新型泛摆线齿轮齿形设计的研究

哈尔滨工业大学工学硕士学位论文
摘 要
传统摆线齿轮齿廓是由圆摆线拼接形成，具有重合度大、不根切齿数小、 磨损小且均匀的优点。在对小体积、轻量化、高效率要求日益迫切的现代生产 中，摆线齿轮的优势被关注，制造水平的提高很容易满足摆线齿轮对精度的要 求。目前对摆线齿轮的研究主要集中在参数选取和圆摆线的拼接方法，但摆线 齿轮不具有可分性，这样的研究不能改变摆线啮合的本质，使得其应用受到很 大局限。本文介绍的齿廓是传统圆摆线齿廓的变形，称之为新型泛摆线齿轮， 既保留摆线齿轮传动的优点，解决了中心距问题，又使轮齿强度有一定提升。 该齿轮齿廓由变形内摆线、渐开线和变形外摆线组成，其共轭齿轮由齿轮 啮合原理得到。这种齿廓形成的齿轮在满足重合度的条件下，最小齿数为 6 ， 并且不会产生根切，这大大缩小了齿轮及减速器体积。该齿轮啮合时的滑动率 相对渐开线齿轮较小并且均匀，齿廓啮合的相对曲率半径较渐开线大，并且齿 根的齿廓形状使得齿根强度较大。啮合的一对齿轮中心距变动量为零时，退化 成传统的摆线齿轮，中心距变动量不为零时，成为一般的新型泛摆线齿轮。其 中，封闭齿廓不能用于一般齿轮传动，由其形成的更有效齿廓则可以满足重合 度要求，具有更广泛的应用。 本文通过坐标转换得到直摆线族和直摆线在齿轮坐标系中的表达式，分别 以包络法和运动法建立啮合方程，得到直摆线包络线（新型泛摆线齿廓）的几 何模型，计算直摆线包络的根切界限方程，确定可以形成齿廓的直摆线区域， 根据齿数得到封闭齿廓和更有效齿廓的几何模型。根据啮合条件绘制共轭齿轮 和啮合线，并且对啮合齿轮的重合度、滑动率、压力角、曲率半径和综合曲率 半径、各向受力和应力进行计算并绘制变化图线。通过对齿轮齿廓的研究确定 了齿廓的基本参数和基本齿廓，给出齿轮各部分计算公式以及参数选取的一般 规律和方法。对新型泛摆线齿轮的加工原理进行研究，得到共轭齿轮的插齿原 理。为验证所研究内容，选取一组参数配置满足条件的新型泛摆线齿轮，建立 了 3K-III 型行星齿轮减速器三维模型并进行实际加工，齿廓啮合良好，减速器 运行平稳，证明了齿廓设计的合理性。但是，新型泛摆线齿轮参数没有能够系 列化和标准化，尺寸的简易计算，齿形误差参数与精度控制仍需进一步研究。 关键词：新型泛摆线；中心距；变位系数；根切界限条件；重合度； 3K 型行 星传动
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哈尔滨工业大学工学硕士学位论文
pressure on bearings or gears and stress of this two conjugated gears. Through the studies on the tooth profile of the new universal cycloid gear, the basic parameters of the tooth profile and basic tooth profile are identified, formulas on calculating the various parts of the gear, general rules and parameter selecting methods are give n, the new universal cycloid gear processing principles are researched, and also the shaping principle of a pair of conjugated cycloid gear are gained. In order to verify the contents of the research, a set of new universal cycloid gear’s parameters, which can meet the meshing condition, are chosen to build a 3K-III planetary speed reducer, 3-D models are built and the actual reducer are processed. The tooth profile meshing well and the reducer running smoothly, that proved the tooth profile designing is reasonable. However, the serialization and standardization of the parameters, the formula for calculating the geometrical dimensions, the profile error parameters and the profile error control still need further study. Keywords: the new universal cycloid gear, centerline spacing, modification coefficient, undercutting boundary conditions, contact ratio, the 3K type planetary transmission
硕士学位论文
新型泛摆线齿轮齿形设计的研究
（工学硕士）
RESEARCH AND DESIGN OF THE NEW UNIVERSAL CYCLOID GEAR TOOTH PROFILE
刘建壮
哈尔滨工业大学 2013 年 7 月
国内图书分类号： TH13 国际图书分类号： 621
学校代码： 10213 密级：公开
Dissertation for the Master Degree in Engineering
RESEARCH AND DESIGN OF THE NEW UNIVERSAL CYCLOID GEAR TOOTH PROFILE
Candidate: Supervisor: Academic Degree Applied for: Specialty: Affiliation: Date of Defence: Degree-Conferring-Institution:
Liu Jianzhuang Prof. Chen Ming Master of Engineering Mechanical design and theory School of Mechatronics Engineering July, 2013 Harbin Institute of Technology
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哈尔滨工业大学工学硕士学位论文
Abstract
The tooth profile of traditional cycloid gear is formed by a circular cyc loid with the advantages of large contact ratio, fewer number of teeth with no undercutting, less wear and uniform wear, on the increasingly urgent requirements of small size, light weight, high efficiency in modern production, the advantages of cycloid gear is concerned, and also the accuracy requirements of cycloid gear can be easily met by the raising level of processing. However, the cycloid gear does not have the separability as involute gear, and researches mentioned above lay stress on the appropriate parameters selecting or method of circle cycloid splicing, making the essence is still the traditional cycloid engagement and the application is greatly limited. The tooth profile described in this article, as is called new universal cycloid tooth profile, is the deformation of traditional circular cycloid tooth profile. It remains the advantages of cycloid gear, solves the centerline spacing problem and increases tooth strength. This tooth profile is formed by the deformation of hypocycloid, involute and deformation epicycloid, whose conjugate tooth profile is generated by principles of gear. The least teeth number of gear has this tooth profile is 6, this meets the conditions of the contact ratio and has no undercutting and greatly reduces the volume of the gear and reducer. Compared with involute gear, this new universal cycloid gear has small and uniform sliding rate, bigger comprehensive radius of curvature and higher strength of tooth caused of the figure of tooth profile. A pair of meshing gears degenerate into traditional cycloid gear when the centerline spacing variation is zero, otherwise, became the new universal cycloid gears. Among them, the closed tooth profile cannot be used in general gear transmission while the more effective tooth profile formed by the closed tooth profile can meet the requirements of the contact ratio with a wider range of application. In this paper, expressions of straight cycloid in the coordinate system of gear is generated by cห้องสมุดไป่ตู้ordinates transformation, meshing equation is established by envelop method and relative motion method, geometric model of straight cycloid ’s envelope(the new universal cycloid ) is established, the undercutting boundary equations of straight cycloid envelope is calculated, the region of straight cycloid which can be formed into tooth profile is determined, according to the number of teeth, the geometry of the closed tooth profile and the more effective tooth profile have been established. According to the theory of gearing, calculating and drawing are shown in this paper of conjugate gear and meshing line, the contact ratio, sliding rate, pressure angle, radius of curvature and comprehensive radius of curvature,
硕士学位论文
新型泛摆线齿轮齿形设计的研究
（工学硕士）
硕 士 研 究 生： 刘建壮 导 学 师： 陈明 教授 科： 机械设计及理论 申 请 学 位： 全日制工学硕士 所 在 单 位： 机电工程学院 答 辩 日 期： 2013 年 7 月 授予学位单位： 哈尔滨工业大学
Classified Index: TH13 U.D.C: 621