Analytical model to determine meshing stiffness of spur gears
DOI:
https://doi.org/10.32972/dms.2012.020Keywords:
gear mesh, meshing stiffness, elastic deflection, non-linear dynamicsAbstract
During dynamic analysis of gears correct determination of the meshing stiffness bears great importance. In order to determine meshing stiffness first of all the contact points have to be located. In this work a general method is presented for determining the contact points i.e. the contact curve, and a special method for involute profiles. An analytical method for deflection analysis of spur gears is formulated. During deflection analysis elastic deformation of the teeth is taken into account and as a consequence of the model and the calculation method failure in the base pitch and the profile can be treated.
References
F. L. Litvin: A fogaskerék kapcsolódás elmélete. Műszaki Könyvkiadó, Budapest, 1972.
F. Chaari–W. Baccar–M. S. Abbes–M. Haddar: Effect of spalling or tooth breakage on gearmesh stiffness and dynamic response of a one-stage spur gear transmission. European Journal of Mechanics A/Solids 27 (2008), pp. 691–705. https://doi.org/10.1016/j.euromechsol.2007.11.005
F Chaari–T. Fakhfakh–M. Haddar: Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness. European Journal of Mechanics A/Solids (2009), pp. 461–468. https://doi.org/10.1016/j.euromechsol.2008.07.007
K. Markovic–M. Franulovic: Contact stresses in gear teeth due to tip relief profile modification. Eng. Rev. 31–1. 2011. pp. 19–26.
J.J. Zhang–I.I. Esat–Y.H. Shi: Load analysis with varying mesh stiffness. Computers and structures 70 (1999), pp. 273–280. https://doi.org/10.1016/s0045-7949(98)00185-0
J. Hedlund–A. Lehtovaara: Modeling of helical gear contact with tooth deflection. Tribology Internation 40, 2007. pp. 613–619. https://doi.org/10.1016/j.triboint.2005.11.004
J. I. Pedrero–M. Pleguetuelos–M. Artés–J. A. Antona: Load distribution model along the line of contact for involute external gears. Mechanism and Machine Theory 45, 2010. pp. 780–794. https://doi.org/10.1016/j.mechmachtheory.2009.12.009
L. Walha–T. Fakhfakh–M. Haddar: Nonlinear dynamics of a two-stage gear system with mesh stiffness fluctuation, bearing felxibility and backlash. Mechanism and Machine Theory 44, 2009. pp. 1058–1069. https://doi.org/10.1016/j.mechmachtheory.2008.05.008
A. Andersson–L. Vedmar: A dynamic model to determine vibrations in involute helical gears. Journal of Sound and Vibration 260, 2003. pp. 195–212. https://doi.org/10.1016/s0022-460x(02)00920-3
G. Litak–M. I. Friswell: Vibration in gear systems. Chaos, Solitons and Fractals (2003), p.p. 795-800. https://doi.org/10.1016/s0960-0779(02)00452-6
R. Szűcs–L. Kamondi: Fogaskerekek dinamikai vizsgálatának egy lehetősége. Kolozsvár: Erdélyi Magyar Műszaki Tudományos Társaság, Műszaki Szemle, 2010. pp. 416–419.
R. Szűcs–L. Kamondi: Bevezetés a geometria dinamikai vizsgálatokra gyakorolt hatásába. GÉP LXI. (2010/9-10.), Gépipari Tudományos Egyesület Műszaki Folyóirata, pp. 102–104.
R. Szűcs–L. Kamondi: Bevezetés a fogaskerék kapcsolódás végeselem módszerrel történő vizsgálati lehetőségeibe. GÉP LXII. (2011/11), Gépipari Tudományos Egyesület Műszaki
Folyóirata, pp. 37–39.
James M. Gere–Barry J. Goodno: Mechnanics of Materials, Eighth Edition. 2009 Cengage Learning
M. J. Puttock–E. G. Thwaite: Elastic Compression of Spheres and Cylinders at Point and Line Contact. National Standards Laboratory Technical Paper, No. 25, Commonwealth Scientific and Industrial Research Organization, Australia, Melbourne 1969.
