5 Shafts with Strength According to DIN 743

Please login with your username and your password. Select the module ‘Shaft calculation’ through the tree structure of the project manager by double-clicking on the module or clicking on the button ‘New calculation’.

Figure 5.1:

General overview

This module provides a geometry and a calculation part. The geometry part is the part where you define the shaft geometry, the bearings, the loads as well as the notch effects. The actual calculation then takes place in the calculation part. The calculation part allows to determine bearing forces, deflection, strength or static torsion. Click on the ‘Calculate’ button to switch between the geometry and calculation part.

5.2 The Geometry Part

The geometry part allows you to define the entire shaft geometry including bearings, force elementes and force effects. The upper part of the module provides different input options. The lower part includes the coordinate system as well as the shaft symmetry axis. The input values are taken over immediately and are represented graphically in the lower part. The representation is interactive. That means, you can select, move, copy or delete shaft elements. Use the ‘3D’ view button to move quickly between 2D and 3D view.

Figure 5.2:

Geometry part

5.2.1 Shaft Properties

When you start the calculation module, the general shaft properties are automatically displayed. Use the ‘Shaft properties’ button to modify the properties at any time you want.

Figure 5.3:

Shaft properties

The shaft properties allows you to select the shaft material. You can also specify your own material. Define speed, direction of rotation and the position of the shaft in space. The speed is defined as revolutions per minute. Please keep in mind: When you change the speed of the shaft, the torques will change because of the entered power and speed. This happens when a power instead of a torque is given for the force elements. Select the material by using the listbox or material number. Click the button ‘Material selection’ and you get detailed information on the material (e.g., material type, density, yield point).

Figure 5.4:

Material selection

In case there is no material appropriate for your application, simply define your own material. Select ‘User-defined‘ from the listbox and click the button ‘Material selection’ or click directly on the button ‘Material selection’ to open the material database. When you select the option ‘User defined’, then all inputs and options are enabled and you can specify your individual material very easily. Click on the button ‘OK’ to confirm your entries and to return to the shaft geometry part. Please be advised that changing the material will delete your defined inputs and you have to enter the inputs again.

Figure 5.5:

Materal selection

Please note: It is important to consider the fact that the integrated strength calculation according to DIN 743 is valid or steels only.

5.2.2 Coordinate System

The calculation module uses a coordinate system that is a clockwise system where the Y-axis is the axis of symmetry as well as the axis of rotation of the shaft. In the two-dimensional view, the Z-axis shows upwards and the X-axis shows out of the screen. A rotation of the shaft around the Y-axis is defined as a clockwise rotation. The left end of the shaft is the point of origin. The forces and torques have to be entered in positive direction without signs and in negative direction with a minus sign.

Please Note: The direction of torques is usually defined by the input ‘driving’ and ‘driven’. The input ‘driving’ means that the shaft is driving and the torque counteracts the direction of rotation.

Figure 5.6:

The coordinate system

5.2.3 Relative and Absolute Position

You get more information about the respective elements, for example about the absolute position. It is important that you have to differentiate between a relative position and an absolute position.

Figure 5.7:

The relative and absolute position

Relative Position

The positioning of an element occurs always from a shaft section related to the left side of the element. This means that the relative position corresponds to the input value ‘Position’ of the respective element.

Figure 5.8:

Relative position

Absolute Position

The position of an element is displayed from the origin of the coordinate system to the left side of the element.

Figure 5.9:

Absolute position

5.2.4 Creating a Shaft Segment

There are segments for the outer contour and axial holes for the inner contour available. Click on the button ‘Segment’ to create a shaft segment.

Figure 5.10:

Create a shaft segment

Figure 5.11:

Representation of the shaft segment

Input fields for the entry of length and diameter are displayed. To add a conic segment, activate the option ‘Conic segment’.

Figure 5.12:

Activate conic segment

If this option is activated, enter a left diameter ‘1’ and a right diameter ‘2’ for the segment. To add another segment, please click on the ‘Segment’ button again.

5.2.5 Creating a Hole

To create a hole (an inner contour), click on the button ‘Hole (axial)’. The different possibilities for a data input are now displayed.

Figure 5.13:

Add an axial hole

In addition, you can extend the axial hole by clicking the button ‘Adjust to shaft length’. This button adapts the length of the axial hole to the shaft length automatically. Then the entire inner contour goes exactly to the end of the outer contour.

Figure 5.14:

Adjust to shaft length

Please Note: For the strength calculation notch effects, such as shoulders, are not considered in the inner contour. There is no applicable calculation method right now.

5.2.6 Creating a Bearing

You can add as many bearings as you need. A calculation of statically over-determined shafts with more than two bearings is possible. Select a shaft segment to position the bearing on the shaft, then click on the button ‘Bearing’.

Figure 5.15:

Button ‘Bearing’

Figure 5.16:

Add bearing

To define the bearing, different options for an input are available: position, width, diameter, stiffness, and pressure angle. Further you can define the kind of bearing arrangement: fixed bearing, unfixed bearing, axial bearing or swimming bearing.

Figure 5.17:

Define a bearing

Please note that the position refers to respective shaft segment, that means a relative position has to be entered. The absolute position, related to the point of origin and with it related to the left end of the shaft, is indicated with the element info (see section 5.2.3 ‘Relative and absolute position’).

The width is the overall width of the bearing and the diameter is the outer diameter of the bearing for the correct representation. For bearings with a pressure angle the changed point of application of load can be considered for the calculation of the support reactions. In case the (radial) stiffness of the bearing is known, the stiffness can be considered by appropriate settings for the calculation as well.

5.2.7 Force Elements: Cylindrical Gear

The shaft module offers different possibilities to define loads. Besides a direct input of forces and torques in coordinate direction, so-called intelligent elements for application of load can be positioned on the shaft. Click on the ‘Force elements’ button and you can select cylindrical gear, bevel gear, coupling/motor and load.

At first select the shaft segment on which you want to create the cylindrical gear. Click on the button ‘Force elements’ and select the menu item ‘Cylindrical gear’.

Figure 5.18:

Select ‘Cylindrical gear’

Figure 5.19:

Add the cylindrical gear

For the positioning of the shaft, the relative position of the left shaft side is given. Based on further inputs for pitch circle, helix angle, pressure angle, position of action and power/torque, the calculation of forces, that influence the shaft, is determined.

Figure 5.20:

Define the cylindrical gear

In particular the input of power of action is important for the point of application of load. The power of action indicates the position of the point of the interference with the gear pair.

Figure 5.21:

Power of action

For cylindrical gears with a profile shift modification, reference circle and pitch circle are not equal. When you enter the reference circle of the cylindrical gear, the calculated forces are not completely accurate - in particular with very large profile shift modifications. For an exact calculation of the forces, you have to enter the pitch circle diameter instead of the reference diameter and instead of the pressure angle you have to enter the working transverse pressure angle.

The Button ‘T/P’

The ‘T/P’ button allows you to enter either the power or torque. The description of the input field will be changed accordingly in torque or power.

Figure 5.22:

Input of power or torque

Multiple Position of Action

Here you can define a multiple position of action, that means that the cylindrical gear, which is on the shaft, is in mesh with several cylindrical gears. Set a checkmark into the field next to ‘Use multiple position of action’ and click on the button ‘Multiple position of action’.

Figure 5.23:

Button ‘Multiple position of action’

Select the number of position of action from the listbox. Further you can indicate either ‘Power’ or ‘Torque’. Confirm your inputs with the button ‘Ok’.

Figure 5.24:

Define multiple position of action

Helix Angle and Direction of Helix Angle

If two helical gears are in mesh, both gears have the same, but opposite direction of the helix angle $β$ . The direction of the helix angle has to be opposite that a left-hand mates a right-hand. Therefore, you have to differentiate between right-handed helix angle and left-handed helix angle. Please specify here right or left-hand helix angle.

Figure 5.25:

Right-handed or left-handed

Driving and Driven Gear

A driving gear and a driven gear always co-operate and form a gear pair. For the most force elements the direction of torques is specified by the input of driving and driven. The input ‘driving’ means that the shaft drives or that the moment counteracts the direction of rotation. Define here the driving and driven cylindrical gear. You can also define it with the ‘Multiple position of action’.

Figure 5.26:

Driving and driven cylindrical gear

5.2.8 Force Elements: Bevel Gear

To add a bevel gear, please mark the shaft segment onto which you want to generate the bevel gear. Then click on the button ‘Force elements’. Select the menu item ‘Bevel gear’.

Figure 5.27:

Select ‘Bevel gear’

Figure 5.28:

Add bevel gear

When you add a bevel gear, additionally inputs are available, for example an input for a bevel angle or for the direction of the bevel angle.

Figure 5.29:

Define bevel gear

5.2.9 Force Elements: Coupling / Motor

The force element ‘Coupling / Motor’ allows the input and output of torques. Just like the spur and bevel gears you can enter a mass additionally. The positioning occurs relative to the selected shaft segment. The position refers to the left side of the force element. First select a shaft segment to position the force element.

Figure 5.30:

Select ‘Coupling’

Figure 5.31:

Add coupling

5.2.10 Force Element: Load

The general force element ‘Load’ can be positioned freely on the shaft independently from a selected shaft segment. Click on the button ‘Force elements’ and select the menu item ‘Load’.

Figure 5.32:

Select ‘Load’

Figure 5.33:

Add load

The specification of the position occurs absolutely to the point of origin (left shaft end) and refers, like the other elements, to the left side of the element.

Figure 5.34:

Define load

The element can be defined as a concentrated load (width = 0) or as a stretch load. This general force element offers the possibility to specify lateral forces in X and Z-direction, a axial forces as well as bending moments around the X and Z-axis as a load. Further you can define the power or the torque as driving and driven. The meaning of driven and driving applies here similarly to the other force elements.

5.2.11 Extra Mass

Figure 5.35:

Select ‘Extra mass’

Please enter here position, width and mass. An extra mass can be defined as a concentrated load or as a stretch load.

Figure 5.36:

Add extra mass

5.2.12 Notch Effect

The definition of notch effects is necessary for the strength calculation according to DIN 743. In case you have calculated the equivalent stress before, then it is not necessary to enter all notch effects. Based on the tension peaks, which appear in the process of the equivalent stress, the critical cross sections can be identified very easily and the notch factors can be defined only for these cross sections. All defined types of notch effect according to DIN 743 are available.

The notch factors defined in DIN 743 apply to solid and hollow shafts with wall thicknesses where no interference of the notch by the hole is existing. For rotating notches the condition is used, according to DIN 743-2 (field of application),

Dimensions for Cross Sections

Figure 5.37:

Dimensions for cross sections

When adding a notch effect, please select the shaft element and click the button ‘Notch effects’.

Figure 5.38:

Select ‘Notch effects’

Figure 5.39:

Add notch effect

To run a strength calculation for highly loaded smooth shafts, select the notch effect ‘Smooth shaft’ from the listbox. For this type of notch effect, the notch factor is set to ‘1’. Notch effects can be placed easily on the shaft, independent of a shaft segment. The notch effects can be positioned absolutely to the point of origin (to the left shaft end).

You can enter the exact position into the input field ‘Position’, use the two arrow keys to move the notch effect from one shaft section to the other shaft section. With the left mouse button it is easy to place the notch effects on the shaft.

Figure 5.40:

Define notch effects

Types of Notch Effects

Figure 5.41:

Smooth shaft

Figure 5.42:

Parallel key keyway

Figure 5.43:

Interference fit

Figure 5.44:

Splinded shaft

Figure 5.45:

Serrated shaft

Figure 5.46:

Involute splines

Figure 5.47:

V-groove

Figure 5.48:

Square groove

Figure 5.49:

Shoulder

Figure 5.50:

Round groove

Figure 5.51:

Shoulder with undercut

Figure 5.52:

Cross hole

Set load and notch factors manually

The button ‘Set load and notch factors manually (optional)’ allows you to enter notch factors manually (in addition to the automatic calculation of the notch factors). Here the possibility exists to use experimentally calculated notch factors.

Figure 5.53:

Set load and notch factors manually

Click the button ‘Set load and notch factors manually (optional)’, the following window opens.

Figure 5.54:

Define individual loads

Overlapping Notch Effects

For overlapping notch effects (two notches with notch factors $β1$ and $β2$ ), the notch factors can be estimated according to Niemann ‘Maschinenelemente’ Vol. 1, page 134, equation 3.115 (3. Edition) as follows:

Notches on the Inner Contour

Please note that you cannot use the notch factors according to DIN 743 for notches on the inner contour.

5.3 General Functions

5.3.1 How to Select an Element

Use your left mouse button to select the shaft or force elements. When choosing an element, the color of the selected element changes and it is easier to recognize it.

Please Note: It is also possible to select individual elements by using your keyboard. If you would like to change, for example from the value input of shaft segments to the selection mode, you have to press the ‘Page-down’ key. Afterwards, the two arrow keys enable you to move the elements to the left or to the right side. To move from the shaft segments to the axial hole, please use the cursor keys ‘Up’ and ‘Down’. By using the ‘Page-up’ key you can change to the input value of a selected element.

5.3.2 How to Shift an Element

If an element is selected, then different input possibilities for the element appear in the upper area of the calculation module. The input field ‘Position’ helps to place an element on the shaft. For positioning the element, you can also click on an element, continue holding the left mouse button and then drag the mouse. The arrow keys below the element info allows you to move to the next segment. It is possible to skip certain elements on the shaft.

If a shaft segment is selected, then the segment can be shifted using the arrow key including all elements sitting on the segment. Thus, you can easily re-sort shaft segments.

Figure 5.55:

Arrow keys

5.3.3 How to Copy and Add an Element

The two buttons ‘Copy’ and ‘Add’ allow to copy and add segments, bearings or force elements. If you copy an element, all inputs will be confirmed and you do not have to re-define the element again. Place the element by using the input field ‘Position’ or by clicking or dragging your left mouse button or by clicking the arrow keys on your keyboard.

Figure 5.56:

‘Copy’ and ‘Add’

Figure 5.57:

Select the first bearing

Figure 5.58:

Button ‘Copy’

Figure 5.59:

Select the shaft segment

Figure 5.60:

Button ‘Add’

Figure 5.61:

Add the second bearing

Please Note: If you select an element and click the right mouse button, a new context menu will open. Choose the menu items ‘Copy’ and ‘Add’.

Figure 5.62:

right-click to open context menu

5.3.4 How to Cut Out an Element

Select a segment or an element and click the right mouse button to open the context menu. Choose the menu item ‘Cut out’.

Figure 5.63:

Menu item ‘Cut out’

5.3.5 How to Delete an Element

This button allows you to delete an element. To delete an element, select the element and click the button ‘Delete’. You can also click the right mouse button to open the context menu and to select the menu item ‘Delete’.

Figure 5.64:

Button ‘Delete’

5.3.6 Menu Item ‘Delete All’

Clicking the ‘Delete all’ button deletes not just one element but the entire shaft geometry. Right-clicking opens the context menu where you can select the menu item ‘Delete all’.

Figure 5.65:

Button ‘Delete all’

5.4 2D and 3D View

Clicking this button displays the three-dimensional presentation. This function is available in the geometry part as well as in the calculation part. Using this button, the deflection (inculding the selected planes) of the shaft can be visualized in a three-dimensional manner.

Figure 5.66:

2D and 3D view

The three-dimensional view allows to modify the elements. Select the element and change, for example, the position, length or diameter. To do so, please use the appropriate input fields. Click on the ‘2D / 3D view’ button again to switch back to the two-dimensional representation.

Figure 5.67:

3D view of the shaft

5.5 Toolbar

The toolbar on the left side contains buttons that let you toggle between different views of your shaft quickly. There are zoom options available that allow you to zoom in and out.

Figure 5.68:

Toolbar

Reset view and show the entire shaft

Activate zoom selection with mouse click: By dragging the cursor with the left mouse button, you can select parts of the shaft and enlarge them. Click the button ‘Reset view’, then you can restore the original view of the shaft.

Move view with mouse: Click into the graphical representation,hold the mouse button and move the shaft.

Figure 5.69:

Zoom selection with mouse

Orthogonal view

Perspective view

Perspective wide angle view

3D view of the shaft from left upside

Frontal 3D view of the shaft

3D view of the shaft from right

3D view of the shaft from rear

3D view of the shaft from left

3D view of the shaft from upside

3D view of the shaft from downside

5.6 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.

Figure 5.70:

The message window

5.7 Quick Info

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.

Figure 5.71:

The quick info

5.8 Calculation Part

After defining the entire shaft geometry, bearings, loads and notch effects, you can start your calculation. To start the calculation, click the button ‘Calculate’. The button changes then its description into ‘Geometry’ and you get into the calculation part. The calculation part enables you to carry out the calculation. If you want to modify the geometry of the shaft, you have to go back to the geometry part. To do so, please click the button ‘Geometry’.

Figure 5.72:

The calculation part

In addition to the determination of the bearing forces and static torsion, different diagrams for forces, moments, deflection, bending angle, equivalent stress or torque will be displayed. Move the mouse over the graphical representation to see the values for the deflection at any shaft position. With just one click, the following calculations can be carried out:

Figure 5.73:

Different calculations

5.8.1 Bearing Forces

Click the button ‘Bearing forces’ in order to start the calculation of the bearing forces.

Figure 5.74:

Bearing forces

5.8.2 Deflection

Click the button ‘Deflection’ in order to start the calculation of the deflection, bending angle and bending moment. Select the forces and moments for different planes.

Figure 5.75:

Deflection

The values for the deflection can be selected directly from the graphical representation. The values appear in the text field. Click the button 3D view to toggle between the 2D and 3D view.

Figure 5.76:

Select values with a mouse click

Please note: There is the possibility to compare different deflections (e.g., for shafts with a modified geometry) based on the graphical representation. Go back to the geometry part and change a value. Click on the Calculate button to go to the calculation part again. Click on the ‘Redo’ and ‘Undo’ buttons in the menu bar. Now you can compare the results

5.8.3 Strength

Click the button ‘Strength’ in order to start the strength calculation. The strength calculation provides a complete static and fatigue proof of strength according to DIN 743. The exact values appear in the text field and can be selected with a mouse click from the graphical representation.

Figure 5.77:

Strength calculation according to DIN 743

The calculation report provides all detailed calculation results. In addition, the results for the cross sections are represented in three different colors:

Figure 5.78:

A graphical representation

Please note: Click the button ‘Options’ to modify the settings for the minimum safety, the stress conditions and mechanical kind of material treatment (see section 5.14 ‘The button Options’).

5.8.4 Critical Speed (Bending)

Click the button ‘Critical speed (bending)’ in order to start the calculation of the critical speed. Gyroscopic effects, moments of inertia, deflection due to shear can be taken into consideration. To do so, please activate the appropriate check box.

Figure 5.79:

Calculation of critical speed (bending)

5.8.5 Critical Speed (Torsion)

Click the button ‘Critical speed (torsion)’ in order to start the calculation of the critical speed.

Figure 5.80:

Calculation of critical speed (torsion)

Please note: Please click the button ‘Options’ to modify the default settings regarding the critical speeds (see section 5.14 ‘The button Options’).

5.9 Documentation: Calculation Report

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

Figure 5.81:

Button ‘Report’

Figure 5.82:

Report configuration

During the generation of the report, a waiting screen appears. But you can continue to work with the calculation module. The length of time for the generation of the report depends on the number of diagrams which have to be generated.

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. In HTML format, the figures are displayed in ‘gif’ format. In case a SVG viewer is available, you can display all graphics in SVG format. Right-clicking on the picture allows to zoom in and zoom out.

Figure 5.83:

Calculation report

5.10 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’.

Figure 5.84:

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

Figure 5.85:

Standard 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’.

Figure 5.86:

Save the calculation

5.11 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.

Figure 5.87:

Change measurement unit

5.12 The Button ‘Redo’ and ‘Undo’

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

Figure 5.88:

Button ‘Redo’ and ‘Undo’

5.13 The Button ‘CAD’

The top menu bar of the calculation module provides the button ‘CAD’. The eAssistant plugin for various CAD systems (e.g., SolidWorks, Solid Edge, Autodesk Inventor, Catia, NX and Creo Parametric) enables you to combine calculation and design fast and easily. Based on your eAssistant calculation, you can create the shaft as a 3D part within seconds. Solid and hollow shaft with an unlimited number of cylindrical and conical elements can be generated with just a click.

Figure 5.89:

Button ‘Output for CAD PlugIn’

Generate a shaft by using the calculation module. Click the button ‘CAD $⇒$ Output for CAD PlugIn’. Open your CAD system. The top menu bar of the CAD system shows a button called ‘eAssistant’. Please click this button to start the generation of the 3D model.

Figure 5.90:

eAssistant CAD plugin in CAD system

Please note: Before you can start using the CAD plugin, you need to download and install the plugin from our web site www.eAssistant.eu. Then you have to activate the option ‘Enable file save local’ in the project manager to allow the generation of CAD data.

In case you need further information about the eAssistant CAD plugin, please feel free to contact us. The web site www.eAssistant.de also contains detailed information. There you can also find the CAD plugin manuals for the various CAD system.

5.14 The Button ‘Options’

Click the button ‘Options’ in order to change the default settings for the strength calculation according to DIN 743 as well as for the calculation of the critical speeds.

Figure 5.91:

Button ‘Options’

Figure 5.92:

Additional settings

5.15 Calculation Examples: Shaft According to DIN 743

5.15.1 Start the Calculation Module

Figure 5.93:

Start the calculation module

5.15.2 First Calculation Example

This calculation example shows a winding shaft with a fixed and movable bearing and an extra mass.

Create Shaft Segments

Click the button ‘Segment’ in order to create the first shaft segment. Enter a length of 50 mm and a diameter of 20 mm into the input fields.

Figure 5.94:

Create the first segment

Figure 5.95:

Representation of the created and defined shaft segment

To create the second shaft segment, click the button ‘Segment’ again. The second segment has a length of 400 mm and a diameter of 50 mm.

Figure 5.96:

Create the second segment

Figure 5.97:

Representation of the second segment

The third shaft segment gets the same dimensions as the first shaft segment. That is why we can use the ‘Copy’ and ‘Add’ function to create the third segment. Click on the first segment.

Figure 5.98:

Select the first segment

Figure 5.99:

Copy the first segment

Figure 5.100:

Select the second segment

Figure 5.101:

Add the segment

Figure 5.102:

Add the third shaft segment

Please note: If you select a segment and you click the right mouse button, a new context menu will open. Choose the menu items ‘Copy’ and ‘Add’.

Figure 5.103:

Right-click to open context menu

Create Axial Hole

Click the button ‘Hole (axial)’ in order to create the first hole. Enter a length of 70 mm and a diameter of 0 mm into the input fields.

Figure 5.104:

Create the first axial hole

Click the button ‘Hole (axial)’ again in order to create a second hole. Enter a length of 360 mm and a diameter of 40 mm into the input fields.

Figure 5.105:

Define the second axial hole

Figure 5.106:

Representation of the axial hole

Please note: Use your keyboard to select the individual elements. For example, if you want to change from the value input of a shaft segment to the selection mode, then press the ‘Page down’ key. Then use the two arrow keys to select the elements. Use the cursor keys ‘Up’ and ‘Down’ to move from the shaft segments to the axial holes. In order to change the input values of an element, press ‘Page up’.

Add Bearing

Figure 5.107:

Select a segment

Figure 5.108:

Button ‘Bearing’

A bearing is added. Enter 20 mm for the bearing position, 10 mm for the bearing width and 40 mm for the bearing diameter. As bearing arrangement, select ‘Fixed bearing’ from the listbox.

Figure 5.109:

Add the first bearing

In order to add the second bearing, select the first bearing and click the button ‘Copy’.

Figure 5.110:

Select the first bearing

Select the third shaft segment and click the ‘Add’ button. Because the bearing is copied, it is not necessary to define the position, width and diameter of the bearing, you just need to define the bearing arrangment. Select ‘Movable bearing’ from the listbox.

Figure 5.111:

Define the second bearing

Define Load as Extra Mass

Figure 5.112:

Select a shaft segment

Figure 5.113:

Button ‘Extra mass’

The extra mass will be positioned on the shaft segment. Please define the extra mass with 50 mm for position, 300 mm for width and 950 kg for mass.

Figure 5.114:

Extra mass is added

Define Notch Effect

Figure 5.115:

Button ‘Notch effect’

A notch effect is added and can be placed on the shaft. Enter the position of the notch effect or change the postion with the two arrow keys. Selct the notch effect from the listbox.

Figure 5.116:

Notch effects

5.15.3 Start Calculation

After defining the entire shaft geometry with bearings, loads and notch effects, you can start your calculation. To start the calculation, click the button ‘Calculate’. The button changes then its description into ‘Geometry’ and you get into the calculation part. The calculation part enables you to carry out the calculation. If you want to modify the geometry of the shaft, you have to go back to the geometry part. To do so, please click the button ‘Geometry’.

Figure 5.117:

Calculation part

When you are in the calculation part of the module, it is not possible to change the geometry. In order to change the geometry, please go back to the geometry part by clicking the ‘Geometry’ button.

Here, you can carry out the different calculations, e.g., the strength calculation according to DIN 743.

Figure 5.118:

Different calculations

Calculation of Bearing Forces

In order to start the calculation of bearing forces, click the button ‘Bearing forces’.

Figure 5.119:

Calculation of bearing forces

Calculation of Deflection

Click the button ‘Deflection’ to start the calculation of the deflection, bending angle and bending moment. Open the different diagrams for forces and moments.

Figure 5.120:

Interactive diagrams of forces and moments

You can select all values for deflection directly from the representation with just a mouse click. The values appear in the text field.

Figure 5.121:

Select values by mouse-click

Calculation of Strength According to DIN 743

Start the strength calculation by clicking the button ‘Strength’. The strength calculation provides a complete static and fatigue proof of strength according to DIN 743. The exact values appear in the text field and can be selected with a mouse click from the graphical representation.

Figure 5.122:

Strength calculation with a representation of the cross sections

The text field shows the most important calculation results. The calculation report provides all detailed calculation results. In addition, the results for the cross sections are represented in three different colors:

Calculation of Critical Speed (Bending)

Start the calculation of the critical speeds by clicking the button ‘Critical speed (bending)’. Gyroscopic effects, moments of inertia, deflection due to shear can be taken into consideration.

Figure 5.123:

Critical speed (bending)

Calculation of Critical Speed (Torsion)

Click the button ‘Critical speed (torsion)’ in order to start the calculation of the critical speed.

Figure 5.124:

Critical speed (torsion)

5.15.4 Documentation: Calculation Report

Figure 5.125:

Button ‘Report’

Figure 5.126:

Report configuration

During the generation of the report, a waiting screen appears. During the generation of the report, a waiting screen appears. But you can continue to work with the calculation module. The length of time for the generation of the report depends on the number of diagrams which have to be generated.

Figure 5.127:

Calculation report

5.15.5 Save Calculation

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

Figure 5.128:

The button ‘Save’

Figure 5.129:

Standard Windows dialog for saving the file

Figure 5.130:

Save the calculation

5.15.6 Second Calculation Example

Figure 5.131:

Shaft

Create Shaft Segments

Figure 5.132:

Shaft segments

Add Bearings

Figure 5.133:

Bearing

Create First Cylindrical Gear

In order to create the cylindrical gear, select the first shaft segment. Click on the button ‘Force elements’ and select the menu item ‘Cylindrical gear’ from the submenu. Use the input mask to define the cylindrical gear. Enter the following input values:

Figure 5.134:

Define the first cylindrical gear

Figure 5.135:

First cylindrical gear

Create Second Cylindrical Gear

To create the second cylindrical gear, select the third shaft segment. Click on the button ‘Force elements’ and select the menu item ‘Cylindrical gear’ from the submenu. Please enter the following values into the input mask:

Figure 5.136:

Define the second cylindrical gear

Figure 5.137:

Two spur gears created

Then you can display the shaft in different views. Click the button ‘3D view’ and select the different views from the toolbar and zoom into the graphic. Click on the button ‘Calculate’ and switch from the geometry part into the calculation part. There you can run the calculations (find detail information in the section ‘How to start the calculation’). The button ‘Report’ allows you to generate a report.

Result

Clicking the ‘3D view’ button displays the three-dimensional presentation. The three-dimensional view allows to modify the elements. Select the element and change, for example, the position, length or diameter. To do so, please use the appropriate input fields. Click on the ‘2D / 3D view’ button again to switch back to the two-dimensional representation.

Figure 5.138:

3D view of the shaft

5.15.7 Start Calculation

After defining the entire shaft geometry with the cylindrical gears and the bearings, you can start your calculation. To start the calculation, click the button ‘Calculate’. The button changes then its description into ‘Geometry’ and you get into the calculation part. The calculation part enables you to carry out the calculation. If you want to modify the geometry of the shaft, you have to go back to the geometry part. To do so, please click the button ‘Geometry’. With just one click, the following calculations can be carried out:

Figure 5.139:

Start of calculation

5.15.8 Documentation: Calculation Report

Figure 5.140:

Button ‘Report’

First the report configurator appears. The report configurator allows you to select which diagrams should appear in the calculation report and if the results of the strength calculation should be in the report, too. 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. In HTML format, the figures are displayed in ‘gif’ format. In case a SVG viewer is available, you can display all graphics in SVG format. Right-clicking on the picture allows to zoom in and zoom out.

Figure 5.141:

Calculation report

5.15.9 Save Calculation

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

Figure 5.142:

Button ‘Save’

Figure 5.143:

Standard Windows dialog for saving the file

Figure 5.144:

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

Chapter 5Shafts with Strength According to DIN 743

5.1 Start the Calculation Module

5.2 The Geometry Part

5.2.1 Shaft Properties

5.2.2 Coordinate System

5.2.3 Relative and Absolute Position

Relative Position

Absolute Position

5.2.4 Creating a Shaft Segment

5.2.5 Creating a Hole

5.2.6 Creating a Bearing

5.2.7 Force Elements: Cylindrical Gear

The Button ‘T/P’

Multiple Position of Action

Helix Angle and Direction of Helix Angle

Driving and Driven Gear

5.2.8 Force Elements: Bevel Gear

5.2.9 Force Elements: Coupling / Motor

5.2.10 Force Element: Load

5.2.11 Extra Mass

5.2.12 Notch Effect

Dimensions for Cross Sections

Types of Notch Effects

Set load and notch factors manually

Overlapping Notch Effects

Notches on the Inner Contour

5.3 General Functions

5.3.1 How to Select an Element

5.3.2 How to Shift an Element

5.3.3 How to Copy and Add an Element

5.3.4 How to Cut Out an Element

5.3.5 How to Delete an Element

5.3.6 Menu Item ‘Delete All’

5.4 2D and 3D View

5.5 Toolbar

5.6 Message Window

5.7 Quick Info

5.8 Calculation Part

5.8.1 Bearing Forces

5.8.2 Deflection

5.8.3 Strength

5.8.4 Critical Speed (Bending)

5.8.5 Critical Speed (Torsion)

5.9 Documentation: Calculation Report

5.10 How to Save the Calculation

5.11 How to Change the Unit of Measurement

5.12 The Button ‘Redo’ and ‘Undo’

5.13 The Button ‘CAD’

5.14 The Button ‘Options’

5.15 Calculation Examples: Shaft According to DIN 743

5.15.1 Start the Calculation Module

5.15.2 First Calculation Example

Create Shaft Segments

Create Axial Hole

Add Bearing

Define Load as Extra Mass

Define Notch Effect

5.15.3 Start Calculation

Calculation of Bearing Forces

Calculation of Deflection

Calculation of Strength According to DIN 743

Calculation of Critical Speed (Bending)

Calculation of Critical Speed (Torsion)

5.15.4 Documentation: Calculation Report

5.15.5 Save Calculation

5.15.6 Second Calculation Example

Create Shaft Segments

Add Bearings

Create First Cylindrical Gear

Create Second Cylindrical Gear

Result

5.15.7 Start Calculation

5.15.8 Documentation: Calculation Report

5.15.9 Save Calculation

Chapter 5
Shafts with Strength According to DIN 743