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Vanderbilt University

Modal Parameter Estimation of hydraulic

Axial-piston pumps and Motors

Paul Kalbfleisch, Researcher

Purdue University

Monika Ivantysynova

Fluid Power Innovation & Research Conference

October 10-12, 2016

2FPIRC16

Vibro-

Acoustics

VibroacousticsRadiationPropagation

0 100 200 300

20

40

60

80

100

120

Displacement Chamber Pressure

Angle [°]

Pre

ssure

ΔP

[bar]

Pump noise modeling

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Project Overview Major

Objectives/Deliverables

Next Steps

• Goal: Incrementally validate noise

modeling techniques with experimental

results.

• CCEFP: Thrust Area 3, Effectiveness:

Noise and vibration, leakage,

contamination and human factors.

• Contribution: Understand the

generation of noise by swash plate

type axial piston machines.

• Handful of competing researchers.

• Large simulation errors

• Lack sufficient experimental

validation

• Complete experimental modal

analysis (month 3)

• Measure displacement chamber and

port pressures to verify current

hydraulic model (month 6)

• Can industry donate a laser

vibrometer?

• Set of measurements that include:

• Displacement chamber pressure

• Acceleration on the casing

• Modal parameter estimation

• Sound intensity

• Better understand how internal pressure

forces transmit to external audible noise

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Cremer, L., Heckl, M. and Petersson, B. A. T., 2005. Structure-borne Sound: Structural

Vibrations and Sound Radiation at Audio Frequencies. Berlin: Springer.

GenerationDisplacement

Chamber Pressures

Radiation Case to Air

Propagation Wave Travel

Transmission Active to passive

Structural Acoustic Process

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Task 1: Hydraulic model

GenerationDisplacement

Chamber Pressures

Telemetry

Transmitter

Antenna

AD data acquisition boardKeithley DAS 1802 ST

Pressure sensorKistler 60050 .. 1000 bar

Chargeamplifier

Signal converterManner telemetry

0 100 200 300

20

40

60

80

100

120

Displacement Chamber Pressure

Angle [°]

Pre

ssure

ΔP

[bar]

• Verify current hydraulic model in frequency domain for use

with vibration model

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Task 2: Vibration model

Propagation Wave Travel

Transmission Active to passive

• Experimental Modal analysis

• FEM model of the hydraulic pump case

• Utilize forces found in Task 1 for FEM analysis

• Compare measured pump case vibration to

simulation results

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Task 3: Acoustic model

Radiation Case to Air

Correlate surface vibrations with total sound power

• Measurement of sound power with robot

• Develop an acoustic model to predict

audible noise level based on case

vibration simulated by Task 2

8

Experimental Modal Analysis

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( )( )

( )

X wH w FRF

F w

• Basic Frequency Response Equation (SDOF)

( )H w FRF

(Avitabile, 2003)

Frequency (Hz)

ω2 ω3ω1

Magnitude

(g/N

)

Modal Analysis

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• Measure a structure’s dynamic properties

• Natural frequencies

• Damping ratios

• Residue (effective mass)

• Mode shapes

Measurement Setup

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Data Aquisition• Accelerometer

• Triaxial (X,Y, and Z)

• ±5000 m/s2 measurement range

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Collecting Valuable Data• Valuable Data

• Narrowing of the time sample

• Accessing the Valuable Information

• Data spikes relative to electrical noise floor

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Collecting Valuable Data

• Recording Accelerations

• From impact until specified % of max peak

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H1 Algorithm

*

1

avgN

GXF X F

• Cross Power Spectral Density

• Auto Power Spectral Density

*

1

avgN

GFF F F

• H1 Algorithm

• Minimizes Noise on the Output

1( )GXF

H wGFF

Finds Consistent Data Throughout

a Sample

Finds Consistent Data Between

Two Samples

Generates an Averaged

Frequency Response Function

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Modal Parameter Estimation

• Eigensystem Realization Algorithm

• Time Domain

• Low Order (few accelerometers)

• Multiple Reference

• Basic Equation

• Estimation

•Pseudo-Inverse

•Eigenvalue Decompisition1 2

1 2 1 0 0N N

N Nz z z

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Modal Analysis Results

• Frequency Response Function Example

• More than 1200 FRFs were recorded

- Accel 1

- Accel 2

- Accel 3

Natural

Frequencies

(Hz)

Damping

Ratios (% of

critical

damping)

50 99

671 98

1066 99

2103 82

2496 53

3529 2

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Modal Analysis Results

• Frequency Response Function Example

• More than 1200 FRFs were recorded

- Accel 1

- Accel 2

- Accel 3

Natural

Frequencies

(Hz)

Damping

Ratios (% of

critical

damping)

50 99

671 98

1066 99

2103 82

2496 53

3529 2

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Results (con’t)

• Increasing Amplitude for Z Axis

Red = Accel 1

Green = Accel 2

Blue = Accel 3

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Thank You

Any Questions?

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Mode Shapes

• Modal Shape at 2650 Hz

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Mode Shapes

• Modal Shape at 4900 Hz