An adaptive geometric meshing theory for the face-milled generated spiral bevel gears

Abstract

Tooth surface model is an essential element for the design, analysis, and manufacturing of gears. The tooth surface model of a spiral bevel gear is usually calculated as an implicit representation related to its complex manufacturing process. Recently, the geometric meshing theory is proposed to simplify the calculation by representing the tooth surface model as a closed-form (explicit) result. Unfortunately, this method is not appropriate to the extreme case that the calculated points cannot cover the whole tooth surface area. To fulfill this problem, a new adaptive geometric meshing theory is proposed with an advanced study of cutter geometry and meshing theory. At the beginning, a simple introduction is presented to the tooth surface model of the face-milled generated spiral bevel gear. Subsequently, an existing closed-form representation of face-milled generated spiral bevel gear is briefly introduced, and a new closed-form representation is illustrated in details. Then we make some in-depth discussions on these two representations. On this basis, we propose an adaptive geometric meshing theory (AGMT) to make up for the shortcomings of the aforementioned representations in some aspects. With the proposed AGMT, the tooth surface modeling is implemented effectively. Examples are given to validate the proposed methods.