13 5 1 2 3 1 3 2 0.028 0.174 34.0 0.014

14 5 2 3 1 2 1 3 0.014 0.157 40.2 0.007

15 5 3 1 2 3 2 1 0.011 0.164 42.1 0.006

16 6 1 3 2 3 1 2 —0.004 0.164 51.6 —0.002

17 6 2 1 3 1 2 3 0.019 0.154 37.5 0.009

18 6 3 2 1 2 3 1 0.017 0.156 38.6 0.008

X,Y: displacement value of each axis.

hole either presence or absence. From the spindle motor, bearing housing to each part of the headstock, different rib shapes were analyzed to predict the changes in thermal conduction route which contribute to thermal deformation. Three variations of wall thickness are also investigated, whose change causes thermal capacity balance between the front and rear part of the headstock, which contributes to different thermal   displacement.

To identify the optimum design by analyzing each possible combination of the control factors and levels is time consuming, for instance, the case study of Table 1 requires a total of 4374 analyses, which is far beyond practical. Therefore, the Taguchi method is applied to reduce the total analysis number. For above case with 7 control factors and 6 levels, it is possible to determine the optimal combination by analyzing only 18 conditions using Taguchi method, as explain in the following section.

5. Optimization of headstock structure