# Effect of Multiple Reclosing Time Intervals on Axial Vibration of Winding
## 3 Effect of Reclosing Interval on Winding Vibration
### Vibration Response under Different Short Circuit Intervals  
After a short circuit, the windings vibrate strongly, resulting in relaxation of the winding, and the height of the winding is reduced [28]. Even a relaxed winding will not immediately recover after the short circuit is removed [29]. Additionally, the equivalent stiffness of the winding will change when the axial height of the winding falls. It is necessary to wait before the axial height of the winding is restored after a short circuit [30].  
Figure 5: Change of Acceleration at different cut-off times.  
At the same time, the breaker trips and the transformer short-circuit current cuts off. At that point, the winding has damped free vibration, showing underdamped attenuation, and the vibration energy is variably attenuated. At different degrees of vibration-energy attenuation, such as at 10 ms and 500 ms after the breaker trips, the breaker closes and a short-circuit current enters the transformer winding. At that time, the winding continues to be subjected to the short-circuit electromagnetic force. Figure 7 shows the disk displacement at different positions.  
It can be seen from Figure 7 that the vibration-displacement peak value at 500 ms decreases by more than 20% compared with the vibration-displacement peak value at 10 ms. The displacement peak value of the circuit breaker decreases significantly after reclosing. Therefore, as the short-circuit interval becomes larger, the vibration-displacement peak value decreases.  
After the breaker trips, the transformer short-circuit current is cut off and the winding's free vibration is damped, showing underdamped attenuation. At different degrees of  
Figure 6: Change of displacement at different cut-off times.  
Figure 7: Vibration displacement under different degrees of attenuation.  
vibration-energy attenuation, such as the circuit-breaker action after the trip at 10 ms and 500 ms, the breaker closes and the short-circuit current passes into the transformer winding. At that point, the winding continues to be subjected to the short-circuit electromagnetic force. Figure 8 shows the disk acceleration at different positions.  
According to Figure 8, the vibration-acceleration peak value at 500 ms is lower than the vibration acceleration peak value at 10 ms by about 40%. The vibration-acceleration peak value is significantly lower. Therefore, as the short-circuit interval becomes larger, the vibration acceleration decreases.  
After 10 ms of vibration attenuation, we selected different phase angles to continue the short-circuit closing, where the closing angle was set to different points in the 0-180\({}^{\circ}\) period, each separated by 20\({}^{\circ}\). According to the calculated results of the reclosing short-circuit current, the current through the winding is different at different positions and decays periodically with the change of interval. The electromagnetic force is adjusted by adjusting the secondary short-circuit impulse current, following which the excitation of the winding vibration is changed. The vibration displacement and acceleration of the transformer, in different disks and at different closing phase angles, are shown in Figure 9.  
Figure 8: Vibration acceleration under different degrees of attenuation.  
Figure 9: Vibration displacement and acceleration under different closing phase angles.  
Figure 9 shows the vibration response of the most common single-phase short-circuit fault, which describes the vibration displacement and vibration acceleration law in a closing angle from 0\({}^{\circ}\) to 180\({}^{\circ}\). As the phase angle increases from 0\({}^{\circ}\) to 90\({}^{\circ}\), the vibration displacement and acceleration response become smaller. However, the vibration displacement and acceleration response become larger as the closing phase angle increases from 90\({}^{\circ}\) to 180\({}^{\circ}\). Therefore, the vibration amplitude is the smallest when the closing angle is 90\({}^{\circ}\), and the reclosing phase-angle configuration should be considered.