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Journal of Mechanical Design | Volume 137 | Issue 9 | research-article
Research Papers: Design of Direct Contact Systems

Actual Tooth Contact Analysis of Straight Bevel Gears

[+] Author and Article Information
M. Kolivand

American Axle & Manufacturing, Inc.,
1 Dauch Drive,
Detroit, MI 48211
e-mail: mohsen.kolivand@aam.com

H. Ligata

General Electric,
Global Research Center,
1 Research Cir,
Schenectady, NY 12309

G. Steyer, D. K. Benedict, J. Chen

American Axle & Manufacturing, Inc.,
1 Dauch Drive,
Detroit, MI 48211

1Corresponding author.

2Present address: General Electric, Fairfield, CT 06825.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 3, 2014; final manuscript received June 17, 2015; published online July 22, 2015. Editor: Shapour Azarm.

J. Mech. Des 137(9), 093302 (Jul 22, 2015) Paper No: MD-14-1468; doi: 10.1115/1.4031025 History: Received August 03, 2014
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Theoretically, spherical involutes are used as one of the base topographies for straight bevel gears. Actual bevel gears, however, have deviations from their intended topographies due to manufacturing errors, heat treatment deviations, and finishing processes. Measuring the physical parts with coordinate measuring machines (CMMs), this study proposes a new approach to capture such deviations. The measured deviations from spherical involute are expressed in form of a third-order two-dimensional (2D) polynomial function and added to the base topography to duplicate the geometry of the actual part; tooth thickness deviation is also accounted for and corrected through changing the theoretical tooth thickness. The resultant surfaces are then used to construct ease-off and surface of roll angle topographies and to perform tooth contact analysis (TCA) and calculate motion transmission error (TE). At the end a sample straight bevel gear set is measured and utilizing the proposed approach its predicted TCA is compared to the experimental TCA obtained from roll tester. The results show very good correlation between the predicted and actual TCA of the parts. Utilizing the proposed methodology, the other bevel gear base profile geometries (such as octoids) can also be analyzed. In the proposed approach, the difference between other base geometries and spherical involutes can be treated as deviations from spherical involutes and can be taken into account to perform TCA.
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Figures

Grahic Jump Location
Fig. 1

Spherical involute surface definitions

+Spherical involute surface definitions
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Spherical involute surface definitions
Grahic Jump Location
Fig. 4

Measurements of a sample parts against exact spherical involute for both pinion and gear. LFl stands for left flank and RFl stands for right flank.

+Measurements of a sample parts against exact spherical involute for both pinion and gear. LFl stands for left flank and RFl stands for right flank.
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Measurements of a sample parts against exact spherical involute for both pinion and gear. LFl stands for left flank and RFl stands for right flank.
Grahic Jump Location
Fig. 2

Bevel gear flank sketch

+Bevel gear flank sketch
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Bevel gear flank sketch
Grahic Jump Location
Fig. 3

Typical bevel gear flanks; area within dashed-border lines will be measured by CMM

+Typical bevel gear flanks; area within dashed-border lines will be measured by CMM
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Typical bevel gear flanks; area within dashed-border lines will be measured by CMM
Grahic Jump Location
Fig. 5

Designed modifications of pinion and gear based on microgeometry coefficients defined in Table 2

+Designed modifications of pinion and gear based on microgeometry coefficients defined in Table 2
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Designed modifications of pinion and gear based on microgeometry coefficients defined in Table 2
Grahic Jump Location
Fig. 6

TCA of gear set of Table 1 if pinion and gear microgeometry are as defined in Table 2: (a) ease-off, (b) single tooth contact as seen on the gear, (c) multiple tooth contact as seen on the gear, and (d) TE as seen on the gear axis

+TCA of gear set of Table 1 if pinion and gear microgeometry are as defined in Table 2: (a) ease-off, (b) single tooth contact as seen on the gear, (c) multiple tooth contact as seen on the gear, and (d) TE as seen on the gear axis
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TCA of gear set of Table 1 if pinion and gear microgeometry are as defined in Table 2: (a) ease-off, (b) single tooth contact as seen on the gear, (c) multiple tooth contact as seen on the gear, and (d) TE as seen on the gear axis
Grahic Jump Location
Fig. 7

CMM measurements of sample pinion and gear against design represented in Tables 1 and 2

+CMM measurements of sample pinion and gear against design represented in Tables 1 and 2
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CMM measurements of sample pinion and gear against design represented in Tables 1 and 2
Grahic Jump Location
Fig. 8

Residual error between theory and actual parts for pinion and gear after correction of theoretical surfaces to represent actual parts

+Residual error between theory and actual parts for pinion and gear after correction of theoretical surfaces to represent actual parts
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Residual error between theory and actual parts for pinion and gear after correction of theoretical surfaces to represent actual parts
Grahic Jump Location
Fig. 9

Predicted TCA of actual parts: (a) ease-off, (b) single tooth contact as seen on the gear, (c) multiple tooth contact as seen on the gear, and (d) TE as seen on the gear axis

+Predicted TCA of actual parts: (a) ease-off, (b) single tooth contact as seen on the gear, (c) multiple tooth contact as seen on the gear, and (d) TE as seen on the gear axis
View Large  |  Save Figure  |  Download Slide (.ppt)
Predicted TCA of actual parts: (a) ease-off, (b) single tooth contact as seen on the gear, (c) multiple tooth contact as seen on the gear, and (d) TE as seen on the gear axis
Grahic Jump Location
Fig. 10

Experimental setup: (a) roll tester arbors (b) master gauges that replicate pinion and gear mounting distances

+Experimental setup: (a) roll tester arbors (b) master gauges that replicate pinion and gear mounting distances
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Experimental setup: (a) roll tester arbors (b) master gauges that replicate pinion and gear mounting distances
Grahic Jump Location
Fig. 11

Actual contact pattern on (a) pinion and (b) gear

+Actual contact pattern on (a) pinion and (b) gear
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Actual contact pattern on (a) pinion and (b) gear
Grahic Jump Location
Fig. 12

Contact patterns on gear consecutive gear teeth

+Contact patterns on gear consecutive gear teeth
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Contact patterns on gear consecutive gear teeth

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