Abstract
The paper presents an investigation in the area of planetary gear trains. Based upon previous investigations of the author, methodology for the determination of geometrical boundaries for planetary gear trains is systemized. Precise analytical relationships are analyzed. The objectives of the presented investigation are: to summarize and improve the existing methodology for the determination of the geometry boundaries of internal gear trains; to analyze the influence of the tribological parameters upon the functional capacity of such gear trains, to define and precise the influence of the geometry in internal meshing upon the energy efficiency in such transmission elements and to indicate the approach for finding optimal design solutions considering the energy efficiency of gear trains. The results of the investigation of internal gear trains with small difference between the teeth number of the pinion and the teeth number of the ring (from 1 to 10) give the options for a quick and precise determination of the optimal addendum modification coefficients for the pinion and the ring considering the criteria contact strength and energy efficiency of the gear meshing. Conclusion and recommendations concerning the energy efficiency of planetary gear trains are suggested by the author.
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Abbreviations
- a :
-
Centre distance
- d a1 :
-
Addendum diameter of pinion
- d a2 :
-
Addendum diameter of ring
- d b1 :
-
Base diameter of pinion
- d b2 :
-
Base diameter of ring
- d f1 :
-
Root diameter of pinion
- h a * :
-
Coefficient of the addendum of the tooth depth
- m :
-
Module
- m n :
-
Normal module
- u :
-
Gear ratio of pair
- W :
-
Ratio characterizing special kind of interference
- x 0 :
-
Addendum modification coefficient of cutter
- x 1 :
-
Addendum modification coefficient of pinion
- z 0 :
-
Teeth number of cutter
- z 1 :
-
Teeth number of pinion
- z 2 :
-
Teeth number of ring
- α 0 :
-
Angle of the standard basic tooth profile
- α at1 :
-
Profile angle of tooth at addendum pinion circle
- α at2 :
-
Profile angle of tooth at addendum ring circle
- α w0min :
-
Minimal pressure angle during tooth generation
- α wt :
-
Pressure angle of meshing
- θ 1D :
-
Angle decribing inteference, Eq. (5)
- θ 2D :
-
Angle decribing inteference, Eq. (6)
- μ :
-
Coefficient of friction
- ν :
-
Angle decribing inteference, Eq. (8)
- ψ :
-
Angle decribing inteference, Eq. (7).
References
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DIN 3960. Begriffe und Bestimmungsgroessen fuer Stirnraeder (Zylinderraeder) und Stirnpaare (Zylinderpaare) mit Evolventenverzahning
DIN 3993. Geometrische Auslegung von zylindrischen Innenradpaaren
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ISO 6336 (2006)(E) Calculation of load capacity of spur and helical gears
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Acknowledgments
The work has been funded through the Fund of Scientific research at the University of Ruse.
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Dobreva, A. (2013). Theoretical Investigation of the Energy Efficiency of Planetary Gear Trains. In: Dobre, G. (eds) Power Transmissions. Mechanisms and Machine Science, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6558-0_21
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DOI: https://doi.org/10.1007/978-94-007-6558-0_21
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