Figure 1 illustrates the cross-section of a typical quartz force sensor. This
particular sensor is a General Purpose 208 Series compression/tension model
with built-in electronics.
Figure 1: Compression-Tension-Impact Series 208
When force is applied to this sensor, the quartz crystals generate an
electrostatic charge proportional to the input force. This output is collected
on the electrodes sandwiched between the crystals and is then either routed
directly to an external charge amplifier or converted to a low impedance
voltage signal within the sensor. Both these modes of operation will be
examined in the following sections.
CONVENTIONAL CHARGE OUTPUT SENSORS
A charge mode piezoelectric force sensor, when stressed, generates a high
electrostatic charge from the crystals. This high impedance charge must be
routed through a special "low noise" cable to an impedance converting amplifier
such as a laboratory charge amplifier or source follower for recording
purposes. Connection from the sensor directly to a readout device such as an
oscilloscope is possible for high frequency impact indication, but is not
suitable for most quantitative force measurements.
The primary function of the charge or voltage amplifier is to convert the high
impedance charge output to a usable low impedance voltage signal for recording
purposes. Laboratory charge amplifiers provide added versatility for signal
normalization, ranging and filtering. PCB's "electrostatic" charge amplifiers
have additional input adjustments for quasi static measurements, static
calibration and drift-free dynamic operation. Miniature in-line amplifiers are
generally of fixed range and frequency.
Quartz charge mode force sensors with fallen insulators can be used at operating
temperatures up to 400°F (204°C).
When considering the use of charge mode systems, remember that the output from
the crystals is a pure electrostatic charge. The internal components of the
force sensor and the external electrical connector maintain a very high
(typically 10el3 ohm) insulation resistance so that the electrostatic charge
generated by the crystals does not "leak away". Consequently, any connectors,
cables or amplifiers used must also have a very high insulation resistance to
maintain signal integrity. Environmental contaminants such as moisture, dirt,
oil, or grease can all contribute to reduced insulation, resulting in signal
drift and inconsistent results.
Use of special "low noise" cable is required with charge mode force sensors.
Standard, two-wire or coaxial cable when flexed, generates an electrostatic
charge between the conductors. This is referred to as "triboelectric noise" and
cannot be distinguished from the sensor's crystal electrostatic output. "Low
noise" cables have a special graphite lubricant between the dielectric shield
which minimizes the triboelectric effect.
Figures 2 and 3 show a typical charge amplifier system schematic including:
sensor, low noise cable, and charge amplifier.
Figure 2: Charge Mode System Schematic
Figure 3: Charge Mode System
ICP LOW IMPEDANCE QUARTZ FORCE SENSORS
ICP force sensors incorporate a built-in MOSFET microelectronic amplifier to
convert the high impedance charge output into a low impedance voltage signal
for recording. ICP sensors, powered from a separate constant current source,
operate over long ordinary coaxial or ribbon cable without signal degradation.
The low impedance voltage signal is not affected by triboelectric cable noise
Figure 4: ICP Sensor System Schmatic
Power to operate ICP sensors is generally in the form of a low cost, 24-27 VDC,
2-20 mA constant current supply. Figure 4 schematically illustrates a typical
ICP sensor system. PCB offers a number of AC or battery-powered, single or
multi-channel power/signal conditioners, with or without gain capabilities for
use with force sensors. (See Related Products Section of this catalog for
available models.) In addition, many data acquisition systems now incorporate
constant current power for directly powering ICP sensors. Because static
calibration or quasi-static short-term response lasting up to a few seconds is
often required, PCB manufactures signal conditioners that provide DC coupling.
Figure 5 summarizes a complete 2-wire ICP system configuration.
Figure 5: Typical ICP Sensor System
In addition to ease of operation, ICP force sensors offer significant advantages
over charge mode types. Because of the low impedance output and solid-state,
hermetic construction, ICP force sensors are well suited for continuous,
unattended force monitoring in harsh factory environments. Also, ICP sensor
cost-per-channel is substantially lower, since they operate through standard,
low-cost coaxial cable, and do not require expensive charge amplifiers.
The output voltage polarity of lCP force sensors is positive for compression and
negative for tension force measurements. The polarity of PCB charge mode force
sensors is just opposite: negative for compression and positive for tension.
This is because charge output sensors are usually used with external charge
amplifiers that exhibit an inverting characteristic. Therefore, the resulting
system output polarity of the charge amplifier system is positive for
compression and negative for tension; same as for an ICP sensor system.
(Reverse polarity sensors are also available.)
WHY ONLY DYNAMIC FORCE CAN BE MEASURED WITH PIEZOELECTRIC FORCE SENSORS
The quartz crystals of a piezoelectric force sensor generate an electrostatic
charge only when force is applied to or removed from them. However, even though
the electrical insulation resistance is quite large, the electrostatic charge
will eventually leak to zero through the lowest resistance path. In effect, if
you apply a static force to a piezoelectric force sensor, the electrostatic
charge output initially generated will eventually leak back to zero.
The rate at which the charge leaks back to zero is dependent on the lowest
insulation resistance path in the sensor, cable and the electrical
resistance/capacitance of the amplifier used.
In a charge mode force sensor, the leakage rate is usually fixed by values of
capacitance and resistance in the low noise cable and external charge or source
follower amplifier used.
In a force sensor with built-in ICP electronics, the resistance and capacitance
of the built-in ICP electronics normally determines the leakage rate.
When a rapid dynamic force is applied to a piezoelectric force sensor, the
electrostatic charge is generated quickly and, with an adequate discharge time
constant, does not leak back to zero. However, there is a point at which a slow
speed dynamic force becomes quasi-static and the leakage is faster than the
rate of the changing force. Where is the point at which the force is too slow
for the piezoelectric force sensor to make the measurement? See the next
section on Discharge Time Constant for the answer.
DISCHARGE TIME CONSTANT (DTC)
When leakage of a charge (or voltage) occurs in a resistive capacitive circuit,
the leakage follows an exponential decay. A piezoelectric force sensor system
behaves similarly in that the leakage of the electrostatic charge through the
lowest resistance also occurs at an exponential rate. The value of the
electrical capacitance of the system (in farads), multiplied by the value of
the lowest electrical resistance (in ohms) is called the Discharge Time
Constant (in seconds).
DTC is defined as the time required for a sensor or measuring system to
discharge its signal to 37% of the original value from a step change of
measurand. This is true of any piezoelectric sensor, whether the operation be
force, pressure or vibration monitoring. The DTC of a system directly relates
to the low frequency monitoring capabilities of a system and, in the case of
force monitoring, becomes very important as it is often desired to perform
DTC CHARGE MODE SYSTEM
In a charge mode system, the sensors do not contain built-in amplifiers,
therefore, the DTC is usually determined by the settings on an external charge
amplifier. A feedback resistor working together with a capacitor on the
operational amplifier determines the time constant. PCB Series 460 Charge
Amplifiers feature short, medium and long time constant switch from which DTC
is selected. It is assumed that the electrical insulation resistance of the
force sensor and cable connecting to the charge amplifier are larger than that
of the feedback resistor in the charge amplifier; otherwise, drift will occur.
Therefore, to assure this, the force sensor connection point and cable must be
kept clean and dry.
LOW FREQUENCY RESPONSE OF ICP SYSTEMS
With ICP sensors, there are two factors which must be considered when making low
frequency measurements. These are:
The discharge time constant characteristic of the force sensor.
The discharge time constant of the AC coupling circuit used in the signal
conditioner. (If DC coupling is used, only the above (1) need to be
It is important that both factors be readily understood by the user to assure
accurate low frequency measurements.
DTC IN ICP FORCE SENSORS
The DTC is fixed by the components in the ICP sensors internal amplifier.
Specifications for the ICP force sensors shown in this catalog list the DTC for
each force sensor.
When testing with ICP sensors, there are two time constants that must be
considered for low frequency determination, one being that of the sensor which
is a fixed value, and the other that of the coupling electrical circuit used in
the signal conditioner.
When an ICP sensor is subjected to a step function input, a quantity of charge,
Δq, is produced proportional to the mechanical input. According to the law
of electrostatics, output voltage is ΔV = Δq/C where C is the total
capacitance of the sensing element, amplifier, and ranging capacitor. This
voltage is then amplified by the MOSFET amplifier to determine final sensor
sensitivity. After the initial step input, the charge signal decays according
to the equation q = Qe-t/RC where:
q = instantaneous charge (pC)
Q = initial quantity of charge (pC)
R = Bias resistor value (ohms)
C = Total capacitance (pF) t = time after t0
e = base of natural log (2.71 8)
This equation is also graphically represented in Fig. 6 below:
Figure 6: Standard DTC Curve
The product of R and C represents the DTC (in seconds) of the sensor. Sensor
time constants vary from just a few seconds to >2000 seconds for standard
sensors. Special time constants can be supplied by altering the resistor value,
R, in the sensors built-in microelectronic amplifier.
Most readout instruments have a high input impedance, >1 Megohm. For these
systems, the sensor DTC as previously discussed becomes the dominant value and
can be used in determining signal discharge rate. However, for signals coupled
to low impedance readout devices, generally <1 Megohm, it is necessary to
determine the system time constant. This will be explained further in the
SIGNAL CONDITIONER & READOUT TIME CONSTANTS
The external power supply used with an ICP force sensor may also have a DTC
associated with it. In some ICP signal conditioners, which feature internal
buffer amplifiers or gain amplifiers, the time constant is fixed by various
internal components and may be shorter, or longer, than the sensor DTC. In
signal conditioners with capacitive-coupled outputs, the DTC is not fixed. In
this case, a capacitor used to decouple a ICP force sensor bias voltage acts
with the input impedance of the readout device to create another time constant.
Check the specifications of the signal conditioner to determine if it has a
fixed internal DTC, which sets the low frequency response, or if it has a
capacitive-coupled output. If the output is capacitive-coupled, the time
constant, when fed into the input of the readout can be calculated as follows:
DTC = input impedance of readout x value of power supply coupling capacitor
Note that the output of some capacitive-coupled ICP power conditioners feature a
shunt resistor that overrides the effects of the input resistance of the
readout device if it is 1 Megohm or greater.
AC coupling in the readout device is also an additional type of DTC. Check
specifications for the power conditioners and readout instrument to be sure
they are suitable for your particular dynamic measurement. If you have more
than one DTC in the system, a time constant that is significantly shorter than
the others will usually dominate. Determination of the system DTC for
oscillating and transient inputs can be calculated from these equations:
The TCr, or readout discharge time constant, is calculated from the product of
the ICP power supply coupling capacitor and the readout input impedance, in
seconds. To avoid potential problems, it is recommended to keep the coupling
time constant at least 10 times longer than the sensor time constant. The
discharge time constant of the ICP sensor determines the low frequency response
of the system. It is analogous to a first order high pass RC filter. The
theoretical lower corner cutoff frequency (fc) is illustrated in Fig. 7 below,
and can be calculated from the following relationships:
3 dB down: fc = 0.16/DTC
10% down: fc = 0.34/DTC
5% down: fc = 0.5/DTC
Figure 7: Transfer Characteristics of an ICP Sensor
LONG DURATION EVENTS AND DTC
It is often desired to measure an input pulse lasting a few seconds in duration.
This is especially true with force sensor applications where static calibration
or quasi-static measurements take place. (Before performing tests of this
nature, it is important to DC couple the entire monitoring system to prevent
rapid signal loss. PCB 484 Series signal conditioners have AC/DC mode of
operation and are designed for such applications.)
The general rule of thumb for such measurements is that the output signal loss
and time elapsed over the first 10% of a DTC have a one to one relationship. If
a sensor has a 500 second DTC, over the first 50 seconds, 10% of the original
input signal will have decayed. For 1% accuracy, data should be taken in the
first 1% of the DTC. If 8% accuracy is acceptable, the measurement should be
taken within 8% of the DTC, and so forth. Figure 8 graphically demonstrates
Figure 8: Step Function Response
Left unchanged, the signal will naturally decay toward zero. This will take
approximately 5 DTC. You will notice that after the original step impulse
signal is removed, the output signal dips below the base line reference point
(t0+.01 TC). This negative value is the same value as has decayed
from the original impulse. Further observation will reveal that the signal,
left untouched, will decay upwards toward zero until equilibrium in the system
FORCE SENSOR NATURAL FREQUENCY
Unlike the low frequency response of the sensor, which is determined
electrically through the DTC = RC equation, the high frequency response is
determined mechanically from the sensor components. Each force sensor has an
unloaded resonant frequency specification which should be observed when
determining upper linear limits of operation. The linear response of force
sensors is generally considered to be to 20% of this resonant frequency value.
Proper installation of sensors is essential for accurate dynamic measurements.
Although rugged PCB quartz force sensors are forgiving to some degree, certain
basic procedures should be followed.
Since most PCB force sensors are designed with quartz compression plates to
measure forces applied in an axial direction, aligning the sensor and contact
surfaces to prevent edge loading or bending moments in the sensor will produce
better dynamic measurements.
Having parallelism between the sensor and test structure contact surfaces
minimizes bending moments and edge loading. Flatness of mounting surfaces will
also affect the quality of the measurement. Using a thin layer of)lubricant on
mounting surfaces during installation, creates better contact between sensor
and mounting surface.
The mounting surfaces on PCB force sensors are lapped during their manufacture
to ensure that they are flat, parallel and smooth. Ring style force sensors are
supplied with antifriction washers to minimize shear loading of the sensor
surface when torquing between two surfaces.
Loading to the entire force sensor sensing surface is also important for good
measurements. However, this can be difficult if the surface being brought into
contact with the for sensor is flat but not parallel to the sensor mounting
surface. In this case, an intermediate curved surface ran lessen edge loading
affects. (See Figure 9)
Figure 9: Edge loading vs. center loading
PCB Series 208 force sensors are supplied with a convex curved impact cap to
help spread the forces over the entire surface of the force sensor.
One other consideration when mounting force sensors is try to minimize
unnecessary mechanical high frequency shock loading of the sensors. The high
frequency content of direct metal-to-metal impacts can often create short
duration, high "g" overloads in structures and sensors. This problem can be
minimized by using a thin damping layer of a softer material on the interface
surface between the structure and sensor being impacted. (It should be
considered beforehand whether the slight damping of the high frequency shock is
critical to the force measurement requirements.) The impact surface on Series
200 and the impact caps on Series 208 Force Sensors are supplied with thin
layers of damping material.
PRELOADING FORCE RINGS
PCB ring style force sensors are generally installed between two parts of a test
structure with an elastic beryllium copper bolt or stud. This stud holds the
structure together and applies preload to the force ring. In this type of
installation, part of the force between the two structures is shunted through
the mounting stud. This may be up to 5% for the beryllium copper stud supplied
with the instrument and up to 50% for steel studs. If a stud other than
beryllium copper is used, it is crucial that ring sensors be calibrated in a
preloaded state to assure accurate readings and linearity throughout the entire
working range of the sensor.
PCB in-house calibration procedure requires the installation of a force ring
with BeCu stud in series with a NIST traceable proving ring. A preload of 20%
(full scale operating range of the force ring) but not less than 10 lbs, is
applied prior to recording of measurement data. Allow the static component of
the signal to discharge prior to calibration.
TYPICAL PIEZOELECTRIC SYSTEM OUTPUT
The output characteristic of piezoelectric sensors is that of an AC coupled
system, where repetitive signals will decay until there is an equal area above
and below the original base line. As magnitude levels of the monitored event
fluctuate, the output will remain stabilized around the base line with the
positive and negative areas of the curve remaining equal. Figure 10 represents
an AC signal following this curve. (Output from sensors operating in DC mode
following this same pattern but over an extended time frame associated with
sensor time constant values.)
Figure 10: AC Signal
Example: Assuming a 0 to 4 volt output signal is generated from an AC coupled
force application with a one second steady-state pulse rate and one second
between pulses. The frequency remains constant but the signal quickly decays
negatively until the signal centers around the original base line (where area A
= area B). Peak to peak output remains the same.
REPETITIVE PULSE APPLICATIONS
In many force monitoring applications it is desired to monitor a series of
zero-to-peak repetitive pulses that may occur within a short time interval of
one another. This output signal is often referred to as a "pulse train". As has
been previously discussed, the AC coupled output signal from piezoelectric
sensors will decay towards an equilibrium state, making it look like the
positive force is decreasing and difficult to accurately monitor a continuous
zero-to-peak output signal such as associated with stamping or pill press
applications. With the use of special ICP signal conditioning equipment it
becomes possible to position an output signal positive going above a ground
based zero. Operating in drift-free AC mode, PCB's Model 484B02 provides the
constant current voltage excitation to ICP force sensors and has a zero based
clamping circuit that electronically resets each pulse to zero. As outlined in
Figure 11, this special circuitry prevents the output from drifting negatively
providing a continuous positive polarity signal.
Figure 11: Positive Polarity, zero based AC output
CALIBRATION OF FORCE SENSORS
PCB provides NIST (National Institute of Standards and Technology) traceable
calibration and testing services for all force sensor products. Calibration
procedures follow accepted guidelines as recommended by ANSI (American National
Standards Institute) and ISA (instrument Society of America). Calibration of
force sensors at PCB is in accordance with ISA-37-10 and complies with
MIL-STD-45662A. These standards provide the establishment and management of
complete calibration systems, thus controlling the accuracy of a sensor's
specifications by controlling measuring and test equipment accuracy.
Each individually calibrated force sensor is supplied with a NIST traceable
certificate indicating calibrated sensitivity. Determining the sensitivity of
sensors with operating ranges from 5 000 to 100 000 lbs (22,24 to 444,8 kN) is
performed by placing the force sensor in a hydraulic press stand. In series
with the sensor is a Morehouse proving ring reference force standard selected
for the operating range of the sensor. Reference proving rings are calibrated
and certified every six months to verify calibrated value. A scaled down test
stand is used for lower ranged sensors. Miniature, high sensitivity models are
calibrated by applying a known lightweight mass, letting the signal zero, and
then quickly removing the mass. Output recorded is the sensitivity of the
sensor. Charge mode and longer time constant sensors are calibrated by
statically applying a known force and recording output data.
In each calibration procedure, data points are plotted at 20% intervals of the
sensor's operating range. Each point represents the average of three separate
measurements taken at that range. These averaged points are graphically plotted
and the best straight line through zero is drawn. Should calibrated points fall
outside the specified linearity as provided in published specifications, the
unit fails calibration and is rejected.