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Koyo Technical Information

3. Bearing service life and selection

• Basic dynamic load rating
• Selection based on service life
• Basic static load rating and safety coefficient

a. Basic dynamic load rating

1) Bearing service life

When bearings rotate under loading, material flakes from the surfaces of inner and outer rings or rolling elements by fatigue arising from repeated contact stress. This phenomenon is called flaking. The total number of bearing rotations until flaking occurs is regarded as the bearing “(fatigue) service life”. “(Fatigue) service life” differs greatly depending upon bearing structures, dimensions, materials, and processing methods. Since this phenomenon results from fatigue distribution in bearing materials themselves, differences in bearing service life should be statistically considered. When a group of identical bearings is rotated under the same conditions, the total number of revolutions until 90% of the bearings are left without flaking (i.e. a service life of 90% reliability) is defined as the basic rating life. In operation at a constant speed, the basic rating life can be expressed in terms of time.

In actual operation, a bearing fails because of not only fatigue, but other factors as well, such as wear, seizure, creeping, fretting, brinelling, cracking etc (ref. Bearing failures and countermeasures). Selecting the proper mounting method and lubricant, as well as the bearing most suitable for the application can minimize these bearing failures.

2) Basic dynamic load rating

The basic dynamic load rating is either pure radial (for radial bearings) or central axial load (for thrust bearings) of constant magnitude in a constant direction, under which the basic rating life of 1 million revolutions can be obtained, when the inner ring rotates while the outer ring is stationary, or vice versa. The basic dynamic load rating, which represents the capacity of a bearing under rolling fatigue, is specified as the basic dynamic radial load rating (C_r) for radial bearings, and basic dynamic axial load rating (C_a) for thrust bearings. These load ratings are listed in the specification table.

3) Dynamic equivalent load

Bearings are used under various operating conditions; however, in most cases, bearings receive radial and axial load combined, while the load magnitude fluctuates during operation. The two are compared by replacing the load applied to the shaft center with one of a constant magnitude and in a specific direction, that yields the same bearing service life as under actual load and rotational speed. This theoretical load is reffered to as the dynamic equivalent load, can be obtained using the equivalent load equation.

• Deep groove ball bearings

Dynamic equivalent radial load

P_r=XF_r+YF_a

Factor f₀ is shown in the bearing dimension table.

Static equivalent radial load

P_0r=0.6F_r+0.5F_a

when P_0r<F_r ; P_0r=F_r

• Angular contact ball bearings – Single-row angular contact ball bearings

Dynamic equivalent radial load

P_r=XF_r+YF_a

For i, use 2 for DB & DT arrangements and 1 for single & DT arrangement.

Factor f₀ is shown in the bearing dimension table.

Static equivalent radial load

P_0r=X₀F_r+Y₀F_a

In reference to single-row or tandem arrangement bearings,
when P_0r<F_r; P_0r=F_r

• Angular contact ball bearings – Double-row angular contact ball bearings

Dynamic equivalent radial load

P_r=XF_r+YF_a

Static equivalent radial load

P_0r=X₀F_r+Y₀F_a

• Self-aligning ball bearings

Dynamic equivalent radial load

P_r=XF_r+YF_a

Refer to the bearing specification table for values of e, Y_1, Y_2.

Static equivalent radial load

P_0r=F_r+Y₀F_a

Refer to the bearing specification table for value of Y_0.

• Cylindrical roller bearings

Dynamic equivalent radial load

P_r=F_r

Static equivalent radial load

P_0r=F_r

• Tapered roller bearings – Single-row

Dynamic equivalent radial load

when F_a/F_r≤e ; P_r=F_r

when F_a/F_r>e ; P_r=0.4F_r+Y₁F_a

Refer to the bearing specification table for the values of axial load factors Y₁ and constant e.

Static equivalent radial load

P_0r=0.5F_r+Y₀F_a
when P_0r<F_r ; P_0r=F_r

Refer to the bearing specification table for the value of axial load factors Y_0.

• Tapered roller bearings – Double-row / four-row

Dynamic equivalent radial load

when F_a/F_r≤e ; P_r=F_r+Y₂F_a

when F_a/F_r>e ; P_r=0.67F_r+Y₃F_a

Refer to the bearing specification table
for the values of axial load factors Y_2, Y₃ and constant e.

Static equivalent radial load

P_0r=F_r+Y₀F_a

Refer to the bearing specification table for the value of axial load factors Y_0.

• Spherical roller bearings

Dynamic equivalent radial load

when F_a/F_r≤e ; P_r=F_r+Y₁F_a

when F_a/F_r>e ; P_r=0.67F_r+Y₂F_a

Refer to the bearing specification table
for the values of axial load factors Y_1, Y₂ and constant e.

Static equivalent radial load

P_0r=F_r+Y₀F_a

Refer to the bearing specification table for the values of axial load factors Y₀ and constant e.

• Needle roller bearings

Dynamic equivalent radial load

P_r=F_r

Static equivalent radial load

P_0r=F_r

• Thrust ball bearings

Dynamic equivalent axial load

P_a=F_a

Static equivalent axial load

P_0a=F_a

• Spherical thrust roller bearings

Dynamic equivalent radial load

P_a=1.2F_r+F_a

Static equivalent axial load

P_0a2.7F_r+F_a

Note : F_r/F_a≤0.55

4) Basic rating life

The basic rating life in relation to the basic dynamic load rating and dynamic equivalent load can be expressed using equation (3-1). It is convenient to express the basic rating life in terms of time, using equation (3-2), when a bearing is used for operation at a constant speed; and, in terms of mileage (km), using equation (3-3), when a bearing is used in railway rolling stock or automobiles.

5) Correction of calculated service life

When the bearing is used under heat, adjust the service life by multiplying the basic dynamic load rating indicated in the Bearing Specification Tables by the temperature adjustment factor.

For applications where more than one bearing is used, calculate the service life of the entire bearing system.
Equation for Calculation of Service Life of Entire System

π

Also, adjust the rating life by using reliability factor a1, bearing characteristic factor a2, and operating condition factor a3:

1) Reliability factor a₁

The following table describes reliability factor, a₁, which is necessary to obtain the corrected rating life of reliability greater than 90%.

2) Bearing characteristic factor a₂

The bearing characteristic in relation to bearing life may differ according to bearing materials (steel types and their quality), and may be altered by production process, design, etc. In such cases, the bearing life calculation can be corrected using the bearing characteristic factor a₂.
Koyo has employed vacuum-degassed bearing steel as our standard bearing materials. It has a significant effect on bearing life extension, which was verified through studies at our laboratory. The basic dynamic load rating of bearings made of vacuum-degassed bearing steel is specified in the bearing specification table, taking the bearing characteristic factor as a₂=1. For bearings made of special materials to extend fatigue life, the bearing characteristic factor is treated as a₂>1.

3) Operating condition factor a₃

When bearings are used under operating conditions, which directly affect their service life, including improper lubrication, the service life calculation can be corrected by using a₃.
Under normal lubrication, the calculation can be performed with a₃=1; and, under favorable lubrication, with a₃>1.
In the following cases, the operating condition factor is treated as a₃<1:

• Operation using lubricant of low kinematic viscosity

For ball bearings …  13mm²/s or less

For roller bearings … 20mm²/s or less

• Operation at very slow rotation speed

Product of rolling element pitch diameter and rotational speed is 10000 (mmm/min) or less.

• Contamination of lubricant is expected
• Greater misalignment of inner and outer rings is present

For calculation of the service life in due consideration of a₂ and a₃, use the Calculation Menu entitled Life Calculation.

b. Selection based on service life

The following is an example of how an appropriate bearing can be selected based on the required service life. To determine required service life in actual cases, refer to the selection menu.

1) Initial conditions

Bearing radial load (F_r), bearing axial load (F_a), rotational speed (n), and bearing bore diameter (d)

2) Selection of bearing type 

Select a proper type of bearing from among those listed in the Example Bearing Arrangements.

• Arrangement in which fixed and free sides are distinguished

n : Rotation speed; F_r : Radial load; F_a : Axial load; Q : Aligning capability

Bearing arrangement		n	Fr	Fa	Q	Application example
Fixed side	Free side
		High	Light	Light	Low	Medium size motors, air blowers
		High	Heavy	Light	Low	Traction motors for railway rolling stock
		High	Heavy	Heavy	Low	Speed reducers, lathe spindles
		High	Normal	Normal	Low	Motors
		Middle	Heavy	Normal	Middle	Paper manufacturing calender rollers
		High	Heavy	Light	Low	Speed reducers
		High	Light	Light	Low	Pumps
		High	Light	Normal	Low	Worm gear, speed reducers
		Middle	Heavy	Normal	High	Steel manufacturing table rollers

• Arrangement in which fixed and free sides are not distinguished

n : Rotation speed; F_r : Radial load; F_a : Axial load; Q : Aligning capability

Bearing arrangement	n	Fr	Fa	Q	Application example
	High	Light	Light	Low	Small motors, small pumps
Back-to-back Face-to-face	High	Light	Normal	Low	Machine tool spindles
Back-to-back Face-to-face	High	Heavy	Heavy	Low	Speed reducers, automobile wheels
	High	Normal	Normal	Low	Machine tool spindles
	High	Heavy	Light	Low	Construction equipment

• Application to vertical shafts

n : Rotation speed; F_r : Radial load; F_a : Axial load; Q : Aligning capability

Bearing arrangement	n	Fr	Fa	Q	Application example
Fixed side  Free side	High	Normal	Normal	Low	Vertical motors
Free side Fixed side	Middle	Heavy	Heavy	High	Crane center shafts

3) Determination of required service life 
Determine the required service life of bearings, referring to Table 3-1.

Table 3-1 Recommended bearing service life

4) Determination of required dynamic load rating 

Obtain the required dynamic load rating by means of equation 3-4.

Calculation of required dynamic load rating

C :	basic dynamic load rating	N
P :	dynamic equivalent load	N
	for radial bearings
	Pr : dynamic equivalent radial load	N
	for thrust bearings
	Pa : dynamic equivalent axial load	N
L10h :	required service life	h
n :	rotational speed	min-1
p :	for ball bearings ………..	p=3
	for roller bearings………..	p=10/3

When the axial load is not so large, the rating is provisionally estimated supposing that P equals F_r.

5) Selection of bearing 

Select a bearing that meets the dynamic load rating requirement obtained by the above calculation, from those listed in the Bearing Specification Tables.

6) Calculation of bearing rating life 

Obtain the dynamic equivalent load based on the radial and axial load factor of the selected bearing, and calculate the rating life of the bearing.
As for applications where loads on the bearing may vary, calculate the mean dynamic equivalent load by means of equation 3-5 , and estimate the rating life based on it.

Mean dynamic equivalent load (In case of staged fluctuation)

(Reference) Mean speed nm can be calculated using the following equation:

c. Basic static load rating and safety coefficient

1) Basic static load rating 

A bearing may sustain a local deformation permanently when exposed to an excessively high static load or impact load. If the permanent deformation is beyond a specific extent, smooth rotation is imposed. The static load under which contact surface pressure working between the rolling element and raceway may generate the following sizes of contact stress is called the basic static load rating and is used as a reference to determine a high load.

Other ball bearings … 4200MP_a

2) Static equivalent load 

The static equivalent load is a virtually calculated load, under which contact stress of the same degree as generated under actual loading conditions would occur between the rolling elements and raceway in the section exposed to the maximum load.
It is calculated by means of the equivalent static load calculation equation, using the load factors listed in the tables.

(TO BE CONTINUED)

3) Safety coefficient

A safety coefficient is designated, based on empirical data, so as to ensure safety in relation to basic static load rating.

[Remark] For spherical thrust roller bearings ; f_s≥4

Consult Koyo for further advice regarding safety factors appropriate to individual machines.