Research an Online Monitoring Method of Propulsion Shafting Alignment Adapting to Hull Deformation


 Hull deformations are caused by factors such as loading status, wave load, diving depth of underwater vehicles, etc. This causes a change in the shafting alignment state of the ship's propulsion shafting.This affects the alignment state of the ship propulsion shafting. It is very important for engineering significance to research an online monitoring method of propulsion shafting alignment that adapts to the influence of hull deformation. Based on Euler's rigid body attitude theory, this paper constructs a spatial attitude relationship model of the main and driven shafts of the ship's propulsion shafting. By converting to a fixed earth coordinate system, their absolute position-posture can be obtained. Using laser displacement sensor measurement technology, an online monitoring method of propulsion shafting alignment that adapts to the influence of hull deformation is established, which was verified by experiments. This method is suitable for situations where both the main shaft and the driven shaft may have rigid body posture changes. It can provide shafting alignment control compensation for the influence of hull deformation under different working conditions. This will greatly reduce the operating noise of the shaft system and the mechanical operation failure caused by the misalignment of the ship's propulsion shafting.

The existing shafting alignment measurement technology is basically offline, which is only suitable for shafting installation inspection and measurement. The more common ones are the dial indicator method and the laser alignment instrument method.Garg et al. [9] and Li and Wang [10] used two laser sensors (PSD/LD-PSD, Figure  1(a) and Figure 1(b)) to collect data from three different positions of the laser sensor to calculate the shaft alignment state. The two laser sensors are respectively installed at the main and driven ends of the propulsion shaft system, and the sensor is rotated with the shaft system by cranking the shaft system.These methods are suitable for the nonworking state of the shaft system. Once the shaft system is working normally, the laser sensor cannot be rotated for measure.Therefore, it is impossible to realize the online monitoring of the shaft alignment state, and it is not suitable for shaft alignment measurement under the condition of the deformation of the hull.
(a) Structure of the laser alignment system with dual PSDs [9] (b) Two-beam LD/PSD diagram [10] (c) An example of ship hull FEM model with hull deformations [13] (d) Hull deformation at St5 (Full draught APT empty) condition [15] Figure 1. Monitoring principle and hull deformation Ttraditional reasonable shaft alignment technology [11] ignores dynamic factors such as hull deformation. Dynamic shaft alignment technology is still in the stage of theoretical research, which considers hull deformation and other dynamic factors.The dynamic alignment technology is closer to the actual working conditions of the shaft system, which can better improve the shaft alignment quality and the reliability of the shaft system operation. Shi Lei et al. [12][13], Li Zeyuan et al. [14] and Seo et al. [15] used the FEM to research the relationship between hull deformation and bearing displacement. Shi Lei [13] took a 76,000 DWT product oil tanker as the research object.Hull deformation (Figure 1(c)) is analyzed by an FEM, and the deformation of the bottom hull is transformed into the deformation of the bearing.Compared with the standard line, the bearing offset is estimated.Compared with the azimuth offset in the still water condition, the relative azimuth offset is estimated. Seo et al. [15] took the 300,000 DWT ultralarge crude oil carrier as the research object. According to the ship's draft, five draft conditions were selected to analyze the hull deformation of the overall structure and calculate the bearing offset value. The analysis results (Figure 1(d)) show that the hull deformation may be a key factor affecting the deflection and deformation of each bearing supporting the shafting.Generally, shipyards use the FEM to analyze the influence of hull deformation on the vertical relative deformation of the shafting centerline under floating conditions, ballast conditions and full load conditions to optimize the shaft alignment design.Although the influence of hull deformation on the position offset of the shafting bearing is researched, there is a lack of research on the calculation of parallel misalignment and angular misalignment, and it is impossible to realize the online monitoring of the system's centering state.
Zw et al. [2] used three displacement sensors to monitor diesel engine misalignment, and realized real-time calculation of the misalignment. Two parallel sensors with a fixed relative position quantitatively detect the posture of the output shaft. The relative position of the two sensors will change under the influence of the hull deformation. Bu Wenjun et al. [16] (Figure 2 is the schematic diagram) and Shi Liang et al. [17] used an eddy current displacement sensor to measure the horizontal and vertical displacements of different parts of the propulsion main engine to construct an online shaft alignment monitoring model. In this way, based on the hull (assuming that there is no deformation in the hull), the online alignment monitoring of the propulsion main engine shafting system is realized. Applied to the smart air spring vibration isolation device, the maintaining control of the shafting attitude of the ship propulsion main engine is realized [16][17][18][19].However, these methods do not take into account the impact of hull deformation. They cannot adapt to the impact of hull deformation to achieve accurate online monitoring of shaft alignment. There are two main problems. On the one hand, these methods assume that the driven shaft does not perform any rigid movement. The parallel misalignment and angular misalignment of the main shaft relative to the plane are the alignment values of the shaft system. The hull deformation will affect the position offset of the main shaft and the driven shaft. Therefore, the alignment value is determined by the position states of both the main shaft and the driven shaft at the same time. On the other hand, with the development of floating raft vibration isolation technology, raft bodies are carrying increasing equipment, and raft bodies are developing toward larger and lighter weight [20]. The deformation of the elastic support platform affects the shafting deformation [21].The measurement data of the displacement sensor include the local deformation of the shaft installation platform, which cannot be simply regarded as the pure rigid displacement of the main engine.  Figure 2. Schematic diagram of the displacement sensor layout of the alignment attitude monitoring system [16] Based on Euler's rigid body attitude theory, this paper constructs the space position-posture relationship model of the main shafts and driven shafts of the ship's propulsion shaft system. Their relative space position-posture is converted into the absolute position-posture state of the Earth's fixed coordinate system. Using the measurement technology of laser displacement sensor, an online propulsion shafting that can adapt to the influence of hull deformation is established, and the method is tested and verified.

Principle of the online alignment monitoring method for propulsion shafting
The hull deformation causes position changes of the propulsion motors and bearings. Both the main shaft and the driven shaft will have different rigid body motions and produce displacements of different amplitudes. Therefore, when researching shaft alignment, it is necessary to consider the position and position states of both the main shaft and the driven shaft at the same time. As shown in Figure 3, the relative position-posture of the main shaft and the driven shaft is obtained by two laser sensors. They are respectively fixed on the main and driven shaft fixing brackets. By analyzing the position and position data of the two shafts, the position and position change of the two shafts is obtained, and then the shafting alignment value is calculated. Therefore, the shafting online alignment monitoring system was constructed. The workflow is shown in Figure 4. . The workflow of the shafting online alignment monitoring system This system is mainly composed of a laser displacement sensor, relay bridge module and other modules. Among them, laser sensor A and laser sensor B are used to measure the relative position-posture of the driven shaft and main shaft respectively.The relay bridge module is responsible for controlling the opening and closing of the laser sensor, collecting the laser sensor data and judging whether it is out of range, capturing multiple sets of data for average filtering, and using the centering offset model to calculate the centering change and display it to the user. At the same time, users can set up and perform corresponding data processing and display functions.

Alignment monitoring model
As shown in Figure 5, three coordinate systems are established: a fixed spatial reference coordinate system, a body A coordinate system and a body B coordinate system. _ represents the earth fixed reference coordinate system. _ represents the A body coordinate system fixedly connected to the center point of the laser sensor A. _ represents the B body coordinate system fixedly connected to the center point of the laser sensor B. represents the torsion angle of the laser sensor A.
represents the laser sensor the torsion angle of B. The coordinate of point P , one point on the coupling, is ( , , ) in the _ coordinate system . The _ and _ coordinate systems are the same as the azimuth, and the initial state (state 1) has a different torsion Figure 5. Schematic diagram of the ship propulsion shaft system and coordinate system For any point ( , , ) on the _ coordinate system, since _ rotates around the axis relative to _ , the coordinates of point Q in the coordinate system _ are: is the rotation transformation matrix: In this article, it assumed that the main shaft and driven shaft do not undergo elastic deformation. In the main shaft and driven shaft only rigid body motion occurs. The position-posture of laser sensors A and B on the main shaft and driven shaft can be used to deduce the position-posture of the entire shaft system through the law of rigid body position-posture movement.The Laser sensors A and B emit laser beams opposite to each other along the axis, and form imaging points on each other. As shown in Figure 6, the torsion angles of Laser sensor A and B are 1 and 1 in state 1 respectively, and are 2 and 2 in state 2. Figure 6. Schematic diagram of monitoring model The imaging points of laser sensors A and B in state 1 are ′( 1 , 0, 1 ) and ′( 1 , 0, 1 ), and the imaging points of laser sensors A and B in state 2 are ′′( 2 , 0, 2 ) and ′′( 2 , 0, 2 ). Since laser sensor A is rotated 180° relative to _ , in the _ coordinate system, the coordinates of ′ and ′′ are (− 1 , 0, − 1 ) and (− 2 , 0, − 2 ) .Therefore, transformed to the _ coordinate system, the changes in the direction and direction between the imaging point in state 1 and the imaging point in state 2 are: For 1 、 1 、 2 and 2 are all small angle angles, so Eqs. 3-4 can be simplified to: Eqs. 5-6 are the position-posture changes of the driven shaft. Eqs. 7-8 are the position-posture changes of the main shaft.Generally, parallel misalignment(offset deviation) and angular misalignment(skew deviation) are used to measure the shaft alignment state. The shaft alignment state response vector [22] is: In this article, the axial deformation ∆ is not considered. The torsion angle can be measured by the inclination sensor. The coupling point P is selected as the calculation point of the alignment state change. The alignment state change of any two states is: where b is the axial center distance of the two optical instruments. The horizontal offset change ∆ and the vertical offset change ∆ are: Eqs. 11-14 are the calculation models for the amount of change in the alignment component. In particular, when state 1 is the ideal shaft alignment state, the model is the shaft alignment component calculation model.

Experimental verification
A comprehensive experimental platform for shaft alignment of the main power propulsion system is built. The physical and schematic diagram are shown in Figure 7. In addition, it can make the rotation movement of around the axis ( ) to realize the torsional rotation of the shaft system.Therefore, by controlling the translation and rotation of the A and B components, different alignment states of the shaft system can be achieved, including horizontal parallel misalignment, vertical parallel misalignment and vertical angular misalignment. The main parameters of the experimental platform are shown in Table 1.  ) and B (around the axis) is 0.005° (0.0875 mm/m), and the rotation range is -1°~+1°.
The main parameters of the laser sensor are as follows. The maximum transmitting and receiving distance is 20 m. The receiver range is -8~8 mm. The receiver resolution is 0.001 mm. The linear error is 1%±0.003 mm. The working temperature range is -5℃~50℃. The signal output mode is the RS485 protocol .
To verify the correctness of the shafting alignment model that adapts to the deformation of the hull, three types of targeted tests have been carried out, namely, the purely parallel misalignment condition, the purely angular misalignment condition and the combined misalignment condition test [23] [24].Three types of centering components of horizontal offset, vertical offset and vertical angularity are simulated by controlling the movement of Moving Parts A and B. The offset and angularity of the control movement are recorded. At the same time, using the two-axis relative position-posture obtained by the laser sensor, the corresponding three centering components are calculated. Thus the difference between the control centering component and the solution centering component is calculated, which is Horizontal Offset Error (HOE), Vertical Offset Error (VOE) and Vertical Angularity Error (VAE). So the offset error (Offset Error, OE) is the arithmetic square root of the horizontal offset error and the vertical offset error ( = √ 2 + 2 ). Then an error map will be drawn and the root mean square error will be calculated to evaluate the accuracy of the calculation model. Figure 8. Schematic of rotor with misalignment at a coupling [24] Aiming at the three types of shafting misalignment including parallel misalignment, angular misalignment and combined misalignment [24] (Figure 8), three types of experiments were designed and carried out in purely parallel misalignment conditions, purely angular misalignment conditions and combined misalignment conditions [23]. A total of 6 sets of experiments were carried out. Experiments #1 to #3 are used to verify the purely parallel conditions, corresponding to vertical translation, horizontal translation and combined translation, respectively, and corresponding to verifying vertical offset, horizontal offset and horizontal and vertical offset. Experiment #4 is used to verify pure rotation conditions, corresponding to pitch rotation, and is used to verify vertical deflection. Experiment #5 and Experiment #6 are used to verify the combined parallel-rotation working conditions, corresponding to horizontal translation-pitch rotation and vertical translation-pitch rotation, corresponding to verifying horizontal offset-vertical skew deviation and horizontal offset-vertical straight skew error.The working conditions are shown in Table 2.   . Error diagram of parallel and rotation Experiments #1 to #3 were carried out for purely parallel motion conditions. From the experimental results ( Figure 9a), it can be seen that the horizontal offset error presents a clustered distribution, and the vertical offset error distribution is relatively scattered. The offset errors (OE) are all less than 0.01 mm. Considering the parallel accuracy of the experimental platform (0.01 mm), for the axis system offset state, the offset calculation model for the change component of the shaft alignment state is accurate. Experiment #4 was carried out founder pure rotation conditions. From the experimental results (Figure 9b), it can be seen that the vertical angularity error is concentrated in the range of -0.02~0.02 mm/m. The results of pure translation and pure rotation RMSE are shown in Table 3. Considering the rotation accuracy of the experimental platform(0.0875 mm/m), the angularity calculation model for the change component of the shaft alignment state is accurate for the deflection state of the shaft system.  Figure 10) show that the offset errors are all less than 0.01 mm. The vertical angularity errors are concentrated in the range of -0.05~0.05 mm/m. The results of panning combined movement RMSE are shown in Table 4.
Considering the parallel accuracy motion of the experimental platform (0.01mm) and the rotational accuracy of the experimental platform (0.0875 mm/m), for the shaft system deviation state, the calculation of the offset deflection of the centering state change component model is accurate  The above mentioned three types of experiments, namely, purely parallel motion conditions, purely rotational conditions and combined translational motion conditions, correspond to the three types of shaft alignment offset, deflection, and deviation respectively. The error of the centering component solution proposed in this paper and the actual maneuvering centering component is less than the accuracy of the translational motion of the experimental bench, and the centering component solution proposed in this paper is accurate.

Conclusion
Aiming at the problem of the change of in the alignment state caused by the deformation of the hull, a research on the online method of the propulsion shaft alignment monitoring adapted to the influence of the hull deformation has been carried out. Some important findings are as follows: a) A new shafting alignment calculation model is established. Based on Euler's rigid body attitude theory, the shaft alignment is calculated by calculating the position-posture of the main shaft and the driven shaft b) A shafting alignment monitoring system adapted to the deformation of the hull is constructed. The laser displacement sensor fixed on the main shaft and driven shaft bracket monitors the shaft alignment status, which is suitable for situations which both the main and driven shafts may have position-posture changes.
c) The model has engineering application value and potential. It can be used in engineering to realize online shafting centering monitoring under the running state of the ship's propulsion shafting. Compensation control for the influence of hull deformation under different operating conditions of the ship is realized. d) There are still some problems with the model in this paper. The shaft alignment model is constructed based on the assumption that the main shaft and driven shaft brackets do not undergo axial deformation and are approximated by small angles. Further research is needed to consider shaft deformation monitoring methods and large-angle issues.