Patent Publication Number: US-10788771-B2

Title: Image forming apparatus with charging amount acquisition unit

Description:
INCORPORATION BY REFERENCE 
     This application contains subject matter related to Japanese Patent Application No. 2018-103216 filed in Japanese Patent Office on May 30, 2018, the entire content of which being incorporated herein by reference. 
     BACKGROUND 
     The present disclosure relates to an image forming apparatus that forms an image on a sheet. 
     Conventionally, a known image forming apparatus, which forms an image on a sheet, includes a photoconductive drum (an image carrier), a developing device, and a transfer member. An electrostatic latent image formed on the photoconductive drum is developed on a development nip portion by the developing device, and thus a toner image is formed on the photoconductive drum. The transfer member transfers the toner image to a sheet. As the developing device to be applied to such an image forming apparatus, a two-component developing technique using developer including toner and carrier is known. 
     In the two-component development, the developer is deteriorated due to influences of a number of sheets to be printed, a change in environment, a printing mode (a number of sheets to be sequentially printed per one job), and a page-coverage rate, and thus a toner charging amount changes. Such a phenomenon causes problems such as a decrease in image density, occurrence of tonner fogging, and an increase in toner flying. A conventional technique, which solves such a problem, predicts a change in a charging amount of developer based on a number of sheets to be printed, a change in environment, a printing mode, and a page-coverage rate, and adjusts toner density, a development bias, a surface potential of a photoconductor, a rotational speed of a developing roller, and an output of a suction fan that collects flying toner, thus suppressing a decrease in image density, deterioration of toner fogging, and deterioration of toner flying. 
     However, such a technique is only a combination of individual predictions under conditions of a number of sheets to be printed, a change in environment, a printing mode, and a page-coverage rate, and thus if a plurality of conditions are changed compositively, it is difficult to sufficiently predict a charging amount of developer. 
     Therefore, a technique for accurately predicting a charging amount of toner is proposed. In this technique, a surface potential of a photoconductive drum before development and a surface potential of a toner layer on the photoconductive drum after development are individually measured, whereas a toner developing amount is calculated based on an image density measured result on the developed toner layer. The toner charging amount is calculated based on the measured surface potentials and toner developing amount. 
     In this technique, a value of an electric current flowing into the developing roller that carries developer is measured, and the measured current value is predicted as an amount of toner charges which transfer from the developing roller to the photoconductive drum. A toner developing amount is calculated based on the image density measured result on the developed toner layer. Further, a toner charging amount is calculated based on the amount of toner charges and the toner charging amount. 
     SUMMARY 
     According to one aspect of the present disclosure, an image forming apparatus includes an image carrier, a charging device, an exposing device, a developing device, a transfer unit, a development bias applying unit, a density detecting unit, a storage unit, and a charging amount acquisition unit. The image carrier is rotated and carries a toner image obtained by developing an electrostatic latent image which is formed on a surface of the image carrier. The charging device charges the image carrier to a predetermine charging potential. The exposing device exposes the surface of the image carrier charged to the charging potential, based on predetermined image information so as to form the electrostatic latent image, the exposing device being disposed in a rotational direction of the image carrier downstream with respect to the charging device. The developing device is disposed in a predetermined development nip portion in the rotational direction downstream with respect to the exposing device so as to oppose the image carrier. The developing device includes a developing roller that is rotated, carries developer including toner and carrier on a peripheral surface of the developing roller, and supplies the toner to the image carrier so as to form the toner image. The transfer unit transfers the toner image carried on the image carrier to a sheet. The development bias applying unit applies a development bias obtained by superimposing an alternating current voltage on a direct current voltage to the developing roller. The density detecting unit detects density of the toner image. The storage unit stores reference information in advance for each toner charging amount, the reference information relating to a tilt of a reference straight line representing a relationship between a change amount of a frequency of the alternating current voltage of the development bias and a density change amount of the toner image in a case where the frequency is changed with a potential difference in the direct current voltage between the developing roller and the image carrier being kept constant. The charging amount acquisition unit performs a charging amount acquisition operation for forming a measurement toner image on the image carrier while changing the frequency of the alternating current voltage of the development bias with the potential difference in the direct current voltage between the developing roller and the image carrier being kept constant, acquiring a tilt of a measurement straight line representing a relationship between the change amount of the frequency and a density change amount of the measurement toner image based on the change amount of the frequency and a result of detecting density of the measurement toner image in the density detecting unit, and acquiring a charging amount of the toner included in the measurement toner image formed on the image carrier based on the acquired tilt of the measurement straight line and the reference information in the storage unit. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a cross-sectional view illustrating an internal structure of an image forming apparatus according to an embodiment of the present disclosure; 
         FIG. 2  is a cross-sectional view of a developing device and a block diagram illustrating an electrical configuration of a control unit according to the embodiment of the present disclosure; 
         FIG. 3A  is a pattern diagram illustrating a developing operation of the image forming apparatus according to the embodiment of the present disclosure; 
         FIG. 3B  is a pattern diagram illustrating a level relationship between potentials of an image carrier and a developing roller according to the embodiment of the present disclosure; 
         FIG. 4  is a graph illustrating a relationship between a frequency of a development bias and image density in the image forming apparatus according to the embodiment of the present disclosure; 
         FIG. 5  is a graph illustrating a relationship between a tilt in the graph of  FIG. 4  and a toner charging amount in the image forming apparatus according to the embodiment of the present disclosure; 
         FIG. 6  is a flowchart illustrating a charging amount measuring mode to be executed in the image forming apparatus according to the embodiment of the present disclosure; 
         FIG. 7  is a pattern diagram illustrating a measurement toner image to be formed on the image carrier in the charging amount measuring mode to be executed in the image forming apparatus according to the embodiment of the present disclosure; 
         FIG. 8  is a flowchart illustrating a charging amount distribution measuring mode to be executed in the image forming apparatus according to the embodiment of the present disclosure; and 
         FIG. 9  is a graph illustrating a relationship between the toner charging amount and a ratio of a toner developing amount in the image forming apparatus according to the embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     An image forming apparatus  10  according to an embodiment of the present disclosure will be described in detail below with reference to the drawings. The present embodiment illustrates a tandem color printer as one example of the image forming apparatus. Examples of the image forming apparatus may be a copying machine, a facsimile device, and a complex machine of them. The image forming apparatus may form a single-color (monochrome) image. 
       FIG. 1  is a cross-sectional view illustrating an internal structure of the image forming apparatus  10 . The image forming apparatus  10  includes an apparatus main body  11  having a box-shaped housing structure. The apparatus main body  11  includes a sheet feeding unit  12  that feeds a sheet P, an image forming unit  13  that forms a toner image to be transferred to the sheet P fed from the sheet feeding unit  12 , an intermediate transfer unit  14  (a transfer unit) that primarily transfers the toner image, a toner supply unit  15  that supplies toner to the image forming unit  13 , and a fixing unit  16  that executes a fixing process for fixing an unfixed toner image formed on the sheet P to the sheet P. A sheet ejection portion  17 , onto which the sheet P which has been subject to the fixing process in the fixing unit  16  is ejected, is disposed on an upper portion of the apparatus main body  11 . 
     An operation panel, not illustrated, for inputting output conditions or the like for the sheet P is disposed on an appropriate position on an upper surface of the apparatus main body  11 . The operation panel includes a power key, and a touch panel and various operation keys that are used for inputting the output conditions. 
     The apparatus main body  11  includes a sheet conveyance path  111  that extends vertically on a right position with respect to the image forming unit  13 . A conveyance roller pair  112  that conveys a sheet to an appropriate position is disposed on the sheet conveyance path  111 . A registration roller pair  113  is disposed on an upstream side of a nip portion on the sheet conveyance path  111 . The registration roller pair  113  adjusts skew of a sheet and sends the sheet to the nip portion for secondary transfer, described later, at predetermined timing. The sheet conveyance path  111  is a conveyance path through which the sheet P is conveyed from the sheet feeding unit  12  to the sheet ejection portion  17  via the image forming unit  13  and the fixing unit  16 . 
     The sheet feeding unit  12  includes a sheet feeding tray  121 , a pickup roller  122 , and a sheet feeding roller pair  123 . The sheet feeding tray  121  is detachably attached to a lower portion of the apparatus main body  11 , and a sheet bundle P1 including a plurality of laminated sheets P is stored on the sheet feeding tray  121 . The pickup roller  122  feeds a top sheet P of the sheet bundle P1 stored on the sheet feeding tray  121  one by one. The sheet feeding roller pair  123  sends the sheet P fed by the pickup roller  122  to the sheet conveyance path  111 . 
     The sheet feeding unit  12  includes a manual sheet feeding unit which is mounted to a left side surface, illustrated in  FIG. 1 , of the apparatus main body  11 . The manual sheet feeding unit includes a bypass tray  124 , a pickup roller  125 , and a sheet feeding roller pair  126 . The bypass tray  124  is a tray on which the sheet P to be manually fed is placed, and is opened on a side surface of the apparatus main body  11  as illustrated in  FIG. 1  when the sheet P is manually fed. The pickup roller  125  feeds the sheet P placed on the bypass tray  124 . The sheet feeding roller pair  126  sends the sheet P fed by the pickup roller  125  to the sheet conveyance path  111 . 
     The image forming unit  13  forms a toner image to be transferred to the sheet P, and includes a plurality of image forming units that form toner images of different colors. In the present embodiment, the image forming units are a magenta unit  13 M which uses magenta (M) developer, a cyan unit  13 C which uses cyan (C) developer, a yellow unit  13 Y which uses yellow (Y) developer, and a black unit  13 Bk which uses black (Bk) developer. The units  13 M,  13 C,  13 Y, and  13 Bk are disposed in this order from an upstream side to a downstream side (from left to right illustrated in  FIG. 1 ) in a rotational direction of an intermediate transfer belt  141 , described later. The units  13 M,  13 C,  13 Y, and  13 Bk each have a photoconductive drum  20  (an image carrier), and a charging device  21 , a developing device  23 , a primary transfer roller  24 , and a cleaning device  25  which are disposed around the photoconductive drum  20 . An exposing device  22  which is shared by the units  13 M,  13 C,  13 Y, and  13 Bk is disposed below the image forming units. 
     The photoconductive drum  20  is driven to be rotated about a shaft of the photoconductive drum  20 , and carries a toner image obtained by developing an electrostatic latent image which is formed on a surface of the photoconductive drum  20 . Examples of the photoconductive drum  20  are a publicly-known amorphous silicon (α-Si) photoconductive drum and an organic photoconductive drum (OPC). The charging device  21  charges the surface of the photoconductive drum  20  uniformly to a predetermined charging potential. The charging device  21  includes a charging roller and a charging cleaning brush which removes toner adhered to the charging roller. The exposing device  22  is disposed downstream in the rotational direction of the photoconductive drum  20  with respect to the charging device  21 , and includes various optical systems such as a light source, a polygon mirror, a reflection mirror, and a deflection mirror. The exposing device  22  irradiates the surface of the photoconductive drum  20  charged uniformly to the charging potential with light modulated based on image data (predetermined image information) and exposes the surface of the photoconductive drum  20 , thus forming an electrostatic latent image. 
     The developing device  23  is disposed in a predetermined development nip portion NP ( FIG. 3A ) downstream in the rotational direction of the photoconductive drum  20  with respect to the exposing device  22  so as to oppose the photoconductive drum  20 . The developing device  23  includes a developing roller  231  that is rotated to carry developer including toner and carrier on a peripheral surface of the developing roller  231  and supplies the toner to the photoconductive drum  20  so as to form the toner image. 
     The primary transfer roller  24  and the photoconductive drum  20  form the nip portion across the intermediate transfer belt  141  provided to the intermediate transfer unit  14 . The primary transfer roller  24  primarily transfers the toner image on the photoconductive drum  20  to the intermediate transfer belt  141 . The cleaning device  25  cleans the peripheral surface of the photoconductive drum  20  after the transfer of the toner image. 
     The intermediate transfer unit  14  is disposed in a space between the image forming unit  13  and the toner supply unit  15 , and includes the intermediate transfer belt  141 , a driving roller  142  which is rotatably supported to a unit frame, not illustrated, a driven roller  143 , a backup roller  146 , and a density sensor  100 . The intermediate transfer belt  141  is an endless belt-shaped rotating body, and is installed across the driving roller  142  and the driven rollers  143  and the backup roller  146  so that a peripheral surface side of the intermediate transfer belt  141  makes contact with the peripheral surfaces of the photoconductive drums  20 . The intermediate transfer belt  141  is circularly driven by the rotation of the driving roller  142 . A belt cleaning device  144 , which removes toner remaining on the peripheral surface of the intermediate transfer belt  141 , is disposed near the driven roller  143 . The density sensor  100  (the density detecting unit) is disposed downstream with respect to the units  13 M,  13 C,  13 Y, and  13 Bk so as to oppose the intermediate transfer belt  141 , and detects density of the toner image formed on the intermediate transfer belt  141 . In another embodiment, the density sensor  100  may detect density of a toner image on the photoconductive drum  20 , or density of a toner image fixed to the sheet P. 
     A secondary transfer roller  145  is disposed outside the intermediate transfer belt  141  so as to oppose the driving roller  142 . The secondary transfer roller  145  makes pressure-contact with the peripheral surface of the intermediate transfer belt  141  so that a transfer nip portion is formed between the secondary transfer roller  145  and the driving roller  142 . The toner image, which has been primarily transferred to the intermediate transfer belt  141 , is secondarily transferred to the sheet P supplied from the sheet feeding unit  12  in the transfer nip portion. That is, the intermediate transfer unit  14  and the secondary transfer roller  145  function as a transfer unit that transfers the toner image carried by the photoconductive drum  20  to the sheet P. Further, a roll cleaner  200  which is used for cleaning the peripheral surface of the driving roller  142  is disposed on the driving roller  142 . 
     In the present embodiment, the toner supply unit  15 , which stores toner to be used for forming an image, includes a magenta toner container  15 M, a cyan toner container  15 C, a yellow toner container  15 Y, and a black toner container  15 Bk. These toner containers  15 M,  15 C,  15 Y, and  15 Bk store M, C, Y, and Bk toner to be supplied, respectively. Toner of respective colors is supplied from a toner discharge port  15 H formed on a container bottom surface to the developing devices  23  of the image forming units  13 M,  13 C,  13 Y, and  13 Bk corresponding to M, C, Y, and Bk. 
     The fixing unit  16  includes a heating roller  161  having a built-in heating source, a fixing roller  162  disposed to oppose the heating roller  161 , a fixing belt  163  stretched between the fixing roller  162  and the heating roller  161 , and a pressure roller  164  which is disposed to oppose the fixing roller  162  via the fixing belt  163  and forms a fixing nip portion. The sheet P supplied to the fixing unit  16  passes through the fixing nip portion so as to be heated and pressurized. This fixes the toner image transferred to the sheet P in the transfer nip portion to the sheet P. 
     The sheet ejection portion  17  is formed by recessing a top of the apparatus main body  11 , and includes an output tray  171  that receives the sheet P ejected to a bottom portion of the recessed portion. The sheet P which has been subject to the fixing process is ejected onto the output tray  171  via the sheet conveyance path  111  which extends from an upper portion of the fixing unit  16 . 
     &lt;Developing Device&gt; 
       FIG. 2  is a cross-sectional view of the developing device  23  and a block diagram illustrating an electrical configuration of a control unit  980  according to the present embodiment. The developing device  23  includes a development housing  230 , the developing roller  231 , a first screw feeder  232 , a second screw feeder  233 , and a regulating blade  234 . The developing device  23  employs a two-component developing method. 
     The development housing  230  has a developer housing portion  230 H. The developer housing portion  230 H houses two-component developer including toner and carrier. The developer housing portion  230 H includes a first conveyance portion  230 A and a second conveyance portion  230 B. The first conveyance portion  230 A conveys the developer to a first conveyance direction from one end of a axial direction of the developing roller  231  to the other end (a direction perpendicular to a sheet surface of  FIG. 2 , namely, a rear-front direction). The second conveyance portion  230 B, which is communicated with the first conveyance portion  230 A at both the ends in the axial direction, conveys the developer to a second conveyance direction opposite to the first conveyance direction. The first screw feeder  232  and the second screw feeder  233  are rotated to directions indicated by arrows D 22  and D 23  in  FIG. 2 , respectively, so as to convey the developer to the first conveyance direction and the second conveyance direction, respectively. In particular, the first screw feeder  232  supplies the developer to the developing roller  231  while conveying the developer to the first conveyance direction. 
     The developing roller  231  is disposed so as to oppose the photoconductive drum  20  in the development nip portion NP ( FIG. 3A ). The developing roller  231  includes a sleeve  231 S to be rotated, and a magnet  231 M which is stationarily disposed inside the sleeve  231 S. The magnet  231 M has S1, N1, S2, N2, and S3 poles. The N1 pole functions as a main pole, the S1 and N2 poles function as conveyance poles, and the S2 pole functions as a peeling pole. The S3 pole functions as a draw-up and regulating pole. In one example, magnetic flux density of the S1, N1, S2, N2, and S3 poles is set to 54 mT, 96 mT, 35 mT, 44 mT, and 45 mT, respectively. The sleeve  231 S of the developing roller  231  is rotated to a direction indicated by arrow D 21  in  FIG. 2 . The developing roller  231  is rotated, receives the developer in the development housing  230 , carries a developer layer, and supplies toner to the photoconductive drum  20 . In the present embodiment, the developing roller  231  rotates to an identical direction (a width direction) in a position opposing to the photoconductive drum  20 . 
     The regulating blade  234  (a layer thickness regulating member) is disposed to be away from the developing roller  231  by a predetermined space, and regulates a layer thickness of the developer supplied from the first screw feeder  232  to the peripheral surface of the developing roller  231 . 
     The image forming apparatus  10  having the developing device  23  further includes a development bias applying unit  971 , a driving unit  972 , and the control unit  980 . The control unit  980  includes a central processing unit (CPU), a read only memory (ROM) that stores a control program, a random access memory (RAM) that is used as a work area of the CPU. 
     The development bias applying unit  971 , which includes a direct-current power source and an alternating-current power source, applies a development bias, which is obtained by superimposing an alternating current voltage on a direct current voltage, to the developing roller  231  of the developing device  23  based on a control signal from a bias control unit  982 , described later. 
     The driving unit  972 , which includes a motor and a gear mechanism that transmits a torque of the motor, drives to rotate the developing roller  231 , the first screw feeder  232 , and the second screw feeder  233  in the developing device  23  as well as the photoconductive drum  20  during the developing operation in accordance with a control signal from a driving control unit  981 , described later. 
     The control unit  980  is configured to include the driving control unit  981 , the bias control unit  982 , a storage unit  983 , and a mode control unit  984  by the CPU executing the control program stored in the ROM. 
     The driving control unit  981  controls the driving unit  972 , and drives to rotate the developing roller  231 , the first screw feeder  232 , and the second screw feeder  233 . The driving control unit  981  controls a driving mechanism, not illustrated, and drives to rotate the photoconductive drum  20 . 
     The bias control unit  982  controls the development bias applying unit  971  during the developing operation for supplying toner from the developing roller  231  to the photoconductive drum  20 , and causes a potential difference in the direct current voltage and the alternating current voltage between the photoconductive drum  20  and the developing roller  231 . The potential difference moves the toner from the developing roller  231  to the photoconductive drum  20 . 
     The storage unit  983  stores various information to be seen by the driving control unit  981  and the bias control unit  982 . An example of the stored information is a value of the development bias to be adjusted in accordance with a number of rotations of the developing roller  231  and an environment. The storage unit  983  stores reference information, which relates to a tilt of the reference straight line representing a relationship between a change amount of a frequency of the alternating current voltage of the development bias and a density change amount of the toner image in a case where the frequency is changed with the potential difference in the direct current voltage between the developing roller  231  and the photoconductive drum  20  being kept constant, for each toner charging amount in advance. Data to be stored in the storage unit  983  may be a graph or a table. 
     The mode control unit  984  (the charging amount acquisition unit) executes a charging amount measuring mode (a charging amount acquisition operation) and a charging amount distribution measuring mode (a charging amount distribution acquisition operation). In the charging amount measuring mode, the mode control unit  984  forms the measurement toner image on the photoconductive drum  20  while changing the frequency of the alternating current voltage of the development bias with the potential difference in the direct current voltage between the developing roller  231  and the photoconductive drum  20  being kept constant. The mode control unit  984  acquires the tilt of the measurement straight line representing the relationship between the change amount of the frequency and the density change amount of the measurement toner image based on the change amount of the frequency and a result of detecting density of the measurement toner image in the density sensor  100 , and acquires the charging amount of the toner included in the measurement toner image formed on the photoconductive drum  20  based on the acquired tilt of the measurement straight line and the reference information in the storage unit  983 . The mode control unit  984  performs a first charging amount acquisition operation at a first peak-to-peak voltage of the alternating current voltage of the development bias, and performs a second charging amount acquisition operation at a second peak-to-peak voltage higher than the first peak-to-peak voltage of the alternating current voltage of the development bias. The mode control unit  984  further performs a charging amount distribution acquisition operation for acquiring distribution of the toner charging amount based on the results in the first charging amount acquisition operation and the second charging amount acquisition operation. 
       FIG. 3A  is a pattern diagram of a developing operation in the image forming apparatus  10  according to the present embodiment, and  FIG. 3B  is a pattern diagram illustrating a level relationship in an electric potential between the photoconductive drum  20  and the developing roller  231 . With reference to  FIG. 3A , the development nip portion NP is formed between the developing roller  231  and the photoconductive drum  20 . Toner TN and carrier CA which are carried on the developing roller  231  form a magnetic brush. In the development nip portion NP, the toner TN is supplied from the magnetic brush to the photoconductive drum  20 , and a toner image TI is formed. With reference to  FIG. 3B , the surface of the photoconductive drum  20  is charged to a background portion potential V0 (V) by the charging device  21 . Thereafter, when the exposing device  22  emits exposure light, the surface potential of the photoconductive drum  20  is changed from the background portion potential V0 to at most an image portion potential VL (V) in accordance with the image to be printed. On the other hand, a direct current voltage Vdc of the development bias is applied to the developing roller  231 , and an alternating current voltage, not illustrated, is superimposed on the direct current voltage Vdc. 
     In a case of such a reversal developing method, a potential difference between the surface potential V0 and the direct-current component Vdc of the development bias is a potential difference that suppresses toner fogging on the background portion of the photoconductive drum  20 . On the other hand, a potential difference between a surface potential VL after exposure and the direct-current component Vdc of the development bias is a developing potential difference for moving toner of plus polarity to an image portion of the photoconductive drum  20 . The alternating current voltage to be applied to the developing roller  231  improves the transfer of the toner from the developing roller  231  to the photoconductive drum  20 . 
     On the other hand, toner is triboelectrically charged due to carrier while being circularly conveyed in the development housing  230 . Each of The toner charging amounts has an effect on an amount of toner (a developing amount) moving to the photoconductive drum  20  due to the development bias. Therefore, when the toner charging amount can be accurately predicted in the image forming apparatus  10 , the development bias and the toner density are adjusted in accordance with a number of sheets to be printed, a change in environment, a printing mode, and a page-coverage rate so that satisfactory image quality can be maintained. Thus, accurate prediction of the toner charging amount has been desired. 
     &lt;Prediction of Toner Charging Amount&gt; 
     The disclosers have continued to earnestly conduct a study in view of the above situation, and have gained a new insight that when the frequency of the alternating current voltage of the development bias is changed, the change in the toner developing amount varies depending on the toner charging amount. Specifically, when the toner charging amount is small, an increase in the frequency of the alternating current voltage causes an increase in the toner developing amount. On the other hand, the disclosers have gained a new insight that when the toner charging amount is high, an increase in the frequency of the alternating current voltage causes a decrease in the toner developing amount. With use of this characteristic, the change in the image density in the case where the frequency of the alternating current voltage is changed is measured, and thus the toner charging amount can be accurately predicted. 
       FIG. 4  is a graph illustrating a relationship between the frequency of the development bias and the image density in the image forming apparatus  10  according to the present embodiment.  FIG. 5  is a graph illustrating a relationship between the tilt in the graph of  FIG. 4  and the toner charging amount in the image forming apparatus  10  according to the present embodiment. 
     A potential difference between the direct current voltage of the development bias to be applied to the developing roller  231  and the direct current voltage of the electrostatic latent image on the photoconductive drum  20  is kept constant, and a frequency of an alternating current voltage of the development bias is changed with a peak-to-peak voltage Vpp and a duty ratio of the alternating current voltage being fixed. This results in a tendency that the toner image density detected by the density sensor  100  varies in accordance with the toner charging amount on the developing roller  231  ( FIG. 4 ). That is, as illustrated in  FIG. 4 , when the toner charging amount is 27.5 μc/g, a low frequency f causes a decrease in the image density. On the other hand, when the toner charging amounts are 34.0 μc/g and 37.7 μc/g, the low frequency f causes an increase in image density. As the toner charging amount is smaller, the tilt in the graph illustrated in  FIG. 4  is greater. With reference to  FIG. 5 , relationships between three tilts in the graph of  FIG. 4  and the respective toner charging amounts are represented by straight lines (approximation straight lines). Thus, when information illustrated in  FIG. 5  is stored in the storage unit  983  in advance and the tilts of the straight lines illustrated in  FIG. 4  are derived in the charging amount measuring mode, described later, the toner charging amount at that time can be measured (predicted). 
     &lt;Toner Charging Amount Predicting Effect&gt; 
     In the present embodiment, a surface potential sensor that measures the surface potential of the photoconductive drum  20  does not need to be disposed to predict the toner charging amount. An electric current which flows into the developing roller  231  does not need to be measured in accordance with the development bias for predicting the toner charging amount. The toner charging amount can be stably predicted without any effect of a change in the electric current flowing into the developing roller  231  due to soiling of the surface potential sensor and a change in carrier resistance. This prediction makes selection of a desirable method easy in a case where the density of an image to be printed in the image forming apparatus  10  is decreased. In one desirable method, an increase in the toner density of the developing device  23  causes a reduction in the toner charging amount and thus causes an increase in the image density. In the other method, an increase in a developing potential difference (Vdc−VL) in the development nip portion NP causes the increase in the image density. 
     In general, the reduction in the image density in the image forming apparatus  10  is caused by, for example, “a reduction in the developing potential difference”, “a reduction in a conveyance amount of the developer passing through the regulating blade  234 ”, “a rise in the carrier resistance”, and “a rise in the toner charging amount”. With such a method, the increase in the toner density for reducing the toner charging amount in response to the reduction in the image density caused by a factor other than the increase in the toner charging amount might cause a defect such as toner flying. The toner charging amount is desirably reduced by increasing the toner density in response to the reduction in the image density caused by the increase in the toner charging amount, and a developing electric field (the development bias) is desirably increased in response to the reduction in the image density caused by another factor. Acquisition of the toner charging amount enables optimization of a transfer current to be applied to the secondary transfer roller  145 , thus enabling a whole system of the image forming apparatus  10  to be stable. 
     &lt;Relationship Between Frequency and Toner Charging Amount&gt; 
     The discloser of the present disclosure estimates that the toner charging amount contributes to the change in the image density in the case where the frequency of the alternating current voltage of the development bias is changed as described below. 
     (1) Case of Small Toner Charging Amount 
     In the case of the small toner charging amount, electrostatic adhesion which acts between the toner and the carrier is small, and thus the toner is easily separated from the carrier. However, when the frequency of the alternating current voltage of the development bias is low, a number of toner reciprocating times in the development nip portion NP is decreased. This decrease causes a reduction in the image density. The decrease in the frequency increases a reciprocating distance of the toner per cycle of the alternating current voltage, but in the case of the small toner charging amount, an effect on the decrease in the image density is small because a toner moving distance is originally short. In the case of the small toner charging amount, when the frequency of the alternating current voltage of the development bias is decreased, the image density is decreased. 
     (2) Case of Large Toner Charging Amount 
     The low frequency of the alternating current voltage of the development bias decreases the number of toner reciprocating times in the development nip portion NP, but in the case of the large toner charging amount, an effect of the decrease in the number of the reciprocating times is small because originally the toner is hardly separated from the carrier. On the other hand, the low frequency increases the toner reciprocating distance per cycle of the alternating current voltage, and thus the image density increases in accordance with the large toner charging amount. In the case of the large toner charging amount, when the frequency of the alternating current voltage of the development bias is decreased, the image density increases. 
     &lt;Toner Charging Amount Measuring Mode&gt; 
       FIG. 6  is a flowchart illustrating the charging amount measuring mode to be executed in the image forming apparatus  10  according to the present embodiment.  FIG. 7  is a pattern diagram of the measurement toner image to be formed on the photoconductive drum  20  in the charging amount measuring mode. 
     With reference to  FIG. 6 , when the charging amount measuring mode starts (step S 01 ), the mode control unit  984  sets a variable n for changing the frequency of the alternating current voltage of the development bias to 1 (step S 02 ). The mode control unit  984  controls the driving control unit  981  and the bias control unit  982 , and after rotating the developing roller  231  once or more with a preset reference development bias being applied, sets the frequency of the alternating current voltage of the development bias to a first frequency (n=1) (step S 03 ). The reference development bias is set for preventing the charging amount measuring mode from being affected by a history of previous image forming. Normally, a bias to be used for printing (image forming) is applied to a condition of the reference development bias. It is desirable that the direct current voltage and the alternating current voltage are applied in a superimposed manner because of a less eliminating effect for the history when only the direct current voltage is applied as the reference development bias. 
     The preset measurement toner image is developed at the development bias with which the frequency of the alternating current voltage is set to the first frequency (step S 04 ), and this toner image is transferred from the photoconductive drum  20  to the intermediate transfer belt  141  (step S 05 ). Image density of the measurement toner image is measured by the density sensor  100  (step S 06 ), and the acquired image density as well as the first frequency value is stored in the storage unit  983  (step S 07 ). 
     The mode control unit  984  then determines whether the variable n relating to the frequency reaches a preset prescribed number of times N (step S 08 ). If a relation of n≠N is satisfied (NO in step S 08 ), the value n is counted up by 1 (n=n+1 in step S 09 ), and steps S 03  to S 07  are repeated. It is desirable for heightening the measuring accuracy of the charging amount that the prescribed number of times N is 2 or more, and more desirably set to satisfy a relation of 3≤N. On the other hand, if a relation of n=N is satisfied (YES in step S 08 ), the mode control unit  984  calculates tilts of the approximation straight lines illustrated in  FIG. 4  based on the information stored in the storage unit  983  (step S 10 ). The mode control unit  984  estimates the toner charging amount from the tilts (step S 11 ) based on the graph (the reference information), illustrated in  FIG. 5 , stored in the storage unit  983 , and ends the charging amount measuring mode (step S 12 ). 
       FIG. 7  illustrates an example that when the prescribed number of times N is 3, the frequency f is increased, and thus the image density of the measurement toner image is increased. In this case, the toner charging amount is relatively small as in 27.5 μc/g in  FIG. 4 . 
     When N is 2, the image density measured in step S 06  is defined as ID1 and ID2. The first frequency is defined as f1 (kHz), and the second frequency is defined as f2 (kHz) (f2&lt;f1). In this case, a tilt a of the straight line illustrated in  FIG. 4  is calculated by expression 1.
 
Tilt  a =( ID 1− ID 2)/( f 1− f 2))  (expression 1)
 
     The tilt a, which varies with a toner charging amount, becomes “positive (+)” in the small toner charging amount, and becomes “negative (−)” in the large toner charging amount. When the measurement is conducted under the condition that 3≤N, a tilt of the approximation straight lines in a linear expression obtained by a method of least squares may be used. The reference information illustrated in  FIG. 5  is expressed by expression 2.
 
 Q/M=A ×tilt of straight line+ B   (expression 2)
 
     Symbols A and B are values specific to developer, and are determined in advance by an experiment. Symbol Q/M means the toner charging amount per unit mass. When the tilt a of the approximation straight line calculated by the expression 1 in step S 10  is assigned into the expression 2, the toner charging amount Q/M is calculated. The charging amount measuring mode illustrated in  FIG. 6  may be executed for the developing devices  23  of the respective colors in  FIG. 1 , and the frequency set during the mode may be set to values specific to the developing devices  23 . In particular, when desirable frequencies in accordance with temperature and humidity around the image forming apparatus  10  and a number of durable sheets have been already known, the frequency to be set during the mode may be set near the already known frequency. A frequency to be used for a new measuring mode may be selected with reference to the result of the charging amount measuring mode for the previous toner. In this case, the accuracy of the toner charging amount to be measured can be heightened. 
     &lt;Execution Timing of Charging Amount Measuring Mode&gt; 
     The charging amount measuring mode according to the present embodiment is automatically started and manually started at different timings. It is desirable that the automatic measuring mode is executed at the same timing as a calibration operation by the image forming apparatus  10  (referred to also as a setting-up operation or an image quality adjusting operation). In the calibration operation, the adjusting operation is sufficiently performed for obtaining satisfactory image quality in an intermediate density region (a halftone image). For this operation, a time period required by executing the charging amount measuring mode is sufficiently secured. Therefore, the measuring mode can be executed at the alternating current voltage of the development bias with two different frequencies. In the calibration operation, a halftone image as well as a solid image (100% solid image) is also used as an image pattern for adjusting the image quality. Thus, the predicting accuracy of the toner charging amount can be improved. In the solid image in a high density region, a developing performance in the development nip portion NP is saturated more easily than that in the halftone image. That is, a change amount of the image density is small in the case where the development bias is changed (a sensitivity is low). On the other hand, in the halftone image, the toner charging amount is accurately measured (predicted) because the change amount of the image density is comparatively large. In the case of the halftone image, the density sensor  100  might detect the image density with comparatively low accuracy because the density is relatively low in the halftone image than in the solid image. Therefore, the charging amount measuring mode is executed for both the solid image and the halftone image, and an average value is taken from these images, thus enabling the measurement with higher accuracy. The values A and B in the expression 2 are different between the solid image and the halftone image. This is because a relationship between the image density and the toner developing amount is different between the solid image and the halftone image. 
     It is desirable that a plurality of the density sensors  100  are disposed in a main scanning direction (the axial direction of the photoconductive drum  20 ) and measurement toner images are formed in accordance with the positions of the density sensor  100 . That is, in a case where a measurement toner image is formed corresponding to both the ends in the axial direction of the photoconductive drum  20 , the toner charging amounts at both the ends of the developing device  23  (the developing roller  231 ), respectively, can be predicted. If a difference in the toner charging amount between both the ends is larger than a preset threshold, charging performance might be deteriorated in the developing device  23 . The mode control unit  984  thus can facilitate replacement of the developing device  23  and replacement of developer through a display unit, not illustrated, of the image forming apparatus  10 . 
     It is desirable that the toner charging amount measuring mode is executed when the image forming apparatus  10  is manufactured and is shipped from a factory and when the main body of the image forming apparatus  10  is set up in a place where the image forming apparatus  10  is used. This enables prediction of an influence during suspension of the image forming apparatus  10 . That is, the charging amount of the developer tends to be small when the suspension period is long, and a tendency level varies with a period and an environment in which the image forming apparatus  10  is left. Therefore, the measurement of the toner charging amount at the shipment time and the main body setup time enables prediction of a deteriorated state of the developer due to the state that the developer is left. If the image forming apparatus  10  is left for a very long period or left in a hostile environment, a great difference between the two toner charging amounts (the toner charging amounts at the shipment time and the main body setup time) is detected. In such a case, replacement of the developer can be facilitated in the place of use, similarly as described above. 
     On the other hand, even if the toner charging amounts at the shipment time and the main body setup time are small, the developer is less likely to be deteriorated when the difference between the toner charging amounts is small. Thus, the developer does not have to be replaced in the place of use, and adjustment of the toner density and a developing condition (the development bias, etc.) can improve image quality. The toner charging amount measuring mode according to the present embodiment is executed after the image forming apparatus  10  is not used and left for a predetermined time period, thus acquiring a change in state of the developer. 
     In the toner charging amount measuring mode according to the present embodiment, the toner charging amounts in the developing devices  23  can be acquired without using the surface potential sensor that measures potentials on the photoconductive drum  20  and an ammeter that measures developing currents flowing into the developing rollers  231 . The acquired results enable an accurate determination whether the replacement of the developer in the developing devices  23  is necessary and an accurate determination whether adjustment of the development bias is necessary. 
     In particular, the reference information stored in the storage unit  983  is set such that when the toner charging amount is the first charging amount, the tilt of the reference straight line is negative, when the toner charging amount is the second charging amount smaller than the first charging amount, the tilt of the reference straight line is positive, and as the toner charging amount becomes smaller, the tilt of the reference straight line is greater. Such a configuration enables the accurate toner charging amounts to be acquired based on a relationship between the frequency of the alternating current voltage of the development bias and the density of toner images (the development toner amount) to be formed on the photoconductive drums  20  (the intermediate transfer belt  141 ). 
     &lt;Toner Charging Amount Distribution Measuring Mode&gt; 
     In the present embodiment, the mode control unit  984  can execute the charging amount distribution measuring mode in which a toner charged state more detailed than the charging amount measuring mode can be detected.  FIG. 8  is a flowchart illustrating the charging amount distribution measuring mode to be executed in the image forming apparatus  10  according to the present embodiment.  FIG. 9  is a graph illustrating a relationship between the toner charging amount and a ratio of a toner developing amount in the image forming apparatus  10  according to the present embodiment. 
     With reference to  FIG. 8 , If the charging amount distribution measuring mode starts (step S 21 ), the mode control unit  984  sets the variable n for changing the frequency of the alternating current voltage of the development bias to 1, and sets a variable m for changing the peak-to-peak voltage Vpp of the alternating current voltage to 1 (step S 22 ). After rotating the developing roller  231  once or more with a preset reference development bias being applied, the mode control unit  984  sets the alternating current voltage Vpp of the development bias to a first Vpp (m=1) (step S 23 ). The mode control unit  984  sets the frequency of the development bias to the first frequency (n=1) (step S 24 ). Herein, the reference development bias is set for preventing the charging amount measuring mode from being affected by a history of previous image forming, and normally a bias at a time of use for printing (image forming) is employed. 
     Then, the measurement toner image set in advance at the first Vpp and with the first frequency is developed (step S 25 ), and this toner image is transferred from the photoconductive drum  20  to the intermediate transfer belt  141  (step S 26 ). The image density of the measurement toner image is measured by the density sensor  100  (step S 27 ), and is stored in the storage unit  983  together with the first Vpp and the first frequency (step S 28 ). 
     The mode control unit  984  then determines whether the variable n relating to the frequency reaches the preset prescribed number of times N (step S 29 ). Herein, if a relation of n≠N is satisfied (NO in step S 29 ), the value n is counted up by 1 (n=n+1 in step S 30 ), and steps S 24  to S 28  are repeated. It is desirable for heightening the measuring accuracy of the charging amount distribution that the prescribed number of times N is 2 or more, and more desirably is set to satisfy a relation of 3≤N. On the other hand, if a relation of n=N is satisfied (YES in step S 29 ), the mode control unit  984  calculates tilts of the approximation straight lines illustrated in  FIG. 4  based on the information stored in the storage unit  983  (step S 31 ). The mode control unit  984 , then, estimates the toner charging amounts in the case where m=1 from the tilts based on the graph (the reference information), illustrated in  FIG. 5 , stored in the storage unit  983  (step S 32 ). 
     The mode control unit  984  determines whether the variable m relating to the voltage Vpp reaches the preset prescribed number of times M (step S 33 ). If a relation of m≠M is satisfied (NO in step S 33 ), the value m is counted up by 1 (m=m+1) to satisfy a relation of n=1 (step S 34 ), and steps S 23  to S 32  are repeated. It is desirable for heightening the measuring accuracy of the charging amount distribution that the prescribed number of times M is 3 or more, and more desirably is set to satisfy a relation of 5≤M. On the other hand, if a relation of m=M is satisfied (YES in step S 33 ), the mode control unit  984  estimates the toner charging amount distribution from the toner charging amounts corresponding to the respective voltages Vpp based on the information stored in the storage unit  983  (step S 35 ). The mode control unit  984  then ends the charging amount distribution measuring mode (step S 36 ). 
     In the charging amount measuring mode, the mode control unit  984  changes only the frequencies with the voltages Vpp being fixed so as to estimate and measure the toner charging amounts. This case is conditional upon a state that all the toner charging amounts in the developing devices  23  are the same (average). Normally, states of the developer in the developing devices  23  can be sufficiently acquired even based on the toner charging amounts estimated under such a condition. On the other hand, in the charging amount distribution measuring mode, employment of a method for further heightening the voltage Vpp gradually enables measurement of the toner charging amount distribution. In other words, in the flow illustrated in  FIG. 8 , frequency dependence characteristics of the image density are acquired at a low voltage Vpp. In this case, highly charged toner is hardly separated from the carrier, and thus low-charged toner is mainly developed on the photoconductive drum  20 . The toner charging amount can be predicted ( FIG. 5 ) from “the change in image density/the change in frequency” at this time ( FIG. 4 ). At this time, the mode control unit  984  stores image density with a frequency to be used for the image forming operation (6 kHz in tables 1 and 2, described later) in the storage unit  983 . The mode control unit  984  then increases the voltage Vpp, and acquires the frequency dependence characteristics of the image density similarly in the above method. As a result, the toner charging amounts to be acquired become slightly large, and the image density is also heightened. 
     When such a process is repeated for different voltages Vpp at a plural number of times, graphs (plural pieces of information) representing a relationship between a toner charging amount Q/M and image density ID are acquired. Herein, the mode control unit  984  converts the image density ID into a development toner amount TM on the intermediate transfer belt  141  based on the data stored in the storage unit  983  in advance, and calculates a value QT (=the toner charging amount Q/M×the development toner amount TM) of the measured data for each voltage Vpp so as to obtain a difference ΔQT between this value QT and a value QT at a previous voltage Vpp (ΔQT=QT(n)−QT(n−1): n is a natural number). Similarly, as for the development toner amount TM, the mode control unit  984  obtains a difference ΔTM between the development toner amount TM and a development toner amount TM at a previous voltage Vpp (ΔTM=TM(n)−TM (n−1): n is a natural number). The mode control unit  984  then divides the difference ΔQT by the difference ΔTM, and calculates a difference in (the toner charging amount Q/M×the development toner amount TM)/(the difference in the development toner amount TM)=ΔQT/ΔTM=a calculated toner charging amount Q/Mcal (tables 1 and 2) for each voltage Vpp. 
     In such a manner, in the present embodiment, the charging amount acquisition operation is performed on the peak-to-peak voltages of the plurality of alternating current voltages, and thus the toner charging amount distribution can be acquired. 
     &lt;Ds Gap Correcting Mode&gt; 
     In the present embodiment, the mode control unit  984  further executes a Ds gap correcting mode. A Ds gap is a gap between the photoconductive drum  20  and the developing roller  231  in the development nip portion NP( FIG. 3A ). The Ds gap might affect the toner developing amount. That is, when the Ds gap becomes narrower, the toner developing amount increases. On the other hand, even if the Ds gap changes within a predetermined design range (within tolerance), this change does not have much effect on the tilt in the case where the frequency is changed. However, in a case where the accuracies of the charging amount measuring mode and the charging amount distribution measuring mode are desired to be heightened, the Ds gap correcting mode is executed and then the charging amount measuring mode and the charging amount distribution measuring mode can be executed. The Ds gap correcting mode can be turned ON or OFF by a maintenance staff through an operation unit, not illustrated, of the image forming apparatus  10 . 
     In a case where the Ds gap correcting mode is ON, in the charging amount measuring mode and the charging amount distribution measuring mode, a predetermined correction is made on the image density measured result of the toner image (step S 06  in  FIG. 6  and step S 27  in  FIG. 8 ). The mode control unit  984  starts cumulative counting of driving time periods of the photoconductive drum  20  and the developing roller  231  (or a total number of rotations) when the image forming apparatus  10  starts to be used. When these driving time periods increase, a space regulating member, not illustrated, which intervenes between the photoconductive drum  20  and the developing roller  231  wears out, thus decreasing the Ds gap. As one example, the space regulating member is a disc member (a roller bearing) pivotally supported to the shaft of the developing roller  231  in a rotatable state. The disc member makes contact with the peripheral surface of the photoconductive drum  20 , and thus the Ds gap is retained within a predetermined range. When the driving time periods of the photoconductive drum  20  and the developing roller  231  increase, the mode control unit  984  makes predetermined correction on the image density measured results of the toner image (step S 06  in  FIG. 6  and step S 27  in  FIG. 8 ). As one example, when the driving time period of the photoconductive drum  20  reaches about 100 KPV (100000 sheets), the mode control unit  984  multiples the measured density result by 0.99. That is, 1% of the measured density result is canceled as a reduced portion of the Ds gap. 
     The mode control unit  984  may make correction in accordance with film thinning (wear) of a functional layer formed on the surface of the photoconductive drum  20 . In this case, the film thinning of the functional layer causes an increase in the Ds gap. Therefore, when the driving time period of the photoconductive drum  20  reaches a predetermined value, the mode control unit  984  may multiply the measured density result by 1.005. That is, 0.5% of the measured density result is canceled as an increased portion of the Ds gap. In such a manner, the image density measured result of the toner image is corrected in accordance with a factor in Ds gap fluctuation, and thus the toner charging amount and the charging distribution can be acquired without being affected by disturbance. 
     &lt;Development Bias Control Mode&gt; 
     In the present embodiment, the bias control unit  982  can execute a development bias control mode. In this mode, the bias control unit  982  controls the direct current voltage of the development bias at a time of forming an image in accordance with the toner charging amount acquired in the charging amount measuring mode. As described above, a potential difference between the surface potential V0 of the photoconductive drum  20  and the direct-current component Vdc of the development bias applied to the developing roller  231  in  FIG. 3B  is a potential difference for suppressing toner fogging on the background portion of the photoconductive drum  20 . That is, as |V0−Vdc| is larger, the toner fogging is less. On the other hand, if |V0−Vdc| is larger, negatively (−) charged carrier transfers from the developing roller  231  to the photoconductive drum  20 , namely, a so-called carrier phenomenon easily occurs. When the measured toner charging amount is smaller than the predetermined threshold (the charging amount is small), the carrier phenomenon hardly occurs. Thus, the bias control unit  982  prioritizes the suppression of toner fogging and controls the direct current voltage Vdc so that |V0−Vdc| is large. On the other hand, when the measured toner charging amount is larger than the predetermined threshold (the charging amount is large), toner fogging hardly occurs. Thus, the bias control unit  982  prioritizes suppression of carrier development and controls the direct current voltage Vdc so that |V0−Vdc| is small. In such a manner, the direct-current component of the development bias is controlled in accordance with the toner charging amount so that margins (latitudes) for the toner fogging and the carrier development are widened, and thus stable image forming can be performed. 
     EXAMPLES 
     The embodiment of the present disclosure will be further described in detail below by giving examples, but the present disclosure is not limited only to the following examples. Experimental conditions in conducted comparative experiments are described below. 
     &lt;Common Experimental Conditions&gt; 
     Printing speed: 55 sheets/minute 
     The photoconductive drum  20 : amorphous silicon photoconductor (α-Si) 
     The developing roller  231 : outer diameter; 20 mm, surface shape; knurled grooving, 80 rows of recessed portions (grooves) are formed along the circumferential direction. 
     The regulating blade  234 : made of SUS430, magnetic property, thickness; 1.5 mm 
     Developer conveyance amount after the regulating blade  234 : 250 g/m 2    
     Circumferential velocity of the developing roller  231  with respect to the photoconductive drum  20 : 1.8 (a trailing direction in an opposing position) 
     The distance between the photoconductive drum  20  and the developing roller  231 : 0.30 mm 
     White portion (background portion) potential V0 on the photoconductive drum  20 : +270 V 
     Image portion potential VL on the photoconductive drum  20 : +20 V 
     The development bias of the developing roller  231 : an alternating current voltage square wave in which frequency=6.0 kHz, Duty=50%, and Vpp=1000 V, Vdc (the direct current voltage)=200 V 
     Toner: positively charged toner, volume average particle size; 6.8 μm, toner density; 8% 
     Carrier: volume average particle size; 35 μm, ferrite resin coated carrier 
     &lt;Experiment 1&gt; 
     Under the above conditions, the toner charging amount was adjusted by changing an amount of toner external additive, and the printing operation was performed. Results of the experiment 1 are illustrated in  FIGS. 4 and 5 . In  FIG. 4 , the image density of the toner image on the intermediate transfer belt  141  was measured by the density sensor  100 , and the toner image density is represented as I.D of a toner fixed image by using a correlation curve indicating a correlation between image density (a sensor output), which was acquired in advance, of the toner image and the image density of the toner fixed image formed on a printing sheet (paper). 
       FIG. 5  illustrates a relationship between the toner charging amounts and the tilts of the straight lines (the approximation straight lines) in  FIG. 4 . Expression 3 (described below) of the approximation straight lines illustrated in  FIG. 5  is stored in the storage unit  983  in advance. Use of this expression 3 enables prediction of the toner charging amount.
 
Toner charging amount  Q/M (μc/g)=−442.32×tilt+29.87  (Expression 3)
 
In the expression 3, the tilt=Δ image density/Δ frequency (see the tilts in the graph of  FIG. 4 )
 
&lt;Experiment 2&gt;
 
     An experiment relating to the charging amount distribution measuring mode was conducted. The condition of carrier coating agent was changed for preparing developer A and developer B that indicate different charging amount distributions. The toner density was 8% for both the developer A and the developer B. The condition of the development bias was the same as the condition in the experiment 1 except for the voltage Vpp and the frequency. 
     &lt;Developer&gt; 
     It was confirmed that pulverized toner and core-shell toner produced a similar effect. It was confirmed that a similar effect was produced at the toner density ranging from 3% to 12%. Toner transfer is caused by an alternating electric field notably when a finer magnetic brush is used. Thus, the volume average particle size of the carrier is preferably 45 μm or less, and more preferably 30 μm or more to 40 μm or less. Resin carrier is more preferable because its true specific gravity is smaller than that of ferrite carrier. 
     &lt;Carrier&gt; 
     The carrier was formed by coating a ferrite core having volume average particle size of 35 μm with silicon or fluorine, specifically in the following procedure. 20 parts by mass of silicon resin KR-271 (Shin-Etsu Chemical Co., Ltd.) was dissolved in 200 parts by mass of toluene, and thus an application liquid was prepared for 1000 parts by weight of carrier core EF-35 (made by Powdertech Co., Ltd.). After a fluid bed coating applicator sprayed the application liquid to the carrier core EF-35, and the carrier core EF-35 coated with the application liquid was heated at 200° C. for 60 minutes so that carrier was obtained. In this application liquid, a conductive agent and a charge control agent were mixed within a range between 0 to 20 parts by mass with respect to 100 parts by mass of coating resin and were dispersed. In such a manner, resistance and charging were adjusted. 
     Table 1 indicates experimental results in the developer A, and Table 2 indicates experimental results in the developer B. The charging amounts in Tables 1 and 2 were measured by using a suction-type small-sized charging amount measuring device MODEL212HS manufactured by Trek, Inc. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 DEVELOPER A 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                   
                   
                 DEVELOPING 
               
               
                   
                   
                 DEVELOPING 
                 CALCULATED 
                 AMOUNT 
               
               
                   
                 CHARGING 
                 AMOUNT 
                 CHARGING 
                 RATIO 
               
               
                 Vpp 
                 AMOUNT 
                 WITH 6 kHz 
                 AMOUNT 
                 WITH 6 kHz 
               
               
                 (kV) 
                 (μc/g) 
                 (mg/cm 2 ) 
                 (μc/g) 
                 (%) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 0.2 
                 23 
                 0.25 
                 23.0 
                 75.8 
               
               
                 0.3 
                 23.6 
                 0.257 
                 43.5 
                 2.4 
               
               
                 0.4 
                 24.2 
                 0.265 
                 45.0 
                 2.1 
               
               
                 0.6 
                 25.6 
                 0.281 
                 48.8 
                 4.8 
               
               
                 0.8 
                 27 
                 0.294 
                 57.3 
                 3.9 
               
               
                 1 
                 28.6 
                 0.309 
                 60.0 
                 4.5 
               
               
                 1.2 
                 29.1 
                 0.313 
                 67.7 
                 1.2 
               
               
                 1.4 
                 31.1 
                 0.33 
                 67.9 
                 5.2 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 DEVELOPER B 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                   
                   
                 DEVELOPING 
               
               
                   
                   
                 DEVELOPING 
                 CALCULATED 
                 AMOUNT 
               
               
                   
                 CHARGING 
                 AMOUNT 
                 CHARGING 
                 RATIO 
               
               
                 Vpp 
                 AMOUNT 
                 WITH 6 kHz 
                 AMOUNT 
                 WITH 6 kHz 
               
               
                 (kV) 
                 (μc/g) 
                 (mg/cm 2 ) 
                 (μc/g) 
                 (%) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 0.2 
                 22.4 
                 0.24  
                 22.4 
                 72.7 
               
               
                 0.3 
                 22.5 
                 0.252 
                 24.5 
                 3.6 
               
               
                 0.4 
                 22.7 
                 0.263 
                 25.2 
                 3.9 
               
               
                 0.6 
                 23 
                 0.268 
                 26.0 
                 3.6 
               
               
                 0.8 
                 23.1 
                 0.281 
                 27.3 
                 3.3 
               
               
                 1 
                 23.5 
                 0.289 
                 29.3 
                 3.3 
               
               
                 1.2 
                 23.6 
                 0.301 
                 37 5 
                 2.4 
               
               
                 1.4 
                 23.8 
                 0.312 
                 38.8 
                 1.5 
               
               
                   
               
            
           
         
       
     
     In both the experiments, the experimental results are the toner developing amounts obtained by converting the image density in the case where the frequency of the alternating current voltage of the development bias is set to 6 kHz in accordance with a linear conversion expression stored in the storage unit  983  in advance. The charging amount distributions in the developer A and the developer B are illustrated in  FIG. 9 .  FIG. 9  illustrates a ratio of development toner amount for each voltage Vpp on condition that the amount of toner developed in a relation of Vpp=1.4 kV is 100%. 
     A “developing amount ratio with frequency of 6 kHz” indicated in Tables 1 and 2 will be described. For example, the “developing amount ratio with frequency of 6 kHz” at the voltage Vpp of 0.3 (kV) is calculated according to {(developing amount at the development bias with voltage Vpp 0.3 (kV) and frequency of 6 (kHz))−(developing amount at the development bias with voltage Vpp 0.2 (kV) and frequency of 6 (kHz))}/(developing amount at the development bias with voltage Vpp 1.4 (kV) and frequency of 6 (kHz))×100(%). Herein, the voltage Vpp 1.4 (kV) is a maximum voltage Vpp within the measurement range. Similarly, the “developing amount ratio with frequency of 6 kHz” at the voltage Vpp 0.4 (kV) is calculated according to {(developing amount at the development bias with voltage Vpp 0.4 (kV) and frequency of 6 (kHz))−(developing amount at the development bias with voltage Vpp 0.3 (kV) and frequency of 6 (kHz))}/(developing amount at the development bias with voltage Vpp 1.4 (kV) and frequency of 6 (kHz))×100(%). That is, in the above calculating procedure, the value QT of the measurement data for each voltage Vpp (=toner charging amount Q/M×the development toner amount TM) is calculated, and the difference ΔQT between this value QT and a value QT at a previous voltage Vpp is obtained (ΔQT=QT(n)−QT (n−1); n is a natural number). Much the same is true on the other voltages Vpp, but in a case of a minimum voltage Vpp 0.2 (kV), the “developing amount ratio with frequency of 6 kHz” is calculated according to (the developing amount at the development bias with voltage Vpp 0.2 (kV) and frequency of 6 (kHz))/(the developing amount at the development bias with voltage Vpp 1.4 (kV) and frequency of 6 (kHz))×100(%). A developer ratio (%) calculated in such a manner is plotted along a vertical axis in  FIG. 9 . 
     With reference to  FIG. 9 , it is found from the result in the charging amount distribution measuring mode that the developer A includes toner larger in the charging amount than the developer B, and the charging distribution is wide. On the other hand, the developer B shows narrow charging distribution, and the toner charging amounts are approximate to each another. Such tendency is measured during use of the image forming apparatus  10 , and thus a deteriorated state of the developer can be acquired. This enables secure determination whether replacement of developer is necessary. 
     The embodiment of the present disclosure has been described as above, but the present disclosure is not limited to the embodiment and thus includes following modifications. 
     (1) In the above embodiment, the aspect in which the surface of the developing roller  231  is subject to the knurled grooving has been described, but the surface of the developing roller  231  may have a dimple shape or may be subject to blast working. 
     (2) In the above embodiment, the aspect in which the mode control unit  984  can execute both the charging amount measuring mode and the charging amount distribution measuring mode has been described, but the mode control unit  984  may execute any one of the measuring modes. 
     (3) As illustrated in  FIG. 1 , in the case where the image forming apparatus  10  includes the plurality of developing devices  23 , one or two developing devices  23  execute both or one of the charging amount measuring mode and the charging amount distribution measuring mode according to the embodiment, and another developing device  23  may use the results in the modes. 
     Although the present disclosure has been fully described by way of example with reference to the accompanying drawings, it is to be understood that various changes and modifications will be apparent to those skilled in the art. Therefore, unless otherwise such changes and modifications depart from the scope of the present disclosure hereinafter defined, they should be construed as being included therein.