A Parametric Analysis of the Undeformed Chip Geometry in Gear Hobbing

Abstract

Hobbing is a common manufacturing method when producing helical, involute gears. In order to increase tool life and surface finish, an accurate method to determine chip geometry is needed. Although this accurateness may involve numeric solutions, the geometric description must, as far as possible, be analytic and give a description of the continuously changing chip geometry. In this report, the cutting edges of the tool are mathematically described using parametric and analytically differentiable functions. This gives the possibility to determine the geometry of the three-dimensional surface on the blank each cutting edge will cut with numeric approximations kept to a minimum. By comparing successively cut surfaces, the chip geometry is determined using the tool and process parameters. The mathematical description gives the possibility to calculate the required characteristic properties of the chips. These are needed for increasing the tool life in order to develop more efficient tools and processes. An example is given in which characteristics, as the maximum chip thickness, the chip cross-section area, and the mean chip thickness are calculated. The reported theory describes in detail how the chip geometry is determined.