Patent Publication Number: US-9891550-B2

Title: Developing device which can detect rotational position of developing roller

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is based on Japanese Patent Application No. 2015-202839 filed with the Japan Patent Office on Oct. 14, 2015, the entire content of which is hereby incorporated by reference. 
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     This invention relates to a developing device, an image forming apparatus, and a control program of a developing device. More specifically, this invention relates to a developing device, an image forming apparatus, and a control program of a developing device, which can detect a rotational position of a developing roller, preventing complication of the device configuration. 
     Description of the Related Art 
     As electrophotographic image forming apparatuses, there are an MFP (Multi Function Peripheral) which has a scanner function, a facsimile function, a copying function, a function of a printer, a data transmitting function and a server function, a facsimile device, a copying machine, a printer, and so on. 
     An image forming apparatuses generally develop an electrostatic latent image formed on an image supporting body to form a toner image After transferring the toner image onto a sheet, a fixing device fixes the toner image on the sheet to form an image on the sheet. Some image forming apparatuses develop an electrostatic latent image on a surface of a photo conductor by using a developing device, to form a toner image, and transfer the toner image to a secondary transfer belt by using a primary transfer roller. The toner image on the secondary transfer belt is secondary transferred to a sheet by using a secondary transfer roller. In this instance, the photo conductor and the secondary transfer belt act as image supporting bodies. 
     In an electrophotographic process, density ununiformity (periodical ununiformity) may occur in the developing cycle in the sub scanning direction of the toner image, due to runout of an outer shape of the developing roller, when an electrostatic latent image is developed with toner by the developing roller of the developing device. An idea of a method for suppressing the density ununiformity is to adopt stricter screening criteria (inspection criteria) relating to runout of developing rollers at the time of manufacture of image forming apparatuses, to employ only image rollers of which the runout is small. However, since the method causes decreasing in yield of developing rollers, the method has a problem in that it causes increasing the cost of an image forming apparatus. 
     Another method for suppressing the periodical ununiformity above mentioned is to match phases of both a rotation period of a developing roller and a cycle of density ununiformity in the circumferential direction of the developing roller, wherein the density ununiformity is detected by an image density reading sensor. According to the method, the periodical ununiformity is reduced and suppressed. According to the method, a disk with slits is installed on the rotation shaft of the developing roller. The disk is detected by a photo sensor, such as a photo interrupter, or an encoder, so that the rotational position of the developing roller is detected. 
     The Document 1 below discloses a technique for detecting a rotational position of a developing roller by using a photo interrupter. According to the technique, a detection plate is directly connected to the rotation shaft of the developing roller. The detection plate rotates in conjunction with the developing roller. The detection plate has a slit. The photo interrupter detects the slit of the detection plate on every rotation of the detection plate, to detect the rotational position of the developing roller. 
     [Document 1] Japan Patent Publication No. 2000-98675 
     However, according to the another method above mentioned, a detector such as a photo interrupter or an encoder should be newly installed on a developing device. It has a problem which causes the complication of the device configuration and increase in the cost. Especially, from the viewpoint of the cost, the increase in a cost when a detector is newly installed is almost of the same as the increase in a cost when adopting stricter screening criteria relating to runout of developing rollers. Therefore, the another method above mentioned does not receive benefit by cost reduction. 
     SUMMARY OF THE INVENTION 
     This invention is to solve the above problems. The object is to provide a developing device, an image forming apparatus, and a control program of a developing device which can detect a rotational position of a developing roller, preventing the device configuration from being complex. 
     To achieve at least one of the above-mentioned objects, a developing device reflecting one aspect of the present invention comprises: a developing roller rotationally driven, for developing an electrostatic latent image formed on a surface of an image supporting body with toner, a screw rotationally driven, of which a ratio of number of rotations to number of rotations of the developing roller being rotationally driven is constant, and a processor, wherein the processor is configured to detect first toner density in developer by using a sensor installed facing the screw, during rotationally drive of the screw, and detect information indicating a rotational position of the developing roller, based on ripples which occur in the first toner density detected. 
     Preferably, the processor is further configured to: detect second toner density in a toner image formed on the surface of the image supporting body, during rotationally drive of the screw, and detect the information indicating the rotational position of the developing roller, further based on the second toner density detected. 
     Preferably, the processor is further configured to: detect a deviation amount between periodicity of the ripples and periodicity of the second toner density detected. 
     Preferably, the processor is further configured to: calculate a curved line which indicates relationship between the rotational position of the developing roller and a developing bias, based on the second toner density detected and the deviation amount, wherein the developing bias is an electrical voltage applied to the developing roller when the developing roller develops the electrostatic latent image. 
     Preferably, the processor is further configured to: detect the first toner density and the second toner density, in a state that system speed is slower than system speed of normal image forming. 
     Preferably, the processor is further configured to: detect the first toner density and the second toner density, in a state that a ratio of the rotational speed of the developing roller to a rotational speed of the image supporting body is reduced from normal image forming. 
     Preferably, the processor is further configured to: detect the first toner density and the second toner density, in a state that the toner density in the developer is lowered from normal image forming. 
     Preferably, the processor is further configured to: detect the first toner density and the second toner density, when a new developing device is installed on an image forming apparatus. 
     Preferably, a rotational speed of faster of the developing roller and the screw is an integral multiple of a rotational speed of slower of the developing roller and the screw. 
     Preferably, the developing device further comprises: a housing in which developer is stored, an agitating screw to convey the developer, agitating the developer, and a feeding screw to provide the developer conveyed by the agitating screw for the developing roller, wherein the housing includes a partition wall which separates the agitating screw and the feeding screw, and the sensor is provided near an aperture which is made on the wall, facing the agitating screw. 
     Preferably, the developing device further comprises: a detection subsidiary part which is fixed to the screw at a location facing the sensor, to improve sensitivity of the ripples. 
     Preferably, the detection subsidiary part extends parallel with an axis of rotation of the screw between spiral protruding portions which are formed on an outer periphery of a rotation shaft of the screw, wherein the spiral protruding portions constitute the screw. 
     Preferably, the detection subsidiary part gets thinner, with distance from the rotation shaft of the screw, viewed from an extending direction of the axis of rotation. 
     Preferably, the detection subsidiary part is made of an elastic body, and keeps contact with the housing contains the screw. 
     To achieve at least one of the above-mentioned objects, an image forming apparatus reflecting one aspect of the present invention comprises: the developing device, and a transfer device to transfer a toner image obtained by developing of the developing roller, to a recording medium. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows a cross sectional view of a structure of image forming apparatus  100 , according to the first embodiment of this invention. 
         FIG. 2  shows a block diagram of a control structure of image forming apparatus  100 , according to the first embodiment of this invention. 
         FIG. 3  shows a cross sectional view of a structure of developing device  107 , according to the first embodiment of this invention. 
         FIG. 4  shows a cross sectional view along IV-IV of  FIG. 3 . 
         FIGS. 5A and 5B  show a cross sectional view of a structure adjacent to agitating screw  132  in developing device  107  of the first embodiment of this invention. 
         FIGS. 6A-6C  is for explanation pertaining to behavior at clock time tm 1  of developing device  107 , according to the first embodiment of this invention. 
         FIGS. 7A-7C  is for explanation pertaining to behavior at clock time tm 2  of developing device  107 , according to the first embodiment of this invention. 
         FIG. 8  schematically shows a developing bias correction curve calculated by image forming apparatus  100 , according to the first embodiment of this invention. 
         FIG. 9  shows a flowchart of behavior of image forming apparatus  100 , according to the first embodiment of this invention. 
         FIG. 10  shows a subroutine of the first toner density fluctuation detection process (S 3  and S 13 ) in  FIG. 9 . 
         FIG. 11  shows a subroutine of the second toner density fluctuation detection process (S 9  and S 19 ) in  FIG. 9 . 
         FIGS. 12A and 12B  shows a cross sectional view of a structure adjacent to agitating screw  132  in developing device  107 , according to the second embodiment of this invention. 
         FIGS. 13A and 13B  shows a cross sectional view of a structure adjacent to agitating screw  132  in developing device  107 , according to the third embodiment of this invention. 
         FIG. 14  schematically shows a graph of ripples generated by detection subsidiary part  135  of the first, the second, and the third embodiments. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The embodiments of this invention will be explained in the followings with the figures. 
     In the following embodiments, an image forming apparatus as an MFP is explained. An image forming apparatus may be a facsimile device, a copying machine, a printer, or the like. 
     [The First Embodiment] 
     Firstly, a structure of an image forming apparatus of the embodiment will be explained. 
       FIG. 1  shows a cross sectional view of a structure of image forming apparatus  100 , according to the first embodiment of this invention. 
     Referring to  FIG. 1 , image forming apparatus  100  according to the embodiment is an MFP which is basically equipped with sheet conveying unit  10 , toner image forming unit  20 , and fixing device  30 . 
     Sheet conveying unit  10  includes paper feeding tray  102 , paper feeding roller  103   a , conveying rollers  103   b ,  103   c ,  103   e ,  103   f  and  103   g , paper ejection roller  103   d , and copy receiving tray  115 . Paper feeding tray  102  stores sheets on which images are to be formed. Paper feeding tray  102  may include a plurality of paper feeding trays. Paper feeding roller  103   a  is provided between paper feeding tray  102  and conveying path TR 1 . Conveying rollers  103   b  and  103   c  are provided along with conveying path TR 1 . Conveying rollers  103   e ,  103   f  and  103   g  are provided along with conveying path TR 2 . Paper ejection roller  103   d  is provided at the most downstream side of conveying path TR 1 . Copy receiving tray  115  is provided at the top of the main body  101  of the image forming apparatus  100 . 
     Toner image forming unit  20  synthesizes images of four colors of Y (yellow), M (magenta), C (cyan) and K (black) by so-called a tandem system, and transfers the toner image onto a sheet. Toner image forming unit  20  includes four image forming units  21 Y,  21 M,  21 C and  21 K, expose device (laser unit)  106 , secondary transfer belt  109 , primary transfer rollers  108   a ,  108   b ,  108   c  and  108   d , secondary transfer roller  111 , cleaning device  112 , and so on. 
     Image forming units  21 Y,  21 M,  21 C and  21 K are parallely placed immediately below secondary transfer belt  109 . Image forming unit  21 Y includes photo conductor  104   a , electrostatic charging roller  105   a , developing device  107   a , cleaning device  110   a , and so on. Photo conductor  104   a  is rotationally driven in the direction shown by arrow AR 1  in  FIG. 1 . Electrostatic charging roller  105   a , developing device  107   a , and cleaning device  110   a  are placed around photo conductor  104   a.    
     Image forming unit  21 M includes photo conductor  104   b , electrostatic charging roller  105   b , developing device  107   b , cleaning device  110   b , and so on Image forming unit  21 C includes photo conductor  104   c , electrostatic charging roller  105   c , developing device  107   c , cleaning device  110   c , and so on. Image forming unit  21 K includes photo conductor  104   d , electrostatic charging roller  105   d , developing device  107   d , cleaning device  110   d , and so on. Each of image forming units  21 M,  21 C and  21 K has a same structure as image forming unit  21 Y. 
     Expose device  106  is provided at the lower part of image forming units  21 Y,  21 M,  21 C, and  21 K. Secondary transfer belt  109  is provided at the upper part of image forming units  21 Y,  21 M,  21 C, and  21 K. Secondary transfer belt  109  is in the form of a ring, and is rotationally driven in the direction shown by arrow AR 2  in  FIG. 1 , in conjunction with sheet conveying unit  10 . Primary transfer rollers  108   a ,  108   b ,  108   c , and  108   d  face photo conductors  104   a ,  104   b ,  104   c  and  104   d  respectively, interposing secondary transfer belt  109 . Secondary transfer roller  111  is placed in contact with secondary transfer belt  109  at conveying path TR 1 . The distance between secondary transfer roller  111  and secondary transfer belt  109  is adjustable, by using a pressure contact and separation mechanism which is not shown in the figures. Cleaning device  112  is provided near secondary transfer belt  109 . Primary transfer rollers  108   a ,  108   b ,  108   c ,  108   d , secondary transfer belt  109 , and secondary transfer roller  111  constitute a transfer device which transfers a toner image developed by developing roller  131  onto recording media. 
     Fixing device  30  includes heating roller  116  and pressure roller  117 . Fixing device  30  pinches and conveys a sheet which holds a toner image, by a nip portion of heating roller  116  and pressure roller  117 , along with conveying path TR 1 , to fix the toner image onto the sheet. 
     When image forming apparatus  100  receives an instruction of performing a printing job, recording media such as sheets stored in paper feeding tray  102  are one by one taken by paper feeding roller  103   a , and conveyed along with conveying path TR 1  by conveying rollers  103   b  and  103   c . In parallel to the paper feeding, the surfaces of photo conductors  104   a ,  104   b ,  104   c  and  104   d  for YMCK colors are electrostatic charged by electrostatic charging rollers  105   a ,  105   b ,  105   c  and  105   d  of YMCK colors. After that, expose device  106  performs exposure based on image data. Herewith, electrostatic latent images are formed on the surfaces of photo conductors  104   a ,  104   b ,  104   c  and  104   d . These electrostatic latent images are developed by developing devices  107   a ,  107   b ,  107   c  and  107   d  for YMCK colors with toner. Herewith, toner images are formed on the surfaces of photo conductors  104   a ,  104   b ,  104   c  and  104   d . These toner images are transferred onto secondary transfer belt  109 , by a transfer bias which is applied to primary transfer rollers  108   a ,  108   b ,  108   c  and  108   d  for YMCK colors. Herewith, toner images of YMCK colors are overlapped and formed on secondary transfer belt  109 . After that, residual toner on the surface of photo conductors  104   a ,  104   b ,  104   c  and  104   d  is removed by cleaning devices  110   a ,  110   b ,  110   c  and  110   d  for YMCK colors. 
     A toner image on secondary transfer belt  109  is transferred onto a recording medium being conveyed between secondary transfer belt  109  and secondary transfer roller  111 , by a secondary transfer bias applied to secondary transfer roller  111 . After that, residual toner on secondary transfer belt  109  is removed by cleaning device  112 . 
     Heat and pressure are applied to the toner image formed on the recording medium, when the recording medium passes through fixing device  30 , to fix the toner image onto the recording medium. The recording medium on which the toner image was fixed is discharged onto copy receiving tray  115  by paper ejection roller  103   d.    
     When toner in the inner part of one of developing devices  107   a ,  107   b ,  107   c  and  107   d  is reduced by image forming, toner stored in the inner part of corresponding one of toner bottles  114   a ,  114   b ,  114   c  and  114   d  of YMCK colors is supplied to the one of developing devices  107   a ,  107   b ,  107   c  and  107   d . Toner bottles  114   a ,  114   b ,  114   c  and  114   d  are detachable. When toner in the inner part of a toner bottle among toner bottles  114   a ,  114   b ,  114   c  and  114   d  is exhausted, a user replaces the toner bottle. Herewith, toner is continuously supplied to image forming apparatus  100 . 
     When images are to be formed on both sides of the recording medium, paper ejection roller  103   d  is reversely rotated after the recording medium passed through fixing device  30 , so that the recording medium enters conveying path TR 2 . The recording medium is conveyed by conveying rollers  103   e ,  103   f  and  103   g , and fed into conveying path TR 1  again. Then, a toner image is formed on the rear surface of the recording medium. After that, the recording medium is discharged onto copy receiving tray  115 , by paper ejection roller  103   d.    
     Hereinafter, a photo conductor, an electrostatic charging roller, and a developing device in an arbitrary image forming unit among image forming units  21 Y,  21 M,  21 C, and  21 K may be referred to as photo conductor  104  (an example of an image supporting body), electrostatic charging roller  105 , and developing device  107  (an example of a developing device), respectively. 
       FIG. 2  shows a block diagram of a control structure of image forming apparatus  100 , according to the first embodiment of this invention. 
     Referring to  FIG. 2 , image forming apparatus  100  is equipped with control unit  200 , electrostatic charging control unit  211 , expose control unit  212 , developing control unit  213 , transfer control unit  214 , fixing control unit  215 , TCR (Toner Carrier Ratio) sensor SE 1 , and IDC (Image Density Control) sensor SE 2 . 
     Control unit  200  includes CPU (Central Processing Unit)  201 , ROM (Read Only Memory)  202 , and RAM (Random Access Memory)  203 . CPU  201 , and each of ROM  202 , RAM  203 , electrostatic charging control unit  211 , expose control unit  212 , developing control unit  213 , transfer control unit  214 , fixing control unit  215 , TCR sensor SE 1  and IDC sensor SE 2  are bilaterally connected with each other. 
     CPU  201  controls entire behavior of image forming apparatus  100 . CPU  201  executes processing based on control programs. 
     ROM  202  stores control programs or the like, executed by CPU  201 . 
     RAM  203  is a working memory for CPU  201 , and temporarily stores data relating to various jobs. 
     Electrostatic charging control unit  211  controls behavior of electrostatic charging roller  105 , such as electrical voltage applied to electrostatic charging roller  105 , rotational speed of electrostatic charging roller  105 , and so on. 
     Expose control unit  212  controls behavior of expose device  106 , such as exposure light intensity, irradiate timing when photo conductors  104  is irradiated with exposure light. 
     Developing control unit  213  controls behavior of developing device  107 , such as developing bias of developing device  107 , suppliance of toner to developing device  107 , rotational speed of motor  141  which drives parts in developing device  107 , and so on. 
     Transfer control unit  214  controls behavior of each of primary transfer rollers  108 , secondary transfer belt  109 , and secondary transfer roller  111 , such as primary transfer bias, primary transfer electrical current, contact pressure of primary transfer roller  108  to secondary transfer belt  109 , rotational speed of secondary transfer belt  109 , secondary transfer bias, and so on. 
     Fixing control unit  215  controls behavior of fixing device  113 , such as temperature of heating roller  116 , rotational speed of pressure roller  117 , and so on. 
     TCR sensor SE 1  outputs electrical voltage corresponding to magnetic permeability of developer present in a detection range. 
     IDC sensor SE 2  outputs electrical voltage corresponding to toner density of a toner image formed on the surface of photo conductor  104 . 
       FIG. 3  shows a cross sectional view of a structure of developing device  107 , according to the first embodiment of this invention.  FIG. 4  shows a cross sectional view along IV-IV of  FIG. 3 . 
     Referring to  FIGS. 3 and 4 , developing device  107  includes developing roller  131 , agitating screw  132 , feeding screw  133 , and housing  134 . Each of agitating screw  132  and feeding screw  133  has a circulating route which is formed oblique two axes with respect to developing roller  131 . 
     Developer is stored in the inner part of housing  134 . The inner part of housing  134  is partitioned into agitation tank  137  and feeding tank  138  by partition wall  134   a . Agitating screw  132  is installed in agitation tank  137 . Agitating screw  132  conveys developer in the direction shown by arrow AR 3 , agitating it to frictionally electrify toner in the developer. Aperture  134   b  is provided on partition wall  134   a  at the most downstream side in the direction shown by arrow AR 3 . The developer in agitation tank  137  is drawn into feeding tank  138 , via aperture  134   b.    
     Feeding screw  133  is installed in feeding tank  138 . Feeding screw  133  provides developing roller  131  with developer conveyed by agitating screw  132 , which includes toner electrostatically charged, conveying the developer in the direction shown by arrow AR 4 . The residual developer which was not provided for developing roller  131  is drawn down from feeding tank  138  to agitation tank  137 . 
     Developing roller  131  is rotationally driven in the direction shown by arrow AR 6 , to catch developer from feeding screw  133  by magnetic force. When developer is conveyed on developing roller  131 , a conveying amount of developer is quantified by a regulation blade (which is not shown in Figures), and the developer is frictionally electrified. After that, toner contained in the developer conveyed by developing roller  131  is supplied to the surface of photo conductor  104  at the developing location DV, by difference in electrical potential between a developing bias (electrical voltage applied to developing roller  131  when developing roller  131  develops an electrostatic latent image) and the surface electrical potential of photo conductor  104 . The developing location DV is a portion which faces photo conductor  104 . Herewith, an electrostatic latent image formed on the surface of photo conductor  104  is developed with toner, so that a toner image is formed on the surface of photo conductor  104 . 
     Developing roller  131 , agitating screw  132 , and feeding screw  133  are rotationally driven by a same motor  141  via gears. The ratio of revolutions of agitating screw  132  and feeding screw  133  to revolutions of developing roller  131  is 1 to 1, for example. Therefore, rotation phases of developing roller  131 , agitating screw  132 , and feeding screw  133  are same at all times, and not deviated. 
     The ratio of revolutions of agitating screw  132  and feeding screw  133  to revolutions of developing roller  131  during rotational driving is not limited to as presented above 1 to 1. The faster one of the rotational speed of developing roller  131  and the rotational speed of agitating screw  132  is preferably the integral multiple of the slower one of the rotational speed of developing roller  131  and the rotational speed of agitating screw  132 . A structure which makes a ratio of revolutions of agitating screw  132  to revolutions of developing roller  131  constant is arbitrary. The structure may employ gears, belts, transmissions driven, or the like. 
     The toner/carrier ratio Tc of the residual developer remained on developing roller  131  after developing, is decreased from normal developer, since the toner was consumed. The residual developer is recovered into agitation tank  137  via the two axes circulating route, by feeding screw  133 . Image forming apparatus  100  detects toner density in the developer by using TCR sensor SE 1 , during rotational drive of agitating screw  132 . When outputting electrical voltage of TCR sensor SE 1  decreases, image forming apparatus  100  determines that the toner/carrier ratio Tc (the toner density in the developer) of developer in agitation tank  137  is decreased. In such a case, image forming apparatus  100  supplies toner from one of toner bottles  114   a ,  114   b ,  114   c , and  114   d , to restore the toner/carrier ratio Tc. TCR sensor SE 1  is preferably provided near aperture  134   b  provided on partition wall  134   a , facing agitating screw  132 . Since developer is moved from agitating screw  132  to feeding screw  133  around aperture  134   b , so that developer temporarily remains around aperture  134   b , and the powder pressure of the developer tends to be higher. By providing TCR sensor SE 1  near aperture  134   b , the toner/carrier ratio Tc of developer with high powder pressure can be measured, so that the occurrence of ripples can be detected with more precision. 
     Image forming apparatus  100  performs an image stabilization process at necessary timing, to form toner images with proper toner density when developing of developing device  107 . The image stabilization process is to optimize difference in electrical potential between developing roller  131  and photo conductor  104  when developing Image forming apparatus  100  sets difference in electrical potential between developing roller  131  and photo conductor  104  to a preset value, and forms a toner image on the surface of photo conductor  104 . Image forming apparatus  100  measures toner density of the toner image on the surface of photo conductor  104 , by using IDC sensor SE 2 . Image forming apparatus  100  corrects difference in electrical potential between developing roller  131  and photo conductor  104  during developing, based on the measured toner density. IDC sensor SE 2  is provided near the surface of photo conductor  104 . 
     According to the embodiment, information to indicate the rotational position of developing roller  131  is detected, by using TCR sensor SE 1  and IDC sensor SE 2  installed in a conventional image forming apparatus. More specifically, image forming apparatus  100  detects information to indicate the rotational position of developing roller  131  based on ripples occurred in toner density detected by using TCR sensor SE 1  and fluctuation of toner density detected by using IDC sensor SE 2  during rotational drive of agitating screw  132 . 
     Next, the detection method for information to indicate the rotational position of developing roller  131  according to the embodiment will be explained. 
       FIGS. 5A and 5B  show a cross sectional view of a structure adjacent to agitating screw  132  in developing device  107  of the first embodiment of this invention.  FIG. 5A  is a cross sectional view showing a cross section parallel to the extending direction of rotation shaft  132   a .  FIG. 5B  is a cross sectional view showing a cross section plane of which the normal line extends in the extending direction of rotation shaft  132   a.    
     Referring to  FIGS. 5A and 5B , agitating screw  132  includes rotation shaft  132   a , spiral blade  132   b , and detection subsidiary part  135 . Spiral blade  132   b  is a spiral protruding portion installed on rotation shaft  132   a , with a predetermined pitch. Detection subsidiary part  135  is a paddle, and fixed on an outer periphery of rotation shaft  132   a . Detection subsidiary part  135  extends parallel with rotation shaft  132   a , in a portion of spiral blade  132   b , wherein the portion faces TCR sensor SE 1 . Detection subsidiary part  135  is to improve the sensitivity of ripples. Detection subsidiary part  135  may be integrally molded with rotation shaft  132   a  and spiral blade  132   b . Detection subsidiary part  135  should have magnetic permeability which is different from magnetic permeability of developer. Detection subsidiary part  135  is preferably made of non-magnetic material, such as resin. 
     Agitating screw  132  rotates in the direction shown by arrow AR 5 . Thereby, developer is conveyed in the direction shown by arrow AR 3 . TCR sensor SE 1  outputs electrical voltage corresponding to magnetic permeability of developer presents in detection range RG 1  in agitation tank  137 , wherein detection range RG 1  faces TCR sensor SE 1 . The carrier contained in developer is magnetic material. Therefore, when toner density in the developer decreases, the percentage of carrier in the developer increases. In this case, measured magnetic permeability increases, and toner/carrier ratio Tc decreases. 
     Detection subsidiary part  135  enters detection range RG 1  at time intervals corresponding to the rotation period of agitating screw  132 . Hence, outputting electrical voltage of TCR sensor SE 1  (magnetic permeability in detection range RG 1 ) fluctuates in a rotation period of agitating screw  132 . In consequence, in the output waveform of TCR sensor SE 1 , a ripple is generated in a rotation period of agitating screw  132 . The ripple is noise, in terms of measurement of toner/carrier ratio Tc in developer. Therefore, toner/carrier ratio Tc of developer is typically detected based on magnetic permeability measured, avoiding the ripples. The output waveform of TCR sensor SE 1  tends to include a ripple in the rotation period of agitating screw  132 , by nature. Therefore, ripples can be detected without detection subsidiary part  135 . 
       FIGS. 6A-6C  is for explanation pertaining to behavior at clock time tm 1  of developing device  107 , according to the first embodiment of this invention.  FIG. 6A  is a graph showing alteration of outputting electrical voltage (V) of TCR sensor SE 1  from moment to moment.  FIG. 6B  is a cross sectional view showing a state of agitating screw  132  at clock time tm 1 .  FIG. 6C  is a cross sectional view showing a state of developing roller  131  at clock time tm 1 . The time axis (the horizontal axis) in the graph of  FIG. 6A  corresponds to the rotational position of agitating screw  132 . 
     In the following explanation, IDC sensor SE 2  outputs electrical voltage corresponding to toner density at the developing location DV on the surface of photo conductor  104 . 
     Referring to  FIGS. 6A-6C , in the output waveform of TCR sensor SE 1  (curved line L 1 ), ripples occur with period T 1 . The ripples are caused by detection subsidiary part  135 . Hence, period T 1  corresponds to the rotation period of agitating screw  132 . Clock time tm 1  when the curved line L 1  peaks (clock time when a ripple occurs) corresponds to clock time when detection subsidiary part  135  passes in front of TCR sensor SE 1 . At clock time tm 1 , the rotational position PO which is explained later of developing roller  131  does not reach the developing location DV. 
       FIGS. 7A-7C  is for explanation pertaining to behavior at clock time tm 2  of developing device  107 , according to the first embodiment of this invention.  FIG. 7A  is a graph showing alteration of outputting electrical voltage (V) of IDC sensor SE 2  from moment to moment.  FIG. 7B  is a cross sectional view showing a state of agitating screw  132  at clock time tm 2 .  FIG. 7C  is a cross sectional view showing a state of developing roller  131  at clock time tm 2 . The time axis (the horizontal axis) in the graph of  FIG. 7A  corresponds to the rotational position of photo conductor  104 . 
     Referring to  FIGS. 7A-7C , in parallel with detection by TCR sensor SE 1 , image forming apparatus  100  forms a solid image of which the length in the sub scanning direction corresponds to at least one round of developing roller  131  (an image to form a toner image covering the entire image forming area), on the surface of photo conductor  104 . The toner density is detected by using IDC sensor SE 2 . 
     When the solid image was formed on the surface of photo conductor  104 , toner density (curved line L 2 ) of the toner image periodically changes with period T 2 . This periodical fluctuation of toner density is caused by density ununiformity in the circumferential direction of developing roller  131 , generated by runout of developing roller  131 . Hence, period T 2  corresponds to the rotation period of developing roller  131 . Clock time tm 2  is when curved line L 2  reaches the maximum value. At clock time tm 2 , the distance between the rotational position PO and photo conductor  104  becomes the minimum value, and the rotational position PO of developing roller  131  passes through the developing location DV. 
     The clock time when curved line L 2  reaches a minimum value can be employed as clock time tm 2 . In this instance, clock time tm 2  is when a portion of developing roller  131  to which the distance from photo conductor  104  shown in  FIG. 7C  is a maximum passes through developing location DV. 
     Image forming apparatus  100  calculates time ΔT which is the difference between clock time tm 1  and clock time tm 2 . Time ΔT corresponds to a deviation amount between periodicity of ripples detected by using TCR sensor SE 1  and periodicity of toner density detected by using IDC sensor SE 2  (a deviation amount between a phase in which a ripple occurs and a phase in which the toner density becomes a maximum value). Time ΔT is information indicates the rotational position of developing roller  131 . 
     More specifically, when the ratio of revolutions of agitating screw  132  to revolutions of developing roller  131  is 1:1, the rotational position of developing roller  131  can be calculated based on time ΔT and ripple period T 1 . In case that the ratio of revolutions of developing roller  131  to revolutions of agitating screw  132  is not 1:1, the rotational position of developing roller  131  can be calculated, as long as the ratio of revolutions of developing roller  131  to revolutions of agitating screw  132  is comprehended. 
     Since the developing location DV and the detecting location of IDC sensor SE 2  are different in actuality, the difference may be corrected. However, the deviation amount between the developing location DV and the detecting location of IDC sensor SE 2  is constant at all times. Then, there is no problem even if the correction is not performed. 
     Next, image forming apparatus  100  calculates a developing bias curved line (a density correction Vdc curved line), based on toner density detected by using IDC sensor SE 2  and calculated time ΔT. 
       FIG. 8  schematically shows a developing bias correction curve calculated by image forming apparatus  100 , according to the first embodiment of this invention. 
     Referring to  FIG. 8 , the developing bias correction curve is a curved line which indicates the relationship between the rotational position of developing roller  131  and the developing bias. Image forming apparatus  100  calculates the developing bias correction curve, based on toner density detected by using IDC sensor SE 2 , to alleviate fluctuation of toner density which is based on the rotational position of developing roller  131 . The period of the developing bias correction curve is equal to period T 2  (the rotation period of developing roller  131 ). As an example, at a rotational position of the developing roller (which corresponds to clock time tm 2 ) which the toner density reaches a maximum value in curved line L 2 , the developing bias in the developing bias correction curve is set as a minimum value. At a rotational position of the developing roller (which corresponds to clock time tm 3 ) which the toner density reaches a minimum value in curved line L 2 , the developing bias in the developing bias correction curve is set as a maximum value. 
     The reference location of the developing bias correction curve is preferably set to when the distance between developing roller  131  and photo conductor  104  is narrow due to runout of developing roller  131  (where toner density reaches a maximum value, namely, the rotational position of developing roller  131  which corresponds to clock time tm 2 ). The fluctuation of toner density based on the rotational position of developing roller  131  changes according to the environment and the number of printed sheets. Then, the developing bias correction curve is preferably updated each time an image stabilization process is performed. 
     When actual printing, image forming apparatus  100  confirms ripples in outputting electrical voltage of TCR sensor SE 1 , during preliminary behavior of starting up, after starting the printing. After entering the printable state, developing bias is begun to be applied in accordance with the developing bias correction curve at the timing of “ripple detection timing+the deviation amount”, more specifically, the timing the rotational position of developing roller  131  where toner density becomes a maximum value reaches the developing location DV. 
     After starting applying developing bias in accordance with the developing bias correction curve, whether fluctuation of toner density is remedied or not may be confirmed by using IDC sensor SE 2 . In this instance, the detection result of IDC sensor SE 2  is feed backed, to correct the developing bias correction curve and the deviation amount, so that images with little unevenness can be obtained. 
       FIG. 9  shows a flowchart of behavior of image forming apparatus  100 , according to the first embodiment of this invention. 
     Referring to  FIG. 9 , CPU  201  of image forming apparatus  100  determines whether attachment of a new developing device  107  is detected or not (S 1 ). Density ununiformity (periodical ununiformity) of developing roller  131  in the circumferential direction is caused by runout of developing roller  131 . The runout of developing roller  131  is caused by the mechanical shape of developing roller  131  (a shape of the mag roller). Therefore, whether density ununiformity of developing roller  131  in the circumferential direction is occurred or not is preferably confirmed, when attachment of a new developing device  107  is detected. 
     At step S 1 , when attachment of new developing device  107  is detected (YES at S 1 ). CPU  201  executes the first toner density fluctuation detecting process (S 3 ). 
       FIG. 10  shows a subroutine of the first toner density fluctuation detection process (S 3  and S 13 ) in  FIG. 9 . 
     Referring to  FIG. 10 , in the first toner density fluctuation detection process, CPU  201  decreases developing θ from 1.8 which is a value of normal image forming to 1.2, and decreases the system speed to a speed that is half of a speed of normal image forming (S 51 ). Developing θ is a ratio of the rotational speed of developing roller  131  to the rotational speed of photo conductor  104 . Whether fluctuation of toner density caused by the rotational position of developing roller  131  is detected or not depends on process conditions of image forming apparatus  100 . Since developing properties decrease by decreasing developing θ, detection sensitivity of fluctuation of toner density based on rotation of developing roller  131  can be enhanced. The detection accuracy of the rotational position of agitating screw  132  when a ripple occurs can be improved, by decreasing the system speed to half of the normal speed. 
     In the process of step S 51 , the toner density in the developer may be decreased from when normal image forming. 
     After step SM, CPU  201  forms a solid image on the surface of photo conductor  104  (S 53 ), and detects the toner density by using IDC sensor SE 2  (S 55 ). CPU  201  converts outputting electrical voltage of IDC sensor SE 2  to toner density (ID). Next, CPU  201  calculates PP (peak to peak, the amplitude) of fluctuation of toner density (S 59 ). Next, CPU  201  calculates the difference ΔID between a reference value for PP which is a quality target of image forming apparatus  100  and the calculated PP value (S 61 ). Next, CPU  201  determines whether the fluctuation of the toner density coincides with the developing period (the rotation period of developing roller  131 ) or not (S 63 ). The developing period is calculated by the rotational speed and size of developing roller  131 . 
     At step S 63 , when the fluctuation of toner density coincides with the developing period (YES at S 63 ), CPU  201  determines whether the difference ΔID is more than or equal to 0.1, or not (S 65 ). 
     At step S 65 , when the difference ΔID is more than or equal to 0.1 (YES at S 65 ), CPU  201  determines that fluctuation of toner density caused by rotation of developing roller  131  is detected (S 67 ), and returns to the main flowchart. 
     When the fluctuation of toner density does not coincide with the developing period at step S 63  (NO at S 63 ), or when the difference ΔID is less than 0.1 at step S 65  (NO at S 65 ), CPU  201  determines that fluctuation of toner density caused by rotation of developing roller  131  is not detected (S 69 ), and returns to the main flowchart. 
     Referring to  FIG. 9 , after step S 3 , CPU  201  determines whether fluctuation of toner density was detected at the process of step S 3  or not (S 5 ). 
     At step S 5 , when fluctuation of toner density was detected (YES at S 5 ), CPU  201  calculates a deviation amount between the ripple periodicity detected by using TCR sensor SE 1  and the toner density periodicity detected by using IDC sensor SE 2  (S 7 ). The deviation amount does not change as long as rotation phases of developing roller  131  and agitating screw  132  does not deviate. Then, the deviation amount should be calculated once for one developing device  107 . 
     After step S 7 , CPU  201  executes the second toner density fluctuation detecting process (S 9 ). 
       FIG. 11  shows a subroutine of the second toner density fluctuation detection process (S 9  and S 19 ) in  FIG. 9 . 
     Referring to  FIG. 11 , in the second toner density fluctuation detection process, CPU  201  sets developing θ to normal 1.8, and sets the system speed to the normal speed (S 81 ). After step S 81 , CPU  201  executes processes similar to step S 53  and the following steps in the first toner density fluctuation detection process (S 3 ) of  FIG. 10 , and returns to the main flowchart. 
     Referring to  FIG. 9 , after step S 9 , CPU  201  determines whether fluctuation of toner density was detected in the process of step S 9  or not (S 11 ). 
     At step S 11 , when fluctuation of toner density was detected (YES at S 11 ), CPU  201  determines that fluctuation of toner density (periodical ununiformity) occurs, under the normal printing condition. In this instance, CPU  201  calculates the developing bias correction curve (S 23 ), and steps in the process of step S 18 . 
     At step S 11 , when fluctuation of toner density was not detected (NO at S 11 ), CPU  201  determines that fluctuation of toner density (periodical ununiformity) does not occur under the normal printing condition. In this instance, CPU  201  determines that detection of a deviation amount and calculation of the developing bias correction curve are unnecessary when the detection of new developing device  107 , and steps in the process of step S 18 . 
     When attachment of new developing device  107  is not detected at step S 1  (NO at S 1 ), or fluctuation of toner density was not detected at step S 5  (NO at S 5 ), CPU  201  determines that detection of a deviation amount and calculation of the developing bias correction curve are unnecessary when the detection of new developing device  107 , and steps in the process of step S 12 . 
     At step S 12 , CPU  201  determines whether printings were done on the prescribed number of paper sheets or not (S 12 ). Until printings are done on the prescribed number of paper sheets, CPU  201  continues the process of step S 12 . 
     At step S 12 , when printings were done on the prescribed number of paper sheets (YES at S 12 ), CPU  201  executes the first toner density fluctuation detection process (S 13 ). When the number of printed sheets increases, there is the potential that fluctuation of toner density becomes tangible. Therefore, as presented above, the presence or absence of fluctuation of toner density is preferably detected, at the timing (for example, at the timing of an image stabilization process) when the number of printed sheets reaches a predetermined number (for example, a few hundreds to a few thousands). 
     After step S 13 , CPU  201  determines whether fluctuation of toner density was detected or not at the process of step S 13  (S 15 ). 
     At step S 15 , when fluctuation of toner density was not detected (NO at S 15 ), CPU  201  steps in the process of step S 12 . 
     At step S 5 , when fluctuation of toner density was detected (YES at S 15 ), CPU  201  calculates a deviation amount between periodicity of ripples detected by using TCR sensor SE 1  and periodicity of toner density detected by using IDC sensor SE 2  (S 17 ). 
     After step S 17 , CPU  201  determines whether paper sheets of the prescribed number were printed or not (S 18 ). Until paper sheets of the prescribed number are printed, CPU  201  continues the process of step S 18 . 
     At step S 18 , when paper sheets of the prescribed number were printed (YES at S 18 ), CPU  201  executes the second toner density fluctuation detection process (S 19 ). Next, CPU  201  determines whether fluctuation of toner density was detected or not at the process of step S 19 , or not (S 21 ). 
     At step S 21 , when fluctuation of toner density was detected (YES at S 21 ), CPU  201  calculates the developing bias correction curve (S 23 ), and steps in the process of step S 18 . 
     At step S 21 , when fluctuation of toner density was not detected (NO at S 21 ), CPU  201  determines that fluctuation of toner density (periodical ununiformity) does not occur under normal printing condition, and continues the normal printing mode. In this instance, CPU  201  steps in the process of step S 18 . 
     According to the embodiment, the rotational position of the developing roller is detected by using ripples in the output waveform of the TCR sensor, which are generated for each rotation of the agitating screw. A TCR sensor is installed by nature to detect magnetic permeability of developer filled in a developing device. Hence, the embodiment eliminates the need to install an expensive detector, such as a photo interrupter, an encoder, or the like. In consequence, the rotational position of the developing roller can be detected, preventing complication of the device configuration. 
     In addition, according to this embodiment, an IDC sensor is further used. Hence, the rotational position of the developing roller which causes unevenness of toner density (periodical ununiformity) is identified. Since the developing bias is corrected, based on the identified rotational position of the developing roller, unevenness of toner density which is caused by runout of the developing roller can be suppressed. 
     [The Second Embodiment] 
       FIGS. 12A and 12B  shows a cross sectional view of a structure adjacent to agitating screw  132  in developing device  107 , according to the second embodiment of this invention.  FIG. 12A  is a cross sectional view showing a cross section parallel to the extending direction of rotation shaft  132   a .  FIG. 12B  is a cross sectional view showing a cross section plane of which the normal line extends in the extending direction of rotation shaft  132   a.    
     Referring to  FIGS. 12A and 12B , detection subsidiary part  135  according to the embodiment has a plate shape as shown in the cross section of  FIG. 12B , and tapers toward housing  134 . The width W of detection subsidiary part  135  gets thinner little by little, with distance from rotation shaft  132   a  to approach housing  134 . 
     The structure and behavior of image forming apparatus  100  other than the above mentioned are similar to the first embodiment. The explanations are not repeated. 
     A ripple occurs in the output waveform of TCR sensor SE 1 , at timing when the tip of detection subsidiary part  135  arrives at the center of detection range RG 1 . According to this embodiment, outputting electrical voltage of TCR sensor SE 1  rapidly changes when a ripple occurs. The width of the ripple narrows in the direction of the rotational position of agitating screw  132 . In consequence, the rotational position of agitating screw  132  equipped with detection subsidiary part  135  can be identified with more precision, and degree of detection accuracy of the rotational position of agitating screw  132  improves. 
     [The Third Embodiment] 
       FIGS. 13A and 13B  shows a cross sectional view of a structure adjacent to agitating screw  132  in developing device  107 , according to the third embodiment of this invention.  FIG. 13A  is a cross sectional view showing a cross section parallel to the extending direction of rotation shaft  132   a .  FIG. 13B  is a cross sectional view showing a cross section plane of which the normal line extends in the extending direction of rotation shaft  132   a.    
     Referring to  FIGS. 13A and 13B , according to detection subsidiary part  135  of the embodiment, the tip is placed in contact with an inner periphery of housing  134 . Detection subsidiary part  135  has a plate shape section as shown in the cross section of  FIG. 13B . Detection subsidiary part  135  is preferably made of an elastic body. When detection subsidiary part  135  is made of an elastic body, detection subsidiary part  135  can be bent by force (force to prevent the rotation) received from housing  134 . 
     The structure and behavior of image forming apparatus  100  other than the above mentioned are similar to the first embodiment. The explanations are not repeated. 
     According to this embodiment, the volume ratio of detection subsidiary part  135  to detection range RG 1  when detection subsidiary part  135  passes through detection range RG 1  can be increased. Herewith, a ripple which occurs in outputting electrical voltage of TCR sensor SE 1  becomes larger. In consequence, the rotational position of agitating screw  132  equipped with detection subsidiary part  135  can be identified with more precision, and degree of detection accuracy of the rotational position of agitating screw  132  improves. 
       FIG. 14  schematically shows a graph of ripples generated by detection subsidiary part  135  of the first, the second, and the third embodiments. 
     Referring to  FIG. 14 , the width of ripple N 2  when using detection subsidiary part  135  according the second embodiment is narrower, as compared to ripple N 1  generated by detection subsidiary part  135  of the first embodiment. Ripple N 3  by using detection subsidiary part  135  of the third embodiment is larger, as compared to ripples N 1  and N 2 . 
     [Effect of the Embodiments] 
     According to the embodiments, a developing device, an image forming apparatus, and a control program for a developing device which can detect the rotational position of the developing roller can be provided, preventing a complication of the device configuration. 
     [Others] 
     An image forming apparatus of this invention may be an MFP, a black-and-white printer, a color printer, a copying machine, a facsimile device, or the like. 
     According to the above mentioned embodiment, a TCR sensor is installed facing the agitating screw. The TCR sensor may be installed facing a screw which agitates or conveys developer including toner. The screw is rotationally driven, wherein the ratio of the number of rotation of the screw to the developing roller is constant. The TCR sensor may be installed facing a feeding screw. 
     The above mentioned embodiments can be appropriately combined with each other. For example, the structure of detection subsidiary part  135  which tapers toward housing  134  in the second embodiment, and the structure of detection subsidiary part  135  of which the tip keeps contact with an inner periphery of housing  134  in the third embodiment can be combined. 
     The processes in the above mentioned embodiments can be performed by software and a hardware circuit. A computer program which executes the processes in the above embodiments can be provided. The program may be provided recorded in recording media of CD-ROMs, flexible disks, hard disks, ROMs, RAMs, memory cards, or the like to users. The program is executed by a computer of a CPU or the like. The program may be downloaded to a device via communication lines like the internet. The processes explained in the above flowcharts and the description are executed by a CPU in line with the program. 
     Although the present invention has been described and illustrated in detail, it is clearly understood that the same is by way of illustration and example only and is not to be taken by way of limitation, the spirit and scope of the present invention being limited only by the terms of the appended claims.