Page 312 - Intro Predictive Maintenance

Failure-Mode Analysis 303

Because this is a friction-driven motion, the cage turns much slower than the inner
race of the bearing. Generally, the rate of rotation is slightly less than one-half of the
shaft speed. The FTF is calculated by the following equation:

1 È BD ˘
FTF = f r 1 -
2 Î Í PD˚ ˙

Ball-Spin Frequency. Each of the balls or rollers within a bearing rotates around its
own axis as it rolls around the bearing races. This spinning motion is referred to as
ball spin, which generates a ball-spin frequency (BSF) in a vibration signature. The
speed of rotation is determined by the geometry of the bearing (i.e., diameter of the
ball or roller, and bearing races) and is calculated by:

1 PD È Ê BD ˆ 2 ˘
2
BSF = ¥ f r 1 - ¥ cos b ˙
Í
2 BD Î Ë PD ¯ ˚
Ball-Pass Outer-Race. The ball or rollers passing the outer race generate the ball-pass
outer-race frequency (BPFO), which is calculated by:

n Ê BD ˆ
BPFO = ¥ f r 1 - ¥ cosb
2 Ë PD ¯
Ball-Pass Inner-Race. The speed of the ball/roller rotating relative to the inner race
generates the ball-pass inner-race rotational frequency (BPFI). The inner race rotates
at the same speed as the shaft, and the complete set of balls/rollers passes at a slower
speed. They generate a passing frequency that is determined by:

n Ê BD ˆ
BPFI = ¥ f r 1 + ¥ cosb
2 Ë PD ¯

Defect Frequencies

Rolling-element bearing defect frequencies are the same as their rotational frequen-
cies, except for the BSF. If there is a defect on the inner race, the BPFI amplitude
increases because the balls or rollers contact the defect as they rotate around the
bearing. The BPFO is excited by defects in the outer race.

When one or more of the balls or rollers have a defect such as a spall (i.e., a missing
chip of material), the defect impacts both the inner and outer race each time one
revolution of the rolling element is made. Therefore, the defect vibration frequency is
visible at two times (2¥) the BSF rather than at its fundamental (1¥) frequency.

14.2.2 Bearings: Sleeve (Babbitt)
In normal operation, a sleeve bearing provides a uniform oil film around the supported
shaft. Because the shaft is centered in the bearing, all forces generated by the