Table of contents

Friction and increases in temperature

  • Heat dissipation
  • Determining the friction values
  • Load P1 for ball bearings, tapered roller bearings, spherical roller bearings
  • Frictional torque for axially loaded radial cylindrical roller bearings

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
of lubricant

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


Increase in the bearing factor f0

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
ball bearings, single row

Fa – 0,1 · Fr

1,4 · Fa – 0,1 · Fr

Angular contact
ball bearings, double row

1,4 · Fa – 0,1 · Fr

‒

Four point contact bearings

1,5 · Fa + 3,6 · Fr

‒

Tapered roller bearings

2 · Y · Fa or Fr,
use the larger value

1,21 · Y · Fa or Fr,
use the larger value

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

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