CEMB USA N500 User 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)