Mulder, Andrew

Skelley, Stephen

English

NASA Technical Reports Server

Estimating Inducer Blade 
Damping in Water with On-
Blade Strain Measurements
Andrew Mulder and Stephen Skelley
Fluid Dynamics Branch
NASA Marshall Space Flight Center
2/14/2020 Approved for public release 1
https://ntrs.nasa.gov/search.jsp?R=20200001005 2020-03-28T19:06:48+00:00Z
Introduction
2/14/2020 Approved for public release 2
A water flow test of a 
subscale inducer (RS25 Low 
Pressure Fuel Pump) was 
conducted at MSFC in July 
2017 and Feb-May 2018
Objective: Measure on-blade 
strain response to various 
forms of excitation, with 
intent to estimate critical 
damping ratio of blade 
structural natural frequencies 
in real operating conditions
Strain Gauge Instrumentation
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Slip ring with amplifiers and  
bridge completion circuitsStrain gauge info
Strain Gauge Instrumentation
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Waterproofing 
(rubber coating + metal foil)
Gauges installed on blades
Excitation Method: Ping Test
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An ‘electric hammer’ was used to strike the inducer shaft 
Excitation Method: Ping Test
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Strike location
Ping Data Analysis
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Example ping response
FFT shows frequency of the response
Ping Data Analysis
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• Filter data around natural 
frequency
• Compute amplitude envelope of 
blade response
• Compute critical damping with 
impulse response formula
𝜔𝜔𝑑𝑑:
𝜁𝜁 = 11 + 𝜔𝜔𝑑𝑑𝛽𝛽 2
Damped natural frequency
𝛽𝛽: Exponential decay rate of amplitude envelope 
Ping Test Results
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Histograms show the frequency distribution of 
the highest amplitude responses over many pings
Ping Test Results
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Damping histogram for ~2 kHz response Peak strain vs damping ratio for ~2 kHz response
Ping Test Results
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Average critical damping ratio for various conditions 
Ping Test Results
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Ping test data show quite a bit of variation over many pings
Excitation Method: Stator Plate
2/14/2020 Approved for public release 139-Vane 27-Vane
Given facility speed limits, the 26th harmonic of shaft speed 
(27N) crosses the fundamental blade modes. Two stator plate 
designs were tested 
Stator Plate Data Analysis 
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• Dwell at a series of frequencies 
around the natural frequency
• Compute the frequency 
response function using strain 
amplitude measured at 27N
• Apply half quadratic gain 
formula to estimate damping
𝜁𝜁 = 12 − 4 + 4 𝑓𝑓𝑢𝑢 − 𝑓𝑓𝑙𝑙𝑓𝑓𝑝𝑝 2 − 𝑓𝑓𝑢𝑢 − 𝑓𝑓𝑙𝑙𝑓𝑓𝑝𝑝 4 − ⁄1 2
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Stator Plate Testing
Both stator plates did appear to 
generate a forcing function at 27N, 
with some caveats:
1) Response was noted only at very 
high (off-design) flow coefficients
2) The middle and downstream 
gauge locations responded more 
than the upstream location
3) Response is only at ~1.5-1.7 kHz 
Damping Summary
• On average, results showed blade critical damping 
ratios of 4-7% when operating in realistic conditions
• There was significant variation in damping estimates
• Different excitation methods resulted in different 
frequencies responding
• Damping increased from air to still water, and again 
from quiescent to spinning
• Damping had moderate correlation with response 
amplitude
• Damping had no significant correlation with cavitation 
number or flow coefficient (?!?)
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Acknowledgements
This test effort was sponsored by the SLS Liquid Engine Project 
Office at Marshall Spaceflight Center
MSFC Test Branch ET20 operated the facility and provided/installed 
instrumentation
MSFC Fluid Dynamics Branch ER42 designed strain gauge circuitry, 
generated requirements, conducted test and data acquisition, and 
performed data reduction/analysis
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BACKUP
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Critical Damping Ratio 
Analysis
Identify blade natural frequencies
Ping Test
• Filter data around natural frequency
• Compute amplitude envelope of blade response
• Compute critical damping with impulse response formula
Stator Test 
• Sweep shaft speed 
• Track strain response at 27N
• Compute pseudo-frequency response function with half-
quadratic gain formula
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Ping Data Analysis
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𝜇𝜇 𝑡𝑡 = 𝐴𝐴e−𝜁𝜁𝜔𝜔𝑛𝑛𝑡𝑡 cos 𝜔𝜔𝑑𝑑𝑡𝑡 + 𝜙𝜙
𝜁𝜁 = 11 + 𝜔𝜔𝑑𝑑𝛽𝛽 2
Single degree of freedom impulse response
𝜔𝜔𝑑𝑑 = 𝜔𝜔𝑛𝑛 1 − 𝜁𝜁2
Amplitude envelope
𝑋𝑋 𝑡𝑡 = 𝐴𝐴e−𝜁𝜁𝜔𝜔𝑛𝑛𝑡𝑡 = 𝐴𝐴e− 𝜔𝜔𝑑𝑑𝜁𝜁1−𝜁𝜁2 𝑡𝑡 = 𝐴𝐴e−𝛽𝛽𝑡𝑡log 𝑋𝑋 𝑡𝑡 = log 𝐴𝐴 − 𝛽𝛽𝑡𝑡
Ping Hydro Set Points
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~90-110% rated flow
Non-cav
to approaching breakdow
n
Damping vs Hydro Conditions
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Damping vs Flow Coeff Damping vs Cav Number


Estimating Inducer Blade Damping in Water with On-Blade Strain Measurements

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