5.4. Solving a Harmonic Analysis with Synchronous or Asynchronous Rotating Forces

To perform a harmonic analysis of an unbalanced excitation, the effect of the unbalanced mass is represented by forces in the two directions perpendicular to the spinning axis. (See Defining Rotating Forces.) The forces are applied on a node located on the axis of rotation. The SYNCHRO command is used to specify that the frequency of excitation is synchronous with the rotational velocity.

Note:  The SYNCHRO command's RATIO argument is not valid in the case of an unbalanced force.

This linear approach can be used for beam models as well as for solid models.

For solid models, your analysis may require a more precise determination of displacements and stresses in the wheel/disk containing the unbalanced mass. In this case, you can model the unbalance using a MASS21 element and performing a nonlinear transient analysis.

 

5.4.1. Specifying Rotational Velocity with OMEGA

You can specify the rotational velocity using the OMEGA command. When the SYNCHRO command is activated, the OMEGA command defines the rotational velocity direction vector. The spin is specified automatically with the HARFRQ command. See the following example:

harfrq,100           ! 100 Hz  
synchro   
omega,1.,1.,1.       ! direction vector of the rotational velocity

The above commands denote:

  • an excitation frequency of 100 Hz,

  • a spin of (100) (2π) rd/sec

  • a rotational velocity vector of

 

5.4.2. Specifying Rotational Velocity with CMOMEGA

You can specify the rotational velocity using the CMOMEGA command. The rotational velocity definition is different when tabular input is used. See below for the details of tabular and non-tabular input.

 

5.4.2.1. Non-Tabular Input

When the SYNCHRO command is activated, the CMOMEGA command only defines the rotational velocity direction vector for the component. If there are several components, the ratios between their different spins are also calculated from the CMOMEGA input. The spin of the driving component (specified by Cname in the SYNCHRO command) is derived from the HARFRQ command, as noted in the following example:

harfrq,100.               ! excitation 100 Hz
synchro,,SPOOL1           ! driving component is SPOOL1
cmomega,SPOOL1,1.,1.,1    ! direction vector  of the rotational velocity for SPOOL1 
cmomega,SPOOL2,2.,2.,2.   ! direction vector  of the rotational velocity for SPOOL2 (also spin ratio between the 2 components)

The above commands denote:

  • an excitation frequency of 100Hz

  • the spin of SPOOL1 is (100) (2π) rd/sec, with a rotational velocity vector of:

  • the spin of SPOOL2 is twice the spin of SPOOL1 with the same rotational velocity vector

 

5.4.2.2. Tabular Input

Using tabular input may sometimes be necessary, for example when rotors' rotational velocities are not proportional. In this case, all rotating components must be defined with the CMOMEGA command and a tabular rotational velocity OMEGAX(%tab%) with primary variable FREQ.

For each harmonic analysis solution, the rotational velocity of the driving component is directly obtained from the excitation frequency and the two points provided. It is scaled with the asynchronous ratio if provided (RATIO on SYNCHRO).

For all other rotating components, the spin is calculated as the spin of the driving component multiplied by the ratio of the tabular inputs.