AN INTEGRATED APPROACH TOWARD THE DYNAMIC ANALYSIS OF HIGH-SPEED SPINDLES .1. SYSTEM MODEL

Experimental evidence (Shin, 1992) has shown that the natural frequenc ies of high-speed spindles with angular contact ball bearings decrease with increasing rotational speed. A recent study (Wang et al., 1991) illustrated that this phenomenon is caused by stiffness change of the bearings. A simplified approximation was used in the past analysis to examine the bearing radial stiffness at high speeds. While the investi gation explained the experimental observations in a qualitative sense, the analytical results so far are not sufficient to quantitatively de scribe the spindle behavior under high speed and load operations due t o the assumptions and approximations made in the modeling process. Thi s paper presents an integrated approach toward the modeling of flexibl e spindles with angular contact ball bearings from basic principles. T he local dynamics of the bearings are coupled with the global shaft mo tion. The model derived includes both the longitudinal and transverse vibrations of the shaft interacting with the nonlinear bearings. The i nfluences of shaft speed on the bearing stiffness matrix and the syste m frequencies are studied. It is shown that the spindle dynamic behavi or can vary substantially as speed increases due to the bearing gyrosc opic moment and centrifugal force. These effects have been ignored in most of the previous spindle models. This unique characteristic, which is critical to high-speed machinery, is rigorously studied for the fi rst time. Lab tests are conducted to validate the model. The analytica l predictions are quantitatively verified by the experimental results.