Abstract:
The invention relates to a measuring apparatus comprising a sensing head ( 15 ) for determining the position of a primary part ( 27 ) on a secondary part. The sensing head ( 15 ) is fixedly connected to a primary part ( 27 ) or is integrated therein while the primary part ( 27 ) and the secondary part form a linear motor ( 30 ). Furthermore, the secondary part is embodied as a rack ( 16 ) which is provided at least with ferromagnetic material and preferably equidistant teeth ( 18 ) in a preferred direction ( 13 ), said teeth ( 18 ) containing at least ferromagnetic material. The sensing head ( 15 ) can be moved in the preferred direction ( 13 ) and opposite thereto. An air gap is located between the sensing head ( 15 ) and the rack ( 16 ) while the sensing head ( 15 ) is equipped with at least one sensor ( 1 - 12, 19, 31 ), by means of which magnetic fields can be measured in order to determine a position.

Description:
BACKGROUND OF THE INVENTION 
     The invention relates to a measuring apparatus with a measuring head for determining the position of a primary part on a secondary part and to a method for determining the position of a primary part on a secondary part with a measuring head. 
     Electric motors are used in a very large number of technical fields. In the case of electric motors it is necessary to distinguish between DC motors, AC motors and three-phase motors. Electric motors can furthermore be split into rotary motors and linear motors. In order to approach a specific rotary angle in the case of rotary motors or specific path distances in the case of linear motors, it is necessary to measure the present rotary angle or the present path distance. In this case, the measurement should take place as precisely as possible in order that the corresponding rotary angle or the corresponding path distance can be approached precisely and quickly by means of a suitable regulating device. 
     Previous measurement systems for position determination for linear motors are based on an optical measurement, for example. 
     Disadvantages with an optical measurement, however, are the fact that it is expensive to implement and that the optical measurement is very easily impaired or made impossible by contamination in the linear motor or in its surrounding environment, so that failure of the regulating device results. 
     SUMMARY OF THE INVENTION 
     Against this background, the invention is based on the object of specifying a measuring head and a method for position determination for a linear motor, with which the costs are reduced in comparison with the previous optical solution and the reliability is increased in comparison with conventional solutions. 
     This object is achieved according to the invention by a measuring apparatus with a measuring head for determining the position of a primary part on a secondary part,
         the measuring head being fixedly connected to a primary part or integrated in it,   the primary part and the secondary part forming a linear motor,   the secondary part being in the form of a toothed rack,   the toothed rack having at least ferromagnetic material   and, in a preferred direction, having teeth with predeterminable spacings, which teeth have at least ferromagnetic material,   the measuring head being capable of moving in the preferred direction and at least in the opposite direction thereto,   an air gap being located between the measuring head and the toothed rack, and   the measuring head having at least one sensor, by means of which magnetic fields can be measured for the purpose of position determination.       

     Furthermore, the object is achieved by a linear motor according to the invention and by a method for determining the position of a primary part on a secondary part. 
     Advantageously, the costs in comparison with a previous optical solution for position determination are reduced by the measuring apparatus according to the invention with a measuring head. Furthermore, the reliability is markedly increased since contamination cannot result in the measurement being impaired in contrast to an optical solution. 
     The toothed rack can either correspond to the secondary part of the linear motor or else also in addition be installed in the linear motor for the purpose of position determination. In this case, the toothed rack is fitted in the vicinity of the movable part in the linear motor. The toothed rack is in this case, for example, constructed from laminates. 
     It is advantageous if the measuring head is fixedly connected to a primary part or is integrated in it and the primary part and the toothed rack form a linear motor and the toothed rack acts as the secondary part. That is to say that, in combination with a linear motor, the measuring apparatus according to the invention with a measuring head can be used in an advantageous manner by the measuring head being fixedly connected to the primary part of the linear motor and measuring the position of the primary part relative to the stationary secondary part. The measuring head according to the invention can in this case also be completely integrated in the primary part, with the result that it is even no longer possible to identify it as an independent object. In the latter case, the sensors are therefore installed directly in the primary part. It is therefore possible to design the unit comprising the primary part and the measuring head to be compact. 
     In this case, the teeth are preferably arranged equidistantly in a preferred direction on the toothed rack. However, the teeth can also have different spacings. 
     In a first configuration, the measuring head has at least two sensors, which can be used to detect magnetic fields, the sensors being arranged on the measuring head offset in the preferred direction of the toothed rack. Advantageously, improved position determination is therefore achieved in comparison with the case with only one sensor. 
     The measuring head has a position relative to the toothed rack in which the sensors are located either directly over the teeth of the toothed rack or next to the toothed rack at the height of the teeth. Alternatively, the sensors can also be shaped in such a way that they surround the teeth, but do not touch them. 
     The measuring apparatus according to the invention with a measuring head can be characterized by the fact that
         at least one sensor has at least ferromagnetic material,   a sensor has at least two sensor heads, which are arranged so as to follow on from one another in the preferred direction of the toothed rack or in the preferred direction of the toothed rack parallel to one another and are connected to one another by a connecting element,   the connecting element and/or one or both sensor heads are also surrounded by an exciter coil, to which an excitation AC voltage can be applied,   the connecting element and/or one or both sensor heads is surrounded by a measuring coil, at which an induced voltage can be tapped off,   the air gap between the sensor and the toothed rack in the region of the connecting element is greater than in the region of the sensor heads, with the result that, when the excitation AC voltage is applied, the amplitudes of the induced voltage are increased if the sensor is located centrally over one tooth since in this case the magnetic circuit is closed over the tooth.       

     The induced voltage is therefore a measure of whether a sensor is located directly over a tooth, only partially overlaps it or is located over a tooth interspace. If the sensor is located over a tooth, the magnetic circuit over the tooth is closed, and the amplitudes of the induced voltage are at a maximum. In this embodiment, at least one AC voltage source, which provides the excitation AC voltage, is associated with the exciter coils. The air gap in the region of the connecting element can alternatively also correspond to that in the region of the sensor heads. 
     A further embodiment of the measuring apparatus according to the invention with a measuring head can be characterized by the fact that
         at least one sensor has at least ferromagnetic material,   a sensor has at least two sensor heads, which are arranged so as to follow on from one another in the preferred direction of the toothed rack or in the preferred direction of the toothed rack parallel to one another and are connected to one another by a connecting element, which has a measuring element for measuring the magnetic field, such as a magnetic dependent resistor or a Hall sensor,   the sensors and/or the teeth of the toothed rack have permanent magnets,   the air gap between the sensor and the toothed rack in the region of the connecting element is greater than in the region of the sensor heads.       

     The position of the sensor relative to the toothed rack can therefore be determined since the teeth and/or the sensors have permanent magnets, as a result of which, when the measuring head moves, the magnetic field in the sensor changes, which can be measured by a magnetic dependent resistor or a Hall sensor. The air gap in the region of the connecting element can alternatively also correspond to that in the region of the sensor heads. In this case, an electronic evaluation circuit is associated with the magnetic dependent resistors or the Hall sensors. 
     Advantageously, an electronic evaluation device, by means of which the position of the measuring head on the toothed rack can be determined from the measured values of the sensors, is associated with the measuring head. In this case, the measured values are in the form of induced or output voltages. During the determination of the position, use is made of the profile of the induced voltages or measured values as a function of the position of the measuring head on the toothed rack. 
     Furthermore, a correction device, which takes into consideration temperature-dependent changes in length of the toothed rack and/or shape or positional errors of individual teeth in the determination of the position of the measuring head, can be associated with the measuring head. Advantageously, precise determination of the position of the measuring head on the toothed rack is therefore also possible when the teeth have tolerances or the toothed rack has been lengthened or shortened as a result of a change in temperature. The temperature is measured by a temperature sensor. Tolerances of the teeth are measured before the linear motor is first brought into operation and stored in the correction device. 
     The position regulation and velocity regulation of the linear motor can be further improved in accordance with the teaching in the document DE10024394A1 by an acceleration and/or velocity sensor being associated with the measuring head. 
     Advantageously, an electrical circuit, in which at least one group of measuring coils or measuring elements is formed and the measuring coils of each group are connected either in parallel or in series, is associated with the measuring head. Alternatively, for each group the measuring coils, which follow on from one another in the preferred direction of the toothed rack, are connected with alternating polarity either in parallel or in series. The corresponding exciter coils are connected in parallel or in series. As a result of the interconnection in the form of a series or parallel circuit, there is advantageously only one voltage level, which needs to be evaluated in a downstream evaluation device. If the measuring coils, which follow on from one another in the preferred direction of the toothed rack, are connected with alternating polarity in series, the function of the envelopes of the induced voltage as a function of the position of the measuring head is similar to a sine function. 
     The advantages of the position determination on toothed racks are realized in particular in a linear motor according to the invention with a primary part and a secondary part,
         the secondary part being in the form of a toothed rack,   the toothed rack comprising at least a ferromagnetic material   and, in the preferred direction, having preferably equidistant teeth, which comprise at least ferromagnetic material,   the primary part being capable of being moved in the preferred direction and in the opposite direction thereto,   an air gap being located between the primary part and the toothed rack, and   the primary part having a measuring head according to the invention for position determination or a corresponding measuring head being integrated in the primary part in such a way that the two form one piece.       

     In this case, the toothed rack is therefore one component part, which is required for operating the linear motor and for operating the measuring head. That is to say that a further toothed rack is advantageously no longer required. 
     The invention can also be used in the case of a rotary motor. In this case, the toothed rack corresponds to the stator, which has teeth, and the primary part corresponds to the rotor. A variant according to the invention is also conceivable in which the toothed rack corresponds to the rotor and the primary part corresponds to the stator. 
     Furthermore, the measuring head can be used, for example, in a further type of linear motor, to be precise in permanent magnet synchronous motors, which have at least one secondary part, at least sections of which are free of permanent magnets. In this case, the primary part comprises a structure comprising toothed modules, which are arranged in the preferred direction, point towards the air gap and are each surrounded by a coil, each toothed module having at least one permanent magnet. In a particularly preferred embodiment, the secondary part is also configured completely without permanent magnets. 
     In the text which follows, supplementary embodiments and configurations relating to the measuring apparatus according to the invention with a measuring head and also to the method for position determination will be represented. 
     The measuring head according to the invention measures the present path position in the event of a path displacement of a cyclically split toothed rack or alternatively also of a magnet holder as a material measure. 
     A direct measurement system is required for the operation of linear motors. As a result of the force-fitting coupling between the direct measurement system and linear motors, a rigid position regulation response in the axial direction is provided. On the basis of previous experience, linear motor axles in the case of lightweight machines can be run with a high proportion of feedforward control. As a result, a narrow contour guidance of a tool driven by the linear motor is possible. Direct optical measurement systems for position determination are in this case relatively expensive. 
     A newly developed permanent magnet synchronous motor, which has at least one secondary part, at least sections of which are free of permanent magnets, no longer requires any permanent magnets in the secondary part. Instead, a structure similar to a toothed rack is used as the secondary part. The newly developed motor is a linear motor. This arrangement provides the opportunity of using novel, inexpensive measurement methods alongside a high resolution. In the explanations below, the term toothed rack is used for a material measure similar to a toothed rack, both for the secondary part of the newly developed motor and for the primary parts, which are provided with magnets, of the conventional linear motors. 
     The subject of the invention is, inter alia, the special arrangement of the individual sensors in the measuring head for detecting a position of the toothed rack. As a result, first a coarse geometric resolution of the toothed rack pitch is achieved prior to the electrical/digital fine resolution. This takes place by means of an array of staggered individual sensors. 
     The material measure of the sensor array in the position measuring head is at a specific pitch ratio with respect to the material measure of the toothed rack. In combination with the interpolation of the sensor signals, finally a resolution in the sub-mm range is achieved. 
     One feature of the proposed solution is the further resolution of the toothed rack pitch in a step sequence which preferably has an even number of steps. In this case, each step has an alternating polarity with respect to the next step, or an opposite electrically produced mathematical sign. Advantageously, the sensors are arranged in such a way that one sine or cosine period per toothed rack pitch results. Other subdivisions with a plurality of sine or cosine periods per toothed rack pitch are also conceivable. 
     On the one hand for displacement direction detection, and on the other hand for further electrical subdivision in the superordinate processor, a sine system and a cosine system, which is shifted through 90° with respect thereto, can be required in the measuring head. 
     The overall resolution is formed, inter alia, by the following chain:
         Module or toothed rack pitch.   Number of sensors for the intermediate geometric resolution.   Interpolation of the transmitter evaluation.       

     The solution provides the advantage that, in the basic scope, no additional optical or magnetic material measure in the form of a glass scale or a magnetic strip for the direct measurement system is required if a uniformly divided toothed rack is available. In the event of more stringent requirements, the solution can be combined with additional measurement systems. 
     The absolute and cyclic tolerance of the toothed rack can be corrected by means of a measurement system error correction in the superordinate processor system (CNC) by means of measurement and measure comparison with a comparison scale (laser interferometer). 
     Furthermore, the temperature-dependent length extent of the toothed rack can be corrected by an automatic temperature compensation in the superordinate processor system (CNC) if the temperature change is detected by a sensor. 
     In the case of a sensor which is based on induction, the highest amplitude is present in the case of complete coverage by the fed carrier frequency, and in the case of partial coverage the corresponding amplitude as a function of a cosinusoidal function of the path increment of the part-period. The minimum amplitude is present between two full overlaps. In order to achieve a cosine form which is as effective as possible, various measures can be taken, for example the shape of the sensor heads can be correspondingly optimized. The sensor array is arranged in such a way that, with a given displacement direction, in each case one negative half-cycle follows on from a positive half-cycle, and vice versa. 
     In the case of the inductive head, the changes in mathematical sign of the transmitter signals are achieved, for example, by virtue of the fact that the measuring coils are connected with different polarity in parallel or in series, while the exciter coils are all interconnected with the same polarity; alternatively, the exciter coils can be interconnected with different polarities and the measuring coils can be interconnected with the same polarity. Different polarities can therefore be achieved either by swapping over the terminals or by a different winding sense. In the case of a primary voltage which always has the same polarity, an identical phase angle, or one rotated through 180°, results depending on the polarity of the measuring coil, or vice versa. This solution has the advantage that no electronic active parts are required in the sensor head. 
     As a result of the technically simpler embodiment, only the series or parallel circuit comprising all the coil elements or individual sensors is described. Alternatively, the electrical individual detection of the sensor signals is also possible, with electronic overall evaluation in the superordinate electronics or processor assembly. 
     The arrangement of the sensors can be such that it covers or even overlaps the teeth. 
     The sensors according to the invention can be compared in terms of their physical operation with a transformer, which only induces the desired rated voltage in the secondary winding when the magnetic circuit is closed. This is the case when the position of the measuring head is such that the sensor heads of the relevant sensor are positioned in each case as centrally as possible over the teeth of the secondary part. 
     Depending on the linear displacement of the poles, in the case of a sinusoidal voltage on the exciter coils with a carrier frequency of conventionally 4 to 10 kHz and with a constant amplitude, a similar induced voltage results on the receiving coils, whose amplitude has a sinusoidal dependency on the displacement path. This amplitude is digitized. Independently of the evaluation method used, the evaluation electronics produce a position value with a correspondingly high resolution. As a result of a special arrangement and embodiment, the measuring head can also be used for path detection via material measures by means of permanent magnets. 
     Furthermore, coil parts or other structural elements of the primary or secondary part of the linear motor can also be used exclusively or partially for the function of the measurement method described. 
     Alternatively, the invention also relates to solutions in which a separately fitted toothed rack is used exclusively for path detection. This can also be a comb-like structure, which is inserted into the gaps between the teeth of the motor tooth system. 
     As an alternative to the described measuring apparatus with a measuring head, an inductosyn-like arrangement is also conceivable. In this case, the geometric step arrangement described is printed onto a printed circuit board with a magnetically conductive background. In the case of the toothed rack solution, a highly precise solution can also be used as the conventional inductosyn solution if the inductosyn slider is designed to overlap the teeth and the scales are pushed in the manner of a comb into the gaps between the teeth and adjusted. 
     When using a capacitive, optical or other measurement method, the gaps between the teeth can be used unchanged or for accommodating a special sensor mating piece. Likewise, the teeth can be used unchanged or for accommodating a special sensor mating piece. This also includes an additionally rastered fine subdivision of the gaps between the teeth and/or teeth in interaction with the path measuring head. 
     In order to use the proposed solution as a virtually absolute measurement system, corresponding additional markings/codings can be introduced along the toothed rack, which are also detected and evaluated by the measuring head; it is therefore then possible not only for the relative position within a toothed rack pitch but also the absolute position within the entire displacement path to be detected. 
     The described solution does not exclude the combination with another measurement system. It is advantageous to use the described solution possibly for commutation and for the velocity control loop, and to use a suitable additive measurement system for absolute positioning. 
     In addition to the proposed solution, the teeth of the toothed rack can additionally be provided with windings. These windings then in one case act as exciter coils, with the result that the measuring head sliding over them only needs to be available over the measuring coils, or in another case as measuring coils, with the result that the measuring head sliding over them only needs to be available over the exciter coils. The additional windings can in this case exclusively be used in the mentioned function or whilst also using another function. 
     The abovedescribed method can be used equally for rotary motors. In this case, the measuring head has a segment-like embodiment. Instead of a toothed rack, the material measure in this case comprises a wheel with inner toothing or a structure with a form similar to a wheel with permanent magnets or coil elements. 
     In addition to the case of two track signals which are shifted through 90°, in particular the case of three track signals is of interest. It is thus possible to compensate for, for example, a third harmonic of the track signals. 
     As described, a plurality of transmitter signal periods can be produced by the configuration of the measuring head per toothed rack period. However, it is also possible to produce further synthetic transmitter signals from the original transmitter signals, which synthetic transmitter signals have a plurality of signal periods per period of the original transmitter signals. 
     In arrangements in which magnetic dependent resistors are used, Hall sensors can in principle also be used. With magnetic dependent resistors, only the absolute value of the B field is measured, and with Hall sensors the mathematical sign is also measured. 
     The toothed rack can also be sampled based on the gearwheel transmitter principle. The difference from conventional gearwheel transmitters consists in two points:
         linear instead of round material measure   more coarse structure (longer period length of the teeth) than is conventional in gearwheel transmitters.       

     In this case, the measuring head comprises a magnet and a magnetic field sensor. The magnetic field produced by the magnet is in this case influenced by a magnetic toothed structure which is located in front of the measuring head, with the result that the magnetic field sensor measures a different magnetic field depending on the relative position with respect to the toothed structure. 
     The sensor principles which have been described up to this point are based on the measurement of magnetic fields. However, other sensor principles are also conceivable. For example, the toothed rack can also be sampled optically or capacitively. Optical sampling, however, is not possible, for example, when the toothed rack (with an opaque material) is cast in such a way that the toothed rack structure cannot be optically identified from the outside. 
     Mere position measurement is only sufficient, under certain circumstances, for the positioning and position regulation, but not for velocity regulation with sufficient dynamics. This can be remedied in this case by acceleration or velocity sensors, with the aid of which an improved velocity signal can be obtained. In this case, in particular the Ferrari sensor should be mentioned, which measures the relative acceleration. For the advantages which can be achieved by the use of a Ferrari sensor, see DE10024394A1, for example. This document highlights the fact that an improved velocity/actual value signal can be obtained using the Ferrari sensor. 
     However, there are also two further points where the Ferrari sensor could be advantageous:
         The actual position measurement system has an error which also has a systematic content. This systematic content can be compensated for, under certain circumstances, at least partially by advance or online learning of the positional error curve.   If the actual position measurement system has comparatively poor dynamics (a poor time response), this can be compensated for by the Ferrari sensor if the latter has correspondingly good dynamics.
 
Similar advantages to those associated with the Ferrari sensor are also conceivable with other acceleration or velocity sensors.
       

     Advantages could also be provided by the additional application of a modified regulation method. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
       The invention and further advantageous configurations of the invention in accordance with the features of the dependent claims are explained in more detail below with reference to schematically illustrated exemplary embodiments in the drawing, without the invention thereby being restricted to these exemplary embodiments; in the drawing: 
         FIG. 1  shows a measuring head according to the invention on a toothed rack; 
         FIG. 2  shows a measuring head according to the invention with an associated electrical circuit; 
         FIG. 3  shows the envelope of the induced voltage of sensor  1  in  FIG. 2  as a function of the path distance x; 
         FIG. 4  shows the envelopes of the induced voltages of the sensors  1  to  6  in  FIG. 2  as a function of the path distance x; 
         FIG. 5  shows the envelope of the voltage at the output of the electrical circuit from  FIG. 2 ; 
         FIG. 6  shows a further sensor according to the invention on a toothed rack; 
         FIG. 7  shows the envelopes of the induced voltages of the sensors  1  to  6  corresponding to  FIG. 6  as a function of the path distance x and the envelope of the voltage at the output of an electrical circuit; 
         FIG. 8  shows a further measuring head according to the invention on a toothed rack; 
         FIG. 9  shows a further measuring head according to the invention on a toothed rack; 
         FIG. 10  shows a further measuring head according to the invention on a toothed rack with a further sensor according to the invention; 
         FIG. 11  shows a further arrangement of the sensors on a toothed rack; 
         FIG. 12  shows an exemplary embodiment of a sensor from  FIG. 11 ; 
         FIG. 13  shows a further exemplary embodiment of a sensor similar to that in  FIG. 11 ; 
         FIG. 14  shows a linear motor, on whose primary part a measuring head is fixed; 
         FIG. 15  shows a toothed module for a primary part of a permanent magnet synchronous motor; and 
         FIG. 16  shows a further measuring head according to the invention on a toothed rack with a further sensor according to the invention; and 
         FIG. 17  shows the linear motor of  FIG. 14  with evaluation device, correction device, and acceleration and/or velocity sensor. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       FIG. 1  shows a measuring head  15  according to the invention on a toothed rack  16  in plan view. The toothed rack  16  has teeth  18  and slots  17 . The toothed rack pitch of the toothed rack  16  is L, i.e. the distance from tooth center to tooth center is L. The measuring head  15  is capable of moving in a first direction, also called “preferred direction”  13  of the toothed rack  16  or in a second opposite direction  14 . The measuring head  15  has twelve sensors  1 ,  2 ,  3 ,  4 ,  5 ,  6 ,  7 ,  8 ,  9 ,  10 ,  11  and  12 . The sensors  1  to  12  are in this case arranged offset with respect to one another in the preferred direction  13  of the toothed rack  16 . The figure also shows the profile of the sinusoidal envelope  37  and the profile of the cosinusoidal envelope  38 . The position of the measuring head  15  can be determined from the two profiles. 
     The toothed rack  16  and the teeth  18  are in this case manufactured at least from ferromagnetic material, but can also contain other materials. With the aid of the sensors  1  to  12 , magnetic fields or changes in these magnetic fields can be measured. An air gap is located between the toothed rack  16  and the measuring head  15 . The sensors  1  to  6  in this case form one group of sensors, and the sensors  7  to  12  form a further group of sensors. In the exemplary embodiment shown in  FIG. 1 , the sensors have a length which corresponds to the width of a tooth  18 . 
       FIG. 2  shows a measuring head  15  according to the invention with an associated electrical circuit  24  on a toothed rack  16 .  FIG. 2  shows, by way of example, the sensors  1  and  6 . The sensors each have two sensor heads  20  and a connecting element  21  between the two sensor heads  20 . The sensor heads  20  are arranged so as to follow on from one another in the preferred direction  13  or  14  of the toothed rack  16 , but they can also be arranged parallel to one another in the preferred direction  13  or  14  of the toothed rack  16 , as is shown in  FIGS. 11 ,  12  and  13 . The connecting element  21  is surrounded by an exciter coil  22 , to which an excitation AC voltage Up is applied. Furthermore, the connecting elements  21  of the sensors  1  to  6  are surrounded by in each case one measuring coil  23 , at which in each case one induced voltage U 1 , U 2 , U 3 , U 4 , U 5  and U 6 , respectively, can be tapped off, only U 1  and U 6  being shown in  FIG. 2 . All of the exciter coils  22  and all of the measuring coils  23  are applied in the same way to the connecting element  21  and have the same winding sense. 
     In the example shown in  FIG. 2 , the measuring coils are connected in series. In this case, however, the measuring coil  23  of the sensor  6  is connected into the series circuit  24  with reverse polarity. This is denoted in  FIG. 2  by an arrow in the measuring coil  23  of the sensor  6 , which is in the opposite direction from the measuring coil  23  of the sensor  1 . The voltage Us can be tapped off at the series circuit comprising the measuring coils  23  of the sensors  1  to  6 . Alternatively, it is also conceivable for the voltages induced at the measuring coils  23  to be passed to a superordinate controller and evaluated there. The voltage Us is digitized for further processing purposes. 
       FIG. 2  furthermore shows the position measuring head with a three-fold reduction in the toothed rack pitch. In the event of movement in the displacement direction, three sine/cosine periods are produced in the case of three-fold reduction per toothed rack pitch or each toothed rack pitch is split into twelve individual steps or quadrants. In this case, the sensors  1  to  6  correspond to the sine system and the sensors  7  to  12  correspond to the cosine system. In this case, the sine system produces the profile  37  and the cosine system produces the profile  38 . 
     The air gap between the sensors  1  to  12  and the toothed rack  16  in the region of the connecting element  21  is greater than in the region of the sensor heads  20 , with the result that, when the excitation AC voltage Up is applied, for example, the amplitude of the induced voltage U 1  is at a maximum if the sensor  1  is located centrally over a tooth  18 , since the magnetic circuit is closed over the tooth  18 . The sensors  1  to  12  are advantageously manufactured from at least ferromagnetic material, for this purpose. 
       FIG. 3  shows the envelope of the induced voltage U 1 , denoted by EU 1 , of sensor  1  in  FIG. 2  as a function of the path distance x along the preferred direction  13  of the toothed rack  16 . If sensor  1  is located over a tooth  18  of the toothed rack  16 , the envelope of the induced voltage U 1  is at a maximum and falls to a minimum value if sensor  1  is located over a slot  17 . As can be seen, position determination using only one sensor is made more difficult in particular when the latter is located over a slot  17 . 
       FIG. 4  shows the envelopes EU 1 ( x ) to EU 6 ( x ) of the induced voltages U 1 ( 1 ) to U 6 ( x ) of the sensors  1  to  6  from  FIG. 2  as a function of the path distance x. 
       FIG. 5  shows the envelope EUs(x) of the voltage at the output of the electrical circuit Us(x) from  FIG. 2 . The voltages are combined in the series circuit correspondingly: Us(x)=U 1 ( x )−U 2 ( x )+U 3 ( x )−U 4 ( x )+U 5 ( x )−U 6 ( x ). As can be seen in  FIG. 5 , a sinusoidal signal results, with the aid of which the position of the measuring head  15  can be determined. This would not yet have been possible from the signal U 1 ( x ) according to  FIG. 3 . Clear position determination within a toothed rack pitch is possible by virtue of the fact that the measuring coils  23  of the second group of sensors  7  to  12  are combined in a similar manner, with the result that a further phase-shifted sinusoidal voltage profile is produced. 
     A plurality of groups of sensors are also conceivable. In the case of two groups of sensors, a sinusoidal profile as a function of the path distance can be produced, for example, with a first group of sensors as shown in  FIG. 5  and a cosinusoidal profile, i.e. a profile shifted through 90°, can be produced with a second group. Both of these profiles can be used to clearly determine the position of the measuring head within a toothed rack pitch. In particular, the second profile, which is shifted through 90°, can be used to identify in which direction the measuring head is moving. 
     It can be seen from  FIG. 5  that, as a result of the convenient series circuit, a plurality of, in this case three, signal periods can be produced in the envelopes EUs(x) of Us(x) using the signal Us(x) per toothed rack pitch L. 
     The profiles of the amplitudes of the individual sensors can deviate from the ideal profile. These deviations can be described by offset, amplitude, phase and waveform errors. In this case, it needs to be assumed that these errors for the various individual sensors do not, or at least not in all cases, correspond to one another. Therefore, the profile of the signal Us will also have these errors, but sine periods following on from one another will generally have various errors. When using a track signal correction method, as is described, for example, in DE10163504A1 or DE10163528A1, this can be taken into consideration correspondingly. 
     The just mentioned waveform errors can be minimized by suitable shaping of the sensor heads  20 . Preferably, the sensor heads  20  of the sensors  1  to  12  will in this case be correspondingly configured, but in principle the structure of the toothed rack  16  can also be correspondingly configured. 
       FIG. 6  shows a further sensor  1  according to the invention on a toothed rack  16 . In this exemplary embodiment, the sensor  1  is shorter than the width of a tooth  18 . 
       FIG. 7  shows the envelopes EU 1 ( x ) to EU 6 ( x ) of the induced voltages U 1 ( x ) to U 6 ( x ) of the sensors  1  to  6  corresponding to  FIG. 6  as a function of the path distance x and the envelope EUs(x) of the voltage Us at the output of an electrical series circuit, in which the induced voltages are combined according to the formula
 
 Us ( x )= U 1( x )− U 2( x )+ U 3( x )− U 4( x )+ U 5( x )− U 6( x ).
 
In this example, a cyclic function results, from which the position of the measuring head  15  on the toothed rack  16  can be determined.
 
       FIGS. 8 and 9  show further measuring heads  15  according to the invention on a toothed rack  16 . The sensors can in this case be as long, for example, as the width of a tooth  18  or else longer. The sensors are in this case arranged offset with respect to one another in the preferred direction  13  of the toothed rack  16 . In this case, in each case the two sensors  19  which are illustrated at the top form one group of sensors and the two sensors which are illustrated at the bottom form a further group of sensors. 
       FIG. 10  shows a further measuring head  15  according to the invention on a toothed rack  16  with a further sensor  31  according to the invention. Sensor  31  comprises at least ferromagnetic material. Sensor  31  has at least two sensor heads  20 , which are arranged so as to follow on from one another in the preferred direction  13  or  14  of the toothed rack  16 . The sensor heads  20 , however, can also be arranged parallel to one another in the preferred direction  13  or  14  of the toothed rack  16 . The sensor heads  20  are connected to one another by a connecting element  21 , which has a magnetic dependent resistor  25  or a Hall sensor for measuring the magnetic field. The sensor heads  20  and/or the teeth  18  of the toothed rack  16  have permanent magnets  26 . The air gap between the sensor  31  and the toothed rack  16  in the region of the connecting element  21  is greater than in the region of the sensor heads  20 . 
     If the sensor  31  is moved over the toothed rack  16 , the change in the magnetic field is measured via the sensor heads  20  and the magnetic dependent resistor  25 . This is used for determining the position of the measuring head  15 . One advantageous factor is the fact that no excitation by means of an excitation AC voltage and no demodulation for transmitter evaluation needs to take place. 
     In the case of a measuring head with magnetic dependent resistors or Hall sensors, the changes in the mathematical sign of the transmitter signals are preferably achieved by virtue of the fact that the magnetic dependent resistors or Hall sensors are connected to an electronic circuit, which forms a suitable linear combination, such as addition and subtraction, for example, from the signals of the individual Hall sensors or magnetic dependent resistors. 
       FIG. 11  shows a further arrangement of the sensors  19  on a toothed rack  16 . In this case, the sensors  19  can be designed corresponding to the sensors  1  to  12  or else  31 . In the exemplary embodiment shown in  FIG. 11 , the sensor heads  20  are arranged parallel to one another in the preferred direction  13  or  14  of the toothed rack  16 . In this case, the two sensors  19  illustrated on the left form one group of sensors and the two sensors illustrated on the right form a further group of sensors. 
       FIG. 12  and  FIG. 13  show corresponding exemplary embodiments of the sensors  19 . The sensor in  FIG. 12  in this case corresponds to one of the sensors illustrated in  FIG. 11 . In  FIG. 13 , on the other hand, a slightly modified sensor is illustrated in comparison with the sensor in  FIG. 12 , namely the teeth  18  are surrounded laterally by the sensor heads  20  in this FIG. This has the advantage that a change in the spacing between the sensor  19  and the toothed rack  16  has less of an effect on the sensor signals than in the case of the sensor in  FIG. 12 . 
       FIG. 14  shows a linear motor  30 , on whose primary part  27  a measuring head is fixed in position  29 . As an alternative to this, the measuring head can also be fitted in position  28  on the primary part  27 . By position  28 , the movement path of the primary part is not restricted. Furthermore, the teeth  18  of the toothed rack  16  can have additional markings or codings which can be read, for example, optically or electromagnetically. The position of the measuring head  15  is therefore defined in particular when the linear motor  30  is switched on. The coding can be stored, for example, by means of RFID transponders. As shown in  FIG. 17 , at least one electronic evaluation device  40  is provided to determine the position of the measuring head on the toothed rack  16  in response to a measured value transmitted by the sensor. In addition, a correction device  41  is operatively connected to the measuring head to correct a determination of the position of the measuring head in response to a temperature-dependent change in length of the toothed rack  16 , flaw in shape of individual teeth  18 , or positional inaccuracy of individual teeth  18 .  FIG. 17  also shows the presence of an acceleration and/or velocity sensor  42  operatively connected with the measuring head. 
     A particularly advantageous embodiment is provided when the coding of the teeth  18  or segments of the toothed rack  16  can be programmed. This programming could take place during a setup run, in which the entire movement path is covered and an apparatus for programming is carried along with the primary part  27 . The advantage here is the fact that it is thus easily possible to ensure that a clear conclusion can be drawn on the position from the readable code. It is therefore not necessary to take care, for example during the production of the segments, that no two segments are produced with identical codes. 
     Even if the segments cannot be programmed, but are provided with a fixed code in advance, the sequence of the code along the displacement path is under certain circumstances not known in advance. Thus, for example, a secondary part can comprise a plurality of secondary part sections, which for their part in turn in each case contain a plurality of segments. In this case, it is advantageous if it is not necessary to prescribe in which sequence the secondary part sections need to be arranged next to one another in a row. An already existing code sequence can also be changed if a secondary part needs to be replaced by a replacement part as a result of a defect. For this reason, it may be expedient to learn the code sequence first during a setup run. 
       FIG. 15  shows a toothed module  35  for a primary part of a permanent magnet synchronous linear motor, which has at least one secondary part, at least sections of which are free of permanent magnets. In this case, the primary part comprises a structure comprising toothed modules  35 , which are arranged in the preferred direction, point towards the air gap and are in each case surrounded by a coil  36 , each toothed module  35  having at least one permanent magnet  34 . The secondary part (not illustrated here) is located in the position illustrated in  FIG. 15  of the toothed module  35  beneath this toothed module  35 . The exemplary toothed module has webs  33 , which are separated from one another by interspaces  32 . In this way, a plurality of toothed modules can be joined together to form a primary part. Instead of the webs  33 , a solid basic body can also be used, however. Instead of the permanent magnet  34 , permanent magnets can also be fitted on the underside of the toothed module  35 . 
       FIG. 16  shows a further measuring head  15  according to the invention on a toothed rack  16  with a further sensor  31  according to the invention. Sensor  31  comprises at least ferromagnetic material. Sensor  31  has at least two sensor heads  20 , which are arranged so as to follow on from one another in the preferred direction  13  or  14  of the toothed rack  16 . However, the sensor heads  20  can also be arranged parallel to one another in the preferred direction  13  or  14  of the toothed rack  16 . The sensor heads  20  are connected to one another by a connecting element  21 , which has a magnetic dependent resistor  25  or a Hall sensor for measuring the magnetic field. The sensor heads  20  have permanent magnets  26  on the side of the air gap. The air gap between the sensor  31  and the toothed rack  16  in the region of the connecting element  21  is greater than in the region of the sensor heads  20 . 
     If the sensor  31  is moved over the toothed rack  16 , the change in the magnetic field is measured via the sensor heads  20  with the permanent magnets  26  and the magnetic dependent resistor  25 . This is used to determine the position of the measuring head  15 . One advantageous factor is the fact that no excitation by means of an excitation AC voltage and no demodulation for the transmitter evaluation need to take place. 
     In the case of a measuring head with magnetic dependent resistors or Hall sensors, the changes in the mathematical signs of the transmitter signals are preferably achieved by virtue of the fact that the magnetic dependent resistors or Hall sensors are connected to an electronic circuit, which forms a suitable linear combination, such as addition and subtraction, for example, from the signals of the individual Hall sensors or magnetic dependent resistors.