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A Charge-Based Magneto-Electric Test Procedure. Scott P. Chapman & Joseph T. Evans, Jr. Radiant Technologies, Inc. Aug 9, 2011 IWPMA 2011. Summary.
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A Charge-Based Magneto-Electric Test Procedure Scott P. Chapman & Joseph T. Evans, Jr. Radiant Technologies, Inc. Aug 9, 2011 IWPMA 2011
Summary The goal is to describe an experiment to characterize the charge response of a piezoelectric or multiferroic sample in the presence of a magnetic (B) field by: P = aH B = mH P = a/mB For a multiferroic, H induces P directly. For our piezoelectric sample, P results from direct force (dc) or torque (dt) applied to the sample ferroelectric.
Summary • I will present: • Mathematics and theory relating predictive and measured polarization response to the magnetic field and magnetic field geometry. • Experimental considerations. • Experimental design and configuration. • Measured results. • Measured comparison to predictive.
Magnetic Force • These three statements apply to understanding Magnetic Force: • Magnetic force is generated only by moving electric charges. • For two objects to exert magnetic force both must contain moving charges. • Magnetic force calculation proceeds as follows: • Calculate a mathematical field, H, that sums the motion of all charge particles at the point of interest in the field. • Multiply H by the magnetic permeability factor, m, to convert it to a force field, B. • Use B to calculate magnetic force on the target. This requires the calculation of both the HH coil force and the target force, and their multiplication.
Geometry Bsingle coil = m0NIR2 x 0.5(R2+x2)-3/2 (1) BHHC = 0.5 m0NIR2 / [(R2+(x+K/2)2)3/2+[(R2+(x-K/2)2) 3/2] (2) N = Number of Coils R = Coil Radius (m) I = Current Through Loop (Amps) K = Coil Separation (m) B = 0.716 m0NI/R (3) For: K = R and x = 0 (Centered Between Coils)
Plot Measured Charge Vs Field Arbitrary Data P H P is Measured but H may be inferred
Independent Field Values • The independent (Field) axis in the data presentation can be determined by: • Assumed Field by DRIVE Volts into the Current Amplifier. This experiment presented here uses this approach. • Assumed Field by Measured Current into the Helmholtz Coil. This reduces the number of error sources in the first option by half. • Field Measured Field by magnetic sensor. Most accurate.
Improved Test Configuration - Direct Field Measurement at Sample
Measured Piezo Constants • The constants we measured: • Parallel to the magnetic axis: • 61.2 pC/N (10 g = 0.98 N) • 71.4 pC/N (20 g = 1.96 N) • 71.4 pC/N (50 g = 4.9 N) • 68.0 pC/N (Average) • Torque: 765.0 pC/N • When applying magnetic torque, the force must be calculated from the lever arm length and then multiplied by the equivalent torque piezo constant
Primary Error Sources • There are three primary sources of error: • Frequency response of the current amplifier with the attached HH coil. Slow the measurement to ensure the amplifier can provide the requested HH coil input power. • Parasitic charge resulting from magnetic induction in the RETURN cable. This effect is reduced by slowing the measurement. Measure the effect and subtract from the final measurement. • Charge measurement accuracy reduced by charge deterioration over long tests. This effect is reduced by speeding the test.
Pre-Measurement Steps • To prepare for the Magneto-Electric Response Task measurement, perform these steps: • Calculate the magnetic field at the point where the sample is located. • Measure the induced current in the cable, under measurement test conditions, and retain to subtract from the measured data. • Reduce the test speed to reduce inductive current, but no slower than 1000.0 ms. • Determine through experimentation the maximum frequency and ensure 1/Test Period does not exceed this value.
Predictive Modelm || B - Centered in HH Coil Define, for our force inducing magnet: m = MV M = Magnetization of Magnet V = Volume For B || m F = Ñ[m ·B] (1) For constant m, as with our magnets: F = mdB/ dx (2) For constant B, as in the center of the Helmholtz coil: F = 0 => DQ = 0
Predictive Modelm ^B - Centered in HH Coil Piezo Constant: dt = 0.75 V x 100 pC/10g (Sense Capacitor) = 75 pC/0.098 N = 765 pC/N Ftorque (t): m = 4 x 1.08 T/4p x10-7 x (0.00252px 0.006) = 0.4 A/m Estimated Charge (DQ) at 45.0 Gauss: DQ = dt x 0.4 A/m x B / Height = 765 pC/N x 0.4 A/m x 45 e-4 T / 0.006 m = 229.5 pC
Predictive Model m ||B - At 1 K From Closest Coil x = 1.5 K = 1.5 R ÑB = -0.319 m0NI/R2 DQ = dc x 0.4 A/m x ÑB = d33 x 0.037 x I What is d33, is 0.037 the Amps/Gauss and How do I use this to predict DQ?
Predictive Modelm ^B - At 1 K From Closest Coil At x = 0: B = 0.716 m0NI/R => m0NI/R = B/0.716 = 45.0/0.716 = 62.85 G At x = 1.5 K = 1.5 R: BHHC = 0.5 m0NIR2/(R2+(x+K/2)2)3/2+ 0.5 m0NIR2/(R2+(x-K/2)2) 3/2 G = 0.5 m0NIR2/(R2+(1.5R + R/2)2)3/2+ 0.5 m0NIR2/(R2+(1.5R-K/2)2)3/2 = 0.1727 m0NI/R G = 10.855 G DQ = dt x 0.4 A/m x B / Height = 765 pC/N x 0.4 A/m x 10.855 e-4 T / 0.006 m = 55.36 pC/m3
Error Sources • Amps/DRIVE Volts conversion for the KEPCO 36-6M current amplifier. -1.75 Volts/Amp used. Expected current = 45.0 G X 0.0373 Amps/Gauss = 1.68 Amps. Post-data measurement showed 1.799 Amps. Generated 48.15 G. • Current/Gauss conversion for the Lakeshore MH-6 Helmholtz coil. Used the Lakeshore published conversion of 26.76 G/A => 0.0373 A/G. Did not measure the actual ratio. • Manual dc and dt measurements. • Unstable measurement surface. • Unfixed sample subject to bending an shear. • Joe, please add.
Conclusion • Radiant successfully tested the magneto-electric response of a piezoelectric force sensor coupled to a magnet using Radiant’s Magnetoelectric Response Task • The system was able to cleanly capture the measurements that generated 100 pC of Response • The sample response differed from our predictions but there were several possible error sources in the test fixture and predictive models.
