Patent Publication Number: US-10317814-B2

Title: Powder supply device and image forming apparatus incorporating same

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This patent application is based on and claims priority pursuant to 35 U.S.C. § 119(a) to Japanese Patent Application No. 2015-241515, filed on Dec. 10, 2015, in the Japan Patent Office, the entire disclosure of which is hereby incorporated by reference herein. 
     BACKGROUND 
     Technical Field 
     Embodiments of the present invention generally relate to a powder supply device and an image forming apparatus, such as a copier, a printer, a facsimile machine, or a multifunction peripheral or MFP having at least two of copying, printing, facsimile transmission, plotting, and scanning capabilities. 
     Description of the Related Art 
     There are developer supply devices including a developer reservoir to temporarily store developer (i.e., powder) to be discharged to a developing device, a developer amount detector to detect the amount of developer in the developer reservoir, and a developer container to contain the developer to be supplied to the developer reservoir. In such developer supply devices, the developer is supplied to the developer reservoir from the developer container based on a detected amount of developer in the developer reservoir. 
     SUMMARY 
     An embodiment of the present invention provides a powder supply device that includes a powder reservoir including a rotator having a rotation shaft, to temporarily store powder supplied from a powder container; and a powder amount detector to detect an amount of the powder in the powder reservoir. The powder amount detector includes a detected member disposed in the powder reservoir, a contact member attached to the rotation shaft of the rotator to rotate together with the rotation shaft, to contact the detected member to vibrate or move the detected member, a detector to detect one of vibration and a displacement of the detected member, and a detection result processor to detect the amount of the powder in the powder reservoir based on a detection result generated by the detector. The powder supply device further includes a controller to supply the powder from the powder container to the powder reservoir based on a detection result generated by the powder amount detector. The controller is configured to rotate the rotator in discharging the powder from the powder reservoir to a supply destination and in supplying the powder from the powder container to the powder reservoir. 
     In another embodiment, an image forming apparatus includes an image bearer, a latent image forming device to form a latent image on the image bearer, a developing device to develop, with developer, the latent image on the image bearer, and a powder supply device to supply the developer to the developing device. The powder supply device includes the powder reservoir and the powder amount detector described above. The image forming apparatus further includes a controller to supply the developer from the powder container to the powder reservoir based on a detection result generated by the powder amount detector. The controller is configured to rotate the rotator in discharging the developer from the powder reservoir to the developing device and in supplying the developer from the powder container to the powder reservoir. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A more complete appreciation of the disclosure and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein: 
         FIG. 1  is a schematic diagram illustrating an image forming apparatus according to an embodiment of the present disclosure; 
         FIG. 2  is a perspective view illustrating a developer supply device according to an embodiment; 
         FIG. 3  is a perspective view illustrating developer supply drivers according to an embodiment; 
         FIG. 4  is a front view of the developer supply drivers illustrated in  FIG. 3 ; 
         FIG. 5  is a perspective view of a sub-hopper of the developer supply device illustrated in  FIG. 2 ; 
         FIG. 6  is a perspective view of the sub-hopper, in which an upper side is open to illustrate an interior thereof; 
         FIG. 7  is a block diagram illustrating an exemplary configuration of principal portions of control circuitry of in the developer supply device according to an embodiment; 
         FIG. 8  is an explanatory view for explaining the movement of the developer when the developer is supplied to a developer reservoir of the sub-hopper from a developer bottle of the developer supply device illustrated in  FIG. 2 ; 
         FIG. 9  is an explanatory view for explaining the movement of the developer when the developer is supplied to a developing device according to an embodiment; 
         FIG. 10  illustrates circuitry of a magnetic flux sensor according to an embodiment; 
         FIG. 11  is a chart of counting of a signal output from the magnetic flux sensor; 
         FIG. 12  is a perspective view illustrating an exterior of the magnetic flux sensor; 
         FIG. 13  is a schematic block diagram of a controller to acquire the signal from the magnetic flux sensor, according to an embodiment; 
         FIG. 14  illustrates relative positions of the magnetic flux sensor and a vibration plate, according to an embodiment; 
         FIG. 15  illustrates actions of magnetic flux penetrating the vibration plate; 
         FIG. 16  is a graph of oscillation frequency of the magnetic flux sensor corresponding to a distance between the magnetic flux sensor and the vibration plate; 
         FIG. 17  is a perspective view illustrating a component layout around the vibration plate; 
         FIG. 18  is a side view illustrating a rotation position of the rotation shaft, at which the torsion spring is about to contact a projection on the vibration plate; 
         FIG. 19  is a side view of the torsion spring rotated further from the position illustrated in  FIG. 18 ; 
         FIG. 20  is a side view of the torsion spring rotated further from the position illustrated in  FIG. 19 ; 
         FIG. 21  is a top view of the vibration plate; 
         FIG. 22  schematically illustrates a state of developer, which is represented by dots, stored in the sub-hopper; 
         FIG. 23  is a graph of changes in the count of the oscillation signal from the magnetic flux sensor from when the torsion spring flips the projection until the vibration of the vibration plate ceases; 
         FIG. 24  is a flowchart of developer amount detection in the sub-hopper, according to an embodiment; 
         FIG. 25  is a table of data in count value analysis according to an embodiment; 
         FIG. 26  is a chart of count values sampled during a single vibration cycle of the vibration plate; 
         FIG. 27A  is a perspective view of a structure to vibrate the vibration plate, according to an embodiment; 
         FIG. 27B  is a perspective view of a torsion spring in the structure illustrated in FIG.  27 A; 
         FIG. 28  is a schematic view illustrating a state before the torsion spring, which is attached via a holder to the rotation shaft, contacts the projection on the vibration plate in the structure illustrated in  FIG. 27A ; 
         FIG. 29  is a timing chart illustrating an example of driving respective members in a developer supply device according to Embodiment 1; 
         FIG. 30  is a block diagram illustrating an exemplary configuration of principal portions of control circuitry of a developer supply device according to Embodiment; 
         FIG. 31  is a timing chart illustrating an example of driving respective members in the developer supply device according to Embodiment 2; 
         FIG. 32  is a block diagram illustrating an exemplary configuration of principal portions of control circuitry of a developer supply device according to Embodiment; and 
         FIG. 33  is a timing chart illustrating an example of driving respective members in the developer supply device according to Embodiment 3. 
     
    
    
     The accompanying drawings are intended to depict embodiments of the present invention and should not be interpreted to limit the scope thereof. The accompanying drawings are not to be considered as drawn to scale unless explicitly noted. 
     DETAILED DESCRIPTION 
     In describing embodiments illustrated in the drawings, specific terminology is employed for the sake of clarity. However, the disclosure of this patent specification is not intended to be limited to the specific terminology so selected, and it is to be understood that each specific element includes all technical equivalents that operate in a similar manner and achieve a similar result. 
     As an example, descriptions are given below of detection of the amount of developer (i.e., powder) including toner and carrier, in an electrophotographic image forming apparatus. In particular, the present embodiment concerns detection of the amount of developer in a sub-hopper to store developer between a developing device, which develops an electrostatic latent image on a photoconductor, and a container from which the developer is supplied to the developing device. Although the developer in the present embodiment is a mixture of toner and carrier, the powder can be one-component developer (i.e., toner) or another powder. Although the descriptions below concern developer being the powder, one or more of aspects of the present disclosure can adapt to a powder supply device to handle powder such as flour, metal powder, resin powder, and the like. 
     Referring now to the drawings, wherein like reference numerals designate identical or corresponding parts throughout the several views thereof, and particularly to  FIG. 1 , an image forming apparatus according to an embodiment of the present invention is described. 
     It is to be noted that the suffixes Y, M, C, and K attached to each reference numeral indicate only that components indicated thereby are used for forming yellow, magenta, cyan, and black images, respectively, and hereinafter may be omitted when color discrimination is not necessary. 
     Referring now to the drawings, an embodiment of the present invention is described below. 
       FIG. 1  is a schematic view of an image forming apparatus  100  according to the present embodiment. As illustrated in  FIG. 1 , the image forming apparatus  100  employs a so-called tandem system and includes image forming units  106 K,  106 C,  106 M, and  106 Y (collectively “image forming units  106 ”) corresponding to different colors, lined along an intermediate transfer belt  105 . 
     The image forming apparatus  100  includes a sheet feeding tray  101  and a sheet feeding roller  102  to feed sheets  104  from the sheet feeding tray  101 . A registration roller pair  103  stops the sheet  104  and forwards the sheet  104  to a secondary transfer position where the image is transferred from the intermediate transfer belt  105 , timed to coincide with image formation in the image forming units  106 . Although the colors of toner images formed thereby are different, the multiple image forming units  106  are similar in internal structure. The image forming unit  106 K forms black toner images, the image forming unit  106 M forms magenta toner images, the image forming unit  106 C forms cyan toner images, and the image forming unit  106 Y forms yellow toner images. 
     The image forming unit  106 Y is described in detail below. Since the image forming units  106  have a similar structure, descriptions of the image forming units  106 M,  106 C, and  106 K are omitted. The intermediate transfer belt  105  is an endless belt entrained around a driving roller  107  and a driven roller  108 . The driving roller  107 , a driving motor to rotate the driving roller  107 , and the driven roller  108  together drive the intermediate transfer belt  105 . 
     Among the multiple image forming units  106 , the image forming unit  106 Y is the first to transfer toner images onto the intermediate transfer belt  105 . The image forming unit  106 Y includes a photoconductor drum  109 Y and components disposed around the photoconductor drum  109 Y, namely, a charging device  110 Y, a developing device  112 Y, a photoconductor cleaner  113 Y, and a discharger. The image forming unit  106 Y, together with an optical writing device  111 , serves as an image forming section. The optical writing device  111  is configured to irradiate, with light, the photoconductor drums  109 Y,  109 M,  109 C, and  109 K (collectively “photoconductor drums  109 ”). 
     To form images, the charging device  110 Y uniformly charges the outer face of the photoconductor drum  109 Y in the dark, after which the optical writing device  111  directs light from a light source corresponding to yellow images to the photoconductor drum  109 Y. Thus, an electrostatic latent image is formed on the photoconductor drum  109 Y, and the optical writing device  111  serves as a latent image forming device. The developing device  112 Y develops the electrostatic latent image into a visible image with yellow toner. Thus, a yellow toner image is formed on the photoconductor drum  109 Y. A transfer device  115 Y transfers the toner image onto the intermediate transfer belt  105  at a primary transfer position, where the photoconductor drum  109 Y contacts or is closest to the intermediate transfer belt  105 . Thus, the yellow toner image is formed on the intermediate transfer belt  105 . Subsequently, the photoconductor cleaner  113 Y removes toner remaining on the outer face of the photoconductor drum  109 Y, and the discharger discharges the outer face of the photoconductor drum  109 Y. Then, the photoconductor drum  109 Y is on standby for subsequent image formation. 
     The yellow toner image formed on the intermediate transfer belt  105  by the image forming unit  106 Y is then transported to the image forming unit  106 M as the intermediate transfer belt  105  rotates. The image forming unit  106 M forms a magenta toner image on the photoconductor drum  109 M through the processes similar to the processes performed by the image forming unit  106 Y. The magenta toner image is transferred from the photoconductor drum  109 M and superimposed on the yellow toner image. While rotating, the intermediate transfer belt  105  transports the yellow and magenta toner images further to the image forming units  106 C and  106 K. Then, cyan and black toner images are transferred from the photoconductor drums  109 C and  109 K, respectively, and superimposed on the toner image on the intermediate transfer belt  105 . Thus, a multicolor (i.e., full-color) intermediate toner image is formed on the intermediate transfer belt  105 . 
     The sheets  104  contained in the sheet feeding tray  101  are sent out from the top sequentially. At a position where a conveyance path of the sheet  104  contacts or is closest to the intermediate transfer belt  105 , the intermediate toner image is transferred from the intermediate transfer belt  105  onto the sheet  104 . Thus, an image is formed on the sheet  104 . The sheet  104  carrying the image is transported to a fixing device  116 , where the image is fixed on the sheet  104 . Then, the sheet  104  is ejected outside the image forming apparatus  100 . The intermediate transfer belt  105  is provided with a belt cleaner  118 . The belt cleaner  118  includes a cleaning blade pressed against the intermediate transfer belt  105  to scrape off toner from the surface of the intermediate transfer belt  105  at a position downstream from the secondary transfer position and upstream from the photoconductor drums  109  in the direction in which the intermediate transfer belt  105  rotates. 
     Referring to  FIG. 2 , descriptions are given below of structures for developer supply to the developing devices  112 , which are similar among cyan (C), magenta (M), yellow (Y), and black (B). Thus,  FIG. 2  illustrates the structure to supply the developer to one of the four developing devices  112 . The developer is contained in a developer bottle  117  serving as an upstream powder container. In  FIG. 2 , a first developer supply passage  119  extends from a sub-hopper  90  to the developing device  112 , and a second developer supply passage  120  extends from the developer bottle  117  to the sub-hopper  90 . The developer is supplied from the developer bottle  117  through the second developer supply passage  120  to the sub-hopper  90 . The sub-hopper  90  temporarily stores the developer supplied from the developer bottle  117  and supplies the developer to the developing device  112  according to the amount of developer remaining in the developing device  112 . From the sub-hopper  90 , the developer is supplied through the first developer supply passage  119  to the developing device  112 . When no or almost no toner remains in the developer bottle  117 , developer is not supplied to the sub-hopper  90 . An aspect of the present embodiment is to detect a situation in which the amount of developer remaining in the sub-hopper  90  is small. 
     Next, the driving of respective members for supplying the developer will be described. 
       FIG. 3  is a perspective view illustrating developer supply drivers  80 Y,  80 M,  80 C, and  80 K, and  FIG. 4  is a front view of the developer supply drivers  80 Y,  80 M,  80 C, and  80 K. 
     The developer supply drivers  80 Y,  80 M,  80 C, and  80 K serve as supply-use drivers used when the developer within the developer bottles  117  is supplied to the sub-hoppers  90 Y,  90 M,  90 C, and  90 K of developer supply devices, respectively. The developer supply drivers  80 Y,  80 M,  80 C, and  80 K drive bottle agitators  117 A ( 117 A 1  and  117 A 2 ) and conveying screws  117 B of the developer bottles  117  and first and second stirring conveyors  96  and  97  (refer to  FIG. 6 ) within the sub-hoppers  90 Y,  90 M,  90 C, and  90 K, which will be described later. The bottle agitators  117 A can be screws, coils, paddles, or the like. To supply the developer from the developer bottle  117 , at least one of the bottle agitator  117 A and the conveying screw  117 B disposed inside the developer bottle  117  is driven, thereby causing the developer flowing down from an outlet of the developer bottle  117  into the sub-hopper  90 . Alternatively, a conveying screw (or a conveying coil) is provided to convey the developer from the outlet of the developer bottle  117  toward the sub-hopper  90 , and the conveying screw is driven to supply the developer from the developer bottle  117  toward the sub-hopper  90 . 
     The developer supply drivers  80 Y,  80 M,  80 C, and  80 K include second driving motors  81 Y,  81 M,  81 C, and  81 K (supply-use motors), respectively, each of which serves as a second driving source. The developer supply drivers  80 Y,  80 M,  80 C, and  80 K are also provided with gear trains each including a plurality of gears. Those gears are supported on plates  86 Y,  86 M,  86 C, and  86 K, respectively, so as to freely rotate. In addition, the developer supply drivers  80 Y,  80 M,  80 C, and  80 K include conveying-use joints  83 Y,  83 M,  83 C, and  83 K, respectively, each of which is coupled to the conveying screw  117 B of the developer bottle  117 . The developer supply drivers  80 Y,  80 M, and  80 C for colors also include driving-side couplings  85 Y,  85 M, and  85 C, respectively, each of which is coupled to a coupling of the developer bottle  117 . Meanwhile, the developer supply driver  80 K for black includes a first driving-side coupling  85   a K coupled to a coupling attached to a shaft of a first bottle agitator  117 A 1  of the developer bottle  117 . The developer supply driver  80 K also includes a second driving-side coupling  85   b K coupled to a coupling attached to a shaft of a second bottle agitator  117 A 2  of the developer bottle  117 . 
     Driving forces of the respective second driving motors  81 Y,  81 M,  81 C, and  81 K are transmitted to the conveying screws  117 B of the developer bottles  117  for respective colors via a worm gear, a plurality of gears, and the conveying-use joints  83 Y,  83 M,  83 C, and  83 K, thereby the conveying screws are rotated. The driving forces of the respective second driving motors  81 Y,  81 M,  81 C, and  81 K are further transmitted to agitator-driving gears  84 Y,  84 M, and  84 C and a first agitator-driving gear  84   a K from the conveying-use joints  83 Y,  83 M,  83 C, and  83 K via a plurality of gears. Subsequently, the driving forces are transmitted to the agitators of the developer bottles  117  via the driving-side couplings  85 Y,  85 M, and  85 C disposed coaxially with the agitator-driving gears  84 Y,  84 M, and  84 C, respectively, thereby driving the agitators. The driving force is also transmitted to the first bottle agitator  117 A 1  of the developer bottle  117  via the first driving-side coupling  85   a K disposed coaxially with the first agitator-driving gear  84   a K, thereby driving the first agitator. In addition, as for the developer supply driver  80 K for black, the driving force of the second driving motor  81 K is transmitted to a second agitator-driving gear  84   b K from the first agitator-driving gear  84   a K. Subsequently, the driving force is transmitted to the second bottle agitator  117 A 2  of the developer bottle  117  via the second driving-side coupling  85   b K disposed coaxially with the second agitator-driving gear  84   b K, thereby driving the second agitator. 
     The driving forces of the second driving motors  81 Y,  81 M,  81 C, and  81 K are also transmitted to second-driving one-way clutches  82 Y,  82 M,  82 C, and  82 K, respectively, each of which is attached to an end portion on a rear side of a rotation shaft  96   c  of the first stirring conveyor  96  (refer to  FIG. 6 ) serving as a rotator (stirrer), which will be described later. Subsequently, the driving forces of the respective second driving motors  81 Y,  81 M,  81 C, and  81 K are transmitted to the first stirring conveyor  96  and the second stirring conveyors  97  described later via the second-driving one-way clutches  82 Y,  82 M,  82 C, and  82 K. 
     Next, the sub-hoppers  90 Y,  90 M,  90 C, and  90 K will be described. Note that, because the sub-hoppers  90 Y,  90 M,  90 C, and  90 K of respective colors are similar in structure and operation, the sub-hopper for black will be described here and subscripts, namely, Y, M, C, and K will be omitted as appropriate in the following description. 
       FIG. 5  is a perspective view of the sub-hopper  90 .  FIG. 6  is a perspective view illustrating an interior of the sub-hopper  90 . The upper side of the sub-hopper  90  is open in  FIG. 6 . 
     As illustrated in  FIGS. 5 and 6 , the sub-hopper  90  includes a case  93   b , which contains a first stirring conveyor  96 , a second stirring conveyor  97 , a first conveyor  98 , and a second conveyor  99  and is open on the upper side. The sub-hopper  90  further includes an upper cover  93   a  as a lid of the case  93   b . The upper cover  93   a  includes an inlet  91  to receive the developer supplied from a supply opening of the developer bottle  117 . 
     The sub-hopper  90  includes, inside the case  93   b , a developer reservoir  90   a  (i.e., a downstream powder container or a powder reservoir) to temporarily store the developer supplied from the developer bottle  117  and a conveyance compartment  90   b  to transport the stored developer to the developing device  112 . The developer reservoir  90   a  is separated from the conveyance compartment  90   b  by a partition  92 . First and second openings  92   a  and  92   b  are secured at both ends of the partition  92 . The first opening  92   a  is on the rear side (upper side in the drawing or a driving unit side), and the second opening  92   b  is on the front side (lower side in the drawing). 
     The first stirring conveyor  96  and the second stirring conveyor  97  are disposed side by side in the developer reservoir  90   a . On the right wall (in  FIG. 6 ) of the case  93   b  of the sub-hopper  90 , a magnetic flux sensor  10  serving as a vibration detector is disposed. On the inner face of the right wall (in  FIG. 6 ) of the case  93   b , a vibration plate  201  (a detected member) is disposed to face the magnetic flux sensor  10  via the case  93   b . The first stirring conveyor  96 , which is disposed on the right side, in the drawing, of the developer reservoir  90   a , includes a rotation shaft  96   c  and a spiral screw blade  96   b  whose pitch is relatively large. Additionally, a torsion spring  203 , serving as a contact member (to vibrate the vibration plate  201 ), to flip the vibration plate  201  is disposed on the first stirring conveyor  96 . The second stirring conveyor  97 , which is on the side of the partition  92  in the developer reservoir  90   a , includes a rotation shaft  97   c , a spiral blade  97   b  whose pitch is relatively large, and paddles  97   a . The paddles  97   a  are disposed on the rotation shaft  97   c  and positioned to face the first opening  92   a  and the second opening  92   b , respectively. 
     The conveyance compartment  90   b  is partitioned by a partition  901  into a first passage  902 A and a second passage  902 B. An opening  901   a  for conveyance is disposed on the front side of the partition  901  so that the first passage  902 A and the second passage  902 B communicate with each other. The first conveyor  98  is disposed in the first passage  902 A, and the second conveyor  99  is disposed in the second passage  902 B. The first conveyor  98  has a rotation shaft  98   b  and a spiral blade  98   a . The second conveyor  99  has a rotation shaft  99   b  and a spiral blade  99   a . The pitch of the spiral blade  98   a  of the first conveyor  98  is reduced in a range facing the opening  901   a.    
     The pitch of the spiral blade  99   a  of the second conveyor  99  is uniform in the axial direction thereof. The first conveyor  98  transports the developer in the first passage  902 A toward the opening  901   a  (from the rear side to the front side). The second conveyor  99  transports the developer in the second passage  902 B from the front side to the rear side. The downstream end of the second passage  902 B communicates with a developer outlet formed in the bottom of the case  93   b . The developer outlet communicates with a supply inlet of the developing device  112 . The developer transported through the second passage  902 B by the second conveyor  99  is supplied through the developer outlet to the developing device  112 . 
     The sub-hopper  90  is provided with a driving part  130  (illustrated in  FIG. 5 , serving as a replenishment-use driver) to replenish the developing device  112  with the developer supplied from the sub-hopper  90 . The driving part  130  is disposed on the front side of the sub-hopper  90  and includes a first driving motor  131  (i.e., a first driving source or replenishment-use motor) and a gear train including multiple gears. The driving force of the first driving motor  131  is transmitted, via a one-way clutch  132  (disposed at a lower end in the drawing of the rotation shaft  96   c  of the first stirring conveyor  96 ), to the first stirring conveyor  96 . Then, the first stirring conveyor  96  rotates. The driving force of the first driving motor  131  is transmitted further from the first stirring conveyor  96  via the multiple gears to the second stirring conveyor  97 . Then, the second stirring conveyor  97  rotates. Additionally, the driving force of the first driving motor  131  is transmitted via the multiple gears to the first and second conveyors  98  and  99 . Then, the first and second conveyors  98  and  99  rotate. 
     In the present embodiment, the developer reservoir  90   a  stores the developer. Even when the developer bottle  117  becomes empty, the developer can be supplied from the developer reservoir  90   a  to the developing device  112 . With this structure, preferable images can be produced while uses are preparing a new developer bottle  117 . 
       FIG. 7  is a block diagram illustrating an exemplary configuration of principal portions of control circuitry of the developer supply device. 
     In  FIG. 7 , a controller  210  includes a central processing unit (CPU), a read only memory (ROM) storing a control program or various types of data, a random access memory (RAM) temporarily storing various types of data, and so on. The controller  210  receives a detection result on the toner concentration from a toner concentration sensor  211  that detects the toner concentration in developer contained in the developing device  112 . The controller  210  compares a target value stored in the RAM and the detection result from the toner concentration sensor  211  and controls a first driving motor  131  to supply, to the developing device  112 , developer in accordance with the comparison result. In specific terms, the first driving motor  131  is driven for a time period corresponding to the amount to be supplied. Then, the developer is supplied from the developer supply device to the developer in which the toner concentration has decreased due to toner consumption during image development. For example, the supplied developer has a toner content of 25 to 35 percent by weight, which is larger than the content of toner in the developer in the developing device  112  (e.g., 4 to 10 percent by weight). Accordingly, when the developer is supplied into the developing device  112 , the toner concentration in developer in the developing device  112  increases and thus, the toner concentration in developer in the developing device  112  is kept near the target value. 
     The developer supply device can include the controller  210 . Alternatively, the image forming apparatus  100  can include the controller  210 . 
     In addition, in response to a signal from the magnetic flux sensor  10  indicating that the amount of the developer in a developer reservoir  90   a  is less than a predetermined amount (i.e., “no developer”), the controller  210  drives the second driving motor  81  to supply the developer. The magnetic flux sensor  10  functions as a vibration detector of a powder amount detector, and details of a detection principle thereof will be described later. Subsequently, in response to a signal from the magnetic flux sensor  10  indicating that the amount of the developer in the developer reservoir  90   a  is equal to or greater than the predetermined amount, the controller  210  stops driving the second driving motor  81  to end the supply of the developer. Meanwhile, when the signal from the magnetic flux sensor  10  does not change even after the second driving motor  81  is driven for a predetermined time period (12 seconds in the present embodiment), the controller  210  stops driving the second driving motor  81 . Subsequently, deeming that the developer bottle  117  has no developer, the controller  210  causes a display of the image forming apparatus  100  to display a message prompting the replacement of the developer bottle  117 . 
     Next, the movement of the developer in the sub-hopper  90  will be described. 
       FIG. 8  is a view for explaining the movement of the developer when the developer is supplied to the developer reservoir  90   a  from the developer bottle  117 . 
     As illustrated in  FIG. 8 , while the developer is supplied to the developer reservoir  90   a  from the developer bottle  117 , as described earlier, the second driving motor  81  is driven. Once the second driving motor  81  is driven, the first stirring conveyor  96  and the second stirring conveyor  97  are rotated via the second-driving one-way clutch  82 . At this time, the rotation shaft  96   c  of the first stirring conveyor  96  rotates idle with respect to a first-driving one-way clutch  132  and thus, the first-driving one-way clutch  132  does not rotate. The first and second stirring conveyors  96  and  97  rotate clockwise in the drawing when viewed from a front side. 
     The developer in the developer bottle  117  is supplied onto the second stirring conveyor  97  of the developer reservoir  90   a . The developer supplied to the second stirring conveyor  97  is conveyed to the front side and the rear side by the second stirring conveyor  97 . The developer conveyed to the end portion on the rear side by the second stirring conveyor  97  passes through the first opening  92   a  to the conveyance compartment  90   b . At this time, since the conveyors  98  and  99  of the conveyance compartment  90   b  are not rotating, the developer is accumulated in the vicinity of the first opening  92   a  of the conveyance compartment  90   b . When the developer is blocked from being conveyed to the conveyance compartment  90   b  due to this accumulated developer, the developer conveyed to the end portion on the rear side is conveyed to the first stirring conveyor  96 . The developer conveyed to the end portion on the front side by the second stirring conveyor  97  passes through the second opening  92   b  to the conveyance compartment  90   b . Subsequently, when the developer is blocked from being conveyed to the conveyance compartment  90   b  due to the developer accumulated in the vicinity of the second opening  92   b  of the conveyance compartment  90   b , the developer conveyed to the end portion on the front side is also conveyed to the side of the first stirring conveyor  96 . 
     As illustrated in  FIG. 8 , the first stirring conveyor  96  conveys the developer toward a region where a vibration plate is disposed, which serves as a detected member whose vibration is detected by the magnetic flux sensor  10 . The developer conveyed to the region where the vibration plate  201  is disposed is conveyed vertically below the inlet  91  by a paddle-shaped cleaner  96   a . While the developer is thus supplied to the developer reservoir  90   a  from the developer bottle  117 , the developer is circulated in the developer reservoir  90   a  by the first and second stirring conveyors  96  and  97 . 
       FIG. 9  is a view for explaining the movement of the developer when the developer is supplied to the developing device  112 . 
     While the developer is supplied to the developing device  112 , the first driving motor  131  is driven. As the first driving motor  131  drives, the first and second stirring conveyors  96  and  97  and the first and second conveyors  98  and  99  rotate. In the present embodiment, the first and second stirring conveyors  96  and  97  and the first conveyor  98  rotate clockwise when viewed from the front side of the apparatus, whereas the second conveyor  99  rotates counterclockwise when viewed from the front side. The developer in the first passage  902 A is conveyed to the front side from the rear side by the first conveyor  98 . Subsequently, the first conveyor  98  forwards the developer from the end portion on the front side through the opening  901   a  to the second passage  902 B. In the second passage  902 B, the second conveyor  99  conveys the developer to the rear side from the front side. At the rear end, the developer drops through the supply inlet to the developing device  112 . 
     Meanwhile, the developer in the developer reservoir  90   a  is conveyed similarly to the above description. During the supply of developer, however, the first conveyor  98  and the second conveyor  99  are rotated, and the developer is not accumulated in the vicinity of the first and second openings  92   a  and  92   b  of the conveyance compartment  90   b  but is conveyed further. Accordingly, the developer in the developer reservoir  90   a  is not circulated in the developer reservoir  90   a  but is sequentially forwarded to the conveyance compartment  90   b.    
     As the developer in the developer reservoir  90   a  is sequentially forwarded through the first and second openings  92   a  and  92   b  to the conveyance compartment  90   b  as described above, the amount of the developer in the developer reservoir  90   a  decreases gradually. As a result, the height of the developer becomes lower than the region where the vibration plate  201 , the vibration of which is detected by the magnetic flux sensor  10 , is disposed. Consequently, the vibration of the vibration plate  201  no longer changes due to the developer. At this point, as will be described later, the controller  210  detects that there is no developer in the developer reservoir  90   a  based on the output value from the magnetic flux sensor  10  detecting the vibration of the vibration plate  201 . Then, the second driving motor  81  is driven to start supplying the developer to the developer reservoir  90   a . Once the second driving motor  81  is driven, the driving force is transmitted to the second-driving one-way clutch  82 . Thus, the second-driving one-way clutch  82  is rotated. In the present embodiment, the rotation speed of the second-driving one-way clutch  82  is set faster than the rotation speed of the first stirring conveyor  96  rotated by the first driving motor  131 . Before the second-driving one-way clutch  82  is caused to rotate, the rotation shaft  96   c  of the first stirring conveyor  96  rotates clockwise, relative to the second-driving one-way clutch  82 , as viewed from the front side of the apparatus, in the present embodiment. By contrast, when the second-driving one-way clutch  82  rotates, the rotation shaft  96   c  of the first stirring conveyor  96  rotates counterclockwise, relative to the second-driving one-way clutch  82 , as viewed from the front side. As a result, the second-driving one-way clutch  82  is coupled. Accordingly, the first and second stirring conveyors  96  and  97  are rotated by the driving force of the second driving motor  81 . As the first stirring conveyor  96  starts rotating, due to the driving force of the second driving motor  81 , the rotation speed of the rotation shaft  96   c  of the first stirring conveyor  96  becomes faster than the rotation speed of the first-driving one-way clutch  132 . With this configuration, the rotation shaft  96   c  of the first stirring conveyor  96  rotates idle with respect to the first-driving one-way clutch  132 . In addition, the first and second conveyors  98  and  99  are continuously driven to rotate by the first driving motor  131 . 
     Thus, by setting the rotation speed of the first stirring conveyor  96  rotated by the second driving motor  81  to a speed different from the rotation speed of the first stirring conveyor  96  rotated by the first driving motor  131 , driving sources can be switched to each other with inexpensive one-way clutches. In a configuration in which the driving sources are switched using an electromagnetic clutch or the like, it is necessary to control a timing for coupling the clutch. By contrast, the present embodiment dispenses with controlling such a timing to couple the clutch or the like and is advantageous in that software configuration can be simplified. 
     Next, descriptions are given below of an internal structure of the magnetic flux sensor  10  according to the present embodiment with reference to  FIG. 10 . The magnetic flux sensor  10  is an oscillator circuit based on a Colpitts-type LC oscillator circuit (L represents a inductor and C represents a capacitor) and includes a coil pattern  11 , a resistor pattern  12 , first and second capacitors  13  and  14 , a feedback resistor  15 , unbuffered integrated circuits (ICs)  16  and  17 , and an output terminal  18 . 
     The coil pattern  11  is a planar coil made from conducting wire (signal wire) printed on a board  300  (illustrated in  FIG. 12 ) of the magnetic flux sensor  10 . As illustrated in  FIG. 10 , the coil pattern  11  has an inductance L attained by the coil. In the coil pattern  11 , the inductance L changes depending on the magnetic flux passing through a space opposing a board face on which the coil pattern  11  is printed. The magnetic flux sensor  10  in the present embodiment is used as a signal generator to output signals having a frequency corresponding to the magnetic flux passing through the space opposed to the face bearing the coil pattern  11 . 
     Similar to the coil pattern  11 , the resistor pattern  12  is a planar resistor made of a planar pattern of a conducting wire printed on the board  300 . The resistor pattern  12  in the present embodiment has a serpentine or zigzag pattern, thereby better inhibiting flow of electrical current compared with a resistor having a linear pattern. Incorporating the resistor pattern  12  is one aspect of the present embodiment. The term “zigzag” means the shape in which the wire is bent and folded back, like a serpentine, multiple times to reciprocate in a predetermined direction. Referring to  FIG. 10 , the resistor pattern  12  has a resistance value R p . The coil pattern  11  and the resistor pattern  12  are connected in series with each other. 
     The first and second capacitors  13  and  14  serve as a capacitance and a part of the Colpitts-type LC oscillator circuit including the coil pattern  11 . Accordingly, the first and second capacitors  13  and  14  are connected serially with the coil pattern  11  and the resistor pattern  12 . A loop including the coil pattern  11 , the resistor pattern  12 , and the first and second capacitors  13  and  14  serves as a resonance current loop. 
     The feedback resistor  15  is inserted to stabilize a bias voltage. With a function of the unbuffered ICs  16  and  17 , fluctuations in potential of a part of the resonance current loop are output as a rectangular wave corresponding to the resonance frequency from the output terminal  18 . 
     With this configuration, the magnetic flux sensor  10  oscillates at a frequency f corresponding to the inductance L, the resistance value R P , and a capacitance C of the first and second capacitors  13  and  14 . The frequency f is expressed by Formula 1 below. 
     
       
         
           
             
               
                 
                   f 
                   = 
                   
                     
                       1 
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         π 
                       
                     
                     ⁢ 
                     
                       
                         
                           1 
                           LC 
                         
                         - 
                         
                           
                             ( 
                             
                               
                                 
                                   R 
                                   L 
                                 
                                 + 
                                 
                                   R 
                                   P 
                                 
                               
                               
                                 2 
                                 ⁢ 
                                 L 
                               
                             
                             ) 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   Formula 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   1 
                 
               
             
           
         
       
     
     The inductance L changes depending on the presence and density of the magnetic material adjacent to the coil pattern  11  (planar coil). Thus, according to the oscillation frequency of the magnetic flux sensor  10 , the magnetic permeability in the space adjacent to the coil pattern  11  can be determined. 
     It is to be noted that a circuit resistance R L  (resistance value) is caused by a conducting wire or signal wire (e.g., the length of the wire) forming the circuit illustrated in  FIG. 10 . Most of the conducting wire is used to form the coil pattern  11  in the magnetic flux sensor  10  according to the present embodiment. Accordingly, the circuit resistance R L  is substantially identical to the resistance value attained by the conducting wire forming the coil pattern  11 . 
     As described above, the magnetic flux sensor  10  faces the vibration plate  201  via the case  93   b  of the sub-hopper  90  in the present embodiment. Accordingly, the magnetic flux generated by the coil pattern  11  passes through the vibration plate  201 . That is, the vibration plate  201  affects the magnetic flux generated by the coil pattern  11  and affects the inductance L. Consequently, the vibration plate  201  affects the frequency of signal of the magnetic flux sensor  10 . 
       FIG. 11  is a chart of counting of signal output from the magnetic flux sensor  10  according to the present embodiment. If the magnetic flux generated by the coil pattern  11  does not change, the magnetic flux sensor  10  keeps oscillating at a constant frequency basically. Consequently, the count value of the output signal increases constantly with elapse of time as illustrated in  FIG. 11 . For example, in  FIG. 11 , at time points t 1 , t 2 , t 3 , t 4 , and t 5 , count values aaaah, bbbbh, cccch, ddddh, and AAAAh are acquired respectively. 
     The count values are calculated based on Periods T 1 , T 2 , T 3 , and T 4  . . . , respectively, to obtain the frequency in each of Periods T 1 , T 2 , T 3 , and T 4  in  FIG. 11 . For example, in a case where an interrupt signal is output each time a reference clock equivalent for 2 milliseconds (ms) is counted, the count value in each period is divided with 2 ms. Thus, the frequency f (Hz) of the magnetic flux sensor  10  in each of Periods T 1 , T 2 , T 3 , and T 4  in  FIG. 11  is calculated. In the case where the upper limit of the count value is FFFFh as in  FIG. 11 , the oscillation frequency f (Hz) in Period T 4  can be calculated as follows. Deduct ddddh from FFFFh and divide, with 2 ms, the sum of the AAAAh and FFFFh—ddddh. 
     Thus, the image forming apparatus  100  according to the present embodiment acquires the frequency of signal generated by the magnetic flux sensor  10  and determines, based on the result of acquisition, a phenomenon corresponding to the oscillation frequency of the magnetic flux sensor  10 . In the magnetic flux sensor  10  according to the present embodiment, the inductance L changes in response to the state of the vibration plate  201  disposed facing the coil pattern  11 , and the frequency of signal output from the output terminal  18  changes accordingly. Consequently, the controller  210  to acquire the signal recognizes the state of the vibration plate  201  disposed facing the coil pattern  11 . The controller  210  determines the state of developer inside the sub-hopper  90  based on the state of the vibration plate  201 . It is to be noted that, although the frequency is obtained by dividing the count value of the signal by the period in the description above, alternatively, in a case where the period during which the count value is acquired is fixed, the acquired count value itself can be used as the parameter indicating the frequency. 
       FIG. 12  is a perspective view illustrating an exterior of the magnetic flux sensor  10  according to the present embodiment. In  FIG. 12 , the face of the board  300 , on which the coil pattern  11  and the resistor pattern  12  (described above with reference to  FIG. 10 ) are disposed, is faced up. That is, a detection face for detecting magnetic permeability, which is to oppose the space subjected to magnetic permeability detection, is faced up. As illustrated in  FIG. 12 , the resistor pattern  12 , which is connected serially to the coil pattern  11 , is printed on the detection face on which the coil pattern  11  is printed. As described above with reference to  FIG. 10 , the coil pattern  11  is made of conducting wire (signal line) printed in a spiral shape on the board face. Additionally, the resistor pattern  12  is made of conducting wire printed in a serpentine or zigzag pattern on the board face, and the above-described function of the magnetic flux sensor  10  is established by these patterns. The coil pattern  11  and the resistor pattern  12  serve as a detecting portion of the magnetic flux sensor  10  according to the present embodiment. The magnetic flux sensor  10  is attached to the sub-hopper  90  with the detecting portion facing the vibration plate  201 . 
     Next, descriptions are given below of a structure to acquire outputs from the magnetic flux sensor  10  in the image forming apparatus  100  according to the present embodiment, with reference to  FIG. 13 . 
       FIG. 13  is a schematic block diagram of the controller  20  to acquire the signal from the magnetic flux sensor  10 . The controller  20  includes a central processing unit (CPU)  21 , an application specific integrated circuit (ASIC)  22 , a timer  23 , a crystal-oscillator circuit  24 , and an input-output control ASIC  30 . The controller  20  can be a part of the controller  210  illustrated in  FIG. 7 . Alternatively, the controller  20  is connected to the controller  210  to be controlled thereby. 
     The CPU  21  is a computation unit and executes computation according to programs stored in a memory, such as a read only memory (ROM), to control operation of the entire controller  20 . The ASIC  22  functions as a connection interface between a system bus, to which the CPU  21  and a random access memory (RANI) are connected, and another device. The timer  23  outputs an interrupt signal to the CPU  21  each time the count of reference clock input from the crystal-oscillator circuit  24  reaches a predetermined count. In response to the interrupt signal input from the timer  23 , the CPU  21  outputs the read signal for acquiring the output value of the magnetic flux sensor  10 . The crystal-oscillator circuit  24  generates the reference clock to operate respective elements inside the controller  20 . The input-output control ASIC  30  acquires the signal output from the magnetic flux sensor  10  and converts the signals into data processable inside the controller  20 . As illustrated in  FIG. 13 , the input-output control ASIC  30  includes a magnetic permeability counter  31 , a read signal acquisition unit  32 , and a count value output  33 . As described above, the magnetic flux sensor  10  according to the present embodiment is an oscillator circuit that outputs a rectangular wave having the frequency corresponding to the magnetic permeability of the space as a detection target. 
     The magnetic permeability counter  31  increments the value according to the rectangular wave output from the magnetic flux sensor  10 . That is, the magnetic permeability counter  31  serves as a target signal counter to count the number of the signal whose frequency is to be calculated. It is to be noted that, in the present embodiment, multiple magnetic flux sensors  10  are provided for the respective sub-hoppers  90  coupled to developing devices  112 Y,  112 M,  112 C, and  112 K, and multiple magnetic permeability counters  31  are used accordingly. The read signal acquisition unit  32  acquires, from the CPU  21  via the ASIC  22 , the read signal, which is a command to acquire the count value of the magnetic permeability counter  31 . Acquiring the read signal from the CPU  21 , the read signal acquisition unit  32  inputs, to the count value output  33 , a signal instructing output of the count value. According to the signal from the read signal acquisition unit  32 , the count value output  33  outputs the count value of the magnetic permeability counter  31 . 
     The CPU  21  has an access to the input-output control ASIC  30 , for example, via a register. Accordingly, the CPU  21  writes a value in a predetermined register of in the input-output control ASIC  30  to output the above-described read signal. Additionally, the count value from the count value output  33  is stored in a predetermined register of the input-output control ASIC  30 , from which the CPU  21  acquires the count value. The controller  20  illustrated in  FIG. 13  is disposed in an apparatus (e.g., the image forming apparatus  100 ) or a device other than the magnetic flux sensor  10  in one embodiment. In another embodiment, the controller  20  is mounted, as a circuit including the CPU  21 , on the board  300  of the magnetic flux sensor  10 . 
     In the above-described structure, the CPU  21  detects the vibration state of the vibration plate  201  based on the count value acquired from the count value output  33  and, based on the detection result, detects the amount of developer in the sub-hopper  90 . The count value output  33  serves as a frequency-related data output. That is, a detection result processor is implemented by the CPU  21  performing computation according to a predetermined program. The count value acquired from the count value output  33  is used as frequency-related data indicating the frequency of the magnetic flux sensor  10 , which changes corresponding to the vibration of the vibration plate  201 . 
     Next, descriptions are given below of effects of the vibration plate  201  on the oscillation frequency of the magnetic flux sensor  10  according to the present embodiment. As illustrated in  FIG. 14 , the board face of the magnetic flux sensor  10  bearing the coil pattern  11  faces the vibration plate  201  via the case  93   b  of the sub-hopper  90 . Then, a magnetic flux arises, centering around a center of the coil pattern  11 , and the magnetic flux penetrates the vibration plate  201 . 
     For example, the vibration plate  201  is made of a stainless steel plate. As illustrated in  FIG. 15 , an eddy current is generated in the vibration plate  201  as a magnetic flux G 1  penetrates the vibration plate  201 . A magnetic flux G 2  is generated by the eddy current and acts to cancel the magnetic flux G 1  generated by the coil pattern  11 . As the magnetic flux G 1  is thus canceled, the inductance L in the magnetic flux sensor  10  decreases. As defined by Formula 1 above, the oscillation frequency f increases as the inductance L decreases. 
     The strength of the eddy current, which occurs inside the vibration plate  201  due to the magnetic flux generated by the coil pattern  11 , changes according to the strength of the magnetic flux as well as a distance between the coil pattern  11  and the vibration plate  201 .  FIG. 16  is a graph of oscillation frequency of the magnetic flux sensor  10  corresponding to the distance between the coil pattern  11  and the vibration plate  201 . The strength of the eddy current occurring inside the vibration plate  201  is inversely proportional to the distance between the coil pattern  11  and the vibration plate  201 . Accordingly, as the distance between the coil pattern  11  and the vibration plate  201  decreases, the oscillation frequency of the magnetic flux sensor  10  becomes higher. When the distance is smaller than a threshold, the inductance L is too low, and the magnetic flux sensor  10  does not oscillate. 
     In the sub-hopper  90  according to the present embodiment, the CPU  21  uses the characteristics illustrated in  FIG. 16  to detect the vibration of the vibration plate  201  based on the oscillation frequency of the magnetic flux sensor  10 . The amount of developer in the sub-hopper  90  is detected based on the vibration of the vibration plate  201  thus detected. In other words, the vibration plate  201  and the magnetic flux sensor  10  illustrated in  FIG. 14  as well as the structure to process the signal output from the magnetic flux sensor  10  is used as a powder detector according to the present embodiment. The magnetic flux sensor  10  serves as a vibration detector. 
     The vibration of the vibration plate  201  flipped by the torsion spring  203  is expressed by an eigenfrequency and an attenuation ratio determined by external factors that absorb the vibration energy. The eigenfrequency is defined by rigidity of the vibration plate  201  and weight of the projection  202  (refer to  FIG. 17 ). The external factors to absorb the vibration energy include the presence of developer that contacts the vibration plate  201  in the sub-hopper  90 , in addition to fixed factors such as the holding strength of the mount  201   a  cantilevering the vibration plate  201  and air resistance. The amount or state of developer that contacts the vibration plate  201  in the sub-hopper  90  changes depending on the amount of developer in the sub-hopper  90 . Accordingly, by detecting the vibration of the vibration plate  201 , the amount of developer remaining in the sub-hopper  90  is detected. In the sub-hopper  90  according to the present embodiment, the torsion spring  203 , disposed on the first stirring conveyor  96  to stir developer, flips the vibration plate  201  and vibrates the vibration plate  201  periodically according to the rotation cycle. 
     Next, descriptions are given below of placement of components around the vibration plate  201  in the sub-hopper  90  and the structure for the torsion spring  203  to flip the vibration plate  201 .  FIG. 17  is a perspective view illustrating a component layout around the vibration plate  201 . As illustrated in  FIG. 17 , the vibration plate  201  is secured via a mount  201   a  to the case  93   b  of the sub-hopper  90 .  FIG. 18  is a side view illustrating a rotation position of the rotation shaft  96   c , at which the torsion spring  203  is about to contact the projection  202 . Specifically, the portion of the torsion spring  203  that contacts the projection  202  is referred to as a contact portion  203   a . The rotation shaft  96   c  rotates so that the torsion spring  203  rotates clockwise in  FIG. 18 . The torsion spring  203  is an elastic body attached to the rotation shaft  96   c  via a holder  205  (illustrated in  FIG. 27A ). The torsion spring  203  is constantly biased in the direction in which the rotation shaft  96   c  rotates (clockwise in the drawing). 
     As illustrated in  FIG. 18 , the projection  202  projects from a face (on the front side of paper on which the drawing is drawn) of the vibration plate  201  and inclined relative to the face of the vibration plate  201  when viewed from a lateral side. Specifically, the projection  202  has an inclined face  202   a  that approaches the rotation shaft  96   c  along the direction of rotation of the torsion spring  203 . When the torsion spring  203  flips the vibration plate  201  to vibrate, the contact portion  203   a  of the torsion spring  203  pushes the inclined face  202   a  of the projection  202 . 
       FIG. 19  is a side view of the torsion spring  203  positioned downstream in the direction indicated by arrow Y 1  from the position illustrated in  FIG. 18 . As the torsion spring  203  rotates further with the contact portion  203   a  kept in contact with the projection  202 , the vibration plate  201  is pushed and deformed along the inclined face  202   a . In  FIG. 19 , broken lines represent positions of the vibration plate  201  and the projection  202  in a state in which no external force is applied thereto (hereinafter “stationary state”). As illustrated in  FIG. 19 , the contact portion  203   a  of the torsion spring  203  pushes the projection  202  on the vibration plate  201 . 
     Since the vibration plate  201  is secured via the mount  201   a  to the case  93   b  of the sub-hopper  90 , the position of the first end of the vibration plate  201  on the side of the mount  201   a  does not change. By contrast, the opposite end (i.e., a free end) of the vibration plate  201 , in which the projection  202  is disposed, is pushed by the torsion spring  203  and moves to the side opposite to the rotation shaft  96   c . Consequently, the vibration plate  201  deforms, starting from the mount  201   a . Energy to vibrate the vibration plate  201  is accumulated in the vibration plate  201  being in the deformed state. 
       FIG. 20  is a side view of the torsion spring  203  positioned downstream in the direction indicated by arrow Y 1  from the position illustrated in  FIG. 19 . In  FIG. 20 , broken lines represents the position (i.e., a predetermined position) of the vibration plate  201  being in the stationary state, and alternate long and short dashed lines represent the position of the vibration plate  201  illustrated in  FIG. 19 . When the vibration energy, which has been accumulated by the contact portion  203   a  of the torsion spring  203  pushing the vibration plate  201 , is released, the vibration plate  201  deforms to the opposite side as represented by solid lines.  FIG. 21  is a top view of the vibration plate  201 . As illustrated in  FIG. 20 , when the pushing force given to the projection  202  by the torsion spring  203  is released, owing to the energy of deformation accumulated in the vibration plate  201 , the free end of the vibration plate  201 , provided with the projection  202 , deforms and moves to the opposite side. In the state illustrated in  FIGS. 20 and 21 , the vibration plate  201  is away from the magnetic flux sensor  10 , which faces the vibration plate  201  via the case  93   b  of the sub-hopper  90 . Subsequently, while vibrating, the vibration plate  201  repeatedly approaches the magnetic flux sensor  10  closer than the stationary state and draws away therefrom further than the stationary state. Then, the vibration plate  201  returns to the stationary state as the vibration attenuates. 
       FIG. 22  schematically illustrates a state of developer (represented by dots) stored in the sub-hopper  90 . When the developer is present in the sub-hopper  90  as illustrated in  FIG. 22 , the vibration plate  201  and the projection  202  contact the developer while vibrating. Accordingly, compared with a state in which the sub-hopper  90  is empty, the vibration of the vibration plate  201  attenuates early. According to changes in attenuation of vibration, the amount of developer in the sub-hopper  90  is detected. 
       FIG. 23  is a graph of changes in the count value of the oscillation signal from the magnetic flux sensor  10  per counting period from when the torsion spring  203  flips the projection  202  until the vibration of the vibration plate  201  attenuates to cease. The count value of the oscillation signal increases as the oscillation frequency becomes higher. Accordingly, the count value indicated by the ordinate in  FIG. 23  is replaceable with the oscillation frequency. As illustrated in  FIG. 23 , at Time point t 1 , the contact portion  203   a  of the torsion spring  203  contacts and pushes the projection  202 , and the vibration plate  201  approaches the magnetic flux sensor  10 . Then, the oscillation frequency of the magnetic flux sensor  10  increases, and the count value per counting period increases. At Time point t 2 , the torsion spring  203  stops pushing the projection  202 . Subsequently, the vibration plate  201  vibrates owing to the accumulated vibration energy. As the vibration plate  201  vibrates, the distance between the magnetic flux sensor  10  repeatedly increases and decreases from that distance in the stationary state. Consequently, the frequency of the oscillation signal of the magnetic flux sensor  10  fluctuates inherent to the vibration of the vibration plate  201 , and the count value per counting period fluctuates similarly. 
     The amplitude of vibration of the vibration plate  201  becomes narrower as the vibration energy is consumed. That is, the vibration of the vibration plate  201  attenuates with elapse of time. Accordingly, the change in distance between the vibration plate  201  and the magnetic flux sensor  10  decreases with elapse of time. Similarly, the change in count value changes with elapse of time. As described above, the vibration of the vibration plate  201  attenuates earlier when the amount of developer remaining in the sub-hopper  90  is greater. Accordingly, how the vibration of the vibration plate  201  attenuates is recognizable based on the analysis of the attenuation manner of the oscillation signal from the magnetic flux sensor  10  illustrated in  FIG. 23 . Then, the amount of developer in the sub-hopper  90  is recognizable. Referring to  FIG. 23 , when P 1 , P 2 , P 3 , P 4  . . . represent the peaks of the count values of the oscillation signal, respectively, an attenuation ratio ζ of the vibration of the vibration plate  201  can be obtained by, for example, Formula 2 below. 
     
       
         
           
             
               
                 
                   ζ 
                   = 
                   
                     
                       
                         P 
                         6 
                       
                       - 
                       
                         P 
                         5 
                       
                     
                     
                       
                         P 
                         2 
                       
                       - 
                       
                         P 
                         1 
                       
                     
                   
                 
               
               
                 
                   Formula 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
               
             
           
         
       
     
     Referring to the change ratio between one peak value and another peak value acquired at different time points as expressed by Formula 2, errors caused by environmental changes are canceled, thereby attaining more accurate attenuation ratio. Specifically, in Formula 2, the ratio between the difference between P 2  and P 1 , and the difference between P 6  and P 5  is calculated. In other words, the CPU  21  according to the present embodiment obtains the attenuation ratio based on the ratio of the count values acquired at different time points. 
     It is to be noted that, in Formula 2, use of Peaks P 1  and P 2 , and Peaks P 5  and P 6 , out of the peaks illustrated in  FIG. 23 , is an example, and other peaks can be used instead. However, it is preferable to exclude the peak at Time point t 2 , at which the vibration plate  201  pushed by the torsion spring  203  is closest to the magnetic flux sensor  10 , since the peak at Time point t 2  includes error. For example, the friction between the torsion spring  203  and the projection  202  causes a sliding noise, which is superimposed on the peak. Even if the developer in the sub-hopper  90  accelerates the attenuation of the vibration, as illustrated in  FIG. 22 , the vibration frequency of the vibration plate  201  does not change significantly. Accordingly, the attenuation of amplitude in the specific period can be calculated from the calculated ratio of the amplitude of specific peaks as expressed in Formula 2. 
     Next, descriptions are given below of detection of developer amount in the sub-hopper  90  according to the present embodiment with reference to a flowchart illustrated in  FIG. 24 . 
       FIG. 24  illustrates a flow of actions of the CPU  21  illustrated in  FIG. 13 . As illustrated in  FIG. 24 , at S 1 , the CPU  21  detects the occurrence of vibration as the torsion spring  203  pushes the projection  202  as illustrated in  FIG. 19 . As described above, the CPU  21  acquires, from the count value output  33 , the count value of the signal output from the magnetic flux sensor  10  per counting period. In the stationary state, the count value is C 0  as illustrated in  FIG. 23 . By contrast, as the projection  202  is pushed as illustrated in  FIG. 19  and the vibration plate  201  approaches the magnetic flux sensor  10  accordingly, the count value increases. Accordingly, at S 1 , the CPU  21  detects the occurrence of vibration when the count value acquired from the count value output  33  exceeds a threshold. 
     Regardless of step S 1 , the CPU  21  keeps acquiring the count value per counting period. At S 2 , the CPU  21  acquires the peak value of fluctuation of the count value, which accords with the vibration of the vibration plate  201  illustrated in  FIG. 23 . The CPU  21  continuously analyzes the count value acquired in each counting period, thereby identifying the peak. 
       FIG. 25  is a table of data of count analysis. The data in  FIG. 25  include “number n”, “count value S n ” acquired in each counting period, and the sign (+ or −) of the difference (S n−1 −S n ) between each count value S n  and the immediately preceding count value S n−1 . The “number n”, “count value S n ”, and the sign (+ or −) are arranged in the order of acquisition. In the data illustrated in  FIG. 25 , the peak is immediately before the sing of “S n−1 −S n ” is inverted. In the case illustrated in  FIG. 25 , “5” and “10” are adopted as peaks. That is, subsequent to S 1 , the CPU  21  calculates “S n−1 −S n ” in  FIG. 25  regarding the count values sequentially acquired. The count value S n  of the number n immediately before the sign of “S n−1 −S n ” is inverted is adopted as P 1 , P 2 , P 3  . . . illustrated in  FIG. 23 . 
     As described above, it is preferred to avoid the count value at Timing t 2 , which is an initial peak after the step S 1 . Accordingly, the CPU  21  discards the initial peak of the extracted peaks through the analysis illustrated in  FIG. 25 . Additionally, in practice, it is possible that the count value include noise of high frequency component, and the sign of “S n−1 −S n ” may be inverted at a timing different from the timing at which the vibration of the vibration plate  201  is at the peak. To avoid erroneous detection in such cases, preferably the CPU  21  smooths the values acquired from the count value output  33 , before analyzing the values as illustrated in  FIG. 25 . The acquired values can be smoothed through common methods such as moving average. 
     Using the peak values thus obtained, at S 3 , the CPU  21  calculates the attenuation ratio ζ according to Formula 2 mentioned above. For that, the count value analysis illustrated in  FIG. 25  is continued at S 2  until the peaks used in the attenuation ratio calculation are attained. In the case of Formula 2, the CPU  21  analyzes the count values until the peak value equivalent to Peak P 6  is attained. 
     At S 4 , the CPU  21  determines whether the attenuation ratio ζ calculated at S 3  is equal to or smaller than the threshold. In other words, the CPU  21  determined whether the amount of developer in the sub-hopper  90  is below the predetermined amount based on the comparison between the rate of the count values acquired at different time points and the threshold. As described above with reference to  FIG. 22 , when a sufficient amount of developer is in the sub-hopper  90 , the vibration of the vibration plate  201  attenuates early, and the attenuation ratio ζ is smaller. 
     As the amount of developer in the sub-hopper  90  decreases, the attenuation of the vibration of the vibration plate  201  is slowed, and the attenuation ratio increases. Accordingly, when the threshold is set to the attenuation ratio ζ corresponding to the amount of remaining developer to be detected, whether the amount of developer remaining in the sub-hopper  90  falls to the amount to be detected (hereinafter “prescribed amount”) can be determined based on the calculated attenuation ratio ζ. 
     The amount of developer in the sub-hopper  90  does not directly affect the attenuation manner of vibration of the vibration plate  201 . According to the amount of remaining developer, the manner of contact of developer with the vibration plate  201  changes, and the manner of contact defines the manner of attenuation of vibration of the vibration plate  201 . Therefore, even if the amount of developer in the sub-hopper  90  is the same, the vibration of the vibration plate  201  attenuates differently if the manner of contact between the vibration plate  201  and developer is different. By contrast, in the present embodiment, the torsion spring  203  constantly stirs the developer in the sub-hopper  90 , in detection of developer amount in the sub-hopper  90 . Accordingly, to a certain degree, the state of contact of developer with the vibration plate  201  is determined with the amount of remaining developer. This configuration can avoid the inconvenience that the detection result differs depending on the manner of contact between the vibration plate  201  and developer even if the remaining amount is the same. 
     When the CPU  21  determines that the calculated attenuation ratio ζ is below the threshold (No at S 4 ), the CPU  21  determines that the amount of developer in the sub-hopper  90  is equal to or greater than the prescribed amount and completes the processing. By contrast, when the calculated attenuation ratio ζ is equal to or greater than the threshold (Yes at S 4 ), the CPU  21  determines that the amount of developer in the sub-hopper  90  is below the prescribed amount and, at S 5 , detects the developer end in the sub-hopper  90 . Then, the processing is completed. Detecting the developer end at S 5 , the CPU  21  outputs a signal indicating that the amount of remaining developer is below the prescribed amount, to an upper level controller to control the image forming apparatus  100 . With this signal, the controller of the image forming apparatus  100  recognizes the end of developer of specific color and becomes capable of supplying developer from the developer bottle  117 . 
     Next, descriptions are given below of the relation between the oscillation frequency of the magnetic flux sensor  10 , the cycle in which the CPU  21  acquires the count values (hereinafter “sampling cycle”), and the eigenfrequency of the vibration plate  201 .  FIG. 26  is a chart of count values sampled during a single vibration cycle of the vibration plate  201 . In  FIG. 26 , the vibration cycle of the vibration plate  201  is represented by “T plate ”, and the sampling cycle is represented by “T sample ”. 
     To calculate, at a higher degree, the attenuation ratio ζ of the vibration of the vibration plate  201  through the method illustrated in  FIGS. 23 through 25 , it is necessary to acquire the peak value of vibration of the vibration plate  201  accurately. For that, preferably, the number of sampled count values in the vibration cycle T plate  is sufficient, and the sampling cycle T sample  is small enough relative to the vibration cycle T plate . 
     In the case illustrated in  FIG. 26 , the number of count values sampled in one vibration cycle T plate  is  10 . That is, the sampling cycle T sample  is 1/10 of the vibration cycle T. In the case illustrated in  FIG. 26 , the count value S i  is inevitably sampled during a peak period T peak  of the count value, and thus the peak value can be acquired with a higher degree of accuracy. 
     Accordingly, for example, when the sampling cycle T sample  for the CPU  21  to acquire the count values is 1 ms, the vibration cycle T plate  of the vibration plate  201  is preferably 10 ms or greater. In other words, regarding a sampling frequency 1000 Hz of the CPU  21 , the eigenfrequency of the vibration plate  201  is preferably about 100 Hz and, more preferably, not greater than 100 Hz. Such an eigenfrequency of the vibration plate  201  is attained by adjusting the material of the vibration plate  201 , the dimension (including thickness) of the vibration plate  201 , and the weight of the projection  202 . 
     By contrast, if the count value acquired per each sampling cycle is too small, changes in the sampled count values corresponding to the vibration of the vibration plate  201  are small, and accurately calculating the attenuation ratio ζ becomes difficult. Here, the count value sampled conforms to the oscillation frequency of the magnetic flux sensor  10 . Typically, the oscillation frequency of the magnetic flux sensor  10  is of the order of several megahertz (MHz). When the sampling is performed at a sampling frequency of 1000 Hz, 1000 count values or greater are obtained at each sampling timing. According to the order of the vibration cycle T plate  and the sampling cycle T sample , the attenuation ratio ζ can be calculated accurately. 
     However, the amplitude of fluctuation of the count values relative to time illustrated in  FIG. 23  is small if the change in the oscillation frequency of the magnetic flux sensor  10  is insufficient relative to the change in distance between the magnetic flux sensor  10  and the vibration plate  201 . The change in distance therebetween is defined by the vibration of the vibration plate  201 . As a result, the change in the attenuation ratio also becomes smaller, thereby degrading the accuracy in detecting the amount of remaining developer, using the vibration of the vibration plate  201 . To increase the change in oscillation frequency of the magnetic flux sensor  10  corresponding to the change in distance between the magnetic flux sensor  10  and the vibration plate  201 , the distance therebetween is determined based on the characteristics illustrated in  FIG. 16 . For example, the distance between the magnetic flux sensor  10  and the vibration plate  201  (in the stationary state) is preferably set to the distance that corresponds to the range in which the oscillation frequency changes steeply corresponding to the distance therebetween, such as the range FL in  FIG. 16 . 
       FIG. 27A  is a perspective view of a structure to vibrate the vibration plate  201 .  FIG. 27B  is a perspective view of the torsion spring  203 . 
     In the present embodiment, the torsion spring  203  is used to vibrate the vibration plate  201 . The vibration plate  201  is secured to the case  93   b  of the sub-hopper  90  via the mount  201   a , which is disposed on one end of the vibration plate  201  in the direction parallel to the axial direction of the rotation shaft  96   c  (see  FIG. 6 ). The projection  202  (i.e., a weight) that is triangular in cross section is disposed on the other end of the vibration plate  201 . The projection  202  projects from the face of the vibration plate  201  facing the rotation shaft  96   c . The projection  202  includes the first inclined face  202   a , an apex  202   b , and a second inclined face  202   c  arranged in that order in the rotation direction of the rotation shaft  96   c  (see  FIG. 28 ). The first inclined face  202   a  is inclined to approach the rotation shaft  96   c  in the rotation direction of the rotation shaft  96   c . The second inclined face  202   c  is inclined to draw away from the rotation shaft  96   c  in the rotation direction of the rotation shaft  96   c . That is, the second inclined face  202   c  is inclined to reduce the projecting amount of the projection  202  in the rotation direction of the torsion spring  203 . The first inclined face  202   a  and the second inclined face  202   c  are connected together at the apex  202   b.    
     The torsion spring  203  is secured via the holder  205  to the rotation shaft  96   c  of the first stirring conveyor  96 . As the rotation shaft  96   c  rotates, the torsion spring  203  rotates together with the rotation shaft  96   c . As the torsion spring  203  rotates, the contact portion  203   a  thereof contacts the projection  202 . Then, the torsion spring  203  pushes the projection  202  to the case  93   b , and the vibration plate  201  elastically deforms. As the torsion spring  203  rotates further from the position to push the projection  202 , the contact portion  203   a  of the torsion spring  203  is disengaged from the projection  202 , flipping the vibration plate  201 . Then, the vibration plate  201  vibrates with the force to return to the predetermined position in the stationary state. 
     A preferable material for the torsion spring  203  is elastic wire made of, for example, hard drawn steel wire type C (SW-C), piano wire type A (SWP-A), piano wire type B (SWP-B), or stainless steel spring wire, for example, Steel Special Use Stainless (SUS) 304-WPB according to Japanese Industrial Standards (JIS). However, the material for the torsion spring  203  is not limited thereto. Although the torsion spring  203  in the present embodiment is a single torsion spring, in which a torsion coiled spring is disposed on one side, the shape of the torsion spring  203  is not limited thereto. For example, a double torsion spring can be used instead. The force with which the torsion spring  203  pushes the vibration plate  201  is adjustable with the material of the torsion spring  203  or the number of turns of the coiled portion thereof. Thus, the force of the torsion spring  203  to push the vibration plate  201  can be changed as required. For example, the force is changed between the case where one-component developer (i.e., toner) is used and the case where two-component developer is used. It is to be noted that the contact member to flip the vibration plate  201  is not limited to the torsion spring  203 . For example, a wire piece or a rod can be used. This configuration can reduce the area of contact between the projection  202  of the vibration plate  201  and the contact member and accordingly inhibit toner aggregation. 
       FIG. 28  is a schematic view illustrating a state before the contact portion  203   a  of the torsion spring  203  contacts the projection  202  attached to the vibration plate  201 . 
     The torsion spring  203  is attached, via the holder  205 , to the rotation shaft  96   c  of the first stirring conveyor  96 . The torsion spring  203  rotates clockwise in  FIG. 28 , together with the rotation shaft  96   c  of the first stirring conveyor  96 . The projection  202  attached to the vibration plate  201  includes the first inclined face  202   a  (i.e., an upstream inclined face), the apex  202   b , and the second inclined face  202   c  (i.e., a downstream inclined face) disposed in the rotation direction of the torsion spring  203  (the rotation shaft  96   c ) indicated by arrow Y 1 . The first inclined face  202   a  is inclined to rise, from the face of the vibration plate  201  facing the rotation shaft  96   c , in the rotation direction indicated by arrow Y 1 . The second inclined face  202   c  is inclined to descend, toward the face of the vibration plate  201  facing the rotation shaft  96   c , in the rotation direction indicated by arrow Y 1 . At the apex  202   b  connecting the first inclined face  202   a  to the second inclined face  202   c , the height of the projection  202  from the face of the vibration plate  201  facing the rotation shaft  96   c  is highest. The shape of the apex  202   b  is not limited to a pointed shape but can be a rounded shape or a flat shape. 
     Next, descriptions are given below of examples (Embodiments 1 through 3) of driving timings of respective members in the developer supply device. 
     Embodiment 1 
       FIG. 29  is a timing chart illustrating driving of the respective members in the developer supply device according to Embodiment 1. 
     In  FIG. 29 , when the first driving motor  131  is turned on according to a control instruction from the controller  210 , the first and second stirring conveyors  96  and  97  to stir the developer in the sub-hoppers  90  as well as the first and second conveyors  98  and  99  to transport the developer from the sub-hopper to the developing device  112  simultaneously start driving. The torsion spring  203  disposed at the rotation shaft  96   c  taps the vibration plate  201  as the first stirring conveyor  96  rotates. Detecting the vibration of the vibration plate  201 , the vibration plate  201  outputs a detection signal. The magnetic flux sensor  10  outputs the detection signal with a slight delay after the first driving motor  131  is turned on. Based on this detection signal, the controller  210  detects whether the developer is present (smaller or not smaller than the predetermined amount) in the developer reservoir  90   a . When the controller  210  does not detect the signal indicating “no developer” in the developer reservoir  90   a , and a sufficient amount of the developer is supplied to the developing device  112 , the controller  210  turns off the first driving motor  131 . At this point, the first and second stirring conveyors  96  and  97  and the first and second conveyors  98  and  99  stop driving. Additionally, as the first stirring conveyor  96  is stopped, the magnetic flux sensor  10  stops outputting the detection signal. 
     Thereafter, the first driving motor  131  is turned on again, and the first and second stirring conveyors  96  and  97  and the first and second conveyors  98  and  99  simultaneously start driving. Then, the magnetic flux sensor  10  outputs the detection signal in accordance with the driving of the first stirring conveyor  96 . Here, when the controller  210  detects the detection signal, from the magnetic flux sensor  10 , indicating “no developer” in the developer reservoir  90   a , the controller  210  turns on the second driving motor  81 . Consequently, the developer is supplied to the developer reservoir  90   a  from the developer bottle  117 , and, at the same time, rotation speeds of the first and second stirring conveyors  96  and  97  increase to promote stirring of the developer in the developer reservoir  90   a.    
     Subsequently, once a sufficient amount of the developer is supplied to the developing device  112 , the controller  210  turns off the first driving motor  131 . The first and second conveyors  98  and  99  stop driving since the first driving motor  131  has stopped. The first and second stirring conveyors  96  and  97 , however, are continuously driven by the second driving motor  81 . When the controller  210  detects the detection signal from the magnetic flux sensor  10  indicating that the developer is present in the developer reservoir  90   a , the controller  210  turns off the second driving motor  81  after a predetermined time period (e.g., one second) elapses. Consequently, the first and second stirring conveyors  96  and  97  stop driving. Since the first stirring conveyor  96  is stopped, the magnetic flux sensor  10  stops outputting the detection signal. Later on, the controller  210  repeats the control operation described above. 
     Here, in a case where a pressure (piezoelectric) sensor is used, the amount of the developer (or whether the developer is present or not) in the developer reservoir  90   a  can be constantly detected. By contrast, in Embodiment 1, the detection is limited to a time period during which the first stirring conveyor  96  is driven and the magnetic flux sensor  10  outputs the detection signal. Specifically, the detection of the amount of the developer (whether the developer is present) by the controller  210  is limited to the time period during which the first stirring conveyor  96  is driving. When a detection time period for the amount of the developer is short, there is a risk of detection failure. For example, detection failure occurs near the end of the developer, at which the developer remaining amount in the developer bottle  117  is small and the amount, per unit time, of developer discharged is reduced. Detection failure can also occur while the sub-hopper  90  (in particular, the developer reservoir  90   a  thereof) is filled with developer (i.e., recovery filling) immediately after the developer bottle  117  is replaced with a new one. Due to detection failure, the developer supply from the developer bottle  117  may become insufficient, resulting in the shortage of the developer in the developer reservoir  90   a  or insufficient toner concentration in the developing device  112 . 
     In Embodiment 1, at least while the second driving motor  81  is driven to supply the developer from the developer bottle  117  to the developer reservoir  90   a , the first stirring conveyor  96  is driven to enable the magnetic flux sensor  10  to output the detection signal for the developer amount detection. This configuration secures the time period to detect the amount of developer in the developer reservoir  90   a  and inhibits detection failure. Accordingly, the detection accuracy can be further enhanced than a case where a powder amount is detected by the pressure sensor or the like, and a state in which the amount of powder remaining in a powder reservoir is small can be detected with a high precision. In addition, the amount of powder supplied into the powder reservoir can be controlled with a high degree of accuracy, and overflow of powder is inhibited. Furthermore, even near the end of developer in the developer bottle  117  or during the recovery filling of the developer reservoir  90   a  immediately after replacement of the developer bottle  117 , the shortage of developer in the developer reservoir  90   a  or an insufficient toner concentration in the developing device  112  can be prevented. 
     Embodiment 2 
     In Embodiment 1 described above, the first driving motor  131  drives the first and second stirring conveyors  96  and  97  and the first and second conveyors  98  and  99 . By contrast, an electromagnetic clutch can be disposed therebetween such that the drive transmission to the first and second conveyors  98  and  99  is blocked. 
       FIG. 30  is a block diagram illustrating an exemplary configuration of principal portions of control circuitry of a developer supply device according to Embodiment 2.  FIG. 31  is a timing chart illustrating driving of respective members in the developer supply device according to Embodiment 2. The drive control of an electromagnetic clutch  135  and the drive control of the first and second conveyors  98  and  99  are similar to each other and represented by a single timing chart in  FIG. 31 . 
     As illustrated in  FIG. 30 , the electromagnetic clutch  135  is connected to the controller  210 . The electromagnetic clutch  135  is disposed where driving is transmitted from the first and second stirring conveyors  96  and  97  to the first and second conveyors  98  and  99 . Accordingly, when the electromagnetic clutch  135  is turned on, the clutch is connected. Then, the driving force of the first driving motor  131  is transmitted to the first and second conveyors  98  and  99  via the first and second stirring conveyors  96  and  97 . On the other hand, when the electromagnetic clutch  135  is turned off, the clutch is disconnected. Thus, the driving force is not transmitted to the first and second conveyors  98  and  99 , while the first and second stirring conveyors  96  and  97  are driven by the first driving motor  131 . The first and second conveyors  98  and  99  are driven when both of the first driving motor  131  and the electromagnetic clutch  135  are on. 
     In  FIG. 31 , in a case where the controller  210  attempts to obtain the detection signal from the magnetic flux sensor  10  to detect whether the developer is present in the developer reservoir  90   a  of the sub-hopper  90 , the first driving motor  131  is turned on, and the first and second stirring conveyors  96  and  97  are driven. As the first stirring conveyor  96  drives, the magnetic flux sensor  10  outputs the detection signal. Based on the detection signal from the magnetic flux sensor  10 , the controller  210  detects whether or not the developer is present in the developer reservoir  90   a . Here, the electromagnetic clutch  135  is kept being off. Thus, the first and second conveyors  98  and  99  do not receive the driving force of the first driving motor  131  and are consequently not driven. 
     When the controller  210  detects that the developer is present in the developer reservoir  90   a , the controller  210  turns off the first driving motor  131 , thereby stopping the first and second stirring conveyors  96  and  97 . Additionally, as the first stirring conveyor  96  is stopped, the magnetic flux sensor  10  stops outputting the detection signal. 
     Thereafter, when the developer in the developing device  112  becomes insufficient and additional developer is supplied thereto, the controller  210  turns the first driving motor  131  on, thereby driving the first and second stirring conveyors  96  and  97 . Simultaneously, the electromagnetic clutch  135  is turned on such to transmit the driving force to the first and second conveyors  98  and  99  to drive these conveyors. Then, the developer is supplied to the developing device  112 . Meanwhile, as the first stirring conveyor  96  drives, the magnetic flux sensor  10  outputs the detection signal. Based on the detection signal from the magnetic flux sensor  10 , the controller  210  detects whether or not the developer is present in the developer reservoir  90   a . Subsequently, detecting the detection signal from the magnetic flux sensor  10  indicating that there is no developer in the developer reservoir  90   a , the controller  210  turns on the second driving motor  81 . Consequently, the developer is supplied to the developer reservoir  90   a  from the developer bottle  117 . At this time, the rotation speed of the first and second stirring conveyors  96  and  97  is accelerated with the driving force of the second driving motor  81 , and stirring of the developer in the developer reservoir  90   a  is promoted. 
     Subsequently, once a sufficient amount of the developer is supplied to the developing device  112 , the controller  210  turns off the electromagnetic clutch  135  to stop the first and second conveyors  98  and  99 , thereby stopping supply of developer from the sub-hopper  90  (the developer reservoir  90   a ). At this time, although the first driving motor  131  is turned off simultaneously, the first and second stirring conveyors  96  and  97  are continuously driven by the second driving motor  81 . Thereafter, detecting the detection signal from the magnetic flux sensor  10  indicating that the developer is present in the developer reservoir  90   a , the controller  210  turns off the second driving motor  81  after a predetermined time period (e.g., one second) elapses. With this action, the first and second stirring conveyors  96  and  97  stop driving. Since the first stirring conveyor  96  is stopped, the magnetic flux sensor  10  stops outputting the detection signal. Later on, the controller  210  repeats the control operation described above. 
     According to Embodiment 2, the controller  210  can drive only the first and second stirring conveyors  96  and  97  by switching the electromagnetic clutch  135  and can obtain the detection signal from the magnetic flux sensor  10  by driving the first stirring conveyor  96 . Therefore, regardless of the timing of developer supply to the developer reservoir  90   a  or the timing of developer supply to the developing device  112 , the controller  210  can detect the amount of the developer (whether the developer is present) in the developer reservoir  90   a  at an appropriate timing. Consequently, a sufficient detection time period is secured, and the detection failure is inhibited. 
     Embodiment 3 
     In Embodiment 2 described above, the electromagnetic clutch  135  is disposed between the stirrers (the first and second stirring conveyors  96  and  97 ) to stir developer in the sub-hopper  90  and the developer conveys (the first and second conveyors  98  and  99 ) to supply developer from the sub-hopper  90 . By contrast, separate driving motors can be employed to stir the developer in the sub-hopper  90  and to supply the developer from the sub-hopper  90 , as in Embodiment 3. 
       FIG. 32  is a block diagram illustrating an exemplary configuration of principal portions of control circuitry of a developer supply device according to Embodiment 3. FIG. is a timing chart illustrating driving of respective members in the developer supply device according to Embodiment 3. The drive control of the first first-driving motor  133  and that of the first and second stirring conveyors  96  and  97  are similar to each other and represented by a single timing chart in  FIG. 33 . Likewise, the drive control of the second first-driving motor  134  and that of the first and second conveyors  98  and  99  are similar to each other and represented by a single timing chart. 
     As illustrated in  FIG. 32 , the first first-driving motor  133 , which drives the first and second stirring conveyors  96  and  97 , and the second first-driving motor  134 , which drives the first and second conveyors  98  and  99 , are connected to the controller  210 , respectively. The driving of the first and second stirring conveyors  96  and  97  and the driving of the first and second conveyors  98  and  99  are separated from each other, and the first and second stirring conveyors  96  and  97  are driven independently of the first and second conveyors  98  and  99 . In addition, the driving of the first and second stirring conveyors  96  and  97  is separate from the driving of the second driving motor  81  (to supply developer from the developer bottle  117  to the sub-hopper  90 ). Thus, the members to stir the developer in the sub-hopper  90  are driven independently of the second driving motor  81 . 
     In  FIG. 33 , in a case where the controller  210  attempts to obtain the detection signal from the magnetic flux sensor  10  to detect whether the developer is present in the developer reservoir  90   a , the first first-driving motor  133  is turned on. Then, the first and second stirring conveyors  96  and  97  are driven simultaneously. As the first stirring conveyor  96  is driven, the magnetic flux sensor  10  outputs the detection signal with a slight delay after the first first-driving motor  133  is turned on. Based on the detection signal from the magnetic flux sensor  10 , the controller  210  detects whether or not the developer is present in the developer reservoir  90   a.    
     Subsequently, detecting that the developer is present in the developer reservoir  90   a , the controller  210  turns off the first first-driving motor  133 , thereby simultaneously stopping the driving of the first and second stirring conveyors  96  and  97 . Additionally, as the first stirring conveyor  96  is stopped, the magnetic flux sensor  10  stops outputting the detection signal. 
     Thereafter, when the developer in the developing device  112  becomes insufficient and additional developer is supplied thereto, the controller  210  turns on the second first-driving motor  134 , thereby driving the first and second conveyors  98  and  99  to supply the developer to the developing device  112 . At this time, the first first-driving motor  133  is simultaneously turned on to drive the first and second stirring conveyors  96  and  97 . As the first stirring conveyor  96  drives, the magnetic flux sensor  10  outputs the detection signal. Subsequently, detecting the detection signal from the magnetic flux sensor  10  indicating that there is no developer in the developer reservoir  90   a , the controller  210  turns on the second driving motor  81 . Consequently, the developer is supplied to the developer reservoir  90   a  from the developer bottle  117 . At this time, the rotation speed of the first first-driving motor  133  is accelerated. As a result, the rotation speed of the first and second stirring conveyors  96  and  97  is accelerated to promote stirring of the developer in the developer reservoir  90   a.    
     Subsequently, once a sufficient amount of the developer is supplied to the developing device  112 , the controller  210  turns off the second first-driving motor  134 , thereby stopping developer supply by the first and second conveyors  98  and  99 . The first and second conveyors  98  and  99  stop driving since the second first-driving motor  134  has stopped. The first and second stirring conveyors  96  and  97 , however, are continuously driven by the first first-driving motor  133 . Thereafter, detecting the detection signal from the magnetic flux sensor  10  indicating that the developer is present in the developer reservoir  90   a , the controller  210  turns off the second driving motor  81  after a predetermined time period (e.g., one second) elapses. In addition, the first first-driving motor  133  is simultaneously turned off to stop the driving of the first and second stirring conveyors  96  and  97 . Since the first stirring conveyor  96  is stopped, the magnetic flux sensor  10  stops outputting the detection signal. Later on, the controller  210  repeats the control operation described above. 
     According to Embodiment 3, the controller  210  can drive, with the first first-driving motor  133 , only the first and second stirring conveyors  96  and  97  to obtain the detection signal from the magnetic flux sensor  10 , which accompanies the driving of the first stirring conveyor  96 . Therefore, regardless of the timing of developer supply to the developer reservoir  90   a  or the timing of developer supply to the developing device  112 , the controller  210  can detect the amount of the developer (whether the developer is present) in the developer reservoir  90   a  at an appropriate timing. Consequently, a sufficient detection time period is secured, and the detection failure is inhibited. 
     Alternatively, in the aforementioned embodiments, the developer amount detector to detect the amount of developer in the sub-hopper can use displacement of a detected member. Such a configuration includes a detected member (e.g., a sheet to be pressed) disposed to move in the sub-hopper, a contact member, e.g., a stirring sheet) to make the detected member to move, and a detector to detect displacement of the detected member. The contact member is disposed on the rotation shaft of a rotator that is rotated in the sub-hopper and to contact and move the detected member while rotating together with the rotation shaft. 
     The various aspects of the present specification can attain specific effects as follows. 
     Aspect A 
     A powder supply device such as the developer supply device includes: a downstream powder container such as the developer reservoir  90   a  of the sub-hopper  90  to temporarily store powder supplied from an upstream powder container such as the developer bottle  117  accommodating the powder such as the developer and then discharge the temporarily stored powder toward a supply destination such as the developing device  112 ; and a powder amount detector to detect an amount of the powder in the downstream powder container. The powder supply device is configured to supply the powder from the upstream powder container to the downstream powder container based on a detection result generated by the powder amount detector. The powder amount detector includes: a detected member, such as the vibration plate  201 , disposed in the downstream powder container so as to vibrate or move; a contact member, such as the torsion spring  203 , disposed on the rotation shaft  96   c  of a rotator, such as the first stirring conveyor  96 , to rotate in the downstream powder container. While rotating together with the rotation shaft  96   c , the contact member contacts the detected member to cause the detected member to vibrate or be displaced. The powder amount detector further includes a detector, such as the magnetic flux sensor  10 , to detect a vibration state or a displacement state of the detected member; and a detection result processor, such as the controller  20 , to detect the amount of the powder in the downstream powder container based on a detection result by the detector. The powder supply device further includes a controller such as the controller  210  to cause the rotator to rotate when the powder is discharged from the downstream powder container to the supply destination and when the powder is supplied from the upstream powder container to the downstream powder container. 
     According to this aspect, as described above, when the powder is discharged from the downstream powder container and when the powder is supplied to the downstream powder container, the rotator including the rotation shaft  96   c  provided with the contact member is rotated. Consequently, the detected member is caused to vibrate or displaced by the contact member. The detector detects vibration or displacement of the detected member, and the detection result processor can detect the amount of the powder in the downstream powder container based on a detection result generated by the detector. As described above, at both of a timing of discharging the powder from the downstream powder container and a timing of supplying the powder to the downstream powder container, at which the amount of the developer in the downstream powder container is expected to change, the amount of the powder in the downstream powder container can be reliably detected. In particular, even in a case where the powder is supplied from the upstream powder container to the downstream powder container prior to discharging the powder from the downstream powder container, the amount of the powder in the downstream powder container can be reliably detected. 
     Besides, the detected member, which contacts the powder in the downstream powder container, vibrates or is displaced when touched by the contact member rotating together with the rotator. Consequently, the powder is unlikely to adhere to the detected member. Therefore, an influence of the powder adhesion is unlikely to occur on the vibration state or the displacement state of the detected member, which is used to detect the amount of the powder and thus, erroneous detection of the amount of powder due to the powder adhesion is unlikely to occur. 
     Aspect B 
     In the aforementioned aspect A, the powder supply device further includes a stirrer such as the first stirring conveyor  96  to stir the powder in the downstream powder container, and the stirrer serves as the rotator having the rotation shaft  96   c  to which the contact member, such as the torsion spring  203 , is attached. 
     According to this aspect, as described above, the stirrer of the downstream powder container is rotated when the powder is discharged from the downstream powder container and when the powder is supplied to the downstream powder container. Consequently, while the powder in the downstream powder container is stirred, the detection result processor can detect the amount of the powder in the downstream powder container. 
     Aspect C 
     In the aforementioned aspect B, the powder supply device further includes: a powder conveyor, such as the first conveyor  98 , to convey the powder from the downstream powder container to the supply destination; an powder supply member, such as the second bottle agitator  117 A (or the conveying screw  117 B) of the developer bottle  117 , to supply the powder from the upstream powder container to the downstream powder container through a supply opening; a first driving source, such as the first driving motor  131 , to drive the stirrer of the downstream powder container and the powder conveyor; and a second driving source, such as the second driving motor  81 , to drive the powder supply member and the stirrer. The first driving source drives the stirrer of the downstream powder container and the powder conveyor when the powder is discharged from the downstream powder container to the supply destination. Meanwhile, the second driving source drives the powder supply member and the stirrer of the downstream powder container when the powder is supplied from the upstream powder container to the downstream powder container. 
     According to this aspect, as described above, the stirrer, to which the detected member used in powder amount detection is driven by both of the first driving source and the second driving source. Therefore, the powder amount detector can reliably detect the amount of the powder in the downstream powder container when the powder is discharged from the downstream powder container to the supply destination and when the powder is supplied from the upstream powder container to the downstream powder container. 
     Aspect D 
     In the aforementioned aspect C, drive transmission from the first driving source to the stirrer of the downstream powder container and drive transmission from the second driving source to the stirrer are respectively carried out by way of first and second one-way clutches, such as the one-way clutch  132  (first-driving side) and the one-way clutch  82  (second-driving side), and a rotation speed of the stirrer being driven by the first driving source is made different from a rotation speed of the stirrer being driven by the second driving source. 
     According to this aspect, as described above, the driving of the stirrer by the first driving source and the driving of the stirrer by the second driving source can be switched to each other with ease by using inexpensive one-way clutches. In addition, in a case where the first driving source and the second driving source are simultaneously driven, the stirrer can be driven by the faster of the first driving source and the second driving source. 
     Aspect E 
     In the aforementioned aspect D, the rotation speed of the stirrer being driven by the second driving source is faster than the rotation speed of the stirrer being driven by the first driving source. 
     According to this aspect, as described above, the stirrer rotates at a higher speed in a case where the powder is supplied from the upstream powder container to the downstream powder container than a case where the powder is discharged from the downstream powder container to the supply destination. Accordingly, stirring of the powder in the downstream powder container is promoted during powder supply. 
     Aspect F 
     In any one of the aforementioned aspects C to E, the second driving source drives the stirrer constantly at least while the powder supply device is operating. 
     According to this aspect, as described above, the stirrer is constantly driven while the powder supply device is operating, and, in the meantime, the amount of the powder in the downstream powder container is detected by the powder amount detector. Therefore, the powder amount detector can detect the amount of the powder in the downstream powder container at an arbitrary timing while the powder supply device is operating. 
     Aspect G 
     In any one of the aforementioned aspects C to F, the powder supply device further includes an electromagnetic clutch (e.g., the electromagnetic clutch  135 ), and the driving force of the first driving source is transmitted from the stirrer to the powder conveyor via the electromagnetic clutch. 
     According to this aspect, as described above, when the electromagnetic clutch is turned off to block the drive transmission to the powder conveyor, the first driving source can drive the stirrer only. Therefore, regardless of a timing of discharging the powder from the downstream powder container to the supply destination or a timing of supplying the powder from the upstream powder container to the downstream powder container, the amount of the powder in the downstream powder container can be detected at an arbitrary timing, similar to a configuration using a piezoelectric sensor. 
     Aspect H 
     In any one of Aspects A through D, the contact member includes an elastic body, such as the torsion spring  203 , being constantly biased to one side in the rotation direction of the rotation shaft. 
     With this aspect, as described above, the elastic body exerts a resilience to cause the contact member to quickly pass the area opposed to the vibration plate. Accordingly, the vibration of the vibration plate is not hindered. 
     Aspect I 
     In the aforementioned aspect H, the torsion spring  203  is used as the elastic body. 
     With this aspect, as described above, the torsion spring exerts a spring resilience to quickly pass the area opposed to the vibration plate, and the vibration of the vibration plate is not hindered. Further, the durability of the contact member is enhanced. 
     Aspect J 
     An image forming apparatus such as the image forming apparatus  100  includes an image bearer (e.g., the photoconductor drum  109 ), a developing device (e.g., the developing device  112 ), and the powder supply device according to Aspect I, to supply the developer to the developing device as the supply destination. 
     According to this aspect, as described above, the amount of the developer in the downstream powder container can be detected at both of when the developer is discharged from the downstream powder container and when the developer is supplied to the downstream powder container. Additionally, erroneous detection of developer amount due to developer adhesion is unlikely to occur. 
     The above-described embodiments are illustrative and do not limit the present invention. Thus, numerous additional modifications and variations are possible in light of the above teachings. For example, elements and/or features of different illustrative embodiments may be combined with each other and/or substituted for each other within the scope of the present invention.