1 © 2015 ANSYS, Inc. June 28, 2016

Johannes Einzinger

ANSYS

Enhancement regarding the Statistical Analysis of Mistuned Compressor

Wheels by Model Order Reduction using the software SoS

2 © 2015 ANSYS, Inc. June 28, 2016

Outline

3 © 2015 ANSYS, Inc. June 28, 2016

What is Mistuning?

• Why does Blade x break?• Local Production Error?

• Local Material Error?

• Local Overload?

• Local Erosion?

• …

• Non cyclic System due to• Allowed Production Tolerances

• Small Erosion

• …

• Mistuned System

Rotor Damage at Blade x

CAD-Model (=Tuned System)

Real-Model(=Mistuned)

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Model Order Reduction Cyclic Reduction

Modal Reduction

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Flutter Margin

Blade Flutter

Aerodamping EO Forcing

Forced Response

)()()( tFxkkxccxm aeroaero

Aero Mechanic - Reduced Oder Model

6 © 2015 ANSYS, Inc. June 28, 2016

Aero Mechanic - Mistuning

Reduced

mass

Excitation

frequency Reduced

damping

Reduced

stiffness

Single sector

engine order

forcing

Projection to

modal space

and expansion

from cyclic

domain

Mistuning

terms

Aero

stiffness

Cyclic Modes are approximated

by cantilevered ModesModal

Participation Factors q

8 © 2015 ANSYS, Inc. June 28, 2016

optiSLang Set-Up • Reference=Mean Value=0, i.e. Tuned

• 22 Blades 22 Random Variables

• Standard Deviation=0.1% 1.0% 10% 100%

• DoE with 400 and 800 dps

• Objective: Variation of Meximal Stress

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Meta Modell of Optimal Prognosis

CoP=33 CoP=22 CoP=22 CoP=1

CoP=35 CoP=35 CoP=34 CoP=3

400 Design

Points

800 Design

Points

Std. Dev. d

=0.1%

Std. Dev. d

=1.0%Std. Dev. d

=10%

Std. Dev. d

=100%

10 © 2015 ANSYS, Inc. June 28, 2016

Important Parameters

CoP=33 CoP=22 CoP=22 CoP=1

CoP=35 CoP=35 CoP=34 CoP=3

400 Design

Points

800 Design

Points

Std. Dev. d

=0.1%

Std. Dev. d

=1.0%Std. Dev. d

=10%

Std. Dev. d

=100%

11 © 2015 ANSYS, Inc. June 28, 2016

Apply Best-Practice Guide Lines

Number of Design Points for Meta-Model depends on:• Number of important Parameters

• Nonlinearity of Response Surface

Reason for small Coefficient of Prognosis:• Parameterization Input (TWC vs. discrete)

• Parameterization Output (Scalar, Signal, Field)

• Number Design Points

• Number of Input Parameter

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Parameterization – Input

Mistuning Patter=

Direct InputFourier Series

+Fourier Sieries:• Independent of #Blades• Parameter Reduction• High Flexibility• 100% accurate

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Parameterization – Input as Fourier Series

N=1 N=2

N=3 N=4

...Parameters per Imp-Wave:• Amplitude• Phase Position:

• N=1: 0-360° [0-1]• N=2: 0-180° [0-1]• N=3: 0-120° [0-1]• …

Mistuning Patter Imperfection Wave

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Simulation – ResultsExcitation Frequency

Rang

Eigen Frequencies

Modal Response @ Resonance

Nominal Exsitation

Mistuning

Response @ Tip Node @ Resonance

for Blades

Frequency Response @ Tip

Node

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Response @ Tip Node @ Resonance

for Blades

• Scalar– Global Maximum

– Local Maximum @ Blades

• Signal– Local Maximum @ Blades

• Field SoS– Value @ Surface

Parameterization – Output

16 © 2015 ANSYS, Inc. June 28, 2016

Investigation: Number of Design Points

90%

20%

#Design Points

Coefficient of Prognosis

Monotonic convergence of CoP with increading

#Design Points

?

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• Parameter Reduciton

• CoP wrt:– #Imperfection Waves

• Amplitudes

• Phase

– #Design Points

• Increased with Imp. Waves

Investigation: Number of Input Parameters

#Design Points100 200 200 400 1200

100%

75%Imperfection Wave

Coefficient of Prognosis

18 © 2015 ANSYS, Inc. June 28, 2016

Parameter Impact & Response Surface

Blade 1 Blade 2 Blade 3

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• Parameter Reduciton

• CoP wrt:– #Imperfection Waves

• Phase

– #Design Points

• Increased with Imp. Waves

Investigation: Number of Input Parameters

100%

80%

Coefficient of Prognosis

#Design Points100 200 400 1000 1300

Imperfection Wave

20 © 2015 ANSYS, Inc. June 28, 2016

Robustness Evalution

Nominal Exsitation Response

Nominal Exsitation Response

Pro

bab

ility

Imp

erfe

ctio

n P

has

e 2

Amplitudes (1-4) Normal Distribution

Phase Position (1-4) Uniform Random

2x4 Parameter, 100 Design

Points

21 © 2015 ANSYS, Inc. June 28, 2016

Imperfection Shapes - Statistic on Structures

...

Reconstruction of single Design Point by Imperfection Shapes

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Final Result with Statistic on Structures

Mean Value Standard Deviation ~ 0

23 © 2015 ANSYS, Inc. June 28, 2016

Summary

• Full automatic

• Reliable - Physics and Numerics

• Efficient - fast Simulation

Number of Design Points for Meta-Model depends on:• Number of important Parameters

• Nonlinearity of Response Surface

Beat-Practice Analysis:• Parameterization Input

• Parameterization Output (Scalar, Signal, Field)

• Numerical Error

• Number of Design Points

• Number of Input Parameter

• Systematic Error