复杂轮系基本单元的运动特征状态数学建模
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摘要
提出了复杂齿轮轮系运动分析的单元运动特征状态建模方法。通过研究复杂齿轮轮系构成规律,并分解其构成,定义了轮系基本单元;以齿轮原型机构为基础,利用机构拓扑特征构建了轮系基本单元构型图谱;构建了运动特征状态向量用以描述运动的类型和方向特征等属性,并利用状态方程建立了轮系基本单元的运动特征状态模型,为后续的轮系运动方案设计提供了理论基础。
This paper presented a new modeling approach for unit kinematic characteristic state on the motion analysis of compound gear trains. Gear basic units were defined according to studying the composite rules and decomposing the constitution of compound gear trains. Based on prototypes of gear basic units,gear mechanism diagrams of basic units were set up using topological characteristics of mechanism. Kinematic vector was built to describe the type and direction characteristics of motion. The kinematic characteristic model was established by using state equation. All of them provides a solid theoretical basis for kinematic conceptual design of gear trains.
This paper presented a new modeling approach for unit kinematic characteristic state on the motion analysis of compound gear trains. Gear basic units were defined according to studying the composite rules and decomposing the constitution of compound gear trains. Based on prototypes of gear basic units,gear mechanism diagrams of basic units were set up using topological characteristics of mechanism. Kinematic vector was built to describe the type and direction characteristics of motion. The kinematic characteristic model was established by using state equation. All of them provides a solid theoretical basis for kinematic conceptual design of gear trains.
引文
[1]薛隆泉,雷亚荣.周转轮系系统化的数学模型[J].机械工程学报,2008,44(4):80-86.Xue Longquan,Lei Yarong.System Mathematic Model of Epicyclic Gear Trains[J].Chinese Journal of Mechanical Engineering,2008,44(4):80-86.
[2]雷亚荣,薛隆泉.周转轮系系统化研究的图论方法[J].西安理工大学学报,2007,23(1):98-101.Lei Yarong,Xue Longquan.Graph Method of Epicyclic Trains Systematic Research[J].Journal of Xi’an University of Technology,2007,23(1):98-101.
[3]陈良钰,薛隆泉.周转轮系自由度及运动分析的图论方法[J].西安理工大学学报,2008,24(1):98-102.Chen Liangyu,Xue Longquan.Graph Theory Method to the Freedom and Motion Analysis of Epicyclic Gears[J].Journal of Xi’an University of Technology,2008,24(1):98-102.
[4]Chen Dar-Zen,Shiue Shuen-Chen.Kinematic Characteristics and Classification of Geared Mechanisms Using the Concept of Kinematic Fractionation[J].Journal of Mechanical Design,2008,130(8):2-7.
[5]Liu Chia-Pin,Chen Dar-Zen.On the Application of Kinematic Units to the Topological Analysis of Geared Mechanisms[J].Journal of Mechanical Design,2001,123(2):240-246.
[6]卢存光,段钦华.3K型行星轮系的单元分析法[J].机械设计与研究,2009,25(6):22-24.Lu Cunguang,Duan Qinhua.The Unit Analysis Method of 3K Type Planetary Gear[J].Mechine Design and Research,2009,25(6):22-24.
[7]杨实如,段钦华.NGW型差动变速机构的特点与设计[J].机械设计与研究,2003,19(6):29-30.Yang Shiru,Duan Qinhua.The Characteristics and Design of NGW Differential Gear Mechanism[J].Mechine Design and Research,2003,19(6):29-30.
[8]段钦华,杨实如.复杂周转轮系的单元求解法[J].机械设计与研究,2001,17(1):55-56.Yang Shiru,Duan Qinhua.The Finite Element Method for Solving the Complex Epicyclic Gear Trains[J].Mechine Design and Research,2001,17(1):55-56.
[9]Hsu Cheng-Ho.A New Graph Representation for the Automatic Kinematic Analysis of Planetary[J].Journal of Mechanical Design,1992,114:196-200.
[10]Hsu Cheng-Ho,Lam Kin-Tak.An Analytic Methodology for the Kinematic Synthesis of Epicyclic Gear Mechanisms[J].Journal of Mechanical Design,2002,124:574-589.
[11]Hsu Cheng-Ho,Lam Kin-Tak.Automatic Analysis of Kinematic Structure of Planetary Gear Trains[J].Journal of Mechanical Design,1993,115:631-638.
[12]张利萍,王德伦.混联机械系统方案设计特征状态空间理论与方法[J].机械工程学报,2006,42(12):26.Zhang Liping,Wang Delun.New Approach to Automated Conceptual Design of Hybrid Mechanical System by Means of Characteristics State Space[J].Chinese Journal of Mechanical Engineering,2006,42(12):26.
[13]王德伦,张德珍,马雅丽.机械运动方案设计的状态空间方法[J].机械工程学报,2003,39(3):22-27.Wang Delun,Zhang Dezhen,Ma Yali.New Approach to Automated Conceptual Design of Mechanical System by Means of State-Space[J].Chinese Journal of Mechanical Engineering,2003,39(3):22-27.
[14]张德珍.基于状态空间方法的机械运动方案设计的理论基础[J].计算机集成制造系统-CIMS,2005,11(1):127-132.Zhang Dezhen.Theory of Mechanical Kinematic Scheme Design Based on State-space[J].Computer Integrated Manufacturing Systems,2005,11(1):127-132.
[15]马雅丽.机械系统方案设计的能量特征状态模型[D].大连:大连理工大学,2001.
[16]张德珍.串联机械系统运动方案设计的状态空间理论与方法的研究[D].大连:大连理工大学,2002.
[2]雷亚荣,薛隆泉.周转轮系系统化研究的图论方法[J].西安理工大学学报,2007,23(1):98-101.Lei Yarong,Xue Longquan.Graph Method of Epicyclic Trains Systematic Research[J].Journal of Xi’an University of Technology,2007,23(1):98-101.
[3]陈良钰,薛隆泉.周转轮系自由度及运动分析的图论方法[J].西安理工大学学报,2008,24(1):98-102.Chen Liangyu,Xue Longquan.Graph Theory Method to the Freedom and Motion Analysis of Epicyclic Gears[J].Journal of Xi’an University of Technology,2008,24(1):98-102.
[4]Chen Dar-Zen,Shiue Shuen-Chen.Kinematic Characteristics and Classification of Geared Mechanisms Using the Concept of Kinematic Fractionation[J].Journal of Mechanical Design,2008,130(8):2-7.
[5]Liu Chia-Pin,Chen Dar-Zen.On the Application of Kinematic Units to the Topological Analysis of Geared Mechanisms[J].Journal of Mechanical Design,2001,123(2):240-246.
[6]卢存光,段钦华.3K型行星轮系的单元分析法[J].机械设计与研究,2009,25(6):22-24.Lu Cunguang,Duan Qinhua.The Unit Analysis Method of 3K Type Planetary Gear[J].Mechine Design and Research,2009,25(6):22-24.
[7]杨实如,段钦华.NGW型差动变速机构的特点与设计[J].机械设计与研究,2003,19(6):29-30.Yang Shiru,Duan Qinhua.The Characteristics and Design of NGW Differential Gear Mechanism[J].Mechine Design and Research,2003,19(6):29-30.
[8]段钦华,杨实如.复杂周转轮系的单元求解法[J].机械设计与研究,2001,17(1):55-56.Yang Shiru,Duan Qinhua.The Finite Element Method for Solving the Complex Epicyclic Gear Trains[J].Mechine Design and Research,2001,17(1):55-56.
[9]Hsu Cheng-Ho.A New Graph Representation for the Automatic Kinematic Analysis of Planetary[J].Journal of Mechanical Design,1992,114:196-200.
[10]Hsu Cheng-Ho,Lam Kin-Tak.An Analytic Methodology for the Kinematic Synthesis of Epicyclic Gear Mechanisms[J].Journal of Mechanical Design,2002,124:574-589.
[11]Hsu Cheng-Ho,Lam Kin-Tak.Automatic Analysis of Kinematic Structure of Planetary Gear Trains[J].Journal of Mechanical Design,1993,115:631-638.
[12]张利萍,王德伦.混联机械系统方案设计特征状态空间理论与方法[J].机械工程学报,2006,42(12):26.Zhang Liping,Wang Delun.New Approach to Automated Conceptual Design of Hybrid Mechanical System by Means of Characteristics State Space[J].Chinese Journal of Mechanical Engineering,2006,42(12):26.
[13]王德伦,张德珍,马雅丽.机械运动方案设计的状态空间方法[J].机械工程学报,2003,39(3):22-27.Wang Delun,Zhang Dezhen,Ma Yali.New Approach to Automated Conceptual Design of Mechanical System by Means of State-Space[J].Chinese Journal of Mechanical Engineering,2003,39(3):22-27.
[14]张德珍.基于状态空间方法的机械运动方案设计的理论基础[J].计算机集成制造系统-CIMS,2005,11(1):127-132.Zhang Dezhen.Theory of Mechanical Kinematic Scheme Design Based on State-space[J].Computer Integrated Manufacturing Systems,2005,11(1):127-132.
[15]马雅丽.机械系统方案设计的能量特征状态模型[D].大连:大连理工大学,2001.
[16]张德珍.串联机械系统运动方案设计的状态空间理论与方法的研究[D].大连:大连理工大学,2002.