# Harmonic frequency components in vibration test of reducer variable speed integrated gear

When the input speed is 560 R / min, the theoretical frequency component of gear vibration response is calculated by formula.

The calculation formula of excitation frequency of time-varying meshing stiffness of gear teeth is as follows:

The calculation formula of excitation frequency of time-varying instantaneous center of gear tooth is as follows:

Set the sampling frequency to 1000Hz, balance and clear the test and analysis system. Test the vibration acceleration signal of the reducer variable speed integrated gear system under the condition of input speed of 560r / min and load torque of 10nm. After the gear system runs stably and the signal image on the recorder tends to be stable, the signal acquisition is started. The vibration acceleration data is sampled by MATLAB The file format is saved to the computer, and the time domain and amplitude frequency curves of the vibration signal under the working condition are obtained after signal processing such as noise reduction and filtering.

Figure a) is the time-domain signal of radial vibration acceleration of non-circular gear measured by the sensor, and the amplitude frequency curve of Fig. b) is obtained by Fourier transform. It can be seen that the main vibration frequencies are 134.2 Hz, 2.1 Hz and 268.5 Hz, which are close to the theoretical calculation values F1, F2 and 2F1 respectively. Meanwhile, the frequencies of 134.2hz and 268.5hz in Fig. b) are close to 2.1hz It is obvious that there is a frequency doubling of 2.1 Hz in the frequency component. The above phenomena also exist in the vibration signals measured in other directions of spur gears and non-circular gears.

Therefore, from the amplitude frequency curve of the test data, it can be verified that there are fundamental frequency f1, F2 and their multiple frequency of time-varying instantaneous center and time-varying stiffness, and there are also F1 and F2 in the vibration of the gear The results show that the elastic rotation angle function of the reduced speed integrated gear set in the approximate analytical solution is reasonable. 