Patent Publication Number: US-2015063869-A1

Title: Image forming apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is related to, and claims the priority benefit of, Korean Patent Application No. 10-2013-0103950, filed on Aug. 30, 2013 in the Korean Intellectual Property Office, the disclosure of which is incorporated herein by reference. 
     BACKGROUND 
     1. Field 
     Embodiments relate to an image forming apparatus and more particularly to an image forming apparatus that may form color images using a plurality of photosensitive drums. 
     2. Description of the Related Art 
     In general, an image forming apparatus refers to an apparatus that forms electrostatic latent images, which are electrified with a prescribed potential, by scanning a photosensitive drum with light, develops the electrostatic latent images with a single color or multiple color toner, and then transfers and fixes the developed toner images on a paper to form color images. 
     The image forming apparatus for color images includes a toner having a plurality of color toners such as cyan, magenta, yellow, and black that are called CMYK, and the like. Through combination between the respective color toners, the colors of print data may be implemented. The plurality of color toners may be printed on one surface a plurality of times when printing of a color document is performed, unlike usual printing of a black-and-white document. While printing the plurality of color toners on one surface, a problem may arise such that each color cannot be exactly printed at a desired position due to several causes. This may be referred to as color mis-registration. 
     Many photosensitive drums (OPC drum) have a periodic speed variation. This phenomenon occurs in most rotor systems unless the system is an ideally complete rotor system. The periodic speed variation of the photosensitive drum have several fundamental causes such as a shape error (eccentricity or run-out), alignment, and mountability of the photosensitive drum, a shape error of gears of a driving system, a transmission error of gears, structural imperfection of gears, a coupling angular velocity transfer error, and the like. The speed variation of the photosensitive drum that occurs due to these causes may be a direct cause of the color mis-registration. In order to maintain the constant-speed property of the photosensitive drum that has a relationship, e.g., direct relationship with such a color mis-registration phenomenon, efforts to improve individual control technology such as individually driving each of the plurality of photosensitive drums using a plurality of motors in order to cancel a difference in the speed variation for each of the plurality of photosensitive drums as well as efforts to minimize a mechanical deviation such as structural stability of a driving unit and a developing unit, a gear/coupling degree, tolerance management, and the like are desired. 
     SUMMARY 
     It is an aspect to provide an image forming apparatus that may mechanically synchronize eccentricity and run-out deviation for each photosensitive drum of an image forming apparatus which does not individually drive the photosensitive drums. 
     Additional aspects are set forth in part in the description that follows and, in part, will be obvious from the description, or may be learned by practice of the invention. 
     In accordance with an aspect of an embodiment, an image forming apparatus includes a plurality of photosensitive drums, a single motor, a plurality of driving gears installed in accordance with a predetermined phase so as to cancel deviation therebetween and simultaneously driven by the single motor, a plurality of driving side couplers provided in each of the plurality of driving gears and rotated together with the plurality of driving gears, and a plurality of driven side couplers provided in each of the plurality of photosensitive drums and coupled to the plurality of driving side couplers, wherein, when at least one of the plurality of photosensitive drums is coupled to at least one of the plurality of driving gears, the driving side coupler and the driven side coupler are coupled to each other in an one-direction coupling method, and therefore the plurality of photosensitive drums follow the predetermined phase of the plurality of driving gears. 
     A single fastening groove having directivity may be formed in the plurality of driven side couplers, a single protrusion having directivity may be formed in the plurality of driving side couplers, and the protrusion of the plurality of driving side couplers may be inserted into the fastening groove of the plurality of driven side couplers in accordance with the directivity when the plurality of photosensitive drums are coupled to the plurality of driving gears. 
     The fastening groove of the plurality of driven side couplers may be asymmetrically formed so as to have the directivity. 
     An elastic body may be provided in each of the plurality of driving side couplers, and when at least one of the plurality of photosensitive drums is coupled to at least one of the plurality of driving gears, the plurality of driving side couplers may be pressurized toward the plurality of driven side couplers by the elastic body so that a bonding force between the plurality of driving side couplers and the plurality of driven side couplers is maintained. 
     At least two fastening grooves having mutually different directivity may be formed in the plurality of driven side couplers, at least two protrusions having mutually different directivity may be formed in the plurality of driving side couplers, and when the plurality of photosensitive drums are coupled to the plurality of driving gears, the at least two protrusions of the plurality of driving side couplers may be inserted into the fastening groove having corresponding directivity of the plurality of driven side couplers so that the plurality of photosensitive drums and the plurality of driving gears are coupled to each other in the one-direction coupling method. 
     The at least two fastening grooves of the plurality of driven side couplers may be formed into mutually different shapes so as to have the directivity. 
     The at least two fastening grooves of the plurality of driven side couplers may be formed to have mutually different sizes so as to have the directivity. 
     An elastic body may be provided in each of the plurality of driving side couplers, and when at least one of the plurality of photosensitive drums is coupled to at least one of the plurality of driving gears, the plurality of driving side couplers may be pressurized toward the plurality of driven side couplers by the elastic body so that a bonding force between the plurality of driving side couplers and the plurality of driven side couplers is maintained. 
     An insertion port in which a rotating shaft of the driving gear is inserted and fixed may be formed in a center portion of each of the plurality of driving side couplers, and the elastic body may be installed at an inlet side of the insertion port. 
     A groove position detecting protrusion may be formed in at least one of the plurality of driving gears, and the image forming apparatus may further include a single groove position sensing unit for detecting the groove position detecting protrusion. 
     The groove position detecting protrusion may be formed on a surface of at least one of the plurality of driving gears so as to have a semicircular arc shape. 
     The groove position sensing unit may include a light emitting unit and a light receiving unit, and a groove position of the photosensitive drum may be determined through a difference between a light receiving state when the groove position detecting protrusion is positioned between the light emitting unit and the light receiving unit of the groove position sensing unit and a light receiving state when the groove position detecting protrusion is deviated from between the light emitting unit and the light receiving unit. 
     In accordance with an aspect of an embodiment, an image forming apparatus includes a plurality of photosensitive drums, a single motor; a plurality of driving gears installed in accordance with a predetermined phase so as to cancel deviation therebetween and simultaneously driven by the single motor, a plurality of driving side couplers provided in each of the plurality of driving gears and rotated together with the plurality of driving gears, and a plurality of driven side couplers provided in each of the plurality of photosensitive drums and coupled to the plurality of driving side couplers, wherein a single fastening groove having directivity is formed in the plurality of driven side couplers, a single protrusion having directivity is formed in the plurality of driving side couplers, and when at least one of the plurality of photosensitive drums is coupled to at least one of the plurality of driving gears, the driving side coupler and the driven side coupler are coupled in an one-directional coupling method by the directivity of the single protrusion and the directivity of the single groove, and therefore the plurality of photosensitive drums follow the predetermined phase of the plurality of driving gears. 
     In accordance with an aspect of an embodiment, an image forming apparatus includes a plurality of photosensitive drums, a single motor, a plurality of driving gears installed in accordance with a predetermined phase so as to cancel deviation therebetween and simultaneously driven by the single motor, a plurality of driving side couplers provided in each of the plurality of driving gears and rotated together with the plurality of driving gears, and a plurality of driven side couplers provided in each of the plurality of photosensitive drums and coupled to the plurality of driving side couplers, wherein at least two fastening grooves having mutually different directivity are formed in the plurality of driven side couplers, at least two protrusions having mutually different directivity are formed in the plurality of driving side couplers, and when at least one of the plurality of photosensitive drums is coupled to at least one of the plurality of driving gears, the driving side coupler is coupled to the driven side coupler in an one-directional coupling method by the directivity of the at least two protrusions and the directivity of the at least two grooves, and therefore the plurality of photosensitive drums follow the predetermined phase of the plurality of driving gears. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and/or other aspects will become apparent and more readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which: 
         FIG. 1  illustrates a configuration of an image forming apparatus in accordance with an embodiment; 
         FIG. 2  illustrates a control system of an image forming apparatus in accordance with an embodiment; 
         FIGS. 3A and 3B  illustrate characteristics of a photosensitive drum having eccentricity and run-out; 
         FIG. 4  is an exploded perspective view illustrating a connection relationship between a photosensitive drum and a motor of an image forming apparatus in accordance with an embodiment; 
         FIG. 5  illustrates an exemplary connection relationship between the photosensitive drum and the motor of the image forming apparatus illustrated in  FIG. 4 ; 
         FIGS. 6A to 6D  illustrate an exemplary embodiment of a coupler that connects a driving gear and a photosensitive drum of an image forming apparatus in accordance with one embodiment; 
         FIGS. 7A to 7D  illustrate an exemplary embodiment of a coupler that connects a driving gear and a photosensitive drum of an image forming apparatus in accordance with one embodiment; 
         FIGS. 8A and 8B  illustrate a groove position detecting protrusion and a groove position sensing unit that are provided in a driving gear of an image forming apparatus in accordance with an embodiment; 
         FIG. 9  illustrates phase synchronization of a driving gear of an image forming apparatus in accordance with an embodiment; 
         FIGS. 10A and 10B  illustrates a detection result of AC components of a photosensitive drum of an image forming apparatus in accordance with an embodiment; 
         FIG. 11  illustrates a test pattern for performing automatic color registration (ACR) of a photosensitive drum in an image forming apparatus in accordance with one embodiment; and 
         FIG. 12  illustrates results of phase synchronization control and AC average control of an image forming apparatus in accordance with one embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to the embodiments, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to like elements throughout. 
       FIG. 1  illustrates a configuration of an image forming apparatus in accordance with an embodiment. 
     As illustrated in  FIG. 1 , the image forming apparatus in accordance with an embodiment includes a paper feed unit  100 , image forming units  110   k ,  110   m ,  110   c , and  110   y , a transfer unit  120 , and a fixing unit  130 . The paper feed unit  100  feeds a recording medium (S) such as a paper, and the recording medium (S) loaded in a paper feed cassette may be picked up by a pick-up roller  112  to be conveyed. The image forming units  110   k ,  110   m ,  110   c , and  110   y  may be disposed above the paper feed unit  100 , and form developer images with predetermined colors such as black (K), magenta (M), cyan (Y), and yellow (Y) on the recording medium (S). 
     The image forming units  110   k ,  110   m ,  110   c , and  110   y  include, for example, four photosensitive drums  111   k ,  111   m ,  111   c , and  111   y . The photosensitive drums  111   k ,  111   m ,  111   c , and  111   y  may be disposed in parallel with each other at prescribed intervals so as to face an intermediate transfer belt  122  of the transfer unit  120 . The photosensitive drums  111   k ,  111   m ,  111   c , and  111   y  may contact the intermediate transfer belt  122  at a constant pressure by four transfer rollers  121   k ,  121   m ,  121   c , and  121   y  of the transfer unit  120  to thereby form a nip, and may be rotated counterclockwise by a gear member to which power is transmitted from a motor. Four electrifying units  112   k ,  112   m ,  112   c , and  112   y , four laser scanning units  113   k ,  113   m ,  113   c , and  113   y , and four developing units  114   k ,  114   m ,  114   c , and  114   y  may be disposed around the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y.    
     Each of the electrifying units  112   k ,  112   m ,  112   c , and  112   y  includes an electrifying roller. The electrifying units  112   k ,  112   m ,  112   c , and  112   y  respectively contact surfaces of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y . The first, second, third, and fourth electrifying units  112   k ,  112   m ,  112   c , and  112   y  may be applied with a prescribed electrification bias voltage, and form a prescribed electrification potential on the surface of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y , for example, form an electrification potential of about 600 V when a developer has a negative (−) polarity. 
     The laser scanning units  113   k ,  113   m ,  113   c , and  113   y  irradiate the surface of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y  electrified by the electrifying units  112   k ,  112   m ,  112   c , and  112   y  with a laser beam so that a model corresponding to image signals input from a computer, a scanner, or the like is formed, thereby forming electrostatic latent images having a prescribed potential lower than the electrification potential, for example, a low potential area of about −50 V. 
     The developing units  114   k ,  114   m ,  114   c , and  114   y  apply a developer with a color corresponding to the image signal to the surface of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y  in which the electrostatic latent images are formed, thereby developing the electrostatic latent images into visible developer images. The developing units  114   k ,  114   m ,  114   c , and  114   y  include four developing rollers  115   k ,  115   m ,  115   c , and  115   y , and four developer feed rollers  116   k ,  116   m ,  116   c , and  116   y.    
     The developing rollers  115   k ,  115   m ,  115   c , and  115   y  are rotated while being engaged with the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y , and apply the developer to the electrostatic latent images of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y , thereby developing the electrostatic latent images into visible developer images. The developing rollers  115   k ,  115   m ,  115   c , and  115   y  may be disposed adjacent to the surface of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y , and may be rotated clockwise by a power transmission gear connected to the gear member that drives the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y . A prescribed developing bias voltage lower by 100 to 400 V than that of the developer feed rollers  116   k ,  116   m ,  116   c , and  116   y , for example, a voltage of −250 V may be applied to the developing rollers  115   k ,  115   m ,  115   c , and  115   y.    
     The developer feed rollers  116   k ,  116   m ,  116   c , and  116   y  feed the developer to the developing rollers  115   k ,  115   m ,  115   c , and  115   y  using a potential difference with the developing rollers  115   k ,  115   m ,  115   c , and  115   y . The developer feed rollers  116   k ,  116   m ,  116   c , and  116   y  may be disposed so as to contact a lower portion of one side surface of the developing rollers  115   k ,  115   m ,  115   c , and  115   y , thereby forming a nip. The developer of black (K), magenta (M), cyan (C), and yellow (Y) may be conveyed to a lower space between the developer feed rollers  116   k ,  116   m ,  116   c , and  116   y  and the developing rollers  115   k ,  115   m ,  115   c , and  115   y.    
     A prescribed developer feed bias voltage higher by 100 to 400 V than that of the developing rollers  115   k ,  115   m ,  115   c , and  115   y , for example, a voltage of −500 V may be applied to the developer feed rollers  116   k ,  116   m ,  116   c , and  116   y . Thus, the developer which has been conveyed to the lower space between the developer feed rollers  116   k ,  116   m ,  116   c , and  116   y  and the developing rollers  115   k ,  115   m ,  115   c , and  115   y  has a charge due to a charge injected by the developer feed rollers  116   k ,  116   m ,  116   c , and  116   y , may be applied to the developing rollers  115   k ,  115   m ,  115   c , and  115   y  having a relatively low potential, and conveyed to the nip between the developer feed rollers  116   k ,  116   m ,  116   c , and  116   y  and the developing rollers  115   k ,  115   m ,  115   c , and  115   y.    
     Four cleaning units  117   k ,  117   m ,  117   c , and  117   y  clean waste developer remaining on the surface of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y  after rotation, e.g, one-cycle rotation of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y.    
     The transfer unit  120  includes transfer rollers  121   k ,  121   m ,  121   c , and  121   y , an intermediate transfer belt  122 , and a final transfer roller  125 . The developer images formed in the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y  may be transferred to the intermediate transfer belt  122  by the transfer rollers  121   k ,  121   m ,  121   c , and  121   k , and the images transferred to the intermediate transfer belt  122  are transferred to the recording medium (S) that is fed from the paper feed unit  100  and passes between the final transfer roller  125  and the intermediate transfer belt  122 . 
     The intermediate transfer belt  122  may be provided so as to be wound around a support roller  124  that contacts driving rollers  123  disposed so as to be laterally spaced apart from each other and an inner surface of the intermediate transfer belt  122 , and provided so as to travel from the first developing unit  114   k  toward the fourth developing unit  114   y.    
     The transfer rollers  121   k ,  121   m ,  121   c , and  121   y  are transfer voltage applying members that apply a prescribed transfer bias voltage to the intermediate transfer belt  122 , and may be disposed so as to respectively pressurize the intermediate transfer belt  122  against the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y  on an inner side of the intermediate transfer belt  122  at a constant pressure. A prescribed transfer bias voltage may be applied to the transfer rollers  121   k ,  121   m ,  121   c , and  121   y.    
     The final transfer roller  125  may be installed so as to face the intermediate transfer belt  122 . The final transfer roller  125  may be spaced apart from the intermediate transfer belt  122  while the developer image is transferred to the intermediate transfer belt  122 , and may be brought into contact with the intermediate transfer belt  122  at a prescribed pressure when the developer image is completely transferred to the intermediate transfer belt  122 . A prescribed transfer bias voltage may be applied to the final transfer roller  125  so as to transfer the developer image transferred to the intermediate transfer belt  122  to the recording medium (S). 
     The fixing unit  130  fixes the developer image transferred to the recording medium (S), and includes a heating roller  131  and a pressure roller  132 . The heating roller  131  includes a heater provided therein so as to fix the developer image to the recording medium (S) by a high-temperature heat. 
     The pressure roller  132  is installed to be pressurized against the heating roller  131  by an elastic pressing member so as to pressurize the recording medium (S). The number of respective units, drums, etc. illustrated in  FIG. 1  is exemplary and may be a number different than four. 
       FIG. 2  is a schematic diagram illustrating a control system of an image forming apparatus in accordance with an embodiment. 
     As illustrated in  FIG. 2 , the image forming apparatus in accordance with an embodiment includes a control unit  160  that performs control, e.g, overall control, a groove position sensing unit (for example,  170   k ), e.g, a single groove position sensing unit that detects a groove position of a photosensitive drum (for example,  111   k ) e.g., a single photosensitive drum, a pattern detecting unit e.g., single pattern detecting unit  180  that detects a color mis-registration detecting pattern P transferred to the intermediate transfer belt  122  by each of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y , and a motor driving unit  190  that drives a motor, e.g, a single motor  140  corresponding to the four photosensitive drums  111   k ,  111   m ,  111   c , and  111   y.    
     The groove position sensing units  170   k ,  170   m ,  170   c , and  170   y  include optical sensors, and detect a position of a groove position detecting protrusion  111   b   —   k  formed on a side, e.g., one side of the driving gear  111   a  connected to the drum, e.g., single photosensitive drum  111   k  that is a reference, thereby detecting a groove position of the single photosensitive drum  111   k  that is the reference. Groove position detecting protrusions  111   b   —   c ,  111   b   —   m , and  111   b   —   y  are illustrated in  FIG. 4 . 
     The pattern detecting unit  180  includes a color toner density (CTD) sensor. The pattern detecting unit  180  irradiates the color mis-registration detecting pattern P, which is transferred to the intermediate transfer belt  122  for each of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y , with, for example, infrared rays, and detects intensity of reflected light reflected from the color mis-registration detecting pattern P or a non-pattern area. 
     The control unit  160  forms the color mis-registration detecting pattern P in corresponding photosensitive drums  111   k ,  111   m ,  111   c , and  111   y  through the corresponding laser scanning units  113   k ,  113   m ,  113   c , and  113   y  for each of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y , and transfers the color mis-registration detecting pattern P formed in the corresponding photosensitive drums  111   k ,  111   m ,  111   c , and  111   y  to the intermediate transfer belt  122 . 
     The control unit  160  detects the color mis-registration detecting pattern P transferred to the intermediate transfer belt  122  for each of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y , and performs auto color registration in order to improve the color mis-registration of the photosensitive drum  111 . The number of respective units, drums, etc. illustrated in  FIG. 2  is exemplary and may be a number different than four 
       FIGS. 3A and 3B  illustrate exemplary characteristics of a photosensitive drum having eccentricity and run-out. In  FIG. 3A , a radius of a cross-section of the photosensitive drum  111  when the photosensitive drum  111  that is a rotor has eccentricity and run-out characteristics is illustrated. In  FIG. 3B , an exemplary alternate current (AC) component of the photosensitive drum  111  having eccentricity and run-out characteristics is illustrated. 
     As illustrated in  FIG. 3A , a radius (r) of a general rotor has the following geometric variation characteristics through a geometric relationship illustrated in  FIG. 3A . 
         r   o  sin(θ o −θ)= e  cos θ  [Equation 1]
 
         e  sin θ+ r=r   o  cos(θ o −θ)  [Equation 2]
 
     From Equation 1, θ0 may be represented as in the following Equation 3. 
     
       
         
           
             
               
                 
                   
                     θ 
                     o 
                   
                   = 
                   
                     θ 
                     + 
                     
                       
                         sin 
                         
                           - 
                           1 
                         
                       
                        
                       
                         
                            
                            
                           
                               
                           
                            
                           cos 
                            
                           
                               
                           
                            
                           θ 
                         
                         
                           r 
                           o 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     3 
                   
                   ] 
                 
               
             
           
         
       
     
     When substituting Equation 3 in Equation 2, r represented as the following Equation 4 may be obtained. 
     
       
         
           
             
               
                 
                   r 
                   = 
                   
                     
                       
                         r 
                         o 
                       
                        
                       
                         cos 
                          
                         
                           ( 
                           
                             
                               sin 
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               
                                  
                                  
                                 
                                     
                                 
                                  
                                 cos 
                                  
                                 
                                     
                                 
                                  
                                 θ 
                               
                               
                                 r 
                                 o 
                               
                             
                           
                           ) 
                         
                       
                     
                     - 
                     
                        
                        
                       
                           
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       θ 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 4, r denotes an amount of change in a radius having entire run-out, rc denotes a radius of a rotor (photosensitive drum), rA denotes a magnitude of run-out variation, θA denotes a run-out variation phase, and e denotes eccentricity. 
     When r0 of a general rotor has sinusoidal run-out represented as r0=rc+rA sin(θ+θA), Equation 4 may be represented as the following Equation 5. 
     
       
         
           
             
               
                 
                   r 
                   = 
                   
                     
                       
                         ( 
                         
                           
                             r 
                             c 
                           
                           + 
                           
                             
                               r 
                               A 
                             
                              
                             
                               sin 
                                
                               
                                 ( 
                                 
                                   θ 
                                   + 
                                   
                                     θ 
                                     A 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         ) 
                       
                        
                       
                         cos 
                          
                         
                           ( 
                           
                             
                               sin 
                               
                                 - 
                                 1 
                               
                             
                              
                             
                               
                                  
                                  
                                 
                                     
                                 
                                  
                                 cos 
                                  
                                 
                                     
                                 
                                  
                                 θ 
                               
                               
                                 
                                   r 
                                   c 
                                 
                                 + 
                                 
                                   
                                     r 
                                     A 
                                   
                                    
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         θ 
                                         + 
                                         
                                           θ 
                                           A 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                     - 
                     sinθ 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
     In Equation 5, rc denotes a radius of a rotor (photosensitive drum), rA denotes a magnitude of run-out variation, and θA denotes a run-out variation phase. 
     Thus, when accuracy of a component used for fixing the photosensitive drum  111  is not sufficiently managed, run-out characteristics of each of the photosensitive drums  111  may be highly likely to have mutually different phases and sizes as found by Equation 5. According to an exemplary embodiment, couplers (see, for example,  402  and  404  of  FIGS. 4 and 5 ) having an improved structure for mechanically fastening the photosensitive drum  111  to the plurality of driving gears (see  111   a   —   k ,  111   a   —   c ,  111   a   —   m , and  11   a   —   y  of  FIG. 4 ) for transmitting a driving force (rotatory power) of the motor  140  to the photosensitive drum  111  may be used. Therefore, when the plurality of photosensitive drums  111  are fastened to the plurality of driving gears, a phase of each of the plurality of photosensitive drums  111  may be synchronized with a phase of each of the plurality of driving gears that may be set in advance. 
       FIG. 3B  illustrates an exemplary entire run-out profile (AC component) when a run-out variation phase θA is 0, 90, 180, and 270 degrees, respectively. 
       FIG. 4  is an exploded perspective view illustrating a connection relationship between a photosensitive drum and a motor of an image forming apparatus in accordance with an embodiment, and  FIG. 5  is a side view illustrating an exemplary connection relationship between a photosensitive drum and a motor of an image forming apparatus illustrated, for example, in  FIG. 4 . 
     As illustrated in  FIGS. 4 and 5 , the plurality of driving gears  111   a  that are provided so as to correspond to each of the four photosensitive drums  111  disposed in parallel with each other in a tandem method may be rotatably fixed and installed inside the image forming apparatus. The groove position detecting protrusion  111   b  is formed on one side surface of the driving gear (for example,  111   a   —   k ) that is a reference among the four driving gears  111   a  as illustrated in  FIG. 2 , and the groove position sensing unit  170  may be fixed and installed above the groove position detecting protrusion  111   b  while being spaced apart from the driving gear  111   a . When the driving gear  111   a  is rotated, the groove position detecting protrusion  111   b  of the driving gear  111   a  passes the groove position sensing unit  170  in a fixed state, and therefore the groove position sensing unit  170  may detect both ends (groove position) of the groove position detecting protrusion  111   b . The groove position detecting protrusion  111   b  may be provided even in the remaining driving gears  111   a   —   c ,  111   a   —   m , and  111   a   —   y  except the driving gear  111   a   —   k  that is a reference. In an image forming apparatus in accordance with an embodiment, the groove position detection through the groove position sensing unit  170  may be performed only with respect to a single driving gear  111   a  that is a reference. This is because the image forming apparatus in accordance with an embodiment simultaneously drives the plurality of driving gears  111   a  and the plurality of photosensitive drums  111  using the single motor  140 . Thus, the groove position detecting protrusion  111   b  may not be formed in each of the driving gears  111   a , and the groove position sensing unit  170  may not be formed in each of the driving gears  111   a.    
     On another surface of each of the driving gear  111   a , a driving gear rotating shaft  406  of the driving gear  111   a  may be provided while being extended in a fixed length in a normal direction of the other surface of the driving gear  111   a . A driving gear side coupler (driving side coupler)  402  may be fastened to the driving gear rotating shaft  406 . An insertion port  410  in which the driving gear rotating shaft  406  is inserted and fixed may be formed in a center portion of the driving gear side coupler  402 , and an elastic body  408  (for example, spring) is provided at an inlet side of the insertion port  410 . An inner diameter of the insertion port  410  of the driving gear side coupler  402  coincides with an outer diameter of the driving gear rotating shaft  406  of the driving gear  111   a , and the driving gear side coupler  402  may be mechanically fastened to the driving gear  111   a  so as to be rotated together with the driving gear  111   a  in a state in which the driving gear side coupler  402  is inserted into the insertion port  410  of the driving gear  111   a . For example, the insertion port  410  and the driving gear rotating shaft  406  have different concavo-convex structures and the concavo-convex structures are coupled to each other, and therefore the driving gear side coupler  402  is rotated together with the driving gear  111   a  without running idle, when the driving gear  111   a  is rotated. An inner diameter of the elastic body  408  may be larger than or equal to an outer diameter of the driving gear rotating shaft  406 . Thus, the driving gear rotating shaft  406  may pass through the inner diameter of the elastic body  408 , and may be inserted into the insertion port  410  of the driving gear side coupler  402 . When the driving gear side coupler  402  is fastened to the driving gear  111   a , a length of the elastic body  408  may be set so that only a part of the elastic body  408  is compressed rather than a 100% compressed state. That is, when the driving gear side coupler  402  is fastened to the driving gear  111   a , it is preferable that the elastic body  408  be additionally compressed by an external force applied to the driving gear side coupler  402 , whereby elasticity is created. This is to enable a photosensitive drum side coupler (driven side coupler)  404  provided in the photosensitive drum  111  and the driving gear side coupler  402  to be softly and completely fastened to each other when the photosensitive drum  111  is coupled to the driving gear  111   a . Exemplary shapes and structures of the photosensitive drum side coupler  404  and the driving gear side coupler  402  are described with reference, for example, to  FIGS. 6A-6D . 
     As illustrated in  FIGS. 4 ,  5 A, and  5 B, the driving gear  111   a  and the photosensitive drum  111  may be mechanically coupled to each other through the driving gear side coupler  402  and the photosensitive drum side coupler  404 , and therefore rotatory power of the driving gear  111   a  may be transmitted to the photosensitive drum  111 . In an embodiment, the driving gear side coupler  402  and the photosensitive drum side coupler  404  are devices that enable a relative position on a rotation plane of the photosensitive drum  111  with respect to the driving gear  111   a  to maintain a constant relationship. For example, in a case in which the driving gear  111   a  is positioned in a groove position, when an angle on the rotation plane of the photosensitive drum  111  is 0, the driving gear side coupler  402  and the photosensitive drum side coupler  404  may act in such a manner that angles on the rotation planes of the plurality of photosensitive drums  111  all have displacement of 45 degrees when the driving gear  111   a  is rotated clockwise by 45 degrees in the groove position. When all of the four photosensitive drums  111  are coupled to the corresponding driving gears  111   a  through the driving gear side coupler  402  and the photosensitive drum side coupler  404  and all of the four driving gears  111   a  are simultaneously driven by the single motor  140 , the four photosensitive drums  111  may be all synchronized with an initially set phase to be rotated. By such a structure of the driving gear side coupler  402  and the photosensitive drum side coupler  404 , when at least one of the plurality of photosensitive drums  111  is coupled to at least one of the plurality of driving gears  111   a , the driving gear side coupler  402  and the photosensitive drum side coupler  404  are coupled to each other in an one-directional coupling method, and therefore the plurality of photosensitive drums  111  follow a predetermined phase of the plurality of driving gears  111   a . A one-directional coupling method may indicate that even when the driving gear side coupler  402  and the photosensitive drum side coupler  404  are attempted to be coupled to each other at any angle on the rotation plane, actual coupling is performed only at a predetermined single angle. Exemplary actions of the photosensitive drum side coupler  404  and the driving gear side coupler  402  associated are disclosed, for example, with reference to  FIG. 9 . 
     As illustrated in  FIG. 5 , the motor  140  that provides a driving force for rotating the photosensitive drum  111  may be mechanically connected to the driving gear  111   a  through a gear member  150 . The photosensitive drum  111  may be rotated by receiving the driving force (rotatory power) of the motor  140  through the action of the gear member  150 . 
       FIGS. 6A to 6D  illustrate an embodiment of a coupler that connects a driving gear and a photosensitive drum of an image forming apparatus in accordance with one embodiment. 
       FIG. 6A  illustrates the photosensitive drum side coupler  404 ,  FIG. 6B  illustrates the driving gear side coupler  402 ,  FIG. 6C  illustrates a state in which the driving gear side coupler  402  and the photosensitive drum side coupler  404  are not coupled to each other, and  FIG. 6D  illustrates a state in which the driving gear side coupler  402  and the photosensitive drum side coupler  404  are coupled to each other. 
     As illustrated in  FIG. 6A , a single fastening groove  404   a  having directivity may be formed in a part of one side surface (a surface facing the driving gear side coupler  402  at the time of coupling) of the photosensitive drum side coupler  404 . The directivity of the fastening groove  404   a  may indicate that the photosensitive drum side coupler  404  and the driving gear side coupler  402  are fastened to each other only in a state of mutually facing one specific direction when the driving gear side coupler  402  is coupled to the photosensitive drum side coupler  404 . The fastening groove  404   a  of  FIG. 6A  may be formed into an asymmetric fan shape in order to have directivity, but the present invention is not limited only thereto. That is, the fastening groove  404   a  may be formed into other various shapes as long as it has directivity. A single protrusion  402   a  is formed in the driving gear side coupler  402  illustrated in  FIG. 6B . When the driving gear side coupler  402  and the photosensitive drum side coupler  404  are coupled to each other, the protrusion  402   a  of the driving gear side coupler  402  is inserted into the fastening groove  404   a  of the photosensitive drum side coupler  404  illustrated in  FIG. 6A . Thus, a cross-section of the protrusion  402   a  of the driving gear side coupler  402  may be smaller than or equal to a cross-section of the fastening groove  404   a  of the photosensitive drum side coupler  404 . According to an embodiment, the cross-section of the protrusion  402   a  of the driving gear side coupler  402  and the cross-section of the fastening groove  404   a  of the photosensitive drum side coupler  404  have the same size and shape in order to enable a stable fastening state to be maintained by preventing a gap from being created when the driving gear side coupler  402  and the photosensitive drum side coupler  404  are coupled to each other. 
     According to an embodiment, when the protrusion  402   a  of the driving gear side coupler  402  is not accurately fastened to the fastening groove  404   a  of the photosensitive drum side coupler  404 , the driving gear side coupler  402  and the photosensitive drum side coupler  404  are not coupled to each other as illustrated in  FIG. 6C . As illustrated in  FIG. 6D , only when the protrusion  402   a  of the driving gear side coupler  402  is accurately fastened to the fastening groove  404   a  of the photosensitive drum side coupler  404 , the driving gear side coupler  402  and the photosensitive drum side coupler  404  are coupled to each other. This indicates that any one of the driving gear side coupler  402  and the photosensitive drum side coupler  404  is dependent on the other one thereof. In order to couple the photosensitive drum side coupler  404  to the driving gear side coupler  402  in a state in which the driving gear side coupler  402  is fixed, a position of the fastening groove  404   a  of the photosensitive drum side coupler  404  may be adjusted so as to correspond to a position of the protrusion  402   a  of the driving gear side coupler  402 . To couple the photosensitive drum side coupler  404  to the driving gear side coupler  402  in a state in which the driving gear side coupler  402  is rotated clockwise at an angle of 45 degrees to be fixed, the position of the fastening groove  404   a  of the photosensitive drum side coupler  404  may be rotated clockwise at an angle of 45 degrees so as to correspond to the position of the protrusion  402   a  of the driving gear side coupler  402 . Thus, the driving gear side coupler  402  and the photosensitive drum side coupler  404 , the driving gear side coupler  402  and the photosensitive drum side coupler  404  are coupled to each other in the one-directional coupling method when at least one of the plurality of photosensitive drums  111  is coupled to at least one of the plurality of driving gears  111   a . Therefore, the plurality of photosensitive drums  111  follow a predetermined phase of the plurality of driving gears  111   a . The one-directional coupling method indicates that even when the driving gear side coupler  402  and the photosensitive drum side coupler  404  are attempted to be coupled to each other at any angle on the rotation plane, actual coupling is performed only at a predetermined single angle. 
       FIGS. 7A to 7D  illustrate an embodiment of a coupler that connects a driving gear and a photosensitive drum of an image forming apparatus in accordance with an embodiment.  FIG. 7A  illustrates a photosensitive drum side coupler  704 ,  FIG. 7B  illustrates a driving gear side coupler  702 ,  FIG. 7C  illustrates a state in which the driving gear side coupler  702  and the photosensitive drum side coupler  704  are not coupled to each other, and  FIG. 7D  illustrates a state in which the driving gear side coupler  702  and the photosensitive drum side coupler  704  are coupled to each other. 
     As illustrated in  FIG. 7A , two fastening grooves  704   a  and  704   b  having directivity are formed in a part of one side surface (a surface facing the driving gear side coupler  702  at the time of coupling) of the photosensitive drum side coupler  704 . Both the fastening groove  704   a  and  704   b  of  FIG. 7A  are formed into a fan shape, but may be formed in various shapes while not limited only thereto. The two fastening grooves  704   a  and  704   b  may have mutually different sizes or shapes to enable directivity of any one of the driving gear side coupler  702  and the photosensitive drum side coupler  704  to be dependent on the other one thereof when the driving gear side coupler  702  and the photosensitive drum side coupler  704  are coupled to each other. The directivity indicates that the photosensitive drum side coupler  704  and the driving gear side coupler  702  are fastened to each other only in a state of mutually facing one specific direction when the driving gear side coupler  702  is coupled to the photosensitive drum side coupler  704 . Two protrusions  702   a  and  702   b  may be formed in the driving gear side coupler  702  illustrated in  FIG. 7B . When the driving gear side coupler  702  and the photosensitive drum side coupler  704  are coupled to each other, the protrusions  702   a  and  702   b  of the driving gear side coupler  702  are inserted into the fastening grooves  704   a  and  704   b  of the photosensitive drum side coupler  704  illustrated in  FIG. 7A . Thus, a cross-section of each of the protrusions  702   a  and  702   b  of the driving gear side coupler  702  should be smaller than or equal to a cross-section of each of the fastening grooves  704   a  and  704   b  of the photosensitive drum side coupler  704 . The cross-section of each of the protrusions  702   a  and  702   b  of the driving gear side coupler  702  and the cross-section of each of the fastening grooves  704   a  and  704   b  of the photosensitive drum side coupler  704  may have the same size and shape in order to enable a stable fastening state to be maintained by preventing a gap from being created when the driving gear side coupler  702  and the photosensitive drum side coupler  704  are coupled to each other. In a geometric relationship between the fastening grooves  704   a  and  704   b  and the protrusions  702   a  and  702   b , only in a case of a structure in which the protrusion  702   b  is not fastened to the fastening groove  704   a  and the protrusion  702   a  is not fastened to the fastening groove  704   b  in the opposite structure in which the protrusion  702   a  is fastened to the fastening groove  704   a  and the protrusion  702   b  is fastened to the fastening groove  704   b , directivity of any one of the driving gear side coupler  702  and the photosensitive drum side coupler  704  is dependent on the other one thereof. 
     When the protrusions  702   a  and  702   b  of the driving gear side coupler  702  are not accurately fastened to the fastening grooves  704   a  and  704   b  of the photosensitive drum side coupler  704 , the driving gear side coupler  702  and the photosensitive drum side coupler  704  are not coupled to each other as illustrated in  FIG. 7C . As illustrated in  FIG. 7D , only when the protrusions  702   a  and  702   b  of the driving gear side coupler  702  are accurately fastened to the fastening grooves  704   a  and  704   b  of the photosensitive drum side coupler  704 , the driving gear side coupler  702  and the photosensitive drum side coupler  704  are coupled to each other. This indicates that any one of the driving gear side coupler  702  and the photosensitive drum side coupler  704  is dependent on the other one thereof. To couple the photosensitive drum side coupler  704  to the driving gear side coupler  702  in a state in which the driving gear side coupler  702  is fixed, a position of each of the fastening grooves  704   a  and  704   b  of the photosensitive drum side coupler  704  may be adjusted so as to correspond to a position of each of the protrusions  702   a  and  702   b  of the driving gear side coupler  702 . To couple the photosensitive drum side coupler  704  to the driving gear side coupler  702  in a state in which the driving gear side coupler  702  is rotated clockwise at an angle of 45 degrees to be fixed, the position of each of the fastening grooves  704   a  and  704   b  of the photosensitive drum side coupler  704  may be also rotated clockwise at an angle of 45 degrees so as to correspond to the position of each of the protrusions  702   a  and  702   b  of the driving gear side coupler  702 . Consequently, in order to couple the driving gear side coupler  702  and the photosensitive drum side coupler  704  to each other, any one of the driving gear side coupler  702  and the photosensitive drum side coupler  704  is dependent on the other one thereof. By such a structure of the driving gear side coupler  702  and the photosensitive drum side coupler  704 , the driving gear side coupler  702  and the photosensitive drum side coupler  704  are coupled to each other in the one-directional coupling method when at least one of the plurality of photosensitive drums  111  according to an embodiment is coupled to at least one of the plurality of driving gears  111   a , and therefore the plurality of photosensitive drums  111  follow a predetermined phase of the plurality of driving gears  111   a . The one-directional coupling method provides that even when the driving gear side coupler  702  and the photosensitive drum side coupler  704  are attempted to be coupled to each other at any angle on the rotation plane, actual coupling is performed only at a predetermined single angle. 
       FIGS. 8A and 8B  illustrate a groove position detecting protrusion and a groove position sensing unit that are provided in a driving gear of an image forming apparatus in accordance with one embodiment.  FIG. 8A  is a perspective view illustrating the driving gear  111   a  and the groove position sensing unit  170 , and  FIG. 8B  is a side view showing the driving gear  111   a  and the groove position sensing unit  170 . As illustrated in  FIG. 8A , the groove position sensing unit  170  includes a light emitting unit  170   a  and a light receiving unit  170   b . A groove position detecting protrusion  111   b  passes between the light emitting unit  170   a  and the light receiving unit  170   b  of the groove position sensing unit  170 . There is no signal received to the light receiving unit  170   b  while the groove position detecting protrusion  111   b  passes between the light emitting unit  170   a  and the light receiving unit  170   b  of the groove position sensing unit  170 , but when the groove position detecting protrusion  111   b  is deviated from between the light emitting unit  170   a  and the light receiving unit  170   b  of the groove position sensing unit  170 , light radiated from the light emitting unit  170   a  is received to the light receiving unit  170   b , and therefore it is possible to detect that at least one end of both ends of the groove position detecting protrusion  111   b  is deviated from or enters between the light emitting unit  170   a  and the light receiving unit  170   b  of the groove position sensing unit  170 . The groove position detecting protrusion  111   b  may be formed on a surface of the driving gear  111   a  so as to have a semicircular arc shape, and disposed on a concentric circle from a virtual rotating shaft at a center of the driving gear  111   a . A length of the groove position detecting protrusion  111   b  may be changed. When rotation of the driving gear  111   a  is sufficiently performed, at least one end of both ends of the groove position detecting protrusion  111   b  is deviated from or enters between the light emitting unit  170   a  and the light receiving unit  170   b  of the groove position sensing unit  170 . By detecting that the at least one end of both ends of the groove position detecting protrusion  111   b  is deviated from or enters between the light emitting unit  170   a  and the light receiving unit  170   b  of the groove position sensing unit  170 , a groove position (that is, kind of reference position) of the driving gear  111   a  may be detected. 
       FIG. 9  illustrates phase synchronization of a driving gear of an image forming apparatus in accordance with an embodiment. As illustrated in  FIG. 9 , in order to drive four photosensitive drums  111  for representing C, M, Y, and K colors, four driving gears  111   a  are rotatably installed. As illustrated in  FIG. 2 , the four driving gears  111   a  are rotated by receiving power from the single motor  140 . When each of the driving gears  111   a  is independently controlled by connecting a motor to each of the driving gears  111   a , an increase in a product price, an increase in a product size, a maintenance problem, or the like due to use of the multiple motors may occur. Thus, when driving the four driving gears  111   a  using the single motor  140 , a product price and a product size may be reduced, and the maintenance may be facilitated. 
     However, it should be noted that, in a case of rotating a large number of rotors (for examples, photosensitive drums or the like) using a single motor, a color registration error may occur when eccentricity and run-out characteristics of each rotor (photosensitive drum) are not sufficiently controlled. The color registration error in the image forming apparatus may cause degradation of print quality, and therefore the color registration error should be minimized in order to obtain more improved print quality. Thus, in the image forming apparatus in accordance with an embodiment, a large number of photosensitive drums are simultaneously driven using only the single motor  140 , and phases of components for fixing the photosensitive drums  111  are synchronized, thereby predicting and controlling drive of the large number of photosensitive drums  111  whose phases are synchronized. 
     In an image forming apparatus in accordance with an embodiment, a phase difference existing between the four driving gears  111   a  in a state in which the groove positions of the four driving gears  111   a  coincide with each other as illustrated in  FIG. 9  may be detected, and phases of the remaining driving gears  111   a   —   c ,  111   a   —   m , and  111   a   —   y  except the driving gear  111   a   —   k  may be adjusted by θ1, θ2, and θ3, respectively, so that the phase difference becomes 0. Therefore, the four driving gears  111   a  are in a state in which the phase difference is adjusted through synchronization. As illustrated in  FIGS. 6A-6D  and  7 A- 7 D, when the driving gear side coupler  402  and the photosensitive drum side coupler  404  are coupled to each other, any one of the driving gear side coupler  402  and the photosensitive drum side coupler  404  is dependent on the other one thereof. Thus, when the driving gear  111   a  and the photosensitive drum  111  are coupled to each other through the driving gear side coupler  402  and the photosensitive drum side coupler  404 , the photosensitive drum  111  is dependent on the phase of the driving gear  111   a , and therefore the plurality of photosensitive drums  111  coupled to the plurality of driving gears  111   a  are synchronized in the same manner as the driving gear  111   a , and an operation for image forming may be performed in a state in which the phase difference is removed. That is, according to an embodiment, by the structure of the driving gear side coupler  402  and the photosensitive drum side coupler  404 , when at least one of the plurality of photosensitive drums  111  is coupled to at least one of the driving gears  111   a , the driving gear side coupler  402  and the photosensitive drum side coupler  404  are coupled to each other in the one-directional coupling method, and therefore the plurality of photosensitive drums  111  follow a predetermined phase of the plurality of driving gears  111   a . Thus, the plurality of photosensitive drums  111  coupled to the plurality of driving gears  111   a  are rotated in accordance with the predetermined (adjusted) phase of the plurality of driving gears  111   a , and therefore deviation between the plurality of photosensitive drums  111  that may occur during rotation of the plurality of photosensitive drums  111  may be significantly reduced. 
       FIGS. 10A-10B  illustrate an exemplary detection result of AC components of a photosensitive drum of an image forming apparatus in accordance with an embodiment. As illustrated in  FIG. 10A-10B , when a rotor such as the photosensitive drum  111  is driven, run-out characteristics of a component for fixing the rotor appear as an AC component, and a size of the AC component may be in proportion to run-out of the component for fixing the rotor. Thus, when phase information is obtained from the run-out characteristics of the component for fixing the photosensitive drum  111 , the AC component that is generated when the photosensitive drum  111  is driven may be predicted, for example, using Equation 5. A phase of the driving gear  111   a  may be represented in consideration of a pitch between the respective photosensitive drums  111  and a diameter of each of the photosensitive drums  111  when the photosensitive drum  111   k  is a reference photosensitive drum.
         Y: 3θp   M: 2θp   C: 1θp       

     Here, θp=(πD ? p)÷πD×360° is satisfied, where
         p: pitch of photosensitive drum, and   D: diameter of photosensitive drum.       

     That is, when each of the driving gears  111   a  is assembled and the photosensitive drum  111  is coupled to the assembled driving gear  111   a  so that C has a phase difference by 1θp compared to K using K phase as a reference, M has a phase difference by 2θp compared to K, and Y has a phase difference by 3θp compared to K, the phases of each of the four photosensitive drums  111  are synchronized with the phase of each of the four driving gears  111   a  as illustrated in  FIG. 9  using the action of the coupler as an example. 
       FIG. 11  illustrates a test pattern for performing automatic color registration (ACR) of a photosensitive drum in an image forming apparatus in accordance with an embodiment. As illustrated in  FIG. 11 , in order to determine a gap variation that occurs by speed variation of the photosensitive drum, the color mis-registration detecting pattern (P) transferred to the intermediate transfer belt  122  includes a large number of rod-shaped patterns (P1, P2, P3, . . . , P24, P25). Each rod-shaped pattern may be designed to have the same thickness and have a gap ( 110 ) with the same distance. 
     The color mis-registration detecting pattern (P) has a length corresponding to an integer multiple of a circumferential length of the photosensitive drum. This may be effective to obtain stable data and increase error fitting accuracy. 
     The control unit  160  forms black (K), magenta (M), cyan (C), and yellow (Y) patterns with respect to the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y , respectively, and transfers the formed patterns to the intermediate transfer belt  122 . 
     The control unit  160  repeatedly transfers the color mis-registration detecting pattern (P) to the intermediate transfer belt  122  for each of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y  more than once. This is, for example, to detect more accurate data and remove an unexpected measurement value. When transferring each color mis-registration detecting pattern (P) more than once, the control unit  160  forms each color mis-registration detecting pattern (P) in the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y  at the same time using a groove position of each of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y  as a reference. The control unit  160  may fit the gap variation due to periodic flux variation of each of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y  with a sine function to determine a gap variation function, and a motor speed function may be obtained using the gap variation function to vary a speed of each of the motors  140   k ,  140   m ,  140   c , and  140   y , and therefore speed variation of the photosensitive drums  111   k ,  111   m ,  111   c , and  111   y  may be suppressed, thereby significantly reducing color mis-registration. 
     The photosensitive drum  111  that is a rotor may have a periodic speed variation. Such a speed variation of the photosensitive drum  111  may cause the gap variation of the color mis-registration detecting pattern transferred to the intermediate transfer belt  122 , and such a gap variation is generally represented as a sine curve due to characteristics of the periodic speed variation. 
     In order to ascertain a relationship between the speed variation of the photosensitive drum  111  and the gap variation of the color mis-registration detecting pattern that occurs due to the speed variation, the gap variation may be represented as follows as a sine function in Equation 6. 
       gap variation= A  sin(ω t +θ)  (Equation 6)
 
     In Equation 6, A denotes a variation magnitude, ω denotes an angular velocity (2πf), f denotes a speed variation frequency, and θ denotes a phase. 
     The gap variation may occur by flux variation of the photosensitive drum  111 , and therefore a linear velocity of the photosensitive drum  111  may be represented as follows in Equation 7. 
       Linear velocity of photosensitive drum= Vo+θA  cos(θ t +θ)  (Equation 7)
 
     In Equation 7, Vo denotes a process speed of the photosensitive drum. 
     Thus, since the variation magnitude (Av) of the linear velocity of the photosensitive drum is ωA, a position variation magnitude may be obtained as follows in Equation 8. 
       Position variation magnitude ( A )= Av/ω=Av /(2 πf )  (Equation 8)
 
     A speed of the motor  140  to be controlled may be represented as follows in Equation 9. 
       Motor speed= VM+ωAVM/Vo  sin(ω t+θM )  (Equation 9)
 
     In Equation 9, VM denotes a speed of the motor  140  that provides an average speed of the photosensitive drum  111 , and θM denotes a speed phase of the motor  140 . 
     From Equation 9, for example, it can be seen that the gap variation is in proportion to a magnitude of the speed variation, and in reverse proportion to the variation frequency. That is, an amount of gap variation may be increased along with an increase in the speed variation of the photosensitive drum  111  or a reduction in the frequency of the speed variation thereof. Thus, in order to improve the gap variation, for example, the speed variation of the photosensitive drum  111  should be alleviated. 
     Even when the motor  140  provides constant rotatory power, an error mechanism may be created while being subjected to multiple transmission processes, and a defect such as color mis-registration may occur. Conversely, when a relationship between the gap variation of the color mis-registration detecting pattern and the speed of the motor  140  is known, the gap variation may be improved through appropriate motor speed variation control. 
     Thus, in order to suppress inherent periodic speed variation of a rotor that is a direct cause of the color mis-registration, the gap variation of the color mis-registration detecting pattern that occurs by linear velocity variation of the photosensitive drum  111  may be determined, and a relationship between the gap variation and the motor speed may be determined based on the determined gap variation to thereby alleviate the linear velocity variation of the photosensitive drum  111 , thereby reducing the color mis-registration. 
       FIG. 12  illustrates results of phase synchronization control and AC average control of an image forming apparatus in accordance with an embodiment.  FIG. 10A  is a graph illustrating exemplary values before performing AC average control, and  FIG. 12  is a graph illustrating exemplary values after performing the AC average control. Through comparison between the graphs of  FIGS. 10B and 12 , it can be seen that a phase displacement of each of the photosensitive drums  111  is significantly reduced through mechanical phase synchronization between the driving gear  111   a  and the photosensitive drum  111  of the image forming apparatus in accordance with an embodiment. 
     The image forming apparatus according an embodiment may mechanically synchronize eccentricity and run-out deviation for each photosensitive drum of an image forming apparatus that does not individually drive the photosensitive drums. Accordingly, a color registration error can be reduced by controlling a linear velocity variation of the photosensitive drum in order to stabilize a deviation of mass production quality of a mechanical approach. 
     Although a few embodiments have been shown and described, it would be appreciated by those skilled in the art that changes may be made in these embodiments without departing from the principles and spirit of the invention, the scope of that is defined in the claims and their equivalents.