Design of Screw Tooth Profile Based on Backlash and Design Method of Forming Cutter

Abstract

Screw pump product often exhibits low volumetric efficiency and low service life due to the complicated screw rotor design, manufacturing and the non-uniform clearance. On the basis of analyzing the formation mechanism of screw clearance, a new design method of screw tooth profile based on the given clearance is proposed by using the analytic geometry theory in three dimensions. The transformation equations related to the feed path, screw tooth profile and the clearance in screw manufacturing process are then established. In combination with the isometric surface configuration of differential geometry, the screw cross tooth profile with the predetermined clearance is obtained. Furthermore, after investigating the spatial enveloping characteristics and geometry characteristics between screw and cutter in manufacturing process, as well as the shape and spatial position parameters of contact lines resulting from the movement for three combinations of machine tool, screw and cutter, a novel design method of forming cutter—shaped-position method is proposed, which is based on the discrete points for tooth profiles of screw manufacturing forming cutter. The method simplifies the solving model by virtue of converting the abstract spatial envelop into plane analytic geometry. It is shown to solve the problem that traditional meshing theory for cutter designing can not accurately calculate the cusp of tooth profile curves, and it therefore improves the tooth profile accuracy of forming cutter.