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8.2. Using a Stationary Reference Frame

The primary application for a stationary (rather than a rotating) frame of reference is in the field of rotordynamics where a rotating structure (rotor) is modeled along with a stationary support structure. Examples of such an application include a gas turbine engine rotor-stator assembly or an electric turbo generator, where the rotor spins inside a specially designed housing.

The rotating part of the structure to be modeled must be axisymmetric. The gyroscopic damping matrix generated is valid only for a linear analysis.

ANSYS computes the displacement field with respect to the global coordinate system (CORIOLIS,Option = ON,,,RefFrame = ON), referred to as the stationary reference frame.

Elements Supported

Elements that are part of the rotating structure generate the gyroscopic matrix that arises due to the rotational angular velocity. The gyroscopic matrix is available for the elements listed in the notes section of the CORIOLIS command.

For a beam element, the angular velocity vector is aligned along the length and the point mass is aligned along one of the principal axes. The rotating structure must be axisymmetric about the spin axis.

For SHELL281 and other triangular-shaped elements with midside nodes, modeling a shell structure with the gyroscopic matrix turned on (CORIOLIS,ON, , ,ON) may yield anomalies with the QRDAMP eigensolver. This is especially true when only a limited number of modes are extracted. In this case, use the damped eigensolver (MODOPT, DAMP).

Analysis Types Supported

The following analysis types support rotating structure analysis using a stationary reference frame:

•Modal (ANTYPE,MODAL)

•Transient (ANTYPE,TRANS)

•Harmonic (ANTYPE,HARMIC)

For transient and harmonic analyses, the mode-superposition method (TRNOPT, MSUP, or HROPT,MSUP) is supported for instances where the gyroscopic matrix does not need updating (see below). For the mode-superposition method, only the QR Damp mode-extraction method (MODOPT,QRDAMP) is supported.

For a varying rotational velocity, mode superposition analysis (transient or harmonic) is not supported, since the modal gyroscopic matrix is not updated. This is especially true for cases where:

•an unbalance or asynchronous rotating force exists in a harmonic analysis (SYNCHRO command)

•a start-up or stop simulation is performed in a transient analysis (use the KBC command to ramp the rotational velocity within one loadstep).

To include unbalance or general asynchronous rotating forces in a harmonic analysis, use the SYNCHRO command.

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Using a Stationary Reference Frame

For a transient analysis involving a rotating structure with a stationary reference frame, support for a start or stop simulation is available. Issue the KBC command to ramp the rotational velocity.

For a prestressed analysis that includes gyroscopic effects, issue the CORIOLIS, ON,,,ON command in the static prestress portion of the analysis.

Postprocessing

Besides general results, the following specific outputs are available:

• Campbell diagram (PRCAMP and PLCAMP) see Campbell Diagram (p. 225)

Note

For a prestressed structure, set the Campbell key (CAMPBELL,ON) in the first solution pass. Doing so allows a Campbell diagram analysis.

•Orbits (PRORB and PLORB) see Orbits (p. 228)

•Animation of the whirl (ANHARM)

8.2.1. Campbell Diagram

In a modal analysis with multiple load steps corresponding to different angular velocities ω, a Campbell diagram (PLCAMP or PRCAMP) shows the evolution of the natural frequencies.

ANSYS determines eigenfrequencies at each load step. The plot showing the variation of eigenfrequency with respect to rotational speed may not be readily apparent. For example, if the gyroscopic effect is significant on an eigenmode, its frequency tends to split so much that it crosses the other frequency curves as the speed increases. For more information, see Generating a Successful Campbell Diagram below.

Critical Speeds

The PRCAMP command also prints out the critical speeds for a rotating synchronous (unbalanced) or asynchronous force. The critical speeds correspond to the intersection points between frequency curves and the added line F=s.ω (where s represents SLOPE > 0 as specified via PRCAMP). Because the critical speeds are determined graphically, their accuracy depends upon the quality of the Campbell diagram.

To retrieve and store critical speeds as parameters, use the *GET command.

Whirls and Stability

As eigenfrequencies split with increasing spin velocity, ANSYS identifies forward (FW) and backward (BW) whirls, and unstable frequencies. To obtain more information to help you determine how a particular frequency becomes unstable, issue the PLCAMP or PRCAMP command and specify a stability value (STABVAL) of 1. You can also view the logarithmic decrements by specifying STABVAL = 2. For more

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information about complex eigenvalues and corresponding logarithmic decrements, see Complex Eigensolutions in the Mechanical APDL Theory Reference.

Note

For a rotating structure meshed in shell elements lying in a plane perpendicular to the rotational velocity axis - such as a thin disk - the whirl effects are not plotted or printed by the PRCAMP or PLCAMP commands. However, they can be visualized using the ANHARM command.

To retrieve and store frequencies and whirls as parameters, use the *GET command.

Prestressed Structure

For a prestressed structure, set the Campbell key (CAMPBELL,ON) in the static solution portion of the analysis. Doing so modifies the result file so that it can accommodate a subsequent Campbell diagram analysis. In this case, static and modal solutions are calculated alternately and only the modal solutions are retained.

Generating a Successful Campbell Diagram

To help you obtain a good Campbell diagram plot or printout, the sorting option is active by default (PLCAMP,ON or PRCAMP,ON). ANSYS compares complex mode shapes and pairs similar mode shapes. (Because eigenmodes at zero velocity are real modes, ANSYS does not pair them with complex modes.)

If the plot is unsatisfactory even with sorting enabled, try the following:

•Start the Campbell analysis with a non-zero rotational velocity.

Modes at zero rotational velocity are real modes and may be difficult to pair with complex modes obtained at non-zero rotational velocity.

•Increase the number of load steps.

It helps if the mode shapes change significantly as the spin velocity increases.

•Change the frequency window.

To do so, use the shift option (PLCAMP,,,FREQB or PRCAMP,,,FREQB). It helps if some modes fall outside the default frequency window.

Overcoming Memory Problems

To run the Campbell analysis (PRCAMP or PLCAMP), the scratch memory needed may be important as complex mode shapes are read from the result file for two consecutive load steps. If your computer has insufficient scratch memory, try the following:

•Decrease the number of extracted modes (MODOPT,,NMODE)

•Generate the result file for a reduced set of selected nodes (for example, nodes on the axis of rotation). Issue OUTRES,ALL,NONE and then OUTRES,Item,Freq,Cname where Item=NSOL, Freq=ALL and Cname is the name of a node-based component.

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Using a Stationary Reference Frame

For the sorting process and whirl calculation to be successful, the set of selected nodes must represent the dynamics of the structure. In general, nodes on the spin axis contribute to the bending mode shapes that are needed in the Campbell analysis.

Example Analysis

For an example of a rotating structure analysis using a stationary reference frame, see Example Campbell Diagram Analysis (p. 231).

8.2.2. Harmonic Analysis for Unbalance or General Rotating Asynchronous Forces

Some forces may rotate synchronously (for example, unbalance) or asynchronously with the structure. In such cases, use the SYNCHRO command to update the amplitude of the rotational velocity vector with the frequency of excitation at each frequency step of the harmonic analysis.

Forces are defined as static (F), as shown in this example where X is the assumed spin axis:

Force	Real (VALUE)	Imaginary (VALUE2)
FY	F0cosα	-F0sinα
FZ	-F0sinα	-F0cosα
where:

F0 is the amplitude of the force. For unbalance, the amplitude is equal to the mass times the distance of the unbalance mass to the spin axis.

α is the phase of the force, needed only when several such forces, each with a different relative phase, are defined.

If the forces are caused by an unbalance mass, multiplication of the amplitude of the static forces (F) by the square of the spin velocity is unnecessary. ANSYS performs the calculation automatically at each frequency step.

Because the rotational velocity commands (OMEGA and CMOMEGA) define only the orientation of the spin axis, a harmonic analysis using the SYNCHRO command requires that you define the frequency

of excitation (HARFRQ) instead. For example, if the frequency of excitation is f, then:

ω = 2πf/RATIO

where:

ω is the new magnitude of the rotational velocity vector used to calculate the gyroscopic matrices.

RATIO is the ratio between the frequency of excitation and the frequency of the rotational velocity of the structure, as specified via the SYNCHRO command. If no RATIO value is specified, an unbalance force is assumed; in all other cases, a general rotating force is assumed.

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