Patent Publication Number: US-11385567-B2

Title: Image forming apparatus with developer amount prediction

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based on and claims priority under 35 USC 119 from Japanese Patent Application No. 2020-182830 filed Oct. 30, 2020. 
     BACKGROUND 
     (i) Technical Field 
     The present disclosure relates to an image forming apparatus. 
     (ii) Related Art 
     In the related art, a technology related to replenishment of a developer to a developing device in an image forming apparatus has already been proposed in, for example, JP-A-2006-301537. 
     JP-A-2006-301537 discloses a configuration including a replenishing amount predicting unit configured to predict a replenishing amount of replenishment developer that is replenished from a replenishing device to a developing device, and a forced replacing unit configured to, w % ben the replenishing amount predicted by the replenishing amount predicting unit is smaller than a predetermined value, supply toner in the developing device to an image carrier to be forcibly consumed, and to forcibly replenish the replenishing device with the replenishment developer from the replenishing device. 
     SUMMARY 
     Aspects of non-limiting embodiments of the present disclosure relate to, in an image density control operation that supplies toner to an inside of a developing device to control an image density, preventing a decrease in the image density caused by the toner consumed by adhering to a surface of an image carrier by a potential difference between the image carrier and a developer carrier at a start or end of an image forming operation. 
     Aspects of certain non-limiting embodiments of the present disclosure address the above advantages and/or other advantages not described above. However, aspects of the non-limiting embodiments are not required to address the advantages described above, and aspects of the non-limiting embodiments of the present disclosure may not address advantages described above. 
     According to an aspect of the present disclosure, there is provided an image forming apparatus including: an image carrier configured to carry an image; a developing unit configured to develop the image carried by the image carrier with a developer; and a developer replenishing unit configured to supply the developer to the developing unit, the developer replenishing unit being configured to predict, in advance, an amount of developer consumed by the image carrier at a start or an end of image formation apart from developer consumed in the image formation, to replenish the predicted amount of the developer. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Exemplary embodiment(s) of the present disclosure will be described in detail based on the following figures, wherein: 
         FIG. 1  is an overall configuration view illustrating an image forming apparatus according to a first exemplary embodiment of the present disclosure: 
         FIG. 2  is a cross-sectional configuration view illustrating a process cartridge serving as an image forming device of the image forming apparatus according to the first exemplary embodiment of the present disclosure; 
         FIG. 3  is a cross-sectional configuration view illustrating a developing device; 
         FIG. 4  is a graph illustrating a relationship between a cumulative number of printings and a cumulative consumption amount of toner; 
         FIG. 5  is a graph illustrating a relationship between a cumulative number of printings and a cumulative consumption amount of toner; 
         FIG. 6  is a block diagram illustrating a controller of the image forming apparatus according to the first exemplary embodiment of the present disclosure; 
         FIG. 7  is a flowchart of a toner replenishing operation of the image forming apparatus according to the first exemplary embodiment of the present disclosure: 
         FIG. 8  is a flowchart of the toner replenishing operation of the image forming apparatus according to the first exemplary embodiment of the present disclosure; 
         FIG. 9  is a flowchart of the toner replenishing operation of the image forming apparatus according to the first exemplary embodiment of the present disclosure; 
         FIG. 10  is a graph illustrating a relationship between a cumulative number of printings and a cumulative consumption amount of toner in the image forming apparatus according to the first exemplary embodiment of the present disclosure; 
         FIG. 11  is a block diagram illustrating a controller of an image forming apparatus according to a second exemplary embodiment of the present disclosure; 
         FIG. 12  is a block diagram illustrating a controller of an image forming apparatus according to a third exemplary embodiment of the present disclosure; and 
         FIG. 13  is a block diagram illustrating a controller of an image forming apparatus according to a fourth exemplary embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, exemplary embodiments of the present disclosure will be described with reference to the accompanying drawings. 
     First Exemplary Embodiment 
       FIG. 1  is a configuration view illustrating an overall outline of an image forming apparatus to which a developing device according to a first exemplary embodiment of the present disclosure is applied, and  FIG. 2  is a configuration view illustrating an image forming device of the image forming apparatus. 
     Overall Configuration of Image Forming Apparatus 
     An image forming apparatus  1  according to the first exemplary embodiment is configured as, for example, a color printer. As illustrated in  FIG. 1 , the image forming apparatus  1  includes plural image forming devices  10  that form a toner image developed with toner that constitutes a developer, an intermediate transfer device  20  that carries the toner images formed by the respective image forming devices  10  and finally transports to a secondary transfer position at which the toner images are secondarily transferred to a recording sheet  5  as an example of a recording medium, a sheet feeding device  30  that accommodates and transports the required recording sheet  5  to be fed to the secondary transfer position of the intermediate transfer device  20 , and a fixing device  40  that fixes the toner images on the recording sheet  5  secondarily transferred in the intermediate transfer device  20 . The reference numeral  1   a  in the drawing indicates an apparatus body of the image forming apparatus  1 . The apparatus body  1   a  includes a support structure member, an outer cover, and the like. 
     The image forming device  10  includes four image forming devices  10 Y,  10 M,  10 C, and  10 K that exclusively form toner images of four colors of yellow (Y), magenta (M), cyan (C), and black (K), respectively. The four image forming devices  10 (Y, M, C, K) are disposed to be arranged in one row in an oblique state in the inner space of the apparatus body  1   a.    
     The four image forming devices  10  include the image forming devices  10 (Y, M, C) of colors of yellow (Y), magenta (M), and cyan (C), and the image forming device  10 K of black (K). The black image forming device  10 K is disposed on the most downstream side along a moving direction B of an intermediate transfer belt  21  of the intermediate transfer device  20 . The image forming apparatus  1  has a full color mode in which the color image forming devices  10 (Y, M. C) and the image forming device  10 K of black (K) are operated to form a full-color image, and a black-and-white mode in which only the image forming device  10 K of black (K) is operated to form a black-and-white (monochrome) image, as an image forming mode. 
     As illustrated in  FIG. 2 , each of the image forming devices  10 (Y, M, C, K) includes a rotating photoconductor drum  11  as an example of an image carrier. Around the photoconductor drum  11 , the following devices are disposed as examples of a toner image forming unit. The main devices are a charging device  12  that charges a circumferential surface (an image carrying surface) of the photoconductor drum  11  on which an image may be formed to a required potential, an exposure device  13  that irradiates light based on image information (signal) on the charged circumferential surface of the photoconductor drum  11  to form an electrostatic latent image (for each color) having a potential difference, a developing device  14 (Y, M, C, K) that develops the electrostatic latent image into a toner image with toner of a developer of corresponding colors (Y, M, C, K), a primary transfer device  15 (Y, M, C, K) (see  FIG. 1 ) as an example of a primary transfer unit that transfers each toner image to the intermediate transfer device  20 , and a drum cleaning device  16 (Y, M, C, K) that removes and cleans adhering substances such as toner remaining and adhering on the image carrying surface of the photoconductor drum  11  after the primary transfer. 
     The photoconductor drum  11  is obtained by forming an image carrying surface having a light conductive layer (a photoconductive layer) made of a photoconductive material on a circumferential surface of a cylindrical or a columnar substrate to be grounded. The photoconductor drum  11  is supported so as to be rotated in a direction indicated by the arrow A when power is transmitted from a driving device (not illustrated). 
     The charging device  12  is configured as a contact type charging roller disposed in a state of being in contact with the photoconductor drum  11 . A charging voltage is supplied to the charging device  12 . As the charging voltage, when the developing device  14  performs reverse development, a voltage or current having the same polarity as the charging polarity of the toner supplied from the developing device  14  is supplied. A cleaning roller  121  that cleans the surface of the charging device  12  is disposed to be in contact with the rear side of the charging device  12 . Examples of the charging device  12  may include a non-contact type charging device such as a Scorotron disposed on the surface of the photoconductor drum  11  in a non-contact state. 
     As illustrated in  FIG. 1 , the exposure device  13  is commonly configured in each of the image forming devices  10 (Y, M, C, K), and deflects and scans a laser beam LB configured according to the image information along the axial direction of each photoconductor drum  11 . As the exposure device  13 , an LED print head that irradiates the photoconductor drum  11  with light according to the image information by light emitting diodes (LED) as plural light emitting elements disposed along the axial direction of the photoconductor drum  11  to form an electrostatic latent image may be used, of course. 
     Each of the developing devices  14 (Y, M, C, K) includes a developing roller  141  that carries a developer  4  and transports the developer  4  to a developing area facing the photoconductor drum  11 , a supply transport member  142  and an agitation transport member  143  such as two screw augers that transport the developer  4  so as to pass through the developing roller  141  while agitating the developer  4 , and a layer thickness regulating member  144  that regulates an amount (the thickness of the layer) of the developer  4  carried on the developing roller  141 , inside the device housing  140  serving as a device body in which an opening and a developer accommodating chamber are formed. In the developing device  14 , a developing voltage is supplied from a power supply device (not illustrated) between the developing roller  141  and the photoconductor drum  11 . Further, the developing roller  141  or the supply transport member  142  and the agitation transport member  143  is rotated in a required direction by transmitting power from a driving device (not illustrated). Further, as the four color developers  4 (Y, M, C, K), a two-components developer containing non-magnetic toner and a magnetic carrier is used. The developing device  14  will be described in detail later. 
     The primary transfer device  15 (Y, M, C, K) is a contact type transfer device having a primary transfer roller that is in contact with the periphery of the photoconductor drum  11  via the intermediate transfer belt  21  and rotates, and is supplied with a primary transfer voltage. A DC voltage having a polarity opposite to the charging polarity of the toner is supplied from a power supply device (not illustrated) as the primary transfer voltage. 
     The drum cleaning device  16  includes a body  16   a  having a container shape with an opening, a cleaning plate  16   b  disposed to be in contact with the circumferential surface of the photoconductor drum  11  with a required pressure after the primary transfer and removes the adhering substances such as residual toner to clean, a delivery member  16   c  such as a screw auger that recovers the adhering substances such as toner removed by the cleaning plate  16   b  and delivers the adhering substances to a recovery system (not illustrated), and the like. 
     As illustrated in  FIG. 1 , the intermediate transfer device  20  is disposed so as to be located at a position above each of the image forming devices  10 (Y, M, C, K). The intermediate transfer device  20  includes the intermediate transfer belt  21  passing through a primary transfer position between the photoconductor drum  11  and the primary transfer device  15  (the primary transfer roller) and rotating in a direction indicated by the arrow B, plural belt support rollers  22  to  25  holding the intermediate transfer belt  21  in a desired state from the inner surface thereof to rotatably support, a secondary transfer device  26  as an example of a secondary transfer unit disposed on the outer peripheral surface (an image carrying surface) side of the intermediate transfer belt  21  supported by the belt support roller  22  and secondarily transferring the toner image on the intermediate transfer belt  21  to the recording sheet  5 , and a belt cleaning device  27  removing and cleaning the adhering substances such as toner and paper dust remaining and adhering on the outer peripheral surface of the intermediate transfer belt  21  after passing through the secondary transfer device  26 . 
     An endless belt made from a material in which, for example, a resistance adjusting agent such as a carbon black is dispersed in a synthetic resin such as polyimide resin or polyamide resin is used as the intermediate transfer belt  21 . Further, the belt support roller  22  is configured as a rear surface support roller for the secondary transfer, the belt support roller  23  is configured as a driving roller that is rotatably driven by a driving device (not illustrated), the belt support roller  24  is configured as a surface shaping roller that forms an image formation surface of the intermediate transfer belt  21 , and the belt support roller  25  is configured as a tension applying roller that applies tension to the intermediate transfer belt  21 . Further, the belt support roller  23  also serves as an opposing roller facing the belt cleaning device  27 . 
     The secondary transfer device  26  is a contact type transfer device having a secondary transfer roller rotating in contact with the peripheral surface of the intermediate transfer belt  21  in the secondary transfer position that is the outer peripheral surface portion of the intermediate transfer belt  21  supported by the belt support roller  22  of the intermediate transfer device  20 , and to which a secondary transfer voltage is supplied. Further, a DC voltage having a polarity opposite to or the same as the charging polarity of the toner is supplied to the secondary transfer device  26  or the belt support roller  22  of the intermediate transfer device  20  as the secondary transfer voltage from a power supply device (not illustrated). 
     As illustrated in  FIG. 1 , the fixing device  40  includes a heating rotary body  41  having a roller form or a belt form that is rotated in the direction indicated by the arrow and is heated by a heating unit such that the surface temperature is maintained at a predetermined temperature, and a pressurizing rotary body  42  having a roller form or a belt form that rotates in accordance with the rotation of the heating rotary body  41  with being in contact with the heating rotary body  41  at a predetermined pressure in a state of substantially extending along the axial direction of the heating rotary body  41 , inside a housing (not illustrated) including an introducing port and a discharging port for the recording sheet  5 . In the fixing device  40 , a contact portion where the heating rotary body  41  and the pressurizing rotary body  42  are in contact with each other serves as a fixing processing portion that performs necessary fixing processing (heating and pressurizing). 
     The sheet feeding device  30  is disposed so as to be located at a position below the image forming device  10 (Y, M, C. K). The sheet feeding device  30  includes a single (or plural) sheet accommodating body  31  that accommodates the recording sheet  5  of a desired size, type, or the like in a loaded state, and a delivery device  32  that delivers the recording sheet  5  one by one from the sheet accommodating body  31 . The sheet accommodating body  31  is provided such that, for example, the user of the apparatus body  1   a  may pull it out from the front surface (left side in the drawing) which is a side surface facing during an operation. 
     Examples of the recording sheet  5  may include, for example, a plain sheet used in an electrophotographic copying machine and printer, a thin sheet such as a tracing paper, and an OHP sheet. In order to further improve the smoothness of the image surface after fixing, it is desired that the surface of the recording sheet  5  is also as smooth as possible, and for example, a so-called thick sheet having a relatively large basis weight such as a coated sheet obtained by coating the surface of a plain sheet with resin, or an art sheet for printing may be properly used. 
     A sheet feeding transport path  34  including a single or plural sheet transport roller pairs  33  that transports the recording sheet  5  delivered from the sheet feeding device  30  to the secondary transfer position or a transport guide (not illustrated) is provided between the sheet feeding device  30  and the secondary transfer device  26 . The sheet transport roller pair  33  disposed at a position immediately before the secondary transfer position in the sheet feeding transport path  34  is configured as, for example, a roller (registration roller) that adjusts the transport timing of the recording sheet  5 . Further, a sheet transport path  35  that transports the recording sheet  5  after the secondary transfer delivered from the secondary transfer device  26  to the fixing device  40  is provided between the secondary transfer device  26  and the fixing device  40 . Further, a discharge transport path  38  including a sheet discharge roller pair  37  that discharges the recording sheet  5  after fixing delivered from the fixing device  40  to a sheet discharge unit  36  provided on the upper portion of the apparatus body  1   a  is provided in a portion near the discharging port for the sheet formed in the apparatus body  1   a.    
     A switching gate G switching the sheet transport path is provided between the fixing device  40  and the sheet discharge roller pair  37 . The sheet discharge roller pair  37  is configured so that the rotation direction may be switched between a forward rotation direction (discharge direction) and a reverse rotation direction. When an image is formed on both sides of the recording sheet  5 , after the rear end portion of the recording sheet  5  having an image on one side passes through the switching gate G, the rotation direction of the sheet discharge roller pair  37  is switched from the forward rotation direction (discharge direction) to the reverse rotation direction. The transport path of the recording sheet  5  transported in the reverse rotation direction by the sheet discharge roller pair  37  is switched by the switching gate G rotated in the counterclockwise direction in the drawing, and the recording sheet  5  is transported to a duplex transport path  39  formed along the substantially vertical direction along the rear surface of the apparatus body  1   a . The duplex transport path  39  includes a sheet transport roller pair  39   a  transporting the recording sheet  5  in a state where the front and back sides are inverted to the sheet transport roller pair  33 , a transport guide  39   b , and the like. 
     In  FIG. 1 , the reference numeral  145 (Y, M. C. K) respectively indicates a toner cartridge disposed in plural along a direction orthogonal to the sheet surface and accommodating the developer containing at least toner supplied to the corresponding developing device  14 (Y, M, C, K). The toner cartridge  145 (Y, M, C, K) supplies each color toner to the corresponding developing device  14 (Y, M, C, K) at a predetermined timing via a toner supply device (not illustrated). 
     Further, the reference numeral  100  in  FIG. 1  indicates a controller that collectively controls the operation of the image forming apparatus  1 . The controller  100  includes a central processing unit (CPU), a read only memory (ROM), a random access memory (RAM) (not illustrated), or a bus connecting these CPU and ROM, and a communication interface. 
     Operation of Image Forming Apparatus 
     Hereinafter, descriptions will be made on a basic image forming operation by the image forming apparatus  1 . 
     Here, an operation in the full color mode that forms a full-color image that is a combination of toner images of four colors (Y, M, C. K) using the four image forming devices  10 (Y, M. C. K) will be described. 
     In the image forming apparatus  1 , when command information of requirement for a full-color image forming operation (print) is received from an user interface or a printer driver (both are not illustrated), the four image forming devices  10 (Y, M, C. K), the intermediate transfer device  20 , the secondary transfer device  26 , the fixing device  40 , and the like are started. 
     Then, as illustrated in  FIGS. 1 and 2 , in each of the image forming devices  10 (Y, M, C, K), each photoconductor drum  11  first rotates in the direction indicated by the arrow A. and each charging device  12  charges the surface of each photoconductor drum  11  at a required polarity (negative polarity in the first exemplary embodiment) and potential. Subsequently, the exposure device  13  irradiates the laser beam LB which is deflected and scanned based on an image signal obtained by converting the image information input to the image forming apparatus  1  into the respective color components (Y, M, C, K) to the surface of the photoconductor drum  11  after charging, thereby forming an electrostatic latent image of each color component formed with a required potential difference on the surface. 
     Subsequently, each of the image forming devices  10 (Y, M, C, K) supplies toner of the corresponding color (Y, M, C, K) charged to the required polarity (negative polarity) from the developing roller  141  to cause the toner electrostatically to adhere to the electrostatic latent image of the corresponding color component formed on the photoconductor drum  11  for development. By this development, the electrostatic latent image of each color component formed on each photoconductor drum  11  is developed as toner images of the four colors (Y, M, C, K) respectively developed with toner of the corresponding color. 
     Subsequently, when the toner image of each color of the respective image forming devices  10 (Y, M, C, K) formed on the photoconductor drum  11  is transported to the primary transfer position, the primary transfer device  15 (Y, M, C, K) primarily transfers the toner image of each color in a sequentially overlapped state with respect to the intermediate transfer belt  21  of the intermediate transfer device  20  rotating in the direction indicated by the arrow B. 
     Further, in each of the image forming devices  10 (Y, M, C, K) in which the primary transfer is completed, the drum cleaning device  16  removes the adhering substances by scraping to clean the surface of the photoconductor drum  11 . Therefore, each of the image forming devices  10 (Y, M, C. K) becomes a state where the next image forming operation is possible. 
     Subsequently, the intermediate transfer device  20  carries the toner image primarily transferred and transports the toner image to the secondary transfer position by the rotation of the intermediate transfer belt  21 . Meanwhile, the sheet feeding device  30  delivers the required recording sheet  5  to the sheet feeding transport path  34  in accordance with the image forming operation. In the sheet feeding transport path  34 , the sheet transport roller pair  33  serving as a registration roller delivers and feeds the recording sheet  5  to the secondary transfer position in accordance with a transfer timing. 
     In the secondary transfer position, the secondary transfer device  26  secondarily transfers the toner image on the intermediate transfer belt  21  collectively to the recording sheet  5 . Further, in the intermediate transfer device  20  in which the secondary transfer is completed, the belt cleaning device  27  removes the adhering substances such as toner remaining on the surface of the intermediate transfer belt  21  after the secondary transfer to clean. 
     Subsequently, the recording sheet  5  to which the toner image is secondarily transferred is separated from the intermediate transfer belt  21 , and then transported to the fixing device  40  through the sheet transport path  35 . In the fixing device  40 , the recording sheet  5  after the secondary transfer is introduced into and passed through the contact portion between the heating rotary body  41  and the pressurizing rotary body  42  that are rotating, and thus, an unfixed toner image is fixed on the recording sheet  5  by performing the necessary fixing processing (heating and pressurizing). Finally, when the image forming operation in which an image is formed on one surface is performed, the recording sheet  5  after completing the fixing is discharged to the sheet discharge unit  36  provided in the upper portion of the apparatus body  1   a  by the sheet discharge roller pair  37 . 
     By the above operation, the recording sheet  5  on which a full-color image formed by combining toner images of four colors is formed is output. 
     The recording sheet  5  on which a monochrome image is formed is output by operating only the image forming device  10 K of black (K). 
     Configuration of Process Cartridge 
     In the exemplary embodiment, a process cartridge  80 (Y, M, C. K) as an example of an image forming unit is configured by integrally unitizing and assembling the image forming member including the photoconductor drum  11 , the charging device  12  disposed around the photoconductor drum  11 , the developing device  14 , and the drum cleaning device  16 . 
       FIG. 2  is a cross-sectional configuration view illustrating the process cartridge  80  that constitutes the image forming device of the image forming apparatus. 
     As illustrated in  FIG. 2 , the process cartridge  80  includes a process cartridge body as an example of an image forming unit body in which the photoconductor drum  11 , the charging device  12 , the developing device  14 , and the drum cleaning device  16  are integrally unitized and mounted. In the illustrated exemplary embodiment, the process cartridge body includes the device housing  140  of the developing device  14  or the body  16   a  of the drum cleaning device  16 , further, frame members (not illustrated) disposed on the front end portion and the inner end portion of the process cartridge  80  along the mounting direction, and the like. 
     The photoconductor drum  11  is rotatably mounted to the frame member (not illustrated) of the process cartridge body. Meanwhile, as illustrated in  FIG. 3 , in the developing device  14 , the developing roller  141  is swingable in a direction in which the developing roller  141  comes into contact with and separates from the photoconductor drum  11 , with a swing fulcrum  146  as the center with respect to the process cartridge body. Further, in the developing device  14 , the developing roller  141  is pressurized to be in contact with the surface of the photoconductor drum  11  by an elastic member such as a coil spring (not illustrated) that is hooked between the device housing  140  of the developing device  14  and the frame member of the process cartridge body to which the photoconductor drum  11  is rotatably mounted. 
     Configuration of Developing Device 
       FIGS. 2 and 3  are cross-sectional configuration views respectively illustrating the process cartridge including the developing device and the developing device according to the first exemplary embodiment. 
     As illustrated in  FIGS. 2 and 3 , the developing device  14  includes the device housing  140  as an example of a device body of the developing device  14 . When roughly classifying, the device housing  140  includes a lower housing  140   a  disposed at the lower portion of the developing device  14  and an upper housing  140   b  disposed at the upper portion of the developing device  14 . The lower housing  140   a  and the upper housing  140   b  are airtightly joined with each other, and as illustrated in  FIG. 2 , a developer accommodating chamber  150  that accommodates the two-components developer  4  is formed inside the device housing  140 . An opening  151  is provided in the area of the device housing  140  facing to the photoconductor drum  11 . Further, inside the device housing  140 , the developing roller  141  as an example of a developer carrier is disposed to be rotatable along the arrow direction C to be partially exposed to the opening  151 . The developing roller  141  includes a magnet roller  141   a  as an example of a magnetic field generating unit that is fixedly disposed inside, and in which a magnetic pole having the required polarity is disposed at the required position along the circumferential direction, and a cylindrical developing sleeve  141   b  as an example of a developer transport member disposed on the outer periphery of the magnet roller  141   a  to be rotatable at a required rotational speed along the direction of the arrow C. The developing sleeve  141   b  is formed in a cylindrical shape by a non-magnetic material made of aluminum, non-magnetic stainless steel, or the like. 
     In the first exemplary embodiment, the rotation direction of the developing sleeve  141   b  is set to a direction opposite to the rotation direction of the photoconductor drum  11 . That is, while the rotation direction A of the photoconductor drum  11  is set to the clockwise direction as illustrated in  FIG. 2 , the rotation direction C of the developing sleeve  141   b  is set to the counterclockwise direction. As a result, the outer peripheral surface of the developing sleeve  141   b  moves in the same direction as the movement direction of the surface of the photoconductor drum  11  in the developing area facing the photoconductor drum  11 . The rotation direction of the developing sleeve  141   b  may be set to the same direction as the rotation direction A of the photoconductor drum  11 . 
     The rotation speed of the developing sleeve  141   b  is determined in accordance with the productivity of the image forming apparatus  1  determined by the rotation speed (process speed) of the photoconductor drum  11 . The productivity of the image forming apparatus  1  is indicated by, for example, the number of recording sheets  5  having A4 size (LEF) on which an image may be formed per unit time. 
     The magnet roller  141   a  includes a developing magnetic pole S 1  disposed at a position that is a developing area facing to the photoconductor drum  11  and is slightly displaced upstream side along the rotation direction of the photoconductor drum  11  from the closest position, a transport magnetic pole N 1  positioned at the end portion on the downstream side along the rotation direction of the developing sleeve  141   b  in the opening  151  of the device housing  140  and transporting the developer  4  that is disposed to be adjacent to the downstream side of the developing magnetic pole S 1  along the rotation direction of the developing sleeve  141   b  and used for developing to the inside of the device housing  140 , a pick-off magnetic pole S 2  disposed on the downstream side of the transport magnetic pole N 1  along the rotation direction of the developing sleeve  141   b , serving as a transport magnetic pole that transports the developer  4  to the inside of the device housing  140  together with the transport magnetic pole N 1 , and separating the developer  4  from the surface of the developing sleeve  141   b , a pick-up magnetic pole S 3  disposed on the downstream side of the pick-off magnetic pole S 2  along the rotation direction of the developing sleeve  141   b  and adsorbing the new developer  4  supplied while being agitated by the supply transport member  142  to the surface of the developing sleeve  141   b , and a trimming magnetic pole N 2  disposed on the downstream side of the pick-up magnetic pole S 3  along the rotation direction of the developing sleeve  141   b  and uniformalizing the developer layer together with the layer thickness regulating member  144 . The layer thickness regulating member  144  that regulates the amount (layer thickness) of the developer  4  carried on the surface of the developing sleeve  141   b  is disposed at the position facing the trimming magnetic pole N 2  of the magnet roller  141   a . The layer thickness regulating member  144  is made of a magnetic material formed in a columnar shape, and regulates the layer thickness of the developer  4  to a required value in a state where the magnetic force of the trimming magnetic pole N 2  acts. The developer  4  that is transported while being adsorbed by the magnetic poles of the magnet roller  141   a  forms a layer in a magnetic brush form on the surface of the developing sleeve  141   b.    
     Inside the device housing  140 , the supply transport member  142  as an example of a developer supply unit including, for example, a screw auger (supply auger) that pumps the developer  4  accommodated inside the developer accommodating chamber  150  and supplies the developer  4  to the developing roller  141  is disposed below obliquely along the vertical direction of the developing roller  141 . The supply transport member  142  is rotatably driven in the counterclockwise direction by a driving device (not illustrated). Further, inside the device housing  140 , the agitation transport member  143  as an example of a developer transport unit including, for example, a screw auger (admix auger) that transports the developer  4  supplied to the inside of the device housing  140  while agitating the developer  4  is disposed on the rear surface of the supply transport member  142 . The agitation transport member  143  is also rotatably driven in the clockwise direction by a driving device (not illustrated). 
     The lower housing  140   a  is provided with a first accommodating portion  147  and a second accommodating portion  148  formed in a substantially semi-cylindrical cross-sectional shape in order to accommodate the supply transport member  142  and the agitation transport member  143 . The first accommodating portion  147  and the second accommodating portion  148  are partitioned by a partition wall  152  provided in the lower housing  140   a . Further, the upper housing  140   b  is provided with a third accommodating portion  153  that accommodates the developer  4  together with the first accommodating portion  147  of the lower housing  140   a  and supplies the developer  4  to the developing roller  141 . In  FIGS. 2 and 3 , the reference numeral  103  indicates a toner concentration sensor that detects the toner concentration of the developer  4  accommodated inside the device housing  140 . 
     Further, as illustrated in  FIG. 3 , at both end portions of the partition wall  152  along the longitudinal direction, a first passage  154  and a second passage  155  that transport the developer  4  between the supply transport member  142  and the agitation transport member  143  are provided, respectively. Further, the inner end portion of the agitation transport member  143  along the axial direction extends to protrude toward the rear surface of the device housing  140 . A supply unit  156  having a substantially cylindrical shape is provided in the extending portion of the agitation transport member  143 . Further, in the supply unit  156  having a cylindrical shape, a supply port  157  through which the developer  4  of the corresponding color is supplied from the toner cartridge  145 (Y, M, C, K) is opened. The supply port  157  is covered with a shutter member (not illustrated) to be opened/closed. 
     In the meantime, in the developing device  14 , the toner in the developer  4  accommodated inside the device housing  140  is consumed by developing the electrostatic latent image formed on the surface of the photoconductor drum  11 , and is gradually decreased. 
     As a result, in the image forming apparatus  1 , the pixel amount of the image (electrostatic latent image) formed on the surface of the photoconductor drum  11  of each image forming device  10 (Y, M, C, K) by the exposure device  13  is counted and the toner concentration of the developer  4  accommodated in the developing device  14  is directly or indirectly measured. Then, the toner amount supplied from the toner cartridge  145 (Y, M, C, K) via a toner supply device (not illustrated) to the developing device  14  is controlled based on the pixel amount of the image (electrostatic latent image) formed on the surface of the photoconductor drum  11  and the toner concentration of the developer  4  in the developing device  14 . 
     At this time, when the image (electrostatic latent image) formed on the surface of each photoconductor drum  11  has a normal image density, as illustrated in  FIG. 4 , the cumulative consumption amount of the toner is within the range controlled by a toner concentration control operation, and thus, the decrease in the image density caused by the insufficient supply of the toner to the developing device  14  does not occur. 
     In  FIGS. 4 and 5 , cycle up &amp; down indicated represents an operation in which, when a series of image forming operations is started in the image forming apparatus  1 , the photoconductor drum  11  or the developing device  14  is driven, and the surface of the photoconductor drum  11  is charged to a required charging potential by the charging device  12 , and a developing bias voltage is applied to the developing roller  141  of the developing device  14 . 
     Further, when a series of image forming operations is ended in the image forming apparatus  1 , the photoconductor drum  11  or the developing device  14  is stopped, and when the photoconductor drum  11  or the developing device  14  is stopped, the charging of the surface of the photoconductor drum  11  by the charging device  12  or the application of the developing bias voltage to the developing roller  141  of the developing device  14  is stopped. 
     When a series of image forming operations is started or ended in this image forming apparatus  1 , when the surface potential of the photoconductor drum  11  is suddenly raised or lowered by the charging device  12  or when the developing bias voltage applied to the developing roller  141  of the developing device  14  is suddenly raised or lowered, due to the potential difference between the surface potential of the photoconductor drum  11  and the developing bias voltage of the developing roller  141 , a technical problem called bead carry-over occurs in which carriers in the developer  4  adhering to the developing roller  141  adhere to the surface of the photoconductor drum  11 . 
     Therefore, in the image forming apparatus  1 , when a series of image forming operations is started or ended, the carriers in the developer  4  are prevented or suppressed from adhering to the surface of the photoconductor drum  11  by raising or lowering the surface potential of the photoconductor drum  11  and the developing bias voltage of the developing roller  141  with a required potential difference. 
     However, as described above, in the image forming apparatus  1 , when a series of image forming operations is started or ended, the carriers in the developer  4  may be prevented or suppressed from adhering to the surface of the photoconductor drum  11  by raising or lowering the surface potential of the photoconductor drum  11  and the developing bias voltage of the developing roller  141  with a required potential difference. On the other hand, the toner charged in the polarity opposite to the carrier is transferred and adhering to the surface of the photoconductor drum  11 , and thus, the toner in the developing device  14  is consumed. 
     As a result, in the image forming apparatus  1 , when the image (electrostatic latent image) formed on the surface of each photoconductor drum  11  is an image having a low image density lower than a normal image density, as illustrated in  FIG. 5 , due to the toner consumed at the start or end of a series of image forming operations, the cumulative consumption amount of the toner is out of the range controlled by the toner concentration control operation at a low image density, and as a result, there is a technical problem of causing a decrease in image density. 
     Therefore, the image forming apparatus  1  according to the first exemplary embodiment includes a developer replenishing unit that supplies the developer to the developing unit, and predicts, in advance, an amount of developer consumed by the image carrier at a start or an end of image formation, or both the start and the end of the image formation apart from developer consumed in the image formation, to replenish the predicted amount of the developer. 
     Further, in the image forming apparatus  1  according to the first exemplary embodiment, the developer replenishing unit predicts the amount of the developer consumed by the image carrier at the start or end of the image formation or both the start and the end of the image formation apart from the developer consumed in the image formation, in accordance with the characteristics of the developer, to replenish the predicted amount of the developer. 
     Further, in the image forming apparatus  1  according to the first exemplary embodiment, when the density of the image carried by the image carrier is equal to or less than a predetermined density, the developer replenishing unit predicts, in advance, the amount of the developer consumed by the image carrier apart from the developer consumed in the image formation to replenish the predicted amount of the developer. 
       FIG. 6  is a block diagram illustrating a controller  100  of the image forming apparatus  1  according to the first exemplary embodiment. 
     In  FIG. 6 , the reference numeral  100  indicates the controller of the image forming apparatus  1 , the reference numeral  10 (Y, M, C, K) indicates each of the image forming devices of yellow (Y), magenta (M), cyan (C), and black (K), the reference numeral  30  indicates the sheet transport device, the reference numeral  101   a  indicates a toner replenishing screw that transports toner of a toner replenishing device  101  that replenishes the developing device  14 (Y, M, C, K) with toner from each of the toner cartridges  145 (Y, M, C, K) of yellow (Y), magenta (M), cyan (C), and black (K), the reference numeral  102  indicates an image formation counter that counts the number of recording sheets  5 , which is the number of images formed in the image forming apparatus  1 , the reference numeral  103  indicates a toner concentration sensor that detects the toner concentration in the developer  4  provided in the developing device  14  of each of the image forming devices  10 (Y, M, C, K), and the reference numeral  104  indicates a dot counter device that counts the dot, which is an amount of pixels (number of pixels) of the image formed on the surface of the photoconductor drum  11  of each of the image forming devices  10 (Y, M, C, K). 
     Effect of Image Forming Apparatus 
     In the image forming apparatus  1  according to the first exemplary embodiment, as described in the following, in an image density control operation that supplies toner to the inside of the developing device to control an image density, the decrease in the image density caused by the toner that is consumed by adhering to the surface of the image carrier by the potential difference between the image carrier and the developer carrier at the start or end of the image forming operation is prevented. 
     That is, in the image forming apparatus  1  according to the first exemplary embodiment, as illustrated in  FIG. 7 , when command information (job) for requesting a full color or a monochrome image forming operation (print) from a user interface or a printer driver (both are not illustrated) is received (step  101 ), the controller  100  adds (cumulatively counting) the number of pixels, which is the image information of the received print command (step  102 ). 
     Here, the number of pixels, which is the image information of the received print command, is, for example, the number of pixels in consideration of a desired resolution (for example, 400 dpi or 600 dpi, or 1,200 dpi), and a desired tonality (for example, 256 tones), based on the image information of the print command on the A4 size recording sheet  5 . 
     Subsequently, the controller  100  determines whether the print command is for full color or monochrome (step  103 ), and when it is determined to full color, pixels corresponding to fogging are added to each of the image forming devices  10 (Y, M, C, K) of yellow (Y), magenta (M), cyan (C), and black (K) (step  104 ). 
     Here, pixels corresponding to fogging represents the toner that is predicted to be consumed at the start or the end of a series of jobs (image forming operations) as the number of pixels. The addition of the pixels corresponding to fogging is performed for each developing device  14  of each of the image forming devices  10 (Y, M, C, K) of yellow (Y), magenta (M), cyan (C), and black (K) used in the image determined to be a full-color image. Then, the controller  100  calculates the toner replenishment time (step  105 ), and respectively stores the toner replenishment time, which is the calculated result, in a buffer as an example of a storage unit (not illustrated) provided in each developing device  14  of yellow (Y), magenta (M), cyan (C), and black (K) (step  106 ). 
     When it is determined to be full color, the controller  100  executes the above-described processing for each color of yellow (Y), magenta (M), cyan (C), and black (K). 
     Meanwhile, when it is determined that the print command is for monochrome, the controller  100  adds the pixel corresponding to fogging to black (K) (step  107 ), calculates the toner replenishment time (step  108 ), stores the toner replenishment time, which is the calculated result, in the buffer as an example of a storage unit (not illustrated) provided in the developing device  14  of black (K) (step  109 ), and ends the processing. 
     The controller  100  executes the above processing until the print command of the example is ended. 
     Further, the controller  100  executes a calculation operation of the toner replenishment time according to the toner concentration in the developing device  14 , apart from a calculation operation of the toner replenishment time according to the number of pixels of the image described above. The calculation operation of the toner replenishment time according to the toner concentration in the developing device  14  may be executed at a timing different from the calculation operation of the toner replenishment time according to the number of pixels of the image, or at the same timing as the calculation operation of the toner replenishment time according to the number of pixels of the image. 
     When the calculation operation of the toner replenishment time according to the toner concentration in the developing device  14  is executed, as illustrated in  FIG. 8 , the controller  100  detects the toner concentration of the developer  4  accommodated in the device housing  140  for each of the developing devices  14  of yellow (Y), magenta (M), cyan (C), and black (K) by the toner concentration sensor  103  (step  201 ). 
     Subsequently, the controller  100  respectively calculates the toner replenishment time for replenishing each of the developing devices  14  of yellow (Y), magenta (M), cyan (C), and black (K) based on the toner concentration in each detected developing device  14  (step  202 ), and then, stores the calculated toner replenishment time for replenishing each developing device  14  in the buffer (not illustrated) provided corresponding to each developing device  14  (step  203 ), and ends the processing. 
     Then, as illustrated in  FIG. 9 , when it is determined to be a predetermined toner replenishment timing such as the start or the end of the print operation, or when an image is formed on the required number of recording sheets  5 , the controller  100  executes the toner replenishing operation. 
     In the toner replenishing operation, the controller  100  reads and calculates the toner replenishment time according to the number of pixels of the image from the buffer (not illustrated) provided corresponding to each of the developing devices  14  of yellow (Y), magenta (M), cyan (C), and black (K) (step  301 ). 
     Subsequently, the controller  100  reads and calculates the toner replenishment time corresponding to the toner concentration of each of the developing devices  14  of yellow (Y), magenta (M), cyan (C) and black (K) from the buffer (not illustrated) (step  302 ). 
     Then, the controller  100  adds the toner replenishment time according to the number of pixels of the image read from the buffer (not illustrate) provided corresponding to each of the developing devices  14  of yellow (Y), magenta (M), cyan (C), and black (K), and the toner replenishment time corresponding to the toner concentration of each of the developing devices  14  of yellow (Y), magenta (M), cyan (C), and black (K) to determine the toner replenishment time for replenishing each of the developing devices  14  (step  302  and step  304 ). 
     The controller  100  determines whether it is the timing at which the toner replenishing operation is allowed (step  305 ), and, when it is determined to be the timing at which the toner replenishing operation is allowed, executes the toner replenishing operation (step  306 ). 
     Here, as the determining whether or not it is the timing at which the toner replenishing operation is allowed, since the image density may fluctuate when the toner is replenished to the developing device  14  while performing the image forming operation, for example, in a case where any one of the image forming devices  10  of yellow (Y), magenta (M), cyan (C), and black (K) is performing the image forming operation, a processing that does not allow the toner replenishing operation is performed. 
     Meanwhile, when it is determined that it is not the timing at which the toner replenishing operation is allowed, the controller  100  ends the processing without executing the toner replenishing operation. 
     As described above, in the image forming apparatus  1  configured as described above, when the toner replenishment time for supplying to each of the developing devices  14  of yellow (Y), magenta (M), cyan (C), and black (K) is calculated according to the number of pixels of the image, it is considered adding the pixels corresponding to fogging, which is the toner to be consumed, due to the start and the stop of the print job. As a result, the image forming apparatus  1  executes the toner replenishing operation including the toner to be consumed, due to the start and the stop of the print job. 
     The image forming apparatus  1  does not necessarily need to add the pixels corresponding to fogging, which is the toner to be consumed, due to both the start and the stop of the print job. For example, in a case where there is a difference in the toner amount consumed due to the start and the stop of the print job, and one is largely smaller than the other one, the image forming apparatus  1  may add the pixels corresponding to fogging, which is the toner to be consumed, due to one of the start and the stop of the print job. 
     Therefore, as illustrated in  FIG. 10 , in the above image forming apparatus  1 , even in a case where the image forming operation with a low image density is continuously executed, the toner is replenished by predicting (assuming) the toner to be consumed due to the start and the stop of the print job, and thus, it is possible to prevent or suppress the decrease in image density due to insufficient replenishment of the toner. 
     Second Exemplary Embodiment 
       FIG. 11  is a block diagram illustrating a controller of an image forming apparatus according to a second exemplary embodiment of the present disclosure. 
     As illustrated in  FIG. 11 , the image forming apparatus  1  according to the second exemplary embodiment includes an environmental sensor  110  that detects temperature and humidity as an example of an environment detector that detects environmental conditions in which the image forming apparatus  1  is provided. The developer supply unit corrects the amount of the developer consumed apart from the developer consumed in the image formation in accordance with the detection result of the environmental sensor  110 . 
     That is, the controller  100  of the image forming apparatus  1  according to the second exemplary embodiment detects the temperature and the humidity of the environment in which the image forming apparatus  1  is provided detected by the environmental sensor  110 . 
     Then, the controller  100  determines whether it is normal temperature and normal humidity, high temperature and high humidity, or low temperature and low humidity, based on the temperature and the humidity of the environment detected by the environmental sensor  110 . 
     When it is determined that the temperature is high and the humidity is high based on the temperature and the humidity of the environment detected by the environmental sensor  110 , in  FIG. 7 , when the pixels corresponding to fogging are added, the controller  100  changes the added value of the pixels corresponding to fogging to a larger value than the normal (normal temperature and normal humidity) value. 
     As described above, in the image forming apparatus  1  according to the second exemplary embodiment, when it is determined that the temperature and the humidity in the environment in which the image forming apparatus  1  is provided, which is detected by the environmental sensor  110 , are high temperature and high humidity, the added value of the pixels corresponding to fogging is changed to a larger value than the normal value (normal temperature and normal humidity). Therefore, even when the fogging toner adhering to the surface of the photoconductor drum  11  at the start and the end of the print operation and consumed at high temperature and high humidity increases, it is possible to replenish the toner corresponding to the increase in the fogging toner. 
     Since other configurations and operations are the same as those in the first exemplary embodiment, the description thereof is omitted. 
     Third Exemplary Embodiment 
       FIG. 12  is a block diagram illustrating a controller of an image forming apparatus according to a third exemplary embodiment of the present disclosure. 
     As illustrated in  FIG. 12 , the image forming apparatus  1  according to the third exemplary embodiment includes a first counting device  120  that cumulatively counts the number of rotations of the developing roller  141 , as an example of a first usage history detector that detects a usage history of the developing unit. 
     The first counting device  120  does not necessarily count the number of rotations of the developing roller  141  directly, and may indirectly count the number of rotations of the developing roller  141  based on the size of the image developed by the developing device  14 . 
     The controller  100  determines whether or not the number of rotations of the developing roller  141  is equal to or less than the required threshold value by the first counting device  120 , and when it is determined that the number of rotations of the developing roller  141  exceeds the required threshold value, changes the added value of the pixels corresponding to fogging, which corresponds to the normal case where the number of rotations of the developing roller  141  is equal to or less than the required threshold value, to a larger value than the normal value, when the pixels corresponding to fogging are added in  FIG. 7 . 
     As described above, in the image forming apparatus  1  according to the third exemplary embodiment, the number of rotations of the developing roller  141  is cumulatively counted by the first counting device  120 , and the added value of the pixels corresponding to fogging, which corresponds to the normal case where the number of rotations of the developing roller  141  is equal to or less than the required threshold value, is changed to a larger value than the normal value. Therefore, even when the number of rotations of the developing roller  141  exceeds the required threshold value and the developer  4  deteriorates, and the amount of the fogging toner consumed increases, it is possible to replenish the toner corresponding to the increase in the fogging toner. 
     Since other configurations and operations are the same as those in the first exemplary embodiment, the description thereof is omitted. 
     Fourth Exemplary Embodiment 
       FIG. 13  is a block diagram illustrating a controller of an image forming apparatus according to a fourth exemplary embodiment of the present disclosure. 
     The image forming apparatus  1  according to the fourth exemplary embodiment includes a second usage history detector that detects the usage history of the image carrier. The developer supply unit corrects the amount of the developer consumed apart from the developer consumed in the image formation in accordance with the detection result of the second usage history detector. 
     Further, in the image forming apparatus  1  according to the fourth exemplary embodiment, the developer supply unit corrects the amount of the developer consumed apart from the developer consumed in the image formation to be increased as the detection result of the second usage history detector increases. 
     That is, as illustrated in  FIG. 13 , the image forming apparatus  1  according to the fourth exemplary embodiment includes a second counting device  130  that cumulatively counts the number of rotations of the each photoconductor drum  11 , as an example of the second usage history detector that detects the usage history of each photoconductor drum  11  serving as an image carrier. 
     The second counting device  130  does not necessarily count the number of rotations of each photoconductor drum  11  directly, and may indirectly count the number of rotations of each photoconductor drum  11  based on the size of the recording sheet  5  on which an image is formed by the photoconductor drum  11 . 
     The controller  100  determines whether or not the number of rotations of the photoconductor drum  11  is equal to or less than the required threshold value by the second counting device  130 , and when it is determined that the number of rotations of the photoconductor drum  11  exceeds the required threshold value, in  FIG. 7 , changes the added value of the pixels corresponding to fogging, which corresponds to the normal case where the number of rotations of the photoconductor drum  11  is equal to or less than the required threshold value, to a larger value than the normal value, when the pixels corresponding to fogging are added. 
     As described above, in the image forming apparatus  1  according to the fourth exemplary embodiment, the number of rotations of the photoconductor drum  11  is cumulatively counted by the second counting device  130 , and the added value of the pixels corresponding to fogging, which corresponds to the normal case where the number of rotations of the photoconductor drum  11  is equal to or less than the required threshold value, is changed to a larger value than the normal value. Therefore, even when the number of rotations of the photoconductor drum  11  exceeds the required threshold value and the photoconductive layer of the photoconductor drum  11  is worn, and the amount of the fogging toner consumed increases, it is possible to replenish the toner corresponding to the increase in the fogging toner. 
     Since other configurations and operations are the same as those in the first exemplary embodiment, the description thereof is omitted. 
     In the above exemplary embodiments, the image forming apparatus that forms a full-color image as an example of an image forming apparatus has been described. It is noted that the present disclosure is not limited thereto. Of course, an image forming apparatus that forms a black-and-white image may be used as the image forming apparatus. 
     The foregoing description of the exemplary embodiments of the present disclosure has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure to the precise forms disclosed. Obviously, many modifications and variations will be apparent to practitioners skilled in the art. The embodiments were chosen and described in order to best explain the principles of the disclosure and its practical applications, thereby enabling others skilled in the art to understand the disclosure for various embodiments and with the various modifications as are suited to the particular use contemplated. It is intended that the scope of the disclosure be defined by the following claims and their equivalents.