The analysis result shows that headstock structure of No. 11 will produce the best result with smallest thermal displacement and No. 9 will cause the largest displacement in minus direction of

X.   To   verify   this   result,   two   headstocks   are    manufactured

correspondingly and installed on the real NC lathes. The experiments were performed with spindle speed  at  500,  1000, 1500 and 2000 rpm. The thermal displacement was measured for 10 h to ensure displacement stabilization was reached  after spindle start rotation. Fig. 7 shows X axis displacement of the headstock in three cases: basic structure, structure of No. 11 and No.  9  at  different spindle speed.

While the basic headstock shows a proportional increase in thermal displacement with spindle speed, the No. 11 displaced less than 0.001 mm even at full spindle speed. Also in conformity with the above analysis results, structure of No. 9 contributed large displacement in minus direction of X. Fig. 8 shows the three cases’

comparison of thermal displacement in Y axis. All three   headstock

structures have the same tendency of enlarging thermal displace- ment in Y direction as the spindle speed  increases.

Fig. 9 shows the three cases’ comparison results of front and rear wall temperature change. For the basic headstock, the   front

wall is approximately 2.4 8C higher than the rear wall. This means the headstock will tilt backward, resulting in an X displacement shift  into  the  positive direction.

At the front wall, headstock No. 11 was 0.4 8C lower than the basic headstock, while the rear wall was 0.6 8C warmer, resulting in an approximately 1 8C difference reduction between the front and rear walls compared to the basic headstock’s case. This means that headstock No. 11 will tilt relatively forward compared to the tilting degree of the basic headstock’s case. This results in a displacement reduction for headstock at the steady state condition when is mounted on an actual machine. For headstock No. 9, the rear wall temperature was approximately 0.2 8C higher than the front wall, and the tendency of tilting forward was stronger than headstock No. 11, resulting in displacement shift into the minus direction of X.

7. Conclusions

A novel method is  proposed  for  designing  the  headstock structure for NC lathe with minimized thermal displacement in X direction using CAE techniques and Taguchi Method. With the proposed design method, an optimal headstock design immune to thermal displacement was possible after analyzing only  18 patterns, which dramatically reduces development time and costs comparing  to  the  traditional  trial  and  error    approach.

An optimal headstock is determined from the analysis results and manufactured with Full Mold Casing method. The thermal displacement of the headstock in X direction at spindle speed of 500, 1000, 1500 and 2000 rpm was measured respectively. The result was less than 0.001 mm, showing the consistency between the analysis and actual experiment result, which confirms the efficiency  of  the  proposed method.

References

[1] Moriwaki T, Shamoto E (1998) Analysis of Thermal Deformation of an Ultra- precision Air Spindle System. Annals of the CIRP   47(1):315–319.

[2] Brecher C, Hirsche B (2004) Compensation of Thermo-elastic Machine Tool Deformation Based on Control internal Data. Annals of the CIRP   53(1):299–304.

[3] Spur G, Hoffmann E, Paluncic Z, Benzinger K, Nymoen H (1988) Thermal Behavior Optimization of Machine Tools. Annals of the CIRP    37(1):401–405.