Принципы нанометрологии (1027623), страница 26
Текст из файла (страница 26)
Capacitivesensors measure the change in capacitance as a conducting target is displacedwith respect to the sensor. Figure 5.7 shows a capacitive sensor andmeasurement target. In this parallel plate capacitor arrangement, thecapacitance, C, is given byC ¼3Ad(5.20)where 3 is the permittivity of the medium between the sensor and target, A isthe effective surface area of the sensor and d is the distance between thesensor and the target surface.
This relationship is not highly dependent onthe target conductivity and hence capacitance sensors can be used withFIGURE 5.7 A typical capacitance sensor set-up.99100C H A P T ER 5 : Displacement measurementa range of materials. Note that capacitance sensors can also be used tomeasure dielectric thickness and density by varying 3 and keeping d constant.Due to the effect of stray capacitance and the need to measure very lowvalues of capacitance (typically from 0.01 pF to 1 pF), capacitance sensorsusually require the use of a guard electrode to minimise stray capacitance.Capacitance sensors are used in the semiconductor, disk drive andprecision manufacturing industries, often to control the motion of a rotatingshaft.
Modern MEMS devices also employ thin membranes and comb-likestructures to act as capacitance sensors (and actuators) for pressure, acceleration and angular rate (gyroscopic) measurement [37,38]. High-accuracycapacitance sensors are used for control of MNT motion devices [39] andform the basis for a type of near-field microscope (the scanning capacitancemicroscope) [40].The non-linear dependence of capacitance with displacement can beovercome by using a cylindrical capacitor or by moving a flat dielectric platelaterally between the plates of a parallel plate capacitor [41]. These configurations give a linear change of capacitance with displacement.The environment in which it operates will affect the performance ofa capacitance sensor.
As well as thermal expansion effects, the permittivity ofthe dielectric material (including air) will change with temperature andhumidity [42]. Misalignment of the sensor and measurement surface willalso give rise to a cosine effect.Capacitance sensors are very similar to some inductive or eddy currentsensors (i.e. sensors that use the electromagnetic as opposed to the electrostatic field).
Many of the points raised above relate to both types of sensor. See[42] for a fuller account of the theory and practice behind capacitive sensors.5.4 Inductive displacement sensorsAs discussed above, inductive sensors are very similar to capacitive sensors.However, inductive sensors are not dependent upon the material in thesensor/target gap so they are well adapted to hostile environments wherefluids may be present in the gap.
They are sensitive to the target material andmust be calibrated for each material that they are used with. They alsorequire a certain thickness of target material to operate (usually fractions ofa millimetre, dependent on the operating frequency). Whilst they may havenanometre resolutions, their range of operation is usually some millimetres.Their operating frequencies can be 100 kHz and above.Another form of contacting sensor, based on inductive transduction, isthe linear variable differential transformer (LVDT).
An LVDT probe consistsInductive displacement sensorsof three coils wound on a tubular former. A centre-tapped primary coil isexcited by an oscillating signal of between 50 Hz and 30 kHz and a nonmagnetic rod, usually with an iron core, moves in and out of the tube.Figure 5.8 illustrates this design. As the rod moves the mutual inductancebetween the primary and two other, secondary, coils changes. A voltageopposition circuit gives an output potential difference that is directlyproportional to the difference in mutual inductance of the two secondarycoils that is in turn proportional to the displacement of the rod within thetube. When the core is central between the two secondary coils, the LVDTprobe is at its null position and the output potential difference is zero.LVDTs have a wide variety of ranges, typically 100 mm to 500 mmand linearities of 0.5 % or better.
LVDTs have a number of attractive features.First, there is no physical contact between the movable core and the coilstructure, which results in frictionless measurement. The zero output at itsnull position means that the signal can be amplified by an unlimited amount,and this essentially gives an LVDT probe infinite resolution, the only limitation being caused by the external signal-conditioning electronics. There iscomplete isolation between the input and output, which eliminates the needfor buffering when interfacing to signal-conditioning electronics.
Therepeatability of the null position is inherently very stable, making an LVDTFIGURE 5.8 Schematic of an LVDT probe.101102C H A P T ER 5 : Displacement measurementFIGURE 5.9 Error characteristic of an LVDT probe.probe a good null-position indicator. Insensitivity to radial core motionallows an LVDT probe to be used in applications where the core does notmove in an exactly straight line. Lastly, an LVDT probe is extremely ruggedand can be used in relatively harsh industrial environments (although theyare sensitive to magnetic fields).Figure 5.9 shows the ‘bow-tie’ error characteristic of a typical LVDT probeover its linear or measuring range.
Probes are usually operated around thenull position, for obvious reasons, although, depending on the displacementaccuracy required, a much larger region of the probe’s range can be used.LVDTs find uses in advanced machine tools, robotics, construction,avionics and computerised manufacturing. Air-bearing LVDTs are nowavailable with improved linearities and less damping. Modern LVDTs canhave multiple axes [43] and use digital signal processing [44] to correct fornon-linearities and to compensate for environmental conditions and fluctuations in the control electronics [45].5.5 Optical encodersOptical encoders operate by counting scale lines with the use of a light sourceand a photodetector.
They usually transform the light distribution into twosinusoidal electrical signals that are used to determine the relative positionbetween a scanning head and a linear scale. The grating pitch (resolution) ofthe scales varies from less than 1 mm to several hundred micrometres. Aswith interferometers, electronic interpolation of the signals can be used toOptical encodersproduce sub-nanometre resolution [5] and some of the more advanced opticalencoders can have accuracies at this level [46–48].The most common configuration of an optical encoder is based upona double grating system; one grating acts as the scale and the other is placedin the reading head.
The grating pair produces a fringe pattern at a certaindistance from the second grating (usually a Lau or moiré pattern). Thereading head has a photodetector that transforms the optical signal into anelectrical signal. When a relative displacement between the reading head andthe scale is produced, the total light intensity at the photodetector variesperiodically. The electronic signals from the photodetector are analysed inthe same manner as the quadrature signals from an interferometer (seesection 5.2.4). Figure 5.10 is a schema of a commercial optical encodersystem capable of sub-nanometre resolution. The period of the grating is512 nm. The reading head contains a laser diode, collimating optics and anindex grating with a period of 1024 nm (i.e.
twice the period of the scale). Thesignals collected by the detectors are transformed into quadrature signalswith a period of 128 nm (i.e. a quarter of the scale period).There are a number of errors that can affect the performance of an opticalencoder, which can be mechanical, electrical or optical [49]. MechanicalFIGURE 5.10 Schema of an optical encoder.103104C H A P T ER 5 : Displacement measurementerrors arise from deformation of the parts, thermal expansion and vibration.There may also be errors in the production of the gratings or dust particles onthe gratings. Variations in the light intensity, mechanical rotations betweenthe two gratings or variations in the amplification of the optical signals mayalso occur.
Correct design of the scanning head so that the encoder is robustto variations in the distances between the parts, rotations, variations inillumination conditions, etc. can minimize many of the error sources.Optical encoders can be linear or rotary in nature. The rotary versionsimply has the moving grating encoded along a circumference. The linear andangular versions often have integral bearings due to the difficulty of aligningthe parts and the necessity for a constant light intensity.
Optical encoders areoften used for machine tools, CMMs, robotics, assembly devices and precision slideways. A high-accuracy CMM that uses optical encoders is discussedin section 9.4.1.1. Some optical encoders can operate in more than one axisby using patterned gratings [50].5.6 Optical fibre sensorsOptical fibre displacement sensors are non-contact, relatively cheap and canhave sub-nanometre resolution, millimetre ranges at very high operatingfrequencies (up to 500 kHz). Optical fibres transmit light using the propertyof total internal reflectance; light that is incident on a media’s interface willbe totally reflected if the incident angle is greater than a critical angle (knownas Brewster’s angle [51]).
This condition is satisfied when the ratio of therefractive index of the fibre and its cladding is in proper proportion (seeFigure 5.11). The numerical aperture, NA, of an optical fibre is given byNA ¼ sin1 ðn21 n22 ÞFIGURE 5.11 Total internal reflectance in an optical fibre.(5.21)Optical fibre sensorswhere n1 and n2 are the refractive indexes of the fibre core and claddingrespectively.This refractive index ratio also governs the efficiency at which light fromthe source will be captured by the fibre; the more collimated the light fromthe source, the more light that will be transmitted by the fibre.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
