Vibration and Acceleration Sensors

1 Piezoelectric Transducers

Piezoelectric transducers depend upon the characteristics of certain materials that are capable of generating electric voltage when they deform. Piezoelectric materials, when subjected to mechanical force or stress along specific planes, generate electric charge. The property of generating an electric charge when deformed makes piezoelectric materials useful as primary sensors in instrumentation.

The best-known natural material is quartz crystal (SiO2). Rochelle salt is also considered a natural piezoelectric material. Artificial materials using ceramics and polymers, such as PZT (lead zirconium titanate), PVDF (polyvinylidene fluoride), BaTio3 (barium titanate), and LS (Lithium Sulfate) also exhibit the piezoelectric phenomenon.

ILL. 46 PIEZOELECTRIC EFFECT IN A CRYSTAL

Piezoelectric Effect A piezoelectric material such as a quartz crystal can be cut along its axes in x, y, and z directions. Ill. 46 shows a view along the z-axis. In a single-crystal cell, there are three atoms of silicon and six atoms of oxygen. Oxygen atoms are lumped in pairs. Each silicon atom carries four positive charges, and oxygen atoms carry two negative charges. A pair of oxygen atoms carries four negative charges. When there is no external force applied on the quartz crystal, the quartz cell is electrically neutral.

When compressive forces are applied along the x-axis, as shown in Ill. 46(b), the hexagonal lattices become deformed. The forces shift the atoms in the crystal in such a manner that positive charges are accumulated at the silicon atom side and negative charges at the oxygen pair side. The crystal tends to exhibit electric charges along the y-axis. On the other hand, if the crystal is subjected to tension along the x-axis, as in Ill. 46(c), a charge of opposite polarity is produced along the y-axis. To transmit the charge which has been developed, conductive electrodes are applied to the crystal at the opposite side of the cut.

ILL. 47 LONGITUDINAL EFFECT

ILL. 48 TRANSVERSE EFFECT

The piezoelectric material acts as a capacitor with the piezoelectric crystal acting as the dielectric medium. The charge is stored because of the inherent capacitance of the piezoelectric material itself.

The piezoelectric effect is reversible. If a varying potential is applied to the proper axis of the crystal, it changes the dimension of the crystal, thereby deforming it. A piezoelectric element used for converting mechanical motion to electrical signals is thought of as both a charge generator and a capacitor. This charge appears as a voltage across the electrodes. The magnitude and polarity of the induced surface charges are proportional to the magnitude and direction of the applied force.

For the arrangements shown in Ill. 47 and 3-48, the charge generated, Q, is defined as:

Q = dF (Longitudinal effect)

Q = dF a/b (Transverse effect)

Here d is the piezoelectric coefficient of the material. it's also known as the charge sensitivity factor of the crystal. For a typical quartz crystal, d = 2.3 = 10_12 F/N or 2.3 pF/N where F is the applied force, in newtons.

If the ratio of is greater than one, the transverse effect produces more charge than the longitudinal effect. The force, F, results in a change in thickness of the crystal. If the original thickness of the crystal is t and _t is the change in thickness due to the applied force, Young's modulus, E, can be expressed as the ratio of stress and strain:

Rewriting the expression, we have where A = area of the crystal, m^2 t = thickness of the crystal, m

Piezoelectric Output From Equations 56 and 57, we have […]

The charge at the electrodes produces the voltage:

The capacitance of the piezoelectric material between the two electrodes is

Here is the dielectric constant (permitivity) of the material, and o is that for free space. Thus, e_r

Expressing g as the crystal voltage sensitivity factor, the voltage can be written as […]

Piezoelectric materials are used in a variety of applications where force, pressure, acceleration, and vibration measurements are taken. The major application of the piezoelectric sensor is in situations where the charge does not have much time to leak off. it's also used as the sensor in ceramic- or crystal-type pick ups, where the needle causes distortion of the crystal and the voltages generated are amplified by charge amplifiers, which have the additional capacity of reducing loading effects on piezoelectric transducers.

TBL. 4 BASIC CHARACTERISTICS OF PIEZOELECTRIC MATERIALS

Sensitivity, natural frequency, nonlinearity, hysteresis, and temperature effects are the primary considerations when selecting piezoelectric transducers. Piezoelectric pressure sensors are used for the measurement of rapidly varying pressures as well as shock pressures. Sensors made of quartz materials generally exhibit stbl. frequency response from 1 Hz to 20 kHz-the natural frequency being of the order of 50 kHz. Quartz crystals can be used over a temperature range of _185 to 288 °C compared to ceramic devices, which are limited to _185 to 100 °C.

Equivalent Circuit of a Piezoelectric Transducer

The dynamic properties of a piezoelectric transducer can be represented by an equivalent circuit derived from the electrical and mechanical parameters of the transducer. The basic equivalent circuit is shown in Ill. 49. The charge generated, Q, is across the capacitance C_c, and its leakage resistance is R_c. The charge source can be replaced by a voltage source, as per Equation 63 and drawn in series with a capacitance Cc and resistance Rc.

ILL. 49 EQUIVALENT CIRCUIT

When the piezoelectric crystal is coupled with leads and cables as well as a readout device, the voltage depends not only on the element but also on the capacitance of cables, charge amplifier, and display. The total capacitance is expressed as: A typical arrangement is shown in Ill. 50, where the sensing element and charge amplifiers are presented.

CT = C_c + C_cable + C_display

ILL. 50 CHARGE AMPLIFIER FOR PIEZOELECTRIC TRANSDUCER

The feedback resistance of the charge amplifier is kept high so that this circuit draws very low current and produces a voltage output that is proportional to the charge. Ill. 51 shows the piezoelectric crystal interface, and the combined equivalent circuit is shown in Ill. 52.

ILL. 51 PIEZOELECTRIC CRYSTAL INTERFACE

ILL. 52 COMBINED EQUIVALENT CIRCUIT

Ill. 54 presents a photograph of a piezoelectric translator used for high-precision motion measurement.

Ill. 55 presents a photograph of a rotating cutting force dynamometer for machine-tool applications.

Analogy Equations Using mathematical models, solutions of equations describing one physical form can be applied to analogous systems in other fields. The analogy approach is discussed in detail in earlier chapters. These analogies also can be applied to a piezoelectric transducer element. Using mechanical elements (such as inertial elements, spring, and damper), a mechanical system can be analyzed. C, L, and R represent mechanical parameters of compliance, mass, and viscous resistance of the element, respectively. The mechanical analogy in terms of displacement can be expressed as

Differential equations in terms of current and velocity are also developed. R, L and C represent the viscous resistance of an element, mass, and parameters of mechanical parameters of compliance. In a R-L-C series electrical network, the applied voltage equals the drop across the resistor, plus the drop across the inductor, plus the drop across the capacitor.

The configuration of the piezoelectric element is an important consideration in the industrial use of these elements. The shape of the element could be a disc, plate, or in tubular form. It may be operated under normal, transverse, or shear modes. e.g., a small piezoelectric transducer 4 mm in diameter and 10 mm long weighs around 2 grams, operates at 177 °C, and has voltage sensitivity of 0.1 mV/N.

Acceleration Measurement by Piezoelectric Transducer The piezoelectric accelerometer is constructed as follows. It consists of a housing and contains a mass attached to the mechanical axis of the crystal. The piezoelectric element in the form of a cylinder is first bonded to a central pillar.

Then a cylinder mass is bonded to the outside of the PZT element. Acceleration in the direction of the cylinder axis causes a shear force on the element, which provides its own spring force. The acceleration of the piezoelectric material generates electric potential when subjected to mechanical strain along a predetermined axis. The initial calibrating force is predetermined between the mass and spring using a preloaded spring.

As the housing of the accelerometer is subjected to vibrations, the force exerted on the piezoelectric element by the mass is altered. The charge generated on the crystal is sensed using a charge amplifier. A force F applied to the crystal develops a charge, Q = dF. When a varying acceleration is applied to the mass crystal assembly, the crystal experiences a varying force.

Here a is the acceleration and V is the voltage produced. Thus, the output is a measure of the acceleration. Ill. 56 presents a photograph of a typical accelerometer.

Because of the high stiffness of the piezoelectric material, the natural frequency of such devices can be as high as 125 kHz, which provides an ability to measure at high frequencies. The accelerometer (Ill. 57) is of small size and has a small weight (0.25 kg). The crystal is a source with high output impedance, and the electrical matching of the impedance between the transducer and the circuitry is usually a critical matter in the design of the display system. Piezoelectric materials used as sensing elements for acceleration have been employed in seismic instrumentation.

The base of the device is attached to the object whose motion is to be measured. Inside the piezoelectric acceleration transducer, mass m is supported on spring of stiffness k and a viscous damper with damping coefficient c. The motion of the object results in the motion of the mass relative to the frame. A transducer equation is obtained by considering the inertial forces of the mass and the restoring force of the spring and the damper.

ILL. 56 ACCELEROMETER

ILL. 57 PIEZOELECTRIC ACCELEROMETER where y = absolute motion of the mass.

The relative motion, z = y = x, is expressed as […]

where, D = d /dt

The equation is of second order and relates the input and output of the transducer.

Velocity Measurement by Piezoelectric Transducer it's possible to measure velocity by first converting the velocity into a force using a viscous damping element and then measuring the resulting force with a PZT sensor. If acceleration data is available through an accelerometer, the velocity is obtained by integrating this device. Velocity transducers are constructed using piezoelectric accelerometers and integrating amplifiers. Double integration provides displacement information. The principle of piezoelectric velocity transducer is illustrated in Ill. 58.

ILL. 58 VELOCITY TRANSDUCER

2 Active Vibration Control

Active vibration control can be defined as a technique in which the vibration of a structure is reduced by applying a counterforce to the structure that is appropriately out of phase but equal in force and amplitude with the original vibration. As a result, two opposing forces cancel with each other, and the structure essentially stops vibrating. A schematic of a representative active vibration control system is shown in Ill. 59.

ILL. 59 SCHEMATIC OF ACTIVE VIBRATION CONTROL SYSTEM

The vibration control system consists of a high-speed microprocessor-based system, a vibrating structure, and an actuator. The structural vibrations are monitored by a motion sensor, such as an accelerometer. The resulting output voltage from the motion sensor is fed into a high-speed digital signal processing device. The processing device calculates the appropriate phase inversion and the counterforce amplitude needed to reduce the original vibration characteristics. The output voltage from the computer is amplified and drives the actuator. The expansion and contraction of the actuator produces a force which counteracts the original vibration amplitude and reduces the vibration of the structure. It should be noted that this vibration control must theoretically take place in real time with the original vibration. It also should be noted at this point that, in practice, the vibration of a structure can not be stopped-it can only be reduced. This is essential due to the response-time limitations of the control system, the response-time limitations of the actuator itself, and the high rate of change of the structural vibration's spectral characteristics.

There are several areas where active vibration control can be applied. One such area is in isolating a mass from another vibrating mass rather than using traditional passive devices, such as springs and dampers. This is especially useful in the isolation of microelectronics and signal processing units that are extremely sensitive to even the slightest vibrations. Another use of active vibration control is in the precision manufacturing area. Vibrations and resultant acoustic emissions have the ability to damage the instrumentation and can be harmful for human health.

Chatter and vibrations, if present in a machine-tool structure, also can make a severe impact on machining accuracies and can reduce surface quality. Elimination of unwanted vibrations created by a process can improve process accuracy. By controlling the vibrations of the cutting tools, closer tolerances can be achieved, and tool wear can be reduced. The advantage of active vibration control over other passive methods (i.e., springs and dampers) is that the structural vibrations can be reduced at a much faster rate.

3 Magnetostrictive Transducers for Vibration Control

The piezoelectric type of actuator has been popular in active vibration control because of its fast response times. However, very high voltages are required to produce only micro-cm strains.

Magnetostrictive materials, on the other hand, produce fairly substantial strains in the presence of relatively low magnetic fields. Magnetostrictive materials are also able to produce much higher counter forces. Magnetostrictive materials, however, do have high-frequency limitations, whereas the piezoelectric materials can oscillate well into the megahertz range. The actuator with the best promise for real-time vibration control is the magnetostrictive transducer.

Magnetostrictive Transducer Principle Magnetostriction is a property of certain materials, namely iron, nickel, cobalt, and respective alloys, whereby the material strains in the presence of a magnetic field. There are fifteen such rare earth elements that are part of the periodic tbl. The magnetic field is imposed by feeding a current through a coil surrounding the magnetostrictive material. The rare earth materials, especially magnetostrictive materials, are capable of producing strains of the order of 2,000 ppm. Certain alloys of iron and rare earth elements are capable of producing strains in excess of 2,000 ppm under certain circumstances. One such material is an alloy of terbium, iron, and dysprosium. Known commercially as Terfenol-D, it exhibits good magnetostrictive properties and is the most commonly used actuator element.

The basic elements of the actuator is shown in Ill. 60. It consists of the coil which encloses the magnetostrictive rod, magnetic poles that conduct the flux to the rod, the DC flux from the permanent magnet to the rod, the air gap that allows the rod to expand and contract freely, the head and tail mass or the base, and spring systems that are used to provide the proper preload to the rod.

When a magnetostrictive material is surrounded by a coil and an AC current is fed to the coil, both the positive and negative portions of the cycle produce positive strains in the magnetostrictive material. However, this presents a problem when one wants to produce both positive and negative strains. This phenomenon is of importance while using the materials to actively control vibrations.

ILL. 60 BASIC ELEMENTS OF THE TERFENOL-D ACTUATOR: Coils enclosing magnetostrictive core; Pre-loaded spring system; Base; Magnet flux path

In other words, the oscillating structure is pulled down (counterforce is applied in the negative direction) when the vibration amplitude is positive and pushes the oscillating structure up (i.e., counterforce is applied in the positive direction) when the vibration amplitude is negative. In both cases, the goal is to push or pull the vibration amplitude toward its neutral position so that the structural vibrations are significantly reduced.

The magnetostrictive strain, S, can be defined as the ratio of the expansion length, _l to the original length, l, due to the applied magnetic field intensity, H. The magnetic field intensity, H, pro vided by the coil to the magnetostrictive material is defined as:

..where I is the current through the coil, N is the number of coil turns, and lc is the axial length of coil turns. The magnetostrictive actuator, if used in the linear region, converts electrical energy into mechanical energy. It also can be used to convert mechanical energy into electrical energy. It can be seen that the device may be used as both a transducer and an actuator.

Applications In the design of magnetostrictive transducer for real-time applications, the problem of the material straining in only one direction in the presence of both positive and negative currents is addressed by introducing a biasing field. The bias is usually accomplished either by placing a permanent magnet around the material or by introducing a DC bias field into the circuit. Due to the magnetic field from the permanent magnet, the material experiences an initial expansion or strain.

The design size of the permanent magnet is suitably chosen so that the initial expansion is about one half the total expansion limit of the magnetostrictive material used. When the positive cycle of the AC current is presented, the field from the magnet and the field from the coil gets added, resulting in positive expansion of the material. When the negative cycle of the current is presented, the two fields cancel each other, and the material shrinks. Through the use of biasing, the actuator can be used to control the oscillating structures. If the use of the magnetostrictive actuator is limited to positive strain, a bias is not required for the application.

Magnetostrictive materials can operate from cryogenic temperatures up to 200°C. The transducer is highly reliable because of the minimal number of moving parts. Some of the current applications of magnetostrictive transducers include robotics, valve control, micro-positioning, and active vibration control. Other areas of applications include fast-acting relays, high-pressure pumps, and as high-energy, low-frequency sonic sources.

SUMMARY Piezoelectric Transducer

Piezoelectric materials, when subjected to mechanical force or stress along specific planes, generate electric charge. The best-known natural material is quartz crystal (SiO2). Rochelle salt is also considered a natural piezoelectric material.

For the arrangement shown in Ill. 61, the charge generated, Q, is defined as

Q = dF (Longitudinal effect)

= (Transverse effect)

Here d is the piezoelectric coefficient of the material.

Magnetostrictive Transducer Theory

Magnetostriction is a property of certain materials, namely iron, nickel, cobalt, and respective alloys, whereby the material strains in the presence of a magnetic field. The most commonly used actuator element is commercially known as "Terfenol-D." When a magnetostrictive material is surrounded by a coil and an AC current is fed to the coil, both the positive and negative portions of the cycle produce positive strains in the magnetostrictive material. This phenomenon is of importance while using the materials to actively control vibrations.

Applications

• Piezoelectric materials are used in a variety of applications where force, pressure, acceleration, and vibration measurements are taken.

• Used as the sensor in ceramic- or crystal-type pick ups where the needle causes distortion of the crystal and the voltages generated are processed.

Features

• Sensitivity, natural frequency, nonlinearity, hysteresis, and temperature effects are the primary selection considerations.

• Sensors made of quartz materials generally exhibit stbl. frequency response from 1 Hz to 20 kHz, with the natural frequency being of the order of 50 kHz.

• Quartz crystals can be used over a temperature range of _185 to 288 °C compared to ceramic devices, which are limited to _185 to 100 °C.

Applications of Magnetostrictive Transducers

Current applications include micro-positioning, stress measurement. Other engineering applications include inspection of steel pipes and tubes, condition monitoring of machinery such as combustion engines, and onboard sensing of crash events for vehicle safety system operations.

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