# Reverse Engineering Used to Profile a Gerotor Pump Rotor
## 1 Introduction
To ensure a smooth rotation, the profiles of the inner and outer elements of all gerotors, regardless of the number of lobes, are conjugate to each other, meaning the common normal at all contact points between the two elements passes through a fixed point, thus maintaining a constant angular speed [29]. Studying the energy efficiency problems of these pumps involves establishing mathematical models of their profiles, comparing various geometric parameters [30], or using simulations and graphical methods [31; 32; 33; 34; 35; 36; 37]. Although the construction of the pumps is robust enough, operational incidents can sometimes lead to damage to the fluid drive elements through more or less uniform wear of some of the lobes as an effect of the erosive process due to the working environment or the cavitation phenomenon as a result of the turbulent flow through the pump body of the working fluids. In this way, in order to reconstruct such components of the pumps, it starts with the identification of the shape, usually of the solid 3D model, starting from the existing construction, identifiable by measurement, in the discrete form of the active surfaces of the rotor, using working methods specific to reverse engineering. Basically, reverse engineering is the process of analyzing an object or an environment in the real world in order to collect data on its shape, structure, and appearance so that it can be used later to build digital 3D models [38]. By means of such a technique, [PERSON] et al. [39] established the parametric equation of the theoretical contour curve by analyzing the radius of curvature of the cycloidal gearing using NX10.0 software. Reverse engineering problems have been developed in graphical design environments [40; 41; 42], with applications, especially in the field of virtual modeling of generating tools of pumps and compressors rotor channels or of different working components whose profiles comprise different shapes, such as circular arcs, straight segments, helical curves, involute-cycloids, cycloidal curves, or various non-analytical curves [43; 44], in which profiling solutions were proposed using a set of software products, such as MATLAB for calculation and CATIA for virtual representation. The existing problem in the reconditioning processes of rotors within pumps consists in making the tools that generate the profiles of the rotors, starting from the existingphysical characteristics, for which, often, there is no specific technical documentation. In such situations, the constructive form of the rotors can be obtained by actually measuring them, making 3D models of the rotors, and, starting from them, by profiling the generating tools with which the profiles of the parts will be processed. The specialized literature has addressed multiple and various aspects regarding the study of gerotor pumps, a fact that makes this topic still relevant. However, from the point of view of reverse engineering techniques, there are no approaches that clearly highlight the 3D geometry of the pump components through non-contact optical methods and 3D analysis of deviations in relation to a nominal mathematical model. Thus, the technique used in this paper has an essential role in the correlation of images, respectively the projection of light fringes, intended for measuring 3D surfaces with the possibility of performing measurements in hostile environmental conditions (dust, high humidity, vibrations, large temperature variations), to which is added the speed of generating 3D surfaces of digitized objects, materialized through a network of polygons (3D mesh). The paper highlights the advantages of the use of reverse engineering techniques versus theoretical algorithms and traditional CAD design, obtaining a reduced time for the creation of numerical models of pump rotors, the possibility of redesigning these rotors in order to improve the volumetric efficiency of the pump, and the ability of the \"virtual pole\" method to be applied in the study of the specific enwrapping problems of hydraulic pump profiles.