 Mathematical Modelling of Beveloid Gears  Methods for Avoiding Undercutting  Verification with Finite Element Analysis Figure A. Designing process and the stress values of the FEM analysis for the beveloid gear model. Purpose: The purpose of this study is to obtain a mathematical model for the beveloid gear types to have a 3 dimensional CAD model and also implement methods to prevent undercutting. Theory and Methods: For obtaining the mathematical models and forming the cross sectional and 3 dimensional geometries of the gears, MATLAB and SOLIDWORKS software has been used. The finite element analysis has been done by aid of ABAQUS. Results: With the aid of the mathematical models, 3 dimensional beveloid gear models has been generated for different design parameters. To avoid undercutting, two different modelling technics such as positive profile shifting and modelling with asymmetrical rack cutter has been used and cross sectional views have showed that especially for the regions around the gear roots, undercutting occurrence is reduced. Also the maximum stress values on the gear roots which received from the finite element analysis are σ = 28.06 MPa and σ = 25.50 MPa for the regular conical model and asymmetrical rack cutter application respectively. Conclusion: The analysis results indicate that the strength of the gear teeth can be increased by avoiding undercutting. To provide that, positive profile shifting and asymmetric rack cutter methods can be used. For this purpose, modifications on the mathematical models can easily be used and, CAD models can be imported into the finite element analyzing programs.

İç ve dış dişlerin imalat simülasyonu  Yan boşluksuz çalışan profil kaydırmalı dişliler  Örnek uygulamalar ile doğrulama Makale Bilgileri ÖZET

ÖZETBu çalışmada pinyon-tipi takımla imal edilen evolvent dişlilerin bilgisayar simülasyonu ele alınmıştır. Dişli teorisinden hareketle kesici takımların ve imal edilen iç ve dış dişlilerin matematik modelleri verilmiştir. İmal edilen evolvent bölgenin diş başında sonlanmasını sağlayan tasarım parametresinin efektif limitinin bulunması araştırılmıştır. Kesici takımın ve imal edilen dişlinin grafiklerini elde etmek için bilgisayar programları geliştirilmiştir. Böylelikle çeşitli takım parametrelerinin imal edilen dişli geometrisindeki etkileri önceden incelenebilmektedir.Anahtar Kelimeler: Evolvent profil, helisel dişli, pinyon takım DETERMINATION OF EFFECTIVE INVOLUTE PARAMETER LIMIT IN GENERATION SIMULATION OF GEARS MANUFACTURED BY PINION-TYPE CUTTERS ABSTRACTThis paper studies the computerized tooth profile generation of involute gears cut with pinion-type cutters. Based on the theory of gearing the mathematical models of generating cutters and generated external and internal gears with involute teeth are given. Effective limits of design parameters that determine the actual tip circle radii of the generated gears are investigated. Computer simulation programs are developed to obtain graphs of generating tools and generated teeth surfaces. The effect of tool parameters on generated gear can be investigated before manufacturing.