Giovanni Bonandrini

Theoretical analysis of internal epitrochoidal and hypotrochoidal machines

Abstract In this article, a complete and original method to analyse both the epitrochoidal and the hypotrochoidal rotary machines is presented. The internal trochoidal machines consist of two rotors: the first rotor is an envelope of a trochoid, the second rotor is its conjugate. In particular, in this article, the profiles of the trochoidal rotor and its conjugate are expressed by original and particularly synthetic equations using a method based on the theory of gearing. Then the geometry of these machines is completely defined by the choice of four non-dimensional parameters. Once these parameters are selected, the geometric and kinematic characteristics of the rotor profiles are obtained in an original analytic form; hence, the main theoretical performance indexes are computed by a proper method. The results of the analysis allow us to choose the best geometric configuration for a specific application.

Theoretical Analysis of an Original Rotary Machine

In this study an original analysis of the geometric design of a particular internal rotary machine and an investigation on its theoretical performances are presented. The first part of the work is focused on the geometry of the machine, characterized by more complex rotor profiles compared with the classical epitrochoidal pumps. Suitable parameters are pointed out to completely define the geometry of the machine. In the second part of the study, proper indices are set and evaluated as functions of the design parameters, in order to evaluate the performance of the machine. Finally a specific configuration of the considered pump is compared with the conventional trochoidal pumps in terms of flow-rate indices. The analysis performed allows one to highlight the basic advantages and drawbacks of this original design in comparison with the classical trochoidal profiles and can be used as a basis for CAD/CAE (Computer-Aided Design and Engineering) or experimental studies.

On Design and Performance of Internal Epitrochoidal Pumps

In this study an analysis of rotor profiles geometry in internal epitrochoidal pumps and a systematic study of their performance as a function of the geometrical parameters are introduced. Internal pumps are used in various fields, like automotive, alimentary, or medical-scientific. This machines consist of two rotors: generally the inner rotor has epitrochoidal profile and the profile of the outer rotor is determined as conjugate to the inner one. The rotor geometry and the final performance of the whole machine has been studied by many researchers, using different methods. In this paper the construction of the profiles is performed by the theory of gearing, in order to calculate performance indexes. In particular the pump type with epitrochoidal outer rotor has been considered. Even if it is impossible to establish an optimal profile valid for every application, the analysis of the results obtained allows to choose the design parameters, in order to optimize the shape of the rotors for any particular application.Copyright

Solutions of the Equation of Meshing for Planar Gear Profiles

This paper illustrates the possibility of obtaining an explicit solution for the equation of meshing for any type of regular two-dimensional curve of a planar gearing, in order to compute the conjugate profile of the curve. The analysis of the equation of meshing permits to express its explicit solution when the relative motion between the considered reference systems occurs with a constant transmission ratio (for example internal or external gears and rack). The solution is expressed with the general conventions of the theory of gearing. In this way, when we have a generating curve in homogeneous coordinates, and the transformation matrixes which define the relative motion between the profiles considered, we can directly find the solution of the equation of meshing, and consequently the profile conjugated to the generating one by a simple coordinate transformation. The method here presented can be successfully applied to the profiles of planar gears and rotary machines.