Free-Form Conjugation Theory

Abstract

The paper presents the first theory and practice for free-form conjugation design and extends the conventional conjugate tooth profiles to free-form tooth profiles. It presents a conjugation theory that offers a rigorous correspondence between a conjugate pair and the cutter profile or contact path, discovers the necessary and sufficient conditions for non-undercutting with differential curves, and thus extends the traditional free-form single surface modeling to dual conjugate surface modeling. Free-form conjugation modeling and synthesis can be carried out through the cutter profile or the contact path surface. The paper offers a general theory and methodology for free-form modeling and synthesis of planar conjugation, extend the traditional single surface free-form modeling to dual-surface conjugation modeling, and establishes the foundation that will offer much needed design freedom enabling one searching for conjugate surfaces with optimal or desired performance in any transmission involving contact surfaces. The theory is demonstrated in gear tooth profile design through splines and thus provides a fresh perspective on gearing.