3.1 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 and tolerances for dimensional, form, and positional deviations (Figure 3.1-1). The term ‘dimension’ refers both to the diameter of rotationally symmetrical work- pieces and to distances and angles between planes and straight lines and to cone angles. The sensors used for measurement can be classified according to the method used to acquire the measured value into mechanical, electrical, and optoelectronic sensors. A small proportion work by other methods, eg, pneumatic measuring methods. The sensors mainly work with point-by-point, usually tactile measured value ac- quisition. Contactless and wide-area measurements of characteristic variables of the rough shape are possible with optical sensors. 71 3 Sensors for Workpieces Fig. 3.1-1 Deviations of the macro shape of workpieces Sensors in Manufacturing. Edited by H.K. Tönshoff, I. Inasaki Copyright © 2001 Wiley-VCH Verlag GmbH ISBNs: 3-527-29558-5 (Hardcover); 3-527-60002-7 (Electronic) 3.1.1 Mechanical Measurement Methods By far the greatest number of measuring systems used in dimensional metrology work with tactile probes and mechanical transmission of the measured value. For acquisition and indication of the measured value, a linear scale is usually used or the measured value is transmitted to deflection of a needle, say, by means of a rack 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 depth measurements. The measured length is transmitted mechanically and a scale with millimeter divisions that can be read absolutely is used. Use of a Vernier scale provides 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 at which a graduation mark on the main scale is aligned with a graduation mark on the 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 of the Vernier scale with 10 graduation marks. Except for the depth gage, the scale of a caliper and the measuring object can- 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 included linearly in the result error. We therefore refer to it as a first-order error. 3 Sensors for Workpieces72 Fig. 3.1-2 Vernier caliper 3.1.1.2 Protractors A measuring instrument which works in an analogous way to the caliper is the universal protractor for measuring angles (Figure 3.1-4). The universal protractor also has an absolute angular scale and a Vernier scale, which allows the user to read off angular dimensions in steps of 5'. Models with a digital display are also available. 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 cali- pers. Micrometer calipers (Figure 3.1-5) are used for outside measurements and inside measurements (measuring range usually about 25 mm) and depth micro- meters for depth measurements. Drill-hole diameters can be measured using three-point inside micrometer gages. A threaded spindle is used to transfer the measured value to the scale on the sleeve. The graduations on the sleeve indicate steps, each of which corresponds to one turn of the threaded spindle. A further, finer subdivision is also marked on a circumferential 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 3.1 Macro-geometric Features 73 Fig. 3.1-3 Violation of the comparator principle on a caliper Tab. 3.1-1 Sine deviation for a measuring arm length l =40 mm Angular deviation, u 1' 5' 10' 1 8 Sine deviation, f (lm) 11.6 58.2 116.4 698.1 Fig. 3.1-4 Universal protractor (courtesy: Brown and Sharpe) that heat from the hands is not transferred to the measuring instruments, which could otherwise cause a thermally induced alteration in length. Special inserts for the fixed anvil and the measuring surface of the spindle per- mit an extension of the application range. For example, if a notch and cone are used, it is possible to measure flank diameters on threads, and larger measuring contacts are used to measure tooth widths. Models with numerical or digital dis- plays also exist. Micrometer gages ensure that the measuring object and the scale are aligned. Since the comparator principle is not violated, no first-order measuring error can occur; 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 13 lm (DIN 863-1). 3 Sensors for Workpieces74 Fig. 3.1-5 Micrometer caliper with measuring head Fig. 3.1-6 Cosine deviation in measure- ment using a micrometer caliper 3.1.1.4 Dial Gages With their comparatively short plunger travel (3 or 10 mm), dial gages (Fig- ure 3.1-7a, 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 required specified dimension with a material measure, say, a parallel gage block, and then to adjust the needle to a defined deflection (calibration). The displacement of the measuring bolt is transmitted to a gear-wheel mecha- nism via a rack, converting the distance measured to needle deflection. The result is displayed on a circumferential scale with a scale interval of typically 0.01 mm. Since dial gages indicate a width of backlash, measurements should be performed only touching the measuring object in the same direction as when calibrating. Ra- dial run-out measurements can therefore be afflicted with systematic errors. On dial gages, the needle can revolve around the scale several times over the entire plunger travel; a small pointer then counts the number of revolutions. Dial gages are also available in digital versions. The probe tip diameter is usually 3 mm, but numerous other probe styluses are available, eg, pointed, cutting edge, plane or ball measuring contacts, balls of other diameters, or measuring rollers. According to the measuring range, the maximum total discrepancy span is specified between 9 and 17 lm (DIN 878). 3.1 Macro-geometric Features 75 Tab. 3.1-2 Cosine deviation for spindle length d =20 mm Angular deviation, u 1' 5' 10' 1 8 Cosine deviation, f ( lm) 0.001 0.021 0.85 3.046 a) Dial gage b) Comparator dial c) Lever-type test indicator Fig. 3.1-7 Dial gage, comparator dial, and lever-type test indicator (courtesy: Mahr) 3.1.1.5 Dial Comparators Dial comparators (Figure 3.1-7b) are also mainly used for differential measure- ments, but the measuring range is smaller than that of dial gages, usually under 1 mm, with a smaller scale interval, starting at 0.5 lm according to the standards (DIN 879-1, DIN 879-3). The needle deflection only extends over the angular range of the scale, and the motion of the measuring bolt is transmitted to the point via a lever mechanism or a torsion spring, indicating a negligible width of backlash. Comparator dials with contact limits are used, for example, to indicate violation of tolerance ranges with a special display unit. The maximum total dis- crepancy span is specified as 1.2 times the scale interval (DIN 879-1). 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 dial gage, multiple revolutions of the needle around the scale are not recorded with an additional 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 mea- surement (Figure 3.1-8): 3 Sensors for Workpieces76 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 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 the measuring 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 sensors have in common is a reference mark that they require to permit absolute mea- surements. The incrementally determined intervals then refer to this reference mark which is approached as soon as the instrument is switched on. 3.1.2.1 Resistive Displacement Sensors Resistive displacement sensors in the form of potentiometers permit the measure- ment of lengths and angles. The resistance is varied in direct proportion to the linear or angular displacement via a sliding contact. The voltage, which depends on the resistance, is measured (Figure 3.1-9). Given a sufficiently high input resis- tance in the voltmeter, the following applies: U a  s s 0 Á U 0 or U a  u u 0 Á U 0 : 3:1-1 Resistance displacement pickups are available with a wound resistance wire on an insulating main body, or with a continuous resistive layer applied to a material substrate. The disadvantage is the wear on the sliding contact. 3.1.2.2 Capacitive Displacement Sensors Capacitive displacement measurement makes use of the effect that the capaci- tance of a plate capacitor depends on the distance between the capacitor plates. 3.1 Macro-geometric Features 77 Fig. 3.1-9 Potentiometer length and angle measurement On electrically conductive workpieces, contactless measurement is possible; the surface 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 high speed. One of its applications is therefore in-process monitoring of spindles in machine tools. On workpieces with insufficient electrical conductivity, the dimen- sional measurement has to be transmitted to a moving capacitor plate via a rigid measuring 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 U a depending on length s (Figure 3.1-10 shows a setup of a capacitive displacement sensor). The fol- lowing applies: U a  s 2s 0 Á U 0 : 3:1-2 In dimensional measurement, capacitive displacement sensors are actually used fairly rarely. They have become common as filling level meters and for the con- tactless measurement of material thicknesses. 3.1.2.3 Inductive Displacement Sensors Most electrical dimensional measurement sensors function inductively, there being 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 two coils varies as a function of the length measured. Inductive probes make use of the effect that in a coil carrying AC, an AC volt- 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 be varied 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 a differential circuit on inductive probes that produce an output signal that depends linearly 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 the plunger core sensor principle and LVDT probes on the transformer sensor princi- ple (Figure 3.1-11). 3 Sensors for Workpieces78 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 U a the following applies: U a  1 2K Á DL L Á U 0 3:1-3 where DL 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 central position toward one of the two coils. The maximum value is present if only one coil is completely covered by the plunger core. If it is moved further along the coil in the same direction, the induction voltage decreases again. The linearity 3.1 Macro-geometric Features 79 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 displace- ment of the plunger core is smaller than and included in the unambiguity range (Figure 3.1-13). LVDT probes, on the other hand, have one primary coil and two secondary coils that are arranged concentrically around the moveable plunger core. The primary coil receives an AC voltage of approximately 5 kHz that is transmitted to the sec- ondary coils in phase opposition. The measurement signal U a derived from the differential connection of the two secondary coils is directly proportional to the displacement s of the measuring bolt. The following applies: U a  K Á s Á U 0 : 3:1-4 Inductive displacement sensors can be operated with very small measuring forces (down to 0.02 N) on some types. Resolutions down to 0.01 lm and small linearity errors of below 1% permit high-precision dimensional measurements. They are also suitable for static and dynamic measurements. They are frequently used in multi-gaging measuring instruments and automatic measuring machines. When using inductive probes, the thermally induced zero point drift in lm/K, stating how the measured value indicated varies as a function of the temperature for a constant measured quantity, must be taken into account. Eddy current measurement is a special case of inductive dimensional measure- ment, which is suitable for contactless distance measurement, if the workpiece material is electrically conductive. If a coil that forms a magnetic field is brought close to an electrically conductive body, eddy currents form within it which, in turn, form a magnetic flux with opposite polarity. This causes a reduction in in- ductance in the coil, which is electrically measurable. The change in inductance depends on the distance between the coil and the measuring object. For eddy cur- rent sensors in a differential circuit, a linear relationship is established between the distance and the change in inductance. 3 Sensors for Workpieces80 Fig. 3.1-13 Unambiguity and linearity of the measurement signal of an inductive displacement sensor