INCREASING THE DURABILITY OF BEVEL GEARS WITH BICONVEX-CONCAVE TEETH

А. В. Кузнецова

Abstract


The article presents theoretical and practical approaches to increasing the service life of bevel gears with biconvex-concave (BCC) teeth by selecting optimal meshing parameters based on wear modeling. Theoretical studies involve the development of mathematical models: 1. Meshing of BCC teeth in bevel gears, which contains a description of the lateral three-dimensional surfaces of the teeth and enables the determination of geometric (radii of curvature of profiles), kinematic (rolling and sliding velocities) and strength (normal meshing force, contact stresses, and bending stresses) parameters for further wear; 2. Wear of BCC teeth in bevel gears, which takes into account the wear in the pole zone of engagement and the reduction in surface hardness due to the degradation of the cemented layer. This model ensures sufficient accuracy in calculating tooth surface wear (with a relative error not exceeding 10%).

Analytical dependencies between wear and profile shift coefficients, modulus, number of teeth, width of the gear ring were established using mathematical models of meshing and wear. This allowed to substantiate rational meshing parameters (according to the criterion of wear resistance of the teeth) to ensure increased durability of the gears. A method for the experimental determination of wear in the BCC teeth of bevel gears has been developed. It is based on the laser scanning method and allows the coordinates of points on the lateral three-dimensional surface of the teeth to be determined with a maximum absolute error of 0.02 mm. The results of the experimental wear determination, conducted under production conditions, confirmed the accuracy and adequacy of the developed theoretical principles. A method for predicting the durability of bevel gears with BCC teeth at the design stage has been developed. It takes into account changes in their geometric, kinematic, and strength parameters resulting from the alteration of the side surface profile of the teeth due to wear after each load cycle. A program has been developed to select rational engagement parameters for bevel gears with BCC teeth. It is based on the durability-prediction method. Using this program rational parameters for bevel gears with biconvex-concave teeth have been selected, increasing their service life by a factor of 1.93.


Keywords


bevel gears, biconvex-concave teeth, pinion, gear, wear, profile of worn teeth, geometric, kinematic and load parameters of contact

References


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Friction, Lubrication, and Wear Technology, ASM Handbook, Edited By George E. Totten, ASM International, Vol. 18, 2017. DOI: https://doi.org/10.31399/asm.hb.v18.9781627081924.

M. Vaishya, D.R. Houser, Modeling and Analysis of Sliding Friction in Gear Dynamics, Proceedings of the ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Volume 6: 8th International Power Transmission and Gearing Conference, Baltimore, Maryland, USA, September 10–13, 2000, 601-610. DOI: https://doi.org/10.1115/DETC2000/PTG-14431.

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T. Bercsey, P. Horak, Modeling of the contact and tribological relations of spatial gear pairs, VDI Berichte, NR.1665, 2002, 91–105.

Ikejo, K., Nagamura, K. Power Loss of Spur Gear Drive Lubricated With Traction Oil, Proceedings of the ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Volume 4: 9th International Power Transmission and Gearing Conference, Parts A and B, Chicago, Illinois, USA, September 2–6, 2003, 1079-1084. DOI: https://doi.org/10.1115/DETC2003/PTG-48130.

Bair, B. W., M.H. Sung, J.S. Wang, C.F. Chen, Tooth profile generation and analysis of oval gears with circular-arc teeth, Mechanism and Machine Theory 44/6 (2009) 1306-1317. DOI: https://doi.org/10.1016/j.mechmachtheory.2008.07.003.

Batsch, M. Mathematical model and tooth contact analysis of convexo-concave helical bevel Novikov gear mesh, Mechanism and Machine Theory, 149, 2020, 103842. DOI: https://doi.org/10.1016/j.mechmachtheory.2020.103842.

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Bajpai, P. A surface wear prediction methodology for helical gear pairs / P. Bajpai, A. Kahraman, N.E. Anderson // Journal of Tribology. – Transaction of ASME, Vol. 126, 2004. – pp.275-287.

Bajpai, P. A Surface Wear Prediction Model for Parallel-Axis Gear Pairs / P. Bajpai, A. Kahraman, N. E. Anderson // ASME J. Tribol. – Vol. 126, 2004. – pp. 597-604.

Flodin, A. Simulation of Mild Wear in Helical Gears / A. Flodin, S. Andersson // Wear. – France, Elsevier Science Publishing Company, Inc., Vol. 241, 2000, pp. 123-128.

Flodin, A. A Simplified Model for Wear Prediction in Helical Gears / A. Flodin, S. Andersson // Wear. – France, Elsevier Science Publishing Company, Inc., Vol. 249, 2001. – pp. 285-292.

Kahraman, A. Influence of Tooth Profile Deviations on Helical Gear Wear / A. Kahraman, P. Bajpai, N. E. Anderson // ASME, Journal of Mechanical Design, JULY 2005. – Vol. 127, 2005. – pp. 656-663.

Wojnarowski, J. Tooth wear effects on spur gear dynamics / J. Wojnarowski, V. Onishchenko // Mechanism and Machine Theory. – Vol. 38, 2003, pp. 161-178.

Winkelbach, S. Low-Cost Laser Range Scanner and Fast Surface Registration Approach / S. Winkelbach, S. Molkenstruck, F.M. Wahl. – DAGM 2006, LNCS 4174, 2006. – pp. 718–728.

Kuznetsova, A. Changing the load-kinematic parameters of bevel gears with biconvex-concave teeth during operation / A. Kuznetsova // International Journal of Applied Mechanics and Engineering. – Zielona Gora, Poland, Vol.17, №3, 2012. – R. 885-892.

Bostan, V. I. Bostan, M. Vaculenco, Mechanical Transmissions with Convex–Concave Multipair Contact of Teeth in Precessional Gearing, Designs, 8/4, 2024, 71. DOI: https://doi.org/10.3390/designs8040071.

Brumercik, F., M. Lukac, J. Caban, Z. Krzysiak, A. Glowacz, Comparison of Selected Parameters of a Planetary Gearbox with Involute and Convex–Concave Teeth Flank Profiles, Applied Sciences, 10/4, 2020, 1417. DOI: https://doi.org/10.3390/app10041417.




DOI: https://doi.org/10.32620/oikit.2025.104.15

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