Image forming apparatus

Abstract

The present invention provides an image forming apparatus. The bias condition determination section of the image forming apparatus respectively performs: a first approximation formula determination operation of obtaining the DC component of the developing current at at least three inter-peak voltages included in a first measurement range and determining a first approximation formula representing the relationship between the inter-peak voltage and the DC component of the developing current; a second approximation formula determination operation of obtaining the DC component of the developing current at at least three inter-peak voltages included in a second measurement range larger than the first measurement range and determining a second approximation formula representing the relationship between the inter-peak voltage and the DC component of the developing current; and a reference voltage determination operation of determining the inter-peak voltage at the intersection of the first approximation formula and the second approximation formula as the reference inter-peak voltage.

Description

Technical Field

[0001] The present invention relates to an image forming apparatus including a developing device that applies a two-component developing method. Background Art

[0002] Conventionally, as an image forming apparatus for forming an image on a thin sheet, an image forming apparatus including a photosensitive drum (image carrier), a developing device, and a transfer member is known. If an electrostatic latent image formed on the photosensitive drum is developed by a toner using the developing device, a toner image is formed on the photosensitive drum. The toner image is transferred to the thin sheet by the transfer member. As a developing device applied to such an image forming apparatus, a two-component developing technique using a developer containing a toner and a carrier is known.

[0003] In the two-component developing technique, the developing device has a developing roller, and a suitable toner image is formed by applying a developing bias in which an AC bias is superimposed on a DC bias to the developing roller. In particular, if the Vpp (peak-to-peak voltage) in the AC bias is set high, the image density increases, and there is a tendency to improve the texture of a halftone image and to improve the half pitch unevenness that easily occurs in the rotation cycle of the developing roller. On the other hand, if Vpp is set too high, leakage may occur in the developing nip portion where the photosensitive drum and the developing roller face each other. Therefore, a technique for appropriately setting Vpp of the AC bias in the developing bias has been proposed.

[0004] In the above prior art, the image forming conditions are changed based on the developing current and the charge amount of the toner. If Vpp of the developing bias is increased as described above, the DC component in the developing current increases because the developing amount of the toner increases. Therefore, in the prior art, while increasing Vpp, the developing current is confirmed, and a suitable Vpp is set to achieve a target image density (developing current).

[0005] However, in the adjustment of the image density based on such Vpp, there are the following problems: If the charge amount of the toner in the developing device changes, the image density changes, and if the developing gap corresponding to the distance between the photosensitive drum and the developing roller changes, the AC electric field formed between the two changes, and thus the image density also changes. That is, if Vpp is continuously changed, the image density will indeed change. Therefore, the problem is that although Vpp can be selected as an adjustment parameter for the image density, in reality, the image density depends on the setting region of Vpp and is liable to change due to interference. Summary of the Invention

[0006] In order to solve the above problems, an object of the present invention is to set a peak-to-peak voltage having robustness against changes in image density due to interference with respect to the AC bias of the developing bias of a developing device that applies a two-component developing method in an image forming apparatus.

[0007] An image forming apparatus according to one aspect of the present invention is capable of performing an image forming operation of forming an image on a sheet, and includes: an image carrier that rotates and has a surface that allows an electrostatic latent image to be formed and bears a toner image after the electrostatic latent image is developed by toner; a charging device that charges the image carrier to a predetermined charging potential; an exposure device that is disposed downstream of the charging device in the rotational direction of the image carrier and forms the electrostatic latent image by exposing the surface of the image carrier charged to the predetermined charging potential according to predetermined image information; a developing device that is disposed opposite to the image carrier in a predetermined developing nip portion downstream of the exposure device in the rotational direction, and includes a developing roller that rotates and has a circumferential surface that bears a developer composed of toner and a carrier, and forms the toner image by supplying toner to the image carrier; a transfer unit that transfers the toner image borne on the image carrier to a sheet; a developing bias application unit that can apply a developing bias in which an alternating voltage is superimposed on a direct current voltage to the developing roller; a current detection unit that can detect a direct current component of a developing current flowing between the developing roller and the developing bias application unit; and a bias condition determination unit that executes a bias condition determination mode for determining a reference peak-to-peak voltage based on the direct current component of the developing current, the direct current component of the developing current being detected by the current detection unit when the developing bias is applied to the developing roller in response to a predetermined measurement latent image formed on the image carrier and the measurement latent image is developed by toner, the reference peak-to-peak voltage being a reference for the peak-to-peak voltage of the alternating voltage of the developing bias applied to the developing roller in the image forming operation, and the bias condition determination unit respectively executes in the bias condition determination mode: a first approximation formula determination operation of respectively obtaining the direct current component of the developing current and determining a first approximation formula that represents the relationship between the first measurement peak-to-peak voltages within the first measurement range and the obtained direct current component of the developing current, under the condition that the peak-to-peak voltages of the alternating current component of the developing bias are respectively set to at least three first measurement peak-to-peak voltages included in a predetermined first measurement range; a second approximation formula determination operation of respectively obtaining the direct current component of the developing current and determining a second approximation formula that represents the relationship between the second measurement peak-to-peak voltages within the second measurement range and the obtained direct current component of the developing current, under the condition that the peak-to-peak voltages of the alternating current component of the developing bias are respectively set to at least three second measurement peak-to-peak voltages included in a second measurement range, the second measurement range being set such that the minimum value is larger than the maximum value of the first measurement range, and the second approximation formula being a unary approximation formula that represents the relationship between the second measurement peak-to-peak voltages within the second measurement range and the obtained direct current component of the developing current;As well as a reference voltage determination operation, the peak-to-peak voltage at the intersection where the first approximation formula determined by the first approximation formula determination operation and the second approximation formula determined by the second approximation formula determination operation intersect is determined as the reference peak-to-peak voltage.

[0008] According to the present invention, for the alternating current bias of the developing bias of a developing device that employs a two-component developing method in an image forming apparatus, it is possible to set a peak-to-peak voltage that has robustness such that the image density is less likely to change with respect to changes in interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 is a cross-sectional view showing the internal structure of an image forming apparatus according to an embodiment of the present invention.

[0010] Figure 2 is a block diagram showing a cross-sectional view of a developing device and the electrical structure of a control unit according to an embodiment of the present invention.

[0011] Figure 3A is a schematic diagram showing the developing operation of an image forming apparatus according to an embodiment of the present invention.

[0012] Figure 3B is a schematic diagram showing the magnitude relationship between the potentials of an image carrier and a developing roller according to an embodiment of the present invention.

[0013] Figure 4 is a flowchart of AC calibration performed in an image forming apparatus according to an embodiment of the present invention.

[0014] Figure 5 is a flowchart of a first approximation formula determination step of AC calibration performed in an image forming apparatus according to an embodiment of the present invention.

[0015] Figure 6 is a flowchart of a second approximation formula determination step of AC calibration performed in an image forming apparatus according to an embodiment of the present invention.

[0016] Figure 7 is a graph showing the relationship between Vpp and developing current in AC calibration performed in an image forming apparatus according to an embodiment of the present invention.

[0017] Figure 8 is a graph showing the relationship between Vpp and developing current in AC calibration performed in an image forming apparatus according to an embodiment of the present invention.

[0018] Figure 9 is a graph showing the relationship between Vpp and developing current in AC calibration performed in an image forming apparatus according to an embodiment of the present invention.

[0019] Figure 10 This is a flowchart of the second approximation formula determination step of AC calibration performed in the image forming apparatus according to a modified embodiment of the present invention.

[0020] Figure 11 This is a flowchart of a part of the second approximation formula determination step of AC calibration performed in the image forming apparatus according to a modified embodiment of the present invention. Detailed Embodiment

[0021] Hereinafter, based on the accompanying drawings, the image forming apparatus 10 according to the embodiment of the present invention will be described in detail. In the present embodiment, as an example of the image forming apparatus, an in-line color printer is illustrated. The image forming apparatus may also be, for example, a copying machine, a facsimile machine, and a digital multifunction machine thereof. In addition, the image forming apparatus may also form a monochrome (black and white) image. The image forming apparatus 10 is capable of performing an image forming operation of forming an image on a sheet P.

[0022] Figure 1 This is a sectional view showing the internal structure of the image forming apparatus 10. The image forming apparatus 10 includes a device main body 11 having a box-shaped housing structure. Inside the device main body 11, there are provided: a paper feeding unit 12 for supplying the sheet P; an image forming unit 13 for forming a toner image to be transferred onto the sheet P supplied from the paper feeding unit 12; an intermediate transfer unit 14 (transfer unit) for first transferring the toner image; a toner supply unit 15 for supplying toner to the image forming unit 13; and a fixing unit 16 for performing a process of fixing the unfixed toner image formed on the sheet P to the sheet P. In addition, a paper discharging unit 17 is provided at the upper part of the device main body 11, and the sheet P on which the fixing process has been performed in the fixing unit 16 is discharged to the paper discharging unit 17.

[0023] At an appropriate position on the upper surface of the device main body 11, an operation panel (not shown) for inputting operations such as output conditions of the sheet P is provided. On the operation panel, there are provided a power key, a touch panel for inputting output conditions, and various operation keys.

[0024] Inside the device main body 11 and at a position to the right of the image forming unit 13, a sheet conveying passage 111 extending in the vertical direction is formed. In the sheet conveying passage 111, a pair of conveying rollers 112 for conveying the sheet to an appropriate position is provided. In addition, a pair of alignment rollers 113 for correcting the skew of the sheet and feeding the sheet into the nip portion of the secondary transfer described later at a predetermined timing is provided upstream of the nip portion of the sheet conveying passage 111. The sheet conveying passage 111 is a conveying passage for conveying the sheet P from the paper feeding unit 12 to the paper discharging unit 17 via the image forming unit 13 and the fixing unit 16.

[0025] The paper feeding unit 12 includes a paper feed tray 121, a sheet feeding roller 122, and a paper feed roller pair 123. The paper feed tray 121 is removably installed below the apparatus main body 11 and stores a stack of sheet bodies P1 in which a plurality of sheet bodies P are stacked. The sheet feeding roller 122 extracts the topmost sheet body P from the stack of sheet bodies P1 stored in the paper feed tray 121 one by one. The paper feed roller pair 123 feeds the sheet body P extracted by the sheet feeding roller 122 to the sheet body conveyance path 111.

[0026] The paper feeding unit 12 includes a manual paper feeding unit installed on the Figure 1 left side surface shown in the figure. The manual paper feeding unit includes a manual paper feed tray 124, a sheet feeding roller 125, and a paper feed roller pair 126. The manual paper feed tray 124 is a tray for carrying the manually fed sheet body P, and opens from the side surface of the apparatus main body 11 as shown in Figure 1 the figure when manually feeding the sheet body P. The sheet feeding roller 125 extracts the sheet body P carried on the manual paper feed tray 124. The paper feed roller pair 126 feeds the sheet body P extracted by the sheet feeding roller 125 to the sheet body conveyance path 111.

[0027] The image forming unit 13 is configured to form a toner image to be transferred onto the sheet body P, and includes a plurality of image forming units that form toner images of different colors. In the present embodiment, as the image forming units, there are provided a magenta unit 13M that uses a magenta developer, a cyan unit 13C that uses a cyan developer, a yellow unit 13Y that uses a yellow developer, and a black unit 13Bk that uses a black developer, which are arranged in order from the upstream to the downstream in the rotation direction of the intermediate transfer belt 141 described later (from the Figure 1 left side to the right side shown in the figure). Each of the units 13M, 13C, 13Y, and 13Bk includes a photosensitive drum 20 (image carrier) and a charging device 21, a developing device 23, a primary transfer roller 24, and a cleaning device 25 disposed around the photosensitive drum 20. In addition, an exposure device 22 shared by each of the units 13M, 13C, 13Y, and 13Bk is disposed below the image forming unit.

[0028] The photosensitive drum 20 is driven to rotate about its axis and has a cylindrical surface that allows the formation of an electrostatic latent image and carries a toner image in which the electrostatic latent image is visualized by a toner. As an example of the photosensitive drum 20, a well-known amorphous silicon (α-Si) photosensitive drum or an organic (OPC) photosensitive drum is used. The charging device 21 uniformly charges the surface of the photosensitive drum 20 at a predetermined charging potential. The charging device 21 includes a charging roller and a charging cleaning brush for removing the toner attached to the charging roller. The exposure device 22 is arranged on the downstream side of the rotation direction of the photosensitive drum 20 relative to the charging device 21, and has various optical devices such as a light source, a polygonal mirror, a reflecting mirror, and a deflecting mirror. The exposure device 22 performs exposure by irradiating the surface of the photosensitive drum 20 uniformly charged at the charging potential with light modulated based on image data (predetermined image information), thereby forming an electrostatic latent image.

[0029] The developing device 23 is located at a predetermined developing nip portion NP ( Figure 3A ) is disposed opposite to the photosensitive drum 20. The developing device 23 includes a developing roller 231 having a peripheral surface that rotates and carries a developer composed of a toner and a carrier, and forms the toner image by supplying the toner to the photosensitive drum 20.

[0030] The primary transfer roller 24 forms a nip portion with the photosensitive drum 20 via the intermediate transfer belt 141 provided in the intermediate transfer unit 14. The primary transfer roller 24 primarily transfers the toner image on the photosensitive drum 20 onto the intermediate transfer belt 141. The cleaning device 25 cleans the peripheral surface of the photosensitive drum 20 after the toner image is transferred.

[0031] The intermediate transfer unit 14 is arranged in a space provided between the image forming unit 13 and the toner supply unit 15, and includes an intermediate transfer belt 141, a driving roller 142 rotatably supported by a unit frame (not shown), a driven roller 143, a support roller 146, and a density sensor 100. The intermediate transfer belt 141 is an endless belt-shaped rotating member, and is stretched on the driving roller 142, the driven roller 143, and the support roller 146 in such a manner that the circumferential surface side thereof abuts against the circumferential surface of each photosensitive drum 20. The intermediate transfer belt 141 is driven in the circumferential direction by the rotation of the driving roller 142. A belt cleaning device 144 is arranged near the driven roller 143 to remove the toner remaining on the circumferential surface of the intermediate transfer belt 141. The density sensor 100 (density detection unit) is disposed opposite to the intermediate transfer belt 141 on the downstream side of the units 13M, 13C, 13Y, and 13Bk, and detects the density of the toner image formed on the intermediate transfer belt 141 by reflected light (reflection type). In other embodiments, the density sensor 100 may detect the density of the toner image on the photosensitive drum 20, or may detect the density of the toner image fixed on the sheet P.

[0032] Opposite to the driving roller 142, a secondary transfer roller 145 is disposed outside the intermediate transfer belt 141. The secondary transfer roller 145 is pressed against the circumferential surface of the intermediate transfer belt 141, and a transfer nip portion is formed between the secondary transfer roller 145 and the driving roller 142. The toner image transferred onto the intermediate transfer belt 141 for the first time is secondarily transferred onto the sheet P fed from the paper supply unit 12 in the transfer nip portion. That is, the intermediate transfer unit 14 and the secondary transfer roller 145 function as a transfer unit for transferring the toner image carried on the photosensitive drum 20 onto the sheet P. In addition, a roller cleaner 200 for cleaning the circumferential surface is disposed on the driving roller 142.

[0033] The toner supply unit 15 is for storing toner for image formation. In the present embodiment, it includes a magenta toner container 15M, a cyan toner container 15C, a yellow toner container 15Y, and a black toner container 15Bk. These toner containers 15M, 15C, 15Y, 15Bk store the replenishing toner of each color of M / C / Y / Bk respectively. Toner of each color is supplied from the toner discharge port 15H formed on the bottom surface of the container to the developing devices 23 of the image forming units 13M, 13C, 13Y, 13Bk corresponding to the colors of M / C / Y / Bk.

[0034] The fixing unit 16 includes: a heating roller 161 having a heating source inside; a fixing roller 162 disposed opposite to the heating roller 161; a fixing belt 163 tensioned between the fixing roller 162 and the heating roller 161; and a pressure roller 164 disposed opposite to the fixing roller 162 with the fixing belt 163 therebetween to form a fixing nip portion. The sheet P supplied to the fixing unit 16 passes through the fixing nip portion and is heated and pressed. Thus, the toner image transferred onto the sheet P in the transfer nip portion is fixed on the sheet P.

[0035] The paper discharge unit 17 is formed by recessing the top of the apparatus main body 11, and a paper discharge tray 171 for receiving the discharged sheet P is formed at the bottom of the recess. The sheet P on which the fixing process has been performed is discharged to the paper discharge tray 171 via a sheet conveying passage 111 extending from the upper part of the fixing unit 16.

[0036] <Regarding the developing device>

[0037] Figure 2 FIG. is a cross-sectional view of the developing device 23 according to the present embodiment and a block diagram of the electrical structure of the control unit 980. The developing device 23 includes a developing housing 230, a developing roller 231, a first screw feeder 232, a second screw feeder 233, and a restricting blade 234. The two-component developing method is applied in the developing device 23.

[0038] The developing housing 230 includes a developer accommodating portion 230H. A two-component developer composed of toner and carrier is accommodated in the developer accommodating portion 230H. Further, the developer accommodating portion 230H includes: a first conveying portion 230A that conveys the developer in a first conveying direction ( Figure 2 a direction perpendicular to the paper surface and from back to front) from one end side in the axial direction of the developing roller 231 toward the other end side; and a second conveying portion 230B that communicates with the first conveying portion 230A at both axial end portions and conveys the developer in a second conveying direction opposite to the first conveying direction. The first auger 232 and the second auger 233 rotate in the directions of arrows D22 and D23 of Figure 2 to convey the developer in the first conveying direction and the second conveying direction, respectively. In particular, the first auger 232 conveys the developer in the first conveying direction and supplies the developer to the developing roller 231.

[0039] The developing roller 231 is disposed opposite to the photosensitive drum 20 at the developing nip portion NP ( Figure 3A ). The developing roller 231 includes a rotating sleeve 231S and a magnet 231M fixedly disposed inside the sleeve 231S. The magnet 231M has poles S1, N1, S2, N2, and S3. The N1 pole functions as a main pole, the S1 and N2 poles function as conveying poles, and the S2 pole functions as a peeling pole. Further, the S3 pole functions as a sucking pole and a restricting pole. As an example, the magnetic flux densities of the S1, N1, S2, N2, and S3 poles are set to 54 mT, 96 mT, 35 mT, 44 mT, and 45 mT. The sleeve 231S of the developing roller 231 rotates in the direction of arrow D21 of Figure 2 . The developing roller 231 rotates, receives the developer in the developing housing 230, bears a developer layer, and supplies toner to the photosensitive drum 20. In addition, in the present embodiment, the developing roller 231 rotates in the same direction at a position opposite to the photosensitive drum 20. Further, as an example, in the axial direction (width direction) of the developing roller 231, the range where the magnetic brush of the two-component developer is formed is 304 mm.

[0040] The restricting blade 234 (layer thickness restricting member) is disposed at a predetermined interval from the developing roller 231 to restrict the layer thickness of the developer supplied from the first auger 232 to the circumferential surface of the developing roller 231.

[0041] The image forming apparatus 10 having the developing device 23 further includes a developing bias application unit 971, a driving unit 972, a galvanometer 973 (current detection unit), and a control unit 980. The control unit 980 is composed of a CPU (Central Processing Unit), a ROM (Read Only Memory) that stores a control program, a RAM (Random Access Memory) used as a work area of the CPU, and the like.

[0042] The developing bias application unit 971 is composed of a DC power supply and an AC power supply, and applies a developing bias in which an AC voltage is superimposed on a DC voltage to the developing roller 231 of the developing device 23 based on a control signal from a bias control unit 982 described later.

[0043] The driving unit 972 is composed of a motor and a gear mechanism that transmits its torque, and drives the developing roller 231, the first auger feeder 232, and the second auger feeder 233 in the developing device 23 to rotate in addition to the photosensitive drum 20 according to a control signal from a drive control unit 981 described later during the developing operation.

[0044] The galvanometer 973 detects a direct current (DC component of the developing current) flowing between the developing roller 231 and the developing bias application unit 971.

[0045] The control unit 980 functions in such a manner as to include a drive control unit 981, a bias control unit 982, a storage unit 983, and a calibration execution unit 984 (bias condition determination unit) by the CPU executing the control program stored in the ROM.

[0046] The drive control unit 981 controls the driving unit 972 to drive the developing roller 231, the first auger feeder 232, and the second auger feeder 233 to rotate. In addition, the drive control unit 981 controls a driving mechanism (not shown) to drive the photosensitive drum 20 to rotate.

[0047] During the developing operation (image forming operation) in which toner is supplied from the developing roller 231 to the photosensitive drum 20, the bias control unit 982 controls the developing bias application unit 971 to set a potential difference between a DC voltage and an AC voltage between the photosensitive drum 20 and the developing roller 231. Through the potential difference, the toner moves from the developing roller 231 to the photosensitive drum 20.

[0048] The storage unit 983 stores various information referred to by the drive control unit 981, the bias control unit 982, and the calibration execution unit 984. As an example, it stores the value of the developing bias adjusted according to the rotation speed and environment of the developing roller 231. In addition, the storage unit 983 stores the printing rate and the number of lines set according to each toner image when forming a plurality of measurement toner images. Further, the data stored in the storage unit 983 may be in the form of a graph, a table, or the like.

[0049] The calibration execution unit 984 executes the AC calibration (bias condition determination mode) described later. During the AC calibration, the calibration execution unit 984 controls the photosensitive drum 20, the charging device 21, the exposure device 22, and the developing device 23 while forming a plurality of measurement toner images on the photosensitive drum 20. Then, based on the DC current detected by the ammeter 973 when developing the measurement latent image corresponding to a prescribed measurement latent image formed on the photosensitive drum 20 by applying the developing bias to the developing roller 231 and using toner, the calibration execution unit 984 determines the reference peak-to-peak voltage, which serves as the reference for the peak-to-peak voltage of the AC voltage of the developing bias applied to the developing roller 231 during the image forming operation.

[0050] <Regarding the developing operation>

[0051] Figure 3A is a schematic diagram of the developing operation of the image forming apparatus 10 according to the present embodiment, Figure 3B is a schematic diagram showing the magnitude relationship of the potentials of the photosensitive drum 20 and the developing roller 231. Refer to Figure 3A , a developing nip portion NP is formed between the developing roller 231 and the photosensitive drum 20. The toner TN and the carrier CA carried on the developing roller 231 form a magnetic brush. In the developing nip portion NP, the toner TN is supplied from the magnetic brush toward the photosensitive drum 20 side to form a toner image TI. Refer to Figure 3B , the surface potential of the photosensitive drum 20 is charged to the background potential V0 (V) by the charging device 21. Thereafter, if exposure light is irradiated by the exposure device 22, the surface potential of the photosensitive drum 20 changes from the background potential V0 to the maximum image portion potential VL (V) according to the printed image. On the other hand, a DC voltage Vdc of the developing bias is applied to the developing roller 231, and an AC voltage (not shown) is superimposed on the DC voltage Vdc.

[0052] In the case of such a reversal development method, the potential difference between the surface potential V0 and the DC component Vdc (DC bias) of the development bias is a potential difference that suppresses the toner fogging to the background portion of the photosensitive drum 20. On the other hand, the potential difference between the surface potential VL after exposure and the DC component Vdc of the development bias is a development potential difference that moves the positive polarity toner to the image portion of the photosensitive drum 20. In addition, the AC component (AC bias) of the development bias applied to the development roller 231 promotes the movement of the toner from the development roller 231 to the photosensitive drum 20.

[0053] <Regarding the Relationship between Development Bias Voltage and Image Density>

[0054] Here, when the charge amount of the toner in the developing device 23 changes, or when the developing gap changes due to the vibration of the developing roller 231, etc., either the DC bias or the AC bias has the property of changing the moving force F (= the charge amount Q of the toner × the magnitude E of the electric field) applied to the toner, thereby changing the image density. However, strictly speaking, the DC bias and the AC bias have different characteristics from each other. In the case of the AC bias, if the Vpp (peak-to-peak voltage) is increased, the image density rises, but the image density hardly rises soon, and if it is further increased, the image density decreases instead. On the other hand, if the development potential difference (Vdc-VL) in the DC bias is increased, the image density continues to rise, and the amount of increase in the image density becomes smaller soon, but the image density decreases as in the AC bias. This is presumably because the AC electric field forms a bidirectional electric field (reciprocating electric field) between the photosensitive drum 20 and the developing roller 231 in the developing nip, while the DC electric field forms an electric field in one direction.

[0055] In more detail, the reciprocating electric field of the AC bias is composed of two electric fields in opposite directions, namely, a developing electric field for supplying toner from the developing roller 231 to the photosensitive drum 20 and a recovery electric field for recovering toner from the photosensitive drum 20 to the developing roller 231. Furthermore, when Vpp is increased, both electric fields increase, but the toner supply amount of the developing electric field reaches a maximum soon. Thereafter, if Vpp is further increased, the toner recovery amount increases due to the increase in the recovery electric field, but the toner supply amount of the developing electric field has already reached a maximum. As a result, according to the relationship between the supply and recovery of toner between the photosensitive drum 20 and the developing roller 231, the final toner development amount decreases in accordance with the increase in Vpp.

[0056] <About the relationship between Vpp and developing current>

[0057] As described above, it is possible to grasp the relationship between the DC bias and the AC bias and the developing amount of the toner. On the other hand, it is not possible to fully understand how the developing current flowing between the developing roller 231 and the developing bias applying unit 971 changes when the Vpp of the AC bias is increased.

[0058] Presumably, the reason is that the developing current generated in the developing nip portion NP is composed of "toner movement current flowing due to the movement of the toner", "brush current of the magnetic brush of the developer flowing in the image portion (image portion magnetic brush current)", and "brush current of the magnetic brush of the developer flowing in the non-image portion (non-image portion magnetic brush current)". Since the toner movement current changes corresponding to the movement amount of the toner, if the Vpp is increased, the toner movement current rises and then falls. However, since the image portion magnetic brush current is the current flowing through the magnetic brush in the developing nip portion NP, it has a tendency to rise with the increase of the Vpp. In addition, the non-image portion magnetic brush current has a tendency to increase the current in the opposite direction with the increase of the Vpp in the non-image forming regions at both ends in the long side direction of the image forming region. Therefore, it is not possible to fully understand how the developing current, which is so complexly affected by the combined current change of the toner movement current, the image portion magnetic brush current, and the non-image portion magnetic brush current, changes corresponding to the increase of the Vpp.

[0059] Therefore, the inventors of the present application have newly discovered that there are various modes in the change tendency through the experiment of determining the change of the developing current when the Vpp of the AC bias of the developing bias is increased by earnestly implementing the experiment. That is, it is clarified that there are the following modes: if the Vpp of the AC bias is increased, the developing current (DC current) rises, but soon reaches the change point of the slope change, and thereafter the developing current also rises slowly; and the developing current conversely starts to fall from the change point.

[0060] Based on this mode of the developing current, the inventors of the present application newly focused on setting the Vpp of the AC bias in the region where the change of the image density is small. As a result, even if the charge amount of the toner and the developing gap change, the change of the image density can be reduced. Hereinafter, the details of the AC calibration for setting such a Vpp will be described.

[0061] <Regarding AC Calibration>

[0062] Figure 4 It is a flowchart of the AC calibration executed in the image forming apparatus 1 according to the present embodiment. Figure 5 It is a flowchart of the first approximation formula determination step of the AC calibration executed in the image forming apparatus 1 according to the present embodiment. Figure 6 It is a flowchart of the second approximation formula determination step of the AC calibration executed in the image forming apparatus 1 of the present embodiment.

[0063] In this embodiment, at a timing when no image forming operation is performed, the calibration execution unit 984 executes AC calibration (bias condition determination mode). The AC calibration is a mode for determining the reference peak-to-peak voltage (target voltage), which serves as the reference for the peak-to-peak voltage (Vpp) of the alternating current voltage of the developing bias applied to the developing roller 231 during the image forming operation.

[0064] If the AC calibration is started, the calibration execution unit 984 sequentially executes a first approximation formula determination step ( Figure 4 step S01), a second approximation formula determination step ( Figure 4 step S02), and a target voltage determination step ( Figure 4 step S03).

[0065] Referring to Figure 5 , the first approximation formula determination step will be described in detail. If the first approximation formula determination step is started, the calibration execution unit 984 acquires information related to the first measurement range stored in the storage unit 983. The first measurement range is information related to the range and interval of the Vpp of the alternating current bias applied to the developing roller 231 in the first approximation formula determination step. In this embodiment, as an example, the calibration execution unit 984 acquires information related to four first measurement peak-to-peak voltages. As a result, the first measurement range in the first approximation formula determination step is determined (step S11).

[0066] Next, the calibration execution unit 984 forms a measurement latent image on the photosensitive drum 20 and develops the measurement latent image by applying a developing bias to the developing roller 231. Specifically, similar to during image formation, the photosensitive drum 20 rotates, and the circumferential surface of the photosensitive drum 20 is uniformly charged to 250 V by the charging device 21. Additionally, as an example, the charging range in the axial direction (width direction) of the photosensitive drum 20 is set to 322 mm. And, by the exposure light irradiated from the exposure device 22, the potential of a part of the photosensitive drum 20 drops to 10 V, and a measurement latent image is formed on the photosensitive drum 20. In this embodiment, with respect to the sheet body width of 297 mm (A4 landscape), the width of the measurement latent image is set to 287 mm, and the width of the magnetic brush of the developing roller is set to 304 mm. The difference between the width of the magnetic brush and the width of the measurement latent image becomes the region where the non-image magnetic brush current flows.

[0067] On the other hand, on the developing roller 231, an AC bias voltage with a frequency of 10 kHz and a Duty (duty ratio) of 50% is superimposed on a DC voltage of 150 V. In addition, the Vpp of the AC bias voltage is sequentially set to the four first measured peak-to-peak voltages. As a result, for each of the first measured peak-to-peak voltages, when developing the above-mentioned latent image for measurement by the developing roller 231, the galvanometer 973 measures the DC component (DC current Idc) of the developing current flowing between the developing roller 231 and the developing bias application unit 971 respectively (step S12). As a result, four developing currents corresponding to the four first measured peak-to-peak voltages are obtained, and four sets of data related to the first measured peak-to-peak voltage and the developing current are obtained. In addition, the calculation of the developing current is preferably performed based on the average current over more than one rotation of the developing roller 231, and more preferably, the average is taken for rotations that are an integer multiple of one week.

[0068] Next, the calibration execution unit 984 regresses the relationship between the four first measured peak-to-peak voltages and the four developing currents with a linear equation and calculates the correlation coefficient R (step S13). As an example, the calibration execution unit 984 calculates the above-mentioned linear equation by the least squares method and obtains the correlation coefficient R.

[0069] Next, the calibration execution unit 984 compares the magnitude relationship between the correlation coefficient R obtained in the above manner and the threshold value R1 pre-stored in the storage unit 983 (step S14). As an example, the threshold value R1 is set to 0.90. Among them, when the threshold value R1 ≤ the correlation coefficient R (yes in step S14), the calibration execution unit 984 determines the linear equation regressed in the above manner as the first approximation formula (step S15). On the other hand, when the threshold value R1 > the correlation coefficient R in step S14 (no in step S14), the calibration execution unit 984 recalculates the correlation coefficient R based on the remaining three data in the state where the data with the maximum Vpp in the above four sets of data is removed. After that, the calibration execution unit 984 executes steps S14 and S15 in the same manner as above. In addition, when the relationship of the threshold value R1 ≤ the correlation coefficient R is not satisfied even after removing the data with the maximum Vpp in step S16, the calibration execution unit 984 can further remove a part of the data and repeat the steps, or can interrupt the execution of the AC calibration and refer to the result of the previous AC calibration.

[0070] As described above, if the first approximation formula determination step is completed, the second approximation formula determination step is started. Refer to Figure 6, the second approximation determination step will be described in detail. If the second approximation determination step starts, the calibration execution unit 984 acquires information related to the second measurement range stored in the storage unit 983. The second measurement range is information related to the range and interval of Vpp of the alternating current bias applied to the developing roller 231 in the second approximation determination step. In the present embodiment, as an example, the calibration execution unit 984 acquires information related to three second measurement peak-to-peak voltages. As a result, the second measurement range in the second approximation determination step is determined (step S21). In addition, the minimum value of the second measurement range (three second measurement peak-to-peak voltages) is set to be larger than the maximum value of the first measurement range (four first measurement peak-to-peak voltages).

[0071] Next, the calibration execution unit 984 forms a latent image for measurement on the photosensitive drum 20 in the same manner as Figure 5 step S12, and develops the latent image for measurement by applying a developing bias to the developing roller 231. At this time, on the developing roller 231, an alternating current bias with a frequency of 10 kHz and a duty of 50% is superimposed on the direct current voltage of 150 V, and the Vpp of the alternating current bias is sequentially set to the three second measurement peak-to-peak voltages. As a result, for each second measurement peak-to-peak voltage, when the latent image for measurement is developed by the developing roller 231, the galvanometer 973 measures the direct current component (direct current Idc) of the developing current flowing between the developing roller 231 and the developing bias application unit 971 respectively (step S22). As a result, three developing currents corresponding to the three second measurement peak-to-peak voltages are obtained, and three sets of data related to the second measurement peak-to-peak voltage and the developing current are obtained.

[0072] Next, the calibration execution unit 984 regresses the relationship between the three second measurement peak-to-peak voltages and the three developing currents with a linear equation (first judgment approximation formula), and calculates its slope L (step S23). As an example, the calibration execution unit 984 calculates the linear equation by the least squares method and obtains the slope L.

[0073] Next, the calibration execution unit 984 compares the size relationship between the slope L obtained in the above manner and the threshold value L1 previously stored in the storage unit 983 (step S24). As an example, the threshold value L1 is set to 0 (zero). Among them, when the slope L < the threshold value L1 (yes in step S24), the calibration execution unit 984 determines the linear equation regressed in the above manner as the second approximation formula (step S25). On the other hand, when the slope L ≥ the threshold value L1 in step S24 (no in step S24), the calibration execution unit 984 calculates the average value of the Vpp of the above three sets of data, and sets the linear formula with a fixed change of the average value with respect to the peak-to-peak voltage as the second approximation formula (step S26).

[0074] IfFigure 5 , Figure 6 When the first approximation formula determination step and the second approximation formula determination step shown end respectively, the calibration execution unit 984 executes the target voltage determination step ( Figure 4 step S03). In this target voltage determination step, the calibration execution unit 984 determines the peak-to-peak voltage at the intersection of the first approximation formula and the second approximation formula as the reference peak-to-peak voltage (target voltage VT). As a result, it is possible to set the peak-to-peak voltage during the image forming operation near the boundary (near the peak value) of the relationship between the peak-to-peak voltage and the developing current in each of the first measurement range and the second measurement range. In addition, in the present embodiment, considering a specified safety factor, the peak-to-peak voltage obtained by multiplying the reference peak-to-peak voltage determined in the above manner by 1.2 is applied as the actual peak-to-peak voltage during the image forming operation.

[0075] Hereinafter, the AC calibration in the present embodiment will be described in further detail based on data. The data described later was obtained under the following conditions.

[0076] <Common conditions>

[0077] · Printing speed: 55 sheets per minute

[0078] · Photoconductor drum 20: Amorphous silicon photoconductor (α-Si)

[0079] · Developing roller 231: Outer diameter 20 mm, surface shape: Rolled groove processing + Shot peening (80 columns of recesses (grooves) are formed in the circumferential direction)

[0080] · Restricting blade 234: Made of SUS430, magnetic, thickness 1.5 mm

[0081] · Developing agent conveyance amount after the restricting blade 234: 250 g / m 2

[0082] · Peripheral speed of the developing roller 231 relative to the photoconductor drum 20: 1.8 (in the locus direction at the relative position)

[0083] · Distance between the photoconductor drum 20 and the developing roller 231: 0.25 mm

[0084] · White bottom (background part) potential V0 of the photoconductor drum 20: +250 V

[0085] · Image part potential VL of the photoconductor drum 20: +10 V

[0086] · Developing bias of the developing roller 231: AC voltage rectangular wave with a frequency = 7 kHz and Duty = 50% (Vpp is adjusted according to each experimental condition), Vdc (DC voltage) = 150 V

[0087] Toner: Positively charged polar toner, volume average particle size 6.8 μm, toner concentration 6%

[0088] Carrier: Volume average particle size 35μm, ferrite / resin coating carrier

[0089] <About Developer>

[0090] The toner is a pulverized toner, and the same effect is confirmed for any toner of a core-shell structure. In addition, the same effect is confirmed for the toner concentration in the range of 3% to 12%. Since the finer the magnetic brush, the easier it is for the toner to move significantly due to the AC electric field, the volume average particle size of the carrier is preferably 45 μm or less, more preferably 30 μm or more and 40 μm or less. In addition, a resin carrier with a smaller true specific gravity (true density) is more preferred than a ferrite carrier.

[0091] <About the carrier>

[0092] The carrier is made by coating silicon or fluorine on a ferrite core with a volume average particle size of 35 μm, and is specifically made in the following steps. 20 parts by weight of silicone resin KR-271 (manufactured by Shin-Etsu Chemical Co., Ltd.) is dissolved in 200 parts by weight of toluene in 1000 parts by weight of carrier core EF-35 (manufactured by Paudatek) to prepare a coating liquid. After the coating liquid is spray-coated by a fluidized bed coating device, it is heat-treated at 200°C for 60 minutes to obtain a carrier. In the coating liquid, a conductive agent and a charge control agent are mixed and dispersed in a range of 0 to 20 parts relative to 100 parts of the coating resin, thereby adjusting the resistance and charging.

[0093] Figure 7 , Figure 8 and Figure 9 Each of the graphs shows the relationship between Vpp and the developing current in the AC calibration performed in the image forming apparatus 1 according to the present embodiment. In each graph, the vertical axis (Y axis) shows the developing current, and the horizontal axis (X axis) shows Vpp.

[0094] Tables 1 and 2 show Figure 7 The relationship between Vpp and developing current in the first measurement range and the second measurement range is shown.

[0095] [Table 1]

[0096]

[0097] [Table 2]

[0098]

[0099] exist Figure 7 In, byFigure 5 In the first approximation formula determination step shown, a linear equation of y = 0.01x + 7 is calculated as the first approximation formula. On the other hand, in Figure 6 In the second approximation formula determination step shown, since the slope L is negative (L < L1 = 0), a linear equation of y = -0.0075x + 20.767 is calculated as the second approximation formula in step S25. As a result, in the target voltage determination step S03, as the intersection point of the first approximation formula and the second approximation formula, Vpp = target voltage VT = 787V is calculated, and 1.2 is set as the safety factor. Thus, Vpp = 787×1.2 = 944 (V) during the image forming operation is selected.

[0100] Tables 3 and 4 show the relationship between Vpp and the developing current within the first measurement range and the second measurement range shown in Figure 8

[0101] [Table 3]

[0102]

[0103] [Table 4]

[0104]

[0105] In Figure 8 , in Figure 5 In the first approximation formula determination step shown, a linear equation of y = 0.01x + 7 is calculated as the first approximation formula. On the other hand, in Figure 6 In the second approximation formula determination step shown, since the slope L is positive (L > L1 = 0), the average value of the developing current is calculated in step S026, and a linear equation of y = 14.1 is calculated as the second approximation formula. As a result, in the target voltage determination step S03, as the intersection point of the first approximation formula and the second approximation formula, Vpp = target voltage VT = 710V is calculated, and by setting 1.2 as the safety factor, Vpp = 710×1.2 = 852 (V) during the image forming operation is selected.

[0106] Tables 5 and 6 show the relationship between Vpp and the developing current within the first measurement range and the second measurement range shown in Figure 9

[0107] [Table 5]

[0108]

[0109]

[0110] [Table 6]

[0111] ​​

[0112] In Figure 9 it, the first approximation determination step shown by Figure 5 calculates a linear equation of y = 0.0042x + 6.71 as the first approximation. On the other hand, in the second approximation determination step shown by Figure 6 since the slope L is positive (L > L1 = 0), the average value of the developing current is calculated in step S026, and a linear equation of y = 12.4 is calculated as the second approximation. As a result, in the target voltage determination step S03, as the intersection point of the first approximation and the second approximation, Vpp = target voltage VT = 1310 V is calculated, and by setting 1.2 as the safety factor, Vpp = 1310 × 1.2 = 1572 (V) is selected during the image forming operation.

[0113] <Reason for the peak (change point) of the developing current (DC component)>

[0114] Next, the reason for the peak (change point) of the developing current (DC component) with respect to Vpp as described above for each data is speculated. As described above, the developing current is composed of "toner movement current + image area brush current + non-image area brush current", but when obtaining the developing current, in the part corresponding to the image area (solid image part) of the electrostatic latent image, both the "toner movement current + image area brush current" flow, but in the white background part at the end in the width direction, only the "non-image area brush current" flows in the direction opposite to the image area. Therefore, if Vpp is increased, the non-image area brush current in this white background part increases, and the total developing current decreases.

[0115] In addition, although the image area brush current in the image area also increases corresponding to the increase in Vpp, the toner layer formed by attaching toner to the surface of the photosensitive drum 20 becomes a resistance layer, suppressing the extreme increase in the image area brush current. On the other hand, in the white background part, although some toner moves to the sleeve surface of the developing roller 231, since the amount is very small compared to the image area, the toner layer attached to the sleeve surface does not become a large resistance compared to the image area. As a result, the non-image area brush current in the white background part increases significantly with the increase in Vpp, and this brush current flows in the direction opposite to the toner movement current, so it is speculated that the developing current has a change point (peak).

[0116] The inventors of the present application newly discovered the above relationship between the developing current and Vpp through repeated intensive experiments. In addition, it was further found that the smaller the resistance of the carrier, the easier this phenomenon occurs, based on a parallel flat plate with a gap of 1 mm (area 240 mm 2) was filled with 0.2 g of a carrier and a voltage of 1000 V was applied, and the resistance value of the carrier was calculated by the current flowing through the carrier. This phenomenon was significantly observed below 10 to the 9th power ohms.

[0117] That is, if a two-component developer is present between the photosensitive drum 20 and the developing roller 231, and a latent image for measurement is formed in the central part of the electrostatic latent image in the axial direction (width direction) and white background portions are arranged at both ends thereof, the above-mentioned change point is generated at the boundary between the first measurement range and the second measurement range of the present embodiment. In particular, the phenomenon that the slope of the second approximate equation is distributed in a wide range of positive and negative values is caused by the fact that a current flows in the opposite direction to the central part at both ends of the axial direction of the developing roller 231. In particular, in the present embodiment, in the axial direction, the range of the magnetic brush on the developing roller 231 is narrower than the charged range on the photosensitive drum 20, and the range of the image portion (solid image portion) in the latent image for measurement formed on the photosensitive drum 20 is set to be narrower than the range of the magnetic brush. As a result, as described above, a region where a magnetic brush flows in the opposite direction to the image portion is formed at both ends of the axial direction of the developing roller 231. This phenomenon is a unique phenomenon in the developing nip portion, which does not appear in the discharge current generated between the photosensitive drum 20 and the charging roller in contact with the peripheral surface thereof, and was discovered through the above-mentioned repeated experiments. In particular, since there is no developer that causes the resistance change of the carrier between the charging roller and the photosensitive drum 20, it is difficult to produce the characteristic that the current decreases soon after the peak-to-peak voltage increases.

[0118] As described above, in the present embodiment, the reference peak-to-peak voltage is set according to the intersection of the first approximation and the second approximation representing the relationship between the peak-to-peak voltage of the AC bias and the developing current within the respective ranges of the first measurement range and the second measurement range. There is a change point of the relationship between the peak-to-peak voltage of the AC bias and the developing current near the above-mentioned intersection, so it is difficult to be affected by the slope of the first approximation within the first measurement range, thereby suppressing the image density from changing due to the charge amount of the toner and the change of the developing gap. In addition, it is possible to suppress the setting of the reference peak-to-peak voltage in the region where the slope of the second approximation is smaller than the prescribed threshold value corresponding to the change of the resistance of the carrier, etc., and in the region where the developing current is likely to decrease corresponding to the increase of the peak-to-peak voltage. As a result, it is possible to set the AC bias of the developing bias that can output a stable image density during the image forming operation. In addition, the actual peak-to-peak voltage during the image forming operation can directly use the value of the reference peak-to-peak voltage, or multiply the reference peak-to-peak voltage by a fixed ratio, or add a fixed value, or add a fixed value to the reference peak-to-peak voltage.

[0119] In addition, in the present embodiment, the calibration execution unit 984 determines the first approximate formula by the least squares method based on the DC components of the development currents respectively obtained at the at least three first measurement peak-to-peak voltages included in the first measurement range. With this configuration, the first approximate formula can be determined by simple arithmetic processing based on the first measurement peak-to-peak voltages included in the first measurement range.

[0120] In addition, in the present embodiment, when the slope of the first determination approximate formula of the linear approximate formula determined by the least squares method based on the DC components of the development currents respectively obtained at the at least three second measurement peak-to-peak voltages included in the second measurement range is greater than a preset first threshold L1, the calibration execution unit 984 sets a linear formula in which the change of the average value of the DC components of the development currents respectively obtained at the at least three second measurement peak-to-peak voltages with respect to the peak-to-peak voltage is fixed as the second approximate formula. When the slope of the first determination approximate formula is less than the first threshold L1, the first determination approximate formula is set as the second approximate formula. With this configuration, in the process of determining the second approximate formula whose slope is likely to change due to the influence of the resistance value of the carrier, etc., a more suitable approximate formula can be selected as the second approximate formula based on the slope of the first determination approximate formula.

[0121] In addition, in the present embodiment, the intervals of the plurality of first measurement peak-to-peak voltages in the first measurement range and the intervals of the plurality of second measurement peak-to-peak voltages in the second measurement range are respectively set to be smaller than the interval between the maximum value of the first measurement range and the minimum value of the second measurement range. With this configuration, the first measurement range and the second measurement range are clearly distinguished, and further, the intervals of the peak-to-peak voltages are finely set within each measurement range, thereby enabling improvement of the determination accuracy of the first approximate formula and the second approximate formula.

[0122] In addition, in the first approximate formula determination operation, when the correlation coefficient of the first approximate formula is smaller than a preset second threshold, the calibration execution unit 984 determines the first approximate formula based on the DC components of the development currents with respect to the peak-to-peak voltages remaining after excluding at least one peak-to-peak voltage from the at least three first measurement peak-to-peak voltages. With this configuration, when the correlation coefficient is small in the process of determining the first approximate formula, a first approximate formula with higher accuracy can be determined by excluding the data of at least one peak-to-peak voltage.

[0123] Specifically, in the first approximation formula determination operation, when the correlation coefficient of the first approximation formula is smaller than a preset second threshold R1, the calibration execution unit 984 determines the first approximation formula based on the DC component of the development current with respect to the inter-peak voltages remaining after excluding the maximum inter-peak voltage among the at least three first measurement inter-peak voltages. With this configuration, when the correlation coefficient is small during the determination process of the first approximation formula, by excluding data of the inter-peak voltages close to the second measurement range, a first approximation formula with higher accuracy can be determined.

[0124] In addition, the calibration execution unit 984 excludes in advance from the second measurement range the maximum inter-peak voltage or the minimum inter-peak voltage excluded in the second approximation formula determination operation, and executes the next bias condition determination mode. With this configuration, by excluding from the very beginning in the next bias condition determination mode the data excluded in the previous bias condition determination mode, the mode execution time can be shortened, and a reference inter-peak voltage with higher accuracy can be determined.

[0125] In addition, in the present embodiment, the number of the at least three first measurement inter-peak voltages in the first measurement range is set to be larger than the number of the at least three second measurement inter-peak voltages in the second measurement range. With this configuration, by obtaining relatively more data in the first measurement range where the slope of the first approximation formula is positive and the development current is likely to change significantly, a reference inter-peak voltage with higher accuracy can be determined.

[0126] In addition, in the present embodiment, the change point of the balance (the sum of each current) change of the toner movement current, the image portion magnetic brush current, and the non-image portion magnetic brush current can be predicted by the intersection point of the two approximation formulas, and thus the reference inter-peak voltage can be determined.

[0127] In addition, in the present embodiment, the setting of the reference inter-peak voltage is determined based on the development current. In the past, it was also considered to measure the image density and determine the reference inter-peak voltage according to its stability. However, for example, the density sensor that measures the image density on the photosensitive drum 20 or the intermediate transfer belt 141 is likely to have a decrease in measurement accuracy when the image density becomes high, and thus the image density in the second measurement range of the present invention cannot be detected with high accuracy. From this point of view, the data for determining the reference inter-peak voltage in the first measurement range and the second measurement range is also preferably the development current.

[0128] In addition, since the developing current is likely to vary significantly within the first measurement range, it is preferable to perform the measurement within a range of the inter-peak voltage as large as possible. On the other hand, within the second measurement range, the change in the developing current is small. If the inter-peak voltage is set too large, leakage may occur in the developing nip portion. Therefore, it is preferable that the second measurement range is narrower than the first measurement range, and the number of measurement points is set to be small. As a result, the pattern execution time can be shortened and the toner consumption amount can be suppressed.

[0129] In addition, the measurement of the developing current can be performed in the circuit within the developing bias application unit 971. Further, although the movement current of the toner can also be measured on the side of the photosensitive drum 20, since the current flowing in from the transfer roller is also included in the photosensitive drum 20, these currents cannot be separated. Therefore, it is preferable to measure the developing current on the side of the developing bias application unit 971.

[0130] The embodiments of the present invention have been described above, but the present invention is not limited thereto. For example, the following modified embodiments can be adopted.

[0131] (1) In the above embodiment, the method of performing rolling groove processing + shot peening processing on the surface of the developing roller 231 has been described. However, it may also be a method of performing concave shape (pit) + shot peening processing on the surface of the developing roller 231, or only shot peening processing, only rolling groove processing, only concave shape (pit), or electroplating processing.

[0132] (2) As Figure 1 shown, in the case where the image forming apparatus 10 has a plurality of developing devices 23, the AC calibration of the above embodiment can be performed in one or two developing devices 23, and the result can be applied to the other developing devices 23.

[0133] (3) Figure 10 is a flowchart of a second approximation formula determination step of the AC calibration performed in the image forming apparatus of the modified embodiment of the present invention. Figure 11 is a flowchart of a part of the second approximation formula determination step. In this modified embodiment, compared with the previous embodiment, Figure 10 steps S22A, S22B, and S22C are different. That is, in step S22, the DC component (DC current Idc) of the developing current is measured. At this time, in this modified embodiment, in the same manner as the first approximation formula determination step, the DC components of the four developing currents corresponding to the four second measurement inter-peak voltages are obtained, and four sets of data related to the second measurement inter-peak voltage and the DC component of the developing current are obtained.

[0134] Among them, the calibration execution unit 984 calculates the correlation coefficient R (step S22A) in the same way as in the first approximation formula determination step. Then, the calibration execution unit 984 compares the magnitude relationship between the correlation coefficient R and the threshold value R2 pre-stored in the storage unit 983 (step S22B). As an example, the threshold value R2 is set to 0.90. Among them, when the threshold value R2 ≤ the correlation coefficient R (yes in step S22B), the calibration execution unit 984 calculates the slope L in step S23 and calculates the second approximation formula in step S25 or step S26 respectively based on the judgment result in step S24, as in the previous embodiment. On the other hand, in step S22B, when R2 > R (no in step S22B), the calibration execution unit 984 determines the corrected correlation coefficient R in step S22C.

[0135] Referring to Figure 11 , if the determination step of the corrected correlation coefficient R is started, then in step S31, the calibration execution unit 984 calculates the correlation coefficient Rm based on the remaining three data in the state where the data with the maximum Vpp is removed from the above four groups of data (step S31). Next, the calibration execution unit 984 calculates the correlation coefficient Rn based on the remaining three data in the state where the data with the minimum Vpp is removed from the above four groups of data (step S32). Then, the calibration execution unit 984 compares the magnitude relationship between the correlation coefficients Rm and Rn calculated in the above manner and selects the larger correlation coefficient as the corrected correlation coefficient R (step S33). After that, it returns to Figure 10 , and based on the selected corrected correlation coefficient R, the processes after step S22B are repeated.

[0136] Thus, in this modified embodiment, in the second approximation formula determination step, when the correlation coefficient is small, data with a higher correlation coefficient is selected, and the second approximation formula is set based on this data. Therefore, by excluding at least one of the peak-to-peak voltage data, a second approximation formula with higher accuracy can be determined.

[0137] In particular, the calibration execution unit 984 compares the correlation coefficient Rm of the second determination approximate formula determined based on the DC component of the development current with respect to the remaining peak-to-peak voltages after relatively excluding the maximum peak-to-peak voltage among the at least three second measurement peak-to-peak voltages, and the correlation coefficient Rn of the third determination approximate formula determined based on the DC component of the development current with respect to the remaining peak-to-peak voltages after relatively excluding the minimum peak-to-peak voltage among the at least three second measurement peak-to-peak voltages, and determines the determination approximate formula with the larger correlation coefficient among the second determination approximate formula and the third determination approximate formula as the second approximate formula. According to this configuration, when the correlation coefficient is small in the process of determining the second approximate formula, by excluding either the minimum peak-to-peak voltage closest to the first measurement range in the second measurement range or the data of the maximum peak-to-peak voltage that is prone to discharge leakage and prone to include noise, a second approximate formula with higher accuracy can be determined.

Claims

1. An image forming apparatus capable of performing an image forming operation of forming an image on a sheet-like body, characterized in that the image forming apparatus includes: An image carrier that rotates and has a surface that allows an electrostatic latent image to be formed and that bears a toner image developed from the electrostatic latent image by toner; A charging device that charges the image carrier to a predetermined charging potential; An exposure device disposed downstream of the charging device in the rotation direction of the image carrier, and forms the electrostatic latent image by exposing the surface of the image carrier charged to the charging potential according to predetermined image information; A developing device disposed opposite to the image carrier in a predetermined developing nip portion downstream of the exposure device in the rotation direction, including a developing roller that rotates and has a circumferential surface that bears a developer composed of toner and a carrier, and forms the toner image by supplying toner to the image carrier; A transfer unit that transfers the toner image borne on the image carrier to a sheet-like body; A developing bias application unit capable of applying a developing bias in which an AC voltage is superimposed on a DC voltage to the developing roller; A current detection unit capable of detecting a DC component of a developing current flowing between the developing roller and the developing bias application unit; And A bias condition determination unit that, based on the DC component of the developing current, executes a bias condition determination mode for determining a reference peak-to-peak voltage, the DC component of the developing current being detected by the current detection unit when the developing bias is applied to the developing roller in response to a predetermined measurement latent image formed on the image carrier and the measurement latent image is developed by toner, and the reference peak-to-peak voltage being a reference for the peak-to-peak voltage of the AC voltage of the developing bias applied to the developing roller in the image forming operation; The bias condition determination unit respectively executes in the bias condition determination mode: A first approximation formula determination operation of respectively obtaining the DC component of the developing current and determining a first approximation formula under the condition that the peak-to-peak voltage of the AC voltage of the developing bias is respectively set to at least three first measurement peak-to-peak voltages included in a predetermined first measurement range, the first approximation formula being a unary approximation formula representing the relationship between the first measurement peak-to-peak voltages in the first measurement range and the obtained DC component of the developing current; A second approximation formula determination operation of respectively obtaining the DC component of the developing current and determining a second approximation formula under the condition that the peak-to-peak voltage of the AC voltage of the developing bias is respectively set to at least three second measurement peak-to-peak voltages included in a second measurement range, the second measurement range being set such that it has a minimum value larger than the maximum value of the first measurement range, the second approximation formula being a unary approximation formula representing the relationship between the second measurement peak-to-peak voltages in the second measurement range and the obtained DC component of the developing current; And The reference voltage determination operation determines the peak-to-peak voltage at the intersection where the first approximation formula determined by the first approximation formula determination operation and the second approximation formula determined by the second approximation formula determination operation cross each other as the reference peak-to-peak voltage.

2. The image forming apparatus according to claim 1, wherein The bias condition determination unit determines the first approximation formula by the least squares method based on the DC components of the development currents respectively obtained at the at least three first measurement peak-to-peak voltages included in the first measurement range.

3. The image forming apparatus according to claim 1, wherein When the slope of the first determination approximation formula, which is a linear approximation formula, is greater than a preset first threshold, the bias condition determination unit sets a linear formula in which the change of the average value of the at least three second measurement peak-to-peak voltages with respect to the peak-to-peak voltage is fixed as the second approximation formula. When the slope of the first determination approximation formula is less than the first threshold, the bias condition determination unit sets the first determination approximation formula as the second approximation formula. Here, the linear approximation formula is determined by the least squares method based on the DC components of the development currents respectively obtained at the at least three second measurement peak-to-peak voltages included in the second measurement range.

4. The image forming apparatus according to claim 1, wherein The intervals of the multiple first measurement peak-to-peak voltages within the first measurement range and the intervals of the multiple second measurement peak-to-peak voltages within the second measurement range are respectively set to be smaller than the interval between the maximum value of the first measurement range and the minimum value of the second measurement range.

5. The image forming apparatus according to claim 1, wherein, In the first approximation formula determination operation, when the correlation coefficient of the first approximation formula is smaller than a preset second threshold, the bias condition determination unit determines the first approximation formula based on the DC components of the development currents corresponding to the peak-to-peak voltages remaining after excluding at least one peak-to-peak voltage from the at least three first measurement peak-to-peak voltages.

6. The image forming apparatus according to claim 5, wherein, In the first approximation formula determination operation, when the correlation coefficient of the first approximation formula is smaller than the second threshold, the bias condition determination unit determines the first approximation formula based on the DC components of the development currents corresponding to the peak-to-peak voltages remaining after excluding the maximum peak-to-peak voltage from the at least three first measurement peak-to-peak voltages.

7. The image forming apparatus according to claim 1, wherein In the second approximation formula determination operation, when the correlation coefficient of the second approximation formula is smaller than a preset third threshold, the bias condition determination unit determines the second approximation formula based on the DC components of the development currents corresponding to the peak-to-peak voltages remaining after excluding at least one peak-to-peak voltage from the at least three second measurement peak-to-peak voltages.

8. The image forming apparatus according to claim 7, wherein In the second approximation formula determination operation, when the correlation coefficient of the second approximation formula is smaller than the third threshold value, the bias condition determination unit compares the correlation coefficient of the second determination approximation formula determined based on the DC component of the development current corresponding to the remaining peak-to-peak voltages after excluding the maximum peak-to-peak voltage among the at least three second measurement peak-to-peak voltages with the correlation coefficient of the third determination approximation formula determined based on the DC component of the development current corresponding to the remaining peak-to-peak voltages after excluding the minimum peak-to-peak voltage among the at least three second measurement peak-to-peak voltages, and determines the determination approximation formula with the larger correlation coefficient among the second determination approximation formula and the third determination approximation formula as the second approximation formula.

9. The image forming apparatus according to claim 7, wherein The bias condition determination unit pre-excludes the maximum peak-to-peak voltage or the minimum peak-to-peak voltage excluded in the second approximation formula determination operation from the second measurement range, and executes the next bias condition determination mode.

10. The image forming apparatus according to claim 1, wherein The number of the at least three first measurement peak-to-peak voltages in the first measurement range is set to be larger than the number of the at least three second measurement peak-to-peak voltages in the second measurement range.

11. The image forming apparatus according to claim 1, characterized in that, The bias condition determination unit obtains a change point, which is a point where the balance of the three currents constituting the DC component of the development current changes corresponding to the change in the peak-to-peak voltage, through the intersection point of the first approximation formula and the second approximation formula, and determines the peak-to-peak voltage corresponding to the change point as the reference peak-to-peak voltage. The three currents are: the toner movement current, which is a current generated by the movement of the toner from the developing roller to the image carrier in the image forming portion of the developing nip; the image portion brush current, which is a current flowing in the same direction as the toner movement current along the brush formed by the toner and the carrier across the developing roller and the image carrier; and the non-image portion brush current, which is a current flowing in the opposite direction to the toner movement current along the brush formed by the toner and the carrier across the developing roller and the image carrier in the non-image forming portion of the developing nip.

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