# Reverse Engineering Used to Profile a Gerotor Pump Rotor
## 1 Introduction  
The gerotor pumps with trochoidal (cycloidal, epitrochoidal, hypotrochoidal, etc.) profile rotor are special types of rotary pumps with internal gear that contain a profile, most often called a straight cycloidal profile, having a rotor consisting of two components: one known as an inner rotor and the other as an outer rotor [1, 2, 3]. The inner rotor and outer rotor come into contact with each other and create a gap between them and as the pump enters operating mode, the volume of the gap expands and shrinks continuously. The expansion of the gap creates a vacuum, and the fluid is drawn into the pump. As the gap shrinks, compression occurs, and the fluid is pumped out [4, 5]. The inner rotor is fixed to the pump drive shaft and acts as the outer rotor. The inner rotor has four or more lobes (\(Z_{1}\)), while the outer rotor has one more lobe (\(Z_{2}\)) than the inner one and therefore rotates at \(n/(n+1)\) rotations per minute, orbital or satellite [6]. Although they have a lower efficiency and work at pressures of up to 150 bar, they are found in lubrication systems or as compensation pumps (booster pumps) located on the same shaft as the main pump. For these reasons, these constructions are used, in particular, as motors, being superior in many ways to classic hydrostatic motors, even if the operating principle remains similar to pumps in terms of the conversion of mechanical energy (in the form of moment and speed) into hydraulic energy (pressure and flow) [7]. [PERSON] [8] defined, from a geometrical point of view, the main profiles of the gearing components, with applicability to cycloidal gears. Also based on a method derived from the gearing theory, [PERSON] [9] analyzed the epitrochoidal and hypotrochoidal profiles, defining synthetic equations that led to the calculation of some performance indices such as the specific flow rate, the volumetric compression ratio, or the pressure angle. [PERSON] et al. [10] define and extend a study regarding the use of geometric profiles of asymmetric lobes formed by elliptical arcs, with multiple advantages over the traditional profile, while [PERSON] et al. [11] propose a new gerotor with the shape of a lobe with 2 expanded cardioids in order to reduce the noise of the oil pump used in automatic automobile transmissions. For the efficiency of the gerotor pumps for various industrial applications, a great emphasis was placed on the geometry of gerotor pump rotors and the role they have in increasing the performance of hydraulic machines [12; 13; 14; 15], and modeling and simulations of several gerotor pump geometries and kinematics were realized, whose results were compared with experimentally obtained values [16; 17; 18; 19; 20]. [PERSON] [21] used finite element analysis to demonstrate theoretical calculations regarding the influence of the profile geometry of the gerotor pump lobes on stress variation and volumetric flow results. [PERSON] et al. [22; 23] used a computer-aided design program developed in the C++ language to define the inner profile of the rotor as a combination of two circular arcs, as well as a genetic algorithm as a technique to optimize the wear rate proportional factor. Another genetic algorithm was also used by [PERSON] [24], through which he studied the pitting in a pump with the circular geometry of the gerotor gearing. Obviously, not only the geometry of the rotor profile has a decisive role in the good operation and efficiency of such hydraulic constructions; the influence of the characteristics of the transported fluids, such as the density of the fluid or the kinematic viscosity, but also the mechanical characteristics and the physical working quantities, such as the flow rate, pressure, or working speed, they also have an extremely important role [25; 26; 27; 28].