When the instantaneous center line (pitch circle) of the cam rolls purely, two tooth profile curves formed by the auxiliary tooth profiles fixedly connected with the auxiliary instantaneous center line on the big wheel and the small wheel are yoked with each other, which is Camus's theorem. It considers the meshing state of two tooth surfaces; The modern theory of contact point trajectory is clearly established.
Concept. 1765, L. Euler of Switzerland put forward the mathematical basis for the analytical study of involute tooth profile, and expounded the relationship between the curvature radius and the curvature center position of a pair of meshing gear tooth profile curves. Later, Savari further improved this method and became the present Eu-let-Savary equation. Roteft WUlls contributed to the application of involute tooth profile, and he proposed that involute gear has the advantage of constant angular velocity ratio when the center distance changes. 1873, German engineer Hoppe put forward the involute tooth profile of gears with different numbers of teeth when the pressure angle changes, which laid the ideological foundation for modern modified gears.
At the end of 19, the principle of generating tooth cutting and the appearance of special machine tools and tools using this principle made involute tooth profile show great advantages after gears were equipped with more complete tools. When cutting teeth, as long as the gear cutter is slightly moved from the normal meshing position, the corresponding modified gear can be cut on the machine tool with the standard cutter. During the period of 1908, MAAG of Switzerland studied the modification method and manufactured the generating gear shaper. Later, British BSS, American AGMA and German DIN successively put forward various calculation methods of gear modification.
In order to improve the service life of power transmission gear and reduce its size, in addition to improving the material, heat treatment and structure, arc tooth profile gear is also developed. 1907, the British Frank Humphris first published the circular tooth profile. 1926, Swiss Eruest Wildhaber obtained the patent right of normal circular arc bevel gear. 1955, M.L. Novikov of the Soviet Union completed the practical research of circular-arc gears and won the Lenin Medal. 1970, R.M.Studer, an engineer of Rolh—Royce Company in England, obtained the patent of double circular arc gear in the United States. People pay more and more attention to this kind of gear and play an important role in production.
Gear is a kind of toothed mechanical parts that can mesh with each other, which is widely used in mechanical transmission and the whole mechanical field. Modern gear technology has reached: the gear module is 0.004 ~100 mm; Gear diameters range from 1mm to150m; The transmission power can reach 10 million kilowatts; The rotating speed can reach100000 rpm; The maximum circumferential speed is 300m/s.
The application of gears in transmission appeared very early. More than 300 years BC, the ancient Greek philosopher Aristotle expounded the problem of transmitting rotary motion with bronze or cast iron gears in Mechanical Problems. The South Compass invented by China in ancient times has used a whole set of gear trains. However, the gears in ancient times were all made of wood or metal, which could only transmit the rotary motion between shafts, and could not guarantee the stability of transmission, and the bearing capacity of gears was also very small.
With the development of production, the stability of gear operation has been paid attention to. 1674, the Danish astronomer Romer first proposed using epicycloid as the tooth profile curve to get a smooth running gear.
/kloc-during the industrial revolution in the 0 th and 8 th centuries, gear technology developed rapidly, and people did a lot of research on gears. 1733, the French mathematician Camille published the basic law of tooth profile meshing; 1765, the Swiss mathematician Euler suggested using involute as the tooth profile curve.
/kloc-gear hobbing machine and gear shaper appeared in the 0/9th century, which solved the problem of mass production of high-precision gears. 1900, Pfeiffer installed a differential device on the gear hobbing machine, which can process helical gears on the gear hobbing machine. Since then, hobbing machines have become popular, and gear generation method has an overwhelming advantage, and involute gears have become the most widely used gears.
1899, Lasher first realized the scheme of modifying gears. The modified gear can not only avoid undercutting, but also match the center distance and improve the bearing capacity of the gear. 1923, Wilder Haber of the United States first proposed the circular-arc tooth profile gear. 1955, Sunovikov made an in-depth study on circular-arc gear, and circular-arc gear was applied to production. This kind of gear has high bearing capacity and high efficiency, but it is not as easy to manufacture as involute gear and needs further improvement.
Gears are generally composed of teeth, tooth grooves, end faces, normal faces, tooth top circles, tooth root circles, base circles and indexing circles.
Gear teeth, referred to as gear teeth for short, are each convex part on the gear for meshing. These convex parts are generally arranged radially, and the teeth on the paired gears are in contact with each other, so that the gears can run continuously during meshing. Cogging is the space between two adjacent teeth on the gear; The end face is a plane on the cylindrical gear or worm, perpendicular to the axis of the gear or worm; Normal plane refers to the plane perpendicular to the tooth line of gear teeth; Tooth tip circle refers to the circle where the tooth tip is located; Tooth root circle refers to the circle where the groove bottom is located; The base circle is the circle in which the generatrix of involute makes pure rolling; The dividing circle is the reference circle for calculating the geometric dimensions of the face gear.
Gears can be classified according to tooth profile, gear shape, tooth line shape, surface where gear teeth are located and manufacturing method.
The tooth profile of gear includes tooth profile curve, pressure angle, tooth height and displacement. Involute gears are relatively easy to manufacture, so among the gears used in modern times, involute gears account for an absolute majority, while cycloidal gears and circular arc gears are less used.
In terms of pressure angle, the bearing capacity of small pressure angle gear is small; The gear with large pressure angle has high bearing capacity, but it increases the bearing load under the same transmission torque, so it is only used in special circumstances. The tooth height of gears has been standardized, and the standard tooth height is generally adopted. Modified gears have many advantages and have been used in various mechanical equipment.
In addition, gears can be divided into cylindrical gears, bevel gears, non-circular gears, racks and worm gears according to their shapes; According to the shape of tooth line, it is divided into spur gear, helical gear, herringbone gear and curved gear; According to the surface of gear teeth, it is divided into external gear and internal gear; According to the manufacturing method, it can be divided into casting gear, cutting gear, rolling gear and sintering gear.
The manufacturing materials and heat treatment process of gears have great influence on the bearing capacity, size and weight of gears. Carbon steel was used for gears before 1950s, alloy steel was used in 1960s, and surface hardened steel was used in 1970s. According to hardness, tooth surface can be divided into soft tooth surface and hard tooth surface.
The gear with soft tooth surface has lower bearing capacity, but it is easy to manufacture and has good running-in. It is mostly used in general machinery with no strict restrictions on the size and weight of transmission, and in small batch production. Because the small wheel bears a heavy burden in the paired gears, the tooth surface hardness of the small wheel is generally higher than that of the big wheel in order to make the working life of the big and small gears roughly equal.
Hard tooth surface gear has high bearing capacity. After the gear is finely cut, it is quenched, surface quenched or carburized to improve the hardness. However, in the process of heat treatment, the gear will inevitably deform, so it is necessary to grind, grind or finish cut after heat treatment to eliminate the error caused by deformation and improve the accuracy of the gear.
The steels commonly used in manufacturing gears are quenched and tempered steel, hardened steel, carburized and hardened steel and nitrided steel. The strength of cast steel is slightly lower than that of forged steel, and it is often used for larger gears. Gray cast iron has poor mechanical properties and can be used for light load open gear transmission. Ductile iron can partially replace steel to make gears; Plastic gears are mostly used in places with light load and low noise requirements, and the matching gears are generally steel gears with good thermal conductivity.
In the future, gears are developing in the direction of heavy load, high speed, high precision and high efficiency, striving for small size, light weight, long service life, economy and reliability.
The development of gear theory and manufacturing technology will further study the mechanism of gear tooth damage, which is the basis for establishing a reliable strength calculation method and the theoretical basis for improving gear bearing capacity and prolonging gear life. Develop a new tooth profile represented by circular arc tooth profile; Research on new gear materials and new gear manufacturing technology: The elastic deformation, manufacturing and installation errors and temperature field distribution of gears are studied, and the gear teeth are modified to improve the stability of gear operation and increase the contact area of gear teeth when fully loaded, thus improving the bearing capacity of gears.
Friction, lubrication theory and lubrication technology are the basic work of gear research. Studying the theory of elastohydrodynamic lubrication, popularizing the use of synthetic lubricating oil and adding extreme pressure additives to the oil can not only improve the bearing capacity of the tooth surface, but also improve the transmission efficiency.