Sommario
Si studiano le vibrazioni lineari d'un asse leggermente sbilanciato che ruota su cuscinetti lubrificati, tenendo conto dell'azione delle forze e momenti generati dalla presenza del lubrificante. L'analisi (sviluppata sulla traccia di precedenti lavori di Sternlicht, Warner ed altri) mentre mostra che l'effetto dei momenti è trascurabile nel normale campo di variabilità dei parametri, mette invece in risalto l'effetto ammortizzante totale del lubrificante. Appare così importante, in sede di progetto di dispositivi ruotanti, la determinazione delle ampiezze di vibrazione alle varie velocità di rotazione piuttosto che delle sole velocità critiche.
Summary
Amplitudes of linear vibrations of a slightly unbalanced shaft, rotating on lubricated bearings near one of its critical speeds, are determined, taking into account the damping action of lubricant forces and couples on the journal movement. The analysis (carried out on the lines of earlier work by Sternlicht, Warner and others) shows that the effect of lubricant couples is never relevant in the normal range of variability of parameters. The analysis puts instead in evidence the effect of the total damping action of the lubricant and hence the importance in design of forecasts of amplitude of vibration at running speed. The attention s often limited to forecasts of critical speeds; such procedure may be misleading particularly near higher critical speeds.
Abbreviations
- A :
-
cccentricity ratio (eccentricity/clearance) of journal centre in the steady state under load
- B :
-
[u 1(L/2,t)2+u 2(L/2,t)2]1/2
- C :
-
centre of disc
- b, c, R :
-
width, radial clearance, radius of bearing
- d :
-
modulus of displacement of centre of gravity from centre of disc
- E :
-
modulus of clasticity
- G :
-
centre of gravity of disc
- I :
-
second moment of area of cross-section of shaft
- L :
-
length of shaft
- m :
-
mass of disc
- O :
-
centre of journal
- v 1,v 2,e :
-
components and modulus of displacement of centre of journal
- w 1,w 2 :
-
components of displacement of centre of gravity of disc
- 2W :
-
weight of rotor (W=(W 21 +W 22 )1/2)
- W 1,W 2 :
-
components of load on each bearing
- η :
-
viscosity of lubricant
- ζ, σ, γ, λ :
-
non dimensional parameters characterizing bearings and shaft, see formulae (10) and Sect. 3
- ω :
-
rotational speed of shaft (radian-unit time)
- ω c :
-
critical speed of shaft on pin-jointed supports.
References
P. C. Warner andR. J. Thoman,The Effect of the 150-Degree Partial Bearing on Rotor-Unbalance Vibration, J. Basic Eng., D 86, pp. 337–347, 1964.
P. C. Warner,Static and Dynamic Properties of Partial Journal Bearings, J. Basic Eng., D 85, pp. 247–257, 1963.
J. W. Lund andB. Sternlicht,Rotor-Bearing Dynamics with Emphasis on Attenuation, J. Basic Eng., D 84, pp. 491–502, 1962.
R. Holmes,The Vibration of a Rigid Shaft on Short Sleeve Bearings, J. Mech. Engineering Sc. 2, pp. 337, 1960.
Communications on five papers on Bearing Stability, Proc. Inst. Mech. Engrs., 176, pp. 591–593, 1962.
L. Galletti-Manacorda andG. Capriz,Torque produced by misalignement in short lubricated bearings, J. Basic Eng., 87 D, pp. 847–849, 1965.
G. Capriz andS. J. Denison,A Method for the calculation of the response of rotating shafts to excitation, Internal Report C.S.C.E., no. 2, 8.
G. Capriz,Numerical method for evaluating the response of rotating shafts to excitation, Meccanica, no. 2, pp. 213–217, 1967.
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Capovani, M. Vibrations of rotors: The effect of lubricant damping. Meccanica 3, 252–258 (1968). https://doi.org/10.1007/BF02186944
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DOI: https://doi.org/10.1007/BF02186944