Patent Publication Number: US-10324394-B2

Title: Developing device

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present disclosure relates to a developing device used for an image forming apparatus of an electrophotographic type, an electrostatic recording type, or the like. 
     Description of the Related Art 
     In an existing image forming apparatus employing an electrophotographic system, an electrostatic latent image formed on an image bearing member such as a photosensitive drum is developed with a resin containing colorant or the like, to form a visible image. In an existing developing device used for such development, two-component developer (hereinafter, referred to as developer) that contains non-magnetic toner and magnetic carrier is widely used as developer. 
     In the developing device using the two-component developer, in a developing region where the image bearing member and a developer bearing member (hereinafter, referred to as developing sleeve) face each other, the developer forms a brush shape (hereinafter, magnetic brush) by a magnet that is fixed and disposed inside the developing sleeve. In other words, the developer is borne on the developing sleeve by the magnet disposed in the developing sleeve, and the magnetic carrier forms the magnetic brush along magnetic field lines of the magnet. The magnetic brush is conveyed through rotational driving of the developing sleeve; however, conveyance failure may occur due to shortage of conveyance force when the magnetic brush is conveyed in the developing region. Such conveyance failure of the developer the developing region may cause deterioration of image density in some cases. 
     To enhance conveyance performance of the developer by the developing sleeve to solve such an issue, a developing device in which concave parts are provided on a surface of the developing sleeve, and the magnetic brush is formed with the carrier engaged with the concave parts as starting points has been proposed. As a form of each of the concave parts, for example, a random shape (see Japanese Patent Application Laid-Open. No. 2-64561), a groove shape parallel to an axis direction of the developing sleeve (see Japanese Patent. Application Laid-Open No. 2-50182), and a linearly-continuous elliptical shape (see Japanese Patent Application Laid-Open No. 2011-100003) have been proposed. Such developing devices make it possible to improve followability of the magnetic brush with respect to the rotation of the developing sleeve. 
     In the development using the two-component developer, when the developer is conveyed to a region where the developing sleeve comes close to the image bearing member, the magnetic brush comes into contact with the image bearing member. Thereafter, the magnetic brush is separated from the image bearing member after passing through a region where the developing sleeve comes closest to the image bearing member. The region where the magnetic brush is in contact with the image bearing member is called a contact nip, and the toner adheres to the electrostatic latent image on the image bearing member mainly in the contact nip, and the toner image is accordingly formed. In the image forming process, roughness of the image particularly relates to a region where the magnetic brush starts to separate from the image bearing member on the downstream end of the contact nip in the conveyance direction. For example, if the contact state of the magnetic brush to the image bearing member before separation is non-uniform, the toner image formed in the contact nip is disturbed, which increases roughness of the output image. 
     Non-uniformity of the contact state of the magnetic brush on the downstream end of the contact nip in the conveyance direction easily occurs when a length of the magnetic brush and the distance between the bristles of the magnetic brush formed on the developing sleeve are non-uniform. The length of the magnetic brush and the distance between the bristles of the magnetic brush closely relate to the surface shape of the developing sleeve. As Japanese Patent Application Laid-Open Nos. 2-64561, 2-50182, and 2011-100003, in the developing sleeve having irregularity on the surface to improve the conveyance force of the developing sleeve, the conveyance force of the concave parts is strong and the magnetic brush tends to be collected in the concave parts. Consequently, in the developing devices discussed in Japanese Patent Application Laid-Open Nos. 2-64561, 2-50182, and 2011-100003, the distance between the bristles of the magnetic brush and the length of the magnetic brush on the developing sleeve are non-uniform. The non-uniform contact state of the magnetic brush on the downstream end of the contact nip in the conveyance direction occurs, which adversely affects roughness of the image. 
     First, in the developing device discussed in Japanese Patent Application Laid-Open No. 2-64561, the sizes and the distance of the concave parts vary because irregularity is randomly provided on the surface of the developing sleeve. Accordingly, the bristles of the magnetic brush are densely present in a region where the concave parts are densely provided, and the bristles of the magnetic brush are sparsely present in a region where the distance between the concave parts is wide, which causes non-uniformity of the distances between the bristles of the magnetic brush. Further, the magnetic brush typically has a conical shape in which a root is thick and a thickness is gradually reduced toward a tip. Therefore, a large amount of carrier is easily collected in a large concave part and the magnetic brush having a large root and a long length is easily formed. If the sizes of the concave parts are non-uniform, the length of the formed magnetic brush also becomes non-uniform. 
     Moreover, in the developing device discussed in Japanese Patent Application Laid-Open No. 2-50182, the groove parallel to the axis direction is provided on the surface of the developing sleeve. In this configuration, the developer is easily collected in the grove and the amount of the developer carried on the groove is larger than the amount of the developer carried on the surface other than the groove. As a result, the magnetic brush in the groove becomes larger in length than the magnetic brush on the surface other than the groove. 
     Furthermore, in the developing device discussed in Japanese Patent Application Laid-Open No. 2011-100003, the concave parts are regularly provided to regularly form the magnetic brush; however, the developer exists on the surface other than the concave parts because the distance between the concave parts in a circumferential direction is large. As a result, the magnetic brush is not sufficiently regulated in the pattern of the concave parts, which results in the non-uniform state of the magnetic brush. 
     SUMMARY OF THE INVENTION 
     The present disclosure is directed to a developing device that makes it possible to stabilize a state where magnetic brush is in contact with an image bearing member on a downstream end of a contact nip in a conveyance direction. 
     According to an aspect of the present disclosure, a developing device includes a developer bearing member configured to be rotatable and to carry non-magnetic toner and magnetic carrier, a magnet provided inside the developer bearing member, and a plurality of concave parts provided on a surface of an entire region where developer is carried, in a rotation axis direction of the developer bearing member. Each of the concave parts has a surface size larger than a volume average particle diameter of the carrier, and the plurality of concave parts are arranged to make a shortest distance between the concave parts adjacent to each other smaller than the volume average particle diameter of the carrier. 
     Further features of the present disclosure will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  a cross-sectional view illustrating a schematic configuration of an image forming apparatus according to an exemplary embodiment. 
         FIG. 2  a cross-sectional view illustrating a schematic configuration of a developing device according to the exemplary embodiment. 
         FIG. 3  is a cross-sectional view illustrating the developing device according to the exemplary embodiment in a planar view. 
         FIGS. 4A and 4B  are plan views in a wide range and in an enlarged view, respectively, each illustrating a surface of a developing sleeve of the developing device according to the exemplary embodiment. 
         FIGS. 5A and 5B  are plan views in a wide range and in an enlarged view, respectively, each illustrating a surface of a developing sleeve of a developing device according to another exemplary embodiment. 
         FIGS. 6A, 6B, 6C, and 6D  are enlarged views each illustrating a modification of the surface of the developing sleeve of the developing device according to the exemplary embodiment, in a case where a concave part has a regular hexagonal shape, in a case where the concave part has a regular triangle shape, in a case where the concave part has a circular shape, and in a case where the concave part has an elliptical shape, respectively. 
         FIG. 7A  is an enlarged view illustrating a surface of a developing sleeve of a developing device according to an example,  FIG. 7B  is a vertical cross-sectional view illustrating a concave part of the developing sleeve of the developing device according to the example, and  FIG. 7C  is an enlarged view illustrating a surface of a developing sleeve of a developing device according to a second comparative example. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     A developing device according to an exemplary embodiment of the present disclosure will be described in detail below with reference to  FIGS. 1 to 4 . In the present exemplary embodiment, a case where the developing device is applied. to a tandem full-color printer as an example of an image forming apparatus is described. The present disclosure, however, is not limited to the developing device of the tandem image forming apparatus, and may be a developing device of an image forming apparatus of other type. In addition, the present disclosure is not limited to full color and may be monochrome or mono-color. Alternatively, the present disclosure may be implemented for various applications such as a printer, a printing apparatus, a copier, a facsimile machine, and a multifunction apparatus by including necessary device, equipment, and housing structure. In the present exemplary embodiment, an image forming apparatus  1  includes an intermediate transfer belt  44   b , and primarily transfers toner images of respective colors from a photosensitive drum  81  to the intermediate transfer belt  44   b , and then collectively secondarily transfers a composite toner image of the colors to a sheet S. The method, however, is not limited thereto, and the image forming apparatus  1  may adopt a method of directly transferring the image from the photosensitive drum to a sheet conveyed by a sheet conveyance belt. 
     Further, in the present exemplary embodiment, a two-component developer that is a mixture of non-magnetic toner and magnetic carrier, is used as developer. The toner contains binder resin, colorant, colored resin particles containing other additive as necessary, and colored particles that are externally added with an external additive such as colloidal silica fine powder. The toner contains colorant, a wax component, etc. in a resin such as negatively-charged polyester or styrene, and is powdered through grinding or polymerization in the present exemplary embodiment, volume average particle diameter of the toner is 7.0 μm. The carrier is formed by performing resin coating on a surface layer of a core including a ferrite particle or a resin particle kneaded with magnetic powder. 
     As the carrier, for example, metals such as surface-oxidized or non-oxidized iron, nickel, cobalt, manganese, chromium, and rare earths, and an alloy thereof, or oxide ferrite may be suitably used. In the present exemplary embodiment, the carrier having the oxide ferrite as a core are used; however, the method of manufacturing the magnetic particles is not particularly limited. The contact of the magnetic brush with the photosensitive drum  81  becomes uniform to obtain favorable image quality as the particle diameter of the carrier becomes smaller; however, carrier adhesion to the photosensitive drum  81  becomes remarkable, which causes image failure. Accordingly, an average particle diameter  2 R (hereinafter, “particle diameter” in brief indicates volume average particle diameter) of the volume distribution reference of the carrier is desirably approximately 20 μm to 50 μm. A mixing ratio of the developer in the present exemplary embodiment is 10% in a ratio of the toner to the total weight. The carrier, however, is not limited thereto as a matter of course. 
     As illustrated in  FIG. 1 , the image forming apparatus  1  includes an image forming section  40 , a sheet conveyance unit  50 , a control unit  60 , and the like inside an unillustrated apparatus body. The sheet conveyance unit conveys the sheet S that has been fed from an unillustrated sheet feeding unit, to an unillustrated sheet discharging unit from the image forming section  40  The sheet S serving as a recording medium is to be formed with toner images, and specific examples of the sheet S include a regular paper, a resin sheet as a substitute for the regular paper, a thick paper, and an overhead projector sheet. 
     The image forming section  40  includes an image forming unit  80 , a toner bottle  41 , a toner container  42 , a laser scanner  43 , an intermediate transfer unit  44 , a secondary transfer unit  45 , and a fixing device  46 . The image forming section  40  can form an image on the sheet S, based on image information The image forming apparatus  1  according to the present exemplary embodiment supports full color, and image forming units  80   y ,  80   m ,  80   c , and  80   k  are respectively provided with similar configurations for four colors of yellow (y) , magenta (m) , cyan (c) , and black (k). Likewise, toner bottles  41   y ,  41   m ,  41   c , and  41   k  and toner containers  42   y ,  42   m ,  42   c , and  42   k  are respectively provided with similar configurations for the four colors of yellow (v), magenta (m), cyan (c), and black (k). Accordingly, in  FIG. 1 , a color identifier is added after the same reference numeral for configurations of the respective four colors; however, in  FIG. 2 ,  FIG. 3 , and The specification, description is given only with a reference numeral without addition of the color identifier in some cases. 
     The toner container  42  is, for example, a cylindrical bottle which houses the toner, and is disposed above The corresponding image forming unit  80  so as to be coupled to the corresponding image forming unit  80  via the toner bottle  41 . The laser scanner  43  exposes a surface of the photosensitive drum  81  that has been charged by a charging roller  82 , thereby forming an electrostatic latent image on the surface of the photosensitive drum  81 . 
     The image forming unit  80  includes the four image forming units  80   y ,  80   m ,  80   c , and  80   k  to form the toner images of the four colors. The image forming unit  80  includes the photosensitive drum  81  forming the toner image, the charging roller  82 , the developing device  20 , and an unillustrated cleaning blade. The photosensitive drum  81 , the charging roller  82 , the developing device  20 , and a developing sleeve  24  described later are also separately provided with similar configurations for each of the four colors of yellow (y), magenta (m), cyan (c), and black (k). 
     The photosensitive drum  81  includes a photosensitive layer and rotates in an arrow direction at a predetermined process speed (circumferential speed). The photosensitive layer is provided so as to have a negative charge polarity on an outer peripheral surface of an aluminum cylinder. The charging roller  82  comes into contact with the surface of the photosensitive drum  81  to charge the surface of the photosensitive drum  81  to, for example, homogeneous negative dark portion potential. After charging, an electrostatic image is formed on the surface of the photosensitive drum  81  by the laser scanner  43 , based on the image information. The photosensitive drum  81  revolves while carrying the formed electrostatic image, and an image is developed with the toner by the developing device  20 . A detailed configuration of the developing device  20  is described later. The developed toner image is primarily transferred to the intermediate transfer belt  44   b  described later. The surface of the photosensitive drum  81  after the primary transfer is discharged by an unillustrated pre-exposure unit. 
     The intermediate transfer unit  44  is disposed above the image forming units  80   y ,  80   m ,  80   c , and  80   k . The intermediate transfer unit  44  includes a plurality of rollers including a driving roller  44   a , primary transfer rollers  44   y ,  44   m ,  44   c , and  44   k , and the intermediate transfer belt  44   b  wound on these rollers. The primary transfer rollers  44   y ,  44   m ,  44   c , and  44   k  are disposed to respectively face the photosensitive drums  81   y ,  81   m ,  81   c , and  81   k , and come into contact with the intermediate transfer belt  44   b.    
     When positive transfer bias is applied to the intermediate transfer belt  44   b  through the primary transfer rollers  44   y ,  44   m ,  44   c , and  44   k , the negative toner images on the photosensitive drums  81   y ,  81   m ,  81   c , and  81   k  are sequentially transferred on the intermediate transfer belt  44   b  in a multiple manner. Thereafter, the intermediate transfer belt  44   b  moves while the toner image that has been obtained by developing the electrostatic image on the surfaces of the respective photosensitive drums  81   y ,  81   m ,  81   c , and  81   k  is transferred thereon. 
     The secondary transfer unit  45  includes a secondary inner transfer roller  45   a  and a secondary outer transfer roller  45   b . Positive secondary transfer bias is applied to the secondary outer transfer roller  45   b  to transfer the full-color image formed on the intermediate transfer belt  44   b  to the sheet S. The fixing device  46  includes a fixing roller  46   a  and a pressurizing roller  46   b . The sheet S is held and conveyed between the fixing roller  46   a  and the pressurizing roller  46   b . As a result, the full-color image transferred on the sheet S is heated and pressurized, and is fixed to the sheet S. 
     The control unit  60  includes a computer, and includes, for example, a central processing unit (CPU), a read only memory (ROM) that stores programs controlling respective units, a random access memory (RAM) that temporarily stores data, and an input/output circuit (I/F) that exchanges signals with outside. The CPU is a microprocessor that performs whole control of the image forming apparatus  1 , and is a main component of a system controller. The CPU is connected to, for example, the sheet feeding unit, the image forming section  40 , and the sheet conveyance unit  50  through the input/output circuit, and exchanges the signals with the respective units and controls operation of the respective units. 
     Next, image forming operation by the image forming apparatus  1  having such a configuration will be described. When the image forming operation is started, the photosensitive drum  81  first rotates and the surface thereof is charged by the charging roller  82 . Thereafter, a laser beam is applied from the laser scanner  43  to the photosensitive drum  81 , based on the image information, and the electrostatic latent image is accordingly formed on the surface of the photosensitive drum  81 . When the toner adheres to the electrostatic latent image, the electrostatic latent image is developed and is visualized as the toner image, and the toner image is transferred to the intermediate transfer belt  44   b.    
     In contrast, the sheet conveyance unit  50  operates in parallel with such formation operation of the toner image, and conveys the sheet S fed from the sheet feeding unit, to the secondary transfer unit  45  while matching the timing with the toner image on the intermediate transfer belt  44   b . Thereafter, the image is transferred from the intermediate transfer belt  44   b  to the sheet S. The sheet S is conveyed to the fixing device  46 , and the unfixed toner image is fixed to the surface of the sheet S through heating and pressurization, and the sheet S is then discharged to the sheet discharging unit. 
     Next, the developing device  20  will be described with reference to  FIG. 2  and  FIG. 3 . The developing device  20  is detachable to the apparatus main body, and includes a developer container  21  housing the developer, a first conveyance screw  22 , a second conveyance screw  23 , the developing sleeve (developer bearing member)  24 , a regulation blade  25 , and an inductance sensor  26 . The developer container  21  includes an opening  21   a  from which the developing sleeve  24  is exposed, at a position facing the photosensitive drum  81 . 
     The developer container  21  includes, at a substantially center, a partition wall  27  that extends in a longitudinal direction The developer container  21  is partitioned in the horizontal direction by the partition wall  27  into a developing chamber  21   b  and an agitating chamber  21   c . The developer is housed in the developing chamber  21   b  and the agitating chamber  21   c . The developing chamber  21   b  supplies the developer to the developing sleeve  24 . The agitating chamber  21   c  communicates with the developing chamber  21   b , and recovers and agitates the developer from the developing sleeve  24 . The partition wall  27  between the developing chamber  21   b  and the agitating chamber  21   c  includes two communication portions  27   a  and  27   b  that communicates the developing chamber  21   b  and the agitating chamber  21   c  with each other, at both end parts. In the developing device  20  of the present exemplary embodiment, the developing chamber  21   b  and the agitating chamber  21   c  are disposed in the horizontal direction; however, the configuration is not limited thereto. The developing chamber and the agitating chamber may be disposed in a vertical direction, or a developing device may have other form. 
     The first conveyance screw  22  is disposed, in the developing chamber  21   b , in substantially parallel to the developing sleeve  24  along an axis direction of the developing sleeve  24 , and conveys the developer in the developing chamber  21   b  while agitating the developer. The first conveyance screw  22  includes a shaft part  22   a , and a spiral conveyance blade  22   b . The shaft part  22   a  is rotatably provided. in the developer container  21  and has magnetism. The conveyance blade  22   b  rotates integrally with the shaft part  22   a  and conveys the developer inside the developer container  21  in a conveyance direction D 1  through rotation. 
     The second conveyance screw  23  is disposed, in the agitating chamber  21   c , in substantially parallel to an axis of the first conveyance screw  22 , and conveys the developer in the agitating chamber  21   c  in a direction opposite to the conveyance direction of the first conveyance screw  22 . The second conveyance screw  23  includes a shaft part  23   a  and a spiral nonmagnetic conveyance blade  23   b . The shaft part  23   a  is rotatably provided in the developer container  21  and has magnetism. The conveyance blade  23   b  rotates integrally with the shaft part  23   a  and conveys the developer in the developer container  21  the conveyance direction D 1  through rotation. The developing chamber  21   b  and the agitating chamber  21   c  configure a developer circulation path. through which the developer agitated and conveyed. The screws  22  and  23  convey the developer in directions opposite to each other, and convey the developer toward the facing screw at a position where the screws  22  and  23  face each other. The toner is rubbed with the carrier through agitation by the screws  22  and  23 , and is frictionally charged to negative polarity. 
     In the present exemplary embodiment, the first conveyance screw  22  has a screw structure in which the conveyance blade  22   b  is spirally provided around the shaft part  22   a , and a screw diameter is set to 20 mm, a screw pitch is set to 20 mm, and a rotation speed is set to 400 rpm. The second conveyance screw  23  also has a screw structure in which the conveyance blade  23   b  is spirally provided around the shaft part  23   a . A screw diameter of the second conveyance screw  23  is set to 20 mm. A screw pitch is set to 30 mm on side provided with a replenishing port  28  and is set to 20 mm on side not provided with the replenishing port  28 , and thus a conveying property on the side provided with the replenishing port  28  is made larger. A rotation speed is set to 400 rpm. 
     In the agitating chamber  21   c , the replenishing port  28  that opens upward is provided at an end on the upstream in the conveyance direction D 1  of the developer, and the toner bottle  41  (see  FIG. 1 ) is connected to the replenishing port  28 . The toner bottle  41  houses the two-component developer for replenishment (normally, toner/developer for replenishment=100% to 80%) that is a mixture of the toner and the carrier. The toner supplied from the toner bottle  41  is replenished to the agitating chamber  21   c  through the replenishing port  28 . 
     As illustrated in  FIG. 2 , the developing sleeve carries the developer that contains the nonmagnetic toner and the magnetic carrier, and conveys the developer to a developing region  30  facing the photosensitive drum  81 , through rotation. The developing sleeve  24  contains, for example, a nonmagnetic material such as aluminum and nonmagnetic stainless steel. In the present exemplary embodiment, the developing sleeve  24  contains aluminum having the diameter of 20 mm. A roller-shaped magnetic roller  29  is fixed and disposed inside the developing sleeve  24  so as not to rotate relative to the developer container  21 . The magnet roller  29  includes a developing magnetic pole N 2 , and magnetic poles N 1 , S 1 , S 2 , and N 3  that convey the developer. The pole N 3  and the pole N 1  of the same polarity are adjacently disposed inside the developer container  21 . The developer peeled off from the surface of the developing sleeve  24  so as to be separated therefrom recovered in the developing chamber  21   b  because repulsive magnetic field is formed between the poles N 1  and N 3 . The developing sleeve  24  includes a plurality of concave parts  31  on the surface, and detail thereof will be described later. 
     The developer in the developing device  20  is carried on the developing sleeve  24  by the magnet roller  29 . Thereafter, the developer on the developing sleeve  24  is regulated in layer thickness by the regulation blade  25 , and is conveyed to the developing region  30  that faces the photosensitive drum  81 , through rotation of the developing sleeve  24 . In the developing region  30 , the developer on the developing sleeve  24  is napped to form magnetic brush. The magnetic brush is brought into contact with. the photosensitive drum  81  to supply the toner to the photosensitive drum  81 , and the electrostatic latent image of the photosensitive drum  81  is accordingly developed as the toner image. 
     The regulation blade  25  includes a plate-like nonmagnetic member that contains aluminum, etc., and extends along the axial line of the developing sleeve  24  in the longitudinal direction The regulation blade  25  is disposed on upstream of the developing region  30  in the rotation direction of the developing sleeve  24 . Further, both of the toner and the carrier of the developer pass between a front end part of the regulation blade  25  and the developing sleeve  24 , thereby being fed to the developing region  30 . Adjusting a gap between the regulation blade  25  and the surface of the developing sleeve  24  regulates a nap cut amount of the magnetic brush of the developer carried on the developing sleeve  24 , thereby adjusting the developer amount conveyed to the developing region  30 . 
     The inductance sensor  26  is provided on a side wall of the agitating chamber  21   c  and is connected to the control unit  60 . The inductance sensor  26  detects toner density of the developer conveyed in the agitating chamber  21   c  and transmits an electric signal to the control unit  60 . The control unit  60  uses the inductance sensor  26  to execute automatic toner replenishment (ATR). As a result, the control unit  60  causes the second conveyance screw  23  to agitate and convey the toner supplied from the replenishing port  28  and the developer in the agitating chamber  21   c , thereby controlling the toner density of the developer to he constant. 
     Next, the configuration of the surface of the developing sleeve  24  described above will be described in detail with reference to  FIG. 4 . In  FIG. 4 , the conveyance direction of the developing sleeve  24  is illustrated as a rotation direction R, upstream side and downstream side thereof are respectively illustrated as UP and DN, and a direction intersecting the rotation direction R is illustrated as a width direction W. Further, a volume average particle diameter (average particle diameter) of carrier C carried on the developing sleeve  24  is regarded as 40 μm. 
     As illustrated in  FIG. 4A , the plurality of concave parts  31  are provided on the surface of the developing sleeve  24 . The concave parts  31  are disposed periodically in each of the rotation direction R and the width direction W of the developing sleeve  24 . The concave parts  31  are disposed with predetermined intervals G in the width direction W. Further, in the rotation direction R, the concave parts  31  are oriented. in a direction inclined to the rotation direction R. The concave parts  31  each have a square shape in which one side extends along the width direction W in a planar view. As illustrated in FIG.  4 B, the concave parts  31  are disposed at equal intervals G. The interval G is the shortest distance between the concave parts  31  adjacent to each other. A region other than the concave parts  31  on the surface of the developing sleeve  24 , namely, a region among the concave parts  31  serves as a non-concave part  51 . In other words, a width of the non-concave part  51  equal to the interval G of the concave parts  31 . In the present exemplary embodiment, the interval G of the concave parts  31  is equal to a width between the concave parts  31  in the longitudinal direction of the developing sleeve. 
     If the interval G between the concave parts  31  adjacent to each. other is large, effect of collecting the magnetic brush in the concave parts  31  is weakened, which increases possibility that the magnetic brush is formed in the non-concave part  51 . Therefore, in the present exemplary embodiment, the width of the non-concave part  51 , namely, the interval G of the concave parts  31  is made smaller than the volume average particle diameter of the carrier C and is set to approximately 30 μm, for example. With this configuration, a circular surface having a diameter equal to the volume average particle diameter of the carrier C is not included in the non-concave part  51  which are not the concave parts  31 , so that it is difficult for the carrier u to exist stably in the non-concave part  51 . As a result, the carrier C is less likely to be carried on the non-concave part  51 , and the magnetic brush is less likely to be formed in the non-concave part  51 , accordingly. Therefore, the magnetic brush is regulated. and formed in the pattern of the concave parts  31 , which makes it possible to make uniform the distance between the bristles of the magnetic brush and the length of the magnetic brush formed on the developing sleeve  24 . 
     The concave parts  31  each have a shape that can house the circular shape having the diameter equal to the volume average particle diameter of the carrier C, and are all formed with the same dimension. If the size of each of the concave parts  31  in a planar view can include a projected surface of the carrier C, the carrier C held by the concave parts  31 , and the magnetic brush can easily and stably exist at the positions of the concave parts  31 . In other words, if each particle of the carrier C is a sphere having a diameter equal to the volume average particle diameter, each of the concave parts  31  includes a circular surface that has the diameter equal to the diameter of the sphere. Further, the magnetic brush typically has a conical shape in which a root is thick and a thickness is gradually reduced toward a tip. Therefore, area of each of the concave parts  31  in a planar view is desirably equal to or larger than the size of four carrier particles in order to more stably hold the magnetic brush. Further, if each of the concave parts  31  has the area equal to or larger than the size of 30 or more carrier particles, the concave part  31  including two the bristles of the magnetic brush appears, and the number of magnetic brush becomes different among the concave parts  31 . In this case, the magnetic brush may become non-uniform over the entire developing sleeve  24 . Accordingly, each of the concave parts  31  preferably has the area that can house four or more and less than 30 circular shapes each having the diameter equal to the volume average particle diameter of the carrier C. In the present exemplary embodiment, each of the concave parts  31  is formed in a square shape in which one side has a length of 100 μm. The square shape has an area corresponding to a total cross-sectional area of approximately eight carrier C particles having the volume average particle diameter of 40 μm. 
     The concave parts  31  each desirably have a depth equal to or larger than the volume average particle diameter of the carrier C in order to stably hold the carrier C in the concave parts  31 . When the concave parts each have an excessively-large depth, however, the conveyance performance becomes excessively high, and peeling of the developer in a non-magnetic field cannot be sufficiently performed. This may cause a dragging phenomenon in which the developer after the development is conveyed to the developing region again without going through the agitating process. The dragging phenomenon becomes remarkable when the maximum depth of each of the concave parts  31  becomes equal to or larger than four times the volume average particle diameter of the carrier C. Accordingly, the concave parts  31  each preferably have the depth. that is equal to or larger than the volume average particle diameter of the carrier C and smaller than four times the volume average particle diameter of the carrier C. In the present exemplary embodiment, the concave parts  31  each have the maximum depth of 60 μm, and are each formed in a U-shaped concave shape in a cross-sectional view (see  FIG. 7B ). 
     For example, the concave parts  31  may be arranged in. a lattice form in which the concave parts  31  are arranged with linearly equal intervals G in each of the width direction W and the rotation direction R. In this case, however, a region where the non-concave part  51  is continuously present is formed over the entire circumference of the developing sleeve  24  in the rotation direction R. In this case, the following possibility is considered. First, when the developer carried on the developing sleeve  24  is conveyed to the region facing the photosensitive drum  81 , the developer on the developing sleeve  24  is compressed at a pressure by the photosensitive drum  81 . In addition, the circumferential speed of the developing sleeve  24  is typically higher than the circumferential speed of the photosensitive drum  81  for enhancement of developing efficiency of the toner. Accordingly, the speed of the tip of the magnetic brush in contact with the photosensitive drum  81  is reduced in a region where the contact nip starts. At this time, constraint force of the concave parts  31  with respect to the root of the magnetic brush is present, and accordingly, the reduction of the speed is suppressed. The root of the magnetic brush slips on the developing sleeve  24  in the region where the constraint force with respect to the magnetic brush is weak, which reduces the speed of the magnetic brush. As a result, accumulation of the developer in the contact nip easily occurs. 
     In the case of the configuration in which the non-concave part  51  does not include the circular surface having the diameter equal to the volume average particle diameter of the carrier C as with the present exemplary embodiment, the magnetic brush is less likely to exist in the non-concave part  51 . The developer, however, is compressed at the pressure by the photosensitive drum  81  near the region where the developing sleeve  24  and the photosensitive drum  81  come closest to each other in the contact nip. Therefore, the magnetic brush may be present in the non-concave part  51 . In this case, in the configuration where the square-shaped concave parts  31  are arranged in a lattice form, the non-concave part  51  is continuously present in the rotation direction R in some part. Consequently, the above-described slip of the magnetic brush may occur, which may cause retention. 
     In contrast, in the present exemplary embodiment, the concave parts  31  are arranged with linearly equal intervals G in the width direction W, and are arranged with equal intervals G in the rotation direction R such that adjacent columns of the concave parts  31  are shifted by substantially half of a pitch P of the cycle in the width direction W. As a result, another concave part  31  is disposed on an extension of the non-concave part  51 , located between the concave parts  31  arranged side by side in the width direction W, in the rotation direction R. Therefore, even if the root of the magnetic brush slips on the non-concave part  51  due to compression by the photosensitive drum  81  in the developing region, the carrier C is constrained by the subsequent other concave part  31 , and smoothly passes through the developing region. 
     The concave parts  31  of the developing sleeve  24  described above may be formed through, for example, electrocasting or etching, or may be formed by mechanically pressing square molds against the surface of the developing sleeve  24  to dent the surface. 
     As describe above, according to the developing device  20  of the present exemplary embodiment, the concave parts  31  are periodically arranged in each of the rotation direction R and the width direction W of the developing sleeve  24 . Further, the concave parts  31  each have the shape that can house tan circular shape having the diameter equal to the volume average particle diameter of the carrier C carried on the developing sleeve  24 . Further, the interval G of the concave parts  31  is smaller than the volume average particle diameter of the carrier C. As a result, the carrier C is less likely to be carried between the concave parts  31 , and the magnetic brush is less likely to be formed between the concave parts  31 . Therefore, the magnetic brush is regulated and formed in the pattern of the concave parts  31 . This makes it possible to make uniform the distance between the bristles of the magnetic brush and the length of the magnetic brush formed on the developing sleeve  24 , and to make uniform the contact state of the magnetic brush to the photosensitive drum  81  on the downstream of the contact nip in the rotation direction, thereby improving quality of the output image. 
     Further, according to the developing device  20  of the present exemplary embodiment, the concave parts  31  are arranged with the linearly equal intervals G in the width direction W, and are arranged with the equal intervals G in the rotation direction R such that the adjacent columns of the concave parts  31  are shifted by substantially half of the pitch P of the cycle in the width direction W. As a result, another concave part  31  disposed on the extension of the non-concave part  51 , located between the concave parts  31  arranged side by side in the width direction W, in the rotation direction R. Therefore, even if the root of the magnetic brush slips on the non-concave part  51  due to compression by the photosensitive drum  81  in the developing region, the carrier C is constrained by the subsequent other concave part  31 , and smoothly passes through the developing region. As a result, the carrier C is less likely to be carried on the non-concave part  51 , and the magnetic brush is less likely to be formed in the non-concave part  51 . Therefore, the magnetic brush is regulated and formed in the pattern of the concave parts  31 , which makes it possible to make uniform the distance between the bristles of the magnetic brush and the length of the magnetic brush formed on the developing sleeve  24 . 
     In the above-described developing device  20  of the exemplary embodiment, the case where the concave parts  31  each have the square shape in which the one side extends along the width. direction W has been described; however, the concave parts are not limited thereto. For example, as illustrated in  FIG. 5A , concave parts  32  each may have a square shape in which one side is inclined by approximately 45 degrees with respect to the width direction W in a planar view. In this case, as illustrated in  FIG. 5B , the concave parts  32  are arranged with linearly equal intervals G in each of two directions that are inclined by about  45  degrees with respect to the width direction W. In this case as well, the carrier C are less likely to be carried between the concave parts  32 , and the magnetic brush is less likely to be formed. Therefore, the magnetic brush is regulated and formed in a pattern of the concave parts  32 . Further, also in this case, other concave part  32  is disposed on an extension of a non-concave part  52 , located between the concave parts  32  arranged side by side in the width direction W, in the rotation direction R. Therefore, even if the root of the magnetic brush slips on the non-concave part  52  due to compression by the photosensitive drum  81  in the developing region, the carrier C is constrained by subsequent other concave part  32 , and smoothly passes through the developing region. For these reasons, is possible to make uniform the distance between the bristles of the magnetic brush and the length of the magnetic brush formed on the developing sleeve  24 , and to make uniform the contact state of the magnetic brush to the photosensitive drum  81  on the downstream of the contact nip in the rotation direction, thereby improving quality of the output image. In particular, according to the concave parts  32  illustrated in  FIG. 5B , since a vertex of the square shape is located on the upstream side UP in the rotation direction R in a planar view, the carrier C tends to be concentrated in the vertex. This makes it possible to concentrate the position of the root of the magnetic brush and to make uniform the distance between the bristles of the magnetic brush and the length of the magnetic brush at a high degree. 
     Further, in the developing device  20  of the exemplary embodiment described above, the case where the concave parts  31  and  32  each have the square shape has been described; however, the concave parts  31  and  32  each may have other shapes. For example, as illustrated in  FIG. 6A , concave parts  33  each may have a regular hexagonal shape. In this case, the concave parts  33  may be arranged such that one side of each of the concave parts 33 is aligned along the width direction W or the rotation direction R or is appropriately inclined in a planar view. Further, as illustrated in  FIG. 6B , concave parts  34  each may have a regular triangle shape. In this case, the concave parts  34  may be arranged such that one side of each of the concave parts  34  is aligned along the width direction W, and a vertex facing the one side alternately faces the upstream side UP and the downstream side DN in the rotation direction R. As described above, the case where the concave parts each have any of the regular triangle shape, the square shape, and the regular hexagonal shape is preferable for making the distance between the bristles of the magnetic brush and the length of the magnetic brush uniform because the concave parts are arranged with minimum equal intervals G. 
     Furthermore, as illustrated in  FIG. 6C , concave parts  35  each may have a circular shape. in this case, the concave parts  35  may be arranged such that a center of each of the concave parts  35  is aligned along the width direction W or the rotation direction R, or is appropriately inclined in a planar view, In a case where the concave parts  35  each have a perfect circular shape, the concave parts  35  may be formed through cutting. Further, as illustrated in  FIG. 6D , concave parts  36  each may have an elliptical shape. In this case as well, the concave parts  36  may be arranged such that a long axis of each of the concave parts  36  is aligned in the width direction W or the rotation direction R, or is appropriately inclined in a planer view, as with the case of the circular shape. 
     In particular, when the elliptical shape has a long axis in the width direction W, freedom of movement of the magnetic brush in the rotation direction R is small as compared with the circular shape. In other words, slip of the root of the magnetic brush due to compression by the photosensitive drum  81  in the developing region hardly occurs inside the concave parts  36 . This makes it possible to further improve conveyance force of the developing sleeve  24  conveying the magnetic brush. 
     Also in the case of the above-described concave parts  33 ,  34 ,  35 , and  36 , the interval G between the concave parts is smaller than the volume average particle diameter of the carrier C. Therefore, the carrier C is less likely to be carried between the concave parts and the magnetic brush is less likely to be formed, and the magnetic brush is accordingly regulated and formed in the pattern of the concave parts  33 ,  34 ,  35 , and  36 . This makes it possible to make uniform the distance between the bristles of the magnetic brush and the length of the magnetic brush formed on the developing sleeve  24 , and to make uniform the contact state of the magnetic brush to the photosensitive drum  81  on the downstream of the contact nip in the rotation direction, thereby improving quality of the output image. 
     An image was output by using the developing device  20  of the present exemplary embodiment described above, and roughness was evaluated. One side of each of the square-shaped concave parts  31  was set to 100 μm and an interval between the concave parts  31  was set to 30 μm in a planar view as illustrated in  FIG. 7A . Each of the concave parts  31  was formed in a concave shape having a U-shaped bottom shape in cross-section and a maximum depth of 60 μm, as illustrated in  FIG. 7B . 
     An average particle diameter of the volume distribution reference of used magnetic carrier was measured with use of a multi-image analyzer (manufactured by Beckman Coulter, Inc.). As the particle diameter, 50% particle diameter (D 50 ), which is an accumulated value of the volume distribution, was determined. Control and analysis were performed with use of accompanying software (version 10.3.3-202D). Measurement conditions were as follows. SetZero time was set to 10 seconds, a measurement time was set to 10 seconds, the number of measurement times was set to once, a particle refractive index was set to 1.81, a particle shape was set to a non-spherical shape, a measurement upper limit was set to 1208 μm, a measurement lower limit was set to 0.243 μm, and a measurement environment was set to a normal-temperature normal-humidity environment (23° C. and 50% RH). The particle size distribution measurement was performed with use of a laser diffraction/scattering particle size distribution measuring apparatus “Microtrac MT3300EX” (manufactured by Nikkiso Co., Ltd). A sample supplier for identification measurement “one-shot dry-type sample conditioner Turbotrac” (manufactured by Nikkiso Co., Ltd) was attached to perform the measurement. As supplying conditions of Turbotrac, a dust collector was used as a vacuum source, a quantity of air was set to about 33 liters/sec, and pressure was set to 17 kPa. The control was automatically performed on the software. As a result of the measurement, the volume average particle diameter of the carrier C was 40 μm. 
     The conditions used for output of an image were as follows. A circumferential speed of the photosensitive drum  81  was set to 240 mm/sec, and a circumferential speed of the developing sleeve  24  was set to 432 mm/sec. A charged potential V D  was set to 500 V, an applied direct current voltage V dc  was set to 400 V, an alternating current voltage superimposed was a rectangular wave having a peak-to-peak voltage of 1.3 kV with a frequency of 10 kHz. The output images were an entirely solid-black image and an entirely half-tone image in A4 size. The solid-black image used herein indicates an image that has density of approximately 1.4 when the density is measured with use of a reflection spectral densitometer 500 series manufactured by X-Rite Inc., and the half-tone image indicates an image having density of 40% relative to the density of the solid-black image. Results are illustrated in Table 1. As illustrated in Table 1, favorable result and particularly-favorable result were obtained in both. of the solid-black image and the half-tone image. 
     
       
         
           
               
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                   
                 Roughness Evaluation 
               
            
           
           
               
               
               
            
               
                   
                 Solid--Black Image 
                 Half-Tone Image 
               
               
                   
               
               
                 Example 
                 Particularly 
                 Favorable 
               
               
                   
                 Favorable 
                   
               
               
                 Comparative 
                 Favorable 
                 Particularly 
               
               
                 Example 1 
                   
                 Unfavorable 
               
               
                 Comparative 
                 Favorable 
                 Unfavorable 
               
               
                 Example 2 
               
               
                   
               
            
           
         
       
     
     A comparative example 1 will be described. The developing sleeve obtained by subjecting the surface to blast processing with use of regular-shaped beads and having a surface roughness Rz of 11 μm was used. Other conditions were similar to those in the example. Results are illustrated in Table 1. As illustrated in Table 1, favorable result was obtained in the solid-black image but particularly-unfavorable result was obtained in the half-tone image. 
     A comparative example 2 will be described. The developing sleeve used in the comparative example 2 has square-shaped concave parts  37  periodically arranged similarly to the above-described exemplary embodiment, but an interval between the concave parts  37  adjacent to each other is set to 100 μm as illustrated in  FIG. 7C . In other words, a circular surface having a diameter equal to the volume average particle diameter of the carrier C was included in a non-concave part  57 . Results are illustrated in Table 1. As illustrated in Table 1, favorable result was obtained in the solid-black image but unfavorable result was obtained. in the half-tone image. 
     As described above, remarkable difference of roughness appeared in the results of the half-tone image, and roughness became favorable in the case where the developing sleeve  24  of the exemplary example was used as compared with the comparative examples 1 and 2. This is because the magnetic brush is arranged in the pattern of the concave parts  31  provided on the sleeve surface, which makes uniform the state of the magnetic brush. It is inferred that small difference of roughness evaluation in the black-solid image is due to small influence caused by disturbance by non-uniformity of the magnetic brush at the rear end of the contact nip because of a large applied amount of the toner. While the difference of roughness becomes small in the solid-black image, the difference of roughness due to influence of the magnetic brush was observed. As described above, it was confirmed that quality of the output image can be improved by configuring the sleeve surface in such a manner that each of the concave parts  31  has the area larger than the size of one carrier C particle and the non-concave part  51  does not have the area equal to the size of one carrier C particle, and the magnetic brush is arranged in the pattern of the concave parts  31 . 
     While the present disclosure has been described with reference to exemplary embodiments, it is to be understood that the disclosure is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Application No. 2017-021511, filed Feb. 8, 2017, which is hereby incorporated by reference herein in its entirety.