As shown in the figure, the included angles between the five contact paths and the root cone on the convex surface of the big wheel are different. The contact paths in the figure are roughly divided into two categories: one is contact paths ①, ② and ③, which can be classified as inner diagonal contact. The contact mode is that the contact path of the convex surface of the big wheel is from the top of the big end tooth to the root of the small end tooth, and the design coincidence degree ε R is ① < ② < ③; The starting and ending points of the contact path are on the top cone of the big and small wheels. The other is ④ and ⑤. The contact path runs through the whole tooth surface along the tooth length direction, and its starting point and ending point are on the inner and outer cones of the tooth; The contact path ④ is in the middle of the tooth width and is basically parallel to the pitch cone line. It is applicable to the case that the helix angle at the midpoint is greater than 30 °. Its design coincidence degree is only related to the tooth width, while the contact path ⑤ has a certain inclination angle with the pitch cone line, so the design coincidence degree is ε R is ④ < ⑤, which is applicable to the case that the helix angle at the midpoint is less than 30 °, and its purpose is to increase the design coincidence degree and the area of tooth surface impression; When the helix angle at the midpoint is small, the contact path along the tooth length will cause the included angle between the meshing line and the contact path to be very small, so as to reduce the area of the tooth surface impression, and it is not easy to form lubricating oil film, which will lead to the premature failure of spiral bevel gear.
From the above analysis, it can be seen that the design coincidence obtained by contact paths ① and ② is too small to meet the design requirements of large coincidence degree. Contact path ③ is the main design method with large coincidence degree at present. Its relative sliding speed is large, which mostly occurs at the root or top of the tooth. Therefore, it is prone to tooth surface scratch and gluing. It is sensitive to installation error and easy to form edge contact. It is not generally applicable to some transmission occasions with high speed and heavy load. The contact path ④ is similar to the contact path of helical gear. The contact path basically coincides with the pitch cone line without friction. However, because the bevel gear generally adopts the tooth height displacement design, if the contact path design coincides with the pitch cone line, it will inevitably lead to the tooth surface impression too close to the top of big gear or the root of small gear, which is easy to cause premature edge contact and reduce the bearing capacity, Therefore, the contact path is generally designed in the middle of the tooth width. The relative sliding speed of the tooth surface of the contact path ⑤ is greater than that of the contact path ④, which increases the probability of tooth surface scratch and gluing.