Patent Publication Number: US-9846383-B2

Title: Image formation device having determination of charge voltage

Description:
The entire disclosure of Japanese Patent Application No. 2016-017785 filed on Feb. 2, 2016 including description, claims, drawings, and abstract are incorporated herein by reference in its entirety. 
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to an image formation device configured such that a charge voltage formed by superimposition of an AC voltage on a DC voltage is supplied to a charging member to charge an image carrier. 
     Description of the Related Art 
     Examples of the technique of charging an image carrier such as a photosensitive drum in an image formation device such as a printer include the technique of charging an image carrier by a charging member, such as a charging roller and a charging brush, disposed in contact with a surface of the image carrier or disposed close to the surface of the image carrier with a certain spacing. In this charging technique, it is often configured such that a charge voltage formed by superimposition of an AC voltage on a DC voltage is supplied to the charging member. 
     JP 2001-201920 A discloses a configuration in which the level of peak-to-peak voltage is set to a proper value to stably perform discharging between an image carrier and a charging member based on the premise that there is the effect of averaging charge of the image carrier when a peak-to-peak voltage of an AC voltage has a value of equal to or greater than twice as great as a charge start voltage. 
     Specifically, in each of a first range in which the peak-to-peak voltage is lower than twice as high as the charge start voltage and a second range in which the peak-to-peak voltage is equal to or higher than twice as high as the charge start voltage, AC voltages with different detection peak-to-peak voltages are sequentially applied to the charging member, and the value of alternating current flowing through the charging member is sequentially detected. 
     Based on each detection value of the alternating current flowing through the charging member, an approximate function fI 1 (Vpp) of the alternating current value for the peak-to-peak voltage in the first range and an approximate function fI 2 (Vpp) of the alternating current value for the peak-to-peak voltage in the second range are obtained. Then, a peak-to-peak voltage value when a difference [=fI 2 (Vpp)−fI 1 (Vpp)] between the approximate functions fI 1 (Vpp), fI 2 (Vpp) is a predetermined value D is determined as a proper value. 
     However, as a result of experiment by the inventor(s) of the present invention, it has been found that the proper peak-to-peak voltage value is not always obtained in the configuration in which the above-described difference is fixed to the predetermined value D. 
     Specifically, even when the peak-to-peak voltage value obtained from the predetermined value D is proper in a brand-new state of the image carrier, if an image carrier surface is progressively worn out due to repeated printing for a long period of time, the peak-to-peak voltage value obtained from the same predetermined value D becomes extremely greater than a proper value at each point due to, e.g., a decrease in an electric resistance value of the image carrier. This leads to great damage on the image carrier. As a result, wearing out of the image carrier is further accelerated, and the image carrier early reaches the end of the life thereof. 
     SUMMARY OF THE INVENTION 
     The present invention has been made in view of the above-described problems, and an object of the present invention is to provide an image formation device being able to obtain a more proper peak-to-peak voltage value. 
     To achieve the abovementioned object, according to an aspect, an image formation device in which an image carrier is charged by a charging member, reflecting one aspect of the present invention comprises: a power source configured to supply a charge voltage to the charging member, the charge voltage being formed such that an AC voltage is superimposed on a DC voltage; a detection unit configured to detect an alternating current value flowing through the charging member; and a control unit configured to control a peak-to-peak voltage value of the AC voltage, wherein the control unit executes: first processing of sequentially supplying a plurality of charge voltages from the power source to the charging member in non-image formation, the charge voltages having different peak-to-peak voltage values in a first discharge range in which only charge transfer from the charging member to the image carrier occurs and a second discharge range in which charge transfer occurs in both directions between the image carrier and the charging member; second processing of obtaining, from an alternating current value detection result obtained by the detection unit when each charge voltage is supplied by the first processing, a third approximate function indicating a difference value between a first approximate function and a second approximate function, the first approximate function indicating an alternating current value for each peak-to-peak voltage value in the first discharge range and the second approximate function indicating an alternating current value for each peak-to-peak voltage value in the second discharge range; and third processing of determining one of different predetermined ranges to which a detection value of the alternating current value in supply of one of the charge voltages with an associated one of the peak-to-peak voltage values in the second discharge range belongs, and determining, as a peak-to-peak voltage value in image formation, a peak-to-peak voltage value at a point at which a change amount of the difference value per unit peak-to-peak voltage is coincident with a predetermined change amount value corresponding to the determined range in the third approximate function. 
     The associated one of the peak-to-peak voltage values is preferably one of the peak-to-peak voltage values in the second discharge range. 
     The associated one of the peak-to-peak voltage values is preferably a greatest one of the peak-to-peak voltage values in the second discharge range. 
     The third approximate function is preferably obtained by subtraction of the first approximate function from the second approximate function, and the associated one of the peak-to-peak voltage values is preferably one of peak-to-peak voltage values which are included in the peak-to-peak voltage values in the second discharge range and for which the difference value is greater than zero. 
     The image formation device preferably further comprises: a detection unit configured to detect an environmental condition inside or outside a machine, wherein for each of the different predetermined ranges, different values of the change amount is, in advance, associated respectively with different environmental conditions, and in the third processing, one of the different values of the change amount associated in advance with the determined range and corresponding to one of the different environmental conditions detected by the detection unit is set as the predetermined change amount value. 
     The environmental condition is preferably at least one of a temperature or a humidity inside the machine. 
     The charging member is preferably in a roller, brush, or blade shape contacting the image carrier or disposed close to the image carrier. 
     To achieve the abovementioned object, according to an aspect, there is provided a non-transitory recording medium storing a computer readable control program of an image formation device in which an image carrier is charged by a charging member, wherein the image formation device includes: a power source configured to supply a charge voltage to the charging member, the charge voltage being formed such that an AC voltage is superimposed on a DC voltage; and a detection unit configured to detect an alternating current value flowing through the charging member, the program reflecting one aspect of the present invention causes a computer to execute: a first processing step of sequentially supplying a plurality of charge voltages from the power source to the charging member in non-image formation, the charge voltages having different peak-to-peak voltage values in a first discharge range in which only charge transfer from the charging member to the image carrier occurs and a second discharge range in which charge transfer occurs in both directions between the image carrier and the charging member; a second processing step of obtaining, from an alternating current value detection result obtained by the detection unit when each charge voltage is supplied by the first processing, a third approximate function indicating a difference value between a first approximate function and a second approximate function, the first approximate function indicating an alternating current value for each peak-to-peak voltage value in the first discharge range and the second approximate function indicating an alternating current value for each peak-to-peak voltage value in the second discharge range; and a third processing step of determining one of different predetermined ranges to which a detection value of the alternating current value in supply of one of the charge voltages with an associated one of the peak-to-peak voltage values in the second discharge range belongs, and determining, as a peak-to-peak voltage value in image formation, a peak-to-peak voltage value at a point at which a change amount of the difference value per unit peak-to-peak voltage is coincident with a predetermined change amount value corresponding to the determined range in the third approximate function, and a peak-to-peak voltage value of the AC voltage is controlled by the first to third processing steps. 
     The associated one of the peak-to-peak voltage values is preferably one of the peak-to-peak voltage values in the second discharge range. 
     The associated one of the peak-to-peak voltage values is preferably a greatest one of the peak-to-peak voltage values in the second discharge range. 
     The third approximate function is preferably obtained by subtraction of the first approximate function from the second approximate function, and the associated one of the peak-to-peak voltage values is preferably one of peak-to-peak voltage values which are included in the peak-to-peak voltage values in the second discharge range and for which the difference value is greater than zero. 
     The image formation device preferably further includes a detection unit configured to detect an environmental condition inside or outside a machine, for each of the different predetermined ranges, different values of the change amount is preferably, in advance, associated respectively with different environmental conditions, and in the third processing step, one of the different values of the change amount associated in advance with the determined range and corresponding to one of the different environmental conditions detected by the detection unit is preferably set as the predetermined change amount value. 
     The environmental condition is preferably at least one of a temperature or a humidity inside the machine. 
     The charging member is preferably in a roller, brush, or blade shape contacting the image carrier or disposed close to the image carrier. 
     To achieve the abovementioned object, according to an aspect, a method for controlling an image formation device in which an image carrier is charged by a charging member and which includes a power source configured to supply a charge voltage to the charging member, the charge voltage being formed such that an AC voltage is superimposed on a DC voltage, and a detection unit configured to detect an alternating current value flowing through the charging member, reflecting one aspect of the present invention comprises: a first processing step of sequentially supplying a plurality of charge voltages from the power source to the charging member in non-image formation, the charge voltages having different peak-to-peak voltage values in a first discharge range in which only charge transfer from the charging member to the image carrier occurs and a second discharge range in which charge transfer occurs in both directions between the image carrier and the charging member; a second processing step of obtaining, from an alternating current value detection result obtained by the detection unit when each charge voltage is supplied by the first processing, a third approximate function indicating a difference value between a first approximate function and a second approximate function, the first approximate function indicating an alternating current value for each peak-to-peak voltage value in the first discharge range and the second approximate function indicating an alternating current value for each peak-to-peak voltage value in the second discharge range; and a third processing step of determining one of different predetermined ranges to which a detection value of the alternating current value in supply of one of the charge voltages with an associated one of the peak-to-peak voltage values in the second discharge range belongs, and determining, as a peak-to-peak voltage value in image formation, a peak-to-peak voltage value at a point at which a change amount of the difference value per unit peak-to-peak voltage is coincident with a predetermined change amount value corresponding to the determined range in the third approximate function, wherein a peak-to-peak voltage value of the AC voltage is controlled by the first to third processing steps. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other objects, advantages and features of the present invention will become more fully understood from the detailed description given hereinbelow and the appended drawings which are given by way of illustration only, and thus are not intended as a definition of the limits of the present invention, and wherein: 
         FIG. 1  is a schematic view of an entire configuration of a printer; 
         FIG. 2  is a block diagram of configurations of a control section and a power source; 
         FIG. 3  is a flowchart of contents of charge voltage determination processing; 
         FIG. 4  is a configuration example of an environmental step table; 
         FIG. 5  is a configuration example of a detection voltage table; 
         FIG. 6  is a flowchart of contents of a subroutine of peak-to-peak voltage value determination processing; 
         FIG. 7  is a graph of a relationship between a peak-to-peak voltage value and an alternating current value; 
         FIG. 8  is a graph of an example of the relationship between the peak-to-peak voltage value and the alternating current value at initial and terminal stages of the life of a photosensitive drum; 
         FIG. 9  is an example of a graph with a difference function at the initial and terminal stages of the life of the photosensitive drum; 
         FIG. 10  is a configuration example of a slope determination table; 
         FIG. 11  is a table for comparting between a peak-to-peak voltage value obtained by the method using ΔIac fixed to a certain value D and a peak-to-peak voltage value obtained by the method using a constant value k as dΔIac/dVpp; 
         FIG. 12A  is an example of a graph with a difference function when a detection value of the alternating current value is equal to or less than 2400 μA, and  FIG. 12B  is an example of a graph with a difference function when the detection value of the alternating current value is equal to or greater than 2561 μA and equal to or less than 2630 μA; 
         FIG. 13  is a table of an experimental result example in an example and a comparative example; 
         FIG. 14  is a graph for comparing the magnitude of difference ΔVd among new articles and durable articles in the example and the comparative example; and 
         FIG. 15  is a table of an experimental result example under each type of LL environment and HH environment when the durable article is placed under each of these types of environment. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, a tandem color printer (hereinafter merely referred to as a “printer”) will be described as an example of an embodiment of an image formation device of the present invention with reference to the drawings. However, the scope of the invention is not limited to the illustrated examples. 
     (1) Entire Configuration of Printer 
       FIG. 1  is a schematic view of an entire configuration of a printer  1 . 
     As illustrated in  FIG. 1 , the printer  1  is configured to form an image by an electrophotographic technique. The printer  1  includes an image processing section  10 , an intermediate transfer section  20 , a feeding section  30 , a fixing section  40 , and a control section  50 , and is configured to execute color image formation (printing) based on a job execution request from an external terminal device (not-shown) via a network (e.g., a LAN). 
     The image processing section  10  includes image formation sections  10 Y,  10 M,  10 C,  10 K corresponding respectively to colors of yellow (Y), magenta (M), cyan (C), and black (K). 
     The image formation section  10 K includes, for example, a photosensitive drum  11  configured to rotate in a direction indicated by an arrow A, a charging roller  12  disposed at the periphery of the photosensitive drum  11 , an exposure section  13 , a development section  14 , and a cleaner  15 . 
     The charging roller  12  is in a shape elongated along the axial direction of the photosensitive drum  11 , and is configured to charge the photosensitive drum  11  while rotating in contact with a peripheral surface of the photosensitive drum  11  in a direction indicated by an arrow B. Such charging is performed in such a manner that a charge voltage is supplied from a power source  60  ( FIG. 2 ) to the charging roller  12 . 
     The exposure section  13  is configured to expose the charged photosensitive drum  11  with a light beam to form an electrostatic latent image on the photosensitive drum  11 . 
     The development section  14  is configured to develop, with toner in the color K, the electrostatic latent image on the photosensitive drum  11 . In this manner, a toner image in the color K is formed on the photosensitive drum  11 . The toner image formed in the color K on the photosensitive drum  11  is primarily transferred onto an intermediate transfer belt  21  of the intermediate transfer section  20 . 
     The cleaner  15  is configured to remove, e.g., toner and paper dust remaining on the surface of the photosensitive drum  11  after primary transfer to clean up the surface of the photosensitive drum  11 . Note that the other image formation sections  10 Y,  10 M,  10 C also have configurations similar to that of the image formation section  10 K, and therefore, reference numerals for these sections are omitted from  FIG. 1 . 
     The intermediate transfer section  20  includes the intermediate transfer belt  21  bridging between a drive roller  22  and a driven roller  23  and configured to circulatably run in a direction indicated by arrows, a primary transfer roller  24  disposed to face an associated one of the photosensitive drums  11  of the image formation sections  10 Y to  10 K with the intermediate transfer belt  21  being sandwiched therebetween, and a secondary transfer roller  25  disposed to face the drive roller  22  with the intermediate transfer belt  21  being interposed therebetween. 
     The feeding section  30  includes a cassette  31  configured to house sheets, e.g., paper sheets S in the present embodiment, a feeding roller  32  configured to feed, one by one, the paper sheets S from the cassette  31  to a delivery path  35 , and delivery rollers  33 ,  34  configured to deliver the fed paper sheets S. 
     The fixing section  40  includes a fixing roller  41  and a pressure roller  42  pressed against the fixing roller  41 . 
     The control section  50  is configured to control operation of the image processing section  10  to the fixing section  40  in a comprehensive manner to smoothly execute a job. 
     Specifically, in each of the image formation sections  10 Y to  10 K, the photosensitive drum  11  is charged by the charging roller  12  to which the charge voltage has been supplied. Then, each exposure section  13  of the image formation sections  10 Y to  10 K emits a light beam based on printing image data contained in a received job. 
     In each of the image formation sections  10 Y to  10 K, an electrostatic latent image is formed on the charged photosensitive drum  11  by the light beam emitted from the exposure section  13 . Then, such an electrostatic latent image is developed using the toner, thereby forming a toner image. Subsequently, the toner image is primarily transferred onto the intermediate transfer belt  21  by electrostatic action of the primary transfer roller  24 . 
     The operation of image formation in the colors corresponding respectively to the image formation sections  10 Y to  10   k  is, at timings shifted from each other, executed from an upstream side toward a downstream side in a running direction such that toner images in the above-described colors are transferred to overlap with each other at the same position of the running intermediate transfer belt  21 . 
     The paper sheet S is, in timing with such image formation, delivered from the cassette  31  of the feeding section  30  toward the secondary transfer roller  25 . When the paper sheet S passes through a secondary transfer position  251  as a contact position between the secondary transfer roller  25  and a surface of the intermediate transfer belt  21 , the overlapping toner images transferred in the above-described colors onto the intermediate transfer belt  21  are collectively secondarily transferred onto the paper sheet S by electrostatic action of the secondary transfer roller  25 . 
     After secondary transfer of the toner images in the above-described colors, the paper sheet S is delivered to the fixing section  40 , and then, is heated and pressurized when passing between the fixing roller  41  and the pressure roller  42  of the fixing section  40 . In this manner, the toner on the paper sheet S is fused and fixed onto the paper sheet S. The paper sheet S having passed through the fixing section  40  is discharged to a catch tray  39  by discharge rollers  38 . 
     A temperature detection sensor  71  and a humidity detection sensor  72  are, as a temperature/humidity detection unit, arranged right below the image processing section  10 . The temperature detection sensor  71  is configured to detect a temperature (a machine inner temperature) in the printer  1 , and the humidity detection sensor  72  is configured to detect a relative humidity (a machine inner humidity) in the printer  1 . A detection result of each sensor is transmitted to the control section  50 . 
     (2) Configuration of Control Section 
       FIG. 2  is a block diagram of the configuration of the control section  50 , and also illustrates the image formation section  10 K and the power source  60  and a current detection section  70  provided corresponding to the image formation section  10 K. 
     The power source  60  is configured to supply a charge voltage (a voltage formed such that an AC voltage is superimposed on a DC voltage) Vg to the charging roller  12  of the image formation section  10 K. In the present embodiment, the DC voltage has the same negative polarity as the charge polarity of the photosensitive drum  11 , but may have a positive polarity depending on a device configuration. 
     The current detection section  70  is configured to detect an alternating current value Iac flowing through the charging roller  12  via the photosensitive drum  11  when the charge voltage Vg is supplied to the charging roller  12 . Note that the power source  60  and the current detection section  70  are also provided corresponding to each of the other image formation sections  10 Y to  10 C. However, these sections basically have the same configuration as those of the image formation section  10 K, and therefore, are not shown in  FIG. 2 . The image formation section  10 K and the power source  60  and the current detection section  70  corresponding to the image formation section  10 K will be described below. 
     The control section  50  includes, as main components, a central processing unit (CPU)  51 , a read only memory (ROM)  52 , a random access memory (RAM)  53 , and a storage section  54 . 
     The CPU  51  is configured to read a required program from the ROM  52  and control, in a comprehensive manner, operation of the image processing section  10 , the intermediate transfer section  20 , the feeding section  30 , and the fixing section  40  at certain timing, thereby smoothly executing printing operation based on job data. Moreover, the CPU  51  is configured to provide the power source  60  with the request of outputting the charge voltage Vg. Such a request contains a request for a peak-to-peak voltage level (a peak-to-peak voltage value) Vpp of the AC voltage contained in the charge voltage Vg. 
     The RAM  53  serves as a work area of the CPU  51 . 
     The storage section  54  is a non-volatile storage section, and is configured to store an environmental step table  81 , a detection voltage table  82 , a slope determination table  83 , etc. 
     The power source  60  includes a combination of a DC power source circuit  61  and an AC power source circuit  62 . 
     The DC power source circuit  61  is configured to output a predetermined DC voltage Vdc under control of the control section  50 . Note that in the present embodiment, it is not particularly important to change the DC voltage Vdc for each image formation section. For this reason, it will be described below, for the sake of convenience, that the DC voltage Vdc is the same value among the image formation sections. 
     The AC power source circuit  62  includes, e.g., an AC transformer, and can change the magnitude of peak-to-peak voltage value Vpp of an AC voltage Vac to be output. Based on the request output from the control section  50 , the AC power source circuit  62  outputs the AC voltage Vac including the requested magnitude of peak-to-peak voltage value Vpp. Note that as in the DC voltage Vdc, it will be described that the peak-to-peak voltage value Vpp of the AC voltage Vac is the same among the image formation sections. 
     An output end of the AC power source circuit  62  is connected to an output end of the DC power source circuit  61 , and therefore, the charge voltage Vg is generated such that the AC voltage Vac is superimposed on the DC voltage Vdc. The generated charge voltage Vg is supplied to the charging roller  12 . 
     In such a configuration, in non-image formation other than printing (image formation) onto the paper sheet S, the CPU  51  executes the charge voltage determination processing of determining, for each of the image formation sections  10 Y to  10 K, an optimal value of the peak-to-peak voltage value Vpp of the AC voltage of the charge voltage Vg in subsequent printing (subsequent image formation). The charge voltage Vg is hereinafter distinguished between a charge voltage Vg 1  in printing and a charge voltage Vg 2  output from the power source  60  during the charge voltage determination processing. 
     (3) Charge Voltage Determination Processing 
       FIG. 3  is a flowchart of contents of the charge voltage determination processing in the image formation section  10 K. Note that the same processing is simultaneously executed in the other image formation sections  10 Y to  10 C. 
     As illustrated in  FIG. 3 , an existing machine inner temperature and an existing machine inner humidity are obtained (step S 1 ). Such an obtaining step is performed in such a manner that detection results of a machine inner temperature St and a machine inner humidity Sh of the temperature detection sensor  71  and the humidity detection sensor  72  are received. 
     Next, an environmental step is obtained (step S 2 ). Such an obtaining step is performed by reference to the environmental step table  81  stored in the storage section  54  of the control section  50 . 
       FIG. 4  illustrates a configuration example of the environmental step table  81 . 
     As illustrated in  FIG. 4 , an environmental step  1 ,  2  . . . as an indicator of an absolute humidity level for each combination between the machine inner temperature and the machine inner humidity is written in the environmental step table  81 . Note that, e.g., a machine inner temperature of “&lt;15” in the environmental step table  81  indicates a temperature of lower than 15° C., and “&lt;20” indicates a temperature within a range of equal to or higher than 15° C. and lower than 20° C. The same applies to, e.g., other temperature ranges of “&lt;24” . . . and a machine inner humidity of “&lt;18.” The environmental step table  81  is produced in advance by, e.g., experiment at a fabrication stage or a development stage of the printer  1 . Similarly, other tables described later are also produced in advance by, e.g., experiment. 
     In the present embodiment, the environmental steps are classified into 16 levels. The environmental steps  1  to  3  indicate low-temperature low-humidity environment (LL environment), the environmental steps  4  to  7  indicate normal-temperature normal-humidity environment (NN environment), the environmental steps  13  to  16  indicate high-temperature high-humidity environment (HH environment), and environmental steps  8  to  12  indicate environment which is between the NN environment and the HH environment and under which the machine inner temperature and the machine inner humidity are higher than those under the NN environment. 
     For example, when the existing machine inner temperature St is between 15° C. and 19° C. and the machine inner humidity Sh is between 18% and 31%, the environmental step “ 2 ” is obtained. 
     Referring back to  FIG. 3 , the group of detection peak-to-peak voltage values Vpp corresponding to the environmental step is obtained at step S 3 . Such an obtaining step is performed by reference to the detection voltage table  82  stored in the storage section  54  of the control section  50 . 
       FIG. 5  illustrates a configuration example of the detection voltage table  82 . 
     As illustrated in  FIG. 5 , groups A to D each including a plurality of different detection peak-to-peak voltage values Vpp (ten values in the present embodiment) are written for environmental step ranges in the detection voltage table  82 . For each of a positive discharge range (a first discharge range) and a reverse discharge range (a second discharge range), each of the groups A to D includes at least two of ten detection peak-to-peak voltage values Vpp. 
     The positive discharge range described herein is a peak-to-peak voltage value Vpp range (see  FIG. 7 ) of less than (Vth×2) when a charge start voltage at which charging of the photosensitive drum  11  begins is Vth. Such a range is a peak-to-peak voltage range in which charge transfer (charge transfer in a single direction) only occurs from the charging roller  12  to the photosensitive drum  11  when the charge voltage Vg is applied to the charging roller  12 . 
     On the other hand, the reverse discharge range is a range ( FIG. 7 ) of equal to or greater than (Vth×2). Such a range is a range in which charge transfer occurs in both directions between the photosensitive drum  11  and the charging roller  12 . 
     In the present embodiment, (Vth×2) is 1500 V.  FIG. 5  shows the example where for each of the groups A to D, first to fourth detection peak-to-peak voltage values Vpp in a positive discharge range of less than 1500 V are written and fifth to tenth detection peak-to-peak voltage values Vpp in a reverse discharge range of equal to or greater than 1500 V are written. 
     For example, when the environmental step obtained at step S 2  belongs to a range of  1  to  3 , the group A of the detection peak-to-peak voltage value Vpp in  FIG. 5  is assigned. When the environmental step belongs to a range of  4  to  7 , a range of  8  to  12 , or a range of  13  to  16 , the group B, C, D is assigned. 
     Referring back to  FIG. 3 , a first counter value n is initialized to one at step S 4 . The value of n indicates the number of the first to tenth detection peak-to-peak voltage value written in the detection voltage table  82  of  FIG. 5 . 
     In  FIG. 3 , an existing n-th detection peak-to-peak voltage value Vpp in the group selected at step S 3  is obtained at step S 5 . For example, in the case where the group B is obtained, the existing n-th detection peak-to-peak voltage value Vpp which is a first detection peak-to-peak voltage value Vpp of 1020 V ( FIG. 5 ) is obtained. 
     Then, at step S 6 , the AC voltage Vac and the DC voltage Vdc to be output from the power source  60  corresponding to the image formation section  10 K are set, and the request of outputting the set AC voltage Vac and the set DC voltage Vdc is provided to the power source  60 . Specifically, the peak-to-peak voltage value Vpp of the AC voltage Vac to be output from the AC power source circuit  62  of the power source  60  corresponding to the image formation section  10 K is set to the detection peak-to-peak voltage value Vpp (1020 V in the above-described example) obtained at step S 5 . Moreover, the DC voltage Vdc to be output from the DC power source circuit  61  of the power source  60  is set to a preset value. Note that this value of the DC voltage Vdc is equivalent to a voltage value required for charging the photosensitive drum  11  to a predetermined potential in printing. 
     By execution of step S 6 , the charge voltage Vg 2  formed such that the AC voltage having the detection peak-to-peak voltage value Vpp is superimposed on the DC voltage Vdc is output from the power source  60 , and then, the output charge voltage Vg 2  is supplied to the charging roller  12 . 
     When output of the charge voltage is stabilized, specifically when a predetermined time period required for stabilization is elapsed (“Yes” at step S 7 ), a second counter value m is initialized to one (step S 8 ). 
     Next, the alternating current value Iac detected by the current detection section  70  corresponding to the image formation section  10 K is obtained, and the obtained alternating current value Iac is stored in the RAM  53  (step S 9 ). 
     Then, it is determined whether or not the second counter value m is equal to a predetermined value y (step S 10 ). The predetermined value y described herein is a sampling number per rotation of the photosensitive drum  11 , and is a natural number of equal to or greater than one. When m is not equal to the predetermined value y (“No” at step S 10 ), an existing second counter value m is incremented by one (step S 11 ), and then, the process returns to step S 9 . 
     Steps S 9  to S 11  are repeated until it is determined that m is equal to the predetermined value y. In this manner, each of the alternating current values Iac measured at y locations different from each other in a circumferential direction is held in the RAM  53  while the photosensitive drum  11  of the image formation section  10 K rotates one time. When it is determined that m is equal to the predetermined value y (“Yes” at step S 10 ), the average of the y alternating current values Iac is obtained, and the obtained average is stored as the alternating current value Iac corresponding to the n-th peak-to-peak voltage value Vpp in the RAM  53  (step S 12 ). With such an average, variation in the detection value of the alternating current value Iac due to variation in the thickness of the photosensitive drum  11  can be smoothed. 
     Next, it is determined whether or not the first counter value n is 10 (step S 13 ). When it is determined that n is not 10 (“No” at step S 13 ), an existing first counter value n is incremented by one (step S 14 ), and the process returns to step S 5 . 
     For example, when the existing value of n is two and the group obtained at step S 3  is B, a second detection peak-to-peak voltage value Vpp of 1080 V ( FIG. 5 ) is obtained at step S 5 . 
     Then, the processing of steps S 6  to S 13  is executed based on the obtained second detection peak-to-peak voltage value Vpp. Accordingly, the average of the alternating current values Iac when the charge voltage Vg 2  including the AC voltage having the second detection peak-to-peak voltage value Vpp is supplied to the charging roller  12 , and then, is stored in the RAM  53 . 
     Then, it is determined again whether or not the first counter value n is 10 (step S 13 ). When it is determined that n is not 10 (“No” at step S 13 ), the existing first counter value n is incremented by one (step S 14 ). Subsequently, the process returns to step S 5 , and the processing of step S 5  and subsequent steps is executed. 
     The processing of steps S 5  to S 14  is repeatedly executed until it is determined that the first counter value n is 10. Accordingly, the average of the alternating current values Iac when the charge voltage Vg 2  including the AC voltage having the detection peak-to-peak voltage value Vpp is supplied to the charging roller  12  is obtained sequentially for each of the third to tenth detection peak-to-peak voltage values Vpp in the obtained group, and then, is stored in the RAM  53 . 
     That is, when four charge voltages Vg 2  each having the peak-to-peak voltage value in the positive discharge range and six charge voltages Vg 2  each having the peak-to-peak voltage value in the reverse discharge range are sequentially applied to the charging roller  12  of the image formation section  10 K, the total of ten detected alternating current values Iac (ten averages) are stored in the RAM  53 . 
     Each alternating current value Iac is stored in the RAM  53  such that the n-th detection peak-to-peak voltage value Vpp and the alternating current value Iac detected in supply of such a peak-to-peak voltage value Vpp are in one-to-one correspondence with each other. A one-to-one combination, which is stored in the RAM  53 , of the detection peak-to-peak voltage value Vpp and the alternating current value Iac is hereinafter collectively referred to as “(Vpp, Iac).” 
     Execution of steps S 1  to S 14  by the control section  50  as described above can be regarded as execution of the first processing of sequentially supplying, in non-image formation, a plurality of charge voltages Vg 2  from the power source  60  to the charging roller  12 , the charge voltages Vg 2  having the different peak-to-peak voltage values Vpp in the positive discharge range (the first discharge range) and the reverse discharge range (the second discharge range). 
     Then, when it is determined that the first counter value n is 10 (“Yes” at step S 13 ), the peak-to-peak voltage value determination processing of determining an optimal value Vpp 1  of the peak-to-peak voltage value is executed (step S 15 ), and then, the charge voltage determination processing ends. 
     (4) Peak-to-Peak Voltage Value Determination Processing 
       FIG. 6  is a flowchart of contents of a subroutine of the peak-to-peak voltage value determination processing. Moreover,  FIG. 7  is a graph of a relationship between the alternating current value Iac and the peak-to-peak voltage value Vpp obtained by steps S 1  to S 14  of the above-described charge voltage determination processing. In  FIG. 7 , points P 1  to P 4  in the positive discharge range indicate points of the alternating current values Iac for the above-described detection peak-to-peak voltage values Vpp of n=1 to 4, and points P 7  to P 10  in the reverse discharge range indicate points of the alternating current values Iac for the above-described detection peak-to-peak voltage values Vpp of n=7 to 10. 
     First, a first approximate function is obtained as shown in  FIG. 6  (step S 31 ). The first approximate function is obtained in such a manner that values of (Vpp, Iac) at the points P 1  to P 4  in the positive discharge range shown in  FIG. 7  are selected and data of the selected four points is linearly approximated by, e.g., a least-square technique. In this manner, a linear graph L 1  ( FIG. 7 ), i.e., a first approximate function of Iac=f 1 (Vpp) (note that Vpp&lt;2×Vth), is obtained by approximation of properties (hereinafter referred to as “Vpp-Iac properties”) of the alternating current value Iac with respect to the peak-to-peak voltage value Vpp in the positive discharge range. 
     Next, a second approximate function is obtained (step S 32 ). The second approximate function is obtained in such a manner that values of (Vpp, Iac) at the points P 7  to P 10  in the reverse discharge range shown in  FIG. 7  are selected and data of the selected four points is curve-approximated. In this manner, a curved graph L 2  ( FIG. 7 ), i.e., a second approximate function of Iac=f 2 (Vpp) (note that 2×Vth≦Vpp), is obtained by approximation of the Vpp-Iac properties in the reverse discharge range. Note that curve approximation is performed at step S 32  because actual Vpp-Iac properties in the reverse discharge range are closer to a curved line than to a linear line. 
       FIG. 8  is a graph of an example of the Vpp-Iac properties at an initial stage of the life of the photosensitive drum  11  and a terminal stage of the life of the photosensitive drum  11 . A graph L 3  indicates the initial stage of the life, and a graph L 4  indicates the terminal stage of the life. 
     As shown in  FIG. 8 , it can be seen that not only the graph L 3  indicating the initial stage of the life but also the graph L 4  indicating the terminal stage of the life show, in the reverse discharge range, an exponential increase in the alternating current value Iac with an increase in the peak-to-peak voltage value Vpp. Moreover, the graph L 4  indicating the terminal stage of the life is, as a whole, on an upper side of the graph L 3  indicating the initial stage of the life, i.e., the graph L 4  shows a greater alternating current value Iac than that of the graph L 3 . 
     This is because of the following reasons. That is, the thickness of the photosensitive drum  11  is generally reduced due to repeated printing operation. A greater number of printed sheets (i.e., closer to the terminal stage of the life) results in a smaller thickness, and an electric resistance value of the photosensitive drum  11  decreases by a thickness decrease. 
     Thus, even when the same peak-to-peak voltage value Vpp between the initial stage of the life and the terminal stage of the life is applied to the charging roller  12 , a greater alternating current flows at the terminal stage of the life than at the initial stage of the life. 
     Note that as described above, the first approximate function is obtained from the values of (Vpp, Iac) at four points P 1  to P 4  in the positive discharge range, and the second approximate function is obtained from the values of (Vpp, Iac) at four points P 7  to P 10  in the reverse discharge range. However, the present invention is not limited to above. Each of the first and second approximate functions can be obtained from the values of (Vpp, Iac) at two or more points. 
     In each of the positive discharge range and the reverse discharge range, two or more different peak-to-peak voltage values Vpp each preferably have a difference of equal to or greater than a certain value, e.g., equal to or greater than 100 V, from an AC voltage value (=2×Charge Start Voltage Vth) indicating a boundary between the positive discharge range and the reverse discharge range. This is because a greater difference results in easier indication of the graph of the Vpp-Iac properties of each of the positive and reverse discharge ranges by the approximate function. Note that points indicating the above-described detection peak-to-peak voltage values Vpp of n=5 and n=6 are omitted from  FIG. 7 , but in some cases, one or both of these points may be added for calculation of the second approximate function. 
     Referring back to  FIG. 6 , a difference function (a third approximate function) indicating a discharge current amount ΔIac with respect to the peak-to-peak voltage value Vpp is obtained at step S 33 . Specifically, a value obtained by subtraction of the first approximate function from the second approximate function, i.e., f 2 (Vpp)−f 1 (Vpp), is derived as the difference function indicating ΔIac (a difference value of the alternating current value Iac:  FIG. 7 ). In this light, execution of step S 33  by the control section  50  can be regarded as execution of the second processing of obtaining the third approximate function indicating the difference value between the first and second approximate functions from detection results of the alternating current value Iac. 
       FIG. 9  is an example of a graph with the difference function at the initial stage of the life and the terminal stage of the life of the photosensitive drum  11 . A graph L 5  indicates an example of the difference function at the initial stage of the life, and a graph L 6  indicates an example of the difference function at the terminal stage of the life. 
     As shown in  FIG. 9 , the graph L 6  indicating the terminal stage of the life shows, for the same peak-to-peak voltage value Vpp, a greater discharge current amount ΔIac than that of the graph L 5  indicating the initial stage of the life, and also shows a greater increment of the discharge current amount ΔIac per unit peak-to-peak voltage. 
     This is because of the following reasons: it is considered that the increment of the discharge current amount ΔIac is greater at the terminal stage of the life than at the initial stage of the life due to, e.g., a decrease in the electric resistance value of the photosensitive drum  11 , and increases with an increase in the peak-to-peak voltage value Vpp in the reverse discharge range. This can be also seen from the graph L 4  (the terminal stage of the life) showing, in  FIG. 8 , a greater difference value (=ΔIac) from the first approximate function (a dashed line) than that of the graph L 3  (the initial stage of the life). 
     The graph L 6  (the terminal stage of the life) is in more upright shape than that of the graph L 5  (the initial stage of the life) in  FIG. 9 . This is because of the following reasons. That is, at the initial stage of the life, the photosensitive drum  11  has a great thickness and a high electric resistance value. Thus, an alternating current is difficult to flow, and the discharge current amount ΔIac tends to be small. For these reasons, the graph L 5  (the initial stage of the life) tends to have a lying-down shape as illustrated in  FIG. 9 . Conversely, at the terminal stage of the life, the electric resistance value of the photosensitive drum  11  decreases by a decrease in the thickness of the photosensitive drum  11 , and therefore, an alternating current easily flows. Thus, the discharge current amount ΔIac tends to be great. For these reasons, the graph L 6  (the terminal stage of the life) tends to transition to a more upright shape than that of the graph L 5  (the initial stage of the life). 
     Referring back to  FIG. 6 , the alternating current value Iac detected when the peak-to-peak voltage value Vpp is 2000 V is obtained at step S 34 . In the example of  FIG. 7 , when Vpp is 2000 V at the point P 10 , an Iac of 4000 μA is obtained at the point P 10 . This value of 2000 V is one of six detection peak-to-peak voltage values Vpp in the reverse discharge range, and is herein determined in advance. 
     By referring, at step S 35 , to the slope determination table  83  stored in the storage section  54 , the range to which the alternating current value Iac obtained at step S 34  belongs is determined from different ranges written in the slope determination table  83 . Then, a value k corresponding to the determined range is obtained. 
       FIG. 10  illustrates a configuration example of the slope determination table  83 . 
     As shown in  FIG. 10 , the slope determination table  83  is a table in which for each of the different predetermined ranges (to 2400, 2401 to 2460, etc.) of the alternating current value Iac detected by the current detection section  70  when a peak-to-peak voltage value Vpp of 2000 V is supplied to the charging roller  12 , a single value k (3.6, 3.3, etc.) is written corresponding to the environmental step ( 1  to  2 ,  3  to  4 , etc.). The way to determine the value k will be described later. 
     For example, in the case where the environmental step obtained at step S 2  as described above is two, if the alternating current value Iac obtained at step S 34  is 2300 μA, such a value falls within a range of equal to or less than 2400 μA, and therefore, a k of 3.6 corresponding to the environmental step  2  is read. If the obtained alternating current value Iac is 2600 μA, such a value falls within a range of 2561 to 2630 μA, a k of 2.5 corresponding to the environmental step  2  is read. 
     Referring back to  FIG. 6 , the discharge current amount ΔIac is, at step S 36 , obtained at such a point that a change amount (i.e., a derivative value (dΔIac/dVpp)) of the discharge current amount ΔIac per unit peak-to-peak voltage is coincident with the inverse of the value k obtained at step S 35 , i.e., 1/k (a predetermined change amount value), in the difference function obtained at step S 33 . 
     For example, in the example of the graph L 5  with the difference function as shown in  FIG. 9 , when the value k obtained at step S 35  is ka, a value Id of the discharge current amount ΔIac at a point Pa at which the change amount (the slope of a tangent) of ΔIac is coincident with 1/ka is obtained. Moreover, in, e.g., the graph L 6  with the difference function, when the value k obtained at step S 35  is kb, a value Ie of the discharge current amount ΔIac at a point Pb at which the change amount of ΔIac is coincident with 1/kb is obtained. Note that as shown in  FIG. 9 , the change amount of ΔIac per unit peak-to-peak voltage in the difference function is only an increment in the present embodiment. 
     Referring back to  FIG. 6 , the peak-to-peak voltage value Vpp corresponding to the discharge current amount ΔIac obtained by step S 36  in the above-described difference function is, at step S 37 , determined as the optimal peak-to-peak voltage value Vpp 1  in image formation, and the process returns to a main routine. 
     For example, a peak-to-peak voltage value Vma at the point Pa is determined as the optimal value Vpp 1  in the graph L 5  shown in  FIG. 9 , and a peak-to-peak voltage value Vmb at the point Pb is determined as the optimal value Vpp 1  in the graph L 6 . The optimal peak-to-peak voltage value Vpp 1  determined by the peak-to-peak voltage value determination processing is stored in the storage section  54 . 
     In subsequent printing at the image formation section  10 K, the peak-to-peak voltage value Vpp of the AC voltage Vac to be output from the AC power source circuit  62  is set at the peak-to-peak voltage value Vpp 1  currently stored in the storage section  54 , and the DC voltage Vdc to be output from the DC power source circuit  61  is set at a predetermined value. As a result, the charge voltage Vg 1  having the peak-to-peak voltage value Vpp 1  determined as the optimal value as described above is supplied from the power source  60  to the charging roller  12  of the image formation section  10 K in printing, and in this manner, the photosensitive drum  11  of the image formation section  10 K is charged. 
     In this light, execution of steps S 34  to S 37  by the control section  50  can be regarded as execution of the third processing of determining one of the different predetermined ranges to which the detected alternating current value Iac in supply of the charge voltage Vg 2  with one of the peak-to-peak voltage values Vpp in the reverse discharge range (the second discharge range) belongs, and determining, as the peak-to-peak voltage value in image formation, the peak-to-peak voltage value Vpp at the point at which the change amount of ΔIac in the difference function (the third approximate function) is coincident with the predetermined change amount value (=1/k) corresponding to the determined range. 
     The charge voltage determination processing can be executed at predetermined timing such as timing every time printing of a predetermined number of sheets (e.g., 1000 sheets) is executed, timing every time the number of rotation of the photosensitive drum  11  reaches a predetermined value, and timing when the change amount of the machine inner temperature/humidity per unit time exceeds a predetermined value (when an environment change amount exceeds a predetermined range). 
     The peak-to-peak voltage value Vpp 1  stored in the storage section  54  by a single execution of the charge voltage determination processing is set as the peak-to-peak voltage value Vpp, which is to be output in printing, of the charge voltage Vg 1  until subsequent charge voltage determination processing is executed. When the subsequent charge voltage determination processing is executed, the peak-to-peak voltage value Vpp 1  stored in the storage section  54  is updated to a newly-determined peak-to-peak voltage value Vpp 1 . The same applies to the image formation sections  10 Y to  10 C other than the image formation section  10 K. 
     (5) Reasons for Determining Peak-to-Peak Voltage Value by Using Slope Determination Table 
     As shown in  FIG. 8  described above, when the same peak-to-peak voltage value Vpp is applied to the charging roller  12 , the alternating current value Iac is greater at the terminal stage of the life than at the initial stage of the life due to an electric resistance value decrease caused by reduction in the thickness of a photosensitive layer of the photosensitive drum  11 . 
     Moreover, not only a decrease in the electric resistance value of the photosensitive drum  11  but also the electric resistance value of the charging roller  12  are involved. Specifically, a lower resistance value of the charging roller  12  results in a greater alternating current value Iac, and a higher resistance value of the charging roller  12  results in a smaller alternating current value Iac. 
     When the resistance value reaches a lower value side within a specification tolerance range of the electric resistance value of the charging roller  12 , the alternating current value Iac increases. When toner particles are accumulated on, e.g., a roller surface due to long-term use of the charging roller  12 , the resistance value might increase by such particle accumulation, leading to a smaller alternating current value Iac. 
     Thus, the peak-to-peak voltage value Vpp substantially the same as the optimal value at the initial stage of the life of the photosensitive drum  11  is not always the optimal value at the terminal stage of the life. 
     According to experiment conducted by the inventor(s) of the present invention, when the optimal value of the peak-to-peak voltage value Vpp is Vma at the initial stage of the life in the example of  FIG. 9 , the optimal value decreases to Vmb at the terminal stage of the life. Such an optimal value is properly determined as a value with which a high-quality reproduced image can be visually obtained, for example. 
     When these experimental results are found, if the above-described method of JP 2001-201920 A, i.e., the method for obtaining the peak-to-peak voltage value Vpp for which ΔIac is a predetermined value D, is employed, a peak-to-peak voltage value Vmc at a point Pc corresponding to ΔIac=Id (equivalent to the predetermined value D) in the graph L 6  is obtained at the terminal stage of the life of the photosensitive drum  11  as shown in  FIG. 9 . 
     The voltage value Vmc is extremely greater than an optimal value Vmb, and cannot be taken as the optimal value corresponding to the terminal stage of the life of the photosensitive drum  11  or a value close to such an optimal value. 
     On the other hand, in the present embodiment, the method for obtaining the peak-to-peak voltage value Vpp 1  by using the above-described difference functions and the slope determination table  83  is employed. This is because of the following reasons. 
     That is, the inventor(s) of the present invention has obtained the difference function at a point after a brand-new state of the photosensitive drum  11  and before the end of the life of the photosensitive drum  11 . As a result, it has been found that the discharge current amount ΔIac indicated by each difference function increases with an increase in the peak-to-peak voltage value Vpp at both of the initial and terminal stages of the life of the photosensitive drum  11 . Moreover, it has also been found that the change amount (=dΔIac/dVpp) of the discharge current amount ΔIac per unit peak-to-peak voltage tends to begin increasing from a smaller peak-to-peak voltage value Vpp at the terminal stage of the life than at the initial stage of the life. 
     Such tendency is applicable to the graph L 5  at the initial stage of the life and the graph L 6  at the terminal stage of the life in  FIG. 9 . 
     Specifically, the change amount of the discharge current amount ΔIac for the same peak-to-peak voltage value Vpp, i.e., the slope of the tangent, is greater in the graph L 6  than in the graph L 5 . This shows that the slope of the tangent begins increasing from a smaller peak-to-peak voltage value Vpp in the graph L 6  than in the graph L 5 . 
     Although not shown in  FIG. 9 , the difference function obtained for each period between the initial stage of the life and the terminal stage of the life similarly shows the tendency that the change amount of ΔIac begins increasing from a smaller peak-to-peak voltage value Vpp in a latter period than in a certain period. 
     That is, the entire graph of the difference function transitions, as in the graphs L 5 , L 6  of  FIG. 9 , to shift in a direction in which the peak-to-peak voltage value Vpp decreases from the initial stage of the life toward the terminal stage of the life of the photosensitive drum  11  and to rise by rotation movement in a counterclockwise direction. 
     When the graph of the difference function is obtained for each point from the initial stage of the life to the end of the life based on the presence of graph transition as described above, and points at which the slope of the tangent is the same among these graphs are plotted, the peak-to-peak voltage value Vpp at each point decreases toward the end of the life. 
     Specifically, when the graph of the difference function at the initial stage of the life of the photosensitive drum  11  in  FIG. 9  is L 5 , and each period between the initial and terminal stages of the life is A, B, C, . . . , a peak-to-peak voltage value at a point with the same slope (=1/ka) of the difference function of the point A as that at the initial stage of the life is Vma 1  (&lt;Vma), a peak-to-peak voltage value at a point with the same slope (=1/ka) of the difference function of the point B as that at the initial stage of the life is Vma 2  (&lt;Vma 1 ), a peak-to-peak voltage value at a point with the same slope (=1/ka) of the difference function of the point C as that at the initial stage of the life is Vma 3  (&lt;Vma 2 ), and so forth. 
     That is, transition of the photosensitive drum  11  from the brand-new state to the terminal stage of the life due to repeated printing is, in a linked manner, followed by a change in the peak-to-peak voltage value Vpp at the point with the same slope from a greater value to a smaller value. It can be said that such a relationship is substantially the same as the following relationship: as the photosensitive drum  11  transitions from the brand-new state to the terminal stage of the life, the resistance values of the photosensitive drum  11  and the charging roller  12  decrease, and accordingly, the optimal value of the peak-to-peak voltage value Vpp decreases. 
     The inventor(s) of the present invention has focused on such transition followed by the change in the peak-to-peak voltage value Vpp, and has derived as follows by experiment. 
     (a) The change amount (the slope of the tangent) of the discharge current amount ΔIac per unit peak-to-peak voltage at the point (the point Pa of the graph L 5  in the example of  FIG. 9 ) indicating the discharge current amount ΔIac corresponding to the optimal peak-to-peak voltage value Vpp in the difference function obtained at the initial stage of the life of the photosensitive drum  11  is 1/ka. 
     (b) The peak-to-peak voltage value Vpp (e.g., Vmd at the point Pd of the graph L 6  in the example of  FIG. 9 ) at the point with the slope 1/ka, which is the same as that at the initial stage of life, of the difference function obtained for, e.g., each point between the initial stage of the life and the end of the life of the photosensitive drum  11  and at the terminal stage of the life of the photosensitive drum  11  is the value close to the optimal value of the peak-to-peak voltage value Vpp at such a point. 
     According to above, as compared to the method for obtaining the peak-to-peak voltage value Vpp by at least using the fixed predetermined value D (=Id), the peak-to-peak voltage value Vpp closer to the optimal value properly obtained for each point is, as can be seen from  FIG. 9 , obtained until the end of the life of the photosensitive drum. 
     In other words, in the method using the fixed predetermined value D, an extremely-greater peak-to-peak voltage value Vpp than the optimal value is, at a certain point, obtained toward the terminal stage of the life as described above. However, this can be prevented. 
     In fact, an experimental machine was used to calculate the peak-to-peak voltage values at the initial and terminal stages of the photosensitive drum by both of the method using ΔIac fixed to the predetermined value D (=Id) and the method using a constant value of the slope (=dΔIac/dVpp) of the difference function. Consequently, results as shown in  FIG. 11  were obtained. 
     As shown in  FIG. 11 , in the method using ΔIac fixed to the predetermined value D, a difference ΔVd between the optimal value of the peak-to-peak voltage and the calculated peak-to-peak voltage value Vpp is 0 V at the initial stage of the life, but the difference ΔVd is 260 Vat the terminal stage of the life. The peak-to-peak voltage value Vpp calculated at the terminal stage of the life is a value extremely greater than the optimal value (=1480 V) at such a point. 
     A difference ΔVd of 260 V greatly deviates from an acceptable peak-to-peak voltage value range assumed as not causing damage of the photosensitive drum, supposing that the acceptable range is, e.g., about 5% to 10% at a maximum with respect to the optimal value. Note that the acceptable range can be determined in advance by, e.g., experiment, and may be a voltage value range such as a range of equal to or greater than 50 V and less than 150 V, instead of the above-described percentage. 
     On the other hand, in the method using the constant value of the slope of the difference function, the difference ΔVd is 0 V at the initial stage of the life, and is only 20 V at the terminal stage of the life. These values are within the above-described acceptable range. Thus, it can be seen that the optimal peak-to-peak voltage value or the value close to such an optimal value is obtained. 
     Based on the above-described relationship between the life of the photosensitive drum  11  and the peak-to-peak voltage value Vpp, the inventor(s) of the present invention has further set plural groups of the photosensitive drum  11  and the charging roller  12 , such as a group formed such that one of the photosensitive drum  11  or the charging roller  12  has a greater electric resistance value and the other one of the photosensitive drum  11  or the charging roller  12  has a smaller electric resistance value within the specification tolerance and a group formed such that both of the photosensitive drum  11  and the charging roller  12  have electric resistance values close to a center value of the tolerance, and has conducted various types of experiment, such as an endurance test and an environmental test, for the printers  1  with the above-described different groups. As a result, the inventor(s) has found as follows. 
     That is, in the experiment shown in  FIG. 11 , only a particular group of the photosensitive drum and the charging roller was used. However, in the case where the photosensitive drum and the charging roller with different properties, such as the electric resistance value, even within the design specification tolerance are combined together, the following has been found: due to influence of a change in charging properties between the initial stage of the life and the end of the life of the photosensitive drum, the calculated peak-to-peak voltage value Vpp might deviate from a proper range (a range in which an image is obtained with a certain image quality level or higher) when the slope of the difference function remains fixed to 1/ka at any points. 
     Such a charging property change mainly occurs due to a difference in the degree of a chronological resistance value change or the degree of time degradation between the photosensitive drum and the charging roller, variation in the resistance value of the charging roller, and an environmental change, for example. 
     Meanwhile, when a certain short time period of a long time period between the initial stage of the life and the end of the life of the photosensitive drum is focused, the photosensitive drum and the charging roller both exhibit a less change in the resistance value etc. and a much less change in the charging properties. In such a short time period, the optimal peak-to-peak voltage value Vpp or the value (the value within the above-described proper range) closer to such an optimal value as compared to that obtained by the method using the fixed predetermined value D is obtained even for the same slope. 
     The above-described short time period can be regarded as a period for which the charging property change is within a certain range. Considering a relationship in which a greater charging property change generally results in a greater change amount of the detection value of the alternating current value Iac, it can be said that the above-described short time period is a period for which the detection value of the alternating current value Iac is within a certain range. 
     Thus, the inventor(s) of the present invention has derived the following range from experiment: a certain alternating current value range which is included in an entire available range of the alternating current value Iac detected at a certain peak-to-peak voltage value Vpp such as 2000 V and in which the optimal peak-to-peak voltage value Vpp or the value close to such an optimal value can be obtained using the same (common) slope of the difference function. 
     A relationship between the range of the alternating current value Iac and the slope of the difference function will be described with reference to  FIGS. 12A and 12B . 
       FIG. 12A  shows examples of graphs L 11 , L 12 , L 13 , L 14  with difference functions obtained for each point in the case where the detection value of the alternating current value Iac is within a range of equal to or less than 2400 μA when the charge voltage with a peak-to-peak voltage value Vpp of 2000 V is supplied to the charging roller  12  in a certain short time period after the brand-new state to the end of the life of the photosensitive drum  11 . 
     Each of the graphs L 12  to L 14  shown in  FIG. 12A  is in such a shape that the graph L 11  moves parallel to a direction in which the discharge current amount ΔIac increases. This is because of the following reasons. In the short time period, the thickness of the photosensitive drum  11  slightly decreases with an increase in the cumulative number of printed sheets, leading to an increase in the alternating current value Iac. 
     When printing was performed with such settings that peak-to-peak voltage values Vm 1 , Vm 2 , Vm 3 , Vm 4  at points P 11 , P 12 , P 13 , P 14  with the same value (k=3.6) of the slope 1/k of the tangent in each of the graphs L 11  to L 14  with the difference functions are set to the peak-to-peak voltage value Vpp 1  at each point, a favorable image quality was visually obtained, and it was confirmed that almost no damage of the photosensitive drum  11  is caused. 
     On the other hand,  FIG. 12B  shows examples of graphs L 21 , L 22 , L 23 , L 24  with difference functions obtained for each point in the case where the detection value of the alternating current value Iac is within a range of equal to or greater than 2561 μA and equal to or less than 2630 μA when the charge voltage with a peak-to-peak voltage value Vpp of 2000 V is supplied to the charging roller  12  in a short time period different from that of  FIG. 12A . 
     As in  FIG. 12A , each of the graphs L 22  to L 24  shown in  FIG. 12B  is in such a shape that the graph L 21  moves parallel to the direction in which the discharge current amount ΔIac increases. 
     When printing was performed with such settings that peak-to-peak voltage values Vm 5 , Vm 6 , Vm 7 , Vm 8  at points P 21 , P 22 , P 23 , P 24  with the same value (k=2.5) of the slope 1/k of the tangent in each of the graphs L 21  to L 24  with the difference functions are set to the peak-to-peak voltage value Vpp 1  at each point, a favorable image quality was visually obtained, and it was confirmed that almost no damage of the photosensitive drum  11  is caused. 
     Results similar to above were obtained for a greater range of the detection value of the alternating current value Iac than the ranges shown in  FIGS. 12A and 12B . 
     Thus, the available range of the alternating current value Iac was divided into a plurality of different ranges, and information indicating the value k corresponding to the environmental step in each range was obtained. Such obtained information is used for the slope determination table  83  shown in  FIG. 10  as described above. 
     The alternating current value Iac corresponds to an associated one of the environmental steps  1  to  16  in the slope determination table  83 . This is because of the following reasons: even in the case of the same peak-to-peak voltage value Vpp, when a discharge amount by the charging roller  12  changes due to a change in the machine inner temperature/humidity, the detection value of the alternating current value Iac also changes, and therefore, the value k suitable for the alternating current value Iac is obtained for each environmental step. 
     As seen from the slope determination table  83 , the available range of the alternating current value Iac is divided into eight different ranges. For example, when the range of the alternating current value Iac for the environmental step  1  is equal to or less than 2400 μA, the value k is 3.6. Moreover, the value k is 3.3 in the case of a range of equal to or greater than 2401 μA and equal to or less than 2460 μA. It can be seen that a greater alternating current value Iac tends to result in a smaller value k. The different values k correspond, for the same environmental step, respectively to the different ranges of the alternating current value Iac because other factors than an environmental factor, such as a change in the thickness of the photosensitive drum  11  and the electric resistance value of the charging roller  12  due to the lives of the photosensitive drum  11  and the charging roller  12 , can be also handled. 
     In addition, for each range of the alternating current value Iac, the value k varies according to the different environmental steps. Specifically, when the alternating current value Iac is within, e.g., a range of equal to or less than 2400 μA, the value k is 3.6 for the environmental step  2 , and is 2.5 for the environmental step  4 . 
     As shown in the slope determination table  83 , there is a great difference in the alternating current value Iac detected in application of the same peak-to-peak voltage value, i.e., 2000 V, because this results from the change in the resistance values of the photosensitive drum  11  and the charging roller  12  and deterioration of the photosensitive drum  11  and the charging roller  12  as described above. 
     In the present embodiment, the slope determination table  83  produced considering the charging property change due to the above-described resistance value change of the photosensitive drum  11  and the charging roller  12  is stored in the storage section  54  in advance (e.g., in manufacturing of the printer  1 ). Thus, after delivery of the printer  1  to a user, the above-described charge voltage determination processing is performed at each point between the brand-new state to the end of the life of the photosensitive drum  11 , and in this manner, the optimal peak-to-peak voltage value Vpp 1  at each point can be obtained. 
     (6) Experimental Results 
       FIG. 13  is a table of results obtained by experimental calculation of the peak-to-peak voltage value Vpp in a configuration (an example) in which the value k is determined by the charge voltage determination processing and a configuration (a comparative example) in which the value k is fixed to a constant value. 
     The present experiment was performed for each of the following articles under the LL (low-temperature low-humidity) environment corresponding to the above-described environmental step  1 : a configuration (a new article) in which a set of a new photosensitive drum  11  and a charging roller  12  with the upper electric resistance limit within the specification tolerance is mounted; and a configuration (a durable article) in which a set of a photosensitive drum  11  after 600 krot (six hundred thousand rotations) and a charging roller  12  with the lower electric resistance limit within the specification tolerance is mounted. 
     For the new article and the durable article, a peak-to-peak voltage value Vppt (equivalent to the optical value) optimal for obtaining a reproduced image with a favorable image quality was obtained in advance by, e.g., experiment. The peak-to-peak voltage value Vppt for the new article was 2400 V, and the peak-to-peak voltage value Vppt for the durable article was 1560 V. 
     In the case of the new article of the example, a k of 3.6 was, from the slope determination table  83 , obtained for a detected alternating current value Iac of 2370 μA when a peak-to-peak voltage value Vpp of 2000 V is supplied to the charging roller  12 , and a peak-to-peak voltage value Vpp of 2460 V was calculated. When the difference ΔVd between the calculated value and Vppt was taken, the difference ΔVd was 60 V. In the comparative example, a peak-to-peak voltage value Vpp of 2414 V was calculated for k (4 in the comparative example). When the difference ΔVd between the calculated value and Vppt was taken, the difference ΔVd was 14 V. 
     On the other hand, in the case of the durable article of the example, a k of 2.3 was obtained for a detected alternating current value Iac of 3582 μA in supply of a peak-to-peak voltage value Vpp of 2000 V. A peak-to-peak voltage value Vpp of 1623 V was calculated, and the difference ΔVd was 63 V. In the comparative example, a peak-to-peak voltage value Vpp of 1342 V was calculated, and the difference ΔVd was −218 V. 
       FIG. 14  is a graph for comparing the magnitude of difference ΔVd among the new articles and the durable articles in the example and the comparative example. 
     As shown in  FIG. 14 , the difference ΔVd is extremely small in both of the new article and the durable article of the example, whereas the difference ΔVd (=−218 V) for the durable article is extremely great in the comparative example. 
     The difference ΔVd being great on a negative side indicates that the calculated peak-to-peak voltage value Vpp is extremely less than the optimal value Vppt. As a result, scattering of dot-shaped toner images, i.e., so-called “fog,” easily occurs in the printed reproduced image. 
     For both of the new article and the durable article of the example, the difference ΔVd falls within the above-described acceptable range (within a range of 5% to 10% with respect to the optimal value of the peak-to-peak voltage value), and it has been found that the peak-to-peak voltage value Vpp can be set within the proper range. 
     On the other hand, the value for the durable article of the comparative example falls outside the above-described acceptable range, and it has been found that the peak-to-peak voltage value Vpp might not be set within the proper range until the end of the life. 
     Note that  FIGS. 13 and 14  do not show results of comparison between the example and the method using ΔIac fixed to the predetermined value D as described above. However, it has been found that when the peak-to-peak voltage value Vpp is obtained by the method using the fixed constant value D, such a value is extremely greater than the optimal value as shown in  FIG. 9 , and it has been confirmed that the peak-to-peak voltage value Vpp can be more properly obtained in the example. 
       FIG. 15  is a table of an experimental result example when the above-described durable article was placed under the HH (high-temperature high-humidity) environment corresponding to the environmental step  15  instead of the LL environment and the peak-to-peak voltage value Vpp was obtained by the method of the example.  FIG. 15  also shows, for comparison, experimental results under the LL environment. 
     Under the LL environment, a peak-to-peak voltage value Vpp of 1623 V was calculated, and the difference ΔVd was 63 V, as shown in  FIG. 15 . 
     On the other hand, for the durable product under the HH environment, the peak-to-peak voltage value Vppt optimal for obtaining the reproduced image with the favorable image quality was obtained as 1300 V in advance by, e.g., experiment. Since the detection value of the alternating current value Iac was 4246 μA, a k of 1.8 was obtained from the slope determination table  83 . Then, a peak-to-peak voltage value Vpp of 1386 V was calculated. The difference ΔVd was 86 V. This magnitude of difference ΔVd falls within the above-described acceptable range. 
     If a k of 1.8 was also obtained under the LL environment as in the HH environment, a peak-to-peak voltage value Vpp of 1749 V was calculated, and the difference ΔVd was 189 V, as shown in  FIG. 15 . Moreover, if a k of 2.3 was also obtained under the HH environment as in the LL environment, a peak-to-peak voltage value Vpp of 1272 V was calculated, and the difference ΔVd was −28 V, as shown in  FIG. 15 . 
     When the same value k as that under the LL environment is applied under the HH environment, the difference ΔVd might be a negative value. In this case, the calculated value falls below the optimal value Vppt, and there is a probability that fog occurs in the reproduced image. For this reason, it has been found that the value k suitable for environment is preferably applied. 
     As described above, in the present embodiment, the values k for obtaining the optimal peak-to-peak voltage value Vpp in the printer  1  are obtained in advance and written in the slope determination table  83 . Then, the charge voltage determination processing is executed using the slope determination table  83  at each of optional points between the brand-new state and the end of the life of the photosensitive drum  11 . In this manner, the optimal peak-to-peak voltage value Vpp at each point can be obtained with a favorable accuracy. 
     This can maintain a high-quality reproduced image for a long period of time without great damage on the photosensitive drum  11  and occurrence of fog etc. 
     Moreover, the slope determination table  83  has a versatile configuration in which each value k corresponds to an associated one of the different ranges of the alternating current value Iac. In such a configuration, a storage area can be significantly reduced as compared to a configuration with an enormous amount of information, such as a configuration in which each value k corresponds to an associated one of the alternating current values Iac within the available range of the alternating current value Iac. Consequently, the low-capacity inexpensive storage section  54  can be used. 
     Note that the configuration example where the inverse (=1/k) of the value k written in the slope determination table  83  is used as the change amount (the slope of the tangent) of the discharge current amount ΔIac per unit peak-to-peak voltage has been described above, but the present invention is not limited to the inverse. It may be configured such that a value indicating the change amount (the slope) itself is written in the slope determination table  83 . 
     The present invention is not limited to the image formation device, and may relate to the method for determining the charge voltage. Further, the present invention may relate to the program for executing such a method by a computer. In addition, the program of the present invention can be recorded in various computer-readable recording media including, e.g., a magnetic tape, a magnetic disk such as a flexible disk, an optical recording medium such as a DVD-ROM, a DVD-RAM, a CD-ROM, a CD-R, a MO, and a PD, and a flash memory-type recording medium. Such a program may be produced and assigned in the form of the above-described recording medium, or may be transmitted and supplied in the form of program via various types of wired and wireless networks including the Internet, broadcasting, a telecommunications circuit, and satellite communication, for example. 
     &lt;Variations&gt; 
     The present invention has been described above with reference to the embodiment. Needless to say, the present invention is not limited to the above-described embodiment, and the following variations are conceivable. 
     (1) In the above-described embodiment, the value k is, with reference to the slope determination table  83 , obtained from the alternating current value Iac detected when the charge voltage with a detection peak-to-peak voltage value Vpp of 2000 V is supplied to the charging roller  12 . However, the peak-to-peak voltage value (hereinafter referred to as “Vppk”) for obtaining the value k is not limited to 2000 V. It may be configured such that one, e.g., the maximum value, of the different peak-to-peak voltage values Vpp in the reverse discharge range is set as Vppk. 
     Note that in the case where the maximum value of the detection peak-to-peak voltage value varies according to the environmental step, specifically the case where the maximum value of the detection peak-to-peak voltage in the group A for the environmental steps  1  to  3  is, in  FIG. 5 , 2300 V and the maximum value of the detection peak-to-peak voltage in the group D for the environmental steps  13  to  16  is 2000 V, the slope determination table  83  is separately produced for each group. 
     Alternatively, it may be configured such that any one, at which the discharge current amount ΔIac (the difference value of the alternating current value:  FIG. 7 ) is greater than zero, of the different detection peak-to-peak voltage values Vpp in the reverse discharge range is selected as Vppk instead of the maximum value. 
     For example, in the case where the charge voltage determination processing is executed at a certain point between the initial stage of the life and the terminal stage of the life, when each of the seventh to tenth ones of the fifth to tenth detection peak-to-peak voltage values Vpp in the group A shown in  FIG. 5  satisfies a relationship of ΔIac&gt;0, any one of the seventh to tenth values is selected as Vppk. 
     In this configuration, the detection peak-to-peak voltage values Vpp satisfying the relationship of ΔIac&gt;0 cannot be specified in advance by the time point at which the charge voltage determination processing is executed. Thus, for each of the fifth to tenth detection peak-to-peak voltage values Vpp, the slope determination table  83  to be used when such a detection peak-to-peak voltage value Vpp is selected as Vppk is produced in advance. 
     Note that in any case, a greatest possible value is preferably set or selected as the peak-to-peak voltage value Vppk.  FIG. 7  etc. show such properties that a greater peak-to-peak voltage value Vpp results in a greater alternating current value Iac. Thus, a greater detection range of the alternating current value Iac can be taken by a greater Vppk. Accordingly, the options for the value k for the alternating current value Iac can be increased. 
     (2) When the peak-to-peak voltage value Vppk is a voltage value in the reverse discharge range, it may be configured such that, e.g., a peak-to-peak voltage value Vppz different from the fifth to tenth detection peak-to-peak voltage values written in the detection voltage table  82  is used. 
     In such a configuration, a slope determination table  831  for the peak-to-peak voltage value Vppz is obtained in advance. When the first and second approximate functions are obtained, the peak-to-peak voltage values Vpp written in the detection voltage table  82  are, as described above, supplied sequentially to the charging roller  12 . Subsequently, when the value k is obtained, the peak-to-peak voltage value Vppz is newly supplied to the charging roller  12 , and the alternating current value Iac is determined at such a point. Then, the value k corresponding to one, to which the detected alternating current value Iac belongs, of different ranges of the alternating current value Iac written in the slope determination table  831  is read from the slope determination table  831 . 
     (3) In the above-described embodiment, the tandem color printer has been described, but the present invention is not limited to such a printer. The present invention may relate to a black-and-white printer, other types of copiers, a facsimile device, and a combined machine thereof. 
     Moreover, the configuration example where an image carrier charged by a charging member is the photosensitive drum  11  has been described above, but the image carrier is not limited to the drum shape. The image carrier may be in a belt shape, for example. 
     Further, the configuration example where the charging roller  12  is used as the charging member, but the charging member is not limited to the roller shape. The charging member may be in a brush or blade shape. In addition, the contact arrangement configuration example where the charging roller  12  contacts the peripheral surface of the photosensitive drum  11  has been described, but the present invention is not limited to such an example. For example, the present invention is applicable to a configuration in which the charging member such as the charging roller  12  is disposed close to the peripheral surface of the image carrier such as the photosensitive drum  11  with a certain spacing. 
     (4) In the above-described embodiment, the configuration example where the power source  60  and the current detection section  70  are provided for each of the image formation sections  10 Y to  10 K, but the present invention is not limited to such an example. As long as the above-described charge voltage determination processing can be executed for each image formation section, it may be configured that a common power source and a common current detection section are provided for the image formation sections, for example. 
     (5) In the above-described embodiment, the example where the approximate function of f 2 (Vpp)−f 1 (Vpp) is taken as the difference function (the third approximate function) has been described, but the present invention is not limited to such an example. For example, f 1 (Vpp)−f 2 (Vpp) may be taken as the difference function. In this case, the current change amount in the difference function is a decrement. 
     Moreover, the approximate function f 1  and the approximate function f 2  are obtained, and the difference between these functions is taken as the difference function. However, as long as the function (the third approximate function) indicating the difference value ΔIac between the approximate function f 1  and the approximate function f 2  can be obtained, e.g., the following method may be used. 
     First, the first approximate function is obtained. Then, the difference ΔIac from the obtained first approximate function is calculated for each of four points P 7  to P 10  in  FIG. 7 . 
     The calculated difference ΔIac is plotted on the Y-axis, and each of the peak-to-peak voltage values Vpp at four points P 7  to P 10  is plotted on the X-axis. An approximate expression (an exponential function) indicating the difference ΔIac for the peak-to-peak voltage value Vpp is obtained as the third approximate function. Specifically, f(Vpp)=α·exp(β·Vpp). In such an expression, α and β are coefficients. 
     In this method, the second approximate function itself is not calculated, but the function substantially the same as the above-described difference function is obtained. A method to be used can be determined in advance according to the device configuration. 
     (6) In the above-described embodiment, both of the machine inner temperature and the machine inner humidity are used as environmental conditions, but the present invention is not limited to these conditions. As long as the proper peak-to-peak voltage value Vpp 1  at each point from the brand-new state to the end of the life of the photosensitive drum  11  can be determined, a configuration using only one of the temperature or the humidity as the environmental condition may be employed, for example. 
     In a device configuration providing almost no influence of a temperature/humidity change on determination of the peak-to-peak voltage value Vpp 1 , a configuration not taking the environmental steps into consideration can be employed, for example. In this configuration, only information indicating the different detection peak-to-peak voltages is written in the detection voltage table  82 , and only information on correspondence between the alternating current value Iac and the value k is written in the slope determination table  83 . 
     Further, the configuration example where the machine inner temperature and the machine inner humidity are detected by the temperature detection sensor  71  and the humidity detection sensor  72  as the detection unit has been described, but the present invention is not limited to the machine inner temperature/humidity. A configuration with a detection unit such as a sensor configured to detect a temperature and a humidity outside a machine (e.g., at the periphery of the printer  1 ) may be employed. This is because the charging properties etc. sometimes change due to a change in the temperature/humidity outside the machine. In the case of employing such a configuration, environmental steps corresponding to the temperature/humidity outside the machine are obtained in advance. 
     The values written in the environmental step table  81 , the detection voltage table  82 , and the slope determination table  83  and the above-described values for voltage, current, temperature/humidity, etc. are not limited to those described above. Proper values are set according to the device configuration. 
     Moreover, the above-described embodiment and each variation thereof may be used in combination to the extent possible. 
     The present invention can be broadly applied to an image formation device configured such that an image carrier is charged by a charging member. 
     The processing in the above-described embodiment may be implemented by software, or may be implemented using a hardware circuit. Moreover, the program for executing the processing in the above-described embodiment may be provided. Such a program may be recorded in a recording medium such as a CD-ROM, a flexible disk, a hard disk, a ROM, a RAM, and a memory card, and then, may be provided to a user. The program is executed by a computer such as a CPU. Moreover, the program may be downloaded to a device via a communication line such as the Internet. 
     Although the present invention has been described and illustrated in detail, it is clearly understood that the same is by way of illustrated and example only and is not to be taken by way of limitation, the scope of the present invention being interpreted by terms of the appended claims.