Patent Publication Number: US-2023134616-A1

Title: Control device, image forming apparatus, image forming method, and storage medium

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This patent application is based on and claims priority pursuant to 35 U.S.C. § 119(a) to Japanese Patent Application Nos. 2021-176789, filed on Oct. 28, 2021, and 2022-140572, filed on Sep. 5, 2022, in the Japan Patent Office, the entire disclosure of which is hereby incorporated by reference herein. 
     BACKGROUND 
     Technical Field 
     Embodiments of the present disclosure relate to a control device, an image forming apparatus, an image forming method, and a storage medium. 
     Related Art 
     Some technologies have been proposed that control the rotation speed of an image bearer to correct density unevenness that occurs according to a rotation cycle of the image bearer due to an eccentricity of the image bearer in an image forming apparatus including multiple image bearers. 
     SUMMARY 
     In an embodiment of the present disclosure, there is provided a control device that includes circuitry. The circuitry detects density unevenness of a toner image occurring according to a rotation cycle of a first image bearer for a first color among a plurality of rotatable image bearers, based on a rotation phase of the first image bearer and a density of the toner image formed on the first image bearer, detects density unevenness of a toner image occurring according to a rotation cycle of a second image bearer for a second color among the plurality of image bearers, based on a rotation phase of the second image bearer and a density of the toner image formed on the second image bearer, controls rotation phases of the plurality of image bearers based on detection results of the plurality of image bearers and rotation speeds of the plurality of image bearers, corrects the rotation phase of the first image bearer based on a detection result of the first image bearer and a rotation speed of the first image bearer, corrects the rotation phase of the second image bearer based on a detection result of the second image bearer and a rotation speed of the second image bearer, controls the rotation speeds of at least two of the plurality of image bearers to be a specified rotation speed, and starts a detection operation of the rotation phases of the plurality of image bearers after a difference between each of the rotation speeds of the at least two of the plurality of image bearers and the specified rotation speed falls within a specified range. 
     In another embodiment of the present disclosure, there is provided an image forming apparatus that includes the control device, the plurality of image bearers, and a plurality of forming devices that form toner images on the plurality of image bearers. 
     In still another embodiment of the present disclosure, there is provided an image forming method for an image forming apparatus that includes forming toner images on a plurality of rotatable image bearers with a plurality of forming devices of the image forming apparatus, detecting density unevenness of a toner image occurring according to a rotation cycle of a first image bearer among the plurality of image bearers, based on a rotation phase of the first image bearer and a density of the toner image formed on the first image bearer, detecting density unevenness of a toner image occurring according to a rotation period of a second image bearer among the plurality of image bearers, based on a rotation phase of the second image bearer and a density of the toner image formed on the second image bearer, controlling rotation phases of the plurality of image bearers based on detection results of the plurality of image bearers and rotation speeds of the plurality of image bearers, correcting the rotation phase of the first image bearer based on a detection result of the first image bearer and a rotation speed of the first image bearer, correcting the rotation phase of the second image bearer based on a detection result of the second image bearer and a rotation speed of the second image bearer, controlling rotation speeds of at least two of the plurality of image bearers to be a specified rotation speed, and starting a detection operation of the rotation phases of the plurality of image bearers after a difference between each of the rotation speeds of the at least two of the plurality of image bearers and the specified rotation speed falls within a specified range. 
     In still yet another embodiment of the present disclosure, there is provided a non-transitory storage medium storing a plurality of instructions which, when executed by one or more processors, cause the processors to execute a method that includes forming toner images on a plurality of rotatable image bearers with a plurality of forming devices of an image forming apparatus, detecting density unevenness of a toner image occurring according to a rotation cycle of a first image bearer among the plurality of image bearers, based on a rotation phase of the first image bearer and a density of the toner image formed on the first image bearer, detecting density unevenness of a toner image occurring according to a rotation period of a second image bearer among the plurality of image bearers, based on a rotation phase of the second image bearer and a density of the toner image formed on the second image bearer, controlling rotation phases of the plurality of image bearers based on detection results of the plurality of image bearers and rotation speeds of the plurality of image bearers, correcting the rotation phase of the first image bearer based on a detection result of the first image bearer and a rotation speed of the first image bearer, correcting the rotation phase of the second image bearer based on a detection result of the second image bearer and a rotation speed of the second image bearer, controlling rotation speeds of at least two of the plurality of image bearers to be a specified rotation speed, and starting a detection operation of the rotation phases of the plurality of image bearers after a difference between each of the rotation speeds of the at least two of the plurality of image bearers and the specified rotation speed falls within a specified range. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A more complete appreciation of embodiments of the present disclosure and many of the attendant advantages and features thereof can be readily obtained and understood from the following detailed description with reference to the accompanying drawings, wherein: 
         FIG.  1    is a diagram illustrating an overall configuration of an image forming apparatus according to a first embodiment of the present disclosure; 
         FIG.  2 A  is a block diagram illustrating a configuration of the image forming apparatus of  FIG.  1   ; 
         FIG.  2 B  is a block diagram illustrating a hardware configuration of a control device of the image forming apparatus of  FIG.  1   ; 
         FIG.  2 C  is a block diagram illustrating a functional configuration of the control device of the image forming apparatus in  FIG.  1   ; 
         FIG.  3    is a diagram illustrating density unevenness according to a comparative example; 
         FIG.  4    is a diagram illustrating color unevenness when the density unevenness of  FIG.  3    is transferred to a recording sheet; 
         FIG.  5    is a diagram illustrating density unevenness of colors in the image forming apparatus of  FIG.  1   ; 
         FIG.  6    is a diagram illustrating color unevenness when the density unevenness of  FIG.  5    is transferred to the recording sheet; 
         FIG.  7    is a diagram illustrating a state at the start of control by the image forming apparatus of  FIG.  1   ; 
         FIG.  8    is a diagram illustrating a state at the end of control by the image forming apparatus of  FIG.  1   ; 
         FIG.  9    is a diagram illustrating density unevenness in the image forming apparatus of  FIG.  1   ; 
         FIG.  10    is a flowchart of an operation of the image forming apparatus of  FIG.  1   ; 
         FIG.  11    is a timing chart illustrating an operation of the image forming apparatus of  FIG.  1   ; 
         FIG.  12    is a flowchart of a detection operation of rotation phase of a photoconductor drum of the image forming apparatus of  FIG.  1   ; 
         FIG.  13    is a first diagram illustrating a detection operation of the density-unevenness phase difference of the image forming apparatus of  FIG.  1   ; 
         FIG.  14    is a second diagram illustrating the detection operation of the density-unevenness phase difference of the image forming apparatus of  FIG.  1   ; 
         FIG.  15    is a diagram illustrating an overall configuration of an image forming apparatus according to a first modification of the present disclosure; 
         FIG.  16    is a block diagram illustrating a functional configuration of a control device of an image forming apparatus according to a second embodiment of the present disclosure; 
         FIG.  17    is a diagram illustrating an operation of a second determination unit according to the second embodiment of the present disclosure; 
         FIG.  18    including  FIGS.  18 A and  18 B  is a flowchart of an operation of the image forming apparatus according to the second embodiment of the present disclosure; 
         FIG.  19    is a diagram illustrating a switching operation between enabling and disabling of an abnormality detection unit; 
         FIG.  20    is a diagram illustrating density unevenness according to a comparative example of a second modification of the present disclosure; 
         FIG.  21    is a diagram illustrating color unevenness when the density unevenness in  FIG.  20    is transferred to a recording sheet; 
         FIG.  22    is a diagram illustrating density unevenness of colors in an image forming apparatus according to the second modification of the present disclosure; 
         FIG.  23    is a diagram illustrating color unevenness when the density unevenness in  FIG.  22    is transferred to the recording sheet; 
         FIG.  24    is a diagram illustrating a state at the start of control by the image forming apparatus according to the second modification of the present disclosure; 
         FIG.  25    is a diagram illustrating a state at the end of control by the image forming apparatus according to the second modification of the present disclosure; 
         FIG.  26    is a diagram illustrating the density unevenness in the image forming apparatus according to the second modification of the present disclosure; 
         FIG.  27    is a diagram illustrating a detection operation of the density-unevenness phase difference of the image forming apparatus according to the second modification of the present disclosure; 
         FIG.  28    is a flowchart of a first example of an operation of the image forming apparatus according to the second modification of the present disclosure; 
         FIG.  29    is a timing chart of the operation of the image forming apparatus according to the second modification of the present disclosure; 
         FIG.  30    including  FIG.  30 A  and  FIG.  30 B  is a flowchart of a second example of the operation of the image forming apparatus according to the second modification of the present disclosure; and 
         FIG.  31    is a diagram illustrating an overall configuration of an image forming apparatus according to a third modification of the present disclosure. 
     
    
    
     The accompanying drawings are intended to depict embodiments of the present disclosure and should not be interpreted to limit the scope thereof. The accompanying drawings are not to be considered as drawn to scale unless explicitly noted. Also, identical or similar reference numerals designate identical or similar components throughout the several views. 
     DETAILED DESCRIPTION 
     In describing embodiments illustrated in the drawings, specific terminology is employed for the sake of clarity. However, the disclosure of this specification is not intended to be limited to the specific terminology so selected and it is to be understood that each specific element includes all technical equivalents that have a similar function, operate in a similar manner, and achieve a similar result. 
     Referring now to the drawings, embodiments of the present disclosure are described below. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. 
     An image forming apparatus including a control device according to an embodiment is described below as an example. 
       FIG.  1    is a diagram illustrating an overall configuration of an image forming apparatus  100  according to an embodiment of the present disclosure. The image forming apparatus  100  is an electrophotographic image forming apparatus and is a quadruple-tandem-type full-color machine employing an intermediate transfer method. However, the embodiment can also be applied to other image forming apparatuses such as a quadruple-tandem-type full-color machine employing a direct transfer method, a one-drum-type full-color machine employing an intermediate transfer method, and a one-drum-type monochrome machine employing a direct transfer method. 
     As illustrated in  FIG.  1   , the image forming apparatus  100  includes an intermediate transfer belt  1 . The image forming apparatus  100  further includes photoconductor drums  2 Y,  2 M,  2 C, and  2 K (serving as image bearers) arranged along an extension surface, in other words, a stretched surface of the intermediate transfer belt  1 . One of the photoconductor drums  2 Y,  2 M,  2 C, and  2 K corresponds to an image bearer for a first color. One of the photoconductor drums  2 Y,  2 M,  2 C, and  2 K other than the image bearer for the first color corresponds to an image bearer for a second color. One of the photoconductor drums  2 Y,  2 M,  2 C, and  2 K other than the image bearers for the first and second colors corresponds to an image bearer for a third color. 
     Suffixes Y, M, C, and K represent yellow, magenta, cyan, and black, respectively. When an image forming station (serving as an image forming device) for yellow is described as a representative, the image forming apparatus  100  includes the following configuration around the photoconductor drum  2 Y in an order of the rotation direction thereof. The photoconductor drums  2 Y,  2 M,  2 C, and  2 K are collectively referred to as photoconductor drums  2  without suffixes when the photoconductor drums  2 Y,  2 M,  2 C, and  2 K are not particularly distinguished from one another. Similarly, components provided for the respective colors, such as a toner density sensor, a charger, an optical writing unit, and a developing unit, which are described later, are collectively referred to without suffixes when the components are not distinguished from each other. 
     The image forming apparatus  100  includes a charger  3 Y and a photointerrupter  18 Y (serving as a rotation-phase detection device) that detects a rotation phase of the photoconductor drum  2 Y The image forming apparatus  100  further includes an optical writing unit  4 Y that writes an electrostatic latent image by exposing the photoconductor drum  2 Y and a toner density sensor  19 Y that detects the density of the toner image formed on the photoconductor drum  2 Y. 
     The toner density sensor  19 Y includes, for example, an optical sensor. The image forming apparatus  100  further includes a developing unit  5 Y, a primary transfer roller  6 Y, a photoconductor cleaning unit  7 Y including a blade and a brush, and a charge eliminating unit  8 Y. 
     A forming unit that forms a toner image on the photoconductor drum  2 Y includes the charger  3 Y, the optical writing unit  4 Y, and the developing unit  5 Y. The image forming apparatus  100  can transfer the toner image formed on the photoconductor drum  2 Y by the forming unit onto the intermediate transfer belt  1  by the primary transfer roller  6 Y. The same applies to other colors. 
     The intermediate transfer belt  1  is rotatably supported by a plurality of rollers  11 ,  12 , and  13 . The image forming apparatus  100  includes a belt cleaning unit  15  including a blade and a brush at a position opposite the roller  12 . An intermediate transfer unit  33  includes the intermediate transfer belt  1 , the rollers  11 ,  12 , and  13 , and the belt cleaning unit  15 . The image forming apparatus  100  includes a secondary transfer roller  16  for secondarily transferring the toner image formed on the intermediate transfer belt  1  onto a recording sheet  20  at a position opposite the roller  13 . 
     The image forming apparatus  100  further includes, for example, a scanner  9  as an image reader and an automatic document feeder (ADF)  10  as an automatic document feeder vertically above the optical writing unit  4  including the optical writing units  4 Y,  4 C,  4 M, and  4 K. 
     The image forming apparatus  100  includes sheet trays  17  in a lower portion of an apparatus body  99 . In the image forming apparatus  100 , a control unit  37  controls a pickup roller  21  and a sheet feed roller  22  to feed the recording sheet  20  as a recording medium stored in each sheet tray  17  and controls a conveying roller pair  23  to convey the recording sheet  20 . In the image forming apparatus  100 , the control unit  37  controls a registration roller pair  24  to send the recording sheet  20  at a specified timing to a nip portion N 2  which is a secondary transfer portion where the intermediate transfer belt  1  and the secondary transfer roller  16  face each other. 
     The image forming apparatus  100  includes a fixing unit  25  as a fixing device downstream from the nip portion N 2  in a sheet conveyance direction. In  FIG.  1   , the image forming apparatus  100  includes an output tray  26 , a switchback roller pair  27 , and the control unit  37 . 
     The developing units  5 Y,  5 C,  5 M, and  5 K include developing rollers  5 Ya,  5 Ca,  5 Ma, and  5 Ka which are rotators as developer bearers disposed opposite the photoconductor drums  2 Y,  2 C,  2 M, and  2 K with developing gaps of specified distances, respectively. The developing rollers  5 Ya,  5 Ca,  5 Ma and  5 Ka bear two-component developer containing toner and carrier stored in the developing units  5 Y, SC,  5 M and  5 K, respectively. The developing rollers  5 Ya,  5 Ca,  5 Ma, and  5 Ka cause the toner in the borne two-component developer to adhere to the photoconductor drums  2 Y,  2 C,  2 M, and  2 K at developing nips opposite the photoconductor drums  2 Y,  2 C,  2 M, and  2 K, thereby forming the toner images on the photoconductor drums  2 Y,  2 C,  2 M, and  2 K, respectively. 
     In the present embodiment, the image forming apparatus  100  includes the photointerrupters  18 Y,  18 C,  18 M, and  18 K as detection devices that detects rotation positions of the photoconductor drums  2 Y,  2 C,  2 M, and  2 K. However, the present disclosure is not limited thereto, and the image forming apparatus  100  may include a configuration for detecting the rotation position of, for example, a rotary encoder  230 . The same applies to the rotation position detection device that detects the rotation positions, i.e., phases of the developing rollers  5 Ya,  5 Ca,  5 Ma, and  5 Ka. 
     A laser controller causes the optical writing units  4 Y,  4 C,  4 M, and  4 K to drive four semiconductor lasers based on image data. The optical writing units  4 Y,  4 C,  4 M, and  4 K emit four writing lights in the dark to irradiate the photoconductor drums  2 Y,  2 C,  2 M, and  2 K which are uniformly charged by the chargers  3 Y,  3 C,  3 M, and  3 K, respectively. The optical writing units  4 Y,  4 C,  4 M, and  4 K scan the photoconductor drums  2 Y,  2 C,  2 M, and  2 K in the dark with the writing lights to write electrostatic latent images for Y, C, M, and K on the surfaces of the photoconductor drums  2 Y,  2 C,  2 M, and  2 K, respectively. 
     In the present embodiment, the optical writing units  4 Y,  4 C,  4 M, and  4 K perform optical scanning with laser beams emitted from the laser diodes as follows. In the optical writing unit  4 Y,  4 C,  4 M, and  4 K, the laser beams emitted by the laser diodes are deflected by a polygon mirror, reflected by a reflection mirror, and passed through the optical lenses. Thus, the optical writing unit  4 Y,  4 C,  4 M, and  4 K perform optical scanning. Each of the optical writing units  4 Y,  4 C,  4 M, and  4 K may include a unit that performs optical writing using a light-emitting diode (LED) array instead of the laser diode. 
     An image forming operation of the image forming apparatus  100  is described below. In response to an input of an order to start a print job, the rollers around the photoconductor drums  2 Y,  2 C,  2 M, and  2 K, the intermediate transfer belt  1 , and a feed conveyance passage start rotating at their specified timings. Thus, the recording sheet  20  is fed from one of the sheet trays  17 . 
     On the other hand, the surfaces of the photoconductor drums  2 Y,  2 M,  2 C, and  2 K are charged to a uniform potential by the chargers  3 Y,  3 M,  3 C, and  3 K, and the surfaces of the photoconductor drums  2 Y,  2 M,  2 C, and  2 K are exposed by the writing lights emitted from the optical writing units  4 Y,  4 M,  4 C, and  4 K according to the image data. A potential pattern after exposure is called an electrostatic latent image. Toner is supplied from the developing units  5 Y,  5 M,  5 C, and  5 K to the surfaces of the photoconductor drums  2 Y,  2 M,  2 C, and  2 K bearing the electrostatic latent images, so that the electrostatic latent images borne on the photoconductor drums  2 Y,  2 M,  2 C, and  2 K are developed into specified colors. 
     In the configuration of  FIG.  1   , since the photoconductor drums  2 Y,  2 M,  2 C, and  2 K have four colors, the toner images of yellow, magenta, cyan, and black (the order of colors differs depending on the system) are developed on the photoconductor drums  2 Y,  2 M,  2 C, and  2 K, respectively. 
     The toner images developed on the photoconductor drums  2 Y,  2 M,  2 C, and  2 K are transferred onto the intermediate transfer belt  1  at nip portions N 1  (serving as primary transfer portions), which are contact points between the photoconductor drums  2 Y,  2 M,  2 C, and  2 K and the intermediate transfer belt  1 , respectively. That is, the toner image is transferred onto the intermediate transfer belt  1  by a primary transfer bias and a pressing force applied to each of the primary transfer rollers  6 Y,  6 M,  6 C, and  6 K disposed opposite the photoconductor drums  2 Y,  2 M,  2 C, and  2 K. The image forming apparatus  100  forms a full-color toner image on the intermediate transfer belt  1  by repeating this primary transfer operation for four colors while adjusting the timing. 
     In the image forming apparatus  100 , the full-color toner image formed on the intermediate transfer belt  1  is transferred to the recording sheet  20  conveyed by the registration roller pair  24  at a proper timing in the nip portion N 2 . At this time, the secondary transfer is performed by a secondary transfer bias and a pressing force applied to the secondary transfer roller  16 . The image forming apparatus  100  causes the recording sheet  20  to which the full-color toner image is transferred to pass through the fixing unit  25 , thereby heating and fixing the toner image borne on the surface of the recording sheet  20 . 
     In the case of single-sided printing, the image forming apparatus  100  linearly conveys the recording sheet  20  as it is to the output tray  26 . In the case of double-sided printing, the image forming apparatus  100  changes the conveyance direction to downward and conveys the recording sheet  20  to a sheet reverse unit. In the image forming apparatus  100 , the conveyance direction of the recording sheet  20  that has reached the sheet reverse unit is reversed by the switchback roller pair  27 , and the recording sheet  20  is ejected from the sheet reverse unit from a trailing end of the sheet. This is called a switchback operation. The front and back of the recording sheet  20  are reversed by this operation. The reversed recording sheet  20  does not return to the fixing unit  25 , passes through a refeed conveyance passage, and joins an original sheet feed passage. Thereafter, the image forming apparatus  100  transfers the toner image in the same manner as in the front surface printing, passes the toner image through the fixing unit  25 , and ejects the sheet. This is a double-sided print operation. 
     The photoconductor drums  2 Y,  2 M,  2 C, and  2 K that have passed through the nip portions N 1  bear primary-transfer residual toner on the surfaces thereof. The photoconductor cleaning units  7 Y,  7 M,  7 C, and  7 K of the image forming apparatus  100  remove the primary-transfer residual toner. Thereafter, the charge eliminating units  8 Y,  8 M,  8 C, and  8 K of the image forming apparatus  100  uniformly eliminate charge of the surfaces thereof to prepare for charging of the next image formation. The intermediate transfer belt  1  that has passed through the nip portion N 2  also bears the secondary-transfer residual toner on the surfaces thereof. The belt cleaning unit  15  of the image forming apparatus  100  removes the secondary-transfer residual toner to prepare for the transfer of the next toner image. The image forming apparatus  100  performs single-sided printing or double-sided printing by repeating such operations. 
     The image forming apparatus  100  includes a toner-image detection sensor  30  as an optical sensor unit that includes the optical sensor. The toner-image detection sensor  30  detects density of the toner image formed on an outer circumferential surface of the intermediate transfer belt  1 . 
     The toner-image detection sensor  30  functions as a toner-adhesion-amount detection sensor that detects the density of a toner image that is the image on the intermediate transfer belt  1  in order to detect the adhesion amount of toner on the intermediate transfer belt  1  and detect density unevenness of the image. 
     The toner-image detection sensor  30  of the image forming apparatus  100  detects the density of the toner image of an image pattern for correction control formed on the surface of the intermediate transfer belt  1  for use in correction control of unevenness of the image. 
     In the configuration example illustrated in  FIG.  1   , the image forming apparatus  100  includes the toner-image detection sensor  30  in a position P 1  before secondary transfer, which is a position facing a portion of the intermediate transfer belt  1  wound around the roller  11 . The image forming apparatus  100  may include the toner-image detection sensor  30  at a position P 2  after the secondary transfer, which is a position downstream from the nip portion N 2 . In a case where the toner-image detection sensor  30  is disposed downstream from the nip portion P 2  such as the position P 2 , the toner-image detection sensor  30  as follows is preferably disposed. A roller  14  for preventing vibration of the intermediate transfer belt  1  inside the intermediate transfer belt  1  is preferably disposed, and the toner-image detection sensor  30  is preferably disposed to face the roller  14 . 
     Of the two kinds of arrangement positions in the toner-image detection sensor  30 , the position P 1  before the secondary transfer is a position where the toner pattern on the intermediate transfer belt  1  before the secondary transfer step is detected. This configuration is often adopted if there is no restriction on the layout of the apparatus. Since the toner image of the image pattern for correction control is detected immediately after the toner image is formed, the waiting time is short and the toner image of the image pattern does not need to be passed through the nip portion N 2 . Thus, a contrivance therefor is not required. 
     However, there are many models in which the position immediately downstream from the image forming station of the fourth color (black in the example of  FIG.  1   ) is a secondary transfer position such as the nip portion N 2 . In such a case, installing a sensor in the position P 1  is difficult in terms of space. In such a case, the toner-image detection sensor  30  is disposed at the position P 2  which is the position after the secondary transfer, and the toner image of the image pattern formed on the intermediate transfer belt  1  is passed through the nip portion N 2 . Thus, the density of the toner image is detected by the toner-image detection sensor  30 . As a method of passing through the nip portion N 2 , for example, separation of the secondary transfer roller  16  from the intermediate transfer belt  1  or application of a reverse bias to the secondary transfer roller  16  can be considered. The way is not particularly limited here. 
       FIG.  2 A  is a block diagram illustrating a configuration of the image forming apparatus  100 . As illustrated in  FIG.  2 A , the image forming apparatus  100  includes a control device  200 , the photointemipters  18 , the toner density sensors  19 , forming devices  220 , a motor M, the photoconductor drums  2 , and rotary encoders  230 . The photointerrupters  18 K,  18 C,  18 M, and  18 Y are disposed corresponding to the photoconductor drums  2 Y,  2 C,  2 M, and  2 K, respectively. Although the toner density sensors are not disposed for the respective colors, the toner density sensors  19 K,  19 C,  19 M, and  19 Y are disposed in the image forming apparatus  100 . The forming devices  220 K,  220 C,  220 M and  220 Y for the respective colors and the motors MK, MC, MM and MY for the respective colors are disposed in the image forming apparatus  100 . The rotary encoders  230 K,  230 C,  230 M, and  230 Y are also disposed for the respective colors in the image forming apparatus  100 . 
       FIG.  2 B  is a block diagram illustrating the hardware configuration of the control device  200 . As illustrated in  FIG.  2 B , the control device  200  includes a central processing unit (CPU)  241 , a read only memory (ROM)  242 , a random access memory (RAM)  243 , and an input-and-output (I/O) port  244 . 
     The CPU  241  is an arithmetic device that sequentially executes, e.g., branching processing or iterative processing by executing a program stored in the ROM  242 . The ROM  242  is a non-volatile memory in which a program executed in the CPU  241  is stored. 
     The RAM  243  is a memory that functions as a work area (working area) for the operation of the CPU  241 . A bus line  245  is, e.g., an address bus or a data bus to electrically connect the components such as the CPU  241 . 
     The I/O port  244  is an interface to which an output signal of the photointerrupter  18 , an output signal of the toner density sensor  19 , an output signal of the rotary encoder  230 , and the like are input. The I/O port  244  is also an interface that outputs a control signal for controlling the forming device  220  and a control signal for controlling the motor M. 
     The functions of the control device  200  may be implemented with an electronic circuit such as an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA) instead of the CPU  241 . Each of the functions described below may be implemented with, for example, s a CPU, an ASIC, or an FPGA, or the functions may be implemented with a common CPU, ASIC, or FPGA. 
       FIG.  2 C  is a block diagram illustrating a functional configuration of the control device  200 . A description is given with reference to  FIG.  2 A  as appropriate. The control device  200  includes a detection unit  210  and the control unit  37 . 
     The detection unit  210  detects the density unevenness of the toner image generated according to the rotation cycle of the photoconductor drum  2  based on the rotation phase of each of the four photoconductor drums  2  detected by the photointerrupters  18  and the density of the toner image formed on the photoconductor drum  2  detected by the toner density sensor  19 . 
     In the present embodiment, the detection unit  210  starts the detecting operation of the rotation phase of each of the four photoconductor drums  2  when the difference between the rotation speed of at least two photoconductor drums  2  and a specified rotation speed is within a specified range. 
     The detection unit  210  includes a calculation unit  211 . In the present embodiment, the calculation unit  211  starts a calculation for calculating the rotation phase when the operation for detecting the rotation phase of at least two photoconductor drums  2  among the four photoconductor drums  2  have ended. 
     The control unit  37  controls the rotation speed of the photoconductor drum  2  by controlling the rotation of the motor M based on the detection result by the detection unit  210  and the rotation speed of each of the four photoconductor drums  2  detected by the rotary encoder  230 . 
     In the present embodiment, the control unit  37  performs control such that at least two of the four photoconductor drums  2  have the specified rotation speed when the four photoconductor drums  2  start to rotate. 
     The control unit  37  includes a correction unit  371 . In the present embodiment, the correction unit  371  starts the correction of the density unevenness when the calculation for calculating the rotation phases of at least two photoconductor drums  2  among the four photoconductor drums  2  has ended. 
     A control method by the image forming apparatus  100  is described with reference to  FIGS.  3  to  6   .  FIG.  3    is a diagram illustrating density unevenness according to a comparative example.  FIG.  4    is a diagram illustrating color unevenness when the density unevenness of  FIG.  3    is transferred to the recording sheet  20 .  FIG.  5    is a diagram illustrating density unevenness of each color according to the present embodiment.  FIG.  6    is a diagram illustrating color unevenness when the density unevenness of  FIG.  5    is transferred to the recording sheet  20 . Horizontal axes in  FIGS.  3  to  6    indicate a sub-scanning direction (i.e., recording-sheet conveyance direction). Vertical axes in  FIGS.  3  and  5    indicate the density unevenness D. The vertical axes in  FIGS.  4  and  6    indicate L*, a*, and b* that are color evaluation index. 
     As illustrated in  FIGS.  3  and  4   , when the photoconductor drums  2  of the respective colors are independently driven with respect to the density unevenness D (variations of the toner adhesion amount) of the toner image generated according to the rotation cycle of the photoconductor drum  2 , the density unevenness of the image on the recording sheet  20  may be emphasized and increased when the toner images of two or more colors are superimposed. 
     As illustrated in  FIGS.  5  and  6   , in the present embodiment, a phase matching control that drives the photoconductor drums  2  is performed so that the phases of the density unevenness of the toner images formed on the photoconductor drums  2  of respective colors coincide with each other on the image on the recording sheet  20 . Density unevenness of the image is reduced by the phase matching control. 
       FIG.  7    is a diagram illustrating a state at the start of phase matching control by the image forming apparatus  100 .  FIG.  8    is a diagram illustrating a state at the end of the phase matching control by the image forming apparatus  100 .  FIG.  9    is a diagram illustrating density unevenness in the image forming apparatus  100 . 
     In  FIGS.  7  to  9   , in the phase matching control by the image forming apparatus  100 , the rotation speeds of the photoconductor drums  2  are corrected so that phases φt of the density unevenness at which the density unevenness D peaks in the four photoconductor drums  2  coincide with each other on the image on the recording sheet  20  before the photoconductor drums  2  contact the intermediate transfer belt  1 . As an initial phase B of the phase φpt of the density unevenness with respect to a rotation origin HP of the photoconductor drum  2 , a phase separately acquired in advance is used. 
     In the present embodiment, the adhesion amount phase of the density unevenness of each color is detected with respect to the density unevenness generated according to the rotation cycle of the photoconductor drum  2  along the sub-scanning direction. Thus, the photoconductor drum  2  is driven to match the detected phase on the recording sheet  20 . As a result, the density unevenness of each color is canceled with respect to the superimposed image with more than secondary color. 
     The control according to the present embodiment includes a start-up period, a phase detection period, a calculation period, and a phase correction period. The start-up period is a period from when the rotation of the photoconductor drum  2  for each color is started until the rotation speed is stabilized at the specified rotation speed. The phase detection period is a period in which the rotation phase of each photoconductor drum  2  is detected by the photointerrupter  18  attached to the photoconductor drum  2  after the start-up has completed. In the phase detection period, the error of the rotation phase difference is reduced by equalizing the rotation speeds of the respective photoconductor drums  2 . 
     The calculation period is a period in which the phases of the density unevenness are detected by detecting the relationship between the density unevenness generated based on the detection result and the rotation phases of the photoconductor drums  2 C,  2 M, and  2 Y after the detection of the rotation phases of the photoconductor drums  2 C,  2 M, and  2 Y has completed. The phase correction period is a period in which the phase of the density unevenness is adjusted by accelerating or decelerating the rotation speed of the photoconductor drum  2  using information on the phase of the detected density unevenness after the calculation period ends. 
       FIG.  10    is a flowchart of an image forming operation of the image forming apparatus  100 . In  FIG.  10   , a case where the image formation is performed with four colors of Y, M, C, and K and the phase matching control is performed on the photoconductor drums  2 Y,  2 M, and  2 C is described as an example. 
     The image forming apparatus  100  starts an image forming operation in response to an instruction to start image formation from an external apparatus such as a personal computer (PC) or an operation input to start image formation to an operation unit disposed in the image forming apparatus  100 . 
     First, in step S 61  of  FIG.  10   , the image forming apparatus  100  causes the control unit  37  to start rotation of the photoconductor drums  2 Y,  2 M,  2 C, and  2 K. 
     Subsequently, in step S 62  of  FIG.  10   , the image forming apparatus  100  causes the control unit  37  to determine whether the difference between the rotation speed of the photoconductor drums  2 Y,  2 M, and  2 C and the specified rotation speed is within a specified range. The specified rotation speed is, for example, a specified target rotation speed. 
     In a case where it is determined in step S 62  that the difference is not within the specified range (No in step S 62  of  FIG.  10   ), the image forming apparatus  100  causes the control unit  37  to perform the operation of step S 62  again. On the other hand, in Step S 63  of  FIG.  10   , in a case where it is determined that the difference is within the specified range (Yes in step S 62  of  FIG.  10   ), the image forming apparatus  100  causes the detection unit  210  to start detection of the rotation phases of the photoconductor drums  2 Y,  2 M, and  2 C. 
     Subsequently, in step S 64  of  FIG.  10   , the image forming apparatus  100  causes the detection unit  210  to determine whether the detection of the rotation phases of the photoconductor drums  2 Y,  2 M, and  2 C has completed. 
     In a case where it is determined in step S 64  that the processing has not completed (No in step S 64  of  FIG.  10   ), the image forming apparatus  100  causes the control unit  37  to perform the operation of step S 64  again. On the other hand, in a case where it is determined in step S 64  that the processing has completed (Yes in step S 64  of  FIG.  10   ), the image forming apparatus  100  causes the calculation unit  211  to calculate phase correction values of the photoconductor drums  2 Y,  2 M, and  2 C in step S 65 . 
     Subsequently, in step S 66  of  FIG.  10   , the image forming apparatus  100  causes the correction unit  371  to correct the rotation phases of the photoconductor drums  2 Y,  2 M, and  2 C after completion of the calculation by the calculation unit  211 . 
     Subsequently, in step S 67  of  FIG.  10   , the image forming apparatus  100  causes the control unit  37  to determine whether the correction of the rotation phases of the photoconductor drums  2 Y,  2 M, and  2 C has completed. 
     In a case where it is determined in step S 67  that the processing has not completed (No in step S 67  of  FIG.  10   ), the image forming apparatus  100  causes the control unit  37  to perform the operation of step S 67  again. On the other hand, in a case where it is determined that the processing has completed (Yes in step S 67  of  FIG.  10   ), the image forming apparatus  100  causes the control unit  37  to bring each of the photoconductor drums  2  into contact with the intermediate transfer belt  1  in step S 68 . 
     Subsequently, in step S 69  of  FIG.  10   , the image forming apparatus  100  causes the control unit  37  to start image formation on the recording sheet  20 . 
     Subsequently, in step S 70  of  FIG.  10   , after the end of the image formation, the image forming apparatus  100  causes the control unit  37  to stop the photoconductor drum  2 . Thus, the operation ends. 
     As described above, the image forming apparatus  100  can form an image on the recording sheet  20  while performing phase matching control. Note that the number of colors for which image formation is performed is not particularly limited as long as two or more colors are used. An order in which detection or correction is performed on each photoconductor drum  2  can be appropriately changed. In the description of  FIG.  10   , a description of control of components other than the photoconductor drum  2  is omitted. 
       FIG.  11    is a timing chart illustrating an operation of the image forming apparatus  100 . As illustrated in  FIG.  11   , the period after the start of rotation of each photoconductor drum  2  transitions in the order of a start-up period, a phase detection period, a calculation period, a phase correction period, and a speed control period. 
     In the start-up period, the control unit  37  starts up the motor M in the photoconductor drum  2  on which the phase matching control is performed, that is, performs an operation of causing the photoconductor drum  2  to converge to the specified rotation speed. In the phase detection period, the detection unit  210  detects the rotation phase of the photoconductor drum  2  based on a rising edge of the rotation origin detection signal of each photoconductor drum  2  by the photointerrupter  18 . 
     In the calculation period, the calculation unit  211  calculates the phase correction value from the relationship between the rotation phase difference and the phase of the density unevenness in each photoconductor drum  2 . In the phase correction period, the correction unit  371  outputs the phase correction value calculated in the calculation period to the motor M of the corresponding photoconductor drum  2  and corrects the rotation phase of the photoconductor drum  2 . In the speed control period, the control unit  37  controls the rotation speed of the motor M in the photoconductor drum  2 . Since the rotation speed is changed during the phase correction period, the contact of the photoconductor drum  2  with the intermediate transfer belt  1  is performed when the rotation speed of the photoconductor drum  2  transitions to a stable speed control period after the end of the phase correction period. 
       FIG.  12    is a flowchart of the detection operation of rotation phase of the photoconductor drum  2  by the image forming apparatus  100 . In the phase detection period, the image forming apparatus  100  starts the detection operation of rotation phase of the photoconductor drum  2  in response to the first interruption of the signal that the photointerrupter  18  has detected the rotation origin HP of the photoconductor drum  2 . 
     In step S 81  of  FIG.  12   , the image forming apparatus  100  stores the number of pulses output from the rotary encoder  230  in the photoconductor drum  2 Y, which is a specified photoconductor drum, in a volatile memory disposed in the control unit  37  and detects the rotation phase differences of the respective photoconductor drums  2 . An operation of storing the number of pulses output from the rotary encoder  230  in the photoconductor drum  2 Y is exemplified. The number of pulses output from the rotary encoder  230  in the photoconductor drum  2  of another color may be stored. 
       FIG.  13    is a first diagram illustrating a detection operation of the density-unevenness phase difference by the image forming apparatus  100 .  FIG.  13    illustrates the phase of density unevenness of the photoconductor drum  2 Y.  FIG.  14    is a second diagram illustrating the detection operation of the density-unevenness phase difference by the image forming apparatus  100 .  FIG.  14    illustrates the phase of density unevenness of the photoconductor drum  2 M. 
     In the calculation period, the density-unevenness phase difference between the different photoconductor drums  2  are obtained by calculating from the rotation phase differences between the photoconductor drum  2 Y and the photoconductor drum  2 M detected in the phase detection period, and the relationship between the rotation origins of the photoconductor drums  2  and the peaks of the density unevenness phases acquired in advance. 
     In the examples illustrated in  FIGS.  13  and  14   , it is assumed that the phases of the photoconductor drum  2 Y and the photoconductor drum  2 M are matched, and the number of pulses output from the rotary encoder  230  of the photoconductor drum  2 Y is stored, for example, in the volatile memory during the phase detection period. 
     A density-unevenness phase difference A between the photoconductor drum  2 Y and the photoconductor drum  2 M is calculated from the following expression A=C−(By−Bm). Here, C represents a difference in rotation origin detection timing between the photoconductor drum  2 Y and the photoconductor drum  2 M, and By and Bm represent initial phases. 
     The correction unit  371  can assign phase correction values that cancel the density-unevenness phase difference to the photoconductor drum  2 Y and the photoconductor drum  2 M based on the calculated phase difference A of the density unevenness. 
     As described above, the control device  200  includes the detection unit  210  that detects the density unevenness of the toner image generated according to the rotation cycle of the photoconductor drum  2  based on the rotation phase of each of the plurality of rotatable photoconductor drums  2  (image bearers) and the density of the toner image formed on the photoconductor drum  2 . The control device  200  includes the control unit  37  that controls the rotation phase of the photoconductor drum  2  based on the detection result by the detection unit  210  and the rotation speed of each of the plurality of photoconductor drums  2 . 
     The control unit  37  performs control so that at least two photoconductor drums  2  among the plurality of photoconductor drums  2  have the specified rotation speed when the plurality of photoconductor drums  2  start to rotate. The detection unit  210  starts the operation of detecting the rotation phase when the difference between the rotation speed of at least two photoconductor drums  2  and the specified rotation speed is within the specified range. As a result, the control device  200  can rotate the photoconductor drums  2  such that the phases of the density unevenness in the plurality of photoconductor drums  2  coincide with each other on the image on the recording sheet  20 . Thus, the rotation phases of the photoconductor drums  2  can be accurately controlled. The image forming apparatus  100  can reduce density unevenness for each color and can reduce color unevenness of the image formed on the recording sheet  20 . 
     For example, in the present embodiment, the detection unit  210  starts the calculation for calculating the rotation phase when the operation that detects the rotation phases of at least two photoconductor drums  2  has completed. The control unit  37  starts the correction of the density unevenness when the calculation for calculating the rotation phases of at least two photoconductor drums  2  has completed. The control unit  37  starts the control of the rotation speeds of the photoconductor drums  2  when the operation for correcting the density unevenness of at least two photoconductor drums  2  has completed. As a result, the control device  200  can accurately control the rotation phases of the photoconductor drums  2 . 
     In the present embodiment, the detection unit  210  further detects the rotation origin HP disposed on the photoconductor drum  2 , and the rotation origin HP rotates together with the rotation of the photoconductor drum  2 . As a result, the control device  200  can detect the initial phase of the photoconductor drum  2  with an inexpensive configuration. 
     In the present embodiment, the detection unit  210  detects the rotation phase difference between at least two photoconductor drums  2 . The control unit  37  corrects the density unevenness by matching the phases of the density unevenness in at least two photoconductor drums  2  based on the rotation phase difference and the phase of the density unevenness. The control unit  37  controls the rotating speed of the photoconductor drums  2  so that the phases of the density unevenness in at least two photoconductor drums  2  are matched. As a result, the control device  200  can accurately control the rotation phases of the photoconductor drums  2 . 
     First Modification 
       FIG.  15    is a diagram illustrating an overall configuration of an image forming apparatus  100   a  according to a first modification. In  FIG.  15   , the same members and devices as those of the image forming apparatus  100  of  FIG.  1    are denoted by the same reference numerals, and redundant description thereof is appropriately omitted. 
     The image forming apparatus  100   a  is the quadruple-tandem-type direct-transfer-type full-color machine and includes a transfer unit  29  that transfers toner images formed on the photoconductor drums  2 Y,  2 M,  2 C, and  2 K to the recording sheet  20  vertically below the four sets of the image forming stations. The transfer unit  29  includes an endless transfer conveying belt  29   a  rotatably supported from a drive roller  11   a  to a driven roller  11   d  as a plurality of supporters. The transfer conveying belt  29   a  is wound around the drive roller  11   a,  a driven roller  11   b,  and the driven roller  11   d,  and bears and conveys the recording sheet  20  to pass through the transfer position N of each image forming station while being rotationally driven in the counterclockwise direction in  FIG.  15    at a specified timing. The image forming apparatus  100   a  includes the primary transfer rollers  6 Y,  6 M,  6 C, and  6 K for applying transfer charges at transfer positions N to transfer toner images on the respective photoconductor drums  2 Y,  2 M,  2 C, and  2 K to the recording sheet  20  inside the transfer conveying belt  29   a.    
     The image forming apparatus  100   a  performs the following operation when, for example, a full-color mode that is superimposed with four color is selected by the operation unit. That is, the image forming apparatus  100   a  performs an image forming process that forms the toner images of the respective colors on the photoconductor drums  2 Y,  2 M,  2 C, and  2 K of the image forming stations of the respective colors in synchronization with the conveyance of the recording sheet  20 . 
     On the other hand, the recording sheet  20  is fed from the sheet trays  17 , sent out at the specified timing by the registration roller pair  24 , and borne on the transfer conveying belt  29   a.  The image forming apparatus  100   a  conveys the recording sheet  20  to pass through the transfer position N of each image forming station. The image forming apparatus  100  transfers the toner images of the respective colors to form a four color superimposed color image onto the recording sheet  20 . The fixing unit  25  fixes the toner images on the recording sheet  20 . Thus, the image forming apparatus  100  ejects the recording sheet  20  onto the output tray  26 . 
     The image forming apparatus  100   a  includes the toner-image detection sensor  30 . The toner-image detection sensor  30  is disposed at a pre-fixing position P 4  which is a position opposite a portion where the transfer conveying belt  29   a  is wound around the drive roller  11   a  most downstream from the transfer unit  29  in the recording-sheet conveyance direction. The present embodiment can also be applied to the image forming apparatus  100   a  described above. 
     Second Embodiment 
     An image forming apparatus  100   b  according to a second embodiment is described. 
     The same components as the components described in the first embodiment are denoted by the same reference numerals, and redundant description is omitted as appropriate. 
     When the control device disposed in the image forming apparatus includes an abnormality detection unit that detects an abnormality in the rotation speed of the photoconductor drum  2 , the abnormality detection unit may erroneously detect a change in the rotation speed of the photoconductor drum  2  during the phase matching control. In the present embodiment, the abnormality in the rotation speed of the photoconductor drum  2  can be detected while preventing erroneous detection by the abnormality detection unit. 
       FIG.  16    is a block diagram illustrating a functional configuration of a control device  200   b  of the image forming apparatus  100   b.  The hardware configuration of the control device  200   b  in  FIG.  16    is substantially the same as the hardware configuration in above-described configuration illustrated in  FIG.  2 B . The description is given with reference to above-described  FIG.  2 A  as appropriate. 
     As illustrated in  FIG.  16   , the control device  200   b  includes a control unit  37   b  and an abnormality detection unit  240 . The control unit  37   b  includes a correction unit  371 , a first determination unit  372 , a second determination unit  373 , and a switching unit  374 . 
     The first determination unit  372  determines whether the difference between the rotation speed of the photoconductor drum  2  and the specified rotation speed is within the specified range. The first determination unit  372  can determine that the difference between the rotation speed of the photoconductor drum  2  and the specified rotation speed is not within the specified range when the rotation speed of the photoconductor drum  2  deviates from the specified range from the minimum speed to the maximum speed for a specified time. 
     When the first determination unit  372  determines that the difference is not within the specified range, the second determination unit  373  determines whether the detection by the abnormality detection unit  240  is to be enabled. In the present embodiment, the second determination unit  373  can output a determination result of enabling the detection by the abnormality detection unit  240  in the position detection period, the position correction value calculation period, and the speed control period and disabling the detection by the abnormality detection unit  240  in the start-up period and the position correction period. 
     The switching unit  374  switches between enabling and disabling of the detection by the abnormality detection unit  240 . Based on the determination result by the second determination unit, the switching unit  374  can switch between enabling and disabling of the detection by the abnormality detection unit  240 . 
     The abnormality detection unit  240  has a function of detecting an abnormality in the rotation speed of the photoconductor drum  2 . A method of abnormality detection is not particularly limited. For example, the abnormality detection unit  240  can detect the abnormality based on the output of the rotary encoder  230  disposed in the motor M of the photoconductor drum  2 . 
       FIG.  17    is a diagram illustrating an operation of the second determination unit  373 . In  FIG.  17   , the horizontal axis represents time, and the vertical axis represents the number of output pulses of the rotary encoder  230 . 
     In order to prevent the photoconductor drum  2  from rotating at an unexpected speed, the abnormality detection unit  240  can determine that the rotation speed is abnormal when the number of output pulses of the rotary encoder  230  deviates from a specified minimum speed and maximum speed for the specified time. 
     In  FIG.  17   , a graph Pu indicates changes in the number of output pulses of the rotary encoder  230 . The maximum speed Gt indicates the maximum rotation speed of the motor M, and the minimum speed Gb indicates the minimum rotation speed of the motor M. A period Tv indicates a period in which the abnormality detection is enabled, and the specified time Ti indicates the specified time for determining the abnormality of the rotation speed. 
       FIG.  18    including  FIGS.  18 A and  18 B  is a flowchart of the operation of the image forming apparatus  100   b.  In  FIG.  18   , a case where an image formation is performed with four colors of Y, M, C, and K, and phase matching control is performed on the photoconductor drums  2 Y,  2 M, and  2 C is described as an example. Description of the components or portions described with reference to  FIG.  10    is omitted as appropriate. 
     The image forming apparatus  100   b  starts an image forming operation in response to an instruction to start image formation from an external apparatus such as a personal computer or an operation input to start image formation to an operation unit disposed in the image forming apparatus  100   b.    
     First, in step S 181  of  FIG.  18   , the image forming apparatus  100   b  causes the control unit  37   b  to switch between enabling and disabling of the detection by the abnormality detection unit  240 . This switching operation is described separately with reference to  FIG.  19   . The same applies to steps S 184 , S 187 , S 189 , and S 192  in subsequent operations. 
     Subsequently, in step S 182  of  FIG.  18   , the image forming apparatus  100  causes the control unit  37   b  to start rotation of the photoconductor drums  2 Y,  2 M,  2 C, and  2 K. 
     Subsequently, in step S 183  of  FIG.  18   , the image forming apparatus  100   b  causes the first determination unit  372  to determine whether the difference between the rotation speed of the photoconductor drums  2 Y,  2 M, and  2 C and the specified rotation speed is within the specified range. 
     In a case where it is determined in step S 183  that the difference is not within the specified range (No in step S 183  of  FIG.  18   ), the image forming apparatus  100   b  performs the operation of step S 183  again. On the other hand, in a case where it is determined that the difference is within the specified range (Yes in step S 183  of  FIG.  18   ), the image forming apparatus  100   b  causes the control unit  37   b  to switch between enabling and disabling of the detection by the abnormality detection unit  240  in step S 184 . 
     Subsequently, in step S 185  of  FIG.  18   , the image forming apparatus  100   b  causes the detection unit  210  to start the detection of the rotation phases of the photoconductor drums  2 Y,  2 M, and  2 C. 
     Subsequently, in step S 186  of  FIG.  18   , the image forming apparatus  100   b  causes the detection unit  210  to determine whether the detection of the rotation phases of the photoconductor drums  2 Y,  2 M, and  2 C has completed. 
     In a case where it is determined in step S 186  that the processing has not completed (NO in step S 186  of  FIG.  18   ), the image forming apparatus  100   b  performs the operation of step S 186  again. On the other hand, in a case where it is determined that the detection has completed (Yes in step S 186  of  FIG.  18   ), the image forming apparatus  100   b  causes the control unit  37   b  to switch between enabling and disabling of the detection by the abnormality detection unit  240  in step S 187 . 
     Subsequently, in step S 188  of  FIG.  18   , the image forming apparatus  100   b  causes the calculation unit  211  to calculate the phase correction values of the photoconductor drums  2 Y,  2 M, and  2 C. 
     Subsequently, in step S 189  of  FIG.  18   , the image forming apparatus  100   b  causes the control unit  37   b  to switch between enabling and disabling of the detection by the abnormality detection unit  240 . 
     Subsequently, in step S 190  of  FIG.  18   , the image forming apparatus  100   b  causes the correction unit  371  to correct the rotation phases of the photoconductor drums  2 Y,  2 M, and  2 C after completion of the calculation by the calculation unit  211 . 
     Subsequently, in step S 191  of  FIG.  18   , the image forming apparatus  100   b  causes the control unit  37   b  to determine whether the correction of the rotation phases of the photoconductor drums  2 Y,  2 M, and  2 C has completed. 
     In a case where it is determined in step S 191  that the processing has not completed (NO in step S 191  of  FIG.  18   ), the image forming apparatus  100   b  performs the operation of step S 191  again. On the other hand, in a case where it is determined that the detection has completed (Yes in step S 191  of  FIG.  18   ), the image forming apparatus  100   b  causes the control unit  37   b  to switch between enabling and disabling of the detection by the abnormality detection unit  240  in step S 192 . 
     Subsequently, in step S 193  of  FIG.  18   , the image forming apparatus  100   b  causes the control unit  37   b  to bring each of the photoconductor drums  2  into contact with the intermediate transfer belt  1 . 
     Subsequently, in step S 194  of  FIG.  18   , the image forming apparatus  100   b  starts image formation on a recording sheet. 
     Subsequently, in step S 195  of  FIG.  18   , the image forming apparatus  100   b  stops the photoconductor drum  2  after the end of the image formation. Thus, the operation ends. 
     In this way, the image forming apparatus  100   b  can form an image on the recording sheet while performing the phase matching control. 
       FIG.  19    is a flowchart of an operation of switching between enabling and disabling of the rotation speed abnormality detection. The image forming apparatus  100   b  starts the switching operation of enabling or disabling the rotation speed abnormality detection at the beginning of each of the start-up period, the phase detection period, the calculation period, the phase correction period, and the speed control period. 
     First, in step S 201  of  FIG.  19   , the image forming apparatus  100   b  causes the second determination unit  373  to determine whether the detection by the abnormality detection unit  240  is to be enabled. In this determination, the second determination unit  373  determines that the detection by the abnormality detection unit  240  is to be enabled in the position detection period, the position correction value calculation period, and the speed control period. Then, the second determination unit  373  determines that the detection by the abnormality detection unit  240  is to be disabled in the start-up period and the position correction period. Thus, the determination result is output. 
     In a case where it is determined in step S 201  that the abnormality detection is to be enabled (Yes in step S 201  of  FIG.  19   ), the image forming apparatus  100   b  causes the switching unit  374  to enable the detection by the abnormality detection unit  240  in step S 202 . On the other hand, in a case where it is determined that the abnormality detection is not to be enabled (No in step S 201  of  FIG.  19   ), the image forming apparatus  100   b  causes the switching unit  374  to disable the detection by the abnormality detection unit  240  in step S 203 . 
     In this way, the image forming apparatus  100   b  can switch between enabling and disabling of the detection by the abnormality detection unit  240 . 
     As described above, the control device  200   b  includes the abnormality detection unit  240 , the first determination unit  372 , the second determination unit  373 , and the switching unit  374 . The abnormality detection unit  240  detects the abnormality in the rotation speed of the photoconductor drum  2 . The first determination unit  372  determines whether the difference between the rotation speed of the photoconductor drum  2  and the specified rotation speed is within the specified range in addition to the configuration of the control device  200  according to the first embodiment. Further, when the first determination unit  372  determines that the difference between the rotation speed of the photoconductor drum  2  and the specified rotation speed is not within the specified range, the second determination unit  373  determines whether the detection by the abnormality detection unit  240  is to be enabled. The switching unit  374  switches between enabling and disabling of the detection by the abnormality detection unit  240 . 
     For example, when the rotation speed of the photoconductor drum  2  is out of the specified range from the predetermined maximum speed to the minimum speed for the specified time, the first determination unit  372  determines that the difference between the rotation speed of the photoconductor drum  2  and the specified rotation speed is not within the specified range. 
     For example, the second determination unit  373  outputs a determination result of enabling the detection by the abnormality detection unit  240  in the position detection period, the position correction value calculation period, and the speed control period and disabling the detection by the abnormality detection unit  240  in the start-up period and the position correction period is output. 
     For example, the switching unit  374  switches between enabling and disabling of the detection by the abnormality detection unit  240  based on the determination result by the second determination unit  373 . 
     Such a configuration can disable the detection by the abnormality detection unit  240  in the period in which the rotation speed of the photoconductor drum  2  changes during the phase matching control, thus allowing an erroneous detection by the abnormality detection unit  240  to be prevented. Such a configuration can also enable the detection by the abnormality detection unit  240  in the period in which the rotation speed of the photoconductor drum  2  does not change during the phase matching control. As a result, the abnormality in the rotation speed of the photoconductor drum  2  can be detected while preventing the erroneous detection by the abnormality detection unit  240 . Advantageous effects other than the effects described above are similar to the effects of the first embodiment. 
     Second Modification 
     With reference to  FIGS.  20  to  30   , a description is given of a case where an image composed of two colors of C and M is printed by the image forming apparatus of  FIG.  1   . 
       FIG.  20    is a diagram illustrating density unevenness according to a comparative example of a second modification.  FIG.  21    is a diagram illustrating color unevenness when the density unevenness illustrated in  FIG.  20    is transferred to a recording sheet.  FIG.  22    is a diagram illustrating density unevenness of each color in the image forming apparatus according to the second modification.  FIG.  23    is a diagram illustrating color unevenness when the density unevenness of  FIG.  22    is transferred to a recording sheet.  FIG.  24    is a diagram illustrating a state at a start of control by the image forming apparatus according to the second modification.  FIG.  25    is a diagram illustrating a state at an end of control by the image forming apparatus according to the second modification.  FIG.  26    is a diagram illustrating density unevenness in the image forming apparatus according to the second modification.  FIG.  27    is a diagram illustrating the detection operation of rotation phase of the photoconductor drum of the image forming apparatus according to the second modification.  FIG.  28    is a flowchart of an operation of the image forming apparatus according to the second modification.  FIG.  29    is a timing chart illustrating the operation of the image forming apparatus according to the second modification.  FIG.  30    is a flowchart of a second example of the operation of the image forming apparatus according to the second modification. 
     The functions and operations of the image forming apparatus  100   b  are the same as those of the image forming apparatus  100  before the image forming process. In  FIGS.  20  to  28   , the function and operation are the same as those in a case where the two color image of C and M is printed by the image forming apparatus  100 . In  FIG.  20   , the description of  FIG.  3    except for Ye can be applied as it is. The descriptions of  FIGS.  4 ,  5 , and  6    can be applied to  FIGS.  21 ,  22 , and  23   , respectively. The descriptions of  FIGS.  7  and  8    can be applied to  FIGS.  24  and  25   , respectively. The descriptions of  FIGS.  13  and  14    can be applied to  FIGS.  26  and  27    by replacing the photoconductor drum  2 Y with  2 C and replacing A=C−(Be−Bm). The description of  FIG.  10    can be applied to  FIG.  28    by replacing the operation after S 202  with that of  FIG.  10    except for the photoconductor drum  2 Y. The description of  FIG.  11    can be applied to  FIG.  29    except for the photoconductor drum  2 Y. The description of  FIG.  10    can be applied to  FIG.  30    except for the photoconductor drum  2 Y from step S 303  of  FIG.  30   . 
     Third Modification 
       FIG.  31    is a diagram illustrating an overall configuration of the image forming apparatus  100   b  according to a third modification. 
     The image forming apparatus  100   b  causes the optical writing units  4 Y,  4 M,  4 C, and  4 K to form latent images on the photoconductor drums  2 Y,  2 M,  2 C, and  2 K, respectively. The image forming apparatus  100   b  causes the chargers  3 Y,  3 M,  3 C, and  3 K and the developing units  5 Y,  5 M,  5 C, and  5 K to develop the latent images formed on the photoconductor drums  2 Y,  2 M,  2 C, and  2 K, respectively. 
     The image forming apparatus  100   b  primarily transfers the toner images developed on the photoconductor drums  2 Y,  2 M,  2 C, and  2 K to the intermediate transfer belt  1  using transfer biases from the primary transfer rollers  6 Y,  6 M,  6 C, and  6 K, respectively. The image forming apparatus  100   b  secondarily transfers the toner images transferred on the intermediate transfer belt  1  onto the conveyed recording sheet by using the secondary transfer unit including a secondary transfer belt  400 . The image forming apparatus  100   b  transfers the toner image not to the recording sheet but to the secondary transfer belt  400 , and detects the toner density by a sensor  401  on the secondary transfer belt  400  to detect the density unevenness. Also in the image forming apparatus  100   b  described above, the substantially same effects as those of the image forming apparatus  100  can be obtained. Further, by generating the latent image in accordance with the detection of the rotation origin HP of the photoconductor drum  2 , the initial phase of the rotation origin HP and the phase φt of the density unevenness can be acquired by using the sensor  401  on the secondary transfer belt  400 . 
     The above-described embodiments are just examples and do not limit the present disclosure. Modifications and variations of the embodiments can be made without departing from the spirit and scope of the disclosure described in the claims unless limited in the above description. 
     The numbers such as ordinal numbers and numerical values that indicates quantity are all given by way of example to describe the technologies to implement the embodiments of the present disclosure, and no limitation is indicated to the numbers given in the above description. In addition, the above-described connections among the components are examples for specifically describing the technology of the present disclosure, and connections for implementing functions of the present disclosure are not limited to the above-described examples. 
     Each function of the embodiments described above can be implemented by one or more processing circuits. The “processing circuit” in the present specification includes a processor programmed to execute each function by software like a processor implemented by an electronic circuit, and a device such as an application specific integrated circuit (ASIC), a digital signal processor (DSP), a field programmable gate array (FPGA), or a conventional circuit module designed to execute each function described above. 
     Aspects of the present disclosure are, for example, as follows. 
     First Aspect 
     A control device includes a detection unit and a control unit. The detection unit detects density unevenness of a toner image occurring according to a rotation cycle of a first image bearer for a first color among a plurality of rotatable image bearers, based on a rotation phase of the first image bearer and a density of the toner image formed on the first image bearer, and detects density unevenness of a toner image occurring according to a rotation cycle of a second image bearer for a second color among the plurality of image bearers, based on a rotation phase of the second image bearer and a density of the toner image formed on the second image bearer. The control unit controls rotation phases of the plurality of image bearers based on detection results of the plurality of image bearers by the detection unit and rotation speeds of the plurality of image bearers, corrects the rotation phase of the first image bearer based on a detection result of the first image bearer by the detection unit and a rotation speed of the first image bearer, corrects the rotation phase of the second image bearer based on a detection result of the second image bearer by the detection unit and a rotation speed of the second image bearer, and controls the rotation speeds of at least two of the plurality of image bearers to be a specified rotation speed. The circuitry starts a detection operation of the rotation phases of the plurality of image bearers after a difference between each of the rotation speeds of the at least two of the plurality of image bearers and the specified rotation speed falls within a specified range. 
     Second Aspect 
     The control device according to aspect 1 further includes a detection unit that detects density unevenness of a toner image on a third image bearer for a third color occurring according to a rotation phase of the third image bearer and a rotation cycle of the third image bearer. The control unit corrects the rotation phase of the third image bearer based on a detection result of the third image bearer and a rotation speed of the third image bearer. 
     Third Aspect 
     The control device according to aspect 2 that the detection unit starts calculating rotation phases of the at least two of the plurality of image bearers after a detection operation of the rotation phases of the at least two of the plurality of image bearers has ended. 
     Fourth Aspect 
     The control device according to aspect 3 that the control unit starts correcting density unevenness of the at least two of the plurality of image bearers after the calculating of the rotation phases of the at least two of the plurality of image bearers has ended. 
     Fifth Aspect 
     The control device according to aspect 4 that the control unit starts controlling the rotation speeds of the plurality of image bearers after the correcting of the density unevenness of the at least two of the plurality of image bearers has ended. 
     Sixth Aspect 
     The control device according to any one of aspects 1 to 5 that the detection unit detects a rotation origin of the first image bearer, a rotation origin of the second image bearer, and a rotation origin of the third image bearer. The detection unit detects the density unevenness of the toner image occurring according to each of the rotation cycle of the first image bearer, the rotation cycle of the second image bearer, and the rotation cycle of the third image bearer. 
     Seventh Aspect 
     The control device according to aspect 6 that the rotation origin of the first image bearer rotates with the rotation of the first image bearer. The rotation origin of the second image bearer rotates with the rotation of the second image bearer. The rotation origin of the third image bearer rotates with the rotation of the third image bearer. 
     Eighth Aspect 
     The control device according to any one of aspects 1 to 7 that the detection unit detects a difference between rotation phases of the at least two of the plurality of image bearers. 
     Ninth Aspect 
     The control device according to aspect 8 that the control unit matches phases of density unevenness between the at least two of the plurality of image bearers, based on the phases of the density unevenness and the difference between the rotation phrases of the at least two of the plurality of image bearers, to correct the density unevenness of the at least two of the plurality of image bearers. 
     Tenth Aspect 
     The control device according to any one of aspects 1 to 9 that the control unit controls the rotation phases of the plurality of image bearers to match phases of density unevenness between the at least two of the plurality of image bearers. 
     Eleventh Aspect 
     The control device according to any one of aspects 1 to 10 further includes an abnormality detection unit that detects the rotation speeds of the plurality of image bearers. The control unit determines whether a difference between each of the rotation speeds of the plurality of image bearers and the specified rotation speed falls within the specified range, determines whether detection by the abnormality detection unit is to be enabled, in response to a determination that the difference does not fall within the specified range, and switches between enabling and disabling of the detection by the abnormality detection unit. 
     Twelfth Aspect 
     The control device according to aspect 11 that the control unit determines that the difference between each of the rotation speeds of the plurality of image bearers and the specified rotation speed does not fall within the specified range, in a case where any one of the rotation speeds of the plurality of image bearers deviates from a predetermined range from a minimum speed to a maximum speed for a specified time. 
     Thirteenth Aspect 
     The control device according to aspect 11 or 12 that the control unit outputs a determination result of enabling the detection by the abnormality detection unit in a position detection period, a position correction value calculation period, and a speed control period, and disabling the detection by the abnormality detection unit in a start-up period and a position correction period. 
     Fourteenth Aspect 
     The control device according to any one of aspects 11 to 13 that the control unit switches between enabling and disabling of the detection by the abnormality detection unit, based on the determination result. 
     Fifteenth Aspect 
     An image forming apparatus includes the control device according to any one of aspects 1 to 14, the plurality of image bearers, and a plurality of forming devices that form devices form the toner images on the plurality of image bearers. 
     Sixteenth Aspect 
     An image forming method for an image forming apparatus, the method includes forming toner images on a plurality of rotatable image bearers with a plurality of forming devices of the image forming apparatus, detecting density unevenness of a toner image occurring according to a rotation cycle of a first image bearer among the plurality of image bearers, based on a rotation phase of the first image bearer and a densify of the toner image formed on the first image bearer, detecting density unevenness of a toner image occurring according to a rotation period of a second image bearer among the plurality of image bearers, based on a rotation phase of the second image bearer and a density of the toner image formed on the second image bearer, controlling rotation phases of the plurality of image bearers based on detection results of the plurality of image bearers and rotation speeds of the plurality of image bearers, correcting the rotation phase of the first image bearer based on a detection result of the first image bearer and a rotation speed of the first image bearer, correcting the rotation phase of the second image bearer based on a detection result of the second image bearer and a rotation speed of the second image bearer, controlling rotation speeds of at least two of the plurality of image bearers to be a specified rotation speed, and starting a detection operation of the rotation phases of the plurality of image bearers after a difference between each of the rotation speeds of the at least two of the plurality of image bearers and the specified rotation speed falls within a specified range. 
     Seventeenth Aspect 
     A storage medium storing a plurality of instructions which, when executed by one or more processors, cause the processors to execute a method that includes forming toner images on a plurality of rotatable image bearers with a plurality of forming devices of an image forming apparatus, detecting density unevenness of a toner image occurring according to a rotation cycle of a first image bearer among the plurality of image bearers, based on a rotation phase of the first image bearer and a densify of the toner image formed on the first image bearer, detecting density unevenness of a toner image occurring according to a rotation period of a second image bearer among the plurality of image bearers, based on a rotation phase of the second image bearer and a density of the toner image formed on the second image bearer, controlling rotation phases of the plurality of image bearers based on detection results of the plurality of image bearers and rotation speeds of the plurality of image bearers, correcting the rotation phase of the first image bearer based on a detection result of the first image bearer and a rotation speed of the first image bearer, correcting the rotation phase of the second image bearer based on a detection result of the second image bearer and a rotation speed of the second image bearer, controlling rotation speeds of at least two of the plurality of image bearers to be a specified rotation speed, and starting a detection operation of the rotation phases of the plurality of image bearers after a difference between each of the rotation speeds of the at least two of the plurality of image bearers and the specified rotation speed falls within a specified range. 
     The above-described embodiments are illustrative and do not limit the present invention. Thus, numerous additional modifications and variations are possible in light of the above teachings. For example, elements and/or features of different illustrative embodiments may be combined with each other and/or substituted for each other within the scope of the present invention. 
     Any one of the above-described operations may be performed in various other ways, for example, in an order different from the one described above. 
     The functionality of the elements disclosed herein may be implemented using circuitry or processing circuitry which includes general purpose processors, special purpose processors, integrated circuits, application specific integrated circuits (ASICs), digital signal processors (DSPs), field programmable gate arrays (FPGAs), conventional circuitry and/or combinations thereof which are configured or programmed to perform the disclosed functionality. Processors are considered processing circuitry or circuitry as they include transistors and other circuitry therein. In the disclosure, the circuitry, units, or means are hardware that carry out or are programmed to perform the recited functionality. The hardware may be any hardware disclosed herein or otherwise known which is programmed or configured to carry out the recited functionality. When the hardware is a processor which may be considered a type of circuitry, the circuitry, means, or units are a combination of hardware and software, the software being used to configure the hardware and/or processor.