Johannes Einzinger ANSYS

Transcription

1 Enhancement regarding the Statistical Analysis of Mistuned Compressor Wheels by Model Order Reduction using the software SoS Johannes Einzinger ANSYS ANSYS, Inc. June 28, 2016

2 Outline ANSYS, Inc. June 28, 2016

3 What is Mistuning? Rotor Damage at Blade x 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 CAD-Model (=Tuned System) Real-Model (=Mistuned) ANSYS, Inc. June 28, 2016

4 Model Order Reduction Cyclic Reduction Modal Reduction ANSYS, Inc. June 28, 2016

5 Aero Mechanic - Reduced Oder Model Aerodamping EO Forcing Flutter Margin m x ( c c ) x ( k k ) x F( t) aero aero Forced Response Blade Flutter ANSYS, Inc. June 28, 2016

6 Aero Mechanic - Mistuning Cyclic Modes are approximated by cantilevered Modes Modal Participation Factors q Excitation frequency Reduced mass Reduced damping Reduced stiffness Mistuning terms Aero stiffness Projection to modal space and expansion from cyclic domain Single sector engine order forcing ANSYS, Inc. June 28, 2016

7 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 ANSYS, Inc. June 28, 2016

8 Meta Modell of Optimal Prognosis Std. Dev. d =0.1% Std. Dev. d =1.0% Std. Dev. d =10% Std. Dev. d =100% CoP=33 CoP=22 CoP=22 CoP=1 400 Design Points CoP=35 CoP=35 CoP=34 CoP=3 800 Design Points ANSYS, Inc. June 28, 2016

9 Important Parameters Std. Dev. d =0.1% Std. Dev. d =1.0% Std. Dev. d =10% Std. Dev. d =100% CoP=33 CoP=22 CoP=22 CoP=1 400 Design Points CoP=35 CoP=35 CoP=34 CoP=3 800 Design Points ANSYS, Inc. June 28, 2016

10 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 ANSYS, Inc. June 28, 2016

11 Parameterization Input Mistuning Patter= Direct Input Fourier Series +Fourier Sieries: Independent of #Blades Parameter Reduction High Flexibility 100% accurate ANSYS, Inc. June 28, 2016

12 Parameterization Input as Fourier Series Mistuning Patter Imperfection Wave N=1 N=2 Parameters per Imp-Wave: Amplitude Phase Position: N=1: [0-1] N=2: [0-1] N=3: [0-1] N=3 N= ANSYS, Inc. June 28, 2016

13 Simulation Results Excitation Frequency Rang Frequency Tip Node Eigen Frequencies Tip Resonance for Blades Modal Resonance Mistuning Nominal Exsitation ANSYS, Inc. June 28, 2016

14 Parameterization Output Scalar Global Maximum Local Blades Tip Resonance for Blades Signal Local Blades Field SoS Surface ANSYS, Inc. June 28, 2016

15 Investigation: Number of Design Points 90% Coefficient of Prognosis? Monotonic convergence of CoP with increading #Design Points 20% #Design Points ANSYS, Inc. June 28, 2016

16 Investigation: Number of Input Parameters Parameter Reduciton CoP wrt: #Imperfection Waves Amplitudes Phase #Design Points Increased with Imp. Waves 100% Coefficient of Prognosis #Design Points % Imperfection Wave ANSYS, Inc. June 28, 2016

17 Parameter Impact & Response Surface Blade 1 Blade 2 Blade ANSYS, Inc. June 28, 2016

18 Investigation: Number of Input Parameters Parameter Reduciton CoP wrt: #Imperfection Waves Phase #Design Points Increased with Imp. Waves 100% Coefficient of Prognosis #Design Points % Imperfection Wave ANSYS, Inc. June 28, 2016

19 Imperfection Phase 2 Probability Robustness Evalution Amplitudes (1-4) Normal Distribution Nominal Exsitation Response Phase Position (1-4) Uniform Random 2x4 Parameter, 100 Design Points Nominal Exsitation Response ANSYS, Inc. June 28, 2016

20 Imperfection Shapes - Statistic on Structures... Reconstruction of single Design Point by Imperfection Shapes ANSYS, Inc. June 28, 2016

21 Final Result with Statistic on Structures Mean Value Standard Deviation ~ ANSYS, Inc. June 28, 2016

22 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 ANSYS, Inc. June 28, 2016