Free Form Conjugation Modeling and Gear Tooth Profile Design

Abstract

The paper presents the first theory and practice of freeform conjugation modeling. It introduces the concept of masterslave that broadens the traditional computer aided single geometry modeling to dual geometry modeling. The concept is then applied to gear geometry to establish the first freeform conjugation modeling technique, in which a fictitious freeform rackcutter or freeform contact path is proposed as the master geometry. Simple geometric relationship suitable for conjugation modeling and undercutting analysis is found between the master and the conjugate profiles. With a freeform master geometry, freeform conjugation modeling has desirable properties of guaranteed continuity, flexibility, and controllability. It offers unlimited representation capability crucial for conjugation modification and optimization. Undercutting is examined rigorously and extensively under the freeform technique via differential geometry. For general planar conjugation, including noncircular gearing, necessary and sufficient undercutting conditions in terms of the master geometry are obtained. Simple geometric explanation of undercutting is demonstrated in terms of the distance between a contact path and two centrode centers. The technique is demonstrated with Bspline as the master geometry.