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.