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.