The Effect of Friction on the Nonlinear Vibration of the Cracked One-Stage Power Transmission
Authors
Abstract
: The gear systems are widely used in industry to transmit the power or change the direction of the torque. Due to the extensive usage of the gears, the detailed designing and the subsequent maintenance of these systems are more and more evident. System recognition can be achieved through modeling the system, investigating the system behavior, and comparing the results obtained through the model with the actual system behavior. Up to now, the effect of dry friction has not been taken into account in nonlinear vibration analysis and modeling of a cracked one-stage gear power transmission system. In this paper, the nonlinear vibration of a pair of cracked spur-gear system in presence of dry friction, static transmission error, clearance and time-variant mesh stiffness is investigated. To this end, the time-variant mesh stiffness of an intact tooth is calculated analytically. Then, the tooth root crack is modeled as a cracked cantilever beam. The governing nonlinear equation of motion is extracted accordingly, and in order to consider the effect of dry friction, the governing equation solved by Rung- Kutta method in three separate time spans. Finally, the frequency response and bifurcation diagrams are used to study the effect of the friction and tooth root crack on the nonlinear vibration behavior of the system.
Keywords
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15. Chaari, F., Fakhfakh, T., and Haddar, M., “Analytical Modeling of Spur Gear Tooth Crack and Influence on Gear Mesh Stiffness”, European Journal of Mechanics A/Solids, Vol. 28, pp. 461-468, 2009.
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17. Endo, H., Randall, R. B., and Gosselin, C., “Differential Diagnosis of Spall Vs. Crack in Gear Tooth Fillet Region: Experimental Validation”, Mechanical Systems and Signal Processing, Vol. 23, pp. 636-651, 2009.
18. Howard, I., Jia, Sh., and Wang, J., “The Dynamic Modelling of a Spur Gear in Mesh Including Friction and a Crack”, Mechanical Systems and Signal Processing, Vol. 15, No. 5, pp. 831-853, 2001.
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21. Wang, J., Zheng, J., and Yang, A., “An Analytical Study of Bifurcation and Chaos in a Spure Gear Pair with Sliding Friction”, Procedia Engineering, Vol. 31, pp. 563-570, 2012.
22. Shen, Y., Yang, S., and Liu, X., “Nonlinear Dynamic of a Spur Gear Pair with Time-Varying Stiffness and Backlash Based on Incremental Harmonic Balance Method”, Journal of Mechanical Sciences, Vol. 48, pp. 1256-1263, 2006.
2. Vinayak, H., and Singh, R., “Multi-body dynamics and modal analysis”, Journal of Sound and Vibration, Vol. 210, No. 2, pp. 171-214, 1998.
3. Vinayak , H., Singh, R., and Padmanabhan, C., “Linear Dynamic Analysis of Multi-mesh Transmissions Containing External Rigid Gears”, Journal of Sound and Vibration, Vol. 185, No. 1, pp. 1-32, 1995.
4. Fakhfakh, T., Chaari, F., and Haddar, M., “Numerical and Experimental Analysis of a Gear System with Teeth Defects”, The International Journal of Advanced Manufacturing Technology , Vol. 25, pp. 542-550, 2005.
5. Kahraman, A., and Singh, R., “Non-Linear Dynamics of Spur Gear Pair”, Journal of Sound and Vibration, Vol. 142, No. 1, pp. 49-75, 1990.
6. Wang, J., li, R., and Peng, X., “Survey of Nonlinear Vibration of Gear Transmission Systems”, Applied Mechanics Reviews, Vol. 56, No. 3, pp. 309-329, 2003.
7. Theodossiades, S., and Natsiavas, S., “Nonlinear Dynamics of Gear-pair Systems with Periodic Stiffness and Backlash”, Journal of Sound and Vibration, Vol. 229, No. 2, pp. 287-310, 2000.
8. Chang-Jian, C., and Chang, Sh., “Bifurcation and Chaos Analysis of Spur Gear Pair with and without Nonlinear Suspention, Nonlinear Analysis”, Real World Application,Vol. 12, pp. 979-989, 2011.
9. Vaishya, M., and Singh, R., “Sliding Friction-Induced Nonlinearity and Parametric Effects in Gear Dynamics”, Journal of Sound and Vibration, Vol. 248, No. 4, pp. 671-694, 2001.
10. Velex, P., and Sainsot, P., “An Analytical Study of Tooth Friction Excitations in Errorless Spur and Helical Gears”, Mechanism and Machine Theory, Vol. 37 pp. 641-658, 2002.
11. He, S., Gunda, R., and Singh, R., “Effect of Sliding Friction on the Dynamics of Spur Gear Pair with Realistic Time-Varying Stiffness”, Journal of Sound and Vibration, Vol. 301, pp. 927-949, 2007.
12. He, S., Cho, S., and Singh, R., “Pridiction of Dynamic Friction Forces in Spur Gears Using Alternate Sliding Friction Formulations”, Journal of Sound and Vibration, Vol. 309, pp. 843-851, 2008.
13. Parey, A., and Tandon, N., “Spur Gear Dynamic Models Including Defects–A review”, The shock and Vibration Digest, Vol. 35, No. 6, pp. 465-478, 2003.
14. Chaari, F., Baccar, W., Abbes, M. S., and Haddar, M., “Effect of Spalling or Tooth Breakage on Gearmesh Stiffness and Dynamic Response of a One-Stage Spur Gear Transmission”, European Journal of Mechanics A/Solid, Vol. 27, pp. 691-705, 2008.
15. Chaari, F., Fakhfakh, T., and Haddar, M., “Analytical Modeling of Spur Gear Tooth Crack and Influence on Gear Mesh Stiffness”, European Journal of Mechanics A/Solids, Vol. 28, pp. 461-468, 2009.
16. Wu, S., Zuo, M. J., and Pary, A., “Simulation of Spur Gear Dynamics and Estimation of Fault Growth”, Journal of Sound and Vibration, Vol. 317, pp. 608-624, 2008.
17. Endo, H., Randall, R. B., and Gosselin, C., “Differential Diagnosis of Spall Vs. Crack in Gear Tooth Fillet Region: Experimental Validation”, Mechanical Systems and Signal Processing, Vol. 23, pp. 636-651, 2009.
18. Howard, I., Jia, Sh., and Wang, J., “The Dynamic Modelling of a Spur Gear in Mesh Including Friction and a Crack”, Mechanical Systems and Signal Processing, Vol. 15, No. 5, pp. 831-853, 2001.
19. Lewicki, D. G., “Effect of Rim Thickness on Gear Crack Propagation Path, NASA Technical Memorandum 107229”, 7th International Power Transmission and Gearing Conference sponsored by the American Society of Mechanical Engineers, San Diego, California, 1996.
20. Just Agosto, F. A., “Damage Detection Based on the Geometric Interpretation of the Eigenvalue Problem”, Ph.D. Thesis, Virginia Polytechnic Institute and State University, 1997.
21. Wang, J., Zheng, J., and Yang, A., “An Analytical Study of Bifurcation and Chaos in a Spure Gear Pair with Sliding Friction”, Procedia Engineering, Vol. 31, pp. 563-570, 2012.
22. Shen, Y., Yang, S., and Liu, X., “Nonlinear Dynamic of a Spur Gear Pair with Time-Varying Stiffness and Backlash Based on Incremental Harmonic Balance Method”, Journal of Mechanical Sciences, Vol. 48, pp. 1256-1263, 2006.
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