JP2014235350A - Belt heating device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To heat an endless belt in a shorter period of time.SOLUTION: A belt heating device 10 comprises: a heat transfer member 11; and a surface heater 12. The heat transfer member 11 is in pressure contact with an inner peripheral surface of a heated belt 23 which is extended in such a manner that it is freely movable in a loop-shaped route. The pressure contact surface 111 of the heat transfer member 11, which is in contact with the inner peripheral surface of the heated belt 23, is a convex surface curved along a moving direction 91 of the heated belt 23. The surface heater 12 is in contact with a contact surface 112 of the heat transfer member 11 and heats the heat transfer member 11. The surface heater 12 has line-shaped heat generating bodies 121, 122 extended in a width direction of the heated belt 23. A heat generating bodies 121, 122 are disposed at the ends in the perpendicular direction 93 to a width direction of the surface heater 12.

Description

  The present invention relates to a belt heating device configured such that a planar heater heats an endless belt via a heat transfer member.

  Among the fixing devices mounted on the electrophotographic image forming apparatus, there are a fixing roller, a belt heating device, an endless belt stretched between the fixing roller and the belt heating device, and a pressure contact with the fixing roller across the endless belt. There is a configuration in which an unfixed toner is fixed to a sheet by heating and pressing a sheet passing between the endless belt and the pressure roller.

  As a belt heating device provided in such a fixing device, for example, a heat transfer member and a ceramic heater are provided, and the heat transfer member is a convex surface having a curved pressure contact surface with the inner peripheral surface of the endless belt and is opposite to the convex surface. Some ceramic heaters are provided on the flat surface of the heat transfer member (see, for example, Patent Document 1). In this belt heating device, since the heat generated by the ceramic heater is configured to be transmitted to the endless belt via the heat transfer member, the endless belt is compared with the configuration in which heat is conducted using the heating roller. Heating time is shortened.

Japanese Patent No. 4796177

  However, in the conventional belt heating apparatus described in Patent Document 1, in order to efficiently conduct heat to the endless belt, it is preferable to uniformly press the heat transfer member and the endless belt. Need to be small. For this reason, in the ceramic heater, the heat transfer member between the ceramic heater and the endless belt is thicker at the center in the direction perpendicular to the width direction of the endless belt than at the end. Therefore, when the heating element is disposed in the central portion in the orthogonal direction, the heat conduction path from the ceramic heater to the endless belt becomes longer, and the heating time of the endless belt becomes longer.

  The objective of this invention is providing the belt heating apparatus which can shorten the heating time of an endless belt more.

  The belt heating device of the present invention includes a heat transfer member and a planar sheet heater. The heat transfer member is in pressure contact with the inner peripheral surface of the endless belt that is movably stretched around the loop path. The pressure contact surface of the heat transfer member with the inner peripheral surface of the endless belt is a convex surface curved along the moving direction of the endless belt. The planar heater abuts against a contact surface that is the surface opposite to the pressure contact surface of the heat transfer member to heat the heat transfer member. The planar heater has a linear heating element extending in the width direction of the endless belt. A heat generating body is arrange | positioned in the edge part of the orthogonal | vertical direction with respect to the said width direction in a planar heater.

  In this configuration, the heat transfer member between the planar heater and the endless belt is thinner at the end of the planar heater in the orthogonal direction than at the center. Since the heat generating member is disposed at the end portion in the orthogonal direction where the heat transfer member is thin, the heat conduction path from the heat generating member to the endless belt is shortened as compared with the case where the heat generating member is disposed at the center portion.

  In the above-described configuration, the heat transfer member preferably has a concave portion extending in the width direction at a central portion in the orthogonal direction of the contact surface.

  In this configuration, the concave portion is provided on the central portion side of the heating element in the orthogonal direction, so that the thermal conduction from the heating element to the central portion side is limited, and the thermal conduction path from the heating element to the endless belt is the shortest path. Be directed. Moreover, the heat capacity of the heat transfer member is reduced.

  Further, it is preferable that the planar heater is fixed to the contact surface at both end portions straddling the concave portion in the orthogonal direction.

  Further, the heating elements are arranged at both ends of the planar heater in the orthogonal direction, and are electrode lines for supplying power to the heating elements, and for heating only a part of the heating elements in the width direction. However, it can be configured to be provided between the heating elements in the orthogonal direction.

  In this configuration, only a part of the endless belt in the width direction can be heated. For this reason, even when a toner image is fixed on a small size paper, it is possible to prevent overheating of the sheet heater in a portion where the paper does not pass in the width direction. In addition, since the electrode wires are provided between the heating elements in the orthogonal direction, the space in the planar heater is effectively utilized, and an increase in the size of the planar heater is suppressed.

  Moreover, it is preferable that the press-contact surface of a heat-transfer member has a small diameter part with a smaller curvature radius than a center part in the said moving direction in both ends.

  In this configuration, when the heat transfer member between the planar heater and the endless belt becomes thin, the radius of curvature of the pressure contact surface excluding the small diameter portion increases in the moving direction, but the small diameter portions are formed at both ends of the pressure contact surface. By providing, even if a heat-transfer member becomes thin, the bending degree of the endless belt in the both ends of a press-contact surface is eased, and the crack of an endless belt is suppressed. Further, by reducing the thickness of the heat transfer member, the heat conduction path from the heating element to the endless belt is shortened. Therefore, the heat conduction path from the heating element to the endless belt can be shortened while suppressing cracking of the endless belt.

  Further, by increasing the radius of curvature of the pressure contact surface, the contact pressure between the endless belt and the heat transfer member in the vicinity of the central portion of the small diameter portion in the moving direction forms the entire area of the pressure contact surface with the same curvature radius. It becomes higher than the case. For this reason, the thermal conductivity by contact also improves. Furthermore, since the heating element is arranged at the end of the planar heater in the orthogonal direction, the heat conduction efficiency in the short heat conduction path from the heating element to the endless belt can be increased.

  According to this invention, the heating time of the endless belt can be further shortened.

1 is a cross-sectional view illustrating a schematic configuration of an image forming apparatus including a fixing device having a belt heating device according to an embodiment of the present invention. FIG. 3 is an enlarged cross-sectional view of a fixing device. It is an expanded sectional view of a belt heating device. It is a block diagram of the planar heater with which a belt heating apparatus is equipped. It is sectional drawing of the belt heating apparatus which concerns on a comparative example. It is a block diagram of the planar heater with which the belt heating apparatus which concerns on the said comparative example is equipped. It is a figure which shows the experimental result about the time required to heat up a heating belt to predetermined temperature. It is sectional drawing of the belt heating apparatus which concerns on other embodiment.

  Below, belt heating device 10 concerning an embodiment of this invention is explained using a drawing. As an example, the belt heating device 10 is provided in a fixing device 20 mounted on an electrophotographic image forming apparatus 100.

  As shown in FIG. 1, in addition to the fixing device 20, the image forming apparatus 100 includes four image forming stations 30A, 30B, 30C, and 30D, an intermediate transfer unit 40, a secondary transfer unit 50, and a paper feed tray 60. It has.

  The image forming stations 30B to 30D are configured in the same manner as the image forming station 30A. The image forming station 30A forms a toner image having a black hue. The image forming stations 30B to 30D form images having hues of cyan, magenta, and yellow, respectively.

  The image forming station 30A includes a photosensitive drum 31A, and a charger 32A, an exposure unit 33A, a developing unit 34A, a primary transfer roller 35A, a cleaning unit 36A, and a static eliminator 37A arranged in this order around the photosensitive drum 31A. It has.

  The intermediate transfer unit 40 includes an intermediate transfer belt 41, a driving roller 42, and a driven roller 43. The intermediate transfer belt 41 is stretched between the driving roller 42 and the driven roller 43, and rotates along a predetermined loop path as the driving roller 42 rotates. The intermediate transfer belt 41 is disposed so as to face the photosensitive drums 31A of the four image forming stations 30A to 30D.

  The photosensitive drum 31A is an electrostatic latent image carrier. The charger 32A charges the peripheral surface of the photosensitive drum 31A to a predetermined potential. The exposure unit 33A forms an electrostatic latent image by irradiating the peripheral surface of the photosensitive drum 31A with laser light based on image data. The developing unit 34A supplies toner to the peripheral surface of the photosensitive drum 31A, thereby visualizing the electrostatic latent image and forming a toner image.

  The primary transfer roller 35A is disposed so as to face the photosensitive drum 31A with the intermediate transfer belt 41 interposed therebetween. The facing position between the photosensitive drum 31A and the primary transfer roller 35A in each of the image forming stations 30A to 30D is a primary transfer position. The primary transfer roller 35 </ b> A applies a predetermined voltage to primarily transfer the toner image on the photosensitive drum 31 </ b> A to the outer peripheral surface of the intermediate transfer belt 41. As the intermediate transfer belt 41 rotates, the toner images are transferred so as to overlap each other at each primary transfer position. The superimposed toner images are conveyed to a predetermined secondary transfer position by the rotational movement of the intermediate transfer belt 41.

  The cleaning unit 36A removes and collects residual toner from the peripheral surface of the photosensitive drum 31A after the toner image is transferred to the intermediate transfer belt 41. The static eliminator 37A sets the potential of the peripheral surface of the photosensitive drum 31A after the residual toner is removed and collected to 0V.

  The secondary transfer unit 50 includes a secondary transfer roller, and is arranged so that the secondary transfer roller is in pressure contact with the driving roller 42 with the intermediate transfer belt 41 interposed therebetween. The pressure contact position between the secondary transfer roller and the intermediate transfer belt 41 is the secondary transfer position. A sheet is conveyed from the sheet feed tray 60 to the secondary transfer position at a predetermined timing. The secondary transfer unit 50 secondarily transfers the toner image on the outer peripheral surface of the intermediate transfer belt 41 to the sheet at the secondary transfer position by applying a predetermined voltage to the secondary transfer roller. The sheet on which the toner image is transferred is conveyed to the fixing device 20.

  The fixing device 20 heats and pressurizes the paper to melt and fix the unfixed toner to the paper, thereby firmly fixing the toner to the paper. The paper on which the image is formed is discharged to the paper discharge tray 70.

  As shown in FIG. 2, the fixing device 20 includes a fixing roller 21, a pressure roller 22, a heating belt 23, a belt heating device 10, and a temperature detection sensor (not shown).

  The heating belt 23 is constituted by an endless belt, is stretched between the fixing roller 21 and the belt heating device 10, and rotates and moves on the loop path as the fixing roller 21 rotates. For example, as the heating belt 23, a polyimide base material having a thickness of 70 μm, an elastic layer made of silicon rubber having a thickness of 150 μm provided on the outer peripheral surface of the base material, and a thickness of 20 μm covering the outer peripheral surface of the elastic layer The thing provided with the mold release layer comprised by this PFA tube is used. As the heating belt 23, a belt having a two-layer structure without an elastic layer can be used.

  The belt heating device 10 is in pressure contact with the inner peripheral surface of the heating belt 23 and heats the heating belt 23 from the inner peripheral surface. A control unit (not shown) controls the belt heating device 10 based on the temperature information of the heating belt 23 detected by the temperature detection sensor. Details of the configuration of the belt heating device 10 will be described later.

  The pressure roller 22 is in pressure contact with the fixing roller 21 with the heating belt 23 interposed therebetween. The pressure roller 22 has a heater lamp 221 inside. The heater lamp 221 heats the outer peripheral surface of the pressure roller 22 from the inside. The heater lamp 221 is controlled so that the outer peripheral surface of the pressure roller 22 has a predetermined temperature.

  While the sheet carrying the unfixed toner is conveyed between the pressure roller 22 and the heating belt 23, the unfixed toner is melted and pressed against the sheet, and the toner is firmly fixed to the sheet.

  As shown in FIG. 3, the belt heating device 10 includes a heat transfer member 11 and a planar heater 12.

  The heat transfer member 11 is formed of a material having high thermal conductivity. For example, the material of the heat transfer member 11 includes an aluminum material, a composite material with copper, and ceramics such as aluminum nitride.

  The heat transfer member 11 is disposed so that the pressure contact surface 111 is in pressure contact with the inner peripheral surface of the heating belt 23. The pressure contact surface 111 has a convex surface curved along the moving direction 91 of the heating belt 23. The cross section of the pressure contact surface 111 has a circular arc shape.

  The contact surface 112 which is the surface opposite to the pressure contact surface 111 in the heat transfer member 11 has a shape in which a concave portion 113 is provided on a flat surface. As described above, the heat transfer member 11 has a substantially bowl shape except for having the recess 113.

  The recess 113 extends along the width direction 92 of the heating belt 23 (a direction orthogonal to the paper surface in FIG. 3, see FIG. 4). In addition, the recess 113 is provided at the center of the contact surface 112 in the direction 93 perpendicular to the width direction 92. The orthogonal direction 93 is a direction in a plane parallel to the contact surface 112.

  The planar heater 12 has a planar shape and is in contact with the contact surface 112 of the heat transfer member 11. The planar heater 12 is fixed to the abutting surface 112 at both end portions straddling the recess 113 in the orthogonal direction 93. For this reason, although the recessed part 113 extended in the width direction 92 is provided in the heat-transfer member 11, the intensity | strength with respect to the bending along the orthogonal direction 93 of the heat-transfer member 11 improves. Therefore, the contact property of the heat transfer member 11 with respect to the heating belt 23 when the heat transfer member 11 is brought into pressure contact with the heating belt 23 can be improved.

  The heat transfer member 11 and the planar heater 12 are fixed at the center in the width direction 92, and fixed at both ends with a contact pressure that can absorb the difference in elongation between the heat transfer member 11 and the planar heater 12. It is preferable to do. This is to prevent deformation due to expansion in consideration of the difference in linear expansion coefficient between the heat transfer member 11 and the planar heater 12.

  As shown in FIGS. 3 and 4, the planar heater 12 includes linear heating elements 121 and 122 extending in the width direction 92. In this embodiment, a steel heater is used as the planar heater 12, and heating elements 121 and 122 are provided on the surface of a stainless steel plate via an insulating layer.

  The heating elements 121 and 122 are disposed at the end portions of the planar heater 12 in the direction 93 perpendicular to the width direction 92. In this embodiment, the heating elements 121 and 122 are respectively disposed at both ends of the planar heater 12 in the orthogonal direction 93. In addition, the orthogonal direction 93 with respect to the width direction 92 in the contact surface 112 and the orthogonal direction 93 with respect to the width direction 92 in the planar heater 12 are the same. In this embodiment, as the heating elements 121 and 122, a resistor based on silver palladium is used. The lengths of the heating elements 121 and 122 in the width direction 92 are 366 mm, and the length in the orthogonal direction 93 is 15.8 mm.

  The heating elements 121 and 122 generate heat when supplied with power. As a result, the heating elements 121 and 122 heat the heat transfer member 11, and the heat transfer member 11 heats the heating belt 23. Thus, the heat generated from the heating elements 121 and 122 is conducted to the heating belt 23 through the heat transfer member 11.

  The heat transfer member 11 between the planar heater 12 and the heating belt 23 is thinner at the end of the planar heater 12 in the orthogonal direction 93 than at the center. Since the heat generating members 121 and 122 are disposed at the end portions in the thin orthogonal direction 93 of the heat transfer member 11, the heat conduction from the heat generating members 121 and 122 to the heating belt 23 as compared with the case where the heat generating members 11 and 122 are disposed at the center portion. The route becomes shorter. Therefore, the heating time of the heating belt 23 can be shortened.

  In addition, by providing the recess 113 on the center side with respect to each of the heating elements 121 and 122 in the orthogonal direction 93, thermal conduction from the heating elements 121 and 122 to the center side is limited, and the heating elements 121 and 122. To the heating belt 23 is directed to the shortest path. Moreover, the heat capacity of the heat transfer member 11 is reduced. Therefore, the heating time of the heating belt 23 can be further shortened.

  As shown in FIG. 4, the end portions of the heating elements 121 and 122 in the width direction 92 are connected to the first power supply terminal 123, respectively. In addition, a second power supply terminal 124 is provided between the heating element 121 and the heating element 122 in the orthogonal direction 93. The power supply terminals 123 and 124 are connected to the power source of the image forming apparatus 100 via connection terminals (not shown).

  A heating region changing electrode 125 is provided in a portion corresponding to the edge of the small size paper in the width direction 92. The heat generating region changing electrode 125 is provided in the orthogonal direction so as to span the heat generating member 121 and the heat generating member 122. Further, the heat generating region changing electrodes 125 are respectively connected to the second power supply terminals 124 by electrode wires 126 provided so as to extend in the width direction 92 between the heat generating elements 121 and 122 in the orthogonal direction 93. .

  When power supply from the first power supply terminal 123 is stopped and power is supplied from the second power supply terminal to the heat generating elements 121 and 122, only a part of the heat generating elements 121 and 122 in the width direction 92 generates heat. As a result, when forming an image on small-size paper, only the portion of the heating elements 121 and 122 facing the small-size paper in the width direction 92 can generate heat.

  For this reason, even when the toner image is fixed on the small size paper, it is possible to prevent the sheet heater 12 from overheating in the width direction 92 where the paper does not pass. Further, since the electrode wire 126 is provided between the heating elements 121 and 122 in the orthogonal direction 93, the space in the planar heater 12 is effectively utilized, and the increase in size of the planar heater 12 is suppressed.

  It should be noted that the heat generating area changing electrode 125 can be additionally installed at different locations in the width direction 92 so that the heat generating areas of the heat generating elements 121 and 122 can be switched corresponding to a larger number of sheets.

  As shown in FIGS. 5 and 6, in the belt heating device 80 according to the comparative example, the heat transfer member 81 does not include a recess, and the heating element 821 is provided at the center of the planar heater 82 in the orthogonal direction 93. It has been.

  The heat transfer member 81 between the sheet heater 82 and the heating belt 23 is thicker at the center of the sheet heater 82 in the orthogonal direction 93 than at the end. In the belt heating device 80, since the heat generating member 821 is disposed at the central portion in the orthogonal direction 93 where the heat transfer member 81 is thick, the heat generating member 821 is arranged from the heat generating member 821 to the heating belt 23 as compared with the case where it is disposed at the end. The heat conduction path becomes longer.

  In contrast, in the belt heating apparatus 10 of the present invention, as described above, since the heat transfer members 11 and 122 are arranged at the end portions in the orthogonal direction 93 where the heat transfer member 11 is thin, the heat conduction path is shortened. Therefore, according to the belt heating device 10, the heating time of the heating belt 23 can be shortened.

  Further, in the belt heating device 80 according to the comparative example, the heat transfer member 81 does not have the recess 113, so that the direction of the heat conduction path from the heating element 821 to the heating belt 23 is wide. In addition, the heat capacity of the heat transfer member 81 is larger than when the recess is provided.

  On the other hand, in the belt heating apparatus 10 of the present invention, as described above, the recess 113 is provided on the center side with respect to each of the heating elements 121 and 122 in the orthogonal direction 93, so that the heating elements 121 and 122 are provided. Therefore, the heat conduction from the heating elements 121 and 122 to the heating belt 23 is directed to the shortest path. Moreover, the heat capacity of the heat transfer member 11 is reduced. Therefore, according to the belt heating device 10, the heating time of the heating belt 23 can be further shortened.

  Further, in the belt heating device 80 according to the comparative example, since the electrode wire 826 for supplying power to the heat generating region changing electrode 825 is provided on the side of the heat generating element 821 in the orthogonal direction 93, the planar heater 82 is enlarged. There is a fear.

  On the other hand, in the belt heating apparatus 10 of the present invention, as described above, the electrode wire 126 is provided between the heating elements 121 and 122 in the orthogonal direction 93, so that the space in the planar heater 12 is effectively utilized. Thus, an increase in the size of the planar heater 12 is suppressed.

  FIG. 7 shows experimental results comparing the belt heating device 10 according to the example and the belt heating device 80 according to the comparative example with respect to the time required to raise the temperature of the heating belt 23 to a predetermined temperature. In this experiment, 820 W was fed to the planar heater, and the time from the start of feeding until the heating belt 23 reached 160 ° C. was measured. The heat transfer member 11 of the belt heating device 10 was 35.8 g, and the heat transfer member 81 of the belt heating device 80 was 41.2 g. This difference in weight is due to whether or not there is a recess 113.

  As a result of the experiment, it was found that the belt heating device 80 took 33.7 seconds, whereas the belt heating device 10 took 30 seconds, and the heating time of the heating belt 23 could be shortened.

  Note that the temperature of the planar heaters 12 and 82 when the heating belt 23 reached 160 ° C. was 198 ° C. in the belt heating device 80, whereas that when the heating belt 23 reached 160 ° C. and 203 ° C. It was almost the same level.

  As shown in FIG. 8, in the belt heating device 10A according to another embodiment, the pressure contact surface 111 of the heat transfer member 11 has a small diameter portion 114 having a smaller radius of curvature than the central portion in the moving direction 91 at both ends. Except for this, the configuration is the same as that of the belt heating device 10.

  In the belt heating device 10 </ b> A, the radius of curvature at the center of the pressure contact surface 111 of the heat transfer member 11 is larger than the radius of curvature at both ends in the moving direction 91 of the heating belt 23.

  In this embodiment, the curvature radius of the central portion of the pressure contact surface 111 of the heat transfer member 11 in the moving direction 91 is 20 mm. In addition, the curvature radius of a center part can also be 20 mm or more.

  In the belt heating apparatus 10A, when the heat transfer member 11 between the planar heater 12 and the heating belt 23 becomes thin, the radius of curvature of the pressure contact surface 111 excluding the small diameter portion 114 increases in the moving direction 91. By providing the small-diameter portions 114 at both ends of 111, the degree of bending of the heating belt 23 at both ends of the pressure contact surface 111 is reduced even if the heat transfer member 11 becomes thin, and cracking of the heating belt 23 is suppressed. Further, by reducing the thickness of the heat transfer member 11, the heat conduction path from the heating elements 121 and 122 to the heating belt 23 is shortened. Therefore, the heat conduction path from the heating elements 121 and 122 to the heating belt 23 can be shortened while suppressing cracking of the heating belt 23.

  Further, by increasing the radius of curvature of the pressure contact surface 111, the contact pressure between the heating belt 23 and the heat transfer member 11 in the central portion side vicinity 115 of the small diameter portion 114 in the moving direction 91 is spread over the entire pressure contact surface 11. Compared with the case of forming with the same radius of curvature, it becomes higher. For this reason, the thermal conductivity by contact also improves. Further, since the heating elements 121 and 122 are arranged at the end portions of the planar heater 12 in the orthogonal direction 93, the heat conduction efficiency in the short heat conduction path from the heating elements 121 and 122 to the heating belt 23 can be increased. .

  In the belt heating devices 10 and 10A according to the above-described embodiment, the heating elements 121 and 122 are disposed at both ends of the planar heater 12 in the orthogonal direction 93, respectively, but are disposed only at one end. Even in this case, the effect that the heating time of the heating belt 23 can be shortened can be obtained.

  The belt heating device according to the present invention is not limited to being provided in a fixing device mounted on an electrophotographic image forming apparatus, and can also be applied to devices other than the fixing device.

  The above description of the embodiment is to be considered in all respects as illustrative and not restrictive. The scope of the present invention is shown not by the above embodiments but by the claims. Furthermore, the scope of the present invention is intended to include all modifications within the meaning and scope equivalent to the scope of the claims.

DESCRIPTION OF SYMBOLS 10,10A Belt heating apparatus 11 Heat-transfer member 111 Pressure contact surface 112 Contact surface 113 Recessed part 12 Planar heater 121,122 Heating element 126 Electrode wire 20 Fixing device 23 Heating belt 91 Movement direction 92 Width direction 93 Orthogonal direction

Claims (5)

A heat transfer member that is in pressure contact with an inner peripheral surface of an endless belt that is movably stretched in a loop path, and the pressure contact surface with the inner peripheral surface is a convex surface that is curved along the moving direction of the endless belt. A thermal member;
A planar surface heater that heats the heat transfer member in contact with a contact surface that is the surface opposite to the pressure contact surface of the heat transfer member;
The planar heater has a linear heating element extending in the width direction of the endless belt,
The said heating element is a belt heating apparatus arrange | positioned at the edge part of the said planar heater at the orthogonal direction with respect to the said width direction.   The belt heating device according to claim 1, wherein the heat transfer member has a recess extending in the width direction at a central portion of the contact surface in the orthogonal direction.   The belt heating device according to claim 2, wherein the planar heater is fixed to the contact surface at both end portions straddling the concave portion in the orthogonal direction. The heating elements are respectively disposed at both ends of the planar heater in the orthogonal direction,
The electrode wire for supplying electric power to the heating element for heating only a part of the heating element in the width direction is provided between the heating elements in the orthogonal direction. 4. The belt heating device according to any one of items 1 to 3.   The belt heating device according to any one of claims 1 to 4, wherein the pressure contact surface has a small diameter portion having a smaller radius of curvature than a central portion at both ends in the moving direction.

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