Gear is an important part of mechanical transmission device, which has the characteristics of high efficiency, compact structure, high reliability and low manufacturing and maintenance cost. It is widely used in mechanical processing, transportation, aviation, chemical industry, metallurgy, mining and other engineering fields. As an important form of gear transmission, bevel gear transmission plays an extremely important role. The tooth direction line of ordinary spiral bevel gear is a general curve, so it is stable in the transmission process, from one end to the other, and the number of teeth entering the mesh is also more than that of ordinary straight bevel gear. The helix angle of spiral bevel gear is equal in size and opposite in direction. The coincidence degree is better than that of straight bevel gear. At the same time, in order to reduce the noise of the gear during high-speed operation and obtain compact structure and large transmission ratio, the number of teeth of the pinion can be relatively reduced. However, in the transmission process of traditional spiral bevel gears, due to the unequal spiral angles at different meshing points, it brings a series of problems in the transmission process, such as serious tooth surface friction and wear, low power transmission efficiency, unstable transmission and so on.
With the continuous progress of science and technology and the development of society, spiral bevel gears are used more and more widely, and users’ requirements for spiral bevel gears are more and more strict. With the improvement of the bearing capacity of spiral bevel gears, spiral bevel gears are more and more used in the process of high-speed transmission. Although the materials and heat treatment methods of spiral bevel gears are continuously improved, the vibration and noise of spiral bevel gears are still prominent problems in the operation of machines in the transmission process. With the improvement of the working accuracy of the machine and the improvement of the rules of environmental protection law, people urgently hope that the spiral bevel gear transmission is as stable and accurate as possible, so as to reduce vibration and noise and prolong the service life of spiral bevel gear transmission components. The development trend of these two aspects makes the problems of spiral bevel gear such as vibration, noise and service life more and more prominent, which is paid more and more attention by spiral bevel gear theoretical researchers and manufacturers.
As a new type of spiral bevel gear, the logarithmic spiral is introduced into the tooth direction line. This curve meets the characteristics that the helix angles of each point on the same logarithmic spiral are equal everywhere, and the logarithmic spiral is congruent with its isometric curve, so as to form a new type of gear transmission form – logarithmic spiral bevel gear transmission, The spiral angle of the gear is equal everywhere in the transmission process, which greatly improves the transmission mode of the logarithmic spiral bevel gear, improves the transmission efficiency of the logarithmic spiral bevel gear, and makes it more stable in the transmission process.
Logarithmic spiral bevel gear is affected by many factors in the actual transmission process. On the one hand, the machining error of the tooth surface of the logarithmic spiral bevel gear itself reduces the machining accuracy of the logarithmic spiral bevel gear due to the influence of the machining parameters of the machine tool, resulting in the deviation between the theoretical meshing point and the actual meshing point of the tooth surface, resulting in the tooth surface error, which will cause the speed ratio fluctuation in the transmission process; On the other hand is the installation error and deformation of the logarithmic spiral bevel gear. When transmitting power and force, the logarithmic spiral bevel gear is mainly subject to torque and torque. After a long time of work, the gear box and the gear shaft will be deformed to a certain extent. In this way, the logarithmic spiral bevel gear will be subject to a certain additional dynamic load in the transmission, and a certain jitter will occur. It seriously affects the transmission accuracy. In order to reduce the dynamic load and noise and improve the service life of logarithmic spiral bevel gear, one method is to improve the machining accuracy and make the tooth surface close to the required theoretical tooth surface, but the improvement of machining accuracy has a certain limit and the cost is very high; Another method is to compensate the error, such as measuring the machining error and heat treatment deformation of the tooth surface. The possible error after heat treatment of these milling teeth will be compensated during milling. The latter method is often more economical and feasible. However, due to the errors on the tooth surface (including machining errors and heat treatment deformation), the classical logarithmic spiral bevel gear meshing theory can no longer be used to calculate the contact trace, contact area and speed ratio fluctuation of the real tooth surface; Therefore, for the tooth surface with machining error and heat treatment deformation, based on the perfection of the theoretical meshing system of logarithmic spiral bevel gear and the existing logarithmic spiral bevel gear, reverse engineering is needed to study the error between the real tooth surface and the theoretical tooth surface of logarithmic spiral bevel gear.