Pinyon-Tipi Takımla İmal Edilen Evolvent Düz Dişlilerinin Matematiksel Modellerinin Karşılaştırılması

Yıl 2019, Cilt: 60 Sayı: 696, 178 - 191, 30.10.2019

Cüneyt Fetvacı

Öz

Bu çalışmanın amacı evolvent dişlilerin imalatında kullanılan pinyon-tipi takımın literatürde mevcut matematik modellerinin karşılaştırılmasıdır. İncelemede Litvin’in Vektör Yaklaşımını esas alan çalışmalar göz önüne alınmıştır. Kesici takımın profil denklemleri, koordinat dönüşüm, diferansiyel geometri ve dişli teorisi uygulanarak imal eden ve imal edilen yüzeyler tanımlanmıştır. Verilen matematik modellerden hareketle evolvent düz dişli grafiklerini oluşturmak için bilgisayar programları geliştirilmiştir. Karşılaştırılan makalelerde farklı düzenlemiş denklemlerle özdeş geometrilerin elde edildiği görülmüştür.  

Anahtar Kelimeler

Evolvent dişliler, pinyon-tipi takım

Comparison of Mathematical Models of Involute Spur Gears Generated by Pinion-Type Cutters

Öz

The purpose of this study is to make a comparison of mathematical models of pinion-type cutters that generate involute gears in the literature.  Journal papers based on Litvin’s Vector Approach are taken into consideration in this investigation.  The equations of the profile of the cutter, the principle of coordinate transformation, the theory of differential geometry and the theory of gearing are applied for describing generating and generated surfaces. Based on the given mathematical models, computer simulation programs are developed to obtain the tooth profile of involute spur gears. It has been seen that in comparative models, identical geometries are obtained with differently arranged equations. 

Anahtar Kelimeler

Involute gears, pinion-type cutter

Kaynakça

• Jelaska, D. T. 2012. Gears and Gear Drives, ISBN: 978-111-99-4130-9, John Wiley & Sons, West Sussex.
• Litvin, F. L. 1994. Gear Geometry and Applied Theory, ISBN: 978-013-21-1095-2 PTR Prentice Hall, New Jersey.
• Chang, S. L., Tsay, C. B. 1998. “Computerized Tooth Profile Generation and Undercut Analysis of Noncircular Gears Manufactured with Shaper Cutters,” Journal of Mechanical Design, vol. 120, no. 1, p. 92-99.
• Tsay, C. B., Liu, W. Y., Chen, Y. C. 2000. “Spur Gear Generation by Shaper Cutters,”  Journal of Materials Processing Technology, vol. 104, no. 3, p. 271-279.
• Figliolini, G., Angeles, J. (2003). “The Synthesis of Elliptical Gears Generated by Shaper-Cutters.” Journal of Mechanical Design, vol. 125, no. 4, p. 793-801.
• Wu, J. L., Liu, C. C., Tsay, C. B., Nagata, S. 2003. “Mathematical Model and Surface Deviation of Helipoid Gears Cut by Shaper Cutters,” Journal of Mechanical Design, vol. 125, no. 2, p. 351-355.
• Liu, C. C. ,Wang, S. F. 2007. “Tooth Contact Analysis and Contact Ellipse Simulation of Internal Conical Gear Pairs,” 12th IFToMM World Congress, June 17-21, Besancon, France.
• Tsay, M. F., Fong, Z. H. 2007. “Novel Profile Modification Methodology for Moulded Face-Gear Drives,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 221, no. 6, p. 715-725.
• Liu, C. C., Chen, Y. C., Peng, Y. L. 2015. “Contact Pattern Simulation and Stress Analysis of Intersected Concave Conical Involute Gear Pairs Generated by Shaper Cutters,” 14th IFToMM World Congress, October 25-30, Taiwan.
• 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, p. 449-455.
• Chen, Q., Song, C., Zhu, C., Du, X., Ni, G. 2017. “Manufacturing and Contact Characteristics Analysis of Internal Straight Beveloid Gear Pair,” Mechanism and Machine Theory, vol. 114, p. 60-73.