Patent Publication Number: US-6216512-B1

Title: Method and apparatus for forming a processed portion of a workpiece

Description:
This application is a Continuation-in-Part of U.S. application Ser. No. 09/192,403, filed Nov. 16, 1998, now U.S. Pat. No. 6,067,833 which is incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of Invention 
     The invention relates to a method for forming a portion of a workpiece, such as a cylinder or shell, and an apparatus therefor, especially the method and apparatus for forming the portion of the workpiece by spinning to form a changed diameter portion having a central axis that is at least one of offset from and oblique to a central axis of an unprocessed portion of the workpiece. 
     2. Description of Related Art 
     In Japanese Patent Laid-open Publication No. 3-226327, disclosed is a method for forming an end portion of a cylindrical member (hereinafter, simply referred to as a cylinder) made of metal to form a reduced diameter portion on the end portion. According to the Publication, a spinning process is performed by supporting the cylinder with a chuck and rotating it about its axis, and moving a roller for forming toward the axis to reduce the diameter of the cylinder, thereby to form the reduced diameter portion having a neck portion and a tapered portion. In general, the spinning process is employed to form a plate into a shell. Likewise, a flange and neck portion can be formed by spin flow forming into a cylindrical can body, as disclosed in U.S. Pat. No. 4,563,887. Furthermore, a computerized spinning machine has been proposed in Japanese Patent No. 2,534,530. 
     Recently, it has been requested to form a reduced diameter end portion having an oblique axis inclined against the central axis of the metal cylinder. When the metal cylinder is used for an outer shell of a muffler of an automotive vehicle, for example, the cylinder will be easily mounted in a vehicle. Also, when the metal cylinder is used for a housing of a catalytic converter, it will be easily located near an engine, to reduce the time of increasing the temperature of the catalyst. Furthermore, dual converters may be easily assembled, with their neck portions positioned close to each other. 
     According to the prior methods for forming the cylinder or shell by the spinning process, the reduced diameter portion was formed to be coaxial with the main body of the cylinder, but the reduced diameter end portion having the oblique axis could not be formed. In order to produce the cylinder like the shell or housing as described above, therefore, the portions corresponding to the main body and the reduced diameter portion were formed by press working, and then these components were connected together by welding or the like. According to these methods, however, the produced cylinder can not be expected to be so strong, comparing with that of the integral construction. Furthermore, they need the connecting process, different from the forming process, so that it is difficult to produce the cylinder by those methods, and it is almost impossible to produce the cylinder by the computerized forming process as described in the prior publication. As a result, the manufacturing cost of the cylinder shall be increased, comparing with the cylinder of the coaxial type formed by the spinning process. 
     SUMMARY OF THE INVENTION 
     Accordingly, it is an object of the invention to provide a method for forming a changed diameter portion of a workpiece having a central axis that is at least one of offset from and oblique to a central axis of an unprocessed portion of the workpiece, easily and properly by a spinning process. 
     It is another object of the invention to provide an apparatus for forming a changed diameter portion having a central axis at least one of offset from and oblique to a central axis of an unprocessed portion of the workpiece, easily and properly by a spinning process. 
     In accomplishing the above and other objects, the method for forming the changed diameter portion of the workpiece by spinning may comprise supporting the workpiece so that a central axis of the portion to be processed is at least one of offset from and oblique to a forming target axis and molding the portion to be processed by a spinning process so that the central axis of the portion to be processed is matched to the forming target axis and simultaneously changing the diameter of the portion to be processed. 
     The apparatus for forming the changed diameter portion of the workpiece by spinning may comprise devices for performing the steps as described above. For example, the apparatus may include at least one roller operatively mounted on a rotatable member rotatable about a main axis to be radially movable to and from the main axis, and in contact with a surface of the portion to be processed. In the apparatus, a first driving device may be provided for moving at least one of the workpiece and the at least one roller relative to each other so that a central axis of the portion to be processed is at least one of offset from and oblique to a forming target axis that at least partially overlaps the main axis. A second driving device may be provided for moving the at least one roller radially toward the forming target axis, with the at least one roller being in substantial contact with a surface of the portion to be processed, and rotating the at least one roller about the main main axis relative to the workpiece. A controller controls the first and second driving devices to form the portion to be processed into a changed diameter portion having the forming target axis. 
     According to the method and apparatus as described above, the changed diameter portion may be formed to provide a tapered portion, with the diameter of the workpiece gradually changed from an unprocessed portion toward an end of the changed diameter portion. The changed diameter portion may be formed to provide the tapered portion and a neck portion of a tubular configuration extending from the tapered portion. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above stated objects and following descriptions will become readily apparent with reference to the accompanying drawings, wherein like reference numerals denote like elements, and in which: 
     FIG. 1 is a schematic block diagram illustrating a spinning apparatus according to an embodiment of the invention; 
     FIG. 2 is a side view of a spinning apparatus with a portion thereof sectioned according to an embodiment of the invention; 
     FIG. 3 is a plan view of a spinning apparatus with a portion thereof sectioned according to an embodiment of the invention; 
     FIG. 4 is a perspective view showing a clamp section according to an embodiment of the invention; 
     FIG. 5 is a perspective view of a finished cylinder according to an embodiment of the invention; 
     FIG. 6 is a plan view of a cylinder showing a first spinning process applied thereto according to an embodiment of the invention; 
     FIG. 7 is a plan view of a cylinder showing a first spinning process applied thereto according to an embodiment of the invention; 
     FIG. 8 is a plan view of a cylinder formed by a first spinning process according to an embodiment of the invention; 
     FIG. 9 is a plan view of a cylinder showing a second spinning process applied thereto according to an embodiment of the invention; 
     FIG. 10 is a plan view of a cylinder showing a second spinning process applied thereto according to an embodiment of the invention; 
     FIG. 11 is a plan view of a cylinder showing a second spinning process applied thereto according to an embodiment of the invention; 
     FIG. 12 is a plan view of a cylinder showing a second spinning process applied thereto according to an embodiment of the invention; 
     FIG. 13 is a plan view of a cylinder showing a second spinning process applied thereto according to an embodiment of the invention; 
     FIG. 14 is a plan view of a cylinder formed by a second spinning process according to an embodiment of the invention; 
     FIG. 15 is a plan view of a cylinder showing a second spinning process applied thereto according to an embodiment of the invention; 
     FIG. 16 is a plan view of a cylinder showing a second spinning process applied thereto according to an embodiment of the invention; 
     FIG. 17 is a plan view of a cylinder formed by a second spinning process according to an embodiment of the invention; 
     FIG. 18 is a flowchart showing a spinning process according to an embodiment of the invention; 
     FIG. 19 is a side view of a finished cylinder according to an embodiment of the invention; 
     FIG. 20 is a side view of dual converters for use in an exhaust purifying system employing a cylinder formed according to an embodiment of the invention; 
     FIG. 21 is a side view of a spinning apparatus with a portion thereof sectioned according to another embodiment of the invention; 
     FIG. 22 is a plan view of a spinning apparatus with a portion thereof sectioned according to another embodiment of the invention; 
     FIG. 23 is a diagram showing a basic concept for reducing the diameter of an end portion of a cylinder formed according to an embodiment of the spinning apparatus; 
     FIG. 24 is a front view and side view of an end portion of a cylinder formed according to an embodiment of the spinning apparatus; 
     FIG. 25 is a plan view of a cylinder showing a third spinning process applied thereto according to an embodiment of the invention; 
     FIG. 26 is a plan view of a cylinder showing a third spinning process applied thereto according to an embodiment of the invention; 
     FIG. 27 is a plan view of a cylinder showing a third spinning process applied thereto according to an embodiment of the invention; 
     FIG. 28 is a plan view of a cylinder showing a third spinning process applied thereto according to an embodiment of the invention; 
     FIG. 29 is a plan view of a cylinder showing a third spinning process applied thereto according to an embodiment of the invention; 
     FIG. 30 is a side view of a spinning apparatus with a portion thereof sectioned according to a further embodiment of the invention; 
     FIG. 31 is a plan view of a spinning apparatus with a portion thereof sectioned according to a further embodiment of the invention; 
     FIG. 32 is a plan view of a cylinder showing a bending process applied thereto according to a further embodiment of the invention; 
     FIG. 33 is a plan view of a cylinder a showing a bending process applied thereto according to a further embodiment of the invention; 
     FIG. 34 is a plan view of a cylinder bent and reduced by a bending process according to a further embodiment of the invention; 
     FIG. 35 is a plan view of a cylinder bent and reduced by a bending process and spinning process according to a further embodiment of the invention; 
     FIG. 36 is a plan view of a cylinder showing a bending process applied thereto according to a further embodiment of the invention; 
     FIG. 37 is a plan view of a cylinder bent and reduced at its opposite ends by a bending process and spinning process according to a further embodiment of the invention; 
     FIG. 38 is a schematic block diagram illustrating a spinning apparatus according to an embodiment of the present invention; 
     FIG. 39 is a side view of a spinning apparatus with a portion thereof sectioned according to an embodiment of the present invention; 
     FIGS. 40 and 41 are front and top views, respectively, of a cylinder set so with a central axis of the portion to be processed offset from a forming target axis in a first direction; 
     FIGS. 42 and 43 are front and side views, respectively, of a cylinder set with a central axis of the portion to be processed offset from a forming target axis in a second direction; 
     FIGS. 44 and 45 are front and top views, respectively, of a cylinder set with a central axis of the portion to be processed oblique to a forming target axis; 
     FIGS. 46 and 47 are front and top views, respectively, of a cylinder set with a central axis of the portion to be processed skewed relative to a forming target axis; 
     FIGS. 48A-48D illustrate a spinning process according to an exemplary embodiment of the invention; 
     FIGS. 49-51 are top, front, and side views, respectively, of a cylinder having a changed diameter portion with a central axis skewed relative to a central axis of an unprocessed portion; 
     FIGS. 52A-52C illustrate a spinning process according to an exemplary embodiment of the invention; and 
     FIG. 53 illustrates a spinning process according to an exemplary embodiment of the invention. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     Referring to FIGS. 1-3, there is schematically illustrated a spinning apparatus according to an embodiment of the invention, which is adapted to configure an end portion of a cylindrical member  4  (i.e., cylinder) having a central axis Xt and an oblique axis Xe inclined against the axis Xt, as shown in FIG. 5, to be used for an outer shell (not shown) of a muffler for an automobile, a case (not shown) of a catalytic converter, or the like. The cylinder to be formed according to the invention is the one made of stainless steel, while it is not limited to this, and may be selected from other metallic cylinders. In FIGS. 1-3, the spinning apparatus according to the invention includes a first driving mechanism  2  and a second driving mechanism  3 , both of which are operatively mounted on a base  1 . 
     In the first driving mechanism  2 , a central axis Xt of a cylinder  4  is employed as X-axis, in parallel with which a pair of X-axis guide rails  5  are fixedly secured to one side (right side in FIGS. 2 and 3) on the base  1 . A case  20  is arranged to be movable along the X-axis guide rails  5 . The case  20  has a ball socket  7  secured under its base, which is engaged with a spline shaft  8 . This shaft  8  is mounted on the base  1  in parallel with the X-axis guide rails  5 , to be rotated by a servo motor  9 . Accordingly, when the spline shaft  8  is rotated by the servo motor  9 , the case  20  is moved along the X-axis. On the other hand, a bed la is formed on the other side (left side in FIGS. 2 and 3) of the base  1 . Fixedly secured to the bed la are a pair of Y-axis guide rails  10 , on which a pair of sliders  11  for supporting a sliding table  6  and a clamp device  12  are movably mounted, respectively. The clamp device  12  includes a lower clamp  13  rotatably mounted on the table  6 , and an upper clamp  17  arranged upward of the lower clamp  13 , to clamp the cylinder  4  between the lower clamp  13  and upper clamp  17 . The table  6  has a ball socket  14  secured thereunder, which is engaged with a spline shaft  15 . This shaft  15  is mounted on the base  1   a  in parallel with the Y-axis guide rails  10 , to be rotated by a servo motor  16 . When the spline shaft  15  is rotated by the motor  16 , the table  6  and clamp device  12  are moved along the Y-axis relative to the case  20 . A rotating device such as a motor  31  is embedded in the table  6 , and an output shaft  31  a of the motor  31  extends upward in FIG. 2, or vertically to the base  1 , to be engaged with the lower clamp  13 , which is rotated about the shaft  31   a . On the upper surface of the table  6 , there is formed a guide groove  32  which has a circular configuration with its center located on the shaft  3  la, and into which a guide roller  33  is fitted. The guide roller  33  is rotatably mounted on the lower clamp  13 , so that the lower clamp  13  is guided by the groove  32  to be rotated about the shaft  31   a.    
     Above the clamp device  12 , an actuator  18 , which is activated by oil pressure, for example, and which serves as a driving device, is arranged to support the upper clamp  17  and drive it vertically. When the cylinder  4  is set to or removed from the clamp device  12 , the upper clamp  17  is lifted by the actuator  18  upward. A clamp face  13   a  of a half cylinder configuration is formed on the upper surface of the lower clamp  13 , and a clamp face  17   a  of a half cylinder configuration is formed on the lower surface of the upper clamp  17 . Therefore, when the cylinder  4  is clamped between the clamp faces  13   a  and  17   a , it is secured not to be rotated or moved. On the clamp device  12 , a stopper  19  is disposed at the opposite side to the case  20 , to abut on a one end portion of the cylinder  4 . The stopper  19  is secured to the lower clamp  13 , so as to be movable together with the clamp device  12 . If the stopper  19  is connected to the lower clamp  13  to be adjustable along the central axis Xt of the cylinder  4 , positioning of the cylinder  4  in its axial direction can be made properly and easily. Accordingly, when the cylinder  4  is set on the clamp face  13   a  of the lower clamp  13 , with the one end portion of the cylinder  4  abutted on the stopper  19 , and then the upper clamp  17  is actuated to move downward by the actuator  18 , the cylinder  4  is clamped at a predetermined position between the lower clamp  13  and upper clamp  17 . In this case, the cylinder  4  is positioned such that its axis Xt is located on the same plane as the plane where the longitudinal central axis Xr of a main shaft  21 , which will be described later, is located in parallel with the base  1 , i.e., on the same height from the base  1  as the height of the axis Xr from the base  1 . 
     With respect to the second driving mechanism  3 , the main shaft  21  is positioned on the same plane as the plane, on which the axis Xt of the cylinder  4  is located, and which is parallel with the base  1 . The main shaft  21  is placed opposite to the cylinder  4 , and mounted on the case  20  to be rotated about its axis Xr by a motor  22 , which serves as the rotating device, through a connecting belt  23 . A rotary member  24  is secured to one end portion of the main shaft  21  opposite to the cylinder  4 , so that the rotary member  24  is rotated about the axis Xr in accordance with the rotation of the main shaft  21  about the axis Xr. The rotary member  24  is formed into a cylindrical case with a bottom, at the center of which the main shaft  21  is secured to the rotary member  24 . In the case  20 , a pair of actuators  25  of a pressure cylinder actuated by oil, air or the like are received and mounted on the case  20  through brackets  25   b . Each actuator  25  has a rod  25   a  slidably received therein in parallel with the axis Xr of the main shaft  21 , and moved back and forth in response to the pressurized oil or air fed into the actuator  25 . A force transmitting member  26  of a circular ring plate configuration is secured to the tip ends of the rods  25   a , and disposed within the rotary member  24  to be moved to and from the cylinder  4  in response to the sliding movement of the rods  25   a . The transmitting member  26  has a tapered surface  26   a  formed on the inner surface of its open end portion, extending toward its tip end to enlarge its inner diameter gradually. 
     As shown in FIGS. 2 and 4, a plurality of support members  27  (three support members in the present embodiment) are disposed around the periphery of the rotary member  24  with an even space defined between them, and operatively mounted on the rotary member  24  to be movable in parallel with the main shaft  21 , and movable in a radial direction to and from the central axis Xr of the main shaft  21 . Each support member  27  has a tapered surface  27   a  formed on the inner side of the rotary member  24  to abut on the tapered surface  26   a  of the transmitting member  26 . A roller  28  is mounted on the tip end of each support member  27  to be rotated about its axis. Also disposed in the rotary member  24  is a biasing device for urging each support member  27  toward the outer periphery of the rotary member  24 , such as a compression spring  29  as shown in FIG.  2 . Accordingly, when the transmitting member  26  is activated by the actuators  25  to move forward (leftward in FIG.  2 ), each support member  27  engaged with the transmitting member  26  through the tapered surfaces  26   a ,  27   a , and each roller  28  mounted on the support member  27  are moved in a radial direction toward the axis Xr of the main shaft  21 . Whereas, when the transmitting member  26  is retracted by the actuators  25  to move rearward (rightward in FIG.  2 ), each support member  27  and roller  28  are moved outwardly in a radial direction. 
     Only roller  28  may be provided, but it is preferable to provide a plurality of rollers, so as to reduce intermittent impacts. The course traced by the roller  28  is not necessarily limited to a straight line in the radial direction, but any course may be selected as long as the roller  28  can be moved to and from the axis Xr of the main shaft  21 . Instead of the actuator  25  of the pressure cylinder, other devices such as those of a screw type, lever type or the like may be employed as the device for actuating the roller  28 . As a further embodiment of the device for actuating the roller  28  to be moved in a radial direction toward the axis Xr, may be employed a mechanism having a main shaft of dual tubes, which are connected to the roller  28  through differential gear units (e.g., planetary gear system, not shown herein), respectively, and wherein the rotation of the main shaft will produce a difference between the rotational speeds of the tubes, so as to cause the roller  28  to be moved in the radial direction. 
     The motors  9 ,  16 ,  22 ,  31  and actuators  18 ,  25  are electrically connected to a controller CT as shown in FIG. 1, from which control signals are output to the actuators to control them numerically. The controller CT includes a central processor MP, memory ME, input interface IT and output interface OT, which are connected with each other through a bass bar, as shown in FIG.  1 . The central processor MP is adapted to execute a program for spinning according to the present embodiment, and the memory ME is adapted to memorize the program and temporarily memorize variable data needed to execute the program. An input device IP is connected to the input interface IT to input initial conditions, operating conditions or the like of each actuator into the central processor MP, e.g., by operating a key board or the like manually. There are provided various sensors (not shown), if necessary, and signals detected by those sensors are fed to the controller CT, in which the signals are input from the input interface IT to the central processor MP through amplifying circuits AD or the like. The control signals are output from the output interface OT and fed into the motors  9 ,  16 ,  22 ,  31  and actuators  18 ,  25 , through driving circuits AC 1  to AC 6 . Instead of the controller CT, a control circuit may be provided for each device to perform a predetermined individual control, respectively. 
     According to the spinning apparatus as constituted above, various methods can be contemplated for reducing the diameter of the end portion having the oblique axis. Referring to FIGS. 6-8, there will be explained an embodiment of the method for reducing the diameter of the end portion of the cylinder by the above-described spinning apparatus, to form the reduced diameter end portion having the oblique axis, by means of a single rotating process in setting the oblique axis. In FIG. 6, “C 0 ” indicates the center of rotating motion of the cylinder  4  held by the clamp device  12 , and rotated about the shaft  31   a  of motor  31 . “C 1 ” indicates the center of the innermost end section of the oblique end portion of the cylinder  4  to be formed. “R 1 ” is the distance between the centers C 0  and C 1 . 
     The axis Xr of the main shaft  21  is fixed on the plane in parallel with the base  1 , while the cylinder  4  is rotated about the shaft  31  a, i.e., center C 0 , to produce an oblique angle θ as shown in FIG.  6 . In this case, the oblique axis Xe in parallel with the axis Xr and including the center C 1  of the oblique end portion is apart from the axis Xr by a distance S in the direction perpendicular to the axis Xr, or parallel with the Y-axis. Therefore, the distance S is calculated as S=R 1 ·sin(θ). If each roller  28  is moved toward the axis Xr, it will trace each locus or path as indicated by two-dot chain lines in FIG. 6, whereby the end portion of the cylinder  4  will not be formed properly. In order to form a proper end portion, the main shaft  21  should be set on the axis Xe. Accordingly, the axis Xe is used for a forming target axis in this embodiment, so that the cylinder  4  is moved perpendicularly to the axis Xr along the Y-axis guide rails  10 , downward in FIG. 6, by the distance S. The geometric relationship between the main shaft  21  (represented by the axis Xr) and the cylinder  4  will be as shown in FIG. 7, wherein the axis Xr and the forming target axis Xe are overlapped. Thus, out of five paths shown by two-dot chain lines in FIG. 7, the last path indicates the configuration to be formed, which has the central axis corresponding to the forming target axis Xe, i.e., the oblique axis of the reduced diameter portion to be formed. As a result, the one end portion of the cylinder  4  is formed into the tapered portion  4   b  and neck portion  4   c  having the oblique axis Xe inclined against the central axis Xt of the cylinder  4  as shown in FIG.  8 . 
     In operation, referring to FIG. 2, when the upper clamp  17  is lifted upward, the cylinder  4  to be formed is placed on the clamp face  13   a  of the lower clamp  13 , and set at the predetermined position where the one end portion of the cylinder  4  is abutted on the stopper  19 . Then, the actuator  18  is driven, so that the upper clamp  17  is moved downward, and the cylinder  4  is clamped between the lower clamp  13  and upper clamp  17 , and held not to be rotated. In this case, the cylinder  4  is positioned such that the axis Xt of the cylinder  4  is aligned with the axis Xr of the main shaft  21 . The transmitting member  26  is positioned at a retracted position, i.e., the right side to the position as shown in FIG. 2, so that each roller  28  is retracted outside of the outer periphery of the cylinder  4 . Next, the motor  31  is driven to rotate the lower clamp  13  about the its output shaft  31   a  by the predetermined oblique angle θ. Since the guide roller  33  mounted on the lower clamp  13  is fitted into the guide groove  32  formed on the upper surface of the table  6 , the lower clamp  13  can be rotated along the guide groove  32  about the shaft  31   a  (i.e., the center C 0 ) to form the oblique angle θ between the axis Xr and the axis Xt as shown in FIG.  6 . Therefore, the oblique axis or forming target axis Xe is set. Then, the spline shaft  15  is rotated by the motor  16 , so that the clamp device  12  and the cylinder  4  are moved along the Y-axis guide rails  10  to position the forming target axis Xe in line with the axis Xr of the main shaft  21 . Accordingly, the forming target axis Xe and the axis Xr are overlapped, as shown in FIG.  7 . Next, the spline shaft  8  is rotated by the motor  9 , so that the case  20  is advanced along the X-axis guide rails  5  (moved leftward in FIGS.  2  and  3 ), and stopped at a position for starting the spinning process, which corresponds to the center C 1  in FIG. 7, and which position is set as an origin. 
     From the state as described above, the rotary member  24  is rotated by the motor  22 , and the transmitting member  26  is advanced by the actuator  25 , so that each roller  28  is moved toward the center of the rotary member  24 , or the axis Xr. At the same time, the spline shaft  8  is rotated by the motor  9 , the case  20  and the roller  28  are retracted along the X-axis guide rails  5  (rightward in FIGS.  2  and  3 ). Consequently, each roller  28  is rotated about its axis and rotated about the axis Xr of the main shaft  21 , which is overlapped with the forming target axis Xe in this case, simultaneously, and moved radially toward the axis Xe, being pressed to be in contact with the outer surface of the cylinder  4 , thereby to perform the spinning process. Thus, each roller  28  is started to move from the starting position, until the end portion of the cylinder is deformed by spinning, to form the tapered portion for the first cycle. In the case where each roller  28  is retracted further, exceeding the predetermined distance, the roller  28  is held to be in its state, so that the end portion of the cylinder  4  is deformed in accordance with the retracting movement of each roller  28  to form the cylindrical neck portion for the first cycle, which has the oblique axis inclined against the axis Xt by the oblique angle θ, and which is integrally connected to the smallest diameter side of the tapered portion  4   b.    
     Thereafter, the cylinder  4  and roller  28  are returned to the starting positions, thereby to provide a reciprocating motion together with the initial path for reducing the diameter of the cylinder  4 , so that the spinning process is completed. For simplifying the explanation about the spinning process, the operation for reducing the diameter is performed only in a single path of the reciprocating motion according to the present embodiment. However, the operation for reducing the diameter of the cylinder  4  may be performed in another path of the reciprocating motion as well, to perform the spinning process in both of the paths in one cycle, thereby to improve the forming efficiency. Furthermore, in view of the energy efficiency and tact-time, each roller  28  is continuously rotated about the axis Xr, without being stopped every cycle. 
     After the spinning process in the first cycle was completed and each roller  28  was returned to the starting position, the spinning process in the second cycle is performed. In practice, the spline shaft  8  is rotated by the motor  9 , the case  20  and each roller  28  are advanced, and stopped in the state where each roller  28  is located in a second position retracted from the tip end of the cylinder  4  by a predetermined length. Then, the rotary member  24  is rotated, and the transmitting member  26  is advanced, so that each roller  28  is driven radially toward the axis Xr, and then each roller  28  is retracted along the X-axis guide rails  5 , being pressed to be in contact with the outer surface of the cylinder  4  thereby to perform the spinning process. By repeating the process as described above three more times, in the present embodiment, the end portion of the cylinder  4  is formed into the reduced diameter portion  4   d  with the tapered portion  4   b  and neck portion  4   c  having the oblique axis as shown in FIG.  8 . 
     According to the above-described embodiment, the diameter of the end portion of the cylinder is reduced along the oblique axis Xe, in accordance with a single relative rotating motion between the axis Xr and the axis Xt in setting the oblique axis. Therefore, if the distance between the oblique axis Xe and the axis Xr is large, the diameter of the rotating motion of the roller  28  about the cylinder  4  will be large and inertia moment of the roller will be large. As a result, the apparatus will have to be large in scale. Furthermore, each roller  28  abuts on only a part of the outer surface of the cylinder  4  for a long period of time, an impact will be applied to the cylinder  4  to cause a vibration and noise. 
     In the case where those problems are to be solved, a plurality of relative rotating motions between the axis Xr and the axis Xt are performed in setting the oblique axis, in accordance with another embodiment as explained hereinafter with reference to FIGS. 9-17. FIG. 9 illustrates a state where the cylinder  4  (axis Xt) is rotated about the center C 0  relative to the main shaft  21  (axis Xr) by an angle θ 1 . In this case, the forming target axis Xe is offset from the axis Xr of the main shaft  21 , along the Y-axis by a distance (S 1 =R 1 ·sin θ 1 ). Also, the center C 1  is offset along the X-axis by a distance γ=R 1 ·tan(θ 1 )·sin(θ 1 ). According to the present embodiment, therefore, by moving the cylinder  4  relative to the main shaft  21  by the distance S 1  and distance γ (hereinafter omitted for simplicity), the axis Xr and the forming target axis Xe are overlapped, as shown in FIG.  10 . Accordingly, the cylinder  4  as shown in FIG. 11 is formed with the tapered portion  4   b   1  and neck portion  4   c   1  having the oblique axis Xe overlapped with the axis Xr of the main shaft  21  and inclined against the central axis Xt of the cylinder  4  by the angle θ 1 . FIG. 12 illustrates a state where the cylinder  4  (axis Xt) is rotated about the center C 0  relative to the main shaft  21  (axis Xr) further, to provide an angle  02  added to the angle θ 1  by an angle A 0 , and the cylinder  4  is moved relative to the main shaft  21  by the distance S 2 . Therefore, the axis Xr and the forming target axis Xe are overlapped, as shown in FIG. 13, and then the cylinder  4  is produced to form the tapered portion  4   b   2  and neck portion  4   c   2  in addition to the tapered portion  4   b   1  and neck portion  4   c   1 , having the oblique axis Xe overlapped with the axis Xr of the main shaft  21  and inclined against the central axis Xt of the cylinder  4  by the angle θ 2 , as shown in FIG.  14 . Then, as shown in FIG. 15, the cylinder  4  (axis Xt) is rotated further relative to the main shaft  21  (axis Xr) to provide an angle θ 3  added to the angle θ 2  by the angle Δθ, and the cylinder  4  is moved relative to the main shaft  21  by the distance S 3 , so that the axis Xr and the forming target axis Xe are overlapped, as shown in FIG.  16 . Accordingly, the cylinder  4  is formed with the tapered portions  4   b   1 ,  4   b   2 ,  4   b   3  and neck portions  4   c   1 ,  4   c   2 ,  4   c   3  having the oblique axis Xe, as shown in FIG.  17 . 
     Next will be explained the operation of the spinning process as explained above with reference to FIGS. 9-17, which will be performed by the controller CT in accordance with a flowchart as shown in FIG.  18 . At the outset, various basic data are input by the input device IP at Step  101 . The data input into the controller CT are the distance R between the center C 0  and the center C 1 , target oblique angle θ and the number N of forming cycles. And, the oblique angle per one cycle θ 1  is calculated (θ 1 =θ/N) at Step  102 . Then, the program proceeds to step  103  where a counter for forming the cylinder is incremented (k=k+1), and a rotating angle On is set to the angle per one cycle θ 1  at Step  104 . The program proceeds to Step  105  where a position of the roller  28  to be located on the X-axis is calculated as X=R·sin(θn). And, the program proceeds to Step  106  where each rollers  28  is moved along the X-axis to be located at the position set at Step  105 . Then, the program proceeds to Step  107  where the position of the roller  28  to be located on the Y-axis is calculated as Y=R−R·cos(θn), and proceeds to Step  108  where each roller  28  is moved along the Y-axis to be located at the position set at Step  107 . With each roller  28  and the cylinder  4  located as described above, the spinning process is performed at a Step  109 . When the counter has counted up the predetermined value N at Step  110 , the program proceeds to Step  111  where the spinning process is terminated, so that each component will be returned to its starting position and the program will end. Whereas, when the counter has not counted up the predetermined value N at Step  110 , Steps  103 - 109  are repeated. 
     According to the above-described spinning apparatus, therefore, the cylinder  4  with the tapered portion  4   b  (including  4   b   1 - 4   b   3 ) and neck portion  4   c  (including  4   c   1 - 4   c   3 ) formed at its opposite end portions is produced, as shown in FIG. 19, and may be used for the housing of catalytic converter. Furthermore, two cylinders  4   x ,  4   y  of similar configuration to the cylinder  4  may be combined to produce an exhaust purifying system having dual converters, as shown in FIG.  20 . 
     FIGS. 21 and 22 illustrate the spinning apparatus according to another embodiment. In the embodiment as disclosed in FIGS. 2 and 3, the case  20  is moved along the X-axis and the cylinder  4  moved along the Y-axis, so that they are moved relative to each other, whereas according to the present embodiment, the case  20  is secured to the base  1 , while the cylinder  4  is moved along the X-axis and Y-axis, and rotated about the shaft  31   a  of the motor  31 . That is, the first driving mechanism  2  that serves as the first driving device according to the present invention are gathered in the left side in FIGS. 21 and 22. The rest of the components such as the second driving mechanism  3  are the same as those in the aforementioned embodiment. Therefore, the components in FIGS. 21 and 22 having substantially the same function as those in FIGS. 2 and 3 are identified by the same reference numerals in FIGS. 2 and 3. 
     In the first driving mechanism  2 , a pair of X-axis guide rails  5  are fixedly secured to the base  1  at the left side thereof in FIGS. 21 and 22. A sliding base plate  30  is provided for mounting thereon the sliding table  6 , the clamp device  12  and etc., and arranged to be movable along the X-axis guide rails  5 . The ball socket  7  is secured to the base plate  30  thereunder, and the spline shaft  8  to be engaged with the ball socket  7  is mounted on the base  1  in parallel with the X-axis guide rails  5 , to be rotated by the motor  9 . Accordingly, when the spline shaft  8  is rotated by the motor  9 , the base plate  30  is moved along the X-axis. Furthermore, a pair of Y-axis guide rails  10  are secured to the base plate  30  thereon, and a pair of sliders  11  are movably mounted on the Y-axis guide rails  10 . The same clamp device  12  as shown in FIGS. 2 and 3 is mounted on the sliders  11 , so that when the spline shaft  15  is rotated by the motor  16 , the clamp device  12  is moved along the Y-axis relative to the base plate  30 . 
     According to the invention, when the shaft  31   a  is driven by the motor  31 , the clamp device  12  is rotated about the shaft  31   a . When the spline shaft  8  is rotated by the motor  9 , the clamp device  12  is advanced along the X-axis guide rails  5  (i.e., moved rightward in FIGS.  21  and  22 ), and when the spline shaft  15  is rotated by the motor  16 , the clamp device  12  is moved along the Y-axis guide rails  10  (i.e., moved downward in FIG.  17 ). Accordingly, the clamp device  12  is stopped when the cylinder  4  is located at a position where it is moved to position the end portion of ;the cylinder  4  on the forming target axis. Then, the motor  22  is rotated by the rotary member  24 , the transmitting member  26  is advanced by the actuator  25 , and each roller  28  is moved toward the center of the rotary member  24  (i.e., the axis Xr). At the same time, the spline shaft  8  is rotated by the servo motor  9 , so that the clamp device  12  and the cylinder  4  are retracted along the X-axis guide rails  5  (i.e., moved leftward in FIGS.  21  and  22 ). Consequently, each roller  28  is rotated about its axis and rotated about the axis Xr of the main shaft  21  simultaneously, to be moved radially toward the axis Xr, being biased to be in contact with the outer surface of the cylinder  4 , thereby to perform the spinning process, in the same manner as in FIGS. 2 and 3. 
     In the embodiment as disclosed in FIGS. 2 and 3, the axis Xt of the cylinder  4  is fixed to a position of a predetermined height above the base  1 , so as to be placed on the same plane as the axis Xr of the main shaft  21  in parallel with the base  1 . The height of the axis Xt of the cylinder  4  to the base  1  may be adapted to be variable, and the axis Xt may be adjusted vertically relative to the axis Xr of the main shaft  21 . In other words, the apparatus may be provided with a third driving mechanism (not shown) that drives the cylinder  4  vertically, in addition to the first driving mechanism  2  and second driving mechanism  3  as those shown in FIGS. 2 and 3. In this case, therefore, the axis Xt of the cylinder  4  can be adjusted to be located at a predetermined vertical position relative to the base  1 , and the axis Xt can be adjusted vertically relative to the axis Xr of the main shaft  21 , so that a fine adjustment will be made easily in the spinning process. 
     Referring to FIGS. 23 and 24, there will be explained a method for reducing the end portion of a cylinder  4  by means of the aforementioned spinning apparatus to form a reduced diameter end portion having an eccentric axis offset from the central axis of the cylinder  4 . A thick solid line in FIG. 23 indicates an estimated configuration of the finished cylinder  4 , which includes the main body  4   a , and the tapered portion  4   bo  and neck portion  4   co  which form the reduced diameter portion  4   do . At the outset, a starting position O 1  for starting the spinning process is set to a position retracted from the tip end of the cylinder  4   a  forming distance L 1 . When the tapered portion  4   bo  is formed, the offset amount H is divided by a number N of predetermined forming cycles (N=5, according to the embodiment in FIG.  23 ), so that a moving distance toward the eccentric axis every cycle. i.e., moving distance H 1  along the Y-axis per one cycle, is set. In this embodiment, each moving distance amount may be altered in accordance with the forming process to be required. For example, the moving distance between the cycles in an initial stage of the forming process may be made relatively long to reduce the forming time period, or the moving distance between the cycles in a terminating stage of the forming process may be made relatively short to improve the finished accuracy of the product. Likewise, with respect to the longitudinal length, a tapered length LT is divided by the predetermined forming cycles (N=5), so that a moving distance X 1  along the X-axis per one cycle, is set. 
     In FIG. 23, “D” indicates a diameter of the main body  4   a  of the cylinder  4 , “RD” indicates the smallest diameter of the tapered portion  4   bo  which is equal to the diameter of a portion  4   co . “V 1 ” indicates a reduced amount of the diameter of a portion to be formed to a large extent, and “V 2 ” indicates a reduced amount of the diameter of a portion to be formed to a small extent. “CY 1 ” to “CY 5 ” indicate the cycles of the forming process. The number N of forming cycles is selected properly in view of the limit for reducing the diameter of the cylinder  4 . According to the invention, the moving distance per one cycle is set to a value which does not exceed the limit for reducing the diameter of the cylinder. The limit for reducing the diameter of the cylinder is the limit at which plastic deformation working of the cylinder can not be made appropriately due to a material characteristic of the cylinder. 
     In operation, referring to FIG. 2, when the upper clamp  17  is lifted upward, the cylinder  4  to be formed is placed on the clamp face  13   a  of the lower clamp  13 , and set at the predetermined position where the one end portion of the cylinder  4  is abutted on the stopper  19 . Then, the actuator  18  is driven, so that the upper clamp  17  is moved downward, and the cylinder  4  is clamped between the lower clamp  13  and upper clamp  17 , and held not to be rotated. In this case, the clamp device  12  is positioned such that the axis Xt of the cylinder  4  is aligned with the axis Xr of the main shaft  21 . The transmitting member  26  is positioned at a retracted position, i.e., the right side to the position as shown in FIG. 2, so that each roller  28  is retracted outside of the outer peripheral of the cylinder  4 . Next, the spline shaft  8  is rotated by the motor  9 , so that the case  20  is advanced along the X-axis guide rails  5  (moved leftward in FIGS.  2  and  3 ), and stopped at a position where each roller  28  is retracted from the tip end of the cylinder  4  the forming length (L 1  in FIG.  23 ). In other words, each roller  28  is positioned at the position  01  for starting the spinning process as shown in FIG. 23, which position is set as the origin. Then, the spline shaft  15  is rotated by the motor  16 , and the clamp device  12  is moved along the Y-axis guide rails  10  (moved downward in FIG.  3 ), and stopped at a position where the cylinder  4  is moved along the Y-axis guide rails  10  by the offset moving distance H 1  moved toward the eccentric shaft per one cycle. The starting position of the cylinder  4  may be set to a position where the axis Xt of the cylinder  4  is moved toward the axis Xr of the main shaft  21  along the Y-axis by the moving distance H 1 . 
     From the state as described above, the rotary member  24  is rotated by the motor  22 , and the transmitting member  26  is advanced by the actuator  25 , so that each roller  28  is moved toward the center of the rotary member  24 , or the axis Xr. At the same time, the spline shaft  8  is rotated by the motor  9 , the case  20  and the roller  28  are retracted along the X-axis guide rails  5  (rightward in FIGS.  2  and  3 ). Consequently, each roller  28  is rotated about its axis and rotated about the axis Xr of the main shaft  21  simultaneously, and moved radially toward the axis Xr, being pressed to be in contact with the outer surface of the cylinder  4 , thereby to perform the spinning process. Thus, each roller  28  is started to move from the starting position  01 , until each roller  28  moves the moving distance X 1 , the end portion of the cylinder is deformed by spinning, to form a tapered portion  4   bo   1  with its axis offset from the axis Xt of the main body  4   a  by the moving distance H 1 , as shown in CY 1  of FIG. 24, because the axis Xr, about which the roller  28  is rotated, is offset relative to the axis Xt of the cylinder  4  by the moving distance H 1 . 
     In the case where each roller  28  is retracted further, exceeding the moving distance X 1 , the roller  28  is held to be in its state (i.e., the position moved the predetermined distance H 1 ). Therefore, the end portion of the cylinder  4  is deformed in accordance with the retracting movement of each roller  28  to form a cylindrical neck portion  4   co   1 , which was the central axis offset relative to the axis Xt of the main body  4   a  by the distance H 1 , and which is integrally connected to the smallest diameter side of the tapered portion  4   bo   1 . Thereafter, the cylinder  4  and roller  28  are returned to the starting positions, thereby to provide a reciprocating motion together with the initial path for reducing the diameter of the cylinder  4 , so that the spinning process in the first cycle CY 1  is completed. The operation for reducing the diameter of the cylinder  4  may be performed in another path of the reciprocating motion as well. After the spinning process in the first cycle CY 1  was completed an each roller  28  was returned to the starting position, the spinning process in the second cycle CY 2  is performed in the same manner as described above. By repeating the process as described five times, in the present embodiment, the reduced diameter portion  4   do  with the tapered portion  4   bo  and neck portion  4   co  having the eccentric axis is formed. 
     FIGS. 25-29 relate to a further embodiment of the spinning method, wherein the end portion of the cylinder  4  is formed into the reduced diameter end portion having the eccentric axis and the oblique axis, by means of the apparatus as shown in FIGS. 2 and 3. At the outset, according to the method as explained with reference to FIGS. 23 and 24, the end portion of the cylinder  4  is formed into the tapered portion  4   bo  and neck portion  4   co  having the axis, as shown in FIG. 25, wherein the two-dot chain line indicates the configuration to be formed, which was the oblique axis and the eccentric axis. Next, the axis Xr of the main shaft  21  is fixed on the plane in parallel with the base  1 , while the cylinder  4  is rotated about the center C 0 , to produce the oblique angle θ as shown in FIG.  26 . In this case, the oblique axis, or forming target axis Xe is positioned to be in parallel with the axis Xr and to include the center C 1  of the oblique end portion, which center is apart from the axis Xr by the distance S=R 1 ·sin(θ) in the direction parallel with the Y-axis. Therefore, the cylinder  4  is moved perpendicularly to the axis Xr along the Y-axis guide rails  10 , downward in FIG. 26, by the distance S, so that the axis Xr and the forming target axis Xe are overlapped. 
     Then, as shown by two-dot chain line in FIG. 27, each roller  28  is rotated its axis and about the axis Xr (the forming target axis Xe) simultaneously, and moved radially toward the axis Xr, being pressed to be in contact with the outer surface of the cylinder  4 , thereby to perform the spinning process. As a result, the one end portion of the cylinder  4  is formed into the tapered portion  4   bp  and neck portion  4   cp  having the oblique axis inclined against the axis Xt of the cylinder  4 , as shown in FIG. 28, then its tip end portion is cut out to form the tapered portion  4   bp  and neck portion  4   cp , as shown in FIG.  29 . 
     FIGS. 30 and 31 illustrate the spinning apparatus according to a further embodiment, wherein a mandrel  40  of a columnar configuration, with its tip end  41  configured to correspond to the inner surface of the end portion of the cylinder to be formed, is supported above the base  1  in parallel therewith. The mandrel  49  is arranged to penetrate the main shaft  21  longitudinally, and movably supported in a coaxial relationship therewith by an actuator  42  activated by oil pressure for example, which is mounted on the bracket  1   c  secured to the base  1 . Instead of the motor  31  in FIGS. 2 and 3, a motor  50  and gear box  51  engaged therewith are mounted on the sliding table  6 , so as to rotate a rotating table  52 , on which the clamp device  12  is mounted, about a vertical axis (not shown) at the center C 0  in FIG.  6 . The rest of the components in FIGS. 30 and 31 have substantially the same function as those in FIGS. 2 and 3. Therefore, the components in FIGS. 30 and 31 having substantially the same function as those in FIGS. 2 and 3 are identified by the same reference numerals in FIGS. 2 and 3. 
     Referring to FIGS. 32-37, there will be explained a further embodiment of the method for forming the end portion of the cylinder, wherein a bending device for bending the one end portion of the cylinder is used to form a bent portion at its end, in advance to the spinning process. Referring to FIG. 32, a lower die  80  and upper die (not shown) are provided to form a bore  81  having the same configuration as that of the cylinder to be bent and reduced at its end portion, as shown in FIG.  34 . then, a cylinder  4   z  having slant open ends  4   ze  at its opposite ends is pushed into the bore  81  of the die  80 , as shown in FIG. 33, and then removed from the die  81 . Through this process, the end portion of the cylinder  4   z  is formed into a bend and reduced portion  4   zf  having a substantially oblique axis Xf inclined against the central axis Xt of the cylinder  4   z , as shown in FIG.  34 . At the same time, the slant open end  4   ze  of the cylinder  4   z  pushed into the bore  81  is formed into such an open end face of the bent and reduced portion  4   zf  that is perpendicular to the axis Xf. Thus, it will be unnecessary to cut out the open end of the cylinder  4   z  after the spinning process. As for the bending and reducing process, other processes may be employed, such as a combination of known bending process and reducing process, hydraulic forming or bulging process, high-frequency heating process, or the like. If anything is to be inserted in the cylinder  4   z , like a catalyst CA as shown by broken lines in FIGS. 32-37, it is preferable to insert it into the cylinder  4   z  at the stage as shown in FIG. 32, or before pushing the cylinder  4   z  into the bore  81 . 
     Next, the cylinder  4   z  having the bent and reduced portion  4   zf  is set on the clamp device  12  of the spinning apparatus as shown in FIGS. 30 and 31. In this case, the cylinder  4   z  is positioned so as to align its axis Xf with the axis Xr of the main shaft  21 . Then, by spinning the end portion  4   zf  of the cylinder  4  along the axis Xf (and, the axis Xr), the cylinder  4   z  with a tapered end portion  4   zb  and a neck portion  4   zc  having the oblique axis Xf is formed as shown in FIG. 35, with the catalyst CA held therein. The spinning process may be performed in accordance with the same manner as described with reference to FIGS. 6-17. The opposite end of the cylinder  4   z  may be formed in the same manner as shown in FIG. 36, to produce the cylinder  4   z  with the tapered end portion  4   ab  and the neck portion  4   zc  formed at its opposite ends, and the catalyst CA held therein, as shown in FIG.  37 . According to the method as shown in FIGS. 32-37, therefore, it is easy to form the cylinder  4   z  provided with the tapered end portion  4   zb  and the neck portion  4   zc  having the oblique axis Xf, so that its manufacturing cost and time can be reduced, compared with the aforementioned methods. 
     Referring to FIGS. 38 and 39, there will be explained another exemplary embodiment according to the invention. The bed la is slidably mounted on Z-axis guide posts  38  for movement in the Z direction so that the axis Xt of the cylinder  4  can be adjusted relative to the axis Xr of the main shaft  21 . The first driving mechanism  2  may also include a gear box  35  between the bed  1   a  and the base  1 . The gear box  35  is engaged with a spline shaft  34  that is engaged with a hole defined in the bed  1   a . The gear box  35  is also connected to a servo motor  37  secured to the base  1  through a connecting shaft  36 . When the connecting shaft  36  is rotated by the servo motor  37 , the spline shaft  34  is rotated through the gear box  35  so that the bed  1   a  is moved in the Z direction. Therefore, the axis Xt of the cylinder  4  can be adjusted to be located at a predetermined position relative to the base  1  and the axis Xt can be adjusted relative to the axis Xr of the main shaft  21 . Consequently, the axis Xt of the cylinder  4  can be offset along not only the Y-axis but also along the Z-axis so that a fine adjustment can be easily made in the spinning process. Although not shown in FIGS. 38 and 39, it should be appreciated that the servo motor  37  can also be controlled by a controller CT as shown in FIG. 1 through a driving circuit. 
     As shown in FIGS. 40 and 41, the cylinder  4  may be supported so that the axis Xt of the cylinder  4  is offset from the axis Xr of the main shaft along the Y-axis by an offset distance H. The cylinder  4  is moved along the Y-axis by moving the table  6  along the Y-axis guide rails  10  by driving the servo motor  16 . The cylinder  4  may also be supported so that the axis Xt is offset from the axis Xr of the main shaft along the Z-axis by an offset distance H, as shown in FIGS. 42 and 43. The cylinder  4  is moved along the Z-axis by moving the bed la along the Z-axis guide posts  38  by driving the servo motor  37 . 
     Although the axis Xt of the cylinder  4  has been shown in FIGS. 40-43 as offset from the axis Xr of the main shaft  21  along either the Y-axis or the Z-axis, it should be appreciated that the axis Xt of the cylinder  4  may be offset from the axis Xr of the main shaft  21  along both the Y-axis and the Z-axis and that the offset distance along each axis may be the same or different. 
     As shown in FIGS. 44 and 45, cylinder  4  may be supported so that the axis Xt of the cylinder  4  is at an oblique angle θ to the axis Xr of the main shaft  21 . The axis Xt of the cylinder  4  is in the same plane as the axis Xr of the main shaft  21  and the axes Xt and Xr intersect. 
     As shown in FIGS. 46 and 47, the cylinder  4  may be supported so that the axis Xt of the cylinder  4  is offset along the Z-axis from the axis Xr of the main shaft  21  by an offset distance H and is at an oblique angle  0  to the axis Xr of the main shaft  21 . 
     As shown in FIG. 46, the axes Xt and Xr are skewed relative to another as they are not in the same plane nor do they intersect one another. 
     Referring to FIGS. 48A-48D, there will be explained an exemplary embodiment of a process of forming a changed diameter portion of the cylinder  4 . The cylinder  4  includes two portions, an unprocessed portion UP and a processed portion PP. The length of the unprocessed portion UP and the processed portion PP are determined before processing begins. The processed portion PP may be formed so that its central axis Xpp is offset from the central axis Xt of the unprocessed portion UP of the cylinder  4 , oblique to the central axis Xt of the unprocessed portion UP, or skewed to the central axis Xt of the unprocessed portion UP. A final oblique angle  0 , similar to that shown in FIGS. 26 and 27, may be initially determined and a final offset distance H, similar to that shown in FIG. 23, may be determined for the processed portion PP. 
     As shown in FIG. 48A, the central axis Xpp of the processed portion PP before processing begins overlaps the central axis Xt of the unprocessed portion UP of the cylinder  4 . As shown in FIG. 48B, the cylinder  4  is moved by the second driving mechanism  3  and the servo motor  16 , similar to the process shown in FIGS. 6 and 7, to set the central axis Xpp of the process portion PP at an initial oblique angle  01 , which is less than the final oblique angle θ, relative to a forming target axis Xe that overlaps the axis Xr of the main shaft  21 . The processed portion PP of the cylinder  4  is then subjected to a spinning process in which the rollers  28  rotate about the forming target axis Xe while simultaneously moving in the Y direction. The rollers  28  are moved in the X direction by the first driving mechanism  2 . The rollers  28  engage the outer surface of the process portion PP of the cylinder  4  to force the central axis Xpp of the processed portion PP to match the forming target axis Xe while simultaneously reducing the diameter of the processed portion PP. 
     As shown in FIG. 48D, the cylinder  4  is then moved again by the first driving mechanism  2  to set the central axis Xpp of the processed portion PP at an oblique angle θ 2 , which is also less than the final oblique angle θ, relative to the forming target axis Xe that overlaps the axis Xr of the main shaft. The cylinder  4  is again subjected to the spinning process to force the central axis Xpp of the processed portion PP to match the forming target axis Xe while simultaneously reducing the diameter of the processed portion PP. The processes shown in FIGS. 48B-48D may be repeated until the desired oblique angle θ and the desired offset distance H of the processed portion PP are formed. 
     Although not shown in FIGS. 48A-48D, it should be appreciated that in addition to setting the cylinder  4  so that the central axis Xpp of the processed portion PP is initially set at an oblique angle to the forming target axis Xe, as shown in FIG. 48B, the cylinder  4  may also be set so that the central axis Xpp of the processed portion PP is offset along the Z-axis from the forming target axis Xe. The cylinder  4  would be moved along the Z-axis by the first driving mechanism  2  and set an initial offset distance from the Z-axis, as shown in FIGS. 46 and 47, so that the central axis Xpp and the forming target axis Xe are skewed relative to each other. It should also be appreciated that the cylinder  4  could be initially set so that the central axis Xpp is offset from the forming target axis Xe along either the Y-axis, as shown in FIGS. 40 and 41, or the Z-axis, as shown in FIGS. 42 and 43, or offset from both the Y-axis and Z-axis, without setting the central axis Xpp oblique to the forming target axis Xe. It should also be appreciated that the initial step of supporting the cylinder  4  shown in FIG. 48A may be omitted and the cylinder  4  may be set directly as shown in FIG.  48 B. Although the processes shown in FIGS. 48B-48D are shown as being repeated, it should be appreciated that the cylinder  4  may be set in FIG. 48B at the final desired oblique angle and/or final desired offset and the process shown in FIG. 48B may be performed only once. However, the processes shown in FIGS. 48B-48D may be performed a number N of cycles and the initial oblique angle θ 1  and subsequent oblique angles θ 2  may be determined by dividing the final desired oblique angle θ by the number N of cycles or the oblique angles set during the terminating cycles may be made relatively short to improve the finished accuracy of the product. 
     Referring to FIGS. 49-51, there is shown an example of a cylindrical member  4  having a processed portion with a central axis Xpp skewed from the central axis Xt of the unprocessed portion. The cylinder  4  is initially supported as shown in FIGS. 46 and 47 and processed according to the process shown in FIGS. 48B-48D. The central axis Xpp of the processed portion is offset from the central axis Xt of the unprocessed portion UP by a distance H and is also oblique to the central axis Xt at an angle θ. 
     Referring to FIGS. 52A-52C, there is shown another exemplary embodiment of a process of forming a changed diameter portion of the cylinder  4 . As shown in FIG. 52A, the cylinder  4  includes an unprocessed portion UP and a processed portion PP. As shown in FIG. 52B, a forming target axis Xe 1  of the processed portion PP of the cylinder  4  at least partially overlaps the axis Xr and is defined by a curve containing the points “a” and “b”. The intermediate forming target axis Xe may extend in three dimensions, i.e., in the along the X-axis, Y-axis, and Z-axis. The cylinder  4  is supported by the clamp device  12  as shown in FIGS. 38 and 39 and while the rollers  28  are moved along the X-axis by the first driving mechanism  2  and engaged with the outer surface of the processed portion PP of the cylinder  4 , the unprocessed portion UP of the cylinder  4  in the clamp device  12  is simultaneously moved along the Y-axis by the servo motor  16  moving the table  6  along the Y-axis guide rails  10  and/or along the Z-axis by the servo motor  37  moving the bed  1   a  along the Z-axis guide posts  38  and by the motor  31  pivoting the clamp device  12  on the table  6 . Moving the unprocessed portion UP of the cylinder  4  while the rollers  28  are engaged with the processed portion PP allows forming of the processed portion PP along a curved forming target axis that extends along the X-axis, Y-axis, and Z-axis so that the central axis of the processed portion PP matches the curved forming target axis while the diameter of the processed portion PP is simultaneously reduced. 
     As shown in FIG. 52C, the cylinder  4  may be further processed by forming the processed portion PP about another forming target axis Xe 2  at least partially overlapping the axis Xr and defined by a curve containing the points “c” and “d”. While the processed portion PP is engaged by the rollers  28 , the unprocessed portion UP is simultaneously moved along the Y-axis and/or the Z-axis by the first driving mechanism  2  and the second driving mechanism  3  to further form the processed portion PP. It should be appreciated that the processes shown in FIGS. 52B and 52C may be repeated until the central axis of the processed portion matches a desired final curved forming target axis and the diameter is reduced to a final desired diameter. It should also be appreciated that the processed portion PP may be formed by a single spinning process with simultaneous movement of the unprocessed portion UP. 
     Although the forming target axes Xe 1  and Xe 2  are shown in FIGS. 52B and 52C as being of constant curvature, it should be appreciated that the forming target axis may have a compound curvature. As shown in FIGS. 52B and 52C, the processed portion PP having a curvilinear target forming axis produces a smooth outer shape and substantially reduces the gap between the processed portion PP and the unprocessed portion PP due to the diameter change. 
     Although the previous embodiments have been described in relation to diameter reduction processes, it should be appreciated that the diameter of the processed portion PP may be enlarged by the rollers  28  engaging an inner surface of the cylinder  4  during the spinning process as shown in FIG.  53 . It should be apparent to one skilled in the art that the above-described embodiments are merely illustrative of but a few of the many possible specific embodiments of the present invention. Numerous and various other arrangements can be readily devised by those skilled in the art without departing from the spirit and scope of the invention as defined in the following claims.