Due to the different speed ratio characteristics of non-circular gears with different parameters, the design and processing of non-circular gears will also have different effects. Therefore, it is necessary to theoretically analyze the feasibility of the pitch curve function of the working section of the non-circular gear. According to the inclusion characteristics of the speed ratio function between the working section and the transition section of the non-circular gear, the relationship between the number of paired branches of the non-circular gear, the angle range of the working section and the speed ratio function of the working section can be obtained as shown in Figure 1.
In the ordered plane shown in Figure 1, each plane represents the same velocity ratio function. When the required speed ratio is constant, the theoretical distribution angle of the working section angle of the non-circular gear decreases with the increase of the number of branches of the paired non-circular gear. The dotted line divides the plane into three parts:
1) In the lower left corner, the coincidence degree of pitch curve is less than 1, which means that the pitch curve of non-circular gear obtained when the number of branches is matched with the rotation range is incomplete, and the corresponding integrated output speed ratio function fluctuates, as shown in Figure 2.
2) On the dotted line, the coincidence degree of pitch curve is equal to 1, which means that the pitch curve of non-circular gear is just complete and meets the design requirements when the number of groups is matched with the rotation range; But in the actual use process, instantaneous switching is needed, otherwise the output speed ratio function will fluctuate. In this switching mode, the load between gear pairs and gear teeth changes sharply, which is easy to cause adverse conditions such as life reduction and excessive vibration impact.
3) In the upper right corner, the coincidence degree of pitch curve is greater than 1, which means that the pitch curve of non-circular gear obtained by matching the number of groups with the rotation range has coincidence or output
In this matching mode, if the pitch curve is designed completely, the overlapping part of the output speed ratio can give the phase switching mechanism enough actuation time.
Compared with case 1 and case 2, case 3 not only meets the integrity of pitch curve of single gear pair, but also meets the demand of stepless speed regulation mechanism. It has a certain coincidence degree of its working angle, which provides buffer space and time for phase switching and reduces the impact of fast switching.