Patent Publication Number: US-9417564-B2

Title: Image forming apparatus having rollers, belt and a tension applying unit

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to an image forming apparatus. 
     2. Description of the Related Art 
     In Japanese Patent Application Publication No. 2007-225969, Ito describes an electrophotographic color printer. This printer includes image forming units for four colors of black, yellow, magenta, and cyan. Each of the image forming units includes a photosensitive drum, a charging unit that charges the surface of the photosensitive drum, an exposure unit that illuminates the charged surface to form an electrostatic latent image, a developing unit that develops the electrostatic latent image with toner to form a toner image. The printer further includes an endless belt stretched around a drive roller and a tension roller, and transfer rollers disposed to face the respective photosensitive drums with the endless belt therebetween. As a sheet is conveyed by the endless belt, the toner images of the respective colors are sequentially transferred onto the sheet in a superposed manner by the transfer rollers, so that a color toner image is formed on the sheet. The color toner image is fixed to the sheet by a fixing unit. 
     However, in an image forming apparatus having a belt, an abnormal sound may occur when the belt runs. 
     SUMMARY OF THE INVENTION 
     An aspect of the present invention is intended to reduce the occurrence of abnormal sound when the belt runs. 
     According to an aspect of the present invention, there is provided an image forming apparatus including a plurality of rollers including a first roller rotated by receiving rotation from a drive unit and a second roller rotated with the rotation of the first roller; a belt stretched around the plurality of rollers, the belt having an inner surface; and a tension applying unit that applies tension to the belt. The inner surface of the belt has an uneven shape. Each of at least one roller of the plurality of rollers satisfies conditions expressed by μkmax≦0.73 and Δμk=(μkmax−μkmin)≦0.51, where μkmax is a maximum dynamic friction coefficient between the inner surface of the belt and the roller, and μkmin is a minimum dynamic friction coefficient between the inner surface of the belt and the roller. 
     Further scope of applicability of the present invention will become apparent from the detailed description given hereinafter. However, it should be understood that the detailed description and specific embodiments, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the attached drawings: 
         FIG. 1  is a schematic view of a printer in a first embodiment of the invention; 
         FIG. 2  is a block diagram of the printer in the first embodiment; 
         FIG. 3  shows a transfer unit in the first embodiment; 
         FIG. 4  shows a belt in a first state in the first embodiment; 
         FIG. 5  shows the belt in a second state in the first embodiment; 
         FIG. 6  shows the belt in a third state in the first embodiment; 
         FIG. 7  is a schematic view of a measurement device for measuring a dynamic friction coefficient based on the Euler&#39;s belt theory in the first embodiment; 
         FIG. 8  shows an example of a temporal variation of the dynamic friction coefficient in the first embodiment; 
         FIG. 9  shows results of abnormal sound evaluations in the first embodiment; 
         FIG. 10  is a schematic view of a printer in a second embodiment; and 
         FIG. 11  shows a transfer unit in the second embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Embodiments of the invention will now be described with reference to the attached drawings. Each embodiment illustrates a printer as an image forming apparatus. 
     First Embodiment 
       FIG. 1  is a schematic view showing a printer  10  in the first embodiment.  FIG. 2  is a block diagram of the printer  10 . 
     In  FIG. 1 , the printer  10  includes image forming units Bk, Y, M, and C for black, yellow, magenta, and cyan, and a sheet cassette Ct. Each of the image forming units Bk, Y, M and C includes a photosensitive drum  11  as an image carrier, a charging roller  12  as a charging device, an LED head (Light Emitting Diode) ed as an exposure device, a developing unit  13 , a cleaning blade  14  as a first cleaning member, and other components. The photosensitive drum  11  is rotatably disposed and connected to a drive motor  81  as a drive unit for image formation. The charging roller  12  is rotatably disposed in contact with the photosensitive drum  11  and uniformly charges a surface of the photosensitive drum  11 . The LED head ed is disposed to face the photosensitive drum  11  and illuminates the photosensitive drum  11  charged by the charging roller  12  to form an electrostatic latent image as a latent image. The developing unit  13  is disposed to face the photosensitive drum  11  and develops the electrostatic latent image formed on the surface of the photosensitive drum  11 . The cleaning blade  14  is disposed in contact with the photosensitive drum  11  at its tip. The developing unit  13  includes a toner cartridge  23  as a developer container and a developing roller  33  as a developer carrier, and other components. The toner cartridge  23  stores toner as developer. The developing roller  33  is disposed in contact with the photosensitive drum  11 , carries toner supplied from the toner cartridge  23 , and supplies the toner to the electrostatic latent image to form a toner image as a developer image. The sheet cassette Ct serves as a sheet feeding unit and a medium storage unit, and stores sheets of paper P as media. 
     The printer  10  further includes a transfer unit u 1  disposed below the image forming units Bk, Y, M, and C. 
     The transfer unit u 1  includes a drive roller  19  as a first roller, a driven roller  20  as a second roller, a backup roller  21  as a third roller, an endless belt  24  as a transfer medium, transfer rollers (primary transfer rollers)  25  as first transfer members, a transfer roller (secondary transfer roller)  26  as a second transfer member, a cleaning blade  28  as a second cleaning member, and other components. The drive roller  19  is disposed near the image forming unit Bk, connected to a belt drive motor  82  as a drive unit for driving the belt  24  to run, and rotated by receiving rotation from the belt drive motor  82 . The driven roller  20  is disposed near the image forming unit C and rotated with the rotation of the drive roller  19 . The backup roller  21  is disposed below the drive roller  19  and driven roller  20 , and rotated with the rotation of the drive roller  19 . The belt  24  is stretched around the drive roller  19 , driven roller  20 , and backup roller  21 , and driven to run in the direction indicated by arrow A in  FIG. 1  in accordance with the rotation of the drive roller  19 . Each of the transfer rollers  25  is disposed to face the corresponding photosensitive drum  11  with the belt  24  therebetween. The transfer roller  26  is disposed to face the backup roller  21  with the belt  24  therebetween. The cleaning blade  28  is disposed to face the drive roller  19  with the belt  24  therebetween and in contact with the belt  24  at its tip. 
     Specifically, the belt  24  has an inner surface and an outer surface, and the drive roller  19 , driven roller  20 , and backup roller  21  are disposed in contact with the inner surface of the belt  24 . The belt  24  is rotated or moved by the rotation of the drive roller  19  by friction between the drive roller  19  and the inner surface of the belt  24 . The driven roller  20  is rotated by the movement of the belt  24  by friction between the driven roller  20  and the inner surface of the belt  24 . The backup roller  21  is rotated by the movement of the belt  24  by friction between the backup roller  21  and the inner surface of the belt  24 . 
     Each of the transfer rollers  25  forms a primary transfer portion together with the corresponding photosensitive drum  11  and the belt  24 . As the belt  24  runs, toner images of the respective colors formed on the respective photosensitive drums  11  are transferred in a superposed manner onto the belt  24  at the primary transfer portions, so that a color toner image is formed. The transfer roller  26  forms a secondary transfer portion together with the backup roller  21  and belt  24 . The color toner image formed on the belt  24  is transferred onto a sheet P fed from the sheet cassette Ct at the secondary transfer portion. 
     The printer  10  further includes pairs of conveying rollers m 1  and m 2 , a fixing unit  17  as a fixing device, and a stacker Sk. Each of the pairs of conveying rollers m 1  and m 2  is connected to a conveying motor  83  as a drive unit for conveyance, is rotated by receiving rotation from the conveying motor  83 , and conveys a sheet P fed from the sheet cassette Ct. The fixing unit  17  fixes, to the sheet P, the color toner image transferred on the sheet P to form a color image. The sheet P with the color image formed thereon is discharged from a main body (i.e., an apparatus main body) of the printer  10 , and is stacked on the stacker Sk. 
     The fixing unit  17  includes a heating roller  35  as a first fixing roller, a pressure roller  36  as a second fixing roller, and other components. The heating roller  35  is rotatably disposed, connected to a fixing motor  84  as a drive unit for fixing, and rotated by receiving rotation from the fixing motor  84 . The pressure roller  36  is rotatably disposed in contact with the heating roller  35  and rotated by receiving the rotation of the heating roller  35 . A halogen lamp (not shown) is disposed as a heating body in the heating roller  35 . The color toner image formed on the sheet P is heated by the heating roller  35  and pressured by the pressure roller  36 , thereby being fixed to the sheet P. 
     The toner of each color is formed by an emulsion polymerization method using a styrene-acrylic copolymer as a main component, in which  9  parts by weight of paraffin wax is included. The toner has an average particle diameter of 7 μm and a sphericity of 0.95. The use of such a toner makes it possible to improve the reproducibility and resolution of dots developed by the developing unit  13  and the transfer efficiency of the transfer unit u 1 , and eliminates the need for a release agent in the fixing unit  17 , thereby improving image quality. 
     The printer  10  further includes a controller  85  that controls respective parts, including the drive motor  81 , belt drive motor  82 , conveying motor  83 , and fixing motor  84 , in the printer  10  to control the operation of the printer  10 . 
     The operation of the printer  10  will now be described. 
     In each of the image forming units Bk, Y, M, and C, the surface of the photosensitive drum  11  is uniformly charged by the charging roller  12 . Then, the respective LED heads ed are supplied with image data of the respective colors and driven to illuminate the photosensitive drums  11 , so that electrostatic latent images corresponding to the image data of the respective colors are formed on the surfaces of the respective photosensitive drums  11 . Toners of the respective colors are applied to the electrostatic latent images by the respective developing units  13 , so that toner images of the respective colors are formed. 
     In the transfer unit u 1 , as the drive roller  19  rotates and the belt  24  runs in the direction of arrow A, the toner images of the respective colors are sequentially transferred in a superposed manner onto the belt  24  by the respective transfer rollers  25 , so that a color toner image is formed on the belt  24 . In each of the image forming units Bk, Y, M, and C, the toner (i.e., residual toner) remaining on the photosensitive drum  11  after the transfer of the toner image onto the belt  24  by the transfer roller  25  is scraped off and removed by the cleaning blade  14 , together with other foreign matter. 
     Meanwhile, a sheet P is taken from the sheet cassette Ct, conveyed by the pairs of conveying rollers m 1  and m 2 , and fed between the backup roller  21  and the transfer roller  26 . The color toner image on the belt  24  is transferred onto the fed sheet P by the transfer roller  26 . The toner (i.e., residual toner) remaining on the belt  24  after the transfer of the color toner image onto the sheet P by the transfer roller  26  is scraped off and removed by the cleaning blade  28 , together with other foreign matter. 
     The sheet P is conveyed to the fixing unit  17 , in which the color toner image is fixed to the sheet P, so that a color image is formed on the sheet P. Then, the sheet P is discharged outside the apparatus main body to be stacked on the stacker Sk. 
     The transfer unit u 1  will now be described. 
       FIG. 3  shows the transfer unit u 1  in the first embodiment;  FIG. 4  shows the belt  24  in a first state in the first embodiment;  FIG. 5  shows the belt  24  in a second state in the first embodiment;  FIG. 6  shows the belt  24  in a third state in the first embodiment. 
     Referring to  FIGS. 3 to 6 , the transfer unit u 1  further includes a support member  30  that supports the cleaning blade  28 , flanges  31  as restriction members (or guide members), and a spring  32  that serves as a tension applying unit, a stretching device, or a urging member and applies tension to the belt  24 . The cleaning blade  28  and support member  30  constitute a cleaning device  51 . 
     Each of the drive roller  19 , driven roller  20 , and backup roller  21  has a cylindrical body with an outer diameter of 25 mm and a surface in contact with the belt  24 , the surface being made of a urethane material. The outer diameter of each of the drive roller  19 , driven roller  20 , and backup roller  21  may be 10 mm or more and 50 mm or less. The surface in contact with the belt  24  may be made of a metal material such as stainless steel (SUS) or aluminum, a resin material such as polyacetal or acrylonitrile-butadiene-styrene (ABS) resin, or a rubber material such as acrylonitrile butadiene rubber (NBR) or ethylene-propylene-diene rubber (EPDM). 
     The method of manufacturing the belt  24  will now be described. 
     Polyamide-imide (PAI) and carbon black are mixed and stirred in a solution with N-methylpyrrolidone (NMP) or the like as a solvent (organic polar solvent) to form a mixed solution. Then, the mixed solution is poured into a cylindrical mold, is heated for a predetermined period of time at a temperature of 80° C. or more and 120° C. or less while the mold is rotated, and then is further heated for a predetermined period of time at a temperature of 200° C. or more and 350° C. or less, so that a belt original tube with a thickness of 100±10 μm and a circumferential length of 1210.5±1.5 mm is formed in the mold. The belt original tube is taken out from the mold and cut into widths of 350±0.5 mm, each constituting one belt  24  having a structure consisting of one layer, that is, a single layer structure. 
     To form the belt original tube, instead of pouring the mixed solution into a cylindrical mold and rotating the mold, it is also possible to pour the mixed solution into a gap between two cylinders with different diameters, to rotate a cylindrical mold and apply the mixed solution to the peripheral surface of the mold, or to dip a cylindrical mold into the mixed solution. The belt original tube may be formed by extrusion molding, inflation molding, or other methods. No mixed solution is used in the extrusion molding and inflation molding. 
     After the belt  24  is formed, an uneven shape is formed on the inner surface of the belt  24  by an abrasive such as a variety of lapping films, which may be formed by coating a polymer film of polyester or the like with fine particles of alumina, chromic oxide, silicon carbide, or the like. As the lapping film, this embodiment uses ‘finishing paper’ (manufactured by Sumitomo 3M Ltd.) coated with particles (abrasive grains) of alumina of 5 μm, 9 μm, 30 μm, etc. 
     The polyamide-imide is a polymeric resin material having repeating units in which an amide group is bonded to one or two imide groups through an organic group. Polyamide-imides are classified as an aliphatic polyamide-imide or an aromatic polyamide-imide depending on whether the organic group is aliphatic or aromatic. This embodiment uses an aromatic polyamide-imide in which the organic group has one or two benzene rings. 
     The use of the aromatic polyamide-imide makes it possible to prevent edge portions of the belt  24  from wearing, bending, or cracking due to sliding contact of the belt  24  with the flanges  31 , thereby improving the durability of the belt  24 . Further, since tension occurs when the belt  24  runs, it is possible to prevent the belt  24  from deforming, thereby improving the mechanical properties of the belt  24 . 
     The polyamide-imide may be one in which the imide ring closure is completed or one containing amide acids before the imide ring closure. The use of a polyamide-imide with a low imidization rate containing amide acids leads to a high rate of dimensional change of the belt  24 . Thus, this embodiment uses a polyamide-imide having an imidization rate of 50% or more, preferably 70% or more. 
     The imidization rate is calculated based on a ratio between the intensity of the absorption at 1780 cm −1  due to imide groups and the intensity of the absorption at 1510 cm −1  due to benzene rings, by using a Fourier transform infrared spectrophotometer (referred to below as ‘FT-IR’). 
     In general, the use of a material having a molecular structure rich in aromatic rings, such as benzene rings, and imide groups makes it possible to increase the Young&#39;s modulus of the belt  24  and improve the durability and mechanical properties of the belt  24 . 
     Thus, as the material of the belt  24 , materials having high Young&#39;s moduli may be used separately or in combination (in a mixed manner). Such materials include resins of polyimide (PI), polycarbonate (PC), polyamide (PA), polyether ether ketone (PEEK), polyvinylidene fluoride (PVDF), and ethylene-tetrafluoroethylene copolymer (ETFE), which have, like polyamide-imide, Young&#39;s moduli of 3.0 GPa or more. 
     This embodiment uses the N-methylpyrrolidone as the solvent for mixing and stirring the polyamide-imide and carbon black, but besides the N-methylpyrrolidone, the following may be used: N,N-dimethylacetamides such as N,N-dimethylformamide, N,N-dimethylacetamide, N,N-diethylformamide, N,N-diethylacetamide, and dimethylsulfoxide, pyridine, tetramethylenesulfone, dimethyltetramethylenesulfone, etc. These solvents may be used separately or in combination. 
     In view of the thickness, thickness profile, or other properties of the belt  24 , the rotation speed of the mold during formation of the belt original tube is set at 5 rpm or higher and 1000 rpm or lower, and preferably 10 rpm or higher and 500 rpm or lower. When the belt original tube is formed by rotating a cylindrical mold and applying the mixed solution to the peripheral surface of the mold, the rotation speed of the mold is set at 5 rpm or higher and 1000 rpm or lower, and preferably 10 rpm or higher and 500 rpm or lower. 
     There are many types of carbon black, such as furnace black, channel black, kitchen black, acetylene black. These types may be used separately or in combination. The type of carbon black may be selected according to the electrical conductivity required for the belt  24 . It is preferable to use carbon black subjected to a treatment, such as an oxidation treatment or a graft treatment, for preventing oxidation degradation or improving the dispersibility in the solvent. 
     The content of the carbon black in the belt  24  is determined depending on the mechanical strength required for the belt  24  or other factors. The weight ratio of the carbon black to the polyamide-imide is set at 3% or more and 40% or less, preferably 5% or more and 30% or less, and more preferably 5% or more and 25% or less. 
     Although this embodiment uses a lapping film to form the uneven shape on the inner surface of the belt  24 , the uneven shape may be formed by other methods. For example, when the belt original tube is formed by rotating a cylindrical mold, the uneven shape may be formed during the formation of the belt original tube, by appropriately setting the molding conditions, without using a lapping film. 
     When the belt original tube is formed by rotating a cylindrical mold and applying a mixed solution to the peripheral surface of the mold or by dipping a cylindrical mold into a mixed solution, machining marks may be formed, as the uneven shape, on the inner surface of the belt  24  by concavities and convexities on the peripheral surface of the mold. When the belt original tube is formed by extrusion molding, inflation molding, or the like, machining marks may be formed, as the uneven shape, by concavities and convexities of the nozzle of the extrusion apparatus. The uneven shape may be formed on the inner surface of the belt  24  by using a mold with a surface subjected to blast processing. 
     The uneven shape is an irregular uneven shape in this embodiment, but may be a regular uneven shape. In one preferred aspect, the uneven shape is formed in parallel with the direction (referred to below as the running direction) in which the belt  24  runs. 
     In order to improve the surface slidability of the belt  24 , the mixed solution is added with a proper amount of water repellent agent, such as fluorine or silicone resin, so that the surface of the belt  24  has, with respect to stainless steel, a static friction coefficient lie of 0.1 or more and 1.0 or less. 
     If the static friction coefficient lie of the surface of the belt  24  is less than 0.1, the friction force occurring between the tip of the cleaning blade  28  and the belt  24  is insufficient to adequately scrape off the residual toner, foreign matter, and the like. On the other hand, if the static friction coefficient μe of the surface of the belt  24  is greater than 1.0, the friction force occurring between the tip of the cleaning blade  28  and the belt  24  is so large that an abnormal sound may occur between the tip of the cleaning blade  28  and the belt  24  or turning-up of the cleaning blade  28  may occur. 
     If an excessive amount of water repellent agent is added to the resin material, as the printer  10  is used over a long period of time, the water repellent agent is likely to bleed out on the surface of the belt  24 . When the bled water repellent agent, i.e., the bled substance, adheres to the photosensitive drums  11 , it becomes impossible to form toner images accurately, resulting in degradation of image quality. 
     In this embodiment, the static friction coefficient μe is measured by using a portable friction meter Muse Type:94i-II (manufactured by Heidon). 
     In order to adequately scrape off the residual toner, foreign matter, or the like on the belt  24 , the surface of the belt  24  is roughened to have a specularity SPOT of 60 or more and 200 or less (in this embodiment, 120±10). The inner surface of the mold for forming the belt original tube is subjected to a predetermined surface treatment so as to give a predetermined specularity SPOT to the surface of the belt  24 . When the belt original tube is formed without using a mold, the surface of the belt original tube is provided with a predetermined specularity SPOT by means of an abrasive such as a variety of lapping films. 
     If the specularity SPOT is less than 60, as the printer  10  is used for a long period of time, the residual toner, foreign matter, and the like cannot be scraped off adequately and may pass between the tip of the cleaning blade  28  and the belt  24 . 
     If the specularity SPOT is greater than 200, the tip of the cleaning blade  28  and the belt  24  make a large contact area and produce a large friction force, so that turning-up of the cleaning blade  28  may occur. 
     In this embodiment, the specularity SPOT measured by a specularity measurement device Mirror SPOT AHS-100S (manufactured by Archarima Co., Ltd.). 
     The cleaning device  51  will now be described. In the cleaning device  51 , the cleaning blade  28  is an elastic body made of a rubber material. In this embodiment, the cleaning blade  28  is formed of a urethane rubber blade having a hardness according to Japanese Industrial Standards (JIS) A of 72° and a thickness of 1.5 mm, and disposed so that its tip abuts against the belt  24  at a line pressure of 4.3 g/mm. Since urethane rubber has not only high hardness and elasticity but also superior abrasion resistance, mechanical strength, oil resistance, ozone resistance, and other properties, it allows the cleaning blade  28  not only to remove the residual toner, foreign matter, and the like certainly but also to have high durability. 
     Although this embodiment uses, as the cleaning blade  28 , a urethane rubber blade having a hardness (JIS A) of 72°, it is also possible to use a urethane rubber blade having a hardness (JIS A) of 60° or more and 90° or less, and preferably 70° or more and 85° or less. 
     Further, this embodiment uses urethane rubber having a breaking elongation of 250% or more and 500% or less, preferably 300% or more and 400% or less, a permanent elongation of 1.0% or more and 5.0% or less, preferably 1.0% or more and 2.0% or less, and a rebound resilience of 10% or more and 70% or less, preferably 30% or more and 50% or less. Each of these properties can be measured according to JIS K6301 (modified JIS K6251). 
     Further, although the line pressure of the cleaning blade  28  is set at 4.3 g/mm in this embodiment, it may be set at 1 g/mm or more and 6 g/mm or less, and preferably 2 g/mm or more and 5 g/mm or less. 
     If the line pressure is too low, the cleaning blade  28  does not contact the belt  24  adequately, causing cleaning failure. On the other hand, if the line pressure is too high, the cleaning blade  28  makes surface contact with the belt  24 , causes excessively large frictional resistance, and presses the belt  24  with a pressing force larger than the force required to scrape off residual toner, causing cleaning failure such as the so-called filming phenomenon or turning-up of the cleaning blade  28 . In this embodiment, since the line pressure of the cleaning blade  28  is set at a proper value, the cleaning failure and turning-up of the cleaning blade  28  can be prevented from occurring. 
     The flanges  31  are attached to the both ends of a predetermined roller (in this embodiment, the driven roller  20 ) of the drive roller  19 , driven roller  20 , and backup roller  21 . Specifically, when viewed from the running direction of the belt  24 , the flanges  31  are attached to a left end  20 L and a right end  20 R of the driven roller  20 . Each of the flanges  31  has a circular shape and satisfies
 
 df&gt;dr+tb  
 
where df is the outer diameter of the flange  31 , dr is the outer diameter of the driven roller  20 , and tb is the thickness of the belt  24 .
 
     When the belt  24  runs in accordance with the rotation of the drive roller  19 , it may approach either of the left end  20 L or the right end  20 R of the driven roller  20  to contact one of the flanges  31 . Thus, in this embodiment, the driven roller  20  is provided with an elevating mechanism  91  as an inclination mechanism. The elevating mechanism  91  is configured to incline the driven roller  20  so as to return the belt  24  to the position shown in  FIG. 4 . Specifically, when the belt  24  approaches the left end  20 L and comes into contact with the left flange  31  as shown in  FIG. 5 , the elevating mechanism  91  is driven to move the left end  20 L upward, so that the driven roller  20  is slightly inclined. Thereby, the belt  24  moves on the driven roller  20  in the direction of arrow a and returns to the position shown in  FIG. 4 . 
     When the belt  24  approaches the right end  20 R and comes into contact with the right flange  31  as shown in  FIG. 6 , the elevating mechanism  91  is driven to move the left end  20 L downward, so that the driven roller  20  is slightly inclined. Thereby, the belt  24  moves on the driven roller  20  in the direction of arrow b and returns to the position shown in  FIG. 4 . 
     When the belt  24  moves to the left end  20 L side, the left flange  31  abuts against the left edge of the belt  24  to restrict the belt  24  from further moving leftward; when the belt  24  moves to the right end  20 R side, the right flange  31  abuts against the right edge of the belt  24  to restrict the belt  24  from further moving rightward. Thus, belt  24  can be prevented from meandering. 
     Although the elevating mechanism  91  lifts and lowers the left end  20 L of the driven roller  20  in this embodiment, it may lift and lower the right end  20 R of the driven roller  20 . Further, although the flanges  31  are disposed at both of the left end  20 L and right end  20 R of the driven roller  20  in this embodiment, such flanges may be disposed at only one end (e.g., right end  20 R) of the driven roller  20 . In this case, the driven roller  20  is slightly inclined in advance in such a manner that the left end  20 L is above the right end  20 R so that the belt  24  is biased toward the right end  20 R and abuts against the flange  31 . 
     Although the flanges  31  are attached to the driven roller  20  in this embodiment, such flanges may be attached to the drive roller  19  or backup roller  21 , or to two or more of the drive roller  19 , driven roller  20 , and backup roller  21 . Further, although the flanges  31  are attached to the both ends of the driven roller  20  in this embodiment, such flanges may be attached to only one end of a predetermined roller. Further, although the flanges  31  are disposed as guide members in this embodiment, it is possible to dispose a belt support device that supports the belt  24  during running of the belt  24  at a predetermined position and provide, as a guide member, a piece for restricting movement of the belt  24  to the belt support device. 
     The spring  32  is disposed between a support member Fr 1  provided in the apparatus main body and a shaft sh 1  of the backup roller  21  to urge the backup roller  21  toward the transfer roller  26  with a stretching force of 6±10% kg=6±(6×0.1) kg. 
     Although the stretching force is 6±10% kg in this embodiment, it may be set appropriately depending on the material of the belt  24 , the torque generated by the belt drive motor  82 , or other factors, and may be set to 2±10% kg or more and 8±10% kg or less. 
     Although the spring  32  is used as a tension applying unit in this embodiment, a pneumatic piston or the like may be used. 
     The above printer  10  causes the belt  24  to run so as to form an image. Depending on the condition of the inner surface of the belt  24 , when the belt  24  runs, it may move in an axial direction (referred to below as the roller axial direction) in which the drive roller  19 , driven roller  20 , and backup roller  21  extend, and generate an abnormal sound. In particular, when the elevating mechanism  91 , which is for preventing the belt  24  from meandering, is driven to move the belt  24  on the driven roller  20 , an abnormal sound is likely to occur. 
     In general, when the inner surface of the belt  24  and the surface of each of the drive roller  19 , driven roller  20 , and backup roller  21  are smooth, an abnormal sound, such as a chattering sound, a high-frequency frictional sound (squeak) is likely to occur at positions at which the belt  24  is in contact with the rollers. This is thought to be because a vibration phenomenon called chattering, i.e., a stick-slip phenomenon, occurs between the belt  24  and the rollers. 
     Specifically, in a state where the belt  24  is in intimate contact with the rollers, when an external force is applied to the belt  24  in the roller axial direction, the contact surfaces of the belt  24  with the rollers receive friction forces. If the external force is insufficient, the belt  24  does not move in the roller axial direction due to the friction forces. When a further external force is applied to the belt  24  and the internal stress in the belt  24  becomes larger than a predetermined value, the belt  24  momentarily slides on the rollers, is released from the external force, and comes again into intimate contact with the rollers at the position at which the sliding ends. The repetition of this action causes a stick-slip phenomenon and vibrates the belt  24 , causing an abnormal sound. 
     The smoother the inner surface of the belt  24  and the surfaces of the rollers are, the larger the contact area between the belt  24  and the rollers is, the larger the friction forces exerted on the contact surfaces are, and the more the stick-slip phenomenon is likely to occur. 
     Further, the lower the speed at which the belt  24  runs (i.e., a belt linear speed) is, the more the stick-slip phenomenon is likely to occur. Even if the belt linear speed during image formation is high, when the belt  24  is accelerated to start running or when the belt  24  is decelerated to stop running, the stick-slip phenomenon is likely to occur. Thus, the abnormal sound is likely to occur when the belt  24  moves at low speed relative to the rollers (e.g., when the belt  24  moves in the roller axial direction, or when the belt  24  moves in the running direction at low speed during acceleration or deceleration). 
     Next, the relationship between a dynamic friction coefficient μk and abnormal sound occurring when the belt  24  runs will be described. The dynamic friction coefficient μk represents a friction coefficient between the inner surface of the belt  24  and the peripheral surface of a roller (the drive roller  19 , driven roller  20 , or backup roller  21 ) in contact with the belt  24  when the belt  24  runs. 
     The method of measuring the dynamic friction coefficient μk will be described first. 
       FIG. 7  is a schematic view showing a measurement device  39  for measuring the dynamic friction coefficient based on the Euler&#39;s belt theory. 
     In  FIG. 7 , the measurement device  39  includes a pulley  40 , a belt  41 , a weight  42 , and a load cell  43 . The pulley  40  has the same dimensions as and is made of the same material as the drive roller  19 , driven roller  20 , and backup roller  21 . The pulley  40  is unrotatably attached to a frame or other parts of the measurement device  39 . The belt  41  is made of the same material as and by the same method as the belt  24 . The belt  41  is wound around a part of the pulley  40  over an angle of 90° (π/2 rad). The weight  42  is attached to one end of the belt  41 . As the load cell  43 , a digital force gauge ZP-50N (manufactured by IMADA Co., Ltd.) is used. 
     The weight W of the weight  42  is 320 gf. The width of the belt  41  is 25 mm. In an environment having an ambient temperature of 23±3° C. and a relative humidity of 55±10%, the force F required to move the load cell  43  at a constant speed in the direction of arrow B is measured by the load cell  43 , and the dynamic friction coefficient μk is obtained according to the Euler&#39;s belt formula:
 
μ k =(2/π)×ln( F/W ).
 
Hereinafter, the speed at which the load cell  43  moves during the measurement (i.e., the above constant speed) will be referred to as the cell speed.
 
     From the above measurement, a temporal variation of the dynamic friction coefficient μk is obtained.  FIG. 8  shows an example of the temporal variation of the dynamic friction coefficient. In  FIG. 8 , the horizontal axis represents the time and the vertical axis represents the dynamic friction coefficient μk. In the measurement by the measurement device  39 , when the load cell  43  moves, a stick-slip phenomenon occurs between the belt  41  (corresponding to the belt  24 ) and the pulley  40  (corresponding to the drive roller  19 , driven roller  20 , or backup roller  21 ), and the dynamic friction coefficient μk varies as shown in  FIG. 8 . 
     From the temporal variation of the dynamic friction coefficient μk, a maximum value of the dynamic friction coefficient μk (i.e., a maximum dynamic friction coefficient μkmax), a minimum value of the dynamic friction coefficient μk (i.e., a minimum dynamic friction coefficient μkmin), and an amplitude Δμk represented by the difference between the maximum dynamic friction coefficient μkmax and the minimum dynamic friction coefficient μkmin are obtained as follows. The largest of local maximum values of the dynamic friction coefficient μk is determined to be the maximum dynamic friction coefficient μkmax; the smallest of local minimum values of the dynamic friction coefficient μk is determined to be the minimum dynamic friction coefficient μkmin; the difference between the maximum dynamic friction coefficient μkmax and the minimum dynamic friction coefficient μkmin is determined to be the amplitude Δμk, according to the equation: Δμk=μkmax−μkmin. 
     Next, a method of obtaining the relationship between the dynamic friction coefficient μk and abnormal sound occurring when the belt runs will be described. 
     Twelve types of belt samples #1 to #12 with different irregular uneven shapes on their inner surfaces were manufactured. Each of the samples #1 to #12 was individually mounted as the belt  41  in the measurement device  39  and its maximum dynamic friction coefficient μkmax, minimum dynamic friction coefficient μkmin, and amplitude Δμk were obtained according to the above method. 
     For each sample, the measurement was carried out at each of the following cell speeds: 3.54 mm/s and 0.2 mm/s. Thus, for each of the samples #1 to #12, at each of the two cell speeds, the maximum dynamic friction coefficient μkmax, the minimum dynamic friction coefficient μkmin, and the amplitude Δμk were obtained. The two cell speeds were determined in view of the speed of movement of the belt in the roller axial direction in the printer  10 . 
     Twelve types of belts #1 to #12 were also manufactured so as to have the same uneven shapes and dynamic friction coefficients as the samples #1 to #12, respectively. The belt #12 had its inner surface applied with zinc stearate so as to have high slidability, and thus the dynamic friction coefficient μk between the belt #12 and each roller is significantly small. For each of the belts #1 to #12, an abnormal sound evaluation was carried out as follows. The belt to be evaluated was actually mounted as the belt  24  in a printer having the configuration shown in  FIG. 1  and is driven to run. At this time, it was determined whether an abnormal sound occurred. 
     The results of the measurements and abnormal sound evaluations will now be described. 
       FIG. 9  shows the results of the measurements and abnormal sound evaluations in the first embodiment. 
       FIG. 9  lists the maximum dynamic friction coefficient μkmax, the minimum dynamic friction coefficient μkmin, and the amplitude Auk at each of the cell speeds of 3.54 mm/s and 0.2 mm/s, and the result of the abnormal sound evaluation, for each of the belts #1 to #12. FIG. 9 uses the maximum dynamic friction coefficients μkmax, minimum dynamic friction coefficients μkmin, and amplitudes Δμk of the samples #1 to #12 as those of the belts #1 to #12, respectively. 
     In the results of the abnormal sound evaluations, the word Good indicates that no abnormal sound occurred, the word Fair indicates that a slight abnormal sound with no practical problems in the printer  10  occurred, and the word Poor indicates that an abnormal sound with practical problems in the printer  10  occurred. 
     As can be seen from the results for the belts #1 to #11 in  FIG. 9 , the occurrence of abnormal sound due to running of the belt  24  is reduced when the following conditions are satisfied: the maximum dynamic friction coefficient μkmax is 0.73 or less and 0.10 or more, and the amplitude Δμk is 0.51 or less (preferably 0.45 or less). 
     The occurrence of abnormal sound due to running of the belt  24  is reduced when the following conditions are satisfied: the maximum dynamic friction coefficient μkmax is 0.73 or less and 0.12 or more, and the amplitude Δμk is 0.51 or less (preferably 0.45 or less) when the speed of the belt  24  is 0.2 mm/s. 
     The occurrence of abnormal sound due to running of the belt  24  is reduced when the following conditions are satisfied: the maximum dynamic friction coefficient μkmax is 0.54 or less and 0.10 or more, and the amplitude Δμk is 0.23 or less (preferably 0.22 or less) when the speed of the belt  24  is 3.54 mm/s. 
     For the belt #12, no abnormal sound occurred, but color shift occurred in an image formed using the belt #12. This is thought to be because slippage occurred between the inner surface of the belt  24  and the drive roller  19  since the dynamic friction coefficient μk between the belt  24  and the drive roller  19  was small. Thus, from the results for the belts #1 to #12, the occurrence of abnormal sound due to running of the belt  24  is reduced when the following conditions are satisfied: the maximum dynamic friction coefficient μkmax is 0.73 or less and 0.05 or more, and the amplitude Δμk is 0.51 or less (preferably 0.45 or less). Further, the occurrence of abnormal sound due to running of the belt  24  is reduced and the occurrence of color shift in the image is prevented when the following conditions are satisfied: the maximum dynamic friction coefficient μkmax is 0.73 or less and 0.10 or more, and the amplitude Δμk is 0.51 or less (preferably 0.45 or less). 
     The occurrence of abnormal sound due to running of the belt  24  is reduced when the following conditions are satisfied: the maximum dynamic friction coefficient μkmax is 0.73 or less and 0.06 or more, and the amplitude Δμk is 0.51 or less (preferably 0.45 or less) when the speed of the belt  24  is 0.2 mm/s. Further, the occurrence of abnormal sound due to running of the belt  24  is reduced and the occurrence of color shift in the image is prevented when the following conditions are satisfied: the maximum dynamic friction coefficient μkmax is 0.73 or less and 0.12 or more, and the amplitude Δμk is 0.51 or less (preferably 0.45 or less) when the speed of the belt  24  is 0.2 mm/s. 
     The occurrence of abnormal sound due to running of the belt  24  is reduced when the following conditions are satisfied: the maximum dynamic friction coefficient μkmax is 0.54 or less and 0.05 or more, and the amplitude Δμk is 0.23 or less (preferably 0.22 or less) when the speed of the belt  24  is 3.54 mm/s. Further, the occurrence of abnormal sound due to running of the belt  24  is reduced and the occurrence of color shift in the image is prevented when the following conditions are satisfied: the maximum dynamic friction coefficient μkmax is 0.54 or less and 0.10 or more, and the amplitude Δμk is 0.51 or less (preferably 0.45 or less) when the speed of the belt  24  is 3.54 mm/s. 
     The amplitude Δμk has no lower limit and can be equal to zero in principle. 
     Since the minimum dynamic friction coefficient μkmin is smaller than the maximum dynamic friction coefficient μkmax, the smaller the maximum dynamic friction coefficient μkmax is, the smaller the amplitude Δμk is. 
     As above, in this embodiment, an uneven shape is provided on the inner surface of the belt  24 . This reduces the contact area between the surfaces of the rollers and the inner surface of the belt  24 , and reduces electrostatic attractive force occurring between the rollers and the belt  24 , thereby lowering the maximum dynamic friction coefficient μkmax of the belt  24 . Further, the amplitude Δμk can be reduced. Thus, the occurrence of the stick-slip phenomenon can be reduced, and the occurrence of abnormal sound can be reduced. 
     Specifically, the belt  24  is configured to satisfy, with respect to each of the three rollers (the drive roller  19 , driven roller  20 , and backup roller  21 ) in contact with the inner surface of the belt  24 , the following conditions: the maximum dynamic friction coefficient μkmax is 0.73 or less and 0.10 or more, and the amplitude Δμk is 0.51 or less (preferably 0.45 or less). This reduces the occurrence of abnormal sound due to running of the belt  24 . 
     More specifically, the belt  24  is configured to satisfy, with respect to each of the three rollers, the following conditions: the maximum dynamic friction coefficient μkmax is 0.73 or less and 0.12 or more, and the amplitude Δμk is 0.51 or less (preferably 0.45 or less) when the speed of the belt  24  is 0.2 mm/s. In addition or alternatively, the belt  24  is configured to satisfy, with respect to each of the three rollers, the following conditions: the maximum dynamic friction coefficient μkmax is 0.54 or less and 0.10 or more, and the amplitude Δμk is 0.23 or less (preferably 0.22 or less) when the speed of the belt  24  is 3.54 mm/s. These reduce the occurrence of abnormal sound due to running of the belt  24 . 
     Further, in this embodiment, since an uneven shape is provided on the inner surface of the belt  24 , the surfaces of the rollers need neither be roughened nor undergo friction reducing treatment. Thus, the drive roller  19  can ensure the force for driving the belt  24  to run and drive the belt  24  to run stably without slippage of the belt  24 . In addition, if uneven shapes are formed on the surfaces of the rollers, they may affect the surface of the belt  24  and cause cleaning failure at the cleaning blade  28 . However, this embodiment can eliminate such a problem since no uneven shapes need to be formed on the surfaces of the rollers. Further, since there is no need to perform, on the inner surface of the belt  24 , a friction reducing treatment other than the formation of the uneven shape, it is possible to reduce the cost of the belt  24  and form the belt  24  easily. 
     Second Embodiment 
     A second embodiment will now be described. Descriptions of parts that are the same as in the first embodiment will be omitted or simplified in the description below, and the same reference characters will be used for elements that are the same as or correspond to those in the first embodiment. Parts that are the same as in the first embodiment provide the same advantages in the first embodiment. 
       FIG. 10  is a schematic view showing a printer  10  in the second embodiment. The printer  10  in the second embodiment is configured to transfer toner images formed on the photosensitive drums  11  of the image forming units Bk, Y, M, and C onto a sheet P. 
     In  FIG. 10 , the printer  10  includes the transfer unit u 1  disposed below the image forming units Bk, Y, M, and C. 
     The transfer unit u 1  includes a drive roller  59  as a first roller, a driven roller  60  as a second roller, an endless belt  64  as a transfer medium, transfer rollers  65  as transfer members, a cleaning blade  68  as a second cleaning member, and other components. The drive roller  59  is disposed below and near the image forming unit Bk, connected to the belt drive motor  82  as a drive unit for driving the belt  64 . The driven roller  60  is disposed below and near the image forming unit C. The belt  64  is stretched around the drive roller  59  and driven roller  60 , and is driven to run in the direction indicated by arrow C in  FIG. 10 . Each of the transfer rollers  65  is disposed to face the corresponding photosensitive drum  11  with the belt  64  therebetween. The cleaning blade  68  is disposed in contact with the belt  64  to face the drive roller  59  with the belt  64  therebetween. 
     The respective photosensitive drums  11 , belt  64 , and respective transfer rollers  65  form transfer portions. As the belt  64  runs, toner images of the respective colors formed on the respective photosensitive drums  11  are transferred onto a sheet P fed from the sheet cassette Ct in a superposed manner in the transfer portions, so that a color toner image is formed. 
     The printer  10  further includes a pair of conveying rollers m 3  that is connected to the conveying motor  83  and conveys a sheet P fed from the sheet cassette Ct, and a pair of conveying rollers m 4  that is connected to the conveying motor  83  and conveys a sheet P discharged from the fixing unit  17 . 
     The operation of the printer  10  will now be described. 
     In each of the image forming units Bk, Y, M, and C, the surface of the photosensitive drum  11  is uniformly charged by the charging roller  12 . Then, the respective LED heads ed are supplied with image data of the respective colors and driven to illuminate the photosensitive drums  11 , so that electrostatic latent images corresponding to the image data of the respective colors are formed on the surfaces of the respective photosensitive drums  11 . Then, in the respective image forming units Bk, Y, M, and C, the toners of the respective colors are applied to the electrostatic latent images by the developing units  13 , so that toner images of the respective colors are formed. 
     Meanwhile, a sheet P is taken from the sheet cassette Ct, conveyed by the pair of conveying rollers m 3 , and fed to the transfer unit u 1 . 
     In the transfer unit u 1 , the belt  64  is driven by the drive roller  59  and conveys the fed sheet P in the direction of arrow C. As the sheet P is conveyed on the belt  64 , the toner images of the respective colors are sequentially transferred onto the sheet P in a superposed manner by the respective transfer rollers  65 , so that a color toner image is formed on the sheet P. 
     Then, the sheet P is conveyed to the fixing unit  17 , in which the color toner image is fixed to the sheet P, so that a color image is formed on the sheet P. Then, the sheet P is discharged outside the apparatus main body and is stacked on the stacker Sk. 
     The transfer unit u 1  will now be described. 
       FIG. 11  shows the transfer unit in the second embodiment. 
     In  FIG. 11 , the transfer unit u 1  includes the flanges  31  as the restriction members (or guide members), drive roller  59 , driven roller  60 , belt  64 , cleaning blade  68 , and a support member  70  that supports the cleaning blade  68 . The driven roller  60  is provided with a spring  62  as a tension applying unit or a stretching device that applies tension to the belt  64 . The spring  62  is disposed between a support member Fr 2  provided in the apparatus main body and a shaft sh 2  of the driven roller  60 , and urges the driven roller  60  in a direction away from the drive roller  59  with a predetermined stretching force. 
     In this embodiment, the belt  64  is configured to satisfy, with respect to each of the two rollers (the drive roller  59  and driven roller  60 ) in contact with the inner surface of the belt  64 , the following conditions: the maximum dynamic friction coefficient μkmax is 0.73 or less and 0.10 or more, and the amplitude Δμk is 0.51 or less (preferably 0.45 or less). This makes it possible to reduce the occurrence of abnormal sound due to running of the belt  64 . 
     The belt  64  is configured to satisfy, with respect to each of the two rollers, the following conditions: the maximum dynamic friction coefficient μkmax is 0.73 or less and 0.12 or more, and the amplitude Δμk is 0.51 or less (preferably 0.45 or less) when the speed of the belt  64  is 0.2 mm/s. In addition or alternatively, the belt  64  is configured to satisfy, with respect to each of the two rollers, the following conditions: the maximum dynamic friction coefficient μkmax is 0.54 or less and 0.10 or more, and the amplitude Δμk is 0.23 or less (preferably 0.22 or less) when the speed of the belt  64  is 3.54 mm/s. This makes it possible to reduce the occurrence of abnormal sound due to running of the belt  64 . 
     Although the flanges  31  are provided on the drive roller  59 , such flanges may be provided on the driven roller  60  or on both the drive roller  59  and the driven roller  60 . Further, although the flanges  31  are provided at the both ends of the drive roller  59 , such flanges may be provided at only one end of the drive roller  59 . 
     Although each of the first and second embodiments illustrates the printer  10  as an image forming apparatus, the present invention is applicable to other types of image forming apparatus such as a copier, a facsimile machine, a multi-function peripheral. 
     Although the first and second embodiments illustrate the transfer belts  24  and  64 , the present invention is applicable to other types of endless belts such as a photosensitive belt, a fixing belt, or a conveying belt. 
     Further, each of the first and second embodiments illustrates a case where the belt satisfies the conditions with respect to each of the rollers in contact with the belt. However, the belt may satisfy the conditions with respect to each of at least one of the rollers in contact with the belt. With this configuration, for the at least one roller, the occurrence of abnormal sound can be reduced. 
     While the preferred embodiments of the present invention have been illustrated in detail, it should be apparent that modifications and improvements may be made to the invention without departing from the spirit and scope of the invention as described in the following claims.