Abstract:
A method and system for automatically correcting image registration in an image transfer system utilizing a plurality of moving image-forming media on each of which an image is formed in response to a corresponding start-of-page signal, and an image carrier moving past each of the image-forming media and brought into contact therewith in a transfer zone, wherein the image-forming media are driven independently from one another and the timing of the start-of-page signals and/or the speed of the image-forming media are controlled to maintain a fixed relationship between the longitudinal image distortions occurring in each transfer zone and the timing of the associated start-of-page signals.

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to a method and system for automatically correcting image registration in an image transfer system comprising a plurality of moving, image-forming media on each of which an image is formed in response to a corresponding start-of-page (SOP) signal. An image carrier is moved past each of the image-forming media and is brought into contact therewith in a respective transfer zone. 
     The problem of correcting image registration occurs, for example, in a color copier or printer, in which it is essential for obtaining a good image quality that the various color separations are superimposed correctly on the image carrier. For example, a four color reproduction system comprises four image-forming media corresponding to the four basic colors, i.e. yellow, cyan, magenta and black. 
     The image-forming media may be drums or belts on which a developed toner image in the corresponding color can be formed by any known process, e.g. by a direst induction process or by a xerographic process. In the latter case, the surface of the image-forming medium is formed by a photoconductor on which a charge image is formed by image-wise exposure with light and then the charge image is developed with toner. 
     The image carrier may be a sheet of copying paper on which the desired image is to be recorded or an intermediate carrier (belt or drum) from which the color image is then transferred to the final recording medium in a second transfer step. In any case, the image carrier is successively moved through the various transfer zones, so that the developed single-color images (color separations) are superposed on the image carrier to form the desired multiple-color or full-color image. 
     In each transfer zone the image carrier is brought into contact with the corresponding image-forming medium in a nip which may be constituted by the image-forming medium and the image carrier themselves or, in case of a belt, by rollers supporting the belt. In order to obtain a correct registration of the superimposed images, the mechanical components of the transfer system have to be adjusted correctly, and the timings of the SOP signals, which define the positions of the leading edge of the image on the respective image-forming medium, have to be selected properly, such that the leading edges of all images will coincide on the image carrier. In the course of time, however, the mechanical components are subject to wear or aging, thermal expansion and the like, so that the image registration may be altered to an extent which is not acceptable in a high resolution system. 
     U.S. Pat. No. 4,937,664 discloses a laser printer in which the image registration can be checked and corrected automatically, for example in the warming-up phase each time the printer is switched on. To this end, the image-forming units are arranged to form registration marks on the image carrier. A detector for detecting these registration marks is arranged downstream of the image-forming units and compares the timings at which the registration marks are detected to corresponding target values. In case of a deviation, a mechanical component of the associated image-forming unit, e.g. the optical exposure system is readjusted by means of an actuator in order to compensate for the misregistration. The registration marks formed on the image carrier are then erased again, so that the system will not be confused when new marks are generated in a subsequent correction cycle. 
     In conventional color copiers or printers, in general, the drive systems for the various image-forming media and the image carrier are mechanically coupled to one another through gears or the like, so that all image-forming media are forcibly driven at the same speed as the image carrier. This facilitates the adjustment of image registration, but has the drawback that a rather complex mechanical system is required. With increasing resolution of the printer and, accordingly, increasing accuracy requirements, it becomes increasingly difficult and expensive to suppress effects resulting from gear play, manufacturing tolerances of the gear teeth and the like to an acceptable limit. 
     Theoretically, the speeds of all image-forming media should be exactly identical, because they are all held in contact with the same image carrier. However, it is found that in practice the natural speeds of the image-forming media, i.e. the speeds the image-forming media would acquire if they were allowed to idle, are slightly different from one another. These speed differences may for example result from variations in the thickness of the image carrier belt, variations in the thickness of the toner layer, and from slight elastic deformation of the image-forming medium or the image carrier due to forces acting in the nip in the transfer zone. When the image-forming media are forcibly driven at the same speed, these differences in the natural speeds may result in undesirably high tangential forces or torques which act upon the image carrier in the transfer zone and may impair the image quality or the lifetime of the image carrier and other mechanical components. 
     U.S. Pat. No. 4,705,385 discloses a color printer in which the image carrier and the image-forming medium are driven independently from one another with controllable speeds. There is only provided a single image-forming medium in the form of a photoconductive belt,the length of which is an integer multiple of the circumferential length of the image carrier. The various color separations are formed one after the other on the same photoconductive belt and are transferred to the image carrier after each complete revolution of the latter. The drive system for the photoconductor serves as a master to which the drive system of the image carrier is slaved. More specifically, servo control devices keep track of the displacements of the photoconductor and the image carrier, and when the image carrier has fallen behind or gotten ahead of the photoconductor belt, the displacement of the image carrier is corrected within a short time interval in which image free seam areas of the belts are in contact with each other. Thus, all color separations will be superimposed on the image carrier with correct image registration. Since this system employs only a single image-forming medium, there is no need to cope with registration errors resulting from speed differences between image-forming media. However, the use of only a single image-forming medium leads to losses in productivity. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide a method and system for automatically correcting image registration, which requires little mechanical complexity and nevertheless corrects image registration errors accurately while maintaining tangential forces in the image transfer zones within acceptable limits. 
     According to the present invention, this object is achieved by the method and system as specified herein. 
     The method is characterized in that the image-forming media are driven independently from one another and the timing of the SOP signals and/or the speeds of the image-forming media are controlled to maintain a fixed relationship between the longitudinal image distortions occurring in each transfer zone and the timings of the associated SOP signals. 
     Any slip or differential speed between the image carrier and the individual image-forming media leads to a longitudinal image distortion in the transfer process, that is, the length of the developed image in the image-forming medium, as measured in the direction of movement of this medium, will be different from the length of the image after it has been transferred onto the image carrier. The longitudinal image distortion is defined as the ratio between these lengths. Since the image-forming media are driven independently, the image distortions may be different from one another, and these differences would generally give rise to image registration errors. Even if the leading edges of the images are exactly in registry, the different image distortions would lead to a mismatch gradually increasing towards the trailing edges of the images. As is generally known in the art, this kind of registration errors can be avoided by synchronizing the line pulses of the image-forming units with the displacement of the image carrier. Then, the distance between the image lines formed on the image-forming medium varies in accordance with the speed difference between the image-forming medium and the image carrier, so that a first image distortion already occurs when the image is formed. When the image is then transferred onto the image carrier, the same speed difference gives rise to an image distortion in the opposite sense, so that the two distortions cancel each other. However, the speed of the image-forming medium will still have an effect on the exact position at which the leading edge of the image is transferred onto the image carrier. More precisely, when two image-forming units are so arranged that the path of travel of the image-forming medium from the image-forming position to the transfer position has the same length L for both systems, and DS is the difference in the image distortions (longitudinal scaling factors) in the two units, as compared to the situation existing when the system was calibrated, then the resulting registration error will be DR=DS L. 
     Thus, when the image distortions S of all image-forming media are known, it is possible to calculate the image registration errors resulting therefrom and to compensate these errors by appropriately adjusting the timing of the respective start-of-page signals (SOP) relative to the displacement of the image carrier. Accordingly, a fixed relationship will be established between the image distortions and the timings of the associated SOP signals. When the image distortions tend to change in the course of time, for example as a result of changes in the hardness of the nip-forming rollers or changes of the nip pressure due to mechanical stains in the machine frame, then the SOP timings and/or the speeds of the image-forming media are controlled in order to maintain this fixed relationship. 
     This concept permits the use of a system with idling image-forming media, i.e. a system in which the image-forming media are not actively driven but are driven solely by the frictional contact with the image carrier in the transfer zone. This greatly reduces the mechanical complexity and also eliminates the undesirable tangential forces in the transfer zones. 
     On the other hand, if the image-forming media are actively driven, then it is possible to control the speeds or displacements of the image-forming media and hence the associated image distortions instead of or in addition to controlling the SOP timing. In this case, it is, for example, possible to control all image-forming media to a target speed derived from the movement of the image carrier, so that all DS are reduced to zero. The effect would be comparable to a mechanical coupling by gears, but this effect would now be achieved with less mechanical complexity and also by avoiding errors resulting from gear play, irregularities of the gear teeth and the like. 
     A particular advantage of this system is that the target speed of the image-forming media can easily be varied. If, for example, the surfaces of the image-forming media have become harder due to material aging, and accordingly the natural speeds of the image-forming media have become higher, it is possible to increase the target speed for all image-forming media in the same proportion to the speed of the image carrier, so that the tangential forces in the image-forming zones will not become unduly high. This will change all image distortions by the same amount, so that the various DS remain zero. If desired, it is also possible to change the target speeds independently from one another (DS  0 ) and to correct the registration errors by adjusting the SOP timing, accordingly. 
     It is also possible to modify the natural speed of the image-forming media by changing the nip pressures in the transfer zones. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention will become more fully understood from the detailed description given hereinbelow and the accompanying drawings which are given by way of illustration only, and thus, are not limitative of the present invention, and wherein: 
     FIG. 1 is a diagram of an image transfer system according to one embodiment of the present invention; 
     FIG. 2 is an enlarged schematic view of a transfer zone; 
     FIGS. 3 and 4 are diagrams illustrating the function principles of modified embodiments of the invention; and 
     FIG. 5 shows an embodiment wherein the last three image-forming drums are driven by respective motors. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     As is illustrated in FIG. 1, an image carrier is formed by an endless belt  10  which is passed over a drive roller  12 , a measuring roller  14 , support rollers  16 , a deflection roller  18  and through a transfuse station  20 . The drive roller  12  is driven by a motor  22 , so that the belt  10  is moved in the direction of arrow A. The motor  22  drives the drive roller  12  with a constant speed and may optionally be feedback-controlled by a signal from the measuring roller  14  which detects the displacement of the belt  10 . 
     Four image-forming units  24 A,  24 B,  24 C and  24 D are equidistantly disposed along the path of the belt  10  and are each adapted to form a toner image in one of the four colors yellow, cyan, magenta and black. The image-forming units have essentially the same construction and each comprises a drum  26 A,  26 B,  26 C and  26 C (commonly designated by  26 ) serving as the image-forming medium, and an image-forming system  28 . In the shown example, it is assumed that the image-forming units employ a so-called direct induction printing (DIP) process. Thus, as is generally known in the art, the drum  26  comprises a large number of parallel, circumferentially extending electrodes which can individually be energized in accordance with an image signal, and the image-forming system  28  is formed by a magnetic knife by which the toner image is developed line-by-line in accordance with the energizing pattern of the electrodes. Such direct induction printing process is described more in detail e.g. in European Patent No. 0 191 521. Each of the drums  26 A,  26 B,  26 C and  26 D is arranged opposite to one of the support rollers  16  and forms a nip  30  through which the belt  10  is passed so that it is brought into contact with the surface of the drum. The nip  30  thus defines a transfer zone in which the image formed on the surface of the drum  26  is transferred onto the belt  10 . 
     The drive roller  12 , the measuring roller  14 , the deflection roller  18 , the rollers of the transfuse station  20  and the drums  26  of the four image-forming units are mounted in a common rigid frame (not shown), so that a fixed positional relationship is established. The support rollers  16  are elastically biased against the corresponding drum so as to generate an appropriate nip pressure. In this embodiment, the drums  26  are designed as idling rollers which are driven to rotate in the direction of arrow B solely by frictional engagement with the moving belt  10 . The center lines of each pair of adjacent nips  30  are spaced by the same distance D. Preferably, at each of the support rollers  16  the belt  10  is deflected by the same angle, so that the mechanical configurations of the image-forming units are practically identical. 
     The toner images formed on each of the drums  26 A- 26 D are superimposed on the belt  10  to form a multiple-color or full-color image which is then transferred onto a sheet of paper (not shown) in the transfuse station  20 . A belt tensioner  34  arranged between the transfuse station  20  and the drive roller  12  absorbs any changes in belt tension or belt speed which might be induced by the paper sheets brought into contact with the belt  10  in the nip of the transfuse station  20 . 
     In each of the image-forming units the magnetic knife  28  (schematically shown in FIG.  1  and enclosed in detail in European Patent No. 0 191 521, referred to hereinabove), defines an image-forming position at the circumference of the associated drum  26 . The circumferential length L between the image-forming position and the transfer position defined by the nip  30  is the same for all image-forming units. 
     The measuring roller  14  is connected to a controller  36  via a line  38  and transmits a signal representative of the displacement of the belt  10 . As is generally known in the art, the measuring roller  14  may include an encoder which generates a high-frequency pulse signal the frequency of which is proportional to the rotation of the roller  14  and hence the displacement of the belt  10 . The frequency of the encoder should be relatively high in order to provide a high resolution. This resolution may be enhanced further by electronic interpolation techniques, as is also known in the art. 
     The control system further includes a timing circuit  40 A,  40 B,  40 C and  40 D for each of the image-forming units. The timing circuits may be incorporated in the controller  36  and have been shown separately only for illustration purposes. On a line  42  the controller  36  delivers a clock signal to each of the timing circuits. This clock signal is synchronized with the displacement of the belt  10 . When a printing command for printing an image is supplied on a line  44 , each timing circuit causes the associated image-forming unit to start printing the first line of the image with a predetermined delay, expressed in pulses derived from roller  14  and thus being related to the displacement of the belt  10 . 
     At first, the first line of an image is formed by the magnetic knife  28  on the drum  26 A of the first image-forming unit  24 A. When the drum  26 A has travelled the distance L, this first image line is transferred onto the belt  10 . While the leading edge of the image on the belt  10  moves towards the second image-forming unit  24 B, the printing of the first image line in this second image-forming unit  24 B is initialized. The delay set in the counting circuit  40 B is so adjusted that the leading edge of the image on the drum  26 B and the leading edge of the image on the belt  10  reach the nip  30  of the second image-forming unit exactly at the same time, so that the images are superposed without any registration error. The same applies to the image-forming and transfer processes in the units  24 C and  24 D, so that all four color separations are superposed correctly. 
     In each of the image-forming units the printing of a new image line is triggered by a line pulse supplied from the associated timing circuit  40 A- 40 D. These line pulses are also derived from the clock signal on line  42  and are accordingly synchronized with the movement of the belt  10 . 
     If the circumferential speeds of each of the drums  26 A- 26 D is identical with the speed of the belt  10 , then the image registration can be maintained with high accuracy, once the appropriate delays have been adjusted. In practice, however, the circumferential speeds of the drums  26  may differ from each other and from the speed of the belt  10 , as will now be explained in conjunction with FIG.  2 . 
     In FIG. 2, an image-forming drum  26  and the associated support roller  16  forming a nip  30  with the belt  10  passing therethrough are shown in an enlarged scale. The image-forming position defined by the magnetic knife  28  is disposed at a circumferential distance L from the transfer nip  30 . In the shown example, a toner layer  46  corresponding to the dark areas of a developed image has been formed on the surface of the drum  46 , and the leading edge of the image has just reached the nip  30 . 
     The support roller  16  is biased against the drum  26  by a spring  48 , and, in this case as illustrated, the biasing force, i.e. the nip pressure is adjustable by means of an actuator  50 . Since neither the support roller  16  nor the belt  10  nor the drum  16  are absolutely rigid, these members are slightly compressed in the vicinity of the nip  30 . This has exaggeratedly been illustrated as a slight depression of the drum  26 . As a result, the effective radius of the drum  26 , i.e. the distance between the axis of rotation  52  of the drum and the surface of the belt  10  facing the drum may slightly differ from the nominal radius R 0  of the drum. The effective radius R, among other factors, is influenced by the thickness of the toner layer (which is generally non-uniform over the area of the image) and by the amount of deformation of the drum  26  which is approximately proportional to the nip pressure. 
     As was mentioned before, the line pulses which trigger the formation of subsequent image lines at the position of the magnetic knife  28  are derived from the displacement of the belt  10 , so that the time interval t between two subsequent line pulses corresponds to d/Vb, wherein d is the desired line pitch of the image on the belt  10 . During this time interval t, the surface of the drum  26  travels the distance d′=t Vd=d Vd/Vb. Thus, the image formed on the drum  26  is distorted by a factor S=Vd/Vb in the direction of movement of the drum. When the image is transferred from the drum  26  to the belt  10  at the nip  30 , it is again distorted, but this time by a factor 1/S, so that the two distortions cancel each other. 
     However, the distortion S may nevertheless cause an image registration error for the following reason. Let it be assumed that the leading edge of an image, i.e. the first line of the image is to be transferred to a predetermined position P on the belt  10 . Then, when the distortion S is neglected, the start-of-page signal should be applied to the drum  26  at the time when the position P is just the distance L ahead of the nip  30 , so that the first line of the image will reach the nip  30  simultaneously with the position P. However, when the distortion factor S is different from 1, the first line of the image will travel the distance L S while the position P travels the distance L. This results in a positioning error of L (S−1). 
     When the drums  26 A,  26 B,  26 C and  26 D in FIG. 1 all have the same distortion S, then all images would be shifted by the same amount, and the images would nevertheless be superposed correctly. But when the distortions of any two drums differ from each other by an amount DS, the result is a registration error D=DS L. Such differences in the distortion may easily occur during long-term operation of the system due to changes in the compressibility of the support rollers  16 , the drums  26  or the belt  10 , a change of nip pressure, and the like. 
     A method for correcting the registration error resulting from such effects will now be described in conjunction with FIG.  1 . 
     Each of the drums  26  is provided with an encoder  54  (see unit  24 A) which detects the angular displacement and hence the surface displacement of the drum. The corresponding displacement signals are transmitted to the controller  36  via lines  56 . 
     In a correction cycle, which may for example be performed each time the main power has been switched on, while the transfuse station is warming up, the belt  10  is driven with its normal operating speed. The controller  36  receives the displacement signals from the encoders  54  of each image-forming unit and measures the displacement (numbers of encoder pulses) of the individual drums  26 A- 26 D. 
     Each number of encoder pulses is measured and averaged over a preferably integral number of drum revolutions, so that the result will not be influenced by any possible eccentricities of the drums. The number of revolutions should be as large as practical, in order to improve the accuracy. 
     The measurements for the individual drums are conducted with a delay which corresponds to the time it takes the belt  10  to move from one nip  30  to the other. Thus, the measurements are carried out while the drums roll over the same portion of the belt  10 , so that any possible thickness variations of the belt will influence the measurement results for all drums in the same manner. To this end, the belt  10  may be provided with a mark which is detected every time when it enters a nip  30 . Alternately, this mark can be formed on the belt  10  by the first drum  24 A at the start of the measuring cycle and be detected in the other image-forming units ( 24 B,  24 C,  24 D) upon entering the nips  30 . 
     The measurement for the individual drums is controlled by the controller  36  on the basis of the belt  10  displacement counts delivered by roller  14 , which for achieving an even higher accuracy, preferably has a circumferential length D, corresponding to the distance D between the transfer nips  30  of two successive image-forming units. For each individual drum ( 26 A- 26 D) the controller  36  counts the number of control signals (pulse) that is generated by roller  14  during the predetermined number of revolutions of each drum ( 26 A- 26 D). The number of counts for each drum is compared with a reference number stored in a memory. Based on this comparison and the (fixed) distances L and D, the controller calculates the new SOP-signal for each image-forming unit, which is expressed in count numbers of the roller  14  and stored in a control memory. The reference numbers stored in the memory are set when the machine is manufactured and are obtained in a well-known way in a calibration step, in which for instance, color prints of a specifically designed test image are printed and the SOP signals are adjusted, based upon the registration failures in several test prints, until a print with no registration failures is obtained. 
     Of course, the correction cycle described above may be carried out more frequently, e.g. each time a predetermined number of prints has been made, or at larger intervals, e.g. only upon request of the user, when the image quality has been found to be unsatisfactory. Also, it will be clear that a correction cycle is executed after replacement of a part of the image-forming system, e.g. the belt  10 , a drum  26  or a roller  16 . The correction cycles might also be performed continuously while the system is operating. 
     Alternatively, it would of course be possible to calculate the distortion differences DS and the delay timings for the pairs of image-forming units A-B, B-C and C-D. 
     As will be understood from the above description, the registration errors to be corrected are proportional to the distance L. It will accordingly be preferable to select this distance L as small as possible in order to further enhance the registration accuracy. 
     As has been described above, the nip pressure is one of the factors which influences the drum speed and the image distortion S. Accordingly, instead of or in addition to adjusting the delay counts, it would also be possible to correct the image distortions by adjusting the nip pressures by means of the actuators  50 . 
     As will be understood from FIG. 2, minor short-term variations of the distortion S may also be caused by thickness variations of the belt  10 . However, as the distance L is the same for each of the drums, these variations will not cause a substantial registration error. 
     Since the line pulses are derived from the signal of the measuring roller  14  in the embodiment shown in FIG. 1, the eccentricity of the measuring roller  14  may cause slight irregularities in the line pitch of the printed image. By making the circumference of the measuring roller  14  equal to the distance D between successive transfer nips, it is assured that these variations will be the same for all image-forming units and will not lead to registration errors. 
     In a modified embodiment the measuring roller  14  can be replaced by a stationary detector which detects line pulse encodings that are permanently provided on the belt  10 . 
     FIG. 3 illustrates a further modification, according to which line pulse encodings  58  are provided on the belt  10  and a detector  60  detecting these encodings is provided for each of the drums  26 A- 26 D. In this case, the encodings  58  provide a fixed pattern for the print lines formed in each image-forming unit. The SOP-signal for the image-forming units ( 26 B- 26 D) is released when a specific line number is counted by the respective detector  60 , after release of the SOP-signal for unit  26 A. The control and correction of the count numbers is done as described above with reference to FIG.  1 . 
     FIG. 4 shows another embodiment, in which a single reference mark  62  is provided on the belt  10 . This reference mark  62  is detected by each of the detectors  60  disposed a short distance in front of the transfer nip of each image-forming unit and provides a reference for the start-of-page signal. The timing circuits  40 A- 40 D then have to provide only comparatively short delay times which in the simplest case may consist only of the correction delay times calculated by the controller  36 . Optionally, a relatively short fixed standard delay time may be added, which corresponds to the positioning of the detector relative to the transfer position. 
     In the embodiment according to FIG. 4, the line pulses may be generated in the same manner as in FIG.  1 . 
     According to yet another modification, the first detector  60  associated with the drum  26 A in FIG. 4 may be replaced by a writer which writes line pulse encodings derived from a drum encoder on the belt  10 . To this end, the belt  10  may, for example, be provided with a magnetic recording strip. These line pulse encodings are then read by the detectors  60  of the other three units. The first encoding written after the receipt of a print command signal serves as a start-of-page signal which is appropriately delayed by the timing circuits  40 B- 40 D. Thus, this embodiment combines the advantages of the embodiments shown in FIGS. 3 and 4. In the embodiments described so far, each of the drums  26 A- 26 D is directly driven by the belt  10  (idling drums). In a full color printer, where several toner layers are superposed in order to obtain mixed colors, the total thickness of the toner layer  46  (FIG. 2) may become so large that its influence on the image distortion S can no longer be neglected. Since the thickness of the toner layer will generally vary over the length of the image, the image distortions and the differences therebetween can no longer be regarded as constant. In order to obtain a proper image registration over the whole length of the image it may then become necessary either to correct the timings of the SOP signals and of the line pulse signals continuously or to control the speeds or displacements of the drums  26  in order to forcibly provide constant image distortion differences DS among the various units. In this respect, FIG. 5 shows an embodiment in which at least the last three image-forming drums  26 B,  26 C and  26 D are driven by respective motors  64 . 
     In the shown embodiment, a writer  66  is associated with the first drum  26 A and writes encodings  58  on the belt  10  as has already been described above. The writer  66  is synchronized with the pulse signals obtained from the encoder  54  associated with the drum  26 A. 
     The encodings  58  are read by the detectors  60  each of which delivers a signal indicative of the local displacement of the belt  10  to a respective controller  68 . The controller  68  further receives a signal from the encoder of the associated drum  26  and feedback-controls the drive motor  64  for this drum, so that the displacement of the drums  26 B- 26 D is piloted by the encodings  58 . An eraser  70  is arranged behind the last image-forming unit  24 D to erase the encodings. 
     The system shown in FIG. 5 can be operated in various ways. 
     For example, each controller  68  may be programmed to control the motor  64  such that the pulses obtained from the drum  26  coincide with the pulses obtained from the detector  60 . In this case, the distortion S for each of the drums  26 B- 26 D will be locked to that of the drum  26 A, and all DS will be equal to zero, so that no correction delay times for the SOP signals are necessary. 
     The first image-forming drum  26 A is an idling drum as in the previous embodiments. This is possible because the toner layer applied to the belt  10  is still relatively thin and will not cause substantial deviations in the image distortion. When the thickness or compressibility of the belt  10  varies over the length of the belt, this may cause changes in the speed and the image distortion of the drum  26 A. When the corresponding part of the belt  10  then reaches the subsequent drums, these drums are controlled to forcibly show the same speed changes, so that the variations in the properties of the belt  10  will not give rise to excessive tangential forces or torques in the nips of the units  24 B- 24 D. 
     If the mechanical properties of the drums  26  (and/or the support rollers  16 ) are different, this may give rise to different natural speeds of the drums  16 . When the speeds of the drums  26 B- 26 D are locked to that of the drum  26 A, this may cause tangential forces in the transfer nips. However, the system permits the elimination of these forces by selecting a different target speed for each of the drums  26 B- 26 D. Preferably, these target speeds are still proportional to the speed of the drum  26 A but not necessarily identical therewith (i.e. the ratio between the numbers of pulses from the drum  26  and the detector  60  will be different for each image-forming unit). Of course, the different speeds then lead to image distortion differences DS which have to be compensated by appropriately delaying the SOP signal as in the first embodiment. 
     According to a modification of the system shown in FIG. 5, the writer  66  is replaced by another detector  60 , and all detectors detect encodings (e.g. line pulse encodings) that are permanently provided on the belt  10 . In the first image-forming unit the number of pulses derived from the drum  26 A is compared to the (larger) number of pulses derived from the belt encodings, and the ratio between these pulse counts is stored in a shift register. With a time delay corresponding to the movement of the belt  10  from one nip to the other this ratio is then read by the controllers  68  of the subsequent units and is used to derive the target values for the displacement of the drums  26 B- 26 D on the basis of the signals delivered by the respectively associated detectors  60 . Again, the target displacements may either be selected to fulfill the condition DS=0 or may be varied to obtain a DS which is fixed for each image-forming unit and may be compensated for by correction delay times for the SOP signals. In a practical example, the encoders of the drums  26  may deliver a pulse for every surface displacement of the drum by 20 mm. In the case of a 400 dpi. printer this displacement of 20 mm corresponds to 1240 image lines. Thus, 1240 line pulses detected by the detectors  60  will correspond to one pulse of the drum  26 , so that the frequency ratio can be varied in steps of approximately one per thousand. 
     In yet another embodiment, it is possible to define fixed pulse ratios either individually for each image-forming unit or an identical pulse ratio for all units. The first alternative will essentially correspond to the embodiment described in conjunction with FIG. 1 in which each drum  26  has a different image distortion S, with the difference however, that these image distortions are now forcibly held constant and will not be altered by varying thicknesses of the toner layer. The second alternative (all drums controlled in accordance with the same pulse ratio) corresponds to the effect achieved with a conventional mechanical gear coupling. However, the solution according to the present invention has the advantage that the image distortions may now be varied in order to avoid excessive tangential forces in the nips  30 . 
     Instead of using controllers  68  for feedback-controlling the displacements of the drums  26 B as in the embodiments described above, it is also possible to use conventional servo control systems which feedback-control the drums  26  to a given target speed. The target speed will then be derived from the speed of the belt  10  and may be modified by an appropriate correction factor in order to take account for the different mechanical properties of the image-forming units and to limit the tangential forces in the transfer nips. 
     In order to determine the appropriate target speeds or target image distortions S for each image-forming unit, it is desirable to measure the natural speed of each drum  26  in the idling state. On the other hand, in order to provide a stable feedback control system, it is desirable that the drum  26  is rigidly coupled to its drive motor  64 , and it would be undesirable to provide a releasable coupling between the motor and the drum. In view of this conflict, the following procedure is proposed for determining the natural speed of the drum. 
     The transfer nip  30  is opened so that the drum  26  is no longer in contact with the belt  10 . Then, the drum is driven by the motor  64  (e.g. a DC motor with PID control) at its normal operating speed. Then the driving torque of the motor  24  is determined under this condition, for example from the I-component of the PID controller or from the controlled input voltage applied to the motor. The torque determined in this way is the offset torque which is necessary for overcoming the frictional resistance in the bearing of the drum  26  and the like. The difference between the driving torque of the motor when the nip  30  is closed and the above offset torque is a measure for the torque transmitted via the nip  30 , i.e. the torque which has to be limited by appropriately setting the target speed of the drum. In order to determine the desired target speed, the motor can be driven with the determined offset torque, and the speed can then be measured by the procedure described in conjunction with FIG. 1, i.e. by means of the encoders  54 . 
     In case of a PID-controlled motor, the following procedure is possible: The transfer nip  30  is closed, and the current supply to the motor is limited to the value determined above as a measure for the offset torque. Then, the target speed of the motor is increased to maximum, so that the drum will achieve its natural speed in which the torque of the motor is just sufficient to overcome the frictional resistance. This speed is then measured and is taken as the target speed for the PID controller. After resetting the PID-controller, the limitation of the current supply is removed, so that the controller is fully operative. The drum  26  will then be driven with its natural speed as if it were an idling roller (with no toner layer present in the nip  30 ). During printing operation the PID controller will constantly drive the drum  26  with this speed, irrespective of whether or not toner is present in the nip  30 . 
     In a similar manner, it is possible to determine the appropriate target speeds for any non-zero torque or tangential force at the nip  30 . Once a gauge curve for the relation between the drum speed (image distortion S) and the torque or force transmitted at the nip  30  has been established, any desired torque can be adjusted by appropriately setting the target value for the drum speed. 
     An alternative possibility to control the speeds of the drums  26  without using drive motors  64  is to vary the nip pressure exerted by the actuator  50  and the spring  48  (FIG.  2 ). Once the relation between the nip pressure and the image distortion is known, the image distortion can be feedback-controlled by means of the actuator  50 . 
     While only specific embodiments of the invention have been described above, it will occur to a person skilled in the art that various modifications can be made within the scope of the invention which is defined in the appended claims.