When single-row radial ball bearings are used, several critical speeds take place in a vertical shaft at certain rotating speeds lower than the major critical speed. When the bearing center line of both bearing pedestals is not in alignment and the shaft is not in a perfectly straight line, there is the possibility that these critical speeds occur. The frequencies of vibrations of these critical speeds are represented by zω₁, zω₁+1 and zω₁-1, where ω₁ is the precessional rotating speed of balls in bearing and z is the number of balls. The whirling motions of these critical speeds are those of both forward and backward precessions. When self-aligning double-row ball bearings are used, these critical speeds do not occur ; they occur only in the shaft supported by single-row radial ball bearings.