Abstract
An improved approach to the reliability function calculation of case-hardened spur and helical gears is presented in the paper. The calculation of the reliability function based on six possible gear failures is substantiated: the pitting of a pinion or wheel, the tooth breakage of a pinion or wheel, the tooth flank fracture of a pinion or wheel. The methodology for the reliability function calculation according to the criterion of surface durability (pitting) takes into account the random nature of the misalignment of the teeth in the mesh, caused by the deformation of the gear elements under the action of the transmitted torque (force misalignment). In the given method under the criterion of bending durability (tooth breakage), applied formulas allow calculating an allowable stress number for bending of the tooth through the parameters of the hardened case. Verification of the calculation formulas for the allowable stress number for bending, taking into account the parameters of the hardened case, was carried out according to the experimental data. The calculation methods analysis of deep equivalent stresses is carried out by the authors. The accuracy of the hardness depth profiles (carbonization, carbonitriding) is estimated. The technique has been developed for the reliability function calculation of case-hardened gears according to the criterion of deep equivalent durability. The verification of the developed methods for calculating the reliability function according to the operation data of case-hardened gears is performed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Rudenko, S.P., Val’ko, A.L.: Contact Fatigue of Gear Wheels of Transmissions of Energy-Saturated Machines, 127 p. Belarusian-Russian Science, Minsk (2014) (In Russ.). ISBN 978-985-08-1694-8
GOST 21354-87: Involute Spur Gears. Strength Calculation, 125 p. Publishing House of Standards, Moscow (1988) (In Russ.)
ISO 6336-2:2019: Calculation of Load Capacity of Spur and Helical Gears—Part 2: Calculation of Surface Durability (Pitting), 36 p. ISO, Switzerland (2019)
Caichao, Z., Shuang, C., Hua, L., Huaqing, H., Guangfu, L., Fei, M.: Dynamic analysis of the drive train of a wind turbine based upon the measured load spectrum. J. Mech. Sci. Technol. 28(6), 2033–2040 (2014). https://doi.org/10.1007/s12206-014-0403-0
Syzrantseva, K., Syzrantsev, V.: Determination of parameters of endurance limit distribution law of material by the methods of nonparametric statistics and kinetic theory of high-cycle fatigue. Key Eng. Mater. 736, 52–57 (2017)
Zachary, A.C., Krantz, T.L.: Statistical distribution of gear surface fatigue lives at high reliability. Int. J. Fatigue (167)B, 107350 (2023). https://doi.org/10.1016/j.ijfatigue.2022.107350
Babichev, D.T., Lebedev, S.Y., Babichev, D.A.: Theoretical fundamentals of spur and helical gear synthesis based on assignment of meshing lines at face section. Int. Rev. Mech. Eng. 9(12), 762–770 (2018). https://doi.org/10.15866/ireme.v12i9.15580
Semenov, Y.A., Semenova, N.S.: Internal vibration active of machines with elastic transmission mechanism. In: Advances in Mechanical Engineering: Selected Contributions from the Conference “Modern Engineering: Science and Education”, pp. 28–37. Springer International Publishing, Saint Petersburg (2022). https://doi.org/10.1007/978-3-030-91553-7_4
ISO 6336-3:2019: Calculation of load capacity of spur and helical gears—Part 3: calculation of tooth bending strength, 52 p. ISO, Switzerland (2019)
Brecher, C., Löpenhaus, C., Brimmers, J., Henser, J.: Influence of the defect size on the tooth root load carrying capacity. Gear Technol. 92–100 (2017). https://doi.org/10.3390/app11052416
Korendyasev, G.K., Salamandra, K.B.: Gear shift analysis in dual-clutch transmissions using impact theory. In: Advances in Mechanical Engineering: Selected Contributions from the Conference “Modern Engineering: Science and Education”, pp. 92–101. Springer Nature Switzerland AG, Cham, Switzerland (2021). https://doi.org/10.1007/978-3-030-62062-2_10
Rudenko, S.P., Val’ko, A.L.: Definition of parameters of chemical and heat treatment for high-stressed gear wheels on basis of computational models. Strength. Technol. Coat. 8(14), 353–358 (2018) (In Russ.)
Tesker, E.I.: Modern Methods for Calculating and Increasing the Bearing Capacity of Surface-Hardened Gears in Transmissions and Drives, 434 p. Engineering, Moscow (2011) (In Russ.)
MackAldener, M., Olsson, M.: Tooth interior fatigue fracture—computational and material aspects. Int. J. Fatigue 23, 329–340 (2001). https://doi.org/10.1016/S0142-1123(00)00099-2
Van Dang, K., Griveau, B., Message, O.: On a new multiaxial fatigue limit criterion: theory and application. Biaxial Multiaxial Fatigue EGF 3, 459–478 (1989)
Karolczuk, A., Macha, E.: A review of critical plane orientations in multiaxial fatigue failure criteria of metallic materials. Int. J. Fract. 134(3), 267–304 (2005). https://doi.org/10.1007/s10704-005-1088-2
Bai, H., Zhu, C., Zhou, Y., Chen, X., Feng, H., Ye, W.: Study on tooth interior fatigue fracture failure of wind turbine gears. Metals 10(1497), 1–18 (2020). https://doi.org/10.3390/met10111497
ISO/TS 6336-4: Calculation of Load Capacity of Spur and Helical Gears—Part. 4: Calculation of Tooth Flank Fracture Load Capacity, 36 p. ISO, Geneva, Switzerland (2019)
Onishkov, N.P., Korotkin, V.I.: To estimation of contact-fatigue durability of thermo-chemically strengthened gears. Vestnik Don State Tech. Univ. 17(3), 5–13 (2017) (In Russ.) https://doi.org/10.23947/1992-5980-2017-17-3-5-13
Pisarenko, G.S., Lebedev, A.A.: Deformation and strength of materials under complex stress state. Academy of Sciences of the Ukrainian SSR, Institute of Strength Problems, 415 p. Naukova Dumka, Kyiv (1976) (In Russ.)
Fujita, K., Yoshida, A.: Effect of carburized layer depth and relative radius of curvature on contact fatigue life of a carburized chromium molybdenum steel roller. Des. Eng. Technol. 2, 115–124 (1981). (In Russ.)
Filipovich, S.I., Kravchuk, V.S., Litvinov, A.M.: Evaluation of the cycle resistance of surface-hardened teeth Machine parts. 48, 30–34 (1989) (In Russ.)
Olsson, E., Olander, A., Öberg, M.: Fatigue of gears in the finite life regime—experiments and probabilistic modelling. Eng. Fail. Anal. 62, 276–286 (2016). https://doi.org/10.1016/j.engfailanal.2016.01.012
Guide R.007-2004: Calculation of Gears for Strength, 91 p. Russian River Register, Moscow (2005) (In Russ.)
Lebedev, S.Yu.: Analysis of methods for calculating tooth interior fatigue fracture. Omskiy Nauchnyy Vestnik 2(182), 43–47 (2022). https://doi.org/10.25206/1813-8225-2022-182-43-47. (in Russ.)
Lebedev, S.Yu., Syzrantsev, V.N.: Probability of failure-free operation of spur gears: tooth interior fatigue fracture. Bull. South Ural State Univ. Ser. Eng. 2(22), 20–32 (2022). https://doi.org/10.14529/engin220202. (in Russ.)
Lobachev, A.A. Study of the loading of the elements of the gearbox of the top drive system. Dissertation for the degree of candidate of technical sciences. St. Petersburg, 166 p. (2017) (In Russ.)
Bolshakova, M.J.: Study of the influence of the composition and structure of the hardened surface layer on the durability of heavily loaded gears. Dissertation for the degree of candidate of technical sciences. Perm, 151 p. (2011) (In Russ.)
Zubarev, N.I., Igdalov, M.P.: Optimization of qualitative parameters of gear mesh. Tract. Agric. Mach. 2, 41–42 (1989). (In Russ.)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Lebedev, S.Y., Syzrantsev, V.N. (2024). The Reliability Function of Case-Hardened Cylindrical Gears. In: Evgrafov, A.N. (eds) Advances in Mechanical Engineering. MMESE 2023. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-48851-1_8
Download citation
DOI: https://doi.org/10.1007/978-3-031-48851-1_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-48850-4
Online ISBN: 978-3-031-48851-1
eBook Packages: EngineeringEngineering (R0)