journal article·2026-01-16Open access

Analysis of the Influence of the Tooth Root Fillet Manufacturing Method on the Bending Strength of Spur Gears

Piotr Strojny, Robert Jakubowski

Applied Sciences· Volume 16· Issue 2

Abstract

This paper presents the results of a numerical study on the influence of the tooth root fillet manufacturing method on the bending strength of spur gears with straight teeth. A mathematical model describing the gear tooth geometry was developed, in which the transition curve at the tooth root was directly related to the applied machining process—either rack-type gear shaping or pinion-type gear shaping. Based on this model, a numerical procedure for calculating the bending stresses at the tooth root was formulated and verified using the finite element method (FEM). The results demonstrated high consistency between the proposed approach and FEM analysis, confirming the accuracy of the developed mathematical model and numerical methodology. The study also examined the effect of the tool fillet radius on the stress distribution in the root region. It was found that increasing the tool radius leads to a reduction in bending stresses, while the differences between the two machining methods gradually diminish. The proposed methodology offers a reliable numerical framework for assessing the strength of spur gears and can be effectively used in the design of lightweight, high-performance gear transmissions for aerospace and automotive applications.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Gear and Bearing Dynamics Analysis · Metallurgy and Material Forming · Advanced machining processes and optimization

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Faculty of Mechanical Engineering and Aeronautics, Rzeszow University of Technology, Ave. Powstanców Warszawy 12, 35-959 Rzeszów, Poland

References (30)

Show source-provided references
1. Kim, M., Lee, S., Yoon, K., Lee, Y., and Chung, Y. (2019). Design 2-Speed Transmission for Compact Electric Vehicle Using Dual Brake System. Appl. Sci., 9.10.3390/app9091793 ↗
2. Álvarez, Á., Calleja, A., Ortega, N., and De Lacalle, L.N.L. (2018). Five-Axis Milling of Large Spiral Bevel Gears: Toolpath Definition, Finishing, and Shape Errors. Metals, 8.10.3390/met8050353 ↗
3. Xu, W., Huang, H., Gao, Y., Qin, X., Wen, T., Yang, S., Zhang, P., Wang, L., and Guo, C. (2022). Influence of the Machining Process on the Service Life and Pitting Morphology of Gear-Tooth Surfaces. Metals, 12.10.3390/met12081382 ↗
4. Boral, P., Gołębski, R., and Kralikova, R. (2023). Technological Aspects of Manufacturing and Control of Gears—Review. Materials, 16.10.3390/ma16237453 ↗
5. Comparison of Bending Stress and Contact Stress of Helical Gear Transmission Using Finite Element Method
6. Bending Stress & Contact Stress Analysis of Spur Gear Tooth Using MATLAB
7. Analysis of the Tooth-Root Stress of External Spur Gears with High Contact Ratio10.1016/j.mechmachtheory.2024.105813 ↗
8. Spur Gear Tooth Root Stress Analysis by a 3D Flexible Multibody Approach and a Full-FE contact-based formulation
9. Eggert, C., Kolouch, M., Lohner, T., and Stahl, K. (2024). Inclusion-Based Model: Calculating Tooth Root Bending Strength. Metals, 14.10.3390/met14121349 ↗
10. Fudali, P., Budzik, G., Oleksy, M., and Sanocki, T. (2025). Machining Simulation of Novikov Profile Gear Models for Finite Element Analysis. Materials, 18.10.3390/ma18051155 ↗
11. What Do Stress Calculations Reveal About Spur Gears?
12. Concli, F., Fraccaroli, L., and Maccioni, L. (2021). Gear Root Bending Strength: A New Multiaxial Approach for Life Estimation. Metals, 11.10.3390/met11060863 ↗
13. Zhang, J., Wang, H., Liu, Y., Hou, S., Liu, Z., and Wang, H. (2023). Research on the Strength Calculation Method and Effects of Gear Parameters on Tooth Root Bending Stress. Processes, 11.10.3390/pr11061807 ↗
14. Cazan, S., Ionescu, F., Simion, I., and Voicu, A. (2023). Developing a Fast-Processing Novel Algorithm for Contact Pressure and von Mises Stress of Spur Gears. Symmetry, 15.10.3390/sym15020554 ↗
15. Bonaiti, L., Geitner, M., Tobie, T., Gorla, C., and Stahl, K. (2023). A Comparison between Two Statistical Methods for Gear Tooth Root Bending Strength Estimation Starting from Pulsator Data. Appl. Sci., 13.10.3390/app13031546 ↗
16. New Method for Strength Analysis of Involute Beveloid Gears Based on Fractal Contact Model10.1007/s12206-024-0817-2 ↗
17. Comparison of Standard and Non-Standard Gear Root Fillet Considering Root Stress and Manufacturing Possibilities10.17973/MMSJ.2023_03_2022108 ↗
18. Effect of Rim and Web Thickness on Tooth Root Stress of Spur Gear10.1007/s12239-024-00020-y ↗
19. Tooth Root Stress Relief Hole Optimization on the Spur and Helical Gears
20. Finite Element Stress Analysis for Shape Optimization of Spur Gear Using ANSYS
21. Modal Analysis of Spur Gears for Varied Teeth Root Crack Characteristics: Finite Element Analysis
22. Concli, F. (2022). Effect of Gear Design Parameters on Stress Histories of Gear Tooth Roots. Appl. Sci., 12.10.3390/app12083950 ↗
23. Krishnamurthy, S.H., and Kurkal, R. (2023). Bending Stresses in Profile Corrected Gears. Eng. Proc., 59.10.3390/engproc2023059109 ↗
24. Concli, F. (2021). Dimensional Effect for Small Gears Having a Module below 5 mm. Appl. Sci., 11.10.3390/app11052416 ↗
25. Zhang, H., and Liu, Y. (2020). A Detailed Investigation of Gear Body-Induced Tooth Deflections. Appl. Sci., 10.10.3390/app10072292 ↗
26. Yılmaz, T.G., and Acar, M. (2022). A Numerical Analysis of Hybrid Spur Gears with Various Materials. Machines, 10.10.3390/machines10111056 ↗
27. Ilincă, C.N., Ramadan, I.N., Neacșa, A., Petrescu, M.G., and Laudacescu, E.V. (2025). Finite Element Analysis of 3D-Printed Gears: Evaluating Mechanical Behaviour Through Numerical Modelling. Materials, 18.10.3390/ma18194530 ↗
28. Fatigue safety factor of a transonic centrifugal compressor impeller subject to blade thickness10.1038/s41598-025-03776-0 ↗
29. Digital geometry generation of high-precision broaching tool cutting edges through image-processing algorithm10.17973/MMSJ.2023_11_2023124 ↗
30. Gong, Z., Chen, B., and Cheng, X. (2024). Assessment of the Uniform Wear Bending Strength of Large Modulus Rack and Pinion Pair: Theoretical vs. Experimental Results. Machines, 12.10.3390/machines12080570 ↗