1. Rotordynamics with ANSYS Mechanical Solutions
Pierre THIEFFRY
Product Manager
ANSYS, Inc.

2. Generalized axisymmetric element Rotordynamics with ANSYS Workbench
Agenda
General features
Generalized axisymmetric element
Rotordynamics with ANSYS Workbench
An ANSYS V12.0 example
Future plans
I’d like to remind everyone that some matters that will be discussed during this presentation may constitute forward-looking statements that involve risks and uncertainties, which could cause actual results to differ from those projected.
In addition, I would also like to mention that we will not be able to discuss or answer any questions regarding previously provided guidance, as our Company policy is that we only comment on company guidance in a public forum.

3. General features

4. Rotordynamics features
Pre-processing:
Appropriate element formulation for all geometries
Gyroscopic moments generated by rotating parts
Bearings
Rotor imbalance and other excitation forces (synchronous and asynchronous)
Rotational velocities
Structural damping
Solution:
Complex eigensolver for modal analysis
Harmonic analysis
Transient analysis

5. Rotordynamics features
Post-processing
Campbell diagrams
Orbit plots
Mode animation
Transient plots and animations
User’s guide
Advanced features:
Component Mode Synthesis for static parts

6. Appropriate element formulation
The following elements are supported for rotordynamics analysis (stationary reference frame):
Mass
MASS21
Beam
BEAM4, PIPE16
BEAM188, BEAM189
PIPE 288/289
Solid
SOLID45, SOLID95
SOLID185, SOLID186, SOLID187
Shell
SHELL63
SHELL181, SHELL281
General axisymmetric
elements
SOLID272, SOLID273
New in ANSYS 12.0
New in ANSYS 12.0

7. Generalized axisymmetric element
The new 272/273 elements:
Are computationally efficient when compared to 3D solid
Support 3D non-axisymmetric loading
Allow a very fast setup of axisymmetric 3D parts:
Slice an axisymmetric 3D CAD geometry to get planar model
Mesh with 272/273 elements
No need to calculate equivalent beam sections
Can be combined with full 3D models, including contact
2D axisymmetric mesh
3D representation
3D results (not necessarily axisymmetric)

8. Bearings
2D spring/damper with cross-coupling terms:
Real constants are stiffness and damping coefficients and can vary with spin velocity w
Bearing element choice depends on:
Shape (1D, 2D, 3D)
Cross terms
Nonlinearities
Description
Stiffness and Damping cross terms
Nonlinear stiffness and damping characteristics
COMBIN14
Uniaxial spring/damper No
COMBI214
2-D spring/damper
Unsymmetric
Function of the rotational velocity
MATRIX27
General stiffness or damping matrix
MPC184
Multipoint constraint element
Symmetric for linear characteristics - None for nonlinear characteristics
Function of the displacement

9. Imbalance and other excitation forces
Possible excitations caused by rotation velocity  are:
Unbalance ()
Coupling misalignment (2* )
Blade, vane, nozzle, diffusers (s* )
Aerodynamic excitations as in centrifugal compressors (0.5* )
Input made as a force on the model z y r

10. Rotating damping structural damping (MP, DAMP or BETAD)
Considered if the rotating structure has:
structural damping (MP, DAMP or BETAD)
or a localized rotating viscous damper (bearing)
The damping forces can induce unstable vibrations.
The rotating damping effect is activated along with the Coriolis effect (CORIOLIS command).
Damper
COMBI214
Beam
BEAM4, PIPE16
BEAM188, BEAM189
Solid
SOLID45, SOLID95
SOLID185, SOLID186, SOLID187
General axisymmetric
SOLID272, SOLID273
(new in V 12.0 )
Elements supporting rotating damping

11. Campbell diagrams & whirl
Variation of the rotor natural frequencies with respect to rotor speed w
In modal analysis perform multiple load steps at different angular velocities w
As frequencies split with increasing spin velocity, ANSYS identifies:
forward (FW) and backward (BW) whirl
stable / unstable operation
critical speeds
Also available for multispool models

12. Orbit plots
In a plane perpendicular to the spin axis, the orbit of a node is an ellipse
It is defined by three characteristics: semi axes A , B and phase y in a local coordinate system (x, y, z) where x is the rotation axis
Angle j is the initial position of the node with respect to the major semi-axis A.
Orbit plots are available for beam models

13. Rotordynamics analysis guide
New at release 12.0
Provides a detailed description of capabilities
Provides guidelines for rotordynamics model setup

14. Sample models available

15. Generalized axisymmetric element

16. New Element Technology
General Axi-symmetric Element: 272/273
3D elements generated based on 2D mesh
Boundary conditions applied in 3D space
Nonlinearities, Node to surface contact
Benefits
Multiple Axis can be defined in any direction
Take advantage of axi-symmetry but deformation is general in 3D
1 element in Θ (hoop) direction I L J K A B Y’ Z’ X’
Structural Mechanics
Exciting new ‘Generalized 3D Axi-symmetric element’ that can be used for a 3D analysis.
SOLID272 is defined by four nodes on the master plane, and nodes created in the circumferential direction based on the four master plane nodes
SOLID272 and SOLID273 elements introduce the Fourier series into interpolation functions to describe the change of displacements in the circumferential (theta) direction. Lagrangian polynomial interpolation in r-z plane, Fourier series interpolation in ө dir.
The elements can therefore apply to any analysis type, including geometric nonlinear analyses, and can support any load and deformation mode. The element allows a triangle as the degenerated shape on the base plane to simulate irregular areas.
The element has plasticity, hyperelasticity, stress stiffening, large deflection, and large strain capabilities. It also has mixed-formulation capability for simulating deformations of nearly incompressible elastoplastic materials, and nearly and fully incompressible hyperelastic materials.
The elements can have any axis as the symmetric axis (defined via SECTYPE and SECDATA commands); you need only define quadrilaterals or triangles on a plane.
At release 12.0, Node-to Surface contact is supported and only with SOLID272 (lower order).
Applications include threaded connections simulations for analyzing piping joints, bio-medical etc.
3D view of shaft

17. Application to rotordynamics
The new 272/273 elements:
Are computationally efficient when compared to 3D solid
Support rotordynamics analysis
Support 3D non-axisymmetric loading
Allow a very fast setup of axisymmetric 3D parts:
Slice an axisymmetric 3D CAD geometry to get planar model
Mesh with 272/273 elements
No need to calculate equivalent beam sections
Can be combined with full 3D models, including contact
2D axisymmetric mesh
3D representation
3D results (not necessarily axisymmetric)

18. Rotordynamics with ANSYS Workbench An example

19. Storyboard
The geometry is provided in form of a Parasolid file
Part of the shaft must be reparametrized to allow for diameter variations
A disk must be added to the geometry
Simulation will be performed using the generalized axisymmetric elements, mixing WB features and APDL scripting
Design analysis will be made with variations of bearings properties and geometry

20. Project view
Upper part of the schematics defines the simulation process (geometry to mesh to simulation)
Parameters of the model are gathered in one location (geometry, bearing stiffness)
Lower part of the schematics contains the design exploration tools

21. Geometry setup Geometry is imported in Design Modeler
A part of the shaft is redesigned with parametric dimensions
Model is sliced to be used with axisymmetric elements
Bearing locations are defined
A disc is added to the geometry
Initial 3D geometry
Final axisymmetric model
Additional disk
Bearings location

22. Geometry details 3D Model sliced to create axisymmetric model
Part of the original shaft is removed and recreated with parametric radius
Additional disk created with parameters (the outer diameter will be used for design analysis)
Bearing locations and named selections are created (named selections will be transferred as node components for the simulation)

23. Mesh
The model is meshed using the WB meshing tools

24. Simulation Simulation is performed using an APDL script that defines:
Element types
Bearings
Boundary conditions
Solutions settings (Qrdamp solver…)
Post-processing (Campbell plots and extraction of critical speeds)
Axisymmetric model with boundary conditions
Expanded view

25. APDL script
Mesh transferred as mesh200 elements, converted to solid272
Spring1 component comes from named selection

26. Simulation results The APDL scripts can create plots and animations
The results can also be analyzed within the Mechanical APDL interface
Results are extracted using *get commands and exposed as WB parameters (showing the performance of the design)

27. Mode animation (expanded view)

28. Design exploration
The model has 2 geometry parameters (disc and shaft radius) as well as a stiffness parameters (bearings stiffness)
4 output parameters are investigated: first and second critical speeds at 2xRPM and 4xRPM (obtained from theCampbell diagrams and *get commands)

29. Sample results
Sensitivity plots: the bearing stiffness has no influence on the first and second critical speeds, the disc radius is the key parameter
A response surface of the model is created using a Design of Experiments
Curves, surfaces and sensitivity plots are created and the design can be investigated
Optimization tools are also available
Evolution of critical speed with shaft and disc radius

30. Optimization
A multi-objective optimization is described and possible candidates are found (usually, there are multiple acceptable configurations)
Trade-off plots give an indication about the achievable performance

31. Future plans (V13 and beyond)

32. Campbell diagrams Multiple steps (modal) X axis is rotational velocity
Rotational velocity scoped on bodies( (multispool analysis) available in modal analysis
Output Quantities:frequencies or stability values

33. Additional enhancements
Provide modal solver choice (QRDAMP, LANB…)
The connection folder hosting bearings:
Location
Damping and stiffness (as functions of w)
Coriolis option available from the Analysis settings (like the large deflection or inertia relief)
Orbit plots for beam models
Exposure of generalized axisymmetric elements

34. Modal post-processing (already available at V12)
Complex eigenshapes
Mode animation similar to ANHARM
For complex modes, tabular data display both imaginary and real parts

35. Results parameterization
The user will probably want to be able to parameterize frequencies (real and/or imaginary part) but also the critical frequencies (from Campbell results)
Doing so, he will be able to perform DX analyses :
to examine the variations of critical frequencies
To examine the evolution of the stability of a mode wrt various parameters