Roller Profiling for Generating the Screw of a Pump with Progressive Cavities 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.To get more news about Screw pump rotor, you can visit hw-screwpump.com official website. Pumps with progressive cavities allow the circulation of fluids with high viscosity at a constant flow and high pressure [1,2,3]. Among the most used progressive cavity pumps are single screw pumps, consisting of an external helical rotor that rotates eccentrically inside a double internal helical stator [4,5]. The active surface of the rotor is a cylindrical helical surface of constant pitch, and the stator, whose active surface is a double helical surface, is also cylindrical and with constant pitch. The stator is usually made of rubber [6,7], and the rotor is made of steel, often superficially hardened. The exploitation activity of the pumps with progressive cavities has highlighted the fact that traditional pumps with a rubber stator, which surrounds the rotor, do not allow the existence of an interstice between them, which limits their activity until the stator wears out [8,9]. Alternatively, a new class of pumps that do not use elastomers has been developed, in which the rotor and the stator are made of metal, and are used in drilling activities in high temperature wells [10,11,12,13]. This eliminates the wear and greatly increases the lifetime of the pump for use with viscous, high density, and abrasive liquids, and with liquids containing material in suspension. To ensure proper operation, there must be a space between the rotor and the stator to ensure the leakage of the fluid. If this space is not well defined in the rotor and stator design stage, the efficiency of the pump will be seriously affected. Consequently, dimensional designs and optimizations of the rotor and stator, respectively, using analytical and dynamic simulations of the fluid flow through these pumps, have previously been explored [14,15,16,17,18]. The productive functioning of pumps with progressive cavities depends on proper design of the rotor profiles, respecting the technical conditions of their form. The cross-section form of helical pump rotors as ensembles of profiles associated with the rolling centrodes are determined based on the fundamental theorems of the enveloping surfaces (curves) and calculated based on Olivier’s first theorem, the Gohman general theorem, or the Willis theorem (normals method) [19,20]. The geometric characteristics of the rotor, namely, the helical surface with long length and rounded profile, determine that it can be processed by volumetric deformation, using tools in the form of profiled rollers with axes parallel to the axis of the processing blank. The algorithm by which the tool profile can be determined contains the following steps: defining the analytical equations in the own reference system of the piece of the generated profile; defining the absolute movements of the piece and the blank during the generating process; defining the relative movements between the piece and the tool; calculation of the trajectories of the points on the piece profile that execute a relative movement towards the tool; defining the condition which allows the determination of these points, called the enveloping condition—these points belong to the trajectory’s family and to the enveloping of that family; and association of the enveloping condition at the equations of the trajectory’s family, a connection that allows the determination of the parametric equations of the tool profile [21,22]. The tool’s profiling for generating surfaces of the rotors and the stators of the pump can start either from a physical model or from 3D models obtained by rapid prototyping. In practical activity, the determination of the rotor and the stator form can be undertaken with the help of measuring machines in high precision coordinates when the axial profiles of the generating tools in numerical form are known [23]. By comparison, these axial and graphical profiles can be determined using facilities of programming and graphical representation environments, such as the CATIA software application [