stage planetary gear with MDESIGN LVRplanet 2012

Transcrição

Detailed load analysis in planetary gears with MDESIGN LVRplanet
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
March 2012 - DriveConcepts GmbH, Dresden
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:
planet
Results of FE calculation and bearing forces for the highest stressed
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-,
Verschleißund
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 450456
[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
Windenergieanlagen. Sierke Verlag 2008, Dissertation TU Dresden
von
[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.
[41] MDESIGN® gearbox 2012, design and calculation software for multi stage gearboxes.

stage planetary gear with MDESIGN LVRplanet 2012

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