Tutorial for stress analysis of a single- stage planetary gear with …€¦ · · 2015-02-05Detailed load analysis in ... DriveConcepts GmbH, Dresden Tutorial for stress analysis

Detailed load analysis in planetary gears with MDESIGN LVRplanet

March 2012 - DriveConcepts GmbH, Dresden

Tutorial for stress analysis of a single- stage planetary gear with MDESIGN LVRplanet 2012

Dipl.-Ing. Christian-Hartmann-Gerlach, DriveConcepts GmbH Dresden Dr.-Ing. Tobias Schulze, DriveConcepts GmbH Dresden

Summary

This is a guide to create a calculation model of a planetary gear for stress analysis with the

Software MDESIGN LVRplanet. It describes the steps of data input the results.

Figure 1: Example gear with MDESIGN LVRplanet



1. Index

Content

1. Index ............................................................................................................................................ 2

2. Start ............................................................................................................................................. 3

3. Input of the gear data .................................................................................................................. 4

3.1. Toothing parameters ............................................................................................................... 4

3.2. Design parameters .................................................................................................................. 6

3.3. Bearing and lubrication .......................................................................................................... 10

3.4. Modification and deviation ..................................................................................................... 12

3.5. Configuration parameters ...................................................................................................... 14

4. Results ....................................................................................................................................... 15

5. Documentation .......................................................................................................................... 21

6. Literature .................................................................................................................................... 22



2. Start

Start the software MDESIGN and select in the left explorer bar in the folder MDESIGN LVRplanet the entry MDESIGN LVRplanet and start it by using a double click. Start a new project by clicking on the main button new reset. All data on the input screen will be set to a default value. Save the dataset (*.mpd) into a folder. To save again the dataset can be overwritten. The input masks can be set by the dropdown menu. The entry “All parameters” opens an overview of all parameters. Otherwise the information of toothing, modification and deviation, bearing and lubrication, design and configuration has to be filled in, in any sequence. The symbols left from the dropdown menu marking complete and incomplete input masks. If the check of input data by the software results in an error, the respective mask is marked by a red cross. A gray dot marks an indefinite status.

Figure 2: Select input page



3. Input of the gear data

3.1. Toothing parameters The data of the tooth profile, tool and load has to be defined in the respective groups.

Figure 3: General parameters

The direction of rotation is can be set by negative or positive speed. The application factor KA can be used later for a quick load variation because the FE calculation in MDESIGN LVRplanet are calculated with nominal torque and approximated by the KA factor. After a correct number of teeth the intermediate results can be calculated.

Figure 4: Toothing parameters



If a nominal addendum modification factor is given a face clearance is generated. Tool profiles can be loaded from database. Only the finishing contour of the toothing is defined so the tool geometry for the contour has to be filed in.

Figure 5: Tool parameters

Figure 6: 2D calculation model

In the 2D calculation model in the lower right corner MDESIGN the input data can be controlled. The positions of the gear elements (gear wheels, shafts, planet carrier) are displayed.



3.2. Design parameters The data for the parametric FE model of the sun, planet, ring and planet carrier can be put in in the construction parameters.

Figure 8: Construction parameters sun shaft

For a fast preallocation of the data, two user buttons on top of the data input can be used. The created FE models can be controlled by user button at the end of each group.

Figure 9: View sun model

The ring gear geometry can be defined as one or two sided. For both connection constructions the moment side has to be defined.



Figure 10: Construction parameter planet and ring gear

Figure 11: Construction parameters planet carrier – part 1

The data for the planet carrier geometry has to be defined with one or two side plates. For a two sided plate the planet bolt can be used in different ways in the FE model. One possibility is the usage of a fit between bolt and plate, which is simulated by an elastic interlayer in the FE model.



Figure 12: Construction parameters planet carrier – part 2

Figure 13: Actions button The input date can be controlled by the 2D view as well as in the 3D CAD graphic, which can be opened by the action button.



Figure 14: 2D view of parametric FE models

Figure 15: 3D CAD view



3.3. Bearing and lubrication The planet bearing influence significantly the load distribution of planetary gears. The lever arm of bearing (bl,br) and the radial bearing stiffness are crucial for restoring torque of the bearing. For using the bearing stiffness there are two possibilities (manual input / calculation with Wieche or stiffness curve). We choose the seccond possibilitie. The calculation witch Wieche requires the inner sizes of the bearing geometrie (length of bearing, numer of bearing bodys). They can be calculated from the bearing geometrie by clicking the user button.

Figure 16: Bearing parameters planet

Figure 17: Stiffnesses of the bearings



The stiffnesses of the other bearings are used for calculating the load distribution factor K A compensating element can be defined by a small bearing stiffness. In this example the sun is the compensating element. The gear body and special tooth stiffnesses are calculated by LVR if a zero is set to the input.

Figure 18: Lubrication parameters



3.4. Modification and deviation Under the topic „Modification and Deviation parameters“ it is possible to set every modification to zero as well as requirering a symmetrical modification for left and right planet flank. In this excample we don’t force any modification.

Figure 19: Profile modifications In the group „Lead modifications“ under “helix angel deviation” the helix angle modification ca be set as well. There are different possibilities of gear wheel modifications. The

parameter of „Deviations“ has influence to the load distribution factor K. Due the manufacturing tolerances the planet will be moved from its original position. Thus the system will interlock and can result in a bad load distribution. By using action buttons it is possible to call illustrations of the profile and lead modifivations.



Figure 20: Lead modifications and deviations

Figure 21: Deviation for load distribution on planets



3.5. Configuration parameters In the topic „Configuration parameters“ options for the load distribution calculation and the meshing can be defined.

Figure 22: Configuration parameters The first calculation has to be done with FE-calculation. Afterwards you can deselect the checkbox “Complete Calculation (inclusive FEM)” for faster calculation to check modifications. Then the input boxes with FEM-influencing values are unchangeable.



4. Results

The calculation starts with (F10) or the calculate button. A calculation window displays the progress. At the end all important results are summarized on the output page.

Figure 23: Common results and load distribution factor The load compensation of sun and use of 3 planets results in a small load distribution factor of 1.062.



Figure 24: Results of FE calculation and bearing forces for the highest stressed planet

Due the irregular load distribution different bearing forces occur for the right and left planet bearing. The bearing radial stiffness refers to the deformation of bearing at gear force (Ft). The deformation differences from the FE calculation for both load cases views the determining share. Sun torsion and planet carrier deformation are the greatest values.



Figure 25: Results of load distribution calculation Due the deformation shares (bearing, sun, planet, ring gear, planet carrier) a flank deviation arise on the right side (positive). This result in a load inflates on the left side of tooth (negative centre of mean load). The ratio of qmax/qm from LVR and the calculated face load factor KHß_C* matches very well. The proposal for load distribution over face width is for engaged sun/planet -52 and planet/ring gear -42 µm



Figure 26: Proposal for constant load distribution over face width

Additional LVR results as well as FE deformation plots can be called by the action buttons.

Figure 27: Action buttons



sun/planet planet/ring gear

Load distribution over Face width

Flank Pressure

Table 1 Results load distribution

In the right corner of the MDESIGN window additional result graphics appear. - Load distribution over Face width sun/planet - Load distribution over Face width planet/ring gear - Results FEM calculation - Bending line pin - Parts of flank deviation (sun-planet) - Parts of flank deviation (planet-ring gear) - …

The FEM results of the single gears can be called by the action buttons. In the menu of CalculiX the element edges as well as deformation animations can be viewed.



Figure 28: View the deformation results for load case 1



5. Documentation

For documentation of the input data and calculation results, they can be printed or saved as a *.rtf, *.html or *.pdf-file. The *.rtf-file can be read and edited by Microsoft Word and others. A print preview can be displayed by the respective entry in the menu. The document scope can be changed.

Figure 29: Print preview



6. 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-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

[17] Linke, H.: Stirnradverzahnung – Berechnung, Werkstoffe, Fertigung. München, Wien : Hanser, 1996



[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.



[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 2012, software for load distribution of multi stage spur- and helical gears. DriveConcepts GmbH, 2012

[40] MDESIGN® LVRplanet 2012, software for load distribution of planetary gear stages. DriveConcepts GmbH, 2012

[41] MDESIGN® gearbox 2012, design and calculation software for multi stage gearboxes. DriveConcepts GmbH, 2012

Documents

Tutorial for stress analysis of a single- stage planetary gear with …€¦ · · 2015-02-05Detailed load analysis in ... DriveConcepts GmbH, Dresden Tutorial for stress analysis