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Research Papers

Impact of Tooth Spacing Errors on the Root Stresses of Spur Gear Pairs

[+] Author and Article Information
M. J. Handschuh

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

A. Kahraman

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

M. R. Milliren

Department of Mechanical
and Aerospace Engineering,
The Ohio State University,
201 W. 19th Avenue,
Columbus, OH 43210
e-mail: markmilliren@gmail.com

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 8, 2013; final manuscript received March 21, 2014; published online May 2, 2014. Assoc. Editor: Qi Fan.

J. Mech. Des 136(6), 061010 (May 02, 2014) (10 pages) Paper No: MD-13-1342; doi: 10.1115/1.4027337 History: Received August 08, 2013; Revised March 21, 2014

In this study, experimental and theoretical investigations of the effect of tooth spacing errors on the root stresses of spur gear pairs are performed. A test setup with instrumentation for the measurement of root stresses has been developed. A number of experiments were performed with gears having deterministic (at one or two teeth only) and random spacing errors (all teeth having a random distribution of errors as in a typical production gear). These experiments were simulated using a deformable-body gear contact model to describe the empirical trends physically. A methodology is proposed to relate increases in root stresses to the spacing error magnitudes directly. Closed-form expressions resulting from this methodology permit the determination of the stress amplification factors due to a certain range of spacing error tolerances as well as quantifying how much spacing error can be tolerated within a user defined stress limit.

FIGURES IN THIS ARTICLE
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Copyright © 2014 by ASME
Topics: Stress , Gears , Errors , Spur gears
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References

Munro, R. G., 1969, “Effect of Geometrical Errors on the Transmission of Motion Between Gears,” Proc. Inst. Mech. Eng., 184, pp. 79–84.
Mark, W. D., 1979, “Analysis of the Vibratory Excitation of Gear Systems. II: Tooth Error Representations, Approximations, and Application,” Acoust. Soc. Am., 66(6), pp. 1758–1787. [CrossRef]
Kohler, H., and Regan, R., 1985, “The Derivation of Gear Transmission Error from Pitch Error Records,” Proc. Inst. Mech. Eng., 199(C3), pp. 195–201.
Hayashi, T., and Hayashi, I., 1976, “The Rotational Vibration of a Spur Gear With a Tooth Profile Error,” Bull. Res. Lab. Precis. Mach. Electron., 38, pp. 35–42.
Umezawa, K., Sato, T., and Kohno, K., 1984, “Influence of Gear Errors on Rotational Vibration of Power Transmission Spur Gears: 1st Report, Pressure Angle Error and Normal Pitch Error,” Bull. Jpn. Soc. Mech. Eng., 27(225), pp. 569–575. [CrossRef]
Umezawa, K., and Sato, T., 1984, “Influence of Gear Errors on Rotational Vibration of Power Transmission Spur Gears: 3rd Report, Accumulative Pitch Error,” Bull. Jpn. Soc. Mech. Eng., 28(246), pp. 3018–3024. [CrossRef]
Wink, C. H., and Serpa, A. L., 2005, “Investigation of Tooth Contact Deviations From the Plane of Action and Their Effects on Gear Transmission Error,” Proc. Inst. Mech. Eng., 219, pp. 501–509.
Bonori, G., and Pellicano, F., 2007, “Non-Smooth Dynamics of Spur Gears With Manufacturing Errors,” J. Sound Vib., 306, pp. 271–283. [CrossRef]
Houser, D. R., and Seireg, A., 1970, “An Experimental Investigation of Dynamic Factors in Spur and Helical Gears,” ASME J. Eng. Ind., 92(2), pp. 495–503. [CrossRef]
Li, S., 2007, “Finite Element Analyses for Contact Strength and Bending Strength of a Pair of Spur Gears With Machining Errors, Assembly Errors, and Tooth Modifications,” J. Mech. Mach. Theory, 42, pp. 88–114. [CrossRef]
Wijaya, H., 2001, “Effect of Spacing Errors and Runout on Transverse Load Sharing and Dynamic Factors and Idler Gear Dynamic Analysis,” M.S. thesis, The Ohio State University, Columbus, OH.
Harianto, J., 1995, “The Effect of Manufacturing Errors on Predicted Dynamic Factors of Spur Gears,” M.S. thesis, The Ohio State University, Columbus, OH.
Kubo, A., Yamada, K., Aida, T., and Sato, S., 1972, “Research on Ultra High Speed Gear Devices,” Trans. Jpn. Soc. Mech. Eng., 38, pp. 2692–2715. [CrossRef]
Tamminnana, V. K., Kahraman, A., and Vijayakar, S., 2007, “A Study on the Relationship Between the Dynamic Factors and Dynamic Transmission Error of Spur Gear Pairs,” ASME J. Mech. Des., 129(1), pp. 75–84. [CrossRef]
Kahraman, A., and Blankenship, G. W., 1999, “Effect of Involute Contact Ratio on Spur Gear Dynamics,” ASME J. Mech. Des., 121(1), pp. 112–118. [CrossRef]
Kahraman, A., and Blankenship, G. W., 1999, “Effect of Involute Tip Relief on Dynamic Response of Spur Gear Pairs,” ASME J. Mech. Des., 121(2), pp. 313–315. [CrossRef]
Hotait, M., 2007, “Influence of Shaft Misalignments on Root Stresses of Helical Gears With Lead Crown”, M.S. thesis, The Ohio State University, Columbus, OH.
Hotait, M., and Kahraman, A., 2008, “Experiments on Root Stresses of Helical Gears With Lead Crown and Misalignments,” ASME J. Mech. Des., 130(7), p. 074502. [CrossRef]
Kubur, M., Kahraman, A., Zini, D., and Kienzle, K., 2004, “Dynamic Analysis of a Multi-Shaft Helical Gear Transmission by Finite Elements: Model and Experiment,” ASME J. Vib. Acoust., 126(3), pp. 398–406. [CrossRef]
Hotait, M., and Kahraman, A., “Experiments on the Relationship Between the Dynamic Transmission Error and the Dynamic Stress Factor of Spur Gear Pairs,” Mech. Mach. Theory, (to be published).
Handschuh, M., 2013, “An Investigation into the Impact of Random Spacing Errors on Static Transmission Error and Root Stresses of Spur Gear Pairs,” M.S. thesis, The Ohio State University, Columbus, OH.
External 2D, 2013, Advanced Numerical Solutions, Inc., Hilliard, OH.

Figures

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Fig. 1

(a) The gearbox of the experimental set-up used in this study, and (b) a top view schematic of the entire test set-up showing its main components

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Fig. 2

(a) Strain gaged tooth positions, (b) definition of a gage position along the root fillet, and (c) a close up view of a gage

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Fig. 3

Measured root stress for driven gear from (a) Test #1, (b) Test #2, (c) Test #3, (d) Test #4, and (e) Test #5 of Table 3 at 200 Nm

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Fig. 4

Measured root stress of driven gear (top) from Test #6 of Table 3 at 200 Nm for teeth (a) 1–10, (b) 11–20, (c) 21–30, (d) 31–40, and (e) 41–50

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Fig. 5

The random spacing error sequence on the driving gear for Test #6 of Table 3

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Fig. 7

A finite element contact model of a test gear pair obtained by using external 2D [22]

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Fig. 8

Simulation of root stresses from tests #1 to #5 ((a)–(e)) in Table 3 corresponding to measurements of Fig. 3

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Fig. 9

Comparison of (a) measured and (b) predicted root stresses of the driven gear for (c) the corresponding spacing error sequence on the driving gear for mesh cycles 1–10 of Test #8 in Table 3

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Fig. 10

Comparison of (a) measured and (b) predicted root stresses for the driven gear for (c) the corresponding spacing error sequence on the driving gear for mesh cycles 21–30 of Test #9 in Table 3

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Fig. 11

Distribution of measured and predicted spacing error stress multipliers on the driven gear as a function of spacing error on the driving gear. All data points from Tests #6 to #9 in Table 3 are included.

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Fig. 12

Distribution of predicted spacing error stress multipliers on the driving and driven gears as a function of random spacing error on the driving gear. All simulation points from Tests #6 to #9 in Table 3 are included.

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