Tutorial for designing and calculation of a multiple-stage gearbox stage using MDESIGN gearbox

Transkript

1 Tutorial for designing and calculation of a multiple-stage 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 multiple-stage gearbox, the calculation of it and how to document the results. Figure 1: Example for a planetary gear stage in MDESIGN gearbox June 2016 DriveConcepts GmbH, Dresden 1

2 Content Table of contents Content Default options for calculation Designing the gearbox Designing of shafts Designing gear wheels Designing the bearing Designing in- and output Assembling the gear Calculation Kinematic calculation Calculation of the gear pairs Shaft calculation Calculation of the bearing Complete calculation Further Opportunities Couplings Power split and accumulation Saving the project data Literature: June 2016 DriveConcepts GmbH, Dresden 2

3 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. June 2016 DriveConcepts GmbH, Dresden 3

4 Display settings Select or drag objects 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. Parameters of a selected element Element Explorer Text based assistant Graphical assistant June 2016 DriveConcepts GmbH, Dresden 4

5 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. 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. June 2016 DriveConcepts GmbH, Dresden 5

6 3. Designing the gearbox 3.1 Designing of shafts In the 3D-designer shafts are being modelled using single sections. For adding a shaft section, choose Element explorer Shaft Shaft section and pull it into the 3D-surface by drag and drop. Clicking on the shaft section displays its parameters in the parameter menu. dal and dar are the left and right diameters while dil and dir represent the respective inner diameters. Set the following parameters for the first section: Figure 8: Definition of shaft_01 The shafts in this example are solid shafts so that the inner diameters are always zero. Now the first shaft section has to be defined in the 3D-space. This is realized using catching layers. Click the Move object -button in the Objects operations menu on the toolbar. Now it is possible to drag the shaft section by click and hold the left mouse button. While dragging an object the yellow catching layers are visible. Pull the shaft section towards the black cross until the layers turn blue. Now MDESIGN has found the connection conditions and automatically catches the left surface to the origin of the coordinate system as soon as the left mouse button is released. Figure 9: Catching the first shaft section at the origin of the coordinate system Create two more shaft sections. Connect them using the catching layers. Choose the following parameters for the sections: June 2016 DriveConcepts GmbH, Dresden 6

7 Figure 10: Parameters for the shaft sections 2 and 3 To drag the whole assembly including the origin of the coordinate system hold the middle mouse button. Use the mouse wheel to zoom. Clicking on the whole shaft makes it possible to define the shaft material in the parameter s menu. In order to do so, click the selection button in the material line. Now it is possible to pick a predefined material. Choose E295 as shaft material. Now create the second and the third shaft on your own using the following parameters (dimensions given in mm): Figure 11: Dimensions Shaft_02 June 2016 DriveConcepts GmbH, Dresden 7

8 Figure 12: Dimensions Shaft_03 The first section of Shaft_02 and Shaft_03 can be placed randomly on the 3D surface. The exact position will be defined later through the contact of the gear wheels. Pay attention to the construction process. The first section of a shaft should always be on the left. All other sections should be connected on the right end of an existing shaft/shaft section. Do not forget to choose the material for the shafts. Shaft_02 and Shaft_03 shall also consist of E295. Furthermore all transition radii shall be set to 1 mm. Now three shafts should be completed. Figure 13: 3D surface with the three created shafts Hint: A click with RMB on an element opens the graphic appearance of it. You can change the color and transparency. June 2016 DriveConcepts GmbH, Dresden 8

9 Figure 14: Appearance menu June 2016 DriveConcepts GmbH, Dresden 9

10 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. Choose the following parameters: Figure 15: Parameters of Gear_01 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 16: Recognizing catching lines June 2016 DriveConcepts GmbH, Dresden 10

11 Figure 17: 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 a second gear wheel on your own and position it next to Shaft_02. Use the following parameters: Figure 18: Parameters planet wheel Connact the gear to the left end of Shaft_02 using the satching lines at positionx = 80 mm. The Cogwheels three and four have the same properties as gears one and two. Potition Gear_03 at the right side of Shaft_02 at positionx = 260 mm and Gear_04 an Shaft_03 at positionx = 80 mm. Now the model should look like this: June 2016 DriveConcepts GmbH, Dresden 11

12 Figure 19: Shafts and cogwheels June 2016 DriveConcepts GmbH, Dresden 12

13 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 20: 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. June 2016 DriveConcepts GmbH, Dresden 13

14 Figure 21: 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 create two bearings for Shaft_02 (Roller_bearing_03 and Roller_bearing_04) und two bearings for Shaft_03 (Roller_bearing_05 and Roller_bearing_06). Here a support bearing with two Tapered roller bearings will be used, too. The dimensions of bearing 3 and 5 are like bearing 1 and the dimensions of bearing 4 and 6 like bearing 2. Place bearing 3 and bearing 4 on Shaft_02 at poritionx = 30 mm respectively 310 mm and bearing 5 and 6 on Shaft_03 at x = 30 mm and 130 mm. Figure 22: Bearings of all three shafts June 2016 DriveConcepts GmbH, Dresden 14

15 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 left side of Shaft_01. The drive is being represented by a green arrow.use the following parameters for the drive: Figure 23: 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 24: 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. Now add an output drive and pull it onto the right end of Shaft_03. Choose calculation for speed and torque and position it to X = 220 mm. June 2016 DriveConcepts GmbH, Dresden 15

16 Figure 25: Output drive on Shaft_03 June 2016 DriveConcepts GmbH, Dresden 16

17 3.5 Assembling the gear In the next step the assembly of Shaft_02 has to be attached to the assembly of Shaft_01. Choose and drag the complete 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. Now yellow catching lines will become visible. Bring them close together by dragging the assembly until they turn blue and release LMB. Do the same with Shaft_03 and the right end of Shaft_02 and connect the gears. That way the tooth contacts are being created. By clicking on the cogwheel symbols the parameters of the tooth contacts can be changed, like the center distance, axial offset, efficiency and lubrication. Change the parameters like it is shown below: Figure 26: Definition and parameters of the gear pair The graphic design of the gearbox is done. Change to the static input page to calculate the Gearbox. June 2016 DriveConcepts GmbH, Dresden 17

18 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 27: Results of the calculation June 2016 DriveConcepts GmbH, Dresden 18

19 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 28: Toothing contact Figure 29: Choose gear pair using the choose detail menu June 2016 DriveConcepts GmbH, Dresden 19

20 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 30: Profile view of the sun Figure 31: Load capacity diagram June 2016 DriveConcepts GmbH, Dresden 20

21 Figure 32: Results of the gear pair calculation sun-planet Exit the gear pair specification mode by clicking the cross within the static input page or the button close gear pair on the actions toolbar tab. Figure 33: Exit the specification mode Now choose the GearPair_02. Change the face load and transverse load factors similar to the first gear pair and start the calculation. Alternatively, you can choose GearPair_02 via the arrow in the line Configuration of gear data for chosen variant. That way you can also change between different bearings or shafts. Figure 34: Changing the element June 2016 DriveConcepts GmbH, Dresden 21

22 The results for GearPair_02 are shown in the figure below. Figure 35: Results of GearPair_02 Exit the specification mode like before. 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. June 2016 DriveConcepts GmbH, Dresden 22

23 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 Shaft_01. Figure 36: Shaft_01 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 37: 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 38: 3D model of the sun shaft June 2016 DriveConcepts GmbH, Dresden 23

24 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 39: Results of the Shaft_01 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 40: Torque path June 2016 DriveConcepts GmbH, Dresden 24

25 Figure 41: 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 Shaft_03 on your own. This shaft is designed as a tooth shaft at the right end. Figure 42: Dimensions toothed shaft Figure 43: Results for Shaft_03 Exit the specification mode by clicking the cross or the close shaft -button in the toolbar. June 2016 DriveConcepts GmbH, Dresden 25

26 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 toolbars 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. 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 June 2016 DriveConcepts GmbH, Dresden 26

27 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. Now define the other 3 bearings. Choose the following types: Roller_bearing_ XA Roller_bearing_ XA Roller_bearing_ XA Roller_bearing_ XA Roller_bearing_ XA 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. June 2016 DriveConcepts GmbH, Dresden 27

28 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: Choose All elements The result is an overview of all calculation results of the single calculations (including all intermediate results). June 2016 DriveConcepts GmbH, Dresden 28

29 Figure 49: Calculation of all elements June 2016 DriveConcepts GmbH, Dresden 29

30 5. Further Opportunities 5.1 Couplings Linking multiple gear stages can be achieved via couplings. Therefor the model of the gear has to be redesigned. Pull off Bearing_04 and Gear_03 from Shaft_02. Afterwards select the fifth section of Shaft_02 with CTRL held down and delete the section. Do the same with the fourth section. Now connect Bearing_04 to the third section of Shaft_02 with positionx = 130 mm. Furthermore, give the sections two and three the following dimensions (given in mm): Figure 50: New dimensions for Shaft_02 On top of that add another shaft to the system, giving it the same dimensions as the new Shaft_02, also two more bearings (7 and 8). Build u the bearings like Bearing_01 and Bearing_02. Now form a new assembly based on the new Shaft_04, Bearings_07 and _08 and Gear_03. The Positions are the same as for the assembly around Shaft_02. Concluding link, the gears three and four like before. To connect the two single gear stages chose a coupling from the element explorer (Force elements Coupling). Link one node of the coupling to the right end of Shaft_02 and the other node to the left end of Shaft_04. Now both shafts are connected rigidly transferring all forces and moments. The adjusted system is shown in the following figure. Figure 51: Coupled system June 2016 DriveConcepts GmbH, Dresden 30

31 5.2 Power split and accumulation A split or accumulation of the power can be done using the force elements drive and output drive. In this example a power accumulation will be realised. In order to do so create a new shaft assembly containing one shaft, two bearings and one pinion identic to the assembly of Shaft_01. Link the gear to Gear_02 using the catching lines, set the axial offset equal zero and select the default lubrication. Take a drive from the element explorer and drag it to the left end of Shaft_05. Chose calculation for the rotational speed and default for the torque moment and set the moment up to 150 Nm. Figure 52: Second drive on Shaft_05 The complete system is shown in the following figure: Figure 53: Power split shaft system June 2016 DriveConcepts GmbH, Dresden 31

32 6. Saving the project data All calculation data (*.XML) of the machine element calculation are 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 June 2016 DriveConcepts GmbH, Dresden 32

33 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 [4] Börner, J.; Senf, M.: Verzahnungsbeanspruchung im Eingriffsfeld effektiv berechnet. Antriebstechnik 34, 1995, 1 [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 Engine GmbH, ( [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 LVR planet. 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 LVR planet, Vortrag anlässlich des SIMPEP Kongresses in Würzburg, 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 [17] Linke, H.: Stirnradverzahnung Berechnung, Werkstoffe, Fertigung. München, Wien : Hanser, 1996 June 2016 DriveConcepts GmbH, Dresden 33

34 [18] Linke, H.; Mitschke, W.; Senf, M.: Einfluss der Radkörpergestaltung auf die Tragfähigkeit von Stirnradverzahnungen. In: Maschinenbautechnik 32 (1983) 10, S [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 [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 ; Antriebstechnik 42 (2003), Teil II, Heft 2, S [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), Mai 2009 [27] Schulze, Tobias: Berechnung der Lastverteilung in Planetengetrieben unter Berücksichtigung aller relevanten Einflüsse, Vortrag auf KT2009 in Bayreuth zur Lastverteilung in Planetengetrieben, [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. June 2016 DriveConcepts GmbH, Dresden 34

35 [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 2016, software for load distribution of multi stage spur- and helical gears. DriveConcepts GmbH, 2016 [40] MDESIGN LVR planet 2016, software for load distribution of planetary gear stages. DriveConcepts GmbH, 2016 [41] MDESIGN gearbox 2016, design and calculation software for multi stage gearboxes. DriveConcepts GmbH, 2016 June 2016 DriveConcepts GmbH, Dresden 35