The primary application for a rotating (rather than a stationary) frame of reference is in the field of flexible body dynamics where, generally, the structure has no stationary parts and the entire non-axisymmetric structure is rotating.
The program computes the displacement field and all other result quantities with
respect to the coordinate system rotating at the specified angular velocity
(CORIOLIS,Option =
ON,,,RefFrame = OFF).
Commands specific to modeling a rotating structure are listed in Commands Used in a Rotordynamic Analysis in the Rotordynamic Analysis Guide.
The procedures for using a rotating reference frame, although similar to the procedures for a stationary reference frame analysis described in the Rotordynamic Analysis Guide, have specificities detailed below. One of them is the application of rotating forces (Defining Rotating Forces in the Rotordynamic Analysis Guide). For example, in a rotating reference frame, a load synchronous with the rotational velocity is a static load (see Example: Unbalance Response of a Jeffcott Rotor). Similarly, a load rotating at twice the rotational velocity is synchronous when considered from a rotating reference frame perspective.
The Coriolis matrix and forces are available for the structural elements listed in the notes section of the CORIOLIS command.
The following options are not supported:
Lumped mass (LUMPM) with translational mass only (
KeyElt= 1) or frame invariant formulation (KeyElt= 2)Layered shell elements
In a dynamic analysis, the Coriolis matrix and the spin-softening matrix contribute to the gyroscopic moment in the rotating reference frame; therefore, the program includes the spin-softening effect by default in dynamic analyses whenever you apply the Coriolis effect in the rotating reference frame (CORIOLIS,ON).
Supercritical Spin Softening
As shown by equations (3-77) through (3-79) in the Mechanical APDL Theory Reference, the diagonal coefficients in the stiffness matrix become negative when the rotational velocity is larger than the resonant frequency.
In such cases, the solver may be unable to properly handle the negative definite stiffness matrix. Additional details follow:
In a static (ANTYPE,STATIC) or a full transient (ANTYPE,TRANS with TRNOPT,FULL), the spin-softening effect is more accurately accounted for by large deflections (NLGEOM,ON). If the stiffness matrix becomes negative definite, a warning message about the negative pivot is issued.
In a modal analysis (ANTYPE,MODAL), apply a negative shift (MODOPT,,,
FREQB) to extract the possible negative eigenfrequencies.If negative frequencies exist, mode-superposition transient and harmonic analyses are not supported.
The following analysis types support rotating structure analysis using a rotating reference frame:
5.3.3.1. Static (ANTYPE,STATIC)
Inertia effects are forces computed by multiplying the Coriolis damping matrix by the initial velocity of the structure defined with the IC and ICROTATE commands.
5.3.3.2. Modal (ANTYPE,MODAL)
Because of the spin-softening effect, the damped eigensolver (MODOPT,DAMP) is recommended.
Depending on your model, the procedure to obtain eigensolutions and generate a Campbell diagram is the following:
If your model uses point mass and beam elements only, the frequencies and mode shapes are directly obtained with the damped modal analysis. In post-processing, the Campbell diagram (PRCAMP and PLCAMP commands) can be generated when multiple rotational velocity load steps are calculated. See Example: Campbell Diagram Analysis of a Jeffcott Rotor.
If your model uses 3D solid or shell elements, as there is mass away from the rotational velocity axis, prestress must be included and the frequencies and mode shapes are obtained with a linear perturbation damped modal analysis. In postprocessing, the Campbell diagram (PRCAMP and PLCAMP commands) can be generated if multiple linear perturbation modal analyses are performed and CAMPBELL,RSTP is activated. See Example: Campbell Diagram Analysis of a 3D Bladed Shaft-Disk Assembly.
Note: Because natural frequencies are subject to sudden changes around critical
speeds in a rotating reference frame, it is recommended that you use a small
rotational velocity increment and not activate the sorting option of the
Campbell diagram commands (Option on
PRCAMP and PLCAMP). Also, it is
often best to not draw the curves (THICK = -1 on
/GTHK), but show only the markers (specified by
/GMARKER).
Frequencies obtained in a rotating reference frame are not the same as those obtained in a stationary reference frame. Depending on your model and when applicable, a transformation can be used to deduce one from the other. See Example: Campbell Diagram Analysis of a Jeffcott Rotor.
5.3.3.3. Linear Transient (ANTYPE,TRANS)
Linear transient analysis is only applicable to mass and beam element models. Transient analysis can be performed at a constant rotational velocity or with varying rotational velocity to simulate a spin-up or spin-down. The procedure is similar to Example: Transient Response of a Startup in the Rotordynamic Analysis Guide, except for the CORIOLIS command (use CORIOLIS,ON,,,OFF).
If bearings (COMBI214) are stationary, periodic coefficients are automatically included when the full Newton-Raphson option is activated (NROPT,FULL) and the stiffness and/or damping properties are not isotropic with respect to the rotational velocity axis.
5.3.3.4. Harmonic (ANTYPE,HARMIC)
The SYNCHRO command is used to specify whether the
excitation frequency is synchronous or asynchronous with the rotational
velocity. Remember that, in a rotating reference frame, the ratio between
excitation frequency and rotational velocity (RATIO
on the SYNCHRO command) needs to be adjusted. It is equal to
the value observed when in a stationary reference frame minus 1.