Rotor Dynamics User’s Guide
Simcenter NastranRotor Dynamics User’s Guide
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TABLE OF n to Rotor Dynamics . 2Overview of the Simcenter Nastran Rotor Dynamics Capabilities . 2Complex Eigenvalue Analysis . 4Frequency Response Analysis . 4Transient Response Analysis . 5Maneuver Load Analysis . 5Ability to Solve the Model in the Fixed or Rotating Reference System . 5Support for General and Line Models . 5Symmetric and Unsymmetric Rotors and Supports . 6Multiple Rotors . 7Modal and Direct Method . 7Synchronous and Asynchronous Analysis . 7Mode Tracking . 7Theoretical Foundation of Rotor Dynamics . 10Additional Terms in the Equations of Motion . 10Coriolis Forces and Gyroscopic Moments . 10Centrifugal Softening . 10Centrifugal Stiffening Due to Centrifugal Forces . 10Damping . 10Equation of Motion for the Fixed Reference System . 11Including Steiner’s Inertia Terms in the Analysis . 14Equation of Motion for the Rotating Reference System . 14Real Eigenvalue Analysis for the Modal Solutions . 17Reduction to the Analysis Set for the Direct Methods . 17Fixed System Eigenvalue Problem . 18Synchronous Analysis . 18Rotating System Eigenvalue Problem . 19Synchronous Analysis . 19Solution Interpretation . 20Equation of Motion for Frequency Response . 26Fixed Reference System: . 26Rotating Reference System: . 27Comparison of the Results with the Campbell Diagram . 27Equations of Motion for the Transient Response Analysis . 30Equations of motion for the Fixed System . 30Equations of motion for the Rotating System . 30Forcing Function and Initial Conditions . 30Asynchronous Analysis . 34Synchronous Analysis . 34Other types of Analysis . 34Comparing the Results with the Campbell Diagram . 34Influence of the Sweep Velocity . 36Instabilities . 38Simcenter Nastran Rotor Dynamics User’s Guidei
.2iiInitial Conditions . 38Gyroscopic Moments in Maneuver Load Analysis . 39Coupled, Time-Dependent Solutions . 40Gyroscopic and Circulation Term Scaling . 42Defining Simcenter Nastran Input for Rotor Dynamics . 45File Management Section . 45Executive Control Section . 45Case Control Section . 45Bulk Section . 46Modeling Bearing Supports . 48Coupled, Time-Dependent Solutions . 53Rotor Speed Specification Options . 54Parameters . 56Mode Tracking Parameters . 58Mode Filtering . 60Solution-Specific Data . 61Superelement Reduction of Supporting Structures . 61Superelement-style Reduction of Rotors . 61Interpretation of Rotor Dynamics Output . 64The F06 File . 64The OP2 File . 64The CSV File for Creating Campbell Diagrams. 65The GPF File for Additional Post-Processing . 67Output for Frequency Response . 68Output for Transient Response . 68Complex Modes . 68Modeling Considerations and Selecting a Reference System . 70Choosing Between the Fixed and Rotating Reference System . 70Translation and Tilt Modes . 70Calculating Geometric Stiffness . 70Steiner’s Term in the Centrifugal Matrix . 71Whirl Motion . 71Damping . 71Multiple Rotors . 72Numerical Problems . 73Other Hints. 74Rotor Dynamics Examples . 76Simple Mass Examples . 76Symmetric Model without Damping (rotor086.dat) . 76Symmetric Model with Physical and Material Damping (rotor088.dat) . 83Unsymmetric Rotor with Damping (rotor089.dat) . 92Symmetric Rotor in Unsymmetric Bearings (rotor090.dat) . 96Laval Rotor Examples . 99The Theoretical Model for the Laval Rotor . 99Analysis of the Laval Rotor (rotor091.dat, rotor092.dat) . 101Simcenter Nastran Rotor Dynamics User’s Guide
.9.1Rotating Shaft Examples . 108Rotating Shaft with Rigid Bearings (rotor098.dat) . 109Rotating Shaft with Elastic Isotropic Bearings (rotor095.dat). 114Rotating Shaft with Elastic Anisotropic Bearings . 115Model with Two Rotors (rotor096.dat) . 116Symmetric Shaft Modeled with Shell Elements (rotor097.dat). 126Frequency Response Examples. 139Rotating Cylinder with Beam Elements . 139Campbell Diagrams . 140Frequency Response Analysis in the Fixed System . 144Synchronous Analysis . 145Asynchronous Analysis . 149Analysis in the rotating system . 153Synchronous Analysis in the Rotating System . 153Asynchronous Analysis . 156Rotating Shaft with Shell Elements . 159Synchronous Analysis . 160Asynchronous Analysis . 164Transient Response Examples. 171Asynchronous Analysis . 171Synchronous Analysis . 178Maneuver Load Analysis Example . 184Example of a Model with two Rotors analyzed with all Methods . 187Model . 188Modes . 189Complex Eigenvalues . 195Damping . 196Model without Damping . 197Damping in the Fixed System . 202Damping in the Rotors. 203Model with two Rotors compared to uncoupled Analysis of the individual Rotors . 210Analysis in the Rotating and the Fixed System . 212The Parameters W3R and W4R . 224Analysis with the Direct Method SOL 107 . 228Relative Rotor Speed . 241Single Rotor Models . 241Models with two Rotors . 248Frequency Response Analysis . 255Modal Solution SOL 111 . 255Direct Solution SOL 108 . 255Transient response Analysis . 267Modal Method . 267Direct Method . 277Analysis of a Model with one Rotor . 280Complex Modes . 280Simcenter Nastran Rotor Dynamics User’s Guideiii
10.9.210.9.310.9.411ivRotating System . 282Frequency Response Analyses . 284Transient Analysis . 298References. 313Simcenter Nastran Rotor Dynamics User’s Guide
CHAPTER1Introduction to Rotor Dynamics
Chapter 11Introduction to Rotor DynamicsIntroduction to Rotor DynamicsSimcenter Nastran includes a rotor dynamics capability that lets you predict the dynamicbehavior of rotating systems. Rotating systems are subject to additional forces not present innon-rotating systems. These additional forces are a function of rotational speed and result insystem modal frequencies that vary with the speed of rotation.In a rotor dynamics analysis, the system’s critical speed is particularly important. The criticalspeed corresponds to a rotation speed that is equal to the modal frequency. Because the criticalspeed is the speed at which the system can become unstable, engineers must be able toaccurately predict those speeds as well as detect possible resonance problems in an analysis.With frequency response analyses, the user can predict the steady-state response for differentrotor speeds. Asynchronous analysis can be done by keeping the rotor speed constant andvarying the excitation frequency. In the synchronous option, the excitation frequency is equalto, or a multiple of the rotor speed. Grid point displacement, velocity and acceleration, elementforces and stresses can be recovered as function of rotor speed or excitation frequency.Transient response in the time domain can be used in order to study the behavior of the rotorwhen passing a critical speed. Here, the user can define a sweep function of the excitation. Inthe transient analysis the grid point displacement, velocity and acceleration, element forces andstresses can be calculated as function of time.Both modal and direct methods can be applied for complex eigenvalues, frequency responseand transient response analyses.Maneuver load analysis is a linear static structural analysis that accounts for inertial loads. TheSimcenter Nastran rotor dynamics capabilities allow you to account for gyroscopic forces andforces due to damping of the rotor in a maneuver load analysis.This guide describes the method of the rotor dynamic analysis in Simcenter Nastran, as well asthe required input and modelling techniques. It also provides information about the differentoutput data formats and describes ways that you can further post-process your data. Finally, thisguide contains a number of example problems in which results from Simcenter Nastran arecompared to theoretical results.1.1Overview of the Simcenter Nastran Rotor Dynamics CapabilitiesIn Simcenter Nastran, you can perform rotor dynamics analyses on structures with up toten spinning rotors using either direct or modal solutions. You perform a rotor dynamicsanalysis in Simcenter Nastran using solution sequence 107 or 110 (Complex eigenvalueanalysis). To compute the response of a rotating system in frequency domain, solutionsequence 108 or 111 (Frequency response analysis) can be used. For transient analysis inthe time domain solution sequence 109 or 112 (Transient response analysis) can be used.For maneuver load analysis, solution sequence 101 (Linear static analysis) can be used.The analysis types that are supported in rotor dynamic analysis are listed in Table 1.2Simcenter Nastran Rotor Dynamics User’s Guide
SolutionsequenceAnalysisResults101Linear staticStress, bearing forces, dampingforces107Direct complexeigenvalueCampbell diagram, criticalspeeds, damping108Direct frequencyresponseSteady-state response in thefrequency domain109Direct transientresponseTransient response in the timedomain110Modal complexeigenvalueCampbell diagram, criticalspeeds, damping111Modal frequencyresponseSteady-state response in thefrequency domain112Modal transientresponseTransient response in the timedomainTable 1 Solution sequences supported in rotor dynamicsSimcenter Nastran commands and entries unique to rotor dynamics include: The RMETHOD case control command which is used to select the appropriateROTORD bulk entry. The ROTORD bulk entry which is used to define rotor dynamic solution options. The ROTORG bulk entry which is used to define the portions of the modelassociated with a specific rotor. The ROTORB and CBEAR bulk entries which are used to model bearings. ThePBEAR bulk entry is used to define bearing properties for bearings modeled usingCBEAR entries.For detailed information on creating Simcenter Nastran input files for rotor dynamicanalysis, see the “Defining Simcenter Nastran Input for Rotor Dynamics” chapter.In a rotor dynamics analysis, Simcenter Nastran takes into account all gyroscopic forces orCoriolis forces acting on the system. It also includes geometric (differential) stiffness andcentrifugal softening (also referred to as spin softening).Simcenter Nastran Rotor Dynamics User’s Guide3
Chapter 1Introduction to Rotor Dynamics1.1.1 Complex Eigenvalue AnalysisWhen you solve your model, Simcenter Nastran calculates the complex eigenvalues foreach selected rotor speed, along with the damping, and the whirl direction. The softwaredetermines the whirl direction from the complex eigenvectors. The points in the rotormove on elliptical trajectories. If the motion is in the sense of rotation, the motion is called forward whirl. If the motion is against the sense of rotation, the motion is called backwardswhirl.In addition to this data, the software also calculates: Whirl modes (system modal frequencies that vary with rotational speed) Critical speeds Complex mode shapes (which you can view in a post-processor that supportsthe visualization of complex modes)Simcenter Nastran writes the results of a rotor dynamics analysis to F06 or OP2 files forpost-processing. You can also use parameters (ROTCSV, ROTGPF) in the input file tohave the software generate additional types of ASCII output files (CSV and GPF files)which contain data that is specially formatted for post-processing your results with othertools. For example, you can generate a CSV file which contains data that are formatted tolet you create a Campbell diagram of the eigenfrequencies using a program like Excel.You can also use the CSV file data to plot the damping as a function of rotor speed to helpdetect resonance points and regions of instability. More information is provided aboutthese files later in this guide.It is recommended to always do a complex eigenvalue analysis and to establish a Campbelland damping diagram. The results can be used as reference for response analysis and thephysical behavior can be checked.1.1.2 Frequency Response AnalysisIn the frequency response analysis the complex nodal displacement, velocity andaccelerations and also element forces and stresses can be plotted as function of frequency orrotor speed. The results can be output in the F06 file, OP2 file. The results can be plottedwith standard Simcenter Nastran output commands in the post-processor. Also the Punchfile can be used by defining XYPUNCH commands in the case control section.For the definition of the dynamic loads, standard Simcenter Nastran commands are used.Rotating forces can be defined by applying forces in x- and y-directions with an appropriatephase lag between the components. If the force is of an unbalance type, the force can bemultiplied by the square of the rotor speed as centrifugal force. The excitation order can bedefined by the user.4Simcenter Nastran Rotor Dynamics User’s Guide
1.1.3 Transient Response AnalysisIn the transient response analysis the nodal displacement velocity or acceleration, as well aselement forces and
Simcenter Nastran includes a rotor dynamics capability that lets you predict the dynamic behavior of rotating systems. Rotating systems are subject to additional forces not present in non-rotating systems. These additional forces are a function of rotational speed and result in syste
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