An Integrated Approach Toward the Dynamic Analysis of High-Speed Spindles: Part I—System Model

Experimental evidence (Shin, 1992) has shown that the natural frequencies 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 investigation explained the experimental observations in a qualitative sense, the analytical results so far are not sufficient to quantitatively describe the spindle behavior under high speed and load operations due to the assumptions and approximations made in the modeling process. This paper presents an integrated approach toward the modeling of flexible spindles with angular contact ball bearings from basic principles. The local dynamics of the bearings are coupled with the global shaft motion. The model derived includes both the longitudinal and transverse vibrations of the shaft interacting with the nonlinear bearings. The influences of shaft speed on the bearing stiffness matrix and the system frequencies are studied. It is shown that the spindle dynamic behavior can vary substantially as speed increases due to the bearing gyroscopic 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 first time. Lab tests are conducted to validate the model. The analytical predictions are quantitatively verified by the experimental results.