15. TECHNICAL DATA
DEFINIONS OF SYMBOLS AND THEIR UNITS
Symbols
a
b
Cr
C0r
15. 1 AXIAL DISPLACEMENT OF BEARINGS
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
(1) Contact Angle and Axial Displacement of
Deep Groove Ball Bearings and Angular Contact Ball Bearings
(2) Axial Load and Axial Displacement of Tapered Roller Bearings
Page
A 128
Ca
C0a
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
A 128
A 128
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
A 130
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
(1) Surface Pressure, Maximum Stress on Fitted Surfaces
and Expansion or Contraction of Raceway Diameter
(2) Interferences or Clearances for Shafts and Inner Rings
(3) Interferences or Clearances for Housing Bores and
Outer Rings
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
A 130
A 130
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
A 130
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
15. 3 RADIAL AND AXIAL INTERNAL CLEARANCES
(1) Radial and Axial Internal Clearances for
Single-Row Deep Groove Ball Bearings
(2) Radial and Axial Internal Clearances for
Double-Row Angular Contact Ball Bearings
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
A 132
A 132
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
A 132
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
A 134
(1) Axial Load and Starting Torque of
Tapered Roller Bearings
(2) Preload and Starting Torque of Angular Contact Ball
Bearings and Double-Direction Angular Contact Thrust
Ball Bearings
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
15. 5 COEFFICIENTS OF FRICTION AND OTHER BEARING DATA
(1) Bearing Types and Their Coefficients of Friction
(2) Circumferential Speed of Rolling Elements
about Their Centers and Bearing Center
(3) Radial Internal Clearance and Fatigue Life
A 134
A 134
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
A 136
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
A 136
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
15. 6 BRANDS AND PROPERTIES OF LUBRICATING GREASES
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
A 136
A 136
A 138
A126-141E.indd 126-127
na
nc
(N){kgf}
ne
ni
(N){kgf}
(N){kgf}
(N){kgf}
pm
P
Q
re
ri
va
De
Di
( mm )
( mm )
( mm )
vc
D0
Dpw
Dw
Housing Outside Diameter
Rolling Element Pitch Diameter
Nominal Rolling Element Diameter
( mm )
( mm )
( mm )
e
E
E(k)
Contact Position of Tapered Roller End
Face with Rib
Modulus of Longitudinal Elasticity
(Bearing Steel)
208 000 MPa{21 200 kgf/mm2 }
β
δa
&a
&d
factor which depends on the geometry of
the bearing components and on the
applicable stress level
h
h0
k
De/D
D/D0
d/Di
K
Constant Determined by Internal
Design of Bearing
Fatigue Life when Effective Clearance is 0
Effective Leng of Roller
Fatigue Life when Effective Clearance is
&
m0
αR
√( )
Function of ε
Axial Load, Preload
Radial Load
L
Lwe
Lε
α0
——
——2
b
1– —
a
Fa
Fr
f (ε)
Distance between Centers of Curvature of
Inner and Outer Rings
ri + re –Dw
Frictional Torque
Spin Friction
Z
α
( mm )
Complete elliptic integral of the 2nd kind
for which the population parameter is
k=
M
Ms
A 126
Symbols
( mm )
f0
15. 4 PRELOAD AND STARTING TORQUE
Units
( mm )
( mm )
Shaft Diameter, Nominal Bearing Bore
Diameter
Housing Bore Diameter, Nominal Bearing
Outside Diameter
Outer Ring Raceway Diameter
Inner Ring Raceway Diameter
d
D
15. 2 FITS
Nomenclature
Contact Ellipse Major Axis
Contact Ellipse Major Axis
Basic Dynamic Load Rating of Radial
Bearings
Basic Static Load Radial of Radial
Bearings
Basic Dynamic Load Rating of Thrust
Bearings
Basic Static Load Rating of Thrust
Bearings
&r
(N){kgf}
(N){kgf}
&D
& De
& Di
ε
μ
( mm )
μe
μs
σt max
Nomenclature
Rotating Speed of Rolling Elements
Revolving Speed of Rolling Elements
(Cape Speed)
Speed of Ouder Ring
Speed of Inner Ring
Surface Pressure on Fitted Surface
Bearing Load
Rolling Element Load
Groove Radius of Outer Ring
Groove Radius of Inner Ring
Circumferential Speed of Rolling Element
about Its Center
Circumferential Speed of Rolling Element
about Beaing Center
Number of Rolling Elements per Row
Contact Angle (when axial load is applied
on Radial Ball Bearning
Initial Confact Angle (Geometri) (when
inner and outer rings of Angular Contact
Ball Bearings are pushed axially)
Initial Contact Angle (Geometric) (when
inner and outer rings Angular Contact
Ball Bearing are pushed radially)
1/2 of Conical Angle of Roller
Relative Axial Displacement of Inner and
Outer Rings
Axial Internal Clearance
Effective Interference of Inner Ring and
Shaft
Radial Internal Clearance
Effective Interference of Outer Ring and
Housing
Contraction of Outer Ring Raceway
Diameter due to Fit
Expansion of Inner Ring Raceway
Diameter dus to Fit
Units
(min–1)
(min–1)
(min–1)
(min–1)
(MPa ){kgf/mm2}
(N){kgf}
(N){kgf}
( mm )
( mm )
(m/sec)
(m/sec)
(° )
(° )
(° )
(° )
( mm )
( mm )
( mm )
( mm )
( mm )
( mm )
( mm )
Load Factor
Coefficient of Dynamic Friction of Rolling
Bearing
Coefficient of Friction between Roller End
Face and Rib
Coefficient of Sliding Friction
Maximum Stress on Fitted Surfaces
(MPa ){kgf/mm2}
( mm )
(N·mm){kgf·mm}
(N·mm){kgf·mm}
A 127
11/20/13 4:53:03 PM
15°
10°
5°
0
0.1
0.2
0.3
0.4
0.5
06C
10C
C
B
03B 04B
A
06B
08B
A
08
A
10
2A
1 4 A ,20A,2
18A
Digits: Bearing Bore Number
C…… α 0 = 15°
A…… α 0 = 30°
B…… α 0 = 40°
0.6
0
10B
14B
20B
18B, B
26
24A
0
500
1000
1500
2000
2500 N
0
50
100
150
200
250 kgf
Axial Load Fa
Fig. 15.3 Axial Load and Axial Displacement of
Angular Contact Ball Bearings
Remarks:
Actual axial displacement may vary depending on
the shaft/housing thickness, material, and fitting
interference with the bearing. Please contact NSK
about such factors of axial displacement which are
not discussed in detail in this catalog.
μm
0°
80
= 10°
α0
60
α 0= 1
α 0 = 15°
40
Se
rie
s
es
HR
32
3J
06
HR
32
2
08
10
12
14
10
12
14
16
18
20
5
14
12
16
14
16
18
20
s
Serie
J
D
3
08D
HR30
D
0
1
14D
6210
6310
20
0
10
10
10
α 0 = 15 °
0°
08
08
HR3
02J
Serie
s
04
α 0=
Axial Displacement δa
Axial Displacement δa
120
100
06
15
06
= 0°
α0
140
JS
eri
ies
Ser
03J
H R3
160
06
20
μm
0
0
500
50
1000
100
1500
150
2000
200
2500
250
3000
300
Axial Load Fa
Fig. 15.2 Axial Load and Axial Displacement of
Deep Groove Ball Bearings
A126-141E.indd 128-129
06
0.010
Fig. 15.1 Fa /Cor and Contact Angle of
Deep Groove and Angular
Contact Ball Bearings
}
00
A
Fa /Cor
Fa0.9 ................. (N)
δ a = 0.000077
1.9
0.9
(sin α) Z L we0.8
(mm)
0.9
0.0006
F
a
δa =
.............. {kgf }
(sin α)1.9 Z 0.9 L we0.8
A 128
04
72
A
0.005
0°
(2) Axial Load F a and Axial Displacement δ a of
Tapered Roller Bearings
(Fig. 15.4)
14C
4C
0.015
26
20°
720
Contact Angle α
}
25°
02
08
)
20°
15°
10°
5°
0°
04
(
)
mm
25°
30°
Deep Groove Ball Bearing and Angular Contact
Ball Bearings
(Figs. 15.1 to 15.3)
1
0.00044 Q 2 3
................... (N)
δ a = sin α
Dw
(mm)
1
0.002 Q 2 3
..................... {kgf }
δ a = sin α
Dw
Fa
Q=
(N), {kgf}
Zsin α
(
α 0=30°
08C
35°
Axial Displacement δa
15. 1 Axial Displacement of Bearings
(1) Contact Angle α and Axial Displacement δ a of
18
C,2
0C
,22
72
C
00
A
TECHNICAL DATA
3500 N
350
kgf
0
0
1000
2000
3000
0
100
200
300
4000 N
400 kgf
Axial Load Fa
Fig. 15.4 Axial Load and Axial Displacement of
Tapered Roller Bearings
A 129
11/20/13 4:53:04 PM
TECHNICAL DATA
MPa kgf/mm2
kgf/mm2 MPa
In case of housing outside dia. D0 ≠∞
Surface
Pressure
E & D (1– h2)(1– h02)
pm =
2 D
1– h2 h02
E &d
(1 – k2 ) In case D0 = ∞
2 2
E &D
pm =
(1– h2)
2 D
(In case of sold shaft)
pm
(MPa )
pm =
{kgf/mm2}
Maximum stress Maximum circumferential
stress on fitted surface of
σ t max
inner ring bore is
(MPa )
1 + k2
{kgf/mm2} σ t max = pm
1 – k2
Expansion of
inner ring
raceway dia.
& Di (mm)
In case of solid shaft
& Di
Maximum circumferential stress on
outer ring bore surface is
2
σ t max = pm
1– h2
In case D0 ≠∞
& De = & D · h
= &d . k
Contraction of
outer ring
raceway dia.
& De (mm)
5
4
3
50
40
30
2
20
250 25
200 20
100 10
p6
n6
k5
10
js5
5
4
3
0.5
0.4
0.3
0.2
2
0.1
1
20
30
50 70 100
200 300
50
40
30
5
4
3
20
2
10
1
5
500 mm
0.5
5
4
3
50
40
30
2
20
p6
n6
m5
k5
100 10
1
10
0.5
0.4
0.3
5
4
3
0.2
2
20
30
50 70 100
200 300
50
40
5
4
30
3
20
2
10
500 mm
1
Nominal Bearing Bore Diameter d (Class Normal)
Fig. 15.5 Surface Pressure m and Maximum Stress
σ t max for Average Fitting Interference
In case D0 = ∞
400 40
300 30
250 25
200 20
150 15
js5
Nominal Bearing Bore Diameter d (Class Normal)
1– h02
1– h2 h02
MPa kgf/mm2
10 100
150 15
m5
1
kgf/mm2 MPa
m
Housing & Bore & Outer Ring
Surface Pressure
Shaft & Inner Ring
Maximum Stress σ t max
Items
Maximum Stress σ t max
Table. 15. 1 Surface Pressure, Maximum Stress on Fitted
Surfaces and Expansion or Contraction
m
(1) Surface Pressure p m , Maximum Stress σ tmax
on Fitted Surfaces and Expansion of Inner Ring
Raceway Diameter & Di or Contraction of Outer
Ring Raceway Diameter & De
(Table 15.1, Figs. 15.5 and 15.6)
(2) Interferences or Clearances of Shafts and Inner
Rings (Table 15.2)
(3) Interferences or Clearances of Housing Bores
and Outer Rings (Table 15.3)
Surface Pressure
15.2 Fits
Fig. 15.6 Surface Pressure m and Maximum Stress
σ t max for Maximum Fitting Interference
& De = & D · h
Remarks
The modulus of longitudinal elasticity and Poisson's ratio for
the shaft and housing material are the same as those for inner
and outer rings.
Reference 1 MPa =1 N/ mm2= 0.102 kgf / mm2
Table 15. 2 Interferences or Clearances
Single Plane
Size
Mean Bore
Classification Dia. Deviation
(Normal)
(mm)
& d mp
over
incl.
high
low
3
6
10
6
10
18
0
0
0
18
30
50
30
50
65
65
80
100
Interferences or Clearances for
f6
g5
Clearance
g6
h5
h6
js5
min.
– 8
– 8
– 8
18
22
27
2
5
8
9
11
14
4
3
2
12
14
17
4
3
2
5
6
8
8
8
8
8
9
11
8
8
8
0
0
0
– 10
– 12
– 15
33
41
49
10
13
15
16
20
23
3
3
5
20
25
29
3
3
5
9
11
13
10
12
15
13
16
19
10
12
15
4.5
5.5
6.5
80
100
120
0
0
0
– 15
– 20
– 20
49
58
58
15
16
16
23
27
27
5
8
8
29
34
34
5
8
8
13
15
15
15
20
20
19
22
22
15
20
20
120
140
160
140
160
180
0
0
0
– 25
– 25
– 25
68
68
68
18
18
18
32
32
32
11
11
11
39
39
39
11
11
11
18
18
18
25
25
25
25
25
25
180
200
225
200
225
250
0
0
0
– 30
– 30
– 30
79
79
79
20
20
20
35
35
35
15
15
15
44
44
44
15
15
15
20
20
20
30
30
30
250
280
315
280
315
355
0
0
0
– 35
– 35
– 40
88
88
98
21
21
22
40
40
43
18
18
22
49
49
54
18
18
22
23
23
25
355
400
450
400
450
500
0
0
0
– 40
– 45
– 45
98
108
108
22
23
23
43
47
47
22
25
25
54
60
60
22
25
25
25
27
27
Remarks
max.
max.
max.
max.
max.
max.
max.
max.
Units : μm
Each Fitting Class
js6
j5
Inter- Clearance Inter- Clearance Inter- Clearance Inter- Clearance Inter- Clearance InterClearance ference
ference
ference
ference
ference
ference
max.
of Shafts and Inner Rings
j6
k5
Inter- Clearance Inter- Interference
Clearance ference
ference
k6
m5
m6
n6
p6
r6
Size
Classification
(mm)
Interference
Interference
Interference
Interference
Interference
Interference
min.
max.
min.
max.
min.
max.
min.
max.
min.
min.
max.
min.
max.
over
incl.
—
15
16
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
3
6
10
6
10
18
4
5
7
19
23
27
2
2
2
21
25
30
2
2
2
25
30
36
—
9
11
—
32
39
—
9
11
—
37
45
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
18
30
50
30
50
65
9.5 24.5
11
31
11
31
7
9
9
27
33
33
2
3
3
30
38
38
2
3
3
36
45
45
11
13
13
39
48
48
11
13
13
45
55
55
20
23
23
54
65
65
—
37
37
—
79
79
—
—
—
—
—
—
65
80
100
80
100
120
32
32
32
12.5 37.5
12.5 37.5
12.5 37.5
11
11
11
39
39
39
3
3
3
46
46
46
3
3
3
53
53
53
15
15
15
58
58
58
15
15
15
65
65
65
27
27
27
77
77
77
43
43
43
93
93
93
63
65
68
113
115
118
120
140
160
140
160
180
13
13
13
37
37
37
14.5 44.5
14.5 44.5
14.5 44.5
13
13
13
46
46
46
4
4
4
54
54
54
4
4
4
63
63
63
17
17
17
67
67
67
17
17
17
76
76
76
31
31
31
90
90
90
50
50
50
109
109
109
77
80
84
136
139
143
180
200
225
200
225
250
46.5
46.5
52.5
16
16
18
42
42
47
16
16
18
51
51
58
16
16
18
51
51
58
4
4
4
62
62
69
4
4
4
71
71
80
20
20
21
78
78
86
20
20
21
87
87
97
34
34
37
101
101
113
56
56
62
123
94
123
98
138 108
161
165
184
250
280
315
280
315
355
52.5
58.5
58.5
18
20
20
47
52
52
18
20
20
58
65
65
18
20
20
58
65
65
4
5
5
69
77
77
4
5
5
80
90
90
21
23
23
86
95
95
21
23
23
97
108
108
37
40
40
113
125
125
62
68
68
138 114
153 126
153 132
190
211
217
355
400
450
400
450
500
max.
max.
max. max.
max.
max.
max.
max.
—
3
4
—
11
12
—
2
3
—
12
13
—
—
4.5 12.5
5.5 13.5
—
2
3
14.5
17.5
21.5
4
5
7
15
18
21
6.5 16.5
8
20
9.5 24.5
6.5
7.5
7.5
21.5
27.5
27.5
7
9
9
21
26
26
25
25
25
9
9
9
34
34
34
11
11
11
29
29
29
30
30
30
10
10
10
40
40
40
35
35
40
32
32
36
35
35
40
11.5
11.5
12.5
40
45
45
36
40
40
40
45
45
12.5
13.5
13.5
max.
1. The figures for tolerance classes where stress caused by the fitting of the shaft and inner ring becomes
excessive are omitted.
2. The tolerance range js is now recommended instead of j.
A 130
A126-141E.indd 130-131
A 131
11/20/13 4:53:06 PM
TECHNICAL DATA
Table 15. 3 Interferences or
Single Plane
Mean O. D.
Size
Deviation
Classification
(Normal)
(mm)
& D mp
over
incl.
high
6
10
18
10
18
30
0
0
0
–
–
–
30
50
80
50
80
120
120
150
180
250
315
400
Interferences or Clearances for
low
G7
H6
H7
H8
Clearance
Clearance
Clearance
Clearance
max.
min.
8
8
9
28
32
37
0
0
0
– 11
– 13
– 15
150
180
250
0
0
0
315
400
500
500 630
630 800
800 1 000
J6
JS6
Clearances of Housing Bores and Outer Rings
J7
JS7
Inter- Clearance Inter- Clearance InterClearance ference
ference
ference
max.
min.
max.
min.
max.
min.
max.
max.
max.
max.
5
6
7
17
19
22
0
0
0
23
26
30
0
0
0
30
35
42
0
0
0
13
14
17
4
5
5
12.5
13.5
15.5
4.5
5.5
6.5
45
53
62
9
10
12
27
32
37
0
0
0
36
43
50
0
0
0
50
59
69
0
0
0
21
26
31
6
6
6
19
22.5
26
– 18
– 25
– 30
72
79
91
14
14
15
43
50
59
0
0
0
58
65
76
0
0
0
81
88
102
0
0
0
36
43
52
7
7
7
0
0
0
– 35
– 40
– 45
104
115
128
17
18
20
67
76
85
0
0
0
87
97
108
0
0
0
116
129
142
0
0
0
60
69
78
0
0
0
– 50
– 75
–100
142
179
216
22
24
26
94
125
156
0
0
0
120
155
190
0
0
0
160
200
240
0
0
0
—
—
—
max.
Units : μm
Each Fitting Class
K6
K7
M6
M7
N6
N7
P6
Size
Classification
(mm)
P7
Inter- Clearance Inter- Clearance Inter- Clearance Inter- Clearance Inter- Clearance Inter- Clearance Inter- Interference
Clearance ference
ference
ference
ference
ference
ference
ference
Interference
max.
max.
max.
min.
max.
over
incl.
16
18
21
7
8
9
15
17
19
7
9
10
10
10
11
7
9
11
13
14
15
10
12
15
5
4
5
12
15
17
8
8
9
15
18
21
1
1∗
2∗
16
20
24
4
3
2
19
23
28
4
7
9
21
26
31
1
3
5
24
29
35
6
10
18
10
18
30
8
9.5
11
25
31
37
11
12
13
23
28
32
12
15
17
14
17
19
13
15
18
18
22
25
18
21
25
7
8
9
20
24
28
11
13
15
25
30
35
1∗
1∗
1∗
28
33
38
3
4
5
33
39
45
10
13
15
37
45
52
6
8
9
42
51
59
30
50
80
50
80
120
30.5
37.5
44.5
12.5
12.5
14.5
44
51
60
14
14
16
38
45
53
20
20
23
22
29
35
21
21
24
30
37
43
28
28
33
10
17
22
33
33
37
18
25
30
40
40
46
2∗
5
8
45
45
51
6
13
16
52
52
60
18
11
11
61
61
70
10
3
3
68
68
79
120
150
180
150
180
250
7
7
7
51
58
65
16
18
20
71
79
88
16
18
20
61
68
76
26
28
31
40
47
53
27
29
32
51
57
63
36
40
45
26
30
35
41
46
50
35
40
45
52
57
63
10
14
18
57
62
67
21
24
28
66
73
80
12
11
10
79
87
95
1
1
0
88
98
108
250
315
400
315
400
500
—
—
—
72
100
128
22
25
28
—
—
—
—
—
—
85
115
145
35
40
45
50
75
100
44
50
56
50
75
100
70
80
90
24
45
66
70
80
90
24
45
66
96
110
124
6
25
44
88
100
112
6
25
44
114
130
146
28
13
0
122
138
156
28
13
0
148
168
190
500
630
630
800
800 1 000
max. max. max. max. max. max. max. max. max. max. max. max. max. max.
Note (∗) Indicates the minimum interference
Remarks The tolerance range JS is now recommended instead of J.
15.3 Radial and Axial Internal
Clearances
Table 15. 4 Constant K
(2) Radial Internal Clearance & r and Axial
Internal Clearance & a in Double-Row
Angular Contact Ball Bearings
(Fig. 15.8)
&a = 2
√
&
m 0 – m 0 cosα R – r
2
2
(
– 2 m 0 sinα R
A 132
A126-141E.indd 132-133
)
2
(mm)
1.14
1.06
1.06
1.11
1.07
1.20
1.19
1.37
1.45
1.57
1.64
1.70
2.09
1.82
1.88
1.95
2.01
2.06
2.11
2.16
2.25
2.32
2.40
2.40
2.49
2.59
2.59
62Series
24~30
21, 22
16, 17
13~15
10~11
07
04~06
00~02
0.50
0.30
0.20
63Series
28, 30
22, 24
17~19
15, 16
10, 11
07
05, 06
01~04
µm
0.10
160Series
26~30
21~24
16~17
11~13
06~08
01~03
0.05
0.04
0.03
60Series
22~28
21
16~17
11~13
07~10
02~05
01
80
°
63XX
0.93
0.93
0.93
0.99
1.06
1.06
1.07
1.25
1.29
1.29
1.33
1.40
1.50
1.54
1.57
1.57
1.64
1.70
1.76
1.82
1.88
1.95
2.01
2.06
2.11
2.11
2.11
ot
25
62XX
—
0.80
0.93
0.93
0.96
0.96
1.01
1.06
1.06
1.11
1.11
1.20
1.20
1.20
1.29
1.29
1.37
1.37
1.44
1.44
1.44
1.54
1.64
1.64
1.70
1.70
1.76
rc
1
2
60XX
—
0.80
0.80
0.80
0.90
0.90
0.96
0.96
0.96
1.01
1.01
1.06
1.06
1.06
1.16
1.16
1.20
1.20
1.29
1.29
1.29
1.37
1.40
1.40
1.54
1.54
1.57
&
K = 2 (re + r i – Dw)
160XX
00
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
24
26
28
30
5320
5315
5310
5305
a=
where
Bore No.
60
&
(mm)
1.00
Axial Internal Clearance & a
& aHK & r
1
2
mm
Values of K
Axial Internal Clearance & a
(1) Radial Internal Clearance & r and Axial
Internal Clearance & a in Single-Row
Deep Groove Ball Bearings
(Fig. 15.7)
5220
40
5215
5205 5210
5200
20
0
0.02
0.001
0.003
0.005
0.01
0.02
0.03
0.05
0.1
Radial Internal Clearance & r
Fig. 15.7 & r and & a in Single-Row Deep Groove Ball Bearings
0.2
mm
0
10
20
30
40
Radial Internal Clearance & r
50
µm
Fig. 15.8 & r and & a in Double-Row Angular
Contact Ball Bearings (52, 53 Series)
A 133
11/20/13 4:53:07 PM
TECHNICAL DATA
(N·mm), {kgf·mm}
M = e μe Fa cosβ
where
μe : 0.20
When bearings with the same number are used in
opposition, the torque M caused by the preload
becomes 2M.
M = Ms Z sinα
where Ms is spin friction
3
Ms = — μs Q a E(k)
8
μs = 0.15
When bearings with the same number are used in
opposition, the torque M caused by the preload
becomes 2M.
F
2β
0
μe Qf
e
(N·mm), {kgf·mm}
where
Dw1
Qf
(N·mm), {kgf·mm}
L
Starting Torque of Duplex Bearings
(for two bearings) 2M
(1) Axial Load Fa and Starting Torque M of Tapered
Roller Bearings (Figs. 15.9 and 15.10)
Qe
kgf . mm N . mm
(2) Preload Fa and Starting Torque M of Angular
Contact Ball Bearings and Double-Direction
Angular Contact Thrust Ball Bearings (Figs. 15.11
and 15.12)
15. 4 Preload and Staring Torque
30
300
20
200
22
10
22 20 0
14 1
00 ries
Se
70C
Qi
α
100
0
20
16 ,10
8
08
1 4
1
,
12 06
04 02 00
ies
Ser
72C
0
Fig. 15.9 Relation between e and β
0
500
1000
1500
2000 N
0
50
100
150
200 kgf
Preload Fa
Fig. 15.11 Preload and Starting Torque for Back-to-Back or Face-to-Face Arrangements
of Angular Contact Ball Bearings (α =15°)
kgf·mm
N·mm
5000
500
kgf . mm N . mm
14
12
4000
400
70
10
14
14
D
200
12
D
10
10
100
14
1000
08
06
0
0
10
5000
0
500
er
ies
HR
30
3
04
s
06
08D
06
04
S
s
3J
rie
30
Se
HR
2J
30
R
H
0
06
D
08
18
,16
12
14
2000
60
Se
DJ
rie
s
HR
32
Se
2J
rie
600
280TAC20
240TAC20
200TAC20
150TAC20
100TAC20
80TAC20
08
Starting Torque M
300
3000
16
Starting Torque M
18
700
rie
s
10000
1000
Axial Load Fa
Fig. 15.10 Relation between Axial Load and Starting
Torque of Tapered Roller Bearings
Se
3J
2
3
HR
15000
1500
50
40
30
500
400
60TAC20
50TAC20
40TAC20
300
20
200
10
100
0
0
240TAC29
170TAC29
140TAC29
120TAC29
100TAC29
80TAC29
60TAC29
N
kgf
0
1000
0
100
2000
200
3000
300
4000
400
5000
500
6000
600
7000
700
8000
800
9000
900
N
kgf
Preload Fa
Fig. 15.12 Preload and Starting Torque of Double-Direction
Angular Contact Thrust Ball Bearings
A 134
A126-141E.indd 134-135
A 135
11/20/13 4:53:08 PM
TECHNICAL DATA
15.5 Coefficients of Dynamic Friction and
Other Bearing Data
(3) Radial Internal Clearance & r and Fatigue Life L
(Fig. 15.13)
(1) Bearing Types and Their Coefficients of Dynamic
Friction μ
For the radial internal clearance & r and the function f
(ε) of the load factor, the following equations are valid:
Table 15. 7 ε and f (ε ), Lε /L
Deep Groove Ball Bearings
ε
For Deep Groove Ball Bearings
μ= M
d
P⋅
f (ε ) =
2
Table 15.5 Coefficients of Dynamic Friction
Bearing Types
Approximate values of μ
Deep Groove Ball Bearings
Angular Contact Ball Bearings
Self-Aligning Ball Bearings
Thrust Ball Bearings
0.0013
0.0015
0.0010
0.0011
Cylindrical Roller Bearings
Tapered Roller Bearings
Spherical Roller Bearings
0.0010
0.0022
0.0028
Needle Roller Bearings
with Cages
Full Complement Needle
Roller Bearings
Spherical Thrust Roller
Bearings
f (ε ) =
1
w 3
&r ⋅ D
& r ⋅ Dw
1
3
....................................{kgf}
2
3
( )
0.002 Fr
Z
....................................(N)
2
3
( )
0.00044 Fr
Z
For Cylindrical Roller Bearings
f (ε ) =
& r ⋅ L we0.8
0.000077
f (ε ) =
0.0015
0.0025
( FZ )
r
& r ⋅ L we
0.9
..................................(N)
0.8
( )
0.0006 Fr
Z
0.9
..................................{kgf}
Cylindrical Roller Bearings
Lε
⎯
L
f (ε)
Lε
⎯
L
f (ε)
0.1
0.2
0.3
33.713
10.221
4.045
0.294
0.546
0.737
51.315
14.500
5.539
0.220
0.469
0.691
0.4
0.5
0.6
1.408
0
0.889
1.0
1.069
1.887
0
− 0.859
− 1.133
0.870
1.0
1.075
0.7
0.8
0.9
− 1.438
− 1.862
− 2.195
1.098
1.094
1.041
− 1.897
− 2.455
− 2.929
1.096
1.065
0.968
1.0
1.25
1.5
− 2.489
− 3.207
− 3.877
0.948
0.605
0.371
− 3.453
− 4.934
− 6.387
0.805
0.378
0.196
1.67
1.8
2.0
− 4.283
− 4.596
− 5.052
0.276
0.221
0.159
− 7.335
− 8.082
− 9.187
0.133
0.100
0.067
2.5
3
4
− 6.114
− 7.092
− 8.874
0.078
0.043
0.017
−11.904
−14.570
−19.721
0.029
0.015
0.005
−10.489
−17.148
0.008
0.001
−24.903
−48.395
0.002
0.0002
5
10
The relation between the load factor ε and f (ε ) and
L ε / L , when the radial internal clearance is & r is as
shown in Table 15.7.
From the above equations, first obtain f (ε ) and then ε
and L ε / L can be obtained.
0.0028
(2) Circumferential Speeds of Rolling Elements
about Their Centers and Bearing Center
1.0
Rotating inner ring, fixed outer ring
Ball rotating speed
na (min–1)
Dpw
cos2 α n i
−
−
Dw
Dpw/Dw 2
(
)
Rotating outer ring, fixed inner ring
+
( DD
pw
w
−
cos2 α n e
Dpw/Dw 2
)
Life Ratio
Items
Lε
L
Table 15.6 Circumferential Speeds of Rolling Elements about
Their Centers and Bearing Center
P=Cr/5 6208
P=Cr/10 Cr=29 100 N
P=Cr/15
0.8
0.6
0.4
Cicumferential
speed around
bearing ball's center
υ a (m/sec)
Revolving
speed around
bearing center
nc (min–1)
Cicumferential
speed around
bearing center
υ c (m/sec)
Dpw
⋅
cos2 α n i
− π Dw
−
3
60 ×10
(D
(
+ 1−
w
Dpw/Dw
)2
cos α n i
Dpw/Dw 2
)
Dpw
⋅
cos2 α n e
+ π Dw
−
3
60 × 10
(D
(
+ 1−
w
Dpw/Dw
)2
cos α n e
Dpw/Dw 2
)
0.2
NU208 P=Cr/5
Cr=43 500 N P=Cr/10
P=Cr/15
−60
−40
−20
0
20
40
60
80
100
Radial Internal Clearance & r
⋅
cos α
− π Dpw 1 −
3
60 × 10
(
Dpw/Dw
ni
)2
⋅
cos α n e
+ π Dpw 1 −
3
60 × 10
(
Dpw/Dw
)2
120
μm
Fig. 15.13 Radial Internal Clearance and Life Ratio
Remarks 1. + sign indicates CW rotation and − sign CCW
Remarks 2. The revolving speed and circumferential speed of the rolling elements are the same as those of the
cage.
A 136
A126-141E.indd 136-137
A 137
11/20/13 4:53:09 PM
TECHNICAL DATA
15. 6 BRANDS AND PROPERTIES OF LUBRICATING GREASES
Table 15. 8 Brands of Lubricating Greases
and Comparison of Properties
Working
Temperature
Range(1)(°C)
Thickeners
Base Oils
Dropping Point (˚C)
Consistency
ADLEX
Lithium
Mineral oil
198
300
0 to +110
APOLOIL AUTOLEX A
Lithium
Mineral oil
198
280
−10 to +110
Brands
Pressure Resistance
Usable Limit Compared
to Listed Limiting
Speed(2)(%)
Good
70
Fair
60
Lithium/Calcium
Mineral oil
177
294
−10 to + 80
Fair
70
EA2 GREASE
Urea (3)
Poly-α-olefin oil
≥260
243
−40 to +150
Fair
100
EA3 GREASE
Urea (3)
Poly-α-olefin oil
≥260
230
−40 to +150
Fair
100
EA5 GREASE
Urea (3)
Poly-α-olefin oil
≥260
251
−40 to +160
Good
60
EA7 GREASE
Urea (3)
Poly-α-olefin oil
≥260
243
−40 to +160
Fair
100
ENC GREASE
Urea (3)
Polyol ester oil + Mineral oil (4)
≥260
262
−40 to +160
Fair
70
ENS GREASE
Urea (3)
Polyol ester oil (4)
≥260
264
−40 to +160
Poor
100
ARAPEN RB 300
Lithium
Poly-α-olefin oil
≥260
235
−10 to +120
Fair
100
Barium Complex
Ester oil + Mineral oil (4)
≥260
280
−30 to +120
Poor
100
ISOFLEX SUPER LDS 18
Lithium
Ester oil (4)
195
280
−50 to +110
Poor
100
ISOFLEX TOPAS NB 52
Barium Complex
Poly-α-olefin oil
≥260
280
−40 to +130
Poor
90
DOW CORNING SH 33 L GREASE
Lithium
Silicone oil (5)
210
310
−60 to +120
Poor
60
DOW CORNING SH 44 M GREASE
Lithium
Silicone oil (5)
210
260
−30 to +130
Poor
60
NS HI-LUBE
Lithium
Polyol ester oil + Diester oil (4)
192
250
−40 to +130
Fair
100
NSC GREASE
Lithium
Alkyldiphenyl ether oil + Polyol ester oil (4)
192
235
−30 to +140
Fair
70
NSK CLEAN GREASE LG2
Lithium
Poly-α-olefin oil + Mineral oil
201
199
−40 to +130
Poor
100
EMALUBE 8030
Urea (3)
Mineral oil
≥260
280
0 to +130
Good
60
MA8 GREASE
Urea (3)
Alkyldiphenyl ether oil + Poly-α-olefin oil
≥260
283
−30 to +160
Fair
70
ECE GREASE
ISOFLEX NBU 15
KRYTOX GPL-524
PTFE
Perfluoropolyether oil
≥260
265
0 to +200
Fair
70
KP1 GREASE
PTFE
Perfluoropolyether oil
≥260
280
−30 to +200
Fair
60
Sodium Terephtalamate
Polyol ester oil + Mineral oil (4)
≥230
227
−40 to +130
Poor
100
G-40M
Lithium
Silicone oil (5)
223
252
−30 to +130
Poor
60
SHELL GADUS S2 V220 2
Lithium
Mineral oil
187
276
0 to + 80
Good
60
COSMO WIDE GREASE WR No.3N
SHELL ALVANIA GREASE S1
Lithium
Mineral oil
182
323
−10 to +110
Fair
70
SHELL ALVANIA GREASE S2
Lithium
Mineral oil
185
275
−10 to +110
Fair
70
185
242
−10 to +110
Fair
70
≥240
280
0 to +120
Fair
70
70
SHELL ALVANIA GREASE S3
CASSIDA GREASE RLS 2
Lithium
Mineral oil
Aluminum Complex
Poly-α-olefin oil
SHELL SUNLIGHT GREASE 2
Lithium
Mineral oil
200
274
−10 to +110
Fair
WPH GREASE
Urea (3)
Poly-α-olefin oil
259
240
−40 to +150
Fair
70
PTFE
Perfluoropolyether oil
≥260
280
−30 to +200
Fair
60
DEMNUM GREASE L-200
NIGACE WR-S
Urea (3)
Synthetic oil
≥260
230
−30 to +150
Poor
70
NIGLUBE RSH
Sodium Complex
Polyalkylene Glycol oil
≥260
270
−20 to +120
Fair
60
Notes (1) If grease will be used at the upper or lower limit sufficient of the temperature range or in a special environment such
as vacuum, it is advisable to consult NSK.
Notes (2) For short-term operation or when cooling is grease may be used at speeds exceeding the above limits provided the
supply of grease is appropriate.
Notes (3) Urea-based grease causes fluorine-based material to deteriorate.
Notes (4) Ester-based grease causes acrylic rubber material to swell.
Notes (5) Silicone-based grease causes silicone-based material to swell.
A 138
A126-141E.indd 138-139
(continued on next page)
A 139
11/20/13 4:53:10 PM
TECHNICAL DATA
Brands
Thickeners
Base Oils
Dropping Point (˚C)
Consistency
Working
Temperature
Range(1)(°C)
Pressure Resistance
Usable Limit Compared
to Listed Limiting
Speed(2)(%)
PALMAX RBG
Lithium Complex
Mineral oil
216
300
−10 to +130
Good
70
BEACON 325
Lithium
Diester oil (4)
190
274
−50 to +100
Poor
100
MULTEMP PS No.2
100
Lithium
Poly-α-olefin oil + Diester oil (4)
190
275
−50 to +110
Poor
MOLYKOTE FS-3451 GREASE
PTFE
Fluorosilicone oil (5)
≥260
285
0 to +180
Fair
70
UME GREASE
Urea
Mineral oil
≥260
268
−10 to +130
Fair
70
RAREMAX AF-1
Urea
Mineral oil
≥260
300
−10 to +130
Fair
70
Notes (1) If grease will be used at the upper or lower limit sufficient of the temperature range or in a special environment such
as vacuum, it is advisable to consult NSK.
Notes (2) For short-term operation or when cooling is grease may be used at speeds exceeding the above limits provided the
supply of grease is appropriate.
Notes (3) Urea-based grease causes fluorine-based material to deteriorate.
Notes (4) Ester-based grease causes acrylic rubber material to swell.
Notes (5) Silicone-based grease causes silicone-based material to swell.
A 140
A126-141E.indd 140-141
A 141
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