Once the measuring procedure is completed, the measured point data are collected and saved in an ASCII format file so that the dimensional error can be calculated. The concept of the projected dimensional error is used in this paper. Assume that the coordinate of the theoretical  candidate  point  T  is [Qx     Qy     Qz      1 ]T and the corresponding measured point M is [Mx     My     Mz     1 ]T. This forms a dimensional error vector

E = [Mx  − Qx My  − Qy Mz  − Qz 0 ]. The outer surface

normal vector K is  [Kx Ky Kz 1 ]T. Therefore, the mag-

these points is to ensure the accuracy of MHZ. If the projected dimensional errors of these points are out of the tolerance, MHZ

Fig. 1. Schematic diagram for measuring the stamping die.

140 C.-H. She et al. / Journal of Materials Processing Technology 177 (2006) 138–141

Fig. 2. Probe path generation and DMIS output.

should be offset appropriately. The offset value can be deter- mined as follows.

Assume that there are n points of the common standard sur- face to be measured. The i-th point has the projected dimensional error Di and normal vector [Kxi    Kyi    Kzi     0 ]T. The XYZ off- set of MHZ can be obtained by the following expressions:

punch, where 22 points are selected to be measured and the corresponding DMIS output file can also be generated.

The punch of the stamping die is measured on the Brown & Sharpe DEA CMM with a Renishaw PH-10M touch-trigger probe, as shown in Fig. 3. Fig. 4 illustrates the measured results

[ X   Y Z 1 ]T =

..n

i=1

DiKxi|Kxi| .n

DiKyi|Kxi| .n

DiKzi|Kzi| .T

i=1|Kxi|

i=1|Kyi|

1

i=1|Kzi|

(4)

Once the MHZ has been offset correctly, the other portion of the die will be measured according to this new MHZ coordinate system.

5. System implementation and verification

A window-based C language program written by Borland C++ Builder and Open GL has been developed to verify the presented methodology. A set of an industrial stamping dies of a rear lid panel is used as an example. The stamping dies often consist of two parts, i.e. the punch and die. The punch is the male part of a stamping die and usually the upper member of the complete die assembly, while the die is the female part of a stamping die as distinguished from the male part.

The CAD models of the punch and die are created in the commercial CAD system and saved in IGES format. The pro- posed system can analyze the NURBS surface in IGES format using the developed IGES parser. After the CAD model has been imported, the wireframe of the surface can be shown and dynamically rotated or zoomed on the screen. To generate the candidate inspection point, the isoparametric step size definition is used as the input of incremental change in each parameter (u and v). Fig. 2 shows the zigzag probe inspection path of the

showing the projected dimensional errors incorporated with the punch CAD model. The upper portion of the displayed win- dow lists the measured data including the inspection sequence number, the coordinate of the candidate inspection point, the coordinate of the measured point, the projected     dimensional

Fig. 3. Measurement of the punch on the CMM with a touch-trigger probe.