Patent Publication Number: US-8535116-B2

Title: Magnetic particle carrying device, and developing unit, process cartridge, and image forming apparatus using the same, and surface treatment method of the same

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional of U.S. Ser. No. 12/013,143 filed Jan. 11, 2008 now U.S. Pat. No. 7,899,374, and is based upon and claims benefit of priority from Japanese Patent Application Nos. 2007-003425, filed on Jan. 11, 2007, and 2007-113883, filed on Apr. 24, 2007 in the Japan Patent Office, the entire contents of each of which are hereby incorporated by reference herein. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present disclosure relates generally to a magnetic particle carrying device such as a developing agent carrier, a developing unit, a process cartridge, an image forming apparatus using the magnetic particle carrying device, and a surface treatment method for the magnetic particle carrying device. 
     2. Description of the Background Art 
     Typically, an image forming apparatus includes a photosensitive drum and a magnetic particle carrying device (e.g., a developing agent carrier) having a hollow structure (e.g., a developing sleeve). In such image forming apparatus, developing agent is carried on an external surface of the developing sleeve and then transported to the photosensitive drum for an image forming operation. 
     Such developing sleeve has an external surface subjected to a surface roughening process, for example sandblasting the external surface or forming grooves therein, so that the developing agent can be reliably carried on the developing sleeve. 
     Further, the developing sleeve has an external surface randomly formed with a number of depressions, each having a substantially elliptical shape when viewed from above. Such depressions in the developing sleeve are of two types, each defined by an orientation of a long axis of the elliptical depression. In a first type of depression, the long axis of the elliptical depression is substantially aligned with an axis of the developing sleeve, whereas in a second type of depression, the long axis of the depression is substantially aligned with a circumferential direction of the developing sleeve, that is, a direction perpendicular to the axial direction. The number of depressions of each type is typically unequal, with the first type predominant. 
     When a developing sleeve, having a hollow structure, is treated by the above-described sandblasting process to form concavities and convexities on its external surface, such concavities and convexities are relatively small. Accordingly, under repeated printing operations, such concavities and convexities are gradually scraped flat or nearly flat by the developing agent or the like, gradually reducing the amount of developing agent that the developing sleeve can transport and adversely affecting image quality, resulting, for example, in faint images. 
     The amount of developing agent that the developing sleeve can transport is enhanced by forming larger concavities and convexities on a surface of the developing sleeve, again by sandblasting. However, such an approach has drawbacks. For example, the more powerful sandblasting that is required to form larger concavities and convexities can deform the developing sleeve itself, adversely affecting its rotation. Failure of the developing sleeve to rotate precisely can cause a predetermined gap set between the developing sleeve and the photosensitive drum to fluctuate, which may result in an unstable supply of the developing agent to the photosensitive drum and a consequent lack of appropriate toner concentration in the formed image. 
     Alternatively, as described above, grooves can be formed in the external surface of the developing sleeve. Such grooves can be larger than the concavities and convexities formed by the above-described sandblasting process, and larger also than the particles of magnetic carrier or the like contained in a developing agent. This larger size of the grooves prevents them from being as thoroughly or as rapidly abraded by the developing agent as the concavities formed by sandblasting tend to be, and therefore the amount of developing agent that can be transported by the developing sleeve does not deteriorate as greatly over time. 
     However, such developing sleeve may have an uneven distribution of developing agent across its external surface because the grooves can carry and transport greater amounts of developing agent than areas having no grooves, which may lead to uneven toner concentration in the resultantly produced images. 
     With respect to the above-described elliptical depressions formed in the external surface of the developing sleeve, these are larger or deeper than dents formed by conventional sandblasting. Therefore, the developing agent is less likely to abrade such elliptical depressions, and therefore the amount of developing agent that the developing sleeve can carry does not deteriorate over time and images having appropriate concentrations of toner can continue to be produced. 
     Further, because such depressions can be formed on the external surface of the developing sleeve randomly, the developing agent can be carried on the developing sleeve randomly as a whole, which means that the developing agent can be uniformly attracted to the developing sleeve as a whole. Therefore, such developing sleeve may suppress image concentration unevenness of resultantly produced images. 
     Further, as noted above, the depressions on the external surface of the developing sleeve include first type depressions, extending in the axial direction of the developing sleeve, and the second type depressions, extending in the circumferential direction of the developing sleeve, and the number of the first type depressions is greater than the number of the second type depressions on the external surface. Accordingly, the developing agent can be picked-up onto the developing sleeve along the axial direction of the developing sleeve. Therefore, even if the developing sleeve rotates, the picked-up developing agent is less likely to drop from the external surface of the developing sleeve. Accordingly, elliptical depressions may be able to carry as much developing agent as the above-described grooves do. 
     However, such depressions in the developing sleeve may include a relatively smaller number of depressions aligned in the circumferential direction of the developing sleeve. Accordingly, adhering density (or amount) of developing agent in the circumferential direction of the developing sleeve may become lower or uneven, and thereby image concentration unevenness in a sheet transport direction may not be effectively suppressed or prevented. In general, image concentration unevenness in a sheet transport direction is more recognizable compared to image concentration unevenness in a sheet width direction, which is perpendicular to the sheet transport direction. 
     In view of such background, a method or an apparatus capable of suppressing image concentration unevenness in a sheet transport direction is desired. 
     SUMMARY 
     The present invention provides a magnetic particle carrying device including a magnetic field generator and a hollow cylindrical structure. The magnetic field generator generates a magnetic field. The hollow cylindrical structure encases the magnetic field generator and attracts magnetic particles on an external surface of the hollow structure using the magnetic field. The external surface of the hollow cylindrical structure is provided with a plurality of elliptical depressions. The depressions include first type depressions and second type depressions. A long axis of a first type of elliptical depression is substantially extending in an axial direction of the hollow cylindrical structure, and a long axis of a second type of elliptical depression is substantially extending in a circumferential direction of the hollow cylindrical structure. The external surface of the hollow cylindrical structure has more elliptical depressions of the second type than elliptical depressions of the first type. 
     The present invention also provides an image forming apparatus including a latent image carrier, a charger, a writer, and a developing unit. The latent image carrier carries a latent image thereon. The charger charges a surface of the latent image carrier. The writer configured to write the latent image on the latent image carrier. The developing unit develops the latent image with a developing agent using a magnetic particle carrying device. The magnetic particle carrying device includes a magnetic field generator and a hollow cylindrical structure. The magnetic field generator generates a magnetic field. The hollow cylindrical structure encases the magnetic field generator and attracts magnetic particles on an external surface of the hollow structure using the magnetic field. The external surface of the hollow cylindrical structure is provided with a plurality of elliptical depressions. The depressions include first type depressions and second type depressions. A long axis of a first type of elliptical depression is substantially extending in an axial direction of the hollow cylindrical structure, and a long axis of a second type of elliptical depression is substantially extending in a circumferential direction of the hollow cylindrical structure. The external surface of the hollow cylindrical structure has more elliptical depressions of the second type than elliptical depressions of the first type. 
     The present invention also provides a method of roughening a surface of an object. The method includes generating and impacting. The generating step generates a rotated magnetic field around the object. The impacting step impacts a plurality of cylindrically shaped abrasive grains against an external surface of the object with an effect of the rotated magnetic field having a frequency of 200 Hz to 400 Hz. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A more complete appreciation of the disclosure and many of the attendant advantages and features thereof can be readily obtained and understood from the following detailed description with reference to the accompanying drawings, wherein: 
         FIG. 1  illustrates a cross-sectional view of a magnetic particle carrying device according to an exemplary embodiment; 
         FIG. 2  illustrates a perspective view of a hollow structure of the magnetic particle carrying device of  FIG. 1 ; 
         FIG. 3  is an expanded surface-pictured view of a hollow structure of the magnetic particle carrying device of  FIG. 1 , in which depressions, having elliptical shape, include first depressions aligned in the axial direction of the hollow structure and second depressions aligned in the circumferential direction of the hollow structure, wherein the first depressions are greater in numbers compared to the second depressions; 
         FIG. 4  illustrates a schematic view of an external surface of the hollow structure of  FIG. 3 ; 
         FIG. 5  is an expanded surface-pictured view of a hollow structure of the magnetic particle carrying device of  FIG. 1 , in which depressions having elliptical shape include first depressions aligned in the axial direction of the hollow structure and second depressions aligned in the circumferential direction of the hollow structure, wherein the second depressions are greater in numbers compared to the first depressions; 
         FIG. 6  illustrates a schematic view of an external surface of the hollow structure of  FIG. 5 ; 
         FIG. 7  illustrates a cross-sectional view of the magnetic particle carrying device using the hollow structure of  FIG. 3 , in which protruded aggregated chains of developing agent are formed on the external surface of the magnetic particle carrying device; 
         FIG. 8  illustrates another cross-sectional view of the magnetic particle carrying device using the hollow structure of  FIG. 5 , in which protruded aggregated chains of developing agent are formed on the external surface of the magnetic particle carrying device; 
         FIG. 9  illustrates a cross-sectional view of a magnetic particle used for a developing agent; 
         FIG. 10  illustrates a cross-sectional view of a developing unit, and a process cartridge according to an exemplary embodiment; 
         FIG. 11  illustrates a cross-sectional view of an image forming apparatus according to an exemplary embodiment; 
         FIG. 12  illustrates a perspective view of a surface treatment machine used for conducting surface roughening process to the external surface of the hollow structure of  FIG. 2 ; 
         FIG. 13  illustrates a cross-sectional view of the surface treatment machine, taken along the line  2 - 2  of  FIG. 12 ; 
         FIG. 14  illustrates a perspective view of a magnetic abrasive grain used in the surface treatment machine of  FIG. 12 ; 
         FIG. 15  illustrates an expanded view of the magnetic abrasive grain of  FIG. 14 , taken along the line  3 - 3  of  FIG. 14 ; 
         FIG. 16  illustrates schematic cross-sectional view of a magnetic abrasive grain and a hollow structure to be treated in the surface treatment machine of  FIG. 12 , in which the magnetic abrasive grain rotates about its center while rotatingly moves along an outer circumference of the hollow structure; 
         FIG. 17  illustrates a schematic cross-sectional view of a magnetic abrasive grain and a the hollow structure, in which the magnetic abrasive grain impacts against an external surface of the hollow structure; and 
         FIG. 18  illustrates a cross-sectional view of a depression having elliptical shape and aligned in a circumferential direction of a hollow structure. 
     
    
    
     The accompanying drawings are intended to depict exemplary 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, and identical or similar reference numerals designate identical or similar components throughout the several views. 
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     A description is now given of exemplary embodiments of the present invention. It should be noted that although such terms as first, second, etc. may be used herein to describe various elements, components, regions, layers and/or sections, it should be understood that such elements, components, regions, layers and/or sections are not limited thereby because such terms are relative, that is, used only to distinguish one element, component, region, layer or section from another region, layer or section. Thus, for example, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the present invention. 
     In addition, it should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the present invention. Thus, for example, as used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. Moreover, the terms “includes” and/or “including”, when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     Furthermore, although in describing exemplary embodiments shown in the drawings, specific terminology is employed for the sake of clarity, the present disclosure is not 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. 
     Referring now to the drawings, a magnetic particle carrying device (e.g., developing sleeve) according to an exemplary embodiment is described with reference to accompanying drawings. 
     A description is now given to a magnetic particle carrying device according to an exemplary embodiment with reference mainly to  FIGS. 1 to 6 ,  10 , and  18 . 
     As illustrated in  FIG. 1 , a developing roller  115 , used as magnetic particle carrying device, includes a cored bar  134 , a magnet roller  133 , and a developing sleeve  132 , for example. The cored bar  134  is disposed so that its longitudinal direction is parallel to the longitudinal direction of a photosensitive drum  108  (see  FIG. 10 ), and is fixed to a casing  125  of a development unit  113  shown in  FIG. 10  in an unrotatable manner. 
     The magnet roller  133 , used as magnetic field generator, may be made of a magnetic material and shaped in a cylindrical shape. The magnet roller  133  is attached with a plurality of fixed magnetic poles (not shown). The magnet roller  133  is fixed to an outer circumference of the cored bar  134 , and thereby is not allowed to rotate about the axial center of the cored bar  134 . 
     Each of the fixed magnetic poles may be a magnet having a long bar-like shape, and is attached to the magnet roller  133 . The fixed magnetic pole extending along the longitudinal direction of the magnet roller  133  (i.e., the developing roller  115 ) is provided throughout the length of the magnet roller  133 . Such configured magnet roller  133  is encased in the developing sleeve  132 , which has a hollow structure having a cylindrical shape, for example. 
     As later described with reference to  FIG. 10 , one of the fixed magnetic poles faces a stirring screw  118 , and used as a pick-up magnetic pole for picking up developing agent to the developing sleeve  132  of the developing roller  115 . As also later described with reference to  FIG. 10 , another fixed magnetic pole faces the photosensitive drum  108 , and used as development magnetic pole. The development magnetic pole forms a magnetic field between the developing roller  115  and the photosensitive drum  108 . 
     The fixed magnetic poles may be used to attract a magnetic carrier  135  (see  FIG. 9 ), made of magnetic particle and included in developing agent  126  (see  FIG. 8 ), to an external surface of the developing sleeve  132 . The magnetic carrier  135  may be stacked one on the other along a magnetic field generated by the fixed magnetic poles, by which a aggregated chain of the magnetic carrier  135  may be formed on the external surface of the developing sleeve  132  in a protruding manner (see  FIGS. 7 and 8 ). The term of “magnetic carrier” may be used in this disclosure while having a meaning of singular or plural magnetic particles. Accordingly, the magnetic carrier  135  or the magnetic carrier  135  may be used in this disclosure. 
     Then, toner particles included in the developing agent  126  may be attracted to the protruded aggregated chain of the magnetic carrier  135 . Accordingly, the developing agent  126  is attracted to on the external surface of the developing sleeve  132  with an effect of magnetic force of the magnet roller  133 . 
     As illustrated in  FIG. 2 , the developing sleeve  132  has a cylindrical shape, for example. The developing sleeve  132  encases the magnet roller  133  therein, and can rotate about the axial center of the developing sleeve  132 . Accordingly, the inner surface of the developing sleeve  132  may sequentially faces each of the fixed magnetic poles when the developing sleeve  132  rotates about its axis. The developing sleeve  132  may be made of a non-magnetic material such as aluminum alloy, stainless steel (SUS), or the like, for example. As described later, the external surface of the developing sleeve  132  may be treated by a surface treatment machine  1  (see  FIG. 12 ) to make the external surface as preferably roughened surface. 
     As a base material of the developing sleeve  132 , aluminum alloy may be preferably used from a viewpoint of its machinability and lightweight. When aluminum alloy is used as base material of the developing sleeve  132 , aluminum alloy having standard of A6063, A5056, or A3003 may be preferably used, for example. When SUS (stainless steel) is used, SUS 303, SUS 304, or SUS 316 may be preferably used, for example. 
     The developing sleeve  132  may have a given outer diameter such as 17 mm to 18 mm and a given axial length such as 240 mm to 350 mm, for example. The size of the developing sleeve  132  may be changed to any values depending on a design concept or the like. The external surface of the developing sleeve  132  has a given surface roughness, which may vary depending on a surface portion of the developing sleeve  132 . For example, a depth of depressions formed on the developing sleeve  132  may become gradually deeper in an axial direction, which starts from a center portion to an each end portion of the developing sleeve  132 . 
     Further, as illustrated  FIGS. 3 to 6 , the external surface of the developing sleeve  132  has a number of depressions  139  having elliptical shape when viewed from above the developing sleeve  132 . As illustrated  FIGS. 3 to 6 , such depressions  139  are randomly formed on the external surface of the developing sleeve  132 . As illustrated  FIG. 3 to 6 , the depressions  139  may have two types of depressions, that is, first depressions  139   a  (see  FIGS. 3 and 4 ) and second depressions  139   b  (see  FIGS. 5 and 6 ). 
     In the first depressions  139   a , a long axis of elliptical shape may be substantially aligned in an axial direction of the developing sleeve  132 . For example, the long axis of elliptical shape of the first depressions  139   a  may have an angle of within ±45 degrees with respect to the axial direction of the developing sleeve  132 . 
     In the second depressions  139   b , a long axis of elliptical shape may be substantially aligned in a circumferential direction of the developing sleeve  132 . For example, the long axis of elliptical shape of the second depressions  139   b  may have an angle of within ±45 degrees with respect to the circumferential direction of the developing sleeve  132 , wherein the circumferential direction of the developing sleeve  132  is a rotation direction of the developing sleeve  132  in this disclosure. In an exemplary embodiment, the developing sleeve  132  may have a greater number of the second depressions  139   b  compared to the first depressions  139   a , for example. Further, the depressions  139  having elliptical shape may have a given major axis length of such as 0.05 mm to 2 mm, and a given minor axis length of such as 0.02 mm to 1 mm, for example. As illustrated in  FIG. 3  to  FIG. 6 , the axial direction and the circumferential direction of the developing sleeve  132  are perpendicular with each other. 
     Further, as illustrated in  FIG. 18 , the depression  139  may have a peripheral end portion  200   a  (i.e., rear edge of depression  139 ), which may be protruded from an external face of the developing sleeve  132 , and a deepest portion  200   c  (i.e., bottom of depression  139 ), from which a hypothetical first line L 1  and a hypothetical second line L 2  are extended. The hypothetical first line L 1  may outwardly extend from the deepest portion  200   c  of the depression  139  in a radial direction of the developing sleeve  132 . The hypothetical second line L 2  may outwardly extend from the deepest portion  200   c  to the peripheral end portion  200   a  of the depression  139 , wherein the peripheral end portion  200   a  is a rearward position of the depression  139  with respect to a direction of rotation (shown by an arrow in  FIG. 18 ) of the developing sleeve  132  when magnetic particles are attracted on the developing sleeve  132 . As illustrated in  FIG. 18 , the hypothetical first and second lines L 1  and L 2  may form an angle α. In an exemplary embodiment, average or mean value of the angle α is preferably set within 45 degrees. If the angle α is set within 45 degrees, the deepest portion  200   c  may come to a position closer to the peripheral end portion  200   a  of the depression  139 . 
     Further, as also illustrated in  FIG. 18 , the depressions  139  may have a hypothetical straight-line segment La and a radius segment Lb. The hypothetical straight-line segment La extends from a rotation center P of the developing sleeve  132  to the peripheral end portion  200   a  of the depression  139 . The radius segment Lb is one half of an outer diameter of the developing sleeve  132 . In an exemplary embodiment, the hypothetical straight-line segment La may be set greater than the radius segment Lb, and preferably, the hypothetical straight-line segment La and the radius segment Lb may have a relationship of “20 μm≧La-Lb&gt;5 μm” as described later. When such relationship is set, the peripheral end portion  200   a  may be preferably protruded from the external surface of the developing sleeve  132 . 
     A description is now given to a process of attracting the developing agent  126  to the external surface of the developing roller  115 . 
     As illustrated in  FIG. 10 , in the development unit  113 , the developing roller  115  and the developing agent  126  face each other with a given gap therebetween, wherein the developing roller  115  is used as developing agent carrier, and the developing agent  126  includes the magnetic carrier  135  used as magnetic particles and toner particles. 
     As above described, the developing roller  115  encases the magnet roller  133  attached with the above-described pick-up magnetic pole. As above described, the pick-up magnetic pole generates a magnetic force over the external surface of the developing sleeve  132  (or developing roller  115 ). With an effect of such magnetic force, the developing agent  126  in a second compartment  121  of a container  117  (see  FIG. 10 ) may be attracted on the external surface of the developing sleeve  132 . 
     Further, the above-described development magnetic pole generates a magnetic force over the external surface of the developing sleeve  132  (or developing roller  115 ). With an effect of such magnetic force, the development magnetic pole forms a magnetic field between the developing sleeve  132  and the photosensitive drum  108 . The development magnetic pole may be used to form magnetic brushes of the magnetic carriers  135  with an effect of the magnetic field so that the developing agent  126  is attracted on the external surface of the developing sleeve  132  and then transferred from the developing roller  115  to the photosensitive drum  108  via the magnetic brushes. 
     Further, at least one fixed magnetic pole may be provided between the pick-up magnetic pole and the development magnetic pole. Such at least one fixed magnetic pole generates a magnetic force over the external surface of the developing sleeve  132  (or developing roller  115 ) so that the developing agent  126 , to be used for a developing process, can be transported to a position facing the photosensitive drum  108 , or such magnetic force generated by such at least one fixed magnetic pole is used to transport the developing agent  126 , already used by a developing process, from the photosensitive drum  108  to the container  117 . 
     A description is now given to a protruded aggregated chain of the developing agent  126  formed on the developing sleeve  132  with reference to  FIGS. 7 and 8 . Specifically, protruded aggregated chain of the developing agent  126  may be formed in a different manner between the first depressions  139   a  and the second depressions  139   b . As described above, the first depressions  139   a  may have elliptical shape, extending along the axial direction of the developing sleeve  132 , and the second depressions  139   b  may have elliptical shape, extending along the circumferential direction of the developing sleeve  132 . 
       FIG. 7  illustrates one state of a cross-sectional view of the developing roller  115  having protruded aggregated chains of the developing agent  126 , in which the number of the first depressions  139   a  is greater than that of the second depressions  139   b .  FIG. 8  illustrates another state of a cross-sectional view of the developing roller  115  having protruded aggregated chains of the developing agent  126 , in which the number of the second depressions  139   b  is greater than that of the first depressions  139   a.    
     As shown in  FIGS. 7 and 8 , an effective length of depressions  139 , which can carry or hold the developing agent  126 , is different between the two states shown in  FIG. 7  or  8 . Specifically, the effective length of depressions  139  along the circumferential direction of the developing roller  115  (used as magnetic particle carrying device) in  FIG. 8  becomes greater than that in  FIG. 7 , wherein the developing roller  115  has a greater number of the first depressions  139   a  in  FIG. 7  and a greater number of the second depressions  139   b  in  FIG. 8  as described above. 
     Because the developing agent  126  is closely attracted in the depressions  139  of the developing sleeve  132 , an adhering density of the developing agent  126  in the circumferential direction of the developing sleeve  132  becomes greater in case of  FIG. 8 . Further, protruded aggregated chains of the developing agent  126  may be formed in each of the second depressions  139   b  more uniformly. 
     As above described, in an exemplary embodiment, the external surface of the developing sleeve  132  may include the number of depressions  139  having elliptical shape, wherein the depressions  139  may include a greater number of the second depressions  139   b  compared to the first depressions  139   a . Accordingly, magnetic particles included in the developing agent  126  may be uniformly attracted on the external surface of the developing sleeve  132  in the circumferential direction of the developing sleeve  132 . Further, such magnetic particles may be attracted on the external surface of the developing sleeve  132  with a greater density in the circumferential direction of the developing sleeve  132  as above described. 
     Therefore, the developing roller  115  can supply the developing agent  126  to a circumferential direction of the photosensitive drum  108  more uniformly. In other words, the developing agent  126  can be supplied to a direction of rotation of the photosensitive drum  108  more uniformly, wherein the direction of rotation of the photosensitive drum  108  is aligned to a transport direction of a transfer member such as sheet, intermediate transfer belt or the like. Accordingly, a toner image can be developed on the photosensitive drum  108  by decreasing unevenness of image concentration, by which an image having higher quality can be produced on a transfer member. 
     Further, the depressions  139  having elliptical shape, formed on the external surface of the developing sleeve  132 , may have a greater size compared to dents formed by a conventional sandblasting process, wherein the depression  139  may have a major axis length of 0.05 mm to 2 mm, and a minor axis length of 0.02 mm to 1 mm, for example. Therefore, compared to the conventional sandblasting process, the developing agent  126  is less likely to abrade such elliptical depressions of the depressions  139 , and therefore the amount of developing agent  126  that the developing sleeve  132  can carry does not deteriorate over time and images having appropriate concentrations of toner can continue to be produced. The amount of developing agent  126  that the developing sleeve  132  can carry may be referred as transportability (or transport amount) of the developing agent  126  by the developing sleeve  132 . 
     Further, as above described with reference to  FIG. 18 , the depressions  139  on the external surface of the developing sleeve  132  includes the deepest portion  200   c  and the peripheral end portion  200   a , wherein the deepest portion  200   c  is closer to the peripheral end portion  200   a  positioning at a rearward position of the depression  139  with respect to the direction of rotation of the developing sleeve  132 . 
     In an exemplary embodiment, as above described, the hypothetical first line L 1  extending outwardly from the deepest portion  200   c  in a radial direction of the developing sleeve  132  and the second line L 2  extending outwardly from the deepest portion  200   c  to the peripheral end portion  200   a  of the depression  139  may form the angle α within 45 degrees. 
     Accordingly, the depressions  139  may scoop up magnetic particles when the developing agent  126  is carried up to the developing sleeve  132  from the second compartment  121  (see  FIG. 10 ), and the depressions  139  may reliably carry or hold the magnetic carriers  135  therein. Therefore, the magnetic carriers  135  may be held on the external surface of the developing sleeve  132  more reliably, by which the developing agent  126  may also be held on the external surface of the developing sleeve  132  more reliably. Therefore, the amount of developing agent  126  that the developing sleeve  132  can carry does not deteriorate over time and images having appropriate concentrations of toner can continue to be produced. 
     Further, a depth of the depression  139  may be set to a relatively smaller value in an exemplary embodiment while maintaining a good level of holding capability of developing agent  126 , by which processing energy (e.g., mechanical force) applied for forming the depressions  139  on the external surface of the developing sleeve  132  can be set smaller, which may be preferable for suppressing a shape deformation of the developing sleeve  132  (e.g., misaligned axis, change of inner/outer diameter, collapsing of sleeve shape). Accordingly, the developing sleeve  132  can be manufactured with a higher precision, and can rotate with a higher precision, by which an image having higher quality can be produced with a good level of toner concentration. 
     Further, the depression  139  on the external surface of the developing sleeve  132  may have the peripheral end portion  200   a  at a rearward position with respect to the direction of rotation of the developing sleeve  132 , wherein the peripheral end portion  200   a  may protrude from the external surface of the developing sleeve  132 . Accordingly, an area extending from the deepest portion  200   c  to the peripheral end portion  200   a  in the depression  139  may become relatively greater in size, by which the magnetic carriers  135  can be carried or held on the external surface of the developing sleeve  132  more reliably, by which the developing agent  126  may also be carried or held on the external surface of the developing sleeve  132  more reliably. Therefore, the amount of developing agent  126  that the developing sleeve  132  can carry does not deteriorate over time and images having appropriate concentrations of toner can continue to be produced. 
     Further, because the depressions  139  may be randomly formed on the external surface of the developing sleeve  132 , the developing agent  126  may randomly be attracted on the external surface of the developing sleeve  132 , by which the developing agent  126  may be uniformly attracted on the external surface of the developing sleeve  132  as a whole. Accordingly, the developing agent  126  can be uniformly transported on the developing sleeve  132 , by which the developing agent  126  can be uniformly supplied to the photosensitive drum  108  from the developing agent  126 , by which an image having higher quality can be produced with a good level of toner concentration. 
     A description is now given to the development unit  113 , which employs the above-described developing roller  115 , with reference to  FIG. 10 . As illustrated in  FIG. 10 , the development unit  113  may include an agent supply compartment  114 , a casing  125 , the developing roller  115 , and a doctor blade  116 , for example. 
     The agent supply compartment  114  may include the container  117 , and a pair of stirring screws  118  for agitating the developing agent  126 . The container  117  may have a length, substantially matched to a length of the photosensitive drum  108 . Further, the container  117  is provided with a separation wall  119 , extending in a longitudinal direction of the container  117 . The separation wall  119  separates the container  117  into a first compartment  120  and a second compartment  121 . Further, the first and second compartments  120  and  121  are communicated with each other at their both end portions. 
     In the container  117 , the developing agent  126  is contained in the first and second compartments  120  and  121 . The developing agent  126  may include toner particles and the magnetic carrier  135  made of magnetic particles (see  FIG. 9 ). Fresh toner particles may be supplied to one end portion of the first compartment  120 , which may be far from the developing roller  115 , for example, in a timely manner. Toner particles may be fine spherical particles, prepared by an emulsion polymerization method or a suspension polymerization method, for example. Toner particles may also be prepared by a pulverization method, in which synthetic resin mixed and dispersed with dyes or pigments may be pulverized. Toner particles may have an average particle diameter of 3 μm to 7 μm, for example. 
     The stirring screw  118 , provided for the first and second compartments  120  and  121 , respectively, has a longitudinal direction parallel to longitudinal directions of the container  117 , the developing roller  115 , and the photosensitive drum  108 . The stirring screw  118 , which is rotatable about its axial center, agitates toner particles and the magnetic carriers  135 , and transports the developing agent  126 . Further, the stirring screw  118  in the first compartment  120  transports the developing agent  126  from the one end portion to other end portion, and the stirring screw  118  in the second compartment  121  transports the developing agent  126  from the other end portion to the one end portion. 
     In the agent supply compartment  114 , toner particles supplied to the one end portion of the first compartment  120  are transported to the other end portion of the first compartment  120  while agitated with the magnetic carriers  135 , and the agitated toner particles and the magnetic carriers  135  are transported to the second compartment  121  from the other end portion of the first compartment  120 . Then, in the agent supply compartment  114 , toner particles and the magnetic carriers  135  are agitatingly transported in the second compartment  121 , and supplied to the external surface of the developing roller  115 . 
     The casing  125 , attached to the container  117  of the agent supply compartment  114 , may encase the developing roller  115  or the like with the container  117 . Further, the casing  125  has an opening  125 , facing the photosensitive drum  108 . 
     The developing roller  115 , formed into a cylindrical shape, is provided between the second compartment  121  and the photosensitive drum  108 , and adjacent to the opening  125   a . The developing roller  115  is disposed parallel to the photosensitive drum  108  and the container  117 . The developing roller  115  faces the photosensitive drum  108  with a given gap therebetween. The developing roller  115  and the photosensitive drum  108  form the developing area  131  at such gap portion, at which toner particles in the developing agent  126  are transferred and adhered to the photosensitive drum  108  to develop an electrostatic latent image formed on the photosensitive drum  108  as toner image. 
     The doctor blade  116 , attached to the casing  125 , is disposed over the external surface of the developing sleeve  132  with a given gap, and may be disposed adjacent to the photosensitive drum  108  in the development unit  113 . The doctor blade  116  scrapes the developing agent  126 , supplied on the external surface of the developing sleeve  132 , to control an amount of the developing agent  126  at a given level, by which a given amount of developing agent  126  can be reliably transported to the developing area  131 . 
     The developing agent  126  may be transported to the developing area  131  in the development unit  113  as follows. 
     In the development unit  113 , toner particles and the magnetic carrier  135  are agitated in the agent supply compartment  114 , and the agitated developing agent  126  is then attracted on the external surface of the developing sleeve  132  with an effect of the fixed magnetic poles in the developing roller  115 . With a rotation of the developing sleeve  132 , such attracted developing agent  126  is transported to the developing area  131 . After controlling a thickness of the developing agent  126  with the doctor blade  116 , the developing agent  126  is adhered onto the photosensitive drum  108 . With such processes, an electrostatic latent image on the photosensitive drum  108  is developed with the developing agent  126  as toner image. After such developing process, the developing agent  126  remaining on the developing roller  115  are removed and recovered into the container  117 . Such recovered developing agent  126  is then agitated with the developing agent  126  in the second compartment  121 , and further used as developing agent for developing another electrostatic latent image on the photosensitive drum  108 . 
     In an exemplary embodiment, the development unit  113  employs the developing roller  115  as magnetic particle carrying device, which can supply the developing agent  126  to a circumferential direction of the photosensitive drum  108  more uniformly. In other words, the developing agent  126  can be supplied to a direction of rotation of the photosensitive drum  108  more uniformly, wherein the direction of rotation of the photosensitive drum  108  is aligned to a transport direction of a transfer member such as sheet, intermediate transfer belt or the like. Accordingly, a toner image can be developed on the photosensitive drum  108  by decreasing unevenness of image concentration, by which an image having higher quality can be produced on a transfer member. 
     A description is now given to the magnetic carrier  135  with reference to  FIG. 9 . As above described, the magnetic carrier  135  is contained in the first and second compartments  120  and  121 . The magnetic carrier  135  may have an average particle diameter of 20 μm to 50 μm, for example. As illustrated in  FIG. 9 , the magnetic carrier  135  may include a core  136 , a resin coat layer  137 , and alumina particles  138 , for example. An external surface of the core  136  is coated with the resin coat layer  137 , and the alumina particles  138  are dispersed in the resin coat layer  137 . 
     If the magnetic carrier  135  may have too small average particle diameter (e.g., less than 20 μm), the magnetic carrier  135  may have smaller magnetic force, which may result into a weaker magnetic attraction to the developing roller  115 , by which the magnetic carrier  135  may be more likely to adhere the photosensitive drum  108 , which is not a desirable phenomenon. 
     If the magnetic carrier  135  may have too great average particle diameter (e.g., more than 50 μm), the magnetic carrier  135  and an electrostatic latent image on the photosensitive drum  108  may form a weaker magnetic field therebetween, which may result into a poor quality image such as uneven toner concentration, which is also not a desirable phenomenon. 
     The core  136  may be made of a magnetic material such as ferrite formed into a spherical shape, for example. The resin coat layer  137  coats an external surface of the core  136 . The resin coat layer  137  may include resin such as cross-linked resin (e.g., melamine resin and thermoplastic resin such as acrylic resin) and a charge control agent. Such resin coat layer  137  has elasticity and strong adhesivity, for example. The alumina particles  138  may have an outer diameter, set greater than a thickness of the resin coat layer  137 , by which the alumina particles  138  may protrude from a surface of the resin coat layer  137 . The alumina particles  138  are held in the resin coat layer  137  by adhesivity of the resin coat layer  137 . 
     In an exemplary embodiment, the development unit  113  may employ the developing agent  126  including the magnetic carrier  135  having an average particle diameter of 20 μm to 50 μm, which may have a good level of sphericity, by which an image can be produced with a good level of toner concentration. 
     A description is now given to a process cartridge with reference to  FIG. 10 . Each of process cartridges  106 Y,  106 M,  106 C, and  106 K may include a cartridge case  111 , a charge roller  109 , the photosensitive drum  108 , a cleaning blade  112 , and the development unit  113 , for example. 
     The cartridge case  111  may be detachable from an image forming apparatus  101  (see  FIG. 11 ), and encases the charge roller  109 , the photosensitive drum  108 , the cleaning blade  112 , and the development unit  113 . The charge roller  109  charges an external surface the photosensitive drum  108  uniformly. The photosensitive drum  108 , facing the developing roller  115  in the development unit  113  with a given gap therebetween, has a cylindrical shape and is rotatable about its axial center. 
     The developing roller  115  (or the developing sleeve  132 ) and the photosensitive drum  108  preferably set a given gap of 0.1 mm to 0.4 mm therebetween, in which protruded aggregated chains of the developing agent  126  may supply toner particles from the developing sleeve  132  to the photosensitive drum  108  reliably, by which an image having higher quality can be produced. 
     If such given gap may become too small (e.g., less than 0.1 mm), the developing sleeve  132  and the photosensitive drum  108  may form too strong magnetic field therebetween, which may cause a transfer of the magnetic carrier  135  to the photosensitive drum  108 , which is not a desirable phenomenon. 
     If such given gap may become too great (e.g., more than 0.4 mm), the developing sleeve  132  and the photosensitive drum  108  may form too weak magnetic field therebetween, which may undesirably decrease developability by toner particles on the photosensitive drum  108 , and such weak magnetic field may cause a greater edge effect on image edges resulting into undesirable image quality such as uneven toner concentration. 
     The process cartridges  106 Y,  106 M,  106 C, and  106 K transfers images to a recording sheet  107  as follows. 
     As illustrated in  FIG. 11 , the image forming apparatus  101  includes an optical writing unit  122 . The optical writing unit  122  irradiates a laser beam on the photosensitive drum  108  in the process cartridge  106  to form an electrostatic latent image on the photosensitive drum  108 . The electrostatic latent image on the photosensitive drum  108  is developed with toner particles supplied from the development unit  113 . Then, the toner image is transferred to a transfer belt  129 , and further transferred to the recording sheet  107 . After such toner image transfer to the recording sheet  107 , the cleaning blade  112  removes toner particles remaining on the surface of the photosensitive drum  108 . 
     In an exemplary embodiment, the process cartridge  106  employs the development unit  113 , which can supply the developing agent  126  to a circumferential direction of the photosensitive drum  108  more uniformly. In other words, the developing agent  126  can be supplied to a direction of rotation of the photosensitive drum  108  more uniformly. Therefore, the amount of developing agent  126  that the developing sleeve  132  can carry does not deteriorate over time and images having appropriate concentrations of toner can continue to be produced. 
     A description is now given to an image forming apparatus with reference to  FIG. 11 . The image forming apparatus  101  may form color images of yellow(Y), magenta(M), cyan(C), and black(K) on the recording sheet  107 . Hereinafter, yellow, magenta, cyan, and black are indicated by suffix letter of Y, M, C, and K, respectively. 
     As illustrated in  FIG. 11 , the image forming apparatus  101  may include a sheet feed unit  103 , a registration roller  110 , a transfer unit  104 , a fixing unit  105 , the optical writing unit  122 , and the process cartridge  106 Y,  106 M,  106 C, and  106 K, for example. 
     The sheet feed unit  103  is provided at a bottom of the image forming apparatus  101 , for example. The sheet feed unit  103  includes a sheet cassette  123  and a feed roller  124 . The sheet cassette  123  stores the recording sheet  107 , and the feed roller  124  is pressed to a top sheet in the sheet cassette  123 . The feed roller  124  feeds the recording sheet  107  to the registration roller  110 . 
     The registration roller  110 , disposed in a transportation route of the recording sheet  107 , includes rollers  110   a  and  110   b . The rollers  110   a  and  110   b  sandwich the recording sheet  107 , and feed the recording sheet  107  to a space between the transfer unit  104  and a secondary transfer roller  16 , to be described later. 
     The transfer unit  104 , provided over the sheet feed unit  103 , includes a drive roller  128 , a driven roller  12 , the transfer belt  129 , and primary transfer rollers  130 Y,  130 M,  130 C, and  130 K, for example. A motor or the like (not shown) drives the drive roller  128 , and the driven roller  12  is rotatably supported in the image forming apparatus  101 . The transfer belt  129 , formed into an endless belt, is extended by the drive roller  128  and the driven roller  12 . The transfer belt  129  travels in a given direction when the drive roller  128  rotates. 
     The primary transfer rollers  130 Y,  130 M,  130 C,  130 K and the photosensitive drum  108  of each of the process cartridges  106 Y,  106 M,  106 C,  106 K sandwich the transfer belt  129 . The transfer unit  104  transfers toner images formed on the photosensitive drum  108  to the transfer belt  129  with an effect of the primary transfer rollers  130 Y,  130 M,  130 C, and  130 K, and then the transfer belt  129  transfers the toner image to the recording sheet  107  with an effect of the secondary transfer roller  16 . Then, the recording sheet  107  is transported to the fixing unit  105 . 
     The fixing unit  105  includes rollers  105   a  and  105   b  for sandwiching the recording sheet  107  therebetween. The rollers  105   a  and  105   b  applies heat and pressure to the recording sheet  107  to fix the toner image on the recording sheet  107 . 
     The optical writing unit  122  attached to the image forming apparatus  101  emits a laser beam to an external surface of the photosensitive drum  108 , uniformly charged by the charge roller  109 , of the process cartridges  106 Y,  106 M,  106 C, and  106 K, to form an electrostatic latent image on the photosensitive drum  108 . 
     The process cartridges  106 Y,  106 M,  106 C, and  106 K may be disposed between the transfer unit  104  and the optical writing unit  122 , and detachable from the image forming apparatus  101 , for example. The process cartridges  106 Y,  106 M,  106 C, and  106 K may be arranged in a tandem manner, for example. 
     After the above-described image forming process, a belt cleaning unit  15  removes toner particles remaining on the transfer belt  129 , and toner particles are recovered to an toner waste bottle (not shown). 
     The above-described secondary transfer roller  16  is applied with a bias voltage opposite to toner particles on the transfer belt  129  to transfer toner image from the transfer belt  129  to the recording sheet  107 . 
     After fixing the toner image on the recording sheet  107 , an ejection roller  24  ejects the recording sheet  107  from the image forming apparatus  101 . 
     Further, the image forming apparatus  101  may include toner bottles  31  storing Y, M, C, and K toner. Respective color toner may be refilled from the toner bottles  31  to each of the process cartridge  106 Y,  106 M,  106 C, and  106 K via a toner transport route (not shown). 
     Accordingly, the image forming apparatus  101  forms images on the recording sheet  107 , which may be summarized as below. When the photosensitive drum  108  rotates, the charge roller  109  charges the photosensitive drum  108 . A laser beam is irradiated on the photosensitive drum  108  to form an electrostatic latent image. When the electrostatic latent image comes to the developing area  131  of the development unit  113 , the electrostatic latent image is developed as toner image by the developing agent  126  supplied from the developing sleeve  132 . The toner image is then transferred to the transfer belt  129 , and further transferred to the recording sheet  107  transported from the sheet feed unit  103 . And the fixing unit  105  fixes the image on the recording sheet  107  as color image. 
     In an exemplary embodiment, the image forming apparatus  101  employs the development unit  113  which can supply the developing agent  126  to a circumferential direction of the photosensitive drum  108  more uniformly. In other words, the developing agent  126  can be supplied to a direction of rotation of the photosensitive drum  108  more uniformly. Accordingly, a toner image can be developed on the photosensitive drum  108  by decreasing unevenness of image concentration, by which an image having higher quality can be produced on a transfer member. Therefore, the amount of developing agent  126  that the developing sleeve  132  can carry does not deteriorate over time and images having appropriate concentrations of toner can continue to be produced. 
     A description is now given to a surface treatment machine and magnetic abrasive grain for forming depressions having elliptical shape on an external surface of a hollow structure (e.g., developing roller  115 ) with reference to  FIGS. 12 to 17 , in which a magnetic abrasive grain  65  is impacted against the external surface of the hollow structure to form depressions on the hollow structure. 
     As illustrated in  FIGS. 12 and 13 , the surface treatment machine  1  may include a base  3 , a fixed holding unit  4 , a electromagnetic coil moving unit  5 , a movable holding unit  6 , a movable chuck unit  7 , an electromagnetic coil  8 , a container unit  9 , a collection unit  10 , a cooling unit  11 , a linear encoder  75 , and a control unit  76 , for example. 
     The base  3  is formed into a plate-like shape, and is installed on a floor, a table or the like in a factory. The base  3  has an upper face maintained parallel to the horizontal direction. The base  3  is formed into a rectangular shape, for example. 
     The fixed holding unit  4  may include a plurality of columns  12 , a holding base  13 , a standing bracket  14 , a cylindrical holding member  15 , and a holding chuck  16 . The columns  12  may be standing on the base  3 , for example. 
     The holding base  13  is formed into a plate-like shape, and attached to an upper end portion of the columns  12 . The standing bracket  14 , formed into a plate-like shape, is protruded from the holding base  13 . 
     The cylindrical holding member  15 , formed into a cylindrical shape, is attached to the standing bracket  14  and the holding base  13 . The cylindrical holding member  15  is disposed closer to a center portion of the base  3  compared to the standing bracket  14 , and the axial center of the cylindrical holding member  15  is parallel to the horizontal direction and the direction shown by an arrow X. The cylindrical holding member  15  houses the flange  51   b ,  51   c , and  51   d  (to be described later) attached to a first end portion  9   a  (to be described later) of the container unit  9 . 
     The holding chuck  16 , disposed near the cylindrical holding member  15  and the holding base  13 , is attached to the base  3 . The holding chuck  16  chucks the container unit  9  having the first end portion  9   a , housed in the cylindrical holding member  15 , to hold the first end portion  9   a  of the container unit  9 . The fixed holding unit  4  also holds the first end portion  9   a  of the container unit  9 . 
     The electromagnetic coil moving unit  5  may include a pair of linear guides  17 , an electromagnetic coil holding base  18 , an electromagnetic coil moving actuator  19 . The linear guides  17  may include rails  20 , and a slider  21 . The rails  20  are installed on the base  3 . The rails  20 , formed into a straight line shape, are disposed to parallel to the longitudinal direction (or an arrow X) of the base  3 . The slider  21  is slidably supported on the rails  20  in the longitudinal direction (or an arrow X) of the rails  20 . In the pair of the linear guides  17 , the rails  20  are arranged with a given distance each other in a width direction (hereinafter, refer to an arrow Y) of the base  3 . The arrow X and the arrow Y, perpendicular to each other, and parallel to the horizontal direction. 
     The electromagnetic coil holding base  18 , formed into a plate-like shape, is attached to the slider  21 . The electromagnetic coil holding base  18  has an upper face, which is parallel to the horizontal direction. The electromagnetic coil holding base  18  holds the electromagnetic coil  8  thereon. 
     The electromagnetic coil moving actuator  19 , attached to the base  3 , is used to slidably move the electromagnetic coil holding base  18  in the direction of the arrow X. The electromagnetic coil moving unit  5  slidably moves the electromagnetic coil holding base  18  and the electromagnetic coil  8  in the direction of the arrow Y by using the electromagnetic coil moving actuator  19 . Further, the electromagnetic coil moving unit  5  can change a moving speed of the electromagnetic coil  8  in a range of 0 mm/sec to 300 mm/sec, for example. Further, the electromagnetic coil moving unit  5  can move the electromagnetic coil  8  in a movable range of 600 mm or so. 
     The movable holding unit  6  may include a pair of linear guides  22 , a holding base  23 , a first actuator  24 , a second actuator  25 , a moving base  26 , a bearing rotation unit  27 , and a holding chuck  28 . 
     The linear guides  22  may include rails  29 , and the slider  30 . The rails  29  are installed on the base  3 . The rails  29 , formed into a straight line shape, are disposed parallel to the longitudinal direction (or the arrow X) of the base  3 . The slider  30  is slidably supported on the rails  29  in the longitudinal direction (or the arrow X) of the rails  29 . The pair of the linear guides  22  are arranged with a given distance each other in the width direction (or the direction shown by the arrow Y) of the base  3 . 
     The holding base  23 , formed into a plate-like shape, is attached to the slider  30 . The holding base  23  has an upper face, which is parallel to the horizontal direction. The first actuator  24 , attached to the base  3 , is used to slidably move the holding base  23  in the direction of the arrow X. 
     The second actuator  25 , attached to the holding base  23 , is used to slidably move the moving base  26  in the direction of the arrow Y. The moving base  26 , formed into a plate-like shape, has an upper face, which is parallel to the horizontal direction. 
     The bearing rotation unit  27  may include a pair of bearings  31 , a hollow object holding member  32 , a drive motor  33 , a chuck cylinder  34 . The pair of bearings  31 , arranged with a given distance each other in the direction of the arrow X, are installed on the moving base  26 . 
     The hollow object holding member  32  may be made of a magnetic material, and formed into a cylindrical shape. The hollow object holding member  32 , supported by the bearings  31 , is rotatable about its axial center. The hollow object holding member  32  has its axial center, which is arranged parallel to the axial center of the cylindrical holding member  15  or the direction of the arrow X. The hollow object holding member  32  has a first end portion  32   a  (see  FIG. 13 ), which is inserted in the container unit  9 , and a second end portion  32   c  (see  FIG. 12 ) disposed over the moving base  26 . As illustrated in  FIG. 13 , the hollow object holding member  32  is inserted in the developing sleeve  132  having a cylindrical shape. Further, the second end portion  32   c  of the hollow object holding member  32  is fixed to a pulley  35  placed over the moving base  26 . The pulley  35  is disposed coaxially with the hollow object holding member  32 . 
     The drive motor  33 , installed on the moving base  26 , has an output shaft attached to a pulley  36 . The output shaft of the drive motor  33  has an axial center, which is parallel to the direction of the arrow X. A timing belt (or endless belt)  37  is extended by the pulleys  35  and  36 . 
     The chuck cylinder  34  includes a cylinder body  38 , and a chuck shaft  39 , wherein the cylinder body  38  is mounted on the moving base  26 , and the chuck shaft  39  is slidably provided to the cylinder body  38 . The chuck shaft  39 , formed into a cylindrical shape, is disposed parallel to the direction of the arrow X. The chuck shaft  39  is arranged coaxially with the hollow object holding member  32  and encased in the hollow object holding member  32 . The chuck shaft  39  is provided with a plurality of chuck claws  40 , which are arranged as a pair of the chuck claws. 
     The chuck claws  40  are protrudingly attached on an outer circumference face of the chuck shaft  39 . Further, the chuck claws  40  may protrude from an outer circumference face of the hollow object holding member  32  in an outer direction of the hollow object holding member  32 . A protruding amount of the chuck claws  40  from the chuck shaft  39  and the hollow object holding member  32  can be changeable. The chuck claws  40  are arranged in the longitudinal direction of the chuck shaft  39  with a given distance each other. As the chuck shaft  39  moves toward the cylinder body  38 , the protruding amount of the chuck claws  40  from the chuck shaft  39  and the hollow object holding member  32  increases. 
     When the chuck shaft  39  moves toward the cylinder body  38 , the chuck claws  40  can be more protruded from the outer circumference face of the chuck shaft  39 , by which the chuck claws  40  are pressed to an inner surface of the developing sleeve  132 , attached to the outer circumference face of the hollow object holding member  32 . With such process, the chuck shaft  39 , the hollow object holding member  32 , and the developing sleeve  132  are fixed together. At this time, the chuck shaft  39 , the hollow object holding member  32 , the developing sleeve  132 , a cylindrical member  50  (to be described later), and the container unit  9  are coaxially arranged. 
     Further, when the chuck claws  40  are set to unprotruded condition with respect to the outer circumference face of the hollow object holding member  32 , the developing sleeve  132  and the hollow object holding member  32  is not fixed by the chuck shaft  39 . In such condition, the developing sleeve  132  is rotatable in its circumferential direction (or rotation direction) about its axis center by electromotive force, which is electromagnetically induced by the electromagnetic coil  8 , to be described later. 
     The chuck cylinder  34  and the chuck claws  40  are used to hold the hollow object holding member  32 , the container unit  9 , and the developing sleeve  132  coaxially. Accordingly, the chuck cylinder  34  and the chuck claws  40  hold the developing sleeve  132  in a center position of the container unit  9  in an axial direction of the container unit  9 . 
     The holding chuck  28  is installed on the moving base  26 . The holding chuck  28  chucks a flange  51   a  (to be described later) attached to a second end portion  9   b  of the container unit  9  to hold the second end portion  9   b  of the container unit  9 . The holding chuck  28  regulates or restricts a rotation of the container unit  9  about its axial center. 
     The movable holding unit  6  moves the holding chuck  28 , the hollow object holding member  32  in perpendicular directions (e.g., directions shown by the arrows X and Y) using the above-described actuators  24  and  25 . Accordingly, the movable holding unit  6  moves the container unit  9 , held by the holding chuck  28  in the perpendicular directions (e.g., directions shown by the arrows X and Y). 
     The movable chuck unit  7  includes a holding base  41 , a linear guide  42 , and a holding chuck  43 . The holding base  41  is fixed to one end portion of the rails  29  of the linear guides  22 , wherein such one end portion is closer to the fixed holding unit  4 . The holding base  41 , formed into a plate-like shape, has an upper face, which is parallel to the horizontal direction. 
     The linear guide  42  may include rails  44 , and a slider  45 . The rails  44  are installed on the holding base  41 . The rails  44 , formed into a straight line shape, are disposed parallel to the width direction (or the direction of the arrow Y) of the base  3 . The slider  45  is slidably supported on the rails  44  in the longitudinal direction or the direction of the arrow Y) of the rails  44 . 
     The holding chuck  43  is installed on the slider  45 . The holding chuck  43  is placed between the holding chucks  16  and  28 . The holding chuck  43  chucks the container unit  9  at a portion closer to the second end portion  9   b  to hold the container unit  9 . The movable chuck unit  7  is used to position the container unit  9  at a given position when the holding chuck  43  holds the container unit  9 . Further, when the holding chuck  43  holds the container unit  9 , the movable chuck unit  7  and the holding chuck  28  cooperates together to hold the container unit  9  during a movement of the container unit  9  in its axial direction so that the container unit  9  does not drop from the bearing rotation unit  27  and the surface treatment machine  1 . 
     As illustrated in  FIG. 13 , the electromagnetic coil  8  includes an outer cover  46 , and a coil unit  47 . The outer cover  46 , formed into a cylindrical shape, encases the coil unit  47 . The electromagnetic coil  8  has an inner diameter greater than an outer diameter of the container unit  9 . Accordingly, a space is formed between inner surface of the electromagnetic coil  8  and the outer circumference face of the container unit  9 . Further, a total length of the electromagnetic coil  8  is smaller than a total length of the container unit  9 . Preferably, the total length of the electromagnetic coil  8  is set two thirds (⅔) or less of the total length of the container unit  9 . For example, the electromagnetic coil  8  has an inner diameter of 90 mm and a length of 85 mm. 
     The outer cover  46  is attached to the electromagnetic coil holding base  18  while aligning the axial center of the outer cover  46  to the axial center of the electromagnetic coil  8 . The electromagnetic coil  8  is arranged coaxially with the hollow object holding member  32 , the chuck shaft  39 , and the container unit  9 . 
     The coil unit  47  may include coils, arranged along the circumferential direction of the outer cover  46  (or the electromagnetic coil  8 ). As illustrated in  FIG. 13 , the coil unit  47  is applied with current by a three-phase alternating current source  48 . The coils of the coil unit  47 , applied with current having different phases, generate magnetic fields having different phases. The electromagnetic coil  8  combines such magnetic fields to form a magnetic field (hereinafter referred as “rotated magnetic field”) having a direction of rotation in the electromagnetic coil  8  about its axial center. 
     The electromagnetic coil  8 , applied with current from the three-phase alternating current source  48  to generate such rotated magnetic field, is moved in the axial direction of the electromagnetic coil  8  (or longitudinal direction of the container unit  9 ) by the electromagnetic coil moving unit  5 . The electromagnetic coil  8  uses such rotated magnetic field to position a magnetic abrasive grain  65 , contained in the container unit  9 , to the outer circumference face of the developing sleeve  132 , and to rotate (or move) the magnetic abrasive grain  65  inside the container unit  9  and around the developing sleeve  132 . The magnetic abrasive grain  65  may be a group of a greater number of magnetic abrasive grains. However, for the simplicity of the expression, the term of “magnetic abrasive grain  65 ” may be used in this disclosure while having a meaning of singular or plural abrasive grains. With such configuration, the electromagnetic coil  8  induces the magnetic abrasive grain  65  to impact against the external surface of the developing sleeve  132  by using such rotated magnetic field. 
     Further, an inverter  49  is provided between the three-phase alternating current source  48  and the electromagnetic coil  8  for changing a magnetic field strength. The inverter  49  can change frequency, current value, and voltage value of power applied to the electromagnetic coil  8  by the three-phase alternating current source  48 . By changing frequency, current value, and voltage value of power applied to the electromagnetic coil  8  by the inverter  49 , power applied to the electromagnetic coil  8  from the three-phase alternating current source  48  can be increased or decreased to change a rotated magnetic field strength generated by the electromagnetic coil  8 . 
     As illustrated in  FIG. 13 , the container unit  9  may include a cylindrical member  50 , a plurality of flanges  51 , a pair of shaving-seal holders  52 , a pair of shaving-seal plates  53 , a pair of positioning members  54 , a plurality of partitioning members  55 , and a pair of seal plates  56 , for example. 
     The cylindrical member  50 , formed into a cylindrical shape, is used as an outer envelope of the container unit  9  and has a single wall structure. Accordingly, the container unit  9  may have an outer shell having a cylindrical shape of single wall structure. For example, the cylindrical member  50  of the container unit  9  preferably has an outer diameter of 40 mm to 80 mm, and a thickness of 0.5 mm to 2.0 mm. Further, the cylindrical member  50  preferably has an axial direction length of 600 mm to 800 mm, for example. The cylindrical member  50  may be made of a nonmagnetic material, for example. 
     The cylindrical member  50  is provided with a plurality of the abrasive grain supply holes  57 . Each of the abrasive grain supply holes  57  passes through the cylindrical member  50  so that the outside and the inside of the cylindrical member  50  can be communicated with each other. Each of the abrasive grain supply holes  57  is attached with a seal cap  58 . The abrasive grain supply holes  57  is used to take in the magnetic abrasive grain  65  into the inside of the cylindrical member  50  or to eject the magnetic abrasive grain  65  to the outside of the cylindrical member  50 . The seal cap  58  caps each of the abrasive grain supply holes  57  so that the magnetic abrasive grain  65  does not run out from the cylindrical member  50  of the container unit  9 . 
     The plurality of flanges  51  may be formed into a circular shape or a cylindrical shape, for example. In an exemplary embodiment, the plurality of flanges  51  includes four flanges, for example, and three of them (hereinafter, the flange  51   b ,  51   c , and  51   d ) are attached to the first end portion  9   a  of the cylindrical member  50 , and one of them (hereinafter, the flange  51   a ) is attached to the second end portion  9   b  of the cylindrical member  50 . 
     The flange  51   b , formed into a circular shape, engages an outer circumference of the cylindrical member  50 . The flange  51   c , formed into a circular shape, engages an outer circumference of the flange  51   b . The flange  51   d  may integrally include a ring portion  59  having a circular shape and a column portion  60  having a cylindrical shape, in which the ring portion  59  may be protruded from an outer edge of the column portion  60 . The ring portion  59  of the flange  51   d  engages an outer circumference of the flange  51   c.    
     As illustrated in  FIG. 13 , the flange  51   d  rotatably supports a driven shaft  73  with a bearing  74 . The driven shaft  73 , formed into a cylindrical shape, is disposed coaxially with the cylindrical member  50  of the container unit  9 . The driven shaft  73  has one end face, which is pressed to the hollow object holding member  32 . The driven shaft  73 , rotates with the hollow object holding member  32 , supports the first end portion  32   a  (or free end side) of the hollow object holding member  32 . 
     As illustrated in  FIG. 13 , the flange  51   a , formed into a circular shape, engages an outer circumference of the second end portion  9   b  of the cylindrical member  50 , wherein the hollow object holding member  32  passes through the flange  51   a . The first end portion  9   a  of the cylindrical member  50  is used as one end portion of the container unit  9 , and the second end portion  9   b  of the cylindrical member  50  is used as other end portion of the container unit  9 . 
     Each of the shaving-seal holders  52  is formed into a circular shape. One of the shaving-seal holders  52  engages an inner circumference of the first end portion  9   a  of the cylindrical member  50 , and other shaving-seal holder  52  engages an inner circumference of the second end portion  9   b  of the cylindrical member  50 , wherein the hollow object holding member  32  passes through the other shaving-seal holder  52 . 
     Each of the shaving-seal plates  53  is formed into a mesh-like shape. One of the shaving-seal plates  53 , formed into a circular shape, is disposed in the inner circumference of the first end portion  9   a  of the cylindrical member  50  and attached to the one of the shaving-seal holders  52 . Further, the driven shaft  73  passes through the one of the shaving-seal plate  53 . 
     Other shaving-seal plate  53 , formed into a circular shape, is disposed in the inner circumference of the second end portion  9   b  of the cylindrical member  50  and attached to the other shaving-seal holder  52 . The hollow object holding member  32  passes through the other shaving-seal plate  53 . 
     The shaving-seal plates  53  prevents shavings (e.g., shaved chip) getting out of the cylindrical member  50  of the container unit  9  when shavings are generated by shaving the external surface of the developing sleeve  132  with the impacted magnetic abrasive grain  65 . 
     Each of the positioning members  54  is formed into a cylindrical shape. One of the positioning members  54  engages the outer circumference of the first end portion  32   a  of the hollow object holding member  32 . Other positioning member  54  engages the outer circumference of a center portion  32   b  of the hollow object holding member  32 , which is closer to the second end portion  9   b  of the container unit  9 . 
     The pair of the positioning members  54  sandwich the developing sleeve  132  therebetween to position the developing sleeve  132  at a given position in the hollow object holding member  32 . The first end portion  32   a  of the hollow object holding member  32  is positioned closer to the fixed holding unit  4  and far from the movable holding unit  6 . The center portion  32   b  of hollow object holding member  32 , positioned in the container unit  9 , is far from the fixed holding unit  4  and closer to the movable holding unit  6 . 
     The partitioning member  55  may include a frame  61 , formed into a circular shape, and a mesh portion  62 . The frame  61  engages and attaches the inner circumference of the cylindrical member  50 , wherein the hollow object holding member  32  passes through the frame  61 . As illustrated in  FIG. 13 , a plurality of the partitioning members  55 , is disposed between the pair of the shaving-seal plates  53  with a given distance each other in the longitudinal direction of the cylindrical member  50 . In  FIG. 13 , seven partitioning members  55  are provided, for example. 
     The frame  61  may include a through hole  63 , to which the mesh portion  62  is attached. The mesh portion  62 , formed into a mesh-like shape, allows a passage of gas and shavings (e.g., shaved chip) but do not allow a passage of the magnetic abrasive grain  65  therethrough. 
     The partitioning members  55  partition or segment a space in the cylindrical member  50  of the container unit  9  in an axial direction of the developing sleeve  132 . The frame  61  and the mesh portion  62  of the partitioning member  55  are made of a nonmagnetic material. 
     Further, the developing sleeve  132  has the rotation center P, which may be aligned to the axial center of the container unit  9  and the hollow object holding member  32 . Accordingly, the rotation center P of the developing sleeve  132  and the longitudinal direction of the container unit  9  are set parallel to each other. 
     The seal plate  56 , formed into a circular shape, is further formed into a mesh-like shape to allow a passage of gas (e.g., air) and the above-described shavings (e.g., shaved chip) but not allow a passage of the magnetic abrasive grain  65 . One of the seal plates  56  is attached to one of the partitioning members  55 , which is closest to the first end portion  9   a , and other seal plate  56  is attached to another one of the partitioning members  55 , which is closest to the second end portion  9   b . A cap sleeve  64  (to be described later), attached to both end of the developing sleeve  132 , passes through each of the seal plates  56 . The seal plates  56  may be used to prevent the magnetic abrasive grain  65  getting out from the cylindrical member  50  of the container unit  9 , wherein the magnetic abrasive grain  65  is contained in spaces partitioned or segmented by the partitioning members  55 . 
     The container unit  9  contains the magnetic abrasive grain  65 , made of magnetic material, in spaces partitioned or segmented by the plurality of the partitioning members  55 , and contains the developing sleeve  132 , attached to the hollow object holding member  32 , in the cylindrical member  50 . Accordingly, the container unit  9  contains the developing sleeve  132  and the magnetic abrasive grain  65  therein. 
     Further, the magnetic abrasive grain  65 , rotated (or moved) by the above-described rotated magnetic field, may impact against the external surface of the developing sleeve  132 . When the magnetic abrasive grain  65  impacts against the external surface of the developing sleeve  132 , parts of the external surface of the developing sleeve  132  are shaved by such impact, by which the external surface of the developing sleeve  132  is roughened. 
     As illustrated  FIG. 13 , the collection unit  10  may include a gas inflow tube  66 , a gas ejection hole  67 , a mesh member  68 , a gas ejection duct  69 , and a dust collector  70  (see  FIG. 12 ). As illustrated  FIG. 13 , the gas inflow tube  66  is disposed into a given position of the cylindrical member  50 , which is closer to the above-described other shaving-seal holder  52  and one end of the container unit  9 , closer to the movable holding unit  6 . The gas inflow tube  66  has an orifice, inserted in the cylindrical member  50  of the container unit  9 . The gas inflow tube  66  is used to supply pressurized gas (e.g., air) to the cylindrical member  50  from a pressurized gas supply source (not shown). 
     The gas ejection hole  67  passes through the cylindrical member  50  so that the inside and outside of the container unit  9  are communicated with each other, and is provided to a given position between the above-described one of the shaving-seal holders  52  and an end portion of the cylindrical member  50  of the container unit  9 , which are far from the movable holding unit  6 . The mesh member  68  is disposed to the gas ejection hole  67  provided to the cylindrical member  50 . The mesh member  68  allows a passage of shavings (e.g., shaved chip) and gas, but do not allow a passage of the magnetic abrasive grain  65 . Accordingly, the mesh member  68  prevents the magnetic abrasive grain  65  getting out from the cylindrical member  50  of the container unit  9 . 
     The gas ejection duct  69 , formed in a tube shape, is attached to a near of the gas ejection hole  67 . The gas ejection duct  69  encircles the outer edge of the gas ejection hole  67 . The gas ejection hole  67  and the gas ejection duct  69  are used to guide gas, supplied to the cylindrical member  50  from the gas inflow tube  66 , to the outside of the cylindrical member  50  of the container unit  9 . 
     The dust collector  70 , coupled to the gas ejection duct  69 , sucks in gas from the gas ejection duct  69 . By sucking gas from the gas ejection duct  69 , the dust collector  70  sucks in the above-described shavings (e.g., shaved chip) from the cylindrical member  50  of the container unit  9  to collect the shavings (e.g., shaved chip). As such, the collection unit  10  collects the shavings (e.g., shaved chip) from the cylindrical member  50  of the container unit  9 . 
     As illustrated in  FIG. 12 , the cooling unit  11  includes a cooling fan  71 , and a cooling duct  72 . The cooling fan  71  supplies pressurized gas (e.g., air) to the cooling duct  72 , which is a tube. The cooling duct  72  guides pressurized gas (e.g., air) supplied from the cooling fan  71  to the electromagnetic coil  8 , and blows pressurized gas (e.g., air) to the electromagnetic coil  8 . By blowing the pressurized gas (e.g., air) to the electromagnetic coil  8 , the cooling unit  11  cools the electromagnetic coil  8 . 
     As illustrated in  FIG. 13 , the linear encoder  75  may include a body  77 , and a detection member  78  slidably disposed to the body  77 . The body  77  may have straight line shape and attached to the base  3 . The body  77  is arranged between the pair of rails  20 , in which the body  77  is parallel to the rails  20 . The body  77  has a total length, which is longer than that of the container unit  9 . The body  77  may have its both end portions, which may protrude from both end portions of the container unit  9  in the longitudinal direction of the container unit  9 . 
     The detection member  78  is slidably provided on the body  77  in the longitudinal direction of the container unit  9 . The detection member  78  is attached to the electromagnetic coil holding base  18 . Accordingly, the detection member  78  is coupled to the electromagnetic coil  8  via the electromagnetic coil holding base  18 . 
     The linear encoder  75  detects a position of the detection member  78  with respect to the body  77  (or the container unit  9 ), and outputs a detection result signal to the control unit  76 . As such, the linear encoder  75  detects a relative position of the electromagnetic coil  8  with respect to the container unit  9  (or the developing sleeve  132 ), and outputs a detection result signal to the control unit  76 . 
     The control unit  76  includes a CPU (central processing unit), a RAM (random access memory), and a ROM (read only memory), or the like. The control unit  76 , connected to the electromagnetic coil moving unit  5 , the movable holding unit  6 , the movable chuck unit  7 , the electromagnetic coil  8 , the inverter  49 , the collection unit  10 , the cooling unit  11 , and the linear encoder  75  or the like to control the surface treatment machine  1  as a whole. 
     The control unit  76  stores a rotated magnetic field strength of the electromagnetic coil  8 , which is determined based on a relative position of the electromagnetic coil  8  with respect to the developing sleeve  132 , wherein such relative position of the electromagnetic coil  8  is detected by the linear encoder  75 , for example. 
     Accordingly, the control unit  76  stores power value to be applied to the electromagnetic coil  8  by the inverter  49 , in which power value is determined based on a relative position of the electromagnetic coil  8  with respect to the developing sleeve  132 . Further, the control unit  76  may store such power value for each type (e.g., product number) of the developing sleeve  132 , for example. 
     In an exemplary embodiment, the control unit  76  stores a given power pattern or profile, in which a power value to be applied to the electromagnetic coil  8  from the inverter  49 , is increased gradually in a longitudinal direction (or axial direction) of the developing sleeve  132  when the electromagnetic coil  8  moves over the developing sleeve  132  from the center portion toward the each end portion of the developing sleeve  132 , for example. The control unit  76  controls the inverter  49  with such given power pattern or profile to change a rotated magnetic field strength generated by the electromagnetic coil  8 . 
     As such, in an exemplary embodiment, the control unit  76  controls the inverter  49  and the electromagnetic coil  8  as above described so that a rotated magnetic field strength generated by the electromagnetic coil  8  becomes greater when to process the both end portions of the developing sleeve  132  compared to when to process the center portion of the developing sleeve  132 , for example. 
     As above described, the control unit  76  stores a rotated magnetic field strength of the electromagnetic coil  8 , which is determined based on a relative position of the electromagnetic coil  8  with respect to the developing sleeve  132 , wherein such relative position of the electromagnetic coil  8  is detected by the linear encoder  75 , and the control unit  76  stores corresponding power value to be applied to the electromagnetic coil  8  by the inverter  49 . 
     Further, the control unit  76  is connected to an input unit such as keyboard, and a display unit such as LCD (liquid crystal display), for example. 
     A description is now given to the magnetic abrasive grain  65 , used for the surface treatment machine  1  with reference to  FIG. 14 . As illustrated in  FIG. 14 , the magnetic abrasive grain  65  has a cylindrical-like shape having a relatively short length. The magnetic abrasive grain  65  may be made of a magnetic material such as austenitic stainless steel, martensitic stainless steel, or the like, for example. Although austenitic stainless steel may be generally used as non-magnetic material, austenitic stainless steel may be provided with magnetic property by processing austenitic stainless steel with a cold work or the like, in which austenitic stainless steel may become martensitic stainless steel having magnetic property. Because such austenitic stainless steel or martensitic stainless steel are materials available on the market, the magnetic abrasive grain  65  can be preferably fabricated with austenitic stainless steel or martensitic stainless steel with reasonable cost or a reduced cost. 
     The magnetic abrasive grain  65  may have a given dimension. For example, the magnetic abrasive grain  65  may have an outer diameter of 0.1 mm to 2.0 mm, for example. When the magnetic abrasive grain  65  has a total length TL and an outer diameter D, the magnetic abrasive grain  65  may be formed into a shape having a TL/D value of 2 to 20, for example. 
     With such configured magnetic abrasive grain  65 , an outer edge  65   a  of the magnetic abrasive grain  65  may reliably impact against the developing sleeve  132 , and the magnetic abrasive grain  65  has a total length, which may preferably form a sufficient depth of concavities and convexities on the external surface of the developing sleeve  132  when the magnetic abrasive grain  65  impacts against the developing sleeve  132 . 
     Further, as illustrated in  FIGS. 14 and 15 , the outer edge  65   a  of the magnetic abrasive grain  65  is chamfered around its periphery and has a circular arc shape in a cross sectional view. The outer edge  65   a  is formed to have a given curvature radius r of 0.03 mm to 0.5 mm, for example. Such magnetic abrasive grain  65  may have a preferable shape for forming concavities and convexities on an external surface of to-be-processed object in a mild manner. 
     As illustrated in  FIG. 16 , with an effect of rotated magnetic field generated in the surface treatment machine  1 , the magnetic abrasive grain  65  rotates about its center of its longitudinal direction while rotatingly moving along the circumferential direction of the developing sleeve  132  and the container unit  9 . 
     A description is now given to a surface roughening process of the developing sleeve  132  using the surface treatment machine  1 , in which the external surface of the developing sleeve  132  is roughened by the magnetic abrasive grain  65 . 
     First, the control unit  76  is input with information such as product number of the developing sleeve  132  by using an input unit such as touch panel. Then, the cap sleeve  64  having a cylindrical shape is engaged to the outer circumference of the developing sleeve  132  at both end portion of the developing sleeve  132 . 
     The above-described other positioning member  54  is then engaged to the outer circumference of the hollow object holding member  32 , and the hollow object holding member  32  is then inserted into the developing sleeve  132 , attached with the cap sleeve  64  to its both end portion. Next, the above-described one of the positioning members  54  is also engaged to the outer circumference of the hollow object holding member  32 . 
     In an exemplary embodiment, the developing sleeve  132  is rotatable in its circumferential direction of about its axial center when the developing sleeve  132  is not fixed to the hollow object holding member  32  by the chuck claws  40 . If the chuck claws  40  may be set to a protruded condition with respect to the outer circumference face of the hollow object holding member  32 , the developing sleeve  132  and the hollow object holding member  32  may be fixed by the chuck shaft  39 . 
     At this time, the developing sleeve  132  is coaxially disposed in the hollow object holding member  32  while maintaining a given level of clearance (e.g., less than one millimeter) between the developing sleeve  132  and the hollow object holding member  32 . 
     Then, the developing sleeve  132  and the hollow object holding member  32  are housed in the container unit  9 , and the magnetic abrasive grain  65  is supplied into the cylindrical member  50  of the container unit  9 . With such process, the magnetic abrasive grain  65  and the developing sleeve  132  are housed in the container unit  9 . 
     Further, the container unit  9  is chucked by the holding chucks  28  and  43 . With such process, the developing sleeve  132  and the container unit  9  are attached to the movable holding unit  6 , in which the cylindrical member  50 , the hollow object holding member  32 , and the developing sleeve  132  are coaxially disposed. 
     The movable holding unit  6  is attached to the developing sleeve  132  and the container unit  9  by adjusting a position of the moving base  26  with the above-described actuators  24  and  25 , and also adjusting a position of the holding base  41 . Then, the first end portion  9   a  of the container unit  9  is held by the fixed holding unit  4  by chucking the first end portion  9   a  of the container unit  9  with the holding chuck  16 . 
     Then, gas is supplied into the container unit  9  through the gas inflow tube  66  of the collection unit  10 , and the dust collector  70  sucks gas from the container unit  9 . Further, the cooling unit  11  blows pressurized gas (e.g., air) to the electromagnetic coil  8 . 
     Then, the electromagnetic coil  8  is applied with power from the three-phase alternating current source  48  to generate a rotated magnetic field having a frequency of 200 Hz or more, for example. With such generated rotated magnetic field, an eddy current is generated in the developing sleeve  132 . Such rotated magnetic field and eddy current may cause an electromagnetic induction electromotive force, by which the developing sleeve  132  rotates with a rotation number substantially corresponding to the frequency of the rotated magnetic field. 
     Further, the magnetic abrasive grain  65 , placed in an area receivable of an magnetic field effect of the electromagnetic coil  8 , rotatingly moves along the outer circumference of the developing sleeve  132  while rotating about the center of the magnetic abrasive grain  65 , by which the magnetic abrasive grain  65  impacts against the external surface of the developing sleeve  132  to roughen the external surface of the developing sleeve  132 . 
     During such roughening process, the electromagnetic coil moving unit  5  may consecutively shift or move the electromagnetic coil  8  in the longitudinal direction of the electromagnetic coil  8  in a timely manner. With such shifting or moving of the electromagnetic coil  8 , the magnetic abrasive grain  65  newly entering an magnetic field space of the electromagnetic coil  8  starts to move (i.e., rotation about its center and rotation around the developing sleeve  132 ) with an effect of the above-described rotated magnetic field, and the magnetic abrasive grain  65  getting out of the magnetic field space of the electromagnetic coil  8  stops its movement. 
     When the magnetic abrasive grain  65  enters an magnetic field space of the electromagnetic coil  8 , the magnetic abrasive grain  65  may randomly and omnidirectionally impact against the surface of the developing sleeve  132 , which may mean magnetic abrasive grains are impacting against the developing sleeve  132  from substantially any directions with respect to the surface of the developing sleeve  132  at a substantially same timing. Accordingly, compared to a conventional sandblasting process which may impact abrasive grains against an object from one direction at one time, the developing sleeve  132  may receive impacting stress uniformly on its surface when forming the depressions  139  by the surface processing machine  1  according to an exemplary embodiment, which may be preferable for suppressing a shape deformation of the developing sleeve  132  (e.g., misaligned axis, change of inner/outer diameter, collapsing of sleeve shape). 
     Further, because the partitioning members  55  partition or segment a space in the container unit  9 , the magnetic abrasive grain  65  is prevented from moving beyond each of the partitioning members  55 , by which the magnetic abrasive grain  65  getting out of the magnetic field space of the electromagnetic coil  8  also gets out from the above-described rotated magnetic field of the electromagnetic coil  8 . When the electromagnetic coil moving unit  5  reciprocally moves the electromagnetic coil  8  in the direction shown by the arrow X with a given number of times, the surface roughening process for the external surface of the developing sleeve  132  has completed. 
     In an exemplary embodiment, a rotated magnetic field strength generated by the electromagnetic coil  8  may be set to a greater value when to process the both end portions of the developing sleeve  132  compared to when to process the center portion of the developing sleeve  132 , for example. In other words, a rotated magnetic field strength generated by the electromagnetic coil  8  may become gradually greater in the direction from the center portion to the both end portion of the developing sleeve  132 , for example. 
     The greater the rotated magnetic field strength, the more vibrant the magnetic abrasive grain  65  moves. Accordingly, as the rotated magnetic field strength increases, the magnetic abrasive grain  65  impacts against a to-be-processed object (e.g., the developing sleeve  132 ) with greater force, by which depth of depressions formed on the surface of the developing sleeve  132  may become gradually greater or deeper in the longitudinal (or axial) direction along the developing sleeve  132 . Accordingly, depressions formed on an end portion of the developing sleeve  132  may have a greater depth compared to depressions formed on a center portion of the developing sleeve  132 . 
     When such surface roughening process for the external surface of the developing sleeve  132  has completed, a power application to the electromagnetic coil  8  is stopped, and a power application to the collection unit  10  and the cooling unit  11  is also stopped. Then, the holding chuck  16  is released from holding the container unit  9  to the fixed holding unit  4 . After such releasing, the moving base  26  is departed from the fixed holding unit  4  in the direction of the arrow X by using the first actuator  24  while holding the container unit  9  with the holding chuck  43  of the movable chuck unit  7  and the holding chuck  28  of the movable holding unit  6 . With such process, the container unit  9  is departed from the fixed holding unit  4 . Then, the developing sleeve  132  having treated with the surface roughening process can be removed from the container unit  9 . 
     With the above-described surface roughing process, the developing sleeve  132  having a roughened external surface (see  FIG. 2 ) can be fabricated, in which depth of depressions on the developing sleeve  132  may gradually become greater or deeper in the direction from the center portion to the both end portions of the developing sleeve  132 . The developing sleeve  132  according to an exemplary embodiment may have such depressions randomly formed on the developing sleeve  132  while changing depth of depressions as above described, for example. Such depth change of depressions may be provided to the developing sleeve  132  to suppress a degradation of developability at end portions of a developing sleeve, which may be caused by given factors other than developing sleeve. 
     Then, another new developing sleeve is set and housed in the container unit  9  for performing another surface roughness process. 
     In an exemplary embodiment, when the surface treatment machine  1  is used for performing the surface roughening process to the external surface of the developing sleeve  132 , the electromagnetic coil  8  generates a rotated magnetic field, which generate an eddy current in the developing sleeve  132 . Such rotated magnetic field and eddy current may cause an electromagnetic induction electromotive force, by which the developing sleeve  132  rotates with a rotation number substantially corresponding to the frequency of the rotated magnetic field. 
     Further, as illustrated in  FIG. 16 , with an effect of the rotated magnetic field, the magnetic abrasive grain  65 , placed in a position inside the electromagnetic coil  8 , rotatingly moves along the outer circumference of the developing sleeve  132  while rotating about the center of the magnetic abrasive grain  65 , by which the magnetic abrasive grain  65  impacts against the external surface of the developing sleeve  132  to roughen the external surface of the developing sleeve  132 . The magnetic abrasive grain  65 , rotating about its center, rotates with a rotation number substantially corresponding to the frequency of the rotated magnetic field. 
     Because the direction of rotation of the magnetic abrasive grain  65 , rotating about its center, and the direction of rotation of the developing sleeve  132  are a same direction as illustrated in  FIG. 16 , the outer edge  65   a  of the magnetic abrasive grain  65  impacts against the developing sleeve  132  with a relative speed, which is proportional to the square value of the frequency of the rotated magnetic field. 
     Accordingly, the greater the frequency of the rotated magnetic field, the greater the relative speed of the magnetic abrasive grain  65 , by which a size of the depressions formed on the external surface developing sleeve  132  by impacting the magnetic abrasive grain  65  per unit time becomes greater in the circumferential direction of the developing sleeve  132 , and the long axis of the depressions on the external surface of the developing sleeve  132  may be more likely to align in the circumferential direction (or rotation direction) of the developing sleeve  132 . 
     Further, because an impact force of the magnetic abrasive grain  65  proportionally increases as the relative speed increases, the outer edge  65   a  of the magnetic abrasive grain  65  may rotatingly impact against the external surface of the developing sleeve  132  to scrape or scoop up the external surface of the developing sleeve  132  if the relative speed is effectively greater. 
     Further, because a greater number of the magnetic abrasive grain  65  may move as illustrated in  FIG. 16 , a greater number of depressions, having elliptical shape and formed on the external surface of the developing sleeve  132 , may be formed on the developing sleeve  132  by aligning the long axis of the elliptical shape in the circumferential direction of the developing sleeve  132 . 
     Further, because a rotation kinetic energy of the magnetic abrasive grain  65  may be consumed when the magnetic abrasive grain  65  impacts against the external surface of the developing sleeve  132  and starts to scrape or scoop up the external surface of the developing sleeve  132  for forming the depressions  139 , the rotation kinetic energy of the magnetic abrasive grain  65  may be substantially lost during a formation of the depressions  139 . When the rotation kinetic energy of the magnetic abrasive grain  65  is substantially lost, the magnetic abrasive grain  65  may be bounced from the developing sleeve  132 . Because such rotation kinetic energy of the magnetic abrasive grain  65  may be substantially lost when the magnetic abrasive grain  65  impacts against the external surface of the developing sleeve  132  and scrapes or scoops up some portions of the developing sleeve  132  right after such initial impacting of the magnetic abrasive grain  65 , the depression  139  may have a cross sectional shape, which may be asymmetrical in its frontward and rearward direction as illustrated in  FIG. 17 , in which the depression  139 , having elliptical shape and formed on the external surface of the developing sleeve  132 , may have the deepest portion  200   c  at a rearward position of the depression  139  with respect to the direction of rotation of the developing sleeve  132 , wherein such direction of rotation may be a rotation direction of developing sleeve  132  when magnetic particles is attracted on developing sleeve  132 . 
     Accordingly, as illustrated in  FIG. 18 , the hypothetical first line L 1  outwardly extending from the deepest portion  200   c  of the depression  139  in a radial direction of the developing sleeve  132 , and the hypothetical second line L 2  outwardly extending from the deepest portion  200   c  to the peripheral end portion  200   a  of the depression  139  may form the angle α set within 45 degrees, wherein the peripheral end portion  200   a  is a rearward position of the depression  139  with respect to a direction of rotation of the developing sleeve  132 , which is shown by an arrow. 
     As illustrated in  FIG. 17 , when the magnetic abrasive grain  65  impacts and scoop ups the external surface of the developing sleeve  132  to form the depression  139 , the depression  139  may have the peripheral end portion  200   a  at its rearward position with respect to the direction of rotation of the developing sleeve  132 , wherein the peripheral end portion  200   a  may protrude from the external surface of the developing sleeve  132 . 
     Accordingly, as illustrated in  FIG. 18 , the depression  139  has the hypothetical straight-line segment La and the radius segment Lb. The hypothetical straight-line segment La extends from the rotation center P of the developing sleeve  132  to the peripheral end portion  200   a  of the depression  139 . The radius segment Lb is one half of an outer diameter of the developing sleeve  132 . In an exemplary embodiment, the hypothetical straight-line segment La may be set greater than the radius segment Lb. 
     Further, because a greater number of the magnetic abrasive grain  65  may rotatingly move along the circumferential direction of the developing sleeve  132  with the effect of the rotated magnetic field generated over the developing sleeve  132 , a greater number of depressions  139 , having elliptical shape and formed on the external surface of the developing sleeve  132 , may be formed on the developing sleeve  132  by aligning the long axis of the elliptical shape in the circumferential direction of the developing sleeve  132 . Such depression  139  may have the deepest portion  200   c  closer to its rearward position, and the peripheral end portion  200   a  at its rearward position while protruding from the external surface of the developing sleeve  132 . 
     As described later with Table 1, when the rotated magnetic field frequency is set greater than 200 Hz or so, a number of depressions aligned in the circumferential direction (or rotation direction) of the developing sleeve  132  may become greater than a number of depressions aligned in the axial direction of the developing sleeve  132 . Further, as described later with Table 1, when the rotated magnetic field frequency is set to 200 Hz to 400 Hz, the angle α may be set less than 45 degrees, and a relationship of “20 μm≧La-Lb&gt;5 μm” may be obtained. 
     As above described, in an exemplary embodiment, the surface treatment machine  1  and the magnetic abrasive grain  65  may be used to effectively form a greater number of the depressions  139  having elliptical shape on the external surface of the developing sleeve  132 . Further, the depressions  139  may include the first depressions  139   a  having elliptical shape extending or aligning in the axial direction of the developing sleeve  132  and the second depressions  139   b  having elliptical shape extending or aligning in the circumferential direction of the developing sleeve  132 , wherein the number of second depressions  139   b  is set greater than that of the first depressions  139   a.    
     Accordingly, magnetic particles included in the developing agent  126  may be uniformly attracted on the external surface along the circumferential direction of the developing sleeve  132 . Further, such magnetic particles may be attracted on the external surface of the developing sleeve  132  with a greater density in the circumferential direction of the developing sleeve  132  as above described. Therefore, the developing roller  115  can supply the developing agent  126  to a circumferential direction of the photosensitive drum  108  more uniformly. In other words, the developing agent  126  can be supplied to a direction of rotation of the photosensitive drum  108  more uniformly, wherein the direction of rotation of the photosensitive drum  108  is aligned to a transport direction of a transfer member such as sheet, intermediate transfer belt or the like. Accordingly, a toner image can be developed on the photosensitive drum  108  by decreasing unevenness of image concentration, by which an image having higher quality can be produced on a transfer member. 
     Although the developing sleeve  132  according to an exemplary embodiment may be configured to suppress unevenness of image concentration in a transport direction of a transfer member such as sheet (e.g., sheet transport direction) as above-described, such developing sleeve  132  can also preferably suppress unevenness of image concentration in a width direction (e.g., sheet width direction) of a transfer member, perpendicular to the transport direction of the transfer member. Accordingly, an image produced by using such developing sleeve  132  according to an exemplary embodiment may have a preferable level of image concentration as a whole. 
     Further, as above described, when the depressions  139  having elliptical shape are formed on the external surface of the developing sleeve  132  by impacting the magnetic abrasive grain  65  against the external surface of the developing sleeve  132 , the magnetic abrasive grain  65  may impact against the surface of the developing sleeve  132  omnidirectionally, which may mean magnetic abrasive grains are impacting against the developing sleeve  132  from substantially any directions with respect to the surface of the developing sleeve  132  substantially at the same timing. Accordingly, compared to a conventional sandblasting process which may impact abrasive grains against an object from one direction at one time, the developing sleeve  132  may receive impacting stress uniformly on its surface when forming the depressions  139  by the surface processing machine  1  according to an exemplary embodiment, which may be preferable for suppressing a shape deformation of the developing sleeve  132  (e.g., misaligned axis, change of inner/outer diameter, collapsing of sleeve shape). 
     Accordingly, the developing sleeve  132  can be manufactured with a higher precision, and can rotate with a higher precision, by which an image having higher quality can be produced with a good level of toner concentration. 
     Further, when the surface treatment machine  1  and the magnetic abrasive grain  65  are used to form the depression  139  having elliptical shape on the external surface of the developing sleeve  132 , the hypothetical first line L 1  extending outwardly from the deepest portion  200   c  in a radial direction of the developing sleeve  132  and the hypothetical second line L 2  extending from the deepest portion  200   c  to the peripheral end portion  200   a  of the depression  139  may form the angle α within 45 degrees. Such depression  139  has the peripheral end portion  200   a  at its rearward position, with respect to the direction of rotation of the developing sleeve  132 , wherein the peripheral end portion  200   a  protrudes from the external surface of the developing sleeve  132 . Accordingly, the depressions  139  may effectively scoop up and hold magnetic particles therein when the developing agent  126  is carried up on the developing sleeve  132 . Therefore, magnetic particles may be held on the external surface of the developing sleeve  132  more reliably, by which the developing agent  126  may be held on the external surface of the developing sleeve  132  more reliably. Therefore, the amount of developing agent  126  that the developing sleeve  132  can carry does not deteriorate over time and images having appropriate concentrations of toner can continue to be produced. 
     Further, a depth of the depression  139  may be set to relatively smaller value in an exemplary embodiment while maintaining a good level of holding capability of developing agent, by which processing energy (e.g., mechanical force) applied to the external surface of the developing sleeve  132  can be set smaller, which may be preferable for suppressing a shape deformation of the developing sleeve  132  (e.g., misaligned axis, change of inner/outer diameter, collapsing of sleeve shape). Accordingly, the developing sleeve  132  can be manufactured with a higher precision, and can rotate with a higher precision, by which an image having higher quality can be produced with a good level of toner concentration. 
     A description is now given to experiments conducted for surface roughening process of a hollow structure using the surface treatment machine  1 . In the experiments, current and frequency values applied to the electromagnetic coil  8  were changed for conducting the surface roughening process to the hollow structure (hereinafter, referred as the developing sleeve  132  or developing sleeve for the simplicity of expression) with a method according to an exemplary embodiment and a conventional surface roughening process. The results of the experiments were evaluated with a sensory evaluation method, which evaluates image concentration unevenness in a sheet transport direction. 
     Example Experiment 1 
     By using the surface treatment machine  1 , a surface roughening process was conducted by randomly impacting the magnetic abrasive grain  65  (outer diameter: 0.8 mm, length: 5 mm, material: SUS 304) to the developing sleeve  132  (outer diameter: 18 mm, length: 240 mm, material: aluminum alloy A6063). When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 10 A and a frequency of 200 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. 
     Example Experiment 2 
     The developing sleeve  132  was prepared as similar to Example Experiment 1. When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 20 A and a frequency of 200 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. 
     Example Experiment 3 
     The developing sleeve  132  was prepared as similar to Example Experiment 1. When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 20 A and a frequency of 300 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. 
     Example Experiment 4 
     The developing sleeve  132  was prepared as similar to Example Experiment 1. When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 20 A and a frequency of 400 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. 
     Example Experiment 5 
     The developing sleeve  132  was prepared as similar to Example Experiment 1. When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 30 A and a frequency of 200 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. 
     Comparison Experiment 1 
     A developing sleeve was prepared by forming grooves on its external surface, wherein the grooves have a length of 220 mm, a width of 0.1 mm, a depth of 0.2 mm, and a groove-to-groove interval of 0.18 mm. 
     Comparison Experiment 2 
     A developing sleeve was prepared by conducting a sandblasting to its external surface using alumina abrasive grain having an average particle diameter of 500 μm with a processing time of 30 sec and a jetting pressure of 4 kgf/cm 2 . 
     Comparison Experiment 3 
     A developing sleeve was prepared by conducting a sandblasting to its external surface using alumina abrasive grain having an average particle diameter of 50 μm with a processing time of 30 sec and a jetting pressure of 4 kgf/cm 2 . 
     Comparison Experiment 4 
     A developing sleeve was prepared as similar to Example Experiment 1. When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 10 A and a frequency of 150 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. 
     Comparison Experiment 5 
     A developing sleeve was prepared as similar to Example Experiment 1. When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 20 A and a frequency of 150 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. 
     Comparison Experiment 6 
     A developing sleeve was prepared as similar to Example Experiment 1. When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 30 A and a frequency of 150 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. 
     Comparison Experiment 7 
     A developing sleeve was prepared as similar to Example Experiment 1. When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 20 A and a frequency of 100 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. 
     Comparison Experiment 8 
     A developing sleeve was prepared as similar to Example Experiment 1. When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 30 A and a frequency of 100 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. 
     The developing sleeves prepared by the above-described Example Experiments and Comparison Experiments were used for the following test. 
     The developing sleeves prepared by the above-described Example Experiments and Comparison Experiments were installed in an image forming apparatus (product name of IPSIO CX400 by Ricoh Co., Ltd.). The photosensitive drum  8  was charged with 620 V, and the developing bias voltage of 385 V was applied. A two-component cyan developing agent, including a carrier having an average particle diameter of 35 μm, was used as the developing agent  126 , and a pick-up amount of the developing agent  126  was set to 50 mg/cm 2 . Under such setting, a solid image of 195 mm×285 mm was output for 10,000 sheets by the image forming apparatus, and image concentration unevenness in a sheet transport direction was evaluated with a sensory evaluation method. Specifically, image concentration unevenness at initial condition of the developing sleeves and image concentration unevenness after outputting 10,000 sheets were evaluated with following criteria, and the results are shown as Table 1. 
     Criteria A: image concentration in a sheet transport direction is uniform, and image concentration unevenness is not observed. 
     Criteria B: image concentration unevenness in a sheet transport direction is observed, but no problem for practical use. 
     Criteria C: image concentration unevenness in a sheet transport direction is observed, and problem arises for practical use. 
     Further, because a surface roughening process according to an exemplary embodiment was conducted with the surface treatment machine  1  in Example Experiments 1 to 5 and Comparison Experiment 4 to 8, depressions having elliptical shape were formed on the developing sleeves. Table 1 also shows a ratio of the second depression  139   b  (see  FIG. 6 ) in the depressions  139 , extending along the circumferential direction of the developing sleeve per unit area on the developing sleeve. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                   
                 Concentration 
                 Ratio of 
                   
               
               
                   
                 unevenness 
                 second 
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 After 
                 depression 
                 Angle α 
                 La-Lb 
                 Frequency 
               
               
                   
                 Initial 
                 10,000 
                 (%) 
                 (degree) 
                 (μm) 
                 (Hz) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Ex. 1 
                 A 
                 A 
                 60 
                 22 
                 7.3 
                 200 
               
               
                 Ex. 2 
                 A 
                 A 
                 60 
                 21 
                 7.9 
                 200 
               
               
                 Ex. 3 
                 A 
                 A 
                 85 
                 33 
                 11.3 
                 300 
               
               
                 Ex. 4 
                 A 
                 A 
                 95 
                 41 
                 19.7 
                 400 
               
               
                 Ex. 5 
                 A 
                 A 
                 60 
                 19 
                 7.2 
                 200 
               
               
                 Ex. 6 
                 A 
                 A 
                 95 
                 44 
                 18.5 
                 450 
               
               
                 Ex. 7 
                 A 
                 A 
                 95 
                 43 
                 11.9 
                 450 
               
               
                 Ex. 8 
                 A 
                 A 
                 95 
                 43 
                 6.1 
                 450 
               
               
                 CEx. 1 
                 C 
                 C 
                 — 
                 — 
                 — 
                 — 
               
               
                 CEx. 2 
                 C 
                 C 
                 — 
                 — 
                 — 
                 — 
               
               
                 CEx. 3 
                 C 
                 C 
                 — 
                 — 
                 — 
                 — 
               
               
                 CEx. 4 
                 B 
                 B 
                 40 
                 17 
                 6.1 
                 150 
               
               
                 CEx. 5 
                 B 
                 B 
                 40 
                 17 
                 5.3 
                 150 
               
               
                 CEx. 6 
                 B 
                 B 
                 40 
                 16 
                 5.8 
                 150 
               
               
                 CEx. 7 
                 B 
                 B 
                 20 
                 13 
                 4.2 
                 100 
               
               
                 CEx. 8 
                 B 
                 B 
                 20 
                 13 
                 3.9 
                 100 
               
               
                 CEx. 9 
                 A 
                 B 
                 95 
                 44 
                 20.8 
                 450 
               
               
                 CEx. 10 
                 B 
                 B 
                 95 
                 44 
                 4.5 
                 450 
               
               
                 CEx. 11 
                 B 
                 B 
                 95 
                 48 
                 11.5 
                 500 
               
               
                   
               
            
           
         
       
     
     In Table 1, “Ex.” represents Example Experiment and “CEx.” represents Comparison Experiment. 
     As shown in Table 1, the developing sleeves of Example Experiments 1 to 5 and Comparison Experiments 4 to 8 prepared by the surface roughening process according to an exemplary embodiment have results that an image concentration unevenness in a sheet transport direction is smaller or little, which is a relatively good result, compared to the developing sleeves of Comparison Experiments 1 to 3 prepared by a conventional surface roughening process, in which Example Experiments 1 to 5 has Criteria A, and Comparison Experiments 4 to 8 has Criteria B. 
     Further, in Example Experiments 1 to 5, the electromagnetic coil was applied with a frequency of 200 Hz or greater. In such Example Experiments 1 to 5, the depressions  139  having elliptical shape formed on the external surface of the developing sleeve  132  had a greater number of the second depressions  139   b , extending or aligning in the circumferential direction of the developing sleeve  132  compared to the first depressions  139   a , extending or aligning in the axial direction of the developing sleeve  132  (see “ratio of second depression” in Table 1). Such Example Experiments 1 to 5 show good results as shown in Table 1. 
     With such Example Experiments 1 to 5, it is confirmed that image concentration unevenness in a sheet transport direction can be suppressed or prevented when the number of the second depressions  139   b , extending or aligning in the circumferential direction of the developing sleeve  132 , is set greater than the number of the first depressions  139   a , extending or aligning in the axial direction of the developing sleeve  132 , on the external surface of the developing sleeve  132 . 
     Further, another experiments were conducted to evaluate an effect of one shape factor of the depressions  139  formed on the external surface of the developing sleeve  132  to the image concentration unevenness in a sheet transport direction. 
     Specifically, the surface roughening process according to an exemplary embodiment was conducted in Example Experiments 1, 2, 3, 5, 7, and Comparison Experiment 11 by changing current values and frequency applied to the electromagnetic coil  8 . 
     As illustrated in  FIG. 18 , the depression  139  formed on the external surface of the developing sleeve  132  has the deepest portion  200   c , and the hypothetical first line L 1  outwardly extends from the deepest portion  200   c  of the depression  139  in a radial direction of the developing sleeve  132 , and the hypothetical second line L 2  outwardly extends from the deepest portion  200   c  to the peripheral end portion  200   a  of the depression  139 , wherein the peripheral end portion  200   a  is a rearward position of the depression  139  with respect to a direction of rotation of the developing sleeve  132 , which is shown by an arrow. The hypothetical first and second lines L 1  and L 2  form the angle α. 
     By changing current values and frequency applied to the electromagnetic coil  8 , developing sleeves having different angles α were prepared to evaluate image concentration unevenness in a sheet transport direction with the above-described sensory evaluation method. Table 1 also shows results of such experiments. 
     Example Experiment 7 
     The developing sleeve  132  was prepared as similar to Example Experiment 1. When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 20 A and a frequency of 450 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. After that, the developing sleeve  132  was rotated at a rotation speed of 1480 rpm (revolution per minute) using a rotation machine, and a tape having a surface roughness of #400 was pressed on the surface of the developing sleeve  132  with a force of 10 kgf for a time of 10 sec to polish the surface of the developing sleeve  132 . Such tape polishing was conducted to scrape the outer edge  200   a  of the depression  139  to reduce the hypothetical straight-line segment La. 
     Comparison Experiment 11 
     A developing sleeve was prepared as similar to Example Experiment 1. When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 20 A and a frequency of 500 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. After that, the developing sleeve  132  was rotated at a rotation speed of 1480 rpm (revolution per minute) using a rotation machine, and a tape having a surface roughness of #400 was pressed on the surface of the developing sleeve  132  with a force of 10 kgf for a time of 15 sec to polish the surface of the developing sleeve  132 . Such tape polishing was conducted to scrape the outer edge  200   a  of the depression  139  to reduce the hypothetical straight-line segment La. 
     With such prepared developing sleeves, image concentration unevenness in a sheet transport direction was evaluated with the above-described sensory evaluation method. Table 1 shows results of such experiments, wherein the angle α of the depression  139  is also shown. The angle α was measured by taking a plurality of depressions  139  as samples and then by averaging the angles of the sampled depressions  139 . 
     Further, in order to confirm a relationship between the angle α and the image concentration unevenness, parameters other than the angle α (e.g., major axis length of elliptical shape, minor axis length of elliptical shape, depth of depression, a length of La and Lb) were set to similar values among the prepared developing sleeves by carefully conducting a surface treatment to the developing sleeves, by which such parameters may not cause some effect on the results. 
     As shown in Table 1, the developing sleeves  132  prepared in Example Experiments 1, 2, 3, 5, and 7 have little image concentration unevenness (i.e., Criteria A) in a sheet transport direction, which is a good result, compared to the developing sleeve prepared in Comparison Experiment 11 having Criteria B. 
     Accordingly, based on Example Experiments 1 to 5, it is confirmed that the depression  139  on the developing sleeve  132  has the angle α of less than 45 degrees (α&lt;45 degrees) when the rotated magnetic field is set to a frequency of 200 Hz to 400 Hz. Further, although a length of “La-Lb (μm)” in Example Experiments 1, 3, 5, and 7 are smaller than a length of “La-Lb (μm)” in Comparison Experiment 11, it is confirmed that the Example Experiments 1, 3, 5, and 7 show good results (i.e., Criteria A) on image concentration due to a factor of the angle α. Based on such results, it is confirmed that the image concentration unevenness in a sheet transport direction can be suppressed or prevented when the depression  139  has the angle α of less than 45 degrees (α&lt;45 degrees). 
     Further, another experiments were conducted to evaluate an effect of another shape factor of the depressions  139  formed on the external surface of the developing sleeve  132  to the image concentration unevenness in a sheet transport direction. Specifically, the surface roughening process according to an exemplary embodiment was conducted in Example Experiments 1 to 8 and Comparison Experiments 9 and 10 by changing current values and frequency applied to the electromagnetic coil  8 . As illustrated in  FIG. 18 , the depression  139  may have the hypothetical straight-line segment La and the radius segment Lb. The hypothetical straight-line segment La extends from the rotation center P of the developing sleeve  132  to the peripheral end portion  200   a  of the depression  139 . The radius segment Lb is one half of an outer diameter of the developing sleeve  132 . By changing current values and frequency applied to the electromagnetic coil  8 , developing sleeves having different values of “La-Lb” were prepared to evaluate image concentration unevenness in a sheet transport direction with the above-described sensory evaluation method. Table 1 also shows a result of such experiment. 
     Example Experiment 6 
     The developing sleeve  132  was prepared as similar to Example Experiment 1. When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 20 A and a frequency of 450 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. After that, the developing sleeve  132  was rotated at a rotation speed of 1480 rpm (revolution per minute) using a rotation machine, and a tape having a surface roughness of #400 was pressed on the surface of the developing sleeve  132  with a force of 10 kgf for a time of 5 sec to polish the surface of the developing sleeve  132 . Such tape polishing was conducted to scrape the outer edge  200   a  of the depression  139  to reduce the hypothetical straight-line segment La. 
     Example Experiment 8 
     The developing sleeve  132  was prepared as similar to Example Experiment 1. When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 20 A and a frequency of 450 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. After that, the developing sleeve  132  was rotated at a rotation speed of 1480 rpm (revolution per minute) using a rotation machine, and a tape having a surface roughness of #400 was pressed on the surface of the developing sleeve  132  with a force of 10 kgf for a time of 20 sec to polish the surface of the developing sleeve  132 . Such tape polishing was conducted to scrape the outer edge  200   a  of the depression  139  to reduce the hypothetical straight-line segment La. 
     Comparison Experiment 9 
     A developing sleeve was prepared as similar to Example Experiment 1. When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 20 A and a frequency of 450 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. 
     Comparison Experiment 10 
     A developing sleeve was prepared as similar to Example Experiment 1. When such surface roughening process was conducted, the electromagnetic coil  8  was applied with power having a current value of 20 A and a frequency of 450 Hz, and such surface roughening process was conducted with a processing time of 30 sec and an amount of the magnetic abrasive grain  65  of 50 g. After that, the developing sleeve  132  was rotated at a rotation speed of 1480 rpm (revolution per minute) using a rotation machine, and a tape having a surface roughness of #400 was pressed on the surface of the developing sleeve  132  with a force of 10 kgf for a time of 23 sec to polish the surface of the developing sleeve  132 . Such tape polishing was conducted to scrape the outer edge  200   a  of the depression  139  to reduce the hypothetical straight-line segment La. 
     With such prepared developing sleeves, image concentration unevenness in a sheet transport direction was evaluated with the above-described sensory evaluation method. Table 1 shows results of such experiment, wherein the length of “La-Lb” of the depression  139  are also shown. The length of “La-Lb” was measured by taking a plurality of depressions  139  as samples and then by averaging the length of the sampled depressions  139 . 
     Further, in order to confirm a relationship between the length of “La-Lb” and the image concentration unevenness, parameters other than the “La-Lb” (e.g., major axis length of elliptical shape, minor axis length of elliptical shape, depth of depression, angles α and β) were set to similar values among the prepared developing sleeves by carefully conducting a surface treatment to the developing sleeves, by which such parameters may not cause some effect on the results. 
     As shown in Table 1, the developing sleeves  132  prepared in Example Experiments 1 to 8 have little image concentration unevenness (i.e., Criteria A) in a sheet transport direction, which is a good result, compared to the developing sleeves  132  prepared in Comparison Experiments 9 and 10 having Criteria B when 10,000 sheets were printed. 
     Accordingly, based on Example Experiments 1 to 5, it is confirmed that the depression  139  on the developing sleeve  132  has the hypothetical straight-line segment La greater than the radius segment Lb having a relationship of “20 μm≧La-Lb&gt;5 μm” when the rotated magnetic field is set to a frequency of 200 Hz to 400 Hz. 
     Further, although the angle α in Example Experiments 6 to 8 are similar to the angle α in Comparison Experiments 9 and 10, it is confirmed that the Example Experiments 6 to 8 show good results on image concentration due to a factor of the “La-Lb.” Based on such results, it is confirmed that the image concentration unevenness in a sheet transport direction can be suppressed or prevented when the depression  139  has the hypothetical straight-line segment La greater than the radius segment Lb having a relationship of “20 μm≧La-Lb&gt;5 μm.” 
     If “La-Lb” becomes too great (e.g., La-Lb&gt;20 μm), an edge of the peripheral end portion  200   a , provided at the rearward position of the depression  139 , may more likely wear, abrade, or tear, by which an amount of developing agent carried on the external surface of the developing sleeve  132  may decrease over time. 
     A cross-sectional shape of concavities and convexities on the external surface of the developing sleeve  132  were measured with a laser focus displacement device “LT-8010” manufactured by KEYENCE CORPORATION at three points along one round of a developing sleeve. The measurement conditions include sampling number of 18000, sampling frequency of 1800 Hz, function of displacement, average measurement times of 2, measurement mode of normal, no darkout, no masking, no transparent member, and minimum light intensity of 130. With such conditions, the angle α and the length of “La-Lb” were computed. 
     As illustrated in  FIGS. 10 and 11 , the above-described image forming apparatus  101  includes the process cartridges  106 Y,  106 M,  106 C, and  106 K, and each of the process cartridges  106 Y,  106 M,  106 C, and  106 K includes the cartridge case  111 , the charge roller  109 , the photosensitive drum  108 , the cleaning blade  112 , and the development unit  113 , for example. However, in an exemplary embodiment, the process cartridges  106 Y,  106 M,  106 C, and  106 K may not need to include all such sub-units or devices therein except the development unit  113 . Accordingly, the cartridge case  111 , the charge roller  109 , the photosensitive drum  108 , or the cleaning blade  112  may be omitted from the process cartridges  106 Y,  106 M,  106 C, and  106 K, for example. Further, although the image forming apparatus  101  may include the process cartridges  106 Y,  106 M,  106 C, and  106 K detachably mounted in the image forming apparatus  101 , the process cartridges  106 Y,  106 M,  106 C, and  106 K can be omitted from the image forming apparatus  101 . In such a case, the image forming apparatus  101  may include the development unit  113  as detachable unit, for example. 
     Further, in an exemplary embodiment, the outer diameter of the developing sleeve  132 , the size of the magnetic abrasive grain  65 , the outer diameter of the cylindrical member  50  of the container unit  9  can be changed to any values as required. Further, the surface shape of the developing sleeve  132  at its both end portion, a curvature radius and a shape size of magnetic abrasive grain  65  are preferably selected and determined based on several factors such as desired surface roughness, processing time (processing condition), number of reciprocating movement of the electromagnetic coil  8 , durability of magnetic abrasive grain  65 , or the like. Further, a total amount of the magnetic abrasive grain  65  contained in the container unit  9  may be preferably determined based on several factors such as desired surface roughness, processing time (processing condition), number of reciprocating movement of the electromagnetic coil  8 , durability of magnetic abrasive grain  65 , or the like. 
     Numerous additional modifications and variations are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the disclosure of the present invention may be practiced otherwise than as specifically described herein. For example, elements and/or features of different examples and illustrative embodiments may be combined each other and/or substituted for each other within the scope of this disclosure and appended claims.