# May/June 1988

Archive > 1988 > May/June 1988

## Technical Articles

Helical Gear Mathematics Formulas and Examples
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.

Computer-Aided Design of the Stress Analysis of an Internal Spur Gear
Although there is plenty of information and data on the determination of geometry factors and bending strength of external gear teeth, the computation methods regarding internal gear design are less accessible. most of today's designs adopt the formulas for external gears and incorporate some kind of correction factors for internal gears. However, this design method is only an approximation because of the differences between internal gears and external gears. Indeed, the tooth shape of internal gears is different from that of external gears. One has a concave curve, while the other has a convex curve.

Curvilinear Cylindrical Gears
The curved tooth cylindrical gear is one of ancient design. Samples which date from the period of the Warring State (475-221 BC) have been excavated from archeological sites in China. One such sample is now on display in the Xi'an Clay figures of Warriors and Horses Exhibition Hall. This example is about 3/4" in diameter and made of bronze. It was used in the famous model, "Ancient Chinese Vehicle With a Wooden Figure Always Pointing to the South." Although this early gear is handmade and somewhat crude, it is a viable model.

Tooth Root Stresses of Spiral Bevel Gears
Service performance and load carrying capacity of bevel gears strongly depend on the size and position of the contact pattern. To provide an optimal contact pattern even under load, the gear design has to consider the relative displacements caused by deflections or thermal expansions expected under service conditions. That means that more or less lengthwise and heightwise crowning has to be applied on the bevel gear teeth.

## Departments

Crisis and Challenge in American Education (Publishers Page)
"We have met the enemy and he is us," says Pogo, the cartoon character. The enemy is the crisis in our educational system, and "crisis" is the only term that accurately describes the situation. It is every bit as serious, if not more so, than the crisis that followed the Soviet launching of Sputnik in 1957 - and for many of the same reasons. Our failing public education system threatens our position int he global political and business arenas; and this time, it's not just the Soviets or the Japanese who need to be taken seriously as competitors. Every country int he world that graduates better prepared students than we do - and there are a great many of them - has us at a competitive disadvantage.