Geometric Design, Additive Manufacturing, and Investigation of Contact Characteristics of a Logarithmic Spiral Spur Gear Pair

Öz

In this study, the parametric design, additive manufacturing, and contact path characteristics of logarithmic spiral spur gear pairs, which fall under the category of non-circular gears, have been examined. Within the scope of this study, a parametric design algorithm has been developed to create logarithmic spiral spur gear profiles. The two-dimensional gear profiles obtained using the developed algorithm have been converted into three-dimensional solid models, and physical prototypes have been produced using the FDM (Fused Deposition Modeling) additive manufacturing method with PLA (polylactic acid) filament. The kinematic behavior of the gear pair was analyzed in a CAD program to determine the contact points formed at different angular positions, and the contact path was obtained by connecting these points. The analysis results have shown that the contact path in logarithmic spiral spur gears exhibits a curved rather than a linear character and that the contact is continuous along the tooth surface. This may contribute to a wider contact area and a more balanced load distribution. The findings indicate that the logarithmic spiral spur gear geometry offers distinct contact characteristics that could serve as an alternative to traditional involute gears and can be successfully manufactured using additive manufacturing methods. This study aims to contribute to the literature by adopting a comprehensive approach to the design, manufacturing, and contact analysis processes of logarithmic spiral spur gears.

Anahtar Kelimeler

• Non-circular gears
• Logarithmic spiral gear
• parametric design
• additive manufacturing
• contact analysis

Etik Beyan

The author(s) of this article declare that the materials and methods used in this study do not require ethical committee permission and/or legal-special permission.

Logaritmik Spiral Düz Dişli Çiftinin Geometrik Tasarımı, Katmanlı İmalatı ve Temas Karakteristiklerinin İncelenmesi

Öz

Bu çalışmada, dairesel olmayan dişli kategorisinde yer alan logaritmik spiral düz dişli çiftlerinin parametrik tasarımı, katmanlı imalatı ve temas yolu karakteristikleri incelenmiştir. Çalışma kapsamında, logaritmik spiral düz dişli profillerinin oluşturulabilmesi amacıyla parametrik bir tasarım algoritması geliştirilmiştir. Geliştirilen algoritma yardımıyla elde edilen iki boyutlu dişli profilleri, üç boyutlu katı modellere dönüştürülmüş ve FDM (Fused Deposition Modeling) tipi katmanlı imalat yöntemi ile PLA (polilaktik asit) filament kullanılarak fiziksel prototipler üretilmiştir. Üretilen dişli çiftinin kinematik davranışı CAD ortamında analiz edilerek farklı açısal konumlarda oluşan temas noktaları belirlenmiş ve bu noktaların birleştirilmesiyle temas yolu elde edilmiştir. Analiz sonuçları, logaritmik spiral düz dişlilerde temas yolunun doğrusal değil eğrisel bir karakter sergilediğini ve temasın diş yüzeyi boyunca süreklilik gösterdiğini ortaya koymuştur. Bu durumun, temasın daha geniş bir alana yayılmasına ve yük dağılımının daha dengeli gerçekleşmesine katkı sağlayabileceği değerlendirilmiştir. Elde edilen bulgular, logaritmik spiral düz dişli geometrisinin geleneksel involüt dişlilere alternatif olabilecek farklı temas karakteristikleri sunduğunu ve katmanlı imalat yöntemleri ile başarılı bir şekilde üretilebildiğini göstermektedir. Bu çalışma, logaritmik spiral düz dişlilerin tasarım, üretim ve temas analizi süreçlerini bütüncül bir yaklaşımla ele alarak literatüre katkı sağlamayı amaçlamaktadır.

Anahtar Kelimeler

• Dairesel olmayan dişliler
• logaritmik spiral dişli
• parametrik tasarım
• katmanlı imalat
• temas analizi

Etik Beyan

Bu makalenin yazar(lar)ı çalışmalarında kullandıkları materyal ve yöntemlerin etik kurul izni ve/veya yasal-özel bir izin gerektirmediğini beyan ederler.

Kaynakça

1. [1] Yazar M. and Yanikören M., “Spur gear design, manufacturing and noise analysis according to rolling method using complex numbers,” Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 12: 78–89, (2022).
2. [2] Litvin F. L., Gonzalez-Perez I., Fuentes A., and Hayasaka K., “Design and investigation of gear drives with non-circular gears applied for speed variation and generation of functions,” Computer methods in applied mechanics and engineering, 197:3783–3802, (2008).
3. [3] Yazar M., “Experimental performance comparison of triangle and spur gear hydraulic pumps energy consumption efficiency standpoint,” Sādhanā, 50:287, (2025).
4. [4] Cunningham F. W., “Designing and using noncircular gears to generate mathematical functions,” Machine Design, 161–164, (1959).
5. [5] Olsson U., “Non-circular cylindrical gears”. Royal Swedish Academy of Engineering Science, (1953).
6. [6] Dooner D., Yoon H. D., and Seireg A., “Kinematic considerations for reducing the circulating power effects in gear-type continuously variable transmissions,” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 212:463–478, (1998).
7. [7] Mckinley J. R., Crane III C., Dooner D. B., and Kammath J.-F., “Planar motion generation incorporating a 6-link mechanism and non-circular elements,” in ASME 29th mechanisms and robotics conference, 393–403, (2005).
8. [8] Ogawa K., Yokoyama Y., and Koshiba T., “Studies on the Noncircular Planetary Gear Mechanisms with Nonuniform Motion,” Bulletin of JSME, 16:1433–1442, (1973).

9. [9] Yazar M. and Özdemi̇r A., “Eliptik Düz Dişli Çifti ile Tahrik Edilen Çubuk Mekanizmaların Dinamik Analizi,” Politeknik Dergisi, 14:1–8, (2011).
10. [10] Danieli G. A. and Mundo D., “New developments in variable radius gears using constant pressure angle teeth,” Mechanism and machine theory, 40: 203–217, (2005).
11. [11] Egerszegi J. and Laczik B., “Nem Kor Alaku Fogaskerekek A Fegyvertechnikaban,” ZMNE Bolyai J. Katonai M\Hoszaki Kar, Budapest, 286–295, (2002).
12. [12] Egorova O. V., Barbashov N. N., Abdullina L. R. and Kiselev R. M., “Non-circular Gears: Innovative Manufacturing Technologies,” in Proceedings of I4SDG Workshop 108, (2021).
13. [13] Sałaciński T., Przesmycki A., and Chmielewski T., “Technological Aspects in Manufacturing of Non-Circular Gears,” Applied Sciences, 10:3420, (2020).
14. [14] Gupta K., Jain N. K., and Laubscher R., “Advanced Gear Manufacturing and Finishing: Classical and Modern Processes”. Academic Press, (2017).
15. [15] Chang S.-L., Tsay C.-B., and Wu L.-I., “Mathematical model and undercutting analysis of elliptical gears generated by rack cutters,” Mechanism and Machine Theory, 31: 879–890, (1996).
16. [16] Laczik B., “Non-circular gears width logarithmic pitch curve,” A Dunaujvarosi Fıiskola Kozlemenyei, 211–229, (2006).
17. [17] Berger U., “A Survey of Additive Manufacturing Processes Applied on the Fabrication of Gears,” in Proceedings of the 1st International Conference on Progress in Additive Manufacturing, Research Publishing Services, 315–320 , (2014).
18. [18] Bodzás D. S. and Nemes D., “Geometric Design, Additive Production and 3D Scanning of a Helical Gear Pair,” Fiability&Durability 2, (2022).
19. [19] Lin C., Fan Y., Zhang Z., Fu G., and Cao X., “Additive manufacturing with secondary processing of curve-face gears,” Int J Adv Manuf Technol, 86:9–20, (2016).
20. [20] Łuszczek J., “Review of the method design and additive manufacturing of gears,” Biuletyn WAT, 70: 15–34, (2021).
21. [21] Yazar M., Yanıkören M., and Pazarkaya İ., “Design, Modal Analysis, Additive Manufacturing, and Flow Performance of An Elliptical Gear Hydraulic Pump,” Iğdır Üniv. Fen Bil Enst. Der., 16: 270–282, (2026).
22. [22] Efa D. A. and Ifa D. A., “Optimization of design parameters and 3D-printing orientation to enhance the efficiency of topology-optimized components in additive manufacturing,” Results in Materials, 26:100702, (2025).
23. [23] Gujrathi T. and Bhaskar D., “Additive manufacturing of polymer gears: A review on FDM materials, parameters, and performance,” Journal of Thermoplastic Composite Materials, (2026).
24. [24] Ramakotaiah D. K., Rao J. K., and Ganesh C. S., “Comparative Analysis of Additive Vs Conventional Manufacturing (Gear)”, International Journal of Innovative Research in Engineering 3:38–56, (2022).
25. [25] Mo J., Luo S., Zeng X., Yuan K., Fu S., and Xu S., “Aligning natural logarithmic spiral with gear drive: How bionic gear design and characteristics are affected by logarithmic spiral parameters,” Results in Engineering, 27:106896, (2025).
26. [26] He Z., Gong X., Fu S., Luo S., and Mo J., “Design and Investigation of an Asymmetric Logarithmic Spiral Gear Drive,” Applied Bionics and Biomechanics, 2022: 1–15, (2022).
27. [27] Liu Y., Xu H., Dong C., and Guo J., “Analysis for meshing stiffness and transmission error of non-circular gear based on finite element method,” J Mech Sci Technol, 39: 7425–7435, (2025).
28. [28] Xiao X., Chen Y., Xie X., and Shao Y., “A miniature non-circular line gear with pure-rolling contact,” JAMDSM, 15:. 66-71, (2021).