Turbomachine assemblies and the challenges of designing them – What’s New
- Alvaro Filho
- Nov 11, 2025
- 5 min read
Turbomachines are made of assemblies of different bladed disks
An interesting exploitation of the periodicity of the structure is to consider cyclic symmetry sectors, instead of the whole 3D structure. When the industrial application requires the machine to be made of different stages, each with a different number of sectors, special care is required when connecting those sectors to ensure a smooth junction between the two stages.
When the periodic structure deviates from its regular axisymmetry shape like at the propellers with few blades, a simulation in a rotating frame can no longer be avoided. The limitations on the non-rotating parts apply for such calculations: indeed, the non-rotating parts (stator and bearings) must be isotropic, which can be a rough assumption for industrial applications.
For such cases, the Simcenter Nastran solver for Rotor Dynamics proposes a method of avoiding model limitations with the use of Coleman transformation. Indeed, with this method, bladed rotors assembled to an anisotropic stator and bearings can be computed! While this is a challenge to complete, it allows you to model the complexities and explore more possibilities when simulating and modeling rotating structures.
For industrial applications like turbochargers, steam turbines, or jet engines, the assembly is made of multiple stages of bladed disks, and the assumption that the rotor has axisymmetry is not always true. Therefore, Simcenter 3D 2506 for Rotor Dynamics has expanded the use of the Coleman transformation to assemblies of multiple stages of cyclic symmetry rotors.ontagens de múltiplos estágios de rotores com simetria cíclica.
Coleman transformation for multiple stages of cyclic symmetry rotors
The Coleman transformation is a solution for producing time invariant matrices in the fixed structure for cyclic symmetric rotors, as described by Kirchgassner 2016. Campbell diagrams and stability analysis are then used to calculate the critical speeds at which resonance occurs. This method is equivalent to the Floquet method when the structure is strictly cyclic symmetric, as described by Skjoldan 2009..
Simcenter 3D advanced capabilities for bladed rotors
Simcenter 3D has taken a step further in the simulation of advanced bladed rotors applications, allowing an assembly to be computed satisfying the hypothesis of rotor dynamics calculations based on the axisymmetry or unsymmetry of the different parts of the system. It allows easy postprocessing including the production of Campbell diagrams and presents modes as output in a fixed reference frame for easy interpretation
Top right, model preparation of different cyclic symmetry sectors connected at the junction; bottom right: the Campbell diagram output in fixed reference frame; left: complex mode; 57Hz at 600rpm, backward whirl.
Complex modal analysis in 5 steps
Step one
In Simcenter 3D, prepare an associative model, where the different stages can be linked to the geometry. It will allow any changes in the geometry to be communicated to the finite element model and adapted in such a way that only the simulation has to be computed again, to account for the changes. This method is called the master model concept.
Step two
Prepare the finite element model of the cyclic symmetry sector of each stage, by identifying the sector as a portion of the structure that can be repeated about the rotor axis. It can contain a single blade or multiple blades.
Step three
Assemble the different stages at the junction
Identify each junction between two connected stages. The solver will take care of the continuity of results at this junction by automatically adding the higher order harmonics.
Step four
Prepare the simulation
Set up a complex modal analysis in the rotating frame and activate the Coleman transformation. The rotating parts modeled in cyclic symmetry will be calculated in multi blade coordinates for different cyclic waves (harmonic index). The Coleman transformation will compute time-invariant matrices that will allow results to be output in a fixed reference frame. The bearings and the stator can be anisotropic and are calculated in the fixed reference frame, allowing for the simulation of the whole assembly.
Step five
Post-process results in Simcenter 3D
The Campbell diagram shows the evolution of the eigenfrequencies with the rotation speed, highlighting the gyroscopic effects for the relevant modes. The advantage of the Coleman transformation is the simultaneous consideration of multiple harmonic indices, which is usually not the case with simulations using cyclic symmetry. Modes at 0-diameter, or 1-diameter are output in our example.
What else can cyclic symmetry do?
For all these applications that show a periodic structure, cyclic symmetry is an interesting alternative to full 3D models, since it enables the use of model reduction and makes the simulation time more reasonable.
But what else? let’s review what Simcenter 3D Rotor Dynamics can do with cyclic symmetry models:
Consider hybrid models, that is, a model that consists of sections that are 1D, 2D, and/or 3D, it is now possible to model a rotor made of a cyclic symmetry sector, in one or multiple stages, with a connection to a 2D Fourier portion of the rotor, a 1D shaft, as well as a 3D portion of the structure. Bearings, springs, dampers, etc can be used to connect the rotor to the ground with stiffness and damping properties or to a casing.
If you want to go further in the model reduction, you can create a super-element of the cyclic symmetry sectors, for one or multiple stages, using Component Mode Synthesis methods. This super-element can then be used in an assembly with bearings, in rotor dynamics solutions. The postprocessing enables you to recover the results for the original cyclic symmetry sectors and for the whole recombined structure.
For bladed rotors that can have large deformations due to centrifugal loads or other types of solicitations, which might occur when the blades are long and thin, it is possible to compute a modal basis of the structure with a preliminary nonlinear prestress. The nonlinear prestress of the structure computes the equilibrium state due to large deformations, and the modal basis is computed around this equilibrium state. Afterwards, you can use that tangent modal basis in a modal frequency response to compute the vibrations of the system due to external loading.
For Campbell diagram, stability study and complex mode calculations, this blog shows that Simcenter 3D Rotor Dynamics can now be used to solve multi-stage rotors modeled in cyclic symmetry, with anisotropic bearings and output results in a fixed reference frame.
Want to know more about simulating rotors in Simcenter 3D? Schedule a meeting with CAEXPERTS and see how to apply these cutting-edge technologies to gain performance, reduce simulation time and deal with real geometries and conditions much more efficiently.
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