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Oil whirl of rotors: A numerical method of prediction

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Sommario

Si suggerisce un procedimento numerico che consente di prevedere l'insorgere in un asse ruotante (anche su più cuscini) di vibrazioni autoeccitate nelle quali il veicolo del trasferimento dell'energia dal moto rotatorio a quello vibratorio è il lubrificante nei cuscini (oil whirl). Il procedimento si basa su sviluppi matriciali del tipo di quelli usati per la previsione di ampiezze di vibrazione in assi sbilanciati.

Summary

A numerical precedure is suggested for the forecast of the onset speed for oil whirl in shafts rotating on lubricated plain bearings. The procedure uses matrix manipulations of the type recently proposed in a generalization of the Myklestadt-Holzer method for the prediction of amplitudes of vibration in unbalanced shafts.

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Abbreviations

A :

ratio of |w b *| to clearancec

A c :

area of cross-section of shaft

b :

width of bearing

b ij :

coefficients of lubricant response

E :

modulus of elasticity

c :

radial clearance in bearing

c3 :

unit vector along shaft axis

g:

acceleration due to gravity

G :

shear modulus of elasticity

I :

second moment of area of cross-section

j k :

moments of inertia per unit length of slice of shaft (j 1=j 2=j)

k :

Timoshenko's constant

M:

bending moment

M*:

value of M in the steady state

M (s) :

see Eq. (4.1)

M(m) :

rate of change of moment of momentum

q :

dimensional factor, see Eq. (4.3)

R :

radius of bearing

S:

shear force

S*:

value of S in the steady state

S (s) :

see Eq. (4.1)

t :

time

y (s) :

see Eq. (4.1)

w:

displacement of centre of cross-section of shaft during vibration

w b :

value of w at a bearing

w*:

value of w in the steady state

z :

coordinate along the shaft axis

Δ b :

jump of a variable at a bearing

η :

viscosity of lubricant

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\eta } \) :

a non-dimensional constant, see (5.3)

θ:

slope due to bending of the shaft

θ*:

value ofθ in the steady state

θ (s) :

see Eq. (4.1)

μ :

weight per unit volume of the shaft

v :

ratio of whirl speed to running speed

v c :

value ofv at transition

ω :

speed of rotation

ω c :

value ofω at transition

References

  1. O. Pinkus andB. Sternlicht,Theory of hydrodynamic lubrication, Mc Graw Hill, New York, 1961.

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  2. A. Laratta,Oil whirl of rotors. Part I: Vertical shafts, Meccanica, Vol. 4, p. 336, 1969.

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  3. A. Laratta,Oil whirl of rotors. Part II: Horizontal shafts, Meccanica, Vol. 5, p. 126, 1970.

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  4. G. Campriz, Sulle vibrazioni delle aste rotanti, Ann. Scuola Norm. Sup., Vol. 17, pp. 31–42, 1963.

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  5. G. Capriz,Numerical method for evaluating the response of rotating shafts to excitation, Meccanica, Vol. 2, pp. 213–217, 1967.

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Authors and Affiliations

  1. Istituto di Elaborazione della Informazione, C.N.R., Pisa

    Gianfranco Capriz

Authors
  1. Gianfranco Capriz
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Capriz, G. Oil whirl of rotors: A numerical method of prediction. Meccanica 5, 203–209 (1970). https://doi.org/10.1007/BF02133576

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  • DOI: https://doi.org/10.1007/BF02133576

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