Geometric modelling for cylindrical and helical gear pumps with circular are teeth

This paper describes a simple approach based on the envelope theory for deriving the geometric models of cylindrical and helical gear pumps with circular are teeth. A gear pump with circular are teeth can be easily obtained through the envelope theory for a one-parameter family of surfaces. In the process of machining a gear blank, the required rack-cutter teeth can be obtained by using the obtained cylindrical and helical gears, whose forms are easily determined by the envelope theory. Here the authors provide geometric modelling of the designed gear pump meshing when assembly errors are present, To illustrate the effectiveness of the approach, an analytical expression of cylindrical and helical gear pumps with circular are teeth is given.