Abstract
The prediction of gear vibration and noise has always been a major concern in gear design. Noise and vibration are inevitable problems that are involved in transmission systems; they have intensified when some nonlinear phenomena such as jump phenomenon, tooth separation and period-doubling bifurcation appear in the system. Tip and/or root modifications are well-known solutions that improve dynamic performance of gears. The present work investigates the complex, nonlinear dynamic behavior of three bevel gear models: (1) model with pure involute profile, (2) model with statically optimized tooth profile, and (3) model with dynamically optimized tooth profile. Tooth profile modification is employed in models by means of genetic algorithm in order to extract the best amount and length of modifications. The dynamic responses obtained from dynamic analyzer were compared qualitatively and quantitatively. By augmenting tooth profile modification, the average value of the dynamic responses is decreased intensely for both statically and dynamically optimized gear pairs. Dynamic load factor is calculated and compared with the involute tooth profile model and the two optimized gear sets. Employing teeth optimization leads to elimination of period-\(2T_{m}\) in both optimized simulations.
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References
Smith, J.: Gear Noise and Vibration. Marcel Dekker Inc., New York (1999)
Åkerblom, M., Pärssinen, M.: A Study of Gear Noise and Vibration. TRITA-MMK 2002:8/ISSN 1400-1179/ISRN/KTH/MMK/R-02/8-SE, Stockholm (2002)
Lin, H.H., Oswald, F.B., Townsend, D.P.: Dynamic loading of spur gears with linear or parabolic tooth profile modifications. Mech. Mach. Theory 29(8), 1115–1129 (1994)
Kahraman, A., Blankenship, G.W.: Effect of involute tip relief on dynamic response of spur gear pairs. J. Mech. Des. 121(2), 313–315 (1999)
Terauchi, Y., Miyao, Y., Fujii, M.: Dynamic behavior of straight bevel gear—1. Dynamic load, torque variation and bending vibration of gears shafts. Bull. JSME 23, 126–131 (1980)
Oda, S., Koide, T., Okamura, Y.: Dynamic behavior of straight bevel gear of Gleason type. Bull. JSME 26, 216–220 (1983)
Oda, S., Koide, T., Okamura, Y.: Study on bending fatique of straigth bevel gears. Bull. JSME 25, 1173–1179 (1982)
Oda, S., Takao, K., Higuchi, K.: Study on bending fatique of straigth bevel gears. Bull. JSME 26, 140–145 (1983)
Nalluveettil, S.J., Muthuveerappan, G.: Finite element modelling and analysis of a straight bevel gear tooth. Comput. Struct. 48(4), 739–744 (1993)
Gagnon, P., Gosselin, C., Cloutier, L.: Analysis of spur and straight bevel gear teeth deflection by the finite strip method. J. Mech. Des. 119, 421–426 (1997)
Elkholy, A., Elsharkawy, A., Yigit, A.S.: Effect of meshing tooth stiffness and manufacturing error on the analysis of straight bevel gears. J. Struct. Mech. 26(1), 41–61 (1998)
Wang, Y., Cheung, H.M.E., Zhang, W.J.: 3D dynamic modelling of spatial geared systems. Nonlinear Dyn. 26(4), 371–391 (2001)
Marambedu, K.R.: Development of a procedure for the analysis of load distribution, stresses and transmission error of straight bevel gears. The Ohio State University (2009)
Bahramighahnavieh, A., Mosaddegh, P., Akbarzadeh, S.: Investigation of the Hertzian stress distribution on the surface of the straight bevel gear. Appl. Mech. Mater. 307, 304–307 (2013)
Yinong, L., Guiyan, L., Ling, Z.: Influence of asymmetric mesh stiffness on dynamics of spiral bevel gear transmission system. Math. Prob. Eng. (2010). doi:10.1155/2010/124148
Chang-Jian, C.-W.: Nonlinear dynamic analysis for bevel-gear system under nonlinear suspension-bifurcation and chaos. Appl. Math. Model. 35, 3225–3237 (2011)
Yassine, D., Hammami, A., Walha, L., Haddar, M.: Effects of gear mesh fluctuation and defaults on the dynamic behavior of two-stage straight bevel system. Mech. Mach. Theory 82, 71–86 (2014)
Barbieri, M., Zippo, A., Pellicano, F.: Adaptive grid-size finite element modeling of helical gear pairs. Mech. Mach. Theory 82, 17–32 (2014)
Maitra, G.: Handbook of Gear Design. Tata McGraw-Hill Education, New York (1994)
Bonori, G.: Static and dynamic modeling of gear transmission error. Ph.D. Thesis, University of Modena and Reggio Emilia (2006)
Kahraman, A., Lim, J., Ding, H.: A dynamic model of a spur gear pair with friction. In: Proceedings of the 12th IFToMM World Congress (2007)
Liu, G., Parker, R.G.: Nonlinear dynamics of idler gear systems. Nonlinear Dyn. 53(4), 345–367 (2008)
Kahraman, A., Blankenship, G.: Experiments on nonlinear dynamic behaviour of an oscillator with clearance and periodically time-varying parameters. J. Appl. Mech. 64, 217–226 (1997)
Bonori, G., Barbieri, M., Pellicano, F.: Optimum profile modifications of spur gears by means of genetic algorithms. J. Sound Vib. 313(3), 603–616 (2008)
Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979)
Nayfeh, A.H., Balachandran, B.: Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods. Wiley, New York (2004)
Kahraman, A.: On the response of a preloaded mechanical oscillator with a clearance: period-doubling and chaos. Nonlinear Dyn. 3(3), 183–198 (1992)
Tamminana, V.K., Kahraman, A.: A study of the relationship between the dynamic factors and the dynamic transmission error of spur gear pairs. J. Mech. Des. 129, 75–83 (2007)
Acknowledgments
The authors would like to thank the Lab SIMECH/INTERMECH MO.RE. (HIMECH District, Emilia Romagna Region) particularly Prof. Francesco Pellicano and Dr. Marco Barbieri for providing FEM code and their guidance during the research.
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Motahar, H., Samani, F.S. & Molaie, M. Nonlinear vibration of the bevel gear with teeth profile modification. Nonlinear Dyn 83, 1875–1884 (2016). https://doi.org/10.1007/s11071-015-2452-z
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DOI: https://doi.org/10.1007/s11071-015-2452-z