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Introduction to Piezoelectric Force Sensors

Quartz Force Sensors are recommended for dynamic force applications. They are not used as 'load cells' for static applications. Measurements of dynamic oscillating forces, impactor high speed compression/tension under varying conditions may require sensors with special capabilities. Fast response, ruggedness, stiffness comparable to solid steel, extended ranges and the ability to also measure quasi-static forces are standard features associated with PCB quartz force sensors.

The following information presents some of the design and operating characteristics of PCB force sensors to help you better understand how they function, which in turn, will "help you make better dynamic measurements".

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.

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® 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 or contaminants.

Figure 4: ICP Sensor System Schematic

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.)

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.

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 quasi-static measurements.

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.

With ICP sensors, there are two factors which must be considered when making low frequency measurements. These are:

1.) The discharge time constant characteristic of the force sensor.
2.) 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 considered.)

It is important that both factors be readily understood by the user to assure accurate low frequency measurements.

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 following section.

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

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 this event.

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 is observed.

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.

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.

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.

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

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.