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Patrick Timmons
Calibration Systems Engineer
New Long Stroke Vibration Shaker Design using Linear Motor Technology
Mark Schiefer
Senior Scientist
The Modal Shop, Inc. A PCB Group Company
Long Stroke Shaker
TMS Model 2129E025
25 cm
Sensor
Mounting
Platform
Accelerometers - Piezoelectric
o Inertial Measurement – Change in Velocity
Ground
Power/Output
Inertial Mass
Piezoelectric
Crystals
Housing
+ + + +
- - - -
+ + + +
- - - -
Preload
Ring
Built-In Microelectronics
Traditional Calibration Shakers
o Air Bearing Shaker
• Superior transverse performance
• Limited displacement: 10 mm
• Broader frequency range
o Flexure Shaker • Limited displacement:
25.4mm
• Sub-optimal transverse performance
• Higher payload capability
Traditional Calibration Shakers
o External amplifier provides current to AC coil
o Amplitude control either open loop or iterative control loop • Iterative control
acceptable at high frequency – significant run time increase with low frequency test points
Back To Back Calibration
o Generate known acceleration level
• Calculate ratio of test accelerometer voltage to test g level
Low Frequency Calibration
o Inherent challenges to low frequency calibration
• Stroke length limits sensor output
• Lower frequency test points drastically increase calibration time
• The effect of transverse motion must be characterized to account
for the contribution to system uncertainty
Frequency and Displacement
o a(t)=-(Xω2)Sin(ωt+φ) Where:
• a(t) = acceleration
• t = time
• ω = angular frequency
• φ = phase
• X = displacement
1 o a(t)=X(2πf)2
Where:
• a(t)= acceleration
• f = frequency
• X = displacement
ω=(2πf)
o Acceleration is proportional to displacement by the square of the frequency
Frequency and Displacement
Acceleration (gPeak)
Frequency (Hz)
Required Displacement (mmpeak-peak)
1 1000 0.00497
1 100 0.0497
1 5 19.87
1 0.5 1987
o For constant acceleration, required displacement increases exponentially with decreasing frequency
Linear Motor
Permanent Magnets
Axial View
Hall Effect Sensors
Forcer with Electromagnetic Coils
Linear Motor
o “Unfolded” rotary electric motor
o 3 Electromagnetic coils/ 3 phases
o Control loop provides vertical support system for armature
Optical Feedback
Optical Encoder Read Head
Scale Tape:
20um pitch
Optical Feedback
o Servo loop control for real time positional control
o Axis homing with integrated limit switch
o Processed quadrature output generates incremental positional output as calibration signal
Signal Processing Considerations
o Servo system closed loop control: High frequency noise present in system
o Signal processing must be narrow band
Air Bearings
o Porous Graphite
• Low flow compared to channel type air bearings
o High Stiffness
• Decrease in ride height increases
stiffness
o Low Friction
• Eliminates “stick slip” at motion reversal
Transverse Sensitivity
o Motion not directed along the direction of travel produces an output from the test accelerometer
o Typically
specified to less than 5%
Transverse Sensitivity
Transverse Performance
o Measurement of transverse motion of the armature via tri-axial accelerometer
Transverse Performance
0%
50%
100%
150%
200%
250%
300%
350%
400%
450%
100 120 140 160 180 200 220 240 260 280
Tra
nsv
ers
e (
%)
Frequency (Hz)
Transverse Motion 2129E025
o Experimental Data
• Peak at approx 190 Hz
Transverse Performance
o Theoretical model estimate: 217 Hz - first bending mode
o Assumed rigid boundary conditions
Transverse Motion
0%
20%
40%
60%
80%
100%
120%
0.1 1 10 100 1000
Tra
nsv
ers
e M
oti
on
(%
)
Frequency (Hz)
Transverse Motion 2129E025
490
590
690
790
890
990
1090
1190
1290
0.1 1 10 100 1000
Sen
sit
ivit
y (
mV
/g)
Frequency (Hz)
Calibration of Q353B51
Optical Encoder
Laser Primary
Back to Back
Random Uncertainty
o Single Mounting – Reduces the effect of transverse sensitivity
o Temperature controlled environment approx ±1 deg C
o Relative Standard Deviation – measure of precision
o RSD(%)=(σ/x̄)*100
• Where:
• σ = Standard Deviation
• x̄ = Mean
Random Uncertainty
0.001
0.01
0.1
1
10
0.1 1 10 100 1000
Rela
tive
Sta
nd
ard
De
via
tio
n (
%)
Frequency (Hz)
Comparison of Relative Standard Deviation of 113AB 6.25" Stroke and 2129E025 10" Long Stroke Shakers
2129E025 Optical
113AB B2B
2129E025 B2B
Calibration Time
o Frequencies (Hz) – Back to Back Reference Accelerometer
• 0.1, 0.2, 0.3, 0.4, 0.5, 0.7, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 110,
120, 130, 140, 150, 160
0
10
20
30
40
50
60
Tim
e (
Min
ute
s)
Traditional Iterative Control Loop
2129E025 Long Stroke Shaker
Calibration Time
o Frequencies (Hz) – Optical Encoder Reference
• 0.1, 0.2, 0.3, 0.4, 0.5, 0.7, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, 10
0
10
20
30
40
50
60
Tim
e (
Min
ute
s)
Traditional Iterative Control Loop
2129E025 Long Stroke Shaker
Summary
o The 2129E025 long stroke shaker provides linear excitation for accelerometer calibration.
o Stroke length becomes critical with decreasing frequency in generating adequate output from the test accelerometer.
o Optical encoder operation in limited in frequency by the structural rigidity of the linear stage.
o The random uncertainty of calibration is reduced with the utilization of the displacement based encoder signal.
o An optical encoder used in a servo feedback loop drastically reduces calibration times.