Gear transmission is one of the most important mechanical transmission. More than 300 BC, Aristotle, the ancient Greek philosopher, expounded the problem of using bronze or cast iron gears to transmit rotary motion in the book mechanical problems. From the end of 17th century to the beginning of 18th century, people began to study the strength of gears. After the European industrial revolution, gear technology has been developed rapidly. Gear transmission is widely used in mechanical transmission and the whole mechanical field. Gear design has become one of the important design contents in mechanical design. At present, the commonly used design formulas of gear strength in the world, in addition to the calculation methods of gear strength in China’s national standard (GB), mainly include: ISO calculation method; AGMA standard calculation method; din calculation method; jg-ma calculation method; BS calculation method, etc. In the teaching of mechanical design, especially gear design, the author found that many knowledge points are relatively simple and not easy to understand. Therefore, in this paper, several problems of gear design, such as the failure mode of gear, the history and current situation of gear strength design, are deeply analyzed, and the historical source of gear strength design in China and some puzzles in gear design are discussed. Through in-depth analysis, we can better understand the meaning and context of gear design formula.

In the process of gear transmission, there will be various forms of failure, or even loss of transmission capacity. The failure mode of gear transmission is related to the gear material, heat treatment, lubrication condition, load size, load change rule and rotation speed. People’s understanding of gear failure is a developing process. In the middle of the 18th century, people began to study the failure of gears. A preliminary understanding of the friction and wear of gears, the formation of pitting and the gluing of gear surfaces has been obtained. In 1928, Buckingham published a paper on gear wear, and divided the tooth surface failure into six failure forms: pitting corrosion, abrasive wear, gluing, peeling, scratching and seizing. In 1939, Rideout divided the gear damage into eight forms: normal wear, pitting, peeling, gluing, scratching, cutting, rolling and hammering. In 1953, borsoff and sorem classified gear damage into six categories. In 1967, according to a large number of tests, Niemann drew a limit diagram of bearing capacity for four failure modes of involute gear, and pointed out that when the speed of gear is low, the main factor affecting the bearing capacity of soft tooth surface gear is pitting, and the factor affecting the bearing capacity of hard tooth surface gear is broken teeth; for high-speed heavy-duty transmission gear, the factor is often gluing [2-6]. Since the 1950s, some countries have classified the damage forms of gears in a standard form, and stipulated terms, performance characteristics, causes, etc. For example, in 1951, the United States divided gear damage into two categories, one is tooth surface damage, including wear, plastic deformation, gluing, surface fatigue, and the other is the fracture of gear teeth. The former kind of tooth surface damage is the surface damage caused by high gear pair due to Tribological reasons; the latter kind of tooth fracture is the damage caused by insufficient volume strength of the tooth as a load-bearing component. In 1968, the Austrian national standard stipulated the terminology of gear damage.

In 1983, China promulgated the national standard for terms, characteristics and causes of gear tooth damage (GB / t3481-83), which divides the damage forms of gears into five categories, namely, wear, tooth surface fatigue (including pitting and peeling), plastic deformation, tooth fracture and other damage, a total of 26 failure forms [7].

In 1997, China promulgated the GB / t3481-1997 national standard revised by GB / t3481-1983. At present, in most of the mechanical design textbooks and mechanical design manuals in China, the failure modes of gears are simplified, which are generally divided into five categories: gear fracture, fatigue pitting, gluing, wear and plastic deformation.