When modeling rotating machinery, there are special considerations for performing a linear perturbation modal analysis that includes Coriolis effects. Details are given below depending on the reference frame chosen for the analysis.
For rotordynamics, where gyroscopic forces are of primary importance, the linear perturbation analysis is performed in the stationary reference frame and caution must be taken regarding the consistency of the base (static) and linear perturbation analysis. By default, (no CORIOLIS command) when rotational velocity is defined, the static analysis includes the centrifugal force. In the case of a nonlinear analysis, it also includes the spin softening effect. These effects are not consistent with a stationary reference frame analysis.
Important: As a consequence, the CORIOLIS command with
RefFrame = ON must be activated in the base
analysis. Failing to do so may lead to non-physical negative or zero frequencies
due to spin softening.
The simple example below demonstrates the use of the stationary reference frame for both the static preload solution and subsequent modal analysis. The model used is of a heavy disk cantilevered on a slender shaft rotating at 400 rad/s about the global Z-axis. In accordance with the assumption in rotordynamics, the geometry is axisymmetric and of primary interest are the whirling effect and mode splitting caused by the gyroscopic forces.
Example input to perform perturbed modal solve in a stationary reference frame:
spin=400 ! rads/sec
/prep7
et,1,185,,2 ! 8 node brick with enhanced strain
mp,ex,1,3e7 ! Steel
mp,nuxy,1,.3
mp,dens,1,0.000754
! Slender Shaft
cylinder,0,0.5,0,36,0,90 ! Build geometry in 90 sectors to get uniform mesh
cylinder,0,0.5,0,36,90,180
cylinder,0,0.5,0,36,180,270
cylinder,0,0.5,0,36,270,360
cylinder,0,0.5,36,38,0,90 ! Heavy Disk
cylinder,0,0.5,36,38,90,180
cylinder,0,0.5,36,38,180,270
cylinder,0,0.5,36,38,270,360
cylinder,0.5,6,36,38,0,90
cylinder,0.5,6,36,38,90,180
cylinder,0.5,6,36,38,180,270
cylinder,0.5,6,36,38,270,360
nummrg,kp
esize,2
vmesh,all
nsel,s,loc,z,0 ! Fix end of slender shaft opposite the disk
d,all,all
nsel,all
fini
/solu
antype,static
F,… ! Preload typically an axial load which can modify bending flexibility of the shaft.
omega,,,spin
coriolis,on,,,on ! Coriolis ON in stationary reference frame
rescontrol,linear,all,1 ! Necessary when model is not nonlinear
solve
fini
/solu
antype,static, restart,,,perturb ! Perform a static restart with perturbation from the last
! substep of the previous static solve
perturb,modal,,, INERKEEP ! Set the analysis options for perturbed modal analysis
solve, elform ! Reform element matrices
modopt,qrdamp,20,,,on ! Request 20 modes and complex mode shapes to animate whirling
mxpand,20
solve
fini
For the case where the structure is not axisymmetric, such as a turbine bladed wheel, the rotating reference frame must be used. Gyroscopic forces are typically not as important in this type of model while stress stiffening and spin softening greatly affect the stiffness and frequency of the blades.
The simple input below demonstrates the procedure for performing a preloaded modal analysis using linear perturbation in the rotating reference frame. The model has 4 slender blades cantilevered from a fixed hub rotating at 750 RPM about the global Z-axis.
Example input to perform perturbed modal solve in a rotating reference frame:
/prep7 et,1,187 ! All tet mesh mp,ex,1,1e7 ! Aluminum mp,nuxy,1,.3 mp,dens,1,.0003 wprot,,30 ! Create the blades block,2,20,-1,1,,.25 *do,iii,1,3 wprot,,-30 wprot,90 wprot,,30 block,2,20,-1,1,,.25 *enddo wprot,,-30 cylind,1.5,3.0,-1,1,0,360 ! Create the hub vadd,all numcmp,volu esize,.25 vmesh,1 csys,1 nsel,s,loc,x,1.5 d,all,all ! Fix center of hub nsel,all fini pi=acos(-1) spin=750*2*pi/60 /solu antype,static rescontrol,linear,all,1 time,1.0 kbc,1 omega,0,0,spin ! Turbine is spinning about Z axis coriolis,on ! Coriolis ON in a rotating reference frame solve finish /solu antype,static,restart,,,perturb perturb,modal,,,inerkeep solve,elform modopt,damp,12 mxpand,12 solve finish