Mathematical Modelling of the Profile Shifted Helical Gears

Year 2019, Volume: 60 Issue: 697, 337 - 350, 27.12.2019

Mahmut Cüneyt Fetvacı

https://doi.org/10.46399/muhendismakina.678031

Abstract

This paper studies the mathematical modelling helical gears manufactured by rack cutters. Based on Litvin’s vector approach the equations that determine the geometries of cutter and generated gears are given. Addendum modification and asymmetric tooth profile are also taken into consideration in the mathematical model. Analytic determination of involute parameter upper limit is investigated. A computer program is developed to generate the tooth profile of involute helical gears and to illustrate the effect of tool geometry on the generated surfaces.

Keywords

Rack cutter, asymmetric tooth profile

Profil Kaydırmalı Helisel Dişli Çarkların Matematik Modellenmesi

Abstract

Bu çalışmada evolvent profilli helisel dişli çarkların kremayer takımla imalatının matematik modellenmesi ele alınmıştır. Litvin’in vektör yaklaşımından hareketle takım ve imal edilen dişli çark geometrisini tayin eden ifadeler verilmiştir. Modellemede profil kaydırma ve asimetrik diş profili de göz önüne alınmıştır. İmal edilen dişlide evolvent bölgenin üst sınırının analitik tayini araştırılmıştır. Bir bilgisayar programı geliştirilerek tasarım parametrelerinin imal edilen dişli geometrisindeki etkileri incelenmiştir.

Keywords

Kremayer takım, asimetrik diş profili

References

• Çakır, A. 1989. Dişli Çark Kinematiği. İTÜ Makina Fakültesi.
• Litvin, F. L. 1994. Gear Geometry and Applied Theory, ISBN: 0-13-211095-4, Prentice Hall, New Jersey, ABD.
• Karpat, F., Dogan, O., Yuce, C., Ekwaro-Osire, S. 2017. “An Improved Numerical Method for the Mesh Stiffness Calculation of Spur Gears with Asymmetric Teeth on Dynamic Load Analysis,” Advances in Mechanical Engineering, vol. 9, no. 8, doi: 10.1177/1687814017721856.
• Tsay, C.-B. 1988. “Helical Gears with Involute Shaped Teeth: Geometry, Computer Simulation, Tooth Contact Analysis and Stress Analysis,” ASME J. Mech. Design, vol. 110, no. 4, pp. 482–491.
• Liu, C.-C., and Tsay, C.-B. 2001. “Tooth Undercutting of Beveloid Gears,” ASME J. Mech. Design, vol. 123, no.4, pp. 569–576.
• Brauer, J. 2004. “A General Finite Element Model of Involute Gears,” Finite Elements in Analysis and Design, vol. 40, no. 13-14, pp. 1857-1872.
• Chen, C.-F., and Tsay, C.-B. 2005. “Tooth Profile Design for the Manufacture of Helical Gear Sets with Small Numbers of Teeth,” International Journal of Machine Tools and Manufacture, vol. 45, no. 12-13, pp. 1531-1541.
• Yang, S.-C. 2005. “Mathematical Model of a Helical Gear with Asymmetric Involute Teeth and its Analysis”, International Journal of Advanced Manufacturing Technology, vol. 26, no 5-6, pp. 448-456.
• Huang, K. J., and Su, H. W. 2010. “Approaches to Parametric Element Constructions and Dynamic Analyses of Spur/helical Gears Including Modifications and Undercutting,” Finite Elements in Analysis and Design, vol. 46, no. 12, pp. 1106-1113.
• Fetvaci, M. C. 2017. “Determination of Effective Involute Parameter Limit in Generation Simulation of Gears Manufactured by Rack-type Cutters,” Mechanics & Industry, vol. 18, no. 4, 405.
• Fetvaci, M. C. 2016. “Determination of Effective Involute Parameter Limit in Generation Simulation of Gears Manufactured by Pinion-type Cutters,” Journal of the Faculty of Engineering and Architecture of Gazi University, vol. 31, no. 2, pp. 449-455.
• Fetvacı, C. 2012. “Tam Dişbaşı Yükseklikli Kremayer Takımla Evolvent Düz Dişli İmalatının Bilgisayar Simülasyonu,” Mühendis ve Makina, cilt 53, sayı 635, s. 34-39.
• Kabus, K. 2006. Maschinenelemente: Tabellen und Diagramme. ISBN: 3-446-21525-5, Carl Hanser Verlag, München.