# Traveling wave vibration analysis of bevel gear

Although there are many harmonics in the meshing force of bevel gear, not all harmonics can arouse the resonance of bevel gear. Generally, the amplitude of the first harmonic excitation force with the harmonic number of 1 is the largest, and the amplitude of the higher harmonic excitation force decreases with the increase of the harmonic number. The necessary condition for arousing the resonance of the bevel gear is that the frequency of the exciting force is equal to the natural vibration frequency of the bevel gear, but for the pitch diameter vibration of the bevel gear, the following conditions must also be met:

1) The frequency of exciting force and the natural vibration frequency of bevel gear belong to the same coordinate system;

2) The frequency of exciting force to excite the pitch diameter traveling wave vibration of bevel gear is

3) The work done by the exciting force on the vibration of bevel gear is positive work, on the contrary, it can not arouse resonance.

The exciting force acts on the bevel gear against the steering of the bevel gear and surrounds the gear. It is known that the excitation frequency of the traveling wave exciting the conical gear is the excitation mode of the conical gear

The exciting force frequency fc applied when the bevel gear rotates is:

Where:

K-harmonic order, k = 0.5, 1.0, 1.5, 2.0;

Z – number of teeth of bevel gear;

N – speed of bevel gear.

The conditions for generating traveling wave vibration are:

Where:

FM – natural vibration frequency of pitch diameter m;

M – number of pitch diameters.

According to the formula, the resonant speed of the front and rear traveling waves generated by the bevel gear is:

Front traveling wave resonance speed:

Backward traveling wave resonance speed:

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