Transient torsional vibration is very important when considering the stability, comfortable performance, and full life cycle of a propulsion system as a whole. During the start-up process, clutch engagement may generate a judder phenomenon [19]-[21]. This prevents the propulsion system from starting smoothly and could even can damage the transmission system. A clutch engagement-disengagement test was performed to confirm the transient load on the magnetic clutch during these operations. Consequently, dominant self-excited vibrations can occur during engagement [22][23]. The testing procedure is as follows.

• Step 1: Start the engine and run it stably at an engine-speed of 700 rpm.
• Step 2: Engage the clutch.
• Step 3: Keep the engine running stably at a speed of 700 rpm.
• Step 4: Disengage the clutch.

The results of torsional vibration measurements at the propeller shaft are shown in Figure 9 and Figure 10. During engagement, the judder phenomenon occurred, but the torque fluctuation was not significant compared with the torque transmitted, as depicted in Figure 9. The vibration behavior was much smoother during clutch disengagement, as shown in Figure 10. The measured torsional vibration stresses indicated that the clutch worked well during the engagement and disengagement processes.

Figure 9: 
Torsional vibration stress during clutch engagement

Figure 10: 
Torsional vibration stress during clutch disengagement

Steady-state measurements under normal operating conditions were also performed to evaluate the vibration characteristics of the propulsion system over the full range of operating speeds. For these measurements, only the engine mode was used. Consequently, after engagement, the propeller speed increased with a slow and steady acceleration from the minimum speed to the nominal speed. The sweep was sufficiently slow to enable the full development of the vibration quantities to be measured. The vibration measurement was in accordance with the ISO 20283-4:2012 standard [24] concerning the measurement and evaluation of the vibration of ship propulsion machinery. Accordingly, the sweep took approximately 10 min to complete, to ensure an acceleration rate of less than 15% of the nominal speed per minute. For the best frequency analysis and harmonic order tracking, a sampling rate of 8192 samples/s was applied for the measurement. Harmonic order was defined as a term that relates to the number of events per shaft revolution. This can be obtained as follows:

A fast Fourier transform (FFT) was performed with a 25600 spectral line resolution, flat top window, and 4096 Hz frequency range. The torsional vibration characteristic can be assessed through dynamic stress measurements using a strain gauge or angular velocity measurement by an encoder. Figure 11 shows the analysis results of the torsional vibration stress measured at the propeller shaft. A vertical color bar to the right of the axis describes the color scale of the stress amplitude. Accordingly, vibration resonance occurred in the propeller speed range of 300-350 rpm at the 3^rd harmonic order. This vibration was caused by the propeller that has three blades. A closer look at the contour map in Figure 11(b) shows that the natural frequency of the vibration appears in the range of 15 to 16 Hz. When the 3^rd order vibration met the natural frequency, resonance occurred.

Figure 11: 
Torsional vibration stress measured at the propeller shaft in engine mode. (a) Waterfall plot; (b) Contour map; (c) All orders plot

The same resonance phenomenon was recorded in the result of the angular velocity analysis at the propeller shaft, as shown in Figure 12. The fluctuation of the angular velocity at resonance was very large owing to the 3^rd order excitation from the propeller blades. This must be confirmed by the clutch manufacturer, considering the safety of the transmission system. The level of torsional vibration resonance was not sufficiently high to damage the shaft, but it could cause the electromagnetic clutch to slip and become damaged. In addition, the power performance was not maximized.

Figure 12: 
Angular velocity measured at the propeller shaft in the engine mode

Structural vibration measurements were performed concurrently with steady-state torsional vibration measurements. A sampling rate of 8192 samples/s was used for the measurement. The sensors were piezoelectric accelerometers that generated acceleration signals. For better evaluation, it is necessary to convert the acceleration data to velocity. For a single-frequency vibration, the velocity vibration in the time domain can be described by

Acceleration is the derivative of the velocity with respect to time. The above vibration can be expressed as an acceleration by

• with:

• where
• - a : acceleration value in the time domain [mm/s²];
• - v : velocity value in the time domain [mm/s];
• - v˙ : derivative of the velocity with respect to time [mm/s²];
• - a^ : peak value of acceleration vibration [mm/s²];
• - v^ : peak value of velocity vibration [mm/s];
• - φ_a : phase of acceleration vibration [rad];
• - φ_v : phase of velocity vibration [rad];
• - ω : circular frequency [rad/s];
• - f : vibration frequency [Hz].
• - t : time [second].

From Equations (2)-(4) the relationship between the velocity and acceleration at every frequency is established. For the peak value,

For the phase of vibration,

By applying this relationship, we obtained the peak values of the velocity vibration from the acceleration data. First, the acceleration signal in the time domain was processed using an FFT in the same manner as the torsional vibration analysis, as described previously. The data were then converted to a frequency-domain representation that showed the peak value of the acceleration at every vibration frequency. Therefore, the peak values of the velocity vibrations can be obtained using Equation (5). Finally, order tracking analysis was performed based on Equation (1) to provide a complete diagnosis of the vibration. Figure 13 and Figure 14 show the order tracking results of the structural vibration analysis on the diesel engine body and hull deck near the stern.

Figure 13: 
Structural vibration measured at the top of engine and aft side in engine mode. (a) Longitudinal direction; (b) transverse direction; and (c) vertical direction.

Figure 14: 
Structural vibration measured on hull deck near stern. (a) Longitudinal direction; (b) transverse direction; and (c) vertical direction

As a result, vibration resonance occurred at the 3^rd harmonic order in the range of 300 to 350 rpm. This phenomenon is similar to the behavior of torsional vibrations. The main excitation source was a 3-blade propeller. The level of the vibration amplitude was much higher than the recommended value of the 30 mm/s peak for the overall vibration amplitude by Lloyd’s Register [25]. It should be clearly understood that this recommended value applies to steel merchant ships. It may not be applicable to small boats using composite materials. This value was only used for reference. However, it is evident that it affects the human experience on board. Equipment installed on the board is highly susceptible to damage owing to strong vibrations.

The noise measurement was carried out at full-speed steady-state operation in both engine and motor modes. The overall noise-level results are listed in Table 3.

Based on the measurement results, the motor mode showed superior noise reduction. The noise level was significantly improved in both the engine and hull decks. The difference in the overall noise levels between the engine and motor modes was greater than 20 dBA. This proves the advantages of the hybrid propulsion system. It was quieter during the motor operation.

The propulsion system transmits torque from the engine to the propeller and obtains the thrust force from the propeller, which affects the hull. Torsional vibrations also lead to increased bearing loads, which then affect the structural vibration. The exciting forces of the engine and propeller are the main causes of torsional vibration. Based on the measurement results, vibration resonance occurred in the propeller speed range of 300 to 350 rpm at the 3^rd harmonic order excited by the 3-blade propeller. The same torsional vibration phenomenon was observed in the angular velocity fluctuation at the propeller shaft. The torsional vibration stress amplitudes were not sufficiently high to damage the shaft, but the angular velocity fluctuation was very large. This can lead to internal slippage of the electromagnetic clutch. The clutch, therefore had a high chance of being damaged. This problem must be confirmed by the clutch manufacturer, considering the safety of the propulsion system. Torsional vibration also affects the structural vibration on the engine and hull deck. The vibration level may not damage the boat hull made of composite material, but it can cause damage to the equipment and impairs the onboard human experience.

The vibration resonance was the result of the 3^rd order propeller excitation and a natural vibration frequency in the range of 15 to 16 Hz. It is recommended to change the propeller design from three to four or five blades. In the case of a 5-blade propeller, the propeller excitation frequency was of the 5^th harmonic order. Using Equation (1) and the same natural frequency of 15–16 Hz, the critical propeller speed was determined in the range of 180 to 192 rpm. Therefore, vibration resonance (if still available) occurs at a lower propeller speed, which is far from the usual operating speed range. In addition, this will change the stiffness and the 2nd moment of inertia of the propeller. A ship design engineer can choose appropriate values to lower the natural frequency while maintaining the propeller efficiency. This change improves the torsional vibration behavior and significantly reduces the structural vibration compared to the current state.