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Ch75-I044963.fm  Page 375  Tuesday, August 1, 2006  5:58 PM
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                            Tuesday, August 1, 2006
                                           5:58 PM
            Ch75-I044963.fm
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                  illustrates an experimental example of detecting an error space for the Z axis. The same procedure can
                  be applied to the directions X and Y which are vertical to Z, and planelike  error  forms  for the Xi and
                  Yj are constructed. Consequently, error space for 3 axes (X, Y, Z) is constructed.  Then it is possible to
                  estimate error components for (X, Y, Z) at arbitrary points among the measurement range of a CMM.
                  The  points on which  errors are directly measured  are discrete. The error at an arbitrary  point can be
                  obtained  by applying  interpolation  or least  squares  method  (LSM).  When  the error  e z(X,  Y, Z) is
                  obtained by interpolation or LSM, the compensation of the error is easily performed by subtracting the
                    from  Z. By applying the method, the measurement  accuracy  is improved  without  any change of
                  e z
                  hardware  configuration.


                              Measurement along the direction ofX axis for j=0. ••-. m
                                    Z x(Xj,Y|.Z 0)  (i=0.-,];j=0,-,m)
                                Calculation of decrepancy A from Z X (X|,Y 0 ,ZQ)
                                                                           ZxpCl.Yo.Zo)
                                       A=Z X(X I,Y,,,Z O)/I
                                     Compensation of A for Z x
                                Z x (X i ,Yj,Z 0 )=Z x (X i ,Yj,Zn)4A  (i=0,-.
                               Measurement along the direction ofY axis for i=0.
                                    ZytXj.Yj.Zp)  (i=0,l;j=0,-,m)
                                  Compensation  of A for Z v  (j=l,-%m)
                              y(X 0,Y j,Z 0)=Z y(X 0,Y j,Z 0HA,Z y(X 1,Yj,Z 0)=Z y(X 1,Y j,Z 0HA
                                Compensation for Z^X^YJ.ZQ )  (i=0.-.l:j=l.--.m)
                                 SO that Z x (X () .Yj.Z 0 )=Z y (X 0 .Yj,Z 0 )  (j=l.-.m)
                                    Verification of measurement
                              by comparing Z X (X|.YJ ; ZQ) and Z (X hYyZQ)  (j=0.-,m)


                                  Figure 4: Flow of composing planelike error form for Z=Zo




                                                           15

                       )                                     )
                       (µm                                (µm  10


                       r  0.5                                r
                       o
                       r                                  o  r  5
                       r                                  r
                       e  0
                                                          e
                       s                                  s
                       s                                  s
                       e  -0.5                            e  0
                       n                                  n
                       t                                  t
                       h                                  h
                       g  -1                              g
                       i                                  i
                       a                                  a  -5
                       r                                  r
                       t                                  t
                       S  -1.5                            S
                       350                          400
                                                          -10
                         300                       350
                           250                   300      -15
                             200               250                                     400
                               150            200           300                    300
                             n              150                 200
                                 100      Feed along X-axis (mm)                200
                                          100
                                                                    100
                                   50   50                   Feed along Y-axis (mm)  100 Feed along X-axis (mm)
                                      0  0                              0  0
                          Feed a   lo g Y-a i x s (     mm)
                           Figure 5 (a) (left): Error curved surface of the straightness motion of the probe
                                      (b) (right): Surface profile of the objective plane
                  CONCLUSION
                  It  was demonstrated  that  the sequential  two points  method  could  be well  applied  to evaluate the
                  straightness error motion of the probe of the CMM. The conclusions could be summarized as follows.
                  1.  It was confirmed  that the straightness  error  form  can be accurately  identified  by the STPM. The
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