双相渐开线活齿传动的研究
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摘要
本文简要介绍了活齿传动的结构特征、传动原理以及基本特点。在此基础上
分析了活齿传动的运动副组成特征，Ⅰ型、Ⅱ型活齿传动的结构模型及低副替代机
构。通过对活齿传动的运动学分析，求解两种基本传动形式的活齿运动规律；分
析组成啮合副的三构件间的运动转换；研究活齿传动传动比的计算方法和确定从
动轮的转向与中心轮齿数、活齿轮齿数之间的关系。活齿传动的齿形研究，对所
提出的活齿传动齿形综合的两类问题——齿形综合正解和齿形综合反解问题用等
效机构法进行了理论分析探讨。在分析活齿传动连续传动条件的基础上，研究活
齿传动的重合度问题及齿廓修形的影响。
在分析一齿差活齿减速器和双相活齿减速器优缺点的基础上，提出了双相渐
开线活齿减速器这一新型活齿减速器的设计问题。中心轮直接采用正移距修正的
渐开线内齿轮，双相激波器的廓线采用多项式—变形渐开线—圆弧组成的复合曲
线。用相似变换法推导出与内齿轮相对应的双相激波器的理论廓线及实际廓线方
程，并用解析法推导出能与工作曲线段光滑连接的多项式和圆弧段曲线方程，根
据激波器的曲线方程推导出内齿轮实际工作段和非工作段的位置，同时也介绍了
活齿的结构形式。对有关的设计参数以及不干涉条件、连续传动条件、重合度等
重要的结构问题也作了较为详细的讨论。对内齿轮的加工、刀具选择及加工参数
进行了分析研究。给出了串联式二级双相渐开线活齿减速器的设计实例，并对所
设计的减速器的运动干涉情况和激波器偏心对活齿传动的影响进行了计算机仿
真。
A brief introduction about structural character of, the transmission principle of and
the basic feature of sliding-teeth transmission is presented in this paper. Based on this,
composing character of motion pair, structural model and lower pair抯 replacement
mechanism of type I and type II sliding-teeth transmission are analyzed. By kinematics
analysis about sliding-teeth transmission, sliding-teeth moving rules of two basic
transmission models are found out, and motion transform among three components
about the mesh pair is analyzed. The calculation method of transmission rate about
sliding-teeth transmission is studied, and the relation between turning of driven wheel
and tooth numbers of center wheel and sliding-teeth wheel is discussed. The research on
sliding-teeth transmission gives theoretical analysis about two problems of the tooth
profile synthesis of sliding-teeth transmission-- tooth profile synthesis positive solution
problem and inverse solution problem by applying the equivalent mechanism method.
Based on analysis the continuous transmission condition of sliding-teeth transmission,
the problems of segistration coefficient and tooth profile trimming are discussed.
Based on discussing the advantages and disadvantages between one tooth
difference sliding- teeth reducer and double cams sliding-teeth reducer, a new
sliding-teeth reducer, i.e. double canis sliding-teeth reducer with involute tooth profile is
presented. Center wheel adopts involute inner gear with positive displacement modified.
The tooth profile of the double generating-wave cams employs compound curves
constituted with multinomial curve, distortion involute and arc. Applying the similarity
transformation method derives out the theoretical profile equation and practical profile
equation of the double wave generating cams corresponding to inner gear. Multinomial
curve equation and arc curve equation are derived out with analysis method, which
curves can be smoothly connected with working curve. The locations of inner gear抯
practical work and non-work portion derive from profile equation of the double
generating-wave cams. The structural style of sliding-teeth is introduced at the same
time. The design parameters and important structural problems such as the
nonintervention condition, continuous transmission condition and segistration
coefficient are discussed in detail as well. Does research on production, choice cutters
and production parameters of inner gear. And gives a design instance about double cams
sliding-teeth reducer with involute tooth profile, which sliding-teeth reducer is two
stages in series. The intervention condition and the infection of the generating-wave
cam that deviated from its center about the reducer are emulated.
分析了活齿传动的运动副组成特征，Ⅰ型、Ⅱ型活齿传动的结构模型及低副替代机
构。通过对活齿传动的运动学分析，求解两种基本传动形式的活齿运动规律；分
析组成啮合副的三构件间的运动转换；研究活齿传动传动比的计算方法和确定从
动轮的转向与中心轮齿数、活齿轮齿数之间的关系。活齿传动的齿形研究，对所
提出的活齿传动齿形综合的两类问题——齿形综合正解和齿形综合反解问题用等
效机构法进行了理论分析探讨。在分析活齿传动连续传动条件的基础上，研究活
齿传动的重合度问题及齿廓修形的影响。
在分析一齿差活齿减速器和双相活齿减速器优缺点的基础上，提出了双相渐
开线活齿减速器这一新型活齿减速器的设计问题。中心轮直接采用正移距修正的
渐开线内齿轮，双相激波器的廓线采用多项式—变形渐开线—圆弧组成的复合曲
线。用相似变换法推导出与内齿轮相对应的双相激波器的理论廓线及实际廓线方
程，并用解析法推导出能与工作曲线段光滑连接的多项式和圆弧段曲线方程，根
据激波器的曲线方程推导出内齿轮实际工作段和非工作段的位置，同时也介绍了
活齿的结构形式。对有关的设计参数以及不干涉条件、连续传动条件、重合度等
重要的结构问题也作了较为详细的讨论。对内齿轮的加工、刀具选择及加工参数
进行了分析研究。给出了串联式二级双相渐开线活齿减速器的设计实例，并对所
设计的减速器的运动干涉情况和激波器偏心对活齿传动的影响进行了计算机仿
真。
A brief introduction about structural character of, the transmission principle of and
the basic feature of sliding-teeth transmission is presented in this paper. Based on this,
composing character of motion pair, structural model and lower pair抯 replacement
mechanism of type I and type II sliding-teeth transmission are analyzed. By kinematics
analysis about sliding-teeth transmission, sliding-teeth moving rules of two basic
transmission models are found out, and motion transform among three components
about the mesh pair is analyzed. The calculation method of transmission rate about
sliding-teeth transmission is studied, and the relation between turning of driven wheel
and tooth numbers of center wheel and sliding-teeth wheel is discussed. The research on
sliding-teeth transmission gives theoretical analysis about two problems of the tooth
profile synthesis of sliding-teeth transmission-- tooth profile synthesis positive solution
problem and inverse solution problem by applying the equivalent mechanism method.
Based on analysis the continuous transmission condition of sliding-teeth transmission,
the problems of segistration coefficient and tooth profile trimming are discussed.
Based on discussing the advantages and disadvantages between one tooth
difference sliding- teeth reducer and double cams sliding-teeth reducer, a new
sliding-teeth reducer, i.e. double canis sliding-teeth reducer with involute tooth profile is
presented. Center wheel adopts involute inner gear with positive displacement modified.
The tooth profile of the double generating-wave cams employs compound curves
constituted with multinomial curve, distortion involute and arc. Applying the similarity
transformation method derives out the theoretical profile equation and practical profile
equation of the double wave generating cams corresponding to inner gear. Multinomial
curve equation and arc curve equation are derived out with analysis method, which
curves can be smoothly connected with working curve. The locations of inner gear抯
practical work and non-work portion derive from profile equation of the double
generating-wave cams. The structural style of sliding-teeth is introduced at the same
time. The design parameters and important structural problems such as the
nonintervention condition, continuous transmission condition and segistration
coefficient are discussed in detail as well. Does research on production, choice cutters
and production parameters of inner gear. And gives a design instance about double cams
sliding-teeth reducer with involute tooth profile, which sliding-teeth reducer is two
stages in series. The intervention condition and the infection of the generating-wave
cam that deviated from its center about the reducer are emulated.
引文
[1] 曲继方，活齿传动理论，北京：机械工业出版社，1993
[2] 饶振纲，行星传动机构设计，北京：国防工业出版社，1994
[3] N．A鲍洛托夫斯基[苏]著；张展 张国瑞译，渐开线齿轮与蜗杆传动几何计算手册，上海：华东化工学院出版社，1990
[4] 陈仰贤，多相凸轮式活齿减速器及共廓线的设计问题，甘肃工业大学学报，1989-2，29～38
[5] 吴昭同 张鄂等，齿轮精度标准与检验手册，北京：中国计量出版社，1994
[6] 曲继方 王志强，二齿差活齿传动齿形综合反解研究，东北重型机械学院学报，1992-1，22～28
[7] 陈仰贤 付顶云，活齿传动齿形综合的第Ⅱ类反解问题及相似变换法，甘肃工业大学学报，1992-4，31～38
[8] 周建军，JH型活齿针轮行星减速器齿形分析，机械，1989-3，23～26
[9] 王剑彬，基于模糊分析的渐开线少齿差行星齿轮传动的可靠性优化设计，机械传动，2000-3，43～45
[10] 濮良贵 纪名刚，机械设计(第六版)，北京：高等教育出版社，1996
[11] 马从谦 陈自修等，渐开线行星齿轮传动设计，北京：机械工业出版社，1987
[12] 曲继方，活齿齿轮副齿形分析的等效机构，天津大学学报，1990增刊，162～165
[13] 谭同德 李综浩，渐开线少齿差行星齿轮传动干涉的探讨，山西矿业学院学报，1987-4，408～417
[14] 邓昭明 胡天明等，推杆减速器的效率、平稳性计算及其存在问题的探讨，全国第五届机构学学术讨论会宣读论文，1987
[15] 《少齿差减速器》编写组，渐开线少齿差行星齿轮减速器，北京：机械工业出版社，1978
[16] 国家标准，渐开线圆柱齿轮模数(GB1357-87)，北京：技术标准出版社，1988
[17] 齿轮手册编委会，齿轮手册，北京：机械工业出版社，1990
[18] 周有强 王宏猷，渐开线少齿差传动的替代齿形探讨，巴黎国际会议论文，1985
[19] 曲纪方 金文林，摆动活齿减速机，全国第五届机构发明创造年会宣读论文，1993
[20] 刘杨松 朱文方，机械设计的模糊学方法，北京：机械工业出版社，1996
[21] 牟致忠 朱文予，机械可靠性设计，北京：机械工业出版社，1993
[22] 《数学手册》编写组，数学手册，北京：高等教育出版社，1978
[23] 袁哲俊，齿轮刀具设计，北京：新时代出版社，1983
[24] 波诺马连科著；华中工学院、天津机械研究所合译，径向柱塞式大扭矩液压马达，北京：机械工业出版社，1977
[25] 尹成湖 曲继方，平面机构组成学及构件静定组的研究，机械研究与应用，1991-1，11～13
[26] 李剑锋 曲继方，活齿齿轮副内齿轮齿形通用方程式及间隙分析，东北重型机械学院学报，1992-1，53～59
[27] 姜启源，数学模型(第二版)，北京：高等教育出版社，1993
[28] 刘惟信，机械可靠性设计，北京：清华大学出版社，1996
[29] Hammock BJ, Dow son D, Ball bearing lubrication, Canada: By John Wiley & Sonic. inc, 1981,
[30] Trackman EG, A continuously variable traction drive Proc, Leeds Tribology, 1981
[31] Van H S et al, A methodology for creative mechanism design, MMT, 1992, 27(3)
[32] B S Bagepalli, et al, Generalized modeling of dynamic cam-follower pairs in mechanisms,Trans, of the ANSME, J. of Mechanical Design, 1991
[33] Alberto Gardena, Kinematics and dynamic of mechanisms with cam, Computer Methods in Applied Mechanics and Engineering, 1993,109: 115-134
[34] Y. Altintas, K. Erkorkmaz, W. H. Zhu, Sliding mode controller design for high speed feed drives, CIRP Annals Manufacturing Technology, 2000, 49(1) : 265-270
[2] 饶振纲，行星传动机构设计，北京：国防工业出版社，1994
[3] N．A鲍洛托夫斯基[苏]著；张展 张国瑞译，渐开线齿轮与蜗杆传动几何计算手册，上海：华东化工学院出版社，1990
[4] 陈仰贤，多相凸轮式活齿减速器及共廓线的设计问题，甘肃工业大学学报，1989-2，29～38
[5] 吴昭同 张鄂等，齿轮精度标准与检验手册，北京：中国计量出版社，1994
[6] 曲继方 王志强，二齿差活齿传动齿形综合反解研究，东北重型机械学院学报，1992-1，22～28
[7] 陈仰贤 付顶云，活齿传动齿形综合的第Ⅱ类反解问题及相似变换法，甘肃工业大学学报，1992-4，31～38
[8] 周建军，JH型活齿针轮行星减速器齿形分析，机械，1989-3，23～26
[9] 王剑彬，基于模糊分析的渐开线少齿差行星齿轮传动的可靠性优化设计，机械传动，2000-3，43～45
[10] 濮良贵 纪名刚，机械设计(第六版)，北京：高等教育出版社，1996
[11] 马从谦 陈自修等，渐开线行星齿轮传动设计，北京：机械工业出版社，1987
[12] 曲继方，活齿齿轮副齿形分析的等效机构，天津大学学报，1990增刊，162～165
[13] 谭同德 李综浩，渐开线少齿差行星齿轮传动干涉的探讨，山西矿业学院学报，1987-4，408～417
[14] 邓昭明 胡天明等，推杆减速器的效率、平稳性计算及其存在问题的探讨，全国第五届机构学学术讨论会宣读论文，1987
[15] 《少齿差减速器》编写组，渐开线少齿差行星齿轮减速器，北京：机械工业出版社，1978
[16] 国家标准，渐开线圆柱齿轮模数(GB1357-87)，北京：技术标准出版社，1988
[17] 齿轮手册编委会，齿轮手册，北京：机械工业出版社，1990
[18] 周有强 王宏猷，渐开线少齿差传动的替代齿形探讨，巴黎国际会议论文，1985
[19] 曲纪方 金文林，摆动活齿减速机，全国第五届机构发明创造年会宣读论文，1993
[20] 刘杨松 朱文方，机械设计的模糊学方法，北京：机械工业出版社，1996
[21] 牟致忠 朱文予，机械可靠性设计，北京：机械工业出版社，1993
[22] 《数学手册》编写组，数学手册，北京：高等教育出版社，1978
[23] 袁哲俊，齿轮刀具设计，北京：新时代出版社，1983
[24] 波诺马连科著；华中工学院、天津机械研究所合译，径向柱塞式大扭矩液压马达，北京：机械工业出版社，1977
[25] 尹成湖 曲继方，平面机构组成学及构件静定组的研究，机械研究与应用，1991-1，11～13
[26] 李剑锋 曲继方，活齿齿轮副内齿轮齿形通用方程式及间隙分析，东北重型机械学院学报，1992-1，53～59
[27] 姜启源，数学模型(第二版)，北京：高等教育出版社，1993
[28] 刘惟信，机械可靠性设计，北京：清华大学出版社，1996
[29] Hammock BJ, Dow son D, Ball bearing lubrication, Canada: By John Wiley & Sonic. inc, 1981,
[30] Trackman EG, A continuously variable traction drive Proc, Leeds Tribology, 1981
[31] Van H S et al, A methodology for creative mechanism design, MMT, 1992, 27(3)
[32] B S Bagepalli, et al, Generalized modeling of dynamic cam-follower pairs in mechanisms,Trans, of the ANSME, J. of Mechanical Design, 1991
[33] Alberto Gardena, Kinematics and dynamic of mechanisms with cam, Computer Methods in Applied Mechanics and Engineering, 1993,109: 115-134
[34] Y. Altintas, K. Erkorkmaz, W. H. Zhu, Sliding mode controller design for high speed feed drives, CIRP Annals Manufacturing Technology, 2000, 49(1) : 265-270
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