Abstract
A theoretical investigation is carried out on the orbital motions of a symmetrical, unbalanced, rigid rotor subjected to a constant vertical load and supported on two lubricated journal bearings. In order to determine the fluid film forces, the short bearing theory is adopted.
A method is illustrated that makes it possible to determine the analytical equation of the orbit as an approximated solution of the system of non-linear differential equations of motion of the journal axis. A procedure is also described for evaluating the stability of the solution found. Diagrams of the curves delimiting, in the working plane of the rotor σ-mσ, the areas of stability of the various periodic solutions determined are provided.
Finally, the results obtained are compared and combined with those provided by a direct integration of the motion equation made using the Runge-Kutta method.
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Abbreviations
- C :
-
radial clearance
- D = 2R :
-
bearing diameter
- E :
-
mass unbalance cecentricity
- Fx, Fy :
-
fluid film force components
- fi = Fi/σW :
-
dimensionless fluid film force components
- L :
-
bearing length
- M :
-
one half rotor mass
- % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqe% fqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0d% Xdh9vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9% pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca% qabeaadaabauaaaOqaaiaad2gacqGH9aqpcaWGnbGaam4qaiabeM8a% 3naaCaaaleqabaGaaGOmaaaakiaac+cacqaHdpWCcaWGxbaaaa!471F!\[m = MC\omega ^2 /\sigma W\]:
-
dimensionless one half rotor mass
- R :
-
bearing radius
- T = 2 π :
-
synchronous orbit period
- t :
-
time
- W :
-
load per bearing
- X, Y, Z :
-
coordinates
- x = X/C; y = y/C; z = Z/L :
-
dimensionless coordinates
- μ:
-
oil dynamic viscosity
- ϱ = E/C :
-
dimensionless mass unbalance eccentricity
- σ = (μωRL/W)/(R/C) 2 (L/D) 2 :
-
modified Sommerfeld number
- τ = ωt :
-
dimensionless time = periodic orbit frequency
- ν = 2π/ω:
-
frequency ratio
- ω:
-
journal angular velocity
- (·):
-
dimensionless time derivative
References
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Brancati, R., Russo, M. & Russo, R. On the stability of periodic motions of an unbalanced rigid rotor on lubricated journal bearings. Nonlinear Dyn 10, 175–185 (1996). https://doi.org/10.1007/BF00045456
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DOI: https://doi.org/10.1007/BF00045456