dX ¼ d — d

(1)

*    Corresponding  author.

X1 X2

2

0007-8506/$ – see front matter © 2009 CIRP. doi:10.1016/j.cirp.2009.03.033

332 M. Mori et al. / CIRP Annals - Manufacturing Technology 58 (2009)   331–334

Fig. 1. Headstock structure and thermal boundary conditions for the analysis model.

Fig. 2. Mounting view of thermal displacement sensor.

dY ¼ d — d

(2)

Fig. 3. Selected features for model  analysis.

Y 1 Y 2

2

where dX: thermal displacement in X axis direction; dY: thermal displacement in Y axis direction; dX1, dX2, dY1, dY2: distance between the sensors (X1, X2, Y1, Y2) and the   workpiece.

3. Thermal analysis model and boundary condition

A CAE model is built to conduct thermal analysis. This model includes the headstock, turret, tailstock and the lathe machine bed. The boundary conditions are given with initial temperature distribution, localized heat sources and external  airflow.

The initial temperature distribution was derived by using the commercial CFD (Computational Fluid Dynamics) software pack- age, FLUENT. With this distribution, thermal strain was calculated and the results were further applied to determine the overall thermal displacements by using the CAE software, IDEAS.

Heat values for sources of front bearing housing, rear bearing housing and the motor, were obtained in the following manner: the power output of spindle motor was acquired from the load meter of the spindle amplifier first; heat values of front and rear bearings were calculated using the bearing housing analysis program, BRAIN; then the heat values of spindle motor was calculated by subtracting the bearing housings’ heat values from the power output of spindle  motor.

Since the heat transmission from the spindle affects the thermal displacement of the whole machine, the machine bed, turret and tailstock were also included in the analysis model. In addition, the machine cover was added to model the airflow caused by spindle rotation more accurately.

To verify analysis result, temperature change was measured at several points for comparison. The measurement was  conducted

under fixed ambient temperature of 22 8C with spindle speed of 1000 rpm. The analysis result shows a 3–12.5% difference of temperature compared to the   experiment.

4. Analysis model of headstock

To design the headstock structure with minimal X axis thermal displacement, the critical features that affects headstock thermal displacement were investigated. Fig. 3 shows these features which are also called control factors: (A) rib shape and cast hole; (B) thickness of headstock cylinder; (C) thickness of front wall; (D) thickness of rear wall; (E) thickness of rib; (F) thickness of right wall; (G) thickness of left  wall.

Table 1  shows  the  control  factor’s  value  at  each  level. The currently used headstock is referred  as  basic  headstock. The bold values in Tables 1 and 2 are conditions of the basic headstock. For control factor A, 6 cases were studied, which are 3 cases with different rib shapes and 3 cases combined with cast

Table 1

Value of control factor at each level.

Control factor Level 1 Level 2