“On the Influence of Force Distribution and Boundary Condition on Helical Gear Stiffness”
Authors: Niels Leergaard Pedersen,Affiliation: Technical University of Denmark
Reference: 2015, Vol 36, No 3, pp. 143-155.
Keywords: Gears, Stiffness, Helical, External, FE
Abstract: The gear stiffness has a direct influence on the dynamic response of transmission systems that include a gear box, the stiffness also controls the load distribution among the teeth in mesh. The stiffness of a gear tooth varies non-linearly as the contact line with the meshing gear tooth moves along the surface of the tooth and the resulting meshing stiffness also includes discontinuities. The stiffness estimation for helical gears can only be done using full 3D analysis contrary to spur gears where 2D often suffice. Besides the usual gear geometry defined by standards two factors are found to have a large influence on the stiffness. These two factors are the rim thickness included in the stiffness calculation and the contact zone size. In the contact zone the distribution of the load is also shown to be important. Simple possible simplifications in relation to the contact load distribution are presented. The gear stiffness is found using the elastic energy of the loaded tooth. In the finite element calculation the true gear tooth root profile is applied.
PDF (874 Kb)
DOI: 10.4173/mic.2015.3.2References:
[1] Arafa, M.H. and Megahed, M.M. (1999). Evaluation of spur gear mesh compliance using the finite element method, Proc. of the Inst. of Mech. Eng. Part K-J. Mech. Eng. Science, 1999. 213(6):569--579.
[2] Choi, M. and David, J. (1990). Mesh stiffness and transmission error of spur and helical gears, SAE Transactions. 99(6):1599--1607.
[3] COMSOL AB. (2015). http://www, comsol.se. Accessed: 2015-08-15.
[4] DIN 867. (1986). Basic rack tooth profiles for involute teeth of cylindrical gears for general engineering and heavy engineering (German standard), 1986.
[5] Hayashi, K. (1963). Load distribution on the contact line of helical gear teeth (part1), Bulletin of the JSME. 6(22):336--343.
[6] Hayashi, K. and Sayama, T. (1963). Load distribution on the contact line of helical gear teeth (part2), Bulletin of the JSME. 6(22):344--353.
[7] Hedlund, J. and Lehtovaara, A. (2006). Modeling of helical gear contact with tooth deflection, Tribology international. 40(4):613--619. doi:10.1016/j.triboint.2005.11.004
[8] Hedlund, J. and Lehtovaara, A. (2008). A parameterized numerical model for the evaluation of gear mesh stiffness variation of a helical gear pair, Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Science. 222(7):1321--1327. doi:10.1243/09544062JMES849
[9] ISO 6336-1. (2006). Calculation of load capacity of spur and helical gears - part 1: Basic principles, introduction and general influence factors, 2006.
[10] Letaief, M.R., Chaari, F., and Haddar, M. (2002). Deformation and bending stress analysis of a three-dimensional thin-rimmed gear, Transactions American Society of Mech. Eng., Journal of Mechanical Design. 124(1):129--135. doi:10.1115/1.1427928
[11] Letaief, M.R., Chaari, F., and Haddar, M. (2008). Influence of internal gears rim thickness and design on gearmesh stiffness, Intl. Review of Mechanical Engineering. 1(1):62--67.
[12] Litvin, F.L. and Fuentes, A. (2004). Gear geometry and applied theory, Cambridge University Press.
[13] Niemann, G. and Winter, H. (1985). Maschinenelemente, Band II, Springer-Verlag.
[14] Norton, R.L. (2000). Machine design - an integrated approach, Prentice-Hall.
[15] Pedersen, N.L. (2009). Reducing bending stress in external spur gears by redesign of the standard cutting tool, Structural and Multidisciplinary Optimization. 38(3):215--227. doi:10.1007/s00158-008-0289-5
[16] Pedersen, N.L. (2015). Minimizing tooth bending stress in spur gears with simplified shapes of fillet and tool shape determination, Engineering optimization. 47(6):805--824. doi:10.1080/0305215X.2014.927452
[17] Pedersen, N.L. and Jorgensen, M.F. (2014). On gear teeth stiffness evaluation, Computer & Structures. 135:109--117. doi:10.1016/j.compstruc.2014.01.023
[18] Pedersen, N.L. and Pedersen, P. (2008). On prestress stiffness analysis of bolt-plate contact assemblies, Archive of Applied Mechanics, 2008. 78(2):75--88. doi:10.1007/s00419-007-0142-0
[19] Pedersen, N.L. and Pedersen, P. (2008). Stiffness analysis and improvement of bolt-plate contact assemblies, Mechanics Based Design of Structures and Machines, 2008. 36(1):47--66. doi:10.1080/15397730701735749
[20] Pedersen, N.L. and Pedersen, P. (2009). Bolt-plate contact assemblies with prestress and external loads: Solved with super element technique, Computers & Structures. 87(21-22):1374--1383. doi:10.1016/j.compstruc.2009.07.004
[21] Pedrero, J.I., Pleguezuelos, M., Artes, M., and Antona, J.A. (2010). Load distribution model along the line of contact for involute external gears, Mechanism and Machine Theory. 45(5):780--794. doi:10.1016/j.mechmachtheory.2009.12.009
[22] Tsay, C. (1988). Helical gears with involute shaped teeth: geometry, computer simulation, tooth contact analysis, and stress analysis, Journal of Mechanisms, Transmissions, and Automation in Design. 110(4):482--491.
[23] Zhang, Y. and Fang, Z. (1999). Analysis of tooth contact and load distribution of helical gears with crossed axes, Mechanism and Machine Theory. 34(1):41--5.
BibTeX:
@article{MIC-2015-3-2,
title={{On the Influence of Force Distribution and Boundary Condition on Helical Gear Stiffness}},
author={Pedersen, Niels Leergaard},
journal={Modeling, Identification and Control},
volume={36},
number={3},
pages={143--155},
year={2015},
doi={10.4173/mic.2015.3.2},
publisher={Norwegian Society of Automatic Control}
};