CEMB USA N500 - Manual (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
BD S
= 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
PD S
= BSP
b - rotating external ring (fixed internal ring)
⎥
⎦
⎤
⎢
⎣
⎡
Θ ⋅ ⎟
⎠
⎞
⎜
⎝
⎛
+ ⋅
cos
PD
BD S
= 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
PD S
= 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)