Spherical Bezier—based fillet construction for spherical involute forge straight bevel gears

Abstract

Spherical involute straight bevel gears exhibit inherent advantages, including conjugate tooth surfaces and reduced sensitivity to assembly errors. However, their unfavorable machinability has limited their widespread adoption over the past two decades, and most practical applications have relied on approximations based on equivalent cylindrical straight gears. Recent advances in manufacturing technologies, such as precision forging and additive manufacturing, have now made the direct production of spherical involute straight bevel gears technically feasible. For small-tooth-number straight bevel gears, the base angle is often greater than the root angle, which leads to a highly constrained and mechanically critical root region. As a result, the design and optimization of the fillet become essential for improving bending strength and load-carrying capacity.

In this work, a new approach for constructing the root transition surface based on third-order spherical Bézier curves is proposed. The analytical formulation of the method is derived, followed by computational geometric modeling, numerical simulation, and parametric optimization. The results demonstrate that the proposed fillet modeling strategy substantially reduces root bending stresses, indicating strong potential for practical industrial implementation.