OS-V: 1030 Rigid Jeffcott Model

This problem describes the Rigid Jeffcott model for rotor dynamics.

図 1. Model


Model Files

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Benchmark Model

The model details are as follows:
  • Unbalanced rigid disc on a massless rigid shaft.
  • CELAS, CTETRA4 and RBE2 elements defined.
  • ASYNC Complex Eigenvalue Analysis with Gyroscopic effects.
  • Rotor speed increments via RSPEED from 0 to 100 Hz, in steps of 10 Hz.

Material

The MAT1 material properties are:
Property
Value
Young's modulus (E)
1.0E+20 ton/s2-mm
Poisson's Ratio (NU)
0.3
Mass Density (RHO)
1.0 ton/mm3

Results

図 2. Eigen Mode Contour Plots


図 3. OptiStruct Results


The reference results are obtained by:
s   =   σ   +   i ω MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbwvMCKfMBHbqee0evGueE0jxy aibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaabiWacqaaaOqaaiaadohacaaMc8Uaey ypa0JaaGPaVlabeo8aZjaaykW7cqGHRaWkcaaMc8UaamyAaiabeM8a 3baa@421F@
Where,
ω =  J p Ω ±  J p 2 Ω 2  + 4 J t K 22 2 J t σ = 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbwvMCKfMBHbqee0evGueE0jxy aibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaabiWacqaaaOqaamaaceaaeaqabeaacq aHjpWDcaaMc8Uaeyypa0JaaGPaVpaalaaabaGaamOsamaaBaaaleaa caWGWbaabeaakiabgM6axjaaysW7cqGHXcqScaaMe8+aaOaaaeaaca WGkbWaa0baaSqaaiaadchaaeaacaaIYaaaaOGaeyyQdC1aaWbaaSqa beaacaaIYaaaaOGaaGjbVlabgUcaRiaaysW7caaI0aGaamOsamaaBa aaleaacaWG0baabeaakiaadUeadaWgaaWcbaGaaGOmaiaaikdaaeqa aaqabaaakeaacaaIYaGaamOsamaaBaaaleaacaWG0baabeaaaaaake aacqaHdpWCcaaMe8Uaeyypa0JaaGjbVlaaicdaaaGaay5Eaaaaaa@5C16@
J p MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbwvMCKfMBHbqee0evGueE0jxy aibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaabiWacqaaaOqaaiaadQeadaWgaaWcba GaamiCaaqabaaaaa@3685@
Inertia moment of polar axis.
J t MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbwvMCKfMBHbqee0evGueE0jxy aibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaabiWacqaaaOqaaiaadQeadaWgaaWcba GaamiDaaqabaaaaa@3689@
Inertia moment of transverse axis.
K 22 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbwvMCKfMBHbqee0evGueE0jxy aibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaabiWacqaaaOqaaiaadUeadaWgaaWcba GaaGOmaiaaikdaaeqaaaaa@3709@
Stiffness of the transverse rotation.
Ω MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbwvMCKfMBHbqee0evGueE0jxy aibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaabiWacqaaaOqaaiabgM6axbaa@3624@
Spinning speed [rad/s].
ω MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbwvMCKfMBHbqee0evGueE0jxy aibaieYlf9irVeeu0dXdh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0d Xdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXdbPYxe9vr0=vr0=vq pWqaaeaabiGaciaacaqabeaabiWacqaaaOqaaiabeM8a3baa@3662@
Whirling frequency [rad/s].
表 1. Comparison
RotorSpeed (Hz) OptiStruct_mode 1* OptiStruct_mode 2** Reference_mode 11 Reference_mode 21
0 246 245 245.7213 245.7213
10 255 236 255.254 236.5446
20 265 227 265.1419 227.7231
30 275 219 275.3828 219.2546
40 286 211 285.9728 211.1353
50 297 203 296.9069 203.3599
60 308 196 308.1784 195.9211
70 319 189 319.7799 188.8141
80 331 182 331.7025 182.0274
90 344 175 343.9369 175.5524
100 356 169 356.4728 169.3789

* mode 1 - Forward Whirl Mode

** mode 2 - Backward Whirl Mode

図 4. Reference versus OptiStruct Results


1 Genta, Giancarlo. “Dynamics of Rotating Systems.” Mechanical Engineering Series, 2005, doi:10.1007/0-387-28687-x.