• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2021, Vol. 57 ›› Issue (3): 107-115.doi: 10.3901/JME.2021.03.107

• 机械动力学 • 上一篇    下一篇

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单齿啮合的齿轮接触等几何分析

陈龙, 郝婵娟, 汪中厚, 冯文斌, 杨易明   

  1. 上海理工大学机械工程学院 上海 200093
  • 收稿日期:2020-03-16 修回日期:2020-10-11 出版日期:2021-02-05 发布日期:2021-03-16
  • 通讯作者: 汪中厚(通信作者),男,1963年出生,博士研究生导师。主要研究方向为机械传动技术、CAE技术及应用。E-mail:wangzhusst@163.com
  • 作者简介:陈龙,男,1978年出生,硕士研究生导师。主要研究方向为产品智能计算设计、机器视觉与机器人等。E-mail:cl@usst.edu.cn;郝婵娟,女,1994年出生,硕士研究生。主要研究方向为CAE。E-mail:805734886@qq.com
  • 基金资助:
    国家自然科学基金资助项目(52075340,51875360)。

Isogeometric Analysis of Gear with Single Tooth Contact

CHEN Long, HAO Chanjuan, WANG Zhonghou, FENG Wenbin, YANG Yiming   

  1. School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093
  • Received:2020-03-16 Revised:2020-10-11 Online:2021-02-05 Published:2021-03-16

摘要: 齿轮应用极其广泛,而齿面损坏是齿轮失效的主要形式,因此齿轮接触分析是齿轮设计的重要手段,最新发展的等几何分析(Isogeometric analysis,IGA)方法在解决接触仿真分析方面具有优良性能而受到青睐。将直齿圆柱齿轮简化为平面模型,首先构建能用于IGA的多片拼接NURBS曲面参数化模型,并比较了IGA模型与标准渐开线齿轮的几何误差;然后推导了平面接触IGA的相关计算公式,实现了一对单齿接触的完整齿轮等几何接触分析。为验证等几何接触分析算法的正确性,一方面将计算结果与齿轮无摩擦赫兹接触分析的理论值进行计算精度对比,另一方面将计算结果与商业软件计算结果进行对比。结果表明,IGA方法在分析接触问题时具有计算效率高、速度快、应力场更加光滑等优势,从而为解决齿轮接触分析问题提供一种有效的方法,同时也为齿轮的建模仿真与优化一体化设计提供新的途径。

关键词: 齿轮接触分析, 等几何分析, 有限元分析, 赫兹接触分析

Abstract: The gear is an ancient transmission equipment and widely used in machine. Damage of tooth surface is the main form of gear failure. Therefore, gear contact analysis is an important means of gear design. The latest development of the isogeometric analysis (IGA) method draws some attention for its excellent performance in solving contact analysis. To cut down the difficulty, the spur gear is simplified into a planar model. Firstly, the planar gear model is built to be suitable for IGA by stitching multi patches of parametric NURBS surface, as well as the deviation between the model for IGA and the model presented by standard involute is discussed. Secondly, calculation formulas for planar contact analysis using IGA is derived. Then the calculation is applied on a pair of gears that are engagement. In order to verify the correctness of contact analysis by IGA, two comparative verification methods are given. One is comparing the analysis result from IGA with the theoretical calculation under the case of Hertz contact. The other is comparing the result from IGA with the result from the business CAE software. The comparison results show that IGA has the potential advantages of high calculation efficiency, fast speed, and smoother stress field when it is applied on contact problem. IGA not only provides a new method for contact analysis of gear, it but also offers a new path for the integration design of gear in the stage of modelling, simulation and optimization.

Key words: gear contact analysis, isogeometric analysis, finite element analysis, Hertz contact analysis

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