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

This paper describes a simple approach based on the envelope theory for der iving the geometric models of cylindrical and helical gear pumps with circu lar are teeth. A gear pump with circular are teeth can be easily obtained t hrough the envelope theory for a one-parameter family of surfaces. In the p rocess of machining a gear blank, the required rack-cutter teeth can be obt ained by using the obtained cylindrical and helical gears, whose forms are easily determined by the envelope theory. Here the authors provide geometri c modelling of the designed gear pump meshing when assembly errors are pres ent, To illustrate the effectiveness of the approach, an analytical express ion of cylindrical and helical gear pumps with circular are teeth is given.