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, runningin 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 runningin 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 n_{ϑ} ➤ 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
M_{R}  Nmm 
Total frictional torque 
M_{0}  Nmm 
Frictional torque as a function of speed 
M_{1}  Nmm 
Frictional torque as a function of load 
N_{R}  W 
Frictional power 
n  min^{–1} 
Operating speed 
f_{0}   
Bearing factor for frictional torque as a function of speed ➤ Figure and ➤ Table to ➤ Table 
f_{1}   
Bearing factor for frictional torque as a function of load ➤ Table to ➤ Table 
ν  mm^{2}/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 
F_{r}, F_{a}  N 
Radial load for radial bearings, axial load for axial bearings 
P_{1}  N 
Decisive load for frictional torque. For ball bearings, tapered roller bearings and spherical roller bearings ➤ section 
d_{M}  mm 
Mean bearing diameter (d + D)/2 
Bearing factors
The bearing factors f_{0} and f_{1} are mean values from series of tests and correspond to the data in accordance with ISO 15312. They are valid for bearings after runningin and with uniform distribution of lubricant. In the freshly greased state, the bearing factor f_{0} 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, f_{0} may be up to three times the value given in the table ➤ Figure.
Increase in the bearing factor f_{0}, as a function of the oil level h = oil level d_{M} = mean bearing diameter (d +D)/2

Bearing factor f_{0}, f_{1} for needle roller bearings, drawn cup needle roller bearings with open ends or with closed end, needle roller and cage assemblies
Series 
Bearing factor f_{0} 
Bearing factor f_{1} 


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 f_{0}, f_{1} for cylindrical roller bearings, full complement
Series 
Bearing factor f_{0} 
Bearing factor f_{1} 


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 f_{0}, f_{1} for cylindrical roller bearings with cage
Series 
Bearing factor f_{0} 
Bearing factor f_{1} 


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 f_{0}, f_{1 }for axial roller bearings
Series 
Bearing factor f_{0} 
Bearing factor f_{1} 


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 f_{0}, f_{1 }for combined bearings
Series 
Bearing factor f_{0} 
Bearing factor f_{1} 


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 · (P_{0} /C_{0})^{0,33} 
ZKLN, ZKLF 
4 
6 
0,001 · (P_{0} /C_{0})^{0,33} 
NKIA, NKIB 
3 
5 
0,0005 
Bearing factor f_{0}, f_{1 }for tapered roller bearings
Series 
Bearing factor f_{0} 
Bearing factor f_{1} 


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 f_{0}, f_{1 }for axial and radial spherical roller bearings
Series 
Bearing factor f_{0} 
Bearing factor f_{1} 


Grease and oil mist 
Oil bath and recirculating oil 

213..E1 
2,3 
3,5 
0,0005 · (P_{0} /C_{0})^{0,33} 
222..E1 
2,7 
4 
0,0005 · (P_{0} /C_{0})^{0,33} 
223 
3 
4,5 
0,0008 · (P_{0} /C_{0})^{0,33} 
238, 239, 230 
3  4,5 
0,00075 · (P_{0} /C_{0})^{0,5} 
231 
3,7 
5,5 
0,0012 · (P_{0} /C_{0})^{0,5} 
232 
4 
6 
0,0016 · (P_{0} /C_{0})^{0,5} 
240 
4,3 
6,5 
0,0012 · (P_{0} /C_{0})^{0,5} 
248, 249, 241 
4,7 
7 
0,0022 · (P_{0} /C_{0})^{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 f_{0}, f_{1 }for toroidal roller bearings
Series 
Bearing factor f_{0} 
Bearing factor f_{1} 


Grease and oil mist 
Oil bath and recirculating oil 

C22..K 
3,7 
5,5 
0,0012 · (P_{0} /C_{0})^{0,5} 
C22..V 
4 
6 
0,0012 · (P_{0} /C_{0})^{0,5} 
C23..K 
3,8 
5,7 
0,0014 · (P_{0} /C_{0})^{0,5} 
C23..V 
4,3 
6,5 
0,0014 · (P_{0} /C_{0})^{0,5} 
C30..K 
3,3 
5 
0,0014 · (P_{0} /C_{0})^{0,5} 
C30..V, C31..V 
4 
6 
0,0014 · (P_{0} /C_{0})^{0,5} 
C31..K 
3,7 
5,5 
0,0014 · (P_{0} /C_{0})^{0,5} 
C32..K 
3,8 
5,7 
0,0016 · (P_{0} /C_{0})^{0,5} 
C39..K 
3,3 
5 
0,0014 · (P_{0} /C_{0})^{0,5} 
C40..K, C41..K 
5 
7,5 
0,0018 · (P_{0} /C_{0})^{0,5} 
C40..V, C41..V 
6 
9 
0,0018 · (P_{0} /C_{0})^{0,5} 
Bearing factor f_{0}, f_{1 }for deep groove ball bearings
Series 
Bearing factor f_{0} 
Bearing factor f_{1} 


Grease and oil mist 
Oil bath and recirculating oil 

618 
1,1 
1,7 
0,0005 · (P_{0} /C_{0})^{0,5} 
160, 60, 619 
1,1 
1,7 
0,0007 · (P_{0} /C_{0})^{0,5} 
622, 623 
1,1 
1,7 
0,0009 · (P_{0} /C_{0})^{0,5} 
62 
1,3 
2 
0,0009 · (P_{0} /C_{0})^{0,5} 
63, 630, 64 
1,5 
2,3 
0,0009 · (P_{0} /C_{0})^{0,5} 
60..C 
1,1 
1,5 
0,0006 · (P_{0} /C_{0})^{0,5} 
62..C 
1,3 
1,7 
0,0007 · (P_{0} /C_{0})^{0,5} 
63..C 
1,5 
2 
0,0007 · (P_{0} /C_{0})^{0,5} 
42..B 
2,3 
3,5 
0,0010 · (P_{0} /C_{0})^{0,5} 
43..B 
4 
6 
0,0010 · (P_{0} /C_{0})^{0,5} 
Bearing factor f_{0}, f_{1 }for angular contact ball bearings
Series 
Bearing factor f_{0} 
Bearing factor f_{1} 


Grease and oil mist 
Oil bath and recirculating oil 

708, 719, 70..B 
1,3 
2 
0,001 · (P_{0} /C_{0})^{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 f_{0}, f_{1 }for selfaligning ball bearings
Series 
Bearing factor f_{0} 
Bearing factor f_{1} 


Grease and oil mist 
Oil bath and recirculating oil 

10, 112 
1,7 
2 
0,0003 · (P_{0} /C_{0})^{0,4} 
12 
1,7 
2,5 

13 
2,3 
3,5 

22 
2 
3 

23 
2,7 
4 
Bearing factor f_{0}, f_{1 }for four point contact bearings
Series 
Bearing factor f_{0} 
Bearing factor f_{1} 


Grease and oil mist 
Oil bath and recirculating oil 

QJ2 
1,3 
2 
0,001 · (P_{0} /C_{0})^{0,33} 
QJ3 
2 
3 
0,001 · (P_{0} /C_{0})^{0,33} 
QJ10 
1,3 
2 
0,001 · (P_{0} /C_{0})^{0,33} 
Bearing factor f_{0}, f_{1 }for axial deep groove ball bearings
Series 
Bearing factor f_{0} 
Bearing factor f_{1} 


Grease and oil mist 
Oil bath and recirculating oil 

511, 512, 513, 514, 532, 533, 534 
1 
1,5 
0,0012 · (F_{a} /C_{0})^{0,33} 
522, 523, 524, 542, 543, 544 
1,3 
2 
0,0012 · (F_{a} /C_{0})^{0,33} 
Load P_{1} for ball bearings, tapered roller bearings, spherical roller bearings
P_{1} for single bearings and bearing pairs
The load value P_{1}, which is the decisive load for frictional torque as a function of load M_{1}, is shown in ➤ Table. If P_{1} ≦ F_{r}, then P_{1} = F_{r}.
Decisive load P_{1}
Bearing type 
Decisive load 


P_{1} 

for single bearings 
for bearing pairs 

Deep groove ball bearings 
3,3 · F_{a} – 0,1 · F_{r} 
‒ 
Angular contact 
F_{a} – 0,1 · F_{r} 
1,4 · F_{a} – 0,1 · F_{r} 
Angular contact 
1,4 · F_{a} – 0,1 · F_{r} 
‒ 
Four point contact bearings 
1,5 · F_{a} + 3,6 · F_{r} 
‒ 
Tapered roller bearings 
2 · Y · F_{a} or F_{r}, 
1,21 · Y · F_{a} or F_{r}, 
Spherical roller bearings 
1,6 · F_{a} /e if F_{a} /F_{r} ＞ e F_{r} {1 + 0,6 · [F_{a} /(e · F_{r})]^{3}} if F_{a} /F_{r} ≦ e 

Cylindrical roller bearings 
For cylindrical roller bearings with additional axial load, M_{2} must be added to the frictional torque M_{1}: M = M_{0} + M_{1} + M_{2} 
Frictional torque for axially loaded radial cylindrical roller bearings
M_{2} = 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 M_{2}. The total frictional torque M_{R} is calculated in accordance with ➤ Equation, the frictional torque as a function of the axial load M_{2} is calculated in accordance with ➤ Equation.
Total frictional torque
Legend
M_{R}  Nmm 
Total frictional torque for axially loaded cylindrical roller bearings 
M_{0}  Nmm 
Frictional torque as a function of speed 
M_{1}  Nmm 
Frictional torque as a function of radial load 
M_{2}  Nmm 
Frictional torque as a function of axial load ➤ Equation 
Frictional torque as a function of axial load
Legend
f_{2}   
Bearing factor as a function of the bearing series and of operating parameter ν · n · d_{M} ➤ Figure and ➤ Figure 
F_{a}  N 
Axial dynamic bearing load 
d_{M}  mm 
Mean bearing diameter (d + D)/2 
Bearing factor A for calculating M_{2}
In order that the bearing factor f_{2} can be determined for the calculation of M_{2} in ➤ Figure and ➤ Figure, bearing parameter A must be obtained in accordance with ➤ Equation.
Bearing parameter
Legend
A   
Bearing parameter 
k_{B}   
Bearing factor as a function of the bearing series ➤ Table 
d_{M}  mm 
Mean bearing diameter (d + D)/2 
The bearing factors f_{2 }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 k_{B}
The bearing factor k_{B} 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 k_{B}
Series 
Factor k_{B} 

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 f_{2} for cylindrical roller bearings
The bearing factor f_{2} 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 f_{2} as a function of the operating parameter ν · n · d_{M} f_{2} = bearing factor ν = operating viscosity n = operating speed d_{M} = mean bearing diameter ν · n · d_{M} = operating parameter F_{a} = axial dynamic bearing load A = bearing parameter 
Cylindrical roller bearing in TB design, bearing factor f_{2} as a function of the operating parameter ν · n · d_{M} f_{2} = bearing factor ν = operating viscosity n = operating speed d_{M} = mean bearing diameter ν · n · d_{M} = operating parameter F_{a} = axial dynamic bearing load A = bearing parameter 