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The processing of the piece surfaces involves the transformation of the blank into a piece, the defining characteristics of the surfaces (the form, dimensions, deviations, etc.), depending to a large extent on the parameters of the generated processes of the surfaces. Generating surfaces by enveloping represents a complex problem, this mode of generating being a constant concern of researchers due to its advantages. A very important issue is the cutting edge profiling of the future tool, which will generate the wanted profile of the piece. Throughout time, researchers have studied the problems of enveloping surfaces and stated theorems related to them, based on which practical solutions have been conceive to determine the generating and generated surfaces form. The paper presents an overview on study methods for reciprocally enwrapping surfaces, as well as methods for profiling tools for generating helical surfaces by the kinematic method and by the method of decomposing the helical movement. This review can represent a basis for future research articles and projects.

Progressive cavity pumps are used in industry for the circulation of high viscosity fluids, such as crude oil and petroleum products, sewage sludge, oils, salt water, and wastewater. Also known as single screw pumps, these pumps are composed of a single rotor which has the shape of a rounded screw, which moves inside a rubber stator. The stator has an double helical internal surface which, together with the helical surface of the rotor, creates a cavity that moves along the rotor. The movement effect of the cavity inside the stator is the movement of the fluid with a constant flow and high pressure. In this paper, an algorithm for profiling the rollers for generating the helical surface of the pump rotor with progressive cavities is proposed. These rollers are constituted as tools for the plastic deformation of the blank (in case the pump rotor is obtained by volumetric deformation) or for its superficial hardening.