Düz Dişli Çark Tasarım Parametrelerinin Tek Diş Rijitliği ve Diş Dibi Mukavemetine Olan Etkisinin İstatistiksel Olarak İncelenmesi

Yıl 2025, Cilt: 12 Sayı: 27, 363 - 374, 24.12.2025

Neşe Doğan , Özdeş Çermik , Muhammed Safa Kamer , Oğuz Doğan

https://doi.org/10.54365/adyumbd.1720523

https://izlik.org/JA59GA84JH

Öz

Bu çalışmada, düz dişli çark tasarımında etkili olan dört temel parametrenin — diş başı yüksekliği (ha), kesici takım uç yarıçapı (ρ), kavrama açısı (α) ve rim oranı (mb) — tek diş rijitliği ve diş dibi gerilmesine olan etkileri nümerik analiz ve istatistiksel yöntemlerle değerlendirilmiştir. Deneysel çalışma kapsamında Taguchi L16 ortogonal deney tasarımı ile 16 farklı dişli konfigürasyonu oluşturulmuş ve her bir tasarım ANSYS Workbench yazılımı ile sonlu elemanlar analizine (SEA) tabi tutulmuştur. Elde edilen sonuçlara göre, ortalama rijitlik 23412 N/mm ile 31985 N/mm, diş dibi gerilmesi ise 90,58 MPa ile 137,18 MPa arasında değişmektedir. Yapılan varyans analizleri ve sinyal/gürültü (S/N) oranları, özellikle kavrama açısının her iki mekanik çıktı üzerinde en yüksek etkiye sahip parametre olduğunu göstermiştir. Optimum tasarım parametreleri ile yapılan doğrulama analizlerinde, Taguchi tahminleri ile SEA sonuçları arasında %1–3 aralığında düşük hata oranları elde edilmiştir. Bu sonuçlar, düz dişli çarkların performansının artırılmasına yönelik tasarım sürecinde Taguchi yönteminin etkin ve güvenilir bir araç olduğunu ortaya koymaktadır.

Anahtar Kelimeler

: Düz dişli çarklar , Minitab , Diş dibi gerilmesi , Diş rijitliği , Sonlu elemanlar analizi

A Statistical Analysis of the Influence of Spur Gear Design Parameters on Single Tooth Stiffness and Root Strength

https://izlik.org/JA59GA84JH

Öz

This study evaluates the effects of four key parameters in spur gear design—addendum height (ha), cutter tip radius (ρ), pressure angle (α), and rim ratio (mb)—on single tooth stiffness and root stress using numerical analysis and statistical methods. In the experimental part, 16 different gear configurations were created using the Taguchi L16 orthogonal array design. Each design was analyzed with finite element analysis (FEA) using ANSYS Workbench software. The results showed that the average stiffness ranged from 23412 N/mm to 31985 N/mm, while the root stress varied between 90.58 MPa and 137.18 MPa. Variance analyses and signal-to-noise (S/N) ratios indicated that the pressure angle had the most significant effect on both mechanical outputs. Validation analyses with optimal design parameters showed a low error rate between 1% and 3% when comparing Taguchi predictions and FEA results. These findings demonstrate that the Taguchi method is an effective and reliable tool for improving the performance of spur gear design.

Anahtar Kelimeler

Spur gears , Minitab , Gear bending stress , Tooth stiffness , Finite element method

Kaynakça

• Alam J, Panda S, Dash P. A comprehensive review on design and analysis of spur gears. International Journal on Interactive Design and Manufacturing. 2022;17(3):993–1019.
• DIN3990: Calculation of load capacity of cylindrical gears: Calculation of tooth strength. 1987.
• ISO 6336-1: Calculation of load capacity of spur and helical gears. 2019.
• Zhou W, Zhu R, Li Z, Liu W, Wang J, Mu F. Theoretical and experimental research on tooth root bending stress of face gear. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 2024;238(14):7172–88.
• Lisle TJ, Shaw BA, Frazer RC. External spur gear root bending stress: A comparison of ISO 6336:2006, AGMA 2101-D04, Ansys finite element analysis and strain gauge techniques. Mechanism and Machine Theory. 2017;111:1–9.
• Pedrero JI, Sánchez MB, Pleguezuelos M, Fuentes-Aznar A. Analysis of the tooth-root stress of external spur gears with high effective contact ratio. Mechanism and Machine Theory. 2024;203:105813.
• Doğan O, Yilmaz TG, Karpat F. Farklı parametrelere sahip evolvent düz dişli çarkların sonlu elemanlar yöntemi ve grafik metot ile gerilme analizi. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi. 2018;33(4):1493–504.
• Raptis KG, Savaidis AA. Experimental investigation of spur gear strength using Photoelasticity. Procedia Structural Integrity. 2018;10:33–40.
• Patil SS, Karuppanan S, Atanasovska I. Experimental measurement of strain and stress state at the contacting Helical Gear Pairs. Measurement. 2016;82:313–22.
• Venkatesh B, Prabhakar Vattikuti SV, Deva Prasad S. Investigate the combined effect of gear ratio, Helix Angle, Facewidth and module on bending and compressive stress of Steel Alloy Helical Gear. Procedia Materials Science. 2014;6:1865–70.
• Saxena A, Chouksey M, Parey A. Effect of mesh stiffness of healthy and cracked gear tooth on modal and frequency response characteristics of geared rotor system. Mechanism and Machine Theory. 2017;107:261–73.
• Karpat F, Yuce C, Doğan O. Experimental measurement and numerical validation of single tooth stiffness for involute spur gears. Measurement. 2020;150:107043.
• Marafona JDM, Marques PMT, Martins RC, Seabra JHO. Approximate expression for the single tooth pair slice mesh stiffness. Mechanism and Machine Theory. 2023;187:105367.
• He Y, Yang H. Analytical model of gear thermal stiffness based on the potential energy method. Applied Sciences. 2023;13(6):3599.
• El Yousfi B, Soualhi A, Medjaher K, Guillet F. New approach for gear mesh stiffness evaluation of spur gears with surface defects. Engineering Failure Analysis. 2020;116:104740.
• Tunçel O. Optimization of charpy impact strength of tough PLA samples produced by 3D printing using the Taguchi Method. Polymers. 2024;16(4):459.
• Dogan O, Kamer MS, Sahan MF. Multi-objective optimization of low-velocity impact and compression behavior of 3D-printed PLA cubic samples. Polymers. 2025;17(5):627.
• Yuce BE, Nielsen PV, Wargocki P. The use of Taguchi, ANOVA, and GRA methods to optimize CFD analyses of ventilation performance in buildings. Building and Environment. 2022;225:109587.
• Canbolat AS, Bademlioglu AH, Arslanoglu N, Kaynakli O. Performance optimization of absorption refrigeration systems using Taguchi, ANOVA and Grey Relational Analysis Methods. Journal of Cleaner Production. 2019;229:874–85.
• Tunçel O, Tüfekçi K, Kahya Ç. Multi-objective optimization of 3D printing process parameters using gray-based Taguchi for composite PLA parts. Polymer Composites. 2024;45:12870-2884.
• Kahya Ç, Tunçel O, Çavuşoğlu O, Tüfekçi K. Thermal annealing optimization for improved mechanical performance of PLA parts produced via 3D printing. Polymer Testing. 2025;144:108735.
• Dogan O, Yuce C, Karpat F. Effects of rim thickness and drive side pressure angle on gear tooth root stress and fatigue crack propagation life. Engineering Failure Analysis. 2021,105260.
• Dogan O, Yuce C, Karpat F. A novel method for tooth bending stress calculation of gears with asymmetric teeth. OKU Journal of The Institute of Science and Technology. 2024,7(5):2139-157.
• Tunçel O, Kahya Ç, Tüfekçi K. Optimization of flexural performance of PETG samples produced by fused filament fabrication with response surface method. Polymers. 2024;16:2020.