INTERSECTION VOLUMES AND SURFACE-AREAS OF CYLINDERS FOR GEOMETRICAL MODELING AND TOLERANCING

Solid geometric modelling is an important medium for communicating part shape-geometry information, and it encourages the study of solid volumes and surface areas. Growing interest in solid-modelling applications which use surface and volume intersection methods is becoming evident. In their previous work, the authors of the paper examined variations of primitive solids to create a means of representing geometric tolerances in a solid modeller. The paper examines the intersection of two cylinders with reference to the parametric tolerance zones that are associated with size, position and orientation tolerances. Intersection surface areas and volumes are examined. This information can be used not only in the building of models with Boolean operations on primitives, but also in the checking of the interference between mating parts which can arise in fittings of various sorts and functional tolerancing. Because of the likely computer implementation of surface-area or volume calculations relating to the intersection of primitives, the inclusion of faceted solids and methods of dealing with solid primitives are considered. The intersection of two cylinders of arbitrary radii at an arbitrary angle, in a complex steam-trap and flash-tank pipe network, is imaged.