Torus Form Inspection Using Coordinate Sampling

Abstract

Flatness, circularity, and straightness have been studied quite extensively in literature. Forms such as torus are seldom studied. Yet, parts such as ball bearings and Toroidal-CVT have torus features that must be inspected for three-dimensional (3D) form. This research studies the torus form tolerances, herein termed torisity. Mathematical representation for coordinate form verification and fitting methods are each developed for torus forms for the very first time through this research. Three known sampling methods (Hammersley, Aligned systematic, and Random), 3 sample sizes (40, 80, and 120), 2 analysis approaches (horizontal and vertical), and 2 fitting algorithms (least squares and linear optimization) are developed and studied within a designed experiment for torus verification. Analysis shows that different combinations of the above factors lead to different outcomes. It is hoped that this analysis provides the foundation for the development of a future decision support system that can further lead to standards and solutions.