# Vibration response of high speed helical gear driven by time varying meshing stiffness

The time-varying meshing stiffness curve obtained above is input into the dynamic equations to obtain the vibration response of single-stage helical gear transmission under the input torque of 80N · m, 100N · m and 120N · m, and the vibration speed diagram as shown in Fig. 1 is drawn.

It can be seen from Fig. 1 that obvious super harmonic resonance occurs at 1 / 3 and 1 / 2 resonance speeds N0; the gear vibration acceleration increases with the increase of load; in the non resonance region, the root mean square value of gear acceleration does not always increase with the increase of speed, but has a slight downward trend after the over resonance region. In other words, when only considering the time-varying meshing stiffness excitation, the effect of rotating speed on the vibration characteristics of the system is not significant in the over resonance region.

In order to analyze the vibration characteristics of single-stage high-speed helical gear transmission, the vibration response of single-stage helical gear transmission under time-varying meshing stiffness excitation at three different speeds is made, as shown in Fig. 2-fig. 4. In the figure, Z1 table z1f represents the tooth frequency of the input tooth pair.

Fig. 2 and Fig. 3 show the vibration response of single stage helical gear transmission at 3000rpm and 6000rpm. It can be seen from the figure that the phase diagram of single-stage helical gear drive under the excitation of time-varying meshing stiffness is a closed curve, and its Poincare cross-section is a single point, so the vibration response is obviously periodic. And the system response frequency only includes tooth frequency and its multiple frequency, and the frequency component is very simple. The frequency response of the system in the figure shows that the amplitude of double tooth frequency is the highest among all response frequencies. This is because the amplitude of one tooth frequency is the largest in the excitation frequency, while the other excitation frequencies are smaller. In addition, the amplitude of double tooth frequency is larger than that of double tooth frequency. This is due to the fact that the natural frequency of the system is between one time of the tooth frequency and two times of the tooth frequency of 01 (degree rigid meshing heald gear tooth 9) m / N at 3000rpm and 6000rpm. At this time, the natural frequency of the system is close to the double tooth frequency, so the response amplitude is high. 