A novel method to generate the tooth surface model of face-milled generated spiral bevel gears

Tooth surface model is a fundamental element used in the design, analysis, and manufacturing of spiral bevel gears. Based on the face-milled generated process, the tooth surface of spiral bevel gears is mathematically calculated as a complicated representation related to cutter parameters and machine settings. With the representation, the discretized points and curves can be easily obtained from the parameterization of tooth surface. However, the discretized curves for the face-milled generated spiral bevel gears are usually too non-equidistant to directly generate 3D (three dimensional) and mesh models in commercial softwares. This paper presents a novel method to recalculate tooth surface points to generate new approximately equidistant points and curves. The tooth surface representation is introduced at the beginning. Subsequently, a mapping between the isoparametric curve and new approximately equidistant curve is used to recalculate the tooth surface points. To solve the nonlinear equation established from the mapping, a new global optimization algorithm, named real-coded relaxation genetic algorithm (RRGA), is proposed to stably obtain the solutions. Examples are given to validate the proposed method.