## 4 Time-History Method for Impact Resistance Calculation
### Impact Response Result Analysis  
This section is based on the time-history method to calculate the maximum impact response value of the propulsion shafting system after being subjected to impact, as shown in Figures 16 and 17, which are the cloud diagrams of displacement response and stress response of the propulsion shafting system in the vertical and lateral directions when subjected to impact. When performing impact calculations using the time-history method, the time set includes two parts as follows: the impact load duration and the response decay time. The impact load duration refers to the combined triangular wave excitation time, while the decay time is selected based on the convergence situation. A total time-history of 1 s is selected in this paper. Due to the large impact of the propeller mass on the after-stern bearing and the forward-stern bearing, and the high-elasticity coupling has a strong displacement compensation under the action of impact load, the time-domain method mainly focuses on the impact displacement response of the after-stern bearing, the forward-stern bearing, and the master and slave ends of the high-elasticity coupling under this working condition, as shown in Figures 18-21.  
From Figures 16 and 17, it can be seen that the vertical impact displacement response of the propulsion shafting system is greater than the lateral impact displacement response; the vertical impact stress response is greater than the lateral impact stress response. Similar to the dynamic design analysis method, the impact stress of the shaft segments is all manifested at the tail shaft, which may be mainly affected by the larger mass of the propeller, increasing the force situation of the latter half of the tail shaft. It may also be that the span between the after-stern bearing and the forward-stern bearing is larger and the distance is further, resulting in larger impact displacement and stress response of the tail shaft.  
Figure 16: Vertical impact response contour map of the propulsion shafting system.  
From Figures 18-21, it can be seen that based on the time-domain method for impact resistance calculation of the propulsion shafting system, the impact displacement of the master and slave ends of the high-elasticity coupling is large, and the displacement amplitude results are equal. This is mainly due to the smaller density of the rubber components of the high-elasticity coupling and the larger Poisson's ratio, which can compensate for the displacement. The vertical impact response and the lateral impact response of different components have the same amplitude and trend, and under the action of the impact load, the displacement response curve fluctuates back and forth between positive and negative. This is mainly because when the system is subjected to impact, it will produce an inertial force opposite to it, making the displacement amplitude and the torque of the impact force in the previous instantaneous state opposite, and finally, the displacement amplitude curve gradually converges and decreases to zero under the action of the system damping.  
Figure 17: Transverse impact response contour map of the propulsion shafting system.  
Figure 18: Impact displacement response curve of the after-stern bearing: (**a**) vertical impact displacement curve; (**b**) transverse impact displacement curve.  
Figure 19: Impact displacement response curve of forward-stern bearing: (**a**) vertical impact displacement curve; (**b**) transverse impact displacement curve.  
Figure 20: Impact displacement response curve of slave end of elastic coupling: (**a**) vertical impact displacement curve; (**b**) transverse impact displacement curve.