高重合度内啮合复合摆线齿轮传动设计与分析

doi:10.3901/JME.2017.01.055

摘要/Abstract

摘要：

重合度是衡量齿轮传动性能的重要指标，较高的重合度对于提高齿轮的承载能力和传动的平稳性具有重要意义。考虑到摆线齿形的优越性，提出一种具有高重合度的新型内啮合复合摆线齿轮副;根据内、外摆线无包心形成法与包心形成法之间的等效关系，阐明内、外齿轮齿顶与齿根之间的齿廓配合关系，给出使重合度最大化的圆弧啮合线位置及其数学描述;结合坐标变换和齿轮啮合原理，建立共轭齿廓的数学方程，并由已知的啮合线推出适用于任意齿廓形状的齿轮端面重合度的统一计算式，推算上述内啮合摆线齿轮副的最大重合度，分析影响重合度的相关因素，指出提高重合度的可能途径。据此，运用Solidworks软件实现了高重合度内啮合摆线齿轮副的参数化建模，结合具体实例与标准渐开线内齿轮副进行比较研究，并就同时参与啮合轮齿的对数情况进行有限元仿真分析和光弹试验测试。结果表明，所设计的内啮合摆线齿轮副具有很大的重合度，可以到达十几甚至更大，且仿真及实测结果与理论分析吻合，验证了该齿轮传动理论的正确性。

关键词: 高重合度, 内啮合传动, 圆弧啮合线, 复合摆线齿轮

Abstract: Contact ratio is an important indicator of measuring gear transmission performance, and a high contact ratio has great significance to improve the bearing capacity and transmission stability of gears. In view of the excellent characteristics of cycloid tooth profile, a new internal compound cycloid gear pair with high contact ratio is proposed. According to equivalent relationship between center encircled and non-encircled formation of internal and external cycloid, the matching relation between addendum and root of tooth profile of internal and external gears is clarified. The position and mathematical description of arc path of contact are given to maximize the contact ratio. In combination with coordinate transformation and gear meshing theory, mathematical equation of conjugate tooth profile is established. Meanwhile, the unification calculation formula of transverse contact ratio suitable for any tooth profile of gear is deduced by the known meshing arc, with which the maximum contact ratio of the above-mentioned internal cycloid gear pair is calculated. The influencing factors and the possible improving ways of contact ratio are analyzed and pointed out. Accordingly, parametric modeling of internal cycloid gear pair with high contact ratio is realized by Solidworks, and finite element simulation analysis and photoelastic test about the number of simultaneous meshing teeth is carried out, with a concrete instance contract to standard involute internal gear pair. Fact shows that the designing internal cycloid gear pair exactly has a high contact ratio, which can reach a dozen, even greater, and the results of simulation and test are consistent with that of theoretical analysis, which verifies the correctness of the gear transmission theory.

Key words: arc path of contact, high contact ratio, internal gear transmission, compound cycloid gear

贵新成, 詹隽青, 叶鹏, 李红勋. 高重合度内啮合复合摆线齿轮传动设计与分析[J]. 机械工程学报, 2017, 53(1): 55-64.

GUI Xincheng, ZHAN Junqing, YE Peng, LI Hongxun. Design and Analysis of Internal Compound Cycloid Gear Transmission with High Contact Ratio[J]. Journal of Mechanical Engineering, 2017, 53(1): 55-64.

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