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Sensors in production systems such as machine tools or robots may be classified into four categories (Figure 2-1). They are activated either during operation or in the set-up phase. Three types of sensors may be applied during the operation: those which measure kinematic values such as position, velocity, orientation or an- gular velocity, sensors which are applied to control the process in adaptive control systems, and sensors which are used to monitor the production systems and to provide diagnostic functions to assure a high availability of the systems. Sensors for process control functions are shown in Chapters 3 and 4 and will not be men- tioned here. Sensors which are applied in the set-up phase are used after assem- bly to adjust or test the accuracy of the systems or to calibrate the interacting members of the kinematic chain. 2.1 Position Measurement In this section sensors are described which measure linear or rotational movements mainly during operations of machine tools and robots. These sensors became of es- 47 2 Sensors for Machine Tools and Robots H. K. Tönshoff, Universität Hannover, Hannover, Germany Fig. 2-1 Sensors in production systems 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) sential importance with the introduction of position control loops for numerical con- trolled machines (Figure 2-2) [1]. The applied electric and in a few cases hydraulic or pneumatic drives are not able to be positioned by themselves in a control chain but need a feedback of a position signal. An exception to these control loop-based drives are the digital controllable stepping motors. Their application is limited because of accuracy, dynamics, and power. Thus every numerical controlled axis of a machine, tool, or robot that means every feed movement needs at least one position sensor. Since the feed movement in a machine tool, eg, the tool movement of a turning ma- chine, determines the accuracy of the machine, properties of the sensors namely their resolution, their repeatability, their drift velocity, and others (see Chapter 1.3) are of fundamental importance for the accuracy of a production system. A sensor can be set either directly or indirectly. Indirect means that the travel or the position of a moved machine part such as a slide or a table of a machine tool or the arm of a robot are not directly measured but by means of a move- ment- transforming device (Figure 2-3). 2 Sensors for Machine Tools and Robots48 Fig. 2-2 Control loop in numerical controlled machine tools Fig. 2-3 Placement of position sensors This is normally a transformer from rotational to translatory movements for lin- ear moving slides such as a ball screw (see Figure 2-2), a pinion-rack, a screw- rack, a roll-band, or a wheel-track device. Strongly speed-reducing transmissions such as harmonic drives, worm drives, and others are used for rotational moving tables or arms. Because of the high speed reduction, the demands on the accu- racy of a rotational sensor are much higher if it is placed behind the transformer than before it. Indirect sensing in general has the advantage that there is no need for cost-effective measuring devices so that simple and reliable seals can be used. It has the disadvantage that errors of the transmission system are introduced in the measured quantity. These can be, for instance, thermal or elastic deformations of the ball screw or geometric and kinematical aberrations of the transmission system in robots (Figure 2-4). Therefore, the direct measuring principle should be used if high accuracy and small aberrations are required, eg, for radial positioning in grinding or turning machines. On the other hand, it has to be considered that indirect measurement very often gives a better chance to follow Abbe’s principle in machine tools (Fig- ure 2-5). This principle demands that the probe, in this case the travel of the ma- 2.1 Position Measurement 49 Fig. 2-4 Direct and indirect position measurement Fig. 2-5 Abbe’s principle for machine tools chine component, and the scale for measuring the travel be in alignment, other- wise errors can occur by non-orthogonality and by tilting effects. It is possible to reach the necessary alignment for indirect measuring systems approximately whereas the direct measuring system is usually placed parallel to the slide and is thus sensitive against tilting errors. Sensors can be separated in accordance with the kind of signal into analog and digital position-measuring devices. An example of an analog system is the voltage divider (Figure 2-6). The sensor is applied for limited relative resolutions. It can be based on a resistance wire or a vapor-deposited layer of carbon. The resistance of this element is R b  q Á l A 2-1 where the specific resistance q and the cross section A of the conducting wire or layer may be erroneous. In addition, the voltage U x has to be measured within the tolerance of the resolution. For example, the technical limit can be assumed to be 0.1 mV of a 10 V maximal voltage. That means a relative resolution of 10 –5 or a positional resolution of 1 lm limits the maximum travel to 100 mm. The digital sensor determines the position either by counting increments (digi- tal-incremental measurement) or by reading coded numbers (digital-absolute mea- surement) (Figure 2-7). The resolution is given by the width of the incremental unit. The length of measurement l and the incremental width s are connected by l  2 n s 2-2 where n is the number of bits necessary to describe the maximum length with a resolution of s. For the example of s =1 lm and l= 250 mm, n  log À l s Á log 2  17:9 2-3 2 Sensors for Machine Tools and Robots50 Fig. 2-6 Potentiometric sensor This means that 18 bits have to be implemented in the counter of an incremental system or 18 channels have to be incorporated in an absolute system. The incre- mental measurement has the disadvantage that the position can only be deter- mined relatively. The digital absolute sensor, on the other hand, has the disadvan- tage that the system needs a large number of channels for a long measuring length and a high resolution and is therefore expensive. All three mentioned kinds of measurement, the analog, the absolute-digital and the incremental-digital principle, have their specific advantages. Therefore, the idea of combining favor- able abilities is not unreasonable. This leads to the cyclic-absolute measuring prin- ciple. It takes advantage of the absolute character of the analog system applying it only on limited measuring lengths and of the incremental sensing principle with its simple structure and robustness. It is shown schematically in Figure 2-8. 2.1 Position Measurement 51 Fig. 2-7 Digital measuring principle Fig. 2-8 Principle of cyclic-absolute position measurement The resolver is an absolute-cyclic measuring system. It is based on the inductive principle and measures angular or rotational movements. The resolver is often ap- plied in an indirect measuring system. It is basically a transformer consisting of three windings (Figure 2-9). The stator has two windings whose active directions are exactly placed at 90 8. The rotor carries a third coil, the secondary system. High-frequency voltages are acting at the two stator systems which are 908 electri- cally phase shifted: U 1  ^ U 0 sin xt U 2  ^ U 0 cos xt They induce corresponding voltages in the secondary coil which is rotated against the stator by a: U i1  k ^ U 0 sin xt cos a U i2  k ^ U 0 cos xt sin a where k is the coupling factor of the transformer. The two voltages U i1 and U i2 are added to give U i  k ^ U 0 sinxt  a2-4 Comparing the phase between U 1 and U i 1,2 , the searched for angle a can be di- rectly determined. A phase comparison can be made by a phase-locked loop. In another kind of implementation the rotor system is supplied with U R = ^ U sin !t. The induced voltage in the stator coils is modulated by the angle of rotation a due to the spatial arrangement: U s1  k ^ U 0 sin xt sin a U s2  k ^ U 0 sin xt cos a 2 Sensors for Machine Tools and Robots52 Fig. 2-9 Operation and construction of a resolver In this implementation the quotient of the stator- induced voltages is calculated by U s1 U s2  sin a cos a  tan a 2-5 The searched for angle a is determined by an arctan algorithm. This is called the ratiometric method. Resolvers are supplied with alternating current of high frequency, hence the space requirement can be minimized. An upper limit is given at 0.4–1 kHz be- cause of the iron within the transmitter. The resolution might reach 1.5·10 –3 de- grees, but the accuracy of the sensor is mainly determined by the manufacturing accuracy, which influences the costs substantially. The resolver is therefore mostly applied for less critical resolutions where it is fairly inexpensive. The resolver principle is also used for linear sensors. The inductosyn ® sensor is basically a resolver which is straightened in the plane. It is a very common ap- plied cyclic absolute measuring device (Figure 2-10). Similarly to the resolver, the scale or the reader can be supplied with a high-fre- quency alternating current (120 kHz). The signal processing methods are the same. If the alternating voltage is applied to the scale the following voltage is in- duced in the reader with coupling constant k: U R1  k ^ U s sin xt cos 2p s x U R2  k ^ U s sin xt sin 2p s x 2-6 because the reader includes a longitudinal phase shift of s/4. The position x can therefore be determined, for instance, by the ratiometric method. Compared with the resolver, the resolution can be 1000 times higher. The measurement is analog within the domain of the division of 2 mm or 0.1 in. The signal is repeated cycli- cally. The divisions have to be counted or resolvers have to be applied additionally 2.1 Position Measurement 53 Fig. 2-10 Principle of the inductosyn ® sensor to provide the coarse measurement. Inductosyn ® devices are available in modules of 250–1000 mm. They can be serially mounted. The assembly has to be very ac- curate to avoid errors at the joints. It is usually made by interferometric means. A digital-incremental sensor is shown in Figure 2-11. The information is given only relatively. The impulses have to be counted. A reference point must be given, for instance, by driving to a micro limit switch when starting the measurement. These sensors often work by the optical principle. The divisions are applied on glass scales by vapor deposition. The sampling can work by direct or transmitted light. The principle is explained by the transmitted light method. Fine lines are applied on the glass scale. The transparent and black lines can be equal in width. Divisions of 10 lm are used in practice. The width is limited because of the wave- length of the applied light. A scanning reticle is moved along the scale with the table whose position or travel is to be measured. Using a scale with several divi- sions means an increase in the light energy which is received by the photo detec- tor. The width ratio of the transparent to the non-transparent slots can vary. Using a narrower sampling slot (d ( s=2), the light intensity at the receiver is stronger. The receiver gives almost a rectangular signal (Figure 2-12; left). The properties of this principle are: · the received light energy is comparatively low; · the signal is of digital nature; · it is only appropriate for coarse divisions; · the information is gained by counting the signal impulses. According to another principle, the non-transparent and the transparent sections are equal in width. The photo receiver delivers a value-continuous signal (Fig- ure 2-12 right). The properties are: · the signal is of analog nature and the resolution is determined only by the sig- nal-to-noise ratio; · the received light energy is comparatively large; · a further increase in resolution is possible. 2 Sensors for Machine Tools and Robots54 Fig. 2-11 Digital-incremental sensor The value of the continuous signal can be used for further improvement of the re- solution as can be seen from Figure 2-13. Instead of the direct shaping of one im- pulse, several impulses are gained from the triangular signal by a comparison with threshold values, a kind of interpolation. The Moiré effect can be used for scanning glass scales (Figure 2-14). The scale and the reader are tilted against each other by a small angle. Moiré’s stripes are generated using the through-light method. These stripes move with much higher speed than the scale. A photo receiver delivers a sine signal of the moving Moiré’s stripes. A sine and a cosine signal are received if two photo receivers which are displaced by one quarter of the period of Moiré’s stripes are applied. Information on the position can be obtained with high accuracy by an electronic interpolation unit. The two signals are amplified by defined factors and added according to the following equation: 2.1 Position Measurement 55 Fig. 2-12 Influence of sampling slot on photosignal Fig. 2-13 Increase of resolution for incremental sensors a sin x  b cos x   a 2  b 2 p sin  x  arctan b a  2-7 Several phase-shifted signals are achieved by this algorithm, which can generate a high resolution of the sensor after an impulse shaping operation (Figure 2-15). The measuring step can be 1/20 or 1/200 of the division period, which is an inter- polation factor up to 1 :100. A resolution of 50 lm can be reached by such incre- mental sensors. The resolution is limited without further means by the scale division or the nor- mal which is applied for digital measuring systems. The required accuracy for high-precision machine tools is <0.5 lm. It is difficult to produce scales with such divisions with the necessary accuracy. One measure to overcome this limitation is the application of interpolation methods. One increment can be divided electroni- cally into an integral number of partitions. 2 Sensors for Machine Tools and Robots56 Fig. 2-14 Scanning with Moiré stripes Fig. 2-15 Magnification of division for incremental sensors [...]... The end of the pendulum is one part of a differential capacitor By this arrangement the electric signal U is proportional to the inclination angle with a good linearity better than 1% The pendulum is strongly damped by oil If the pendulum is built in a mechanical or optical indexing head, any direction can be measured Furthermore, angles can be measured by the resolver principle as shown in Figure 2-9 . 2-2), a pinion-rack, a screw- rack, a roll-band, or a wheel-track device. Strongly speed-reducing transmissions such as harmonic drives, worm drives, and. Using a narrower sampling slot (d ( s=2), the light intensity at the receiver is stronger. The receiver gives almost a rectangular signal (Figure 2-12; left). The