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8.1. Understanding Rotating Structure DynamicsYou can observe inertia effects, applied via the CORIOLIS command, in either a stationary reference frame or a rotating reference frame. In both cases, you specify angular velocity by issuing an OMEGA or CMOMEGA command. The dynamic equation incorporating the effect of rotation is given by where M, C and K are the structural mass, damping, and stiffness matrices, respectively. Kc is the spin softening matrix (described in Spin Softening in the Theory Reference for ANSYS and ANSYS Workbench.) G is a “damping” matrix contribution due to the rotation of the structure specified via the OMEGA or CMOMEGA command (described in Rotating Structures in the Theory Reference for ANSYS and ANSYS Workbench). Without the inertia effect applied via the CORIOLIS command, ANSYS does not generate the G matrix, and the usual effect of the angular rotation velocity specified by the OMEGA or CMOMEGA command applies (as described in Acceleration Effect in the Theory Reference for ANSYS and ANSYS Workbench). An exception exists, however, involving a nonlinear transient analysis using elements MASS21, BEAM188, and BEAM189; in this case, the inertia effect due to rotation applied via an IC command (or a D command over an incremental time) is included without having to issue CORIOLIS and OMEGA or CMOMEGA commands8.2. Using a Stationary Reference FrameThe 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 SupportedElements 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 following elements: BEAM4, PIPE16, MASS21, SOLID45, SOLID95, SOLID185, SOLID186, SOLID187, BEAM188, and BEAM189.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.Analysis Types SupportedThe 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 full (TRNOPT,FULL) and mode-superposition (TRNOPT,MSUP) methods are supported. For the mode-superposition method, only the QR Damp mode-extraction method (MODOPT,QRDAMP) is supported. To include unbalance or general asynchronous rotating forces in a harmonic analysis, use the SYNCHRO command.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.PostprocessingBesides general results, the following specific outputs are available: Campbell diagram (PRCAMP and PLCAMP) see 8.2.1NoteFor 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 8.2.3 Animation of the whirl (ANHARM) 8.2.1. Campbell DiagramIn a modal analysis with multiple load steps corresponding to different angular velocities , 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 SpeedsThe 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. (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 StabilityAs 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 information about complex eigenvalues and corresponding logarithmic decrements, see Damped Method in the Theory Reference for ANSYS and ANSYS Workbench.To retrieve and store frequencies and whirls as parameters, use the *GET command.Prestressed StructureFor 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 DiagramTo 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 ProblemsTo 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. 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 AnalysisFor an example of a rotating structure analysis using a stationary reference frame, see Sample Campbell Diagram Analysis.8.2.2. Harmonic Analysis for Unbalance or General Rotating Asynchronous ForcesSome 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: ForceReal (VALUE)Imaginary (VALUE2)FYF0cos-F0sinFZ-F0sin-F0coswhere: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. 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: = 2f/RATIOwhere: 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.Example AnalysisFor an example of a harmonic analysis for unbalance forces, see Sample Unbalance Harmonic Analysis.8.2.3. OrbitsWhen a structure is rotating about an axis and undergoes vibration motion, the trajectory of a node executed around the axis is generally an ellipse designated as a whirl orbit.In a local coordinate system xyz where x is the spin axis, the ellipse at node I is defined by semi-major axis A, semi-minor axis B, and phase (PSI), as shown:Angle (PHI) defines the initial position of the node (at t = 0). To compare the phases of two nodes of the structure, you can examine the sum + .Values YMAX and ZMAX are the maximum displacements along y and z axes, respectively.You can print out the A, B, PSI, PHI, YMAX, and ZMAX values via a PRORB (print orbits) command. Angles are in degrees and within the range of -180 through +180. The position vector of local axis y in the global coordinate system is printed out along with the elliptical orbit characteristics. You can also animate the orbit (ANHARM) for further examination. For a typical usage example of these commands, see Sample Unbalance Harmonic Analysis.To retrieve and store orbits characteristics as parameters, use the *GET command after issuing the PRORB command.8.3. Using a Rotating Reference FrameThe 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 structure is rotating. Analyses of this type, therefore, consider only the Coriolis force. ANSYS computes the displacement field with respect to the coordinate system attached to the structure and rotating with it at the specified angular velocity (CORIOLIS,Option = ON,RefFrame = OFF).Elements SupportedThe Coriolis matrix and forces are available for the following structural elements: MASS21, SHELL181, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, BEAM188, BEAM189, SOLSH190, and SHELL281. The Coriolis matrix and forces are also available for PLANE223, SOLID226, and SOLID227 coupled-field analyses with structural degrees of freedom.Analysis Types SupportedThe following analysis types support rotating structure analysis using a rotating reference frame: Static (ANTYPE,STATIC)Inertia effects are forces computed by multiplying the Coriolis damping matrix by the velocity of the structure. If you issue the CORIOLIS command in a prestressed analysis, ANSYS does not take the Coriolis force into account in the static portion of the analysis. In a large-deflection prestressed analysis (NLGEOM,ON and PSTRES,ON), ANSYS generates the Coriolis matrix and uses it in the subsequent prestressed modal, harmonic, or transient analysis. In a small-deflection prestressed analysis (PSTRES,ON only), ANSYS does not generate the Coriolis matrix but still takes the Coriolis force into account in the subsequent prestressed modal, harmonic, or transient analysis. Modal (ANTYPE,MODAL)Support is also available for prestressed modal analysis. Transient (ANTYPE,TRANS) Harmonic (ANTYPE,HARMIC)Spin SofteningIn a dynamic analysis, the Coriolis matrix and the spin-softening matrix contribute to the gyroscopic moment in the rotating reference frame; therefore, ANSYS includes the spin-softening effect by default in dynamic analyses whenever you apply the Coriolis effect in the rotating reference frame (CORIOLIS,ON).If your analysis necessitates ignoring spin-softening effects, set the KSPIN = 0 option when issuing the OMEGA or CMOMEGA command to specify angular velocity. Supercritical Spin SofteningAs shown by equations (3-77) through (3-79) in the Theory Reference for ANSYS and ANSYS Workbench, 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), a full transient (ANTYPE,TRANS with TRNOPT,FULL), or a full harmonic (ANTYPE,HARM with TRNOPT,FULL) analysis, the spin-softening effect is more accurately accounted for by large deflections (NLGEOM,ON). If the stiffness matrix becomes negative definite, ANSYS issues a warning message about the negative pivot. 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 .Campbell DiagramBecause natural frequencies are subject to sudden changes around critical speeds in a rotating frame, ANSYS recommends using a stationary reference frame to create a Campbell diagram (PRCAMP or PLCAMP). Example AnalysisFor examples of a rotating structure analysis using a rotating reference frame, see Sample Coriolis Analysis in this guide and Sample Piezoelectric Analysis with Coriolis Effect in the Coupled-Field Analysis Guide.8.4. Choosing the Appropriate Reference Frame OptionThe rotating and stationary reference frame approaches have their benefits and limitations. Use this table to choose the best option for your application:Reference Frame ConsiderationsStationary Reference FrameRotating Reference FrameNot applicable to a static analysis (ANTYPE,STATIC).In a static analysis, a Coriolis force vector is given by where represents the nodal velocity vector (specified via the IC command). You can generate Campbell plots for computing rotor critical speeds.Campbell plots are not applicable for computing rotor critical speeds.Structure must be axisymmetric about the spin axis.Structure need not be axisymmetric about the spin axis.Rotating structure can be part of a stationary structure in an analysis model (such as a gas turbine engine rotor-stator assembly). The stationary structure and supports (such as bearings) need not be axisymmetric.Rotating structure must be the only part of an analysis model (such as a gas turbine engine rotor).Supports more than one rotating structure spinning at different rotational speeds about different axes of rotation (such as a multi-spool gas turbine engine).Supports only a single rotating structure (such as a single-spool gas turbine engine).Supported in these elements: BEAM4, PIPE16, MASS21, SOLID45, SOLID95, SOLID185, SOLID186, SOLID187, BEAM188, and BEAM189.Supported in these elements: MASS21, SHELL181, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, BEAM188, BEAM189, SOLSH190, and SHELL281.Natural FrequenciesNatural frequencies differ according to the reference frame type. In most cases, natural frequencies are known in a stationary reference frame through analytical expressions or experiment, for example. ANSYS therefore recommends using the stationary reference frame for modal analyses. 8.5. Sample Campbell Diagram AnalysisFollowing is a modal analysis of a rotating structure using a stationary reference frame. The analysis generates a Campbell diagram (PLCAMP). 8.5.1. Problem DescriptionThe model is a simply supported beam spinning at up to 30,000 rd/s.8.5.2. Problem SpecificationsThe geometric properties for this analysis are as follows:Length:8mDiameter: 0.2mThe material properties for this analysis are as follows: Youngs modulus (E) = 2e+11 N/m2 Poissons ratio () = 0.3Density = 7800 kg/m3 8.5.3. Input for the AnalysisUse this input file to perform the example modal analysis of a rotating structure using a stationary reference frame./batch,list/title, Spinning simply supported beam!* Parameterslx=8! lengthdia=0.2! diameter!*/PREP7ET,1,16R,1, dia, dia/2MP,EX,1,2e+11MP,DENS,1,7800MP,PRXY,1,0.3n,1n,9,lxfill,1,9e,1,2egen,8,1,-1d,1,uy, ,uz ! simply supported left endd,9,uy, ,uz ! simply supported right endd,all,ux ! supress axial motiond,all,rotx ! supress torsionfinish!*/SOLUantype,modal! Use the QRDAMP eigensolver, request 8 modes,! and specify complex eigensolutionsmodopt,qrdamp,8,on! Apply Coriolis effect and specify ! stationary r