Rapid calculation method suitable for vibration transmission of any complex-section propulsion shafting of naval vessel

Abstract

The invention belongs to the technical field of naval vessel vibration noise, and discloses a rapid calculation method suitable for vibration transmission of a propulsion shafting with any complex section of a naval vessel, which can be used for rapidly modeling the propulsion shafting and rapidly forecasting a vibration transmission calculation result by using the Timoshenko theory and the thought of superposing the thought of multi-section division of the propulsion shaft. According to the method, the characteristics of short propulsion shaft, complex multi-section, variable bearing supporting rigidity, bearing coating and the like are considered, and compared with a current general propulsion shaft system modeling and vibration transmission calculation method, the modeling and calculation efficiency is high, the method is simple and easy to implement, the time cost is low, and the method better conforms to the actual propulsion shaft system condition.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of ship vibration and noise, and particularly relates to a fast calculation method for vibration transmission of a propulsion shafting with an arbitrary complex cross section of a ship. BACKGROUND

[0002] The shafting vibration characteristics of a ship propulsion system, as a main vibration source and sound source path, are one of the objects of focus for the underwater vehicle radiation noise. Traditional ships mostly use long propulsion shafts to transmit power from the middle or front part of the ship to the propeller at the stern, while modern ships mostly use a direct drive arrangement at the stern, with the motor arranged at the stern of the ship body and the pump-jet propeller directly connected to the propulsion motor, effectively reducing the length of the propulsion shaft.

[0003] Current modeling methods for the propulsion shafting include a refined finite element method and a simplified theoretical method. The refined finite element method is complex, time-consuming and slow in calculation, which is not conducive to the rapid evaluation of the shafting vibration characteristics. The simplified theoretical modeling method, such as regarding the propulsion shaft as a uniform Euler-Bernoulli beam, does not consider the complexity of the cross section of the propulsion shaft and the shear deformation; in addition, the bearing is regarded as a three-direction fixed stiffness spring single-point support, ignoring the influence of the bearing span on the propulsion shaft vibration, and not considering the variable stiffness characteristics of the bearing under water lubrication or oil lubrication. Although this simplified modeling method of the propulsion shafting is feasible in studying the general law of the shafting vibration characteristics, it still has a large difference from the real situation in terms of the complex model of the propulsion shaft and the ship body in practical applications, and the calculation results are still not completely reliable.

[0004] In the prior art, patent CN 111749986A discloses a propulsion shaft transverse vibration active control device, which arranges a stern bearing, an intermediate bearing and a thrust bearing in the axial direction of the propulsion shaft, and introduces an electromagnetic bearing assembly, a displacement sensor and a controller on the propulsion shaft to detect and suppress the transverse vibration of the shaft in real time. This scheme mainly focuses on improving the transverse vibration state of the propulsion shaft through active control, so as to reduce the bearing friction noise and vibration transmission.

[0005] However, this prior art scheme still has the following main technical problems: first, the control focus is limited to transverse vibration, and does not cover longitudinal vibration, torsional vibration and vibration coupling transmission under complex cross section and non-uniform support conditions at the same time; second, this scheme focuses on adding control devices to the existing shafting structure, and does not provide a fast vibration transmission calculation method suitable for an arbitrary complex cross section and multi-section variable stiffness support condition, which is difficult to efficiently predict the shafting modal and response in the design stage. SUMMARY

[0006] In view of the problems existing in the prior art, the present application provides a fast calculation method for vibration transmission of a propulsion shafting with an arbitrary complex cross section of a ship.

[0007] The application is implemented by a quick calculation method suitable for vibration transmission of a propulsion shaft system with any complex cross section of a ship, which comprises the following steps:

[0008] Step 1: establishing an equivalent calculation model of the propulsion shaft system; according to a geometric model of the real shaft, bearings are simulated by two or more springs, the spring setting position is determined according to actual measurement; the propeller hub is regarded as a mass point, and its mass property and three-direction inertia moment are considered; a high-elastic coupling is simulated by a spring;

[0009] Step 2: dividing the shaft section; the propulsion shaft is cut at the positions where the cross section size changes and the spring is connected, and is divided into multiple short shafts;

[0010] Step 3: constructing a transmission matrix; the displacement coordination balance equation between adjacent shaft sections is determined, and a deformation transmission matrix of adjacent shaft sections is constructed;

[0011] Step 4: solving the free vibration of the shaft system; the boundary conditions of the start shaft and the end shaft are combined with the deformation coordination connection relationship between the two, a displacement variable equation about the start shaft is constructed, and the mode function constant coefficient of the start shaft is solved; the mode function of each short shaft is solved by using the transmission matrix between the shaft sections and is spliced, and a complete mode function constant coefficient matrix of the propulsion shaft is formed; the free vibration of the shaft system, including the natural frequency and the mode function, is solved according to the complete mode function constant coefficient matrix.

[0012] Further, the free vibration solving of the propulsion shaft comprises: giving an analytic expression of the short thick beam vibration equation according to the Timoshenko theory; determining the boundary conditions of the propulsion shaft system and the displacement coordination conditions between adjacent shaft sections; and a shaft system free vibration solving method.

[0013] Further, the Timoshenko beam free vibration differential equation is:

[0014] Each short shaft of the propulsion shaft can be regarded as a Timoshenko beam, and the differential equation about the deflection and the rotation angle in the local coordinate system can be expressed as:

[0015]

[0016]

[0017] wherein i is the shaft section number, is the mass density; is the cross section area; and are the deflection and the rotation angle about the local coordinate xi and the time t respectively; is the shear correction coefficient, and is generally ; is the Poisson's ratio; is the Young's modulus; is the shear modulus; is the cross-sectional moment of inertia;

[0018] The general solutions of the linear constant coefficient differential equations (1) and (2) can be given by the characteristic equation method, which are specifically:

[0019]

[0020]

[0021]

[0022]

[0023] The expressions of each constant coefficient are respectively:

[0024]

[0025]

[0026]

[0027]

[0028] wherein: and denote the modal shape function of the i-th segment shaft about the local coordinate xi; (rad / s) is the circular frequency; Ci is the integral constant determined by the boundary condition;

[0029] In addition to the bending vibration, the longitudinal vibration and the torsional vibration of each segment shaft also need to be considered, and the vibration control differential equations thereof are respectively:

[0030]

[0031]

[0032] wherein: and are the axial displacement and the torsional angle of the i-th segment shaft about the local coordinate xi and the time t respectively; is the polar moment of inertia of the i-th segment shaft;

[0033] The general solution of the equation and is:

[0034]

[0035]

[0036]

[0037]

[0038] .

[0039] Further, the boundary and connection conditions are:

[0040] (1) The hub end boundary condition

[0041] The end point of the propeller shaft starting section (subscript 1) is connected to the hub, and the inertial force of the hub has corresponding effects on the axial force, torque, bending moment, and shear force. The specific representation is:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048] (2) The coupling end boundary condition

[0049] The end point of the propeller shaft ending section (subscript e) is connected to the propeller motor through the coupling, and the coupling stiffness mainly has corresponding effects on the axial force and shear force. The boundary condition is specifically represented as:

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] (3) Spring connection position

[0056] The spring connection position is regarded as a division interface, and the displacement and force coordination conditions of the two ends of the interface are satisfied. The transverse and vertical vibration boundary conditions are expressed in the form of differential equations as follows:

[0057]

[0058] The above boundary conditions can be written in matrix form as follows:

[0059]

[0060] Wherein:

[0061]

[0062]

[0063] In , the transverse vibration is , and the vertical vibration is ; , , , , , , ,

[0064] Similarly, the force balance conditions of the longitudinal vibration and the torsional vibration on both sides of the spring connection point are as follows:

[0065]

[0066]

[0067] Which can be expressed in matrix form as follows:

[0068]

[0069]

[0070]

[0071]

[0072] .

[0073] Further, the free vibration solving process:

[0074] From the above, the constant coefficient of the vibration shape function of each shaft can be obtained by the constant coefficient of the vibration shape function of shaft 1 through the transfer matrix transformation; therefore, 12 boundary conditions of the hub connecting end and the high carbon coupling connecting end are used to construct 12 equations about the constant coefficient of the vibration shape function of shaft 1, and then the natural frequency and the modal vibration mode of the entire propulsion shaft are solved, and the specific matrix form is expressed as follows:

[0075]

[0076]

[0077]

[0078] wherein: 、 、 、 is the matrix block formed after the introduction of the longitudinal vibration, torsional vibration, transverse vibration and vertical vibration boundary conditions at the hub connecting end, 、 、 、 is the matrix block formed after the introduction of the boundary conditions at the high elastic coupling, which will not be expanded in detail here;

[0079] If the equation has a non-zero solution, then the matrix corresponding to the determinant value is zero, that is:

[0080]

[0081] Therefore, the equation can be used to solve the natural circular frequency and the corresponding natural vibration mode of the propulsion shaft system.

[0082] Step 5, forced vibration solution of shafting; the propeller rotates in the non-uniform flow field to generate unstable hydrodynamic action, the hydrodynamic load is first applied to the hub, and then transmitted to the entire shafting through the propeller shaft; in order to simulate the excitation force, three excitation forces F (Fx, Fy, Fz) are separately applied at the hub connection position, then the shaft axial force balance condition differential equation at the hub center under three excitation forces is respectively changed into:

[0083]

[0084]

[0085]

[0086] Propeller shaft vibration circular frequency control equation Can be rewritten as an equation with excitation force F:

[0087]

[0088] .

[0089] Get the constant matrix C, and bring it into the assumed function equation to obtain the vibration mode of the first section shaft, and then obtain the complete vibration mode of the whole shaft through the transfer matrix, that is, the forced vibration response of the shafting is obtained.

[0090] Another purpose of the present application is to provide a kind of quick calculation system suitable for the vibration transmission of any complex cross section propeller shaft of warship, comprising:

[0091] Equivalent model establishment module, for establishing the equivalent model of propeller shaft calculation;According to the geometric model of real shaft, bearing is simulated with two or more springs, and the spring setting position is actually measured;Hub is regarded as mass point, and its mass attribute and three-direction inertia moment are considered;High elastic coupling is simulated with spring;

[0092] Divide shaft section module, for cutting off propeller shaft at the position of cross section size change and spring connection position, and dividing into multiple sections of shaft;

[0093] Construct transfer matrix module, for determining and establishing displacement coordination balance equation between adjacent shaft sections, and constructing deformation transfer matrix between adjacent shaft sections;

[0094] The shaft vibration mode solving module is used for constructing a displacement variable equation about the starting shaft and solving the vibration mode function of the starting shaft by using the boundary conditions of the starting shaft and the ending shaft and the deformation coordination connection relationship between the two; and the vibration mode of each shaft section is solved and spliced by using the transfer matrix between the shaft sections to form a complete propulsion shaft vibration mode function.

[0095] In combination with the above technical solutions and solved technical problems, the technical solutions to be protected by the application have the following advantages and positive effects:

[0096] The technical solutions of the application have remarkable advantages and positive effects in industrial application. Firstly, in view of the complexity of the geometry structure and support conditions of the ship propulsion shafting, the Timoshenko beam theory and the multi-section division modeling method are adopted, so that the vibration calculation can truly reflect the characteristics of the short shaft, the complex cross section and the multiple support points. The method breaks through the limitations of the traditional Euler-Bernoulli beam model, ensures the accuracy of the calculation results, and adapts to the actual situation that the bearing stiffness changes with the frequency, greatly improving the reliability of numerical prediction.

[0097] The analytical calculation framework of the application organically connects the multi-section short shaft and the elastic support by using the transfer matrix, realizes the unified solution of the arbitrary multi-section variable cross section and the variable stiffness support, and significantly reduces the complexity of modeling and solving while ensuring the calculation accuracy, so that the calculation speed is fast, and the method is particularly suitable for the rapid analysis scene of multiple working conditions and multiple parameters required in the design stage of the ship propulsion system.

[0098] The application can provide a quick reference for the natural frequency and mode prediction of the propulsion shafting in engineering application. Through the response calculation of the hub end and the coupling end, the dangerous frequency range and the key vibration mode characteristics can be effectively identified, which provides prior information for vibration control, vibration reduction design and noise control. This has important value for improving the stealth performance and long-term operation reliability of the ship.

[0099] The method of the application not only meets the needs of scientific research and engineering design, but also is suitable as an analysis tool for teaching and scientific research in the field of ship and ocean engineering. The modeling is simple and the parameters are adjustable, which can provide a quick and intuitive propulsion shaft vibration analysis method for teaching and research personnel in colleges and universities, research personnel and engineering design personnel, and facilitate the popularization and application in experimental teaching, course design and scientific research.

[0100] The present application fills the technical gap in the world in the aspect of complex variable cross-section propulsion shafting analytical modeling and rapid vibration transmission calculation. The prior art often ignores the variability of bearing oil film stiffness and the wrapping effect caused by bearing span, resulting in large deviation of the results. The present application effectively solves this problem through variable stiffness modeling and multi-section short shaft coupling solution, provides a new idea for the design optimization and vibration noise control of ship propulsion system, and has significant engineering application value and commercial transformation potential. BRIEF DESCRIPTION OF DRAWINGS

[0101] Figure 1 is a flow chart of a rapid calculation method for submarine complex cross-section propulsion shafting vibration transmission provided by an embodiment of the present application.

[0102] Figure 2 is a structural block diagram of a rapid calculation system for submarine complex cross-section propulsion shafting vibration transmission provided by an embodiment of the present application.

[0103] Figure 3 is a schematic diagram of a propulsion shafting provided by an embodiment of the present application.

[0104] Figure 4 is a flow chart of a propulsion shafting vibration transmission solution provided by an embodiment of the present application.

[0105] Figure 5 is a propulsion shafting method verification model diagram provided by an embodiment of the present application.

[0106] Figure 6 is a propulsion shaft forced vibration displacement response diagram provided by an embodiment of the present application. DETAILED DESCRIPTION

[0107] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application will be further described in detail below with embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0108] In the prior art system, the propulsion shafting of a submarine and a large ship often has a multi-section variable cross-section structure, accompanied by complex support arrangement and shaft coupling, and its vibration characteristics directly affect the noise level and propulsion efficiency during sailing. However, the traditional finite element modeling method needs to divide the entire long shaft into global mesh, and the calculation scale is large. When facing the change of multi-stage bearing support stiffness and the influence of hub mass inertia, the solution convergence speed is slow, and it is difficult to quickly obtain stable modal analysis results within the engineering design cycle. This problem is particularly prominent in ship stealth and long-period sailing tasks, and has a substantial restriction on industrial application.

[0109] To solve the above problems, the method abstracts complex components such as bearings and couplings into spring and concentrated mass points by establishing an equivalent shafting model, so that the system can be divided into multiple short shafts and coupled by using a transfer matrix. This processing avoids the complex calculation of global finite elements and converts the originally high-dimensional overall problem into a recursive relationship between multiple substructures, greatly improving the calculation efficiency. Especially in the scene where the cross-sectional shape of the shafting changes frequently, the transfer matrix method can adapt to the parameters of each segment flexibly and reduce the dependence on the accuracy of single geometric modeling.

[0110] The present application is based on the Timoshenko beam theory, and each short shaft is regarded as an elastic beam element considering shear deformation and moment of inertia effect. In three degrees of freedom of transverse vibration, longitudinal expansion and torsional vibration, local modal functions can be established by ordinary differential equations. Then, combined with the inertia boundary conditions at the hub end and the stiffness boundary conditions at the coupling end, a complete boundary constraint system is formed. Finally, the modal functions of each segment are spliced by the transfer matrix to form the vibration modal solution of the overall propulsion shafting.

[0111] In the natural vibration analysis, the system uses twelve boundary conditions at the hub and coupling ports to establish a matrix equation, and calculates the characteristic condition that the determinant is zero, so as to solve the natural circular frequency and mode shape of the shafting. Compared with the traditional finite element method, this method can converge to the real mode more quickly, and has a significant advantage in the calculation requirement of complex cross-section propulsion shaft. In the engineering application of ship propulsion system, accurate modal parameters can be provided for the design stage to assist in optimizing the support arrangement and coupling configuration.

[0112] In terms of forced vibration response, the method simulates the hydrodynamic disturbance generated by the propeller in the non-uniform flow field by applying three-direction external excitation at the hub position. Combined with the transfer matrix recursive process, the vibration response of each shaft segment under different frequency excitation can be obtained in real time. This provides a reliable tool for evaluating the vibration transmission path of the propulsion system under specific working conditions and determining the key dangerous frequency range, and can provide a scientific basis for the design of vibration reduction measures.

[0113] The present application not only solves the contradiction between complex shafting modeling and calculation efficiency, but also solves the vibration transmission problem under the conditions of multiple segments, multiple cross-sections and variable stiffness support by using a modular transfer matrix solution method. The principle is clear and has strong scalability, and can be widely applied to the industrial practice of submarine, destroyer, large cargo ship and other ship propulsion systems. It has practical value for reducing navigation noise, improving propulsion reliability and prolonging bearing life.

[0114] As shown in Figure 1 The fast calculation method for vibration transmission of a propulsion shafting with any complex cross-section suitable for a submarine provided by the embodiment of the present application comprises the following steps:

[0115] S101, an equivalent model of a propulsion shaft system is established; bearings are simulated by two or more springs according to a geometric model of a real shaft, the spring setting position is dependent on actual measurement; a hub is regarded as a mass point, and its mass property and three-direction inertia moment are considered; a high-elastic coupling is simulated by a spring;

[0116] S102, the shaft is divided into multiple short shafts; the propulsion shaft is cut at the position where the cross-sectional dimension changes and the spring connection position, and is divided into multiple short shafts;

[0117] S103, a transfer matrix is constructed; displacement coordination balance equations between adjacent shaft segments are determined, and a deformation transfer matrix of adjacent shaft segments is constructed;

[0118] S104, a shaft vibration mode is solved; a displacement variable equation about a starting shaft is constructed by using boundary conditions of the starting shaft and an ending shaft and a deformation coordination connection relationship between the two, and a vibration mode function of the starting shaft is solved; the vibration mode of each short shaft is solved by using the transfer matrix between shaft segments, and is spliced, so that a complete propulsion shaft vibration mode function is formed.

[0119] A propulsion shaft system of an existing warship generally comprises main components such as a propulsion shaft, a hub, a propulsion motor, a thrust bearing, a stern bearing and the like, as shown in (a). Figure 3 The thrust bearing can provide three-direction stiffness dominated by longitudinal stiffness for the shaft, and the stern bearing only provides lateral stiffness and vertical stiffness; the propulsion motor is connected with the end of the propulsion shaft through a high-elastic coupling, and the coupling stiffness is relatively small compared with the bearing. The cross-sectional dimension of the propulsion shaft is variable, as shown in (b), the shaft diameter is non-uniform and variable and can contain a cavity, and is elastically supported by the bearing and the coupling, and the elastic support is simulated by a spring with variable stiffness with frequency in the dynamic modeling, which is more in line with the variable characteristics of the bearing oil film stiffness. Figure 3

[0120] The Timoshenko theory is used to analyze and calculate the vibration characteristics of the propulsion shaft, and the process is gradually performed according to the flow chart in (a). Figure 4

[0121] The propulsion shaft vibration mode function provided by the embodiment of the present application comprises: a short and thick beam vibration equation solution expression given according to the Timoshenko theory; determination of boundary conditions of the propulsion shaft system and displacement coordination conditions between adjacent shaft segments; and a free vibration and forced vibration solving method of the shaft system.

[0122] The Timoshenko beam free vibration differential equation provided by the embodiment of the present application is:

[0123] Each short shaft of the propulsion shaft can be regarded as a Timoshenko beam, and the differential equation about deflection and rotation angle in the local coordinate system can be expressed as:

[0124] ​​

[0125]

[0126] where i is the number of the shaft segment, is the mass density; is the cross-sectional area; and are the deflection and rotation angle with respect to the local coordinate xi and time t, respectively; is the shear correction factor, which is for a general circular cross-section; is the Poisson's ratio; is the Young's modulus; is the shear modulus; is the cross-sectional moment of inertia;

[0127] The general solutions of the linear constant coefficient differential equations (1) and (2) can be given by the eigenvalue equation, which are specifically:

[0128]

[0129]

[0130]

[0131]

[0132] The expressions of each constant coefficient are respectively:

[0133]

[0134]

[0135]

[0136]

[0137] where: and are the mode shape functions of the i-th segment of shaft with respect to the local coordinate xi; (rad / s) is the circular frequency; Ci is the integral constant determined by the boundary conditions;

[0138] In addition to the bending vibration, the longitudinal vibration and torsional vibration of each segment of shaft also need to be considered, and the vibration control differential equations are respectively:

[0139]

[0140]

[0141] wherein: and are the axial displacement and the torsional angle of the i-th segment of shaft with respect to the local coordinate xi and time t, respectively; is the polar moment of inertia of the i-th segment of shaft;

[0142] Similarly, the general solution of equations and are:

[0143]

[0144]

[0145]

[0146]

[0147] .

[0148] The boundary and connection conditions provided by the embodiments of the present application are:

[0149] (1) The hub end boundary condition

[0150] The propeller shaft starting segment (subscript 1) connects the hub at the end point, and the inertial force of the hub has corresponding effects on the axial force, torque, bending moment and shear force, which are specifically expressed as:

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157] (2) Coupling end boundary conditions

[0158] The end point of the propulsion shaft end segment (subscript e) is connected to the propulsion motor through a coupling. The stiffness of the coupling mainly affects the axial force and shear force, and the boundary conditions are specifically expressed as:

[0159]

[0160]

[0161]

[0162]

[0163]

[0164] (3) Spring connection position

[0165] The spring connection position is regarded as a division interface, and the displacement and force coordination conditions are satisfied at both ends of the interface. The transverse and vertical vibration boundary conditions are expressed in the form of differential equations as follows:

[0166]

[0167] The above boundary conditions can be written in matrix form as:

[0168]

[0169] Where:

[0170]

[0171]

[0172] In , when the transverse vibration is , and when the vertical vibration is ; , , , , , , ,

[0173] The force balance conditions of longitudinal vibration and torsional vibration on both sides of the spring connection point are:

[0174]

[0175]

[0176] The matrix form can be expressed as:

[0177]

[0178]

[0179]

[0180]

[0181] .

[0182] The free vibration solving process provided by the embodiment of the application

[0183] From the foregoing, the constant coefficients of the vibration shape functions of the shafts can be obtained by the constant coefficients of the vibration shape functions of the shaft 1 through the transfer matrix transformation; therefore, 12 boundary conditions of the hub connection end and the high-carbon coupling connection end are utilized to construct 12 equations about the constant coefficients of the vibration shape functions of the shaft 1, and then the natural frequency and the modal vibration mode of the entire propeller shaft are solved, and the specific matrix form is expressed as follows:

[0184]

[0185]

[0186]

[0187] Among them: 、 、 、 is the matrix block formed after the introduction of the longitudinal vibration, torsional vibration, transverse vibration and vertical vibration boundary conditions at the hub connection, 、 、 、 is the matrix block formed after the introduction of the boundary conditions at the high-elastic coupling, which will not be expanded here;

[0188] If the non-zero solution exists, then the matrix The corresponding determinant value is zero, that is:

[0189]

[0190] Therefore, the equation is used to solve the natural circular frequency of the propulsion shafting and the corresponding natural vibration mode.

[0191] The forced vibration solving process provided by the embodiment of the present application comprises the following steps:

[0192] The propeller rotates in the non-uniform flow field to generate unstable hydrodynamic force, and the hydrodynamic load is first applied to the hub and then transmitted to the entire shafting through the propulsion shaft; in order to simulate the excitation force, three excitation forces F (Fx, Fy, Fz) are separately applied at the hub connection position, and then the axial force balance condition differential equations of the hub center under the three excitation forces are respectively changed into:

[0193]

[0194]

[0195]

[0196] The propulsion shafting vibration circular frequency control equation can be rewritten as the equation with the excitation force F:

[0197]

[0198] .

[0199] The constant matrix C is obtained, and the vibration mode of the first section shaft is obtained by bringing the constant matrix C into the assumed function equation, and then the complete vibration mode of the entire shaft is obtained through the transfer matrix, that is, the forced vibration response of the shafting is obtained.

[0200] As shown in Figure 2 , the fast calculation system suitable for the vibration transmission of the propulsion shafting with an arbitrary complex section of the submarine provided by the embodiment of the present application comprises:

[0201] ​The equivalent model building module is used to build an equivalent model for propulsion shaft system calculation; based on the geometric model of the real shaft, the bearings are simulated with two or more springs, and the spring positions are determined according to actual conditions; the propeller hub is regarded as a mass point, and its mass properties and triaxial moment of inertia are considered; the high-elasticity coupling is simulated with springs;

[0202] The shaft segmentation module is used to cut the propulsion shaft into multiple short shaft segments at locations where the cross-sectional dimensions change and at spring connection locations.

[0203] The transfer matrix module is used to determine the displacement coordination equilibrium equation between adjacent shaft segments and to construct the deformation transfer matrix between adjacent shaft segments.

[0204] The shaft vibration mode solution module is used to construct the displacement variable equation for the starting shaft and solve for the vibration mode function of the starting shaft by combining the boundary conditions at the ends of the starting shaft and the deformation coordination connection between them; then, the vibration mode function of each short shaft is solved by using the transfer matrix between shaft segments and spliced ​​together to form the complete propulsion shaft vibration mode function.

[0205] Specific implementation of the present invention:

[0206] 1. Case Introduction

[0207] by Figure 5 Taking the computational model as an example, the natural frequencies, mode shapes, and vibration responses of the shafting system are solved. Both the stern bearing and thrust bearing are simulated using two springs with variable stiffness depending on the frequency. The complete propulsion shafting computational model consists of 13 short shaft segments. Each short shaft can be considered as a Timoshenko beam for solving the equations of motion; its outer diameter, inner diameter, and length are shown in Table 1. The thrust bearing and stern bearing are simulated using two variable stiffness springs; their total stiffness values ​​are shown in Table 2. The propeller hub is considered as a point mass with a mass of 420 kg and a moment of inertia Ix = 36 m. 4 Iy = Iz = 20 m 4 .

[0208] Table 1 Propulsion Shaft Dimensions

[0209]

[0210] Table 2 Bearing / Coupling Stiffness Table

[0211]

[0212] 2. Solving for free vibrations

[0213] calculate Figure 3The natural frequencies of the calculation model in (b) up to 410 Hz and the main natural modes are shown in Table 3, and Table 4 shows the first-order longitudinal natural mode and the first five-order vertical bending modes of the propulsion shaft solved by the analytical method. In combination with the natural frequency list and the mode diagram, it can be concluded that there are 18 natural frequencies of the propulsion shaft within 410 Hz, the first-order longitudinal vibration appears at 59.56 Hz, the second-order longitudinal vibration has a natural frequency of 259.98 Hz, and the first-order vertical bending appears at 55.23 Hz.

[0214] Table 3 Natural frequencies within 400 Hz

[0215]

[0216] Table 4 First-order longitudinal vibration and first five-order bending vibration natural modes

[0217]

[0218] 3 Forced vibration solution

[0219] Unit longitudinal (X-direction) excitation force and transverse (Y-direction) excitation force are respectively applied at the hub end, and the vibration displacement response results of the hub excitation origin and the coupling end at 500 Hz are shown in Table 5, and the peak points of the response curve correspond to the natural frequencies. Figure 6

[0220] 4 Case summary

[0221] The above case shows that the analytical method is feasible for the calculation of natural frequencies of the propulsion shaft system and the rapid calculation of vibration transmission, and compared with the conventional finite element modeling method, a series of tedious processes such as meshing, loading setting, and solution calculation are omitted or simplified. The method only needs to manually modify the corresponding parameters and quickly get the calculation results, and has the characteristics of low threshold, high efficiency, and high reliability of calculation results.

[0222] Figure 6 The results shown in Table 5 give the displacement response characteristics of the hub end and the coupling end at different frequencies. From Figure 6 (a), it can be seen that the response amplitude of the hub end is large at low frequencies, and shows obvious resonance peaks at certain natural frequencies. With the increase of frequency, the response gradually decays to below 10^-10 m, but still appears sharp peaks near 200 Hz and 300 Hz, which indicates that when the hub end is excited by the blade hydrodynamic force, the vibration mainly concentrates in the low-order mode interval, and there is a difference between the responses in the transverse and longitudinal directions.

[0223] Figure 6 ​(b) The overall amplitude of the shaft coupling end displacement response is larger than that of the hub end, especially showing stronger vibration energy transmission at low frequencies below 100 Hz. Multiple high-order resonance peaks are distributed in the 200-400 Hz range, with amplitudes significantly higher than the corresponding points of the hub end, indicating that the coupling position is more likely to become a concentrated transmission area of shaft system vibration energy. At the same time, the X and Y direction curves show the phenomenon of mispeaking in multiple frequency bands, reflecting the coupling effect of the shaft system in different directions.

[0224] In summary Figure 6 The response characteristics of the two endpoints can be seen, and the method can effectively capture the influence of different boundary conditions on the vibration energy distribution under the transfer matrix framework. The hub end mainly reflects the input characteristics under hydrodynamic excitation, while the coupling end reflects the overall transmission and amplification of the shaft system. The comparison verifies the effectiveness of the fast calculation method in predicting the response of complex shaft systems, providing a basis for optimizing support arrangement and vibration isolation design in engineering.

[0225] It should be noted that the embodiments of the present application can be realized by hardware, software or a combination of software and hardware. The hardware part can be realized by special logic; the software part can be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or a specially designed hardware. Those skilled in the art can understand that the above devices and methods can be realized by computer executable instructions and / or included in processor control code, such as provided on a carrier medium, such as a magnetic disk, CD or DVD-ROM, a programmable memory, such as a read-only memory (firmware), or a data carrier, such as an optical or electronic signal carrier. The devices of the present application and their modules can be realized by hardware circuits, such as very large scale integrated circuits or gate arrays, semiconductors, such as logic chips, transistors, etc., or programmable hardware devices, such as field programmable gate arrays, programmable logic devices, etc., software executed by various types of processors, or a combination of the above hardware circuit and software, such as firmware.

[0226] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, and any modification, equivalent replacement and improvement within the technical range disclosed by the present application, which is within the spirit and principle of the present application, should be covered within the protection scope of the present application.

Claims

1. A fast calculation method suitable for the vibration transmission of any complex cross-section propulsion shafting of a submarine vessel, characterized in that, The method comprises the following steps: (1) an equivalent calculation model of the propulsion shafting is established, each bearing is simulated by two or more springs, the boss is regarded as a mass point and the mass and three-direction inertia moments are considered, and the high-elastic coupling is represented by a spring model; (2) the shaft body is divided into multiple short shafts at the positions where the cross-sectional size of the propulsion shaft changes and the spring is connected; (3) displacement coordination balance equations between adjacent shaft segments are constructed to form the transfer matrix of transverse, longitudinal and torsional vibration; (4) the natural frequency and mode are obtained by solving the propulsion shaft vibration mode function in combination with the boundary conditions at the boss end and the coupling end; (5) three-direction excitation forces are applied at the boss position, and the forced vibration response of the shafting is calculated in combination with the transfer matrix.

2. The method of claim 1, wherein, The propulsion shaft is divided into multiple short shafts with variable cross sections, and the bearing support regions of each segment have different equivalent stiffnesses and are represented in the form of spatial distribution parameters in the calculation model.

3. The method of claim 1, wherein, The vibration equation of each short shaft is established by using the Timoshenko beam theory, and three types of vibration, i.e., transverse bending, longitudinal stretching and torsion, are described, and the general solution is obtained by using the characteristic equation method.

4. The method of claim 1, wherein, The boundary conditions at the boss end include the axial force, bending moment, shear force and torsional torque constraints corresponding to the boss mass and three-direction inertia moments, and the boundary conditions at the coupling end include the axial force and shear force constraints corresponding to the coupling stiffness.

5. The method of claim 1, wherein, The force and displacement coordination relationship is established at the spring connection position, and the transverse, longitudinal and torsional vibrations are expressed in the form of matrix equations, so that the dynamic responses of adjacent shaft segments are continuous.

6. The method of claim 1, wherein, The natural frequency is obtained by establishing a matrix equation set containing twelve equations, and when the determinant of the coefficient matrix is zero, there is a non-zero solution, and then the natural circular frequency and mode function of the propulsion shaft are obtained.

7. The method of claim 1, wherein, The excitation forces in three coordinate directions are applied at the boss, and the response amplitude, phase and vibration mode distribution of the shafting under the action of external excitation are calculated in combination with the transfer matrix equation.

8. The method of claim 1, wherein, The fast calculation process comprises five steps of signal acquisition and preprocessing, signal segmentation and window function weighting, time-frequency feature extraction and modal identification, phase coordination analysis and vibration mode reconstruction, and is used to verify the consistency of the calculation results and the measured signals.

9. A fast computational system suitable for the vibration transmission of any complex cross-section propulsion shafting of a submarine vessel, characterized by, It comprises: an equivalent model establishment module, a shaft segment division module, a transfer matrix construction module, a shaft vibration mode solving module and a signal processing verification module; The equivalent model establishment module is used to set the number and arrangement position of the springs according to the geometric structure of the propulsion shaft; The shaft segment division module is used to divide the shaft body at the positions where the cross-sectional size changes and the spring is connected; The transfer matrix construction module is used to automatically generate the coupled matrix equations in the transverse, longitudinal and torsional directions; The shaft vibration mode solving module is used to solve the natural frequency and mode function in combination with the boundary conditions; The signal processing verification module is used to obtain the measured vibration signals and perform frequency spectrum comparison and vibration mode reconstruction.

10. The system of claim 9, wherein, The shaft vibration mode solving module connects the mode functions of each short shaft in a splicing manner to form a complete propulsion shaft mode, and outputs the natural frequency, response amplitude and three-dimensional vibration mode curve.

Images