Calculation of Tooth Surface Equation for Spiral Bevel Gears Based on Vector Transformation

A new algorithm to obtain various complicated tooth surface equations like one of spiral bevel gears is presented. The algorithm utilizes the envelope relationship between the cutting tool and the work piece and vector transformation including vector rotation and movement. It only requires individual processing coordinate system. In contrast to the traditional algorithms, the algorithm can not only simplify the establishment of reference frames, but also avoid the matrix operation during coordinate transformation. Finally, through comparing the calculated tooth surface of a pinion with the processed one, the results show that the deviation distributions of both pinion concave and convex surfaces are logical and the algorithm is accurate.