With the development of mechanical industry modernization, the straight bevel gear transmission system with high load-bearing, high efficiency, high speed and low noise has gradually become the main direction of straight bevel gear dynamics research. In order to reduce the vibration and impact of straight bevel gear transmission and improve the dynamic performance of transmission, straight bevel gear researchers have done a lot of theoretical research and experimental analysis, concluded that tooth profile modification is an effective method to improve the working performance of straight bevel gear system, and summarized many ways and theories of tooth profile modification.
The elastic deformation in the meshing process of straight bevel gear leads to the change of angular velocity of straight bevel gear, which produces angular acceleration and inertial force. The dynamic load caused by inertia force will make the straight bevel gear transmission produce greater noise, vibration and impact. According to the basic law of straight bevel gear meshing, when the two tooth profiles mesh at any position, if the position of the node on the centroid of the straight bevel gear remains unchanged, the straight bevel gear can be transmitted with a fixed transmission ratio. Only when the base joints of adjacent teeth of the driving and driven wheels are equal (as shown in Figure 1), the straight bevel gear transmission can meet the above conditions.
In the actual working process of straight bevel gear, the existence of installation error, tooth error and other errors makes the straight bevel gear mesh on the premise that the adjacent tooth base joints of the driving and driven wheels are not equal, that is, abnormal meshing transmission, as shown in Figure 2. The actual meshing state of straight bevel gear deviates from the theoretical meshing state, and the nodes are not at the theoretical position on the connecting line. The transmission ratio of straight bevel gear changes, so the straight bevel gear system will produce dynamic load, impact, vibration and noise.
In order to reduce the vibration, impact and noise in the transmission process of straight bevel gear, part of the involute profile at the tooth top or near the tooth root of straight bevel gear is removed, so that the straight bevel gear profile is not the original involute profile to compensate for the base pitch deviation. The tooth profile modification removes the interference part caused by the deviation of tooth base pitch, reduces the impact load in the process of tooth transmission, improves the transmission stability, and reduces the vibration and noise of the system.
Straight bevel gear transmission is affected by tooth shape error, manufacturing error, deformation between teeth and other factors, which will also make the actual meshing position of teeth in the tooth direction deviate from the theoretical meshing position, make the tooth load change along the tooth direction, and produce the phenomenon of “end meshing” stress concentration. If the gear teeth contact on the full tooth length, but the load distribution in the tooth direction is uneven, it will also lead to different elastic deformation in the tooth width, resulting in stress concentration and “end meshing”, resulting in that the gear teeth can not bear large load and affect the transmission performance of straight bevel gear.
Therefore, in order to compensate the error, various elastic deformation and thermal deformation of the straight bevel gear system, the tooth direction modification must be carried out on the tooth to improve the load distribution of the tooth direction, make the stress of the tooth along the tooth direction more uniform, and the working performance of the straight bevel gear is better. Generally, the modification methods of straight bevel gear in the tooth direction include tooth end modification and tooth direction drum modification, as shown in Figure 3.
When the meshing skew of straight bevel gear is relatively small, the method of tooth end modification is often used. In many cases, the circular arc drum repair with central symmetry and equal radius is adopted for the straight bevel gear to compensate various errors and deformation of the straight bevel gear system, avoid stress concentration and make the contact area more reasonable. When the meshing skew of straight bevel gear is too large or unknown, the ideal modification effect can be obtained by modifying the target variable curvature surface of straight bevel gear according to the specific working conditions.