Three Kinds of Gear Transmission Nonlinear Dynamics Models

Abstract:

Based on the Lagranges equations, a new nonlinear dynamic gear model is established by introducing two variables of relative rotation angleand mean rotation angle. The motion equations derived with Lagranges equation exhibit nonlinear terms which are absent in the equations derived on Newtons equations. Combining with the numerical simulation, the dynamic responses in time domain and frequency domain are deduced, and it can be concluded that the responses at low speed of three different models are different. However, they are similar at the designed speed without the consideration of dissipation energy. On the contrary, the dynamic responses are similar at low speed and the simplified Newtons equation differs at the designed speed including dissipation energy.

• Periodical: Advanced Materials Research (Volume 787)
• Pages: 765-770
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.787.765
• Online since: September 2013
• Authors: Li Juan Wu, Jin Yuan Tang, Si Yu Chen
• Keywords: Cylindrical Gear, Lagranges Equation, Modeling, Nonlinear Dynamics

References

[1] J.R. Barber, K. Grosh, and S. Oh, Energy considerations in systems with varying stiffness. Journal of Applied Mechanics Vol. 70 (2003), pp.465-469.

DOI: 10.1115/1.1574060

[2] S. Oh, K. Grosh, and J.R. Barber, Energy conserving equations of motion for gear systems. Transactions of the ASME-L-Journal of Vibration and Acoustics Vol. 127 (2005), pp.208-212.

DOI: 10.1115/1.1891815

[3] A. Kahraman, and G. Blankenship, Effect of involute contact ratio on spur gear dynamics. Journal of mechanical design Vol. 121 (1999), pp.112-118.

DOI: 10.1115/1.2829411

[4] C. Siyu, T. Jinyuan, L. Caiwang, and W. Qibo, Nonlinear dynamic characteristics of geared rotor bearing systems with dynamic backlash and friction. Mechanism and Machine Theory Vol. 46 (2011), pp.466-478.

DOI: 10.1016/j.mechmachtheory.2010.11.016

[5] J.Y. Tang, Q.B. Wang, L.J. Wu, and S.Y. Chen, Bifurcation Analysis of Impact Model in Gear Transmission System. Applied Mechanics and Materials Vol. 86 (2011), pp.479-482.

DOI: 10.4028/www.scientific.net/amm.86.479

[6] J.R. Barber, K. Grosh, and S. Oh, Energy considerations in systems with varying stiffness. Journal of Applied Mechanics Vol. 70 (2003), pp.465-469.

DOI: 10.1115/1.1574060

[7] S. Oh, K. Grosh, and J.R. Barber, Energy conserving equations of motion for gear systems. Transactions of the ASME-L-Journal of Vibration and Acoustics Vol. 127 (2005), pp.208-212.

DOI: 10.1115/1.1891815

[8] J.D. Smith, Gear Noise and Vibration, Marcel Dekker, (1999), in press.

[9] W. Kim, H.H. Yoo, and J. Chung, Dynamic analysis for a pair of spur gears with translational motion due to bearing deformation. Journal of Sound and Vibration Vol. 329 (2010), pp.4409-4421.

DOI: 10.1016/j.jsv.2010.04.026

[10] A. Kahraman, and R. Singh, Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system. Journal of Sound and Vibration Vol. 146 (1991), pp.135-156.

DOI: 10.1016/0022-460x(91)90527-q

[11] J. Kuang, and Y. Yang, An estimate of mesh stiffness and load sharing ratio of a spur gear pair, Advancing power transmission into the 21 st century 1992, pp.1-9.

DOI: 10.1115/detc1992-0001