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Influence of abradable coating wear mechanical properties on rotor - - PowerPoint PPT Presentation

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Influence of abradable coating wear mechanical properties on rotor stator interaction A. Batailly, M. Legrand, C. Pierre Structural Dynamics and Vibration Laboratory McGill University Introduction Structural model Contact dynamics

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Influence of abradable coating wear mechanical properties on rotor stator interaction

  • A. Batailly, M. Legrand, C. Pierre

Structural Dynamics and Vibration Laboratory – McGill University

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Outline

1 Introduction 2 Structural model 3 Contact dynamics 4 Abradable coating modeling 5 Results 6 Conclusion and perspectives

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 2 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Industrial context

fan booster compressor combustion chamber

  • Modern turbomachines
  • Optimization of power efficiency
  • ⇒ new designs (higher casing conicity, clearance closure...)
  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 3 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Industrial context

  • Compressor stage
  • Possible parasitic leakage
  • ⇒ significant loss of power
  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 3 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Industrial context

CASING BLADE

  • Compressor stage
  • Possible parasitic leakage
  • ⇒ significant loss of power
  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 3 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Industrial context

  • Modeling of abradable coating

◮ Mono-dimensional plastic law ◮ Plastic finite-elements around the casing

  • Blade / abradable coating contact simulations

◮ Variation of the material parameters of the abradable coating ◮ Consequences over the blade’s amplitude of vibration ◮ Consequences in terms of wear level

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 3 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Outline

1 Introduction 2 Structural model 3 Contact dynamics 4 Abradable coating modeling 5 Results 6 Conclusion and perspectives

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 4 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Blade

  • Industrial finite element model

(≃ 65,000 dof)

  • 8 nodes used for contact

management between the leading edge and the trailing edge

  • clamped boundary conditions

between the blade and the disk

  • use of the Craig-Bampton CMS

(ROM contains 85 dof) Both centrifugal stiffening and clearance closure are taken into account

eθ ez er fΩ fΩ clamped boundaries contact nodes

Blade with eight interface nodes

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 5 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Blade

  • ROM of 85 dof
  • Good approximation of the 8

first eigenfrequencies over the rotational frequency range

7 14 21 28 35 frequency 0.1 0.2 0.3 0.4 rotational frequency

Campbell diagram of the ROM

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 5 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Outline

1 Introduction 2 Structural model 3 Contact dynamics 4 Abradable coating modeling 5 Results 6 Conclusion and perspectives

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 6 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Contact dynamics

  • Master/slave approach

(abradable/blade),

  • Contact forces computed from

plastic deformation of the abradable element,

  • Kuhn and Tucker contact

conditions: ∀x ∈ Γm

c (master

surface) tN 0, g(x) 0, tN g(x) = 0

◮ tN discretized contact

pressure

◮ g gap function

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 7 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Contact dynamics

  • Master/slave approach

(abradable/blade),

  • Contact forces computed from

plastic deformation of the abradable element,

  • Kuhn and Tucker contact

conditions: ∀x ∈ Γm

c (master

surface) tN 0, g(x) 0, tN g(x) = 0

◮ tN discretized contact

pressure

◮ g gap function

Algorithm:

  • 1. prediction of the displacements

without considering abradable coating,

  • 2. determination of the gap

function g,

  • 3. abradable internal forces

computation through a deformation increment ∆ε introduced by predicted displacements,

  • 4. displacements correction

compatible with the calculated contact forces.

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 7 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Outline

1 Introduction 2 Structural model 3 Contact dynamics 4 Abradable coating modeling 5 Results 6 Conclusion and perspectives

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 8 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Theoretical description

  • one-dimensional two-node

bar elements

  • nonlinear plastic constitutive

law

  • numerical profile in order to

represent blade width

  • casing is assumed perfectly

rigid

casing θ bar element blade tip rotation abradable profile eθ er

Blade interface node numerical profile

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 9 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Theoretical description

  • one-dimensional two-node

bar elements

  • nonlinear plastic constitutive

law

  • numerical profile in order to

represent blade width

  • casing is assumed perfectly

rigid

casing θ bar element blade tip rotation abradable profile Fc Fc

θ

Fc

r

eθ er

Blade interface node numerical profile

One layer of abradable elements per contact node on the blade tip ⇒ ≃16.000 abradable elements on the casing

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 9 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Theoretical description

Plastic constitutive law

  • Young’s modulus E
  • Plastic modulus K
  • Yield limit σY

ε σ εp σY E K

Plastic law for abradable modeling

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 9 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Case study

  • Blade-tip/casing abradable

interaction,

  • One blade (disk dynamics is

neglected in this example),

  • Imperfections of the casing:

deformation along 2 and 5-nodal diameter free vibration modes,

  • Simulation parameters

(normalized)

◮ E = 11 ◮ K = 0.5 ◮ σY = 1.5 · 10−8 ◮ fΩ ∈ [0; 0.4] ◮ θ = 0

deformed casing disk fΩ abradable coating

Casing shapes for case study

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 10 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Case study

fΩ dependent wear level map

  • Abradable profiles at the end
  • f each simulation pictured

with colour code,

  • Distinct wear profiles with

both odd and even number

  • f lobes,
  • Two critical velocities

appear.

0.08 0.16 0.24 0.32 0.4 fΩ π 2π angular position (rad) 1 2 3 wear

Abradable coating wear patterns

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 10 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Case study

fΩ dependent wear level map

  • Abradable profiles at the end
  • f each simulation pictured

with colour code,

  • Distinct wear profiles with

both odd and even number

  • f lobes,
  • Two critical velocities

appear.

0.08 0.16 0.24 0.32 0.4 fΩ π 2π angular position (rad) 4 l

  • b

e s 5 l

  • b

e s 6 l

  • b

e s 1 l

  • b

e s 1 2 3 wear 1 2 3 4 5

Abradable coating wear patterns

Complementary results: blade response spectrum for fΩ ∈ [0; 0.4]

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 10 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Case study

eo(k = 4) C1 eo(k = 5)

Spectrum of the blade response

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 11 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Case study

eo(6) eo(4)

Spectrum of the blade response

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 11 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Case study

  • Results of this case study highlight potential critical frequencies

(located at the intersection of f1 with some engine order lines),

  • More simulations may be carried out with different parameters and

casing deformed profiles

Most recent results show a good agreement between experiments and simulation

  • abradable profile
  • blade tip displacements
  • critical stress areas within the blade
  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 12 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Outline

1 Introduction 2 Structural model 3 Contact dynamics 4 Abradable coating modeling 5 Results 6 Conclusion and perspectives

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 13 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Material parameters variation

The focus is made on the material properties of the abradable coating (E, K, and θ) Large range of values of the Young’s modulus between two extreme situations:

  • 1. E → 0, no interaction, no abradable material
  • 2. E → ∞, direct blade-tip/casing contact

In total: 9 values of E and 5 values of K are considered.

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 14 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Material parameters variation

Y4 versus E and K f4 versus E and K

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 14 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Material parameters variation

Y6 versus E and K f6 versus E and K

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 14 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Material parameters variation

  • Results are hardly sensitive to E when K is small,
  • No obvious relationship may be found between the evolution of Y 4

(or Y 6) and E or K ⇒ bell-shape evolution,

  • A maximum of vibration of amplitude is identified

(E, K) = (1.1; 0.5), ⇒ Abradable coating may increase vibration level of the blade

  • Contact stiffening phenomenon seems to be essentially dependent
  • n K.
  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 14 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Rotation of abradable elements

  • Influence of the θ parameter controlling the orientation of the

abradable elements,

  • Contact force has both a radial and a tangential component,
  • Investigated values: θ = 0 and θ = 0.15 (usual friction coefficient

for blade-tip/abradable coating ≃ 0.15),

  • Hypothesis: θ > 0 may lead to more realistic results through the

modeling of abradable coating removal force.

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 15 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Rotation of abradable elements

θ=0 rad

Spectrum of the blade response

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 15 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Rotation of abradable elements

θ=0.15 rad

Spectrum of the blade response

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 15 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Rotation of abradable elements

  • Variation of parameter θ does not change the nature of the

interaction phenomena:

◮ first bending mode dominant (design-dependent), ◮ similar interaction speed, similar abradable profiles.

  • θ > 0 → global softening of the contact case:

◮ interaction detected for slightly lower frequencies, ◮ amplitudes of vibration decrease.

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 15 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Outline

1 Introduction 2 Structural model 3 Contact dynamics 4 Abradable coating modeling 5 Results 6 Conclusion and perspectives

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 16 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Conclusion

  • Results show that abradable coating mechanical properties strongly

influence the interaction phenomena and a maximum of vibration of the blade has been identified,

  • The evolution of the abradable coating modeling (θ parameter)

softens the contact case without modifying the nature of the interaction phenomena (number of lobes, interaction speed almost identical),

  • The proposed approach seems well suited for an accurate simulation
  • f industrial experiments. Most recent results are encouraging for

different types of blades.

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 17 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Perspectives

  • The proposed strategy may be of great interest for the optimization
  • f blade design:

◮ reducing amplitude of vibration, ◮ identification of areas where cracks may initiate (maximum

stress detection).

  • Work is in progress for taking into account the deformation rate

⇒ visco-plastic law of abradable coating,

  • Calibration of this visco-plastic law will be carried out by direct

comparison between numerical simulations and experimental results.

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 18 / 19

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Introduction Structural model Contact dynamics Abradable coating modeling Results Conclusion and perspectives

Thank you for your attention.

  • A. Batailly, M. Legrand, C. Pierre

Turbo Expo 2011 June 9 2011 19 / 19