Calculation Example

Rolling Bearings According to

to DIN ISO 281

Release July 2013

c 2013 GWJ Technology GmbH

Rebenring 31  38106 Braunschweig  Tel.: +49 (0) 531 129 399-0
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Contents
0.1

Calculation Examples: Rolling Bearing According to DIN ISO 281

0.1.1 Start the Calculation Module . . . . . . . . . . . . . .
0.1.2 First Calculation Example . . . . . . . . . . . . . . . .
0.1.3 The Calculation . . . . . . . . . . . . . . . . . . . . . .
0.1.4 Calculation Results . . . . . . . . . . . . . . . . . . . .
0.1.5 Documentation: Calculation Report . . . . . . . . . . .
0.1.6 Save the Calculation . . . . . . . . . . . . . . . . . . .
0.1.7 Second Calculation Example . . . . . . . . . . . . . . .
0.1.8 The Calculation . . . . . . . . . . . . . . . . . . . . . .
0.1.9 Calculation Results . . . . . . . . . . . . . . . . . . . .
0.1.10 Documentation: Calculation Report . . . . . . . . . . .
0.1.11 Save the Calculation . . . . . . . . . . . . . . . . . . .

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0.1. Calculation Examples: Rolling Bearing According to DIN ISO 281

0.1

Calculation Examples: Rolling Bearing According to DIN ISO

281

0.1.1

Start the Calculation Module

Please login with your username and your password. Select the module `Rolling bearings calculation' through
the tree structure of the project manager by double-clicking on the module or clicking on the button `New
calculation'.

Figure 1: Start the calculation module

0.1.2

First Calculation Example

Bearing for a Rope Sheave of a Pulley Block

The wrap angle for rope sheaves of pulley blocks is 180 . Therefore, the load on the bearing is twice the rope
pull. The axial forces and the resulting moments are low. When the diagonal pull is 5 , then the axial forces
have to be considered for the calculation of the rating life. Adequate bearing spread for load accommodation
is achieved by mounting either two bearings or one double-row bearing. In the following example the rating
life and expanded modied rating life are to be calculated.
We have taken this example from: J. Braendlein: Die Waelzlagerpraxis: Handbuch zur Berechnung und Gestaltung von Waelzlagern (1995, p. 466-470).
Please enter the following input values:
Bearing load
Type of bearing
Speed n
Built-in bearing
For-life lubrication

65 kN
Tapered roller bearing (single row)
30 min1
Tapered roller bearing (100 x 150 x 67)
Grease with EP-additive
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0.1. Calculation Examples: Rolling Bearing According to DIN ISO 281

Illustration of a rope sheave of a pulley block including the tapered roller bearing. (The following gure: J.
Braendlein: Die Waelzlagerpraxis, p. 467).

Figure 2: Rope sheave of a pulley block

0.1.3

The Calculation

Dene Number of Bearings

In this example we would like to calculate one bearing of a tapered roller bearing pair. When you open the
calculation module, usually one bearing is shown. So it is not necessary to change the number of the bearings.
You can enter a description into the comment eld, for example `Bearing of the rope sheave'.

Figure 3: Number of bearings

Select Manufacturer and Bearing Type

The extensive bearing database provides over 20.000 bearings from dierent manufacturers. Select the bearing
manufacturer `SKF 2007' from the listbox. Next, choose the bearing type `Tapered roller bearing (single row)'.

Figure 4: Select the manufacturer and bearing type

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0.1. Calculation Examples: Rolling Bearing According to DIN ISO 281

Specication of Bearing Load

Enter the values for the bearing load now. Please keep in mind that the values will be entered in `kN'.
Right-clicking allows you to change the unit of measurement.

Figure 5: Values for the bearing load in kN

Bearing Selection
Click on the button `Bearing selection' to open the bearing database.

Figure 6: Button `Bearing selection'

There are `578' bearings in the database right now. Search lters have been developed to assist in searching
this extensive amount of bearings and to quickly nd the bearing you are looking for. You can lter the bearing
types by the inner and outer diameter so that you can only see bearing types with this particular diameter.
Enter the inner and outer diameter and click the button `Search'.
Inner diameter of bearing
Outer diameter of bearing

= 100 mm
= 150 mm

Select the bearing `32020 X/Q' and conrm with the button `OK'.

Figure 7: Found bearings

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0.1. Calculation Examples: Rolling Bearing According to DIN ISO 281

0.1.4

Calculation Results

Rating Life
All results will be calculated during every input and will be displayed in the result panel. A recalculation occurs
after every data input. Any changes that are made to the user interface take eect immediately. First, you
get the result for the rating life as well as the static identication number.

Figure 8: Result for the rating life

The result of the rating life is L10 = 14.237,9 h
For rope sheaves, a rating life from 5.000 to 20.000 hours is required. The bearing is suciently dimensioned.
You will nd a note in the message window but you can ignore this message. When the pair is tted together,
then the correct axial clearance and the necessary axial force for the tapered roller bearing occur.

Figure 9: Message window

Expanded Modied Rating Theory

After you get the result for the rating life, please have a look at the expanded modied rating life Lnm
regarding the operating conditions (lubrication, clearance). The option `Use expanded modied rating theory'
is activated by default.

Figure 10: Expanded modied rating theory

Now you an dene the requisite reliability and the cleanness as well as a lubricant. Please select the grease
`Klueber Kluebersynth BMQ 72-162 (094073)'. Select this lubricant directly from the listbox. If you need
detailed information, please click on the button `Lubricant'.

Figure 11: Lubricant selection

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0.1. Calculation Examples: Rolling Bearing According to DIN ISO 281

Clicking the button `Lubricant' opens the lubricant database. Here you can see that the grease contains active
EP additive.

Figure 12: Lubricant database

Next, you have to estimate the inuence of possible impurities by using the cleanness factor. Actually, it is
assumed that the `highest cleanness' is used for sealed and greased bearings (for-life-lubrication). But during
the entire operating time, a certain wear of the seals could occur which can let light impurities into the bearing.
In this case you can assume light impurities. Therefore, choose `Light impurities' from the listbox.

Figure 13: Light impurities

Now you get immediately the result for the expanded modied rating life.

Figure 14: Expanded modied rating life

The result of the expanded modied rating life is Lnm = 8.911,8 h.. Finally, the expanded modied rating
life Lnm is in the range of the rating life L10 .

Hinweis: Press the `Up' and `Down' arrow to move through the listbox of cleanness parameters. Moving
through the listbox changes the expanded modied rating life and the results will be displayed immediately
in the result panel, making it very easy to compare the expanded modied rating life with dierent levels of
cleanness. You can also navigate through the lubricant listbox.
0.1.5

Documentation: Calculation Report

After the completion of your calculation, you can create a calculation report. Click on the `Report' button.

Figure 15: Button `Report'

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0.1. Calculation Examples: Rolling Bearing According to DIN ISO 281

You can navigate through the report via the table of contents that provides links to the input values, results
and gures. This calculation report contains all input data, the calculation method as well as all detailed
results. The report is available in HTML and PDF format. The calculation report saved in HTML format,
can be opened in a web browser or in Word for Windows.

Figure 16: Calculation report

You may also print or save the calculation report:
- To save the report in the HTML format, please select `File' `Save as' from your browser menu bar.
Select the le type `Webpage complete', then just click on the button `Save'.
- If you click on the symbol `Print', then you can print the report very easily.
- When you click on the symbol `PDF', then the report appears in the PDF format. If you right-click on
the PDF symbol, you should see the `Save Target As' option. Click on that option and you will see the
dialog box for saving the report.

Diagrams
Click on the button `Diagram' next to the listbox. The diagram includes the values for the rating life and for
the expanded modied rating life. The exact values can be selected directly from the graphical representation.
Clicking the `Close' button leads you back to the main mask.

Figure 17: Button `Diagram'

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0.1. Calculation Examples: Rolling Bearing According to DIN ISO 281

0.1.6

Save the Calculation

When the calculation is nished, you can save it to your computer or to the eAssistant server. Click on the
button `Save'.

Figure 18: Button `Save'

Before you can save the calculation to your computer, you need to activate the checkbox `Enable save data
local' in the project manager and the option `Local' in the calculation module. A standard Windows dialog
for saving les will appear. Now you will be able to save the calculation to your computer.

Figure 19: Windows dialog for saving the le

In case you do not activate the option in order to save your les locally, then a new window is opened and
you can save the calculation to the eAssistant server. Please enter a name into the input eld `Filename' and
click on the button `Save'. Then click on the button `Refresh' in the project manager. Your saved calculation
le is displayed in the window `Files'.

Figure 20: Save the calculation

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0.1. Calculation Examples: Rolling Bearing According to DIN ISO 281

0.1.7

10

Second Calculation Example

Bearing of a Fan
The impeller of fans can be arranged either between two bearings or in an overhung position. The impeller of
small and medium-sized fans is generally overhung. Two separated plummer block housings are suitable for
supporting the fan drive shaft.
This calculation example we have taken from: J. Braendlein: Die Waelzlagerpraxis: Handbuch zur Berechnung
und Gestaltung von Waelzlagern (1995, p. 516-520, gures: p. 517).

Figure 21: Bearing unit for fan

The unit (gure 6.66) contains a cylindrical roller bearing A and a deep groove ball bearing B in a common
housing (gure 6.67). The bearing diameter is 70 mm.

Figure 22: Bearing of a fan

Input Values
The input values for bearing A (Cylindrical roller bearing NU 314 ECP)

Load Case No. 1

Time slice q1
Speed n1
Radial force Fr1
Axial force Fa1
Temperature T1

Load Case No. 2

= 50%
= 3.000 min-1
= 8.500 N
=0N
= 70 C

Time slice q2
Speed n2
Radial force Fr2
Axial force Fa2
Temperature T2

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= 50%
= 4.500 min-1
= 11.000 N
=0N
= 70 C

0.1. Calculation Examples: Rolling Bearing According to DIN ISO 281

11

All input values for bearing B (deep groove ball bearing 6314)

Load Case No. 1

Time slice q1
Speed n1
Radial force Fr1
Axial force Fa1
Temperature T1

0.1.8

Load Case No. 2

= 50%
= 3.000 min-1
= 2.000 N
= 5.000 N
= 70 C

Time slice q2
Speed n2
Radial force Fr2
Axial force Fa2
Temperature T2

= 50%
= 4.500 min-1
= 5.000 N
= 5.000 N
= 70 C

The Calculation

Dene the Number of Bearings

In this example we want to calculate the rating life of the cylindrical roller bearing and the deep groove ball
bearing. We have to dierent bearings and we need to change the number of bearings. So enter `2' into the
input eld `Number of bearings to calculate'. Please calculate the bearings one after another separately. The
listbox `Current view' allows you to switch between the two bearings.

Figure 23: Number of bearings

Add a comment for the rst bearing.

Figure 24: Add a comment

Select Manufacturer and Bearing Type

Now select the manufacturer `SKF'. Choose the cylindrical roller bearing from the listbox.

Figure 25: Selection of the manufacturer and bearing type

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0.1. Calculation Examples: Rolling Bearing According to DIN ISO 281

12

Specication of Bearing Load with Load Collectives

Dene the load collective for the rst bearing. Activate the option `Use load collective'. The input options for
the radial and axial force as well as for the speed will be deactivated.

Figure 26: Bearing load

Dene two load cases for the bearing. Enter the time slice, the radial force, axial force, the temperature and
cleanness for each load case. After you made all entries, click the button `OK' to conrm your inputs.

Figure 27: Dene the load collective

Bearing Selection
Click on the button `Bearing selection'.

Figure 28: Bearing selection

It is increasingly convenient to use the search lter to quickly nd the bearing you are looking for. Enter `70
mm' for the inner diameter and click the button `Search'. Now you can choose the cylindrical roller bearing
`NU 314 ECP' from the list. Clicking the button `OK' conrms the bearing and leads you back to the main
mask.

Figure 29: Bearing selection

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0.1. Calculation Examples: Rolling Bearing According to DIN ISO 281

0.1.9

13

Calculation Results

Rating Life of the Cylindrical Roller Bearing (Bearing Location A)

All results will be calculated during every input and will be displayed in the result panel. A recalculation occurs
after every data input. Any changes that are made to the user interface take eect immediately. First, you
get the result for the rating life as well as the static identication number.

Figure 30: Rating life

The result of the rating life is L10 = 188.391,8 h
The cylindrical roller bearing is suciently dimensioned.

Rating Life for the Deep Groove Ball Bearing (Single Row) (Bearing Location B)
Calculate now the rating life for the deep groove ball bearing. Please pay attention that you select `Bearing
No. 2' from the listbox `Current view'.

Figure 31: Deep groove ball bearing

Select the manufacturer `SKF' and the bearing type `Deep groove ball bearing (single row)'.

Figure 32: Bearing selection

Activate the option `Use load collective'.

Figure 33: Button `Load collective'

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0.1. Calculation Examples: Rolling Bearing According to DIN ISO 281

14

Dene the load cases. Enter the time slice, the radial force, axial force, the temperature and cleanness for
each load case. After you made all entries, click the button `OK' to conrm your inputs.

Figure 34: Dene the load collective

Click on the button `Bearing selection'.

Figure 35: Button `Bearing selection'

Choose the bearing `6314' from the list. It is increasingly convenient to use the search lter to quickly nd
the bearing you are looking for. Enter `70 mm' for the inner diameter and click the button `Search'. Then
you can select the bearing `6314' from the list. Clicking the button `OK' conrms the bearing and leads you
back to the main mask.

Figure 36: Deep groove ball bearing

The result for the rating life is L10 = 5.868 h

Figure 37: Nominal rating life

The rating life of the deep groove ball bearing B is lower than the rating life of the cylindrical roller bearing A. This means that bearing B is subjected to higher stresses than bearing A. At least 22.0000 hours
are required for the rating life of deep groove ball bearings. But with this result, the rating life is not suciently dimensioned. It is necessary to take a closer look at the expanded modied rating life Lnm of bearing B.
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0.1. Calculation Examples: Rolling Bearing According to DIN ISO 281

15

Expanded Modied Rating Life of the Deep Groove Ball Bearing

The next step is to determine the expanded modied rating life for the deep groove ball bearing. The
option `Use expanded modied rating theory' is activated by default. Select the grease `Lubcon Turmogrease
Highspeed L 252 (K HC P 2/3 K-50)' from the listbox or click on the button `Lubricant' to open the lubricant
selection. Choose the lubricant and conrm with the button `OK'.

Figure 38: Expanded modied rating life

The result of the expanded modied rating life is Lnm = 34.092,4 h.

Figure 39: Result for the expanded rating life

At least 22.000 hours are required and the bearing is suciently dimensioned. For the calculation with load
collectives, you cannot open all diagrams. But you can open the diagram for the lubricant viscosity.
0.1.10

Documentation: Calculation Report

After the completion of your calculation, you can create a calculation report. Click on the `Report' button.
Click the button `Options' and activate the diagram for the `Lubricant viscosity'. This diagram will then appear
in the calculation report.

Figure 40: Calculation report

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0.1. Calculation Examples: Rolling Bearing According to DIN ISO 281

16

You can navigate through the report via the table of contents that provides links to the input values, results
and gures. This calculation report contains all input data, the calculation method as well as all detailed
results. The report is available in HTML and PDF format. The calculation report saved in HTML format,
can be opened in a web browser or in Word for Windows. You may also print or save the calculation report:
- To save the report in the HTML format, please select `File' `Save as' from your browser menu bar.
Select the le type `Webpage complete', then just click on the button `Save'.
- If you click on the symbol `Print', then you can print the report very easily.
- When you click on the symbol `PDF', then the report appears in the PDF format. If you right-click on
the PDF symbol, you should see the `Save Target As' option. Click on that option and you will see the
dialog box for saving the report.

0.1.11

Save the Calculation

When the calculation is nished, you can save it to your computer or to the eAssistant server. Click on the
button `Save'. Before you can save the calculation to your computer, you need to activate the checkbox
`Enable save data local' in the project manager and the option `Local' in the calculation module. A standard
Windows dialog for saving les will appear. Now you will be able to save the calculation to your computer.

Figure 41: Windows dialog for saving the le

In case you do not activate the option in order to save your les locally, then a new window is opened and
you can save the calculation to the eAssistant server. Please enter a name into the input eld `Filename' and
click on the button `Save'. Then click on the button `Refresh' in the project manager. Your saved calculation
le is displayed in the window `Files'.

Figure 42: Save the calculation

Our manual is improved continually. Of course we are always interested in your opinion, so
we would like to know what you think. We appreciate your feedback and we are looking
for ideas, suggestions or criticism. If you have anything to say or if you have any questions,
please let us know via telephone +49 (0) 531 129 399-0 or email eAssistant@gwj.de.

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