[1]
Lee J. and Van Moorhem W. K., Analytical and experimental analysis of a self compensating dynamic balancer in a rotating mechanism, ASME Journal of Dynamic Systems, Measurement and Control 118 (1996) 468-475.
DOI: 10.1115/1.2801169
Google Scholar
[2]
Thearle E., A new type of dynamic-balancing machine, Trans. ASME 54(APM-54-12) (1932) 131-141.
DOI: 10.1115/1.4021775
Google Scholar
[3]
Chung J. Jang I., Dynamic response and stability analysis of an automatic ball balancer for a flexible rotor. Journal of Sound and Vibration 259(1) (2003) 31-43.[4] Chao C.-P. Huang Y.-D. Sung C.-K., Non-planar dynamic modeling for the optical disk drive spindles equipped with an automatic balancer. Mechanism and Machine Theory 38 (2003) 1289-1305.
DOI: 10.1016/s0094-114x(03)00078-8
Google Scholar
[5]
Green K. Champneys A. R. and Lieven N. J., Bifurcation analysis of an automatic dynamic balancer for eccentric rotors. Journal of Sound and Vibration 291 (2006) 861-881.
DOI: 10.1016/j.jsv.2005.06.042
Google Scholar
[6]
Sperling L. Ryzhik B. Linz Ch. and Duckstein H., Simulation of two-plane automatic balancing of a rigid rotor, Mathematics and computers in simulation 58 (2002) 351-365.
DOI: 10.1016/s0378-4754(01)00377-9
Google Scholar
[7]
Genta G. Delprete C. and Busa E., Some considerations on the basic assumptions in rotordynamics, Journal of Sound and Vibration 227(3) (1999) 611-645. APPENDIX The explicit forms for the kinetic energy T , potential V and Rayleigh's dissapation function F which are derived in Section 2 are given here T = 1 2Ix � ˙φ cos θ cos ψ + ˙θ sin ψ�2 + 1 2Iy �− ˙φ cos θ sin ψ + ˙θ cos ψ�2 + 1 2Iz � ˙φ sin θ + ˙ψ�2 +1 2M � ˙X2 + ˙Y 2 + ˙Z2� 1 2 2n+2X i=1 mi� h ˙X + εi � − sin θ ˙θ cos (ψ + αi) − cos θ sin (ψ + αi) � ˙ψ + ˙αi�� + zi cos θ ˙θi2 + h ˙Y + εi� cos θ ˙θ sin φ cos (ψ + αi) + sin θ cos φ ˙φ cos (ψ + αi) − sin θ sin φ sin (ψ + αi) � ˙ψ + ˙αi� − sin φ ˙φ sin (ψ + αi) + cos φ cos (ψ + αi) � ˙ψ + ˙αi�� + zi �sin θ ˙θ sin φ − cos θ cos φ ˙φ � i2 + h ˙Z + εi� − cos θ ˙θ cos φ cos (ψ + αi) + sin θ sin φ ˙φ cos (ψ + αi) + sin θ cos φ sin (ψ + αi) � ˙ψ + ˙αi� + cos φ ˙φ sin (ψ + αi) + sin φ cos (ψ + αi) � ˙ψ + ˙αi�� + zi �− sin θ ˙θ cos φ − cos θ sin φ ˙φ � i2� , (A-1) V = 1 2 2X j=1 n kxj �X + sin θ ˜lj�2 + kyj �Y − cos θ sin φ ˜lj�2 + kzj �Z − (1 − cos θ cos φ) ˜lj�2 o , (A-2) F = 1 2 2X j=1 n cxj � ˙X + cos θ ˙θ ˜lj�2 + cyj � ˙Y + �sin θ ˙θ sin φ − cos θ cos φ ˙φ � ˜lj�2 czj � ˙Z − �sin θ ˙θ cos φ + cos θ sin φ ˙φ � ˜lj�2 o + 1 2 2n+2X i=3 cb ˙αi. (A-3)
Google Scholar