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图学学报

图学学报 ›› 2022, Vol. 43 ›› Issue (1): 79-84.DOI: 10.11996/JG.j.2095-302X.2022010079

• 计算机图形学与虚拟现实 • 上一篇    下一篇

直齿圆柱齿轮弯曲强度等几何分析

  

  1. 1. 北京航空航天大学机械工程及自动化学院，北京 100191；  2. 北京航空航天大学虚拟现实技术与系统国家重点实验室，北京 100191
  • 出版日期:2022-02-28 发布日期:2022-02-16
  • 基金资助:
    国家自然科学基金项目(61572056)；工信部2017民用飞机专项科研技术研究项目

Isogeometric analysis of bending strength of spur gear  

  1. 1. School of Mechanical Engineering & Automation, Beihang University, Beijing 100191, China;  2. State Key Laboratory of Virtual Reality Technology & Systems, Beihang University, Beijing 100191, China
  • Online:2022-02-28 Published:2022-02-16
  • Supported by:
    National Natural Science Foundation of China (61572056); 2017 Special Scientific Research on Civil Aircraft Project 

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摘要： 齿轮作为一种重要的机械零件，其设计与制造直接影响着机械设备的实际性能与工作质量。由于 齿轮的工作寿命与齿轮的最大弯曲应力的六次方成反比，因此精准地计算齿轮齿根的弯曲强度，是延长其使用寿 命的必要保证。为了更精准地实现齿轮的弯曲应力的求解计算，本文提出了基于等几何法的齿轮弯曲强度分析算 法，实现了对平面齿轮结构力学性能的等几何分析，给出了对二维平面直齿圆柱齿轮的齿根弯曲强度的等几何分 析计算结果。将该方法的计算结果与传统齿根弯曲应力计算公式的理论值、基于有限元法的分析结果进行对比， 结果表明等几何分析技术在分析齿轮齿根弯曲应力时具有较高的精度和效率，且与有限元法所得应力场相比，其 应力场更光滑，从而为求解齿轮齿根弯曲强度问题提供一种有效的方法。

关键词: 等几何分析, 有限元分析, 齿轮弯曲强度, 非均匀有理 B 样条, 线弹性分析

Abstract: As an important mechanical part, gear is widely applied in all kinds of mechanical equipment, and its design and manufacture directly affect the actual performance and work quality of mechanical equipment. Since the working life of the gear is inversely proportional to the sixth power of the maximum bending stress value of the gear, accurate calculation of the bending strength of the gear root is a necessary guarantee to extend its service life. In order to address the bending stress of the gear more accurately, this paper proposed an algorithm of gear bending strength analysis based on isogeometric analysis method, which provided the isogeometric analysis of the mechanical properties for the two-dimensional gear structure. Compared with the traditional calculation formula of tooth root bending stress and the finite element method, our results show that the isogeometric analysis approach is of higher accuracy and efficiency in analyzing the bending stress of the gear tooth root. Compared with the stress field obtained by the finite element method, the result by the isogeometric analysis is smoother, which provides an effective method for solving the bending strength problem of gear root. 

Key words:  isogeometric analysis, finite element analysis, gear bending strength, non uniform rational B-spline, linear elastic analysis

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