When the bevel gear is working, once the frequency of the exciting force generated by the meshing vibration dynamic load is consistent with the traveling wave vibration frequency of a certain vibration mode, it will arouse the pitch diameter traveling wave vibration of the bevel gear. It is one of the vibration forms of disk bevel gear, and its vibration mode is shown in the figure:
As shown in the figure, because the pitch diameter (or pitch line) divides the disk into an even number of sectors, the traveling wave vibration is also called sector vibration. Each point of the through sector makes axial vibration of the through phase, and each point of the adjacent sector makes reverse vibration. The expression is:
Where:
X – lateral displacement of disk surface;
A (R) – radial amplitude of bevel gear, which is a function of radius;
M – number of pitch diameters;
ΞΈβ Circumferential angle, position coordinate of vibration point;
P – angular frequency of sector vibration;
T – time;