Ship diesel engine shafting longitudinal-torsional coupling vibration calculation method

Abstract

The invention provides a marine diesel engine shafting longitudinal-torsional coupling vibration calculation method. The method specifically comprises the following steps: S1, calculating crankshaft longitudinal-torsional coupling rigidity; s2, calculating torsional vibration excitation at the propeller by using a CFD method; s3, establishing a ship propulsion shafting coupling free vibration kinetic equation through the calculated longitudinal-torsional coupling stiffness; s4, calculating a longitudinal-torsional coupling inherent frequency and a vibration mode of the ship propulsion shafting through a coupling free vibration kinetic equation of the ship propulsion shafting; and S5, substituting the propeller excitation calculated in the step S2 into the ship propulsion shafting coupling forced vibration kinetic equation to calculate the longitudinal-torsional coupling forced vibration response of the ship propulsion shafting. According to the marine diesel engine shafting longitudinal-torsional coupling vibration calculation method, the crankshaft longitudinal-torsional coupling rigidity is calculated based on a material mechanical deformation energy method, and related exciting force considering the crankshaft longitudinal-torsional coupling effect is obtained by combining related formulas of marine diesel engine shafting dynamics; and finally, ship shafting longitudinal-torsional coupling vibration inherent characteristics and ship shafting longitudinal-torsional coupling forced vibration response are obtained through calculation.

Description

Technical Field

[0001] The invention belongs to the technical field of ship vibration, and in particular relates to a method for calculating longitudinal-torsional coupled vibration of a ship diesel engine shaft system. Background Art

[0002] In the 1960s, Dort and other scholars studied the torsional-axial coupled vibration based on Dorey's theory, and proposed that the inertial coupled vibration generated by the propeller's additional water mass and the stiffness coupled vibration generated by the crankshaft are the two main forms of torsional-axial coupled vibration of the ship's propulsion system (【1】Dort DV, Visser N J. Crankshaft coupled free torsional-axial vibrations of a ship's propulsion system[J]. International Shipbuilding Progress, 1963, 10(109): 333-350.); Linden calculated the torsional-axial coupled free vibration of the ship's propulsion shaft system based on the torsional-axial coupled vibration theory proposed by Dort (【2】Linden VD, Hart HH, Dolfin E R. Torsional-axial vibrations of a ship's propulsion system[J]. International Shipbuilding Progress, 1963, 10(109): 333-350.). Progress, 1969, 16 (173): 16-26.); Parsons analyzed the torsional-axial coupling vibration of the ship propulsion shaft system caused by the propeller, and concluded that the propeller coupling effect has little effect on the natural frequency of the shaft system, but will greatly change the vibration mode and forced vibration response of the system (【3】Parsons MGMode coupling in torsional and longitudinal shafting vibrations[J]. Marine Technology, 1983, 20 (3): 257-271.); Homori et al. of Japan NK Classification Society used the Dort torsional-axial coupling vibration theory as the basis and used finite element technology for calculation and analysis (【4】Homori S, Kamata M, Sasaki YComprehensive evaluation of the vibration and strength of long-stroke diesel engine crank shafting[J]. 19th International Congress on Combustion Engines CIMAC, 1991, D60: 1-20.); Jakobsen et al. of MAN B&W simplified the crank into a spring-damper system, used a finite element model to determine the torsional, axial and torsional-axial coupling stiffness of the half crank, and used the state space method to calculate the free vibration characteristics and forced vibration response of the shaft system (【5】Jakobsen SB. Coupling axial and torsional vibration calculations on long-stroke diesel engines[J]. SNAME Transactions, 1991, 99Q: 405-4I9.【6】Jakobsen SB, Bryndum L, Fukuda T, et al. Axial vibrations of crankshafts of long-stroke dieselengines, and the control of their influence on crankshaft strength and hullvibration conditions[J]. 19th International Congress on Combustion Engines CIMAC, 1991, D61: 1-14.); Li Bozhong et al. analyzed the measured data of the engine shaft systems of several cargo ships and found that the torsional vibration caused the axial vibration. They designed a single crank model for experiment and concluded that the crank angle and axial deformation rate were linearly related (【7】Song Xigeng, Song Tianxiang, Li Bozhong. Coupled vibration of piston engine shaft system [J]. Journal of Dalian University of Technology, 1989, 29(6): 675-680.); Zhang Zhihua, Zhang Hongtian, Liu Zhigang et al. quantized the actual shaft system and established a spring-mass system for calculating the longitudinal-torsional coupled vibration of the ship propulsion shaft system (【8】Zhang Hongtian, Zhang Zhihua, Wang Lin et al. Calculation and analysis of longitudinal-torsional coupled vibration of ship shaft system [J]. Ship Engineering, 1994, (5): 36-42). .

[0003] In summary, in the field of diesel engine longitudinal-torsional coupled vibration simulation, there are many research results purely from the coupling mechanism aspect. However, when it comes to coupling calculation, the coupling stiffness is often extracted by assuming a coupling coefficient or by finite element calculation commercial software without giving a calculation method. Summary of the invention

[0004] In view of the above problems, the present invention provides a method for calculating the longitudinal-torsional coupled vibration of a ship diesel engine shaft system. The longitudinal-torsional coupled stiffness of the crankshaft is calculated based on the deformation energy method of material mechanics, and the relevant formulas of the propeller excitation calculated by the CFD method and the dynamics of the ship diesel engine shaft system are combined to obtain the relevant excitation force considering the longitudinal-torsional coupling effect of the crankshaft. Finally, the inherent characteristics of the longitudinal-torsional coupled vibration of the ship shaft system and the forced vibration response of the longitudinal-torsional coupled vibration of the ship shaft system are calculated.

[0005] To achieve the above object, the present invention adopts the following technical solution:

[0006] A method for calculating longitudinal-torsional coupled vibration of a ship diesel engine shaft system, comprising the following steps:

[0007] S1. Calculate the crankshaft longitudinal torsional coupling stiffness;

[0008] S2. Calculate the torsional vibration excitation at the propeller using CFD method;

[0009] S3. Establish the coupled free vibration dynamic equation of the ship propulsion shaft system through the calculated longitudinal-torsional coupling stiffness;

[0010] S4. Calculate the longitudinal-torsional coupled natural frequency and vibration mode of the ship propulsion shaft system through the coupled free vibration dynamic equation of the ship propulsion shaft system;

[0011] S5. The longitudinal-torsional coupled forced vibration response of the ship propulsion shafting is calculated by bringing the torsional vibration excitation at the propeller calculated in S2 into the ship propulsion shafting coupled forced vibration dynamics equation.

[0012] Furthermore, the S1 specifically includes the following steps:

[0013] S11. In order to obtain the parameters required for the deformation calculation of the rod in material mechanics, the crankshaft model is simplified by the length and diameter of the main journal and crank pin and the cross-sectional information of the crank arm. The main journal and crank pin are simplified into cylindrical beam units, and the crank arm is simplified into a rectangular beam unit. According to the simplified crank model, the crank angle is set to θ; the cross-sectional diameters of the equivalent space beam units of the main journal and crank pin are d1 and d3, respectively, the lengths are 2L1 and L3, respectively, the cross-sectional areas are A1 and A3, respectively, and the moments of inertia and polar moments of inertia are I1, I3, I P1 , I P3 ; The length of the crank arm equivalent space beam unit is L2, the length and width of the section are h and b respectively, the cross-sectional area is A2, and the moment of inertia is The equilibrium equation of the crankshaft model hyperstatic system is:

[0014] ∑F i (x) = F x +F ax +F bx =0;

[0015] ∑F i (y) = 0;

[0016] ∑F i (z) = F z +F az +F bz =0;

[0017]

[0018] ∑M0(y)=M y -1-F ax L2-F bx L2=0;

[0019]

[0020] where F ax , F az , F bx and F bz F is the support reaction force generated by the bearing limit function. x , F z is the reaction force of the fixed end support, M x , M y and M z is the three-phase balance torque at the center of the crank pin;

[0021] S12. Because there are unknown forces and unknown moments in the previous step, the main journal will not be laterally offset due to the limit effect in the actual operation of the diesel engine, and the lateral and vertical displacements are zero. Then, the unknown forces and moments can be solved by supplementing the deformation coordination conditions. The deformation coordination conditions are as follows:

[0022] δ ax =δ bx =δ az =δ bz

[0023] where δ ax , δ az , δ bx and δ bz They are respectively the lateral displacement close to the fixed shaft end, the displacement away from the fixed shaft end, and the vertical displacement of the main journal; the expression is solved by using Moore's theorem in the deformation energy method in material mechanics:

[0024]

[0025]

[0026]

[0027] , due to the limitation of the bearing ax, δ az , δ bx and δ bz The value of is zero, and then the support reaction force F at each bearing can be solved by the deformation coordination condition simultaneous equations ax 、F bx 、F az 、F bz And the force and moment at the fixed end, then use Moore's theorem to apply unit axial force and unit torque to the crankshaft to solve the longitudinal displacement θ a and torsional displacement x b :

[0028]

[0029]

[0030] Calculated torsional displacement θ at point a a Multiply by 2 to get the torsional displacement flexibility, and calculate the longitudinal displacement x of point b. b It is the longitudinal-torsional coupling flexibility;

[0031] S13. The axial displacement generated under the action of unit axial force is the axial flexibility, and the torsion angle generated under the action of unit torque is the torsion flexibility. Both are parameters in the absolute sense, but the longitudinal-torsion coupling flexibility is a relative parameter. Therefore, in the process of converting flexibility into stiffness, the traditional method of directly taking the inverse of flexibility cannot be used. The inversion must be obtained in matrix form. The specific process is as follows:

[0032]

[0033] Where N is the axial force acting on the main journal, M is the torque acting on the main journal, u0 is the axial displacement caused by the axial force, θ a is the torsion angle caused by torque, x b is the longitudinal-torsional coupling flexibility, and the inversion of the above matrix is ​​obtained:

[0034]

[0035] Among them, K X is the longitudinal stiffness, K T is the torsional stiffness, K XT is the longitudinal-torsional coupling stiffness.

[0036] Furthermore, the S2 specifically includes the following steps:

[0037] S21. According to the accuracy requirement, select 20%, 40%, 60%, 80%, and 100% working conditions from 20% to 100%, and divide the flow domain based on the propeller model under each selected working condition. Divide the cylindrical flow domain with a distance of ten times the propeller diameter and a diameter of six times the propeller diameter into a dynamic domain, and divide the flow domain outside the dynamic domain but still having a greater impact on the propeller into a static domain, thereby generating the corresponding propeller surface mesh, fluid domain surface mesh, and flow domain body mesh to obtain the flow field model;

[0038] S22. Select the SSTkω turbulence model through CFD, set the boundary conditions and the required algorithm, and solve the propeller pulsation pressure under various working conditions;

[0039] S23. Project the pressure of each blade unit onto a plane perpendicular to the axis, and then decompose it into the pressure perpendicular to the line connecting the point of action and the axis and the pressure in the direction of the line connecting the point of action and the axis, then multiply the pressure perpendicular to the line connecting the point of action and the axis with the length of the line to obtain the excitation torque of each blade unit in the plane perpendicular to the axis, and then perform vector summation on the excitation torque to obtain the reduced-order excitation torque generated by the propeller in the torsion direction under each working condition; based on the solved working conditions, perform linear interpolation on the excitation torque of several unsolved working conditions between every two adjacent known working conditions to obtain the reduced-order excitation torque of the propeller under all working conditions;

[0040] S24. The propeller reduced-order excitation torque under all working conditions is directly added to the blade frequency term and the blade-frequency-doubled term of the propeller excitation torque coefficient matrix to obtain the propeller excitation torque coefficient matrix, so as to take it into account in the torsional vibration of the low-speed machine shaft system. Based on the phase matching relationship between the propeller reduced-order excitation and the shaft system structure, the propeller excitation torque coefficient matrix is ​​formed, and then the matrix is ​​loaded to the concentrated inertia where the propeller is located, so as to construct a low-speed machine shaft system torsional vibration coupling model considering the propeller reduced-order excitation;

[0041] S25. Load the obtained propeller reduced-order excitation torque into the initial propeller excitation torque coefficient matrix, that is, the blade frequency term and the blade frequency double term in the zero vector of 1× harmonic order, so as to obtain the propeller excitation torque coefficient matrix.

[0042] Furthermore, the S3 specifically includes the following steps:

[0043] S31. The longitudinal-torsion coupling stiffness obtained in S1 is used as the stiffness coefficient of the mutual influence between torsional vibration and longitudinal vibration at the crankshaft. The longitudinal stiffness matrix and the torsional stiffness matrix are listed as diagonal matrices. The longitudinal-torsion coupling stiffness is substituted into the longitudinal stiffness matrix and the torsional stiffness matrix at the bend. The longitudinal-torsion coupling stiffness matrix formed by coupling is as follows:

[0044]

[0045] Where K is the coupling stiffness matrix, α n-1,n is the axial stiffness, β n-1,n is the torsional stiffness;

[0046] S32. The lumped parameter method is used to couple the mutually independent longitudinal vibration system and torsional vibration system into the longitudinal torsional coupling free vibration dynamics equation of the ship propulsion shaft system through the longitudinal torsional coupling stiffness matrix, as follows:

[0047]

[0048] Where: δ is the column vector of the synthesis of angular displacement and axial displacement, and J is the system's moment of inertia and mass synthesis matrix.

[0049] Furthermore, the S4 specifically includes the following steps: substituting the mass matrix and the longitudinal-torsional coupling stiffness matrix of the ship propulsion shaft system into the ship propulsion shaft system coupled vibration dynamics equation to solve its eigenvalue and eigenvector, the square root of the eigenvalue is the natural frequency, the solved displacement of each concentrated mass point is divided by the specified concentrated mass point displacement to form an amplitude ratio, and the amplitude ratios are arranged in order and plotted into a broken line, which is the vibration mode.

[0050] Furthermore, the S5 specifically includes the following steps:

[0051] S51. The excitation force generated by the ship diesel engine shaft system due to the change of gas pressure is obtained through the diesel engine shaft system piston diameter, stroke, reciprocating mass and simple harmonic coefficient table provided by the manufacturer, and the excitation force is input into the ship propulsion shaft system coupled vibration dynamics equation for calculation;

[0052] S52. The excitation force calculated by inputting the torsional vibration excitation at the propeller calculated by S2 into the coupled vibration dynamic equation of the ship propulsion shaft system;

[0053] S53. Calculate the forced vibration response of the ship diesel engine shaft system based on the obtained excitation force.

[0054] Furthermore, in S51, the calculation formula of the excitation force is:

[0055]

[0056] Among them, P g is the gas pressure per unit area of ​​the piston; α is the crankshaft angle; β is the connecting rod swing angle.

[0057] Furthermore, in the S53, the calculation method of the forced vibration response of the ship diesel engine shaft system is to bring the excitation force into the longitudinal torsional coupling forced vibration dynamics equation, and the longitudinal torsional coupling forced vibration dynamics equation is as follows:

[0058]

[0059] Among them: [J]-----the composite matrix of the moment of inertia and mass of the equivalent system, [K]-----the longitudinal-torsional coupling stiffness matrix of the equivalent system, [C]-----the coupling damping matrix of the equivalent system, {T}-----the composite column vector of the excitation torque and force of the equivalent system, {δ}-----the composite column vector of the angular displacement and axial displacement of the equivalent system.

[0060] The present invention is suitable for predicting and simulating the longitudinal vibration of a ship propulsion shaft system. This patent first establishes a crankshaft longitudinal torsional coupling stiffness calculation model, instead of introducing the longitudinal torsional coupling stiffness coefficient in the traditional method to make assumptions about the coupling stiffness, nor is it directly extracted through commercial software such as Ansys, but is obtained through calculation; based on the calculation of the longitudinal torsional coupling stiffness, the present invention introduces it into the longitudinal torsional coupling stiffness matrix to link the torsional excitation with the longitudinal vibration response, establishes the longitudinal torsional coupling dynamic equation of the ship propulsion shaft system, and introduces the torsional vibration excitation generated by the fluid-solid coupling at the propeller to calculate the inherent characteristics and forced vibration response of the longitudinal torsional coupling of the ship propulsion shaft system. This patent provides a calculation method considering the inherent characteristics and forced vibration response of the longitudinal torsional coupling vibration of the internal combustion engine shaft system, and is verified by the report data provided by the actual ship test.

[0061] The present invention takes into account the influence of the torsional vibration of the diesel engine shaft system on the longitudinal vibration response and makes certain corrections to the longitudinal vibration calculation; 2. It uses MATLAB programming and calculation, which has the characteristics of fast calculation, easy to use, and strong promotion compared to finite element software such as Ansys. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is the simplified force diagram of the crankshaft model.

[0063] Figure 2 It is a schematic diagram of the longitudinal-torsional coupled vibration equivalent system of a low-speed diesel engine.

[0064] Figure 3 It is a flowchart of the calculation of longitudinal-torsional coupled free vibration of ship propulsion shafting.

[0065] Figure 4 It is a flowchart of the calculation of longitudinal-torsional coupled forced vibration of ship propulsion shafting.

[0066] Figure 5 It is a comparison between the calculation method described in the present invention and the inherent characteristics of the actual ship test report.

[0067] Figure 6 The calculation method described in the present invention is compared with the forced vibration response of the actual ship test report. DETAILED DESCRIPTION

[0068] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0069] like Figures 1 to 4 As shown, a method for calculating longitudinal-torsional coupled vibration of a ship diesel engine shaft system specifically comprises the following steps:

[0070] S1. Calculate the crankshaft longitudinal torsional coupling stiffness;

[0071] S2. Calculate the torsional vibration excitation at the propeller using CFD method;

[0072] S3. Establish the coupled free vibration dynamic equation of the ship propulsion shaft system through the calculated longitudinal-torsional coupling stiffness;

[0073] S4. Calculate the longitudinal-torsional coupled natural frequency and vibration mode of the ship propulsion shaft system through the coupled free vibration dynamic equation of the ship propulsion shaft system;

[0074] S5. The longitudinal-torsional coupled forced vibration response of the ship propulsion shafting is calculated by bringing the torsional vibration excitation at the propeller calculated in S2 into the ship propulsion shafting coupled forced vibration dynamics equation.

[0075] The S1 specifically includes the following steps:

[0076] S11. In order to obtain the parameters required for the deformation calculation of the rod in material mechanics, the crankshaft model is simplified by the length and diameter of the main journal and crank pin and the cross-sectional information of the crank arm. The main journal and crank pin are simplified into cylindrical beam units, and the crank arm is simplified into a rectangular beam unit. According to the simplified crank model, the crank angle is set to θ; the cross-sectional diameters of the equivalent space beam units of the main journal and crank pin are d1 and d3, respectively, the lengths are 2L1 and L3, respectively, the cross-sectional areas are A1 and A3, respectively, and the moments of inertia and polar moments of inertia are I1, I3, I P1 , I P3 ; The length of the crank arm equivalent space beam unit is L2, the length and width of the section are h and b respectively, the cross-sectional area is A2, and the moment of inertia is The equilibrium equation of the crankshaft model hyperstatic system is:

[0077] ∑F i (x) = F x +F ax +F bx =0;

[0078] ∑F i (y) = 0;

[0079] ∑F i (z) = F z +F az +F bz =0;

[0080]

[0081] ∑M0(y)=M y-1-F ax L2-F bx L2=0;

[0082]

[0083] where F ax , F az , F bx and F bz F is the support reaction force generated by the bearing limit function. x , F z is the reaction force of the fixed end support, M x , M y and M z is the three-phase balance torque at the center of the crank pin;

[0084] S12. Because there are unknown forces and unknown moments in the previous step, the main journal will not be laterally offset due to the limit effect in the actual operation of the diesel engine, and the lateral and vertical displacements are zero. Then, the unknown forces and moments can be solved by supplementing the deformation coordination conditions. The deformation coordination conditions are as follows:

[0085] δ ax =δ bx =δ az =δ bz

[0086] where δ ax , δ az , δ bx and δ bz They are respectively the lateral displacement close to the fixed shaft end, the displacement away from the fixed shaft end, and the vertical displacement of the main journal; the expression is solved by using Moore's theorem in the deformation energy method in material mechanics:

[0087]

[0088]

[0089]

[0090] , due to the limitation of the bearing ax , δ az , δ bx and δ bz The value of is zero, and then the support reaction force F at each bearing can be solved by the deformation coordination condition simultaneous equations ax 、F bx 、F az 、F bz And the force and moment at the fixed end, then use Moore's theorem to apply unit axial force and unit torque to the crankshaft to solve the longitudinal displacement θ a and torsional displacement x b:

[0091]

[0092]

[0093] Calculated torsional displacement θ at point a a Multiply by 2 to get the torsional displacement flexibility, and calculate the longitudinal displacement x of point b. b It is the longitudinal-torsional coupling flexibility;

[0094] S13. The axial displacement generated under the action of unit axial force is the axial flexibility, and the torsion angle generated under the action of unit torque is the torsion flexibility. Both are parameters in the absolute sense, but the longitudinal-torsion coupling flexibility is a relative parameter. Therefore, in the process of converting flexibility into stiffness, the traditional method of directly taking the inverse of flexibility cannot be used. The inversion must be obtained in matrix form. The specific process is as follows:

[0095]

[0096] Where N is the axial force acting on the main journal, M is the torque acting on the main journal, u0 is the axial displacement caused by the axial force, θ a is the torsion angle caused by torque, x b is the longitudinal-torsional coupling flexibility, and the inversion of the above matrix is ​​obtained:

[0097]

[0098] Among them, K X is the longitudinal stiffness, K T is the torsional stiffness, K XT is the longitudinal-torsional coupling stiffness.

[0099] Furthermore, the S2 specifically includes the following steps:

[0100] S21. According to the accuracy requirement, select 20%, 40%, 60%, 80%, and 100% working conditions from 20% to 100%, and divide the flow domain based on the propeller model under each selected working condition. Divide the cylindrical flow domain with a distance of ten times the propeller diameter and a diameter of six times the propeller diameter into a dynamic domain, and divide the flow domain outside the dynamic domain but still having a greater impact on the propeller into a static domain, thereby generating the corresponding propeller surface mesh, fluid domain surface mesh, and flow domain body mesh to obtain the flow field model;

[0101] S22. Select the SSTkω turbulence model through CFD, set the boundary conditions and the required algorithm, and solve the propeller pulsation pressure under various working conditions;

[0102] S23. Project the pressure of each blade unit onto a plane perpendicular to the axis, and then decompose it into the pressure perpendicular to the line connecting the point of action and the axis and the pressure in the direction of the line connecting the point of action and the axis, then multiply the pressure perpendicular to the line connecting the point of action and the axis with the length of the line to obtain the excitation torque of each blade unit in the plane perpendicular to the axis, and then perform vector summation on the excitation torque to obtain the reduced-order excitation torque generated by the propeller in the torsion direction under each working condition; based on the solved working conditions, perform linear interpolation on the excitation torque of several unsolved working conditions between every two adjacent known working conditions to obtain the reduced-order excitation torque of the propeller under all working conditions;

[0103] S24. The propeller reduced-order excitation torque under all working conditions is directly added to the blade frequency term and the blade-frequency-doubled term of the propeller excitation torque coefficient matrix to obtain the propeller excitation torque coefficient matrix, so as to take it into account in the torsional vibration of the low-speed machine shaft system. Based on the phase matching relationship between the propeller reduced-order excitation and the shaft system structure, the propeller excitation torque coefficient matrix is ​​formed, and then the matrix is ​​loaded to the concentrated inertia where the propeller is located, so as to construct a low-speed machine shaft system torsional vibration coupling model considering the propeller reduced-order excitation;

[0104] S25. Load the obtained propeller reduced-order excitation torque into the initial propeller excitation torque coefficient matrix, that is, the blade frequency term and the blade frequency double term in the zero vector of 1× harmonic order, so as to obtain the propeller excitation torque coefficient matrix.

[0105] The S3 specifically includes the following steps:

[0106] S31. The longitudinal-torsion coupling stiffness obtained in S1 is used as the stiffness coefficient of the mutual influence between torsional vibration and longitudinal vibration at the crankshaft. The longitudinal stiffness matrix and the torsional stiffness matrix are listed as diagonal matrices. The longitudinal-torsion coupling stiffness is substituted into the longitudinal stiffness matrix and the torsional stiffness matrix at the bend. The longitudinal-torsion coupling stiffness matrix formed by coupling is as follows:

[0107]

[0108] Where K is the coupling stiffness matrix, α n-1,n is the axial stiffness, β n-1,n is the torsional stiffness;

[0109] S32. The lumped parameter method is used to couple the mutually independent longitudinal vibration system and torsional vibration system into the longitudinal torsional coupling free vibration dynamics equation of the ship propulsion shaft system through the longitudinal torsional coupling stiffness matrix, as follows:

[0110]

[0111] Where: δ is the column vector of the synthesis of angular displacement and axial displacement, and J is the system's moment of inertia and mass synthesis matrix.

[0112] The S4 specifically includes the following steps: substituting the mass matrix and the longitudinal-torsional coupling stiffness matrix of the ship propulsion shaft system into the ship propulsion shaft system coupled vibration dynamics equation to solve its eigenvalue and eigenvector, the square root of the eigenvalue is the natural frequency, the solved displacement of each concentrated mass point is divided by the specified concentrated mass point displacement to form an amplitude ratio, and the amplitude ratios are arranged in order and plotted into a broken line to form a vibration mode.

[0113] The S5 specifically includes the following steps:

[0114] S51. The excitation force generated by the ship diesel engine shaft system due to the change of gas pressure is obtained through the diesel engine shaft system piston diameter, stroke, reciprocating mass and simple harmonic coefficient table provided by the manufacturer, and the excitation force is input into the ship propulsion shaft system coupled vibration dynamics equation for calculation;

[0115] S52. The excitation force calculated by inputting the torsional vibration excitation at the propeller calculated by S2 into the coupled vibration dynamic equation of the ship propulsion shaft system;

[0116] S53. Calculate the forced vibration response of the ship diesel engine shaft system based on the obtained excitation force.

[0117] Wherein, in said S51, the calculation formula of the excitation force is:

[0118]

[0119] Among them, P g is the gas pressure per unit area of ​​the piston; α is the crankshaft angle; β is the connecting rod swing angle.

[0120] Furthermore, in the S53, the calculation method of the forced vibration response of the ship diesel engine shaft system is to bring the excitation force into the longitudinal torsional coupling forced vibration dynamics equation, and the longitudinal torsional coupling forced vibration dynamics equation is as follows:

[0121]

[0122] Among them: [J]-----the composite matrix of the moment of inertia and mass of the equivalent system, [K]-----the longitudinal-torsional coupling stiffness matrix of the equivalent system, [C]-----the coupling damping matrix of the equivalent system, {T}-----the composite column vector of the excitation torque and force of the equivalent system, {δ}-----the composite column vector of the angular displacement and axial displacement of the equivalent system.

[0123] Combination Figure 1 , Figure 2, based on the crankshaft information given in the drawing, the crankshaft geometric model is simplified (the main journal and crank pin are simplified to cylindrical beam units, and the crank arm is simplified to a rectangular beam unit). Based on the deformation energy method in material mechanics, unit axial force and torque are applied to the end of the main journal respectively, and the longitudinal-torsional coupling flexibility is calculated by the combined rod deformation energy method. The flexibility matrix is ​​inverted to solve the longitudinal-torsional coupling stiffness; based on the longitudinal-torsional coupling mechanism of the diesel engine shaft system, the diesel engine longitudinal-torsional coupling vibration equivalent system is established, such as Figure 2 As shown, the longitudinal stiffness matrix of the ship propulsion shaft system is coupled with the crankshaft part in the torsional stiffness matrix through the longitudinal-torsional coupling stiffness to form a longitudinal-torsional coupling stiffness matrix.

[0124] Combination Figure 3 , Figure 4 , the natural frequency and vibration mode are solved through the mass matrix and stiffness matrix; then the excitation force of the system is obtained through the relevant parameters and simple harmonic coefficient table provided by the manufacturer to solve the forced vibration response.

[0125] Combination Figure 5 , Figure 6 Based on the traditional calculation model and the model proposed this time, the inherent characteristics and forced vibration response of the simulation conditions and the actual ship test report are basically consistent, that is, the error of the inherent frequency is less than 5%, and the error of the forced vibration response and the actual ship test report is no more than 20%. It can be seen that considering the longitudinal torsional coupling of the diesel engine shaft system, the excitation state is consistent with the actual state of the ship propulsion shaft system, and the final prediction result is more consistent with the actual value than the traditional model.

[0126] Those skilled in the art should understand that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calculating longitudinal-torsional coupled vibration of a ship diesel engine shaft system, characterized in that: The specific steps include: S1. Calculate the crankshaft longitudinal-torsional coupling stiffness; S2. Calculate the torsional vibration excitation at the propeller using CFD method; S3. Establish the coupled free vibration dynamic equation of the ship propulsion shaft system through the calculated longitudinal-torsional coupling stiffness; S4. Calculate the longitudinal-torsional coupled natural frequency and vibration mode of the ship propulsion shaft system through the coupled free vibration dynamic equation of the ship propulsion shaft system; S5. The longitudinal-torsional coupled forced vibration response of the ship propulsion shafting is calculated by bringing the torsional vibration excitation at the propeller calculated in S2 into the ship propulsion shafting coupled forced vibration dynamics equation.

2. A method for calculating longitudinal-torsional coupled vibration of a ship diesel engine shaft system according to claim 1, characterized in that: The S1 specifically includes the following steps: S11. In order to obtain the parameters required for the deformation calculation of the rod in material mechanics, the crankshaft model is simplified by the length and diameter of the main journal and crank pin and the cross-sectional information of the crank arm. The main journal and crank pin are simplified into cylindrical beam units, and the crank arm is simplified into a rectangular beam unit. According to the simplified crank model, the crank angle is set to θ; the cross-sectional diameters of the equivalent space beam units of the main journal and crank pin are d1 and d3, respectively, the lengths are 2L1 and L3, respectively, the cross-sectional areas are A1 and A3, respectively, and the moments of inertia and polar moments of inertia are I1, I3, I P1 , I P3 ; The length of the crank arm equivalent space beam unit is L2, the length and width of the section are h and b respectively, the cross-sectional area is A2, and the moment of inertia is The equilibrium equation of the crankshaft model hyperstatic system is: ∑F i (x)=F x +F ax +F bx =0; ∑F i (y)=0; ∑F i (z)=F z +F az +F bz =0; ∑M0(y)=M y -1-F ax L2-F bx L2=0; Among them, F ax , F az , F bx and F bz F is the support reaction force generated by the bearing limit function. x , F z is the reaction force of the fixed end support, M x , M y and M z is the three-phase balanced torque at the center of the crank pin; S12. Because there are unknown forces and unknown moments in the previous step, the main journal will not be laterally offset due to the limit effect in the actual operation of the diesel engine, and the lateral and vertical displacements are zero. Then, the unknown forces and moments can be solved by supplementing the deformation coordination conditions. The deformation coordination conditions are as follows: δ ax =δ bx =δ az =δ bz where δ ax , δ az , δ bx and δ bz They are respectively the lateral displacement close to the fixed shaft end, the displacement away from the fixed shaft end, and the vertical displacement of the main journal; the expression is solved by using Moore's theorem in the deformation energy method in material mechanics: Due to the limitation of the bearing ax , δ az , δ bx and δ bz The value of is zero, and then the support reaction force F at each bearing can be solved by the deformation coordination condition simultaneous equations ax 、F bx 、F az 、F bz And the force and moment at the fixed end, then use Moore's theorem to apply unit axial force and unit torque to the crankshaft to solve the longitudinal displacement θ a and torsional displacement x b : Calculated torsional displacement θ at point a a Multiply by 2 to get the torsional displacement flexibility, and calculate the longitudinal displacement x of point b. b That is, the longitudinal-torsion coupling flexibility; S13. The axial displacement generated under the unit axial force is the axial flexibility, and the torsion angle generated under the unit torque is the torsion flexibility. Both are parameters in the absolute sense, but the longitudinal-torsion coupling flexibility is a relative parameter. Therefore, in the process of converting flexibility into stiffness, the traditional method of directly taking the inverse of flexibility cannot be used. The inversion must be obtained in matrix form. The specific process is as follows: Where N is the axial force acting on the main journal, M is the torque acting on the main journal, u0 is the axial displacement caused by the axial force, θ a is the torsion angle caused by torque, x b is the longitudinal-torsional coupling flexibility, and the inversion of the above matrix is ​​obtained: Among them, K X is the longitudinal stiffness, K T is the torsional stiffness, K XT is the longitudinal-torsional coupling stiffness.

3. The method for calculating the torsional vibration coupling of the low-speed machine shaft system considering the propeller reduced-order excitation according to claim 1 is characterized in that: The S2 specifically includes the following steps: S21. According to the accuracy requirement, select 20%, 40%, 60%, 80%, and 100% working conditions from 20% to 100%, and divide the flow domain based on the propeller model under each selected working condition. Divide the cylindrical flow domain with a distance of ten times the propeller diameter and a diameter of six times the propeller diameter into a dynamic domain, and divide the flow domain outside the dynamic domain but still having a greater impact on the propeller into a static domain, thereby generating the corresponding propeller surface mesh, fluid domain surface mesh, and flow domain body mesh to obtain the flow field model; S22. Select the SSTkω turbulence model through CFD, set the boundary conditions and the required algorithm, and solve the propeller pulsation pressure under various working conditions; S23. Project the pressure of each blade unit onto a plane perpendicular to the axis, and then decompose it into the pressure perpendicular to the line connecting the point of action and the axis and the pressure in the direction of the line connecting the point of action and the axis, then multiply the pressure perpendicular to the line connecting the point of action and the axis with the length of the line to obtain the excitation torque of each blade unit in the plane perpendicular to the axis, and then perform vector summation on the excitation torque to obtain the reduced-order excitation torque generated by the propeller in the torsion direction under each working condition; based on the solved working conditions, perform linear interpolation on the excitation torque of several unsolved working conditions between every two adjacent known working conditions to obtain the reduced-order excitation torque of the propeller under all working conditions; S24. The propeller reduced-order excitation torque under all working conditions is directly added to the blade frequency term and the blade-frequency-doubled term of the propeller excitation torque coefficient matrix to obtain the propeller excitation torque coefficient matrix, so as to take it into account in the torsional vibration of the low-speed machine shaft system. Based on the phase matching relationship between the propeller reduced-order excitation and the shaft system structure, the propeller excitation torque coefficient matrix is ​​formed, and then the matrix is ​​loaded to the concentrated inertia where the propeller is located, so as to construct a low-speed machine shaft system torsional vibration coupling model considering the propeller reduced-order excitation; S25. Load the obtained propeller reduced-order excitation torque into the initial propeller excitation torque coefficient matrix, that is, the blade frequency term and the blade frequency double term in the zero vector of 1× harmonic order, so as to obtain the propeller excitation torque coefficient matrix.

4. A method for calculating longitudinal-torsional coupled vibration of a ship diesel engine shaft system according to claim 1, characterized in that: The S3 specifically includes the following steps: S31. The longitudinal-torsion coupling stiffness obtained in S1 is used as the stiffness coefficient of the mutual influence between torsional vibration and longitudinal vibration at the crankshaft. The longitudinal stiffness matrix and the torsional stiffness matrix are listed as diagonal matrices. The longitudinal-torsion coupling stiffness is substituted into the longitudinal stiffness matrix and the torsional stiffness matrix at the bend. The longitudinal-torsion coupling stiffness matrix formed by coupling is as follows: Where K is the coupling stiffness matrix, α n-1,n is the axial stiffness, β n-1,n is the torsional stiffness; S32. The lumped parameter method is used to couple the mutually independent longitudinal vibration system and torsional vibration system into the longitudinal torsional coupling free vibration dynamics equation of the ship propulsion shaft system through the longitudinal torsional coupling stiffness matrix, as follows: Where: δ is the column vector of the synthesis of angular displacement and axial displacement, and J is the system's moment of inertia and mass synthesis matrix.

5. A method for calculating longitudinal-torsional coupled vibration of a ship diesel engine shaft system according to claim 4, characterized in that: The S4 specifically includes the following steps: substituting the mass matrix and the longitudinal-torsional coupling stiffness matrix of the ship propulsion shaft system into the ship propulsion shaft system coupled vibration dynamics equation to solve its eigenvalue and eigenvector, the square root of the eigenvalue is the natural frequency, the solved displacement of each concentrated mass point is divided by the specified concentrated mass point displacement to form an amplitude ratio, and the amplitude ratios are arranged in order and plotted into a broken line to form a vibration mode.

6. A method for calculating longitudinal-torsional coupled vibration of a ship diesel engine shaft system according to claim 5, characterized in that: The S5 specifically includes the following steps: S51. The excitation force generated by the ship diesel engine shaft system due to the change of gas pressure is obtained through the diesel engine shaft system piston diameter, stroke, reciprocating mass and simple harmonic coefficient table provided by the manufacturer, and the excitation force is input into the ship propulsion shaft system coupled vibration dynamics equation for calculation; S52. The excitation force calculated by inputting the torsional vibration excitation at the propeller calculated by S2 into the coupled vibration dynamic equation of the ship propulsion shaft system; S53. Calculate the forced vibration response of the ship diesel engine shaft system based on the obtained excitation force.

7. A method for calculating longitudinal-torsional coupled vibration of a ship diesel engine shaft system according to claim 6, characterized in that: In the S51, the calculation formula of the excitation force is: Among them, P g is the gas pressure per unit area of ​​the piston; α is the crankshaft angle; β is the connecting rod swing angle.

8. A method for calculating longitudinal-torsional coupled vibration of a ship diesel engine shaft system according to claim 7, characterized in that: In the S53, the calculation method of the forced vibration response of the ship diesel engine shaft system is to bring the excitation force into the longitudinal torsional coupling forced vibration dynamics equation, and the longitudinal torsional coupling forced vibration dynamics equation is as follows: Among them: [J]-----the composite matrix of the moment of inertia and mass of the equivalent system, [K]-----the longitudinal-torsional coupling stiffness matrix of the equivalent system, [C]-----the coupling damping matrix of the equivalent system, {T}-----the composite column vector of the excitation torque and force of the equivalent system, {δ}-----the composite column vector of the angular displacement and axial displacement of the equivalent system.

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