Patent Publication Number: US-11644779-B2

Title: Image forming apparatus with toner density adjustment control

Description:
INCORPORATION BY REFERENCE 
     This application is based upon and claims the benefit of priority from the corresponding Japanese Patent Application No. 2020-152070 filed on Sep. 10, 2020, the entire contents of which are incorporated herein by reference. 
     BACKGROUND 
     The present disclosure relates to an image forming apparatus. 
     An image forming apparatus such as a printer or a copier adopting an electrophotographic system forms an image on a recording medium such as paper based on image data. For the purpose of stabilizing the image quality of a formed image, there is a technique of detecting a developing current flowing into a developing roller when a print check pattern is formed on a photosensitive drum in a developing step, and controlling a charging potential and a developing bias based on the detection result. 
     However, when the charge amount of the toner used in the image forming apparatus varies depending on the environment or time, the toner adhesion amount of the toner image formed on the photosensitive drum varies, and the image density of the output image is not stable in some cases. 
     SUMMARY 
     An image forming apparatus according to this disclosure includes a an image carrier, a developing device, a control unit, and a density measuring unit. 
     An electrostatic latent image is formed on the surface of an image carrier. 
     A developing device supplies toner to the image carrier and develops the electrostatic latent image formed on the image carrier to form a toner image. 
     A control unit controls an applied voltage applied to the developing device when the toner image is developed by the developing device. 
     A density measuring unit measures the toner density of the toner image. 
     The developing device forms a plurality of first patch toner images for measuring toner density. 
     The control unit controls the applied voltage to a different applied voltage, respectively, when the developing device forms the plurality of first patch toner images. 
     The density measuring unit measures the toner density of the plurality of first patch toner images formed by the developing device. 
     The control unit calculates a relationship between the toner density of the plurality of first patch toner images measured by the density measuring unit and the applied voltage applied to the developing device when the plurality of first patch toner images are formed, and adjusts the applied voltage based on a calculation result. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a diagram illustrating an example of a configuration of image forming apparatus  1 . 
         FIG.  2    is a diagram illustrating an example of a configuration of the developing device  64 . 
         FIG.  3    is a diagram showing a plurality of first patch images formed on the sheet of paper p. 
         FIG.  4    is a graph showing the correlation between the toner density and the developing bias voltage in the present embodiment. 
         FIG.  5    is a graph obtained by adding a point at which a desired toner density is obtained to the graph of  FIG.  4   ; 
         FIGS.  6 A and  6 B  are views focusing on the correlation L 1  in the graph of  FIG.  4   . 
         FIGS.  7 A and  7 B  are views focusing on the correlation L 3  in the graph of  FIG.  4   . 
         FIG.  8    is a diagram showing the correlation L 3  when the toner density CTD 4  is lower than the toner density CTD 3 . 
         FIG.  9    is a diagram showing the second patch toner image for predicting the toner charge amount in the present embodiment. 
         FIG.  10    is a flowchart showing the toner charge amount prediction process in the present embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, embodiments of the present disclosure will be described with reference to the drawings. In the drawings, the same or corresponding portions are denoted by the same reference numerals, and description thereof will not be repeated. 
     Referring to  FIG.  1   , the configuration of the image forming apparatus  1  according to the embodiment of the present disclosure will be described.  FIG.  1    is a diagram showing an example of image forming apparatus  1 . The image forming apparatus  1  is, for example, a tandem color printer. 
     As shown in  FIG.  1   , the image forming apparatus  1  includes an operation unit  2 , a paper feed unit  3 , a conveyance unit  4 , a toner replenishing unit  5 , an image forming unit  6 , a transfer unit  7 , a fixing unit  8 , a discharge unit  9 , and a control unit  10 . 
     The operation unit  2  receives an instruction from a user. Upon receiving an instruction from the user, the operation unit  2  transmits a signal indicating the instruction from the user to the control unit  10 . The operation unit  2  includes a liquid crystal display  21  and a plurality of operation keys  22 . The liquid crystal display  21  displays, for example, various processing results. The operation keys  22  include, for example, a ten key and a start key. When the instruction indicating the execution of the image forming process is input, the operation unit  2  transmits a signal indicating the execution of the image forming process to the control unit  10 . As a result, the image forming operation by image forming apparatus  1  is started. 
     The paper feed unit  3  includes a paper feed cassette  31  and a paper feed roller group  32 . The paper feed cassette  31  can accommodate a plurality of sheets of paper P. The paper feed roller group  32  feeds the sheets of paper P stored in the paper feed cassette  31  one by one to the conveyance unit  4 . The sheet of paper p is an example of a recording medium. 
     The conveyance unit  4  includes a roller and a guide member. The conveyance unit  4  extends from the paper feed unit  3  to the discharge unit  9 . The conveyance unit  4  conveys the sheet of paper p from the paper feed unit  3  to the discharge unit  9  via the image forming unit  6  and the fixing unit  8 . 
     The toner replenishing unit  5  replenishes toner to the image forming unit  6 . The toner replenishing unit  5  includes a first mounting portion  51 Y, a second mounting portion  51 C, a third mounting portion  51 M, and a fourth mounting portion  51 K. The toner replenishing unit  5  is an example of a developer replenishing portion. The toner is an example of a developer. 
     The first toner container  52 Y is mounted on the first mounting portion  51 Y. Similarly, the second toner container  52 C is mounted on the second mounting portion  51 C, the third toner container  52 M is mounted on the third mounting portion  51 M, and the fourth toner container  52 K is mounted on the fourth mounting portion  51 K. The configurations of the first mounting portion  51 Y to the fourth mounting portion  51 K are the same except that the types of toner containers to be mounted are different. Therefore, the first mounting portion  51 Y to the fourth mounting portion  51 K may be collectively referred to as a “mounting portion  51 ”. 
     Toner is stored in each of the first toner container  52 Y, the second toner container  52 C, the third toner container  52 M, and the fourth toner container  52 K. In the present embodiment, the first toner container  52 Y contains yellow toner. The second toner container  52 C contains cyan toner. The third toner container  52 M contains magenta toner. The fourth toner container  52 K contains the black toner. 
     The image forming unit  6  includes an exposure device  61 , a first image forming unit  62 Y, a second image forming unit  62 C, a third image forming unit  62 M, and a fourth image forming unit  62 K. 
     Each of the first image forming unit  62 Y to the fourth image forming unit  62 K includes a charging device  63 , a developing device  64 , and a photosensitive drum  65 . The photosensitive drum  65  is an example of an image carrier. 
     The charging device  63  and the developing device  64  are arranged along the circumferential surface of the photosensitive drum  65 . In the present embodiment, the photosensitive drum  65  rotates in a direction (clockwise) indicated by an arrow R 1  in  FIG.  1   . 
     The charging device  63  uniformly charges the photosensitive drum  65  to a predetermined polarity by discharging. In the present embodiment, the charging device  63  positively charges the photosensitive drum  65 . The exposure device  61  irradiates the charged photosensitive drum  65  with laser light. As a result, an electrostatic latent image is formed on the surface of the photosensitive drum  65 . 
     The developing device  64  develops the electrostatic latent image formed on the surface of the photosensitive drum  65  to form a toner image. The developing device  64  is replenished with toner from the toner replenishing unit  5 . The developing device  64  supplies the toner replenished from the toner replenishing unit  5  to the surface of the photosensitive drum  65 . As a result, a toner image is formed on the surface of the photosensitive drum  65 . 
     In the present embodiment, the developing device  64  included in the first image forming unit  62 Y is connected to the first mounting portion  51 Y. Therefore, the developing device  64  of the first image forming unit  62 Y is replenished with yellow toner. Thus, a yellow toner image is formed on the surface of the photosensitive drum  65  of the first image forming unit  62 Y. 
     The developing device  64  included in the second image forming unit  62 C is connected to the second mounting portion  51 C. Therefore, the developing device  64  of the second image forming unit  62 C is replenished with cyan toner. Thus, a cyan toner image is formed on the surface of the photosensitive drum  65  of the second image forming unit  62 C. 
     The developing device  64  included in the third image forming unit  62 M is connected to the third mounting portion  51 M. Therefore, the developing device  64  of the third image forming unit  62 M is replenished with magenta toner. Thus, a magenta toner image is formed on the surface of the photosensitive drum  65  of the third image forming unit  62 M. 
     The developing device  64  included in the fourth image forming unit  62 K is connected to the fourth mounting portion  51 K. Therefore, the developing device  64  of the fourth image forming unit  62 K is replenished with black toner. Thus, a black toner image is formed on the surface of the photosensitive drum  65  of the fourth image forming unit  62 K. 
     The transfer unit  7  transfers the toner images formed on the surfaces of the photosensitive drums  65  of the first image forming unit  62 Y to the fourth image forming unit  62 K onto the sheet of paper p in an overlapping manner. In the present embodiment, the transfer unit  7  transfers the toner images onto the sheet of paper p in overlapping manner by a secondary transfer method. Specifically, the transfer unit  7  includes four primary transfer rollers  71 , an intermediate transfer belt  72 , a driving roller  73 , a driven roller  74 , a secondary transfer roller  75 , and a density sensor  76 . 
     The intermediate transfer belt  72  is an endless belt stretched around four primary transfer rollers  71 , a driving roller  73 , and a driven roller  74 . The intermediate transfer belt  72  is driven in accordance with the rotation of the driving roller  73 . In  FIG.  1   , the intermediate transfer belt  72  rotates counterclockwise. The driven roller  74  is rotationally driven in accordance with the driving of the intermediate transfer belt  72 . 
     The first image forming unit  62 Y to the fourth image forming unit  62 K are disposed to face the lower surface of the intermediate transfer belt  72  along the driving direction D of the lower surface of the intermediate transfer belt  72 . In the present embodiment, the first image forming unit  62 Y to the fourth image forming unit  62 K are arranged in the order of the first image forming unit  62 Y to the fourth image forming unit  62 K from the upstream side to the downstream side in the driving direction D of the lower surface of the intermediate transfer belt  72 . 
     Each primary transfer roller  71  is disposed to face each photosensitive drum  65  via the intermediate transfer belt  72 , and is pressed toward each photosensitive drum  65 . Therefore, the toner images formed on the surfaces of the photosensitive drums  65  are sequentially transferred onto the intermediate transfer belt  72 . In the present embodiment, a yellow toner image, a cyan toner image, a magenta toner image, and a black toner image are transferred onto the intermediate transfer belt  72  so as to overlap each other in this order. Hereinafter, the toner image in which the yellow toner image, the cyan toner image, the magenta toner image, and the black toner image are superimposed may be referred to as a “laminated toner image”. 
     The secondary transfer roller  75  is disposed to face the driving roller  73  via the intermediate transfer belt  72 . The secondary transfer roller  75  is pressed against the driving roller  73 . As a result, a transfer nip is formed between the secondary transfer roller  75  and the driving roller  73 . When the sheet of paper p passes through the transfer nip, the laminated toner image on the intermediate transfer belt  72  is transferred to the sheet of paper p. In the present embodiment, the yellow toner image, the cyan toner image, the magenta toner image, and the black toner image are transferred onto the sheet of paper p in this order from the upper layer to the lower layer. The sheet of paper p on which the laminated toner image is transferred is conveyed toward the fixing unit  8  by the conveyance unit  4 . 
     The density sensor  76  is disposed to face the intermediate transfer belt  72  in a position more downstream than the first image forming unit  62 Y to the fourth image forming unit  62 K, and measures the density (toner density) of the laminated toner image formed on the photosensitive drum  65 . The density sensor  76  may measure the density of the laminated toner image on the intermediate transfer belt  72  or the density of the toner image fixed on the sheet of paper p. 
     The fixing unit  8  includes a heating member  81  and a pressing member  82 . The heating member  81  and the pressing member  82  are disposed to face each other to form a fixing nip. The sheet of paper p conveyed from the image forming unit  6  passes through the fixing nip, and is pressurized while being heated at a predetermined fixing temperature. As a result, the laminated toner image is fixed to the sheet of paper p. The sheet of paper p is conveyed from the fixing unit  8  toward the discharge unit  9  by the conveyance unit  4 . 
     The discharge unit  9  includes a discharge roller pair  91  and a discharge tray  93 . The discharge roller pair  91  conveys the sheet of paper p to the discharge tray  93  via the discharge port  92 . The discharge port  92  is formed on top of the image forming apparatus  1 . 
     The control unit  10  controls the operation of each unit of the image forming apparatus  1 . The control unit  10  includes a processor  11  and a storage unit  12 . The processor  11  includes, for example, a CPU (Central Processing Unit). The storage unit  12  includes a memory such as a semiconductor memory, and may include a HDD (Hard Disk Drive). The storage unit  12  stores a control program. The processor  11  controls the operation of the image forming apparatus  1  by executing the control program. 
     Next, the configuration of the developing device  64  will be described in detail with reference to  FIG.  2   .  FIG.  2    shows an example of a configuration of the developing device  64 . Specifically,  FIG.  2    shows the first developing device  64 Y of the first image forming unit  62 Y. In  FIG.  2   , the photosensitive drum  65  is shown by a two-dot chain line for ease of understanding. In the present embodiment, the first developing device  64 Y develops the electrostatic latent images formed on the surfaces of the photosensitive drums  65  by a two component developing method. As already described with reference to  FIG.  1   , the developing vessel  640  of the first developing device  64 Y is connected to the first toner container  52 Y. Therefore, the developing vessel  640  of the first developing device  64 Y is replenished with the yellow toner through the toner replenishing port  640   h.    
     As shown in  FIG.  2   , the first developing device  64 Y includes a developing roller  641 , a first stirring screw  643 , a second stirring screw  644 , and a blade  645  inside a developing vessel  640 . Specifically, the developing roller  641  is disposed to face the second stirring screw  644 . The blade  645  is disposed to face the developing roller  641 . 
     The developing vessel  640  is partitioned into a first stirring chamber  640   a  and a second stirring chamber  640   b  by a partition wall  640   c . The partition wall  640   c  extends in the axial direction of the developing roller  641 . The first stirring chamber  640   a  and the second stirring chamber  640   b  communicate with each other outside both ends of the partition wall  640   c  in the longitudinal direction. 
     A first stirring screw  643  is disposed on the first stirring chamber  640   a . The magnetic carriers are accommodated in the first stirring chamber  640   a . Non-magnetic toner is supplied to the first stirring chamber  640   a  through the toner replenishing port  640   h . In the example shown in  FIG.  2   , the yellow toner is supplied to the first stirring chamber  640   a.    
     A second stirring screw  644  is disposed on the second stirring chamber  640   b . A magnetic carrier is accommodated in the second stirring chamber  640   b.    
     The yellow toner is stirred by the first stirring screw  643  and the second stirring screw  644  to be mixed with the carrier. As a result, a two component developer including the carrier and the yellow toner is formed. Since the two component developer is an example of the developer, the two component developer may occasionally be abbreviated as “developer” hereinafter. 
     The first stirring screw  643  and the second stirring screw  644  circulate and stir the developer between the first stirring chamber  640   a  and the second stirring chamber  640   b . As a result, the toner is charged to a predetermined polarity. In the present embodiment, the toner is positively charged. 
     The developing roller  641  includes a non-magnetic rotating sleeve  641   a  and a magnet body  641   b . The magnet body  641   b  is fixedly arranged inside the rotating sleeve  641   a . The magnet body  641   b  includes a plurality of magnetic poles. The developer is attracted to the developing roller  641  by the magnetic force of the magnet body  641   b . As a result, a magnetic brush is formed on the surface of the developing roller  641 . 
     In the present embodiment, the developing roller  641  rotates in a direction indicated by an arrow R 2  (counterclockwise) in  FIG.  2   . The developing roller  641  conveys the magnetic brush to a position facing the blade  645  by rotating. The blade  645  is disposed so that a gap is formed between the blade  645  and the developing roller  641 . Thus, the thickness of the magnetic brush is defined by the blades  645 . The blade  645  is disposed upstream of a position where the developing roller  641  and the photosensitive drum  65  face each other in the rotation direction of the magnetic roller  642 . 
     A predetermined voltage (developing bias voltage) is applied to the developing roller  641  under the control of the control unit  10 . As a result, the developer layer formed on the surface is conveyed to a position facing the photosensitive drum  65 , and the toner in the developer adheres to the photosensitive drum  65 . 
     For example, when an instruction indicating execution of the image forming process is input to image forming apparatus  1  by the user, the control unit  10  controls the image forming unit  6  to start the image forming operation of each unit included in the image forming apparatus  1 . To be specific, the control unit  10  controls the charging device  63 , the first developing device  64 Y, the developing power supply  648 , and the exposure device  61 . 
     The charging device  63  charges the surfaces of the photosensitive drums  65  to a predetermined charging potential (surface potential V 0 ) under the control of the control unit  10 . Specifically, when the charging device  63  applies a charging bias to the photosensitive drum  65 , the surfaces of the photosensitive drum  65  are charged to a surface potential V 0 . 
     The developing power supply  648  applies a developing bias voltage to the developing roller  641  under the control of the control unit  10 . The developing bias voltage includes a DC component and an AC component.  FIG.  2    shows a case where a developing bias voltage, in which the magnitude (Vdc 1 ) of DC components is larger than the surface potential V 0 , is applied to the developing roller  641 . The bias voltage does not have to include an AC component. 
     Under the control of the control unit  10 , the exposure device  61  emits laser light to the photosensitive drum  65  whose surface potential V 0  has been charged by the charging device  63 . As a result, an electrostatic latent image is formed on the surface of the photosensitive drum  65 . The charging potential V 1  of the portion where the electrostatic latent images are formed on the surfaces of the photosensitive drums  65  becomes smaller than the surface potential V 0 . 
     When the electrostatic latent images are formed on the surfaces of the photosensitive drums  65 , the first developing devices  64 Y develop the electrostatic latent images formed on the surfaces of the photosensitive drums  65  under the control of the control unit  10 . 
     At this time, the toner developed on the photosensitive drum  65  is measured as a developing current Id. That is, the developing current Id indicates the amount of toner moved from the developing roller  641  to the photosensitive drum  65  according to the difference (contrast voltage) between the surface potential V 0  and the charging potential V 1 . 
     The configuration of the developing device  64  included in each of the first image forming unit  62 Y to the fourth image forming unit  62 K is substantially the same except that the type of toner replenished from the toner replenishing unit  5  is different. Therefore, description of the configuration of the second developing device  64 C to the fourth developing device  64 K included in the second image forming unit  62 C to the fourth image forming unit  62 K will be omitted. 
     Here, in a case where the contrast voltage by the discharge and the exposure is constant and the charge amount of the toner is always constant, the amount of the toner moving from the developing roller  641  to the photosensitive drum  65  is constant, and thus the toner density measured by the density sensor  76  is constant. 
     However, for example, when the photosensitive drums  65  made of different materials from each other are irradiated with laser light having the same exposure energy, the contrast voltages are different from each other. Specifically, in the photosensitive drum  65  made of a-Si (amorphous silicon), the voltage of the contrast voltage is likely to change greatly as compared with the photosensitive drum  65  made of an organic photosensitive member (OPC). 
     Further, since the charge amount of the toner is not always constant due to environmental conditions or the like, even when the contrast voltage is the same, the amount of the toner moving from the developing roller  641  to the photosensitive drum  65  is not always constant. 
     In order to measure a constant toner density by the density sensor  76 , for example, the present embodiment has a developing bias voltage adjustment mode for adjusting the developing bias voltage applied to the developing roller  641 . The developing bias voltage adjustment mode is started, for example, when an instruction indicating execution of the developing bias voltage adjustment mode is input by the user between image forming processes. 
     [Adjustment of Developing Bias Voltage] 
     When the developing bias voltage adjustment mode is started, the image forming unit  6  forms a plurality of first patch images on the sheet of paper p. Specifically, the developing device  64  forms a plurality of first patch toner images. The first patch toner image is, for example, a quadrangle having four 10 mm sides. With such a size, the toner consumption can be suppressed. 
     Next, the first patch image and the first patch toner image will be described with reference to  FIG.  3   .  FIG.  3    is a diagram showing a plurality of first patch images formed on the sheet of paper p. 
     The developing device  64  forms the first patch toner images S 1  to S 4 . When the first patch toner images S 1  to S 4  are formed, respectively different developing bias voltages are applied to the developing roller  641 . For example, under the control of the control unit  10 , the developing bias voltage Vdc 1  is applied when the first patch toner image S 1  is formed; the developing bias voltage Vdc 2  is applied when the first patch toner image S 2  is formed; the developing bias voltage Vdc 3  is applied when the first patch toner image S 3  is formed; and the developing bias voltage Vdc 4  is applied when the first patch toner image S 4  is formed. 
     The density sensor  76  measures the toner density of the first patch toner images S 1  to S 4  formed by the developing device  64 . The control unit  10  acquires the measurement result of the density sensor  76 . For example, the control unit  10  acquires the toner density CTD 1  to CTD 4  of each of the first patch toner images S 1  to S 4  measured by the density sensor  76 . 
     The control unit  10  calculates the correlation between the toner density and the developing bias voltage based on the acquired toner density CTD 1  to CTD 4  and the acquired developing bias voltage “Vdc 1  to Vdc 4 ”. 
     Next, the toner density and the developing bias voltage in the present embodiment will be described with reference to  FIG.  4   .  FIG.  4    is a graph showing the correlation between the toner density and the developing bias voltage in the present embodiment. In  FIG.  4   , the vertical axis represents the toner density and the horizontal axis represents the developing bias voltage. 
     In the present embodiment, it is assumed that the toner density is highest at CTD 4  and decreases in the order of CTD 3 , CTD 2 , CTD 1 . It is assumed that the developing bias voltage is highest at Vdc 4  and decreases in the order of Vdc 3 , Vdc 2 , Vdc 1 . In general, as the developing bias voltage increases, an image having a higher toner density is formed. 
     For example, the control unit  10  selects two first patch toner images from the first patch toner images S 1  to S 4 , and calculates the relationship between the toner densities of the two first patch toner images and the developing bias voltages when the two first patch toner images are formed, as a linear function. In detail, the control unit  10  selects the first patch toner images S 1  and S 2 , and calculates the linear function of the correlation L 1  between the toner density and the developing bias voltage in the first patch toner images S 1  and S 2  based on the toner density CTD 1  and the developing bias voltage Vdc 1 , and the toner density CTD 2  and the developing bias voltage Vdc 2 . 
     Similarly, the control unit  10  calculates a linear function of the correlation L 2  between the toner density and the developing bias voltage in the first patch toner images S 2 , and S 3  based on the toner density CTD 2  and the developing bias voltage Vdc 2 , and the toner density CTD 3  and the developing bias voltage Vdc 3 , and calculates a linear function of the correlation L 3  between the toner density and the developing bias voltage in the first patch toner images S 3 , and S 4  based on the toner density CTD 3  and the developing bias voltage Vdc 3 , and the toner density CTD 4  and the developing bias voltage Vdc 4 . 
     As described above, when the correlation between the toner density and the developing bias voltage is known, it is possible to obtain the developing bias voltage for forming an image having a desired toner density. 
     Next, a method of calculating a developing bias voltage for forming an image having a desired toner density in the present embodiment will be described with reference to  FIGS.  5  to  8   .  FIG.  5    is a graph obtained by adding, to the graph of  FIG.  4   , a point at which a desired toner density is obtained.  FIG.  5    shows a case where the desired toner density is a density is any of the toner densities CTD 1  to CTD 4 . 
     For example, when the desired toner density is a toner density CTDa between the toner density CTD 1  and the toner density CTD 2  (CTD 1 &lt;CTDa&lt;CTD 2 ), the developing bias voltage Vdca for forming an image having the toner density CTDa is calculated by the Equation (1). 
     
       
         
           
             
               
                 
                   Vdca 
                   = 
                   
                     
                       Vdc 
                       ⁢ 
                       1 
                     
                     + 
                     
                       
                         ( 
                         
                           CTDa 
                           - 
                           
                             CTD 
                             ⁢ 
                             1 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               Vdc 
                               ⁢ 
                               2 
                             
                             - 
                             
                               Vdc 
                               ⁢ 
                               1 
                             
                           
                           ) 
                         
                         
                           ( 
                           
                             
                               CTD 
                               ⁢ 
                               2 
                             
                             - 
                             
                               CTD 
                               ⁢ 
                               1 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                         
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     Similarly, when the desired toner density is a toner density CTDb between the toner density CTD 2  and the toner density CTD 3  (CTD 2 &lt;CTDb&lt;CTD 3 ), and when the desired toner density is a toner density CTDc between the toner density CTD 3  and the toner density CTD 4  (CTD 3 &lt;CTDc&lt;CTD 4 ), the corresponding developing bias voltage Vdcb and developing bias voltage Vdcc are calculated by modifying the Equation (1). 
     As described above, when the desired toner density is a toner density between the maximum density and the minimum density among the toner densities of the plurality of first patch toner images, an appropriate developing bias voltage can be obtained by the interpolation method. 
     Next, as shown in  FIGS.  6 A and  6 B , a method of calculating the developing bias voltage when the desired toner density is lower than the minimum density among the toner densities of the plurality of first patch toner images will be described. In this case, the control unit  10  selects two first patch toner images (first patch toner images S 1 , and S 2 ) including the first patch toner image S 1  having the minimum density. In this case, the calculation methods differ depending on the sign of the intercept CTDint of the correlation L 1 .  FIGS.  6 A and  6 B  show correlation L 1  in the graph of  FIG.  4   .  FIG.  6 A  shows a case where the intercept CTDint of the correlation L 1  is 0 or more (CTDint 1 ), and  FIG.  6 B  shows a case where the intercept CTDint of the correlation L 1  is less than 0 (CTDint 2 ). The intercept CTDint is calculated by Equation (2). 
     
       
         
           
             
               
                 
                   CTDint 
                   = 
                   
                     
                       
                         CTD 
                         ⁢ 
                         1 
                         × 
                         Vdc 
                         ⁢ 
                         2 
                       
                       - 
                       
                         CTD 
                         ⁢ 
                         2 
                         × 
                         Vdc 
                         ⁢ 
                         1 
                       
                     
                     
                       
                         Vdc 
                         ⁢ 
                         2 
                       
                       - 
                       
                         Vdc 
                         ⁢ 
                         1 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                         
                     2 
                   
                   ] 
                 
               
             
           
         
       
     
     In the case (CTDint&gt;0) shown in  FIG.  6 A , when the desired toner density is the toner density CTDd lower than the toner density CTD 1  (CTDd&lt;CTD 1 ), the developing bias voltage Vdcd for forming the image of the toner density CTDd is calculated by the Equation (3). 
     By such calculation, it is possible to prevent the developing bias voltage Vdcd from becoming a negative value when the intercept CTDint is 0 or more (CTDint 1 ). 
     
       
         
           
             
               
                 
                   Vdcd 
                   = 
                   
                     
                       CTDd 
                       × 
                       Vdc 
                       ⁢ 
                       1 
                     
                     
                       CTD 
                       ⁢ 
                       1 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                         
                     3 
                   
                   ] 
                 
               
             
           
         
       
     
     On the other hand, in the case shown in  FIG.  6 B  (CTDint&lt;0), when the desired toner density is the toner density CTDd lower than the toner density CTD 1  (CTDd&lt;CTD 1 ), the developing bias voltage Vdcd for forming the image of the toner density CTDd is calculated by the Equation (4) by the extrapolating method. 
     
       
         
           
             
               
                 
                   Vdcd 
                   = 
                   
                     
                       Vdc 
                       ⁢ 
                       1 
                     
                     + 
                     
                       
                         ( 
                         
                           CTDd 
                           - 
                           
                             CTD 
                             ⁢ 
                             1 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         
                           
                             Vdc 
                             ⁢ 
                             2 
                           
                           - 
                           
                             Vdc 
                             ⁢ 
                             1 
                           
                         
                         
                           ( 
                           
                             
                               CTD 
                               ⁢ 
                               2 
                             
                             - 
                             
                               CTD 
                               ⁢ 
                               1 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                         
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
     Next, as shown in  FIGS.  7 A and  7 B , a method of calculating the developing bias voltage when the desired toner density is higher than the maximum toner density among the toner densities of the plurality of first patch toner images will be described.  FIGS.  7 A and  7 B  show a correlation L 3  in the graph of  FIG.  4   . 
     As shown in  FIG.  7 A , when the desired toner density is CTDe which is higher than the toner density CTD 4  (CTD 4 &lt;CTDe), the control unit  10  selects two first patch toner images (first patch toner images S 3  and S 4 ) including the first patch toner image S 4  having the maximum density. In this case, the developing bias voltage Vdce for forming the image having the toner density CTDe is calculated by the Equation (5) by the extrapolating method. 
     
       
         
           
             
               
                 
                   Vcde 
                   = 
                   
                     
                       Vdc 
                       ⁢ 
                       3 
                     
                     + 
                     
                       
                         ( 
                         
                           CTDe 
                           - 
                           
                             CDT 
                             ⁢ 
                             3 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         
                           
                             Vdc 
                             ⁢ 
                             4 
                           
                           - 
                           
                             Vdc 
                             ⁢ 
                             3 
                           
                         
                         
                           ( 
                           
                             
                               CTD 
                               ⁢ 
                               4 
                             
                             - 
                             
                               CTD 
                               ⁢ 
                               3 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                         
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
     When the calculated developing bias voltage Vdce becomes larger than the maximum output value VdcL of the developing bias voltage as shown in  FIG.  7 B , the maximum output value VdcL is set as the developing bias voltage Vdce. 
     Next, as shown in  FIG.  8   , a description will be given of how to calculate the developing bias voltage Vdce for forming an image having a toner density of CTDe which is higher than the toner density CTD 3  when the toner density CTD  4  is lower than the toner density CTD 3  (CTD 4 &lt;CTD 3 &lt;CTDe), for example.  FIG.  8    is a diagram showing the correlation L 3  when the toner density CTD  4  is lower than the toner density CTD 3 . In this case, since the slope of the linear function of the correlation L 3  becomes negative, the developing bias voltage Vdce cannot be correctly calculated by the Equation (5) of the extrapolating method. 
     Therefore, when the slope of the linear function of the correlation L 3  is negative, the developing bias voltage Vdce is set to the maximum output value VdcL of the developing bias voltage or the developing bias voltage Vdc 4 . 
     In the present embodiment, when the developing bias voltage for forming an image having a desired toner density is calculated, the developing bias voltage adjustment mode is ended. 
     [Prediction of Toner Charge Amount] 
     In the present embodiment, when the developing bias voltage for forming an image having a desired toner density is known, the toner charge amount of the toner in the developing vessel  640  can be more accurately known. For example, the present embodiment has a toner charge amount prediction mode for predicting the toner charge amount. 
     Next, with reference to  FIG.  9   , the prediction of the toner charge amount in the present embodiment will be described.  FIG.  9    is a diagram showing a second patch toner image for predicting the toner charge amount in the present embodiment. 
     In the present embodiment, when the toner charge amount prediction mode is started, the developing device  64  forms the second patch toner images S 5 , and S 6 . For example, the second patch toner images S 5 , and S 6  have a W×T rectangular shape. W represents a length of the second patch toner images S 5 , and S 6  in the direction orthogonal to the conveyance direction of the sheet of paper p. T represents a length of the second patch toner images S 5 , and S 6  in the conveyance direction of the sheet of paper p. W is, for example, the maximum length in which an image can be formed in the width direction (axial direction) of the photosensitive drum  65 . T is, for example, the minimum length in which the density sensor  76  can measure the toner density. 
     When the second patch toner images S 5  and S 6  are formed, a developing bias voltage adjusted so that the second patch toner images S 5  and S 6  have a desired toner density calculated in the developing bias voltage adjustment mode is applied to the developing roller  641  under the control of the control unit  10 . 
     To be specific, under the control of the control unit  10 , the developing bias voltage Vdc 5  is applied when the second patch toner image S 5  is formed, and the developing bias voltage Vdc 6  is applied when the second patch toner image S 6  is formed. At this time, the control unit  10  acquires the developing currents Id 5  and Id 6  measured when the second patch toner images S 5  and S 6  are developed. 
     The density sensor  76  measures the toner density of the second patch toner images S 5  and S 6  formed by the developing device  64 . The control unit  10  acquires the measurement result of the density sensor  76 . For example, the control unit  10  acquires the toner densities CTD 5  and CTD 6  of the second patch toner images S 5  and S 6  measured by the density sensor  76 . 
     The control unit  10  calculates the toner charge amount of the toner in the developing vessel  640  based on the acquired difference between the developing currents Id 5  and Id 6 , the difference between the toner densities CTD 5  and CTD 6 , and the length W of the second patch toner images S 5  and S 6  in the direction orthogonal to the conveyance direction of the sheet of paper p. 
     Next, a toner charge amount prediction process according to the present embodiment will be described with reference to  FIG.  10   .  FIG.  10    is a flowchart showing a toner charge amount prediction process in the present embodiment. 
     In the present embodiment, when the developing bias voltage adjustment mode is started (step S 11 ), the developing device  64  forms a plurality of first patch toner images (step S 12 ). 
     The control unit  10  calculates the correlation between the toner density and the developing bias voltage based on the toner density of the plurality of first patch toner images and the plurality of developing bias voltages when forming the plurality of first patch toner images (step S 13 ). 
     The control unit  10  adjusts the developing bias voltage based on the correlation between the toner density and the developing bias voltage so that the second patch toner image having the desired toner density is formed in the toner charge amount prediction mode (step S 14 ). 
     In the toner charge amount prediction mode (step S 15 ), the developing device  64  forms the second patch toner image (step S 16 ) 
     The control unit  10  calculates the toner charge amount of the toner in the developing vessel  640  based on the developing current when the second patch toner image is formed, the toner density of the second patch toner image, and the length W of the second patch toner image in the direction orthogonal to the conveyance direction of the sheet of paper p (step S 17 ). 
     In the present exemplary embodiment, the density sensor  76  is disposed so as to face the intermediate transfer belt  72  and measures the density of the laminated toner image on the intermediate transfer belt  72 . However, without being limited thereto, the density sensor  76  may be disposed so as to face the photosensitive drum  65  and measure the density of the toner image on the photosensitive drum  65 . 
     According to the present disclosure, it is possible to form an image having a stable image density. 
     The embodiments of the present disclosure have been described above with reference to the drawings ( FIGS.  1  to  10   ). However, the present disclosure is not limited to the above-described embodiment, and can be implemented in various aspects without departing from the scope of the disclosure. In the drawings, each component is schematically illustrated for ease of understanding, and the thickness, length, number, and the like of each illustrated component are different from actual ones for convenience of drawing preparation. In addition, the materials, shapes, dimensions, and the like of the respective constituent elements described in the above-described embodiment are merely examples, and are not particularly limited. Various modifications can be made without substantially departing from the effects of the present disclosure.