Reducing bending stress in external spur gears by redesign of the standard cutting tool

Abstract

For the design of gears the stress due to bending plays a significant role. The stress from bending is largest in the root of the gear teeth, and the magnitude of the maximum stress is controlled by the nominal bending stress and stress concentration due to the geometric shape of the tooth. In this work the bending stress of involute teeth is minimized by shape optimizing the tip of the standard cutting tool. By redesign of the tip of the standard cutting tool we achieve that the functional part of the teeth stays the same while at the same time the root shape is changed so that a reduction of the stresses results. The tool tip shape is described by different parameterizations that use the super ellipse as the central shape. For shape optimization it is important that the shape is given analytically. The shape of the cut tooth that is the envelope of the cutting tool is found analytically. The parameterization includes the standard ISO tooth. Practical simple changes in the design of the tool tip is shown to result in large reduction of the bending stress, keeping at the same time the engage part of the tooth unchanged. This leads to gears that have unchanged functionality based on the involute design, and these can be engaged with existing designs. The presented new cutting tools are custom tools specific for a given gear.