Chapter 9
Involute splines, serrated shaft and splined shaft connection according to Niemann

    9.1   Start the calculation module
    9.2   Profile geometry selection
    9.3   Change the unit of measurement
    9.4   Load peaks
    9.5   Kind of load
    9.6   The stepped hub
    9.7   Material shaft and hub
    9.8   The message window
    9.9   The calculation results
    9.10   The documentation: The calculation report
    9.11   How to save the calculation
    9.12   The dimensioning functions
    9.13   The button ‘Redo’ and ‘Undo’
    9.14   The button ‘CAD’
    9.15   The options
    9.16   The calculation example: Splined shaft connection for a lifting gear drive

9.1 Start the calculation module

Please login with your user name and your password. Select the module through the tree structure of the Project Manager by double-clicking on the module or clicking on the button ‘New calculation’.

The calculation module is opened in a new window.

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Figure 9.1: A general overview

Please note: Open this calculation module either through the entry involute splines, serrated shaft or splined shaft from the window ‘Calculation’ which you find in the Project Manager. The module starts then with the corresponding profile type as a pre-setting. If you are already in the calculation module, use the button ‘Selection’ to change the profile type at any time you want.

The profile geometry selection allows you to switch between involute splines, serrated shaft connections and splined shaft connections.

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Figure 9.2: Kind of profile geometry

All input options for the profile types in the main mask are equal for every profile. Only in the profile geometry selection the options as well as the several input parameters change according to the profile type. In addition, you get a graphical representation for every calculation module.

9.2 Profile geometry selection

Click on the button ‘Selection’.

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Figure 9.3: The button ‘Selection’

The window for the profile geometry selection is opened.

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Figure 9.4: The profile geometry selection

Open the listbox ‘Kind of profile geometry’ and change the profile type.

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Figure 9.5: Selection of profile types

Then the appropriate selection parameters conform to the respective profile type.

9.2.1 Involute splines

This module for the profile type ‘Involute gear (toothed shaft)’ allows you to calculate the strength calculation of shaft-hub-connection with involute splines according to DIN 5480. Decide between the complete DIN 5480 or the preference series of DIN 5480 by using the listbox ‘Standard geometry data’. All dimensions can be selected from the database or determined via the profile selection search. You can refine the profile geometry selection by including specific parameters to find the right profile quicker.

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Figure 9.6: Standard geometry data

The different parameters

can be specified for a certain range.

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Figure 9.7: The profile selection search of the involute splines

Please enter your values here. By using the tabulator key, you can jump from one input field to another. After that, the input data are taken over.

Please note: Enter the values into the input fields to reduce the number of profiles. Then you have to decide between only a few profiles. In case you have already entered the values into the input fields and now you would like to have any reference diameter of the profile again, then delete your own value and click into another input field or use the Tab key on your computer keyboard. The option ‘Any’ is used again in the input field. This applies also for the input of data of the other profile types.

Click on the button ‘Search’ to start the profile selection search.

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Figure 9.8: The button ‘Search’

Select the profile from the database and confirm with the button ‘OK’.

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Figure 9.9: Database

Please note: You can sort the selection list in the database by clicking on the column header. To sort the profiles in reverse order, click on the column header again. Then a black arrow appears. The arrow makes the orientation much easier for you.

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Figure 9.10: The column header

Profile details

If you would like to specify profiles, which vary from the standard, then activate the option ‘User-defined’.

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Figure 9.11: The profile details

Please confirm these inputs with the button ‘OK’ and the profile, including your own values, is taken over to the main mask.

9.2.2 Serrated shaft connection

Select the serrated shaft connection as a kind of profile geometry. With it the strength calculation according to DIN 5481 of shaft-hub connections can be accomplished.

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Figure 9.12: Serrated shaft connection

Similar to the involute splines calculation, the dimensions can be selected from the database or via the profile selection search. You can refine the profile geometry selection by including specific parameters to find the right profile quicker.

The following parameters

can be specified for a certain range.

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Figure 9.13: Profile selection search for serrated shaft connection

Please enter your input values. Move from one input field to another by using the tabulator key. The data are taken over.

Please note: Enter the values into the input fields to reduce the number of profiles. Then you have to decide between only a few profiles. In case you have already entered the values into the input fields and now you would like to have any reference diameter of the profile again, then delete your own value and click into another input field or use the Tab key on your computer keyboard. The option ‘Any’ is used again in the input field. This applies also for the input of data of the other profile types.

Click on the button ‘Search’ to start the profile geometry search.

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Figure 9.14: The button ‘Search’

Select the profile from the database and confirm with the button ‘OK’.

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Figure 9.15: Database

Please note: You can sort the selection list in the database by clicking on the column header. To sort the profiles in reverse order, click on the column header again. Then a black arrow appears. The arrow makes the orientation much easier for you.

Profile details

To specify non-standard profiles, activate the option ‘User-defined’.

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Figure 9.16: User-defined input

All input options for your own values are activated. Confirm these inputs with the button ‘OK’ again and the profile with your values is taken over to the main mask.

9.2.3 Splined shaft connection

Select the splined shaft connection. This calculation of profiles is determined according to DIN ISO 14 light and medium series, DIN 5464 heavy series, DIN 5471 and DIN 5472 for machine tools.

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Figure 9.17: Splined shaft connection

For the profile selection search the following parameters can be specified for a certain range:

Please note: If you specify the ‘from ... to’ input fields, you can refine the profile selection search. Click on the button ‘Search’ and just a certain range of profiles is displayed in the database. You can also select a profile from the database directly. Confirm the selection with the button ‘OK’ and the profile is taken over to the main mask. Click on the column header to sort the profiles in the database.

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Figure 9.18: The profile selection search for splined shaft connection

Profile details

Activate the option ‘User define’ to specify non-standard profiles.

The input options for your own values are activated. Use the button ‘OK’ to confirm your input values. The values are taken over to the main mask of the calculation module.

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Figure 9.19: User-defined input

If you selected the profile, you can go on with your inputs in the main mask. All input options in the main mask are equal for every profile type.

9.3 Change the unit of measurement

If you right-click into an input field, you can change the unit. A context menu is opened. The both arrows mark the current setting.

The current field value will be converted automatically into the according unit.

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Figure 9.20: Change the unit of measurement

9.4 Load peaks

The calculation module allows you to consider a number of load peaks for your calculation. If you want to use this option, just activate ‘Consider load peaks’.

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Figure 9.21: Consider load peaks

To specify the number of load peaks, use the corresponding listbox. You can also define an own number of load peaks. Click on the listbox entry ‘User-defined input’. The input field next to the listbox is enabled and you can add your value.

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Figure 9.22: Load peaks: User-defined input

Please note: The load peak torque Tmax  has to be: Tmax > Tnenn ⋅KA

9.5 Kind of load

Specify the kind of an existing alternating torque for your calculation.

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Figure 9.23: Kind of load

In case you have an alternating torque with a slow or fast increase, then the load direction change is activated.

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Figure 9.24: Load direction changes

There is also an option to activate the input ‘User-defined’.

9.6 The stepped hub

Consider here a stepped hub.

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Figure 9.25: The stepped hub

If you enable this option, you can define a smaller hub diameter D1  , the width c as well as the axial distance a0 . Use the graphical representation to make it easier to find these parameters. With these inputs the load distribution factor Klambda  is determined for a different load in and output according to DIN 6892.

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Figure 9.26: The graphical representation

9.7 Material shaft and hub

All materials for shaft and hub can be selected from the database or can be defined individually.

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Figure 9.27: Material selection for shaft and hub

You are able to search and select the material directly via a listbox.

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Figure 9.28: The material selection

Please note: If you move within the listbox, then use the two arrow keys ‘Up’ and ‘Down’ on your computer keyboard. So you will know, how the safeties change with the respective materials.

Select the input ‘User-defined’ from the listbox.

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Figure 9.29: User-defined

Click on the button ‘Material’ to define your individual material.

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Figure 9.30: The button ‘Material’

When choosing the button, you will get further information about the material.

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Figure 9.31: Material details

In addition, you get the possibility to enter an user-defined material.

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Figure 9.32: User-defined material

Add a comment, a source, kind of material, yield point, hardness factor as well as the support factor. Please confirm your inputs with the button ‘OK’. In the main mask the entry ‘User-defined’ is displayed.

Please note: In case you add a comment and own values for the ‘User-defined’ entry, confirm these with the button ’OK’. Please note, that these data are not saved. As soon as you select another material from the database, your predefined material is deleted. Then you have to enter your data for the user-defined material again.

9.8 The message window

The message window provides hints, messages, or warnings. This information will appear in the calculation report later.

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Figure 9.33: The message window

Move the mouse pointer to an input field or to a button and you will get some additional information in the quick info line.

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Figure 9.34: The quick info line

9.9 The calculation results

In the result panel you find all safeties and pressures at operation and maximum load for the shaft and hub. The calculation is determined automatically and the results are displayed in the result panel. After every data input, the result is be calculated again.

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Figure 9.35: The results

9.10 The documentation: The calculation report

After the determination of the calculation, click on the button ‘Report’ to generate a calculation report.

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Figure 9.36: The button ‘Report’

The calculation report is opened.

The calculation report contains a table of contents. Through this all results can be called very fast. All inputs as well as results are clearly listed. The report is available in HTML and PDF format. Calculation reports, saved in HTML format, can be opened in a web browser or in Word for Windows.

9.11 How to save the calculation

After completion the calculation, you can save the calculation. Save it either on the eAssistant server or on your own workstation. Click on the button ‘Save’.

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Figure 9.37: The button ‘Save’

If you have activated the option ‘Enable file save local’ in the Project Manager and the option ‘Local’ in the calculation module, a standard Windows dialog for saving the file on your workstation appears.

Please note: You must not forget that the calculation module has to be closed to activate the option ‘Enable file save local.’

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Figure 9.38: Windows dialog for saving the file

In case you have not activated this option, a new window is opened and you can save the calculation on the eAssistant server.

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Figure 9.39: Save the calculation

Please enter a name into the input field ‘Filename’ and click on the button ‘Save’. Then click on the button ‘Refresh’ in the Project Manager. Your saved calculation file is displayed in the window ‘File’.

9.12 The dimensioning functions

By using the dimensioning functions (the ‘Calculator’ button), the input value is determined so that the minimum safety is fulfilled. The minimum safety is specified usually with the value ‘1.2’. If you would like to change that given safety, click on the button ‘Options’ (see also section ‘Options’). You are supported by the following dimensioning functions:

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Dimensioning of the supporting length ltr  at minimum safety

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Dimensioning of the nominal operation torque Tnenn  at minimum safety

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Dimensioning of the maximum load peak torque Tmax  at minimum safety

Example: The dimensioning of the maximum nominal operation torque

Determine the torque which fulfills the demanded safety of ‘1.2’. Click on the dimensioning button next to the input field for the torque.

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Figure 9.40: The dimensioning button

Now the maximum torque is determined.

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Figure 9.41: The maximum torque

The minimum safety is displayed in the result panel. If you enter a higher value than ‘45546.0 Nm’, the safety has fallen below. The result is marked in red. Click on the dimensioning function again and the value, which fulfills the minimum safety for the maximum torque, is displayed.

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Figure 9.42: The minimum safety

9.13 The button ‘Redo’ and ‘Undo’

The button ‘Undo’ allows you to reset your input to an older state. The button ‘Redo’ reverses the undo.

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Figure 9.43: The button ‘Redo’ and ‘Undo’

9.14 The button ‘CAD’

The eAssistant plugin for various CAD systems (e.g., SolidWorks, Solid Edge, Autodesk Inventor and Catia) enables you to combine calculation and design very easily and intelligently. Based on your eAssistant calculation, you can generate shafts as well hubs of splined shaft and serrated shaft connections as a 3D part within just seconds. However, first you have to download and install the CAD plugin. You can find the plugin on our web site www.eAssistant.de. After installation, an integrated button called ‘eAssistant’ appears in the CAD system. Accomplish the calculation using the eAssistant and click on the button ‘CAD ⇒ SolidKiss_nG Interface’. The values are transferred to the CAD system where you can generate the 3D models through a menu.

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Figure 9.44: The button ‘CAD’

Please note: In case you need further information about our 3D CAD plugin (SolidKiss_nG), feel free to contact us. Get also details on our web site www.eAssistant.de or read the CAD plugin (SolidKiss_nG) manual.

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Figure 9.45: The ‘eAssistant’ button in the CAD system

9.15 The options

The button ‘Options’ allows you to change the minimum safety or number of the decimal places in the report. If you would like to change these values permanently, you can save your desired settings as a ‘standard’ file. For further details, please check the ‘General functions’ chapter.

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Figure 9.46: The button ‘Options’

9.16 The calculation example: Splined shaft connection for a lifting gear drive

We have prepared the following example to guide you through the calculation module. This calculation module refers to: G. Niemann, H. Winter, B.-R. Höhn: Maschinenelemente Band I: Konstruktion von Verbindungen, Lagern, Wellen. Springer Verlag, 3. edition, 2001: p.857 Example 4: Splined shaft for a lifting gear drive.

9.16.1 Start the calculation module

Please login with your user name and your password. Select the module through the tree structure of the Project Manager by double-clicking on the module or clicking on the button ‘New calculation’.

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Figure 9.47: The calculation module ‘Splined shaft’

9.16.2 The input values

A splined shaft connection with a splined shaft according to DIN ISO 14 is given. The safety against pressure is required. For our calculation example the following input values are given:

Diameter d1 = 32 mm

Diameter d2  = 38 mm

Number of keys = 8

Key width = 6

Supporting length ltr  = 40 mm

Manufacturing according to tolerance field = H7/IT7

Application factor = 1

Nominal operation torque Tnenn  = 2400 Nm

Maximum load peak torque Tmax  = 2400 Nm with number of load peaks > 107  , no alternating torque

Outer diameter of hub D2  = 45 mm

Material shaft = C45 hardened and tempered

Material hub = C45 hardened and tempered

9.16.3 The calculation

The profile geometry selection

To find the right profile, click on the button ‘Selection’.

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Figure 9.48: The button ‘Selection’

The profile geometry selection is opened.

Select from the listbox ‘Standard geometry data’ the splined shaft profile according to DIN ISO 14 medium series.

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Figure 9.49: The profile geometry selection

You can refine the profile geometry selection by including specific parameters to find the right profile quicker. Just add the diameter d
 1  , the number of keys as well the key width. Click on the button ‘Search’.

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Figure 9.50: Refine the profile geometry selection

After clicking the button ‘Search’, only one profile remains. Please take over this profile to the main mask with the button ‘OK’.

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Figure 9.51: Profile

Enter ‘40 mm’ for the supporting length ltr  .

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Figure 9.52: The supporting length

The tolerance field

Use the listbox to select the tolerance field ‘H7/IT7’.

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Figure 9.53: The tolerance selection

The field ‘Profile’ displays the corresponding tolerance.

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Figure 9.54: Tolerance

Please add now the application factor as well as the nominal operation factor T
 nenn  .

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Figure 9.55: Application factor and nominal operation torque

The load peaks

Activate the load peaks und enter ‘2400’ for the maximum load peak torque Tmax  .

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Figure 9.56: The load peaks and load peak torque Tmax

Select the number of load peaks from the listbox.

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Figure 9.57: The number of load peaks

The kind of load

There is no change in load direction, so enter the default setting ‘No alternating torque’ for the ‘kind of load’.

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Figure 9.58: The kind of load

Enter the value ‘45 mm’ for the outer diameter of the hub.

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Figure 9.59: Outer diameter of hub

The material of shaft and hub

Select the material ‘C45 hardened and tempered’ for the shaft.

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Figure 9.60: The material for the shaft

Note: In case you need further information on the material, click on the button ‘Material’.

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Figure 9.61: The button ‘Material’

A new window is opened.

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Figure 9.62: The material details

Select the hub material ‘C45 hardened and tempered’ from the listbox.

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Figure 9.63: The material for the hub

9.16.4 The results

The safeties at operation load and maximum load, the pressures for shaft and hub are determined and displayed immediately in the result panel. In general, the results will be calculated and displayed during every input.

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Figure 9.64: The results

For our calculation example the splined shaft is sufficiently dimensioned. In addition, the message window contains the hint that this shaft-hub-connection can be used.

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Figure 9.65: The message window

The documentation: The calculation report

Click on the button ‘Report’ to create a calculation report. The report contains all detailed results and input values. Using the table of contents, all results can be called up very quickly. The report is available in HTML and PDF format. Save the report in HTML format to open the file later in the web browser or in Word for Windows.

How to save the calculation

Finally, selecting the button ‘Save’ allows you to save the calculation either on the eAssistant server or on your own workstation.

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Figure 9.66: The button ‘Save’

A standard Windows dialog for saving the file on your workstation appears, providing that the options ‘Enable file save local’ in the Project Manager and ‘Local’ in the calculation module are activated.

Note: You must not forget that the calculation module has to be closed to activate the option ‘Enable file save local.’

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Figure 9.67: Windows dialog for saving the file

In case you have not activated this option, a new window is opened and you can save the calculation on the eAssistant server.

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Figure 9.68: Save the calculation

Please enter a name into the input field ‘Filename’ and click on the button ‘Save’. Then click on the button ‘Refresh’ in the Project Manager. Your saved calculation file is displayed in the window ‘File’.

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 phone +49 (0) 531 129 399-0 or email eAssistant@gwj.de.