Mathematical Modelling of a Helical Gear and Its Corresponding Cutter

Shinn-Liang Chang, Associate Professor
Department of Power Mechanical Engineering,
National Huwei Institute of Technology, Huwei, Yunlin, Taiwan 632, R.O.C.


Helical gears, such as helical involute gears, splines, worm and worm gears, and so on, are frequently used in the manufacturing industry. In this paper, the mathematical model of a helical gear was formulated. Its corresponding cutter profile was then derived based on the coordinate transformation method and the equation of meshing. A helical spline with straight-sided normal section was subsequently used as the demonstrative example. The equations derived in this paper can be easily adopted for designing other models of helical gears and their corresponding cutters. Therefore, the proposed modelling method is beneficial to the design, analysis, and manufacture of helical gears and their manufacturing cutters.

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