Abstract This work attempts to improve the kinematic geometry model of pure-rolling contact spiral bevel gears (PCSBGs). A systematic report on the analytical design and analysis methods for PCSBGs is presented herein. The tooth surface model of PCSBGs are extended, and a direct relationship between the normal vector and normal pressure angle of PCSBGs is derived, which contributes to building a bridge between the basic geometric parameters and contact characteristics of PCSBGs. The curvature relationships between the tooth surfaces of PCSBGs are derived, and simple equations related to the relative normal curvatures of PCSBGs are obtained from tensor analysis. A logarithmic spiral bevel gear is used as a sample case to demonstrate the application of the kinematic geometry model of PCSBGs and to verify the analytical expressions. The numerical analysis results of the logarithmic spiral bevel gears agree with the analytical model.

中文翻译：

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纯滚动接触螺旋锥齿轮运动几何的解析综合

摘要 这项工作试图改进纯滚动接触螺旋锥齿轮（PCSBGs）的运动学几何模型。本文介绍了有关 PCSBG 的分析设计和分析方法的系统报告。扩展了PCSBGs的齿面模型，推导出了PCSBGs法向量与法向压力角的直接关系，有助于在PCSBGs的基本几何参数和接触特性之间架起一座桥梁。推导了PCSBGs齿面之间的曲率关系，并通过张量分析获得了与PCSBGs相对法向曲率相关的简单方程。以对数螺旋锥齿轮为例，演示PCSBGs运动学几何模型的应用并验证解析表达式。