CEMB N500 - Page 86

C - 6 A rapid guide to interpreting a spectrum
3. FORMULAE FOR CALCULATING TYPICAL BEARING DEFECT
FREQUENCIES
SYMBOLS:
FTF = housing frequency
BPFO = defect on outer track
BPFI = defect on inner track
BSP = defect on roller/ball
The frequencies of bearings can be calculated if we know:
S = number of shaft rpm
PD = primitive diameter
BD = ball/roller diameter
N = number of balls/rollers
Θ = angle of contact
The most common case:
a - fixed external ring (rotating internal ring)
⎥
⎦
⎤
⎢
⎣
⎡
Θ⋅
⎟
⎠
⎞
⎜
⎝
⎛
−⋅ cos
PD
BDS
=FTF 1
2
⎥
⎦
⎤
⎢
⎣
⎡
Θ⋅
⎟
⎠
⎞
⎜
⎝
⎛
−⋅⋅ cos
PD
BD
N
S
=BPFO 1
2
⎥
⎦
⎤
⎢
⎣
⎡
Θ⋅
⎟
⎠
⎞
⎜
⎝
⎛
⋅⋅ cos
PD
BD
+N
S
=BPFI 1
2
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
Θ⋅
⎟
⎠
⎞
⎜
⎝
⎛
−⋅
⎟
⎠
⎞
⎜
⎝
⎛
⋅
2
1
2
cos
PD
BD
BD
PDS
=BSP
b - rotating external ring (fixed internal ring)
⎥
⎦
⎤
⎢
⎣
⎡
Θ⋅
⎟
⎠
⎞
⎜
⎝
⎛
+⋅ cos
PD
BDS
=FTF 1
2
⎥
⎦
⎤
⎢
⎣
⎡
Θ⋅
⎟
⎠
⎞
⎜
⎝
⎛
−⋅⋅ cos
PD
BD
N
S
=BPFO 1
2
⎥
⎦
⎤
⎢
⎣
⎡
Θ⋅
⎟
⎠
⎞
⎜
⎝
⎛
⋅⋅ cos
PD
BD
+N
S
=BPFI 1
2
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
Θ⋅
⎟
⎠
⎞
⎜
⎝
⎛
−⋅
⎟
⎠
⎞
⎜
⎝
⎛
⋅
2
1
2
cos
PD
BD
BD
PDS
=BSP
Approximate calculation formulae (± 20%)
FTF = 0.4 x S (a) or 0.6 x S (b)
BPFO = 0.4 x N x S (a) or (b)
BPFI = 0.6 x N x S (a) or (b)
BSP = 0.23 x N x S (N < 10) (a) or (b)
= 0.18 x N x S (N ≥ 10) (a) or (b)