Investigating the Dynamics of a Ball-Spring Autobalancer in a Rotor with Non-Linear Bearings
Authors
Abstract
Although the traditional automatic ball balancer (ABB) has numerous advantages, it has two major deficiencies, i.e., it has a limited balance stable region and it increases the vibration amplitude of the rotor at transient state. These deficiencies limit the applicability of ABBs. In this regard, a new type of ABB called “the Ball-spring autobalancer” has been proposed to resolve the mentioned deficiencies of the traditional ABBs. In order to investigate the capability of the Ball-spring AB in balancing rotors, it is necessary to study its dynamics accurately. The dynamics of a rotor with linear bearing equipped with a Ball-spring AB has been studied previously; however, in real situations, the bearings have nonlinear characteristics. Here, the dynamics of a rotor with nonlinear bearings equipped with a Ball-spring AB is investigated by the multiple scales method for the first time. The results show that the nonlinearity at the rotor bearings does not impair the advantages of the Ball-spring AB.
Keywords
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2. Kim, W., chung, J., “Performance of Automatic Ball Balancers on Optical Disc Drives”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 216, No. 11, pp. 1071-1080, 2002.
3. Chao, P. C., Sung, C.-K., and Wang, C.-C., “Dynamic Analysis of The Optical Disk Drives Equipped With an Automatic Ball Balancer with Consideration of Torsional Motions”, Journal of Applied Mechanics, Vol. 72, No. 6, pp. 826-842, 2005.
4. Chao, P. C.-P., Sung, C.-K., and Leu, H.-C., “Effects of Rolling Friction of the balancing balls on the Automatic Ball balancer for Optical Disk Drives”, Journal of Tribology, Vol. 127, No. 4, pp. 845-856, 2005.
5. Rajalingham, C., and Rakheja, S., “Whirl Suppression In Hand-Held Power Tool Rotors Using Guided Rolling Balancers”, Journal of Sound and Vibration, Vol. 217, No. 3, pp. 453-466, 1998.
6. E. L, Thearle, “Automatic Dynamic Balancers”, Machine Design, Vol. 22, pp. 119-124, 1950.
7. Alexander, J., “An Automatic Dynamic Balancer", Proceeding of 2nd Southeastern Conference, 415-426.
8. Cade, J., “Self-Compensating Balancing in Rotating Mechanisms”, Design News, Vol. 20, pp. 234-239, 1965.
9. Chung, J., and Ro, D., “Dynamic Analysis of an Automatic Dynamic Balancer for Rotating Mechanisms”, Journal of Sound and Vibration, Vol. 228, No. 5, pp. 1035-1056, 1999.
10. Chung, J., and Jang, I., “Dynamic Response and Stability Analysis of an Automatic Ball Balancer for a Flexible Rotor”, Journal of Sound and Vibration, Vol. 259, No. 1, pp. 31-43, 2003.
11. Lu, C.- J, Wang, M. –C, Huang, S. H., “Analytical Study of the Stability of a Two-Ball Automatic Balancer", Mechanical Systems and Signal Processing, Vol. 23, No. 3, pp. 884-896, 2009.
12. Lu, C.-J., and Hung, C.-H., “Stability Analysis of a Three-Ball Automatic Balancer”, Journal of Vibration and Acoustics, Vol. 130, No. 5, pp. 1-7, 2008.
13. Ehyaei, J., Moghaddam, M. M., “Dynamic Response and Stability Analysis of an Unbalanced Flexible Rotating Shaft Equipped with an Automatic Ball-Balancers”, Journal of Sound and Vibration, Vol. 321, No. 3, pp. 554-571, 2009.
14. Chan, T., Sung, C., and Chao, P. C., “Non-Linear Suspension of An Automatic Ball Balancer”, International Journal of Non-Linear Mechanics, Vol. 46, No. 2, pp. 415-424, 2011.
15. Sung, C., Chan, T., Chao, C., and Lu, C., “Influence of External Excitations on Ball Positioning of an Automatic Balancer”, Mechanism and Machine Theory, Vol. 69, pp. 115-126, 2013.
16. Bykov, B., “Auto-Balancing of a Rotor With an Orthotropic Elastic Shaft”, Journal of Applied Mathematics and Mechanics, Vol. 77, No. 4, pp. 369-379, 2013.
17. Rezaee, M., and Fathi, R., “The Effect of Damping Ratio and Balls Mass on the Stability of Automatic Ball-Balancer and Determining their Optimum Values”, Modares Mechanical Engineering, Vol. 14, No. 3, pp. 110-118, 2014 (In Farsi).
18. Rezaee, M., and Fathi, R., “Dynamic Analysis of an Automatic Double-race Ball-balancer under the Gyroscopic Effect and Optimization of its Parameters Using the Genetic Algorithm”, Journal of Mechanical Engineering, Vol. 46, No. 3, pp. 129-137, 2016 (In Farsi).
19. Majewski, T., Szwedowicz, D., and Melo, M. A. M., “Self-Balancing System of the Disk on an Elastic Shaft”, Journal of Sound and Vibration, Vol. 359, pp. 2-20, 2015.
20. Jung, D., and DeSmidt, H., “Limit-Cycle Analysis of Planar Rotor/Autobalancer System Influenced by Alford's Force”, Journal of Vibration and Acoustics, Vol. 138, No. 2, pp. 1-14, 2016.
21. Rezaee, M., and Fathi, R., “Improving the Working Performance of Automatic Ball Balancer by Modifying Its Mechanism”, Journal of Sound and Vibration, Vol. 358, pp. 375-391, 2015.
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