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RESEARCH PAPERS

Virtual-Power Flow and Mechanical Gear-Mesh Power Losses of Epicyclic Gear Trains

[+] Author and Article Information
Chao Chen

Department of Mechanical Engineering, and Centre for Intelligent Machines, McGill University, Montreal, QC H3A 2K6, Canadachao.chen@mail.mcgill.ca

Jorge Angeles

Department of Mechanical Engineering, and Centre for Intelligent Machines, McGill University, Montreal, QC H3A 2K6, Canadaangeles@cim.mcgill.ca

The loss factor varies at mesh frequency and is also dependent on a large number of gear design parameters, as related to lubrication, speed, load, and surface roughness. Here, we simply assume that the loss factors at hand are perfectly known.

This assumption can be plausible, especially when the variation of the tooth numbers is small.

There is a typographic error in Ref. 20. According to the derivation, the total efficiency must be written as η=1[1+(1η(c))N2N4(N1N3N2N4)].

J. Mech. Des 129(1), 107-113 (Jul 31, 2006) (7 pages) doi:10.1115/1.2359473 History: Received September 07, 2005; Revised July 31, 2006

The concept of virtual power is first defined as the power measured, in a noninertial frame, in an epicyclic gear train. We then introduce the concept of virtual-power ratio, an invariant related to the power loss in an epicyclic system. It is shown that virtual-power flow and balance exist in an epicyclic gear train, based on which a novel algorithm to compute the gear-mesh powerloss and the train efficiency is formulated. This algorithm is general enough to be applied to any given epicyclic gear train. Our results are compared with previous work on the subject.

FIGURES IN THIS ARTICLE
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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Teeth engaged in a conventional gear pair

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Figure 2

Power flowing from link p to link q

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Figure 3

One planetary gear pair

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Figure 4

(a) Power flow and (b) virtual-power flow in the EGT without power losses

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Figure 5

(a) Power flow and (b) virtual-power flow in the EGT with power losses

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Figure 6

An epicyclic gear train

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Figure 7

(a) Power flow and (b) virtual-power flow in the EGT of Fig. 6 without power losses

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Figure 8

(a) Power flow and (b) virtual-power flow in the EGT of Fig. 6 with power losses

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Figure 9

The total efficiency versus the speed ratio of the epicyclic gear drive: ∘ indicates power loss at G1; + indicates power loss at G2; ◻ indicates total power losses; and total efficiency is indicated with continuous line

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Figure 10

One planetary face gear drive

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Figure 11

(a) Power flow and (b) virtual-power flow in the planetary face gear drive without power losses

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Figure 12

(a) Power flow and (b) virtual-power flow in the planetary face gear drive with power losses

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Figure 13

Efficiency of the planetary face gear drive

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