The following excerpt is from the Revised Manual of Gear Design, Section III, covering helical and spiral gears. This section on helical gear mathematics shows the detailed solutions to many general helical gearing problems. In each case, a definite example has been worked out to illustrate the solution. All equations are arranged in their most effective form for use on a computer or calculating machine.

Circular arc helical gears have been proposed by Wildhaber and Novikov (Wildhaber-Novikov gears). These types of gears became very popular in the sixties, and many authors in Russia, Germany, Japan and the People's Republic of China made valuable contributions to this area. The history of their researches can be the subject of a special investigation, and the authors understand that their references cover only a very small part of the bibliography on this topic.

In the gearing industry, gears are lubricated and cooled by various methods. At low to moderate speeds and loads, gears may be partly submerged in the lubricant which provides lubrication and cooling by splash lubrication. With splash lubrication, power loss increases considerably with speed. This is partially because of churning losses. It is shown that gear scoring and surface pitting can occur when the gear teeth are not adequately lubricated and cooled.

Helical gears can drive either nonparallel or parallel shafts. When these gears are used with nonparallel shafts, the contact is a point, and the design and manufacturing requirements are less critical than for gears driving parallel shafts.

The contact lines of a pair of helical gears move diagonally on the engaged tooth faces and their lengths consequently vary with the rotation of the gears.

High speed gearing, operating with low viscosity lubricants, is prone to a failure mode called scoring. In contrast to the classic failure modes, pitting and breakage, which generally take time to develop, scoring occurs early in the operation of a gear set and can be the limiting factor in the gear's power capability.

The fundamental purpose of gear grinding is to consistently and economically produce "hard" or "soft" gear tooth elements within the accuracy required by the gear functions. These gear elements include tooth profile, tooth spacing, lead or parallelism, axial profile, pitch line runout, surface finish, root fillet profile, and other gear geometry which contribute to the performance of a gear train.

Material losses and long production times are two areas of conventional spur and helical gear manufacturing in which improvements can be made. Metalforming processes have been considered for manufacturing spur and helical gears, but these are costly due to the development times necessary for each new part design. Through a project funded by the U.S. Army Tank - Automotive Command, Battelle's Columbus Division has developed a technique for designing spur and helical gear forging and extrusion dies using computer aided techniques.