新型螺旋非圆锥齿轮的数学模型和齿面接触分析

Mathematic model and tooth contact analysis of a new spiral non-circular bevel gear

本文结合非圆锥齿轮的设计原理和面铣螺旋锥齿轮的制造原理,提出了一种可应用于相交轴变速传动的新型螺旋非圆锥齿轮。与直齿非圆锥齿轮不同,螺旋非圆锥齿轮有许多优点,如高接触比、高强度、良好的动态性能和可调节的接触区域。此外,虽然制造直齿非圆锥齿轮很困难,但螺旋非圆锥齿轮可以用6轴锥齿轮切削机床高效、精确地制造。首先,介绍了螺旋非圆锥齿轮的产形原理。接着,建立了一个数学模型,包括产形齿的齿廓、齿轮螺旋度、压力角和该齿轮的产形齿廓。然后,利用有限元进行齿轮接触分析,验证了模型精度,并研究了螺旋非圆锥齿轮的接触模式和应力分布。

A novel spiral non-circular bevel gear that could be applied to variable-speed driving in intersecting axes was proposed by combining the design principles of non-circular bevel gears and the manufacturing principles of face-milling spiral bevel gears.Unlike straight non-circular bevel gears,spiral non-circular bevel gears have numerous advantages,such as a high contact ratio,high intensity,good dynamic performance,and an adjustable contact region.In addition,while manufacturing straight non-circular bevel gears is difficult,spiral non-circular bevel gears can be efficiently and precisely fabricated with a 6-axis bevel gear cutting machine.First,the generating principles of spiral non-circular bevel gears were introduced.Next,a mathematical model,including a generating tooth profile,tooth spiral,pressure angle,and generated tooth profile for this gear type was established.Then the precision of the model was verified by a tooth contact analysis using FEA,and the contact patterns and stress distributions of the spiral non-circular bevel gears were investigated.