域耦合系统全局动力学的研究中占有重要的地位。
本文的研究工作解决了基于键合图理论的多能域耦合多体系统全局动力学建模与仿真研究领域的一系列重要问题,为功能更加完备的动力学分析软件系统的研制提供有力的理论支持。这对进一步提高该类工作的自动化和实用化程度颇具意义,在车辆系统、数控机床、工程机械、机器人、一般机械、航天机械等领域具有广泛的应用前景。
本文系统地阐述了基于键合图理论的多体系统耦合动力学建模与仿真方法。从能量守恒的基本原理出发,讨论了键合图中的多通口元件MTF所具有的的性质:只要知道其输入流和输出流间的关系,就可以通过简单的矩阵变换确定输入势和输出势间的关系,反之亦然。以此为基础阐述了建立平面多刚体系统、非惯性系平面多刚体系统、平面柔性多体系统、非惯性系平面柔性多体系统及空间多刚体系统键合图模型的一般方法及其动力学原理。
多体系统构件间的运动几何约束,使其键合图模型产生微分因果环;构件上任意一点与其质心的非线性速度关系,使其键合图模型具有非线性结型结构。这给用传统标准的键合图法进行计算机自动建模与仿真带来了非常困难的代数问题。本文提出两种各具特色的解决策略:(1)在标准键合图理论框架下,将运动副约束反力视作未知外界势源,加在系统键合图模型相应的0-结处;(2)利用键合图基本元件间的等效转换关系,将标准键合图转换成回转键合图(Gyrobondgraph)。上述两种策略在多能域范围内,实现了对微分因果环及所产生的非线性结型结构的解耦,解决了其给系统全局耦合动力学计算机辅助建模与仿真所带来的代数困难。
对于多体系统动力学逆问题,分别在标准键合图及回转键合图理论框架下,推导出不同形式的便于计算机自动生成的系统状态方程、运动副约束反力方程的统一公式。所述方法特别适用于多种能量形式并存的复杂系统的计算机自动建模与仿真。对于多体系统动力学正问题,分别在标准键合图及回转键合图理论框架下,严格推导出不同形式的便于计算机自动生成的多体系统驱动力矩(或驱动力)及运动副约束反力的统一公式。所述方法特别适用于多种能量形式并存的复杂系统的计算机辅助动态静力分析。同时,无需进行系统加速度分析,可以提高复杂多体系统动态静力分析的效率及可靠性。
此外,基于MATLAB研制了相应的系统动态分析软件,实现了计算机自动建模与仿真。通过典型应用实例说明所述方法及软件的有效性。
To complicated multibody systems, different kinds of computer aided modeling and simulation procedure based on analytic mechanics have been proposed. As a result, some representative system dynamic analysis softwares with powerful function are developed. But these procedures and softwares are only suitable for the partial dynamic analysis of systems with single energy domain such as mechanical system. For the system with the coupling of multi-energy domains, such as the systems with the coupling of machine, electricity, hydraulics, pneumatics, rigidity and flexibility, they can not be used for deriving the forward and inverse system dynamic equations and constraint force equations in a unified manner automatically on a computer. So that the global dynamic analysis of systems can not be carried out. These result in larger error in dynamic analysis. In addition to these, the simulation efficiency of system should be increased further. The above problems have become the ultimate obstacle of analysis, study, development and application for the multibody mechanical systems with the integration of multi-energy domains, and made bond graph theory become very important to the global dynamics of systems with multi-energy domains.
By the research work in this dissertation,a series of important problems of global dynamic modelling and simulation for multibody systems with the coupling of multi-enegy domains based on bond graph theory are solved. As a result, the dynamic analysis software with more powerful function are supported theoretically, and the automatic and reliable level of this kind of work can be raised greatly. The research work in this dissertation can be widely used in the fields such as vehicle system, numerical control machine, engineering machine, robot, general machine,and space machine, etc.
In this dissertation, the modeling and simulation procedure based on bond graph theory for the coupling dynamics of multibody systems is described systematically. From the viewpoint of enegy conservation, the properties of bond graph multiport element MTF are discussed. Thus knowledge of the flow vector relationship across the MTF dictates the effort vector relationship through a simple matrix transposition, and vice versa. Based on this, the generic procedures of modeling planar rigid multibody system, planar rigid multibody system in non-inertial coordinate system, planar flexible multibody system, planar flexible multibody system in non-inertial coordinate system and spatial multibody system by bond graphs and their dynamic principles are described.
The kinematic and geometric constraints between bodies of multibody system result in differential causality loop, and the nonlinear velocity relationship between the mass center and an arbitrary point on a body leads to the nonlinear junction strcture. These bring very difficult algebraic problem for automatic modeling and simulation on a computer by traditional standard bond graph method. To solve this problem, two strategies with different characteristic are proposed in this dissertation. First, in the frame of standard bond graph theory, the constraint forces at joints can be considered as unknown effort sources and added to the corresponding 0-junctions of system bond graph model. Second, by means of the equivalent transformation between basic elements of bond graph, the standard bond graph can be transformed into gyrobondgraph. By means of the two above strategies, the decoupling to differential causality loop and nonlinear junction structure can be realized. As a result, the algebraic difficulty brought by them for computer aided modelling and simulation of system global coupling dynamics can be solved.
For inverse dynamic problem of multibody system, the different form of unified formulae of system state-space equations and constraint force equations at joints are derived in the frame of bond graph and gyrobondgraph theory respectively, they are very suitable for the automatic modeling and simulation on a computer for complex multibody systems with multi-energy domains. For forward dynamic problem, the different form of unified formulae of balancing moments and constraint forces at joints are derived in the frame of bond graph and gyrobondgraph theory respectively, they are very suitable for computer aided static analysis for dynamic of complex multibody systems with multi-energy domains. By these procedure, the acceleration analysis of system is not needed, so that the efficiency and reliability of static analysis for dynamic of complex multibody systems is increased.
In addition to above work, the corresponding system dynamic analysis software is developed based on MATLAB. As a result, the automatic dynamic modeling and simulation on a computer are realized. The validity of the procedures are illustrated by a lot of typical examples of application.
本文的研究工作解决了基于键合图理论的多能域耦合多体系统全局动力学建模与仿真研究领域的一系列重要问题,为功能更加完备的动力学分析软件系统的研制提供有力的理论支持。这对进一步提高该类工作的自动化和实用化程度颇具意义,在车辆系统、数控机床、工程机械、机器人、一般机械、航天机械等领域具有广泛的应用前景。
本文系统地阐述了基于键合图理论的多体系统耦合动力学建模与仿真方法。从能量守恒的基本原理出发,讨论了键合图中的多通口元件MTF所具有的的性质:只要知道其输入流和输出流间的关系,就可以通过简单的矩阵变换确定输入势和输出势间的关系,反之亦然。以此为基础阐述了建立平面多刚体系统、非惯性系平面多刚体系统、平面柔性多体系统、非惯性系平面柔性多体系统及空间多刚体系统键合图模型的一般方法及其动力学原理。
多体系统构件间的运动几何约束,使其键合图模型产生微分因果环;构件上任意一点与其质心的非线性速度关系,使其键合图模型具有非线性结型结构。这给用传统标准的键合图法进行计算机自动建模与仿真带来了非常困难的代数问题。本文提出两种各具特色的解决策略:(1)在标准键合图理论框架下,将运动副约束反力视作未知外界势源,加在系统键合图模型相应的0-结处;(2)利用键合图基本元件间的等效转换关系,将标准键合图转换成回转键合图(Gyrobondgraph)。上述两种策略在多能域范围内,实现了对微分因果环及所产生的非线性结型结构的解耦,解决了其给系统全局耦合动力学计算机辅助建模与仿真所带来的代数困难。
对于多体系统动力学逆问题,分别在标准键合图及回转键合图理论框架下,推导出不同形式的便于计算机自动生成的系统状态方程、运动副约束反力方程的统一公式。所述方法特别适用于多种能量形式并存的复杂系统的计算机自动建模与仿真。对于多体系统动力学正问题,分别在标准键合图及回转键合图理论框架下,严格推导出不同形式的便于计算机自动生成的多体系统驱动力矩(或驱动力)及运动副约束反力的统一公式。所述方法特别适用于多种能量形式并存的复杂系统的计算机辅助动态静力分析。同时,无需进行系统加速度分析,可以提高复杂多体系统动态静力分析的效率及可靠性。
此外,基于MATLAB研制了相应的系统动态分析软件,实现了计算机自动建模与仿真。通过典型应用实例说明所述方法及软件的有效性。
To complicated multibody systems, different kinds of computer aided modeling and simulation procedure based on analytic mechanics have been proposed. As a result, some representative system dynamic analysis softwares with powerful function are developed. But these procedures and softwares are only suitable for the partial dynamic analysis of systems with single energy domain such as mechanical system. For the system with the coupling of multi-energy domains, such as the systems with the coupling of machine, electricity, hydraulics, pneumatics, rigidity and flexibility, they can not be used for deriving the forward and inverse system dynamic equations and constraint force equations in a unified manner automatically on a computer. So that the global dynamic analysis of systems can not be carried out. These result in larger error in dynamic analysis. In addition to these, the simulation efficiency of system should be increased further. The above problems have become the ultimate obstacle of analysis, study, development and application for the multibody mechanical systems with the integration of multi-energy domains, and made bond graph theory become very important to the global dynamics of systems with multi-energy domains.
By the research work in this dissertation,a series of important problems of global dynamic modelling and simulation for multibody systems with the coupling of multi-enegy domains based on bond graph theory are solved. As a result, the dynamic analysis software with more powerful function are supported theoretically, and the automatic and reliable level of this kind of work can be raised greatly. The research work in this dissertation can be widely used in the fields such as vehicle system, numerical control machine, engineering machine, robot, general machine,and space machine, etc.
In this dissertation, the modeling and simulation procedure based on bond graph theory for the coupling dynamics of multibody systems is described systematically. From the viewpoint of enegy conservation, the properties of bond graph multiport element MTF are discussed. Thus knowledge of the flow vector relationship across the MTF dictates the effort vector relationship through a simple matrix transposition, and vice versa. Based on this, the generic procedures of modeling planar rigid multibody system, planar rigid multibody system in non-inertial coordinate system, planar flexible multibody system, planar flexible multibody system in non-inertial coordinate system and spatial multibody system by bond graphs and their dynamic principles are described.
The kinematic and geometric constraints between bodies of multibody system result in differential causality loop, and the nonlinear velocity relationship between the mass center and an arbitrary point on a body leads to the nonlinear junction strcture. These bring very difficult algebraic problem for automatic modeling and simulation on a computer by traditional standard bond graph method. To solve this problem, two strategies with different characteristic are proposed in this dissertation. First, in the frame of standard bond graph theory, the constraint forces at joints can be considered as unknown effort sources and added to the corresponding 0-junctions of system bond graph model. Second, by means of the equivalent transformation between basic elements of bond graph, the standard bond graph can be transformed into gyrobondgraph. By means of the two above strategies, the decoupling to differential causality loop and nonlinear junction structure can be realized. As a result, the algebraic difficulty brought by them for computer aided modelling and simulation of system global coupling dynamics can be solved.
For inverse dynamic problem of multibody system, the different form of unified formulae of system state-space equations and constraint force equations at joints are derived in the frame of bond graph and gyrobondgraph theory respectively, they are very suitable for the automatic modeling and simulation on a computer for complex multibody systems with multi-energy domains. For forward dynamic problem, the different form of unified formulae of balancing moments and constraint forces at joints are derived in the frame of bond graph and gyrobondgraph theory respectively, they are very suitable for computer aided static analysis for dynamic of complex multibody systems with multi-energy domains. By these procedure, the acceleration analysis of system is not needed, so that the efficiency and reliability of static analysis for dynamic of complex multibody systems is increased.
In addition to above work, the corresponding system dynamic analysis software is developed based on MATLAB. As a result, the automatic dynamic modeling and simulation on a computer are realized. The validity of the procedures are illustrated by a lot of typical examples of application.
引文
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67 林 超 李润方 伍 奎等。基于键合图模型的双驱动行星传动系统动态分析与实验研究。中国机械工程,2003,14(2):1002～1003
68 J. J. Granda. The Role of Bond Graph Modelling and Simulation in Mechatronic Systems, An Integrated Software Tool: CAMP-G, MATLAB-Simulink. Mechatronics, 2002, 12: 1271～1295
69 P. C. Breedveld. Port-Based Modelling of Mechatronic Systems. Mathamatics and Computers in Simulation, 2004, 66: 99～127
70 J. V. Amerongen, P. Breedveld. Modelling of Physical Systens for the Design and Control of Mechatronic Systems. Annual Reviews in Control, 2003, 27: 87～117
71 AHMET SA?IRLL, MUHARREM ERDEM BO?OCL, VASFI EMRE ?MüRLü. Modelling the Dynamics and Kinematics of a Telescopic Rotary Crane By the Bond Graph Method( Part one). Nonlinear Dynamics, 2003, 33: 337～351
72 AHMET SA?IRLL, MUHARREM ERDEM BO?OCL, VASFI EMRE ?MüRLü. Modelling the Dynamics and Kinematics of a Telescopic Rotary Crane By the Bond Graph Method( Part two). Nonlinear Dynamics, 2003, 33:353～367
73 朱福民 郑惠强。边坡压实机振动液压控制回路及其动态模型。中国机械工程,2005,15(5):387～390
74 韩兆林,胡纪滨,荆崇波。液压机械传动系统双流工况动态特性研究。北京理工大学学报,2004,24(2):104～108
75 李儒琼,陈兆能,谭迪华。电液集成块液路系统的建模仿真。机床与液压,2003,(3):121～123
76 冯 刚,江峰,宋东峰等。变量柱塞泵的键合图建模和动态仿真研究。机床与液压,2004,(12):20～25
77 Casimir Sié Kama, Geneviéve Dauphin-Tanguyb. Bond graph models of Strctured Parameter uncertainties. Journal of the Franklin Institute ,2005, 342 : 379～399
78 B. O. Bouamama, K. Medjaher, M. Bayart, A. K. Samantaray, et al. Fault Detection and Isolation of Smart Actuators Using Bond Graphs and External Models. Control Engineering Practice, 2005, 13: 159～175
79 W. Borutzky, G. Dauphin-Tanguy. Incremental Bond Graph Approach to the Derivation of State Equations for Robustness Study. Simulation Modelling Practice and Theory, 2004, 12: 41～60
80 H. Shr-Shiung, Y. Pao-Hwa, B. C. Chang. A Computational Issue and Modified Formulas for Nonlinear Dissipative Controller. ASME. Journal of Dynamic Systems, Measurement and Control, 2003, 125: 475～504
81 B. Ould Bouamama, K. Medjaher, A.K. Samantaray, et al. Supervision of an industrial steamgenerator. Part I: Bond graph modeling. Control Engineering Practace. 2006, 14: 71~83
82 K. Medjaher, A.K. Samantaray, B. Ould Bouamama, et al. Supervision of an industrial steamgenerator. Part II: Online implementation. Control Engineering Practace. 2006, 14: 85~96
83 M. J. Krikclis, F. Papadakis. Gas Turbine Modelling Using Pseudo-Bond Graph. Int. J. Systems Sci., 1988, 19(4): 537～550
84 严运兵,王仲范,杜传进等。基于伪键合图的内燃机建模与仿真。内燃机工程,2004,25(5):13～17
85 严运兵,王仲范,杜传进。键合图在内燃机工作过程数学模拟中的应用。武汉理工大学学报·信息与管理工程版,2004,26(1):146～150
86 E. C. Francois, àngela Nebot, Jüregen Greifeneder. Bond graph modeling of heat and humidity budgets of biosphere 2. Envirnonmental Modelling and Software, 2006 , 21: 1598~1606
87 R. C. de Freitas, K. R. Diller, J. R. T. Lakey, et al. Osmotic Behavior and Transport Properties of Human Islets in a Dimethyl Sulfoxide Solution. Crybiology, 1997, 35(3): 230～239
88 D. L. Margolis, M. Tabrizi. Acoustic Modelling of Lung Dynamics Using Bond Graphs. ASME. J. Biomech. Eng., 1983, 105: 84～91.
89 L. A. Wojcik. Modelling of Musculoskeletal Strcture and Function Using a Modular Bond Graph Approach. Journal of The Franklin Institute, 2003, 340: 63～76
90 J. U. Thoma. Simulation, entropy Flux and Chemical Potential. Bio Systems, 1976, 8: 1～9
91 J. Lefevre, J. Barreto. A Mixed Block Diagram Bond Graph Approach to Biochemical Models With Mass Action and Rate Law Kinetics. Journal of The Franklin Institute, 1985, 319(1/2): 201～215
92 M. Hemamalini, P. Thomas Muthiah, R.J. Butcher, et al. The Interplay of Hydrogen-bonding and Metal-coordination Motifs in the Formation of Supramolecular Patterns: Copper/zinc Malonates–aminopyrimidine Complexes. Inorganic Chemistry Communications, 2006, 9: 1155~1160
93 J. Brewer, P. Craig. Bilinear, Dynamic Single-Ports and Bond Graphs of Economic Systems. Journal of The Franklin Institute, 1982, 313(4): 185～196
94 J. Brewer, P. Craig, M. Hubbard. The Bond Graph for Technological Forcecasing and Resource Policy Analysis. Energy, 1982, 7(6): 505～537
95 J. W. Brewer. Structure and Cause and Effect Relations in Social System Simulations. IEEE Trans. Syst. Man. Cybern., 1977, SMC-7(6): 468～474
96 B. Samanta, A. Mukherjee. Application of Bond Graph to Acoustoelastic Systems Using Concepts of Dualism and decomposition. J. Acoust. Soc., 1987, 14(1): 205～210
97 R. Shoureshi, and D. Carey. Dynamic Modelling of Couple Electroacoustic Systems Using Bond Graph. Int. J. Modelling Simulation, 1987, 7(1): 15～19
98 R. R. Allen. Bond Graph Modes for Plant biosystems. Computer Programme Biomed., 1978, 318(8): 148～216
99 G. P. A. Bot, J. J. Van Dixhoorn. Dynamic Modelling of Greenhouse Climate Using a Mini Computer. Acta. Horticult., 1978, 76: 113～120
100 张尚才。工程系统的键合图模拟和仿真。北京:机械工业出版社,1993:1～209
101 王沫然编著。MATLAB与科学计算。北京:电子工业出版社,2003:1～437
102 檀润华,孙立峰,苑彩云等。基于功率键合图的自动符号建模与仿真。中国机械工程,2000,11(9):1058～1061
103 黄洪钟,祖旭,张旭。基于Matlab/Simulink的键合图仿真。大连理工大学学报,2003,43(5):632～635
104 R. R. Allen, S. Dubowsk. Meachanisms as Components of Dynamic Systems: A Bond Graph Approach. ASME Journal of Engineering for Industry, 1977, 99(1): 104～111
105 A. Zeid. Bond Graph Modelling of Planar Mechanisms With Realistic Joint Effects. ASME Journal of Dynamic Systems, Measurement, and Control, 1989, 111(1): 15～23
106 P. C. Breedveld, Proposition of An Unambiguous Vector Bond Graph. ASME Journal of Dynamic Systems, Measurement and Control, 1982, 104: 267～270
107 M. Ingrim, G. Masada. The Extended Bond Graph Notation. ASME Journal of Dynamic Systems, Measurement and Control, 1991, 113: 113～117
108 E. Fahrenthold, J. Wargo. Vector and Tensor Based Bond Graphs for Physical System Modelling. Journal of the Franklin Institute, 1991, 328: 833～853
109 A. Zeid, C. H. Chung. Bond Graph Modelling of Multibody Systems: A Library of Three-Dimensional Joints. Journal of the Franklin Institute, 1992, 329: 605～636
110 J. Jang, C. Han. Proposion of a Modelling Method for Constrained Mechanical Systems Based on Vector Bond Graphs. Journal of the Franklin Institute, 1998, 335: 451～469
111 W. Favre, S. Scavarda. Bond Graph Representation of Multibody Systems with Kinematic Loops. Journal of the Franklin Institute, 1998, 335: 451～469
112 L. Sass, J. Mcphee, C. Schmitke, et al. A Comparision of Different Methods for Modelling Electromechanical Multibody Systems. Multibody System Dynamics, 2004, 12: 209～205
113 张珂,王生泽。平面可控七杆机构键合图动力学分析。中国机械工程, 2006,17(4):367～371
114 赵匀,俞高红,武传宇等。机构数值分析与综合。北京:机械工业出版社,2005:1～388
115 A. Myklebust. Dynamic Response of an Electric Motor-Linkage System During Startup. ASME Journal of Mechanical Design, 1982, (1): 137~142
116 F. S. Tse, I. E. Morse, R. T. Hinkle. Mechanical Vibrations Theory and Applications. Boston: Allyn and Bacon, inc. ,1978:142-300
117 R. C. Rosenberg . On Gyrobondgraph and Their Uses. Trans. ASME. Journal of Dynamic Systems,Measurement,and Control,1978,100(3):76~82
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7 K. Moojin, M. Wonky, B. Daesung. Dynamic Simulation of Electromechanical Robotic Systems Driven by DC Motors. Robotica, 2004, 22: 523～531
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14 P. Flores, J. Ambrosio, J. P. Claro. Dynamic Analysis for Multibody Mechanical Systems with Lubricated Joints. Multibody System Dynamics, 2004, 12: 47～74
15 S. Marcus, M. John. Dynamic Modelling of Electromechanical Multibody Systems. Multibody System Dynamics, 2003, 9: 87～115
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17 H. M. Paynter. Analysis and Design of Engineering Systems. Cambrige: M.I.T. Press, 1961:1～123
18 D. C. Karnopp, D. L. Margolis, R. C. Rosenberg. System Dynamics:A Unified Approach. New York: Wiley, 1990: 1~166
19 R. C. Rosenberg. Reflections on Engineering Systems and Bond Graphs. ASME. Journal of Dynamic Systems, Measurement, and Control, 1993, 115(2): 242～251
20 M. D. Jenny, D. Marisol, B. Claude, et al. A Survey of Bond Graphs: Theory, Applications and Programs. Journal of the Franklin Institute, 1991, 328: 565～606
21 W. Borutzky, G. Dauphin-Tanguy, J. U. Thoma. Advanced in Bond Graph Modelling: Theory, Software, Applications. Mathematics and Computers in Simulation, 1995, 39: 465～475
22 A. S. Ahmed. Flexible Multibody Dynamics: Reviews of Past and Recent Developments. Multibody System Dynamics, 1997, 1: 189～222
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27 陆佑方著。柔性多体系统动力学。北京:高等教育出版社,1996:1～176
28 黄文虎,邵成勋著。多柔体系统动力学。北京:科学出版社,1996:1～212
29 李庆扬,关治,白峰杉。数值计算原理。北京:清华大学出版社,2000:356～393
30 J. U. Thoma. Simulation By Bondgraphs.New York: Springer, 1990: 1～167
31 J. U. Thoma. Thermofluid Systems By Multi-Bondgraphs. J. Franklin Inst., 1992, 329: 999～1009
32 P. Dransfield. Hydraulic Control Systems-Design and Analysis of Their Dynamics. New York: Springer-Verlag, 1981:1～232
33 P. C. Breedveld. Multibond Graph Elements in Physical Systems Theory. J. Franklin Inst., 1985, 319: 1～36
34 P. C. Breedveld. Current Topics in Bond Graph Related Research. J. Franklin Inst., 1991, 328: 15～21
35 R. C. Rosenberg. Exploiting Bong Graph Causality in Physical System Models. Trans. ASME J. Dyn. Syst. Meas. Control, 1987, 109(4): 378～383
36 S. J. Hood, E. R. Palmer, P. M. Dantzig. A Fast, Complete Method for Automatically Assignment Causality to Bond Graphs. Journal of the Franklin Institute, 1989, 326(1): 83～92
37 D. C. Karnopp. Lagrange’s Equations for Complex Bond Graph Systems. ASME J. Dyn. Syst., Meas., 1977, 99(4): 300～306
38 B. J. Joseph, H. R. Martens. The Method of Relaxed Causality in the Bond Graph Analysis of Nonlinear Systems. ASME J. Dyn. Syst., Meas., 1974, 96(1): 95～99
39 W. Marquit-Favre, S. Scavarda. Alternative Causality Assignment Procedures in Bond Graph for Mechanical Systems. ASME J. Dyn. Syst., Meas., 2002, 124(3): 457～463
40 D. L. Margolis. A Survey of Bond Graph Modeling for Interacting Lumped and Distributed Systems. Journal of The Franklin Institute, 1985, 319(1/2):125～136
41 D. C. Karnopp, D. L. Margolis, R. C. Rosenberg. System Dynamics: Modeling and Simulation of Mechatronic Systems. New York: Wiley, 2000: 1~496
42 王艾伦,赵振宇,仇勇。自由界面模态综合法的研究及应用。湘潭大学自然科学学报,2002,24(4):60~64
43 王艾伦,钟掘。模态分析的一种新方法-键合图法。振动工程学报,2003,16(4):465~467
44 王艾伦,钟掘。复杂机电系统的全局耦合建模方法及仿真研究。机械工程学报,2003,39(4):1~5
45 G. Ermer, R. C. Rosenberg, et al. Steps Towards Integrating Function-Based Models and Bond Graphs for Conceptual Design in Engineering. ASME, Automated Modeling for Design, 1993, DSC-Vol.47: 47～62
46 J. E. E. Sharp. Intergrated Computer Support for Interdisciplinary system Design. ASME, 1994, PD-Vol.64-5: 107-114
47 J. E. E. Sharp. Application of Bond Graph Methodology to Concurrent Design of Interdisciplinary Systems. Proc. Of IEEE International Conference on System, Man and Cybenetics, LeTouquet, France, 1993.10, 1: 7～13
48 K. T. Ulrich, W. P. Seering. Synthesis of Schematic Descriptions in Mechnical Design. Research in Engineering Design, 1989, 1(1): 3～18
49 R. V. Welch, J. R. Dixon. Guiding Conceptual Design Through Behavioral Reasoning. Research in Engineering Design, 1994, 6(1): 169～188
50 檀润华,陈鹰,路甬祥。产品多个设计方案的键合图方法。机械设计,1998,15(1):14～16
51 曹东兴,檀润华,苑彩云等。基于功能分解的机械产品概念设计。机械工程学报,2001,37(11):13～17
52 曹东兴,檀润华,苑彩云等。基于状态空间表示法的的机械产品概念设计。计算机辅助设计与图形学学报,2002,14(2):172～175
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54 曹东兴,檀润华,姚广法等。概念设计行为矩阵模型的公理化验证。中国机械工程,2005,16(4):337～340
55 曹东兴,檀润华,耿磊等。基于功能方法树的机械产品概念设计。上海交通大学学报,2004,38(6):888～891
56 G. M. Asher. The Robust Modelling of Variable Topology Circuits Using Bond Graphs. Proceedings of International Conference on Bond Graph Modelling, San Diego, CA, 1993: 126～131
57 J. E. Str?mberg, J. Top, U. S?derman, Variable Causality in Bond Graph Caused by Discrete Effects. Proceedings of International Conference on Bond Graph Modelling, San Diego, CA, 1993: 115～119
58 P. J. Mosterman, G. Biswas. Behaviour Generation Using Model Switching―A Hybrid Bond Graph Modelling Technique. International Conference on Bond Graph Modelling, 1995. Las Vegas, 1995: 177～182
59 P. J. Mosterman, G. Biswas. A Theory of Discontinuities of Physical System Models. Journal of the Franklin Institute, 1998, 335B(3): 401～439
60 Y. Demir, M. Poyraz. Derivation of State and Output Equations for SystemsContaining Switches and a Novel Definition of a Switch Using the Bond Graph Model. Journal of the Franklin Institute, 1997, 334(2): 191～197
61 A. Bruno, H. Hichem, L. Chung-Cheh, et al. Power Converter Average model Computation Using the Bond Graph and Petri Net Techniques. IEEE PESC, 1995: 830～836
62 C. U. Amod, L. Umanand. Modelling of Switching Systems in Bond Graphs Using the Concept of Switched Power Junctions. Journal of the Franklin Institute, 2005, 342(1): 131～147
63 胡晓林,王仲范,廖连莹。变结构系统的键合图仿真。机械设计,2004,21(5):41～43
64 张珂,王生泽。基于功率键合图的混合驱动五杆机构动力学分析。机械设计,2005,22(4):6～8
65 D. L. Margolis, D. C. Karnopp. Bond Graph for Flexible Multibody Systems. Tans. ASME J. Dyn. Syst. Meas. Control, 1979, 101(1): 50～51
66 M. Tiernego, A. M. Bos. Modeling the Dynamics and Kinematics of Mechanical Systems With Mulibond Graphs. Journal of The Franklin Institute, 1985, 319(1/2): 37～50
67 林 超 李润方 伍 奎等。基于键合图模型的双驱动行星传动系统动态分析与实验研究。中国机械工程,2003,14(2):1002～1003
68 J. J. Granda. The Role of Bond Graph Modelling and Simulation in Mechatronic Systems, An Integrated Software Tool: CAMP-G, MATLAB-Simulink. Mechatronics, 2002, 12: 1271～1295
69 P. C. Breedveld. Port-Based Modelling of Mechatronic Systems. Mathamatics and Computers in Simulation, 2004, 66: 99～127
70 J. V. Amerongen, P. Breedveld. Modelling of Physical Systens for the Design and Control of Mechatronic Systems. Annual Reviews in Control, 2003, 27: 87～117
71 AHMET SA?IRLL, MUHARREM ERDEM BO?OCL, VASFI EMRE ?MüRLü. Modelling the Dynamics and Kinematics of a Telescopic Rotary Crane By the Bond Graph Method( Part one). Nonlinear Dynamics, 2003, 33: 337～351
72 AHMET SA?IRLL, MUHARREM ERDEM BO?OCL, VASFI EMRE ?MüRLü. Modelling the Dynamics and Kinematics of a Telescopic Rotary Crane By the Bond Graph Method( Part two). Nonlinear Dynamics, 2003, 33:353～367
73 朱福民 郑惠强。边坡压实机振动液压控制回路及其动态模型。中国机械工程,2005,15(5):387～390
74 韩兆林,胡纪滨,荆崇波。液压机械传动系统双流工况动态特性研究。北京理工大学学报,2004,24(2):104～108
75 李儒琼,陈兆能,谭迪华。电液集成块液路系统的建模仿真。机床与液压,2003,(3):121～123
76 冯 刚,江峰,宋东峰等。变量柱塞泵的键合图建模和动态仿真研究。机床与液压,2004,(12):20～25
77 Casimir Sié Kama, Geneviéve Dauphin-Tanguyb. Bond graph models of Strctured Parameter uncertainties. Journal of the Franklin Institute ,2005, 342 : 379～399
78 B. O. Bouamama, K. Medjaher, M. Bayart, A. K. Samantaray, et al. Fault Detection and Isolation of Smart Actuators Using Bond Graphs and External Models. Control Engineering Practice, 2005, 13: 159～175
79 W. Borutzky, G. Dauphin-Tanguy. Incremental Bond Graph Approach to the Derivation of State Equations for Robustness Study. Simulation Modelling Practice and Theory, 2004, 12: 41～60
80 H. Shr-Shiung, Y. Pao-Hwa, B. C. Chang. A Computational Issue and Modified Formulas for Nonlinear Dissipative Controller. ASME. Journal of Dynamic Systems, Measurement and Control, 2003, 125: 475～504
81 B. Ould Bouamama, K. Medjaher, A.K. Samantaray, et al. Supervision of an industrial steamgenerator. Part I: Bond graph modeling. Control Engineering Practace. 2006, 14: 71~83
82 K. Medjaher, A.K. Samantaray, B. Ould Bouamama, et al. Supervision of an industrial steamgenerator. Part II: Online implementation. Control Engineering Practace. 2006, 14: 85~96
83 M. J. Krikclis, F. Papadakis. Gas Turbine Modelling Using Pseudo-Bond Graph. Int. J. Systems Sci., 1988, 19(4): 537～550
84 严运兵,王仲范,杜传进等。基于伪键合图的内燃机建模与仿真。内燃机工程,2004,25(5):13～17
85 严运兵,王仲范,杜传进。键合图在内燃机工作过程数学模拟中的应用。武汉理工大学学报·信息与管理工程版,2004,26(1):146～150
86 E. C. Francois, àngela Nebot, Jüregen Greifeneder. Bond graph modeling of heat and humidity budgets of biosphere 2. Envirnonmental Modelling and Software, 2006 , 21: 1598~1606
87 R. C. de Freitas, K. R. Diller, J. R. T. Lakey, et al. Osmotic Behavior and Transport Properties of Human Islets in a Dimethyl Sulfoxide Solution. Crybiology, 1997, 35(3): 230～239
88 D. L. Margolis, M. Tabrizi. Acoustic Modelling of Lung Dynamics Using Bond Graphs. ASME. J. Biomech. Eng., 1983, 105: 84～91.
89 L. A. Wojcik. Modelling of Musculoskeletal Strcture and Function Using a Modular Bond Graph Approach. Journal of The Franklin Institute, 2003, 340: 63～76
90 J. U. Thoma. Simulation, entropy Flux and Chemical Potential. Bio Systems, 1976, 8: 1～9
91 J. Lefevre, J. Barreto. A Mixed Block Diagram Bond Graph Approach to Biochemical Models With Mass Action and Rate Law Kinetics. Journal of The Franklin Institute, 1985, 319(1/2): 201～215
92 M. Hemamalini, P. Thomas Muthiah, R.J. Butcher, et al. The Interplay of Hydrogen-bonding and Metal-coordination Motifs in the Formation of Supramolecular Patterns: Copper/zinc Malonates–aminopyrimidine Complexes. Inorganic Chemistry Communications, 2006, 9: 1155~1160
93 J. Brewer, P. Craig. Bilinear, Dynamic Single-Ports and Bond Graphs of Economic Systems. Journal of The Franklin Institute, 1982, 313(4): 185～196
94 J. Brewer, P. Craig, M. Hubbard. The Bond Graph for Technological Forcecasing and Resource Policy Analysis. Energy, 1982, 7(6): 505～537
95 J. W. Brewer. Structure and Cause and Effect Relations in Social System Simulations. IEEE Trans. Syst. Man. Cybern., 1977, SMC-7(6): 468～474
96 B. Samanta, A. Mukherjee. Application of Bond Graph to Acoustoelastic Systems Using Concepts of Dualism and decomposition. J. Acoust. Soc., 1987, 14(1): 205～210
97 R. Shoureshi, and D. Carey. Dynamic Modelling of Couple Electroacoustic Systems Using Bond Graph. Int. J. Modelling Simulation, 1987, 7(1): 15～19
98 R. R. Allen. Bond Graph Modes for Plant biosystems. Computer Programme Biomed., 1978, 318(8): 148～216
99 G. P. A. Bot, J. J. Van Dixhoorn. Dynamic Modelling of Greenhouse Climate Using a Mini Computer. Acta. Horticult., 1978, 76: 113～120
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