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Research Papers: Design of Direct Contact Systems

Impact of Tooth Indexing Errors on Dynamic Factors of Spur Gears: Experiments and Model Simulations

[+] Author and Article Information
D. Talbot

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

A. Sun, A. Kahraman

Department of Mechanical
and Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 18, 2016; final manuscript received July 5, 2016; published online August 1, 2016. Assoc. Editor: Qi Fan.

J. Mech. Des 138(9), 093302 (Aug 01, 2016) (13 pages) Paper No: MD-16-1134; doi: 10.1115/1.4034175 History: Received February 18, 2016; Revised July 05, 2016

This paper investigates the influences of tooth indexing errors on dynamic factors of spur gears. An experimental study is performed using root strain measurements to (i) establish baseline dynamic behavior of gears having negligible indexing errors and (ii) characterize changes caused by tightly controlled intentional indexing errors to this baseline dynamic behavior. For this, test gears having different forms of indexing errors are paired with an instrumented gear having negligible indexing error. Dynamic root strains of teeth in the neighborhood of teeth with indexing error are measured. A dynamic gear load distribution model is employed to simulate these experiments. Both measurements and predictions indicate clearly that the baseline dynamic response, dominated by well-defined resonance peaks, is altered significantly by transient vibrations induced by indexing errors, in the process increasing dynamic factors significantly in comparison to the case of negligible indexing error.

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Figures

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Fig. 1

Test machine used in this study with safety covers removed for demonstration purposes

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Fig. 2

Measured index errors of the test gears: (a) gear #1, (b) gear #2, (c) gear #3, and (d) gear #4

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Fig. 3

(a) Definition of a gauge position in the root fillet region and (b) a test pair assembled in the test machine showing some of the strain gauged teeth

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Fig. 4

Dynamic factor (κ) versus mesh frequency (fm) for test 1 (no-error gears) at (a) T=100 and (b) 300 N·m

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Fig. 5

Measured and predicted normalized dynamic stress time histories (thick lines) for the no-error gear pair at T=100 N·m: (a) fm=83 Hz representing the quasi-static conditions, (b) 417 Hz, (c) 583 Hz, (d) 917 Hz, (e) 1083 Hz, (f) 1417 Hz, (g) 1583 Hz, (h) 1917 Hz, (i) 2083 Hz, (j) 2417 Hz, (k) 2583 Hz, and (l) 2917 Hz. Thin lines in (b)–(l) are quasi-static curves.

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Fig. 6

Measured normalized dynamic stress time histories for the single-error gear pair at T=100 N·m: (a) fm=83 Hz representing the quasi-static conditions, (b) 417 Hz, (c) 583 Hz, (d) 917 Hz, (e) 1083 Hz, (f) 1417 Hz, (g) 1583 Hz, (h) 1917 Hz, (i) 2083 Hz, (j) 2417 Hz, (k) 2583 Hz, and (l) 2917 Hz

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Fig. 7

Predicted normalized dynamic stress time histories for the single-error gear pair at T=100 N·m: (a) fm=83 Hz representing the quasi-static conditions (corresponding to Fig. 6(a)), (b) 583 Hz (Fig. 6(c)), (c) 1083 Hz (Fig. 6(e)), (d) 1583 Hz (Fig. 6(g)), (e) 2083 Hz (Fig. 6(i)), and (f) 2583 Hz (Fig. 6(k))

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Fig. 8

Measured and predicted dynamic factor (κ) versus mesh frequency (fm) for tests 1 (baseline) and 2 (single-error gears) at T=100 N·m

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Fig. 9

Measured and predicted dynamic factor (κ) versus mesh frequency (fm) for tests 1 (baseline) and 2 (single-error gears) at T=300 N·m

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Fig. 10

Measured normalized dynamic stress time histories for the two-error gear pair at T=100 N·m: (a) fm=83 Hz representing the quasi-static conditions, (b) 417 Hz, (c) 583 Hz, (d) 917 Hz, (e) 1083 Hz, (f) 1417 Hz, (g) 1583 Hz, (h) 1917 Hz, (i) 2083 Hz, (j) 2417 Hz, (k) 2583 Hz, and (l) 2917 Hz

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Fig. 11

Predicted normalized dynamic stress time histories for the two-error gear pair at T=100 N·m: (a) fm=83 Hz representing the quasi-static conditions (corresponding to Fig. 10(a)), (b) 583 Hz (Fig. 10(c)), (c) 1083 Hz (Fig. 10(e)), (d) 1583 Hz (Fig. 10(g)), (e) 2083 Hz (Fig. 10(i)), and (f) 2583 Hz (Fig. 10(k))

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Fig. 12

Measured and predicted dynamic factor (κ) versus mesh frequency (fm) for tests 1 (baseline) and 3 (two-error gears) at T=100 N·m

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Fig. 13

Measured and predicted dynamic factor (κ) versus mesh frequency (fm) for tests 1 (baseline) and 3 (two-error gears) at T=300 N·m

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