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# Installing and Mounting Piezoelectric Force Transducers

## Preface

Piezoelectric force transducers serve an important purpose in force measurement. They are small in size and well-suited for applications requiring small components, or measurement of dynamic forces. This article discusses the various concepts and process that relate to the installation and mounting of piezoelectric force transducers.

## What is a Piezoelectric Transducer?

A piezoelectric force transducer is simply a sensor that detects an applied force, deforms under this force, and then generates an electrical signal at its output terminals. This electrical output signal is in the form of electric charges that are proportional to the applied force.

Piezoelectric transducers operate based on the piezoelectric effect. Piezoelectricity is produced when a polarized crystalline material is stressed or deformed. The stress then causes a shift in the orientation of the internal dipoles of the material. It is similar to di-electricity, which occurs when a charge is produced from a shift of electrons in an insulator.

This piezoelectric force sensor is modeled electrically as a charge source in series with a capacitance that has an internal resistance and inductance. Figure 1 and 2 below depict the piezoelectric effect and an electrical model.

:

Serial Inductance

:

Serial Capacitance

:

Serial Resistance

:

Parallel Capacitance

:

Free Capacitance =

Furthermore, the mathematical formula that shows the relationship between the charge produced, the applied force, compliance, and the material constant is expressed below. The compliance of the material is the inverse of Young’s modulus.

Where is the electrical charge generated by force, (in Newtons) applied across the faces of a piezoelectric device with a mechanical compliance of spring rate () and a more complex material constant, , of dimensions .

The piezoelectric material is attached to the body of the transducer such that it lies along the loading axis. The loading axis is an imaginary line along the direction, and at the application point, of the dynamic force being measured.

## Installation Requirements

A piezoelectric transducer must be installed by a well-trained technician who understands the various standard safety requirements and guidelines.

In an industrial setting, installation personnel should follow the installation design details describing the location of installation for the transducer, the sealing of the transducer’s housing unit, the wiring diagrams, cable requirements, and grounding of the system. Also, installers should be able to perform both the pre-installation testing and post-installation loop testing.

### Mounting a Piezoelectric Force Transducer

Mounting the device at the intended location requires attention to these factors:

• Accessibility: The mounting position should be chosen such that the device is easily accessible to the authorized personnel for repairs and maintenance.
• Orientation of the piezoelectric material: As mentioned above, the material inside the sensor must be installed such that the polarity runs along the loading axis.
• The transducer’s geometric shape: The shape of the transducer will affect the orientation of the underlying piezoelectric material, and therefore the orientation of the output electrodes that detect the output electric field. The transducer should be mounted so the position of its output electrodes is perpendicular to the direction of applied stress.
• Resonant frequency: The natural frequency of piezoelectric materials can be as high as 100,000Hz and they are not self-damping. If driving the transducer to this frequency level is unnecessary, then appropriate mounting measures should be taken to prevent it.
• Damping: Damping is necessary if the piezoelectric material typically operates in an environment with vibration, especially at its natural frequency. Mounts using spring elements can dampen by pre-compressing the transducer. This gives more support, better rigidity, and firmness under vibrations of different amplitudes. Damping also greatly improves linearity of the input/output curve.
• Cabling: The transducer’s electrode cables must be properly insulated and short. Altering the cable length after installation requires knowledge of how to adjust for the new capacitance created by the new length. Also during installation, any exposed cable should be kept clean and free of dirt, debris or even human contact. Coaxial cable is the recommended wire type for installing piezoelectric transducers.
• Housing unit: Once installed, the transducer is housed typically in a vacuum. This ensures the absence of air loading and proper damping, and seals against dust and dirt particles.
• Signal conditioning peripherals: These devices should be placed as close as possible to the transducer so to reduce the distance of charge and signal transmission. This reduces unnecessary noise coupling and voltage drops.
• Grounding and shielding: This is a very important step during installation. The transducer should be properly grounded to protect the device. Shielding protects against electromagnetic interference, and the possibility of the reverse piezoelectric effect. This effect is caused when the material begins to vibrate at a certain frequency from exposure to an electrical time-varying signal such as an AC voltage.

### Installation Components

The important installation components are mainly the piezoelectric transducer itself, the connecting cables, and the charge amplifier. The previous section explained cabling considerations. The first section above addressed the operating principles of the transducer. Therefore, this section explains the remaining component, the charge amplifier.

The charge amplifier is an electronic circuit that converts the charge output from the piezoelectric sensor to a voltage output. The design includes an operational amplifier with a high input impedance (usually a MOSFET input stage), a suitable frequency response, and a low output impedance. The charge amplifier also uses a feedback technique to provide gain adjustment and signal filtering.

Figure 3 below shows the schematic of the charge amplifier connected with the modeled cable and sensor parameters.

In the diagram, is the charge source in parallel with the sensor capacitance ; is the cable capacitance which is also in parallel with the sensor parameters; and are the feedback capacitance and resistance respectively. Recall Figure 2 shows a resistance in series with this parallel capacitance (it is labeled in the previous figure). It is this resistance that causes charge leakage.

This type of charge amplifier design ensures the following:

• A calibration factor fixed by the value of the feedback capacitance and resistance and .
• An adjustable dynamic frequency range, as the time constant ( * ), but only for dynamic loading. (It can be made large or small for low and high-frequency operations respectively.)
• Eliminated effects of stray capacitances from the connecting cables and the sensor .

These three results give the piezoelectric transducer a high stability, wide dynamic range, good temperature stability, good linearity, and low hysteresis.

The output terminal of the charge amplifier can then connect to an analog-to-digital and signal processing component, or to a voltage meter.

## Important Transducer Characteristics

A manufacturer’s datasheet for piezoelectric sensors should give values for the following characteristics. They provide more information for an installation process.

• Relative Dielectric Constant: This quantifies displacement under a unit electric field and zero stress.
• Electromechanical Coupling Factor: This indicates the efficiency of the transducer. Efficiency is the relationship between the supplied electrical energy and the output mechanical energy of the material.
• The Piezoelectric Distortion Constant: This is the resulting distortion when an electric field of uniform strength is applied under zero stress.
• The Voltage Output Coefficient: This is the effective electric field strength under uniform stress but zero electrical displacements.
• Resonant Frequency: This is the natural frequency of vibration of the material.
• The Mechanical Quality Factor: This indicates the steepness of the response of the material to a mechanical vibration equal or close to its resonant frequency. Materials with high “Q” resonate at frequencies only close to their resonant frequency and with a high amplitude, while those with lower “Q” values resonate at a wider frequency bandwidth. In each case the resonant frequency is typically at the center of the response frequency band.
• Poisson’s Ratio: This is the ratio of the traverse strain to the axial strain when a constant stress is applied to the material.
• Curie Temperature: This gives the temperature at which the material loses its polarization and piezoelectric properties. At this temperature the once aligned dipoles arrange themselves randomly.
• The Compliance: This is also called the elasticity constant and it is the inverse of Young’s Modulus. That is, it is the ratio of strain (deformation of the material) to stress (force applied).

## Conclusion

The piezoelectric force transducer is most suitable for dynamic measurements. Therefore it commonly appears in ultrasonic applications, shock measuring sensors, airbags, acceleration measurements, etc.. Its compact size makes it preferable for small systems.

A final point is that once mounting and installation is complete, the piezoelectric force measuring system should be calibrated (see Calibrating the Force Measuring System). Calibration simply involves comparing the reading of the piezoelectric transducer to that of a known standard. This will identify systematic errors and improve accuracy.

## References

• The Instrumentation Reference Book, Edited by Walt Boyes
• Jayant Sirohi, Inderjit Chopra , “Fundamental Understanding of Piezoelectric Strain Sensors,” Journal of Intelligent Material Systems and Structures.
• Instrumentation: Transducers and Interfacing by B.R Bannister and and D.G. Whitehead