Power-Flow and Mechanical Efficiency Computation in Two-Degrees-of-Freedom Planetary Gear Units: New Compact Formulas

Esmail, Essam Lauibi; Pennestrì, Ettore; Cirelli, Marco

doi:10.3390/app11135991

Open AccessFeature PaperArticle

Power-Flow and Mechanical Efficiency Computation in Two-Degrees-of-Freedom Planetary Gear Units: New Compact Formulas

by

Essam Lauibi Esmail

^1,†

,

Ettore Pennestrì

^2,*,†

and

Marco Cirelli

³

¹

Department of Mechanical Engineering, University of Al-Qadisiyah, Diwaniya 0964, Iraq

²

Department of Enterprise Engineering, University of Rome Tor Vergata, 00133 Rome, Italy

³

Deparment of Mechanical Engineering, University Niccolò Cusano, 00166 Rome, Italy

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Appl. Sci. 2021, 11(13), 5991; https://doi.org/10.3390/app11135991

Submission received: 31 May 2021 / Revised: 19 June 2021 / Accepted: 24 June 2021 / Published: 28 June 2021

(This article belongs to the Special Issue Frontiers in Hybrid Vehicles Powertrain)

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Abstract

The mechanical efficiency is a computed value for comparing the performance of the multi degrees-of-freedom geared transmissions of hybrid vehicles. Most of the current methods for estimating gear trains mechanical efficiency require the decomposition of gear transmissions in basic structural elements or planetary gear units (PGU). These are two degrees-of-freedom components whose mechanical efficiency has a deep influence on the overall device. The authors (E.L.E., E.P.) already evidenced that, under certain kinematic conditions, the classic Radzimovsky’s formulas, widely accepted for computing the mechanical efficiency of PGUs, are not adequate. In this paper, more general and reliable formulas for computing the mechanical efficiency are deduced. The proposed formulas herein, exploiting the concept of potential or virtual power, evidence the dependency between kinematics and efficiency. A numerical example compares our results with previous work on the subject.

Keywords: planetary gear trains; mechanical efficiency; power-flow; hybrid vehicles

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MDPI and ACS Style

Esmail, E.L.; Pennestrì, E.; Cirelli, M. Power-Flow and Mechanical Efficiency Computation in Two-Degrees-of-Freedom Planetary Gear Units: New Compact Formulas. Appl. Sci. 2021, 11, 5991. https://doi.org/10.3390/app11135991

AMA Style

Esmail EL, Pennestrì E, Cirelli M. Power-Flow and Mechanical Efficiency Computation in Two-Degrees-of-Freedom Planetary Gear Units: New Compact Formulas. Applied Sciences. 2021; 11(13):5991. https://doi.org/10.3390/app11135991

Chicago/Turabian Style

Esmail, Essam Lauibi, Ettore Pennestrì, and Marco Cirelli. 2021. "Power-Flow and Mechanical Efficiency Computation in Two-Degrees-of-Freedom Planetary Gear Units: New Compact Formulas" Applied Sciences 11, no. 13: 5991. https://doi.org/10.3390/app11135991

APA Style

Esmail, E. L., Pennestrì, E., & Cirelli, M. (2021). Power-Flow and Mechanical Efficiency Computation in Two-Degrees-of-Freedom Planetary Gear Units: New Compact Formulas. Applied Sciences, 11(13), 5991. https://doi.org/10.3390/app11135991

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Power-Flow and Mechanical Efficiency Computation in Two-Degrees-of-Freedom Planetary Gear Units: New Compact Formulas

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