Guide to Measurement and Instrumentation -- Translational Motion, Vibration, and Shock Measurement (part 1)

1 Introduction

2 Displacement

3 Velocity

4 Acceleration

5 Vibration

6 Shock

7 Summary

8 Quiz and Problems

1 Introduction

Movement is an integral part of many systems and therefore sensors to measure motion are an important tool for engineers. Motion occurs in many forms. Simple movement causes a displacement in the body affected by it, although this can take two alternative forms according to whether it’s motion in a straight line (translational displacement) or angular motion about an axis (rotational displacement). Displacement only describes the fact that a body has moved but does not define the speed at which the motion occurs. Speed is defined by the term velocity. As for displacement, velocity occurs in two forms-translational velocity describes the speed at which a body changes position when moving in a straight line and rotational velocity (sometimes called angular velocity) describes the speed at which a body turns about the axis of rotation.

Finally, it’s clear that changes in velocity occur during the motion of a body. To start with, the body is at rest and the velocity is zero. At the start of motion, there is a change in velocity from zero to some nonzero value. The term acceleration is used to describe the rate at which the velocity changes. As for displacement and velocity, acceleration also comes in two forms-translational acceleration describes the rate of change of translational velocity and rotational acceleration (sometimes called angular acceleration) describes the rate of change of rotational velocity.

With motion occurring in so many different forms, a review of the various sensors used to measure these different forms of motion would not fit conveniently within a single section. Therefore, this section only reviews sensors used for measuring translational motion, with those used for measuring rotational motion being deferred to the next section. The following sections therefore look in turn at the measurement of translational displacement, velocity, and acceleration.

The subjects of vibration and shock are also included in final sections of this section. Both of these are related to translational acceleration and therefore properly belong within this section on translational displacement. Vibrations consist of linear harmonic motion, and measurement of the accelerations involved in this motion is important in many industrial and other environments. Shock is also related to acceleration and characterizes the motion involved when a moving body is suddenly brought to rest, often when a falling body hits the floor. This normally involves large-magnitude deceleration (negative acceleration).

2 Displacement

Translational displacement transducers are instruments that measure the motion of a body in a straight line between two points. Apart from their use as a primary transducer measuring the motion of a body, translational displacement transducers are also widely used as a secondary component in measurement systems, where some other physical quantity, such as pressure, force, acceleration, or temperature, is translated into a translational motion by the primary measurement transducer. Many different types of translational displacement transducers exist and these, along with their relative merits and characteristics, are discussed in the following sections of this section. Factors governing the choice of a suitable type of instrument in any particular measurement situation are considered in the final section at the end of the section.

2.1 Resistive Potentiometer

The resistive potentiometer is perhaps the best-known displacement-measuring device. It consists of a resistance element with a movable contact as shown in Figure 1. A voltage, Vs, is applied across the two ends A and B of the resistance element, and an output voltage, VO, is measured between the point of contact C of the sliding element and the end of resistance element A. A linear relationship exists between the output voltage, VO, and distance AC, which can be expressed by [...]

Figure 1 -- Resistance element; Sliding contact

The body whose motion is being measured is connected to the sliding element of the potentiometer so that translational motion of the body causes a motion of equal magnitude of the slider along the resistance element and a corresponding change in the output voltage, VO.

Three different types of potentiometers exist, wire wound, carbon film, and plastic film, so named according to the material used to construct the resistance element. Wire-wound potentiometers consist of a coil of resistance wirewound on a nonconducting former. As the slider moves along the potentiometer track, it makes contact with successive turns of the wire coil.

This limits the resolution of the instrument to the distance from one coil to the next. Much better measurement resolution is obtained from potentiometers using either a carbon film or a conducting plastic film for the resistance element. Theoretically, the resolution of these is limited only by the grain size of the particles in the film, suggesting that measurement resolutions up to 10_4 should be attainable. In practice, resolution is limited by mechanical difficulties in constructing the spring system that maintains the slider in contact with the resistance track, although these types are still considerably better than wire-wound types.

Operational problems of potentiometers all occur at the point of contact between the sliding element and the resistance track. The most common problem is dirt under the slider, which increases the resistance and thereby gives a false output voltage reading or, in the worst case, causes a total loss of output. High-speed motion of the slider can also cause the contact to bounce, giving an intermittent output. Friction between the slider and the track can also be a problem in some measurement systems where the body whose motion is being measured is moved by only a small force of a similar magnitude to these friction forces.

\The life expectancy of potentiometers is normally quoted as a number of reversals, that is, as the number of times the slider can be moved backward and forward along the track. The values quoted for wire-wound, carbon film, and plastic film types are, respectively, 1, 5, and 30 million.

In terms of both life expectancy and measurement resolution, therefore, the carbon and plastic film types are clearly superior, although wire-wound types do have one advantage in respect of their lower temperature coefficient. This means that wire-wound types exhibit much less variation in their characteristics in the presence of varying ambient temperature conditions.

A typical inaccuracy value that is quoted for translational motion resistive potentiometers is _1% of full-scale reading. Manufacturers produce potentiometers to cover a large span of measurement ranges. At the bottom end of this span, instruments with a range of _2 mm are available, while instruments with a range of _1 m are produced at the top end.

The resistance of the instrument measuring the output voltage at the potentiometer slider can affect the value of the output reading, as discussed in Section 3. As the slider moves along the potentiometer track, the ratio of the measured resistance to that of the measuring instrument varies, and thus the linear relationship between the measured displacement and the voltage output is distorted as well. This effect is minimized when the potentiometer resistance is small relative to that of the measuring instrument. This is achieved by (1) using a very high impedance measuring instrument and (2) keeping the potentiometer resistance as small as possible. Unfortunately, the latter is incompatible with achieving high measurement sensitivity as this requires high potentiometer resistance. A compromise between these two factors is therefore necessary. The alternative strategy of obtaining high measurement sensitivity by keeping the potentiometer resistance low and increasing the excitation voltage is not possible in practice because of the power-rating limitation. This restricts the allowable power loss in the potentiometer to its heat dissipation capacity.

The process of choosing the best potentiometer from a range of instruments that are available, taking into account power rating and measurement linearity considerations, is illustrated in the following example.

Example 1 The output voltage from a translational motion potentiometer of stroke length 0.1 meter is to be measured by an instrument whose resistance is 10 KO. The maximum measurement error, which occurs when the slider is positioned two-thirds of the way along the element (i.e., when AC = 2AB/3 in Figure 1), must not exceed 1% of the full-scale reading. The highest possible measurement sensitivity is also required.

A family of potentiometers having a power rating of 1 watt per 0.01 meter and resistances ranging from 100 to 10 K-Ohm in 100-Ohm steps are available. Choose the most suitable potentiometer from this range and calculate the sensitivity of measurement that it gives.

Solution---Referring to the labeling used in Figure 1, let the resistance of portion AC of the resistance element Ri and that of the whole length, AB of the element be Rt. Also, let the resistance of the measuring instrument be Rm and the output voltage measured by it be Vm. When the voltage-measuring instrument is connected to the potentiometer, the net resistance across AC is the sum of two resistances in parallel...

Let the excitation voltage applied across the ends AB of the potentiometer be V and the resultant current flowing between A and B be I. Then I and V are related by...

Vm can now be calculated as...

If we express the voltage that exists across AC in the absence of the measuring instrument as V0, then we can express the error due to the loading effect of the measuring instrument as error = V0 _ Vm.

2.2 Linear Variable Differential Transformer (LVDT)

The linear variable differential transformer, which is commonly known by the abbreviation LVDT, consists of a transformer with a single primary winding and two secondary windings connected in the series-opposing manner shown in Figure 2. The object whose translational displacement is to be measured is attached physically to the central iron core of the transformer so that all motions of the body are transferred to the core.

Because of the series opposition mode of connection of secondary windings, Vo =Va_Vb, and hence with the core in the central position, Vo = 0. Suppose now that the core is displaced upward (i.e., toward winding A) by distance x. If then Ka = K1 and Kb = K2 , we have ...

If, alternatively, the core were displaced downward from the null position (i.e., toward winding B) by distance x, the values of Ka and Kb would then be Ka = K2 and Kb = K1, and we would have:

Thus for equal magnitude displacements +x and _x of the core away from the central (null) position, the magnitude of the output voltage, Vo, is the same in both cases. The only information about the direction of movement of the core is contained in the phase of the output voltage, which differs between the two cases by 180_. If, therefore, measurements of core position on both sides of the null position are required, it’s necessary to measure the phase as well as the magnitude of the output voltage. The relationship between the magnitude of the output voltage and the core position is approximately linear over a reasonable range of movement of the core on either side of the null position and is expressed using a constant of proportionality ...

The only moving part in an LVDT is the central iron core. As the core is only moving in the air gap between the windings, there is no friction or wear during operation. For this reason, the instrument is a very popular one for measuring linear displacements and has a quoted life expectancy of 200 years. The typical inaccuracy is _0.5% of full-scale reading and measurement resolution is almost infinite. Instruments are available to measure a wide span of measurements from _100 mm to _100 mm. The instrument can be made suitable for operation in corrosive environments by enclosing the windings within a nonmetallic barrier, which leaves the magnetic flux paths between the core and windings undisturbed. An epoxy resin is used commonly to encapsulate the coils for this purpose. One further operational advantage of the instrument is its insensitivity to mechanical shock and vibration.

Some problems that affect the accuracy of the LVDT are the presence of harmonics in the excitation voltage and stray capacitances, both of which cause a nonzero output of low magnitude when the core is in the null position. It’s also impossible in practice to produce two identical secondary windings, and the small asymmetry that invariably exists between the secondary windings adds to this nonzero null output. The magnitude of this is always less than 1% of the full-scale output and, in many measurement situations, is of little consequence.

Where necessary, the magnitude of these effects can be measured by applying known displacements to the instrument. Following this, appropriate compensation can be applied to subsequent measurements.

2.3 Variable Capacitance Transducers

Like variable inductance, the principle of variable capacitance is used in displacement measuring transducers in various ways. The three most common forms of variable capacitance transducers are shown in Figure 3.In Figure 3a, capacitor plates are formed by two concentric, hollow, metal cylinders. The displacement to be measured is applied to the inner cylinder, which alters the capacitance. The second form, Figure 3b, consists of two flat, parallel, metal plates, one of which is fixed and one of which is movable. Displacements to be measured are applied to the movable plate, and the capacitance changes as this moves. Both of these first two forms use air as the dielectric medium between the plates. The final form, Figure 3c, has two flat, parallel, metal plates with a sheet of solid dielectric material between them. The displacement to be measured causes a capacitance change by moving the dielectric sheet.

Inaccuracies as low as _0.01% are possible with these instruments, with measurement resolutions of 1 mm. Individual devices can be selected from manufacturers' ranges that measure displacements as small as 10_11m or as large as 1 m. The fact that such instruments consist only of two simple conducting plates means that it’s possible to fabricate devices that are tolerant to a wide range of environmental hazards, such as extreme temperatures, radiation, and corrosive atmospheres. As there are no contacting moving parts, there is no friction or wear in operation and the life expectancy quoted is 200 years. The major problem with variable capacitance transducers is their high impedance. This makes them very susceptible to noise and means that the length and position of connecting cables need to be chosen very carefully. In addition, very high impedance instruments need to be used to measure the value of the capacitance. Because of these difficulties, use of these devices tends to be limited to those few applications where high accuracy and measurement resolution of the instrument are required.

Figure 3 --- Concentric hollow metal cylinders Displacement; Displacement; Displacement (a) (c) (b) Air dielectric Solid dielectric Movable metal plate Fixed metal plate Fixed metal plate Movable metal plate

2.4 Variable Inductance Transducers

Figure 4.

One simple type of variable inductance transducer was shown earlier. This has a typical measurement range of 0_10mm. An alternative form of variable inductance transducer, shown in Figure 4a, has a very similar size and physical appearance to the LVDT, but has a center-tapped single winding. The two halves of the winding are connected to form two arms of a bridge circuit that is excited with an alternating voltage.

With the core in the central position, the output from the bridge is zero. Displacements of the core either side of the null position cause a net output voltage that is approximately proportional to the displacement for small movements of the core. Instruments in this second form are available to cover a wide span of displacement measurements. At the lower end of this span, instruments with a range of 0_2 mm are available, while at the top end, instruments with a range of 0_5 m can be obtained.

Figure 5 --- Displacement Wedge Beams; Strain gauges

2.5 Strain Gauges

The principles of strain gauges were covered earlier in Section 13. Because of their very small range of measurement (typically 0-50 mm), strain gauges are normally only used to measure displacements within devices such as diaphragm-based pressure sensors rather than as a primary sensor in their own right for direct displacement measurement. However, strain gauges can be used to measure larger displacements if the range of displacement measurement is extended by the scheme illustrated in Figure 5. In this, the displacement to be measured is applied to a wedge fixed between two beams carrying strain gauges. As the wedge is displaced downward, the beams are forced apart and strained, causing an output reading on the strain gauges. Using this method, displacements up to about 50 mm can be measured.

2.6 Piezoelectric Transducers

The piezoelectric transducer is effectively a force-measuring device used within many instruments designed to measure either force itself or the force-related quantities of pressure and acceleration. It’s included within this discussion of linear displacement transducers because its mode of operation is to generate an e.m.f. proportional to the distance by which it’s compressed. The device is manufactured from a crystal, which can be either a natural material, such as quartz, or a synthetic material, such as lithium sulfate. The crystal is mechanically stiff (i.e., a large force is required to compress it); consequently, piezoelectric transducers can only be used to measure the displacement of mechanical systems that are stiff enough themselves to be unaffected by the stiffness of the crystal. When the crystal is compressed, a charge is generated on the surface that is measured as the output voltage.

Unfortunately, as is normal with any induced charge, the charge leaks away over a period of time. Consequently, the output voltage-time characteristic is as shown in Figure 6.

Because of this characteristic, piezoelectric transducers are not suitable for measuring static or slowly varying displacements, even though the time constant of the charge-decay process can be lengthened by adding a shunt capacitor across the device.

As a displacement-measuring device, the piezoelectric transducer has a very high sensitivity, about 1000 times better than a strain gauge. Its typical inaccuracy is _1% of full-scale reading and its life expectancy is three million reversals.

Figure 7 -- Variable restriction Fixed restriction Flapper plate Measurement chamber

Figure 6

2.7 Nozzle Flapper

The nozzle flapper is a displacement transducer that translates displacements into a pressure change. A secondary pressure-measuring device is therefore required within the instrument. The general form of a nozzle flapper is shown schematically in Figure 7. Fluid at a known supply pressure, Ps, flows through a fixed restriction and then through a variable restriction formed by the gap, x, between the end of the main vessel and the flapper plate. The body whose displacement is being measured is connected physically to the flapper plate. The output measurement of the instrument is the pressure, Po, in the chamber shown in Figure 7, which is almost proportional to x over a limited range of movement of the flapper plate. The instrument typically has a first order response characteristic. Air is used very commonly as the working fluid, which gives the instrument a time constant of about 0.1 second. The instrument has extremely high sensitivity but its range of measurement is quite small. A typical measurement range is _0.05 mm with a measurement resolution of _0.01 mm. One very common application of nozzle flappers is measuring displacements within a load cell, which are typically very small.

Figure 8 --- Sli 2 mm; 0.125 mm Cyclic pitch (s)

2.8 Other Methods of Measuring Small/Medium-Sized Displacements

Apart from the methods outlined earlier, several other techniques for measuring small translational displacements exist, as discussed here. Some of these involve special instruments that have a very limited sphere of application, for instance, in measuring machine tool displacements.

Linear inductosyn:

A linear inductosyn is an extremely accurate instrument widely used for axis measurement and control within machine tools. Typical measurement resolution is 2.5 mm. The instrument consists of two magnetically coupled parts separated by an air gap, typically 0.125 mm wide, as shown in Figure 8. One part, the track, is attached to the axis along which displacements are to be measured. This would generally be the bed of a machine tool. The other part, the slider, is attached to the body that is to be measured or positioned. This would usually be a cutting tool.

The track, which may be several meters long, consists of a fine metal wire formed into the pattern of a continuous rectangular waveform and deposited onto a glass base. The typical pitch (cycle length), s, of the pattern is 2 mm, which extends over the full length of the track. The slider is usually about 50 mm wide and carries two separate wires formed into continuous rectangular waveforms that are displaced with respect to each other by one-quarter of the cycle pitch, that is, by 90 electrical degrees. The wire waveform on the track is excited by an applied voltage given by Vs =V sin(ot).

This excitation causes induced voltages in the slider windings. When the slider is positioned in the null position such that its first winding is aligned with the winding on the track, the output voltages on the two slider windings are given by V1 =0; V2 =V sin(ot).

For any other position, slider winding voltages are given by V1 =V sin(ot)sin(2px/s); V2 =V sin(ot) cos(2px/s), where x is displacement of the slider away from the null position.

Consideration of these equations for the slider-winding outputs shows that the pattern of output voltages repeats every cycle pitch. Therefore, the instrument can only discriminate displacements of the slider within one cycle pitch of the windings. This means that the typical measurement range of an inductosyn is only 2 mm. This is of no use in normal applications, and therefore an additional displacement transducer with coarser resolution but larger measurement range has to be used as well. This coarser measurement is made commonly by translating the linear displacements by suitable gearing into rotary motion, which is then measured by a rotational displacement transducer.

One slight problem with the inductosyn is the relatively low level of electromagnetic coupling between the track and slider windings. Compensation for this is made using a high-frequency excitation voltage (5_10 kHz is common).

Translation of linear displacements into rotary motion

In some applications, it’s inconvenient to measure linear displacements directly, either because there is insufficient space to mount a suitable transducer or because it’s inconvenient for other reasons. A suitable solution in such cases is to translate the translational motion into rotational motion by suitable gearing. Any of the rotational displacement transducers discussed in the next section can then be applied.

Integration of output from velocity transducers and accelerometers

If velocity transducers or accelerometers already exist in a system, displacement measurements can be obtained by integration of the output from these instruments. However, this only gives information about the relative position with respect to some arbitrary starting point.

It does not yield a measurement of the absolute position of a body in space unless all motions away from a fixed starting point are recorded.

Figure 9: First beam splitter; Laser Reference beam; A B f1,f2 f1, f2; Measurement beam f1 f2 f1,f2; Polarizing beam splitter; Movable reflecting cube; Fixed reflecting cube

Laser interferometer:

The standard interferometer has been used for over 100 years for accurate measurement of displacements. The laser interferometer is a relatively recent development that uses a laser light source instead of the conventional light source used in a standard interferometer.

The laser source extends the measurement range of the instrument by a significant amount while maintaining the same measurement resolution found in a standard interferometer. In the particular form of laser interferometer shown in Figure 9, a dual-frequency helium-neon (He-Ne) laser is used that gives an output pair of light waves at a nominal frequency of 5 x 10^14 Hz. The two waves differ in frequency by 2 x 10^6 Hz and have opposite polarization.

This dual-frequency output waveform is split into a measurement beam and a reference beam by the first beam splitter.

The reference beam is sensed by the polarizer and photodetector, A, which converts both waves in the light to the same polarization. The two waves interfere constructively and destructively alternately, producing light-dark flicker at a frequency of 2_106 Hz. This excites a 2-MHz electrical signal in the photodetector.

The measurement beam is separated into the two component frequencies by a polarizing beam splitter. Light of the first frequency, f1, is reflected by a fixed reflecting cube into a photodetector and polarizer, B. Light of the second frequency, f2, is reflected by a movable reflecting cube and also enters B. The displacement to be measured is applied to the movable cube. With the movable cube in the null position, the light waves entering B produce an electrical signal output at a frequency of 2 MHz, which is the same frequency as the reference signal output from A. Any displacement of the movable cube causes a Doppler shift in the frequency, f2, and changes the output from B. The frequency of the output signal from B varies between 0.5 and 3.5 MHz according to the speed and direction of movement of the movable cube. Outputs from A and B are amplified and subtracted.

The resultant signal is fed to a counter whose output indicates the magnitude of the displacement in the movable cube and whose rate of change indicates the velocity of motion.

This technique is used in applications requiring high-accuracy measurement, such as machine tool control. Such systems can measure displacements over ranges of up to 2 m with an inaccuracy of only a few parts per million. They are therefore an attractive alternative to the inductosyn, in having both high measurement resolution and a large measurement range within one instrument.

Fotonic sensor:

The fotonic sensor is one of many recently developed instruments that make use of fiber-optic techniques. It consists of a light source, a light detector, a fiber-optic light transmission system, and a plate that moves with the body whose displacement is being measured, as shown in Figure 10. Light from the outward fiber-optic cable travels across the air gap to the plate and some of it’s reflected back into the return fiber-optic cable. The amount of light reflected back from the plate is a function of the air gap length, x, and hence of plate displacement.

Measurement of the intensity of the light carried back along the return cable to the light detector allows displacement of the plate to be calculated. Common applications of fotonic sensors are measuring diaphragm displacements in pressure sensors and measuring the movement of bimetallic temperature sensors.

Figure 10 -- Emitter Detector Measured displacement; Optical fibers

Figure 11 --- Infrared radiation Reference photodiode Vane Measured displacement Measurement photodiode Output measurement signal

Noncontacting optical sensor:

Figure 11 shows an optical technique used to measure small displacements. The motion to be measured is applied to a vane, whose displacement progressively shades one of a pair of monolithic photodiodes that are exposed to infrared radiation. A displacement measurement is obtained by comparing the output of the reference (unshaded) photodiode with that of the shaded one. The typical range of measurement is_0.5mmwith an inaccuracy of_0.1%of full scale. Such sensors are used in some intelligent pressure-measuring instruments based on Bourdon tubes or diaphragms as described in Section 15.

2.9 Measurement of Large Displacements (Range Sensors)

One final class of instruments that has not been mentioned so far consists of those designed to measure relatively large translational displacements. These are usually known as range sensors and measure the motion of a body with respect to some fixed datum point. Most range sensors use an energy source and energy detector, but measurement using a rotary potentiometer and a spring-loaded drum provides an alternative method.

Figure 12 --- Moving body; Energy detector; Energy source; Fixed boundary

Energy source/detector-based range sensors:

The fundamental components in energy source/detector-based range sensors are an energy source, an energy detector, and an electronic means of timing the time of flight of the energy between the source and the detector. The form of energy used is either ultrasonic or light.

In some systems, both the energy source and the detector are fixed on the moving body and operation depends on the energy being reflected back from the fixed boundary as in Figure 12a. In other systems, the energy source is attached to the moving body and the energy detector is located within the fixed boundary, as shown in Figure 12b.

In ultrasonic systems, the energy is transmitted from the source in high-frequency bursts.

A frequency of at least 20 kHz is usual, and 40 kHz is common for measuring distances up to 5 m. By measuring the time of flight of the energy, the distance of the body from the fixed boundary can be calculated, using the fact that the speed of sound in air is 340 m/s. Because of difficulties in measuring the time of flight with sufficient accuracy, ultrasonic systems are not suitable for measuring distances of less than about 300 mm. Measurement resolution is limited by the wavelength of the ultrasonic energy and can be improved by operating at higher frequencies. At higher frequencies, however, attenuation of the magnitude of the ultrasonic wave as it passes through air becomes significant. Therefore, only low frequencies are suitable if large distances are to be measured. The typical inaccuracy of ultrasonic range finding systems is _0.5% of full scale.

Optical range-finding systems generally use a laser light source. The speed of light in air is about 3_108 m/s, so that light takes only a few nanoseconds to travel a meter. In consequence, such systems are only suitable for measuring very large displacements where the time of flight is long enough to be measured with reasonable accuracy.

Figure 13 --- Moving body Steel wire Pulley Rotary potentiometer Spring-loaded

drum

Rotary potentiometer and spring-loaded drum:

Another method for measuring large displacements that are beyond the measurement range of common displacement transducers is shown in Figure 13. This consists of a steel wire attached to the body whose displacement is being measured: the wire passes round a pulley and on to a spring-loaded drum whose rotation is measured by a rotary potentiometer.

A multiturn potentiometer is usually required for this to give an adequate measurement resolution. With this measurement system, it’s possible to reduce measurement uncertainty to as little as _0.01% of full-scale reading.

2.10 Proximity Sensors

For the sake of completeness, it’s proper to conclude this section on translational displacement transducers with consideration of proximity sensors. Proximity detectors provide information on the displacement of a body with respect to some boundary, but only insofar as to say whether the body is less than or greater than a certain distance away from the boundary. The output of a proximity sensor is thus binary in nature: the body is, or is not, close to the boundary.

Like range sensors, proximity detectors make use of an energy source and detector. The detector is a device whose output changes between two states when the magnitude of the incident reflected energy exceeds a certain threshold level. A common form of proximity sensor uses an infrared light-emitting diode (LED) source and a phototransistor. Light triggers the transistor into a conducting state when the LED is within a certain distance from a reflective boundary and the reflected light exceeds a threshold level. This system is physically small, occupying a volume of only a few cubic centimeters. If even this small volume is obtrusive, then fiber-optic cables can be used to transmit light from a remotely mounted LED and phototransistor. The threshold displacement detected by optical proximity sensors can be varied between 0 and 2 m.

Another form of proximity sensor uses the principle of varying inductance. Such devices are particularly suitable for operation in aggressive environmental conditions and can be made vibration and shock resistant by vacuum encapsulation techniques. The sensor contains a high-frequency oscillator whose output is demodulated and fed via a trigger circuit to an amplifier output stage. The oscillator output radiates through the surface of the sensor and, when the sensor surface becomes close to an electrically or magnetically conductive boundary, the output voltage is reduced because of interference with the flux paths. At a certain point, the output voltage is reduced sufficiently for the trigger circuit to change state and reduce the amplifier output to zero. Inductive sensors can be adjusted to change state at displacements in the range of 1 to 20 mm.

A third form of proximity sensor uses the capacitive principle. These can operate in similar conditions to inductive types. The threshold level of displacement detected can be varied between 5 and 40 mm.

Fiber-optic proximity sensors also exist where the amount of reflected light varies with the proximity of the fiber ends to a boundary, as shown earlier .

2.11 Choosing Translational Measurement Transducers

Choice between the various translational motion transducers available for any particular application depends mainly on the magnitude of the displacement to be measured, although the operating environment is also relevant.

The requirement to measure displacements of less than 2 mm usually occurs as part of an instrument that is measuring some other physical quantity, such as pressure, and several types of devices have evolved to fulfill this task. The LVDT, strain gauges, fotonic sensor, variable capacitance transducers, and noncontacting optical transducer all find application in measuring diaphragm or Bourdon tube displacements within pressure transducers. Load cell displacements are also very small, which are commonly measured by nozzle flapper devices.

For measurements within the range of 2 mm to 2 m, the number of suitable instruments grows.

Both the relatively inexpensive potentiometer and the LVDT, which is somewhat more expensive, are commonly used for such measurements. Variable inductance and variable capacitance transducers are also used in some applications. Additionally, strain gauges measuring the strain in two beams forced apart by a wedge (see Section 2.5) can measure displacements up to 50 mm. If very high measurement resolution is required, either the linear inductosyn or the laser interferometer is used.

Finally, range sensors are normally used if the displacement to be measured exceeds 2 meters.

As well as choosing sensors according to the magnitude of displacement to be measured, the measurement environment is also sometimes relevant. If the environmental operating conditions are severe (e.g., hot, radioactive or corrosive atmospheres), devices that can be protected easily from these conditions must be chosen, such as the LVDT, variable inductance, and variable capacitance instruments.

2.12 Calibration of Translational Displacement Measurement Transducers

Most translational displacement transducers measuring displacements up to 50 mm can be calibrated at the workplace level using standard micrometers to measure a set of displacements and comparing the reading from the displacement transducer being calibrated when it’s reading the same set of displacements. Such micrometers can provide a reference standard with an inaccuracy of _0.003% of full-scale reading. If better accuracy is required, micrometer-based calibrators are available from several manufacturers that reduce the measurement inaccuracy down to _0.001% of full-scale reading.

For sensors that measure displacements exceeding 50 mm (including those classified as range sensors), the usual calibration tool is a laser interferometer. This can provide measurement uncertainty down to _0.0002% of full-scale reading. According to which laser interferometer model is chosen, a measurement range up to 50meters is possible. Obviously, laser interferometers are expensive devices, which are also physically very large for a model measuring up to 50meters, and therefore calibration services using these are usually devolved to specialist calibration companies or instrument manufacturers.

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