Cutting Method for Inner Circumferential Face or Outer Circumferential Face of Work

Abstract

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. To achieve the object, a cutting method is provided 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, making 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 ω = ( C 2 - 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.

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, comprising the step of:
 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 ω changes in association with a change in the distance R so that   
       
         
           
             
               ω 
               = 
               
                 
                   
                     ( 
                     
                       
                         C 
                         2 
                       
                       - 
                       
                         
                           R 
                           . 
                         
                         2 
                       
                     
                     ) 
                   
                   
                     1 
                     2 
                   
                 
                 / 
                 R 
               
             
           
         
       
       is denoted (where {dot over (R)} denotes a time differential of the distance R). 
     
     
         2 . The cutting method for an inner circumferential face or an outer circumferential face of a work according to  claim 1 ,
 wherein a position of the turning center of the main shaft is movable in one of:
 an orthogonal direction and 
 an oblique direction to a plane orthogonal to the turning central axis, and 
   when the position of the turning center of the main shaft is movable in the oblique direction, moving a supporting position of the work on a table on which the work is placed in association with the movement in the oblique direction to maintain a state where cutting is enabled.   
     
     
         3 . The cutting method for an inner circumferential face or an outer circumferential face of a work according to  claim 2 , further comprising the step of moving the position of the turning center of the main shaft in one of the orthogonal direction and the oblique direction, while the turning radius is sequentially changed. 
     
     
         4 . The cutting method for an inner circumferential face or an outer circumferential face of a work according to  claim 2 , further comprising the step of moving the position of the turning center of the main shaft in one of the orthogonal direction and the oblique direction, while the turning radius is changed in a stepwise manner. 
     
     
         5 . The cutting method for an inner circumferential face or an outer circumferential face of a work according to  claim 1 , wherein a position of the turning center of the main shaft is not moved in the orthogonal direction nor the oblique direction, and further comprising the step of forming a ring shape by the following steps:
 (1) in an inner region of the work that is close to the turning center, sequentially increasing the distance from the turning center to the tip of the cutting tool to move the tip along a helical locus, in the case that the distance reaches a maximum state, so that the maximum state is maintained to form an inner wall in a ring shape, and   (2) In an outer region of the work that is away from the turning center, sequentially reducing the distance from the turning center to the tip of the cutting tool to move the tip along a helical locus, in the case that the distance reaches a minimum state, so that the minimum state is maintained to form an outer wall in a ring shape.   
     
     
         6 . The cutting method for an inner circumferential face or an outer circumferential face of a work according to  claim 1 , further comprising the step of adopting a plurality of main shafts and cutting tools projecting from the respective main shafts.