• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2018, Vol. 54 ›› Issue (7): 114-122.doi: 10.3901/JME.2018.07.114

• 摩擦学 • 上一篇    下一篇

线段齿轮法向接触刚度的改进分形模型研究

刘鹏, 赵韩, 黄康, 陈奇, 熊杨寿   

  1. 合肥工业大学机械工程学院 合肥 230009
  • 收稿日期:2017-04-05 修回日期:2017-12-05 出版日期:2018-04-05 发布日期:2018-04-05
  • 通讯作者: 赵韩(通信作者),男,1957年出生,博士,教授,博士研究生导师。主要研究方向为汽车设计理论、机构学、机械传动。E-mail:hanzhaoff@qq.com
  • 作者简介:刘鹏,男,1988年出生,博士研究生。主要研究方向为分形理论和齿轮传动。E-mail:bn605@hotmail.com
  • 基金资助:
    国家自然科学基金资助项目(51775156)。

Research on Normal Contact Stiffness of Micro-segments Gear Based on Improved Fractal Model

LIU Peng, ZHAO Han, HUANG Kang, CHEN Qi, XIONG Yangshou   

  1. School of Mechanical Engineering, Hefei University of Technology, Hefei 230009
  • Received:2017-04-05 Revised:2017-12-05 Online:2018-04-05 Published:2018-04-05

摘要: 为了准确计算微线段齿轮啮合时的法向接触刚度,引入摩擦因素的影响,通过修正考虑摩擦的弹塑性变形临界面积公式、接触面积公式和刚度公式,结合圆柱结合面接触点面积分布公式,基于已有的结合面法向接触刚度的分形模型,推导出适用于微线段齿轮轮齿法向接触刚度分形模型。通过该模型建立法向接触刚度与法向载荷之间的关系,以及分析模型中的参数对法向接触刚度的影响发现:在无摩擦条件下,相同载荷下的接触刚度最大,且接触刚度随着摩擦因数的增大而减小,在摩擦因数较小时,摩擦因数的改变对圆柱体法向接触刚度的影响也较小;表面微观因素对法向接触刚度的影响需综合考虑分形维数和分形粗糙度幅值的相互影响,二者有着较为复杂的关系;内接触形式、增大材料特性参数和圆柱体半径均可使法向接触刚度增大。最后,选取一组不同加工表面粗糙度的微线段齿轮为对象进行仿真,为微线段齿轮加工方法和工艺选择提供参考。

关键词: 法向接触刚度, 分形, 摩擦, 微线段齿轮

Abstract: The friction factor is introduced to calculate the normal contact stiffness of micro-segments gear accurately, when the contact stiffness, the impact of introducing. The fractal model applicable to micro-segments gear teeth is deduced by correcting the critical area formula friction plastic deformation, stiffness and contact area formula based on existing joint surface normal contact stiffness fractal model and combined with the area distribution formula of cylindrical joint surface. The relationship between the load and the normal contact stiffness is established through this model, analysis results show that:In the absence of friction conditions, the normal contact stiffness shows the maximum, decreases with the increasing friction coefficient. When the friction coefficient is small, the impact of the coefficient of friction on the cylinder normal contact stiffness is also small. The influence factors on surface microstructure normal contact stiffness required to consider the interaction of fractal dimension and fractal roughness amplitude which have a complex relationship. Inner contact form, increasing material parameters and the radius of the cylinder can make normal contact stiffness increases. Finally, a group micro-segments gear of different surface roughness is simulated as a reference for machining method and process selection of micro-segments gear.

Key words: fractal, friction, micro-segments gear, normal contact stiffness

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