## 4 Conclusions  
This research presents the novelty in establishing the true dynamic bending moment using only one bridge of strain gauge instead of double bridges. This technique was applied in the experiments on a 50,000 DWT tanker under the rapid turning transient states, such as port turns and starboard turns, that significantly affected the working conditions of propeller. The following is the summary of what the experiment achieved:  
1. The strain gauge method is a high-precision technique for measuring the bending moment vibration. The nominal bending moment during one revolution can be determined by the zero-to-peak value in the time domain or the first-order vibration in the frequency domain. To identify the effect of forces induced by the propeller on the vertical and horizontal positions for each angle of rotation, it is recommended to evaluate the true dynamic bending moment by installing two strain gauge bridges positioned 90 degrees to each other. 2. In case the second bridge, S2, is not available, the true dynamic bending moment can be measured by using the actual bending stress combined with the phase lag stress of the only one bridge of strain gauge at an angle of 90\({}^{\circ}\). The waveform of the established true bending moment was similar to the waveform of the measured displacement. The mean values (average values) of the established true dynamic bending moment were the same as the values of the nominal bending moment obtained by the conventional method. Both waveforms and amplitudes were validated. These confirmed the accuracy of the suggested method. Figure 12: Trajectory plot of bending moment during rapid starboard turn. (**a**) Nominal bending moment; (**b**) True dynamic bending moment (orbit plot). 3. The rapid change in the ship's heading caused a sudden change in the wake-field, which temporarily applied excessive load to the propeller blades and then transmitted to the shaft and bearings. The bending moment of the propeller shaft had moved upward clockwise at the beginning, then returned in the same trajectory at the end of the starboard turn. The propeller operated as a seesaw, which confirmed the increased load on the ASTB. The phenomenon occurred in the opposite direction during the port turn. 4. The moment orbit when the rudder angle was 12 degrees is larger than the other stages with respect to the greater propeller force fluctuation. This occurred more clearly in the case of the starboard turn, resulting in a non-uniform oil film on the bearings. This instability can be referred to as an oil whirl. When the oil whirl becomes intense, it becomes an oil whip, which possibly leads to bearing wear and premature failure. The fluctuation behavior was not significant, but early detection of instability is essential for the safe operation of bearings. 5. In further work, the displacement sensors should be installed on both vertical and horizontal directions to fully cross-verify the behavior of the bending moment. Additionally, the establishing method presented in this research can be applied in the case of a four-blade propeller. In other cases, it is recommended to install two bridges of strain gauge for each shaft cross-section in order to directly establish the true dynamic bending moment. [PERSON] and J.-u.L. have contributed equally to this work. Conceptualization, Q.D.V., J.-w.L. and J.-u.L. ; methodology, J.-u.L. and Q.D.V. ; software, Q.D.V., Y.K. and K.S. ; validation, Q.D.V., J.-w.L., M.-h.S. and J.-u.L. ; formal analysis, Q.D.V. and J.-u.L. ; investigation, J.-w.L., Y.K., K.S. and Q.D.V. ; resources, Q.D.V. and J.-u.L. ; data curation, Q.D.V., K.S., J.H.J. and J.-u.L. ; writing--original draft preparation, J.-w.L., Q.D.V., H.C. and J.-u.L. ; writing--review and editing, M.-h.S., W.-J.L., H.C. and J.-u.L. ; visualization, Q.D.V., Y.K. and J.-w.L. ; supervision, M.-h.S., W.-J.L. and J.-u.L. ; project administration, J.H.J., H.C. and J.-u.L. ; funding acquisition, J.-u.L. All authors have read and agreed to the published version of the manuscript.