February 2015 – DriveConcepts GmbH, Dresden Tutorial for designing and calculation of a single planetary gearbox stage using MDESIGN gearbox Dr.-Ing. Tobias Schulze DriveConcepts GmbH Dresden Summary This is an instruction for designing a gearbox model followed by a kinematic calculation of single machine elements using the program ‘MDESIGN gearbox’. This is a step by step explanation for designing a 3D-model of a single planetary gear stage, the calculation of it and how to document the results. Figure 1: Example for a planetary gear stage in MDESIGN gearbox
Transcript
February 2015 – DriveConcepts GmbH, Dresden 1
Tutorial for designing and calculation of a single planetary gearbox stage using
This is an instruction for designing a gearbox model followed by a kinematic calculation of single machine elements using the program ‘MDESIGN gearbox’. This is a step by step explanation for designing a 3D-model of a single planetary gear stage, the calculation of it and how to document the results.
Figure 1: Example for a planetary gear stage in MDESIGN gearbox
5. Saving the project data......................................................................................................... 32
Literature .................................................................................................................................. 33
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2. Default options for calculation
Start the program MDESIGN and open the gearbox folder in the left explorer menu. Start the gearbox module by double clicking the writing ‘MDESIGN gearbox’. Start a new project. Click on the main-button top left and choose new reset. All parameters within the input page are now reset to the default values. Choose calculation in the ‘Choice calculation’ line. Save the gearbox data (*.mdp / *.xml) into a random directory of your choice. Now you can start working on the dataset and also automatically overwrite it when saving.
Figure 2: Active dataset Now change to the 3D-surface to design the model. In order to do so, open the pull-down menu on the middle window and choose ‘graphical input’.
Figure 3: Choosing graphical input When entering the graphical input, the upper toolbar changes and provides tools for the 3D designing process.
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Figure 4: Toolbar Within the graphic input page there are different areas. The window in the middle of the screen with the coordinate system is the 3D-surface of the gear. The menu to the right shows the element explorer that provides the desired machine elements. The menu to the left displays the parameters of a selected element.
On the lower edge of the screen, graphical and text based assistants can be found to ease the handling of the program. There is a tab ‘Objects operation’ in the toolbar on the top. Use the option ‘Move object’ to move objects.
Figure 5: Areas of the 3D-input page Before designing a gearbox change to the static input page again (pull-down menu). Within the group ‘Material’ there are two tables to choose construction materials for gears and shafts. First of all delete the current default materials in both tables.
Select or drag objects Display settings
Parameters of a selected element
Text based assistant Graphical assistant
Element Explorer
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In order to do so click the line according to the material and remove it using the delete button below. After that use the data base button top right to add a new construction material. (Default MDESIGN data base or choose own data base with own materials)
Figure 6: Deleting default material / adding new material The pop up window provides a listing of standard materials from the MDESGIN data base. Choose 16MnCr5 as the gear material. Choose 16MnCr5 and E295 as shaft materials. Within the group lubrication ‘ARAL Degol BG 320’ is the default lubricant. Furthermore choose circular lubrication for this gear.
Now the tables show the chosen materials and the lubricant. A changing of the parameters can be done within the module ‘Database organization’. Next, change the load data to KA = 1,1 and KAS = 1,5 and chose ‘circular lubrication’. The required securities and life times should be set to:
Figure 7: Definition of the required securities and life times Change back to the graphical input page.
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3. Designing the gearbox
3.1 Designing of shafts
The first step is to add a planet carrier. Open the shaft path in the element explorer and pull a planet carrier into the 3D-surface (drag and drop). Clicking on the planet carrier displays its parameters in the parameter menu. Change the name from ‘Single planetary gearbox_01’ to ‘Planet_carrier’. Here you can also set the number of planets.
Figure 8: Definition of the planet carrier Pull the planet carrier towards the 3D-surface center (black cross). While dragging, yellow layers appear. These are catching layers. If two layers are close to each other they turn blue, which means the program automatically recognizes the catching conditions. Now you can release LMB and the connection will be created. Connect the Planet carrier to the center now.
Figure 9: Catching the planet carrier to the 3D-scene center
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Create the sun shaft by adding three shaft sections and connecting them to one shaft. Shaft sections can be found in the element explorer, next to the planet carrier. Connect them via the catching layers.
Figure 10: Creating a sun shaft out of three shaft sections Now chose the just created shaft and rename it to ‘Sun_shaft’. Changing names is only possible during the kinematic calculation. If the kinematic calculation is not active, you can activate it within the tab ‘calculation’ ‘Actions’ Kinematics.
Figure 11: Choice kinematic calculation
Now double click at the sun shaft so that the 2D shaft editor opens. Here it is easy to change the geometry of the shaft and add forces and notches.
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Figure 12: 2D shaft editor Select the shaft sections one by one and change the parameters like in figure 13. The values at the end of a section will be calculated automatically.
Figure 13: Parameters for the sun shaft Close the 2D shaft editor with the ‘close’ button and confirm the pop up window. To drag the field of view, hold down the mouse wheel. Scroll the mouse wheel to zoom. Click on the sun shaft to open its parameter menu. Click the choice-button within the material line in the parameter window of the sun shaft. Now it is possible to choose between the materials,
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defined at the beginning. The sun shaft shall be realized as a pinion shaft so choose 16MnCr5. It is also possible to change single shaft sections within the 3D-surface. Hold down CTRL and click on the shaft section which is meant to be changed. Pay attention that nothing else is chosen before choosing another element (not marked red).
Figure 14: Sun shaft Change the length of the section to 120 mm. Now the sun shaft is complete. Place the sun shaft next to the planet carrier. Create the planet shaft the same way as the sun shaft. The planet shaft shall be a solid shaft of 60 mm length and a diameter of 45 mm. It is sufficient to add a single shaft section and adjust the parameters. Drag the planet shaft onto the planet carrier using the catching lines. Change the name of the shaft to ‘planet_shaft’ and choose E295 as the shaft’s material. As you can see the shaft is mirrored to the other arms of the planet carrier. For each planet carrier you only need one planet shaft, no matter how many arms exist.
Figure 15: Placing the planet shaft Hint: A click with RMB on an element opens the graphic appearance of it. You can change the color and transparency.
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Figure 16: Appearance menu
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3.2 Designing gear wheels
Gearwheels are being designed quite similar to shaft sections. Add a gear wheel (external) from the element explorer by drag and drop. Name it ‘Sun’ and choose the following parameters:
Figure 17: Parameters of the sun wheel Material and reference profile can be chosen by clicking the choice button in the particular lines. When dragging the sun wheel the catching lines light up similar to the shafts. Drag the sun wheel onto the sun shaft and release LMB when the catching lines turn blue.
Figure 18: Recognizing catching lines
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Figure 19: Catching the sun wheel onto the sun shaft Now the rotation axes of the two elements are connected. Only the position of the sun wheel is not defined. Use the parameter menu of the sun wheel and type 160 mm in the PositionX line. The PositionX function always refers to the coordinate system’s origin of the particular shaft and the middle of the mounted element. Create the second gear wheel on your own and position it next to the planet shaft. Name it ‘Planet’ and use the following parameters:
Figure 20: Parameters planet wheel Within the next step the internal gear wheel is being created. Add an internal gear wheel from the element explorer. Change the name to ‘Ring_gear’ and use the following parameters:
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Figure 21: Parameters of the Ring gear
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3.3 Designing the bearing
Within the graphic input mode the dimension, position and the type of the bearing can be defined. Further parameterization can be done during the calculation of the bearing. Add a roller bearing by drag and drop (similar to all other machine elements). Click the choice button in the ‘bearing type for shaft’-line and choose the left side fixed location bearing. Afterwards the bearing type has to be defined. Choose a tapered roller bearing.
Figure 22: Definition of the first bearing
Choose the default lubricant from the list. Drag the bearing onto the sun shaft and position the bearing on X = 110 mm.
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Figure 23: Parameters of the bearing Create the second bearing like the first one and position it on X = 210 mm. Pay attention to the fixed side of the location bearing which is fixed on the right side this time to realize a support bearing. Now it is to design the bearing of the planet shaft. Create a support bearing with tapered roller bearings. The outer diameter is 70 mm, the inner diameter 45 mm, the width 30 mm.
Figure 24: Bearing of the planet shaft After placing the bearings on the planet shaft the positions should be changed to 15 mm (left bearing) and 45 mm (right bearing).
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3.4 Designing in- and output
The gearbox is now nearly finished. Only the load data are missing to start the calculation. Add an input-drive from the element explorer (force elements path) and drag it onto the sun shaft. Use the following parameters for the drive:
Figure 25: Definition of the drive Within the choice menu of the drive there are two options whether speed and torque are being calculated or default.
Figure 26: Default torque and speed Choose default for both, torque and speed. The prefix of the speed determines the direction of the rotation. It is significant to pay attention that the power (product of speed and torque) is always greater than zero. The ring gear shall be fixed. To realize a fixed ring gear, an output drive has to be mounted with the default rotational speed of 0 min-1. The torque shall be calculated.
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Figure 27: Output drive as a setting for the ring gear Now add an output drive and pull it onto the planet carrier. Choose calculation for speed and torque and position it to X = 0mm.
Figure 28: Output drive on the planet carrier
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3.5 Assembling the gear
Drag the planet gear wheel onto the planet shaft. The planet is being mirrored to all arms of the planet carrier automatically. The position of the planet is X = 30 mm.
Figure 29: Planet assembly In the next step the sun shaft assembly has to be attached in the middle of the planet carrier (center catching line). Choose and drag the sun assembly by holding ALT- and LMB. Hint: Pay attention that the ALT-button is held down. Else the single element that is currently
chosen will be moved and the position has to be defined again. Alternatively you can use the ‘selection’ mode in the Objects operations tab. With this mode it is possible to select single elements. After all elements are marked (red), change back to the ‘move object’ mode and drag the whole assembly.
By catching the assembly on the planet carrier’s central axis a toothing contact will be created between the sun wheel and the planet (blue toothing contact symbol). By clicking the symbol more parameters of the toothing can be changed like the center distance, axial offset, efficiency and lubrication. Change the parameters like below:
Figure 30: Definition and parameters of the gear pair Finally the ring gear needs to be placed. Choose the ring gear with the mounted output drive
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(ALT+LMB) and drag it onto the planet carrier’s central catching line. Change the parameters of the created toothing contact. Axial offset = 0mm, Efficiency = 0,99 and lubricant = default.
Figure 31: Complete planetary stage The graphic design of the gearbox is finished. Change to the static input page to calculate the gear.
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4. Calculation
4.1 Kinematic calculation
Within the static input page choose ‘Kinematics’ from the actions tab in the toolbar. Start the calculation using F10 or the calculation button top left. Change to the output page where you can inspect the calculation results. The calculation includes torques, speeds, power and gear ratios. It is possible to export, save or print the results using the document functions on the toolbar’s document tab. To change the language for the documentation use the document language pull down menu within the document tab.
Figure 32: Results of the calculation
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4.2 Calculation of the gear pairs
Close the output page. For calculating the machine elements there are two possibilities.
1. Choice of the element within the actions tab 2. Double click the toothing contact on the graphic input page
Figure 33: Toothing contact
Figure 34: Choice gearpair using the choose detail menu
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Choose ‘Gearpair_01’ in the following window. Now you are in the specification mode of the toothing. The face load factors and transverse load factors are default 1. If those factors are set to zero MDESIGN will calculate them according to the standard. Start the calculation (F10). After a short calculation period you can inspect the securities of the gear wheels. In case of too small securities MDESIGN will create a red coloured note on top of the output page. All required intermediate results for the calculation will be displayed too. Additionally you can use the bottom right graphic menu to inspect several drawings of your designed gearbox and even save/document them. Some examples would be tooth profile, pitting- and root bearing capacity diagrams and several views of the gear.
Figure 35: Profile view of the sun
BILD
Figure 36: Load capacity diagram
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BILD
Figure 37: Results of the gearpair calculation sun-planet Exit the gearpair specification mode by clicking the cross within the static input page or the button close gearpair on the actions toolbar tab.
Figure 38: Exit the specification mode Now choose the gearpair planet - ring gear. Change the face load and transverse load factors similar to the first gearpair and start the calculation.
Figure 39: Results of the gearpair calculation planet - ring gear Exit the specification mode like before.
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Furthermore there is the possibility of calculating all planetary stages or all stages (planetary and spur gear if existing). Choose this option in the ‘choose detail’ menu in the toolbar’s actions tab.
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4.3 Shaft calculation
To calculate a shaft double click the shaft that is meant to be calculated. The 2D shaft editor opens which displays all bearings, forces and geometric data from the gear model. Choose the sun shaft.
Figure 40: Sun shaft in the 2D shaft editor More notches can be added via the 2D shaft editor’s element explorer. Add a feather key joint with one groove like in the 3D editor by drag and drop. Use the following parameters:
Figure 41: Parameters of the feather key joint To test if all parameters are correct, the 3D graphic assistant helps by displaying a full parameterized 3D model of the shaft, including all forces, torques, bearings, notches and other geometric data. If only a coordinate system is visible the model is incorrect and a calculation would bring no result. Start the calculation with F10.
Figure 42: 3D model of the sun shaft
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The output page provides the resulting securities and all intermediate results of the calculation. There is the option of documenting them using the document tab on the toolbar. The securities against fracture are very high because there is no deflection of the shaft due to the plane load.
Figure 43: Results of the sun shaft calculation Additionally the graphic assistant shown below provides several illustrations and diagrams like force- and torque path, deflection of the shafts, resulting securities with their positions and so forth. All data provided by the assistant can be saved/documented. Exit the shaft calculation mode for now.
Figure 44: Torque path
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Figure 45: Securities against yielding Another way to choose a shaft for the shaft calculation provides ‘choose detail’ menu on the toolbar’s actions tab. Here are all machine elements provided that can be calculated. Calculate the planet shaft on your own. Exit the specification mode by clicking the cross or the ‘close shaft’-button in the toolbar.
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4.4 Calculation of the bearing
There are two ways to calculate a bearing, similar to the calculation of the gear pairs. The first way is to double click the bearing which is meant to be calculated. The second way is via the choice menu ‘choose detail’ in the toolbar‘s actions tab. Choose the first bearing (roller_bearing_01) for the calculation. The parameters for the type of bearing for shaft (location bearing) and type of bearing (tapered roller bearing) are already defined and assumed so that the calculation can be started instantly (F10). A listing with suitable bearings for the defined dimensions and loads for the chosen bearing opens. All listed bearings fulfil the lifetime requirements. Choose the bearing 32009XA from the list.
BILD
Figure 46: Bearing database The results on the output page include expected lifetimes of the chosen bearing and the static security. Because of the plane load of the sun shaft the bearing forces are low. Therefore both values are very high. The graphical assistant provides more specific data for the chosen bearing like the dimensions.
Figure 47: Design of the chosen bearing Use this bearing for the following calculations too by choosing ‘repeat’ in the bearing selection line on the input page. Close the specification mode by clicking the cross in the line ‘advanced parameters roller bearing’.
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Now define the other 3 bearings. Choose the following types: Roller_bearing_02 – 32009XA Roller_bearing_03 – 32009XA Roller_bearing_04 – 32009XA Now the design of the gearbox is complete and defined. Keep in mind that this is only a rough draw of how to create a gear with MDESIGN gearbox.
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4.5 Complete calculation
After all single machine elements are defined a complete calculation including all machine elements can be done. In order to do so, choose ‘All elements’ from the Choice detail menu in the actions toolbar tab.
Figure 48: Choice ‘All elements’ The result is an overview of all calculation results of the single calculations (including all intermediate results).
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Figure 48: Calculation of all elements
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5. Saving the project data
All calculation data (*.XML) of the machine element calculation is saved to the project folder during the work. The default directory is a temporary folder on your computer. While loading other data all temporary data is being deleted from this folder. Because of this a new directory has to be chosen. If you do this in the end of your calculation, all XML-files will be copied to the new project folder. Choose an appropriate path like displayed below and confirm the copy process. Now the gearbox data is saved to a folder of your choice. If you load the data the next time all previews calculation results are already available.
Figure 49: Choosing a project directory
Figure 50: Copy the data from the temporary folder to a new project directory
Figure 51: Saved calculation data in the new project directory
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Literature
[1] Börner, J., Senf, M., Linke, H.; Beanspruchungsanalyse bei Stirnradgetrieben – Nutzung der Berechnungssoftware LVR; Vortrag DMK 2003, Dresden, 23. und 24. September 2003
[2] Baumann, F, Trempler U.: Analyse zur Beanspruchung der Verzahnung von Planetengetrieben, Vortrag DMK 2007, Dresden
[3] Börner, J.: Modellreduktion für Antriebssysteme mit Zahnradgetrieben zur vereinfachten Berechnung der inneren dynamischen Zahnkräfte. Dissertation TU Dresden, 1988
[5] Börner, J.: Genauere Analyse der Beanspruchung von Verzahnungen. Beitrag zur Tagung „Antriebstechnik, Zahnradgetriebe“, Dresden, 09/2000
[6] Bulligk, Chr.: Theoretische Untersuchung zur modularisierten Berechnung und Auslegung von Getrieben, Diplomarbeit, DriveConcepts GmbH, 2009
[7] CalculiX: freies FEM Programm , MTU Aero-engenier-GmbH, (www.calculix.de);
[8] Gajewski, G.: Untersuchungen zum Einfluss der Breitenballigkeit auf die Tragfähigkeit von Zahnradgetrieben. Dissertation TU Dresden, 1984
[9] Gajewski, G.: Ermittlung der allgemeinen Einflussfunktion für die Berechnung der Lastverteilung bei Stirnrädern. Forschungsbericht, TU Dresden, Sektion Grundlagen des Maschinenwesens, 1984
[10] Hartmann-Gerlach, Christian: Erstellung eines Berechnungskerns für die Software MDESIGN LVRplanet. Unveröffentlichte interne Arbeit, DriveConcepts GmbH 2007
[11] Hartmann-Gerlach, Christian: Verformungsanalyse von Planetenträgern unter Verwendung der Finiten Elemente Methode. Unveröffentlichte interne Arbeit, DriveConcepts GmbH 2008
[12] Hartmann-Gerlach, Christian: Effiziente Getriebeberechnung von der Auslegung bis zur Nachrechnung mit MDESIGN gearbox und MDESIGN LVRplanet, Vortrag anlässlich des SIMPEP Kongresses in Würzburg, 18.-19. Juni 2009
[13] Heß, R.: Untersuchungen zum Einfluss der Wellen und Lager sowie der Lagerluft auf die Breitenlastverteilung von Stirnradverzahnungen. Diss. TU Dresden, 1987
[14] Hohrein, A.; Senf, M.: Reibungs-, Schmierungs-, Verschleiß- und Festigkeitsuntersuchungen an Zahnradgetrieben. Forschungsbericht TU Dresden, 1977
[15] Hohrein, A.; Senf, M.: Untersuchungen zur Last- und Spannungsverteilung an schrägverzahnten Stirnrädern. Diss. TU Dresden, 1978
[16] Linke, H.: Untersuchungen zur Ermittlung dynamischer Zahnkräfte. Diss. TU Dresden, 1969
[18] Linke, H.; Mitschke, W.; Senf, M.: Einfluss der Radkörpergestaltung auf die Tragfähigkeit von Stirnradverzahnungen. In: Maschinenbautechnik 32 (1983) 10, S 450-456
[19] Neugebauer, G.: Beitrag zur Ermittlung der Lastverteilung über die Zahnbreite bei schrägverzahnten Stirnrädern. Dissertation TU Dresden, 1962
[20] Oehme, J.: Beitrag zur Lastverteilung schrägverzahnter Stirnräder auf der Grundlage experimenteller Zahnverformungsuntersuchungen. Diss. Technische Universität Dresden. 1975
[21] Polyakov, D..; Entwicklung eines durchgängigen Rechenmodells zur Bestimmung der Gehäusesteifigkeit unter Verwendung der FE Methode, Diplomarbeit, DriveConcepts GmbH
[22] Schlecht, B., Hantschack, F., Schulze, T.; Einfluss der Bohrungen im Kranz auf die Tragfähigkeit von Hohlradverzahnungen; Antriebstechnik 41 (2002), Teil I, Heft 12, S. 45-47; Antriebstechnik 42 (2003), Teil II, Heft 2, S. 51-55
[23] Schlecht, B. Senf, M.; Schulze, T.: Beanspruchungsanalyse bei Stirnradgetrieben und Planetengetrieben - Haus der Technik e.V., Essen, 09./10. März 2010
[24] Schlecht, B.; Schulze, T.; Hartmann-Gerlach, C.: Berechnung der Lastverteilung in Planetengetrieben unter Berücksichtigung aller relevanten Einflüsse - Zeitschriftenbeitrag Konstruktion 06/2009 S12.ff, DriveConcepts GmbH, 2009
[25] Schulze, Tobias: Getriebeberechnung nach aktuellen wissenschaftlichen Erkenntnissen, Vortrag anlässlich des Dresdner Maschinenelemente DMK2007 in Dresden, DriveConcepts GmbH, 2007
[26] Schulze, Tobias: Load Distribution in planetary gears under consideration of all relevant influences, Vortrag anlässlich JSME International Conference on Motion and Power Transmissions, Sendai (Japan), 13.-15. Mai 2009
[27] Schulze, Tobias: Berechnung der Lastverteilung in Planetengetrieben unter Berücksichtigung aller relevanten Einflüsse, Vortrag auf KT2009 in Bayreuth zur Lastverteilung in Planetengetrieben, 08.-09.10.2009
[28] Schulze, Tobias: Ganzheitliche dynamische Antriebsstrangsbetrachtung von Windenergieanlagen. Sierke Verlag 2008, Dissertation TU Dresden
[29] Schulze, Tobias: Load distribution in planetary gears. Danish gear society “Gearteknisk InteresseGruppe”, 11th february 2010 at SDU in Odense, Denmark
[30] Schulze, Tobias: Calculation of load distribution in planetary gears for an effective gear design process. AGMA Fall Technical Meeting 2010, October 17-19, 2010, Milwaukee Wis, USA
Normen | Standards
[31] DIN 867:1986 – Bezugsprofile für Evolventenverzahnungen an Stirnrädern (Zylinderrädern) für den allgemeinen Maschinenbau und den Schwermaschinenbau.
[32] DIN 3960:1987 – Begriffe und Bestimmungsgrößen für Stirnräder (Zylinderräder) und Stirnradpaare (Zylinderpaare) mit Evolventenverzahnung.
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[33] Beiblatt 1 zu DIN 3960:1980 – Begriffe und Bestimmungsgrößen für Stirnräder (Zylinderräder) und Stirnradpaare (Zylinderpaare) mit Evolventenverzahnung; Zusammenstellung der Gleichungen
[34] DIN 3990:1987, Teil 1 - 5 Tragfähigkeit von Stirnrädern.
[35] DIN 743:2008 T1-T4 & Beiblatt 1,2 Tragfähigkeitsberechnung von Wellen und Achsen
[36] DIN ISO 281:2009 Wälzlager – Dynamische Tragzahlen und nominelle Lebensdauer - Berechnung der modifizierten nominellen Referenz-Lebensdauer für Wälzlager
[37] ISO 6336:2008 Calculation of load capacity of spur and helical gears
[38] VDI 2737:2005, Berechnung der Zahnfußtragfähigkeit von Innenverzahnungen mit Zahnkranzeinfluss, VDI-Richtlinie
Software
[39] MDESIGN LVR 2014, software for load distribution of multi stage spur- and helical gears. DriveConcepts GmbH, 2014
[40] MDESIGN LVRplanet 2014, software for load distribution of planetary gear stages. DriveConcepts GmbH, 2014
[41] MDESIGN gearbox 2014, design and calculation software for multi stage gearboxes. DriveConcepts GmbH, 2014
