Abstract:
An image forming apparatus includes image holding bodies that hold latent images and toner images, developer units that form toner images by developing the latent images, a transfer unit that transfers the toner images to a recording medium, a fixing unit that fixes the transferred toner images to the recording medium, container mounting portions on which toner containers are replaceably mounted, and remaining toner amount calculating units that calculate the amount of toners remaining in the toner containers, wherein the remaining toner amount calculating unit includes a primary calculator that calculates plural primary remaining amounts on the basis of bases different from each other, a storage unit that stores empty area data of a remaining amount space, and a secondary calculator that refers to the empty area data stored in the storage unit, and calculates a ratio of a distance.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is based on and claims priority under 35 USC 119 from Japanese Patent Application No. 2011-068493 filed Mar. 25, 2011. 
       BACKGROUND 
       [0002]    (i) Technical Field 
         [0003]    The present invention relates to an image forming apparatus. 
         [0004]    (ii) Related Art 
         [0005]    As an image forming apparatus, there is an image forming apparatus where toner containers storing replenishing toners are replaceably mounted and the toners are replenished to a developer unit from the mounted toner containers in accordance with the decrease of the toners in the developer unit. In the case of this type of image forming apparatus, it is necessary to facilitate the replacement of the toner container through the detection of the life (emptiness) of the mounted toner container. Further, it is preferable to warn a user of the decrease of the remaining amount of toner or to inform a user of the amount (%) of toner remaining in the toner container even before the life of the toner container has come to an end. 
         [0006]    Here, there is proposed a technique that estimates the remaining amount of developer by counting pixels and detects the amount of developer, which remains immediately before the developer runs out, by capacitance. 
         [0007]    Further, there is proposed a technique that predicts the remaining amount of toner from a cumulative value of the amount of replenished toner until the life of a toner cartridge becomes equal to or shorter than a threshold where there is the remaining amount of toner and predicts the remaining amount of developer at the time of emptiness from the cumulative number of pixels. 
       SUMMARY 
       [0008]    According to an aspect of the invention, there is provided an image forming apparatus including: image holding bodies that hold latent images by being subjected to exposure and hold toner images by being developed with toners; developer units that form toner images by developing the latent images held on the image holding bodies with toners; a transfer unit that transfers the toner images formed on the image holding bodies to a recording medium; a fixing unit that fixes the transferred toner images to the recording medium; container mounting portions on which toner containers storing replenishing toners to be supplied to the developer unit are replaceably mounted; and remaining toner amount calculating units that calculate the amount of toners remaining in the toner containers mounted on the container mounting portions, wherein the remaining toner amount calculating unit includes a primary calculator that calculates plural primary remaining amounts by calculating the amount of toner remaining in the toner container on the basis of bases different from each other, respectively, a storage unit that stores empty area data of a remaining amount space where an empty area, where the toner container is empty, in a remaining amount space, which uses the plural primary remaining amounts as variables, is defined, and a secondary calculator that refers to the empty area data stored in the storage unit, and calculates a ratio of a distance between current coordinates and a point reaching the empty area to a distance between an origin and the point reaching the empty area on a straight line, which passes through the origin where the toner container is not in use and the current coordinates that are defined by the plural primary remaining amounts calculated in the primary calculator in the remaining amount space, as the current remaining amount of toner. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0009]    Exemplary embodiments of the present invention will be described in detail based on the following figures, wherein: 
           [0010]      FIG. 1  is a perspective view of the appearance of a copying machine as an example of an image forming apparatus; 
           [0011]      FIG. 2  is an internal configurational diagram of the copying machine of which the appearance is shown in  FIG. 1 ; 
           [0012]      FIG. 3  is a schematic cross-sectional view showing a toner container and a developer unit; 
           [0013]      FIG. 4  is a schematic cross-sectional view showing the toner container and the developer unit; 
           [0014]      FIG. 5  is a block diagram showing a control system of this exemplary embodiment; 
           [0015]      FIG. 6  is a flowchart illustrating a process for calculating the remaining amount of toner that is performed by a main controller when power is supplied to the copying machine shown in  FIG. 1 ; 
           [0016]      FIG. 7  is a flowchart illustrating a process for calculating the remaining amount of toner that is performed when there is a print request; 
           [0017]      FIG. 8  is a view illustrating an algorithm of this exemplary embodiment that calculates the remaining amount of toner. 
           [0018]      FIG. 9  is a view showing a remaining amount space when the remaining amount of toner is calculated on the basis of only a calculated value of the cumulative amount of replenished toner; 
           [0019]      FIG. 10  is a view showing a remaining amount space when the remaining amount of toner is calculated on the basis of only a value of the cumulative number of pixels; and 
           [0020]      FIG. 11  is a view that is based on both a calculated value of the cumulative amount of replenished toner and the cumulative number of pixels but shows a remaining amount space when a warning is displayed for the faster one of them. 
       
    
    
     DETAILED DESCRIPTION 
       [0021]    An exemplary embodiment of the invention will be described below. 
         [0022]      FIG. 1  is a perspective view of the appearance of a copying machine as an example of an image forming apparatus. 
         [0023]    The copying machine  1  includes a document reading section  1 A and an image forming section  1 B. 
         [0024]    The document reading section  1 A is provided with a document feed table  11  on which documents are placed while being stacked. The documents placed on the document feed table  11  are fed one by one, letters or images recorded on the document are read out, and the document is discharged onto a document discharge table  12 . 
         [0025]    Further, the document reading section  1 A includes a hinge, which extends to the left and right sides, on the back side. The document feed table  11  and the document discharge table  12  can be integrally lifted so as to rotate about the hinge as a rotation center, and a document reading plate  13  (see  FIG. 2 ) made of transparent glass is spread below the document feed table  11  and the document discharge table  12 . In the document reading section  1 A, it may be possible to read letters or images from a document placed on the document reading plate  13  by placing only one document on the document reading plate  13  so that the surface of the document to be read faces downward instead of placing documents on the document feed table  11 . 
         [0026]    A display operation section  14  is provided in front of the document reading plate  13 . The display operation section  14  displays various messages to a user, displays various operation buttons, and is subjected to operations, such as an instruction for reading a document and an instruction for forming an image. 
         [0027]    The entire document reading section  1 A is supported by a support frame  15 . 
         [0028]    Further, the image forming section  1 B is provided with a sheet discharge table  21  to which a sheet on which an image has been formed is discharged. Furthermore, a front cover  22 , which is opened to replace a part such as a toner container provided in the image forming section or remove a sheet jammed during transport, is provided on the front surface of the image forming section  1 B. Moreover, three drawer type sheet feed trays  23 _ 1 ,  23 _ 2 , and  23 _ 3 , in which sheets on which images are not formed yet are stored while being stacked, are housed below the front cover  22 . 
         [0029]    Further, a lateral cover  24 , which is opened to remove a sheet jammed during transport, is provided on the left side surface of the image forming section  1 B. 
         [0030]    Furthermore, wheels  251 , which allow the image forming section  1 B to be movable, are mounted on the bottom of the image forming section  1 B. 
         [0031]      FIG. 2  is an internal configurational diagram of the copying machine of which the appearance is shown in  FIG. 1 . 
         [0032]    A document reading optical system  30  is provided below the document reading plate  13  made of transparent glass. The document reading optical system  30  includes a first block  31  that includes a lamp  311  and a mirror  312 , a second block  32  that includes two mirrors  321  and  322 , and a photoelectric sensor  33  that reads light representing an image and generates image signals. 
         [0033]    The first and second blocks  31  and  32  are movable in the directions of arrows A and A′ along the document reading plate  13 , and are at left positions shown in  FIG. 2  in an initial state. 
         [0034]    Documents S placed on the document feed table  11  are fed one by one, and are transported onto a transporting path  17  facing the document reading plate  13  by transport rollers  16 . When being transported while facing the document reading plate  13 , the documents S are irradiated by the lamp  311 . Light reflected from the documents S is reflected by the mirrors  312 ,  321 , and  322  and read by the photoelectric sensor  33 , and image signals representing letters or images recorded on the documents S are generated. The documents S, which are irradiated by the lamp  311 , are further transported and fed onto the document discharge table  12 . 
         [0035]    When a document is placed on the document reading plate  13 , the first and second blocks  31  and  32  move in the direction of the arrow A so that an optical distance between the photoelectric sensor  33  and a document reading position on the document reading plate  13  is always maintained constant. Further, the lamp  311  irradiates the document in the meantime, and letters or images recorded on the document are read by the photoelectric sensor  33  and converted into image signals. 
         [0036]    The image signals obtained by the photoelectric sensor  33  are input to an image processing unit  34 . The image signals obtained by the photoelectric sensor  33  are image signals that represent colors, that is, R (red), G (green), and B (blue). The image processing unit  34  converts these RGB image signals to image data that are formed of Y (yellow), M (magenta), C (cyan), and K (black), and temporarily stores the image data. Moreover, the image data are sent to an exposure controller  41  in time for the exposure for forming a latent image to be described below. 
         [0037]    The image forming section  1 B is provided with an exposure unit  42 . The image data corresponding to Y, M, C, and K are sent to the exposure unit  42  from the exposure controller  41  in accordance with the format of a latent image, and respective exposure lights  421 Y,  421 M,  421 C, and  421 K, which are modulated by the respective image data corresponding to Y, M, C, and K, are radiated from the exposure unit  42 . 
         [0038]    Further, in  FIG. 2 , a main controller  40  is shown at a position adjacent to the exposure controller  41 . The main controller  40  is formed of a microcomputer and a program that is executed by the microcomputer. The main controller  40  is connected to the exposure controller  41 , the display operation section  14  (see  FIG. 1 ), the image processing unit  34 , other various power circuits or drive circuits (not shown), and the like; and is in charge of the control of the entire copying machine  1 . 
         [0039]    The above-mentioned three sheet feed trays  231 ,  232 , and  23 _ 3  are supported by left and right guide rails  24 _ 1 ,  24 _ 2 , and  24 _ 3  and housed in the lower portion of the image forming section  1 B. Sheets P are stored in each of the sheet feed trays  23 _ 1 ,  23 _ 2 , and  23 _ 3  while being stacked. Each of the sheet feed trays  231 ,  232 , and  233  is adapted so as to be capable of being freely drawn while being guided by the guide rails  24 _ 1 ,  24 _ 2 , and  24 _ 3 , for the purpose of the replenishment of sheets P. 
         [0040]    Sheets P are fed from a sheet feed tray (here, for example, the sheet feed tray  23 _ 1 ), which is designated by the operation or the like of the display operation section  14  (see  FIG. 1 ), among these three sheet feed trays  23 _ 1 ,  23 _ 2  and  23 _ 3  by a pickup roll  25  and are separated one by one by retard rolls  26 . One separated sheet P is transported upward by transport rolls  27 . Then, the transport timing of the sheet after standby rolls  28  is adjusted by the standby rolls  28 , and the sheet is further transported upward. The transport of a sheet after the standby rolls  28  will be described below. 
         [0041]    Four image forming units  50 Y,  50 M,  50 C, and  50 K, which form toner images by the toners corresponding to the respective colors, that is, Y, M, C, and K, are disposed in the middle portion of the image forming section  1 B. Since these four image forming units  50 Y,  50 M,  50 C, and  50 K have the same configuration except that colors of toners in use are different from each other, the image forming unit  50 Y is selected here and the configuration of the image forming unit  50 Y will be described. 
         [0042]    The image forming unit  50 Y includes a photoreceptor  51  that rotates in the direction indicated in  FIG. 2  by an arrow B. A charger  52 , a developer unit  53 , and a cleaner  55  are disposed around the photoreceptor  51 . Further, a transfer unit  54  is disposed at a position where an intermediate transfer belt  61  to be described below is interposed between the photoreceptor  51  and the transfer unit  54 . 
         [0043]    The photoreceptor  51  has the shape of a roll, retains electrical charges by charging, discharges the electrical charges by exposure, and holds an electrostatic latent image on the surface thereof. 
         [0044]    The charger  52  charges the surface of the photoreceptor  51  to a certain charged potential. 
         [0045]    Moreover, the image forming section  1 B includes the above-mentioned exposure unit  42 . Image signals are input to the exposure unit  42  from the exposure controller  41 , and the exposure unit  42  outputs the exposure lights  421 Y,  421 M,  421 C, and  421 K that are modulated according to the input image signal. After being charged by the charger  52 , the photoreceptor  51  is irradiated with the exposure light  421 Y output from the exposure unit  42 . Accordingly, an electrostatic latent image is formed on the surface of the photoreceptor  51 . 
         [0046]    After the photoreceptor  51  is irradiated with the exposure light  421 Y and the electrostatic latent image is formed on the surface of the photoreceptor  51 , the electrostatic latent image is developed by the developer unit  53 . Accordingly, a toner image (a toner image formed using a yellow (Y) toner in the image forming unit  50 Y) is formed on the surface of the photoreceptor  51 . 
         [0047]    The developer unit  53  includes two augers  532 _ 1  and  532 _ 2  and a developing roller  533  that are disposed in a case  531  in which a developer formed of a toner and a carrier is stored. The two augers  532 _ 1  and  532 _ 2  agitate the developer, and the developing roller  533  carries the developer to a position facing the photoreceptor  51 . When the electrostatic latent image formed on the photoreceptor  51  is developed, a bias voltage is applied to the developing roller  533  and the toner contained in the developer is attached to the photoreceptor  51  along the electrostatic latent image, which is formed on the photoreceptor  51 , by the action of the bias voltage. Accordingly, a toner image is formed. 
         [0048]    The toner image, which is formed on the photoreceptor  51  through the development performed by the developer unit  53 , is transferred to the intermediate transfer belt  61  by the action of the transfer unit  54 . 
         [0049]    A toner, which remains on the photoreceptor  51  after this transfer, is removed from the photoreceptor  51  by the cleaner  55 . 
         [0050]    The intermediate transfer belt  61  is an endless belt that is wound around plural rolls  62  and rotated in the direction of an arrow C. 
         [0051]    The toner images, which are formed using the respective color toners by the respective image forming units  50 Y,  50 M,  500 , and  50 K, are transferred to the intermediate transfer belt  61  so as to be sequentially stacked, and are transported to a secondary transfer position where a transfer unit  63  is disposed. A sheet, which has been transported to the standby rolls  28 , is transported to the secondary transfer position in synchronization with this and the toner images transferred to the intermediate transfer belt  61  are transferred to the transported sheet by the action of the transfer unit  63 . The sheet to which the toner images have been transferred is further transported, and the toner images transferred to the sheet are fixed to the sheet by being pressed and heated by the fixing unit  64 . Accordingly, an image formed of the fixed toner images is formed on the sheet. The sheet on which the image has been formed is further transported, and is discharged onto the sheet discharge table  21  by discharge rollers  65 . 
         [0052]    The intermediate transfer belt  61  from which the toner images have been transferred to the sheet by the transfer unit  63  is further rotated, and a toner remaining on the surface of the intermediate transfer belt is removed from the intermediate transfer belt  61  by a cleaner  66 . 
         [0053]    Further, container mounting portions  29 Y,  29 M,  29 C, and  29 K are provided above the intermediate transfer belt  61  in the image forming section  1 B. Toner containers  67 Y,  67 M,  67 C, and  67 K, which store the respective color toners corresponding to yellow (Y), magenta (M), cyan (C), and black (K), are mounted on these container mounting portions  29 Y,  29 M,  29 C, and  29 K, respectively. The respective color toners, which are stored in these toner containers  67 Y,  67 M,  67 C, and  67 K, are replenished to the respective developer units  53  according to the consumption of the toners in the corresponding developer units  53 . 
         [0054]    Moreover, in the image forming section  1 B, “process control” is performed with various events, such as the formation of a predetermined number of images or the change of temperature and humidity environment and the replacement of a part. In this process control, uniform images having predetermined image densities (toner patches) are formed, the densities of the toner patches are measured by a detector (not shown) and compared with a reference density, and various elements are adjusted so that the density of the patch becomes a reference. The various elements include, for example, the conversion of the image density of image data, the amount of toner replenished to the developer unit from the toner container, the amount charged by the charger, the amount of exposure light radiated by the exposure unit, the developing bias voltage of the developer unit, and the like. The temporal change of image density is corrected by this process control, so that an image having constant density is formed. When an event where process control should be performed comes, process control cannot be immediately performed since a printing operation or the like is being performed at this point of time. Accordingly, a process control execution request flag is raised and the flag is referred at a timing where process control can be performed, and the process control is performed if the flag is raised. 
         [0055]      FIGS. 3 and 4  are schematic cross-sectional views showing the toner container and the developer unit. Here,  FIG. 3  is a schematic cross-sectional view when seen from the side, and  FIG. 4  is a schematic cross-sectional view when seen from above. 
         [0056]    Here, only one system is typically shown and the respective components are denoted by reference numerals of which Y, M, C, and K are omitted. 
         [0057]    A developer  537  (see  FIG. 3 ), which includes a toner and a carrier, is stored in the developer unit  53  and is agitated by two augers  532 _ 1  and  532 _ 2  so as to circulate in the direction indicated by arrows F, G, H, and I shown in  FIG. 4 . The developer  537  is held by the developing roller  533  rotating in the direction indicated by an arrow E, is subjected to layer thickness regulation performed by a layer thickness regulating member  534 , and is transported to a development position facing the photoreceptor  51 . Meanwhile, the photoreceptor  51  rotates in the direction indicated by an arrow B, is charged by the charger  52 , and is irradiated with exposure light radiated from the exposure unit  42 , so that an electrostatic latent image is formed. The electrostatic latent image is developed by the toner contained in the developer that is transported by the developing roller  533 . Accordingly, a toner image is formed on the photoreceptor  51 . Since the subsequent process of the toner image formed on the photoreceptor  51  has been described with reference to  FIG. 2 , the repeated description thereof will be omitted here. 
         [0058]    When the toner contained in the developer  537  stored in the developer unit  53  is consumed in this way, the toner contained in the developer  537  falls short. Then, an auger  681  provided in a toner replenishing passage  68  rotates, so that a replenishing toner  671  stored in the toner container  67  is transported in the toner replenishing passage  68  in the direction indicated by an arrow J and is supplied to the developer unit  53 . While being transported so as to circulate along the arrows F, G, H, and J shown in  FIG. 4 , the toner supplied to the developer unit  53  is agitated by the two augers  532 _ 1  and  532 _ 2  and mixed with the carrier. 
         [0059]      FIG. 5  is a block diagram showing a control system of this exemplary embodiment.  FIG. 5  shows only elements required for illustrating the characteristic portions of this exemplary embodiment. 
         [0060]    The main controller  40 , the display operation section  14 , the exposure controller  41 , the exposure unit  42 , the developer unit  53 , the toner container  67 , the photoreceptors SOY,  50 M,  50 C, and  50 K, and intermediate transfer belt  61 , which are also shown in  FIG. 1  or  2 , are shown in  FIG. 5 . However, in  FIG. 5 , developer units  53  are shown as the four developer units shown in  FIG. 2  and toner containers  67  are shown as the four toner containers shown in  FIG. 2 . Since these respective elements shown in  FIG. 1  or  2  have been described except for matters concerning the communication between the toner container  67  and the main controller  40 , the repeated description thereof will be omitted and only the matters concerning the communication will be described. 
         [0061]    Nonvolatile memories (not shown) corresponding to the toner containers  67 Y,  67 M,  67 C, and  67 K (see  FIG. 2 ) corresponding to the respective colors, that is, Y, M, C, and K are mounted on the toner containers  67 . The main controller  40  communicates with the nonvolatile memories mounted on these respective toner containers  67 , and reads out the types, past use history, or the like of the toner containers from the nonvolatile memories or writes new use history or the like. 
         [0062]    An image density calculator  91 , a replenished amount calculator  92 , and an image density detector  93  are further shown in  FIG. 5 . 
         [0063]    In the image density calculator  91 , image density is calculated for each of the colors, that is, Y, M, C, and K on the basis of the image data sent to the exposure controller  41  from the image processing unit  34  shown in  FIG. 2 . That is, in the image forming section  1 B shown in  FIGS. 1 and 2 , the images representing the shading of images are formed by the densities of pixels to which toners are attached. In the image density calculator  91 , the number of pixels, to which the toners are attached, for each of the images and the colors, that is, Y, M, C, and K is calculated on the basis of the image data. The information about the calculated number of pixels is sent to the main controller  40 , and the cumulative number of pixels, which is a value of the cumulative number of pixels of images formed until now, is calculated for each of the colors, that is, Y, M, C, and K in the main controller  40 . 
         [0064]    Further, the amount of toner replenished to the developer unit  53  from the toner container  67  is calculated in the replenished amount calculator  92 . However, since the amount of replenished toner is calculated on the basis of the number of rotations of the auger  681  provided in the toner replenishing passage  68  shown in  FIGS. 3 and 4 , the amount of replenished toner may be different from the actual amount of replenished toner. For example, the actual amount of replenished toner fluctuates due to environmental temperature and humidity, and the actual amount of replenished toner fluctuates even when the toner container  67  is filled with a replenishing toner and is substantially empty. The information about the amount of replenished toner, which is calculated in the replenished amount calculator  92 , is transmitted to the main controller  40 , and a calculated value of the cumulative amount of replenished toner, which is a value of the cumulative amount of replenished toner, is calculated in the main controller  40 . Here, the calculation of the amount of replenished toner, which is to be performed in the replenished amount calculator  92 , is also performed for each of the respective color toners corresponding to Y, M, C, and K like the calculation of the number of pixels that is performed in the image density calculator  91 . Accordingly, a calculated value of the cumulative amount of replenished toner, which corresponds to each of the color toners, is calculated in the main controller  40 . 
         [0065]    Furthermore, the densities of the respective toner patches, which are formed in the above-mentioned process control by the respective color toners corresponding to Y, M, C, and K, are detected in the image density detector  93 . The detection results of the densities of these toner patches are also transmitted to the main controller  40 . 
         [0066]    A toner remaining amount calculating process for calculating the amount of toner remaining in the toner container, which is to be performed in the main controller  40 , will be described with reference to the above-mentioned configuration. 
         [0067]      FIG. 6  is a flowchart illustrating a process for calculating the remaining amount of toner that is performed by the main controller when power is supplied to the copying machine shown in  FIG. 1 . 
         [0068]    When power is supplied to the copying machine  1  shown in  FIGS. 1 and 2  (Step S 01 ), the amount of toner remaining in the toner container is displayed on the display operation section  14  shown in  FIG. 1  (Step S 02 ). The remaining amount of toner, which is displayed here, is the remaining amount of toner that is calculated in Step S 23  or S 24  shown in  FIG. 7 , updated according to need (Step S 26 ), and displayed when power has been turned off last time. A method of calculating the remaining amount of toner will be described below. However, when a new toner container is not used yet after being mounted, the remaining amount of toner is displayed as 100%. 
         [0069]    Then, it is determined whether the remaining amount of toner is equal to or smaller than a threshold A (Step S 03 ). If it is determined that the remaining amount of toner is equal to or smaller than the threshold A, a warning is displayed in addition to the remaining amount of toner of Step S 02  (Step S 04 ). Here, the threshold A corresponds to an example of a second threshold of the invention, and is a threshold used to determine that the amount of toner remaining in the toner container is reduced to, for example, 25%. 
         [0070]    Moreover, it is determined in Step S 05  whether the life of the toner container has come to an end, that is, whether the amount of toner remaining in the toner container is 0%. 
         [0071]    If it is determined that the life of the toner container has come to an end, a replacement request message is displayed so that the toner container is replaced with a new toner container (Step S 06 ) and a printing operation is temporarily inhibited (Step S 07 ). When the toner container is replaced, a process (not shown) for resuming a printing operation is performed and a printing operation is allowed again. 
         [0072]    Meanwhile, as shown in  FIG. 2 , four toner containers  67 Y,  67 M,  67 C, and  67 K are mounted on the copying machine  1 . Accordingly, a process or a display is performed for each of the toner containers in Steps S 02  to S 04  and Step S 06 . However, in Step S 05 , it is determined that the life of the toner container has come to an end even if the life of any one toner container of the four toner containers has come to an end. Then, the process proceeds to Step S 06 . In Step S 07 , a printing operation is inhibited even if the life of any one toner container has come to an end. 
         [0073]    If it is determined in Step S 05  that the lives of all the four toner containers have not yet come to an end, the process proceeds to Step S 11  and it is determined whether a process control execution request flag is raised. If a process control execution request flag is not raised, a process at the time of power-on shown in  FIG. 6  is ended. 
         [0074]    If it is determined in Step S 11  that a process control execution request flag is raised, process control is performed (Step S 12 ). Further, the density of a toner patch formed in the process control is detected in the image density detector  93  shown in  FIG. 5 , and it is determined whether the density of the toner patch is lower than a threshold B (Step S 06 ). The threshold B is a threshold used to determine that the concentration of a toner of a developer stored in the developer unit (a ratio of a toner to a carrier) is excessively reduced and thus should be recovered. If it is determined in Step S 13  that the concentration of a toner is not lower than the threshold B, the process shown in  FIG. 6  is ended. The process control itself is simultaneously performed for the respective colors, that is, Y, M, C, and K. However, a process, such as, the determination of whether the concentration of a toner is lower than the threshold B (Step S 13 ) or the subsequent recovery replenishment (Step S 14 ) to be described below, are performed for the respective developer units or toner containers corresponding to the respective color toners corresponding to Y, M, C, and K. 
         [0075]    Meanwhile, if it is determined in Step S 13  that the concentration of a toner is lower than the threshold B, the process proceeds to Step S 14  and recovery replenishment is performed. That is, here, a replenishing operation for replenishing a toner to the developer unit from the toner container is performed to recover the concentration of a toner of a developer stored in the developer unit. Specifically, a process for rotating the auger  681  provided in the toner replenishing passage  68  shown in  FIGS. 3 and 4  is performed here. After that, process control is performed again (Step S 15 ) and it is determined whether the concentration of a toner is recovered (Step S 16 ). If the concentration of a toner is recovered, the process shown in  FIG. 6  is ended. Meanwhile, a toner replenishing operation is not performed only when process control is performed. That is, the amount of toner used is estimated from the amount of a usually used toner and a toner is also replenished by the amount of toner corresponding to the estimated amount of toner used. If the concentration of a toner is still lower than the threshold B (Step S 13 ), recovery replenishment (Step S 14 ) is performed. The recovery replenishment is performed in a normal operating range as described above, but is performed in the following states in terms of the amount of toner remaining in the toner container that is of interest in this exemplary embodiment. That is, for example, a process subsequent to Step S 14  is performed when the toner container on which the nonvolatile memory is mounted is empty due to a certain reason even though it is determined that the life of the toner container has not yet come to an end from the data of the nonvolatile memory mounted on the toner container. That is, the process subsequent to Step S 14  is a process for securing safety when any abnormality occurs in terms of the life of the toner container. 
         [0076]    If it is determined in Step S 16  that the concentration of a toner is not recovered (which means that the remaining amount of toner is actually 0% although it is determined that the life of the mounted toner container has not yet come to an end as described above), a replacement request message for the toner container is displayed on the display operation section  14  (see  FIGS. 1 and 5 ) (Step S 17 ). 
         [0077]    After that, if a new toner container is mounted (Step S 18 ), the recovery replenishment is performed again (Step S 14 ). The communication with a nonvolatile memory mounted on a toner container, of which reliable mounting is determined with the detection of, for example, an operation for opening/closing the front cover  22  shown in  FIG. 1 , is tried and it is determined that the toner container is mounted if the communication with the nonvolatile memory can be performed. 
         [0078]      FIG. 7  is a flowchart illustrating a process for calculating the remaining amount of toner that is performed when there is a print request. Except for the execution of page print (Step S 32 ), the execution of process control (Steps S 36  and S 39 ), and the inhibition of print (Step S 31 ), a process shown in  FIG. 7  is also performed for the respective developer units or toner containers corresponding to the respective color toners corresponding to Y, M, C, and K. 
         [0079]    If the image forming section  1 B shown in  FIGS. 1 and 2  receives a print request (Step S 21 ), it is determined first whether the cumulative number of pixels after the mounting of a new toner container is smaller than a threshold C (Step S 22 ). 
         [0080]    The threshold C corresponds to an example of a first threshold of the invention, and is a threshold used to determine whether a stage is in an early stage where a new toner container is mounted and has just started to be used. A value, which is obtained by converting the cumulative number of pixels into the remaining amount of toner and corresponds to, for example, 90% of the remaining amount of toner, is employed as the threshold C. 
         [0081]    Here, in  FIG. 8  to be described below, a value exceeding 100% from 0% is shown as the cumulative number of pixels and a value exceeding 100% from 0% is shown as a calculated value of the cumulative amount of replenished toner. 0% of the cumulative number of pixels and 0% of a calculated value of the cumulative amount of replenished toner among these values mean a state where the amount of toner remaining in a toner container immediately after the mounting of a new toner container is 100%. Further, 100% of the cumulative number of pixels and 100% of a calculated value of the cumulative amount of replenished toner are the cumulative number of pixels and a calculated value of the cumulative amount of replenished toner that can be regarded as the life of a toner container when an image having normal image density continues to be printed under a normal operating environment. However, actually, the operating environment is also variously changed, so that the image density of an image to be printed is also variously changed. Accordingly, the life of a toner container may be lower than 100%, and may not come to an end yet even though exceeding 100%. 
         [0082]    The description of  FIG. 8  is completed here, and description will be continued returning to  FIG. 7 . 
         [0083]    If it is determined in Step S 22  that the cumulative number of pixels is smaller than the threshold C, a process proceeds to Step S 23  and the remaining amount of toner is calculated on the basis of the cumulative number of pixels. Meanwhile, if it is determined in Step S 22  that the cumulative number of pixels is equal to or larger than the threshold C, the process proceeds to Step S 24  and the remaining amount of toner is calculated on the basis of both the cumulative number of pixels and a calculated value of the cumulative amount of replenished toner. 
         [0084]    A case where a toner is not replenished even though the cumulative number of pixels is increased or a case where a large amount of toner is replenished even though the cumulative number of pixels is almost not increased in contrast to this case is generated due to the false detection, the variation of detection, or the like of the concentration of a toner of a developer stored in the developer unit, in an early stage where the cumulative number of pixels is smaller than the threshold C and a new toner container just starts to be used. Accordingly, in this exemplary embodiment, the remaining amount of toner is calculated on the basis of the cumulative number of pixels that is relatively stable (Step S 23 ) if the cumulative number of pixels is smaller than the threshold C. A specific algorithm for calculating the remaining amount of toner in Steps S 23  and S 24  will be described later with reference to  FIG. 8 . Here, the description of the flowchart of  FIG. 7  will be made first. 
         [0085]    When the amount of toner remaining in the toner container is calculated in Steps S 23  and S 24 , it is determined whether the remaining amount of toner as the calculation result is decreased as compared to the remaining amount of toner calculated last time (Step S 25 ). Only if the remaining amount of toner is decreased compared with the last time, the remaining amount of toner is updated and the updated remaining amount of toner is reflected on the display of the display operation section  14  (Step S 26 ). Accordingly, an uncomfortable feeling in which a remaining amount of toner decreased once on display is increased during the process is excluded. 
         [0086]    Since the process of the subsequent Steps S 27  to S 31  is the same as that of Steps S 03  to S 07  of the flowchart shown in  FIG. 6 , the description thereof will be omitted. 
         [0087]    If it is determined in Step S 29  that the life of any one of the four toner containers  67 Y,  67 M,  67 C, and  67 K (see  FIG. 2 ) has not yet come to an end, the print corresponding to one page is performed (Step S 32 ) and the cumulative number of pixels is further updated by as many as one page (Step S 33 ). 
         [0088]    Meanwhile, separately from the process of which the flowchart is shown in  FIG. 7 , a calculated value of the cumulative amount of replenished toner is updated whenever a toner replenishing operation is performed. 
         [0089]    Moreover, it is determined whether a job formed of the print corresponding to one or plural pages, which are printed by a single print request and includes one page printed this time, is finished (Step S 34 ). If the job is not finished yet, the process subsequent to Step S 22  is repeated. If it is determined in Step S 34  that the job is finished, the process proceeds to the process subsequent to Step S 35 . Since the process of Steps S 35  to S 42  is the same as that of Steps S 11  to S 18  of the flowchart shown in  FIG. 6 , the repeated description will be omitted. 
         [0090]    Next, an algorithm for calculating the amount of toner remaining in the toner container, which is executed in Steps S 23  and S 24  of  FIG. 7 , will be described. 
         [0091]      FIG. 8  is a view illustrating the algorithm of this exemplary embodiment that calculates the remaining amount of toner. 
         [0092]    Here, a remaining amount space, which represents the remaining amount of toner and is a two-dimensional space where a horizontal axis represents a calculated value (%) of the cumulative amount of replenished toner and a vertical axis represents the cumulative number (%) of pixels, is shown. An empty area (area  103 A) of the remaining amount space is previously defined and stored in a storage unit provided in the main controller  40  (see  FIGS. 1 and 5 ). 
         [0093]    In this exemplary embodiment, the empty area of the remaining amount space has been stored in the storage unit provided in the main controller  40 . However, the invention is not limited to this exemplary embodiment. A storage unit may be provided outside the main controller and the empty area of the remaining amount space may be stored in the storage unit. 
         [0094]    Each of the calculated value (%) of the cumulative amount of replenished toner and the cumulative number (%) of pixels corresponds to an example of each of primary remaining amounts of the invention. The meaning of % is the same as described above. Further, in  FIG. 8 , an area  101 A, which is not hatched or shaded, is an area where there is the sufficient remaining amount of toner, a hatched area  102 A is an area where the remaining amount of toner is equal to or lower than 25%, and a shaded area  103 A is an empty area where the life of a toner container has come to an end and the remaining amount of toner is 0%. 
         [0095]    First, an algorithm, which calculates the remaining amount of toner on the basis of both the calculated value of the cumulative amount of replenished toner and the cumulative number of pixels in Step S 24  of  FIG. 7 , will be described here. 
         [0096]    In Step S 24 , a ratio R of a distance between the current coordinates (x %, y %) and the empty area (area  103 A) to a distance between the origin and the empty area (area  103 A) on a straight line, which passes through the origin (0%, 0%) where a toner container is not in use and the current coordinates (x %, y %) defined by the calculated cumulative number of pixels and a calculated value of the cumulative amount of replenished toner in the remaining amount space shown in  FIG. 8 , is calculated as the current remaining amount of toner. 
         [0097]    That is, when the coordinates of a point where the straight line reaches the empty area (area  103 A) is defined by (x 0 %, y 0 %), the ratio R is calculated by Expression (1). 
         [0000]    
       
         
           
             
               
                 
                   
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         [0098]    That is, when the current coordinates are a point_A shown in  FIG. 8 , a ratio R A  of a distance between the point_A and a point where the straight line reaches the empty area (area  103 A) to a distance between the origin (0, 0) and a point where the straight line connecting the origin (0, 0) with the point_A reaches the empty area (area  103 A) is calculated on the basis of Expression (1). The ratio R A  becomes the current remaining amount of toner. 
         [0099]    Further, similar to this, when the current coordinates are a point_B shown in  FIG. 8 , a ratio R B  of a distance between the point_B and a point where the straight line reaches the empty area (area  103 A) to a distance between the origin (0, 0) and a point where the straight line connecting the origin (0, 0) with the point_B reaches the empty area (area  103 A) is calculated on the basis of Expression (1). The ratio R B  becomes the current remaining amount of toner. 
         [0100]    When the current point currently positioned at the point_A moves on the straight line connecting the origin with the point_A as it is and reaches a point_C that is the boundary between the areas  101 A and  102 A, a warning meaning that the remaining amount of toner at that point of time is small is displayed (Step S 28  of  FIG. 7 ). The point_C is a point where the remaining amount of toner is decreased to 25%. 
         [0101]    Further, similar to this, when the current point currently positioned at the point_B moves on the straight line connecting the origin with the point_B as it is and reaches a point_D that is the boundary between the areas  101 A and  102 A, a warning meaning that the remaining amount of toner at that point of time is small is displayed. The point_D is also a point where the remaining amount of toner is decreased to 25%. 
         [0102]    Meanwhile, the invention is not limited to the fact that the current point (coordinate) moves along one straight line, and the current point may approach the empty area (area  103 A) along a line meandering in various patterns according to the operating environment or the like case by case. The remaining amount of toner is calculated by applying the current point (coordinate), which corresponds to that point of time, to Expression (1). 
         [0103]    According to the algorithm for calculating the remaining amount of toner described with reference to  FIG. 8 , the remaining amount of toner is calculated without uncomfortable feeling. 
         [0104]    Next, an algorithm, which calculates the remaining amount of toner based on only the cumulative number of pixels in Step S 23  of  FIG. 7 , will be described. 
         [0105]    Here, while the cumulative number of pixels is referred and a calculated value of the cumulative amount of replenished toner is regarded as the same percentage as the cumulative number of pixels, the remaining amount of toner is calculated. That is, for example, a calculated value of the cumulative amount of replenished toner is also regarded as 5% when the cumulative number of pixels is 5%, and a calculated value of the cumulative amount of replenished toner is also regarded as 10% when the cumulative number of pixels is 10%. In other words, this means that it is regarded that the current point moves along a straight line inclined by an angle of 45° and shown in  FIG. 8 . Here, while it is regarded as described above, a ratio R based on the above-mentioned Expression (1) is calculated. The ratio R is regarded as the remaining amount of toner. The reason to calculate the remaining amount of toner on the basis of only the cumulative number of pixels is that there is a possibility that the amount of replenished toner in an early stage significantly varies as described above. 
         [0106]    Next, various comparative examples of the algorithm for calculating the remaining amount of toner will be described. 
         [0107]      FIG. 9  is a view showing a remaining amount space when the remaining amount of toner is calculated on the basis of only a calculated value of the cumulative amount of replenished toner. 
         [0108]    Areas  101 B,  102 B, and  103 E correspond to the areas  101 A,  102 A, and  103 A shown in  FIG. 8 , respectively. The area  103 B is an empty area where the remaining amount of toner is defined as 0%, and the area  103 B has the extent that is equal to the extent of the empty area  103 A shown in  FIG. 8 . In contrast to this, here, the remaining amount of toner is calculated on the basis of only a calculated value of the cumulative amount of replenished toner. Accordingly, the boundary between the area  101 E where the remaining amount of toner is large and the area  1023  where the remaining amount of toner is small is different from the boundary between the two areas  101 A and  102 A of  FIG. 8 . 
         [0109]    If the calculated value of the cumulative amount of replenished toner and the cumulative number of pixels are equally changed when the remaining amount of toner is calculated on the basis of only a calculated value of the cumulative amount of replenished toner, the correct remaining amount of toner is calculated as shown at a straight line A and a warning meaning that the remaining amount of toner is small is displayed at the point of time where the remaining amount of toner reaches 25%. 
         [0110]    Meanwhile, if the change of the calculated value of the cumulative amount of replenished toner is large and the change of the cumulative number of pixels is small, for example, the current position moves along a straight line B. When the remaining amount of toner is still 45%, a warning meaning that the remaining amount of toner is small is displayed. In this case, whether the current position is changed along the straight line A or the straight line B is not clear in some apparatuses. Accordingly, the remaining amount of toner is displayed as 25% even in this case. However, after the remaining amount of toner is displayed as 25%, a good number of sheets to be printed can be used and a user feels uncomfortable. 
         [0111]    Meanwhile, in contrast to this, if it is considered that the change of the calculated value of the cumulative amount of replenished toner is small, the change of the cumulative number of pixels is large, and the current position moves along a straight line C, a warning meaning that the remaining amount of toner is 25% is displayed at the point of time where the remaining amount of toner is 5%. In this case, a user expects the number of printed sheets corresponding to 25% of the remaining amount of toner. However, since the remaining amount of toner is actually 5%, the current position immediately reaches an empty area. As a result, a user feels uncomfortable even in this case. 
         [0112]      FIG. 10  is a view showing a remaining amount space when the remaining amount of toner is calculated on the basis of only a value of the cumulative number of pixels. 
         [0113]    Areas  1010 ,  1020 , and  1030  correspond to the areas  101 A,  102 A, and  103 A shown in  FIG. 8 , respectively. The area  103 C is an empty area where the remaining amount of toner is defined as 0%, and the area  1030  has the extent that is equal to the extent of each of the empty areas  103 A and  103 B shown in  FIGS. 8 and 9 . In contrast to this, here, the remaining amount of toner is calculated on the basis of only the cumulative number of pixels. Accordingly, the boundary between the area  1010  where the remaining amount of toner is large and the area  102 C where the remaining amount of toner is small is different from the boundary between the two areas  101 A and  102 A of  FIG. 8  and the boundary between the two areas  101 B and  102 B of  FIG. 9 . 
         [0114]    If the calculated value of the cumulative amount of replenished toner and the cumulative number of pixels are equally changed when the remaining amount of toner is calculated on the basis of only the cumulative number of pixels, the correct remaining amount of toner is calculated as shown at a straight line A and a warning meaning that the remaining amount of toner is small is displayed at the point of time where the remaining amount of toner reaches 25%. 
         [0115]    Meanwhile, if the change of the calculated value of the cumulative amount of replenished toner is large and the change of the cumulative number of pixels is small, for example, the current position moves along a straight line B. A warning meaning that the remaining amount of toner is small is displayed at the point of time where the remaining amount of toner is decreased to 10%. In this case, whether the current position is changed along the straight line A or the straight line B is not clear in some apparatuses. Accordingly, the remaining amount of toner is displayed as 25% even in this case. A user expects the number of printed sheets corresponding to 25% of the remaining amount of toner. However, since the remaining amount of toner is actually 10%, the life of the toner container has come to an end when a small number of sheets are printed after the display of the warning. As a result, a user feels uncomfortable. 
         [0116]    In contrast to this, even when the change of the calculated value of the cumulative amount of replenished toner is small, the change of the cumulative number of pixels is large, and the current position moves along a straight line C, a warning meaning that the remaining amount of toner is 25% is displayed at a stage where the remaining amount of toner is 50%. As a result, a user also feels uncomfortable. 
         [0117]      FIG. 11  is a view that is based on both a calculated value of the cumulative amount of replenished toner and the cumulative number of pixels but shows a remaining amount space when a warning is displayed for the faster one of them. 
         [0118]    Here, areas  101 D,  102 D, and  103 D also correspond to the areas  101 A,  102 A, and  103 A shown in  FIG. 8 , respectively. The area  101 D is an empty area where the remaining amount of toner is defined as 0%, and the area  103 D has the extent that is equal to the extent of each of the empty areas  103 A,  103 B, and  103 C shown in  FIGS. 8 to 10 . Meanwhile, the boundary between the area  101 D where the remaining amount of toner is large and the area  102 D where the remaining amount of toner is small is different from each of the boundary between the two areas  101 A and  102 A of  FIG. 8 , the boundary between the two areas  101 B and  102 B of  FIG. 9 , and the boundary between the two areas  101 C and  102 C of  FIG. 10  due to the difference between the algorithms for calculating the remaining amount of toner. 
         [0119]    Even in  FIG. 11 , when the calculated value of the cumulative amount of replenished toner and the cumulative number of pixels are normally changed, the current point moves along a straight line A inclined by an angle of 45° and a warning is displayed at the point of time where the remaining amount of toner reaches 25%. Meanwhile, if the calculated value of the cumulative amount of replenished toner proceeds prior to the cumulative number of pixels, the calculated value of the cumulative amount of replenished toner is employed. For example, if the current position moves along a straight line B, a warning meaning that the remaining amount of toner is 25% is displayed when the remaining amount of toner is 45%. Further, if the cumulative number of pixels proceeds prior to the calculated value of the cumulative amount of replenished toner, the cumulative number of pixels is employed. For example, if the current position moves along a straight line C, a warning meaning that the remaining amount of toner is 25% is displayed when the remaining amount of toner is 50%. 
         [0120]    That is, a user feels significantly uncomfortable in the case of the algorithm that is shown in  FIG. 11  and employs the faster one of the calculated value of the cumulative amount of replenished toner and the cumulative number of pixels. 
         [0121]    Although not shown, a small amount of toner remains and a warning meaning that the remaining amount of toner is 25% is displayed in the case of an algorithm that employs the slower one of the calculated value of the cumulative amount of replenished toner and the cumulative number of pixels. For this reason, a user feels significantly uncomfortable even in this case. 
         [0122]    According to the algorithm of this exemplary embodiment described with reference to  FIG. 8 , the natural remaining amount of toner, which causes a user not to feel uncomfortable, is calculated or displayed in comparison with the algorithms of  FIGS. 9 to 11  and the like. 
         [0123]    Here, process control is used in the above-mentioned exemplary embodiment to determine whether a toner contained in a developer stored in the developer unit runs short. However, instead of process control, in terms of the life of a toner container, a sensor for detecting the concentration of a toner may be provided in the developer unit and whether a toner contained in a developer stored in the developer unit runs short may be determined on the basis of a signal from the sensor. 
         [0124]    Further, here, the calculated value of the cumulative amount of replenished toner and the cumulative number of pixels have been employed as an example of plural primary remaining amounts of the invention. However, for example, a primary remaining amount based on capacitance as disclosed in JP-A-2001-92232 may be employed as an example of plural primary remaining amounts of the invention. Furthermore, two primary remaining amounts, which are a calculated value of the cumulative amount of replenished toner and the cumulative number of pixels, have been employed in the above-mentioned exemplary embodiment. However, for example, three primary remaining amounts, which include a primary remaining amount based on capacitance in addition to a calculated value of the cumulative amount of replenished toner and the cumulative number of pixels, may be employed and a three-dimensional space, which uses these three primary remaining amounts as variables, may be employed as a remaining amount space. 
         [0125]    In addition, an example where the invention is applied to the copying machine shown in  FIGS. 1 and 2  has been described here. However, the invention is applied to not only a copying machine but also various kinds of image forming apparatuses, which have an image forming function, such as a printer and a facsimile machine. 
         [0126]    The foregoing description of the exemplary embodiments of the present invention has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Obviously, many modifications and variations will be apparent to practitioners skilled in the art. The embodiments were chosen and described in order to best explain the principles of the invention and its practical applications, thereby enabling others skilled in the art to understand the invention for various embodiments and with the various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the following claims and their equivalents.