Abstract:
A cutting method in which, in cutting a circumferential face of a work, control is enabled to make a cutting velocity constant accurately by using a cutting tool projecting from a main shaft which turns around a predetermined position serving as a center and for which a turning radius is adjustable, wherein, in the case that a turning angular velocity of the main shaft is represented as ω, a distance from a turning center to a tip of the cutting tool is represented as R, and a cutting velocity of the tip of the cutting tool is set to a constant value C, making the cutting velocity of the cutting tool constant by performing control such that ω0 changes in association with a change in the distance R so that 
       ω=( C   2   −{dot over (R)}   2 ) 1/2 / R  
 
     is formulated (where {dot over (R)} denotes a time differential of the distance R), thus providing an even cut face.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    The present invention relates to a cutting method for an inner circumferential face and an outer circumferential face of a work using a cutting tool of a main shaft which turns around a predetermined position serving as a center and for which a turning radius is adjustable, the cutting being performed by making a cutting velocity of the cutting tool constant. 
         [0002]    The “turning of the main shaft” is not limited to rotation of the main shaft along a central axis thereof but refers to rotations including revolution of the main shaft around the predetermined position serving as a center. 
         [0003]    What is called an orbit machining that a main shaft turns around a predetermined center has been adopted as a method for forming an inner circumferential face and an outer circumferential face of a work into curved faces variously shaped like cylinders, tapered shapes, flanges, or the like, as disclosed in Patent Literature 1. This machining method is technically advantageous in that machining can be achieved at whatever position a table supporting the work is located. 
         [0004]    A cutting velocity needs to be constant in order to provide an even cut face. 
         [0005]    However, for the orbit machining method according to the related art as is described above, no configuration that makes a cutting velocity constant has been adopted. 
         [0006]    Patent Literature 2 discloses a configuration, for cutting method of gear shaped object, needed to maintain a constant cutting velocity from a cutting start point to a cutting end point. 
         [0007]    However, Patent Literature 2 only discloses that the cutting velocity is made constant simply under the control of an NC lathe and fails to clarify what qualitative or quantitative criteria are used to make a cutting velocity constant. 
         [0008]    Patent Literature 3 discloses that a CAM controls the number of rotations of the main shaft to obtain a constant cutting velocity. However, Patent Literature 3 also fails to clarify a specific configuration concerning what criteria are used to make a cutting velocity constant. 
         [0009]    Furthermore, Patent Literatures 2 and 3 are predicted on cutting based on rotation of the main shaft along a central shaft thereof and do not disclose or suggest that the cutting velocity is constant when the main shaft turns around a predetermined position serving as a center as is the case with the present invention. 
         [0010]    Thus, for the cutting of the inner circumferential face or the outer circumferential face of the work based on turning of the main shaft, no cutting method has been proposed in which the cutting velocity of the cutting tool is controlled to be constant. 
         [0011]    Patent literature 4 discloses that a cutting velocity of a cutting tool is set to be constant by changing ω according to a change of a distance R wherein ω is rotational angular velocity of a main shaft, R is the distance from a rotational center to a tip of the cutting tool, and constant value C is set as the cutting velocity in the tip of the cutting tool (paragraph [0040] and  FIG. 7 ( a ) and ( b ) ). 
         [0012]    However, constant cutting velocity in patent literature 4 means that a value of R·ω is constant at most, and patent literature 4 does not disclose obtaining constant velocity with a factor of a time differential of the distance R. 
         [0013]    So, patent literature 4 does not disclose the state of setting the cutting velocity accurately. 
       RELATED ART LITERATURE 
     Patent Literature 
       [0014]    Patent Literature 1: JP H08-126938 A 
         [0015]    Patent Literature 2: JP 2000-190127 A 
         [0016]    Patent Literature 3: JP 2001-113443 A 
         [0017]    Patent Literature 4: JP 2011-131324 A 
       BRIEF SUMMARY OF THE INVENTION 
       [0018]    According to the present invention, there is provided a cutting method in which, in cutting an inner circumferential face or an outer circumferential face of a work based on turning of a main shaft around a predetermined position serving as a center, control is enabled to make a cutting velocity constant accurately. 
         [0019]    According to the present invention, there are further provided a basic configuration ( 1 ); a cutting method for an inner circumferential face or an outer circumferential face of a work using a cutting tool projecting from a main shaft which turns around a predetermined position serving as a center and for which a turning radius is adjustable, wherein, in the case that a turning angular velocity of the main shaft is represented as ω, a distance from a turning center to a tip of the cutting tool is represented as R, and a cutting velocity of the tip of the cutting tool is set to a constant value C, the cutting velocity of the cutting tool is made constant by performing control such that ω changes in association with a change in the distance R so that 
         [0000]      ω=( C   2   −{dot over (R)}   2 ) 1/2 / R  
 
         [0000]    is formulated (where {dot over (R)} denotes a time differential of the distance R), and a basic configuration (2) the cutting method for an inner circumferential face or an outer circumferential face of the work of the basic configuration (1), wherein the work is put on a table, and a position of the turning center of the main shaft is movable in one of: 
         [0020]    an orthogonal direction and 
         [0021]    an oblique direction to a plane orthogonal to the turning central axis, and 
         [0022]    when the position of the turning center of the main shaft is movable in the oblique direction, setting a supporting position of the work on the table on which the work is placed, such as that a distance from the cutting position of the work to the turning center of the cutting tool is R by moving the table along a direction of the plane in association with the movement in the oblique direction to maintain a state where cutting is enabled, and 
         [0023]    a basic configuration (3) the cutting method for an inner circumferential face or an outer circumferential face of the work of the basic configuration (1), wherein the work is put on a rotational table, and the table is put on a pedestal of a machining center which can not only cut the work but also manufacture the work besides cutting, and a position of the turning center of the main shaft is movable in one of: 
         [0024]    an orthogonal direction and 
         [0025]    an oblique direction to a plane orthogonal to the turning central axis, and 
         [0026]    when the position of the turning center of the main shaft is movable in the oblique direction, setting a supporting position of the work on the table on which the work is placed, such as that a distance from the cutting position of the work to the turning center of the cutting tool is R by moving the pedestal of the machining center along a direction of the plane in association with the movement in the oblique direction to maintain a state where cutting is enabled, and 
         [0027]    a basic configuration (4) the cutting method for an inner circumferential face or an outer circumferential face of the work of the basic configuration (1), wherein the work is held by an arm of a robot, and a position of the turning center of the main shaft is movable in one of: 
         [0028]    an orthogonal direction and 
         [0029]    an oblique direction to a plane orthogonal to the turning central axis, and 
         [0030]    when the position of the turning center of the main shaft is movable in the oblique direction, setting a holding position of the work by the arm of the robot, such as that a distance from the cutting position of the work to the turning center of the cutting tool is R by moving the arm of the robot along a direction of the plane in association with the movement in the oblique direction to maintain a state where cutting is enabled. 
         [0031]    In the aspect of the present invention, the basic configuration (1) makes a cutting velocity constant to provide an even cut face, while the basic configurations (2), (3) and (4) enables the inner circumferential face or the outer circumferential face of the work to be formed into any of various curved faces. 
         [0032]    That is, the aspect of the present invention eliminates the need for control based on complicated calculations or operations as disclosed in Patent Literature 2 and 3. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0033]      FIG. 1 ( a ), ( b )  are block diagrams of a system allowing a method of the present invention to be implemented,  FIG. 1 ( a )  denoting an embodiment that a work is put on a table, and  FIG. 1 ( b )  denoting an embodiment that a work is put on a rotational table, and the rotational table is put on a pedestal of a machining center. 
           [0034]      FIGS. 2( a ) and 2( b )  are plan views denoting the state of a plane in a direction orthogonal to a turning central axis of a main shaft,  FIG. 2( a )  denoting that an inner circumferential face is cut, and  FIG. 2( b )  denoting that an outer circumferential face is cut; 
           [0035]      FIGS. 3( a ) and 3( b )  denote a method of forming a normal tapered shape by moving the position of a turning center of the main shaft and sequentially changing a turning radius,  FIG. 3( a )  being a plan view denoting a locus of movement of a tip of a cutting tool, and  FIG. 3( b )  being a side view of the tapered shape formed by the sequential change; 
           [0036]      FIGS. 4( a ) and 4( b )  denote a method of forming a stepped tapered shape by moving the position of the turning center of the main shaft and changing the turning radius in a stepwise manner,  FIG. 4( a )  being a plan view denoting a locus of movement of the tip of the cutting tool, and  FIG. 4( b )  being a side view of the stepped tapered shape formed by the stepwise change; and 
           [0037]      FIGS. 5( a ), 5( b ), and 5( c )  are perspective views denoting a process of forming a ring shape by helically moving and finally circumferentially moving the tip of the cutting tool in an inner region and an outer region of the work without moving the turning center position of the main shaft,  FIG. 5( a )  denoting a process of forming an inner wall in a ring shape,  FIG. 5( b )  denoting a process of forming an outer wall in a ring shape, and  FIG. 5( c )  denoting the finished ring shape. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0038]    As is denoted in  FIG. 1 ( a ), ( b ) , components of the present invention include a main shaft  1  that turns, a cutting tool  2  provided at a tip side of the main shaft  1 , a work  3 , a table  4  that supports the work  3  (denoted in  FIG. 1 ( a ) ), or a table  4  that supports the work  3  and the pedestal  41  of machining center on which the table  4  is put (denoted in  FIG. 1 ( b ) ), or an arm of a robot for holding the work  3  (not denoted in Figures), and a control apparatus  5  that controls movement of the main shaft  1  and the table  4  or the pedestal  41 , or the arm of the robot. 
         [0039]    In  FIG. 1 , blank arrows indicate a moving state of the main shaft  1  associated with adjustment of a turning radius or a moving state of the main shaft  1  in the orthogonal direction or the oblique direction, curved arrows indicate a turning state by revolution of the main shaft  1  and a rotating state of the table  4 , a dotted arrow from the control apparatus  5  indicates a state where signals which allow a turning angular velocity and a rotating angular velocity to be controlled are dispatched, and solid arrows indicate states where signals are dispatched which allow control of movement of the main shaft  1  associated with adjustment of the turning radius of the main shaft  1 , and in the basic configurations (2), (3) and (4), control of movement of the rotating center of the table  4 , or the pedestal  41 , or the arm of the robot associated with movement of the turning center of the main shaft  1  in the orthogonal direction or the oblique direction and movement of the turning center of the main shaft  1  in the oblique direction. 
         [0040]    In the present invention, elements to be controlled are parameters indicative of the turning angular velocity of the main shaft  1  with respect to the turning center, and the turning radius of the main shaft  1  (these elements correspond to the basic configuration (1)), and further the moving position and the moving velocity of the turning center in the orthogonal direction or the oblique direction with respect to a plane orthogonal to a central axis  6  for turning of the main shaft  1  (these elements correspond to the basic configurations (2), (3) and (4)). For the basic configuration (1), the number of the parameters is two, and for the basic configurations (2), (3) and (4), the number of the parameters is three. 
         [0041]    The main shaft  1  and the cutting tool  2  make turning motion around a predetermined central position. A tip of the cutting tool  2  cuts an inner circumferential face of the work  3  as is denoted in  FIG. 2( a )  or cuts an outer circumferential face of the work  3  as is denoted in  FIG. 2( b ) . The turning radius of the main shaft  1  from the central position is adjustable, and thus, the radius of curvature of the tip of the cutting tool  2  is also adjustable, allowing a cutting curved face to be optionally selected. 
         [0042]    That is, circumferential curved faces in  FIGS. 2( a ) and 2( b )  merely denote typical examples based on rotation by the composition of the revolution of the main shaft  1  and the rotation of the table  4 . The cutting curved face is not necessarily limited to the circumferential curved face. 
         [0043]    Criteria based on expressions for the basic configuration (1) and corresponding to a technical demand for provision of an even cut face will be described below. 
         [0044]    As is denoted in  FIGS. 2( a ) and 2( b ) , if the distance from the turning center to the tip of the cutting tool  2  is represented as R, and an angular position of the cutting tool  2  is represented as θ, and that a coordinate position of the cutting tool  2  is represented as (X, Y), then X=R cos θ and Y=R sin θ is formulated and 
         [0000]        X=R  cos θ− R θ sin θ, Y=R  sin θ+ R  θcos θ
 
         [0000]    is formulated (dots over reference characters indicate time differentials). 
         [0045]    Therefore, when the cutting velocity is represented as V, 
         [0000]        V   2   ={dot over (X)}   2   +{dot over (Y)}   2   ={dot over (R)}   2   +{dot over (R)}   2 {dot over (θ)} 2  
 
         [0000]    is formulated. 
         [0046]    According to the above-described relational expressions, wherein, in the case that the turning angular velocity of the main shaft  1  is represented as ω 1  and the rotating angular velocity of the table  4  is represented as ω 2 , the constant value C may be preset and controlled to formulate 
         [0000]      ω={dot over (θ)}=( C   2   −{dot over (R)}   2 ) 1/2   /R  
 
         [0000]    in association with the distance R and {dot over (R)} that is a time differential of the distance R, in order to allow the tip of the cutting tool  2  to operate at a constant cutting velocity V. 
         [0047]    In the present invention, to form each of the inner and outer circumferential faces into any of various cutting shapes, the following embodiment may be adopted. That is, as shown in the basic configuration (2) as is denoted in  FIG. 1 ( a ) , wherein the work  3  is put on a table  4 , and a position of the turning center of the main shaft  1  is movable in one of: 
         [0048]    an orthogonal direction and 
         [0049]    an oblique direction to a plane orthogonal to the turning central axis  6 , and 
         [0050]    when the position of the turning center of the main shaft  1  is movable in the oblique direction, setting a supporting position of the work  3  on the table  4  on which the work  3  is placed, such as that a distance from the cutting position of the work  3  to the turning center of the cutting tool  2  is R by moving the table  4  along a direction of the plane in association with the movement in the oblique direction to maintain a state where cutting is enabled, 
         [0051]    or as shown in the basic configuration (3) denoted in  FIG. 1 ( b ) , wherein the work  3  is put on a rotational table  4 , and the table  4  is put on a pedestal  41  of a machining center which can not only cut the work  3  but also manufacture the work  3  besides cutting, and a position of the turning center of the main shaft  1  is movable in one of: 
         [0052]    an orthogonal direction and 
         [0053]    an oblique direction to a plane orthogonal to the turning central axis  6 , and 
         [0054]    when the position of the turning center of the main shaft  1  is movable in the oblique direction, setting a supporting position of the work  3  on the table  4  on which the work  3  is placed, such as that a distance from the cutting position of the work  3  to the turning center of the cutting tool  2  is R by moving the pedestal  41  of the machining center along a direction of the plane in association with the movement in the oblique direction to maintain a state where cutting is enabled, 
         [0055]    or wherein the work  3  is held by an arm of a robot (not denoted in figures), and a position of the turning center of the main shaft  1  is movable in one of: 
         [0056]    an orthogonal direction and 
         [0057]    an oblique direction to a plane orthogonal to the turning central axis  6 , and 
         [0058]    when the position of the turning center of the main shaft  1  is movable in the oblique direction, setting a holding position of the work  3  by the arm of the robot, such as that a distance from the cutting position of the work  3  to the turning center of the cutting tool  2  is R by moving the arm of the robot along a direction of the plane in association with the movement in the oblique direction to maintain a state where cutting is enabled. 
         [0059]    In a basic configuration (2), it is not always necessary to rotate a table  4 . 
         [0060]    However, in a basic configuration (3), it is necessary that a table  4  is rotational in the case of manufacturing part  40  acting the work  3  besides cutting. 
         [0061]    So, in the case of a basic configurations (2), (3) and (4), when the turning center of the main shaft  1  is movable in the oblique direction, the turning central axis  6  of the main shaft  1  moves by itself, and the position of the table  4  or the pedestal  41  (in the case of a basic configurations (2) or (3)), or the position of the arm of the robot (in the case of a basic configuration (4)) should be moved along the direction of the plane with synchronized state to the position of the turning center in order to maintain a state where the cutting tool  2  can cut the work  3 . 
         [0062]      FIGS. 3( a ) and 3( b )  denote that the outer circumferential face is formed into a normal tapered shape in accordance with the embodiment in which the position of the turning center of the main shaft  1  is moved in the orthogonal direction or the oblique direction, while the turning radius is sequentially changed. 
         [0063]    When the tapered shape has circumferential curved faces at opposite ends thereof, the turning radius may be approximately constant at an initial stage and a final stage of turning as is denoted in  FIGS. 3( a ) and 3( b ) . 
         [0064]      FIGS. 4( a ) and 4( b )  denote that the inner circumferential face is formed into a stepped tapered shape in accordance with the embodiment in which the position of the turning center of the main shaft  1  is moved in the orthogonal direction or the oblique direction, while the turning radius is changed in a stepwise manner. 
         [0065]    As is apparent from  FIGS. 3( a ) and 3( b )  and  FIGS. 4( a ) and 4( b ) , the basic configuration (2) enables the inner circumferential face or the outer circumferential face to be formed into any of various shapes. 
         [0066]    The above-described drawings all denote that the turning center of the main shaft  1  is moved in the direction orthogonal to the plane orthogonal to the turning central axis  6 , that is, in the same direction as that of the turning central axis  6 . When the turning center is moved in the direction oblique to the plane, a tapered shape is obtained which generally changes in the oblique direction. 
         [0067]    Alternatively to the embodiments denoted in  FIGS. 3( a ) and 3( b )  and  FIGS. 4( a ) and 4( b ) , if the turning radius of the main shaft  1  is not changed, the inner circumferential face or the outer circumferential face (not denoted in the drawings) can be formed into a normal cylindrical shape (when the turning center moves in the orthogonal direction) or an oblique cylindrical shape (when the turning center moves the in the oblique direction). 
         [0068]      FIG. 5  denotes an embodiment in which the position of the turning center of the main shaft  1  is not moved in the orthogonal direction nor the oblique direction. In the embodiment, a ring shape is formed as follows. 
         [0000]    (1) In an inner region of the work  3  that is close to the turning center, the distance from the turning center to the tip of the cutting tool  2  is sequentially increased to move the tip along a helical locus, in the case that the distance reaches a maximum state, the maximum state is maintained to form an inner wall in a ring shape.
 
(2) In an outer region of the work  3  that is away from the turning center, the distance from the turning center to the tip of the cutting tool  2  is sequentially reduced to move the tip along a helical locus, in the case that the distance reaches a minimum state, the minimum state is maintained to form an outer wall in a ring shape.
 
         [0069]    In the above-described embodiment, the ring shape can be quickly obtained. 
         [0070]    Thus, in the present invention, the work  3  is cut with a summation of the cutting velocity to allow the inner circumferential face and the outer circumferential face to be quickly formed. The need for special control for the summation is not required to achieve simple control. 
       EXAMPLE 
       [0071]    In an example, a plurality of main shafts  1  and cutting tools  2  projecting from the respective main shafts  1  are adopted. 
         [0072]    In this example, the plurality of cutting tools  2  performs cutting to further increase the cutting velocity, while the properties of the individual cutting tools  2  related to the cut face are averaged to allow a more even cut face to be provided. 
         [0073]    As is described above, the present invention enables the inner circumferential face and the outer circumferential face of the work to be cut into any of various shapes with even cut faces at a constant cutting velocity. Thus, the present invention has enormous applicability. 
       Explanation of Signature 
       [0000]    
       
           1  a main shaft 
           2  a cutting tool 
           3  a work 
           4  a table 
           40  a manufacturing part of a machining center for manufacturing the work besides cutting 
           41  a pedestal in the machining center 
           5  a control apparatus 
           6  a central axis of turning or rotation