Patent Publication Number: US-9841708-B2

Title: Image forming apparatus having power supply that applies reverse-bias voltage to transfer member

Description:
This application is based on Japanese Patent Application No. 2015-064094 filed on Mar. 26, 2015, the content of which is incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to image forming apparatuses using electrophotographic technology, more particularly to an image forming apparatus including a transfer member made with an ion conductive material. 
     2. Description of Related Art 
     The electrographic technology renders it possible to readily obtain a high-quality image and therefore is widely used in image forming apparatuses such as printers. As is well-known, the electrographic technology incorporates a charging step, an exposing step, a developing step, a transferring step, a cleaning step, and a fixing step. Among these steps, in the transferring step, a toner image formed on a photoreceptor drum is transferred either using an intermediate transfer belt or directly onto a print medium, such as a sheet of paper or an overhead projector (OHP) sheet. In the transferring step, a transfer roller is pressed against an image carrier, such as the photoreceptor drum or the intermediate transfer belt, forming a transfer nip therebetween. When the print medium passes through the transfer nip, a transfer bias voltage is applied to the transfer roller, so that a charge having an opposite polarity to toner is provided to the back face of the print medium. Thus, the toner image is transferred from the image carrier onto the print medium. 
     Some transfer rollers have a layer made of an ion conductive material (e.g., a rubber layer). Such a transfer roller passes current by means of ions in the layer carrying electrons. However, during a print operation, if a transfer bias voltage of the same polarity continues to be applied to the transfer roller, the ions are unevenly distributed in the transfer roller. As a result, the ions that carry electrons decrease in number compared to the initial state, so that the resistance of the transfer roller rises. The degree of the uneven ion distribution increases as the amount of current running through the transfer roller, which is determined by the value of current and the time of application, increases. In other words, the resistance of the transfer roller increases proportionally to the increase of the amount of current. 
     In view of the above, for example, in Japanese Laid-Open Patent Publication No. 2006-163266, once the resistance of the transfer roller has exceeded a threshold, a reverse-bias voltage V 2 , which has an opposite polarity to the transfer bias voltage used in the transferring step, is applied to the transfer roller. Consequently, the uneven ion distribution in the transfer roller is lessened, resulting in lower resistance of the transfer roller. 
     Incidentally, the transfer nip includes an area through which the print medium passes (i.e., a passage area) and an area through which no medium passes (i.e., a nip-margin area). Here, the nip-margin area of the transfer roller is not affected by the resistance of the print medium, and therefore, at the initial stage of continuous printing (i.e., serial printing on a plurality of print media), the nip-margin area passes a higher current compared to the passage area. However, the resistance of the ion conductive material rises as the value of current increases, and therefore, the resistance of the nip-margin area rises faster than the resistance of the passage area. In other words, the amount of current in the nip-margin area gradually decreases. As a result, at some point during the continuous printing, the amount of current in the passage area might become excessively high, resulting in a so-called excessive transfer. Here, the excessive transfer refers to a phenomenon where the toner on the image carrier is inversely charged because the current running through the passage area is excessively high relative to the amount of charge in the toner, so that the toner is not properly transferred to the print medium. Such an excessive transfer might lead to print density failure. 
     However, in Japanese Laid-Open Patent Publication No. 2006-163266, the reverse-bias voltage V 2  is applied to the transfer roller depending on the resistance of the entire transfer roller, including a portion on which the print medium is present. In other words, an increase in the current value of the passage area due to an increase in the resistance of the nip-margin area is not taken into consideration. Accordingly, there is a problem where the reverse-bias voltage V 2  is not applied at an appropriate time, leading to susceptibility to print density failure. 
     SUMMARY OF THE INVENTION 
     An image forming apparatus according to an embodiment of the present invention includes: an image carrier being rotatable while carrying a toner image; a transfer member being rotatable while forming a transfer nip by being pressed by the image carrier, the image carrier being made with an ion conductive material; a power supply continuously applying a transfer bias voltage to the transfer member as a plurality of print media pass through the transfer nip, the transfer bias voltage having a predetermined polarity; and a control section determining whether the resistance of a nip-margin area has exceeded a predetermined resistance threshold, the nip-margin area being a marginal portion of the transfer nip through which no print medium passes, wherein, when the determination of the control section is affirmative, the power supply applies a reverse-bias voltage to the transfer member, the reverse-bias voltage having an opposite polarity to the transfer bias voltage. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram illustrating the configuration of an image forming apparatus according to a first embodiment; 
         FIG. 2  is a diagram illustrating in detail the configuration of a current detection section shown in  FIG. 1 ; 
         FIG. 3  is a diagram illustrating a passage area and a nip-margin area of a secondary transfer nip shown in  FIG. 1 ; 
         FIG. 4  is a diagram illustrating temporal changes in currents running through the passage area and the nip-margin area in  FIG. 3 ; 
         FIG. 5  is a diagram describing a problem with Japanese Laid-Open Patent Publication No. 2006-163266; 
         FIG. 6  provides graphs showing current value (upper panel) and resistance (middle panel) of the nip-margin area over the number of passed sheets, along with a graph showing current threshold (lower panel) for each temperature and humidity environment; 
         FIG. 7  is a flowchart illustrating the operation of a control section shown in  FIG. 1 ; 
         FIG. 8  is a graph showing changes in current running through the passage area in  FIG. 3  over the number of passed sheets; 
         FIG. 9  is a diagram illustrating the configuration of an image forming apparatus according to a second embodiment; 
         FIG. 10  is a diagram illustrating the configuration of an image forming apparatus according to a third embodiment; 
         FIG. 11  is a graph showing changes in current value of the passage area and the nip-margin area in accordance with the size of a print medium and other factors; 
         FIG. 12  is a flowchart illustrating the operation of a control section shown in  FIG. 10 ; 
         FIG. 13  is a flowchart illustrating the operation of a control section according to a first modification; and 
         FIG. 14  is a graph showing changes in resistance of the nip-margin area over the number of passed sheets in the first modification. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, embodiments of an image forming apparatus according to the present invention will be described in detail with reference to the drawings. 
     Section 1: Definitions 
     Some figures show x-, y-, and z-axes perpendicular to one another. The x- and z-axes respectively represent the right-left direction and the top-bottom direction of an image forming apparatus  1 A,  1 B, or  1 C. The y-axis represents the front-back direction of the image forming apparatus  1 A,  1 B, or  1 C. The y-axis also represents the direction in which a secondary transfer roller  4  or a photoreceptor drum  5  extends. 
     Section 2: First Embodiment (General Configuration and Print Operation of Image Forming Apparatus) 
     In  FIG. 1 , the image forming apparatus  1 A according to a first embodiment is, for example, a copier, printer, or fax machine, or a multifunction machine provided with all or some of the functions, and is adapted to print a variety of types of images (typically, full-color or monochrome images) on print media M (e.g., paper or OHP sheets) using a tandem system with a well-known electrophotography technology. To this end, the image forming apparatus  1 A typically includes imaging units  2  for the colors yellow (Y), magenta (M), cyan (C), and black (K), an intermediate transfer belt  3 , and a secondary transfer roller  4 . 
     For example, the imaging units  2  for the four colors are arranged side by side in the x-axis direction and include respective photoreceptor drums  5  for their corresponding colors. Each photoreceptor drum  5  is in the shape of a cylinder extending in the y-axis direction, and rotates about its own axis, for example, in the direction of arrow α. Arranged around the photoreceptor drum  5 , from upstream to downstream in the rotational direction α, are, at least, a charger  6 , a developing device  8 , and a primary transfer roller  9 . 
     The charger  6  uniformly charges the circumferential surface of the photoreceptor drum  5  while the photoreceptor drum  5  is rotating. Provided below the photoreceptor drum  5  is an exposing device  7 . The exposing device  7  irradiates an exposure area of the photoreceptor drum  5 , which is immediately downstream from the charged area, with an optical beam B based on image data, thereby forming an electrostatic latent image in a corresponding color. 
     The developing device  8  supplies a developer for the corresponding color to a developing area of the photoreceptor drum  5 , which is immediately downstream from the exposure area, thereby forming a toner image in the corresponding color in the developing area. 
     The intermediate transfer belt  3  is an example of an image carrier. The intermediate transfer belt  3  is stretched between outer circumferential surfaces of at least two rollers arranged, for example, in the x-axis direction and rotates, for example, in the direction of arrow β. The outer circumferential surface of the intermediate transfer belt  3  abuts, for example, the upper end of each photoreceptor drum  5 . 
     The primary transfer roller  9  is positioned opposite to the photoreceptor drum  5  with the intermediate transfer belt  3  positioned therebetween, and presses the inner circumferential surface of the intermediate transfer belt  3  from above, thereby forming a primary transfer nip  91  between the photoreceptor drum  5  and the intermediate transfer belt  3 . During a print operation, the primary transfer roller  9  receives a secondary transfer bias voltage V 1  to be described later, so that the toner image on the photoreceptor drum  5  is transferred onto the intermediate transfer belt  3  at the primary transfer nip  91  while the intermediate transfer belt  3  is rotating. 
     The secondary transfer roller  4  is a typical example of a transfer member. The secondary transfer roller  4  has a layer made of an ion conductive material (e.g., a rubber layer), and is rotatable about its own axis. During a print operation, the secondary transfer roller  4  receives a secondary transfer bias voltage V 1  having an opposite polarity to a toner image carried on the outer circumferential surface of the intermediate transfer belt  3 . The secondary transfer roller  4  is positioned, for example, near the right end of the intermediate transfer belt  3  so as to press the outer circumferential surface of the intermediate transfer belt  3 , forming a secondary transfer nip  41  at the contact between the secondary transfer roller  4  and the intermediate transfer belt  3 . During the print operation, the secondary transfer nip  41  receives an incoming print medium M. 
     The secondary transfer roller  4  is receiving the secondary transfer bias voltage V 1  while the print medium M is passing through the secondary transfer nip  41 , so that the toner image carried on the intermediate transfer belt  3  is transferred onto the print medium M. The print medium M passes through the secondary transfer nip  41  and a fuser of a well-known type, and thereafter is ejected into a tray as a print. 
     The image forming apparatus  1 A is provided with a switchback path for the purpose of allowing double-side printing, although the path is not shown in  FIG. 1  for the sake of clarity. A print medium M having been subjected to printing on one side is introduced to the secondary transfer nip  41  after being turned over via the switchback path. 
     The image forming apparatus  1 A further includes a first power supply  10 , a control section  11 , a temperature and humidity detection section  12 , at least one current detection section  13 , and a second power supply  14 . The first power supply  10 , under control of the control section  11 , applies the secondary transfer bias voltage V 1  to the secondary transfer roller  4 . In addition, the first power supply  10  applies a reverse-bias voltage V 2  to be described later to the secondary transfer roller  4 . 
     The control section  11  includes, for example, a ROM, a CPU, an SRAM, and an NVRAM. The CPU executes a control program pre-stored in the ROM using the SRAM as a workspace. Typically, the control section  11  controls a print operation as described above upon reception of a print job. 
     The temperature and humidity detection section  12  detects the temperature and the humidity inside the image forming apparatus  1 A. 
     The at least one current detection section  13  includes four current detection sections  13   1 ,  13   2 ,  13   3 , and  13   4 , as illustrated in  FIG. 2 . The four current detection sections  13   1  to  13   4  are connected to a plurality of probes  15  (shown as four probes  15   1 ,  15   2 ,  15   3 , and  15   4 ) capable of coming into and out of contact with the surface of the secondary transfer roller  4 . More specifically, the probes  15   1  and  15   4  are disposed at the front and back ends, respectively, of the secondary transfer roller  4 , and the probes  15   2  and  15   3  are disposed between the probe  15   1  or  15   4  and the center of the secondary transfer roller  4  in the front-back direction. 
     Furthermore, the probes  15   1  to  15   4  are connected to the negative terminal of the second power supply  14  via the current detection sections  13   1  to  13   4 . Note that the positive terminal of the second power supply  14  is connected to the secondary transfer roller  4 . 
     Once the current detection sections  13   1  to  13   4  as above receive a constant voltage from the second power supply  14 , the current detection sections  13   1  to  13   4  detect values of currents I 151  to I 154  running through the probes  15   1  to  15   4  and output the detected values to the control section  11 . 
     Section 3: Details of Technical Problems 
     As shown in the upper portion of  FIG. 3 , the secondary transfer nip  41  has a passage area P 1  and a nip-margin area P 2 , which are variable in accordance with the size of the print medium M. During application of the secondary transfer bias voltage V 1 , the print medium M is present in the passage area P 1 , and therefore, the passage area P 1  has a resistance (R 1 +Rm) higher than the resistance R 2  of the nip-margin area P 2 . Here, R 1  is the resistance of the secondary transfer roller  4  in the passage area P 1 , Rm is the resistance of the print medium M, and R 2  is the resistance of the secondary transfer roller  4  in the nip-margin area P 2 . Accordingly, in the case of continuous printing on print media M of the same size, the amount of current (i.e., current value×application time) in the nip-margin area P 2  is normally greater than the amount of current in the passage area P 1 . 
     The electrical characteristics of an equivalent circuit between the first power supply  10  and the intermediate transfer belt  3  are represented by an equivalent circuit diagram shown in the lower portion of  FIG. 3 . It is assumed here that R 1  is 1.0×10 7 Ω, Rm is 1.0×10 9 Ω, and R 2  is equal to R 1 , i.e., 1.0×10 7 Ω. Furthermore, during application of the secondary transfer bias voltage V 1 , the first power supply  10  passes a transfer current I of 600 μA. Under these assumptions, the passage area P 1  and the print medium M pass a current I 1  of about 6 μA, and the nip-margin area P 2  passes a current I 2  of about 594 μA. In this manner, there is a significant difference between the currents I 1  and I 2 . 
     Furthermore, uneven ion distribution in the secondary transfer roller  4  progresses proportionally to the amount of applied current, and therefore, the resistance R 2  rises with the amount of applied current more than the resistance R 1 . Accordingly, during continuous printing, the value of the current I 1  increases over time. In contrast, the current value I 2  decreases over time (see both the upper and lower portions of  FIG. 4 ). In the course of printing, as the number of passed sheets p of print medium M increases (i.e., as more application time elapses), and the value of the current I 1  exceeds a threshold, an excessive transfer might occur, resulting in print density failure. Therefore, in the case where any ion conductive material is used for the secondary transfer roller  4 , it is necessary to pay attention to changes in the resistances R 1  and R 2 . Here, when comparing initial values and post-continuous printing values, as shown in the lower portion of  FIG. 4 , the resistance R 1  changes but only slightly, whereas the resistance R 2  changes considerably. More specifically, the amount of change in the resistance R 2  relative to the number of passed sheets p is significantly greater than the amount of change in the resistance R 1 . Accordingly, using the change in the resistance R 2  renders it easier to determine whether the value of the current I 1  has exceeded the threshold. 
     Note that the amounts of change in the resistances R 1  and R 2  relative to the number of passed sheets p vary depending not only on the size of the print medium M present in the secondary transfer nip  41  but also on the thickness (or grammage) of the medium, as well as depending on other factors, such as the temperature and the humidity inside the image forming apparatus  1 A, whether to perform double-side printing, and the remaining life (i.e., the duration of use) of the secondary transfer roller  4 . 
     Incidentally, in Japanese Laid-Open Patent Publication No. 2006-163266, the resistance of the entire secondary transfer roller (i.e., an average resistance for the nip-margin area and the passage area) is used. More specifically, when the value of the current running upon application of the transfer bias voltage in accordance with the average resistance exceeds a threshold, the reverse-bias voltage is applied to the secondary transfer roller. The average resistance is lower than the actual resistance of the passage area, as shown in the upper panel of  FIG. 5 . Accordingly, in the case of the approach of Japanese Laid-Open Patent Publication No. 2006-163266, the reverse-bias voltage is not applied at an appropriate time, resulting in a problem of susceptibility to print density failure. 
     Furthermore, even if the size of the print medium varies (i.e., the size of the passage area varies), the resistance of the entire secondary transfer roller might remain the same, as shown in the lower panel of  FIG. 5 . In such a case also, a situation might occur where the reverse-bias voltage is not applied at an appropriate time. In addition, the rate of the change in resistance of the passage area at the transfer nip varies depending on the content of the print job. Therefore, the approach of Japanese Laid-Open Patent Publication No. 2006-163266 has difficulty in effectively inhibiting print density failure. 
     Section 4: Essence of Image Forming Apparatus in Relation to Table 
     In view of the problems described in Section 3, experimentation was carried out at the time of, for example, design of the image forming apparatus  1 A in order to obtain linear characteristics of the currents I 1  and I 2  relative to the number of passed sheets p upon application of a predetermined secondary transfer bias voltage V 1  in some representative temperature and humidity environments (see the upper panel of  FIG. 6 ). Here, the number of passed sheets p is in proportion to the duration of current supply to the secondary transfer roller  4  (i.e., the application time of the secondary transfer bias voltage V 1 ). Accordingly, if the secondary transfer bias voltage V 1  continues to be applied even after the number of passed sheets p has increased to a certain degree, an excessive transfer will occur eventually. The value of the current I 1  at which the excessive transfer starts to occur will be referred to below as a current threshold I 1   TH . Furthermore, the resistance R 2  at which the excessive transfer occurs under the aforementioned conditions is derived as a resistance threshold R 2   TH  from the value of the current I 2  and the secondary transfer bias voltage V 1  where the value of the current I 1  is the current threshold I 1   TH  (see the middle panel of  FIG. 6 ). Furthermore, the minimum value of the characteristic line for the value of the current I 1  will be referred to as I 1   min . In addition, the maximum value of the characteristic line for the value of the current I 2  will be referred to as I 2   max , and the resistance R 2  corresponding to this value will be referred to as an initial resistance R 2   ini . 
     Furthermore, the excessive transfer becomes more likely to occur as the amount of charge in the toner carried on the intermediate transfer belt  3  decreases. Accordingly, if the print job settings and the remaining life of the secondary transfer roller  4  are the same for both a so-called low-temperature and low-humidity environment (L/L environment) and a so-called high-temperature and high-humidity environment (H/H environment), the current threshold I 1   TH  tends to be higher in the L/L environment than in the H/H environment (see the lower panel of  FIG. 6 ), and therefore, the resistance threshold R 2   TH  tends to be higher in the L/L environment as well. Here, the amount of charge in the toner also varies depending on other factors, such as the number of printed pages. 
     In view of the above, the resistance threshold R 2   TH  for the nip-margin area P 2  is obtained in advance for each representative temperature and humidity condition, such as the H/H environment and the L/L environment. Note that the resistance threshold R 2   TH  may also be obtained for any other factor that affects the amount of charge in the toner. For example, the NVRAM of the control section  11  stores a first table T 1  listing the resistance threshold R 2   TH  for each temperature and humidity condition, as shown in TABLE 1 below. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 TABLE 1: Contents of Table T 1   
               
            
           
           
               
               
               
            
               
                 Temperature/Humidity 
                 Temperature/Humidity 
                 Resistance 
               
               
                 Condition 
                 (Representing Value) 
                 Threshold R2 TH   
               
               
                   
               
               
                 L/L Environment 
                 10° C., 15% RH 
                 R2 TH1   
               
               
                 N/N Environment 
                 25° C., 60% RH 
                 R2 TH2   
               
               
                 H/H Environment 
                 30° C., 85% RH 
                 R2 TH3   
               
               
                   
               
            
           
         
       
     
     Section 5: Essence of Image Forming Apparatus in Relation to Operation 
     Next, the operation of the image forming apparatus  1 A will be described with reference to  FIG. 7 . Upon reception of a print job, the control section  11  initially obtains a detection result from the temperature and humidity detection section  12 , and retrieves the resistance threshold R 2   TH  that corresponds to the current temperature and humidity condition from the first table T 1  (S 01 ). Next, the control section  11  starts executing the print job (S 02 ). During the execution of the print job, the first power supply  10 , under control of the control section  11 , applies a predetermined secondary transfer bias voltage V 1  to the secondary transfer roller  4 . 
     Next, the control section  11  determines whether to end the execution of the print job (S 03 ). If the determination is “Yes”, the control section  11  ends the execution of the print job, whereas if the determination is “No”, the control section  11  confirms whether the platen gap remains the same as the print medium M has passed through the secondary transfer nip  41  (S 04 ), and causes the probe  154  for an end portion (e.g., for the back-end portion) of the secondary transfer roller  4  to abut on the secondary transfer roller  4  (S 05 ). Thereafter, the second power supply  14 , under control of the control section  11 , applies a constant voltage to the secondary transfer roller  4  (S 06 ), and the control section  11  acquires the value of a current I 154  from the current detection section  13   4  corresponding to the probe  15   4  (S 07 ). Next, the control section  11  divides the value of the constant voltage applied at S 06  by the value of the current I 154  acquired at S 07 , thereby deriving the current resistance R 2  for the nip-margin area P 2  (S 08 ). 
     Next, the control section  11  determines whether the resistance R 2  obtained at S 08  has exceeded the resistance threshold R 2   TH  obtained at S 01  (S 09 ). If the determination is “No”, the control section  11  performs step S 03 , whereas if the determination is “Yes”, the control section  11  stops executing the print job, and thereafter, controls the first power supply  10  to apply a reverse-bias voltage V 2 , which has an opposite polarity to the polarity of the secondary transfer bias voltage V 1 , to the secondary transfer roller  4  (S 010 ). Thereafter, the control section  11  determines whether a predetermined waiting period has elapsed (S 011 ). Here, the predetermined period is a period of time until the resistance R 2  of the nip-margin area P 2  decreases to the initial resistance R 2   ini  (i.e., the period of time in which uneven ion distribution can be lessened), and is determined in advance through experimentation and so on. Note that at S 011 , whether the resistance R 2  has decreased to the initial resistance R min2  may be determined by actual measurements using the second power supply  14  and the current detection section  13 . 
     After the determination at S 011  results in “Yes”, the control section  11  restarts the print job (S 012 ), and performs step S 03 . 
     Section 6: Actions and Effects of Image Forming Apparatus 
     As described earlier, in the image forming apparatus  1 A, once the resistance R 2  of the nip-margin area P 2  exceeds the resistance threshold R 2   TH , the reverse-bias voltage V 2  is applied to the secondary transfer roller  4 . After that, the secondary transfer bias voltage V 1  is applied again. Consequently, temporal changes in the value of the current I 1  running through the passage area P 1  take the shape of a sawtooth waveform, as shown in  FIG. 8 , such that the current value falls from the current threshold I 1   TH  to the minimum I 1   min , and thereafter, rises again to the current threshold I 1   TH  by means of the application of the secondary transfer bias voltage V 1 , and the same pattern is repeated in an approximately cyclic manner. Here, unlike in conventional practice, the timing of applying the reverse-bias voltage V 2  is determined on the basis of the resistance R 2  of the nip-margin area P 2 , as described earlier, and therefore, when compared to conventional practice, it is possible to more accurately estimate the timing of a reverse transfer and thereby reduce the occurrence of a reverse transfer. In this manner, the present embodiment renders it possible to provide the image forming apparatus  1 A resistant to print density failure. 
     Section 7: Second Embodiment 
     In the first embodiment, the second power supply  14  has been described as supplying a constant voltage at S 06  in  FIG. 7 , but this is not limiting, and as in the case of the image forming apparatus  1 B in  FIG. 9 , the second power supply  14  may provide a constant current, and the control section  11  may derive the current resistance R 2  from a voltage value obtained from a voltage detection section  16 , and determine the timing of applying the reverse-bias voltage V 2 . 
     Section 8: Third Embodiment 
     In the first and second embodiments, the timing of applying the reverse-bias voltage V 2  is decided on the basis of the measured resistance R 2 . However, the timing of applying the reverse-bias voltage V 2  may be decided prior to the execution of a print job, considering the content of the print job, as will be described below. 
     In  FIG. 10 , the image forming apparatus  1 C differs from the image forming apparatus  1 A in that the current detection section  13 , the second power supply  14 , and the probes  15  are not included. The image forming apparatus  1 C has no other configurational difference from the image forming apparatus  1 A. Accordingly, in  FIG. 10 , components corresponding to those shown in  FIG. 1  are denoted by the same reference characters, and any descriptions thereof will be omitted herein. 
     Section 9: Essence of Image Forming Apparatus in Relation to Table 
     In the present embodiment also, the NVRAM or suchlike stores a first table T 1  as described in Section 4 (see TABLE 1). 
     Furthermore, the amount of change in the resistance R 2  relative to the number of passed sheets p (referred to below as the first resistance change rate ΔR 2 ) varies depending on the content of the print job and the remaining life of the secondary transfer roller  4 . For example, the value of the current I 1  changes more significantly relative to the number of passed sheets p as the size or thickness (or grammage) of the print medium M increases or as the design life of the secondary transfer roller  4  becomes closer to the end (see  FIG. 11 ). The same can be said of the value of the current I 2 . Correspondingly, the resistance R 2  changes significantly, so that the first resistance change rate ΔR 2  increases. Moreover, the water content of the print medium M decreases during double-side printing, so that the resistance Rm of the print medium M rises. Accordingly, at the time of double-side printing, the value of the current I 1  changes significantly (see  FIG. 11 ) compared to the time of single-side printing, and therefore, the value of the current I 2  and also the resistance R 2  changes significantly, so that the first resistance change rate ΔR 2  increases. 
     In view of the above, the characteristics of the resistance R 2  relative to the number of passed sheets p are obtained in advance in relation to the size and the thickness of the print medium M, the remaining life of the secondary transfer roller  4 , and whether to perform double-side printing, as well as for each combination thereof, and on the basis of the obtained characteristics, first resistance change rates ΔR 2  relative to the number of passed sheets p are derived. For example, the NVRAM of the control section  11  stores a second table T 2  listing the first resistance change rate ΔR 2  for each combination of factors, such as the content of the print job and the remaining life of the secondary transfer roller  4 , as shown in TABLE 2 below. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 TABLE 2: Contents of Table T 2   
               
            
           
           
               
               
               
               
            
               
                 Print Medium 
                 Life of 
                 Double-side 
                 Resistance 
               
            
           
           
               
               
               
               
               
            
               
                 Size 
                 Thickness (mm) 
                 Roller 
                 Printing 
                 Change Rate ΔR2 
               
               
                   
               
               
                 A4T 
                 0.09 
                 Early Stage 
                 No 
                 ΔR2 1   
               
               
                 A4T 
                 0.09 
                 Early Stage 
                 Yes 
                 ΔR2 2   
               
               
                 A4T 
                 0.09 
                 Late Stage 
                 No 
                 ΔR2 3   
               
               
                 A4T 
                 0.09 
                 Late Stage 
                 Yes 
                 ΔR2 4   
               
               
                 . 
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
                 . 
               
               
                 B4T 
                 0.15 
                 Early Stage 
                 Yes 
                  ΔR2 i   
               
               
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
               
               
                   
               
            
           
         
       
     
     As will be described in detail later, the resistance R 2  at the end of the print job (i.e., the last resistance R 2   last ) can be roughly estimated, and in the present embodiment, as in the first embodiment, the resistance R 2  simply takes a value within the limited range from the initial resistance R 2   ini  to the resistance threshold R 2   TH . Moreover, when the application of the secondary transfer bias voltage V 1  stops upon the end of the print job, uneven ion distribution in the secondary transfer roller  4  is lessened over time, so that the resistance of the secondary transfer roller  4  decreases. Accordingly, the characteristic of the temporal change in the resistance R 2  after the end of the application of the secondary transfer bias voltage V 1  is obtained, for example, through experimentation, and a linear approximation thereof is estimated. In this manner, a second resistance change rate Δr 2  over time for the resistance R 2  after the end of the application of the secondary transfer bias voltage V 1  is obtained from the characteristic. In the third embodiment, for example, the NVRAM stores a third table T 3  listing the initial resistance R 2   ini  and the second resistance change rate Δr 2  for each temperature and humidity condition, as shown in TABLE 3 below. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 TABLE 3: Contents of Table T 3   
               
            
           
           
               
               
               
            
               
                 Temperature/Humidity 
                 Initial Resistance 
                 Resistance Change 
               
               
                 Condition 
                 Value R2 ini   
                 Rate Δr2 
               
               
                   
               
               
                 L/L Environment 
                 R2 ini1   
                 Δr2 1   
               
               
                 N/N Environment 
                 R2 ini2   
                 Δr2 2   
               
               
                 H/H Environment 
                 R2 ini3   
                 Δr2 3   
               
               
                   
               
            
           
         
       
     
     Section 10: Essence of Image Forming Apparatus in Relation to Operation 
     Next, the operation of the image forming apparatus  1 C will be described with reference to  FIG. 12 . In the image forming apparatus  1 C, upon reception of a new print job, the control section  11  obtains an elapsed time t 1  since the end of the previous application of the secondary transfer bias voltage V 1 , on the basis of, for example, the count of an internal timer, which has been activated in a manner as will be described later in conjunction with S 113  (S 11 ). 
     The control section  11  further obtains the last resistance R 2   last , which has been stored in a manner as will be described later in conjunction with S 114  (S 12 ). Here, the last resistance R 2   last  is approximately equal to the resistance R 2  at the end of the previous application of the secondary transfer bias voltage V 1 . Next, the control section  11  receives a detection result from the temperature and humidity detection section  12 , and retrieves the second resistance change rate Δr 2  that corresponds to the current temperature and humidity environment, from the third table T 3  (S 13 ). 
     Thereafter, the control section  11  derives the current resistance R 2  of the nip-margin area P 2  from the elapsed time t 1 , the last resistance R 2   last , and the second resistance change rate Δr 2  (S 14 ). The current resistance R 2  is calculated by Δr 2 ·t 1 +R 2   last . Note that the resistance R 2  has to be greater than or equal to 0, and therefore, if the calculation result is negative, the resistance R 2  is considered as 0. 
     Next, the control section  11  retrieves the resistance threshold R 2   TH  that corresponds to the temperature and humidity environment at S 13 , from the first table T 1  (S 15 ). Next, the control section  11  retrieves from the second table T 2  the first resistance change rate ΔR 2  that matches information included in the print job (more specifically, the size and the thickness of the print medium M to be used for the current job and whether to perform double-side printing) and the remaining life of the secondary transfer roller  4  (S 16 ). 
     Next, the control section  11  derives a feeding threshold p TH  which is the number of sheets to be passed until the resistance increases from the initial value R 2   ini  stored in the third table T 3  to the resistance threshold R 2   TH  obtained at S 15 , from the first resistance change rate ΔR 2  obtained at S 16  (S 17 ). Specifically, the feeding threshold p TH  is calculated by (R 2   TH −R 2   ini )/ΔR 2 . Note that it is expected that the value of the elapsed time t 1  is low and hence uneven ion distribution is lessened unsatisfactorily, and therefore, an initial value p TH0 ) for the feeding threshold p TH  may be obtained beforehand with reference to the current resistance R 2  obtained at S 14 . 
     Next, as at S 02  and S 03  described earlier, the control section  11  starts executing the print job (S 18 ), and thereafter determines whether to end the execution of the print job (S 19 ). If the determination at S 19  is “No”, the control section  11  determines whether the number of sheets passed through the secondary transfer nip  41  has exceeded the feeding threshold p TH  (S 110 ). Note that only immediately after the start of the execution of the print job, it is preferable that the control section  11  uses the initial value p TH0  in place of the feeding threshold p TH . 
     If the determination at S 110  is “No”, the control procedure of the control section  11  returns to S 18 . On the other hand, if the determination is “Yes”, the control section  11  considers the resistance R 2  to have exceeded the resistance threshold R 2   TH  and then stops the execution of the print job before controlling the first power supply  10  to apply the reverse-bias voltage V 2  (see the first embodiment for details) to the secondary transfer roller  4  (S 111 ). Thereafter, as at S 11  described earlier, the control section  11  waits for a predetermined period of time (S 112 ), and executes the processing of S 18  again. 
     In the case where the determination at S 19  is “Yes”, the control section  11  terminates the printing process. In the course of the termination, the control section  11  resets the internal timer, starts measuring an elapsed time since the end of the application of the secondary transfer bias voltage V 1  (S 113 ), and stores the current resistance R 2  as the last resistance R 2   last  (S 114 ). Note that the current resistance R 2  is a value obtained by dividing the number of printed pages, which is specified by the print job, by the feeding threshold p TH  and multiplying the remainder of the division by the first resistance change rate ΔR 2 . 
     Section 11: Actions and Effects of Image Forming Apparatus 
     As described above, in the present embodiment, as in the first embodiment, the value of the current I 1  changes over time, as shown in  FIG. 8 , and therefore, it is rendered possible to provide the image forming apparatus  1 C resistant to print density failure. 
     Section 12: Supplementary 
     The first resistance change rate ΔR 2  can also be determined in accordance with the following factors other than the aforementioned factors: 
     (1) the fusing temperature at the time of double-side printing; and 
     (2) the temperature and/or the humidity inside the image forming apparatus  1 C. 
     Furthermore, in the above embodiment, the resistance threshold R 2   TH  is determined in accordance with the temperature and humidity environment. However, this is not limiting, and the resistance threshold R 2   TH  may be determined so as to be proportional to the amount of charge in the toner carried on the intermediate transfer belt  3 . 
     Furthermore, in the above embodiment, the first resistance change rate ΔR 2  has been described as being obtained based on the second table T 2  and other factors. However, this is not limiting, and the control section  11  may have stored therein an arithmetic operation obtained, for example, at the time of design and capable of deriving the first resistance change rate ΔR 2  by assigning the size and the thickness of the print medium M, the remaining life of the secondary transfer roller  4 , and whether to perform double-side printing. In such a case, upon reception of a print job, the control section  11  obtains the first resistance change rate ΔR 2  by assigning necessary variables to the arithmetic operation. 
     Furthermore, in the above embodiment, the image forming apparatus  1 C employs a so-called intermediate transfer system, so that the toner image carried on the intermediate transfer belt  3  is transferred to the print medium M passing through the secondary transfer nip  41 . However, this is not limiting, and the present embodiment can also be applied to an image forming apparatus employing a direct transfer system. In such a case, the photoreceptor drum functions as the image carrier, and the transfer roller functions as the transfer member. The same can be said of the image forming apparatuses  1 A and  1 B. 
     Section 13: First Modification 
     In the foregoing description of the third embodiment, printing on all print media M during the execution of a print job is carried out under the same condition. However, in some cases, a single print job might produce monochrome prints and color prints. Such a print job is also called a color/monochrome mixed job. Here, the toner layer is thicker for the color print than for the monochrome print, and therefore, the resistance is higher for the color print than for the monochrome print. In such a case, unlike in the above embodiment, it is preferable that the control section  11  performs the procedure shown in  FIG. 13  in place of the procedure shown in  FIG. 12 .  FIG. 13  differs from  FIG. 12  in that steps S 26  and S 210  are included in place of steps S 16  and S 110 , and further, step S 17  is omitted. There is no other difference between the procedures shown in both figures, therefore, in  FIG. 13 , steps corresponding to those in  FIG. 12  are denoted by the same reference characters, and any descriptions thereof will be omitted herein. 
     Initially, at S 26  in  FIG. 13 , on the basis of the condition and other factors for the current print job, the control section  11  selects a first resistance change rate ΔR 2   c  for color and a first resistance change rate ΔR 2   m  for monochrome from among various first resistance change rates obtained for both color and monochrome, for example, at the time of design. 
     Furthermore, at S 210  in  FIG. 13 , the control section  11  cumulatively adds the selected first resistance change rate ΔR 2   c  to the current resistance R 2  of the nip-margin area P 2  upon each passing of a color print through the secondary transfer nip  41 . On the other hand, the control section  11  cumulatively adds the selected first resistance change rate ΔR 2   m  to the current resistance R 2  upon each passing of a monochrome print. Thereafter, the control section  11  determines whether the current resistance R 2  has exceeded the resistance threshold R 2   TH  obtained at S 15 . 
     As a consequence of the procedure in  FIG. 13 , the control section  11  cumulatively adds an appropriate one of the first resistance change rates ΔR 2   c  and ΔR 2   m  to the resistance R 2  every time the medium M passes through during the execution of the color/monochrome mixed job, as shown in  FIG. 14 . Once the resistance R 2  exceeds the resistance threshold R 2   TH , the reverse-bias voltage V 2  is applied to the secondary transfer roller  4 . In this manner, in the present modification, the reverse-bias voltage V 2  is applied at an appropriate time even during the execution of the color/monochrome mixed job, and therefore, it is rendered possible to provide the image forming apparatus  1 C resistant to print density failure. 
     Section 14: Second Modification 
     Incidentally, in general, the image forming apparatus  1 C performs raster image processing (RIP), so that a variety of types of electronic data sent along with the print job are plotted on raster image data (i.e., bitmap data). In the third embodiment, at S 16  in  FIG. 12 , the first resistance change rate ΔR 2  is obtained on the basis of the content of the print job and other factors. However, as is apparent from the foregoing, the thickness of the toner layer on the print medium M affects the change in the resistance R 1 . Accordingly, at S 16  in  FIG. 12 , the control section  11  may obtain and analyze raster image data through an RIP operation and obtain information about the toner layer thickness and other factors, so that the first resistance change rate ΔR 2  is determined considering the obtained information for the toner layer thickness and other factors. Note that in such a case, the table T 2  needs to contain first resistance change rates ΔR 2  prepared in advance considering the toner layer thickness and other factors. 
     Although the present invention has been described in connection with the preferred embodiment above, it is to be noted that various changes and modifications are possible to those who are skilled in the art. Such changes and modifications are to be understood as being within the scope of the invention.