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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 176237, 10 pages
http://dx.doi.org/10.1155/2015/176237
Research Article

Mathematical Model of Helical Gear Topography Measurements and Tooth Flank Errors Separation

1School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, China
2School of Mechatronics Engineering, Henan University of Science and Technology, Luoyang, Henan 471003, China

Received 23 June 2015; Revised 7 November 2015; Accepted 29 November 2015

Academic Editor: Jean J. Loiseau

Copyright © 2015 Huiliang Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

During large-size gear topological modification by form grinding, the helical gear tooth surface geometrical shape will be complex and it is difficult for the traditional scanning measurement to characterize the whole tooth surface. Therefore, in order to characterize the actual tooth surfaces, an on-machine topography measurement approach is proposed for topological modification helical gears on the five-axis CNC gear form grinding machine that can measure the modified gear tooth deviations on the machine immediately after grinding. Combined with gear form grinding kinematics principles, the mathematical model of topography measurements is established based on the polar coordinate method. The mathematical models include calculating trajectory of the centre of measuring probe, defining gear flanks by grid of points, and solving coordinate values of topology measurement. Finally, a numerical example of on-machine topography measurement is presented. By establishing the topography diagram and the contour map of tooth error, the tooth surface modification amount and the tooth flank errors are separated, respectively. Research results can serve as foundation for topological modification and tooth surface errors closed-loop feedback correction.