General Mathematical Model of the Intersecting Cross-axis Gear based on Conjugate Curve

Shuhong Liu; Rulong Tan; Xiaodong Guo

doi:10.16578/j.issn.1004.2539.2020.11.007

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General Mathematical Model of the Intersecting Cross-axis Gear based on Conjugate Curve

Design· Calculation | 更新时间：2022-11-10

- General Mathematical Model of the Intersecting Cross-axis Gear based on Conjugate Curve
- Journal of Mechanical Transmission Vol. 44, Issue 11, Pages: 41-48(2020)
- 作者机构：
  
  1.重庆理工大学机械工程学院，重庆 400054
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2020.11.007
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刘书宏,谭儒龙,郭晓东.基于共轭曲线的交错轴齿轮一般数学模型[J].机械传动,2020,44(11):41-48.

Liu Shuhong,Tan Rulong,Guo Xiaodong.General Mathematical Model of the Intersecting Cross-axis Gear based on Conjugate Curve[J].Journal of Mechanical Transmission,2020,44(11):41-48.
刘书宏,谭儒龙,郭晓东.基于共轭曲线的交错轴齿轮一般数学模型[J].机械传动,2020,44(11):41-48. DOI： 10.16578/j.issn.1004.2539.2020.11.007.

Liu Shuhong,Tan Rulong,Guo Xiaodong.General Mathematical Model of the Intersecting Cross-axis Gear based on Conjugate Curve[J].Journal of Mechanical Transmission,2020,44(11):41-48. DOI： 10.16578/j.issn.1004.2539.2020.11.007.

摘要

针对传统共轭曲面啮合交错轴齿轮传动难以完成全周期接触特性控制的问题，提出了一种基于共轭曲线的交错轴齿轮设计分析方法。应用微分几何学、齿轮运动学和共轭曲线啮合理论，推导了共轭曲线交错轴齿轮的一般数学模型，进行了齿轮模型的齿面曲率分析和齿面啮合分析，并给出了样例。研究结果对重载高效交错轴齿轮的设计与制造具有一定的指导意义。

Abstract

In order to solve the problem that it is difficult to complete the full period contact characteristic control of the intersecting cross-axis gear based on the traditional conjugate surfaces meshing theory， a design and analysis method of the intersecting cross-axis gear based on conjugate curves is proposed. In this method， differential geometry and gear kinematics and the conjugate curves meshing theory are applied to deduce the general mathematical model of the conjugate curves intersecting cross-axis gear. The tooth surface curvature analysis and meshing analysis of gear model is carried out and an example is given. The research results have certain guiding significance for the design and manufacture of overload and high-efficiency intersecting cross-axis gear.

关键词

共轭曲线接触交错轴齿轮传动数学模型齿面曲率分析齿面啮合分析

Keywords

Conjugate curve contactIntersecting cross-axis gear transmissionMathematical modelTooth surface curvature analysisTooth surface meshing analysis

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