Rolling-Element Bearing Defect Frequencies

Which is exactly why they are hard to spot and exactly why they identify the damaged part precisely. The physical picture is a rolling element passing a defect once per encounter: a crack in the stationary outer race is struck by each ball as it rolls past, and a crack in the rotating inner race is struck at a HIGHER rate because the race is moving toward the balls. That is the whole reason the inner-race frequency sits above the outer-race one, and why the ratio of a measured peak to shaft speed says WHICH race has failed -- information no overall reading carries at all. Two field facts make these numbers more useful than they look. The non-integer ratio is diagnostic in itself: a peak at 3.56 times running speed cannot be anything mechanical except a bearing, because nothing else in the machine has a non-integer order -- blades, teeth, and rotor bars are all whole numbers. And inner-race defects produce SIDEBANDS spaced at running speed, because the defect moves in and out of the load zone once per revolution, so a set of evenly spaced peaks around a non-integer centre is close to a positive identification. A 6311 deep-groove ball bearing with 9 balls on a 1,780 rpm shaft gives an outer race at 105.68 Hz and 3.56x, an inner race at 161.32 Hz and 5.44x, a ball spin at 68.10 Hz, and a cage at 11.74 Hz. When the bearing number is unknown, the rough approximations of 0.4 times the ball count for the outer race and 0.6 for the inner get close enough to search a spectrum -- 3.6 against 3.56 and 5.4 against 5.44 here. The cage frequency times the ball count equals the outer race frequency exactly, which is a useful arithmetic check on an entered geometry. This computes frequencies from geometry the user supplies. It does not detect a defect, and the frequencies are present in the spectrum of a healthy bearing at low amplitude -- amplitude, trend, and the high-frequency envelope or demodulated spectrum are what find early damage, and a defect frequency at a normal level is not a finding. The formulas assume pure rolling with no slip, and real bearings slip: actual defect frequencies run one to two percent below the calculated values, so a peak that is close but not exact is still the bearing. Contact angle changes with axial load on an angular-contact bearing, which shifts every one of these. It does not evaluate lubrication, clearance, mounting, or the load zone, and it does not compute bearing life. The bearing manufacturer's published defect frequencies for the specific part number, and a qualified vibration analyst, govern.

cage FTF = (fr/2)(1 - (d/D) cos a); outer race BPFO = (n/2)(1 - (d/D) cos a) fr; inner race BPFI = (n/2)(1 + (d/D) cos a) fr; ball spin BSF = (D/2d)(1 - ((d/D) cos a)^2) fr, for n rolling elements of diameter d on pitch diameter D at contact angle a.

The standard rolling-element bearing defect frequency relations as condition monitoring practice, by name. Pure rolling is assumed; real bearings slip, so measured frequencies run one to two percent below these. The bearing manufacturer's published defect frequencies for the specific part number, and a qualified vibration analyst, govern.

Geometry arithmetic on bearing dimensions the user supplies; no manufacturer frequency table is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: rpm, ball_count, ball_diameter_in, pitch_diameter_in, contact_angle_deg, shaft_hz, ftf_hz, bpfo_hz, bpfi_hz, bsf_hz, bpfo_order, bpfi_order

• Pure rolling assumed real slip puts measured frequencies one to two percent lowcondition monitoring practice
• Frequencies are present on a healthy bearing amplitude, trend and the envelope spectrum find damage, not the frequencycondition monitoring practice
• Contact angle shifts with axial load which moves every one of these on an angular-contact bearingthe bearing manufacturer's data