Longitudinal vibration reduction simulation method of shafting for ship

Abstract

The invention relates to the technical field of ship vibration reduction, in particular to a ship shafting longitudinal vibration reduction simulation method, which comprises the following steps of: firstly, determining a transfer matrix of a propeller by simulating a motion process of the propeller, and secondly, determining a transfer matrix of a uniform shaft section by simplifying a thrust shaft into the uniform shaft section, secondly, longitudinal supports of a longitudinal shock absorber and a thrust bearing are simplified into a mass-free linear spring, and a transfer matrix of the mass-free linear spring is determined, so that a shafting transfer matrix of the vibration model is determined through a transfer matrix of a propeller, a transfer matrix of a shaft and the transfer matrix of the mass-free linear spring; therefore, simulation design of the longitudinal vibration reduction process of the ship shafting is achieved, the rigidity of the vibration damper which is finally obtained through calculation is determined based on the multiple matrixes of the simulation design, and the problems that the vibration reduction effect is poor and the operation safety of the shafting cannot be guaranteed due to the fact that the accuracy of determining the rigidity of the vibration damper is not high are solved.

Description

Technical Field

[0001] The invention relates to the technical field of ship vibration reduction, and in particular to a method for simulating longitudinal vibration reduction of a ship shaft system. Background Art

[0002] The shafting system is the only direct channel for transmitting propeller thrust to the hull. The longitudinal vibration of the shafting system has an important impact on the vibration and noise of the entire ship. Therefore, taking longitudinal vibration reduction measures on the shafting system is of great significance to reducing the vibration and noise of the entire ship.

[0003] Chinese patent publication number: CN102297753B discloses a ship propulsion shaft system longitudinal vibration simulation test bench, comprising a dynamic loading module (1), a base (12), a static loading module (3) arranged in sequence on the base (12), a transmission shaft (4), a clamping shell coupling (6), a thrust bearing (7), an elastic coupling (8), a gear box (10) and a variable frequency motor (11), wherein the dynamic loading module (1) is connected to the static loading module (3) through a push rod (2) to provide a longitudinal alternating excitation force for simulating a propeller, the static loading module (3) is connected to one end of the transmission shaft (4), the other end of the transmission shaft (4) is connected to the thrust shaft of the thrust bearing (7) through the clamping shell coupling (6), the other end of the thrust shaft is connected to the output shaft of the gear box (10) through the elastic coupling (8), and the gear box (10) is connected to the variable frequency motor (11). The invention has a compact structure, is easy to operate, safe and reliable, and meets the practical application requirements of teaching and scientific research. It can be seen that the ship propulsion shaft longitudinal vibration simulation test bench has the problem that the stiffness of the shock absorber is not accurately determined, resulting in poor vibration reduction effect and the inability to ensure the safe operation of the shaft system. Summary of the invention

[0004] To this end, the present invention provides a method for simulating longitudinal vibration reduction of a ship's shaft system, so as to overcome the problem in the prior art that the stiffness of the shock absorber is not accurately determined, resulting in poor vibration reduction effect and failure to ensure safe operation of the shaft system.

[0005] To achieve the above object, the present invention provides a method for simulating longitudinal vibration reduction of a ship shaft system, comprising:

[0006] Establish the vibration model of the propulsion shafting with longitudinal vibration damper;

[0007] Determine the transfer matrix of the propeller of the vibration model based on the shafting parameters;

[0008] Determining a transfer matrix of the axis of the vibration model based on motion parameters of the axis of the vessel;

[0009] converting the longitudinal support of the longitudinal damper and the thrust bearing into a massless linear spring of the vibration model;

[0010] A shafting transfer matrix of the vibration model is determined based on the transfer matrix of the propeller, the transfer matrix of the shaft, and the transfer matrix of the massless linear spring.

[0011] Furthermore, the process of establishing the vibration model of the propulsion shaft system of the longitudinal vibration damper includes:

[0012] Obtaining parameters of each component of the propulsion shaft system of the ship;

[0013] The boundary condition of the thrust bearing on the hull side is considered as a fixed constraint;

[0014] combining the components into the vibration model based on the parameters of the components;

[0015] The components include a propeller, a thrust shaft, a support bearing and a thrust bearing, and the parameters include propeller excitation, propeller mass, elastic modulus of shaft segment material, density of shaft segment material, cross-sectional area of ​​shaft segment, longitudinal stiffness of longitudinal vibration absorber, equivalent damping of longitudinal vibration absorber, longitudinal support stiffness of thrust bearing, equivalent damping of thrust bearing, left shaft length of vibration absorber and right shaft length of vibration absorber.

[0016] Further, the process of determining the transfer matrix of the propeller of the vibration model based on the shaft system parameters includes:

[0017] Take the axis system space state vector as (u,N) T , where u is the longitudinal displacement of the shafting section, and N is the shafting section force;

[0018] It is positive when the acceleration direction is the same as the propeller excitation force direction;

[0019] Determine the propeller's equation of motion based on Newton's laws of motion;

[0020] The propeller motion equations are converted into matrices, and the propeller transfer matrix is ​​determined.

[0021] Furthermore, the propeller motion equation is determined according to the following formula:

[0022]

[0023] Among them, u L is the longitudinal vibration displacement of the left end surface, u R is the longitudinal vibration displacement of the right end surface of the propeller, N L Section stress at the left end, N R Section stress at the right end, M p is the propeller mass, t is the time variable;

[0024] Determine the matrix of the propeller motion equation according to the following formula and set

[0025]

[0026] Among them, M p is the propeller mass, ω is the longitudinal vibration angular frequency, and t is the time variable.

[0027] Furthermore, the propeller transfer matrix is ​​determined according to the following formula:

[0028]

[0029] Among them, T 1 represents the transfer matrix of the propeller.

[0030] Further, the process of determining the transfer matrix of the axis of the vibration model based on the motion parameters of the axis of the ship includes:

[0031] Simplifying the thrust shaft into a uniform shaft section and determining the longitudinal free vibration equation of the uniform shaft section;

[0032] Determining the cross-sectional stress of the uniform shaft segment according to the longitudinal free vibration equation;

[0033] The transfer matrix of the uniform shaft segment is obtained by calculation based on the longitudinal free vibration equation and the cross-sectional stress.

[0034] Furthermore, the transfer matrix of the uniform axis segment is determined according to the following formula:

[0035]

[0036] Among them, T 2 represents the transfer matrix of a uniform shaft segment, m is the shaft segment line density, l is the length of the shaft segment,

[0037] Further, the process of determining the transfer matrix of the massless linear spring of the vibration model based on the longitudinal support of the longitudinal damper and the thrust bearing includes:

[0038] Simplifying the longitudinal support of the longitudinal shock absorber and the thrust bearing of the ship into a massless linear spring;

[0039] Determine the relationship between the displacement and force of the left and right ends of the massless linear spring;

[0040] The transfer matrix of the massless linear spring is determined according to the relationship between the displacements of the left and right ends of the massless linear spring and the force.

[0041] Furthermore, the transfer matrix of the massless linear spring is determined according to the following formula, setting

[0042]

[0043] Among them, T S represents the transfer matrix of the massless linear spring, and K represents the stiffness of the massless linear spring. Further, the shafting transfer matrix of the vibration model is determined based on the transfer matrix of the propeller, the transfer matrix of the shaft, and the transfer matrix of the massless linear spring, and is determined according to the following formula:

[0044]

[0045] Where T is the axis transfer matrix, k t is the longitudinal support stiffness of the thrust bearing, c t is the equivalent damping of the thrust bearing, l 1 is the length of the left shaft of the shock absorber, l 2 is the shaft length on the right side of the shock absorber.

[0046] Compared with the prior art, the beneficial effect of the present invention lies in that, by simulating the design of the longitudinal shafting of the ship, the present invention determines many factors in the design process of the longitudinal vibration reduction of the shafting, and determines the stiffness design of the longitudinal vibration absorber of the shafting, so as to improve the accuracy of determining the stiffness of the vibration absorber during the simulation process, thereby improving the effect of the longitudinal vibration reduction of the ship shafting, and at the same time ensuring the safe and stable operation of the shafting.

[0047] Furthermore, the present invention designs the longitudinal vibration reduction of the shafting based on the transfer matrix. First, the motion process of the propeller is simulated to determine the transfer matrix of the propeller. Secondly, the thrust shaft is simplified into a uniform shaft segment to determine the transfer matrix of the uniform shaft segment. Thirdly, the longitudinal vibration damper and the longitudinal support of the thrust bearing are simplified into a massless linear spring and the transfer matrix of the massless linear spring is determined. Thus, the shafting transfer matrix of the vibration model is determined through the transfer matrix of the propeller, the transfer matrix of the shaft and the transfer matrix of the massless linear spring, thereby realizing the simulation design of the longitudinal vibration reduction process of the ship shafting. Based on several matrices of the simulation design, the stiffness of the shock absorber that is finally required to be calculated is determined, and the stiffness of the shock absorber is accurately determined, thereby improving the effect of the longitudinal vibration reduction of the ship shafting, while ensuring the safe and stable operation of the shafting. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a flow chart of a method for simulating longitudinal vibration reduction of a ship shaft system according to an embodiment of the present invention;

[0049] Figure 2 A vibration model diagram of a method for simulating longitudinal vibration reduction of a ship shaft system according to an embodiment of the present invention;

[0050] Figure 3 A flow chart of determining a vibration model in a method for simulating longitudinal vibration reduction of a ship shaft system according to an embodiment of the present invention;

[0051] Figure 4 It is a flow chart of determining the transfer matrix of a propeller in the method for simulating longitudinal vibration reduction of a ship shaft system according to an embodiment of the present invention;

[0052] Figure 5 It is a flow chart of determining the transfer matrix of a uniform shaft section in the method for simulating longitudinal vibration reduction of a ship shaft system according to an embodiment of the present invention;

[0053] Figure 6 The present invention is a flowchart of determining the transfer matrix of a massless linear spring in a method for simulating longitudinal vibration reduction of a ship shaft system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0054] In order to make the objects and advantages of the present invention more clearly understood, the present invention is further described below in conjunction with embodiments; it should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0055] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood by those skilled in the art that these embodiments are only used to explain the technical principles of the present invention and are not intended to limit the protection scope of the present invention.

[0056] It should be noted that, in the description of the present invention, terms such as "up", "down", "left", "right", "inside" and "outside" indicating directions or positional relationships are based on the directions or positional relationships shown in the drawings. This is merely for the convenience of description and does not indicate or imply that the device or element must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it cannot be understood as a limitation on the present invention.

[0057] In addition, it should be noted that in the description of the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For those skilled in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0058] See also Figure 1 and Figure 2 As shown, Figure 1 This is a flow chart of a method for simulating longitudinal vibration reduction of a ship shaft system according to an embodiment of the present invention. Figure 2 This is a vibration model diagram of a method for simulating longitudinal vibration reduction of a ship shaft system according to an embodiment of the present invention.

[0059] The method for simulating longitudinal vibration reduction of a ship shaft system according to an embodiment of the present invention comprises:

[0060] Step S1, establishing a vibration model of a propulsion shaft system of a longitudinal shock absorber;

[0061] Step S2, determining a transfer matrix of the propeller of the vibration model based on shaft system parameters;

[0062] Step S3, determining the transfer matrix of the axis of the vibration model based on the motion parameters of the axis of the ship;

[0063] Step S4, converting the longitudinal support of the longitudinal vibration damper and the thrust bearing into a massless linear spring of the vibration model;

[0064] Step S5, determining the shafting transfer matrix of the vibration model based on the transfer matrix of the propeller, the transfer matrix of the shaft and the transfer matrix of the massless linear spring.

[0065] See also Figure 3 As shown, it is a flow chart of determining the vibration model in the method for simulating longitudinal vibration reduction of a ship shaft system according to an embodiment of the present invention.

[0066] Specifically, in step S1, establishing the vibration model of the propulsion shaft system of the longitudinal vibration damper includes:

[0067] Step S11, obtaining parameters of each component of the propulsion shaft system of the ship;

[0068] Step S12, treating the boundary condition of the thrust bearing on one side of the hull as a fixed constraint;

[0069] Step S13: combining the components into the vibration model based on the parameters of the components.

[0070] In an embodiment of the present invention, the components include a propeller, a thrust shaft, a support bearing and a thrust bearing, and the parameters include propeller excitation, propeller mass, elastic modulus of shaft segment material, density of shaft segment material, cross-sectional area of ​​shaft segment, longitudinal stiffness of longitudinal vibration absorber, equivalent damping of longitudinal vibration absorber, longitudinal support stiffness of thrust bearing, equivalent damping of thrust bearing, left shaft length of vibration absorber and right shaft length of vibration absorber.

[0071] See also Figure 4 As shown, it is a flow chart of determining the transfer matrix of the propeller in the method for simulating longitudinal vibration reduction of the shafting system of a ship according to an embodiment of the present invention.

[0072] Specifically, in step S2, the process of determining the transfer matrix of the propeller of the vibration model based on the shaft system parameters includes:

[0073] Step S21, take the axis system space state vector as (u, N) T , where u is the longitudinal displacement of the shafting section, and N is the shafting section force;

[0074] Step S22, determining that the acceleration direction is positive when it is the same as the propeller excitation force direction;

[0075] Step S23, determining the propeller motion equation according to Newton's laws of motion;

[0076] Step S24: convert the propeller motion equation into a matrix, and determine the propeller transfer matrix.

[0077] Specifically, the propeller motion equation is determined according to the following formula:

[0078]

[0079] Specifically, the matrix of the propeller motion equation is determined according to the following formula:

[0080]

[0081] Among them, u L is the longitudinal vibration displacement of the left end surface, u R is the longitudinal vibration displacement of the right end surface of the propeller, N L Section stress at the left end, N R Section stress at the right end, M p is the propeller mass, ω is the longitudinal vibration angular frequency, and t is the time variable.

[0082] Specifically, the propeller transfer matrix is ​​determined according to the following formula:

[0083]

[0084] Among them, T 1 represents the transfer matrix of the propeller.

[0085] See also Figure 5 As shown, it is a flow chart of determining the transfer matrix of a uniform shaft section in the method for simulating longitudinal vibration reduction of a ship shaft system according to an embodiment of the present invention.

[0086] Specifically, in step S3, the process of determining the transfer matrix of the axis of the vibration model based on the motion parameters of the axis of the ship includes:

[0087] Step S31, simplifying the thrust shaft into a uniform shaft segment, and determining the longitudinal free vibration equation of the uniform shaft segment;

[0088] Step S32, determining the cross-sectional stress of the uniform shaft segment according to the longitudinal free vibration equation;

[0089] Step S33, calculating and obtaining the transfer matrix of the uniform shaft segment according to the longitudinal free vibration equation and the cross-sectional stress.

[0090] Specifically, the longitudinal free vibration equation of the uniform shaft segment is determined according to the following formula:

[0091]

[0092] u(x,t)=U(x)e iωt (6)

[0093] Determine the cross-sectional stress according to the following formula, setting

[0094] Let U(x)=Csin(βx)+Dcos(βx)(7)

[0095]

[0096] Among them, when x=0, When x=l,

[0097] Among them, A is the cross-sectional area of ​​the shaft segment, E is the elastic modulus of the shaft segment material, N is the section stress, U is the longitudinal displacement of the shaft segment section at a certain position, and l is the length of the shaft segment.

[0098] Specifically, the transfer matrix of the uniform axis segment is determined according to the following formula:

[0099]

[0100] Among them, T 2 represents the transfer matrix of the uniform shaft segment, m is the shaft segment line density,

[0101] See also Figure 6 As shown, it is a flow chart of determining the transfer matrix of the massless linear spring in the method for simulating longitudinal vibration reduction of a ship shaft system according to an embodiment of the present invention.

[0102] Specifically, in step S4, the process of determining the transfer matrix of the massless linear spring of the vibration model based on the longitudinal support of the longitudinal damper and the thrust bearing includes:

[0103] Step S41, simplifying the longitudinal support of the longitudinal shock absorber and the thrust bearing of the ship into a massless linear spring;

[0104] Step S42, determining the relationship between the displacement and force of the left and right ends of the massless linear spring;

[0105] Step S43, determining the transfer matrix of the massless linear spring according to the relationship between the displacement and force of the left and right ends of the massless linear spring.

[0106] Specifically, the relationship between the displacement and force of the left and right ends of the massless linear spring is determined according to the following formula:

[0107]

[0108] The matrix of displacement and force at the left and right ends of the massless linear spring is determined according to the following formula:

[0109]

[0110] The transfer matrix of the massless linear spring is determined according to the following formula, setting

[0111]

[0112] Among them, T S represents the transfer matrix of the massless linear spring, and K represents the stiffness of the massless linear spring.

[0113] Specifically, the shafting transfer matrix of the vibration model is determined based on the transfer matrix of the propeller, the transfer matrix of the shaft, and the transfer matrix of the massless linear spring, and is determined according to the following formula:

[0114]

[0115] Where T is the axis transfer matrix, k t is the longitudinal support stiffness of the thrust bearing, c t is the equivalent damping of the thrust bearing, l 1 is the length of the left shaft of the shock absorber, l 2 is the shaft length on the right side of the shock absorber.

[0116] Specifically, the boundary conditions of the shaft system are that the propeller end is free and the thrust bearing end is fixed. When the longitudinal excitation force f is applied to the propeller end, the state space vectors of the left end face of the propeller and the right end face of the thrust bearing are expressed by the following formula:

[0117]

[0118] The relationship between the state vectors at the rightmost and leftmost ends of the propulsion shaft system is expressed by the following formula

[0119]

[0120] Among them, T is the total transfer matrix. Obviously, T is a 2×2 square matrix, so the matrix expression of the formula is

[0121]

[0122] When the excitation force f = 0, that is, the shaft system is in free vibration, T 11 =0, let the total length of the shaft be l, then l1 +l 2 = l, let l 1 / l=γ, then the longitudinal stiffness of the longitudinal shock absorber is

[0123]

[0124] Where a = k t cos[(1-γ)βl]-EAβsin[(1-γ)βl],

[0125] b=EAβsin(γβl)+M p ω 2 cos(γβl),

[0126] c=EAβcos(γβl)-M p ω 2 sin(γβl),

[0127] d=k t sin[(1-γ)βl]+EAβcos[(1-γ)βl].

[0128] Specifically, the modal frequency ω of the shaft system and the installation position of the longitudinal damper, i.e., the shaft segment l 1 The ratio γ to the total length l of the shaft can be calculated according to the formula Obtain the value of β and substitute it into equation (20) to determine the longitudinal stiffness k of the longitudinal shock absorber: r .

[0129] So far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

[0130] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for simulating longitudinal vibration reduction of a ship shaft system, characterized in that: include: Establish the vibration model of the propulsion shafting with longitudinal vibration damper; Determine the transfer matrix of the propeller of the vibration model based on the shafting parameters; Determining a transfer matrix of the axis of the vibration model based on motion parameters of the axis of the vessel; converting the longitudinal support of the longitudinal damper and the thrust bearing into a massless linear spring of the vibration model; A shafting transfer matrix of the vibration model is determined based on the transfer matrix of the propeller, the transfer matrix of the shaft, and the transfer matrix of the massless linear spring.

2. The method for simulating longitudinal vibration reduction of a ship shaft system according to claim 1, characterized in that: The process of establishing the vibration model of the propulsion shaft system of the longitudinal vibration damper includes: Obtaining parameters of each component of the propulsion shaft system of the ship; The boundary condition of the thrust bearing on the hull side is considered as a fixed constraint; combining the components into the vibration model based on the parameters of the components; The components include a propeller, a thrust shaft, a support bearing and a thrust bearing, and the parameters include propeller excitation, propeller mass, elastic modulus of shaft segment material, density of shaft segment material, cross-sectional area of ​​shaft segment, longitudinal stiffness of longitudinal vibration absorber, equivalent damping of longitudinal vibration absorber, longitudinal support stiffness of thrust bearing, equivalent damping of thrust bearing, left shaft length of vibration absorber and right shaft length of vibration absorber.

3. The method for simulating longitudinal vibration reduction of a ship shaft system according to claim 1, characterized in that: The process of determining the transfer matrix of the propeller of the vibration model based on the shafting parameters includes: Take the axis system space state vector as (u,N) T , where u is the longitudinal displacement of the shafting section, and N is the shafting section force; It is positive when the acceleration direction is the same as the propeller excitation force direction; Determine the propeller's equation of motion based on Newton's laws of motion; The propeller motion equations are converted into matrices, and the propeller transfer matrix is ​​determined.

4. The method for simulating longitudinal vibration reduction of a ship shaft system according to claim 3, characterized in that: The propeller motion equation is determined according to the following formula: Among them, u L is the longitudinal vibration displacement of the left end surface, u R is the longitudinal vibration displacement of the right end surface of the propeller, N L Section stress at the left end, N R Section stress at the right end, M p is the propeller mass, t is the time variable; Determine the matrix of the propeller motion equation according to the following formula and set Among them, M p is the propeller mass, ω is the longitudinal vibration angular frequency, and t is the time variable.

5. The method for simulating longitudinal vibration reduction of a ship shaft system according to claim 4, characterized in that: Determine the propeller transfer matrix according to the following formula, setting Where T1 represents the transfer matrix of the propeller.

6. The method for simulating longitudinal vibration reduction of a ship shaft system according to claim 1, characterized in that: The process of determining the transfer matrix of the axis of the vibration model based on the motion parameters of the axis of the ship includes: Simplifying the thrust shaft into a uniform shaft section and determining the longitudinal free vibration equation of the uniform shaft section; Determining the cross-sectional stress of the uniform shaft segment according to the longitudinal free vibration equation; The transfer matrix of the uniform shaft segment is obtained by calculation based on the longitudinal free vibration equation and the cross-sectional stress.

7. The method for simulating longitudinal vibration reduction of a ship shaft system according to claim 1, characterized in that: The transfer matrix of the uniform axis segment is determined according to the following formula: Where T2 represents the transfer matrix of the uniform shaft segment, m is the shaft segment line density, l is the length of the shaft segment, 8. The method for simulating longitudinal vibration reduction of a ship shaft system according to claim 1, characterized in that: The process of determining the transfer matrix of the massless linear spring of the vibration model based on the longitudinal support of the longitudinal damper and the thrust bearing includes: Simplifying the longitudinal support of the longitudinal shock absorber and the thrust bearing of the ship into a massless linear spring; Determine the relationship between the displacement and force of the left and right ends of the massless linear spring; The transfer matrix of the massless linear spring is determined according to the relationship between the displacements of the left and right ends of the massless linear spring and the force.

9. The method for simulating longitudinal vibration reduction of a ship shaft system according to claim 8, characterized in that: The transfer matrix of the massless linear spring is determined according to the following formula, setting Among them, T S represents the transfer matrix of the massless linear spring, and K represents the stiffness of the massless linear spring.

10. The method for simulating longitudinal vibration reduction of a ship shaft system according to claim 1, characterized in that: The shafting transfer matrix of the vibration model is determined based on the transfer matrix of the propeller, the transfer matrix of the shaft and the transfer matrix of the massless linear spring, and is determined according to the following formula: Where T is the axis transfer matrix, k t is the longitudinal support stiffness of the thrust bearing, c t is the equivalent damping of the thrust bearing, l1 is the shaft length on the left side of the shock absorber, and l2 is the shaft length on the right side of the shock absorber.

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