A Mathematical Model for Grinding a Stick Blade Profile to Cut Hypoid Gears

Abstract

Cutter head with multiple stick blades is widely used in the mass production of hypoid and spiral bevel gears because they allow more blades per revolution of the head cutter. However, the stick blade geometry for a head cutter that is used in face-milling and face-hobbing methods to produce hypoid and spiral bevel gears is complicated and difficult to describe. The geometry of a stick blade is defined in terms of cutting parameters such as the rake angle, the hook angle, and the side relief angle that are required to perform cutting and the theoretical cutter profile in the offset plane or the neutral cutter profile in the normal plane of an imaginary generating crown gear. This study uses a 5-axis profile grinder to grind the stick blade. The machine settings for the profile grinder and the corresponding grinding wheel geometry are derived for the grinding of each face of the stick blade. A sensitivity analysis for the machine settings is conducted to determine the accuracy of the profile grinder. The numerical example shows that the proposed mathematical model is sufficiently accurate for industrial applications.