14.6. Analysis and Solution Controls

14.6.1. Modal Analysis

Modal analyses of the 2D axisymmetric model with and without gyroscopic effects included are discussed in this section.

14.6.1.1. Modal Analysis without Gyroscopic Effects

The modal analysis without gyroscopic effects is performed using the Block Lanczos (LANB) solver, extracting twelve modes.

The following input fragment shows the steps to extract these modes:

/solu

antype, modal                      ! Perform Modal analysis
modopt, lanb, 12                   ! Use Block Lanczos solver to extract 12 modes
mxpand, 12                         ! Expands all the modes
solve
finish

14.6.1.2. Modal Analysis with Gyroscopic Effects

The rotational velocity is specified with the OMEGA or CMOMEGA command. The gyroscopic effects of the rotating structure are included using the CORIOLIS command.

The modal analysis with gyroscopic effects is performed on the model using the complex QRDAMP eigensolver.

The following input fragment shows the steps to perform the modal analysis with gyroscopic effects:

/SOLU

/com, Select all the rotating elements supporting Coriolis command

esel,,ename,,272
esel,a,ename,,21
cm,rot_part, elem
esel, all

/com, Specify rotational velocity to the structure/rotating elements.

pival = acos(-1)
spinRpm = 50000                ! Rotational velocity in rpm
spinRds = spinRpm*pival/30
cmomega, rot_part, spinRds     ! Apply rotational velocity along rotating velocity (X)

/com, Activate Coriolis command and choose QRDAMP eigensolver

antype, modal                  ! Perform Modal analysis
modopt, qrdamp, 12,,, on       ! Use QRDAMP solver to extract 12 complex modes
mxpand, 12                     ! Expand all the modes
coriolis, on,,, on             ! Last field specifies stationary reference frame
solve
finish

14.6.2. Campbell Diagram Analysis

Before performing a Campbell diagram analysis, a modal analysis must be performed with multiple load steps corresponding to different angular velocities. A Campbell diagram plot (PLCAMP command) shows the evolution of the natural frequencies with respect to the rotational speed. The PRCAMP command prints out the critical speeds based on the Campbell diagram plot for a synchronous (unbalanced) or asynchronous force.

The following input fragment shows the steps to perform the Campbell Diagram Analysis:

/SOLU

/com, Select all rotating elements supporting Coriolis command

esel,,ename,,272
esel,a,ename,,21
cm, rot_part, elem
esel, all

/com, Activate Coriolis command and pick the QRDAMP eigensolver

antype, modal                  ! Perform Modal analysis
modopt, qrdamp, 12,,,on        ! Use QRDAMP solver to extract 12 complex modes
mxpand, 12                     ! Expand all the modes
coriolis, on,,, on             ! Last field specifies stationary reference frame

/com, Solve modal analysis for different angular velocities

pival = acos(-1) 
spinRpm = 0                    ! Rotational velocity in rpm
spinRds = spinRpm*pival/30
cmomega, rot_part, spinRds
solve

spinRpm = 50000                ! Rotational velocity in rpm
spinRds = spinRpm*pival/30
cmomega, rot_part, spinRds
solve

spinRpm = 100000               ! Rotational velocity in rpm
spinRds = spinRpm*pival/30
cmomega, rot_part, spinRds
solve
finish

/com, Post process the Campbell diagram plot

/POST1

prcamp,, 1.0, rpm,, rot_part   ! Prints Campbell diagram data
/show, png
/rgb, index, 100, 100, 100, 0  ! Set white background
/rgb, index, 0, 0, 0, 15
plcamp,, 1.0, rpm,, rot_part   ! Plots Campbell diagram data
finish

14.6.3. Unbalance Response Analysis

A harmonic analysis of the 2D axisymmetric model is performed within a speed range of 0 to 100,000 rpm (a frequency range of 0 to 1666.67 Hz) using 200 substeps. The first seven modes in this frequency range are excited.

In this analysis, the unbalance is considered as loading. (see Boundary Conditions and Loading for more details).

A structural damping coefficient of 1 percent is considered (DMPSTR).

The frequency of excitation is specified as synchronous with the rotational velocity (SYNCHRO). The rotational velocity (CMOMEGA) determines only the rotational velocity direction vector of the rotating component. The spin of the rotor is automatically calculated (HARFRQ).

The following input fragment shows the steps to perform the unbalance response analysis:

/SOLU

spinRds = 1         ! Rotating velocity of the shaft to specify the spin axis

spinRpm1 = 0                   ! Begin speed in rpm	
spinRpm2 = 100000              ! End speed in rpm
begin_freq = spinRpm1/60  	 ! Equivalent begin frequency in Hz
end_freq = spinRpm2/60         ! Equivalent end frequency in Hz

antype, harmic                 ! Perform Harmonic analysis
hropt, full                    ! Select Full Harmonic analysis option
nsubst, 200
harfrq, begin_freq, end_freq   ! Defines the frequency range  
kbc, 1

dmpstr, 0.01                   ! Specify damping ratio of 1%

synchro,,rot_part            ! Specify synchronous analysis
cmomega,rot_part,spinRds     ! Define the rotational velocity direction vector
coriolis,on,,, on            ! Includes gyroscopic effect
solve

finish