Blocked Force DeterminationExplanation and ExamplesVibro-Acoustics Consortium Web Meeting
University of Kentucky
Vibro-Acoustics Consortium
April 16, 2020
Vibro-Acoustics Consortium
Overview
• Transfer Functions and Superposition
• What are Blocked Forces?
• Similar Approaches
• Example: Small Compressor attached to Structure
• Example: Engine Cover attached to Plate
• Example: Acoustic Duct
• Future Work
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Vibro-Acoustics Consortium 3
Transfer Functions
𝐹
𝑣
𝑣 𝐻 𝐹
𝐹𝑣 𝐻 𝐹
Vibro-Acoustics Consortium 4
Linear Systems and Superposition
𝐹
𝑣
𝐹 𝐹
𝑣 𝑣 𝑣 𝑣 𝑣
𝑣 𝐻 𝐹 𝐻 𝐹 𝐻 𝐹𝑣 𝐻 𝐹 𝐻 𝐹 𝐻 𝐹
𝑣 𝐻 𝐹 𝐻 𝐹 𝐻 𝐹⋮
𝑣 𝐻 𝐹
Vibro-Acoustics Consortium
Overview
• Transfer Functions and Superposition
• What are Blocked Forces?
• Similar Approaches
• Example: Small Compressor attached to Structure
• Example: Engine Cover attached to Plate
• Example: Acoustic Duct
• Future Work
5
Vibro-Acoustics Consortium 6
What Are Blocked Forces?
𝐹 𝑇 𝜔𝑣
𝑣
Vibro-Acoustics Consortium
Infinitely Stiff Bed Plate
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What Are Blocked Forces?
𝜔𝑣 𝐹 𝑇
𝐹
Vibro-Acoustics Consortium 8
What Are Blocked Forces?
𝜔𝑣 𝐹 𝑇
𝐹
𝑣 0
Vibro-Acoustics Consortium 9
What Are Blocked Forces?
𝐹
𝑣
Input Forces Removed
Vibro-Acoustics Consortium 10
What Are Blocked Forces?
𝐹
Blocked forces are independent of the receiver.
Vibro-Acoustics Consortium 11
Blocked Force Analysis
𝐹
𝑣
Vibro-Acoustics Consortium
Overview
• Transfer Functions and Superposition
• What are Blocked Forces?
• Similar Approaches
• Example: Small Compressor attached to Structure
• Example: Engine Cover attached to Plate
• Example: Acoustic Duct
• Future Work
12
Vibro-Acoustics Consortium 13
Classical Transfer Path Analysis
𝐹
𝑣
Vibro-Acoustics Consortium 14
Pseudo Force Analysis
𝐹
𝑣
Vibro-Acoustics Consortium 15
Force Identification Approaches
Measured Transfer FunctionsSource is “off”
Indicator ResponsesSource is “on”
Unknown Blocked ForcesInverse least squares
Vibro-Acoustics Consortium 16
Summary
Method Transfer Function Measurement
Inverse Force Locations
Can Inverse Forces be Used with Modified Receiver?
Classical TPA Remove Source Interface between Source and Receiver
If Source is well Isolated
Blocked Forces Include Source Interface between Source and Receiver
Yes
Pseudo Forces Include Source User Decided Maybe
Vibro-Acoustics Consortium
Overview
• Transfer Functions and Superposition
• What are Blocked Forces?
• Similar Approaches
• Example: Small Compressor attached to Structure
• Example: Engine Cover attached to Plate
• Example: Acoustic Duct
• Future Work
17
Vibro-Acoustics Consortium
Source and Test Structure
Indicator response Target response
1.6 mm Steel
Air CompressorCompressor
0.6 m x 0.6 m
• Classical TPA, pseudo force and blocked force methods are used to predict target response.
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Vibro-Acoustics Consortium 19
Compressor
Blocked Force Locations
Vibro-Acoustics Consortium 20
Input Force Locations
Compressor 20.5 cm 9 cm
22.5 cm
29.5 cm
10 cm
3.5 cm
10 cmClassical TPA Blocked Forces
• For Classical TPA, transfer functions are measured with compressor removed from steel plate.
Vibro-Acoustics Consortium 21
Input Force Locations
001 002003
004 005 006
X
Y
Z
Compressor
• For pseudo force method, 6 input force points should capture all 3 translational and 3 rotational motions of compressor.
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Acceleration Target Comparison
-80
-60
-40
-20
0
20
4012
.5 16 20 2531
.5 40 50 63 80 100
125
160
200
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
Acce
lera
tion
(dB)
Frequency (Hz)
MeasurementClassical TPA8 Blocked Forces4 Blocked ForcesPseudo Forces
Vibro-Acoustics Consortium
Baseline Modified
Modification Added Mass
Compressor
Steel Plate
Steel Frame
Compressor
5 kg Mass
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Vibro-Acoustics Consortium
Measurement Case Target Comparison
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-80
-60
-40
-20
0
20
4012
.5 16 20 2531
.5 40 50 63 80 100
125
160
200
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
Acce
lera
tion
(dB)
Frequency (Hz)
Measurement ModifiedMeasurement Baseline
Vibro-Acoustics Consortium
Measurement Case Results Comparison
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-80
-60
-40
-20
0
20
4012
.5 16 20 2531
.5 40 50 63 80 100
125
160
200
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
Acce
lera
tion
(dB)
Frequency (Hz)
Measurement Modified
Blocked Force Modified
Classical TPA Modified
Pseudo Force Modified
Vibro-Acoustics Consortium
Recommendations
• A spacing (𝑠) of 𝑠 0.5𝜆 is recommended along an interface for plate and shell structures where 𝜆 is the bending wavelength. This spacing has been validated using FEM analyses.
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Vibro-Acoustics Consortium
Overview
• Transfer Functions and Superposition
• What are Blocked Forces?
• Similar Approaches
• Example: Small Compressor attached to Structure
• Example: Engine Cover attached to Plate
• Example: Acoustic Duct
• Future Work
27
Vibro-Acoustics Consortium
Engine Cover
• Engine cover (receiver) is bolted on a plastic plate (source)
0.65 m
0.2 m
0.1 m
2.5 mm thick
Vibro-Acoustics Consortium
Measurement Setup
Foam
Shaker
Engine Cover
Plastic Plate
• Electromagnetic shaker is used to excite plastic plate.• Assembled system is placed on foam to simulate free-free boundary
condition.
Vibro-Acoustics Consortium
Blocked Force Determination
• 14 blocked force input points are chosen on the bolts in normal direction.• 21 indicator points are evenly spaced on engine cover.• 7 target points are chosen on engine cover
Blocked force input points
Target response points
101102103104105106107108
109
110 111 112 113 114
Vibro-Acoustics Consortium
Correlated Single Target Comparison
-80
-60
-40
-20
0
20
0 500 1000 1500 2000
Acce
lera
tion
(dB)
Frequency (Hz)
MeasurementBlocked Force
Vibro-Acoustics Consortium
Correlated Target Average Comparison
Average acceleration level of 7 target points is compared between measurement and blocked force prediction.
0.01
0.10
1.00
10.0050 63 80 10
012
516
020
025
031
540
050
063
080
010
0012
5016
0020
0025
0031
50
Acce
lera
tion
(m/s
2 )
Frequency (Hz)
Measurement14 Blocked Forces11 Blocked Forces8 Blocked Forces5 Blocked Forces2 Blocked Forces
Vibro-Acoustics Consortium 33
• Phase is not included in the calculation.
Uncorrelated Blocked Force
𝑎 𝐻 𝐹
Vibro-Acoustics Consortium
0.01
0.10
1.00
10.0050 63 80 10
012
516
020
025
031
540
050
063
080
010
0012
5016
0020
0025
0031
50
Acce
lera
tion
(m/s
2 )
Frequency (Hz)
Measurement14 Blocked Forces11 Blocked Forces8 Blocked Forces5 Blocked Forces2 Blocked Forces
Uncorrelated Target Average Comparison
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Vibro-Acoustics Consortium
Measurement Case Modification
• Cylinder shaped mass is glued on engine cover to reduce acceleration level.• The added mass is about 1/4 of the engine cover.• Can uncorrelated blocked forces be used to predict the effect of a modification?
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Vibro-Acoustics Consortium
Uncorrelated Averaged at Targets
0.01
0.10
1.00
10.00
50 63 80 100
125
160
200
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
Acce
lera
tion
(m/s
2 )
Frequency (Hz)
Measurement BaselineMeasurement Modified
0.01
0.10
1.00
10.00
50 63 80 100
125
160
200
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
Acce
lera
tion
(m/s
2 )
Frequency (Hz)
8 Blocked Forces Baseline8 Blocked Forces Modified
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Vibro-Acoustics Consortium
Recommendations
• A spacing (𝑠) of 𝑠 0.5𝜆 is recommended along an interface for plate and shell structures where 𝜆 is the bending wavelength. This spacing has been validated using FEM analyses.
• Once 𝑠 0.5𝜆 , it is recommended to use uncorrelated forces.
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Vibro-Acoustics Consortium
Overview
• Transfer Functions and Superposition
• What are Blocked Forces?
• Similar Approaches
• Example: Small Compressor attached to Structure
• Example: Engine Cover attached to Plate
• Example: Acoustic Duct
• Future Work
38
Vibro-Acoustics Consortium 39
Acoustic Blocked Source Analysis
Transfer Functions
Output Response Pressure Volume Velocities - Acoustic Blocked Forces
Vibro-Acoustics Consortium
Reconstructed Input Source Layer
0.1 m 0.1 m 0.2 m 0.2 m
Output Response Pressure Layers
40
• Input source layer has 6 reconstructed sources• Each output response layer has 6 indicators and 1 target.
Acoustic Duct
Source Room
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Measurement Case Baseline Setup
0.7 m 0.7 m 1.2 m
Vibro-Acoustics Consortium 42
Transfer Function Measurement
0.3 m
• Reciprocity method is used to calculate transfer function.• A reference microphone is placed 0.3 m away from the volume source
to calculate the volume velocity.
0.3 m 0.3 mPoint Source
Vibro-Acoustics Consortium 43
Correlated Targets Comparison
30
40
50
60
70
80
90
100
110
50 63 80 100
125
160
200
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000
6300
8000
Soun
d Pr
essu
re L
evel
(dB)
Frequency (Hz)
Measurement5 Blocked Sources3 Blocked Sources1 Blocked Sources
Vibro-Acoustics Consortium 44
Uncorrelated Targets Comparison
30
40
50
60
70
80
90
100
110
50 63 80 100
125
160
200
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000
6300
8000
Soun
d Pr
essu
re L
evel
(dB)
Frequency (Hz)
Measurement5 Blocked Sources3 Blocked Sources1 Blocked Sources
Vibro-Acoustics Consortium 45
Modification Lined Duct
• A lined duct (5 cm fiberglass) is connected to the baseline case• Reconstructed acoustic blocked forces for baseline will be used to
predict sound pressure level for modification case
1 m
Vibro-Acoustics Consortium 46
Correlated Targets Comparison
30
40
50
60
70
80
90
100
11050 63 80 10
012
516
020
025
031
540
050
063
080
010
0012
5016
0020
0025
0031
5040
0050
0063
0080
00
Soun
d Pr
essu
re L
evel
(dB)
Frequency (Hz)
BaselineModified5 Acoustic Blocked Sorces3 Acoustic Blocked Sorces1 Acoustic Blocked Sorces
Vibro-Acoustics Consortium 47
Uncorrelated Targets Comparison
30
40
50
60
70
80
90
100
11050 63 80 10
012
516
020
025
031
540
050
063
080
010
0012
5016
0020
0025
0031
5040
0050
0063
0080
00
Soun
d Pr
essu
re L
evel
(dB)
Frequency (Hz)
BaselineModified5 Acoustic Blocked Sorces3 Acoustic Blocked Sorces1 Acoustic Blocked Sorces
Vibro-Acoustics Consortium 48
Summary
• A spacing (𝑠) of 𝑠 0.5𝜆 is recommended along the cross-section where 𝜆 is the acoustic wavelength.
• Once 𝑠 0.5𝜆 , it is recommended to use uncorrelated acoustic sources.
Vibro-Acoustics Consortium
Overview
• Transfer Functions and Superposition
• What are Blocked Forces?
• Similar Approaches
• Example: Small Compressor attached to Structure
• Example: Engine Cover attached to Plate
• Example: Acoustic Duct
• Future Work
49
Vibro-Acoustics Consortium
Future Work
• Use response measurements for source diagnostics.
𝐹
𝑣
50
Vibro-Acoustics Consortium
Future Work
𝑣
Machine Under Test
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Vibro-Acoustics Consortium
Future Work
• Blocked forces characterize a source with its isolators irrespective of the receiver substructure.
𝐹
𝑣
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Vibro-Acoustics Consortium
References
• Moorhouse, A. T., Elliot, A. S., and Evans, T. A., “In-situ Measurements of the Blocked Force of Structure-Borne Sound Sources,” Journal of Sound and Vibration, Vol. 325, No. 4-5, pp. 679-685 (2009).
• Lennström, D., Olsson, M., Wullends, F., and Nykänen, A., “Validation of the Blocked Force Method for Various Boundary Conditions for Automotive Source Characterization,” Applied Acoustics, Vol. 102, pp. 108-119 (2016).
• Chen, K. and Herrin, D. W., “Technical Note – Blocked Force Determination on Plate Structures using an Offset Interface,” Applied Acoustics, Vol. 158, Paper No. 107044 (2020).
• Chen, K., Herrin, D. W., and Baker, J. R., “Determination of Correlated and Uncorrelated Blocked Forces on an Engine Valve Cover,” Noise-Con 2019, San Diego, CA, August 26-28 (2019).
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