Table of contents
Friction and increases in temperature
Frictional components
The friction in a rolling bearing is made up of several components ➤ Table. Due to the large number of influencing factors, such as dynamics in speed and load, tilting and skewing resulting from installation, actual frictional torques and frictional power may deviate significantly from the calculated values.
If the frictional torque is an important design criterion, please consult Schaeffler.
The calculation module BEARINX Easy Friction, which is available from Schaeffler free of charge, can be used to calculate and analyse the frictional torque.
Frictional component and influencing factor
|
Frictional component |
Influencing factor |
|---|---|
|
Rolling friction |
Magnitude of load |
|
Sliding friction of rolling elements Sliding friction of cage |
Magnitude and direction of load Speed and lubrication conditions, running-in condition |
|
Fluid friction (flow resistance) |
Type and speed Type, quantity and operating viscosity |
|
Seal friction |
Type and preload of seal |
Influencing factors on idling friction
The idling friction is dependent on the lubricant quantity, speed, operating viscosity of the lubricant, seals and the running-in condition of the bearing.
Heat dissipation
Friction is converted into heat. This must be dissipated from the bearing. The equilibrium between the frictional energy and heat dissipation allows calculation of the thermally safe operating speed nϑ ➤ section.
Lubricant
Lubricating oil dissipates a portion of the heat. Recirculating oil lubrication with additional cooling is particularly effective. Grease does not give dissipation of heat.
Shaft and housing
Heat dissipation via the shaft and housing is dependent on the temperature difference between the bearing and the surrounding structure. Any additional adjacent sources of heat or thermal radiation must be taken into consideration.
Determining the friction values
The speed and load must also be known. The type of lubrication, lubrication method and viscosity of the lubricant at operating temperature are further important factors in calculation.
Total frictional torque
Frictional power
For ν · n ≧ 2 000:
Frictional torque as a function of speed
For ν · n ＜ 2 000:
Frictional torque as a function of speed
Frictional torque as a function of load for needle roller and cylindrical roller bearings:
Frictional torque as a function of load
Frictional torque as a function of load for ball bearings, tapered roller bearings and spherical roller bearings:
Frictional torque as a function of load
Legend
| MR | Nmm |
Total frictional torque |
| M0 | Nmm |
Frictional torque as a function of speed |
| M1 | Nmm |
Frictional torque as a function of load |
| NR | W |
Frictional power |
| n | min–1 |
Operating speed |
| f0 | - |
Bearing factor for frictional torque as a function of speed ➤ Figure and ➤ Table to ➤ Table |
| f1 | - |
Bearing factor for frictional torque as a function of load ➤ Table to ➤ Table |
| ν | mm2/s |
Kinematic viscosity of lubricant at operating temperature. In the case of grease, the decisive factor is the viscosity of the base oil at operating temperature |
| Fr, Fa | N |
Radial load for radial bearings, axial load for axial bearings |
| P1 | N |
Decisive load for frictional torque. For ball bearings, tapered roller bearings and spherical roller bearings ➤ section |
| dM | mm |
Mean bearing diameter (d + D)/2 |
Bearing factors
The bearing factors f0 and f1 are mean values from series of tests and correspond to the data in accordance with ISO 15312. They are valid for bearings after running-in and with uniform distribution of lubricant. In the freshly greased state, the bearing factor f0 can be two to five times higher.
If oil bath lubrication is used, the oil level must reach the centre of the lowest rolling element. If the oil level is higher, f0 may be up to three times the value given in the table ➤ Figure.
|
Increase in the bearing factor f0, as a function of the oil level h = oil level dM = mean bearing diameter (d +D)/2
|
 |
Bearing factor f0, f1 for needle roller bearings, drawn cup needle roller bearings with open ends or with closed end, needle roller and cage assemblies
|
Series |
Bearing factor f0 |
Bearing factor f1 |
|
|---|---|---|---|
|
Grease and oil mist |
Oil bath and recirculating oil |
||
|
NA48 |
3 |
5 |
0,0005 |
|
NA49 |
4 |
5,5 |
|
|
RNA48 |
3 |
5 |
|
|
RNA49 |
4 |
5,5 |
|
|
NA69 |
7 |
10 |
|
|
RNA69 |
7 | 10 | |
|
NKI, NK, NKIS, NKS, NAO, RNO, RNAO, K |
(12 · B)/(33 + d) |
(18 · B)/(33 + d) |
|
|
NK..-TW, NKI..-TW, NK..-D |
(10 · B)/(33 + d) |
(15 · B)/(33 + d) |
|
|
HK, BK |
(24 · B)/(33 + d) |
(36 · B)/(33 + d) |
|
|
HN |
(30 · B)/(33 + d) |
(45 · B)/(33 + d) |
|
Bearing factor f0, f1 for cylindrical roller bearings, full complement
|
Series |
Bearing factor f0 |
Bearing factor f1 |
|
|---|---|---|---|
|
Grease and oil mist |
Oil bath and recirculating oil |
||
|
SL1818 |
3 |
5 |
0,00055 |
| SL1829 | 4 | 6 | |
|
SL1830 |
5 |
7 |
|
|
SL1822 |
5 |
8 |
|
|
SL0148, SL0248 |
6 |
9 |
|
|
SL0149, SL0249 |
7 |
11 |
|
|
SL1923 |
8 |
12 |
|
|
SL1850 |
9 |
13 |
|
Bearing factor f0, f1 for cylindrical roller bearings with cage
|
Series |
Bearing factor f0 |
Bearing factor f1 |
|
|---|---|---|---|
|
Grease and oil mist |
Oil bath and recirculating oil |
||
|
LSL1923 |
1 |
3,7 |
0,00020 |
|
ZSL1923 |
1 |
3,8 |
0,00025 |
|
NU2..-E, NNU41 |
1,3 |
2 |
0,00030 |
|
NU3..-E |
1,3 | 2 |
0,00035 |
|
NU4 |
1,3 | 2 |
0,00040 |
|
NU10, NU19 |
1,3 | 2 |
0,00020 |
|
NU22..-E |
2 |
3 |
0,00040 |
|
NU23..-E |
2,7 |
4 |
0,00040 |
|
NU30..-E, NN30..-E |
1,7 |
2,5 |
0,00040 |
Bearing factor f0, f1 for axial roller bearings
|
Series |
Bearing factor f0 |
Bearing factor f1 |
|
|---|---|---|---|
|
Grease and oil mist |
Oil bath and recirculating oil |
||
|
AXK, AXW |
3 |
4 |
0,0015 |
|
810, K810, 811, K811 |
2 |
3 |
|
|
812, K812 |
2 | 3 | |
|
893, K893 |
2 | 3 | |
|
894, K894 |
2 | 3 | |
Bearing factor f0, f1 for combined bearings
|
Series |
Bearing factor f0 |
Bearing factor f1 |
|
|---|---|---|---|
|
Grease and oil mist |
Oil bath and recirculating oil |
||
|
ZARN, ZARF |
3 |
4 |
0,0015 |
|
NKXR |
2 |
3 |
0,0015 |
|
NX, NKX |
2 |
3 |
0,001 · (P0 /C0)0,33 |
|
ZKLN, ZKLF |
4 |
6 |
0,001 · (P0 /C0)0,33 |
|
NKIA, NKIB |
3 |
5 |
0,0005 |
Bearing factor f0, f1 for tapered roller bearings
|
Series |
Bearing factor f0 |
Bearing factor f1 |
|
|---|---|---|---|
|
Grease and oil mist |
Oil bath and recirculating oil |
||
|
302, 303, 329, 320, 330, JK0S, T4CB, T4DB, T7FC |
2 |
3 |
0,0004 |
|
313, 322, 323, 331, 332, T2EE, T2ED, T5ED |
3 |
4,5 |
0,0004 |
Bearing factor f0, f1 for axial and radial spherical roller bearings
|
Series |
Bearing factor f0 |
Bearing factor f1 |
|
|---|---|---|---|
|
Grease and oil mist |
Oil bath and recirculating oil |
||
|
213..-E1 |
2,3 |
3,5 |
0,0005 · (P0 /C0)0,33 |
|
222..-E1 |
2,7 |
4 |
0,0005 · (P0 /C0)0,33 |
|
223 |
3 |
4,5 |
0,0008 · (P0 /C0)0,33 |
|
238, 239, 230 |
3 | 4,5 |
0,00075 · (P0 /C0)0,5 |
|
231 |
3,7 |
5,5 |
0,0012 · (P0 /C0)0,5 |
|
232 |
4 |
6 |
0,0016 · (P0 /C0)0,5 |
|
240 |
4,3 |
6,5 |
0,0012 · (P0 /C0)0,5 |
|
248, 249, 241 |
4,7 |
7 |
0,0022 · (P0 /C0)0,5 |
|
292..-E |
1,7 |
2,5 |
0,00023 |
|
293..-E |
2 |
3 |
0,00030 |
|
294..-E |
2,2 |
3,3 |
0,00033 |
Bearing factor f0, f1 for toroidal roller bearings
|
Series |
Bearing factor f0 |
Bearing factor f1 |
|
|---|---|---|---|
|
Grease and oil mist |
Oil bath and recirculating oil |
||
|
C22..-K |
3,7 |
5,5 |
0,0012 · (P0 /C0)0,5 |
|
C22..-V |
4 |
6 |
0,0012 · (P0 /C0)0,5 |
|
C23..-K |
3,8 |
5,7 |
0,0014 · (P0 /C0)0,5 |
|
C23..-V |
4,3 |
6,5 |
0,0014 · (P0 /C0)0,5 |
|
C30..-K |
3,3 |
5 |
0,0014 · (P0 /C0)0,5 |
|
C30..-V, C31..-V |
4 |
6 |
0,0014 · (P0 /C0)0,5 |
|
C31..-K |
3,7 |
5,5 |
0,0014 · (P0 /C0)0,5 |
|
C32..-K |
3,8 |
5,7 |
0,0016 · (P0 /C0)0,5 |
|
C39..-K |
3,3 |
5 |
0,0014 · (P0 /C0)0,5 |
|
C40..-K, C41..-K |
5 |
7,5 |
0,0018 · (P0 /C0)0,5 |
|
C40..-V, C41..-V |
6 |
9 |
0,0018 · (P0 /C0)0,5 |
Bearing factor f0, f1 for deep groove ball bearings
|
Series |
Bearing factor f0 |
Bearing factor f1 |
|
|---|---|---|---|
|
Grease and oil mist |
Oil bath and recirculating oil |
||
|
618 |
1,1 |
1,7 |
0,0005 · (P0 /C0)0,5 |
|
160, 60, 619 |
1,1 |
1,7 |
0,0007 · (P0 /C0)0,5 |
|
622, 623 |
1,1 |
1,7 |
0,0009 · (P0 /C0)0,5 |
|
62 |
1,3 |
2 |
0,0009 · (P0 /C0)0,5 |
|
63, 630, 64 |
1,5 |
2,3 |
0,0009 · (P0 /C0)0,5 |
|
60..-C |
1,1 |
1,5 |
0,0006 · (P0 /C0)0,5 |
|
62..-C |
1,3 |
1,7 |
0,0007 · (P0 /C0)0,5 |
|
63..-C |
1,5 |
2 |
0,0007 · (P0 /C0)0,5 |
|
42..-B |
2,3 |
3,5 |
0,0010 · (P0 /C0)0,5 |
|
43..-B |
4 |
6 |
0,0010 · (P0 /C0)0,5 |
Bearing factor f0, f1 for angular contact ball bearings
|
Series |
Bearing factor f0 |
Bearing factor f1 |
|
|---|---|---|---|
|
Grease and oil mist |
Oil bath and recirculating oil |
||
|
708, 719, 70..-B |
1,3 |
2 |
0,001 · (P0 /C0)0,33 |
|
718..-B |
1,3 | 2 | |
|
72..-B |
1,3 | 2 | |
|
73..-B |
2 |
3 |
|
|
74..-B |
2,5 |
4 |
|
|
30..-B |
2,3 |
3,5 |
|
|
32..-B |
2,3 | 3,5 | |
|
38..-B |
2,3 | 3,5 | |
|
33..-B |
4 |
6 |
|
|
32..-BD |
2 |
3 |
|
|
33..-BD |
3,5 |
5 |
|
Bearing factor f0, f1 for self-aligning ball bearings
|
Series |
Bearing factor f0 |
Bearing factor f1 |
|
|---|---|---|---|
|
Grease and oil mist |
Oil bath and recirculating oil |
||
|
10, 112 |
1,7 |
2 |
0,0003 · (P0 /C0)0,4 |
|
12 |
1,7 |
2,5 |
|
|
13 |
2,3 |
3,5 |
|
|
22 |
2 |
3 |
|
|
23 |
2,7 |
4 |
|
Bearing factor f0, f1 for four point contact bearings
|
Series |
Bearing factor f0 |
Bearing factor f1 |
|
|---|---|---|---|
|
Grease and oil mist |
Oil bath and recirculating oil |
||
|
QJ2 |
1,3 |
2 |
0,001 · (P0 /C0)0,33 |
|
QJ3 |
2 |
3 |
0,001 · (P0 /C0)0,33 |
|
QJ10 |
1,3 |
2 |
0,001 · (P0 /C0)0,33 |
Bearing factor f0, f1 for axial deep groove ball bearings
|
Series |
Bearing factor f0 |
Bearing factor f1 |
|
|---|---|---|---|
|
Grease and oil mist |
Oil bath and recirculating oil |
||
|
511, 512, 513, 514, 532, 533, 534 |
1 |
1,5 |
0,0012 · (Fa /C0)0,33 |
|
522, 523, 524, 542, 543, 544 |
1,3 |
2 |
0,0012 · (Fa /C0)0,33 |
Load P1 for ball bearings, tapered roller bearings, spherical roller bearings
P1 for single bearings and bearing pairs
The load value P1, which is the decisive load for frictional torque as a function of load M1, is shown in ➤ Table. If P1 ≦ Fr, then P1 = Fr.
Decisive load P1
|
Bearing type |
Decisive load |
|
|---|---|---|
|
P1 |
||
|
for single bearings |
for bearing pairs |
|
|
Deep groove ball bearings |
3,3 · Fa – 0,1 · Fr |
‒ |
|
Angular contact |
Fa – 0,1 · Fr |
1,4 · Fa – 0,1 · Fr |
|
Angular contact |
1,4 · Fa – 0,1 · Fr |
‒ |
|
Four point contact bearings |
1,5 · Fa + 3,6 · Fr |
‒ |
|
Tapered roller bearings |
2 · Y · Fa or Fr, |
1,21 · Y · Fa or Fr, |
|
Spherical roller bearings |
1,6 · Fa /e if Fa /Fr ＞ e Fr {1 + 0,6 · [Fa /(e · Fr)]3} if Fa /Fr ≦ e |
|
|
Cylindrical roller bearings |
For cylindrical roller bearings with additional axial load, M2 must be added to the frictional torque M1: M = M0 + M1 + M2 |
|
Frictional torque for axially loaded radial cylindrical roller bearings
M2 = frictional torque as a function of axial load
In radial cylindrical roller bearings under axial load, sliding friction between the end faces of the rolling elements and the ribs on the rings leads to an additional frictional torque M2. The total frictional torque MR is calculated in accordance with ➤ Equation, the frictional torque as a function of the axial load M2 is calculated in accordance with ➤ Equation.
Total frictional torque
Legend
| MR | Nmm |
Total frictional torque for axially loaded cylindrical roller bearings |
| M0 | Nmm |
Frictional torque as a function of speed |
| M1 | Nmm |
Frictional torque as a function of radial load |
| M2 | Nmm |
Frictional torque as a function of axial load ➤ Equation |
Frictional torque as a function of axial load
Legend
| f2 | - |
Bearing factor as a function of the bearing series and of operating parameter ν · n · dM ➤ Figure and ➤ Figure |
| Fa | N |
Axial dynamic bearing load |
| dM | mm |
Mean bearing diameter (d + D)/2 |
Bearing factor A for calculating M2
In order that the bearing factor f2 can be determined for the calculation of M2 in ➤ Figure and ➤ Figure, bearing parameter A must be obtained in accordance with ➤ Equation.
Bearing parameter
Legend
| A | - |
Bearing parameter |
| kB | - |
Bearing factor as a function of the bearing series ➤ Table |
| dM | mm |
Mean bearing diameter (d + D)/2 |
The bearing factors f2 are subject to wide scatter. They are valid for recirculating oil lubrication with an adequate quantity of oil. The curves must not be extrapolated, ➤ Figure and ➤ Figure.
Bearings in TB design
Higher axial load carrying capacity and lower axial frictional torque in bearings of TB design
In the case of bearings of TB design (rollers with a toroidal roller end), the axial load carrying capacity was significantly improved through the use of new calculation and manufacturing methods. Optimum contact conditions between the roller and rib are ensured by means of a special curvature of the roller end faces. As a result, axial surface pressures on the rib are significantly reduced and a lubricant film with improved load carrying capacity is achieved. Under normal operating conditions, wear and fatigue at the rib contact running and roller end faces is completely eliminated. In addition, axial frictional torque is reduced by up to 50%. The bearing temperature during operation is therefore significantly lower.
Bearing factor kB
The bearing factor kB in the equations takes into consideration the size and thus the load carrying capacity of the hydrodynamic contacts at the bearing ribs➤ Table.
Bearing factor kB
|
Series |
Factor kB |
|---|---|
|
SL1818, SL0148 |
4,5 |
|
SL1829, SL0149 |
11 |
|
SL1830, SL1850 |
17 |
|
SL1822 |
20 |
|
LSL1923, ZSL1923 |
28 |
|
SL1923 |
30 |
|
NJ2..-E, NJ22..-E, NUP2..-E, NUP22..-E |
15 |
|
NJ3..-E, NJ23..-E, NUP3..-E, NUP23..-E |
20 |
|
NJ4 |
22 |
Bearing factor f2 for cylindrical roller bearings
The bearing factor f2 can vary significantly. The values in ➤ Figure and ➤ Equation are valid for recirculating oil lubrication with an adequate quantity of oil; the curves should not be extrapolated.
Rollers without and with toroidal roller end face
➤ Figure gives the values for bearings without toroidal end face, ➤ Figure gives the factors for cylindrical roller bearings with toroidal end face (TB design).
|
Cylindrical roller bearing in standard design, bearing factor f2 as a function of the operating parameter ν · n · dM f2 = bearing factor ν = operating viscosity n = operating speed dM = mean bearing diameter ν · n · dM = operating parameter Fa = axial dynamic bearing load A = bearing parameter |
 |
|
Cylindrical roller bearing in TB design, bearing factor f2 as a function of the operating parameter ν · n · dM f2 = bearing factor ν = operating viscosity n = operating speed dM = mean bearing diameter ν · n · dM = operating parameter Fa = axial dynamic bearing load A = bearing parameter |
 |