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Research Papers

Efficiency of High-Sensitivity Gear Trains, Such as Cycloid Drives

[+] Author and Article Information
Jonathon W. Sensinger

Departments of Physical Medicine and
Rehabilitation/Mechanical Engineering,
Northwestern University,
Room 1309, 345 E, Superior Street,
Chicago, IL 60611
e-mail: Sensinger@ieee.org

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received July 24, 2012; final manuscript received April 5, 2013; published online xx xx, xxxx. Assoc. Editor: Avinash Singh.

J. Mech. Des. 135(7), 071006 (May 24, 2013) (9 pages) doi:10.1115/1.4024370 History: Received July 24, 2012; Revised April 05, 2013

Compact, high torque ratio, high efficiency transmissions are required in many applications, such as robotics. However, compact size and high torque ratios often come at the expense of surprisingly low efficiency. Here we apply Del Castillo's sensitivity framework (Del Castillo, J. M., 2002, “The Analytical Expression of the Efficiency of Planetary Gear Trains,” Mech. Mach. Theory, 37(2), pp. 197–214) to explain the low efficiency of a subset of transmissions that exploit small differences in tooth number between gears to generate high torque ratios. We add adjustment factors for several transmissions within this category, such as cycloids and harmonic drives; demonstrate that the models match empirical results for the case of cycloids across a range of torque ratios, topologies, and roller conditions; and compare and optimize the topologies of the various mechanisms. We demonstrate that for this subset of transmissions, the efficiency approaches a function of the torque ratio.

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References

Figures

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Fig. 1

Diagram of a wolfrom planetary gear train (left) and the circuit structure (right)

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Fig. 2

Diagram of a wolfrom, topologically segmented into two stages, in series, with circuit structures for each stage

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Fig. 3

Wolfrom efficiency, as a function of torque ratio and the maximum number of teeth per gear, ranging from 1–10 in (a) to 1–20 in (b) to 1–30 in (c). Wolfrom designs are plotted in black; two-stage planetary stacks are plotted in gray. The two circled points in (c) refer to the examples noted in the text.

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Fig. 4

Cycloid assembly includes several parts centered around an input–output axis (including the input shaft, rollers, and output disk), and several parts centered around an eccentric cam (including the offset cam cycloid disk).

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Fig. 5

Cycloid planetary gear trains: (a) a simple cycloid and (b) a compound cycloid. Circuit structures are shown to the left. The simple cycloid only uses circuit 1; the compound cycloid uses circuits 1 and 2.

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Fig. 6

Examples of cycloids tested. Two designs used N3 = 10: simple 10:1 cycloids and compound (100:1) cycloids. One design used N3 = 100 simple 100:1 cycloid. Rollers were either fused to the annulus or free to spin

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Fig. 7

Cycloid efficiency: comparison of data from our model and from empirical measurement. Empirical measurements are indicated by asterisk; model estimations are provided by the dashed horizontal line, with a boxed ±0.3% range in friction coefficient. This ±0.3% range without incorporation of the circumference effect (i.e., using η0 instead of ηc) is indicated by the vertical gray lines for those models that used fused rollers. Ys indicate the presence of fused rollers or the inefficient output bushing.

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Fig. 8

Comparison of planetary, wolfrom, and cycloid drive efficiency. Theoretical cycloid efficiencies are overlaid on Fig. 3(c). These include the case when the cycloid uses rollers housed in ball bearings (η = 0.9992), when the cycloid uses free rollers (η = 0.993), and when the cycloid rollers are fused to the grounded annulus (in this case η is a function of the circumference, governed by the geometry, but a representative value of η = 0.985 was chosen based off the designs reported in this paper). Planetary and wolfrom efficiencies are shown for gear-teeth permutations within a 1–30 tooth range.

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Fig. 9

Tuttle's model of harmonic drive gear meshing, modified from Ref. [33]

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