Abstract
Utilizing ball-type auto-balancer in rotating systems is a popular method in industry in order to eliminate the rotational vibration. Recently, by using numerical methods, it is shown that a ball-type auto-balancer equipped with both the radial and peripheral springs, ball-spring automatic balancer (AB), is an improved model. In this paper, due to the advantages of analytical methods over the numerical ones, the complete system dynamics, i.e., the stability analysis and the time response, of the rotor equipped with ball-spring AB is analyzed by the multiple scales method as a unified technique. Therefore, with no need for implementing any other stability theories, the stability analysis is a definite advantage of this method due to the less computation cost. Moreover, the time responses show a good agreement with those obtained through the numerical method. Finally, for the first time, the influence of the peripheral springs on the time responses and the stable equilibrium points of the rotor with ball-spring AB is studied in details. The results show that the peripheral springs decrease the vibration amplitude at the transient and leave some residual imbalance at the steady state and accordingly, there is a compromise between the system working performance at the transient and the steady state.
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References
Chung, J., Ro, D.S.: Dynamic analysis of an automatic dynamic balancer for rotating mechanism. J. Sound Vib. 228(5), 1035–1056 (1999)
Huang, W.Y., Chao, C.P., Kang, J.R., Sung, C.K.: The application of ball-type balancers for radial vibration reduction of high-speed optic disk drives. J. Sound Vib. 250(3), 415–430 (2002)
Kim, W., Chung, J.: Performance of automatic ball balancers on optical disc drives. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 216(11), 1071–1080 (2002)
Chao, P.C.P., Huang, Y.D., Sung, C.K.: Non-planar dynamic modeling for the optical disk drive spindles equipped with an automatic balancer. Mech. Mach. Theory 38(11), 1289–1305 (2003)
Kim, W., Lee, D.J., Chung, J.: Three-dimensional modeling and dynamic analysis of an automatic ball balancer in an optical disk drive. J. Sound Vib. 285(3), 547–569 (2005)
Chao, P.C., Sung, C.K., Wang, C.C.: Dynamic analysis of the optical disk drives equipped with an automatic ball balancer with consideration of torsional motion. J. Appl. Mech. 72(6), 826–842 (2005)
Rajalingham, C., Rakheja, S.: Whirl suppression in hand-held power tool rotors using guided rolling balancers. J. Sound Vib. 217(3), 453–466 (1998)
Thearle, E.L.: Automatic dynamic balancers. Mach. Des. 22, 119–124 (1950)
Alexander, J.D.: An automatic dynamic balancer. Proc. Second Southeast. Conf. 2, 415–426 (1964)
Cade, J.W.: Self-compensating balancing in rotating mechanisms. Des. News 234–239, (1965)
Chung, J., Jang, I.: Dynamic response and stability analysis of an automatic ball balancer for a flexible rotor. J. Sound Vib. 259(1), 31–43 (2003)
Green, K., Champneys, A.R., Lieven, N.J.: Bifurcation analysis of an automatic dynamic balancing mechanism for eccentric rotors. J. Sound Vib. 291(3), 861–881 (2006)
Green, K., Champneys, A.R., Friswell, M.I.: Analysis of the transient response of an automatic dynamic balancer for eccentric rotors. Int. J. Mech. Sci. 48(3), 274–293 (2006)
Lu, C.J.: Stability analysis of a single-ball automatic balancer. J. Vib. Acoust. 128(1), 122–125 (2006)
Lu, C.J., Hung, C.H.: Stability analysis of a three-ball automatic balancer. J. Vib. Acoust. 130(5), 1–7 (2008)
Lu, C.J., Wang, M.C., Huang, S.H.: Analytical study of the stability of a two-ball automatic balancer. Mech. Syst. Signal Process. 23(3), 884–896 (2009)
Ehyaei, J., Moghaddam, M.M.: Dynamic response and stability analysis of an unbalanced flexible rotating shaft equipped with n automatic ball-balancers. J. Sound Vib. 321(3–5), 554–571 (2009)
Chan, T.C., Sung, C.K., Chao, P.C.P.: Non-linear suspension of an automatic ball balancer. Int. J. Non-Linear Mech. 46(2), 415–424 (2011)
Lu, C.J., Wang, M.C.: Stability analysis of a ball-rod-spring automatic balancer. Int. J. Mech. Sci. 53, 846–854 (2011)
Kim, T., Na, S.: New automatic ball balancer design to reduce transient-response in rotor system. Mech. Syst. Signal Process. 37(1), 265–275 (2013)
Rezaee, M., Fathi, R.: A new design for automatic ball balancer to improve its performance. Mech. Mach. Theory. 94, 165–176 (2015)
Rezaee, M., Fathi, R.: Improving the working performance of automatic ball balancer by modifying its mechanism. J. Sound Vib. 358, 375–391 (2015)
Han, Q., Qin, Z., Lu, W., Chu, F.: Dynamic stability analysis of periodic axial loaded cylindrical shell with time-dependent rotating speeds. Nonlinear Dyn. 81, 1649–1664 (2015)
Mirtalaie, S.H., Hajabasi, M.A.: Nonlinear axial-lateral-torsional free vibrations analysis of Rayleigh rotating shaft. Arch. Appl. Mech. 87(3), 1–30 (2017)
Shahgholi, M., Esmaeilzadeh Khadem, S.: Stability analysis of a nonlinear rotating asymmetrical shaft near the resonances. Nonlinear Dyn. 70, 1311–1325 (2012)
Iwatsubo, T., Shimbo, K., Kawamura, S.: Nonlinear vibration analysis of a rotor system using component mode synthesis method. Arch. Appl. Mech. 72, 843–855 (2003)
Nayfeh, A.H.: Introduction to Perturbation Techniques. Wiley, New York (1981)
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Rezaee, M., Ghorbanpour, L. The nonlinear dynamic analysis of the ball-spring automatic balancer by the multiple scales method. Arch Appl Mech 89, 2229–2243 (2019). https://doi.org/10.1007/s00419-019-01573-6
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DOI: https://doi.org/10.1007/s00419-019-01573-6