Optimization of Geometric Characteristics of Cycloidal Profiles of Gerotor Hydraulic Machines

Abstract

Introduction. The performance and reliability of gerotor hydraulic machines depend on the geometry of the cycloidal gearing profile. The existing methods of calculating and optimizing the profile parameters are cumbersome, multicriteria and difficult for practical application. Therefore, the problem of creating the methodology for calculating the parameters of the gerotor machine profile suitable for engineering calculations at the stage of conceptual design is a challenge. In this regard, the objective of this work was to modernize the methodology for designing the geometry of the profiles of the end section of hypocycloidal gears used in gerotor hydraulic machines, and to analyze the possibilities of their optimization during preliminary design. In the course of the study, the Mathcad computer mathematics system was used; numerical experiments were carried out to study the influence of geometric profile parameters on the performance and operability of the gerotor hydraulic machine, based on the data obtained and analyzed; recommendations for the design of optimal profiles of the end section of gerotor hydraulic machines were developed.Materials and Methods. Materials included known methods of profile parameters calculation, based on application of classical formulas of hypocycloidal equidistant used for outlining profiles of teeth of working elements of gerotor machines. The basic research method was modeling the gerotor machine profile using Mathcad computer mathematics system. Calculated data were obtained for the selected ranges of varying parameters, processed through the univariate regression analysis.Results. An algorithm for analyzing the tooth profile smoothness was developed. Two target parameters were defined: the cross-sectional area of the end profile, which affects the productivity; the smallest reduced radius of contact that determines operability of the working body. A technique for calculating the target parameters at the early stage of design was proposed. A number of optimal values of profile parameters according to the criteria of productivity and operability of gerotor machine was obtained. The dependences providing the optimum values of profile parameters at the stage of designing were constructed.Discussion and Conclusion. The developed methodology makes it possible to obtain an assessment of the performance and operability of the gerotor hydraulic machine at the design stage of the working body. The research results can be used in mechanical engineering when designing gerotor hydraulic machines in order to improve their technical and operational characteristics.