球面渐开线螺旋锥齿轮精确模型设计

Accurate Modeling for the Spherical Involute Spiral Bevel Gears

基于以往的螺旋锥齿轮的模型设计的研究成果,充分利用球面渐开线理论的特点与优势,提出了具有球面渐开线齿形的螺旋锥齿轮的模型设计方案。首先,根据球面渐开线形成原理,建立球面坐标系,求解了构成大小端面齿廓曲线的各个部分曲线方程。然后,以齿形曲线为引导线推导了其基本的方程表达式,由大小端面齿廓曲线沿引导线扫略完成齿面的精确模型设计。最后,从两个方面提出了基于该模型设计的改进方案,以保证足够的齿面精度精度,为螺旋锥齿轮的快速精确模型设计提供新途径。

In view of previous studies on the modeling and the basic components of the tooth profile curves for the spiral bevel gears, it made fuU use of characteristics and advantages of the .spherical involute theory, and a modeling schema of the spired bevel gears with the spherical ivalute tooth profile is proposed. Firstly, basing on the theory of forming the spherical involute and building a spherical coordinate system, equation expression of each part of toath profiles curve of the toe and heel are all solved. Then, it makes the derivation of the basic equations of the tooth trace as a guide line, and the modeling is completed by sweeping the accurate tooth profile curves from the toe and heel along the guide line. Lastly, it gives the improved method about this model design from two aspects, in order to ensure sufficient accuracy of the tooth suofaces, which can provide some new access to fast and accurate modeling for spiral bevel gears.