Patent Publication Number: US-9423750-B2

Title: Image forming apparatus and method for controlling image forming apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of co-pending U.S. patent application Ser. No. 14/515,942 filed on Oct. 16, 2014 which claims the benefit of Japanese Patent Application No. 2013-260382 filed Dec. 17, 2013, both applications are hereby incorporated by reference herein in their entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to toner replenishment control for replenishing a containing unit with toner. 
     2. Description of the Related Art 
     There are image forming apparatuses that employ an electrophotographic method. This type of image forming apparatus forms a toner image based on image data input into the image forming apparatus, by consuming toner in a developer contained in a containing unit. It is known that, in this type of image forming apparatus, the density of the image formed by the image forming apparatus varies according to a ratio of the toner to the developer contained in the containing unit. 
     In this connection, one type of conventional image forming apparatuses predicts an amount of toner (a toner consumption amount) to be consumed in a containing unit due to formation of a toner image based on image data, and determines a toner replenishment amount so that a ratio of the toner in the containing unit becomes equal to a target value. Here, the toner consumption amount is theoretically obtained by calculation. Therefore, in reality, there is a slight error between a consumption amount of the toner actually consumed in the containing unit and the determined toner replenishment amount. In other words, the ratio of the toner in the containing unit may not become equal to the target value, even if toner is replenished based on the determined amount. 
     Japanese Patent Application Laid-Open No. 4-304486 discusses an image forming apparatus that corrects a toner replenishment amount according to a toner consumption amount, by using a correction amount calculated based on a ratio of toner in a containing unit. 
     In the image forming apparatus discussed in Japanese Patent Application Laid-Open No. 4-304486, images each consuming a large amount of toner may be formed, after images each consuming a small amount of toner are formed, when the ratio of the toner in the containing unit is higher than a target value. In this case, the containing unit is not immediately replenished with the toner, which is a problem. 
     When the images each consuming a small amount of toner are formed in the case where the ratio of the toner in the containing unit is higher than the target value, the correction amount serves to suppress the toner replenishment amount. In other words, the correction amount is a negative value, when the ratio of the toner in the containing unit is higher than the target value. 
     Therefore, when the image consuming a large amount of toner is formed after the images each consuming a small amount of toner are formed, the toner replenishment amount becomes a value equal to or below 0. The toner replenishment amount is calculated based on the toner consumption amount predicted according to the image consuming a large amount of toner and the correction amount. Therefore, the containing unit is prevented from being replenished with the toner, even when formation of the image consuming a large amount of toner has commenced and the toner in the containing unit has started to decrease. 
     SUMMARY OF THE INVENTION 
     According to an aspect of the present invention, an image forming apparatus comprising: an image forming unit including a containing unit that contains toner, and configured to form an image based on image data, by using the toner contained in the containing unit; a replenishment unit configured to replenish the containing unit with the toner; a first determination unit configured to determined, based on the image data, an amount of the toner consumed in the containing unit; a detection unit configured to detect an amount of the toner contained in the containing unit; a first calculation unit configured to calculate a difference between the amount of the toner detected by the detection unit and a target amount; a second calculation unit configured to calculate a cumulative value of the difference calculated by the first calculation unit; and a second determination unit configured to determine a determination value used for determining whether the replenishment unit replenishes the toner to the containing unit, based on the consumption amount determined by the first determination unit, the difference calculated by the first calculation unit, and the cumulative value calculated by the second calculation unit; a controller configured to control the replenishment unit, based on the determination value determined by the second determination unit, wherein in a case where the determination value determined by the second determination unit at a first timing is less than a threshold, the second calculating unit is prevented from accumulating the difference calculated by the first calculating unit at a second timing following the first timing, on the cumulative value calculated at the first timing. 
     According to another aspect of the present invention, a method for controlling an image forming apparatus that includes, an image forming unit including a containing unit that contains toner and configured to form an image based on image data by using the toner contained in the containing unit, a replenishment unit configured to replenish the containing unit with the toner, and a detection unit configured to detect an amount of the toner contained in the containing unit, the method comprising: detecting, based on the image data, an amount of the toner consumed in the containing unit; calculating a difference between the amount of the toner detected by the detection unit and a target amount; updating a cumulative value of the difference; determining, based on the consumption amount, the difference, and the cumulative value, a determination value used for determining whether the replenishment unit replenishes to the containing unit with the toner; and controlling the replenishment unit based on the determination value, wherein in the updating, the difference is accumulated to the cumulative value in a case where the determination value is above a threshold, whereas the difference is prevented from being accumulated on the cumulative value in a case where the determination value is less than the threshold. 
     Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic structural diagram of an image forming apparatus. 
         FIG. 2  is an essential-part schematic diagram of a developing unit provided in the image forming apparatus. 
         FIG. 3  is a block diagram illustrating an electrical configuration according to toner replenishment of the image forming apparatus. 
         FIG. 4  is a flowchart illustrating toner replenishment control. 
         FIG. 5  is a flowchart illustrating toner replenishment control according to comparative example 1. 
         FIG. 6  is a flowchart illustrating toner replenishment control according to comparative example 2. 
         FIGS. 7A, 7B, and 7C  are transition diagrams each illustrating each parameter at the time when solid images are successively formed. 
         FIGS. 8A, 8B, and 8C  are transition diagrams each illustrating each parameter at the time when a solid image and a blank image are alternately formed. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Various exemplary embodiments, features, and aspects of the invention will be described in detail below with reference to the drawings. 
     Image Forming Apparatus 
       FIG. 1  is a schematic structural diagram of an image forming apparatus. In  FIG. 1 , an image of a document  31  is projected onto an imaging sensor  33  such as a charge-coupled device (CCD), through a lens  32 . This imaging sensor  33  generates an analog image signal corresponding to the density of the image of the document  31 . The analog image signal output from the imaging sensor  33  is sent to an image signal processing circuit  34  that converts the analog image signal to a digital image signal having an output level corresponding to the density of each pixel. The digital image signal is then sent to a pulse width modulation circuit  35 . 
     Based on the input digital image signal, the pulse width modulation circuit  35  outputs a pulse signal of a time width (a duration) according to the density of each pixel. The pulse signal output from the pulse width modulation circuit  35  is supplied to a semiconductor laser  36 . The semiconductor laser  36  emits a laser beam  36   a  based on the time width of the pulse signal. 
     The laser beam  36   a  emitted from the semiconductor laser  36  is deflected by a rotating polygon mirror  37 , and then applied onto a photosensitive drum  40  through a lens such as a f/θ lens and by a mirror  39 . The photosensitive drum  40  is driven to rotate in an arrow direction in  FIG. 1 . The laser beam  36   a  deflected by the rotating polygon mirror  37  scans in a direction (a main scanning direction) parallel to a rotation shaft of the photosensitive drum  40 , due to rotation of the rotating polygon mirror  37 . 
     The photosensitive drum  40  is subjected to static elimination by a static eliminating unit  41 , and then uniformly charged by a charging unit  42 . An exposure device includes the semiconductor laser  36 , the rotating polygon mirror  37 , the lens  38 , and the mirror  39 . This exposure device exposes the photosensitive drum  40  with the laser beam  36   a  modulated according to the digital image signal, so that an electrostatic latent image corresponding to the digital image signal is formed on the photosensitive drum  40 . A developing unit  44  is a containing unit that contains a two-component developer  43  including toner  63  and a carrier. Using the toner  63 , the developing unit  44  develops the electrostatic latent image formed on the photosensitive drum  40 , so that a toner image is formed. A recording-material carrying belt  47  is held by two rollers  45  and  46 , to carry and convey a recording material  48  in an arrow direction in  FIG. 1 . A transfer charging unit  49  transfers the toner image formed on the photosensitive drum  40 , to the recording material  48  carried by the recording-material carrying belt  47 . 
     The recording material  48 , to which the toner image has been transferred, is separated from the recording-material carrying belt  47  and then conveyed to a fixing unit that is not illustrated. The fixing unit includes a heating roller having a heater and a pressure roller pressing the heating roller. Heat and pressure are applied to the recording material  48  on which the toner image has been formed. As a result, the toner image formed on the recording material  48  is fixed thereto. A drum cleaner  50  removes residual toner on the photosensitive drum  40 , after the toner image on the photosensitive drum  40  is transferred to the recording material  48 . 
     The image forming apparatus has been described in which one image forming station includes the photosensitive drum  40 , the static eliminating unit  41 , the charging unit  42 , the developing unit  44 , the transfer charging unit  49 , and the drum cleaner  50 . However, an image forming apparatus including two or more image forming stations may be employed. For example, a full-color image forming apparatus may be employed. The full-color image forming apparatus includes four image forming stations for cyan, magenta, yellow, and black, which are arranged along a conveyance direction of the recording-material carrying belt  47 . In this configuration, an image of a document is separated into colors of cyan, magenta, yellow, and black, and a toner image of a color component corresponding to each of the image forming stations is formed on the photosensitive drum  40 . The toner images of the respective color components on the respective image forming stations are sequentially transferred to the recording material  48  carried by the recording-material carrying belt  47 , so that a full-color toner image is formed. 
       FIG. 2  is an essential-part schematic diagram of the developing unit  44 . The developing unit  44  is disposed to face the photosensitive drum  40 . A partition  51  partitions the inside of the developing unit  44  into a developing chamber  52  and a agitating chamber  53 . In the developing chamber  52 , a nonmagnetic developing sleeve  54  is disposed to rotate in an arrow direction, and a magnet  55  is fixed inside this developing sleeve  54 . 
     A developer  43  is carried by the developing sleeve  54 , and regulated by a regulating blade  56  in terms of layer thickness. The developer  43  carried by the developing sleeve  54  is supplied to the photosensitive drum  40 , in passing through a developing region facing the photosensitive drum  40 , as the developing sleeve  54  rotates in the arrow direction. As a result, the electrostatic latent image on the photosensitive drum  40  is developed. A power supply  57  applies, to the developing sleeve  54 , a developing bias voltage in which an alternating current (AC) voltage is superimposed on a direct current (DC) voltage. 
     A agitating screw  58  stirs and conveys the developer  43  in the developing chamber  52 . Further, a agitating screw  59  stirs the toner  63  and the developer  43 , so that a toner-to-developer ratio (hereinafter referred to as “toner density”) becomes uniform. The toner  63  is supplied from a toner discharge port  61  of a hopper  60  ( FIG. 1 ) by rotation of a conveyance screw  62 . The developer  43  is contained in the agitating chamber  53 . A developer passage that is not illustrated is formed in the partition  51 . The developer passage connects the developing chamber  52  with the agitating chamber  53 . Therefore, the developer  43  contained in the developing chamber  52  and the agitating chamber  53  circulates in the developing unit  44  due to the rotation of the agitating screws  58  and  59 . 
     An inductance sensor  20  is disposed in a bottom wall of the developing chamber  52 . The inductance sensor  20  detects the amount of the toner  63  contained in the developing unit  44 . Specifically, the inductance sensor  20  detects a permeability of the developer  43  contained in the developing chamber  52 , and outputs a signal according to the toner-to-developer ratio. A central processing unit (CPU)  67  detects the amount of the toner  63  in the developer  43 , based on the output signal of the inductance sensor  20 . 
     The developer  43  contained in the developing chamber  52  includes the toner  63  and the carrier having magnetic properties. Therefore, when the toner density of the developing unit increases, the carrier-to-developer ratio decreases and thus, an output value of the inductance sensor  20  decreases. On the other hand, when the toner density of the developing unit decreases, the carrier-to-developer ratio increases and thus, the output value of the inductance sensor  20  increases. In other words, the inductance sensor  20  detects the ratio of the toner  63  to the developer  43  stored in the developing chamber  52 , and outputs a signal according to this ratio to a controller  1100  ( FIG. 3 ). 
     In the present exemplary embodiment, a toner replenishment amount is determined based on a toner consumption amount and the toner density of the developing unit. The toner  63  consumption amount is an amount consumed in the developing unit  44  due to formation of the toner image based on the image data by the image forming station. The toner density of the developing unit  44  is detected by the inductance sensor  20 . Toner replenishment control for determining the toner replenishment amount will be described below. 
       FIG. 3  is a block diagram illustrating an electrical configuration according to toner replenishment of the image forming apparatus. The CPU  67  is a circuit that controls each part so as to control toner replenishment. The inductance sensor  20  has been described with reference to  FIG. 2 , and therefore will not be described here. A motor driving circuit  69  controls a motor  70  that rotates the conveyance screw  62 . 
     A counter  66  counts to obtain the sum of the densities of the respective pixels included in an image for one page, based on the digital image signal output from the image signal processing circuit  34 . The sum (hereinafter referred to as “video count value”) of the densities of the respective pixels obtained by the counter  66  is equivalent to the amount of the toner  63  consumed in the developing unit  44  due to formation of a toner image for one page included in the image data. A method of acquiring the video count value is a known technique and therefore will not be described here. 
     In the present exemplary embodiment, the controller  1100  determines the amount of the toner  63  used for replenishing the developing unit  44 , based on the value output by the inductance sensor  20  and the video count value acquired by the counter  66 . Further, until a cumulative value of the replenishment amount determined by the controller  1100  becomes smaller than a predetermined value, the motor driving circuit  69  rotates the conveyance screw  62 , so that the developing unit  44  is replenished with the toner  63  in the hopper  60  ( FIG. 1 ). 
     Toner Replenishment Control 
     The toner replenishment control of the exemplary embodiment will be described below with reference to  FIG. 4 .  FIG. 4  is a flowchart illustrating operation of the CPU  67 . 
     The CPU  67  starts the toner replenishment control in response to transfer of image data through an interface that is not illustrated. In step S 201 , the video count value is input from the counter  66 . In step S 202 , a first replenishment-amount determination unit  1101  determines a first replenishment amount based on the video count value, by referring to a conversion table indicating a correspondence between the video count value and the toner replenishment amount. 
     In step S 201 , the counter  66  acquires the video count value per page, from a toner image of at least one or more pages included in the image data. Subsequently, at the timing that the image forming station starts forming the toner image of each page, the counter  66  outputs the video count value of the corresponding page to the controller  1100 . In other words, the counter  66  outputs the video count value corresponding to the toner image for one page to be formed by the image forming station, to the controller  1100 . 
     In step S 203 , the controller  1100  receives an output value D 1  of the inductance sensor  20 , before the toner image for one page is formed. In step S 204 , a difference calculation unit  1102  computes a difference ΔD 1  between the output value D 1  of the inductance sensor  20  and a target value D 1 ref output from a toner-density target-value determination unit  1103 . 
     Here, when a toner image of an nth page is formed, the difference between an output value Dn of the inductance sensor  20  and a target value Dnref is computed by an expression (1).
 
Δ Dn=Dn−Dn ref (where “ n ” is the number of pages)  (1)
 
The toner-density target-value determination unit  1103  determines the target value Dnref, based on temperature and humidity around the image forming apparatus detected by an environment sensor (not illustrated) provided in the image forming apparatus.
 
     In step S 205 , a second replenishment-amount determination unit  1104  determines a second replenishment amount, based on the difference ΔDn at the timing that the image of the nth page is formed and a cumulative value ΣΔD n-1  to be described below. In the present exemplary embodiment, for example, the second replenishment-amount determination unit  1104  determines the second replenishment amount based on an expression (2).
 
Second replenishment amount=(α×Δ Dn )+(β×ΣΔ D   n-1 )  (2)
 
Constants α and β each are a gain value determined beforehand by an experiment. In the present exemplary embodiment, the constants α and β each are a positive value smaller than 1.
 
     The cumulative value ΣΔD n-1  is computed based on the output value received from the inductance sensor  20  each time the toner image for one page is formed, and the target value output by the toner-density target-value determination unit  1103 . This cumulative value ΣΔD n-1  is determined in step S 208  or S 209  to be described below. 
     Next, in step S 206 , a replenishment-amount totaling unit  1105  determines a total replenishment amount, by computing the sum of the first replenishment amount and the second replenishment amount. This total replenishment amount will be added to a replenishment-amount buffer value in step S 210  to be described below. If the replenishment-amount buffer value is equal to or above a predetermined value, the conveyance screw  62  starts operation for replenishing the developing unit  44  with the toner  63  from the hopper  60 . 
     Here, when an image using an extremely small amount of toner is formed in a case where the toner density of the developing unit is higher than the target value, the second replenishment amount becomes a negative value, and the total replenishment amount also becomes a negative value. When images each using an extremely small amount of toner are successively formed, the total replenishment amount that is a negative value is added to the replenishment-amount buffer value for each page. Therefore, the replenishment-amount buffer value becomes a negative value. Assume that an image using an extremely large amount of toner is formed after the images that each use an extremely small amount of toner are successively formed. In this case, a problem arises. That is, although the total replenishment amount is a positive value, the replenishment is not started because the replenishment-amount buffer value is not equal to or above the predetermined value. 
     Therefore, in the present exemplary embodiment, a decrease in the replenishment-amount buffer value is suppressed, when an image using an extremely small amount of toner is formed in the case where the toner density of the developing unit is higher than the target value. 
     In step S 207 , after the total replenishment amount is determined in step S 206 , the CPU  67  determines whether the total replenishment amount is a negative value. In step S 208 , when it is determined that the total replenishment amount is a negative value (Yes in step S 207 ), the second replenishment-amount determination unit  1104  maintains the cumulative value without adding the difference ΔDn to the cumulative value ΣΔD n-1 . In other words, in step S 208 , the second replenishment-amount determination unit  1104  sets the cumulative value ΣΔD n-1  as a cumulative value ΣΔDn. 
     In step S 208 , the CPU  67  does not perform difference accumulation. Therefore, even when an image using an extremely small amount of toner is formed in the case where the toner density of the developing unit is higher than the target value, a decrease in the replenishment-amount buffer value can be suppressed. 
     On the other hand, in step S 209 , when it is determined that the total replenishment amount is not a negative value (No in step S 207 ), the second replenishment-amount determination unit  1104  adds the difference ΔDn to the cumulative value ΣΔD n-1 . In other words, in step S 209 , the second replenishment-amount determination unit  1104  sets the sum of the cumulative value ΣΔD n-1  and the difference ΔDn, as the cumulative value ΣΔDn. 
     In step S 207 , the total replenishment amount functions as a value for determining whether to perform updating by adding the difference ΔDn computed at first timing to the cumulative value ΣΔD n-1  computed at the first timing, or to perform updating without such addition. In step S 210 , after the cumulative value ΣΔDn is set by the second replenishment-amount determination unit  1104  in step S 208  or S 209 , a unit-replenishment-amount computing unit  1106  adds the total replenishment amount to the replenishment-amount buffer value. The cumulative value ΣΔDn is used in computation for determining the total replenishment amount when the next toner replenishment control is performed. Timing that the next toner replenishment control is performed corresponds to second timing that follows the first timing. 
     In step S 211 , the CPU  67  determines whether the replenishment-amount buffer value computed in step S 210  is equal to or above the predetermined value. In step S 211 , the predetermined value is, for example, the amount of the toner  63  used for replenishment by one rotation of the conveyance screw  62 . The predetermined value is determined beforehand, based on the amount of the toner  63  used for replenishing the developing unit  44  from the hopper  60  in one replenishment. The predetermined value is stored beforehand in, for example, a read-only memory (ROM) that is not illustrated. 
     In step S 212 , when it is determined that the replenishment-amount buffer value is equal to or above the predetermined value (Yes in step S 211 ), the CPU  67  transmits a drive command to the motor driving circuit  69 . When the drive command is received, the motor driving circuit  69  drives the motor  70  to cause one rotation of the conveyance screw  62 . As a result, the conveyance screw  62  supplies the toner  63  from the hopper  60  to the developing unit  44 . 
     Next, in step S 213 , the CPU  67  subtracts the predetermined value from the replenishment-amount buffer value and then returns to step S 211 . In other words, in the processing from step S 211  to step S 213 , the CPU  67  keeps supplying the toner  63  from the hopper  60  to the developing unit  44 , until the replenishment-amount buffer value falls below the predetermined value. 
     When the CPU  67  determines that the replenishment-amount buffer value is below the predetermined value (No in step S 211 ), the CPU  67  ends the toner replenishment control. 
     Comparative Example 1 
     Here, conventional toner replenishment control (PI control) will be described with reference to a flowchart in  FIG. 5 . As illustrated in  FIG. 5 , processing from step S 201  to step S 206  is similar to that in the present exemplary embodiment and therefore will not be described in detail here. 
     After computing a total replenishment amount in step S 206 , the CPU  67  proceeds to step S 209  where the second replenishment amount determination unit  1104  adds a difference ΔDn to a cumulative value ΣΔD n-1 . Processing in or after step S 210  is similar to that in the present exemplary embodiment and therefore will not be described in detail here. 
     Comparative Example 2 
     Another conventional toner replenishment control (P control) different from comparative example 1 will be described with reference to a flowchart in  FIG. 6 . As illustrated in  FIG. 6 , processing from step S 201  to step S 204  is similar to that in the present exemplary embodiment and therefore will not be described in detail here. 
     After the difference calculation unit  1102  computes a difference ΔDn between an output value Dn of the inductance sensor  20  and a target value Dnref in step S 204 , the CPU  67  proceeds to step S 305 . In step S 305 , the CPU  67  determines a second replenishment amount by multiplying the difference ΔDn by a predetermined gain “α”. Next, in step S 206 , the CPU  67  computes the sum of a first replenishment amount and the second replenishment amount, and then proceeds to step S 210 . Processing in or after step S 210  is similar to that in the present exemplary embodiment and therefore will not be described in detail here. 
     Comparison of Effects 
     Effects in the toner replenishment control of the present exemplary embodiment will be compared with those of the comparative examples 1 and 2, and results will be described below.  FIGS. 7A to 7C  are provided to describe transition in the ratio between the toner density of the developing unit and the target value, and transition in the cumulative value, at the time when toner images of 100% image duty are successively formed. In  FIGS. 7A to 7C , a solid line indicates results of the toner replenishment control in the present exemplary embodiment. Further, a long dashed line indicates results of the toner replenishment control in comparative example 1, and a short dashed line indicates results of the toner replenishment control in comparative example 2. 
       FIG. 7A  indicates the case where the images of 100% image duty are formed successively. The image duty is an area ratio of a toner-adhered region in one page of the recording material. In other words, when a toner image is formed on the entire surface of one page of the recording material, the image duty is 100%. When no toner image is formed in one page of the recording material, the image duty is 0%. Further, a toner image of 100% image duty is defined to have a density value of 1.6. 
     In  FIG. 7B , a vertical axis (the toner density of the developing unit) indicates that the toner density of the developing unit is above the target value when a numerical value is larger than 1, and that the toner density of the developing unit is below the target value when the numerical value is smaller than 1. In  FIG. 7C , a vertical axis indicates the cumulative value ΣΔDn obtained by adding the difference ΔDn between the output value Dn of the inductance sensor  20  and the target value Dnref, to the cumulative value ΣΔD n-1  of up to previous difference. 
     When the image forming station keeps forming the toner images of 100% image duty, the toner density of the developing unit continues to rise from start of the toner-image formation, until the toner image of the 50th page is formed. This indicates that the amount of the toner  63  used for replenishment by one rotation of the conveyance screw  62  is larger than a replenishment amount predicted beforehand by an experiment. This is attributable to temperature or humidity around the image forming apparatus, or tolerance or individual difference of a mechanical component of the conveyance screw  62 . 
     When there is a deviation in the toner replenishment amount as described above, a steady-state deviation of the toner density of the developing unit from the target value remains, in the toner replenishment control of comparative example 2. On the other hand, in the toner replenishment control of the present exemplary embodiment and comparative example 1, the second replenishment amount is corrected based on the cumulative value and therefore, the toner density of the developing unit converges at the target value. 
     Now, another case will be described with reference to  FIGS. 8A to 8C . In this case, there is a period of allowing the recording material to pass without forming a toner image, during formation of the toner images of 100% image duty. 
     As illustrated in  FIGS. 8A and 8B , the toner density of the developing unit rises relative to the target value, while the toner images of 100% image duty are formed for 50 pages. Subsequently, the image duty changes from 100% to 0% ( FIG. 8A ). However, despite this change, the toner density of the developing unit is maintained as illustrated in  FIG. 8B . In a 0% image duty period in which no toner image is formed, the toner  63  in the developing unit  44  cannot be consumed and therefore, the toner density of the developing unit cannot be reduced. 
     Subsequently, when the image duty changes from 0% to 100% in or after the 400th pages, the toner  63  contained in the developing unit  44  is consumed to form the toner images. The toner density of the developing unit in the present exemplary embodiment starts decreasing in or after the 400th pages, and smoothly converges at the target value. 
     On the other hand, the toner density of the developing unit in comparative example 1 significantly decreases from the 400th page to the 450th page. This is because, as illustrated in  FIG. 8C , the cumulative value is excessively accumulated in the period in which no toner image is formed from the 50th page to the 400th page. In other words, in the toner replenishment control of comparative example 1, even if the total replenishment amount becomes a value calling for immediate replenishment, the replenishment is not performed because the replenishment-amount buffer value does not become equal to or above the predetermined value. 
     In comparative example 2, the replenishment amount is not corrected based on the cumulative value. Therefore, the toner density of the developing unit does not significantly fall, as in the comparative example 1. However, the toner density of the developing unit cannot converge at the target value. 
     In the toner replenishment of the exemplary embodiment, the cumulative value is prevented from being excessively accumulated. Therefore, the toner density of the developing unit can converge at the target value, without having an overshoot as in comparative example 1. 
     In addition, in the present exemplary embodiment, the second replenishment-amount determination unit  1104  stops computing the cumulative value of the differences, if the total replenishment amount obtained in forming the toner image for the immediately preceding page is less than a threshold. However, any other configuration may be adopted as long as the second replenishment-amount determination unit  1104  is prevented from adding the difference to the cumulative value. For example, the second replenishment-amount determination unit  1104  may update the cumulative value by considering the value of the difference as “0”, if the total replenishment amount obtained in forming the toner image for the immediately preceding page is less than the threshold. 
     Moreover, in the present exemplary embodiment, each time the image data is transferred to the controller  1100 , the CPU  67  controls the toner replenishment. In this toner replenishment control, the tonner replenishment is performed if the replenishment-amount buffer value is equal to or above the predetermined value before the image forming station forms the toner image for one page of the recording material. However, the timing for controlling the toner replenishment is not limited to this configuration. 
     For example, the CPU  67  may perform the toner replenishment control in  FIG. 4  at predetermined time intervals, while the agitating screws  58  and  59  in the developing unit  44  rotate. In this configuration, the developing unit  44  can be replenished with the toner  63  from the hopper  60 , each time the toner density of the developing unit falls below the target value. Therefore, the density of the toner image formed by the image forming station can be further stabilized. 
     According to the toner replenishment control of the present exemplary embodiment, even if an image using a large amount of toner is formed after images each using a small amount of toner are successively formed, the toner replenishment amount for the developing unit  44  can be precisely controlled. In other words, when the image using a large amount of toner is formed after the images each using a small amount of toner are successively formed, the toner density of the developer contained in the developing unit  44  can converge at the target value. Therefore, it is possible to suppress a density change of an image formed by the image forming apparatus. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions.