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Numerical Investigation of Abradable Coating Wear Through Plastic Constitutive Law Application to Aircraft Engines Mathias Legrand & Christophe Pierre McGill University IDETC/CIE 2009 - DETC2009-87669 San Diego, USA September 1, 2009

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SLIDE 1

Numerical Investigation of Abradable Coating Wear Through Plastic Constitutive Law

Application to Aircraft Engines

Mathias Legrand & Christophe Pierre

McGill University IDETC/CIE 2009 - DETC2009-87669

San Diego, USA

September 1, 2009

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SLIDE 2

Introduction Solution Method Results Conclusion

Outline

1 Introduction

Problem statement Wear or material removal? General strategy

2 Solution Method

Equations of motion Abradable constitutive law: plasticity Proposed algorithm

3 Results

Model convergence Modal interactions Final wear profile maps Animations

4 Conclusion

Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 2 / 13

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SLIDE 3

Introduction Solution Method Results Conclusion

Problem statement

Problem statement

Technologies for improved efficiency

∙ light and composite materials ∙ few turbine and compressor stages with

higher conicity

∙ aerodynamically improved blade designs ∙ higher operating temperatures

New strategy: use of abradable coatings

∙ minimal operating clearance for improved compression rates ∙ capable of undergoing structural contacts through wear ∙ unexpected diverging behaviors?

■CFM56- CFM International Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 3 / 13

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SLIDE 4

Introduction Solution Method Results Conclusion

Problem statement

Problem statement

Technologies for improved efficiency

∙ light and composite materials ∙ few turbine and compressor stages with

higher conicity

∙ aerodynamically improved blade designs ∙ higher operating temperatures

New strategy: use of abradable coatings

∙ minimal operating clearance for improved compression rates ∙ capable of undergoing structural contacts through wear ∙ unexpected diverging behaviors?

modeling of abradable coating wear in aircraft engines

■CFM56- CFM International Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 3 / 13

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SLIDE 5

Introduction Solution Method Results Conclusion

Wear or material removal?

Wear or material removal?

Referenced mechanisms

∙ abrasion, erosion, corrosion, adhesion, fretting ∙ drilling, grinding, turning, milling ∙ high speed tangential velocities

Abradable properties

∙ strength to withstand gas turbine environment ∙ wear characteristics to minimise incurring blade wear

Current knowledge and modeling

∙ Wear: experimental and empirical → Archard’s law ∙ Machining : kinematic relationships ∙ CPU-intensive numerical approaches in the FEM framework

Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 4 / 13

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SLIDE 6

Introduction Solution Method Results Conclusion

General strategy

General strategy

Assumptions

∙ A single blade in contact ∙ Statically distorted casing on

a 2-nodal diameter shape

∙ No friction ∙ No thermomechanical coupling

Solution method

∙ Blade dynamics reduction through

Craig-Bampton technique

∙ Abradable coating wear through

quasi-static plastic constitutive law

∙ Time-marching solution method

casing interface nodes fixed boundaries Ω Ω Ω abradable

■ chosen configuration Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 5 / 13

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SLIDE 7

Introduction Solution Method Results Conclusion

Equations of motion

Equations of motion

Virtual Work Principal

  • Ω1

ρ1¨ u1δu1 dV +

  • Ω1

¯ ¯ σ1(E1) : δ¯ ¯ ǫ1 dV = −

  • Γc

tNδg dS ← blade

  • Ω2

¯ ¯ σ2(E2, ET, σY ) : δ¯ ¯ ǫ2 dV =

  • Γc

tNδg dS ← abradable coating

Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 6 / 13

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SLIDE 8

Introduction Solution Method Results Conclusion

Equations of motion

Equations of motion

Virtual Work Principal

  • Ω1

ρ1¨ u1δu1 dV +

  • Ω1

¯ ¯ σ1(E1) : δ¯ ¯ ǫ1 dV = −

  • Γc

tNδg dS ← blade

  • Ω2

¯ ¯ σ2(E2, ET, σY ) : δ¯ ¯ ǫ2 dV =

  • Γc

tNδg dS ← abradable coating

Finite element discretization

M¨ u + D˙ u + Ku + λ = 0 ← blade λ = Fint ← abradable

Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 6 / 13

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SLIDE 9

Introduction Solution Method Results Conclusion

Equations of motion

Equations of motion

Virtual Work Principal

  • Ω1

ρ1¨ u1δu1 dV +

  • Ω1

¯ ¯ σ1(E1) : δ¯ ¯ ǫ1 dV = −

  • Γc

tNδg dS ← blade

  • Ω2

¯ ¯ σ2(E2, ET, σY ) : δ¯ ¯ ǫ2 dV =

  • Γc

tNδg dS ← abradable coating

Finite element discretization

M¨ u + D˙ u + Ku + λ = 0 ← blade λ = Fint ← abradable

Contact conditions

λ ⩾ 0, g ⩾ 0, λg = 0

Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 6 / 13

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SLIDE 10

Introduction Solution Method Results Conclusion

Equations of motion

Equations of motion

Virtual Work Principal

  • Ω1

ρ1¨ u1δu1 dV +

  • Ω1

¯ ¯ σ1(E1) : δ¯ ¯ ǫ1 dV = −

  • Γc

tNδg dS ← blade

  • Ω2

¯ ¯ σ2(E2, ET, σY ) : δ¯ ¯ ǫ2 dV =

  • Γc

tNδg dS ← abradable coating

Finite element discretization

M¨ u + D˙ u + Ku + λ = 0 ← blade λ = Fint ← abradable

Contact conditions

λ ⩾ 0, g ⩾ 0, λg = 0

Explicit time stepping technique: central finite differences

¨ un = un+1 − 2un + un−1 h2 , ˙ un = un+1 − un−1 2h

Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 6 / 13

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SLIDE 11

Introduction Solution Method Results Conclusion

Abradable constitutive law: plasticity

Abradable constitutive law: plasticity

Assumptions

∙ Uni-axial plasticity in compression only ∙ Isotrope hardening:

f (σ, α) = σ − (σY + Kα)

∙ Linear additive law:

ε = εe + εp σ = Eεe

Integration

∙ Kuhn & Tucker conditions ∙ Prediction-correction incremental approach: Return Map algorithm

▶ if f p ⩽ 0, admissible prediction ▶ if f p > 0, correction of prediction

σ ε εp εe σY K E

■ plastic constitutive law Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 7 / 13

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SLIDE 12

Introduction Solution Method Results Conclusion

Proposed algorithm

Proposed algorithm

  • 1. Displacement prediction by neglecting contact constraints

un+1,p = M h2 + D 2h −1 2M h2 − K

  • un +

D 2h − M h2

  • un−1
  • 2. Determination of gn+1,p by identifying all abradable elements i ∈ I being

penetrated by the blade

  • 3. Abradable internal forces computation

un+1,p → εi∈I → (σi∈I, αi∈I) → Fint εp

i∈I → abradable profil update

  • 4. Displacements correction consistent with abradable internal forces (∼

contact forces) un+1 = un+1,p − M h2 + D 2h −1 Fc

Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 8 / 13

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SLIDE 13

Introduction Solution Method Results Conclusion

Model convergence

Model convergence

Modal convergence

∙ Craig-Bampton reduction technique ∙ frequency deviation

Δf = |ff − fr| ff < 0.1%

▶ initial size : ∼ 80,000 dof ▶ final size : 109 dof ■ First five modes of the blade Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 9 / 13

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SLIDE 14

Introduction Solution Method Results Conclusion

Model convergence

Model convergence

Modal convergence

∙ Craig-Bampton reduction technique ∙ frequency deviation

Δf = |ff − fr| ff < 0.1%

▶ initial size : ∼ 80,000 dof ▶ final size : 109 dof ■ First five modes of the blade ■ CB componant modes ■ CB static modes Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 9 / 13

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SLIDE 15

Introduction Solution Method Results Conclusion

Model convergence

Model convergence

Time-step convergence

∙ Conditionally stable explicit time-stepping scheme: very small time-step ∙ Blade displacement convergence ∙ Abradable wear profile convergence

Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 9 / 13

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SLIDE 16

Introduction Solution Method Results Conclusion

Model convergence

Model convergence

Time-step convergence

∙ Conditionally stable explicit time-stepping scheme: very small time-step ∙ Blade displacement convergence ∙ Abradable wear profile convergence

angular position on the casing (rad) wear level 2π 0.5 1

■ Final abradable profiles for

different densities

time vibratory level Tf

  • 3
  • 2
  • 1

1

■ Vibratory level of the blade for

interface node 1 with different abradable densities

Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 9 / 13

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SLIDE 17

Introduction Solution Method Results Conclusion

Modal interactions

Modal interactions

freq. Ω |FFT(u)| (mm) k=2 k=4 k=6 k=8 0,1 0,2 0,3 0,4 0,5 1 1,5 0,5 1 1,5

■ No wear Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 10 / 13

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SLIDE 18

Introduction Solution Method Results Conclusion

Modal interactions

Modal interactions

freq. Ω |FFT(u)| (mm) 0,1 0,2 0,3 0,4 0,5 1 1,5 0,5 1 1,5

■ Low wear Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 10 / 13

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SLIDE 19

Introduction Solution Method Results Conclusion

Modal interactions

Modal interactions

freq. Ω |FFT(u)| (mm) 0,1 0,2 0,3 0,4 0,5 1 1,5 0,5 1 1,5

■ High wear Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 10 / 13

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SLIDE 20

Introduction Solution Method Results Conclusion

Final wear profile maps

Final wear profile maps

angular position on the casing (rad) Ω two lobes k = 6 k = 4 0.1 0.2 0.3 0.4 2π

■ low ductility – after ten rounds

angular position on the casing (rad) Ω k = 6 k = 4 0.1 0.2 0.3 0.4 2π

■ high ductility – after ten rounds Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 11 / 13

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SLIDE 21

Introduction Solution Method Results Conclusion

Animations

Animations

Ω = Ωc Ω ≃ Ωc

Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 12 / 13

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SLIDE 22

Introduction Solution Method Results Conclusion

Animations

Animations

Ω = Ωc Ω ≃ Ωc

Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 12 / 13

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SLIDE 23

Introduction Solution Method Results Conclusion

Conclusions

Summary

∙ Available numerical tool accounting for macroscopic peudo-wear mechanisms ∙ Convergence + low CPU features ∙ Possibility of experimental measure for abradable identification ∙ Wear + clearance opening → New phenomena compared to the usual

unilateral contact framework

∙ Detection of unexpected high levels of vibration at critical velocities in

agreement with first experimental results

Future work

∙ Addition of friction ∙ More contact and wear interfaces (∼ more CB interface nodes) ∙ More realistic plastic constitutive laws ∙ New scenarios of interaction

Mathias Legrand IDETC-CIE 2009: Numerical Investigation of Abradable Coating Wear 2009-10-01 13 / 13