内啮合斜齿轮高精度三维有限元自动建模方法

doi:10.3901/JME.2022.21.148

机械工程学报 ›› 2022, Vol. 58 ›› Issue (21): 148-160.doi: 10.3901/JME.2022.21.148

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内啮合斜齿轮高精度三维有限元自动建模方法

刘延平¹, 赵永强²

1. 山东科技大学能源与矿业工程学院青岛 266590;
2. 哈尔滨工业大学机电工程学院哈尔滨 150001

收稿日期:2021-12-14 修回日期:2022-03-29 出版日期:2022-11-05 发布日期:2022-12-23
通讯作者: 刘延平(通信作者),男,1985年出生,博士。主要研究方向为齿轮啮合理论和传动系统动力学。E-mail:liuyanpingsd@126.com
作者简介:赵永强,男,1980年出生,博士,副教授。主要研究方向为机械传动系统动力学。E-mail:zhyq_hit@126.com
基金资助:
青岛市博士后应用研究资助项目。

Research on The Automatic Modelling Method for High Precision Finite Element Model of Internal Helical Gear

LIU Yanping¹, ZHAO Yongqiang²

1. College of Energy and Mining Engineering, Shandong University of Science and Technology, Qingdao 266590;
2. School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001

Received:2021-12-14 Revised:2022-03-29 Online:2022-11-05 Published:2022-12-23

摘要/Abstract

摘要： 为提高内啮合斜齿轮有限元接触分析的建模速度和模型精度，提出了一种齿轮高精度三维有限元模型的自动建模方法。基于齿轮插刀齿廓方程，利用齿廓法线法，得到包括齿根过渡曲线的内、外斜齿轮端面齿廓，建立了内、外齿轮参数化粗网格有限元模型。开发了表层六面体网格剖分方法，自动识别齿面接触带单元，进行分级剖分细化，保证了有限元模型的建模精度和网格密度。进行了齿面接触分析，得到了内啮合斜齿轮的弯曲应力、接触应力、接触印痕、传动误差、时变啮合刚度和载荷分配率。粗细网格有限元模型计算结果对比分析表明，该方法提高了内啮合斜齿轮有限元建模效率和计算精度，缩短了计算时间，为快速准确的齿轮接触分析奠定了基础。

关键词: 斜齿内齿轮, 有限元模型, 分级剖分, 齿面接触分析

Abstract: In order to improve the accuracy and efficiency of tooth contact analysis of internal helical gears, an automatic modeling method of high-precision three-dimensional finite element model of internal helical gear is proposed. The dentiform normal method is applied to derive the tooth profile equations of the internal and external helical gear on the basis of the accurate description of the gear cutter. The parameterized coarse mesh finite element model of internal and external gears are established. Local multi-level refinement method of the hexahedral element has been developed to identify the element on the tooth surface in the contact region automatically to ensure the accuracy and mesh density of the gear finite element model. The tooth contact analysis was carried out, to obtain the bending stress, contact stress, contact stress distribution, transmission error, time-varying meshing stiffness as well as load sharing ratio of the helical internal gears. Comparison of the coarse mesh model with the refined mesh model indicate that the methodology proposed in this paper improves the modeling speed and calculation accuracy of the internal gears, but greatly shorten the computing time, which lays the foundation for fast and accurate internal gear tooth contact analysis.

Key words: internal helical gear, finite element model, mesh refinement, tooth contact analysis

中图分类号:

TH132

刘延平, 赵永强. 内啮合斜齿轮高精度三维有限元自动建模方法[J]. 机械工程学报, 2022, 58(21): 148-160.

LIU Yanping, ZHAO Yongqiang. Research on The Automatic Modelling Method for High Precision Finite Element Model of Internal Helical Gear[J]. Journal of Mechanical Engineering, 2022, 58(21): 148-160.

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内啮合斜齿轮高精度三维有限元自动建模方法

Research on The Automatic Modelling Method for High Precision Finite Element Model of Internal Helical Gear

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