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WP 4 - Improved methods for more accurate HCF assessment
TURBO POWER Program Conference 2014 WP 4 - Improved methods for more accurate HCF assessment Salar Sadek (Daniel Sandberg and Mårten Olsson) KTH Solid Mechanics
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WP2 Aerodynamic Damping and Forcing
X WP1 Synthesis WP3 Structural Damping WP2 Aerodynamic Damping and Forcing
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Relation to Synthesis The HCF-results in WP4 contributes to:
Improved accuracy in the LAST STEP IN THE DESIGN LOOP Provide better design guide-lines Optimization, which requires good HCF-methods Reduced margins and better performance
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The Failure Probability, 𝑝 𝑓
is influenced by uncertainty in: Aero-forcing Manufacturing Thermal loading Structural damping Materials Steady & Unsteady forces Assembly Others … This presentation WP4 Design for 𝑝 𝑓
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Develop improved methods for design of gas turbine compressor blades
WP4 - Aim Develop improved methods for design of gas turbine compressor blades
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+ 𝐒 a Re 𝐱 cos (𝜏) + 𝐒 a Im 𝐱 sin (𝜏)
Stress state Material points: 𝐱 Time-varying stress state: 𝐒 𝐱, 𝜏 = 𝐒 m (𝐱) + 𝐒 a Re 𝐱 cos (𝜏) + 𝐒 a Im 𝐱 sin (𝜏) Mean stress: Rotational speed Alternating stress: Vibrations HCF stress criterion 𝐒 𝐱, 𝜏 𝜎 eff 𝐱 Probabilistic models
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𝑝 𝑓 𝑝 𝑓 AROMA-PF 𝛼, 𝜎 th , 𝜎 u and m 𝜎 eff 𝐱 WL parameters
FE simulation 𝛼, 𝜎 th , 𝜎 u and m MATLAB Mean and amplitude stress 𝐒 m 𝐱 , 𝐒 a 𝐱 Choose criterion: S, C, F, M, DV Sines Crossland Findley Matake Dang Van 𝜎 eff 𝐱 VPF - models Weakest-link model 𝑉 ∗ -model 𝑑 -model 𝐴 ∗ -model 𝑉 -model Integration technique Hex-, Tet-, Pyr- elements 𝑝 𝑓 𝑝 𝑓
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Experimental work
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Fatigue tests for 𝑝 𝑓 & Materials: Different load ratios 𝜔
Rotating bending tests Uniaxial fatigue tests 𝐹 smooth 𝜔 𝛽 & Materials: Cr-Steel Titanium IMPAX notched Different load ratios
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Fatigue tests Realistic region for fatigue tests Fatigue loading
Higher tail Lower tail 90% Probability of failure 𝑝 𝑓 Realistic region for fatigue tests 10% Fat. Lim. Fatigue loading
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New probabilistic HCF models VPF models
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The size and depth of the highly stressed volume influence fatigue!
VPF models Volume method for the Probability of Fatigue The size and depth of the highly stressed volume influence fatigue!
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VPF - models 𝑉 ∗ −model 𝑑 −model 𝐴 ∗ −model
𝑝 𝑓 𝑉 ∗ =1− 𝑒 − 𝑞∙ 𝑉 ∗ − 𝑉 th 𝑑 −model 𝑑 =max( 𝑑 ∗ ) 𝐴 ∗ 𝑝 𝑓 𝑑 =1− 𝑒 − 𝑘∙ 𝑑 − 𝑑 th 𝐴 ∗ −model 𝑝 𝑓 𝐴 ∗ =1− 𝑒 − 𝑞∙ 𝐴 ∗ − 𝐴 th
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Volume where initiated fatigue cracks can grow to final failure:
𝑉 −model Volume where initiated fatigue cracks can grow to final failure: 𝑑 0 𝑉 = 𝑉 ∗ − 𝑉 0 ( 𝑑 0 ) 𝑝 𝑓 𝑉 =1− 𝑒 − 𝜆∙ 𝑉 ∗ − 𝑉 0 ( 𝑑 0 ) =1− 𝑒 −𝜆 ∙ 𝑉 x 𝑉 ∗ : 𝜎 eff ≥ 𝜎 eff,th
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Comparison of the models
Rotating bending tests Poor prediction Findley criterion Sum of errors, 𝑅 2 : 𝑅 2 = 𝑖=1 𝑛 𝑝 𝑓,exp,𝑖 − 𝑝 𝑓,model,𝑖 2 Sum of errors, 𝑅 2 WL 𝑝 𝑓 𝑉 ∗ 𝑝 𝑓 𝑑 𝑝 𝑓 𝐴 ∗ Good prediction
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Comparison of criteria models
Uniaxial tests Poor prediction Good prediction
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AROMA-PF Rotor section load case
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Weakest-link applied to a rotor section
Real geometry Real stress history Stress analysis State of the art Sines Method AROMA-PF Weakest-link Comparison
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BLISK-section from GKN
AROMA-PF: Example Stress data have been obtained from GKN for a BLISK-section for three different resonances. Load case 1 BLISK-section from GKN 9,246 rpm; 462 Hz
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𝜎 eff = 𝜎 vM 𝑺 a +𝛼∙ 𝜎 h 𝑺 m ≤ 𝜎 c
Material parameters The material parameters have been fitted to test data for the smooth specimens Sines determinstic 𝜎 eff = 𝜎 vM 𝑺 a +𝛼∙ 𝜎 h 𝑺 m ≤ 𝜎 c 𝑝 𝑓 =1−exp − 1 𝜎 2𝜋 −∞ 𝛽 𝛾−𝜇 2𝜂 2 𝑑𝛾 Sines probabilistic 𝑝 𝑓 =1−exp − 1 𝑉 0 𝑉 𝜎 eff − 𝜎 th 𝜎 u 𝑚 𝑑𝑉 Weakest-link
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Region contributing much to 𝑝 𝑓
Results from AROMA-PF Sines effective stress 𝜎 eff for 𝑝 𝑓 =0.5 Probability of failure per element for 𝑝 𝑓 =0.5 Region contributing much to 𝑝 𝑓 Loadcase 1 9,247 rpm
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𝑝 𝑓 𝑝 𝑓 AROMA-PF 𝛼, 𝜎 th , 𝜎 u and m 𝜎 eff 𝐱 WL parameters
FE simulation 𝛼, 𝜎 th , 𝜎 u and m MATLAB Smooth specimens Mean and amplitude stress 𝐒 m 𝐱 , 𝐒 a 𝐱 Choose criterion: S, C, F, M, DV Sines Crossland Findley Matake Dang Van 𝜎 eff 𝐱 VPF - models Weakest-link model 𝑉 ∗ -model 𝑑 -model 𝐴 ∗ -model 𝑉 -model Integration technique Hex-, Tet-, Pyr- elements 𝑝 𝑓 𝑝 𝑓
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Predictions by WL and Sines method
Failure probability, 𝑝 𝑓 𝑝 𝑓 =0.5 Amplitude scale factor
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Integrate WP4 fully in the computational chain = WP1 Synthesis!
Future work in WP4 Further analysis of AROMA-PF in terms of: More Load cases Study lower failure probability predictions, ≈ 10 −4 Study the WL predictions with other stress criteria for the rotor section Integrate WP4 fully in the computational chain = WP1 Synthesis!
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Reliability design is possible!
Synthesis enables WP4 to find 𝑝 𝑓 , including all uncertainties Reliability design is possible!
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