# The Equation of the Contact Line of the Involute Curvilinear-Tooth Cylindrical Gear Pump for the Agricultural Tractor

Yi-Qiang Jiang*, 1, 2, Li Hou2, Yong Zhao2
1 School of Manufacturing Science and Engineering, Sichuan University, Chengdu 610065, China
2 Leshan Vocational & Technical College, Leshan 614000, China

© 2014 Jiang et al

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: (https://creativecommons.org/licenses/by/4.0/legalcode). This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

## Abstract

In order to derive the equation of the contact line of the involute curvilinear-tooth cylindrical gear pump for the agricultural tractor, the tooth surface of the involute curvilinear-tooth cylindrical gear is firstly generated as that of the spur or helical gear. Then the equation of the tooth surface is derived from changing the settings and orientations of the coordinate systems after the equation of the tooth profile in an arbitrary radial section is calculated by the methods of differential geometry. Based on the equation of the tooth surface, the meshing equation of the two gears is further acquired and then the equation of the contact line. Finally, the tooth surface and the contact line are simulated with mathematical software. The results suggests that the contact line between two curvilinear-tooth cylindrical gears is an arc line in the surface of action; and this line, shaped as an arc line in the generating plane of the tooth surface, is longer than that of the spur or helical gear with the same face width.

Keywords: Curvilinear-shaped tooth , equation of the contact line, gear pump, tractor.