平行轴齿轮轮系运动方案的特征建模及求解方法
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摘要
本论文在国家自然科学基金(No.51075051)资助下完成。本文建立了平行轴齿轮轮系的运动特征模型,初步探讨了平行轴齿轮轮系运动方案的综合求解方法,并初步开发出平行轴齿轮轮系运动方案求解软件。
首先,建立了平行轴齿轮轮系基本单元运动特征模型。以基本单元作为复杂齿轮轮系运动方案求解的基本研究对象,提取出基本单元的运动功能特征；建立了基本单元运动特征模型描述基本单元输入输出运动特征状态的变换,包括建立基本单元运动特征向量和运动特征方程,并提取出运动特征矩阵；将常见基本单元汇总,初步建立了比较完整的基本单元库。
其次,建立了平行轴齿轮轮系运动特征模型。分析基本单元的组合形式,归纳出常见的基本单元组合形式,即串联式、反馈式、并联式及复合式等组合形式；分析基本单元组合时的构件连接形式,确定单元组合过程就是引入约束的过程,为此研究基本单元构件连接约束,并建立构件连接约束方程描述基本单元的组合过程：根据基本单元组合形式建立了单元组合运动特征模型；定义复合单元,与基本单元共同作为齿轮轮系运动方案分析与综合的单元化机构,并建立复合单元运动特征模型,建立复合单元库,基本单元库与复合单元库称作单元库。
接着,初步探讨了平行轴齿轮轮系运动方案求解方法。研究单元传动比,推导出单元库中单元的传动比范围,并得到单元传动比与运动特征矩阵元素之间的关系式；根据单元组合形式,建立了运动特征矩阵的分解规则,为计算机辅助运动方案设计的实现提供了可能性；建立了运动方案设计步骤；分析单元组合约束,建立了综合过程。
最后,初步开发出平行轴齿轮轮系运动方案求解软件。分析功能需求,建立运动方案求解软件的体系结构,开发出齿轮轮系运动方案求解软件；并通过设计实例验证了论文的运动方案求解方法的可行性和正确性
The kinematic characteristic model of gear trains with parallel axis is established. The synthesis solving method for kinematic scheme of gear trains is researched and software for kinematic scheme solving of gear trains is developed in this paper.
The kinematic characteristic model of basic unit is established. Basic units of gear trains are defined, which are used for fundamental research subjects of kinematic scheme design for gear trains. Then the kinematic characteristic vector of the basic unit is expressed and kinematic characteristic equation is established, then kinematic characteristic matrix is abstracted. Base on the method, the kinematic characteristic equation of the basic unit is built, which describes the transformation between input kinematic characteristic states and output kinematic characteristic states of the basic unit. Basic units are stocked in the basic unit database.
The kinematic characteristic model of gear trains with parallel axis is established. The common combination patterns including series combination, feedback combination, parallel combination, multiple combination, are summarized by means of researching on gear trains. The connecting constraint models for combination of basic units are set up by researching on combination patterns and the constraints characteristics of basic units, and then the component connecting constraint equation is built which describes the combination process. According to combination patterns of basic units, kinematic characteristic models of the basic units combination are established. Composite units of gear trains are defined, which are the basic mechanism units of analysis and synthesis as well as basic units. In the next, the kinematic characteristic model and the composite unit database of composite units are established.
The relation equation between transmission ratio and the element in kinematic characteristic matrix is achieved by researching on transmission ratio of units. With decomposition rule of kinematic characteristic matrix complemented, computer aided kinematic scheme design of gear train is developed. The procedure of kinematic scheme design of gear train is established.
The computer aided software system for kinematic scheme solving of gear train with parallel axis is developed. It can give solutions that meet the design requirements when the proposed approach is applied to a design example.
首先,建立了平行轴齿轮轮系基本单元运动特征模型。以基本单元作为复杂齿轮轮系运动方案求解的基本研究对象,提取出基本单元的运动功能特征；建立了基本单元运动特征模型描述基本单元输入输出运动特征状态的变换,包括建立基本单元运动特征向量和运动特征方程,并提取出运动特征矩阵；将常见基本单元汇总,初步建立了比较完整的基本单元库。
其次,建立了平行轴齿轮轮系运动特征模型。分析基本单元的组合形式,归纳出常见的基本单元组合形式,即串联式、反馈式、并联式及复合式等组合形式；分析基本单元组合时的构件连接形式,确定单元组合过程就是引入约束的过程,为此研究基本单元构件连接约束,并建立构件连接约束方程描述基本单元的组合过程：根据基本单元组合形式建立了单元组合运动特征模型；定义复合单元,与基本单元共同作为齿轮轮系运动方案分析与综合的单元化机构,并建立复合单元运动特征模型,建立复合单元库,基本单元库与复合单元库称作单元库。
接着,初步探讨了平行轴齿轮轮系运动方案求解方法。研究单元传动比,推导出单元库中单元的传动比范围,并得到单元传动比与运动特征矩阵元素之间的关系式；根据单元组合形式,建立了运动特征矩阵的分解规则,为计算机辅助运动方案设计的实现提供了可能性；建立了运动方案设计步骤；分析单元组合约束,建立了综合过程。
最后,初步开发出平行轴齿轮轮系运动方案求解软件。分析功能需求,建立运动方案求解软件的体系结构,开发出齿轮轮系运动方案求解软件；并通过设计实例验证了论文的运动方案求解方法的可行性和正确性
The kinematic characteristic model of gear trains with parallel axis is established. The synthesis solving method for kinematic scheme of gear trains is researched and software for kinematic scheme solving of gear trains is developed in this paper.
The kinematic characteristic model of basic unit is established. Basic units of gear trains are defined, which are used for fundamental research subjects of kinematic scheme design for gear trains. Then the kinematic characteristic vector of the basic unit is expressed and kinematic characteristic equation is established, then kinematic characteristic matrix is abstracted. Base on the method, the kinematic characteristic equation of the basic unit is built, which describes the transformation between input kinematic characteristic states and output kinematic characteristic states of the basic unit. Basic units are stocked in the basic unit database.
The kinematic characteristic model of gear trains with parallel axis is established. The common combination patterns including series combination, feedback combination, parallel combination, multiple combination, are summarized by means of researching on gear trains. The connecting constraint models for combination of basic units are set up by researching on combination patterns and the constraints characteristics of basic units, and then the component connecting constraint equation is built which describes the combination process. According to combination patterns of basic units, kinematic characteristic models of the basic units combination are established. Composite units of gear trains are defined, which are the basic mechanism units of analysis and synthesis as well as basic units. In the next, the kinematic characteristic model and the composite unit database of composite units are established.
The relation equation between transmission ratio and the element in kinematic characteristic matrix is achieved by researching on transmission ratio of units. With decomposition rule of kinematic characteristic matrix complemented, computer aided kinematic scheme design of gear train is developed. The procedure of kinematic scheme design of gear train is established.
The computer aided software system for kinematic scheme solving of gear train with parallel axis is developed. It can give solutions that meet the design requirements when the proposed approach is applied to a design example.
引文
[1]杨家军.机械系统创新设计.武汉：华中理.工大学出版社,1999.
[2]Freudenstein F and Dobrjanskyj L. On A Theory for the Type Synthesis of Mechanisms [C]. Proc.11th Int. Conf. Applied Mechanics,420.1964.
[3]Crossley F R E. The Permutations of Kinematic Chains of Eight Members or Less from the Graph Theoretic Viewpoint [J]. Developments in Theoretical and Applied Mechanics 1965,2:467-486.
[4]颜洪森等.机械装置的创造性设计[M].北京：机械工业出版社,2002.
[5]Yan, H S. Hwang W M. A method for the identification of planar chain. ASME Mech. Trans. and Auto, in design,1983,10(5).
[6]Yan H S. A methodology for creative mechanism design[J]. Mechanism and Machine Theory,1992,27(8):235-242.
[7]Yan, H S. Creative design of mechanical devices[D]. Springer-Verlag Singapore Pte. Ltd. 1998.
[8]段饮华,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)：55-56.
[9]杨实如,段钦华.周转轮系创新设计的基本单元组合法[J].机械科学与技术,2003(22)：761-763.
[10]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,(06)：22-24.
[11]Hsin-I Hsieh, Lung-Wen Tsai. Kinematic Analysis of Epicyclic-Type Transmission Mechanisms Using the Concept of Fundamental Geared Entities[J]. Journal of Mechanical Design.ASME,1996, V01116,294-299.
[12]G Chatterjee, Lung-Wen Tsai. Computer-aided sketching of epicyclic-type automatic transmission gear[J]. Journal of Mechanical Design.ASME,1996, Vol118,405-411.
[13]Cheng-Ho Hsu, Kin-Tak Lam. A new graph representation for the automatic kinematic analysis of planetary [J]. Journal of Mechanical Design.ASME,1992, VOL114,196-200.
[14]Cheng-Ho Hsu. An Analytic Methodology for the Kinematic Synthesis of Epicyclic Gear Mechanisms. Journal of Mechanical Design [J].ASME,2002, VOL 124,574-589.
[15]Cheng-Mo Hsu, Kin-Tak Lam. Automatic Analysis of Kinematic Structure of Planetary Gear Trains. Journal of Mechanical Design [J]. ASME,1993, VoL115,631-638.
[16]薛隆泉,汪友明,王慧武,等.周转轮系的分类和综合[J].中国机械工程,2005,16(19)1716-1722
[17]陈良钰,薛隆泉.周转轮系自由度及运动分析的图论方法[J].西安交通大学学报,2008,24(1):98-102.
[18]Shean-Juinn Chiou, Sridhar Kota. Automated Conceptual Design of Mechanisms [J]. Mechanism and Machine Theory.34(3)(1999):467-495.
[19]Yong-Mo Moon and S. kota, Automated synthesis of mechanism using dual-vector algebra [J], Mechanism and Machine Theory 37(2002):143-166.
[20]陈亚琴,孔凌嘉,张春林.机构叠加组合与创新设计[J].机械设计与研究,2001,(04)
[21]张春林,陈亚琴,赵艳红,孔凌嘉,路敦勇.机构封闭组合与创新设计[J].北京理工大学学报,2002,(06).
[22]陈亚琴,路敦勇,孔凌嘉,张春林.机构组合方法的分类[J].机械设计与研究,2002,(06)
[23]邹慧君,顾明敏.机构系统方案设计专家系统初探(一)——知识库管理系统的建立[J].机械设计,1996,13(5)：26-28.
[24]邹慧君,顾明敏.机构系统方案设计专家系统初探(二)——推理系统的建立与用[J].机械设计,1996,13(6)：12-14.
[25]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.
[26]张德珍,马雅丽,王德伦.机械系统的运动传递与变换矩形阵分析方法[J].中国机械工程,2003,14(1)：4-8.2003.1.
[27]张德珍,马雅丽,王德伦.机构类型综合自动求解分析及知识库系统的建立[J].机械l：程学报,2002,38(Supp)：194-199.
[28]张德珍,马雅丽,王德伦.机构类型综合设计过程自动求解分析及算法实现[J].中国机械工程,2003,14(10)：850-854.
[29]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]：(博十学位论文).大连：大连理工大学,2003.
[30]张利萍.机械系统方案设计的特征状态空间理论与方法[D]：(博十学位论文).大连：大连理工大学,2006.
[31]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)：26-35.
[32]Ma W Y, Wang D L, Ting K L Characteristic matrices and conceptual design of hydraul ic systems[J]..Journal of Mechanical Design,2010,132(3):0310051-03100513.
[33]马文勇,王德伦.液压系统方案设计的能量特征状态模型[J].机械工程报,2010(4)：129-135.
[34]马雅丽.机械系统方案设计的能量特征状态模型[D].大连理工大学,2011.
[35]李铭.混合轮系概念设计的能量特征状态方法[1)].大连理工大学，2009.
[36]李团结.周转轮系的计算机辅助运动分析和运动综合[J].机械传动,2001,25(01):4-6.
[37]唐林,邹慧君.用设计单元法实现计算机辅助机械运动方案设计[J].计算机辅助设计与图形学学报,2000,12(8)：614-617.
[38]唐林,邹慧君.计算机辅助机构选型的实现[J].中国机械工程,2001,(08)：918-921.
[39]史晓影,王宏汀,薛隆泉,刘相蕊.基于图论的真实轮系图计算机自动生成[J].铸造技术,2008,(11).
[40]Timothy L K, Bona B E胡饮训,刘颖译.状态空间分析导论.上册[M].北京：人民教育出版社,1981.
[41]饶振纲.行星齿轮传动设计[M].北京：化学工业出版社,2003.
[42]刘基林Visual C# 2008宝典[M].北京：电子工业出版社,2003.
[43]王珊,萨师煊.数据库系统概论[M].北京：高等教育出版社,2006.
[2]Freudenstein F and Dobrjanskyj L. On A Theory for the Type Synthesis of Mechanisms [C]. Proc.11th Int. Conf. Applied Mechanics,420.1964.
[3]Crossley F R E. The Permutations of Kinematic Chains of Eight Members or Less from the Graph Theoretic Viewpoint [J]. Developments in Theoretical and Applied Mechanics 1965,2:467-486.
[4]颜洪森等.机械装置的创造性设计[M].北京：机械工业出版社,2002.
[5]Yan, H S. Hwang W M. A method for the identification of planar chain. ASME Mech. Trans. and Auto, in design,1983,10(5).
[6]Yan H S. A methodology for creative mechanism design[J]. Mechanism and Machine Theory,1992,27(8):235-242.
[7]Yan, H S. Creative design of mechanical devices[D]. Springer-Verlag Singapore Pte. Ltd. 1998.
[8]段饮华,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)：55-56.
[9]杨实如,段钦华.周转轮系创新设计的基本单元组合法[J].机械科学与技术,2003(22)：761-763.
[10]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,(06)：22-24.
[11]Hsin-I Hsieh, Lung-Wen Tsai. Kinematic Analysis of Epicyclic-Type Transmission Mechanisms Using the Concept of Fundamental Geared Entities[J]. Journal of Mechanical Design.ASME,1996, V01116,294-299.
[12]G Chatterjee, Lung-Wen Tsai. Computer-aided sketching of epicyclic-type automatic transmission gear[J]. Journal of Mechanical Design.ASME,1996, Vol118,405-411.
[13]Cheng-Ho Hsu, Kin-Tak Lam. A new graph representation for the automatic kinematic analysis of planetary [J]. Journal of Mechanical Design.ASME,1992, VOL114,196-200.
[14]Cheng-Ho Hsu. An Analytic Methodology for the Kinematic Synthesis of Epicyclic Gear Mechanisms. Journal of Mechanical Design [J].ASME,2002, VOL 124,574-589.
[15]Cheng-Mo Hsu, Kin-Tak Lam. Automatic Analysis of Kinematic Structure of Planetary Gear Trains. Journal of Mechanical Design [J]. ASME,1993, VoL115,631-638.
[16]薛隆泉,汪友明,王慧武,等.周转轮系的分类和综合[J].中国机械工程,2005,16(19)1716-1722
[17]陈良钰,薛隆泉.周转轮系自由度及运动分析的图论方法[J].西安交通大学学报,2008,24(1):98-102.
[18]Shean-Juinn Chiou, Sridhar Kota. Automated Conceptual Design of Mechanisms [J]. Mechanism and Machine Theory.34(3)(1999):467-495.
[19]Yong-Mo Moon and S. kota, Automated synthesis of mechanism using dual-vector algebra [J], Mechanism and Machine Theory 37(2002):143-166.
[20]陈亚琴,孔凌嘉,张春林.机构叠加组合与创新设计[J].机械设计与研究,2001,(04)
[21]张春林,陈亚琴,赵艳红,孔凌嘉,路敦勇.机构封闭组合与创新设计[J].北京理工大学学报,2002,(06).
[22]陈亚琴,路敦勇,孔凌嘉,张春林.机构组合方法的分类[J].机械设计与研究,2002,(06)
[23]邹慧君,顾明敏.机构系统方案设计专家系统初探(一)——知识库管理系统的建立[J].机械设计,1996,13(5)：26-28.
[24]邹慧君,顾明敏.机构系统方案设计专家系统初探(二)——推理系统的建立与用[J].机械设计,1996,13(6)：12-14.
[25]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.
[26]张德珍,马雅丽,王德伦.机械系统的运动传递与变换矩形阵分析方法[J].中国机械工程,2003,14(1)：4-8.2003.1.
[27]张德珍,马雅丽,王德伦.机构类型综合自动求解分析及知识库系统的建立[J].机械l：程学报,2002,38(Supp)：194-199.
[28]张德珍,马雅丽,王德伦.机构类型综合设计过程自动求解分析及算法实现[J].中国机械工程,2003,14(10)：850-854.
[29]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]：(博十学位论文).大连：大连理工大学,2003.
[30]张利萍.机械系统方案设计的特征状态空间理论与方法[D]：(博十学位论文).大连：大连理工大学,2006.
[31]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)：26-35.
[32]Ma W Y, Wang D L, Ting K L Characteristic matrices and conceptual design of hydraul ic systems[J]..Journal of Mechanical Design,2010,132(3):0310051-03100513.
[33]马文勇,王德伦.液压系统方案设计的能量特征状态模型[J].机械工程报,2010(4)：129-135.
[34]马雅丽.机械系统方案设计的能量特征状态模型[D].大连理工大学,2011.
[35]李铭.混合轮系概念设计的能量特征状态方法[1)].大连理工大学，2009.
[36]李团结.周转轮系的计算机辅助运动分析和运动综合[J].机械传动,2001,25(01):4-6.
[37]唐林,邹慧君.用设计单元法实现计算机辅助机械运动方案设计[J].计算机辅助设计与图形学学报,2000,12(8)：614-617.
[38]唐林,邹慧君.计算机辅助机构选型的实现[J].中国机械工程,2001,(08)：918-921.
[39]史晓影,王宏汀,薛隆泉,刘相蕊.基于图论的真实轮系图计算机自动生成[J].铸造技术,2008,(11).
[40]Timothy L K, Bona B E胡饮训,刘颖译.状态空间分析导论.上册[M].北京：人民教育出版社,1981.
[41]饶振纲.行星齿轮传动设计[M].北京：化学工业出版社,2003.
[42]刘基林Visual C# 2008宝典[M].北京：电子工业出版社,2003.
[43]王珊,萨师煊.数据库系统概论[M].北京：高等教育出版社,2006.