Abstract:
A method of determining a relative speed between two separately driven members in an image forming apparatus, includes the steps of: transporting a print medium using a print media transport assembly including a first nip, the print media transport assembly operable at a first transport speed; driving a rotatable member associated with a second nip at a second transport speed which is independent from the first transport speed; printing a first image on the print medium when the print medium is in at least one of the first nip and the second nip; printing a second image on the print medium when the print medium is in each of the first nip and the second nip, the second image overlapping the first image; detecting a moiré pattern caused by the first image and the second image; and determining a speed relationship between the first transport speed and the second transport speed, dependent upon the detected moiré pattern.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to an image forming apparatus, such as an electrophotographic (EP) printer, and, more particularly, to a method of determining a relative speed between two separately driven members in such a printer. 
   2. Description of the Related Art 
   Cost and market pressures promote the design of the smallest possible printer with the shortest possible length of paper path. Short paper paths mean that media (especially legal-length media) are involved in more than one operation at once, and may span adjacent components. For example, a piece of paper in a printer which images directly onto paper may be at more than one imaging station while it is also in the fuser at the same time. 
   Tandem color laser printers which image directly onto paper typically use a paper transport belt to move media past successive imaging stations before fusing the final image onto the media. Velocity variation is a problem created when fuser or machine component tolerances or thermal growth affect the speed ratio between the fuser and the paper transport system upstream from it. Rather than having a constant ratio between the fuser and the paper transport system, this speed ratio varies from machine to machine and from time to time or mode to mode within the same machine. This can cause registration errors, and can cause scrubbing or other print defects as well. 
   For optimal registration of the imaging planes in tandem color laser printers, the surface speeds of the photoconductors and the media (in a direct-to-paper machine) must be precisely controlled. To achieve this, it is important that no external loads disturb the motor system moving the media. In a hot-roll fuser, the fusing nip is typically a high-force nip, with pressures on the order of 20 psi or more. This high-force nip has a sufficient grip on the media that the fuser will attempt to control the speed of the media regardless of what other systems are regulating its speed. The ability of a fuser to overwhelm other media feeding devices, and the problems this causes, may also be shared by other fuser technologies, such as belt fusers or fusers with belt backup members. For certain types of belt fusers, the backup roll is the driven member, so its effective drive diameter controls the speed of the media. 
   In direct-to-paper machines, if media is pulled taut between an imaging nip and a fusing nip operating at a higher speed, the disturbance force transmitted via the media from the fuser to the paper transport belt causes image registration errors. To prevent these, the fuser is often under driven so that a media bubble accumulates between the transport belt and the fuser. Since the fuser runs more slowly, the media never becomes taut, so less disturbance force can be transmitted from the fuser to the transport belt. However, the pursuit of small machines means that media bubbles must be constrained to stay as small as possible. If a machine is designed for a certain maximum bubble size, large velocity variations can make the media try to form a bigger bubble. If this happens, the media will probably make contact with machine features which scrape across the image area, causing print defects. The media might also “snap through”, from the desired bubble configuration into a new one which is undesirable. This snapping action may also disturb the image and create print defects. 
   Ideally, the fuser is just slightly under driven so that a small paper bubble develops, but does not occupy much space in the machine. However, many factors affect the relative speeds of the transport belt and the fuser, potentially creating a large range of relative velocity variation. The nominal under drive of the fuser must be set such that the worst-case velocity variation condition still results in fuser under drive or exact speed matching, but never fuser overdrive (which would create taut media). 
   The speed of the media on a paper transport belt is set by the motion of the transport belt and photoconductive drums which form respective nips with the belt. The speed of the media in the fuser is controlled by the motion of the driven fuser member, roll compliance, drag on the backup roll, and friction coefficients between media and the two fuser rollers. In a hot-roll fuser, the hot roll is usually gear-driven while the backup roll idles on low-friction bearings. Therefore, the surface speed of the hot roll determines the speed of the media in the fuser. In some fuser systems where the backup roll is driven, the speed of that member controls the speed of the media. 
   The transport speed variances of the fuser can be divided into two primary categories: 1) the effect of temperature variations on the fuser roll, and 2) manufacturing variances such as dimensional tolerances, varying physical properties of materials used in components, different preload nip pressures, etc. Effects of temperature variations of the fuser roll at different operating temperatures are addressed in a manner described in a separate patent application entitled “METHOD OF DRIVING A FUSER ROLL IN AN ELECTROPHOTOGRAPHIC PRINTER”, U.S. patent application Ser. No. 10/757,301, filed Jan. 14, 2004, which is assigned to the assignee of the present invention. 
   Manufacturing variances have been addressed heretofore, but in much more complicated and expensive ways. Merely measuring the outside diameter of a fuser roll and its rotational speed and calculating its circumference or surface speed is not good enough because the roll deforms during rotation. This deformation means that the actual distance media travels during one roll revolution through the fuser is not the same as the circumference of the roll. One method is to place a piece of tape on a fuser roll, and then to fuse solid-coverage images using the fuser roll. The tape causes a print defect at the period of the effective roll circumference, allowing distance traveled during one roll revolution to be accurately measured. The reduction in size of the media as it loses moisture during the fusing process complicates this process, since this change must be accounted for in calculating the period of the print defect. The use of tape is also undesirable since it risks roll damage which could cause later print defects. 
   U.S. Pat. No. 5,819,149 describes sensing methods for directly monitoring the size of a backup roll in a belt fuser. As the backup roll changes size, its peripheral velocity will change, so the media velocity going through the fuser will also change. Monitoring roll size allows the printer to maintain a desired media speed through the fuser. However, as discussed above, roll circumference will not strictly match the media advance distance during one roll revolution, so this method introduces errors. 
   U.S. Pat. No. 5,170,215 describes the use of a separate media speed sensor to determine whether a fuser is pulling on continuous-form media. The additional required sensors undesirably increase the cost of the printer. 
   U.S. Pat. No. 5,508,789 describes a speed measurement method for determining the photoconductor drum speed needed to match speeds between an intermediate transfer belt and the photoconductor drum. The speed of the drum is varied while monitoring current to the drum drive motor, while the belt is driven and servo-actuated independently. Over a long-period speed oscillation (200 seconds), large variations in current demand caused by dry friction between the drum and belt materials when their speeds nearly match are monitored. This dry friction phenomenon provides a large physical response at the point of matching speeds. 
   Each of these known patented methods uses additional sensors for sensing continuously available parameters or measuring parameters while components are in direct continuous contact. This increases the complexity and cost of related printers. 
   What is needed in the art is a method of determining and setting a transport speed of a downstream driven member relative to a transport speed of an independent upstream driven member, without requiring additional sensors, etc. 
   SUMMARY OF THE INVENTION 
   The present invention provides a method of setting a transport speed of a downstream driven member relative to a transport speed of an upstream driven member by detecting moiré patterns on multiple printed sheets and determining a speed of the downstream driven member which most closely matches a transport speed of the upstream driven member. 
   The invention comprises, in one form thereof, a method of determining a relative speed between two separately driven members in an image forming apparatus, including the steps of: transporting a print medium using a print media transport assembly including a first nip, the print media transport assembly operable at a first transport speed; driving a rotatable member associated with a second nip at a second transport speed which is independent from the first transport speed; printing a first image on the print medium when the print medium is in at least one of the first nip and the second nip; printing a second image on the print medium when the print medium is in each of the first nip and the second nip, the second image overlapping the first image; detecting a moiré pattern caused by the first image and the second image; and determining a speed relationship between the first transport speed and the second transport speed, dependent upon the detected moiré pattern. 
   An advantage of the present invention is that the relative speed between the independently driven members can be determined without additional sensors. 
   Another advantage is that the transport speed of the downstream member can be set at a predetermined amount less than the upstream member so as to avoid certain print defects. 
   Yet another advantage is that the point at which the transport speed of the downstream driven member matches the transport speed of the upstream driven member can be established using observation or a linear data fit. 
   A still further advantage is that the method of determining and setting the relative transport speed of the downstream driven member can occur during manufacture or upon replacement of the downstream driven member. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above-mentioned and other features and advantages of this invention, and the manner of attaining them, will become more apparent and the invention will be better understood by reference to the following description of an embodiment of the invention taken in conjunction with the accompanying drawings, wherein: 
       FIG. 1  is a simplified side, sectional view of an EP printer which may be used to carry out an embodiment of the method of the present invention; 
       FIG. 2  is a schematic, side view of a portion of the paper transport assembly, fuser and electrical circuit of the EP printer shown in  FIG. 1 ; 
       FIG. 3  is a graphical illustration of regions of interest for moiré patterns on a print sample; 
       FIG. 4  is an example of a moiré print pattern made with a fuser speed of 104.991 mm/s; 
       FIG. 5  is an example of a moiré print pattern made with a fuser speed of 107.030 mm/s; 
       FIG. 6  illustrates how a moiré print pattern similar to that shown in  FIG. 5  can be analyzed to determine an effect of the fuser speed on the transport belt; and 
       FIG. 7  is graphical illustration of a fuser speed estimate matching the transport belt speed based on moiré shift data. 
   

   Corresponding reference characters indicate corresponding parts throughout the several views. The exemplification set out herein illustrates one preferred embodiment of the invention, in one form, and such exemplification is not to be construed as limiting the scope of the invention in any manner. 
   DETAILED DESCRIPTION OF THE INVENTION 
   Referring now to the drawings and particularly to  FIG. 1 , there is shown an embodiment of an EP printer  10  of the present invention. Paper supply tray  12  contains a plurality of print media, such as paper, transparencies or the like. A print medium transport assembly (not numbered) includes a plurality of rolls and/or transport belts for transporting individual print media  14  through EP printer  10 . For example, in the embodiment shown, the print medium transport assembly includes a pick roll  16  and a paper transport belt  18 . Pick roll  16  picks an individual print medium  14  from within paper supply tray  12  and transports print medium  14  to a bump-align nip defined in part by roll  20  to paper transport belt  18 . Paper transport belt  18  transports the individual print medium past a plurality of color imaging stations  22 ,  24 ,  26  and  28  which apply toner particles of a given color to print medium  14  at selected pixel locations. In the embodiment shown, color imaging station  22  is a black (K) color imaging station; color imaging station  24  is a yellow (Y) color imaging station; color imaging station  26  is a magenta (M) color imaging station; and color imaging station  28  is a cyan (C) color imaging station. 
   Paper transport belt  18  transports an individual print medium  14  ( FIG. 2 ) to fuser  32  where the toner particles are fused to print medium  14  through the application of heat and pressure. Fuser  32  includes a hot fuser roll  34  and a back up roll  36 . In the embodiment shown, fuser roll  34  is a driven roll and back-up roll  36  is an idler roll; however, the drive scheme may be reversed depending upon the application. 
   Techniques for the general concepts of heating fuser roll  34  and rotatably driving fuser roll  34  or back-up roll  36  using gears, belts, pulleys and the like (not shown) are conventional and not described in detail herein. Fuser roll  34  is schematically illustrated as being connected via phantom line  38  to drive motor  40 , which is in turn connected to and controllably operated by electrical processing circuit  42 , such as a microprocessor. Electrical processing circuit  42  is also coupled with temperature sensor  58  associated with hot fuser roll  34 . 
   In the embodiment shown, print medium  14  is in the form of a legal length print medium. As is apparent, print medium  14  is concurrently present at the nips defined by a photoconductive (PC) drum  44  of color imaging station  26 ; a nip defined by PC drum  46  of color imaging station  28 ; a nip defined between fuser roll  34  and back-up roll  36 ; a nip defined by fuser exit rolls  48  and a nip defined by machine output rolls  50 . The leading edge of print medium  14  is received within output tray  52  on the discharge side of machine output rolls  50 . 
   PC drum  46  and the corresponding backup roll define an exit nip from the print medium transport assembly, and fuser rolls  34  and  36  define an entrance nip to fuser  32 . As described above, it is undesirable to overdrive fuser roll  34  such that the fuser-controlled media velocity at the nip of fuser roll  34  exceeds the linear transport speed of paper transport belt  18 . The force on media  14  from the nip between fuser roll  34  and back-up roll  36  typically is larger than the combination of the forces from the nips at PC drums  44  or  46  and the electrostatic force acting on the print medium, and thus the nip pressure and transport speed at fuser roll  34  tend to dominate the transport speed of the print medium conveyed on paper transport belt  18 . If fuser roll  34  is overdriven such that the fuser-controlled media velocity is greater than that of paper transport belt  18 , then print defects may occur on print medium  14 . For this reason, fuser roll  34  may be under driven to cause a slight bubble  54  in the gap between the discharge side of paper transport belt  18  and the input side of the nip between fuser roll  34  and back-up roll  36 . This bubble  54  may be more pronounced, as illustrated by phantom line  56  in  FIG. 2 . If the size of bubble  54  becomes too large because of the velocity differences between fuser roll  34  and paper transport belt  18 , then print medium  14  may contact physical features within printer  10  resulting in print defects. That is fuser roll  34  should be under driven, but not to such an extent that defects resulting from scraping, etc. of print medium  14  occur. 
   In the embodiment shown, each of fuser roll  34  and back-up roll  36  have a PFA sleeve at the outside diameter over an elastomeric layer. The outside diameter of fuser roll  34  and back-up roll  36  is approximately  36 mm at the outside diameter of the PFA sleeve when measured cold. It will be appreciated that the outside diameter of fuser roll  34  increases as the operating temperature of fuser roll  34  increases. 
   The method of the present invention accounts for manufacturing tolerances on fuser rolls which affect the speed of media  14  (such as paper  14 ) as it passes through fuser  32 . This measurement operation allows the relative speed between fuser  32  and transport belt  18  to be set in the middle of an acceptable range, so that media  14  will build an optimal paper bubble  54  between the two systems. Otherwise, during some operating modes, fuser  32  pulls media  14  too tight and affects color registration, or it slows down too much during other modes and builds too large of a paper bubble  56 , possibly causing tailflip and image smear. This method is carried out at the end of the printer manufacturing line, and is necessary if a fuser is replaced in the field. 
   More particularly, one method of determining a relative speed between fuser  32  and transport belt  18  is to monitor commanded voltage of motor  40  while sending pages through fuser  32  at different speeds. Such a method is more fully described in U.S. patent application Ser. No. 10/809,095, entitled “METHOD OF DETERMINING A RELATIVE SPEED BETWEEN INDEPENDENTLY DRIVEN MEMBERS IN AN IMAGE FORMING APPARATUS ”, filed Mar. 25, 2004, which is also assigned to the assignee of the present invention. 
   According to an aspect of the present invention, another method of determining a relative speed between fuser  32  and transport belt  18  is to visually detect moiré patterns printed on multiple media  14  while sending pages through fuser  32  at different speeds. 
   Except when a sheet of media  14  is on both transport belt  18  and in the fuser nip between rolls  34  and  36 , media  14  applies very little load to motor  40 . Most of the fuser motor power is used to rotate fuser rolls  34  and  36  (which deform against one another as they rotate under load), fuser exit rolls  48  and machine output rolls  50 . Even when a sheet  14  is on both transport belt  18  and in the fuser nip, if media  14  speed in fuser  32  is slower than the transport belt speed, a paper bubble  54  will develop, and little additional load will be imposed on motor  40 . However, if a sheet is on both transport belt  18  and in the fuser nip, and media  14  speed in fuser  32  is faster than the independently driven transport belt speed, then fuser  32  will pull on media  14  and transport belt  18 , raising the load on motor  40 . During normal operation, this is not desirable since the load on transport belt  18  could lead to color registration errors. However, during a speed measurement sequence of the present invention, this additional load can be monitored by detecting changes in moiré patterns printed on media  14 . The type of print artifact associated with the printed moiré patterns, depending upon the relative speeds of transport belt  18  and fuser  32 , can be used to determine when the speeds are matched. With a known fuser speed which matches the transport belt speed, processor  42  adds an offset to slow fuser  32  so that a desired paper bubble is created, and the resulting sum is stored as a nominal fuser speed. 
   Moiré patterns are interference patterns made of slightly different images in different color planes. In one form, moiré patterns are an undesirable pattern that occurs when a halftone is made from a previously printed halftone. They are caused by the conflict between the dot arrangement produced by the halftone screen and the dots or lines of the original halftone.  McGraw - Hill Dictionary of Scientific and Technical Terms,  Fifth Edition, 1994. They can show subtle shifts in registration between the color planes from one location on media  14  to another. If media  14  speed through fuser  32  is faster than the current speed of paper transport belt  18 , fuser  32  will pull on transport belt  18 . This disturbance force will subtly affect the speed of media  14  on transport belt  18 , either by encouraging slip between components or by allowing gear train windup between the transport belt motor and media  14  being printed. As a result, moiré patterns printed at different fuser speeds will show different registration effects caused by disturbance forces acting on transport belt  18 . The highest fuser speed which doesn&#39;t introduce registration artifacts is assumed to be the fuser speed equal to the transport belt speed. For normal operation of fuser  32 , a speed offset will be subtracted from this fuser speed so that a paper bubble  56  is formed between fuser  32  and transport belt  18 . 
     FIG. 3  shows an example of different regions of print samples.  FIG. 3  represents a letter-size media  14 , and is oriented so that the top of the figure enters the electrophotographic process first. As media  14  enters the process, it progresses from a bump-align nip defined in part by roll  20  onto transport belt  18 , where it is successively imaged by black, yellow, magenta, and cyan transfer stations, after which it enters fuser  32  and then exits from output rolls  50 . In zone  1 , both the black and the cyan image planes are transferred to media  14  before the page enters fuser  32 . Therefore, no forces from fuser  32  act on transport belt  18  during this time. In zone  2 , the black image plane is transferred to media  14  before the page enters fuser  32 , but the cyan image plane is transferred while the top of the page is in fuser  32 . If fuser  32  is moving faster than transport belt  18 , disturbance forces act on the belt while cyan is imaged in this zone, but not while black is imaged. Finally, in zone  3 , both the black and cyan image planes are transferred to media  14  after the leading edge of the page enters fuser  32 , so transport belt  18  is subject to disturbance forces from fuser  32  during this time. Table 1 shows the progress of a page through the printer, and the resulting distances down a page for imaging events. 
   
     
       
             
           
             
             
             
             
           
             
             
             
             
           
         
             
               TABLE 1 
             
           
           
             
                 
             
             
               Paper Path and Imaging Positions on Page 
             
           
        
         
             
                 
               Leading 
                 
                 
             
             
                 
               edge 
               K image 
               C image 
             
             
                 
               position 
               position 
               position 
             
             
               Page position in the process 
               (mm) 
               (mm) 
               (mm) 
             
             
                 
             
           
        
         
             
               Leading edge at bump-align roll 
               0 
                 
                 
             
             
               Leading edge at K, page in bump-align 
               64 
               0 
             
             
               Leading edge at C 
               214 
               150 
               0 
             
             
               Page in K, page still in bump-align 
             
             
               Leading edge past C 
               279.4 
               215.4 
               65.4 
             
             
               Page in K, trailing-edge at bump-align 
             
             
               Leading edge at fuser 
               293 
               229 
               79 
             
             
               Page in K and C 
             
             
               Trailing edge at K 
               343.4 
               279.4 
               129.4 
             
             
               Page in C and fuser 
             
             
               Page still in C, page still in fuser 
             
             
               Trailing edge at C, page still in fuser 
               493.4 
                 
               279.4 
             
             
                 
             
             
               “Leading edge” is position of the leading edge of page, in mm along the paper path from the bump-align nip 
             
             
               “K image” is position on the page of the K image, in mm from the top of the page 
             
             
               “C image” is position on the page of the C image, in mm from the top of the page 
             
             
               Assumes letter-size paper (279.4 mm page length) 
             
             
               Note that A4 media is 297 mm long, and can be in both the bump-align system and fuser 32 at the same time. 
             
           
        
       
     
   
     FIG. 4  shows an example of a moiré print pattern made when the fuser speed is slower than the transport belt speed. Media forms a paper bubble between transport belt  18  and fuser  32  in this condition, so fuser  32  does not impart much of a disturbance force to transport belt  18  in this situation. 
   This moiré pattern was produced by combining a black halftone screen with a cyan halftone screen. The cyan screen is composed of closely-spaced horizontal lines, while the black screen is composed of closely-spaced lines which are tilted at a slight angle. Postscript (TM) functions were used to command a screen angle of 0.3 degrees for the black halftone screen, and 0.0 degrees for the cyan screen. Both screens are printed at 100 lines per inch, at a 33% intensity, in a 600 dpi mode. Since the angle of the black screen is so shallow compared to the print resolution, each black line is composed of horizontal regions connected by stairsteps between them. This means that black and cyan lines sometimes overlap and sometimes run parallel and adjacent to one another. The close spacing of the lines and their relatively wide widths mean that the apparent darkness of a region of the pattern is determined by whether the lines locally overlap or not. If the lines overlap, there will be some adjacent white space, resulting in a light area. If the lines don&#39;t overlap, they will completely fill the spaces between one another, resulting in a dark area. Because the stairsteps occur at regular intervals across the page, the regions of light and dark do as well, resulting in the pattern in  FIG. 4 . 
   If all of the printer components were “perfect,” this moiré pattern would print as vertical bands running from the top to the bottom of media  14 . However, component defects and speed variations during the imaging process cause shifts in media position and laser position which differ between the imaging of the black plane and the imaging of the cyan plane. Process-direction shifts show up in this moiré pattern as right-to-left motion of the vertical bands as they progress down media  14 . For example, if fuser  32  pulls on transport belt  18  in zone  2  of the image, the vertical bands will veer off toward the right as they move down the page. Note that each one box step toward the right represents a process-direction registration shift of a single 600 dpi pixel. 
     FIG. 5  shows a moiré pattern made with a faster fuser speed of 107.030 mm/s, where fuser  32  does affect the speed of transport belt  18  in zone  2  this way. 
     FIG. 6  shows how this moiré pattern can be analyzed to determine the effect of fuser speed on transport belt  18  during the imaging process. The leftmost vertical band entirely present on the page is labeled “Band A,” and the measurements are performed on this band. Since both color planes are imaged in zone  1  before media  14  enters fuser  32 , and both color planes are imaged in zone  3  after media  14  enters fuser  32 , neither of these zones can be used to assess fuser speed. However, black is imaged in zone  2  before media  14  enters fuser  32 , and cyan is imaged in this zone after media  14  enters fuser  32 . Therefore, if fuser  32  causes a transport belt speed increase when media enters fuser  32 , this will show up as a rightward shift of a vertical band as it moves from Line A at the start of zone  2 , down the page to Line B at the end of zone  2 . Table 2 shows the positions of Line A and Line B on a printed page. 
   
     
       
             
           
             
             
             
           
         
             
               TABLE 2 
             
             
                 
             
             
               Line positions for fuser speed measurement 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
                 
               Line A: 
               79 mm down from the top of the page 
             
             
                 
                 
               [above this line, both black and cyan were 
             
             
                 
                 
               imaged before media entered fuser] 
             
             
                 
               Line B: 
               229 mm down from the top of the page 
             
             
                 
                 
               [below this line, both black and cyan 
             
             
                 
                 
               were imaged after media entered fuser] 
             
             
                 
                 
             
           
        
       
     
   
   Table 3 was generated by measuring a series of images at different fuser speeds. The rightward shifts in zone  2  of each sample made at a given speed were then averaged. Next, the rightward shift of the first, slow-fuser run was subtracted from each of the other runs, resulting in the column labeled “relative average.” 
   
     
       
             
           
             
             
           
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
           
         
             
               TABLE 3 
             
           
           
             
                 
             
             
               Speed measurement via moiré patterns 
             
           
        
         
             
               Actual 
               Rightward shift of Moiré pattern between stations (mm) 
             
           
        
         
             
               Fuser 
               Sam- 
               Sam- 
               Sam- 
               Sam- 
               Sam- 
               Average 
                 
             
             
               Speed 
               ple 
               ple 
               ple 
               ple 
               ple 
               of 
               Relative 
             
             
               (mm/sec) 
               #1 
               #2 
               #3 
               #4 
               #5 
               Samples 
               Average 
             
             
                 
             
           
        
         
             
               104.991 
               53 
               39 
               44 
               38 
               32 
               41.2 
               0.0 
             
             
               106.647 
               76 
               92 
               64 
                 
                 
               77.3 
               36.1 
             
             
               107.030 
               69 
               104 
               76 
                 
                 
               83.0 
               41.8 
             
             
               107.540 
               165 
               131 
               166 
                 
                 
               154.0 
               112.8 
             
             
                 
             
           
        
       
     
   
   Finally, a line was fit to the relative average shift data, estimating the lowest fuser speed which would not produce any more rightward shift than the very-slow-fuser setting. This data and the resulting line are plotted in  FIG. 7 . The intercept of the line is 106.36 mm/s, the estimated fuser speed to match the transport belt speed. With the fuser speed which most closely matches the speed of transport belt  18 , the nominal fuser speed is set about 0.4 to 1.8% slower than this speed, preferably 1.05% slower, to put the nominal size of paper bubble 56 in the middle of the range of its possible sizes. 
   The previous scheme for determining relative speeds between fuser  32  and transport belt  18  has been tested and does work. An improved scheme which could perform the whole process on a single page is also possible. For example, instead of printing each entire page at a constant fuser speed, the fuser speed can begin fast and progressively slow during Zone  2  on a single page. This changing speed produces moiré bands with changing slopes in Zone  2 , rather than the relatively constant-slope lines produced by the method described above. Fuser  32  and transport belt have the same speed when the slope becomes vertical in Zone  2 , because fuser  32  is no longer pulling on transport belt  18  at this point. Instead of measuring rightward shifts on each page, the important value is the distance up from Line B to where the slope of the bands becomes vertical. This distance is used to interpolate the fuser speed at that point in the imaging process, and this speed is assumed to match the speed of transport belt  18 . While this require fewer measurements, it also requires nearly perfect machine registration for accurate measurement. Also, it requires fuser  32  to run very fast at the beginning of the sequence to prevent the creation of a bubble  56  which would uncouple fuser speed from registration shifts at known positions on a page. This high-speed operation risks over-current errors which might interrupt the process and prevent successful speed measurement. 
   Another aspect of the invention determines a known fuser speed which matches the transport belt speed and then uses this information to build and maintain a bubble between the two elements. During normal printing in this mode, the fuser is set to run slower than the matched speed at the start of each sheet of media until a small bubble develops. Then, the fuser is accelerated to the matched speed and runs at that speed for the remainder of the sheet, in order to maintain the bubble at a consistent size. 
   These methods could also be automated by measuring the moiré patterns in a printer. A sensor placed at the exit from the transport belt could measure the reflectivity differences caused by the light and dark zones of the moiré pattern and relative speeds could be determined this way. 
   Further, the method of the present invention as described above for determining a relative speed between two separately and independently driven members in an image forming apparatus may be used with independently driven members other than a fuser and a paper transport assembly. For example, a print medium may be transported from an exit nip of an upstream and independently driven bump-align motor to the entry nip of a transport belt. The present invention allows the relative speed between the transport speed at the exit nip of the upstream bump-align motor and the entry nip of a transport belt to be determined, and an adjustment made to one or both transport speeds, if necessary. 
   While this invention has been described as having a preferred design, the present invention can be further modified within the spirit and scope of this disclosure. This application is therefore intended to cover any variations, uses, or adaptations of the invention using its general principles. Further, this application is intended to cover such departures from the present disclosure as come within known or customary practice in the art to which this invention pertains and which fall within the limits of the appended claims.