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Research Papers: Design of Direct Contact Systems

Static and Dynamic Transmission Error Measurements of Helical Gear Pairs With Various Tooth Modifications

[+] Author and Article Information
M. Benatar

Department of Mechanical and Aerospace Engineering,
The Ohio State University,
201 West 19th Avenue, Columbus, OH 43210
e-mail: benatar.8@osu.edu

M. Handschuh

Department of Mechanical and Aerospace Engineering,
The Ohio State University,
201 West 19th Avenue, Columbus, OH 43210
e-mail: handschuh.1@osu.edu

A. Kahraman

Department of Mechanical and Aerospace Engineering,
The Ohio State University,
201 West 19th Avenue, Columbus, OH 43210
e-mail: kahraman.1@osu.edu

D. Talbot

Department of Mechanical and Aerospace Engineering,
The Ohio State University,
201 West 19th Avenue, Columbus, OH 43210
e-mail: talbot.11@osu.edu

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received January 2, 2019; final manuscript received April 16, 2019; published online May 14, 2019. Assoc. Editor: Hai Xu.

J. Mech. Des 141(10), 103301 (May 14, 2019) (11 pages) Paper No: MD-19-1002; doi: 10.1115/1.4043586 History: Received January 02, 2019; Accepted April 20, 2019

This paper presents a set of motion transmission error data for a family of helical gears having different profile and lead modifications operated under both low-speed (quasi-static) and dynamic conditions. A power circulatory test machine is used along with encoder and accelerometer-based transmission error measurement systems to quantify motion transmission behavior within wide ranges of torque and speed. Results of these experiments indicate that the tooth modifications impact the resultant static and dynamic transmission error amplitudes significantly. A design load is shown to exist for each gear pair of different modifications where static transmission error amplitude is minimum. Forced response curves and waterfall plots are presented to demonstrate that the helical gear pairs tested act linearly with no signs of nonlinear behavior such as tooth contact separations. Furthermore, static and dynamic transmission error amplitudes are observed to be nearly proportional, suggesting that static transmission error can be employed in helical gear dynamic models as the main gear mesh excitation. The data presented here is intended to fill a void in the literature by providing means for validation of load distribution and dynamic models of helical gear pairs.

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Load Distribution Program, 2018, Gear and Power Transmission Research Laboratory, The Ohio State University, Columbus, OH.

Figures

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Fig. 1

(a) Gear dynamics test machine used in this study, (b) encoder-based static transmission error measurement system, and (c) accelerometer-based dynamic transmission error measurement system. Some of the safety guards have been removed in these images for demonstration purposes.

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Fig. 2

An image of test gear pair D as specified in Table 3

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Fig. 3

CMM measurements of right flanks of gear #3: (a) profile traces, (b) lead traces, and (c) spacing errors

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Fig. 4

Predicted δs,rms versus T curves for the gear pairs tested

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Fig. 5

An example of (a) measured δs, (b) its Fourier spectrum, and (c) the band-pass filtered δs signal for gear pair A at T = 300 Nm

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Fig. 6

Fourier spectra of δd of gear pair D at steady-state speeds of (a) Ω = 1140 rpm (fmesh = fn/3), (b) Ω = 1720 rpm (fmesh = fn/2), (c) Ω = 2580 rpm (fmesh = 3fn/4), and (d) Ω = 3440 rpm (fmesh = fn). T = 300 Nm.

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Fig. 7

Measured δs,rms versus T

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Fig. 8

Harris maps of gear pairs (a) A—η̅ = 1 µm, λ̅ = 3 µm, (b) B—η̅ = 11 µm, λ̅ = 7 µm, (c) C—η̅ = 7 µm, λ̅ = 11 µm, and (d) D—η̅ = 13 µm, λ̅ = 21 µm

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Fig. 9

Measured δs,rms, δs,1, and δs,2 versus T for gear pair D

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Fig. 10

Measured δd,rms of gear pairs (a) A—η̅ = 1 µm, λ̅ = 3 µm, (b) B—η̅ = 11 µm, λ̅ = 7 µm, (c) C—η̅ = 7 µm, λ̅ = 11 µm, and (d) D—η̅ = 13 µm, λ̅ = 21 µm at different T values

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Fig. 11

Measured δd,rms, δd,1, and δd,2 versus fmesh/fn for gear pair D at T = 300 Nm

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Fig. 12

Waterfall plot of δ̈ for gear pair D at T = 300 Nm: (a) sweep-up and (b) sweep-down

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Fig. 13

Measured δd,rms versus fmesh/fn of all gear pairs at (a) T = 100 Nm (b) T = 200 Nm, (c) T = 300 Nm, and (d) T = 400 Nm

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Fig. 14

Comparison between δs,rms and δd,rms versus T of gear pairs (a) A—η̅ = 1 µm, λ̅ = 3 µm, (b) B—η̅ = 11 µm, λ̅ = 7 µm, (c) C—η̅ = 7 µm, λ̅ = 11 µm, and (d) D—η̅ = 13 µm, λ̅ = 21 µm when δd,rms is taken at fmesh/fn = 0.75 from Fig. 13

Tables

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