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7/24/2019 Basics of Blade and Blisk Vibration
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Imregun
Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -1Basics of Blade & Disk Vibration
Basics of Blade and Disk Vibration
Tuesday, 4 May 1999
14:00
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Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -2Basics of Blade & Disk Vibration
Stresses in a Bladed-disk Assembly Steady stresses
CF loads Gas bending
Thermal stresses
Alternating stresses (HCF) Blade vibration due to BPF excitation
Transient stresses
Impacts (e. g. bird strike) Blade-off Gyroscopic effects Transient thermal effects
Unexpected stresses (HCF) Flutter Low-engine order excitation Acoustic resonance, rotating stall, etc
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Page BD -3Basics of Blade & Disk Vibration
Consequences of Vibration
Noise Discomfort
Malfunction
Shutdown
Structural failure
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Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -4Basics of Blade & Disk Vibration
Modal Properties
Natural frequency
Mode shape
Damping factor
MASS AND STIFFNESS PROPERTIES DETERMINE THENATURAL FREQUENCIES AND MODE SHAPES OF
THE STUCTURE.
EXCITATION LEVELS AND DAMPING DETERMINE
THE ACTUAL AMPLITUDE OF THE VIBRATIONRESPONSE.
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Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -5Basics of Blade & Disk Vibration
Vibration Properties vs Vibration Characteristics
Properties are determined by the structural featuresalone.
Natural frequencies, mode shapes, damping
Characteristics are determined by the vibration
properties AND external forcing
Resonance, response levels, response time histories, etc.
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Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -6Basics of Blade & Disk Vibration
Tools in Structural Dynamics
Experimental route: Modal Testing and Analysis
Theoretical routes:
Closed-form analytical solutions
Lumped parameter models
Finite element method
Boundary element method ...
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Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -7Basics of Blade & Disk Vibration
Theoretical & Experimental Routes
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Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -8Basics of Blade & Disk Vibration
Mathematical Models
The models are interchangeable for linear systems and SHM.
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Imregun
Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -9Basics of Blade & Disk Vibration
Blade Vibration
Vibration terminology Axial, tangential & radial directions
Flapwise, edgewise and torsional vibration: E, T & T
Blade modes
Beam modes: no chordwise bending, (coupled) flap & edgewise
Plate-type modes: chordwise bending is present
Fixture modes Assembly modes
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Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -10Basics of Blade & Disk Vibration
Beam & Plate Modes
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Imregun
Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -11Basics of Blade & Disk Vibration
FE Modelling
1T mode 2F mode
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Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -12Basics of Blade & Disk Vibration
Factors Affecting Blade Vibration - I
End fixings - Roots
Root flexibility may not be negligible
Non-linear behaviour when friction dampers are fitted
End fixings - Shrouds
Very difficult to model the shroud interface Non-linear behaviour may be significant
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Imregun
Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -13Basics of Blade & Disk Vibration
Operating Conditions
CF forces change thedatum position of theblade: untwist
CF forces increase thestiffness
Gas bending changes thedatum position of theblade: untwist
Temperature effectschange the materialproperties, causing naturalfrequency variations.
Factors Affecting Blade Vibration - II
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Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -14Basics of Blade & Disk Vibration
Blade Vibration Testing
For small blades, excitation mechanism may interfere withstructural properties.
Root clamping may be very difficult to achieve.
Air jet excitation is relatively common.
Damping estimates may contain large errors.
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Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -15Basics of Blade & Disk Vibration
Disk Vibration - I
Consider a rectangular plate which has two modes of vibration:
one about height and the other about length. The two modeswill have different frequencies.
Consider now a square plate. The two modes will still exist
but they will occur at the same frequency.
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Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -16Basics of Blade & Disk Vibration
Disk Vibration - II
Disks vibrate in doubleNodal Diameter modes: samefrequency but different orientation of the mode shape
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Disk Vibration - III
The vibration can take place in axial, radial or tangentialdirections.
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Disk Vibration - IV
As one goes up in frequency, the nodal diameter modes will
start exhibiting nodal circles. Therefore, disks vibrate interms of nodal diameters and nodal circles.
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Disk Vibration - V
In summary, disk vibrationis characterised by families
of nodal diameters. The
modes are double, except
the 0 nodal diameter mode,also known as the umbrella
mode.
Each family is associated
with a nodal circle.
F
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e
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Disk Vibration - VI
All circular components such as cylinders, rings, shafts, etcexhibit the same vibration characteristics.
If there are non-uniformities (holes, manufacturing
imperfections, etc), the double modes will split into close-
frequency pairs.
The disk rotation will also have an effect. More of this
later.
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Page BD -21Basics of Blade & Disk Vibration
Bladed-disk Vibration - I
If the disk is rigid (eg fan assembly), the vibration modes will
be dominated by blade modes.
If the disk is flexible (eg turbine disk), disk and blade
characteristics will co-exist.
At low nodal diameters, the
disk will dominate.
At high nodal diameters, the
cantilevered blade modes will
dominate.
F
r
eq
u
e
n
c
y
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Aeroelasticity in Axial Flow Turbomachines von Karman Institute
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Bladed-disk Vibration - II
Bladed-disk modes are also displayed in nodal-diameter family
format. Bladed disk natural frequencies are affected by blade stagger and
disk/blade coupling.
For a discrete lumped-parameter system with N blades, themaximum nodal diameter value is N/2 (even N) or (N-1)/2 (odd N).
For continuous systems, higher values are
possible but these become indistinguishablefrom the corresponding lower nodal diameter
values if N blades only are considered.
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Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -23Basics of Blade & Disk Vibration
Bladed-disk Vibration - II
The addition of a part-span or tip
shroud makes the vibrationcharacteristics even more complicated.
General behaviour is similar to
unshrouded disks, except for
asymptotic behaviour towards
cantilevered blade frequency.
Continuous or non-interlocking
shrouds may have significant effectson dynamic behaviour.
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Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -24Basics of Blade & Disk Vibration
Bladed-disk Vibration - III
Modes with 0 nodal diameters Single mode
Affected by shaft and bearing (axial)
Modes with 1 nodal diameters
May be coupled with shaft bending
N/2 nodal diameters (even blades)
Two such single modes: the nodal diameters go through the blades
or pass symmetrically between the blades.
Split double mode
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Imregun
Aeroelasticity in Axial Flow Turbomachines von Karman Institute
Page BD -25Basics of Blade & Disk Vibration
Analysis Tools for Bladed-disk Vibration
Analytical solution
for cantilever blade
Receptance coupling for
beams, disks and rings
Lumped parameter models
Single blade (or
sector) FE models
Whole-annulus FE models
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Sources of Excitation Self-excitation or flutter
General unsteadiness and random turbulence
Low engine-order excitation
Non-uniformities in working fluid pressure
Blade passing engine-order excitation.
Angular non-uniformity in pressure causesdynamic excitation of rotating blades at
frequencies that are multiples of the
rotation speed AND with spatial
distributions that match nodal diameter
modes.
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Page BD -27Basics of Blade & Disk Vibration
Blade-passing Excitation
Two conditions must be met:
The excitation frequency, n,
must be equal to an assembly
natural frequency.
The excitation pattern must
match the associated nodal
diameter mode shape.
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Page BD -28Basics of Blade & Disk Vibration
Campbell Diagram
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Critical Vibration Modes in Aeroelasticity
Fan Flutter Usually the first family, occasionally the second family
Very stiff disk, hence assembly modes are dominated by the blade
characteristics
Usually the 1-6 nodal diameter modes, arising from the blades 1Fmode
Forced response
Blade passing excitation. Typically, high nodal diameter modes.
General unsteadiness. Typically, low nodal diameter modes.
In both cases, the first 4-5 families may be affected.