Chapter 12
Involute Splines, Serrated Shaft and Splined Shaft Connection According to Niemann

    12.1   Start the Calculation Module
    12.2   Profile Geometry Selection
    12.3   How to Change the Unit of Measurement
    12.4   Application Factor
    12.5   Load Peaks
    12.6   Kind of Load
    12.7   Stepped Hub
    12.8   Material Selection for Shaft and Hub
    12.9   Message Window
    12.10   Quick Info: Tooltip
    12.11   Calculation Results
    12.12   Documentation: Calculation Report
    12.13   How to Save the Calculation
    12.14   Automatic Dimensioning Functions (Calculator Button)
    12.15   The Button ‘Redo’ and ‘Undo’
    12.16   The Button ‘CAD’
    12.17   Options
    12.18   Calculation Example: Splined Shaft for Lifting Gear

12.1 Start the Calculation Module

Please login with your username 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 12.1: General overview

Please note: You can get into the calculation module either through the entry ‘Involute splines’, ‘Serrated shaft’ or ‘Splined shaft’. The module starts then with the selected profile type as default. You can change the profile type by clicking the button ‘Selection’ anytime you want. The profile geometry selection allows you to switch between involute splines, serrated shaft connections and splined shaft connections.

All input options are the same for every profile type. Only the profile geometry selection provides some profile specific input options. Each profile type gets a graphical representation.

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Figure 12.2: Different profile types

12.2 Profile Geometry Selection

In order to select the profile, click the button ‘Selection’.

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Figure 12.3: Button ‘Selection’

The profile geometry selection is opened.

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Figure 12.4: Profile geometry selection

Click the listbox ‘Kind of profile geometry’ and select the profile type - either involute spline, serrated shaft or splined shaft. The selection parameters automatically adjust to the profile type.

12.2.1 Involute Splines

The calculation module ‘Involute splines’ allows the strength calculation of splined connections with involute splines according to DIN 5480. The calculation is based on Niemann „Maschinenelemente“ Vol. 1, 2001. Involute splines are widely used. The splines are usually made with straight sides or cut with an involute. But involute splines are favoured over straight sided splines because of their greater strength. Involute splines can be moved axially, they are strong and are easy to cut and fit. The major advantage of involute splines is that no special machines are required in order to produce involute splines. Involute splines are especially suitable for the transmission of high torques. You can decide between the DIN 5480 standard or the preferred series of the DIN 5480. All dimensions can be easily selected from the database or identified with the profile search function.

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Figure 12.5: Standard geometry data

You can refine the profile geometry selection by including specific parameters to find the right profile quicker. The following parameters can be defined for a certain range:

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Figure 12.6: Profile selection search

Please enter your values. Use the Tab key to jump from field to field. All the inputs are applied. Click on the button ‘Search’ to start the profile selection search. The number of found profiles will be displayed below the ‘Search’ button.

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Figure 12.7: ‘Search’ button

Please note: To narrow your search, type more values in the search box. This way, you have to decide between a few profiles and you will find the right profile faster. If you have already entered values into the input fields and want to change your entry for any reason (e.g., any reference diameter again), please delete the value and click into another input field or use the Tab key. The option ‘Any’ is used again in the input field. This applies also for the input of data of the other profile types.

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

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Figure 12.8: 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. A black arrow appears. The arrow makes the orientation much easier for you.

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Figure 12.9: Column header

Profile Details

In case you cannot find the right profile you are looking for in our extensive database, simply define your individual profile. Activate the option ‘User-defined’. If you select this option, the input fields will be enabled, so that you can enter your own input values.

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Figure 12.10: Profile details

Please confirm these inputs with the button ‘OK’ and the profile, including your own values, will be applied.

12.2.2 Serrated Shafts

The calculation module ‘Serrated shafts’ allows the strength calculation of serrated shafts according to DIN 5481. The calculation is based on Niemann „Maschinenelemente“ Vol. 1, 2001. The teeth of this profile are in the form of adjacent triangular teeth. Serrated shaft usually have 60∘ and can be easily created using broaching.

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Figure 12.11: Serrated shaft connection

You can refine the profile geometry selection by including specific parameters to find the right profile quicker. The following parameters can be defined for a certain range:

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Figure 12.12: Profile selection search

Please enter your values. Use the Tab key to jump from field to field. All the inputs are applied. Click on the button ‘Search’ to start the profile selection search. The number of found profiles will be displayed below the ‘Search’ button.

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Figure 12.13: ‘Search’ button

Please note: To narrow your search, type more values in the search box. This way, you have to decide between a few profiles and you will find the right profile faster. If you have already entered values into the input fields and want to change your entry for any reason (e.g., any tip circle diameter again), please delete the value and click into another input field or use the Tab key. The option ‘Any’ is used again in the input field.

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

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Figure 12.14: 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. A black arrow appears. The arrow makes the orientation much easier for you.

Profile Details

In case you cannot find the right profile you are looking for in our extensive database, simply define your individual profile. Activate the option ‘User-defined’. If you select this option, the input fields will be enabled, so that you can enter your own input values.

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Figure 12.15: User-defined input

Please confirm these inputs with the button ‘OK’ and the profile, including your own values, will be applied.

12.2.3 Splined Shafts

Splined shafts has equally spaced teeth around the circumference parallel to the shafts axis of rotation. This type of profile is used in case of transmission of large forces, especially in case of alternating forces or impact forces. Splined shaft are replaceable and centers the hub on the shaft very accurately. The manufacturing cost of splined shafts is low. Splines are cut on the shaft by milling and on the hub by broaching. Select the splined shaft connection. The calculation module ‘Splined shaft’ allows the strength calculation of serrated shafts according to DIN ISO 14 light and medium series, DIN 5464 heavy series, DIN 5471 and DIN 5472 for machine tools. The calculation is based on Niemann „Maschinenelemente“ Vol. 1, 2001.

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Figure 12.16: Splined shaft connection

A centric position of the hub on the shaft is achieved by:

You can refine the profile geometry selection by including specific parameters to find the right profile quicker. The following parameters can be defined for a certain range:

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Figure 12.17: Profile selection search

Please enter your values. Use the Tab key to jump from field to field. All the inputs are applied. Click on the button ‘Search’ to start the profile selection search. The number of found profiles will be displayed below the ‘Search’ button. 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. A black arrow appears. The arrow makes the orientation much easier for you.

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Figure 12.18: ‘Search’ button

Please note: To narrow your search, type more values in the search box. This way, you have to decide between a few profiles and you will find the right profile faster. If you have already entered values into the input fields and want to change your entry for any reason (e.g., any tip circle diameter again), please delete the value and click into another input field or use the Tab key. The option ‘Any’ is used again in the input field.

Profile Details

In case you cannot find the right profile you are looking for in our extensive database, simply define your individual profile. Activate the option ‘User-defined’. If you select this option, the input fields will be enabled, so that you can enter your own input values.

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Figure 12.19: User-defined input

Please confirm these inputs with the button ‘OK’ and the profile, including your own values, will be applied.

12.3 How to Change the Unit of Measurement

Use this function if you want to change the unit of measurement quickly. Just a right-click on the input field where you want to change the unit. The context menu contains all available units. The two arrows mark the current setting. As soon as you select a unit, the current field value will be converted automatically into the chosen unit of measurement.

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Figure 12.20: Change the unit of measurement

12.4 Application Factor

The application factor KA  evaluates the external dynamic forces that affect the gearing. These additional forces are largely dependent on the characteristics of the driving and driven machines as well as the masses and stiffness of the system, including shafts and couplings used in service.






Application Factors KA  According to DIN 3990-1: 1987-121





Working Characteristics
Working Characteristics of the Driven Machine




of the Driving Machine Uniform Light Shocks Moderate Shocks Heavy Shocks





Uniform 1,0 1,25 1,5 1,75





Light Shocks 1,1 1,35 1,6 1,85





Moderate Shocks 1,25 1,5 1,75 2,0





Heavy Shocks 1,5 1,75 2,0 2,25 or higher





1 from: DIN 3990 Part 1, December 1987, p. 55, table: A1





12.4.1 Examples for Driving Machines with Various Working Characteristics



Examples for Driving Machines with Various Working Characteristics
according to DIN 3990-1: 1987-12


Working

Characteristics



Uniform

Electric motor (e.g. d.c. motor), steam or gas turbine with uniform operation1 and small rarely occurring starting torques



Light shocks

Steam turbine, gas turbine, hydraulic or electric motor (large, frequently occurring starting torques)



Moderate shocks

Multiple cylinder internal combustion engines



Heavy shocks

Single cylinder internal combustion engines



1 Based on vibration tests or on experience gained from similar installations. 


12.4.2 Examples of Working Characteristics of Driven Machines



Examples of Working Characteristics of Driven Machines
according to DIN 3990-1: 1987-12


Working Characteristics

Driven Machines



Uniform

Steady load current generator; uniform loaded conveyor belt or platform conveyor; worm conveyor; light lifts; packing machinery; feed drives of machine tools; ventilators; lightweight centrifuges; centrifugal pumps; agitators and mixers for light liquids or uniform density materials; shears; presses; stamping machines1; vertical gear; running gear2



Light Shocks

Non-uniformly (i.e. with piece or batched components) loaded conveyor belts or platform conveyors; machine tool main drives; heavy lifts; crane slewing gear; industrial and mine ventilator; heavy centrifuges; centrifugal pumps; agitators and mixers for viscous liquids or substances of non-uniform density, multi-cylinder piston pumps, distribution pumps; extruders (general); calenders; rotating kilns; rolling mill stands3 (continuous zinc and aluminium strip mills, wire and bar mills)



Moderate Shocks

Rubber extruders; continuously operating mixers for rubber and plastics; ball mills (light); wood-working machine (gang saw, lathes); billet rolling mills3,4; lifting gear; single cylinder piston pumps



Heavy Shocks

Excavators (bucket wheel drives), bucket chain drives; sieve drives; power shovels; ball mills (heavy); rubber kneaders; crushers (stone, ore); foundry machines; heavy distribution pumps; rotary drills; brick presses; debarking mills; peeling machines; cold strip3,5; briquette presses; breaker mills



1 Nominal torque: maximum cutting, pressing or stamping torque
2 Nominal torque: maximum starting torque
3 Nominal torque: maximum rolling torque, 4 Torque from current limitation
5 KA up to 2,0 because of frequent strip cracking


12.5 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 12.21: Consider load peaks

Click the listbox to select the number of load peaks. It is also possible to define an own number of load peaks. Select the entry ‘User-defined input’. The input field next to the listbox is enabled and you can add your value.

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Figure 12.22: Load peaks: User-defined input

12.6 Kind of Load

Click the listbox to define the kind of load for your calculation. Decide between alternating torque with slow or fast increase or no alternating torque.

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Figure 12.23: Kind of load

In case you have an alternating torque with a slow or fast increase, then the load direction change is automatically activated. You will find the entry ‘User-defined’ in the listbox. If you select this option, the input field will be enabled, so that you can enter your own input value for the load direction change.

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Figure 12.24: Load direction changes

12.7 Stepped Hub

A stepped hub can be taken into account. 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 12.25: Stepped hub

12.8 Material Selection for Shaft and Hub

Select an appropriate material for the shaft and hub directly from the listbox or click on the button ‘Material’ in order to open the material database.

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Figure 12.26: Material selection for shaft and hub

Please select the material from the list.

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Figure 12.27: Material selection

Please note: The two cursor keys ‘Up’ and ‘Down’ of your keyboard allows you to navigate through the material database, so you can compare the different material properties with each other.

To open the material dataabse, please click the button ‘Material’.

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Figure 12.28: ‘Material’ button

The material database provides some detailed information on the several kinds of material.

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Figure 12.29: Material details

You will find the entry ‘User-defined’ in the listbox. If you select this option, the input fields will be enabled, so that you can enter your own input values or add a comment.

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Figure 12.30: 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 be advised that changing the material will delete your defined inputs and you have to enter the inputs again.

12.9 Message Window

The calculation module provides a message window. This message window displays detailed information, helpful hints or warnings about problems. One of the main benefits of the program is that the software provides suggestions for correcting errors during the data input. If you check the message window carefully for any errors or warnings and follow the hints, you are able to find a solution to quickly resolve calculation problems.

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Figure 12.31: Message window

12.10 Quick Info: Tooltip

The quick info feature gives you additional information about all input fields and buttons. Move the mouse pointer to an input field or a button, then you will get some additional information. This information will be displayed in the quick info line.

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Figure 12.32: Quick info line

12.11 Calculation Results

All important calculation 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 effect immediately. Press the Enter key or move to the next input field to complete the input. Alternatively, use the Tab key to jump from field to field or click the ‘Calculate’ button after every input. Your entries will be also confirmed and the calculation results will displayed automatically. If the result exceeds certain values, the result will be marked red.

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Figure 12.33: Calculation results

12.12 Documentation: Calculation Report

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

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Figure 12.34: ‘Report’ button

You can navigate through the report via the table of contents that provides links to the input values, results and figures. 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.

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Figure 12.35: The calculation report

You may also print or save the calculation report:

12.13 How to Save the Calculation

When the calculation is finished, you can save it to your computer or to the eAssistant server. Click on the button ‘Save’.

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Figure 12.36: ‘Save button’

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 files will appear. Now you will be able to save the calculation to your computer.

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Figure 12.37: Windows dialog for saving the file

In case you do not activate the option in order to save your files locally, then a new window is opened and you can save the calculation to the eAssistant server. 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 ‘Files’.

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Figure 12.38: Save the calculation

12.14 Automatic Dimensioning Functions (Calculator Button)

The button for the dimensioning functions is marked by a calculator symbol and is located next to the input fields. If you click on the dimensioning buttons, you get a suggestion for an appropriate input value. The calculation of the value is carried out so that the given minimum safety is fulfilled. The default value for the minimum safety is set to ‘1.2’. Clicking the button ‘Options’ allows you to change this value. The following dimensioning functions (calculator button) provide you with optimal support:

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Dimensioning of the supporting length at min. safety

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Dimensioning of the nominal operation torque at min. safety

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Dimensioning of the max. load peak torque at min. safety

Example: Dimensioning of the Maximum Nominal Operation Torque

Please 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 12.39: Dimensioning button

Now the maximum torque is determined.

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Figure 12.40: Maximum torque

The minimum safety is displayed in the result panel. If you enter a higher value than ‘69648.0 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.

12.15 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 12.41: The button ‘Redo’ and ‘Undo’

12.16 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 fast. Based on your eAssistant calculation, you can generateshafts as well hubs of splined shaft and serrated shaft connections as a 3D part within seconds. A single menu pick in the eAssistant software transfers the eAssistant calculation data to the CAD system. Based on these parameters, the automatic creation of a 3D parametric model starts in the CAD system. First you need to download and install the right CAD plugin for your CAD system. After installation, an integrated button called ‘eAssistant’ appears in the CAD system. Click the button ‘CAD’ and select the CAD plugin. Open the CAD system and start the generation by clicking the integrated button ‘eAssistant’. Do not forget to activate the option ‘Enable save data local’ in the project manager.

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Figure 12.42: ‘CAD’ button

Please note: For further information, please visit our web site www.eAssistant.eu or read the CAD plugin manual.

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Figure 12.43: eAssistant CAD plugin in CAD system

12.17 Options

Click the button ‘Options’ in order to change the default settings.

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Figure 12.44: ‘Options’ button

You can change the minimum safety or number of the decimal places in the report. To make a permanent change to the calculation module, you can save your settings to a template file. For further details, please check the ‘General functions’ chapter.

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Figure 12.45: The options

12.18 Calculation Example: Splined Shaft for Lifting Gear

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

12.18.1 Start the Calculation Module

Please login with your user name and your password. Select the module ‘Splined shaft’ 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 12.46: Calculation module’

12.18.2 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

12.18.3 The Calculation

Profile Geometry Selection

In order to find the right profile, click the button ‘Selection’.

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Figure 12.47: ‘Selection’ button

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

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Figure 12.48: Profile geometry selection

You can narrow your search by entering certain parameters in order 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 12.49: Refine the profile geometry selection

After clicking the button ‘Search’, only one profile remains. Please select the profile and click the button ‘OK’.

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Figure 12.50: Selected profile

Enter ‘40 mm’ for the supporting length l
tr  .

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Figure 12.51: Supporting length

Tolerance Field

Click the listbox in order to choose the tolerance field ‘H7/IT7’.

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Figure 12.52: Tolerance selection

The field ‘Profile’ displays the previously selected tolerance field.

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Figure 12.53: Tolerance field

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

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Figure 12.54: Application factor and nominal operation torque

Load Peaks

Activate the load peaks und enter ‘2400’ for the maximum load peak torque T
 max  .

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Figure 12.55: Load peaks and load peak torque Tmax

Select the number of load peaks from the listbox.

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Figure 12.56: Number of load peaks

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 12.57: Kind of load

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

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Figure 12.58: Outer diameter of hub

Material of Shaft and Hub

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

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Figure 12.59: Material for the shaft

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

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Figure 12.60: Material details

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

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Figure 12.61: Material for the hub

12.18.4 Calculation Results

All results (safeties at operation load and maximum load, the pressures for shaft and hub) 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 effect immediately.

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Figure 12.62: Calculation results

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

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Figure 12.63: Message window

12.18.5 Documentation: Calculation Report

After the completion of your calculation, you can create a calculation report. Click on the ‘Report’ button. You can navigate through the report via the table of contents that provides links to the input values, results and figures. 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:

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Figure 12.64: Calculation report

12.18.6 How to Save the Calculation

When the calculation is finished, you can save it to your computer or to the eAssistant server. Click on the button ‘Save’.

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Figure 12.65: ‘Save’ button

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 files will appear. Now you will be able to save the calculation to your computer.

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Figure 12.66: Windows dialog for saving the file

In case you do not activate the option in order to save your files locally, then a new window is opened and you can save the calculation to the eAssistant server. 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 ‘Files’.

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Figure 12.67: 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 phone +49 (0) 531 129 399-0 or email eAssistant@gwj.de.