Patent Publication Number: US-9891560-B2

Title: Image forming system

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This patent application is a continuation of U.S. patent application Ser. No. 14/718,567 filed May 21, 2015, which is based on and claims priority pursuant to 35 U.S.C. § 119(a) to Japanese Patent Application Nos. 2014-112896 filed on May 30, 2014 and 2014-151327 filed on Jul. 25, 2014, in the Japan Patent Office, the entire disclosure of each of which is hereby incorporated by reference herein. 
    
    
     BACKGROUND 
     Technical Field 
     Embodiments of the present invention generally relates to an electrophotographic image forming apparatus such as a copier, a facsimile machine, a printer, or a multifunction peripheral (MFP, i.e., a multifunction machine) having at least two of copying, printing, facsimile transmission, plotting, and scanning capabilities. 
     Description of the Related Art 
     Image forming apparatuses such as copiers and printers generally include a transfer roller to press against an image bearer, and a contact therebetween is called “transfer nip” (i.e., a transfer position). It is possible that toner transferred from the image bearer adheres to the transfer roller. Then, when a recording medium such as a paper sheet is nipped in the transfer nip, it is possible that a back side or an edge face of the recording medium is soiled with toner transferred from the transfer roller. To prevent such soil of toner of the sheet, for example, a cleaning bias different from a transfer bias is applied to the transfer roller in intervals between sheets transported to the transfer nip between the transfer roller and the image bearer. 
     SUMMARY 
     An embodiment of the present invention provides an image forming apparatus that includes an image bearer to rotate and bear a toner image, a transfer rotator to rotate and contact the image bearer to form a transfer nip therebetween, a bias application device to apply multiple biases to the transfer rotator, and a controller to control the bias application device and set a sheet feeding interval (an interval between sheets) in successive sheet feeding according to a predetermined condition. The multiple biases includes a transfer bias to transfer the toner image from the image bearer onto the sheet transported to the transfer nip, a cleaning bias to remove toner adhering to the transfer rotator, and a non-image area bias smaller in absolute value than the cleaning bias. 
     When the sheet feeding interval exceeds a predetermined threshold, the bias application device executes application of the non-image area bias for an application time Z within the sheet feeding interval, and the time Z is set to an increased length of time as the sheet feeding interval is increased. When X represents the sheet feeding interval, application of the cleaning bias is executed for a time period expressed as X−Z within the sheet feeding interval. 
     In another embodiment, an image forming apparatus includes the above-described image bearer, the transfer rotator, a backup roller disposed to contact the transfer rotator via the image bearer, and a bias application device to apply the multiple biases to at least one of the transfer rotator and the backup roller. The controller controls bias application device as described above. 
     In yet another embodiment, an image forming apparatus includes the above-described image bearer, the transfer rotator, and a bias application device to apply, to the transfer rotator, the transfer bias and the cleaning bias described above. The image forming apparatus further includes a controller to cause the bias application device to keep a current value applied to the transfer rotator at zero for an application time Z within an interval between sheets in successive feeding of sheets. The application time Z is set to an increased length of time as the interval between sheets is increased. When X represents the interval between sheets, the bias application device is to execute application of the cleaning bias for an application time expressed as X−Z within the interval between sheets. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       A more complete appreciation of the disclosure and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein: 
         FIG. 1  is a schematic diagram illustrating a configuration of an image forming apparatus according to an embodiment of the present invention; 
         FIG. 2  is a schematic cross-sectional view of a sheet processing apparatus according to an embodiment; 
         FIG. 3  is a schematic view of a pressure roller of a fixing device according to an embodiment; 
         FIGS. 4A, 4B, and 4C  are timing charts of control of a power supply to apply bias to a transfer roller according to a first embodiment; 
         FIG. 5  is a timing chart of control of the power supply to apply bias to the transfer roller according to an embodiment, for a case where post-processing of sheets is performed; 
         FIG. 6  is a timing chart of control of the power supply to apply bias to the transfer roller according to an embodiment, when overheating of a non-sheet area of a fixing device is recognized; 
         FIG. 7  is a timing chart of control of the power supply to apply bias to the transfer roller according to an embodiment, for a case where temperature adjacent to the photoconductor drum rises; 
         FIG. 8  is a table of correction coefficients of cleaning biases for each process speed when the process speed is variable in multiple stages, according to an embodiment; 
         FIG. 9  is a table of example settings of cleaning biases variable in accordance with absolute humidity, according to an embodiment; 
         FIG. 10  is a graph of experimentally obtained changes over time of cleanliness rating (indicating the degree of adhesion of toner) of edge face of sheets; 
         FIGS. 11A, 11B, and 11C  are timing charts of control of a power supply for a transfer roller according to a second embodiment; 
         FIG. 12A  is a schematic view that illustrates a main part of a multicolor image forming apparatus according to a variation; and 
         FIG. 12B  is a schematic view that illustrates a main part of a multicolor image forming apparatus according to another variation. 
     
    
    
     DETAILED DESCRIPTION 
     In describing preferred embodiments illustrated in the drawings, specific terminology is employed for the sake of clarity. However, the disclosure of this patent specification is not intended to be limited to the specific terminology so selected, and it is to be understood that each specific element includes all technical equivalents that operate in a similar manner and achieve a similar result. 
     Referring now to the drawings, wherein like reference numerals designate identical or corresponding parts throughout the several views thereof, and particularly to  FIG. 1 , an image forming apparatus according to an embodiment of the present invention is described. 
     Firstly, the entire configuration and functions of an image forming apparatus  1  are described with reference to  FIG. 1 . 
     The image forming apparatus  1  illustrated in  FIG. 1  is, for example, a copier and includes a document reader  2 , an exposure device  3 , an image forming unit  4  to form a toner image on a surface of a photoconductor drum  5 , a transfer roller  7 , a document feeder  10  to feed a document D set thereon to the document reader  2 , sheet trays  12  through  14  to accommodate a stack of sheets P (recording media), a registration roller pair  17  (timing rollers), a fixing device  20  to fix the toner image on the sheet P, and a sheet reversal unit  30  to reverse the sheet P upside down and transport the sheet P again to the image forming unit  4  after the toner image is formed on a first side (front side) thereof. The document reader  2  optically reads image data of the document D, according to which the exposure device  3  emits a laser beam L to the surface of the photoconductor drum  5 . The transfer roller  7  transfers the toner image onto the sheet P. The registration roller pair  17  feeds the sheet P to a position where the transfer roller  7  contacts the photoconductor drum  5 . The fixing device  20  includes a fixing belt  21  and a pressure roller  22 . 
     Additionally, reference numeral  50  represents a sheet processing apparatus (post-processing apparatus) to process the sheets P discharged from the image forming apparatus  1 . The sheet processing apparatus  50  includes an internal tray  61  disposed inside the sheet processing apparatus  50 , first, second, and third output trays  71 ,  72 , and  73  to store the sheets P or bundles of sheets P discharged from the sheet processing apparatus  50 , a center-folding plate  86  to fold the sheets P, a stapler  90 , and a punch  95 . The sheet processing apparatus  50  is removably connected to the image forming apparatus  1 . 
     Referring to  FIG. 1 , the image forming unit  4  includes the photoconductor drum  5  serving as an image bearer, a charging roller  41  (i.e., a charging device), a developing device  42 , the transfer roller  7 , a cleaning device  43 , and the like. 
     The photoconductor drum  5  used in the present embodiment is an organic photoconductor charged to a negative polarity and includes a photosensitive layer overlying a drum-shaped conductive base. For example, the photoconductor drum  5  is multilayered, and a base coat serving as an insulation layer, and a photosensitive layer are provided sequentially on the conductive base. The photosensitive layer includes a charge generation layer and a charge transport layer. The photoconductor drum  5  is rotated clockwise in  FIG. 1  by a driving motor. A temperature and humidity sensor  48  is disposed adjacent to the photoconductor drum  5  to detect a temperature of the photoconductor drum  5 . 
     In one embodiment, the charging roller  41  includes a conductive cored bar and an elastic layer of moderate resistivity overlying an outer circumference of the cored bar. The charging roller  41  is disposed to contact the photoconductor drum  5 . Receiving a predetermined voltage from a power source, the charging roller  41  uniformly charges the surface of the photoconductor drum  5  facing the charging roller  41 . 
     The developing device  42  includes a developing roller disposed facing the photoconductor drum  5 , two conveying screws disposed side by side via a partition, and a doctor blade opposed to the developing roller. The developing roller includes stationary magnets or a magnet roller and a sleeve that rotates around the magnets. The magnets generate magnetic poles around the circumferential surface of the developing roller. Developer is borne on the development roller by the multiple magnetic poles. The developing device  42  contains two-component developer including carrier (carrier particles) and toner (toner particles). Additionally, a replaceable toner container to contain fresh toner is removably attached to the developing device  42 . 
     With the developing device  42  having such a structure, toner is transferred from the developing roller to an electrostatic latent image on the photoconductor drum  5  by the electrical field generated in the developing range where the developing roller faces the photoconductor drum  5 . Thus, a desired toner image is formed on the photoconductor drum  5 . 
     It is to be noted that toner dedicated for high speed machines, having a lower melting point, is used in the present embodiment. 
     Specifically, the toner usable in the present embodiment includes a binder resin that includes, at least, crystalline polyester resin (A), noncrystalline resin (B), noncrystalline resin (C), and composite resin (D) that includes a polycondensation resin unit and an addition polymerization resin unit. The noncrystalline resin (B) contains an insoluble chloroform component, and the noncrystalline resin (C) is lower in softening temperature (T½) than the noncrystalline resin (B) by 25° C. or greater. In a molecular-weight distribution according to gel permeation chromatography (GPC) obtained by a soluble tetrahydrofuran (THF) component of toner, a main peak is within 1000 to 10000, and a full width at half maximum of the molecular-weight distribution is at or lower than 15000. 
     Although such a toner has a lower melting point and suitable for high-speed image formation, the possibility of adhesion of paper dust and decreases in amount of charge are high, and the toner is likely to adhere to the transfer roller  7 . Accordingly, cleaning of the transfer roller  7  to remove the toner is effective. 
     The cleaning device  43  includes a cleaning blade to contact the surface of the photoconductor drum  5  and remove toner and the like adhering to the photoconductor drum  5 . In one embodiment, the cleaning blade includes a planar blade body made of rubber, such as urethane rubber, hydrin rubber, silicone rubber, and fluororubber, and a blade support to hold the rubber blade body. The cleaning blade contacts the surface of the photoconductor drum  5  at a predetermined angle and pressure. With this configuration, substance such as toner and dust adhering to the surface of the photoconductor drum  5  is mechanically scraped off and collected in the cleaning device  43 . 
     It is to be noted that the image forming apparatus  1  according to the present embodiment may further includes a recycle toner tube to feed the toner collected by the cleaning device  43  to the developing device  42 . 
     The transfer roller  7  serving as a rotatable transfer device includes a conductive cored bar and an elastic layer overlying an outer circumference of the cored bar, and the elastic layer has a resistance value of about 10 6 Ω to 10 9 Ω under conditions of a temperature of 23° C., a humidity of 50% RH (relative humidity), and application of direct-current (DC) voltage of 1000 V. The transfer roller  7  is pressed against the photoconductor drum  5 , and the contact portion therebetween is hereinafter referred to as “transfer nip”. The transfer roller  7  is rotated in a predetermined direction (counterclockwise in  FIG. 1 ) by a driving motor. In another embodiment, the transfer roller  7  is rotated by not the driving motor but friction force with the photoconductor drum  5 . 
     The image forming apparatus  1  further includes a power supply  35  serving as a bias application device to apply a transfer bias to the transfer roller  7 , thereby transferring the toner image from the photoconductor drum  5  to the sheet P fed to the transfer nip therebetween. Specifically, the transfer bias applied by the power supply  35  to the transfer roller  7  is different in polarity (positive in the present embodiment) from the polarity of toner to transfer the toner image from the photoconductor drum  5  onto the sheet P nipped in between the photoconductor drum  5  and the transfer roller  7 . 
     It is to be noted that, in the present embodiment, the power supply  35  applies the transfer bias using constant current control. In transfer devices employing the constant current control, the bias applied to the transfer roller  7  is adjusted to keep the value of current constant during sheet feeding. Then, the toner image on the photoconductor drum  5  is attracted to the first side of the sheet P by applying electrical charges opposite in polarity to toner to the back side (the side on which the toner image is not to be transferred) of the sheet P. 
     In transfer devices of direct-transfer type, in which toner is directly transferred from the photoconductor drum  5  onto the sheet P nipped therebetween (the transfer nip), the transfer roller  7  directly contacts the photoconductor drum  5  when the sheet P is not nipped therebetween. Accordingly, if the transfer bias is applied to the transfer roller  7  in that state, toner adhering to non-image areas of the photoconductor drum  5  is transferred onto the transfer roller  7 . That is, the transfer roller  7  is soiled with toner. It is to be noted that, when the charge of toner is insufficient or mechanical pressure is applied thereto, toner can adhere to the non-image areas of the photoconductor drum  5 , and this phenomenon is referred to as “background fog” or “background stains”. If the transfer roller  7  is soiled with toner, the toner is transported to the transfer nip and further transferred to the back side or the edge face of the sheet P. 
     Therefore, in the present embodiment, a cleaning bias is applied to the transfer roller  7  in a predetermined period described later (such as interval between sheets) to prevent the transfer current from flowing to the transfer roller  7 , thereby suppressing adhesion of toner to the transfer roller  7 . Alternatively, the cleaning bias is applied to transfer the toner from the transfer roller  7  to the photoconductor drum  5 , thereby cleaning the transfer roller  7 . 
     Standard image forming operation of the image forming apparatus  1  illustrated in  FIG. 1  is described below. 
     In the document feeder  10 , conveyance rollers transport the document D from a document table in a direction indicated by an arrow in  FIG. 1  above the document reader  2 . Then, the document reader  2  optically reads image data of the document D passing above the document reader  2 . 
     The image data read by the document reader  2  is converted to electric signals and transmitted to the exposure device  3 . Then, the exposure device  3  emits the laser beam L according to the electric signals indicating the image data to the surface of the photoconductor drum  5  of the image forming unit  4 . 
     In the image forming unit  4 , the photoconductor drum  5  rotates clockwise in  FIG. 1 , and an image according to the image data is formed on the photoconductor drum  5  through predetermined image forming processes such as charging, exposure, and developing processes. 
     Subsequently, in the transfer nip between the transfer roller  7  and the photoconductor drum  5 , the image is transferred from the surface of the photoconductor drum  5  onto the sheet P transported by the registration roller pair  17 . 
     The sheet P moves to the transfer roller  7  as follows. 
     Initially, one out of the sheet trays  12 ,  13 , and  14  of the image forming apparatus  1  is selected automatically or manually. For example, the sheet tray  12  on the top is selected. 
     Then, the sheet P on the top on the sheet tray  12  is fed to a sheet conveyance path K 1  defined by multiple conveyance rollers arranged between the sheet tray  12  and a discharge roller pair. 
     The sheet P is transported through the sheet conveyance path K 1  to the registration roller pair  17 , which forwards the sheet P to the transfer roller  7 , timed to coincide with arrival of the image borne on the surface of the photoconductor drum  5 . 
     Subsequently, the sheet P is transported further to the fixing device  20  through the sheet conveyance path K 1 . The sheet P is then nipped between the fixing belt  21  and the pressure roller  22 , and the image carried thereon is fixed with heat and pressure exerted from the fixing belt  21  and the pressure roller  22 , which is a fixing process. After the image is fixed thereon, the sheet P is released from the fixing belt  21  and the pressure roller  22  and discharged through a sheet outlet  49  outside the image forming apparatus  1 . The sheet outlet  49  is connectable to the sheet inlet  50   a  of the sheet processing apparatus  50 . 
     Thus, in single-side printing, the sheet P is discharged after the image is fixed on the front side thereof. By contrast, in duplex printing to form images on both sides (front side and back side) of the sheet P, the sheet P is guided to the sheet reversal unit  30  through a sheet reversal path K 2  defined by multiple conveyance rollers arranged between the fixing device  20  and the sheet reversal unit  30  and those provided in the sheet reversal unit  30 . After the direction in which the sheet P is transported (sheet conveyance direction) is reversed in the sheet reversal unit  30 , the sheet P is transported again to the transfer roller  7 . Then, through the image forming processes similar to those described above, an image is formed on the back side of the sheet P and fixed thereon by the fixing device  20 , after which the sheet P is discharged from the image forming apparatus  1 . 
     In the present embodiment, the image forming apparatus  1  is provided with the sheet processing apparatus  50 , and the sheet P discharged from the image forming apparatus  1  enters the sheet processing apparatus  50  for post-processing. 
     Referring to  FIG. 1 , in the sheet processing apparatus  50  according to the present embodiment, depending on post-processing type, the sheet P is transported through one of three sheet conveyance paths (first, second, and third conveyance paths K 3 , K 4 , and K 5 ) defined by multiple conveyance rollers and guides. The first conveyance path K 3  extends from an sheet inlet  50   a  (in  FIG. 2 ) of the sheet processing apparatus  50  to the first output tray  71 , to which the sheet P is transported when no post-processing is performed or only punching by the punch  95  is performed. The second conveyance path K 4  extends from the sheet inlet  50   a  to the internal tray  61  and further to the second output tray  72  (an external tray). The stapler  90  staples a trailing end of a bundle of sheets P placed on the internal tray  61 , after which the bundle of stapled sheets P (hereinafter “sheet bundle PT)” is discharged onto the second output tray  72  by ejection rollers  55  (in  FIG. 2 ) through a sheet outlet  50   b  (in  FIG. 2 ). The third conveyance path K 5  is for transporting the sheet P temporarily to the second conveyance path K 4  and switchbacking the sheet P to the center-folding plate  86  and a center-folding blade  84  (in  FIG. 2 ). The third conveyance path K 5  extends to the third output tray  73 . 
     It is to be noted that the conveyance route of the sheet P can be switched among the first, second, and third conveyance paths K 3 , K 4 , and K 5  by rotating a bifurcating claw  81 . The sheet P transported through the second and third conveyance paths K 4  and K 5  can be punched by the punch  95  similar to the sheet transported through the first conveyance path K 3 . 
     More specifically, referring to  FIG. 2 , a first conveyance roller pair  51  and a sheet sensor are disposed adjacent to the sheet inlet  50   a  of the sheet processing apparatus  50 , and the sheet P detected by the sheet sensor is transported inside the sheet processing apparatus  50  by the first conveyance roller pair  51  and a second conveyance roller pair  52 . When punching is preliminarily selected by a user, the punch  95  punches the sheet P. 
     According to the post-processing selected by the user, the bifurcating claw  81  rotates to guide the sheet P to one of the first, second, and third conveyance paths K 3 , K 4 , and K 5 . 
     When no post-processing is selected, the sheet P transported to the first conveyance path K 3  is discharged by a third conveyance roller pair  53  to the first output tray  71 . 
     A fourth conveyance roller pair  54  is disposed upstream from the ejection rollers  55  in the second conveyance path K 4  in the sheet conveyance direction. The fourth conveyance roller pair  54  is movable in a width direction, which is perpendicular to the surface of the paper on which  FIG. 1  is drawn. When collating (sorting) is selected, each of the sheets P transported to the second conveyance path K 4  is transported while being shifted for a predetermined amount in the width direction by the fourth conveyance roller pair  54 . Then, the ejection rollers  55  (a fifth conveyance roller pair) discharge the sheets P sequentially on the second output tray  72 . 
     Referring to  FIG. 2 , a feeler  82  is disposed above the second output tray  72 . The feeler  82  is rotatable around a support shaft disposed at an upper end thereof in  FIG. 2 , and the second output tray  72  is movable vertically in  FIG. 2  with a position change mechanism. When a sensor disposed adjacent to the support shaft of the feeler  82  detects that a center portion (in the sheet conveyance direction) of the sheet P sequentially placed on the second output tray  72  is in contact with the feeler  82 , a height of the sheets P on the second output tray  72  is recognized. In accordance with increases and decreases in the number of the sheets P on the second output tray  72 , a vertical position of the second output tray  72  is adjusted. When the second output tray  72  is set at a lowest position in a movable range whereof, it is deemed that the number of the sheets P on the second output tray  72  is at an upper limit (the second output tray  72  is filled to its capacity). Then, the sheet processing apparatus  50  transmits a stop signal to a controller  60  of the image forming apparatus  1  to stop image forming operation. It is to be noted that the image forming apparatus  1  consecutively operates while a sequence of post-processing processes including the processes described above or later is performed in the sheet processing apparatus  50 . Specifically, the image forming components such as the photoconductor drum  5  and the transfer roller  7  are driven idle even when the image forming processes on the photoconductor drum  5  are not performed. 
     When stapling is selected, the sheets P transported to the second conveyance path K 4  are sequentially stacked on the internal tray  61  by the fourth conveyance roller pair  54  without being shifted. An alignment roller  64  is disposed above the internal tray  61 . After a designated number of sheets P (a bundle of sheets) are stacked on a sheet mounting face of the internal tray  61 , the alignment roller  64  moves to a position to contact the sheet P on the top on the sheet mounting face. As the alignment roller  64  rotates counterclockwise in  FIG. 2 , the multiple sheets P are moved to a fence  66 . With this action, a trailing end of each of the multiple sheets P contacts the fence  66 , and thus the multiple sheets P are aligned in the sheet conveyance direction. 
     Referring to  FIG. 2 , jogger fences  68  are disposed at both ends in the width direction of the internal tray  61 . At that time, the jogger fences  68  move in the width direction to sandwich the sheets P on the internal tray  61 , thereby aligning the sheets P in the width direction. Then, the stapler  90  staples the trailing end of the bundle of sheets P aligned in the sheet conveyance direction as well as the width direction. 
     After being stapled, the bundle of sheets P moves obliquely upward along a slope of the sheet mounting face of the internal tray  61  as a release claw  67  moves in the direction in which the bundle is discharged. Then, the ejection rollers  55  discharge the bundle to the second output tray  72 . 
     When folding is selected, the sheet P is transported to the second conveyance path K 4  and then switchbacked while the fourth conveyance roller pair  54  rotates in reverse with the trailing end of the sheet P nipped therein. Then, the sheet P is transported to the third conveyance path K 5 . Along the third conveyance path K 5 , conveyance roller pairs  56 ,  57 , and  58  transport the sheet P to a position where a center position of the sheet P faces the center-folding blade  84 . At that time, a leading end of the sheet P is in contact with a stopper  85 , which is movable in the sheet conveyance direction with a slide mechanism. A designated number of sheets P is stacked at that position. 
     The sheet P is pressed at the position of the center-folding plate  86  and folded at the center position by the center-folding blade  84  that moves to the left in  FIG. 2 . Subsequently, the sheet P or bundle of sheets P is transported by a conveyance roller pair  59  and discharged to the third output tray  73 . 
     Next, the fixing device  20  of the image forming apparatus  1  according to the present embodiment is described in further detail below. The fixing device  20  includes the fixing belt  21 , a hollow metal pipe disposed to face an inner circumferential face of the fixing belt  21 , a halogen heater (i.e., a heat source) disposed inside the hollow of the metal pipe, the pressure roller  22 , a nip holder disposed inside the fixing belt  21 , and first and second temperature sensors  28 A and  28 B (in  FIG. 1 , collectively represented by reference numeral “ 28 ”) to detect a surface temperature of the pressure roller  22 , and the like. The nip holder is pressed against the pressure roller  22  via the fixing belt  21 , thereby defining a contact portion between the fixing belt  21  and the pressure roller  22  (i.e., a fixing nip). 
     The fixing belt  21  is a flexible endless belt and relatively thin. The fixing belt  21  rotates clockwise in  FIG. 1 . The fixing belt  21  includes an elastic layer and a release layer sequentially overlying a base material, and an entire thickness of the fixing belt  21  is 1 mm or smaller. 
     Output from the halogen heater disposed inside the fixing belt  21  is controlled according to surface temperature of the fixing belt  21  detected by a thermistor opposed to the surface of the fixing belt  21 . The fixing belt  21  is heated to a desired temperature (i.e., a fixing temperature) via the metal pipe by radiant heat from the halogen heater. Heat is transmitted from the surface of the fixing belt  21  to the toner image on the sheet P, thereby fixing the toner image on the sheet P. 
     The pressure roller  22  serving as a pressure rotator includes a hollow metal core, made of stainless steel or aluminum, and an elastic layer made of foam silicone rubber or silicone rubber in one embodiment. The pressure roller  22  rotates counterclockwise in  FIG. 1 . 
     In the present embodiment, as illustrated in  FIG. 3 , the fixing device  20  includes the two temperature sensors, namely, the first and second temperature sensors  28 A and  28 B, disposed adjacent to a center portion and an end portion of the pressure roller  22  in the width direction to detect the surface temperature of the pressure roller  22 . The first temperature sensor  28 A is to detect the temperature of the center portion of the pressure roller  22  in the width direction, and the second temperature sensor  28 B is to detect the temperature of the end portion of the pressure roller  22  in the width direction. For example, when small size sheets P are successively fed, the first temperature sensor  28 A detects the temperature of the pressure roller  22  corresponding to a small sheet range M, and the second temperature sensor  28 B detects the temperature of the pressure roller  22  corresponding to a non-sheet range N. Then, the controller  60  compares the detection result generated by the first temperature sensor  28 A with that generated by the second temperature sensor  28 B, and determines whether or not the non-sheet range N is overheated. When it is determined that the non-sheet range N is overheated, the image forming apparatus  1  enters a fixing temperature adjustment mode, in which an interval between large size sheets P is set to an increased interval. This adjustment is effective to suppress the occurrence of defective fixing such as hot offset in the end portions in the width direction (corresponding to the non-sheet range N in the case of small sheet size) when images are fixed on large size sheets. In particular, the fixing device  20  according to the present embodiment is of energy-saving type having an enhance efficiency in transmitting heat from the heat source (heater) to the fixing rotator, and the amount of heat diffused in the width direction of the fixing rotator is smaller. Accordingly, the possibility of overheat in the non-sheet range N is higher. Thus, the temperature control is effective. It is to be noted that, control of the power supply  35  in the fixing temperature adjustment mode is described later with reference to  FIG. 6 . 
     It is to be noted that, although the first and second temperature sensors  28 A and  28 B are respectively disposed to face the center portion and the end portion of the pressure roller  22  in the width direction to determine temperature conditions of the non-sheet range N of the fixing device  20  in the present embodiment, in another embodiments, temperature sensors are respectively disposed to face the center portion and the end portion of the fixing belt  21  in the width direction to determine temperature conditions of the non-sheet range N of the fixing device  20 . 
     Additionally, although the descriptions above concern the fixing device  20  including the fixing belt  21 , the pressure roller  22 , and the halogen heater, the present embodiment can adapt to various types of fixing devices. For example, the present embodiment can adapt to a fixing device employing a fixing roller, a fixing device employing a pressure belt, and a fixing device employing a heater including an excitation coil, a heating resistor, or the like. 
     Next, the configuration and operation of the image forming apparatus  1  according to the present embodiment are described in further detail below. 
       FIGS. 4A, 4B, and 4C  are timing charts of control of the power supply  35  for the transfer roller  7  when the multiple sheets P are successively fed (hereinafter “successive sheet feeding” or “continuous sheet feeding”). 
     The power supply  35  (illustrated in  FIG. 1 ) serving as the bias application device is to apply, in addition to the above-described transfer bias, the cleaning bias to the transfer roller  7  to remove toner adhering to the transfer roller  7 . Specifically, the power supply  35  is capable of changing the value of transfer current supplied to the transfer roller  7 . More specifically, the controller  60  including a central processing unit (CPU), a random access memory (RAM), a read only memory (ROM), and the like changes the value of transferring current applied to the transfer roller  7  by the power supply  35 . 
     It is assumed that hereinafter “X” represents a sheet feeding interval (an interval between sheets, which is a variable in milliseconds) from when the sheet P is sent out from the transfer nip to when the subsequent sheet P is nipped therein while the multiple sheets P are successively fed (successive sheet feeding) in a state in which the photoconductor drum  5  (the image bearer) and the transfer roller  7  are driven, and “Y” is a fixed value (in milliseconds) representing a duration of application of the cleaning bias, which is hereinafter referred to as “cleaning bias application time Y”. The controller  60  controls the power supply  35  so that application of the cleaning bias to the transfer rotator (i.e., transfer roller  7 ) is executed in that sheet feeding interval X when a difference expressed as X−Y exceeds a threshold A. The sheet feeding interval X is changed according to predetermined conditions, and the threshold A (in milliseconds) is predetermined. 
     The threshold A and the fixed value serving as the cleaning bias application time Y are stored in a memory of the controller  60 . The CPU of the controller  60  computes the difference expressed as X−Y. 
     In  FIGS. 4B and 4C , reference character “X 1 ” and “X 2 ” represent sheet feeding intervals that are relatively long (&gt;Y+A) and satisfy X−Y&gt;A. When the sheets P are fed at the sheet feeding interval X 1  or X 2 , the cleaning bias application is executed for the cleaning bias application time Y within the sheet feeding interval X 1  or X 2 . In other words, when the above-mentioned formula is satisfied, regardless of the length of the sheet feeding interval X, the cleaning bias application is executed for an identical or similar time period. Then, out of the sheet feeding interval X, a non-image area bias is applied for time Z (=X−Y, hereinafter “non-image bias application time Z”) except the cleaning bias application time Y. 
     By contrast, reference character “X 0 ” in  FIG. 4A  represents a sheet feeding interval that is shorter (≦Y+A). As illustrated in  FIG. 4A , when the above-mentioned formula is not satisfied, the cleaning bias application is not executed in the sheet feeding interval X 0 . 
     It is to be noted that, when the application time of cleaning bias is divided into multiple number of times in one sheet feeding interval X, the cleaning bias application time Y in the above-mentioned formula means a total time in which the cleaning bias is applied within the sheet feeding interval X. 
     The threshold A is preliminarily determined considering the possibility of deviation in position of the sheet P transported to the transfer nip, a switching time of the bias applied to the transfer roller  7 , and the like. If the threshold A is extremely small, it is possible that the timing at which the sheet P is sent out and the timing at which the sheet P is fed into the transfer nip coincide with the cleaning bias application, and image output is not in time. If the threshold A is extremely large, it is possible that frequency of cleaning bias application is lowered. Accordingly, the threshold A is set properly. 
     As described above, in the present embodiment, even when the sheet feeding interval X is long, adhesion of toner to the back side and the edge face of the sheet P is suppressed since the cleaning bias is applied to the transfer roller  7 , thereby transferring the toner from the transfer roller  7  again onto the photoconductor drum  5  in the sheet feeding interval X. Additionally, since the cleaning bias application is executed only when the cleaning bias application time Y is available within the sheet feeding interval X, the sheet feeding interval X is not increased for the cleaning bias application. Accordingly, productivity in successive sheet feeding is not degraded by the cleaning bias application. 
     Yet additionally, since the cleaning bias application time Y is a fixed value in the first embodiment, the cleaning bias application time Y is not increased even when the sheet feeding interval X is longer. This is advantageous in alleviating damage (electrical hazard), caused by the cleaning bias, given to the photoconductor drum  5 , which directly contacts the transfer roller  7  during intervals between sheets P. Consequently, creation of substandard images with streaky image density unevenness is inhibited. 
     It is to be noted that, as illustrated in  FIG. 4A , when the sheet feeding interval X 0  is short, the above-described cleaning of the transfer roller  7  is not performed. When the sheet feeding interval X is short (X 0  in  FIG. 4A ), the amount of toner transferred from the photoconductor drum  5  to the transfer roller  7  in intervals between the sheets P is small, and the small amount of toner adhering to the transfer roller  7  moves to the subsequent sheet P. The amount of toner transferred onto the subsequent sheet P at that time is not noticeable. Thus, the transfer roller  7  is cleaned (i.e., self-cleaning). 
     The cleaning bias application time Y (fixed value) is set to a time period during which the transfer roller  7  makes one revolution (a complete turn) or rotates further. The transfer roller  7  is cleaned entirely in the circumferential direction (in the direction of arc) by applying the cleaning bias for the period equivalent to one revolution or longer. However, it is possible that toner or the like is not thoroughly removed from the transfer roller  7  by application of cleaning bias for the period equivalent to one revolution. Therefore, in the present embodiment, the cleaning bias is applied to the transfer roller  7  for a period equivalent to 3.9 revolutions of the transfer roller  7 . Specifically, a first cleaning bias (CLEANING BIAS  1  in  FIGS. 8 and 9 ) in negative polarity is applied thereto for a period equivalent to three revolutions, and a second cleaning bias (CLEANING BIAS Y 2  in  FIGS. 8 and 9 ) in positive polarity is applied thereto for a period equivalent to 0.9 revolution. 
     Although cleaning effects are enhanced when the application time (Y, fixed value) of those cleaning biases is set to a relatively long duration, the execution of cleaning bias application, which is determined according to the formula X−Y&gt;A, is less likely to occur. Additionally, excessive application of those cleaning biases may damage the photoconductor drum  5 . Accordingly, the application time thereof is determined considering the various factors. 
     Additionally, in the cleaning bias application according to the first embodiment, referring to  FIGS. 4B and 4C , after the first cleaning bias opposite in polarity (negative) to the transfer bias (positive) is applied to the transfer roller  7 , the second cleaning bias (positive) identical in polarity to the transfer bias is applied to the transfer roller  7 . 
     This operation is effective since the toner adhering to the non-image areas (background) of the photoconductor drum  5  includes a small amount of reversely charged toner in addition to normally charged toner, and both are transferred onto the transfer roller  7  in the sheet feeding intervals X. The normally charged toner (having negative charges) is returned to the photoconductor drum  5  by applying the negative first cleaning bias to the transfer roller  7 . By contrast, the reversely charged toner (having positive charges) is returned to the photoconductor drum  5  by applying the positive second cleaning bias to the transfer roller  7 . With this operation, the toner adhering to the transfer roller  7  can be fully removed. 
     It is to be noted that, referring to  FIGS. 4B and 4C , the cleaning bias is smaller in absolute value than the transfer bias (applied in the range of the sheet P in  FIGS. 4A through 4C ). 
     With this setting, damage given to the photoconductor drum  5  by the cleaning bias is reduced. 
     Referring to  FIGS. 4B and 4C , when the cleaning bias application is executed in the sheet feeding interval X according to the above-mentioned formula, the power supply  35  to apply the bias to the transfer roller  7  is controlled not to start cleaning bias application immediately after the start of the sheet feeding interval X but to end the cleaning bias application immediately before the end of that sheet feeding interval X (or prior to a margin B before the end of the sheet feeding interval X). That is, the controller  60  controls the power supply  35  to execute the cleaning bias application not a former part of the sheet feeding interval X but a latter part of the sheet feeding interval X considering the following. 
     In a case where the sheet feeding interval X is long and the cleaning bias application is executed immediately after the start of the sheet feeding interval X, it is possible that the transfer roller  7  is again soiled with toner before the sheet feeding interval X ends. 
     Specifically, a time Z′ from the start of the sheet feeding interval X to the start of application of the cleaning bias is expressed as: 
     
       
         
           
             
               
                 
                   
                     Z 
                     ′ 
                   
                   = 
                     
                   ⁢ 
                   
                     X 
                     - 
                     Y 
                     - 
                     B 
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     Z 
                     - 
                     B 
                   
                 
               
             
           
         
       
     
     wherein X represents the sheet feeding interval (variable), Y represents the cleaning bias application time (fixed value), B represents the margin, and Z represents the non-image bias application time. In this formula, the margin B (in milliseconds) is either a fixed value or a multiplication of the sheet feeding interval X with a predetermined coefficient. 
     With this control, the transfer roller  7  is efficiently cleaned in the sheet feeding interval X. It is to be noted that, in the present embodiment, the non-image area bias is applied to the transfer roller  7  also in the period corresponding to the margin B. 
     Additionally with reference to  FIGS. 4B and 4C , in the present embodiment, the power supply  35  is controlled to set the value of the non-image area bias, which is the transfer current flowing to the transfer roller  7  except the period in which the cleaning bias application is executed out of the sheet feeding interval X, to 0 μA. In  FIG. 4A , similarly, when the cleaning bias application is not executed, the value of transfer current flowing to the transfer roller  7  is set to 0 μA except the period of transfer process in which the transfer bias is applied to the transfer roller  7 . 
     Specifically, If, in the period except the cleaning bias application, the transfer current (non-image area bias) is set to a large value in positive side, the normally charged toner (having negative charges) is attracted to the transfer roller  7 . By contrast, if the transfer current (non-image area bias) is set to a large value in negative side in the period except the cleaning bias application, the reversely charged toner (having positive charges) is attracted to the transfer roller  7 . Then, it is possible that soiling of the transfer roller  7  accumulates as the sheet feeding interval X increases. Therefore, to efficiently remove toner from the transfer roller  7 , the transfer current of 0 μA (non-image area bias) is applied to the transfer roller  7  immediately after the start of the sheet feeding interval X, and subsequently the predetermined cleaning bias is applied to the transfer roller  7 . Thus, adhesion of toner to the back side and the edge face of the sheet P is suppressed. 
     It is to be noted that, in the first embodiment, before a printing job, specifically, before the transfer process onto the sheet P is executed, the power supply  35  applies a cleaning bias to the transfer roller  7  as pre-job cleaning. 
     Specifically, immediately after the start of the image forming operation (printing), the power supply  35  applies a pre-job cleaning bias to the transfer roller  7  for a period equivalent to one revolution of the transfer roller  7  or longer. The pre-transfer cleaning bias is smaller in absolute value than the transfer bias and opposite in polarity to the transfer bias. 
     With this operation, even if floating toner adheres to the transfer roller  7  while the image forming apparatus  1  is left unused before image formation is started, such toner is removed from the transfer roller  7  before the transfer process. 
     As described above, the controller  60  sets and changes the length of the sheet feeding interval X in successive sheet feeding in accordance with the predetermined conditions in the image forming apparatus  1 . 
     The conditions according to which sheet feeding interval is determined in the present embodiment include at least one of an operating condition of the sheet processing apparatus  50  to process the sheets P output from the image forming apparatus  1 , the temperature conditions of the non-sheet range N in the fixing device  20 , recognized according to detection results generated by the first and second temperature sensors  28 A and  28 B, and temperature around the photoconductor drum  5  detected by the temperature and humidity sensor  48 . 
     Specifically, similar to typical image forming apparatuses, in the image forming apparatus  1 , an interval between feeding of a single sheet and another sheet or an interval between one copy (one set) of multiple sheets and another copy of the multiple sheets is increased when the sheet processing apparatus  50  performs post-processing, such as stapling, folding, or punching, of the sheet or a bundle of sheets. That is, the sheet feeding interval X is increased to secure sufficient time for the sheet processing apparatus  50  to perform the post-processing of sheets. 
       FIG. 5  is a timing chart of control of the power supply  35  for the transfer roller  7  when the sheet processing apparatus  50  staples multiple bundles (i.e., multiple copies) each including five sheets P. 
     In this case, the sheet feeding interval X between the first copy including sheets P 1  through P 5  and the second copy including the sheets P 6  through P 10  is set to the increased length of time (sheet feeding interval X 3  in  FIG. 5 ), and the cleaning bias application is executed for the fixed time (Y) in a latter part of the sheet feeding interval X 3 . 
     Additionally, as mentioned above, in the image forming apparatus  1  according to the first embodiment, when the controller  60  recognizes the overheating of the non-sheet range N after successive feeding of small size sheets, the image forming apparatus  1  enters the fixing temperature adjustment mode before a large size sheet is subsequently fed. Then, the sheet feeding interval X is set to the increased length of time. The fixing temperature adjustment mode is to secure time to equalize the distribution of temperature in the fixing rotator in the width direction. 
       FIG. 6  is a timing chart of control of the power supply  35  for the transfer roller  7  when the overheating of the non-sheet area N of the fixing device  20  is recognized. 
     It is assumed that, out of the multiple sheets P N−2  through P N+2 , successively fed to the transfer nip, the sheets P N−2  through P N  are small size sheets and the sheets P N  through P N+2  are large size sheets. In this case, the sheet feeding interval X after successive feeding of small size sheets P N−2  through P N  and before feeding of the large size sheet P N+1  is set to the increased length of time (sheet feeding interval X 4  in  FIG. 6 ), the cleaning bias application is executed for the fixed time (Y) in a latter part of the sheet feeding interval X 4 . 
     Additionally, the image forming apparatus  1  illustrated in  FIG. 1  includes the temperature and humidity sensor  48  serving as a temperature detector to detect a temperature adjacent to the photoconductor drum  5 . The temperature and humidity sensor  48  serves as an environment detector, described later, as well. When the temperature and humidity sensor  48  detects a temperature at or higher than a threshold, the controller  60  sets the image forming apparatus  1  in a low-productivity mode, in which each sheet feeding interval X during successive sheet feeding is set to an increased length of time (sheet feeding interval X 5  in  FIG. 7 ), to restrict temperature rise in the image forming apparatus  1 . If an interior (adjacent to the photoconductor drum  5  in particular) of the image forming apparatus  1  is overheated, there arises a risk of fusing of toner and adhesion of fused toner to the image forming components. The present embodiment particularly addresses this inconvenience since the toner having a lower melting point is used. 
       FIG. 7  is a timing chart of control of the power supply  35  for the transfer roller  7  in the low-productivity mode due to the temperature rise adjacent to the photoconductor drum  5 . 
     In the low-productivity mode, each sheet feeding interval X during successive feeding of sheets P N  through P N+4  in  FIG. 7  is set to the increased length of time (sheet feeding interval X 5  in  FIG. 7 ). Similar to the control described with reference to  FIGS. 4B through 6 , the cleaning bias application is executed for the fixed time (Y) in a latter part of each sheet feeding interval X 5 . 
     It is to be noted that the sheet feeding interval X is also changed depending on sheet type as well (i.e., thickness, smoothness, of the like of the sheet). For example, when the sheet P is thicker (such as cardboard), the sheet feeding interval X is typically set to an increased length of time, and control of the power supply  35  in such a case can be similar to that described above. 
     Additionally, the conditions under which the sheet feeding interval X is increased are not limited to those described above. Alternatively, for example, the sheet feeding interval X is increased when duplex printing is executed. 
     Further, a sheet conveyance speed at which the sheet P is transported to the transfer nip (identical or similar to the process speed defined as the linear velocity of the photoconductor drum  5 ) is variable, and the power supply  35  is controlled to adjust the magnitude of the cleaning bias in accordance with the sheet conveyance speed. 
       FIG. 8  is a table of correction coefficients of the first cleaning bias and the second cleaning bias for each process speed when the process speed is changed in three stages as one example. 
     In the case of  FIG. 8 , a standard process speed is 260 mm/s, and the correction coefficient at that time is 100. When the process speed is reduced from the standard process speed, the magnitude of the cleaning bias is reduced at the rate of the correction coefficient shown in  FIG. 8 . For example, when the process speed is set at 150 mm/s, the magnitude of the first cleaning bias is 83/100 of the first cleaning bias for the standard process speed of 260 mm/s. 
     The magnitude of the cleaning bias is thus adjusted because the bias relative to the value of transfer current changes as the process speed changes. The bias (i.e., current value) is set properly corresponding to the process speed. By adjusting the cleaning bias as described above, the transfer roller  7  can be cleaned reliably even when the process speed changes. It is to be noted that the process peed is changed, for example, to maintain the fixing performance and gloss of the image with a high accuracy even when the property (such as thickness or smoothness) of the sheet P is different. 
     In yet another embodiment, the power supply  35  for the transfer roller  7  is controlled to adjust the magnitude of the cleaning bias according to a detection result such as an absolute humidity detected by the temperature and humidity sensor  48 , serving as the environment detector. 
       FIG. 9  is a table of example settings of the first cleaning bias and the second cleaning bias in accordance with the absolute humidity. 
     The control according to the table shown in  FIG. 9  is effective because the occurrence of soil with toner of the transfer roller  7  is affected largely by environments. The occurrence of soil with toner tends to increase as the absolute humidity increases. Accordingly, as illustrated in  FIG. 9 , when the absolute humidity is higher, the absolute value of output of cleaning bias (i.e., the transfer current value) is set to a higher value to enhance performance of cleaning of the transfer roller  7 . 
     Descriptions are given below of effects of the above-described embodiments confirmed by an experiment executed by the inventor, with reference to  FIG. 10 . 
       FIG. 10  is a graph of experimentally obtained changes over time of cleanliness rating (indicating the degree of adhesion of toner) of the edge face of the sheet P. 
     In  FIG. 10 , the abscissa represents the number of sheets fed to the transfer nip, and The ordinate in  FIG. 10  represents the edge face cleanliness rating, and level 2 means that the soil of the edge face of the sheet P is acceptable. The level ascends as the edge face cleanliness is improved, and level 5 means that the edge face is not soiled. The edge face of the sheet P is likely to be soiled with toner in the image forming apparatus under 1 a temperature of 27° C. and a humidity of 80%, and the experiment was performed under these conditions. Additionally, a transfer roller at or near its end of operational life was used as the transfer roller  7 , and the printing speed was set to 30 copies per minute (CPM). 
       FIG. 10  includes three different graphs, obtained under different conditions: 
     1) a graph indicated by alternate long and short dashed lines, representing the results when the sheet feeding interval was set to a short length of time (X 1  in  FIG. 4B ) and the transfer roller cleaning was not executed; 
     2) a graph indicated by broken lines, representing the results when the sheet feeding interval was set to an increased length of time (X 3  in  FIG. 5 , about 10 seconds) and the transfer roller cleaning was not executed; and 
     3) a graph indicated by a solid line, representing the results when the sheet feeding interval was set to an increased length of time (X 3  in  FIG. 5 , about 10 seconds) and the transfer roller cleaning was executed according to the first embodiment. 
     According to the results illustrated in  FIG. 10 , it is confirmed that the transfer roller  7  is efficiently cleaned in intervals between sheets and the soil with toner is alleviated by controlling the power supply  35  to supply bias thereto according to the first embodiment. 
     As described above, in the first embodiment, the controller  60  controls the power supply  35  so that, when the difference expressed as X−Y (Y is the fixed value representing the cleaning bias application time and X is the variable representing the sheet feeding interval, changed according to the predetermined conditions) exceeds the threshold A during successive sheet feeding, and cleaning of the transfer roller  7  is executed during that sheet feeding interval. 
     In other words, when the sheet feeding interval X between feeding of a sheet to the transfer nip and feeding of a subsequent sheet thereto during successive sheet feeding, which is changed according to the predetermined condition, exceeds a threshold, the non-image area bias is applied to the transfer rotator for the time (non-image bias application time Z) out of the sheet feeding interval X. Then, the cleaning bias is applied for the time Y expressed as X−Z, and the non-image bias application time Z increases as the sheet feeding interval X increases. 
     This control efficiently suppress soil of the back side and the edge face of the sheet P transported to the transfer nip, resulting from the toner transferred from the photoconductor drum  5  and adhering to the transfer roller  7  while inhibiting acceleration of degradation of the photoconductor drum  5  (the image bearer) caused by the cleaning bias and further inhibiting reduction in productivity in successive sheet feeding resulting from the cleaning bias application. 
     Second Embodiment 
     A second embodiment is described below with reference to  FIGS. 11A, 11B, and 11C . 
       FIGS. 11A, 11B, and 11C  are timing charts of control of the power supply  35  for the transfer roller  7  according to the second embodiment.  FIGS. 11A, 11B, and 11C  respectively correspond to  FIGS. 4A, 4B, and 4C . 
     In the second embodiment, the cleaning bias application time Y is a variable, which is different from the above-described first embodiment in which the cleaning bias application time is a fixed value. 
     Similar to the above-described first embodiment, in the second embodiment, the power supply  35  (illustrated in  FIG. 1 ) serves as the bias application device to apply the transfer bias, the cleaning bias, and the non-image bias to the transfer roller  7 . 
     Similar to the above-described first embodiment, in the second embodiment, the sheet feeding interval X represents a duration from when a sheet P is sent out from the transfer nip to when a subsequent sheet P is nipped therein while multiple sheets P are successively fed to the transfer nip in the state in which the photoconductor drum  5  (the image bearer) is driven, and the sheet feeding interval is changed according to the predetermined condition. Additionally, when the sheet feeding interval X exceeds a predetermined threshold, application of the non-image area bias is executed for the non-image bias application time Z, out of the sheet feeding interval X, and application of the cleaning bias is executed for the time expressed as X−Z. In the second embodiment, similarly, the non-image bias application time Z is set to an increased time as the sheet feeding interval X increases. 
     If the cleaning bias application time Y is increased by the amount equal to the increase in the sheet feeding interval X changed according to the predetermined condition, the is a risk that damage (electrical hazard) given by the cleaning bias to the photoconductor drum  5 , which directly contacts the transfer roller  7  during intervals between sheets P, increases accordingly. In this case, the possibility of image failure, such as streaky image density unevenness, increases. 
     By contrast, in the second embodiment, the non-image bias application time Z is increased as the sheet feeding interval X increases similar to the above-described first embodiment. Accordingly, even if the sheet feeding interval X becomes longer, the cleaning bias application time Y (=X−Z) is not made too long. Thus, the damage to the photoconductor drum  5  can be suppressed. 
     In the second embodiment, the cleaning bias application time Y is changed in accordance with the sheet feeding interval X, but not increased by the amount equal to the increase in the sheet feeding interval X. Specifically, referring to  FIGS. 11B and 11C , when the cleaning bias application is to be executed and the sheet feeding interval X is set to the relatively long sheet feeding interval X 2 , the cleaning bias application time Y is set to a cleaning bias application time Y 2  longer than a cleaning bias application time Y 1  for the case in which the sheet feeding interval X is set to the sheet feeding interval X 1  shorter than the sheet feeding interval X 2 . Adjusting the cleaning bias application time Y in accordance with the sheet feeding interval X is advantageous in improving cleaning of the transfer roller  7 . 
     More specifically, it is assumed that “Y 0 ” represents a shortest application time of the cleaning bias applied to the transfer roller  7  (shortest cleaning bias application time Y 0  in milliseconds) to secure cleaning of the transfer roller  7 , and a remaining time (except the shortest cleaning bias application time Y 0  in the sheet feeding interval X, changed according to the predetermined conditions, is expressed as “X−Y 0 ”. The power supply  35  is controlled such that the cleaning bias application is executed during the sheet feeding interval X when the time X−Y 0  exceeds a predetermined threshold Λ′ (X−Y 0 &gt;A′). 
     In  FIG. 11B , the sheets P are fed at the sheet feeding interval X 1  that is sufficiently long and satisfies X−Y 0 &gt;A′. That is, X 1 &gt;Y 0 +A′ is satisfied in  FIG. 11B . In this case, cleaning bias application is executed for the cleaning bias application time Y 1  within the sheet feeding interval X 1 . Similarly, in  FIG. 11C , the sheets P are fed at the sheet feeding interval X 2  (&gt;X 1 &gt;Y 0 +A′), which satisfies the above-described relation (X 2 &gt;Y 0 +A′). In this case, cleaning bias application is executed for the cleaning bias application time Y 2  (&gt;Y 1 ) in the sheet feeding interval X 2 . 
     By contrast, reference character “X 0 ” in  FIG. 11A  represents a sheet feeding interval that is shorter and does not satisfies the above-described relation (X 0 ≦Y 0 +A′). In this case, the cleaning bias application is not executed in the sheet feeding interval X 0 . 
     In the setting in which the time Z is a fixed value and the cleaning bias application time Y is elongated by the amount equal to the increase in the sheet feeding interval X, the cleaning bias application time Y is expressed as Y 2 =Y 1 +(X 2 −X 1 ). As described above, in this setting, there arises the risk that the cleaning bias application time Y 2  is excessively long when the sheet feeding interval is long. Accordingly, the risk of damage to the photoconductor drum  5  resulting from the cleaning bias increases. 
     By contrast, in the second embodiment, the non-image bias application time Z is set to an increased time as the sheet feeding interval X increases. That is, as illustrated in  FIGS. 11B and 11C , the non-image bias application time Z 2  (&gt;Z 1 ) for the case of the longer sheet feeding interval X 2  (&gt;X 1 ) is set to a longer length of time than the non-image bias application time Z 1  for the shorter sheet feeding interval X 1 . Therefore, even in the case of the long sheet feeding interval X 2 , the cleaning bias application time Y 2  is not too long. Thus, damage given to the photoconductor drum  5  by the cleaning bias is reduced while securing cleaning performance. 
     The shortest cleaning bias application time Y 0  is equal to or longer than a time period during which the transfer roller  7  (transfer rotator) makes one revolution. The cleaning bias application time Y 1  or Y 2  for the increased sheet feeding interval X 1  or X 2  is equal to or longer than the shortest cleaning bias application time Y 0 . The transfer roller  7  is cleaned entirely in the circumferential direction (in the direction of arc) by applying the cleaning bias for the period equivalent to one revolution or longer. 
     As described above, also in the second embodiment, when the sheet feeding interval X, which is changed according to the predetermined condition and means an interval between feeding of a sheet to the transfer nip and feeding of a subsequent sheet thereto during successive sheet feeding, exceeds a threshold, the non-image are bias is applied to the transfer rotator for the time Z (non-image bias application time) out of the sheet feeding interval X. Then, the cleaning bias is applied for the time Y (=X−Z), and the non-image bias application time Z increases as the sheet feeding interval X increases. This control efficiently suppress soil of the back side and the edge face of the sheet P transported to the transfer nip, resulting from the toner transferred from the photoconductor drum  5  and adhering to the transfer roller  7  while inhibiting acceleration of degradation of the photoconductor drum  5  (the image bearer) caused by the cleaning bias and further inhibiting reduction in productivity in successive sheet feeding resulting from the cleaning bias application. 
     It is to be noted that, although the description above concerns the monochrome or single-color image forming apparatus  1  that includes the single image forming unit  4  including the single photoconductor drum  5 , the features of the above-described embodiments can adapt to multicolor image forming apparatuses including multiple photoconductor drums each corresponding to a different color toner. 
     Additionally, in the description above, the features of the embodiments are applied to the image forming apparatus  1  in which the toner image is transferred from the photoconductor drum  5  serving as the image bearer directly onto the sheet P. Alternatively, the features of the embodiments can adapt to image forming apparatuses to transfer a toner image from a photoconductive belt serving as an image bearer onto a sheet and image forming apparatuses to transfer a toner image from an intermediate transfer belt or an intermediate transfer drum serving as an image bearer onto a sheet. 
     Additionally, although the description above concerns the image forming apparatus  1  employing the transfer roller  7  as the transfer rotator, the features of the embodiments can adapt to image forming apparatuses in which a transfer belt or a secondary transfer roller is used as the transfer rotator. 
     In such configurations, effects similar to those attained by the embodiments are also attained. 
     Each of  FIGS. 12A and 12B  is a schematic view illustrating a main part of a multicolor image forming apparatus in which the image forming unit  4  includes multiple photoconductor drums  5  ( 5 Y,  5 M,  5 C, and  5 K). Each of the image forming apparatus illustrated in  FIGS. 12A and 12B  includes primary transfer rollers  39 Y,  39 M,  39 C, and  39 K (collectively “primary transfer rollers  39 ”) and an intermediate transfer belt  38  serving as the image bearer. The image forming apparatuses illustrated in  FIGS. 12A and 12B  use the transfer roller  7  as the secondary transfer roller, and a transfer backup roller  36  is disposed to face and contact the transfer roller  7  (serving as the transfer rotator) via the intermediate transfer belt  38 . The intermediate transfer belt  38  is entrained around a support roller  11 , the transfer backup roller  36 , the primary transfer rollers  39 , and the like. 
     It is to be noted that the suffixes Y, M, C, and K attached to each reference numeral indicate only that components indicated thereby are used for forming yellow, magenta, cyan, and black images, respectively, and hereinafter may be omitted when color discrimination is not necessary. Further, except the differences described above or below, the configurations illustrated in  FIGS. 12A and 12B  are similar to that illustrated in  FIG. 1 . Thus, redundant descriptions are omitted. 
     Specifically, the four primary transfer rollers  39  are pressed against the corresponding photoconductor drums  5  via the intermediate transfer belt  38 , and four contact portions between the primary transfer rollers  39  and the corresponding photoconductor drums  5  are hereinafter referred to as primary transfer nips. Each primary transfer roller  39  receives a primary transfer bias opposite in polarity to toner. 
     While rotating in the direction indicated by the arrow shown in  FIG. 12A or 12B , the intermediate transfer belt  38  sequentially passes through the primary transfer nips between the photoconductor drums  5  and the corresponding primary transfer rollers  39 . Then, the single-color toner images are formed on the photoconductor drums  5  through the charging, exposure, and developing processes similar to the above-described embodiments, and transferred from the respective photoconductor drums  5  primarily and superimposed one on another, into a multicolor toner image, on the intermediate transfer belt  38 . 
     Then, the intermediate transfer belt  38  carrying the multicolor toner image reaches a position facing the transfer roller  7 . At that position, the transfer backup roller  36  and the transfer roller  7  press against each other via the intermediate transfer belt  38 , and the contact portion therebetween is hereinafter referred to as a secondary transfer nip. The multicolor toner image formed on the intermediate transfer belt  38  is transferred onto the sheet P (recording medium) transported to the secondary transfer nip (secondary transfer process). 
     In the configuration illustrated in  FIG. 12A , the power supply  35  applies the transfer bias and the cleaning bias to the transfer roller  7  serving as the secondary transfer roller similar to the above described embodiments so that standard transfer process (secondary transfer process) and the transfer roller cleaning are executed. 
     By contrast, in the configuration illustrated in  FIG. 12B , the power supply  35  applies the transfer bias and the cleaning bias to not the transfer roller  7  but the transfer backup roller  36 . In this case, timings at which the transfer bias and the cleaning bias are applied to the transfer backup roller  36  are similar to those described with reference to  FIGS. 4A through 7  or those for the configuration illustrated in  FIG. 12A . However, the polarity of the transfer bias and the cleaning bias applied to the transfer backup roller  36  is opposite the polarity of the transfer bias and the cleaning bias described with reference to  FIGS. 4A through 7  or those biases for the configuration illustrated in  FIG. 12A . For example, the case of low-productivity mode is described with reference to  FIG. 7 . 
     In contrast to those shown in  FIG. 7 , when the target of bias application is the transfer backup roller  36 , the transfer bias negative in polarity is applied to the transfer backup roller  36  for the standard transfer process. In the sheet feeding interval X 3 , the first cleaning bias that is positive in polarity is applied to the transfer backup roller  36 , and subsequently the second cleaning bias that is negative in polarity is applied thereto, thereby cleaning the transfer roller  7 . 
     Additionally, in another embodiment, the transfer bias, the cleaning bias, and the non-image area bias are applied to each of the transfer roller  7  and the transfer backup roller  36 . In this case, application of the transfer bias, the cleaning bias, and the non-image area bias for the configuration illustrated in  FIG. 12A  is concurrent with application of those for the configuration illustrated in  FIG. 12B . In another embodiment, at least one of the transfer bias, the cleaning bias, and the non-image area bias may be applied to the transfer roller  7 , and the rest may be applied to the transfer backup roller  36 . 
     In such configurations, effects similar to those attained by the above-described embodiments are also attained. 
     Additionally, although the non-image area bias is set to 0 μA in the above-described embodiments, the non-image area bias is not limited thereto. Alternatively, the non-image area bias applied to the transfer roller  7  (or the transfer backup roller  36 , or both of the transfer roller  7  and the transfer backup roller  36 ) is set a value smaller in absolute value than the cleaning bias. 
     Specifically, in the non-image bias application time Z, in which the cleaning bias application is not executed in the sheet feeding interval X, the power supply  35  is controlled to keep the value of current that flows to the transfer roller  7  to a predetermined current value smaller in absolute value than the current value of the cleaning bias. For example, when the cleaning bias includes the first cleaning bias opposite in polarity to the transfer bias and the second cleaning bias identical in polarity to the transfer bias, the predetermined current value is smaller in absolute value than each of the first cleaning bias and the second cleaning bias. By contrast, when the cleaning bias includes at least one bias opposite in polarity to the transfer bias and does not include a bias identical in polarity to the transfer bias, the predetermined current value is smaller in absolute value than the at least one opposite polarity bias. The non-image area bias, however, is preferably small not to attract neither the normally charged toner nor the reversely charged toner to the transfer roller  7 . 
     Further, although the power supply  35  (the bias application device) according to the above-described embodiments is controlled under constant current control, alternatively, the power supply  35  is controlled under constant voltage control in another embodiment. In this case, it is preferable that the power supply  35  is controlled, under constant voltage, to keep the value of the non-image area bias at 0 V similarly. 
     In such configurations, effects similar to those attained by the above-described embodiments are also attained. 
     Additionally, the above-described features can be embodied as an image forming method that includes a step of feeding multiple sheets successively to a transfer nip between a transfer rotator and a backup roller, a step of applying, to at least one of the transfer rotator and the backup roller, a transfer bias to transfer a toner image from an image bearer onto a sheet; a step of keeping a current applied to at least one of the transfer rotator and the backup roller at a value (preferably 0 μm) smaller in absolute value than a cleaning bias for a time Z out of a sheet feeding interval X (interval between sheets) during successive feeding of multiple sheets, and a step of applying the cleaning bias (smaller in absolute value than the transfer bias) to at least one of the transfer rotator and the backup roller for a time expressed as X−Z. 
     Numerous additional modifications and variations are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the present disclosure may be practiced otherwise than as specifically described herein. Such variations are not to be regarded as a departure from the scope of the present disclosure and appended claims, and all such modifications are intended to be included within the scope of the present disclosure and appended claims. The number, position, and shape of the components of the image forming apparatus described above are not limited to those described above.