Patent Publication Number: US-2019171151-A1

Title: Image forming apparatus

Description:
The entire disclosure of Japanese patent Application No. 2017-231740, filed on Dec. 1, 2017, is incorporated herein by reference in its entirety. 
     BACKGROUND 
     Technological Field 
     The present disclosure relates to an image forming apparatus, and more particularly to life determination of an image forming apparatus. 
     Description of the Related Art 
     Image forming apparatuses such as multi functional peripherals (MFPs) have become widespread. An image forming apparatus in an electrophotographic system includes, as a printing process, a step of charging a surface of a photoconductor, a step of exposing the surface of the photo according to an input image pattern, a step of attaching a toner to an electrostatic image formed on the surface of the photoconductor by the exposure, and a step of transferring the toner attached on the surface of the photoconductor to a transfer belt. 
     When the steps of forming a toner image on the surface of the photoconductor and transferring the formed toner image are repeated in this way, the surface of the photoconductor is depleted. Therefore, to perform maintenance such as replacement of the photoconductor before the end of life of the photoconductor arrives, estimation of the arrival of the end of life is widely performed on the basis of a depletion amount of the photoconductor. 
     As an example of a technology relating to the life estimation of a photoconductor, JP 2013-50601 A discloses an image forming apparatus that “changes the life of a photosensitive drum according to an average printing rate” (see [Means for Solving Problem] in [Detailed Description of Invention]). 
     Further, J P 2002-207402 A discloses an image forming apparatus that “eliminates error in life estimation of a photosensitive drum due to a difference in a printing rate and increases the life detection accuracy of the photosensitive drum (see [Problem to be Solved] in [Abstract]). 
     However, with the above-described conventional technologies, phenomena that the accuracy of estimating the life of the photoconductor is not sufficient have occurred. Therefore, there is a need for a technology for improving the accuracy of lifetime estimation of the photoconductor. 
     SUMMARY 
     The present disclosure has been made to solve the above problem, and an object of a certain aspect is to improve the accuracy of the life estimation of the photoconductor. 
     To achieve the abovementioned object, according to an aspect of the present invention, an image forming apparatus reflecting one aspect of the present invention comprises: a plurality of photoconductors that is rotatable and has toner images to be formed on respective surfaces; a transfer belt on which the toner images respectively formed on the plurality of photoconductors are sequentially transferred; and a hardware processor that estimates timing of arrival of end of life of one photoconductor of the plurality of photoconductors due to depletion of the surface of the one photoconductor, wherein the hardware processor calculates a depletion amount of the one photoconductor due to a toner, as a first depletion amount, on the basis of a first parameter having a positive correlation with an amount of the toner used for the toner image formed on the surface of another photoconductor that transfers the toner image on the transfer belt before the one photoconductor, and compares the calculated first depletion amount with a predetermined life estimation threshold value to estimate the timing of arrival of end of life of the one photoconductor. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The advantages and features provided by one or more embodiments of the invention will become more fully understood from the detailed description given hereinbelow and the appended drawings which are given by way of illustration only, and thus are not intended as a definition of the limits of the present invention: 
         FIG. 1  is a diagram illustrating an example of an overall structure of an image forming apparatus; 
         FIG. 2  is a block diagram illustrating a hardware configuration of the image forming apparatus; 
         FIG. 3  is a functional block diagram of the image forming apparatus according to a first embodiment; 
         FIGS. 4A and 4B  are diagrams illustrating an example of a rotation number history table; 
         FIG. 5  is a diagram illustrating an example of a depletion amount regulation table; 
         FIG. 6  is a diagram illustrating a relationship between photoconductors and depletion amounts to be calculated; 
         FIG. 7  is a graph illustrating a life estimation method; 
         FIG. 8  is a diagram illustrating a relationship between a printing rate and a measured value of the depletion amount of a photoconductor; 
         FIG. 9  is a histogram illustrating the depletion amounts when photoconductors are rotated to a predetermined rotation number; 
         FIG. 10  is a diagram illustrating a breakdown of depletion of the photoconductors; 
         FIG. 11  is a diagram illustrating a relationship between the printing rate of a one-upstream photoconductor and the depletion amount; 
         FIG. 12  is a diagram illustrating a depletion amount regulation table; 
         FIG. 13  is a flowchart illustrating a procedure of life estimation processing; 
         FIG. 14  is a functional block diagram of an image forming apparatus according to a second embodiment; 
         FIG. 15  is a graph illustrating a life estimation method in the second embodiment; 
         FIG. 16  is a functional block diagram of an image forming apparatus according to a third embodiment; 
         FIG. 17  is a diagram illustrating operation amounts of a developer and a transfer belt and a percentage of a transfer residual toner; 
         FIGS. 18A and 18B  are diagrams illustrating correction coefficients of self depletion amounts with respect to operation amounts of a developer and a transfer belt; 
         FIG. 19  is a diagram illustrating operation amounts of a developer and a transfer belt and a percentage of a reverse transfer toner; 
         FIGS. 20A and 20B  are diagrams illustrating correction coefficients of reverse transfer depletion amounts with respect to operation amounts of a developer and a transfer belt; 
         FIG. 21  is a functional block diagram of an image forming apparatus according to a fourth embodiment; 
         FIG. 22  is a diagram illustrating a rotation number history table according to the fourth embodiment; 
         FIG. 23  is a diagram exemplarily illustrating the magnitude of the depletion amount calculated for each section; and 
         FIG. 24  is a functional block diagram of a life estimation device according to a fifth embodiment. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Hereinafter, one or more embodiments of the present invention will be described with reference to the drawings. However, the scope of the invention is not limited to the disclosed embodiments. In the following description, the same parts and constituent elements are denoted by the same reference numerals. Names and functions of the same parts and constituent elements are also the same. Therefore, detailed description of the same parts and constituent elements is not repeated. Note that the embodiments and modifications described below may be selectively combined as appropriate. 
     First Embodiment 
     [1. Configuration of Image Forming Apparatus  100 ] 
     An image forming apparatus  100  according to an embodiment will be described with reference to  FIG. 1 .  FIG. 1  is a diagram illustrating an example of an overall structure of the image forming apparatus  100 . 
       FIG. 1  illustrates the image forming apparatus  100  as a color printer. Hereinafter, the image forming apparatus  100  as a color printer will be described, but the image forming apparatus  100  is not limited to a color printer. For example, the image forming apparatus  100  may be a monochrome printer or may be a multifunction peripheral (so-called MFP) of a monochrome printer, a color printer, and a facsimile machine. 
     The image forming apparatus  100  includes a scanner  20  as an image reader and a printer  25  including an image former  90  (image formers  90 Y,  90 M,  90 C, and  90 K in detail). The scanner  20  includes a cover  21 , a sheet base  22 , a sheet tray  37  (sheet trays  37 A,  37 B, and  37 C in details), and an auto document feeder (ADF)  24 . One end of the cover  21  is fixed to the sheet base  22 , and the cover  21  is openable/closable with the one end as a fulcrum. 
     A user of the image forming apparatus  100  can set a document on the sheet base  22  by opening the cover  21 . When the image forming apparatus  100  receives a scan instruction in the state where the document is set on the sheet base  22 , the image forming apparatus  100  starts scan of the document set on the sheet base  22 . Further, when the image forming apparatus  100  receives a scan instruction in a state where a document is set on the sheet tray  37 , the image forming apparatus  100  automatically reads the document by the ADF  24  sheet by sheet. 
     The printer  25  includes the image formers  90 Y,  90 M,  90 C, and  90 K, an image density control (IDC) sensor  19 , a transfer belt  30 , a primary transfer roller  31 , a transfer driver  32 , a secondary transfer roller  33 , the sheet trays  37 A,  37 B, and  37 C, a driven roller  38 , a drive roller  39 , a registration roller  40 , a cleaning unit  43 , a fixing device  60 , and a control device  101 . 
     The image formers  90 Y,  90 M,  90 C, and  90 K are arranged in order along the transfer belt  30 . The image former  90 Y receives a toner supply from a toner bottle  15 Y to form a yellow (Y) toner image. The image former  90 M receives a toner supply from a toner bottle  15 M to form a magenta (M) toner image. The image former  90 C receives a toner supply from a toner bottle  15 C to form a cyan (C) toner image. The image former  90 K receives a toner supply from a toner bottle  15 K to form a black (BK) toner image. 
     The image formers  90 Y,  90 M,  90 C, and  90 K are arranged in order in a rotation direction of the transfer belt  30  along the transfer belt  30 . Each of the image formers  90 Y,  90 M,  90 C, and  90 K includes a photoconductor  10  rotatably configured, a charging device  11 , an exposure device  13 , a developer  14 , a cleaning unit  17  including a cleaning blade  42 , and a neutralization device  18 . 
     After the image formers  90 Y,  90 M,  90 C, and  90 K operate as described above, the yellow (Y) toner image, the magenta (M) toner image, the cyan (C) toner image, and the black (BK) toner image are sequentially superimposed and transferred from the photoconductors  10  to the transfer belt  30  by transfer of the transfer driver  32 . As a result, a color toner image is formed on the transfer belt  30 . 
     The IDC sensor  19  detects the density of a toner image  35  formed on the transfer belt  30 . Typically, the IDC sensor  19  is a light intensity sensor including a reflective photosensor, and detects the intensity of reflected light from a surface of the transfer belt  30 . 
     The transfer belt  30  is stretched around the driven roller  38  and the drive roller  39 . The drive roller  39  is connected to a motor (not illustrated). The drive roller  39  is rotated as the control device  101  controls the motor. The transfer belt  30  and the driven roller  38  are rotated in conjunction with the drive roller  39 . As a result, the toner image  35  on the transfer belt  30  is sent to the secondary transfer roller  33 . 
     Different sizes or types of sheets are set to the sheet trays  37 A,  37 B, and  37 C, respectively, for example. The sheets are conveyed sheet by sheet from one set as a feed tray from among the sheet trays  37 A,  37 B, and  37 C to a conveyance path  41 . The sheet is sent to the secondary transfer roller  33  by the registration roller  40 . 
     The control device  101  controls a transfer voltage to be applied to the secondary transfer roller  33  in accordance with timing at which the sheet is sent out. The secondary transfer roller  33  applies a transfer voltage having an opposite polarity to a charge polarity of the toner image  35  to the sheet being conveyed. As a result, the toner image  35  is attracted from the transfer belt  30  to the secondary transfer roller  33 , and the toner image  35  on the transfer belt  30  is transferred. 
     The conveyance timing of the sheet to the secondary transfer roller  33  is controlled by the registration roller  40  in accordance with the position of the toner image  35  on the transfer belt  30 . As a result, the toner image  35  on the transfer belt  30  is transferred to an appropriate position on the sheet. 
     The fixing device  60  pressurizes and heats the sheet passing through the fixing device  60 . As a result, the toner image is fixed on the sheet. Thereafter, the sheet is discharged to a sheet discharge tray  48 . 
     The cleaning unit  43  collects the toner remaining on the surface of the transfer belt  30  after transfer of the toner image from the transfer belt  30  to the sheet. The collected toner is conveyed by a conveying screw (not illustrated) and stored in a waste toner container (not illustrated). 
     [2. Hardware Configuration] 
     An example of a hardware configuration of the image forming apparatus  100  will be described with reference to  FIG. 2 .  FIG. 2  is a block diagram illustrating a hardware configuration of the image forming apparatus  100 . 
     As illustrated in  FIG. 2 , the image forming apparatus  100  includes the control device  101 , a read only memory (ROM)  102 , a random access memory (RAM)  103 , a network interface  104 , an operation panel  105 , the scanner  20 , a temperature sensor  70 , a humidity sensor  80 , the image former  90 , and a storage device  120 . 
     The control device  101  is configured by, for example, at least one integrated circuit. The integrated circuit is configured by, for example, at least one central processing unit (CPU), at least one application specific integrated circuit (ASIC), or at least one field programmable gate array (FPGA), or a combination thereof. 
     The control device  101  executes various programs such as a program  122  for adjusting control parameters of the image forming apparatus  100  to control the operation of the image forming apparatus  100 . The control device  101  reads the program  122  from the storage device  120  to the RAM  103  on the basis of reception of an execution instruction of the program  122 . The RAM  103  functions as a working memory and temporarily stores various data necessary for execution of the program  122 . 
     An antenna (not illustrated) and the like are connected to the network interface  104 . The image forming apparatus  100  exchanges data with an external communication device via the antenna. The external communication device includes, for example, a mobile communication terminal such as a smartphone, and a server. The image forming apparatus  100  may be configured to download the program  122  from the server via the antenna. 
     The operation panel  105  includes a display (not illustrated) and a touch panel (not illustrated). The display and the touch panel are overlapped with each other, and the image forming apparatus  100  receives an operation on the touch panel. 
     The storage device  120  is, for example, a hard disk, a solid state drive (SSD), or another storage device. The storage device  120  may be either a built-in storage device or an external storage device. The storage device  120  stores the program  122  and the like according to the present embodiment. However, the storage location of the program  122  is not limited to the storage device  120 , and may be stored in a storage area (for example, a cache) of the control device  101 , the ROM  102 , the RAM  103 , an external device (for example, a server), or the like. 
     The program  122  may be incorporated in and provided as a part of an arbitrary program, not as a single program. In this case, control processing according to the present embodiment is realized in cooperation with the arbitrary program. Even such a program not including some of modules does not depart from the gist of the program  122  according to the present embodiment. 
     Furthermore, some or all of the functions provided by the program  122  may be realized by dedicated hardware. Furthermore, the image forming apparatus  100  may be configured in a form like a so-called cloud service in which at least one server executes part of the processing of the program  122 . 
     [3. Functional Configuration] 
     A functional configuration in the image forming apparatus  100  according to the first embodiment will be described with reference to  FIG. 3 .  FIG. 3  is a functional block diagram of the image forming apparatus  100  according to the first embodiment. 
     As illustrated in  FIG. 3 , the image forming apparatus  100  includes the control device  101 , the storage device  120 , the photoconductors  10 Y,  10 M,  10 C, and  10 K (hereinafter simply referred to as photoconductor  10  when collectively called), and the transfer belt  30 . The control device  101  includes a rotation controller  121 , a depletion amount calculator  131 , and a life estimator  141 . 
     The rotation controller  121  of the control device  101  controls the rotation of the photoconductor  10  at the time of image formation. Here, the control of rotation includes control of at least either a rotational speed or a rotation number. The photoconductor  10  transfers a toner image T formed on the surface to the transfer belt  30  while being rotated by the rotation controller  121 . 
     More specifically, the photoconductors  10 Y,  10 M,  10 C, and  10 K sequentially transfer the toner images T to the transfer belt, respectively. First, the photoconductor  10 Y transfers the toner image T formed on the surface to the transfer belt  30 , and then the photoconductors  10 M,  10 C, and  10 K subsequently transfer the toner images T formed on the surfaces to the transfer belt in that order. 
     The rotation controller  121  further registers history information obtained by rotation of the photoconductor  10  to a rotation number history table D 1  stored in the storage device  120 . Details of the rotation number history table D 1  will be described below. 
     In depletion amount calculation processing, the depletion amount calculator  131  calculates a depletion amount (corresponding to a second depletion amount) due to the toner formed on the surface of the photoconductor for which the life is estimated on the basis of an operation amount and a printing rate (corresponding to second parameters) of the photoconductor for which the life is estimated. 
     Further, the depletion amount calculator  131  calculates a depletion amount (corresponding to a first depletion amount) due to the toner formed on the surface of another photoconductor that transfers the toner image on the transfer belt  30  before the photoconductor for which the life is estimated on the basis of the operation amount and the printing rate (corresponding to first parameters) of the another photoconductor. 
     The depletion amount calculator  131  integrates the depletion amount due to the toner formed on the surface of the photoconductor and the depletion amount due to the toner formed on the surface of the another photoconductor to calculate the depletion amount of the photoconductor for which the life is estimated. 
     Here, as the operation amount of the photoconductor, an integrated value of rotation numbers of the photoconductor or an integrated value of rotation times of the photoconductor can be used. 
     To realize the above processing, the depletion amount calculator  131  acquires history information of the rotation numbers of the photoconductor for which the life is estimated (corresponding to one photoconductor) and the photoconductor (corresponding to another photoconductor) that transfers the toner image T on the transfer belt  30  before the one photoconductor by reference to the rotation number history table D 1  stored in the storage device  120 . The depletion amount calculator  131  further calculates the depletion amount of the photoconductor for which life estimation processing is performed with reference to a depletion amount regulation table D 2  stored in the storage device  120 . 
     The life estimator  141  of the control device  101  compares the depletion amount of the photoconductor for which the life is estimated, which has been calculated by the depletion amount calculator  131 , with a predetermined life threshold value to estimate arrival of the end of life of the photoconductor for which the life is estimated. Details of the life estimation processing will be described below. 
     [4. Calculation of Depletion Amount] 
     The rotation number history table D 1  will be described with reference to  FIGS. 4A and 4B .  FIGS. 4A and 4B  are diagrams illustrating an example of the rotation number history table D 1 . 
     As illustrated in  FIG. 4A , the rotation number history table D 1  stores the history information of the rotation number of the photoconductor  10  for each image formation performed by the image forming apparatus  100 . More specifically, the rotation number history table D 1  includes, as examples, a photoconductor type  151 , a rotation number  153 , a printing rate  155 , and a printing date and time  157 . 
     The photoconductor type  151  is information for specifying the photoconductor on which the toner image is formed in image formation. The rotation number  153  is a rotation number of the photoconductor in each image formation. The printing rate  155  is a printing rate in each image formation. The printing rate means a rate of an image area to a printing area of a sheet. The printing rate is measured on the basis of an integrated value of the number of dots of the toner at the time of forming the toner image on the surface of the photoconductor. The printing date and time  157  indicates date and time when image formation was performed. 
     When the depletion amount calculator  131  acquires the rotation number history table D 1 , the depletion amount calculator  131  creates a rotation number aggregation table D 1 ′ in which the rotation number  153  is aggregated for each photoconductor type  151  and each printing rate  155 , as illustrated in  FIG. 4B . The depletion amount calculator  131  calculates the depletion amount of the photoconductor for which the life is estimated, using the rotation number aggregation table D 1 ′. Details of the depletion amount calculation by the depletion amount calculator  131  will be described below. 
     The depletion amount regulation table D 2  will be described with reference to  FIG. 5 .  FIG. 5  is a diagram illustrating an example of the depletion amount regulation table D 2 . 
     The depletion amount regulation table D 2  regulates the depletion amount per one rotation of the photoconductor of each printing rate. As illustrated in  FIG. 5 , the depletion amount regulation table D 2  includes, as an example, a printing rate  160 , a self depletion amount  161 , and a reverse transfer depletion amount  163 . The reverse transfer depletion amount  163  further includes a first depletion amount  165 , a second depletion amount  167 , and a third depletion amount  169 . 
     The self depletion amount (corresponding to the second depletion amount) referred to here means the depletion amount of the surface of the photoconductor due to the toner formed on the surface of the photoconductor itself when the photoconductor is rotated once. For example, as illustrated in  FIG. 5 , in a case where the printing rate is 5%, the photoconductor is depleted by 0.0189 nm per one rotation. 
     In contrast, the reverse transfer depletion amount (corresponding to the first depletion amount) means the depletion amount of the surface of the photoconductor for which the life is estimated, which is caused by the toner transferred on the photoconductor (hereinafter, the transfer is also referred to as “reverse transfer”), the toner being formed when the photoconductor (hereinafter, also referred to as “upstream” photoconductor) that transfers the toner image on the transfer belt before the photoconductor for which the life is estimated is rotated once. 
     The first depletion amount  165  indicates the amount of depletion of the surface of the photoconductor for which the life is estimated, which is caused by the toner reversely transferred on the photoconductor, the toner being formed when the photoconductor (hereinafter, referred to as one-upstream photoconductor) that transfers the toner image on the transfer belt one-photoconductor before the photoconductor for which the life is estimated is rotated once. 
     The second depletion amount  167  indicates the amount of depletion of the surface of the photoconductor for which the life is estimated, which is caused by the toner reversely transferred on the photoconductor, the toner being formed when the photoconductor (hereinafter, referred to as two-upstream photoconductor) that transfers the toner image on the transfer belt two-photoconductors before the photoconductor for which the life is estimated is rotated once. 
     The third depletion amount  169  indicates an amount of depletion of the surface of the photoconductor for which the life is estimated, which is caused by the toner reversely transferred on the photoconductor, the toner being formed when the photoconductor (hereinafter, referred to as three-upstream photoconductor) that transfers the toner image on the transfer belt three-photoconductors before the photoconductor for which the life is estimated is rotated once. 
     The depletion amount calculator  131  calculates the depletion amount of the photoconductor for which the life is estimated, as described below on the basis of the rotation number aggregation table D 1 ′ and the depletion amount regulation table D 2 . 
     A method of calculating the depletion amount of the photoconductor for which the life is estimated will be described with reference to  FIG. 6 .  FIG. 6  is a diagram illustrating a relationship between the photoconductors  10 Y to  10 K and depletion amounts to be calculated. 
     As illustrated in  FIG. 6 , methods of calculating the depletion amounts of the photoconductors  10 Y,  10 M,  10 C, and  10 K are different. In a case of calculating the depletion amount of the photoconductor  10 Y, the depletion amount calculator  131  calculates only the self depletion amount by the photoconductor  10 Y. This is because there is no photoconductor that transfers the toner image on the transfer belt  30  before the photoconductor  10 Y, and thus there is no need to consider the depletion amount due to reverse transfer. 
     In contrast, in a case of calculating the depletion amount of the photoconductor  10 M, the depletion amount calculator  131  calculates an integrated value of the self depletion amount and the reverse transfer depletion amount. In this case, as the reverse transfer depletion amount, the first depletion amount caused by a one-upstream photoconductor (corresponding to the photoconductor  10 Y) is calculated. This is because the photoconductor that transfers the toner image on the transfer belt  30  before the photoconductor  10 M is only the photoconductor  10 Y. 
     Further, in a case of calculating the depletion amount of the photoconductor  10 C, the depletion amount calculator  131  calculates an integrated value of the self depletion amount and the reverse transfer depletion amount. In this case, as the reverse transfer depletion amount, an integrated value of the first depletion amount caused by the one-upstream photoconductor (corresponding to the photoconductor  10 M) and the second depletion amount caused by a two-upstream photoconductor (corresponding to the photoconductor  10 Y) is calculated. This is because the photoconductors that transfer the toner image to the transfer belt  30  before the photoconductor  10 C are the photoconductors  10 Y and  10 M. 
     Further, in a case of calculating the depletion amount of the photoconductor  10 K, the depletion amount calculator  131  calculates an integrated value of the self depletion amount and the reverse transfer depletion amount. In this case, as the reverse transfer depletion amount, an integrated value of the first depletion amount caused by the one-upstream photoconductor (corresponding to the photoconductor  10 C), the second depletion amount caused by the two-upstream photoconductor (corresponding to the photoconductor  10 K), and the third depletion amount caused by a three-upstream photoconductor (corresponding to the photoconductor  10 Y) is calculated. This is because the photoconductors that transfer the toner image on the transfer belt  30  before the photoconductor  10 K are the photoconductors  10 Y,  10 M, and  10 C. 
     Hereinafter, the depletion amounts of the photoconductors  10 Y to  10 K will be specifically obtained for the rotation number aggregation table D 1 ′ illustrated in  FIG. 4B  and the depletion amount regulation table D 2  illustrated in  FIG. 5 . The depletion amount calculator  131  calculates the product of the rotation number and the depletion amount for each printing rate in the rotation number aggregation table D 1 ′ and the depletion amount regulation table D 2 , and calculates the sum of the products (hereinafter also referred to as integrated depletion amount). 
     The integrated depletion amount of the photoconductor  10 Y is obtained by the following equation using the relationship illustrated in  FIG. 6 . 
     The integrated depletion amount (photoconductor  10 Y)=the self depletion amount (photoconductor  10 Y) 
     The depletion amount calculator  131  calculates the sum of products of the rotation number and the depletion amount as the self depletion amount, for each printing rate of the depletion amount regulation table D 2  on the basis of the rotation number  153  of the photoconductor  10 Y in the rotation number aggregation table D 1 ′. 
     The self depletion amount (photoconductor  10 Y)=0.0184 (nm)×10000+0.0189 (nm)×5000+0.0193 (nm)×8000+0.0200 (nm)×2000=472.9 (nm)=0.4729 (μm) 
     Therefore, the integrated depletion amount (photoconductor  10 Y)=0.4729 (μm). 
     The integrated depletion amount of the photoconductor  10 M is obtained by the following equation using the relationship illustrated in  FIG. 6 . 
     The integrated depletion amount (photoconductor  10 M)=the self depletion amount (photoconductor  10 M)+the reverse transfer depletion amount (first depletion amount (photoconductor  10 Y)) 
     The depletion amount calculator  131  calculates the sum of products of the rotation number and the depletion amount as the self depletion amount, for each printing rate of the depletion amount regulation table D 2  on the basis of the rotation number  153  of the photoconductor  10 M in the rotation number aggregation table D 1 ′. 
     The self depletion amount (photoconductor  10 M)=0.0184 (nm)×8000+0.0189 (nm)×6000+0.0193 (nm)×7000+0.0200 (nm)×1200=419.7 (nm)=0.4197 (μm) 
     The depletion amount calculator  131  calculates the sum of products of the rotation number and the depletion amount as the first depletion amount, for each printing rate of the depletion amount regulation table D 2  on the basis of the rotation number  153  of the photoconductor  10 Y in the rotation number aggregation table D 1 ′. 
     The reverse transfer depletion amount (first depletion amount photoconductor  10 Y))=0.0002 (nm)×10000+0.00031 (nm)×5000+0.0004 (nm)×8000+0.0005 (nm)×2000=7.75 (nm)=0.00775 (μm) 
     Therefore, the integrated depletion amount (photoconductor  10 M)=0.4197 (μm)+0.00775 (μm)=0.42745 (μm). 
     The integrated depletion amount of the photoconductor  10 C is obtained by the following equation using the relationship illustrated in  FIG. 6 . The integrated depletion amount (photoconductor  10 C)=the self depletion amount (photoconductor  10 C)+the reverse transfer depletion amount (the first depletion amount (photoconductor  10 M)+the second depletion amount (photoconductor  10 Y)) 
     The depletion amount calculator  131  calculates the sum of products of the rotation number and the depletion amount as the self depletion amount, for each printing rate of the depletion amount regulation table D 2  on the basis of the rotation number  153  of the photoconductor  10 C in the rotation number aggregation table D 1 ′. 
     The self depletion amount (photoconductor  10 C)=0.0184 (nm)×11000+0.0189 (nm)×8000+0.0193 (nm)×9000+0.0200 (nm)×1800=563.3 (nm)=0.5633 (μm) 
     The depletion amount calculator  131  calculates the sum of products of the rotation number and the depletion amount as the first depletion amount, for each printing rate of the depletion amount regulation table D 2  on the basis of the rotation number  153  of the photoconductor  10 M in the rotation number aggregation table D 1 ′. 
     The reverse transfer depletion amount (first depletion amount (photoconductor  10 M))=0.0002 (nm)×8000+0.00031 (nm)×6000+0.0004 (nm)×7000+0.0005 (nm)×1200=6.86 (nm)=0.00686 (μm) 
     The depletion amount calculator  131  calculates the sum of products of the rotation number and the depletion amount as the second depletion amount, for each printing rate of the depletion amount regulation table D 2  on the basis of the rotation number  153  of the photoconductor  10 Y in the rotation number aggregation table D 1 ′. 
     The reverse transfer depletion amount (second depletion amount (photoconductor  10 Y))=0.00025 (nm)×10000+0.00038 (nm)×5000+0.00049 (nm)×8000+0.00062 (nm)×2000=9.56 (nm)=0.00956 (μm) 
     Therefore, the integrated depletion amount (photoconductor  10 C)=0.5633 (μm)+0.00686 (μm)+0.00956 (μm)=0.57972 (μm). 
     The integrated depletion amount of the photoconductor  10 K is obtained by the following equation using the relationship illustrated in  FIG. 6 . 
     The integrated depletion amount (photoconductor  10 K)=the self depletion amount (photoconductor  10 K)+the reverse transfer depletion amount (the first depletion amount (photoconductor  10 C)+the second depletion amount (photoconductor  10 M)+the third depletion amount (photoconductor  10 Y)) 
     The depletion amount calculator  131  calculates the sum of products of the rotation number and the depletion amount as the self depletion amount, for each printing rate of the depletion amount regulation table D 2  on the basis of the rotation number  153  of the photoconductor  10 K in the rotation number aggregation table D 1 ′. 
     The self depletion amount (photoconductor  10 K)=0.0184 (nm)×80000+0.0189 (nm)×50000+0.0193 (nm)×70000+0.0200 (nm)×10000=3968 (nm)=3.968 (μm) 
     The depletion amount calculator  131  calculates the sum of products of the rotation number and the depletion amount as the first depletion amount, for each printing rate of the depletion amount regulation table D 2  on the basis of the rotation number  153  of the photoconductor  10 C in the rotation number aggregation table D 1 ′. 
     The reverse transfer depletion amount (first depletion amount (photoconductor  10 C))=0.0002 (nm)×11000+0.00031 (nm)×8000+0.0004 (nm)×9000+0.0005 (nm)×1800=9.18 (nm)=0.00918 (μm) 
     The depletion amount calculator  131  calculates the sum of products of the rotation number and the depletion amount as the second depletion amount, for each printing rate of the depletion amount regulation table D 2  on the basis of the rotation number  153  of the photoconductor  10 M in the rotation number aggregation table D 1 ′. 
     The reverse transfer depletion amount (second depletion amount (photoconductor  10 M))=0.00025 (nm)×8000+0.00038 (nm)×6000+0.00049 (nm)×7000+0.00062 (nm)×1200=8.454 (nm)=0.008454 (μm) 
     The depletion amount calculator  131  calculates the sum of products of the rotation number and the depletion amount as the third depletion amount, for each printing rate of the depletion amount regulation table D 2  on the basis of the rotation number  153  of the photoconductor  10 Y in the rotation number aggregation table D 1 ′. 
     The reverse transfer depletion amount (third depletion amount (photoconductor  10 Y))=0.00028 (nm)×10000+0.00044 (nm)×5000+0.00057 (nm)×8000+0.00071 (nm)×2000=10.98 (nm)=0.01098 (μm) 
     Therefore, the integrated depletion amount (photoconductor  10 C)=3.968 (μm)+0.00918 (μm)+0.008454 (μm)+0.01098 (μm)=3.996614 (μm). 
     As described above, the depletion amount calculator  131  of the control device  101  integrates the self depletion amount with the rotation of the photoconductor to be calculated and the reverse transfer depletion amount due to the toner formed on the upstream photoconductors to calculate the depletion amount in calculating the depletion amount of the photoconductor. 
     [5. Estimation of Life] 
     Life estimation of the photoconductor by the life estimator  141  will be described with reference to  FIG. 7 .  FIG. 7  is a graph illustrating a life estimation method. 
     For simplicity of description,  FIG. 7  illustrates an example in which the depletion amount of the photoconductor calculated by the depletion amount calculator  131  is 10 (μm) and a life threshold value is 20 (μm). Then, assuming that the integrated value of the rotation numbers of the photoconductor at the estimation processing of this time is 500 (krot). Note that, here, (krot) represents 1000 rotations. 
     The life estimator  141  compares the depletion amount (10 μm) with the life threshold value (20 μm), and determines that the photoconductor has not yet reached the end of life. Further, the life estimator  141  estimates the rotation number of the photoconductor, which is predicted at the timing when the end of life arrives, on the basis of the ratio between the depletion amount and the life threshold value. In the example illustrated in  FIG. 7 , since the life threshold value is 20 (μm) with respect to the depletion amount 10 (μm) of the photoconductor, the photoconductor is depleted to half of the life threshold value. Therefore, the life estimator  141  estimates the integrated value of the rotation numbers of the photoconductor at the timing when the end of life arrives as 1000 (krot) on the basis of the fact that the integrated value of the rotation numbers of the photoconductor is 500 (krot). That is, in the present embodiment, the life estimator  141  estimates the life estimation timing of the photoconductor with the integrated value of the rotation numbers of the photoconductor. Note that the life estimation timing may be estimated with another physical amount such as a rotation time of the photoconductor or the number of printed sheets in the image forming apparatus. 
     [6. Method of Creating Depletion Amount Regulation Table D 2 ] 
     Hereinafter, a method of creating the depletion amount regulation table D 2  will be described with reference to  FIGS. 8 to 12 .  FIG. 8  is a diagram illustrating a relationship between the printing rate of the photoconductor  10 Y and a measured value of the depletion amount.  FIG. 9  is a histogram illustrating the depletion amounts when the photoconductors  10 Y,  10 M,  10 C, and  10 K are rotated to a predetermined rotation number.  FIG. 10  is a diagram illustrating a breakdown of depletion of the photoconductors.  FIG. 11  is a diagram illustrating a relationship between the printing rate of a one-upstream photoconductor and the depletion amount.  FIG. 12  is a diagram illustrating the depletion amount regulation table D 2 . 
     As illustrated in  FIG. 8 , the depletion amount of the photoconductor becomes larger as the printing rate becomes higher. This is because as the toner remaining on the photoconductor (hereinafter referred to as transfer residual toner) at the time of transfer to the transfer belt becomes larger as the printing rate is higher, and the toner accumulated on the cleaning blade  42  scrapes the surface of the photoconductor. 
       FIG. 9  illustrates the measured values of the depletion amounts when the photoconductors  10 Y,  10 M,  10 C, and  10 K are rotated by 1000 (krot). At this time, a charge amount and an adhesion amount of the toner formed on the surface of each photoconductor are substantially the same. The printing rate is 5% in each photoconductor. Here, as illustrated in  FIG. 9 , the depletion amount of a more upstream photoconductor is smaller. The difference in the depletion amount is considered due to the reverse transfer toner caused by the toner transferred from the upstream photoconductor to the transfer belt  30 . 
     That is, since there is no upstream photoconductor for the photoconductor  10 Y, no depletion due to the reverse transfer toner occurs. Therefore, the depletion amount (18.87 (μm)) on the photoconductor  10 Y is considered to be caused by the transfer residual toner by the rotation of the photoconductor  10 Y itself. 
     When comparing the depletion amounts between the photoconductor  10 Y and  10 M, the difference is 19.18-18.87=0.31 (μm). The difference between the depletion amounts is considered to be caused by the reverse transfer toner from the photoconductor  10 Y that is one-upstream of the photoconductor  10 M. 
     When comparing the depletion amounts between the photoconductors  10 Y and  10 C, the difference is 19.56-18.87=0.69 (μm). The difference between the depletion amounts is considered to be caused by the reverse transfer toners from the photoconductor  10 M that is one-upstream of the photoconductor  10 C and the photoconductor  10 Y that is two-upstream of the photoconductor  10 C. 
     When comparing the depletion amounts between the photoconductors  10 Y and  10 K, the difference is 20.00-18.87=1.13 (μm). This 1.13 (μm) is considered to be caused by the reverse transfer toners from the photoconductor  10 C that is one-upstream of the photoconductor  10 K, the photoconductor  10 M that is two-upstream of the photoconductor  10 K, and the photoconductor  10 Y that is three-upstream of the photoconductor  10 K. 
     A breakdown of the depletion amounts due to the reverse transfer toners from the upstream photoconductors will be described with reference to  FIG. 10 . As illustrated in  FIG. 10 , in the photoconductors  10 Y to  10 K, the depletion amounts due to the transfer residual toners themselves (that is, the self depletion amounts) are uniformly 18.87 (μm). Then, the depletion amount due to the reverse transfer toner (that is, the reverse transfer depletion amount) on the photoconductor  10 M is 0.31 (μm). 
     As described above, the depletion amount due to the reverse transfer toner on the photoconductor  10 M is considered to be caused by the reverse transfer toner from the photoconductor  10 Y. Therefore, the depletion amount due to the reverse transfer toner from the one-upstream photoconductor is 0.31 (μm). 
     The depletion amount due to the reverse transfer toner on the photoconductor  10 C is 0.69 (μm). As described above, the depletion amount due to the reverse transfer toner on the photoconductor  10 C is caused by the reverse transfer toner from the photoconductor  10 Y and the reverse transfer toner from the photoconductor  10 M. 
     Here, considering the fact that the depletion amount due to the reverse transfer toner from the one-upstream photoconductor  10 M is 0.31 (μm), the depletion amount due to the reverse transfer from the two-upstream photoconductor  10 Y is 0.38 (μm). 
     The depletion amount due to the reverse transfer toner on the photoconductor  10 K is 1.13 (μm). As described above, the depletion amount due to the reverse transfer toner on the photoconductor  10 K is caused by the reverse transfer toner from the photoconductor  10 Y, the reverse transfer toner from the photoconductor  10 M, and the reverse transfer toner from the photoconductor  10 C. 
     Here, considering the fact that the depletion amount due to the reverse transfer toner from the one-upstream photoconductor  10 C is 0.31 (μm) and the depletion amount due to the reverse transfer toner from the two-upstream photoconductor  10 M is 0.38 (μm), the depletion amount due to the reverse transfer from the three-upstream photoconductor  10 Y is 0.44 (μm). 
     As described above, contribution by an upper-stream photoconductor to the depletion amount due to the reverse transfer toner becomes larger. This is because the toner on the transfer belt receives a larger amount of positive changes from a transfer region and becomes more easily separated from the transfer belt as the toner passes through the transfer region on the transfer belt for a longer time. As a result, the amount to be reversely transferred of the toner on the transfer belt  30  increases, and the depletion amount of the reversely transferred photoconductor increases, accordingly. 
     As described above, it is found that the depletion amount due to the reverse transfer toner from an upper-stream photoconductor becomes larger in the case where a plurality of upstream photoconductors exists. Specifically, in the example illustrated in  FIG. 10 , when the depletion amount due to the reverse transfer toner from a one-upstream photoconductor is 1, the ratio of the depletion amount due to the reverse transfer toner from a two-upstream photoconductor is 1.23, and the ratio of the depletion amount due to the reverse transfer toner from a three-upstream photoconductor is 1.42. 
       FIG. 11  illustrates a relationship between the printing rate of a one-upstream photoconductor and the measured value of the reverse transfer depletion amount. As illustrated in  FIG. 11 , it is found that the reverse transfer depletion amount increases as the printing rate of the one-upstream photoconductor increases. From the above, the printing rate of the upstream photoconductor needs to be considered in calculating the depletion amount of the photoconductor for which the depletion amount is calculated. 
     As illustrated in  FIG. 12 , the second depletion amount is defined as 1.23 times the first depletion amount. Further, the third depletion amount is defined as 1.42 times the first depletion amount. By doing so, the depletion amount calculator  131  can calculate the depletion amount such that the reverse transfer depletion amount from an upper-stream photoconductor becomes larger in the case where a plurality of photoconductors exists for the photoconductor for which the life is estimated. Note that, in creating the depletion amount regulation table D 2 , the self depletion amount and the first depletion amount are obtained in measured values, and the second depletion amount and the third depletion amount are calculated on the basis of the measured values. 
     [7. Processing Procedure] 
     A procedure of the life estimation processing according to the first embodiment will be described with reference to  FIG. 13 .  FIG. 13  is a flowchart illustrating a procedure of the life estimation processing. This processing is realized when the CPU functioning as the control device  101  executes a given program, for example. 
     In step S 1210 , the depletion amount calculator  131  of the control device  101  acquires the history information of the rotation number of the photoconductor  10  from the rotation number history table D 1 . 
     In step S 1220 , the depletion amount calculator  131  aggregates the rotation numbers of each printing rate in the rotation number history table D 1  to create the rotation number aggregation table D 1 ′. 
     In step S 1230 , the depletion amount calculator  131  calculates the depletion amount for the photoconductor for which the life is estimated. 
     In step S 1240 , the life estimator  141  performs the life estimation by comparing the calculated depletion amount with the predetermined life threshold value. 
     In step S 1250 , the life estimator  141  determines whether the end of life has arrived. In a case where the life estimator  141  determines that the end of life has arrived (YES in step S 1250 ) as a result of the life estimation, the control device  101  advances the processing to step S 1260 . Otherwise (NO in step S 1250 ), the control device  101  terminates the processing. 
     In step S 1260 , the control device  101  displays, on the operation panel  105 , replacement of the photoconductor determined to have reached the end of life to notify the user. The control device  101  terminates the processing. 
     [6. Conclusion] 
     As described above, the control device  101  according to the present embodiment calculates the depletion amount due to the reverse transfer toner on the basis of parameters having a positive correlation with the amount of the toner used for the toner image formed on the upstream photoconductor of the photoconductor for which the life is estimated. Further, the control device  101  calculates the depletion amount due to the transfer residual toner on the basis of parameters having a correlation with the amount of the toner used for the toner image formed on the photoconductor itself for which the life is estimated. 
     The control device  101  calculates the integrated value of the depletion amount due to the transfer residual toner and the depletion amount due to the reverse transfer toner, and compares the calculated integrated value with the predetermined life estimation threshold value to estimate the timing when the end of life of the one photoconductor arrives. 
     With the above configuration, not only the depletion amount due to the toner formed by the photoconductor for which the life is estimated but also the depletion amount due to the toner formed by the upstream photoconductors are taken into consideration in estimating the life of the photoconductor. Therefore, the life estimation of the photoconductor can be performed with higher accuracy. 
     Second Embodiment 
     [1. Overview] 
     Hereinafter, a second embodiment will be described. The second embodiment is different from the first embodiment in that a calculation result of a depletion amount is stored in a storage device as a history and life estimation is performed on the basis of the history. Note that, in the present embodiment, similar configurations to the configurations of the image forming apparatus  100  according to the above-described embodiment are denoted by the same reference numerals as those of the image forming apparatus  100 . Therefore, description of the similar configurations is not repeated. 
     [2. Details] 
     An image forming apparatus  200  according to the second embodiment will be described will be described with reference to  FIGS. 14 and 15 .  FIG. 14  is a functional block diagram of the image forming apparatus  200  according to the second embodiment.  FIG. 15  is a graph illustrating a life estimation method in the second embodiment. 
     As illustrated in  FIG. 14 , the image forming apparatus  200  includes a control device  201  and a storage device  220  in place of the control device  101  and the storage device  120  with respect to the configuration of the image forming apparatus  100  illustrated in  FIG. 3 . 
     The control device  201  includes a rotation controller  121 , a depletion amount calculator  231 , and a life estimator  241 . The storage device  220  includes a rotation number history table D 1 , a depletion amount regulation table D 2 , and a depletion amount history table D 3 . The depletion amount calculator  231  stores the calculation result of the depletion amount in the depletion amount history table D 3  provided in the storage device  120 , and the life estimator  241  performs life estimation by reference to the depletion amount history table D 3 . 
     The depletion amount history table D 3  includes the calculation result of the depletion amount of the photoconductor at the timing of performing the life estimation processing. The life estimator  241  estimates timing when the end of life of the photoconductor for which the life is estimated has arrived on the basis of the depletion amount of the photoconductor for which the life is estimated, which has been calculated by the depletion amount calculator  231 , and the depletion amount history table D 3 . 
     In the second embodiment, the life estimator  241  performs life estimation on the basis of the depletion amount calculated at the time of life estimation of previous time by reference to the depletion amount history table D 3 . 
     In the example illustrated in  FIG. 15 , a rate of change of the depletion amount to a rotation number of the photoconductor is a slope illustrated by the straight line OA in the life estimation result of the previous time. The timing when the end of life arrives estimated in this case is illustrated by the point C, and is timing when the rotation number of the photoconductor becomes 1000 (krot). 
     In contrast, the rate of change of the depletion amount to the rotation number of the photoconductor is a slope illustrated by the straight line AB in the life estimation result of this time. In this case, the life estimated of this case is illustrated by the point C′, and is timing when the rotation number of the photoconductor becomes 917 (krot). As described above, the change in the depletion amount and the rotation number from the life estimation of the previous time is calculated on the basis of the calculation result of the depletion amount at the time of the life estimation of the previous time. Therefore, the life estimation can be performed with higher accuracy. 
     [3. Conclusion] 
     As described above, in the second embodiment, the life estimation is performed on the basis of the result of the estimation processing of the previous time by reference to the result of the estimation processing of the previous time. 
     With the above configuration, the accuracy of the life estimation can be further improved. 
     Third Embodiment 
     [1. Overview] 
     Hereinafter, a third embodiment will be described. The third embodiment is different from the first embodiment in that a calculated depletion amount of a photoconductor is corrected on the basis of an operation amount of a consumable member provided in an image forming apparatus. Note that, in the present embodiment, similar configurations to the configurations of the image forming apparatus  100  according to the above-described embodiment are denoted by the same reference numerals as those of the image forming apparatus  100 . Therefore, description of the similar configurations is not repeated. 
     [2. Details] 
       FIG. 16  is a functional block diagram of an image forming apparatus  300  according to the third embodiment. As illustrated in  FIG. 16 , the image forming apparatus  300  includes a control device  301  in place of the control device  101  with respect to the configuration of the image forming apparatus  100 . In addition to the configuration illustrated in  FIG. 3 , the control device  301  further includes a depletion amount corrector  351 . The depletion amount corrector  351  corrects the depletion amount calculated by a depletion amount calculator  131  on the basis of the operation amount of a consumable member such as a developer  14  or a transfer belt  30 . 
     More specifically, the depletion amount corrector  351  determines the operation amounts of the developer  14  and the transfer belt  30  on the basis of control information from a rotation controller  121 . The depletion amount corrector  351  corrects the depletion amount of a photoconductor for which the life is estimated, which is calculated by the depletion amount calculator  131 , on the basis of the operation amounts of the developer  14  and the transfer belt  30 . 
     Here, the operation amount of the developer can be any one of the number of printed sheets in the image forming apparatus  300 , a rotation number of the developing roller provided in the developer  14 , and a rotation time of the developing roller. 
     Further, the operation amount of the transfer belt  30  can be any one of the number of printed sheets in the image forming apparatus  300 , a traveling distance of the transfer belt  30 , and a traveling time of the transfer belt  30 . 
     A relationship between the operation amounts of the developer  14  and the transfer belt  30  and a percentage of a transfer residual toner is illustrated with reference to  FIG. 17 .  FIG. 17  is a diagram illustrating the operation amounts of the developer  14  and the transfer belt  30 , and the percentage of the transfer residual toner. Here, the operation amount can be counted by, for example, the number of printed sheets on which image formation is performed. 
     As illustrated in  FIG. 17 , the percentage of the transfer residual toner decreases as the operation amount of the developer  14  increases. This is because a charge amount to a toner decreases as the operation amount of the developer  14  increases, and thus a transfer rate to the transfer belt rises. 
     In contrast, the percentage of the transfer residual toner increases as the operation amount of the transfer belt  30  increases. This is because a belt surface becomes rough and the transfer rate decreases as the operation amount of the transfer belt  30  increases. 
       FIGS. 18A and 18B  are diagrams illustrating correction coefficients of self depletion amounts with respect to the operation amounts of the developer  14  and the transfer belt  30 . Since the amount of the transfer residual toner and the depletion amount of the photoconductor have a positive correlation, the depletion amount can be more accurately calculated by multiplying a self depletion amount  161  in a depletion amount regulation table D 2  in  FIG. 5  by the correction coefficients in  FIGS. 18A and 18B . 
     A relationship between the operation amounts of the developer  14  and the transfer belt  30  and a percentage of a reverse transfer toner is illustrated with reference to  FIG. 19 .  FIG. 19  is a diagram illustrating the operation amounts of the developer  14  and the transfer belt  30 , and the percentage of the reverse transfer toner. 
     As illustrated in  FIG. 19 , the percentage of the reverse transfer toner increases as the operation amount of the developer  14  increases. This is because the charge amount to the toner decreases as the operation amount of the developer  14  increases, and thus the toner becomes easily separated from the transfer belt  30  and becomes easily reversely transferred. 
     In contrast, the percentage of the reverse transfer toner decreases as the operation amount of the transfer belt  30  increases. This is because as the surface of the belt becomes rough, absorption force between the belt and the toner rises, and the toner becomes less easily reversely transferred, as the operation amount of the transfer belt  30  increases. 
       FIGS. 20A and 20B  are diagrams illustrating correction coefficients of reverse transfer depletion amounts with respect to the operation amounts of the developer  14  and the transfer belt  30 . Since the amount of the transfer residual toner and the depletion amount of the photoconductor have a correlation, the depletion amount can be more accurately calculated by multiplying a reverse transfer depletion amount  163  in the depletion amount regulation table D 2  in  FIG. 5  by the correction coefficients in  FIGS. 20A and 20B . 
     [3. Conclusion] 
     As described above, the depletion amount corrector  351  included in the control device  301  corrects the depletion amount calculated by the depletion amount calculator  131  on the basis of the operation amount of the developer  14  or the transfer belt  30 . 
     With the above configuration, the depletion amount of the photoconductor can be accurately corrected according to the operation amount of the consumable member such as the developer  14  or the transfer belt  30 , and the accuracy of the life estimation of the photoconductor can be improved. 
     Fourth Embodiment 
     [1. Overview] 
     Hereinafter, a fourth embodiment will be described. The fourth embodiment is different from the first embodiment in that a depletion amount is calculated for each of a plurality of sections divided in a longitudinal direction of a photoconductor. Note that, in the present embodiment, similar configurations to the configurations of the image forming apparatus  100  according to the above-described embodiment are denoted by the same reference numerals as those of the image forming apparatus  100 . Therefore, description of the similar configurations is not repeated. 
     [2. Details] 
       FIG. 21  is a functional block diagram of an image forming apparatus  400  according to the fourth embodiment. As illustrated in  FIG. 21 , the image forming apparatus  400  includes a control device  401  in place of the control device  101  with respect to the configuration of the image forming apparatus  100 . The control device  401  includes a rotation controller  121 , a life estimator  141 , and a depletion amount calculator  431 . The depletion amount calculator  431  includes a first calculator  433 , a second calculator  435 , and a third calculator  437  for calculating the depletion amount for three sections along the longitudinal direction of the photoconductor. 
       FIG. 22  is a diagram illustrating a rotation number history table D 1  according to the fourth embodiment. As illustrated in  FIG. 22 , the rotation number history table D 1  includes a section  154 . The section  154  means three sections in a case where the photoconductor is divided into the three sections in the longitudinal direction. The rotation number history table D 1  stores a printing rate for each of a first section, a second section, and a third section every time image formation is executed. 
     The first calculator  433  included in the depletion amount calculator  431  calculates the depletion amount in the first section of the photoconductor. The second calculator  435  calculates the depletion amount in the second section of the photoconductor. The third calculator  437  calculates the depletion amount in the third section of the photoconductor. 
       FIG. 23  is a diagram exemplarily illustrating the magnitude of the depletion amount calculated for each section. In the example illustrated in  FIG. 23 , the depletion amount calculated in the second section is larger than the depletion amounts calculated in the other sections. Therefore, the life estimator  141  performs life estimation of the photoconductor, using the depletion amount calculated in the second section. Since the printing rate sometimes differs in the longitudinal direction in the photoconductor, the accuracy of the life estimation is improved by performing the life estimation on the basis of the depletion amount in the section where the depletion amount is the largest. 
     [3. Conclusion] 
     As described above, the depletion amount calculator  431  calculates the depletion amount for each of the sections divided in the longitudinal direction of the photoconductor. 
     With the above configuration, the life estimation can be performed with more accuracy by calculating the depletion amount for each of the sections divided along the longitudinal direction even in the case where the printing rate differs along the longitudinal direction of the photoconductor. 
     Fifth Embodiment 
     [1. Overview] 
     Hereinafter, a fifth embodiment will be described. The present embodiment is different from the first embodiment in that a life estimation device configured as a server performs life estimation. Note that, in the present embodiment, similar configurations to the configurations of the image forming apparatus  100  according to the above-described embodiment are denoted by the same reference numerals as those of the image forming apparatus  100 . Therefore, description of the similar configurations is not repeated. 
     [2. Details] 
     Functions of a life estimation device  550  according to the fifth embodiment will be described with reference to  FIG. 24 .  FIG. 24  is a functional block diagram of the life estimation device  550  according to the fifth embodiment. 
     As illustrated in  FIG. 24 , the life estimation device  550  includes a control device  501 . The control device  501  is configured by, for example, at least one integrated circuit. The integrated circuit is configured by, for example, at least one central processing unit (CPU), at least one application specific integrated circuit (ASIC), or at least one field programmable gate array (FPGA), or a combination thereof. 
     The life estimation device  550  functions as a so-called server and is configured to be able to communicate with an image forming apparatus  500  through a network. The image forming apparatus  500  has a similar configuration to the image forming apparatus  100  illustrated in  FIG. 3 . The life estimation device  550  includes a depletion amount calculator  531  and a life estimator  541 . The life estimation device  550  estimates the life of the photoconductor on the basis of a rotation number history table D 1  and a depletion amount regulation table D 2  transmitted from the image forming apparatus  500 . 
     The life estimation device  550  acquires information such as the temperature and humidity in the image forming apparatus  500 , operation amounts of a developer  14  and a transfer belt  30 , and content of printing images, and analyzes variation in the life estimation from an operation state of the image forming apparatus  500 . Further, the life estimation device  550  may transmit a threshold value of an integrated value of weighting or life exponents to another image forming apparatus in a similar operation state. 
     Further, the life estimation device  550  may modify a threshold value of an integrated value of weighting coefficients or life exponents of a reverse transfer depletion amount according to the degree of image quality requirement by a user, or may be configured to adjust various life determination parameters with respect to a plurality of image forming apparatuses to modify the integrated value of the weighting coefficients or the life exponents according to a region, a season, a company, or a business style. With the configuration, parts can be ordered and replaced at appropriate timing by a plurality of apparatuses, the cost of replacement parts can be reduced, and labor cost reduction and inventory reduction can be realized. 
     [3. Conclusion] 
     As described above, the life estimation device  550  performs the life estimation of the photoconductor for the communicatively configured image forming apparatus  500 . 
     With the configuration, the life estimation for a plurality of image forming apparatuses can be performed by a single life estimation device, and the operation states of the plurality of image forming apparatuses can be centrally managed, whereby the life estimation processing can be efficiently performed. 
     OTHER EMBODIMENTS 
     Note that the scope of application of the technical idea according to the present disclosure is not limited to the above embodiments. For example, in the above-described embodiments, the depletion amount calculator  131  calculates the depletion amount as the integrated value of the self depletion amount and the reverse transfer depletion amount for the photoconductor for which the life is estimated. However, the depletion amount calculator  131  may be configured to calculate only the reverse transfer depletion amount. In this case, as for the self depletion amount, a depletion amount statistically predicted from the integrated value of the rotation numbers of the photoconductor or the operation amount such as the rotation time of the photoconductor may be used. By doing so, the difference in the depletion amounts in the photoconductors  10 Y,  10 M,  10 C, and  10 K can be considered on the basis of the reverse transfer depletion amounts, and the life estimation with higher accuracy can be performed. 
     Although embodiments of the present invention have been described and illustrated in detail, the disclosed embodiments are made for purposes of illustration and example only and not limitation. The scope of the present invention should be interpreted by terms of the appended claims, and it is intended that all modifications within the meaning and scope equivalent to the claims are included.