МОДЕЛИРОВАНИЕ ПРОСТРАНСТВЕННЫХ ДОПУСТИМЫХ ОТКЛОНЕНИЙ СБОРОЧНЫХ ЕДИНИЦ С ПОМОЩЬЮ БИКВАТЕРНИОНОВ

Abstract

Dimensional deviations arising in mechanical assemblies result from the change in the shape, orientation or position of assembly geometrical elements. If these deviations occur between the mating surfaces of assembly components they affect the final result of the assembly. One of the main conditions of successful assembly and assemblability is accounting for these deviations as early as the design stage of assembly units. The purpose of the article is representation of the general approach for the formalized description of permissible spatial tolerances of assembly unit geometrical elements. The study employs mathematical modeling using the biquaternion theory. A new approach has been developed for formalized imaging of the fields of assembly unit geometrical tolerances using the mathematical apparatus of biquaternions. Configuration manifolds of orientation and position tolerances are built and classified. Biquaternions used to describe permissible spatial deviations of assembly unit geometric elements enable comprehensive description of these deviations and consideration of their correlation. The constructed configuration manifolds allow to take into account the permissible spatial tolerances of assembly units at the stage of geometric design.