copyright lms international 10/03/2014 samcef 4 rotors

copyright LMS International

10/03/2014

Samcef 4 Rotors professional solution

P. MORELLE – LMS 3D Division

copyright LMS International - 2010

2

S4R : a professional solution for the simulation of vibration phenomena in fast rotating systems

Centrifugal compressor Jet engines Gas/steam turbines Centrifugal fans

Industrial fans Centrifugal pumps

Turbo chargers

Francis turbines

A common problematic of forced or self excited vibrations

Turbo pumps

Marine propulsion

Rotating machines : a whole system

3 copyright LMS International - 2012

Designing a rotating machine using simulation requires to model the following :

Non rotating parts (casings, …) possibly including the ground itself (very heavy/long machines) Rotating parts (rotors, blade disks, …) including

every dynamic aspects and first of all the gyroscopic effect Bearings and linking devices, which generally

play a very important role in the stability of the whole system. This can possible include magnetic bearings and active control.

Depending on the design phase and the requested tasks, different level of modelling (beam, 2D, cyclic symmetry, 3D, …) may be used. And the different parts of the machine may be defined as “meshed part” or “condensed part/superelement” so to reduce global CPU

What is Samcef Rotor ? What is Rotor Dynamics ?

7


What is Rotor Dynamics modeling needed for ?

8

Rotating machines have a specific dynamic behaviour: Gyroscopic effect: rotation axis orientation changes due to shaft or

bearing deformations Eigenfrequencies depend on rotation speed

(Gyroscopic stiffening or softening)

Gyroscopic effect must be taken into account for:

• High rotation speeds • High polar inertias

Non linearities : clearances, squeeze-films, hydrodynamic bearings and

rubbing


SAMCEF Field pre/post-processor integrating dedicated “rotor” modules:

ROTOR module for critical speed analysis and harmonic response

ROTOR-T module for transient analyses DYNAM for creation and results recovery of

dynamic Super-Element (SE)

ASEF for linear static analysis

INTERFACES: import NASTRAN and ANSYS SE, import Ansys mesh, import Nastran models, import STEP and IGES geometries +

connectors to CAD

UNIQUE Integrated Graphical User Environment LMS Samtech solution : SAMCEF Rotors package


Analysis performed with SAMCEF Rotors

Critical speed and Stability Analysis (Complex eigenvalue problem):

Methods : Sweeping: within ranges of rotational frequencies where the complex

eigen-values have to be computed (For large problems: sparse solver or frontal, Lanczos, subspace bi-iteration)

Direct: It gives the critical speeds as eigensolutions (undamped systems

and constant stiffness only)

λ 2 M + λB (Ω) + K (Ω) q = 0



Critical speed and Stability Analysis (Complex eigenvalue problem): λ 2 M + λB (Ω) + K (Ω) q = 0

Results Complex eigenvalues (circular frequencies and damping coefficients),

associated eigenvectors, generalized quantities and effective masses. Distribution of energies (kinetic energy, strain energy, gyroscopic and

dissipation) Campbell’s Diagram (Frequencies, Damping, Critical Damping and Root

Locus) Whirling modes



Harmonic responses in frequency domains • Non-linear terms as bushing, clearances, rubbing

• Synchronous response (unbalances)

Methods

–ω 2 M + iωB (Ω) + K (Ω q + f (q)= g

Harmonic Response (Linear): Projection on a Modal Basis (Real and Complex) Direct Complex Solver Frontal Method or Sparse Solver for Complex Non Symmetrical Systems

Non-linear harmonic response Direct Solver Newton-Raphson on a Reduced Set of DOF’s Equivalent Linearization (Harmonic Balance)



Harmonic responses in frequency domains

Results For a given Frequency, drawing of Amplitude, Phase or Recombined Value

(Displacements, Reactions and Stresses/Forces Moments) and Animation

Plots versus Frequency of Amplitude & Phase of Displacements, Velocities, Accelerations, Forces, Reactions, Stresses and Moments



Transient analysis For Run-Up, Run-Down, Blade Losses (Unbalances) and Non Linear effects such as Clearances, squeeze-films, hydrodynamic bearings and rubbing

Loading External Applied Forces Overall Accelerations Local Accelerations

With local non-linearity, variable rotating speed, non-symmetrical Stiffness and Damping matrices

Initial Conditions Initially Statically Applied Forces Initial Stepwise Force Initial Dirac Impulse Initial Harmonic Force

Mq + B (Ω) q + K (Ω, Ω) q + f (q, q, Ω) = g (t).. . . .



Transient analysis

Loading External Applied Forces Overall Accelerations Local Accelerations

Results Nodal displacements, rotations, velocities,

accelerations forces and reactions. Forces and moments for the beam, bearing and

bushing elements Stresses for the volumic and shell elements Drawings of deformed structure, stresses and

forces – animation FFT

Solution Techniques Implicit Direct Integration (Newmark Scheme and HHT) Automatic time stepping Frontal Method with Substructuring Technique Newton-Raphson Possible Restart



Transient analysis


How do we model rotating parts ?

17


Samcef Rotor models and formalisms

Possible frames • Inertial

• Rotating

Possible models • 1D • 2D • 3D CC and 3D MSCC • 3D full

Possible formalisms • Lagrangian • Eulerian (ex. of application : FSI)

grt TTTT ++=CCoriolisrt TTTTT +++=


Jet Engine model elaboration : rotating parts

Stage #1

Stage #3

Stage #2 Stage

#4

Beams Solid Multi Harmonics

Cyclic Symmetry Multi Stage CS Mixed




Preliminary 1D Model :

o Simple 1D model for fast mechanical parametric studies o Model made of beams, springs and lumped inertia o Parametric studies with respect to bearing stiffness, bearing supports, …


Advantages & Limitations of beam models

Limited amount of dofs => fast computations

Not so easy to build and validate a model (compute equivalent masses/inertia

for each disk); to be redone for each design change. Shafts profile cannot be deformed => not suited:

- when ovalization appears - When change of thickness appears (conical parts) - for centrifuge models (centrifuge stiffening)




o 2D Fourier Multi Harmonic model

o Possibility to use it condensed or not (Craig-Bampton component mode synthesis method)


Effects • Stiffness Matrix and Geometric Stiffening from Axi-symmetric Stress Field (centrifuge

stiffening effect) • Consistent Mass and Gyroscopic Matrices • Viscous, Proportional and Circulatory Forces damping • Variable viscous damping • Material can be Anisotropic in the Meridian Plane (Composite Structure, anisotropic

bearings)

Modelling of 2D rotor models


What is so special about S4R ?

2D models demo


Example : simulation of semi-rigid link with contact

Samcef Rotor will take into account: Semi-rigid links, including contact, between different parts of a turbine.

Contacts that are active for some speeds of rotation and not active for others

(centrifuge effects) : critical speed analysis, non linear harmonic response, non linear transient analysis



3D model using detailed CAD geometry :

o most of the time condensed in superelement (CPU) o if not, very expensive


What is so special about S4R ?

3D models demo



3D models are current practice for axial machineries and specifically jet engines. However, when cyclic symmetry can be applied, it leads to similar results but with much less CPU. For multi stage design : One sector where some

stages are idealize Several blades by sector

when applicable


The model : one sector of each stage

Calculated 3D mode involving the 3 stages


Example of a 3 stages jet engine model


Modal analysis on industrial case study:

Independent stages Vs coupled study

Stage #1 alone Stage #2 alone

Coupled stages

Multi-stage cyclic symmetry modelling exhibits new eigenmodes related to coupling between stages : A crucial information when coupling simulation and tests

Multi stage analysis at


How do we model non rotating parts ?

33


Non rotating parts


Possibility to use any

type of FE model for non

rotating parts

Most of the time, non

rotating parts are

represented by SEs

We can import SEs

created in ANSYS,

NASTRAN


Whole jet engine model : components


The WJEM allows to include components. Ex : oil tank

Global analysis Local analysis (ex : FSI)

Whole Jet Engine model elaboration : assembly


Whole Engine FEM Model: example of the rotor casing assembly o Casing : super-element assembled with rotor model o Nodes at interfaces o Sensor nodes for clearances closure detection

The fact to work with superelements will help saving CPU but also facilitate the exchange of models between partners which are also sometimes competitors


How do we model linking devices?

37


Gear element with pressure, toothing and conicity angles:

Coupling of bending, torsion and axial deformation

Modelling of linking devices


Linear model of bearings, seals and fluid forces: BEARING element Variable stiffness and damping matrices. These matrices are either function of

the rotational speed, the frequency or time;

Transfer function for magnetic bearing and coupling between sensors and actuators (DIGI element)

Non-linear bushing: BUSHING element

User element (ex : controller programming)



Squeeze Film Dampers:

Natural

With or without end seals (leakage factor)

With or without inlet and outlet pressure


• Incompressible laminar iso-viscous fluid; • The governing equation for pressure is the classical Reynolds lubrication equation; • A simplified 1D equation (short or long bearing theory) is solved based on the adopted squeeze-film damper configuration.


Rolling Element Bearings:

Single-Row Radial Ball Bearing

Cylindrical Roller Bearing

Single-Row Angular Contact

Tapered Roller Bearing



Journal Bearings: Cylindrical ( 1D or 2D ) Tilting pads (1 D – short bearing theory) Multi lobes ( 1D – short bearing theory)



Hydrodynamic Bearings parametric models:

Cylindrical Hydrodynamic Bearing

Hydrodynamic pivoted pad bearing

Hydrodynamic multi lobe bearing



SAMCEF Field pre/post-processor integrating dedicated “rotor” modules:

ROTOR module for critical speed analysis and harmonic response

ROTOR-T/MECANO parallel module for transient analyses

DYNAM parallel for creation and results

recovery of dynamic Super-Element (SE)

ASEF parallel for linear static analysis

INTERFACES: import NASTRAN and ANSYS SE, import Ansys mesh, import Nastran models, import STEP and IGES geometries +

connectors to CAD

UNIQUE Integrated Graphical User Environment LMS Samtech solution : SAMCEF Rotors parallel


45

References


46

Rotor Dynamics Analysis of propeller reduction gear box

Challenge Evaluate the critical speeds and critical bending modes

of a propeller reduction gear box Complex configuration Multiple shafts

Solution 2.5 D Multi-harmonic model with SAMCEF Rotor Coupling of different shafts using the SAMCEF gear

element

Result: Assessment of critical speeds allowed with reasonable

modeling effort and CPU time

Steam turbine at Dongfang Steam Turbine (CN)

47

Challenge : capture not only global bending torsion modes but also local blade modes which are becoming dangerous because of new design

Solution : propose 2D Fourier and 3D MCSS so to detect those modes at reasonable CPU. The capability to simulate assembly conditions (semi rigid links, contact submitted to centrifuge effects) isalso crucial so to simulate properly the machine

Benefits : much better design thanks to a better prediction of real vibration modes


48

Rotor Dynamics Analysis of VINCI LOX turbopump

Challenge Evaluate the critical speeds and critical bending modes

of the LOX turbopump rotating part Sensitivity to clearances Transient rotordynamic analysis (run-up and shut-

down phases)

Solution Elegant and efficient Model building methodology 2.5 D Multi-harmonic models Addressing real 3D physical phenomena Capabilities enabled by SAMCEF for Rotor

Result: Engineering insight in the physical behaviour of the

turbo-pump during its operational rotating speed range Assessment of loads during run-up and shut-down

phases

Picture of Real Application

Logo of customer (if disclosable)

Picture of Engineering Results

Steam turbine at (FR)

49

Challenge : perform a full train dynamic analysis in frequency and unbalance response with configuration Gas turbine, load gear and generator (system made of an assembly of two rotors linked by gear box, plus bearings)

Solution : global model of the whole system able to capture coupled modes, bending torsion modes involved by the connection of two rotors through a gear box

Benefits : Oil film bearing properties, stiffness and damping, are dependent on rotor speed. Gyroscopic effects added to reliable state of bearing lead to satisfying results of unbalance response analysis and Campbell diagram calculation.


The challenges : a complex Thermo-mechanical problem

Very large temperature range : 20 – 900 K Very high internal pressure : up to 200 bars Very high rotation speed : up to 37 000 RPM Clearances and interference fits with microns

precisions Pressed bolts and screws Seals systems Model must include rotating and non rotating

parts + linking devices Need to take into account of the dispersion of

data (min/max)...

The Ariane 5 LH2 and LOX Turbo-Pumps


First and second modes Floating bearing

simulated as 2 hydrodynamics bearings assembled in serie

In the middle : lumped inertia with the rings inertia properties Hydro 1 (between rotor

and ring) one fraction of the rotational speed (80 % for example) Hydro 2 (between ring

and the casing) (20 % for example)

An exemple of turbocharger rotor simulation


Analysis of a TurboCharger using Samcef Rotors


53

ACAE: Rotor Dynamics Performance Drives the Concept Design

Challenge Establish a design process for the rotor dynamics simulation

of jet engine Lack of engineering experience

Solution Comprehensive capability of Samcef for Rotor

• 1D parameterized model for concept design • 2D and 3D approaches for detailed design allowing to

determine : – Critical Speed – Influence of bearing and other support on the rotor

dynamical behaviour

Benefits Very clear and easy-to-use process Accurate result and faster speed


Summary

Samcef Rotors offers the excellent solution package to optimize the design of gas and steam turbines, working in complement with Ansys or standalone.

Versatile, scalable and accurate modeling techniques, from 1D/beam models to full 3D including innovative methods like 2D multi-harmonic, and multi stage cyclic symmetry

Full 3D modes, including ovalization and coupling of torsion, bending, traction and multi stage - that is, full accuracy at reasonable CPU time

A dedicated GUI, for easy building apd postprocessing of Rotor models

Extended library of linking devices, and methods to couple rotating and non rotating parts, with or without model condensation (static or dynamic)

Many analysis possible from classical critical speed and harmonic response to full transient/time history


Customer’s benefits

Understand better/optimise the behavior of a gas/steam turbine by using models providing better accuracy and predicting better coupling phenomena between different type of vibration modes Reduce time and cost of physical test using accurate simulation models to facilitate model updating and comparison with tests. Use together LMS best-of-class testing technology and top level virtual prototyping techniques Decrease costs linked to maintenance and warranty by reducing the amount of failures. Reduce design cycle time and time to market of your products by designing right at the first time.

copyright lms international 10/03/2014 samcef 4 rotors

Documents