Numerical Studies of Nonlinear Gearing Models Using Bond Graph Method
More details
Hide details
Department of Logistics and Aviation Technologies, Silesian University of Technology, Poland
Higher Vocational School in Nowy Sącz, Poland
Department of Computer Science and Automation, University of Bielsko-Biala, Poland
Online publication date: 2018-11-21
Publication date: 2018-11-01
International Journal of Applied Mechanics and Engineering 2018;23(4):885-896
The present paper is dedicated to computer simulations performed using a numerical model of a one-stage gear. The motion equations were derived utilizing the bond graph method. The formulated model takes into consideration the variable stiffness of toothings as well as an inter-tooth clearance which has been represented via discontinuous elements with so called dead zones. As a result of these assumptions, the nonlinear model was obtained which enables representation of the dynamic phenomena of the considered gear. In the paper, an influence of errors of gear wheels’ co-operation on the character of excited dynamic phenomena was studied. The methodology of the analyses consists in utilization of the following tools: color maps of distribution of the maximal Lapunov coefficient and bifurcation diagrams. Based upon them, the parameters were determined, for which the Poincare portrait represents a structure of the chaotic attractor. For the identified attractors, the initial attractors were calculated numerically - which along with the changes of the control parameters are subjected to multiplication, stretching or rotation.
Lorenz E.N. (1963): Deterministic non-periodic flow. – Journal of the Atmospheric Sciences, vol.20, pp.130-141.
Cai-Wan Chang-Jian and Shiuh-Ming Chang (2011): Bifurcation and chaos analysis of spur gear pair with and without nonlinear suspension. – Nonlinear Analysis: Real World Applications, vol.12, pp.979-989.
Khomeriki G. (2016): Parametric resonance induced chaos in magnetic damped driven pendulum. – Physic Letters A, 380, pp.2382-2385.
Awrejcewicz J., Krysko-jr V.A., Pakovleva T.V. and Krysko V.A. (2017): Alternating chaos versus synchronized vibrations of interacting plane with beams. – International Journal of Non-Linear Mechanics, vol.88, pp.21-30.
Armand Eyebe Fouda J.S., Bodo B., Djeufa G.M.D. and Sabat S.L. (2016): Experimental chaos detection in the Duffung oscillator. – Communications in Nonlinear Science and Numerical Simulations, vol.33, pp.259-269.
Sajid I., Xizhe Z., Yanhe Z. and Jie Z. (2014): Bifurcation and chaos in passive dynamic walking, A review. – Robotics and Autonomous System, vol.62, pp.889-909.
Dudkowski D., Jafari S., Kapitaniak T., Kuznetsov N., Leonov G.A. and Prased A. (2016): Hidden attractors in dynamical system. – Physics Reports, vol.637, pp.1-50.
Awrejcewicz J., Krysko A.V., Papkova I.V. and Krysko V.A. (2012): Routes to chaos in continuous mechanica systems. Part 3: The Lyapunov exponents, hyper-hyper and spatial-temporal chaos. – Chaos, Solitons and Fractals, vol.45, pp.721-736.
Cai-Wan Chang-Jian (2012): Bifurcation and chaos analysis of the porous squeeze film damper mounted gearbearing system. – Computer and Mathematics with Application, vol.64, pp.798-812.
Zhao Xin, Chen Changzheng, Liu Jie and Zhang Lei (2015): Dynamics characteristics of a spur gear transmission system for a wind turbine. – International Conference on Automation, Mechanical Control and Computational Engineering, pp.1985-1990.
Kokare D.K. and Patil S.S. (2014): Numerical analysis of vibration in mesh stiffness for spur gear pair with method of phasing. – International Journal of Current Engineering and Technology, Special Issue 3, pp.156-159.
Saghafi A. and Farshidianfar A. (2016): An analytical of controlling chaotic dynamics in a spur gear system. – Mechanism and Machine Theory, vol.96, pp.179-191.
Cai Y. (1995): Simulation on the Rotational Vibration of Helical Gears in Consideration of the Tooth Separation Phenomenon (A New Stiffness Function of Helical Involute Tooth Pair). – “Journal of Mechanical Design”, Transactions of the ASME, vol.117, pp.460-469.
Cai Y. and Hayashi T. (1994): The Linear Approximated Equation of Vibration of a Pair of Spur Gears (Theory and Experiment). – Journal of Mechanical Design, Transactions of the ASME, vol.116, pp.558-564.
Wang J., Guo L. and Wang H. (2013): Analysis of bifurcation and nonlinear control for chaos in gear transmission system. – Research Journal of Applied Sciences, Engineering and Technology, vol.6, No.10, pp.1818-1824.
Xiang L., Yi J. and Aijun H. (2016): Bifurcation and chaos analysis for multi-freedom gear-bearing system with time-varying stiffness. – Applied Mathematical Modelling, vol.40, pp.10506-10520.
Litak G. and Friswell M.I. (2003): Vibration in gear system. – Chaos, Solution and Fractals, vol.16, pp.795-800.
Łuczko J. (2008): Chaotic vibrations in gear mesh systems. – Journal of Theoretical and Applied Mechanics, vol.46, No.4, pp.879-896.
Ghosh S.S. and Chakraborty G. (2016): On optimal tooth profile modification for reduction of vibration and noise in spur gear pairs. – Mechanism and Machine Theory, vol.105, pp.145-163.
Wang J., Zheng J. and Yang A. (2012): An analytical study of bifurcation and chaos in a spur gear pair with sliding friction. – International Conference on Advances in Computational Modeling and Simulation, Procedia Engineering, vol.31, pp.563-570.
Zhang Y., Meng Z. and Sun Y. (2016): Dynamic modeling and chaotic analysis of gear transmission system in a braiding machine with or without random perturbation. – Shock and Vibration, Hindawi Publishing Corporation, Volume 2016, Article ID 8457645, 12 pages.
Lang S.Y.T. (2005): Graph-theoretical modeling of epicyclic gear system. – Mechanism and Machine Theory, vol.40, pp.511-529.
Wojnarowski J., Kopeć J. and Zawiślak S. (2006): Gear and graphs. – Journal of Theoretical and Applied Mechanics, vol.44, No.1, pp.139-151.
Drewniak J. and Zawiślak S. (2010): Linear-graph and contour-graph-based models of planetary gear. – Journal of Theoretical and Applied Mechanics, vol.48, No.2, pp.415-433.
Luo Y. and Tam D. (2011): Dynamics Modeling of Planetary gear set considering meshing stiffness based on bond graph. – Procedia Engineering, vol.24, pp.850-855.
Guo Y., Liu D., Yang S., Li X. and Chen J. (2016): Hydraulic-mechanical coupling modeling by bond graph for impact system of a high frequency rock drill drifter with sleeve distributor. – Automation in Construction, vol.63, pp.88-99.
Al-Shyyab A. and Kahraman A. (2005): Non-linear dynamic analysis of multi-mesh gear train using multi-term harmonics balance method: sub-harmonic motion. – Journal of Sound and Vibration, vol.279, pp.417-451.
Jingyue W., Lixin G. and Haotion W. (2013): Analysis of bifurcation and nonlinear control for chaos in gear transmission system. – Research Journal of Applied Sciences, Engineering and Technology, vol.6, No.10, pp.1818-1824.
Litak, G. and Friswell M.I. (2005): Dynamics of a gear system with faults in meshing stiffness. – Nonlinear dynamics 41.4, pp.415-421.
Shuang L., Jin-Jin W., Jin-Jie L. and Ya-Qian L. (2015): Nonlinear parametrically excited vibration and active control of gear pair system with time-varying characteristic. – Chines Physical Society, vol.214, No.10, 8 pages.
Journals System - logo
Scroll to top