The EMFI-Transducer as a Force Sensor
Introduction. Electro Mechanical Films (EMFI) have found a variety of applications as transducers (e.g. sensor mats) and effecters (e.g. speakers). Basically the polymer film converts force into charge; quoted values are around 10 to 100 pC per Newton1. The charge will leak away at a rate determined by the time constant of the film and the electronic interface. If the the resistance and the capacitance of the film are given by R and C then the time constant may be supposed to be proportional to the product RC. Since R varies as 1/A with the area A of the film, whereas as C is proportional to the area, we expect the time constant to be independent of the area of the film. The fact that the EMFI-sensor reacts only to changes in pressure (or force) is not as such a principal obstacle for using them as pressure sensors because integrating the rate of change dx/dt over time we should get back the signal x(t). However, since the sensor acts as a highpass filter with a cutoff- frequency around 5 Hz this might limit its use for monitoring DC-signals. Also there is a question about the linearity of the sensor. Our measurements indicate that the amplitude of the response is not a linear function of the rate of change of the input.
Kistler, a well known manufacturer of force measurement devices using piezo transducers, has developed a technology which makes it possible to measure static forces with piezo transducers with a drift as low as 0.01 N/s. Piezo films however have some different characteristics than e.g.
quartz crystals, so one cannot automatically expect the same setup to work for these2. To our knowledge it has not been determined how far one could minimize the drift for piezo films without significantly compromising the sensitivity. Using the electronic interface (designed by VTT3) provided with the sensors, we found the time constant to be around 30 ms. This characterizes how fast the EMFI-device looses its "memory" of the impressed force. The slowest measurable change for piezo films is quoted to be aorund 0.001 Hz4.
Eight EMFI-sensors, all of the same design and shape, were used in a series of tests in order to evaluate their applicability as force or pressure sensors. Basically we tried to determine the transfer function of the film (considered as a "black box") by measuring the response to a steplike force.
Experimental setup. The basic setup was designed so as to produce a step-like force input. The force of a weight was transmitted to the sensor via a lever arm. The weight was released by cutting the supporting thread.
1 Actually the charge is drawn from the external circuit by the electric field produced by the deformation of the piezo material. We treat the EMFI-film here as a piezo film. For a review, and for references, on the theory and
experiments with propylene electrets-transducer see R Gerhard-Multhaupt: "Less can be more: Voids in polymers lead to a new paradim of piezoelectricity and to useful elcctret transducers", submitted to IEEE Transactions on Dielectrics and Electrical Insulation, and Mika Paajanen: The Cellular Propylene Electret Material –
Electromechanical Properties. (Thesis) VTT Publications 436 (2001).
2 We did not have the opportunity to test the use of charge amplifiers made by Kistler in combination with the EMFI- sensors. Kistler reports MOSFET leakage currents less than 0.03 pC/s for its charge amplifiers. For piezo quartz crystals it is possible to use charge amplifiers with impedance up to 1014 Ohm making quasistatic measurements possible (amplifier time constant up to 107 sec); for piezo ceramics however the time constant of the amplifier cannot be made to exceed 10 sec (E O Doebelin: Measurement Systems. Applications and Design. 4.ed., McGraw-Hill 1990: p. 775).
3 VTT Technical Research Center, Finland (www.vtt.fi). EMFI-related research has been done at VTT Chemical Technology, Tampere.
4 "Piezo Film Sensors". REV B 02 APR 99. Technical Specialities, Inc. < www.msiusa.com >.
The force acting on the film was independently measured using a strain gauge5. The following figure shows a typical result (units in Volt)6. A step-like change in the force (F) causes a rapid change in the EMFI-output (E) which then returns back to the resting level.
The EMFI-device as a highpass filter. We might expect that the EMFI-signal follows an exponential decay back to the resting level. This is verified if we try fitting the data using a function
(1) f(t)=a⋅eb⋅tc
as shown in the next figure. (For convenience we have changed the sign of the signal.) The fitted exponential curve (EF) coincides very well with the data (ES) using the parameters
5 Raute Precision BA5-10-C3.
6 For data acquisition we used National Instruments DAQ-card NI6036E and PCI-516 with 16-bit resolution.
EMFI
force transducer
to the DAQ system weight
0 1000 2000 3000 4000
1 1.5 2 2.5 2.809 3
1.258 En
Fn
3.999 10× 3
0 n
a = 1.08 V b = 32.68 s-1 c = -2.51 V
Thus, for the time constant we obtain in this case τ= 1/b = 31 ms. The time constant was found to be quite similar for all the sensors and in all the tests, which was also the case for the parameter c (the resting voltage level)7. Since the EMFI-sensors reacts to the changes in the force/pressure we assume that its output y(t) depends on the force x(t) according to (we set the resting value to zero here)
(2) y(t)=
∫
∞
t
h(tu) x(u)du =
∫
x(∞) x(t )
h(tu)dx(u)
where the transfer function h(t) vis à vis the derivative of x is given by
(3) h(t)=a⋅et⁄ τ(t>0) τ=b1
In frequency space (2) becomes (capital letters used for the Fourier transforms of the functions)
(4) Y( f )=i2π f⋅H ( f )⋅X ( f )
7 The response of the interfacing electronics was tested by directly feeding a steplike voltage (changing from 0 V to 4 V) using the Analog Output function of the DAQ-card. The response time was found to be less than 2 ms. The input impedance was measured to be around 84 Mohm (DC).
0 50 100 150 200 250 300
2.6 2.4 2.2 2 1.8 1.6 1.411
−
2.485
− ESk EFk
300
0 k
Therefore, the transfer function from the force signal to the EMFI-signal becomes
(5) Hxy( f )=i2π f⋅H ( f )=a i 2π f 1
τi 2π f
The transfer function (5) acts as highpass filter with a characteristic lower cutoff-frequency of
fc= 1
2π τ=5.2 Hz
if we adopt the above value of 31 ms for τ. The analogous RC-circuit is (with EMFI as a voltage generator):
Uin corresponds to the force input and Uout to the output EMFI-signal with the transfer function given by
(6) HRC( f )= i 2π f R C 1i2π f R C
One can use the RC-model of cell membranes (without the "battery") to model the basic EMFI-film characteristics (EMFI as a current generator). A charge Q over the capacitor at time t = 0 will – if there are no further excitations – leak away through the equivalent sensor resistance R according to
R QQ
C=0 → Q (t)=Q0e
t RC
Uin Uout
C
R
This leads to a relation of the form (2) between the output y (voltage) and the current (dQ/dt) which is assumed to proportional to rate of change of the compression, which in turn is assumed to be proportional to the rate of change of the impressed force, dx/dt.
A characteristic feature of the system (2-3) is that if we have a steadily increasing force; say dx/dt = d (a constant), then the EMFI-signal reaches a saturation level a d τ according to
(7) y(t)=a d τ⋅
(
1eτt)
which is illustrated in the figure (FK is the force, EK is the EMFI-signal) below:
As can be seen from the graph it takes about 0.1 second to reach an almost complete saturation. In reality the EMFI-sensor of course may behave approximately linearly only up to a certain force level.
Force from EMFI-data? The central issue here is whether it is possible to reconstruct the force signal from the EMFI-signal data. Mathematically it seems that we could obtain the force data x(t) from the EMFI-data y(t) simply by inverting the transducer function (5); that is, by first calculating
0 0.02 0.04 0.06 0.08 0.1
0 2 4 6 8 8.3 10
0
d b FKl
EKl
0.083
0 l⋅∆
Y(f) and then determine X(f) as Y(f)/Hxy(f), and finally obtain x(t) by taking the inverse Fourier transform of X(f). The figure below shows an example. F2 is the force output and FR is the
estimated force calculated by the method just explained (used scaling a = 1). Apparently, we have got an artificial trend in the estimated force. This can be partly remedied in the following way.
Integrating equ (2) above we get a new signal z(t) = h * y (t):
(8) z(t)=
∫
∞
t
y(s)ds=
∫
∞
t
h(tu)x(u) du
Thus, we can integrate numerically the EMFI-data y according to (8), then take the Fourier transform Z(f) of z(t), and finally calculate X(f) by
(9) X( f )=(1
τi2π f )⋅Z ( f )
Though mathematically equivalent to the previous procedure the integration of the measurement data produces a result that better follows the step-like change:
0 500 1000 1500 2000 2500
2 1 0 1 1.776 2
1.985
− FRn−FR0
F2n−F20
( )
2.047 10× 3
0 n
F2 is the force data and X is (scaling a = 1) the force estimated from the EMFI-data by the above method. The artifacts (peaks) at the ends of the estimation can be cut away. In the above calculation we have also used a Gaussian lowpass filter at step (9) of the form (σ = 100)
(10) Hl( f )=exp
(
2fσ22)
in order to suppress high frequency noise.
The modelling (2) presumes that the EMFI-sensor is to a good approximation linear in the measure- ment regime. This can be checked by performing measurements using weights of different sizes in the measurement setup and compare the step-size responses calculated using the method (8-9). For a linear sensor the step-size response should increase in proportion to the increase of the weight. Test series were performed using weights of masses 1.423 kg, 5.825 kg and 9.129 kg. The proportion between the first two weights is ca. 4.1 whereas e.g. for the sensor #6 the corresponding ratio between the calculated forces was about 2.4. None of the other sensors seemed to fare any better in terms of linearity8. Thus it seems that the charge build up in the EMFI is not proportional to the impressed force, instead there is some nonlinear relation making a in (3) a function of x. One could also expect a nonlinearity associated with the capacitance. Indeed, it is conceivable that a compression of the film may increase the capacitance and thus decrease the time constant. From listed key specifications of the EMFI we may assume an average Young's modulus of 0.5 MPa. The EMFI sensors used in the tests were circular with a diameter around 17.2 mm. Thus, a mass of 5 kg would correspond to a pressure of ca. 0.2 MPa which in turn would correspond to a compression of 0.2/0.5 = 40% and a similar change in the capacitance9. Curiously enough, no significant shift in the time constant was detected when we measured the impulse response for preloaded sensors with a preloading up to about 20 kg (about 0.8 MPa pressure)10. Only when using an "extreme" loading
8 Nonlinear properties of the EMFI have been studied e.g. by R Kressmann: "Linear and nonlinear piezoelectric response of charged cellular polypropylene". J. Appl. Phys., Vol. 90, No. 7 ( 2001).
9 The quoted Young's modulus seems indeed to be extremely small by comparision - the Young's modulus for PVC is about 2.7× 109 Pa which is more than three orders larger. The softness is due to the void cells in the EMFI.
10 In these measurements we placed the EMFI-sensor under a vertical wooden pole (ca 4.2 cm × 4.5 cm in cross- section) upon which we stacked the weights used for preloading. On top was placed a smaller weight of ca 2.7 kg
0 0.2 0.4 0.6 0.8
4 3 2 1 0 0.5
−4 F2n−F20 Xn
0.682
0 n⋅∆
around 40 kg did we indeed observe significant changes in the way the sensor output returned to the resting level. Thus, under "normal" conditions we may expect a transfer function of the form
(11) hx(t)=a(x)⋅e
t τ
where the amplitude factor a(x) is some decreasing function of the impressed force x. A simple ansatz would be to try a linear function a(x) =α -β x. Of course, there are further complications if we also have to drop the assumption in (2) that the response is linearly related to the rate of change dx/dt.
An alternative method to the Fourier method is to directly integrate (2) numerically. From this one may propose to calculate the force xk = x(tk) using
(12) xk1=xk1
a⋅
(
yke∆ tτ⋅yk1)
where∆t is the sampling time interval. This procedure could be quite straightforwardly extended to include nonlinearities by making a and τ dependent on xk in (12). The following figure shows an example using (12) (constant a = 4.3) to estimate the force (FI) from the EMFI-data as compared with the measured force F.
It should be clear that no mathematical "trick" can faithfully recover a slowly changing force (below 5 Hz) from the EMFI-signal, since, as the sensor acts as a highpass filter, the information about the
which was swiftly removed in order to produce a steplike change in the force acting on the sensor. The variation of the force was checked by sandwiching a resistive film (FlexiForce with a reported rise time < 20 µs) on top of the EMFI-film.
0.4 0.6 0.8
0.5 0 0.371
0.664
− Fn−F0 FIn
0.808
0.229 n⋅∆
slow components of the force are erased. Only a more advanced amplifier, if such one is feasible, could remedy the situation.
Preliminary conclusions. The EMFI sensors seem to require quite sophisticated signal processing and calibration routines if to be used as force transducers for measuring quasistatic force and still a high degree of accuracy is not to be expected. Physically this is due to the leakage problem. Could this problem be alleviated by an improved charge amplifier design? By comparison, using e.g.
resistive films for measuring force is much simpler. The resistive film consists basically of plastic material integrated with silver electrodes and grains of conductive material. We have successfully tested resistive films (FlexiForce) made by Tekscan11. These sensors come in a range from 100 lb to 1000 lb and have a linear behaviour with an error margin typically around ±5% according to the specifications, which is acceptable for biomechanical measurements.
One problem with film sensors is that the same total force may result in different outputs depending on how the force is distributed over the sensor surface.
In principle the EMFI-transducer could be used to measure quasistatic force if we make use of the fact that the amplitude of the response decreases with the force. If the sensor is subjected to a steady vibration, say around 200 Hz, the output will be an amplitude modulated (AM) signal whose amplitude variations should correlate with the impressed force. One might e.g. consider to place two EMFI-films on top of each other, one which works as an effecter and fed with 200 Hz AC, whereas the other works as the force transducer with an AM output.
One may also consider the EMFI-sensor as a basic component in a sensitive vibration sensor. By preloading the film with a mass and a spring it will pick up any vibrations transmitted to the mass.
Patent document. Kari Kirjavainen: "Electromechanical film and procedure for manufacturing same". United States Patent 4,654,546 (Mar. 31, 1987). Can be accessed at the US Patent Office website <http://www.uspto.gov/patft/index.html>.
EMFI key specifications. Data12 from www.emfit.net apply to the type of sensors used in our study:
11 www.tekscan.com
12 Recent measurements are reported in G S Neugschwandter et al.: "Piezo- and pyroelectricity of a polymer-foam space-charge electret". J. Appl. Phys., Vol. 89, No. 8 ( 2001).
The table below shows some results calculated from measurements conducted by Risto Rapila. Test results from sensor #5 were dropped because it seemed to be broken. The I-column cites measurements using the weight 1.423 kg, in II the weight 5.825 kg was used and in III the weight used was 9.129 kg.
I aII/aI II aIII/aI III
mean stdev mean stdev mean stdev
1 1 1 1 1 1
a 1,09 0,01 1,48 1,61 0,05 2,15 2,35 0,04
b -3,25 0,05 -3,15 0 -3,27 0,03
c -2,52 0 -2,46 0 -2,47 0
2 2 2 2 2 2
1,19 0,07 1,36 1,62 0,07 2,01 2,4 0,06
-3,36 0,03 -3,19 0,02 -3,27 0,02
-2,51 0 -2,47 0 -2,5 0,01
3 3 3 3 3 3
0,85 0,06 1,55 1,32 0,05 2,81 2,4 0,09
-3,16 0,07 -3,21 0,05 -3,21 0,02
-2,53 0,01 -2,47 0 -2,49 0
4 4 4 4 4 4
1,23 0,07 1,58 1,94 0,12 2,05 2,52 0,06
-3,37 0,13 -3,31 0,02 -3,35 0,04
-2,51 0,01 -2,5 0 -2,48 0,01
6 6 6 6 6 6
0,94 0,05 2,41 2,26 0,1 2,99 2,81 0,14
-3,2 0,05 -3,57 0,03 -2,87 0,2
-2,53 0 -2,48 0,01 -2,67 0,08
7 7 7 7
1,27 0,02 1,93 2,44 0,13
-3,3 0,01 -3,29 0,02
-2,52 0 -2,49 0
8 8 8 8 8 8
1,42 0,05 1,77 2,51 0,07 1,66 2,36 0,07
-3,45 0,03 -3,38 0,01 -3,25 0,06
-2,5 0 -2,48 0 -2,49 0,01
F0 2,79 3,76 4,47
F1 2,48 2,48 2,47
F1-F0 0,31 4,13 1,28 6,45 2
b in units of 1/10ms
thus the time constant = 10/b in term of ms data fitted using the equation: a*exp(b*t) + c F0 = initial force level in V
F1 = final force level in V
