Beyond ISO Approximations: Tool-Path-Based Analytical Modelling of Root Fillets in Altered-Tooth-Sum Spur Gears
DOI:
https://doi.org/10.24237/djes.2026.19308Keywords:
Gear root fillet, Altered tooth-sum gears , Profile shift , ISO 6336-3, Cutter kinematicsAbstract
The strength of a gear tooth is strongly influenced by its root fillet, where cracks can initiate under repeated loading. Accurate representation of this region is therefore essential for reliable stress prediction. However, design standards such as ISO 6336-3 represent the root fillet using simplified circular approximations rather than the exact cutter-generated geometry. While adequate for standard gears, these approximations may become less representative when substantial profile shifts are introduced, particularly in Altered Tooth-sum Gears (ATG), where systematic profile shifts enable tooth-sum modification while maintaining the prescribed centre distance. This study develops a cutter-tool-path-based analytical formulation for the ATG root fillet. The formulation is first validated geometrically against a simulated cutter envelope, then compared with the ISO 6336-3 circular approximation, and a controlled finite-element analysis is performed to isolate the influence of fillet geometry on tooth-root stress. For a representative ATG configuration, the critical-section thickness deviation from the ISO representation increases from approximately 6% to 12.47% with increasing negative profile shift. The corresponding maximum root stress is approximately 332 MPa for the analytically generated fillet, compared with 443 MPa for the ISO circular approximation, representing a difference of approximately 25%. These results show that, for ATG configurations with substantial profile shifts, the ISO circular approximation can significantly overpredict root stress, underscoring the need for cutter-generated fillet geometry in their design evaluation.
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[1] "ISO 6336-3: Calculation of load capacity of spur and helical gears — Part 3: Calculation of tooth bending strength," Geneva, 2019.
[2] A. A. Dsa and H. Lobo, "Analytical and geometric perspectives on altered tooth-sum spur gears within a unified non-dimensional gear design framework," Mech. Mach. Theory, vol. 225, p. 106455, Sep. 2026. doi: 10.1016/j.mechmachtheory.2026.106455.
[3] V. Mouton, E. Rigaud, C. Chevrel-Fraux, P. Casanova, and J. Perret-Liaudet, "Spur gear tooth root stress analysis by a 3D flexible multibody approach and a full-FE contact-based formulation," Finite Elem. Anal. Des., vol. 242, p. 104264, Dec. 2024. doi: 10.1016/j.finel.2024.104264.
[4] J. I. Pedrero, M. B. Sánchez, M. Pleguezuelos, and A. Fuentes-Aznar, "Analysis of the tooth-root stress of external spur gears with high effective contact ratio," Mech. Mach. Theory, vol. 203, p. 105813, Nov. 2024. doi: 10.1016/j.mechmachtheory.2024.105813
[5] L. Bonaiti and C. Gorla, "Gear tooth root bending strength estimation under the assumption of fatigue limit existence," Mater. Des. Process. Commun., vol. 2022, pp. 1–13, Jun. 2022. doi: 10.1155/2022/5056057.
[6] A. R. Rajesh, J. Gonsalvis, and K. A. Venugopal, "Load sharing analysis of bending strength in altered tooth-sum gears operating between a standard center distance and module," Eur. J. Eng. Technol., vol. 3, no. 1, pp. 50–61, 2015.
[7] A. R. Rajesh, J. Gonsalvis, and K. A. Venugopal, "Investigation of tooth load distribution along the path of contact in altered tooth-sum gears," J. Mod. Eng. Res., vol. 5, no. 4, pp. 42–50, 2015.
[8] A. R. Rajesh, J. Gonsalvis, and K. A. Venugopal, "Design and testing of gears operating between a specified center distance using altered tooth-sum gearing," J. Mech. Eng. Autom., vol. 6, no. 5A, pp. 102–108, 2016.
[9] S. Krishnamurthy and R. Kurkal, "Bending stresses in profile corrected gears," in Proc. Int. Conf. Recent Adv. Sci. Eng. (ICRASE), Dubai, UAE, Oct. 2023, p. 109. doi: 10.3390/engproc2023059109.
[10] T. J. Lisle, B. A. Shaw, and R. C. Frazer, "External spur gear root bending stress: A comparison of ISO 6336:2006, AGMA 2101-D04, ANSYS finite element analysis and strain gauge techniques," Mech. Mach. Theory, vol. 111, pp. 1–9, May 2017. doi: 10.1016/j.mechmachtheory.2017.01.006.
[11] A. C. Ram Kumar, N. Mohammed Raffic, K. Ganesh Babu, and S. Selvakumar, "Static structural analysis of spur gear using ANSYS 15.0 and material selection by COPRAS, MOORA techniques," Mater. Today Proc., vol. 47, pp. 25–36, 2021. doi: 10.1016/j.matpr.2021.03.485.
[12] E. Can and M. Bozca, "Optimisation of gear geometrical parameters using KISSsoft," Int. Sci. J. Mach. Technol. Mater., vol. 13, no. 1, pp. 7–10, 2019.
[13] S. Li, "Finite element analyses for contact strength and bending strength of a pair of spur gears with machining errors, assembly errors and tooth modifications," Mech. Mach. Theory, vol. 42, no. 1, pp. 88–114, Jan. 2007. doi: 10.1016/j.mechmachtheory.2006.01.009.
[14] R. Prabhu Sekar, "Performance enhancement of spur gear formed through asymmetric tooth," Proc. Inst. Mech. Eng., Part J, J. Eng. Tribol., vol. 233, no. 9, pp. 1361–1378, Sep. 2019. doi: 10.1177/1350650119837822.
[15] R. Prabhu Sekar and G. Muthuveerappan, "Estimation of tooth form factor for normal contact ratio asymmetric spur gear tooth," Mech. Mach. Theory, vol. 90, pp. 187–218, Aug. 2015. doi: 10.1016/j.mechmachtheory.2015.03.019.
[16] F. L. Litvin, Gear Geometry and Applied Theory. Englewood Cliffs, NJ: Prentice Hall, 1994.
[17] M. C. Fetvaci and B. G. Şentürk, "Investigation of rack cutter geometry and trochoid curves at transverse section in gear manufacturing simulation," J. Adv. Mech. Des. Syst. Manuf., vol. 18, no. 8, p. JAMDSM0098, 2024. doi: 10.1299/jamdsm.2024jamdsm0098.
[18] C. Spitas and V. Spitas, "A FEM study of the bending strength of circular fillet gear teeth compared to trochoidal fillets produced with enlarged cutter tip radius," Mech. Based Des. Struct. Mach., vol. 35, no. 1, pp. 59–73, Feb. 2007. doi: 10.1080/15397730601182802.
[19] P. Dong, S. Zuo, S. Du, P. Tenberge, S. Wang, X. Xu, and X. Wang, "Optimum design of the tooth root profile for improving bending capacity," Mech. Mach. Theory, vol. 151, p. 103910, Sep. 2020. doi: 10.1016/j.mechmachtheory.2020.103910.
[20] A. Artoni, "Is the root fillet curve in involute gears trochoidal? A geometric reassessment," Mech. Mach. Theory, vol. 217, p. 106228, Dec. 2025. doi: 10.1016/j.mechmachtheory.2025.106228
[21] A. Dsa and J. Gonsalvis, "Enhancing design features of asymmetric spur gears operating on a specified center distance using tooth sum altered gear geometry," Proc. Eng. Technol. Innov., vol. 18, pp. 1–14, Mar. 2021. doi: 10.46604/peti.2021.7074.
[22] G. Maitra, Handbook of Gear Design. New Delhi: Tata McGraw-Hill, 1994.
[23] J. R. Colbourne, The Geometry of Involute Gears. New York, NY: Springer New York, 1987.
[24] A. Dsa and J. Gonsalvis, "Tribological aspects affecting surface durability of tooth-sum altered spur gears: A load sharing approach," Adv. Technol. Innov., vol. 8, no. 2, pp. 81–99, Apr. 2023. doi: 10.46604/aiti.2023.9562.
[25] “ISO 21771:2007, "Gears — Cylindrical involute gears and gear pairs — Concepts and geometry,” Geneva, 2007.
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Copyright (c) 2026 Avil Allwyn Dsa, Helga Lobo, AR Rajesh, Joseph Gonsalves4
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