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The sensors used for measurement can be classified according to the methodused to acquire the measured value into mechanical, electrical, and optoelectronicsensors.. Mechanical Measureme

Macro-geometric Features

A Weckenmann, Universität Erlangen-Nürnberg, Erlangen, Germany

Measurement of macro-geometric characteristic variables involves the acquisition

of features of geometric elements that are defined in design by dimensions andtolerances for dimensional, form, and positional deviations (Figure 3.1-1) Theterm ‘dimension’ refers both to the diameter of rotationally symmetrical work-pieces and to distances and angles between planes and straight lines and to coneangles

The sensors used for measurement can be classified according to the methodused to acquire the measured value into mechanical, electrical, and optoelectronicsensors A small proportion work by other methods, eg, pneumatic measuringmethods

The sensors mainly work with point-by-point, usually tactile measured value quisition Contactless and wide-area measurements of characteristic variables ofthe rough shape are possible with optical sensors

ac-3

Sensors for Workpieces

Fig 3.1-1 Deviations of the macro

shape of workpieces

Copyright © 2001 Wiley-VCH Verlag GmbH ISBNs: 3-527-29558-5 (Hardcover); 3-527-60002-7 (Electronic)

Mechanical Measurement Methods

By far the greatest number of measuring systems used in dimensional metrologywork with tactile probes and mechanical transmission of the measured value Foracquisition and indication of the measured value, a linear scale is usually used orthe measured value is transmitted to deflection of a needle, say, by means of arack and pinion Indication is analog Measuring instruments with a digital dis-play usually use measuring systems with capacitive, inductive, or optoelectronic(Section 3.1.4) measured value acquisition

3.1.1.1 Calipers

The various designs of calipers (DIN 862) are used for outside, inside, and depthmeasurements The measured length is transmitted mechanically and a scale withmillimeter divisions that can be read absolutely is used Use of a Vernier scaleprovides an additional means of displaying 1/10, 1/20, or 1/50 mm graduations(Figure 3.1-2) The function, eg, of the 1/10 mm Vernier scale, is based on provid-ing a length of 39 mm with 10 graduation marks at equal intervals The point atwhich a graduation mark on the main scale is aligned with a graduation mark onthe Vernier scale indicates the number of 1/10 mm on the measured length.Sometimes a division with 20 graduation marks or a rotary dial is used instead ofthe Vernier scale with 10 graduation marks

Except for the depth gage, the scale of a caliper and the measuring object not be fully aligned This violation of Abbe’s comparator principle causes a sine de-viation between the scale and the slider due to an angular deviation (Figure 3.1-3,Table 3.1-1) When expanding into a Taylor series, the angle of the tilt is includedlinearly in the result error We therefore refer to it as a first-order error

can-Fig 3.1-2 Vernier caliper

3.1.1.2 Protractors

A measuring instrument which works in an analogous way to the caliper is theuniversal protractor for measuring angles (Figure 3.1-4) The universal protractoralso has an absolute angular scale and a Vernier scale, which allows the user toread off angular dimensions in steps of 5' Models with a digital display are alsoavailable Their smallest graduation is 1'

3.1.1.3 Micrometer Gages

Some types of micrometer gages (DIN 863) can be used for the same tasks as pers Micrometer calipers (Figure 3.1-5) are used for outside measurements andinside measurements (measuring range usually about 25 mm) and depth micro-meters for depth measurements Drill-hole diameters can be measured usingthree-point inside micrometer gages

cali-A threaded spindle is used to transfer the measured value to the scale on thesleeve The graduations on the sleeve indicate steps, each of which corresponds toone turn of the threaded spindle A further, finer subdivision is also marked on acircumferential division on the scale thimble The scale interval is usually 0.01

mm A slip clutch ensures that the measuring force is limited Insulation ensures

Fig 3.1-3 Violation of the comparator

that heat from the hands is not transferred to the measuring instruments, whichcould otherwise cause a thermally induced alteration in length.

Special inserts for the fixed anvil and the measuring surface of the spindle mit an extension of the application range For example, if a notch and cone areused, it is possible to measure flank diameters on threads, and larger measuringcontacts are used to measure tooth widths Models with numerical or digital dis-plays also exist

per-Micrometer gages ensure that the measuring object and the scale are aligned.Since the comparator principle is not violated, no first-order measuring error canoccur; only a second-order error remains (also called a cosine deviation, Fig-ure 3.1-6), which is much less significant (Table 3.1-2) According to the measur-ing range, the maximum total discrepancy span is specified between 4 and 13lm(DIN 863-1)

Fig 3.1-5 Micrometer caliper with measuring head

Fig 3.1-6 Cosine deviation in ment using a micrometer caliper

measure-3.1.1.4 Dial Gages

With their comparatively short plunger travel (3 or 10 mm), dial gages ure 3.1-7 a, DIN 878) are mostly used for differential measurements Their applica-tions are checking straightness, parallelism, or circularity To determine an abso-lute dimension with a dial gage and stand, it is first necessary to set the requiredspecified dimension with a material measure, say, a parallel gage block, and then

(Fig-to adjust the needle (Fig-to a defined deflection (calibration)

The displacement of the measuring bolt is transmitted to a gear-wheel nism via a rack, converting the distance measured to needle deflection The result

mecha-is dmecha-isplayed on a circumferential scale with a scale interval of typically 0.01 mm.Since dial gages indicate a width of backlash, measurements should be performedonly touching the measuring object in the same direction as when calibrating Ra-dial run-out measurements can therefore be afflicted with systematic errors Ondial gages, the needle can revolve around the scale several times over the entireplunger travel; a small pointer then counts the number of revolutions Dial gagesare also available in digital versions The probe tip diameter is usually 3 mm, butnumerous other probe styluses are available, eg, pointed, cutting edge, plane orball measuring contacts, balls of other diameters, or measuring rollers According

to the measuring range, the maximum total discrepancy span is specified between

3.1.1.6 Lever-type Test Indicators

Lever-type test indicators (Figure 3.1-7 c, DIN 2270) are similar to comparator dials

in both form and function The angular deflection of the stylus is also transmitted

to the needle via a lever mechanism A circumferential scale with a scale interval

of 0.002 mm is used for display The measuring range is smaller than 1 mm.Although lever-type test indicators use a circumferential scale, unlike on a dialgage, multiple revolutions of the needle around the scale are not recorded with anadditional small needle The admissible deviation is specified

3.1.2

Electrical Measuring Methods

Electrical dimensional measurement has clear advantages over mechanical methods:

· low measuring forces;

· small dimensions of the measured value pickup;

· separation of the measured value pickup and the display unit;

· simple amplification and combination of measuring signals;

· possibility of electrical further processing of the measured length;

· easy connection to a computer and data processing

This is offset by a greater handling effort

It is possible to distinguish between three types of electrical dimensional surement (Figure 3.1-8):

mea-Fig 3.1-8 Working principle of electrical dimensional measurements

· resistive displacement sensors;

· capacitive displacement sensors;

· inductive displacement sensors

A length can be acquired either continuously and analog or incrementally In cremental systems, numerous basic measuring elements (eg, magnets) are ar-ranged consecutively at defined intervals on a scale and the number of zero cross-ings that the measuring bolt produces in the measured signal as it passes themeasuring elements is counted The measured value is therefore digitized Com-mon incremental methods of electrical dimensional measurement function mag-netically, capacitively, or inductively What all incremental measured value sensorshave in common is a reference mark that they require to permit absolute mea-surements The incrementally determined intervals then refer to this referencemark which is approached as soon as the instrument is switched on

in-3.1.2.1 Resistive Displacement Sensors

Resistive displacement sensors in the form of potentiometers permit the ment of lengths and angles The resistance is varied in direct proportion to thelinear or angular displacement via a sliding contact The voltage, which depends

measure-on the resistance, is measured (Figure 3.1-9) Given a sufficiently high input tance in the voltmeter, the following applies:

3.1.2.2 Capacitive Displacement Sensors

Capacitive displacement measurement makes use of the effect that the tance of a plate capacitor depends on the distance between the capacitor plates

capaci-Fig 3.1-9 Potentiometer length and angle measurement

On electrically conductive workpieces, contactless measurement is possible; thesurface of the workpiece is then used as a moveable capacitor plate itself The ad-vantage lies in the almost inertialess measured value acquisition which, for exam-ple, permits circular or axial measurement on cylindrical parts rotating at highspeed One of its applications is therefore in-process monitoring of spindles inmachine tools On workpieces with insufficient electrical conductivity, the dimen-sional measurement has to be transmitted to a moving capacitor plate via a rigidmeasuring bolt.

If all the capacitor plates of a capacitive displacement sensor used in the

differ-ential method are identical, it is possible to measure voltage Ua depending on

length s (Figure 3.1-10 shows a setup of a capacitive displacement sensor) The

3.1.2.3 Inductive Displacement Sensors

Most electrical dimensional measurement sensors function inductively, therebeing two different types of inductive displacement sensors: the plunger core sen-sor, in which the inductance of a coil varies as a function of the length measured,and the transformer sensor, in which the transformational coupling between twocoils varies as a function of the length measured

Inductive probes make use of the effect that in a coil carrying AC, an AC age is induced having the opposite polarity to the excitation voltage The magni-tude of the voltage depends on the inductance of the coil This inductance can bevaried by moving a magnetic core (plunger core) in the magnetic field of a coil.Because the inductance measurable via the induction voltage depends on the dis-placement of the magnetic core in a nonlinear way, the coils are connected in adifferential circuit on inductive probes that produce an output signal that dependslinearly on the displacement of the magnetic core after phase-dependent rectifica-tion Two different types of probes are in common use: half-bridge probes on theplunger core sensor principle and LVDT probes on the transformer sensor princi-ple (Figure 3.1-11)

volt-Fig 3.1-10 Capacitive displacement sensors

in the differential method

On half-bridge probes (Figure 3.1-12), both coils are directly fed an AC voltage

of approximately 10 kHz For the measurement signal, the ferrite core functions

as a voltage divider For the measured induction voltage Uathe following applies:

Uaˆ 1

2K
DL

whereDL is proportional to the displacement s and K is a constant If the plunger

core is precisely in the center between the two coils, the induction voltage is zero.The induction voltage increases if the plunger core is moved out of the centralposition toward one of the two coils The maximum value is present if only onecoil is completely covered by the plunger core If it is moved further along thecoil in the same direction, the induction voltage decreases again The linearity

Fig 3.1-11 Working principles of inductive probes

Fig 3.1-12 Design of an inductive half-bridge probe (courtesy: TESA)

range in which the measurement signal is directly proportional to the ment of the plunger core is smaller than and included in the unambiguity range(Figure 3.1-13).

displace-LVDT probes, on the other hand, have one primary coil and two secondary coilsthat are arranged concentrically around the moveable plunger core The primarycoil receives an AC voltage of approximately 5 kHz that is transmitted to the sec-

ondary coils in phase opposition The measurement signal Ua derived from thedifferential connection of the two secondary coils is directly proportional to the

displacement s of the measuring bolt The following applies:

Inductive displacement sensors can be operated with very small measuring forces(down to 0.02 N) on some types Resolutions down to 0.01lm and small linearityerrors of below 1% permit high-precision dimensional measurements They arealso suitable for static and dynamic measurements They are frequently used inmulti-gaging measuring instruments and automatic measuring machines Whenusing inductive probes, the thermally induced zero point drift in lm/K, statinghow the measured value indicated varies as a function of the temperature for aconstant measured quantity, must be taken into account

Eddy current measurement is a special case of inductive dimensional ment, which is suitable for contactless distance measurement, if the workpiecematerial is electrically conductive If a coil that forms a magnetic field is broughtclose to an electrically conductive body, eddy currents form within it which, inturn, form a magnetic flux with opposite polarity This causes a reduction in in-ductance in the coil, which is electrically measurable The change in inductancedepends on the distance between the coil and the measuring object For eddy cur-rent sensors in a differential circuit, a linear relationship is established betweenthe distance and the change in inductance

measure-Fig 3.1-13 Unambiguity and linearity

of the measurement signal of an inductive displacement sensor

3.1.2.4 Magnetic Incremental Sensors

Incremental measuring systems based on magnets use a scale with permanentmagnets as a material measure The magnets are attached to the scale with alter-nating opposite polarity The reading is obtained using ferromagnetic heads intowhich an excitation current with a defined frequency is injected

Depending on the position of the magnetic poles of the reading head with spect to the permanent magnets in the scale, a different voltage will be generated

re-at the output coils If the poles of the magnet head are precisely symmetrical withrespect to one pole of the scale, the magnetic fluxes produced by the excitationcoil are shorted In that case, no signal is present at the output coil However, ifthe two pole shoes are precisely in the center between a north and a south pole ofthe scale, induction is caused in the output coil with double the frequency of theexcitation current (Figure 3.1-14) Because of the different responses of the read-ing head to different positions with respect to the magnetic scale, it is possible tocount how many period lengths of the individual permanent magnets are passedduring motion along the scale The direction of motion can be detected if twomagnet heads are used for reading, which are arranged such that the measure-ment signal determined at the same time has a phase offset of one fourth of aperiod length The direction of motion can be determined from the time se-quence of the signal progressions between the heads

3.1.2.5 Capacitive Incremental Sensors

Capacitive incremental sensors use scales on which a graduation of thin metal foil

is attached An identical metal foil is attached to the measuring element oppositethe scale, so that the measuring element and scale together act as a capacitor Ifthe measuring element moves along the scale, the capacitance varies sinusoidally

It is possible to derive the number of graduation periods passed from the number

of zero crossings Additional interpolation of the sinusoidal signal permits tions up to 0.1lm Here, too, it is possible to detect the direction of movement

resolu-by the fact that a second division is offset resolu-by a fourth of the graduation period.Capacitive incremental scales are used in calipers and micrometer calipers Thelow energy requirement permits uninterrupted use of the measuring instrumentwith a battery for about 1 year

Fig 3.1-14 Working principle of magnetic

incremental linear measuring systems

3.1.2.6 Inductive Incremental Sensors

The best known example of an inductive incremental sensor is the inductosyn.Depending on the type, inductosyn measuring systems can be used for angularmeasurement (rotary inductosyn) or displacement measurement (linear inducto-syn) A meandering conductor path is applied to a nonmagnetic, flat substratematerial, eg, made of glass by means of an etching process A scale with the re-quired measurement length and a shorter, moveable cursor, on which two sepa-rate conductor paths offset by one fourth of a division period are the basic struc-ture of an inductosyn (Figure 3.1-15)

An alternating voltage is applied to the conductor path of the scale This induces avoltage in the conductor paths on the cursor according to the transformer principle.The amplitude of the induced voltage depends on the relative positions of the con-ductor paths on the scale and cursor If the two paths coincide exactly, the amplitude

of the induced voltage is at a maximum If the conductor path of the cursor is cisely in the gap between the conductor paths of the scale, no induction occurs (Fig-ure 3.1-16) The measurement signals are evaluated in an analogous way to themethods described above for magnetic and capacitive incremental sensors.The inductosyn is frequently used for positioning in machine tools because it islargely insensitive to dirt, contrary to optoelectronic measurement methods de-

pre-Fig 3.1-15 Design of the linear inductosyn

Fig 3.1-16 How the measurement signal

is obtained in an inductosyn

scribed below On linear guideways it allows almost any measurement length byadjoining several scales With a pole pitch of typically 1–2 mm, resolutions down

to 1lm can be achieved

3.1.3

Electromechanical Measuring Methods

Each modern coordinate measuring machine (CMM) needs at least one sensingdevice for the workpiece data acquisition Originally, sets of hard probes (spheres,cones, disk, and cylinders) were the only probes available for use with a CMM.Different probe tips are shown in Figure 3.1-17

Today, electromechanical devices are used exclusively The structure of such a sing device system is crucial for the measuring accuracy of the CMM, which is ap-propriate within the range from a fewlm to 0.1 lm Today’s touch trigger probe arealways afflicted by their geometric structure with a first-order error (violation of theAbbé principle, triangle characteristics of the six-point support) (something similarapplies also to measuring sensing devices) While probing the workpiece the touch-ing strength results in a deflection and bending of the stylus shaft via stylus tip Thedeflection is passed on to the measuring element (points of support, Figure 3.1-18)which are not aligned with the stylus shaft and affect the first-order error These er-rors (first-order error, bending of stylus shaft) are compensated nowadays by time-consuming software calibrations The result depends, however, on geometry of link-age, touching rate, touching force, and temperature

sen-Probes are made in a touch trigger or scanning mode

Fig 3.1-17 Different probe tips

3.1.3.1 Touch Trigger Probe

The simplest sensor is the so-called touch trigger probe It possesses a prestressedkink, which can be yielded in five or six coordinate directions and also in each in-termediate direction After sensing, the sensing device moves and returns in aspatially fixed resting position This is uniquely made by three supporting points

A well-known principle is the combination of cylinder and balls

The sensor signal is produced by opening and closing of one or more cal contacts (Figure 3.1-18) or establishing an external electrical contact betweenthe probe and the workpiece This signal leads to immediate freezing of length-measured values in all axes at their current value This measuring procedure iscalled dynamic, since the measurement takes place during the movement of theprobe relative to the workpiece

mechani-For high accuracy, a rigid structure of the device is necessary, otherwise the celeration forces necessary for movement cause deformations and thus inaccura-cies This principle is not completely free from accuracy losses, which are depen-dent on the preload and the measuring direction These problems are overcomewith piezo sensor touch trigger probes generating a trigger signal sensitive to ten-sion and compression Touch trigger probes are used at workpieces whenever in-dividual points should be taken as fast as possible

ac-3.1.3.2 Continuous Measuring Probe System

The tactile three-dimensional precision measuring technique achieved in 1973 anew quality of three-axes probe measurement By this means it is possible to readoff the length-measured values with complete deadlock of the measuring axes ofthe coordinate measuring machines In contrast to dynamic measurement with aswitching probe, the measurement takes place statically (Figure 3.1-19) The resultwas a substantial increase in the measuring accuracy of coordinate measuring ma-chines

Fig 3.1-18 Touch trigger probe

touching a work piece