Underwater towing system towing stability calculation method

Abstract

The invention relates to a method for calculating the towing stability of an underwater towing system. The method comprises the following steps: establishing stability calculation of the underwater towing system by considering the influence of a towing cable, unifying calculation under coupling of a horizontal plane and a vertical plane, analyzing and judging the stability based on characteristic values, and performing design improvement based on characteristic vector judgment. According to the method, the dragging stability of the underwater dragging system can be calculated and used for evaluating the dragging stability of the underwater dragging system, the stability of different parameters of the dragging system is calculated through the method, system optimization is achieved, the dragging stability is improved, and the specific requirements of some dragging systems for tension, position and posture are met.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater towing systems, and mainly relates to a method for calculating the towing stability of an underwater towing system. Background Art

[0002] When the towing system is in use, affected by external disturbances such as the mother ship and ocean currents, the towing system will deviate from the stable working state, resulting in the loss of its functions. Towing stability calculation refers to the ability of the system to return to the original equilibrium state when it is disturbed and deviates from the equilibrium state. Towing stability is generally divided into static stability and dynamic stability. Static stability refers to the movement tendency of the towing system at the initial moment after the disturbing force is removed when it is disturbed and deviates from the equilibrium state. If the tendency is to return to the original equilibrium state, it is called statically stable, otherwise it is statically unstable. Dynamic stability is the ability of the towing system to return to the original equilibrium state after the disturbing force is removed. That is, whether the movement can return to the original equilibrium state over time.

[0003] 1. Basic Composition of Underwater Towing System

[0004] The underwater towing system generally consists of a towing cable 1 and a tow body 2, and is towed by a mother ship 3. The mother ship 3 floats on the waterline surface 4, and the variable depth of the tow body is achieved by adjusting the cable length and the ship speed. For details, see Figure 1 .

[0005] 2. Calculation Method of Underwater Towing System

[0006] The motion of the tow body is described by the six-degree-of-freedom equation as follows:

[0007]

[0008] The meanings of the physical quantities in the formula are as follows:

[0009] m: Mass of the tow body;

[0010] I: Moment of inertia of the tow body, with subscripts corresponding to each axis of rotation;

[0011] x g , y g , z g : Coordinates of the center of gravity of the tow body;

[0012] u, v, w: Longitudinal, lateral, and vertical motion speeds of the tow body;

[0013] p, q, r: Angular velocities of roll, pitch, and yaw of the tow body;

[0014] X, Y, Z: External forces acting on the tow body, mainly including gravity, buoyancy, hydrodynamic force, and towing cable tension;

[0015] K, M, N: External torques acting on the tow body;

[0016] Note: A dot above a physical quantity represents the derivative of that physical quantity with respect to time.

[0017] The transformation matrix between the towed body coordinate system and the global coordinate system is:

[0018]

[0019] φ, θ, ψ: The attitude angles of the towed body, which are the roll angle, pitch angle, and yaw angle respectively.

[0020] The relationship between the attitude angle and the angular velocity is described by the Euler's motion equations:

[0021]

[0022] The external forces acting on the towed body mainly include gravity, buoyancy, hydrodynamic force, and tow cable tension; they can be expressed as:

[0023]

[0024] (1) Calculation of hydrodynamic force and hydrodynamic moment

[0025] It is described by hydrodynamic coefficients. Physical quantities with a prime (') represent the hydrodynamic coefficients of the towed body, and their acting forces are:

[0026]

[0027] (2) Calculation of gravity, buoyancy, and their moments

[0028]

[0029] G: The weight of the towed body;

[0030] B: The buoyancy of the towed body;

[0031] x b ,y b ,z b : The coordinates of the center of buoyancy of the towed body.

[0032] (3) Calculation of tow cable tension and its moment

[0033]

[0034] T x ,T y ,T z : The tension in the global coordinate system;

[0035] x t ,y t ,z t : The coordinates of the towing point.

[0036] The 9 equations composed of equations (1’) and (3’), corresponding to 9 unknown variables, form a system of ordinary differential equations. Among them, the global tensions (T x , T y , T z ) adopt the results obtained by solving under steady state as known parameters to participate in the operation.

[0037] 3. Judgment Criteria for the Stability of the Towing System

[0038] The analysis method adopts the principle of small perturbation linearization, dividing the motion into unperturbed motion and perturbed motion. Linearize the perturbed motion at the equilibrium point, and distinguish between horizontal plane motion and vertical plane motion. Solve the characteristic roots of the small perturbation linearization equations for the horizontal plane and vertical plane. According to the principle of linear systems, if the characteristic roots have negative real parts, it is considered stable. Derive the judgment criteria for the stability of the vertical plane and horizontal plane based on the calculation with negative real parts of the characteristic roots.

[0039] The specific judgment criteria for the horizontal plane and vertical plane in the past are as follows:

[0040] The static stability judgment criterion for the vertical plane is: L′ α = -M′ w / Z′ w , and L′ α < 0 indicates static stability. L′ α is called the dimensionless hydrodynamic center arm.

[0041] The dynamic stability judgment criterion for the vertical plane is: C v > 0 indicates dynamic stability. C v is called the vertical plane stability criterion number.

[0042] The static stability judgment criterion for the horizontal plane is: L′ β = N′ v / Y′ v , and L′ β < 0 indicates static stability. L′ β is called the dimensionless hydrodynamic center arm.

[0043] The dynamic stability judgment criterion for the horizontal plane is: C h > 0 indicates dynamic stability. C h is called the horizontal plane stability criterion number.

[0044] For the above judgment criteria, the horizontal plane and vertical plane are distinguished, and it is considered that the motions of the two are independent of each other. At the same time, only the influence of position - type hydrodynamic coefficients is considered in the static stability judgment criterion. The dynamic stability judgment criterion only considers the terms related to the longitudinal velocity in the Coriolis force and the influence of the damping moment caused by the angular velocity, ignoring other hydrodynamic coefficients, which may lead to calculation deviations in some specific cases.

[0045] In the existing stability calculation criteria, the towing cable tension is used as a known parameter in the operation, and the coupling effect of the towing cable is not considered. At the same time, simplification is carried out, and the stability calculation is divided into horizontal plane and vertical plane for analysis, without considering the coupling effect between the horizontal plane and the vertical plane. The judgment criterion is calculated under simplified conditions, and the influence of some key parameters such as the position of the center of gravity and the transverse hydrodynamic coefficient on the stability is not considered. The stability calculated according to the criterion can only know whether it is stable or not, and cannot judge the key influencing parameters of stability or instability, and cannot support design improvement. Summary of the Invention

[0046] The purpose of the present invention is to overcome the deficiencies of the existing technology, and provide a method for calculating the towing stability of an underwater towing system, which uses a simplified towing cable to realize the coupling connection with the tow body, and judges its stability by calculating the eigenvalues of the parameter matrix.

[0047] The purpose of the present invention is achieved by the following technical solutions. A method for calculating the towing stability of an underwater towing system, a towing stability calculation method based on eigenvalues considering the coupling of various hydrodynamic coefficients and the coupling of the towing cable, specifically including the following steps:

[0048] S1. Establish a calculation model

[0049] The motion of the tow body is described by the six-degree-of-freedom equation as follows:

[0050]

[0051] The meanings of the physical quantities in the formula are as follows:

[0052] m: the mass of the tow body;

[0053] I: the moment of inertia of the tow body, and the subscript corresponds to each axis of rotation;

[0054] x g ,y g ,z g : the center-of-gravity coordinates of the tow body;

[0055] u, v, w: the longitudinal, lateral, and vertical motion speeds of the tow body;

[0056] p, q, r: the transverse tilt, longitudinal tilt, and yaw angular velocities of the tow body;

[0057] X, Y, Z: the external forces acting on the tow body, mainly including gravity, buoyancy, fluid force, and towing cable tension;

[0058] K, M, N: the external torques acting on the tow body;

[0059] A dot above a physical quantity indicates the derivative of the physical quantity with respect to time;

[0060] The transformation matrix between the vehicle coordinate system and the global coordinate system is:

[0061]

[0062] φ, θ, ψ: the attitude angles of the vehicle, which are the roll angle, pitch angle, and yaw angle respectively;

[0063] The relationship between the attitude angle and the angular velocity is described by the Euler motion equation:

[0064]

[0065] The external forces acting on the vehicle include gravity, buoyancy, hydrodynamic force, and towing cable tension, which are expressed as:

[0066]

[0067] (1) Calculation of hydrodynamic force and hydrodynamic moment

[0068] It is described by hydrodynamic coefficients. Physical quantities with a prime denote the hydrodynamic coefficients of the vehicle, and their acting forces are:

[0069]

[0070] (2) Calculation of gravity, buoyancy, and their moments

[0071]

[0072] G: the weight of the vehicle;

[0073] B: the buoyancy of the vehicle;

[0074] x b , y b , z b : the coordinates of the center of buoyancy of the vehicle;

[0075] (3) Calculation of towing cable tension and its moment

[0076] The towing cable is simplified as a rigid body. The transformation matrix between the towing cable coordinate system and the global coordinate system is

[0077]

[0078] Among them, the global tension of the towing cable is expressed according to the towing cable coordinate system as:

[0079]

[0080] α: the yaw angle of the towing cable;

[0081] γ: the pitch angle of the towing cable;

[0082] T: the tension of the towing cable;

[0083] L c : Towing cable length

[0084] T x , T y , T z : Tension in the global coordinate system;

[0085] Substitute the global tension of the towing cable into the external force of the tow body to achieve the coupling of the towing cable;

[0086]

[0087] x t , y t , z t : Towing point coordinates;

[0088] According to the rigid body motion law, the towing cable motion equation is obtained:

[0089]

[0090] Combined with the six-degree-of-freedom motion equation (1) of the tow body, the Euler motion equation (3), and the towing cable motion equation (12) to form a system of ordinary differential equations with 12 variables:

[0091]

[0092] where X = [u, v, w, p, q, r, φ, θ, ψ, T, α, γ];

[0093] S2. Input parameters

[0094] Using the above dynamic model, input the speed V of the mother ship, the cable length L c , the seawater density r, and the relevant parameters of the tow body length, mass, weight, buoyancy, coordinates, and hydrodynamic coefficients;

[0095] S3. Calculate the equilibrium point state

[0096] In the equilibrium point motion state, that is, the steady-state motion and the undisturbed motion X 0 , the time derivative of all unknowns is zero, the angular velocity is zero, and at the same time, the tow body is generally symmetric left and right, the lateral velocity v is zero, the roll angle φ and the yaw angle ψ are zero, and the yaw angle α of the towing cable is zero; the unknowns are u, w, θ, T, γ respectively, and the corresponding description equations are that the external forces X, Z, the external torque M are zero, and the longitudinal and vertical velocity relationships of the towing cable equation are as follows:

[0097]

[0098] The solution result is denoted as u 0 , w 0 , θ 0 , T0 , γ 0 , obtain the unperturbed motion state: X 0 = [u 0 , 0, w 0 , 0, 0, 0, 0, θ 0 , 0, T 0 , 0, γ 0 ;

[0099] S4. Calculate the parameter matrix

[0100] Divide the motion X into perturbed motion and unperturbed motion X 0 , then Substitute X into Equation (13), where X 0 is the known motion, to obtain the perturbed motion equation with respect to . Rearrange the equation to obtain the parameter matrices A and B;

[0101] S5. Calculate the eigenvalues

[0102] Solve the inverse matrix A of matrix A -1 , and multiply it by matrix B to obtain matrix C = A -1 B. Calculate the eigenvalues λ and eigenvectors of matrix C According to the definitions of eigenvalues and eigenvectors obtain |C - λI| = 0, convert it to the characteristic determinant, and use the Jacobi iterative method to solve for the eigenvalues and eigenvectors;

[0103] S6. Judge the towing stability

[0104] If the real parts of all eigenvalues are less than zero, the system is stable, that is, the perturbed motion tends to zero as time increases.

[0105] Furthermore, step S3 specifically includes the following steps:

[0106] S3.1. Determine the equilibrium point motion parameters;

[0107] S3.2. Determine the unperturbed motion X 0 with 5 unknown variables, namely u, w, θ, T, γ, and the perturbed motion of the remaining variables is 0;

[0108] S3.3. Determine the equilibrium point motion equation;

[0109] S3.4. Solve the equation to obtain the values of the unperturbed motion variables u 0 , w 0 , θ 0 , T 0 , γ 0 , and summarize to form the unperturbed motion state: X 0 = [u0 ,0,w 0 ,0,0,0,0,θ 0 ,0,T 0 ,0,γ 0 .

[0110] Furthermore, step S6 specifically includes the following steps:

[0111] S6.1. Determine all the calculated eigenvalues and eigenvectors;

[0112] S6.2. Make a judgment based on the eigenvalues: if the eigenvalue is a complex number and the real part is negative, it is a damped oscillation mode; if the eigenvalue is a complex number and the real part is positive, it is a divergent oscillation mode; if the eigenvalue is a positive real number, it diverges directly; if the eigenvalue is a negative real number, it decays directly; when the real parts of all eigenvalues are negative, the system is stable;

[0113] S6.3. The motion parameter with a large deviation from the equilibrium point in the eigenvector corresponding to the eigenvalue is the main vibration mode, and analyze the motion equation and design parameters related to this motion parameter through vibration mode analysis;

[0114] S6.4. Modify the relevant design parameters, perform a scanning calculation and optimization. The smaller the negative real part of the eigenvalue, the better the stability.

[0115] The beneficial effects of the present invention are as follows: by considering the influence of the tow cable, the present invention establishes a stability calculation method for the underwater towing system, unifies the calculations under the coupling of the horizontal plane and the vertical plane, analyzes and judges the stability based on the eigenvalues, and judges and makes design improvements based on the eigenvectors. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art or ordinary technicians, other drawings can be obtained based on these drawings without creative efforts.

[0117] Figure 1 It is a schematic diagram of the basic composition of the underwater towing system.

[0118] Figure 2 It is a flow chart of the stability calculation of the present invention.

[0119] Figure 3 It is a simplified schematic diagram of the tow cable of the present invention.

[0120] Figure 4 For different K' v Graph of attitude change after transient disturbance of values.

[0121] Description of reference numerals: towing cable 1, head end 1-1, tail end 1-2, towed body 2, mother ship 3, water plane 4. Detailed implementation manners

[0122] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0123] The towing stability of the underwater towing system is mainly related to the underwater towed body. An important link in the design of the towed body is the towing stability design. It is necessary to perform hydrodynamic simulation or towing tank test on the towed body to obtain hydrodynamic coefficients. At the same time, parameters such as the weight, buoyancy, moment of inertia, center of gravity, center of buoyancy, and towing point coordinates of the towed body are also required to establish a dynamic model for analysis. Currently, the commonly used stability determination criterion is similar to that of an underwater unmanned vehicle. The motion of the towed body is divided into horizontal plane motion and vertical plane motion, considered separately, the model is simplified, and the towing cable tension is set as a fixed known parameter to participate in the operation.

[0124] The present invention proposes a method for calculating the towing stability of an underwater towing system, which takes the towing cable into account for stability calculation, considers the mutual coupling effects of the horizontal plane and the vertical plane, and performs unified calculation. The calculation flow chart is shown in Figure 2 .

[0125] S1. Establish a calculation model

[0126] The motion of the towed body is described by a six-degree-of-freedom equation as follows:

[0127]

[0128] The meanings of the physical quantities in the formula are as follows:

[0129] m: mass of the towed body;

[0130] I: moment of inertia of the towed body, with subscripts corresponding to each axis of rotation;

[0131] x g , y g , z g : coordinates of the center of gravity of the towed body;

[0132] u, v, w: longitudinal, lateral, and vertical motion speeds of the towed body;

[0133] p, q, r: rolling, pitching, and yaw angular velocities of the towed body;

[0134] X, Y, Z: External forces acting on the towed body, mainly including gravity, buoyancy, hydrodynamic force, and tow cable tension;

[0135] K, M, N: External torques acting on the towed body;

[0136] Note: A dot above a physical quantity represents the derivative of that physical quantity with respect to time.

[0137] The transformation matrix between the towed body coordinate system and the global coordinate system is:

[0138]

[0139] φ, θ, ψ: Attitude angles of the towed body, namely roll angle, pitch angle, and yaw angle respectively.

[0140] The relationship between the attitude angle and the angular velocity is described by the Euler's equations of motion:

[0141]

[0142] The external forces acting on the towed body, mainly including gravity, buoyancy, hydrodynamic force, and tow cable tension; can be expressed as:

[0143]

[0144] (1) Calculation of hydrodynamic force and hydrodynamic torque

[0145] It is described by hydrodynamic coefficients. Physical quantities with a prime (' ) represent the hydrodynamic coefficients of the towed body, and their acting forces are:

[0146]

[0147] (2) Calculation of gravity, buoyancy, and their torques

[0148]

[0149]

[0150] G: Weight of the towed body;

[0151] B: Buoyancy of the towed body;

[0152] x b , y b , z b : Coordinates of the center of buoyancy of the towed body.

[0153] (3) Calculation of tow cable tension and its torque

[0154] The dynamic model of the towing system specifically includes the tow cable model and the towed body model. In the tow cable model, the tow cable is simplified as a rigid body, such as Figure 3As shown in the figure, variables \(T\), \(\alpha\), and \(\gamma\) are added, representing the tow cable tension, the yaw angle of the tow cable, and the pitch angle of the tow cable, respectively. The length of the tow cable is \(L\). c .

[0155] The head end 1-1 of the tow cable 1 is connected to the mother ship, and the velocity of the head end point is

[0156]

[0157] where \(V\) is the speed of the mother ship.

[0158] The end 1-2 of the tow cable is connected to the towed body, and its velocity is

[0159]

[0160] The tow cable is simplified as a rigid body, and the transformation matrix between the tow cable coordinate system and the global coordinate system is

[0161]

[0162] where the global tension of the tow cable can be expressed according to the tow cable coordinate system as:

[0163]

[0164] \(\alpha\): the yaw angle of the tow cable;

[0165] \(\gamma\): the pitch angle of the tow cable;

[0166] \(T\): the tow cable tension;

[0167] \(L\) c : the length of the tow cable

[0168] \(T\) x , \(T\) y , \(T\) z : the tension in the global coordinate system.

[0169] Substitute the global tension of the tow cable into the external force of the towed body to realize the coupling of the tow cable.

[0170]

[0171] \(x\) t , \(y\) t , \(z\) t : the coordinates of the towing point.

[0172] According to the rigid body motion law, the velocity relationship between the head end and the end is

[0173]

[0174] \(V\) w , \(V\) s Substitute into the above equation to obtain the motion equation of the tow cable:

[0175]

[0176] Combined with the six-degree-of-freedom motion equation (1) of the towed body, the Euler motion equation (3), and the tow cable motion equation (12), a system of ordinary differential equations with 12 variables is formed:

[0177]

[0178] where \(X = [u, v, w, p, q, r, \varphi, \theta, \psi, T, \alpha, \gamma]\).

[0179] The global tension of the tow cable can be expressed according to the tow cable coordinate system. Substituting the global tension of the tow cable into the external forces of the towed body realizes the coupling of the tow cable.

[0180]

[0181] S2. Input parameters

[0182] Using the above dynamic model, input the ship speed \(V\), cable length \(L\) of the mother ship c , seawater density \(r\), and parameters such as the length, mass, weight, buoyancy, coordinates, and hydrodynamic coefficients of the towed body.

[0183] S3. Calculate the equilibrium point state

[0184] In the equilibrium point motion state, that is, the steady-state motion and the undisturbed motion (denoted as \(X\) 0 ), the time derivatives of all unknowns are zero, the angular velocity is zero, and at the same time, the towed body is generally symmetric left and right, the lateral velocity \(v\) is zero, the roll angle \(\varphi\) and yaw angle \(\psi\) are zero, and the yaw angle \(\alpha\) of the tow cable is zero. Therefore, the 12 unknowns become 5, which are \(u\), \(w\), \(\theta\), \(T\), \(\gamma\) respectively. The corresponding description equations are that the external forces \(X\), \(Z\), the external moment \(M\) are zero, the longitudinal and vertical velocity relationships of the tow cable equation, and the equilibrium point motion equation are as follows:

[0185]

[0186] Solve the equilibrium point motion equation to obtain the values of the undisturbed motion variables \(u\) 0 , \(w\) 0 , \(\theta\) 0 , \(T\) 0 , \(\gamma\) 0 . Compared with the stability of the towing system without considering the tow cable, the calculation of the tow cable tension and the longitudinal inclination angle of the tow cable is increased. The undisturbed motion state is obtained: \(X\) 0 = [u 0 , 0, w 0 , 0, 0, 0, 0, \(\theta\) 0 , 0, \(T\) 0 , 0, \(\gamma\) 0 .

[0187] S4. Calculate the parameter matrix

[0188] Divide the motion X into perturbed motion and unperturbed motion X 0 , then Substitute X into Equation (13), where X 0 is the known motion, to obtain the perturbed motion equation with respect to . Rearrange the equation to obtain the parameter matrices A and B

[0189] S5. Calculate the eigenvalues

[0190] Solve the inverse matrix A of matrix A -1 , and multiply it by matrix B to obtain matrix C = A -1 B. Calculate the eigenvalues λ and eigenvectors of matrix C According to the definitions of eigenvalues and eigenvectors , we can get |C - λI| = 0. Convert it into a characteristic determinant and use the Jacobi iteration method to solve for the eigenvalues and eigenvectors

[0191] S6. Judge the towing stability

[0192] If the real parts of all eigenvalues are less than zero, the system is stable, that is, the perturbed motion tends to zero as time increases. If the absolute value of the real part is small, it means that the change of the perturbed motion with time is slow. Therefore, for the real part close to zero, the corresponding eigenvector needs to be examined. The motion parameter with a large deviation from the equilibrium point in the eigenvector is the main influencing parameter, and the vibration mode of the tow body can be determined. Furthermore, the motion equation and design parameters related to this motion parameter can be analyzed to effectively carry out design improvements

[0193] Step S6 specifically includes the following steps

[0194] S6.1. Determine all the calculated eigenvalues and eigenvectors

[0195] S6.2. Make a judgment based on the eigenvalues: If the eigenvalue is complex and the real part is negative, it is a damped oscillation mode; if the eigenvalue is complex and the real part is positive, it is a divergent oscillation mode. If the eigenvalue is a positive real number, it directly diverges; if the eigenvalue is a negative real number, it directly decays. When the real parts of all eigenvalues are negative, the system is stable

[0196] S6.3. The motion parameter with a large deviation from the equilibrium point in the eigenvector corresponding to the eigenvalue is the main vibration mode. Analyze the motion equation and design parameters related to this motion parameter through the vibration mode

[0197] S6.4. Change the relevant design parameters and perform a scan calculation for optimization. The smaller the negative real part of the eigenvalue, the better the stability

[0198] Example

[0199] (1) Establish an underwater towing system as shown in Figure 1 , and the motion equation is Equation (13), which includes the six-degree-of-freedom motion equation of the towed body (1), the Euler motion equation (3), and the tow cable motion equation (12).

[0200] (2) Input parameters

[0201] Input the speed V of the mother ship, the cable length L c , the seawater density r, and parameters such as the length, mass, weight, buoyancy, coordinates, and hydrodynamic coefficients of the towed body, as shown in the following table.

[0202] Table 1 Underwater towing system parameters

[0203]

[0204] (3) Calculate the equilibrium state

[0205] Calculate the equilibrium state according to Equation (14) to obtain the steady-state values of the following 5 variables, and the steady-state values of other variables are 0.

[0206] u 0 = 3, w 0 = -0.006, θ 0 = -0.115, T 0 = 776.26, γ 0 = 134.51

[0207] (4) Calculate the parameter matrix

[0208] Divide the motion X into perturbed motion unperturbed motion X 0 , then where X 0 = [u 0 , 0, w 0 , 0, 0, 0, 0, θ 0 , 0, T 0 , 0, γ 0 , substitute it into Equation (13) to obtain the perturbed motion equation, and rearrange the equation by moving terms to obtain the parameter matrices A and B.

[0209] Table 2 Numerical values of matrix A

[0210]

[0211] Table 3 Numerical values of matrix B

[0212]

[0213] (5) Calculate the eigenvalues

[0214] The eigenvalues and eigenvectors are solved using the Jacobi iteration method.

[0215] Table 4 Calculation of eigenvalues and eigenvectors

[0216]

[0217] (6) Judging the towing stability

[0218] Based on the fact that the real parts of all calculated eigenvalues are negative, it can be known that the towing system is stable. There are three pairs of conjugate complex numbers, indicating a damped oscillation mode, and the others are negative real numbers that directly decay. It can be seen that the towed body is prone to excite three damped oscillation modes after being disturbed. In particular, the absolute value of the negative real part is small, indicating that the damping is small during the vibration process and the stabilization time is long. In the eigenvectors corresponding to the eigenvalues of -0.17235±0.31281i, α and φ are relatively large, indicating that this mode mainly corresponds to the cable yaw and the towed body roll coupling mode, that is, the tow cable and towed body coupling mode. In the eigenvectors corresponding to the eigenvalues of -0.30889±2.3709i, p and φ are relatively large, indicating that this mode mainly corresponds to the pure roll oscillation mode of the towed body. In the eigenvectors corresponding to the eigenvalues of -0.34585±0.20953i, γ is relatively large, indicating that this mode mainly corresponds to the pitch oscillation mode of the towed body.

[0219] Taking the hydrodynamic coefficient K′ v as the scanning parameter, when K′ v is -0.1, 0.1, and 0.16 respectively, the corresponding mode eigenvalues are -0.055091±1.4057i, -0.17172±0.31371i, and 0.25026±4.8102i respectively. It can be seen that when K′ v =-0.1 - 0.1, as the hydrodynamic coefficient increases, the negative real part becomes smaller and the stability increases. When K′ v =0.16, the real part of the eigenvalue becomes positive and it becomes an unstable state. And such hydrodynamic coefficients are not reflected in the existing stability judgment criteria. According to the change of K′ v , after applying a disturbing cross-sea current disturbance, the change of its attitude is shown in Figure 4 as shown, which is also consistent with the eigenvalue judgment result.

[0220] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the scope disclosed by the present invention should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A method for calculating the towing stability of an underwater towing system, characterized in that: The following steps are involved: S1. Establishing the computational model The motion of the towed body is described by the six-degree-of-freedom equation as follows: The meanings of the physical quantities in the formula are as follows: m: the mass of the towed body; I: moment of inertia of the drag body, the subscripts correspond to the rotation axes; x g ,y g ,z g : coordinates of the center of gravity of the towed body; u, v, w: longitudinal, lateral and vertical movement speeds of the towed body; p, q, r: heel, pitch and yaw angular velocity of the towed body; X, Y, Z: external forces acting on the towed body, mainly gravity, buoyancy, fluid force, and towline tension; K, M, N: external torque on the dragged body; The "·" symbol above a physical quantity indicates the derivative of the physical quantity with respect to time; The transformation matrix between the drag body coordinate system and the global coordinate system is: φ, θ, ψ: attitude angles of the towed body, which are heel angle, pitch angle, and yaw angle respectively; The relationship between attitude angle and angular velocity is described by Euler's equation of motion: The external forces acting on the towed body include gravity, buoyancy, fluid force, and towline tension, which can be expressed as: (1) Calculation of fluid force and fluid moment The hydrodynamic coefficients are used for description. The physical quantities with "'" represent the hydrodynamic coefficients of the towed body, and the acting force is: (2) Calculation of gravity, buoyancy and their moments G: weight of the towed body; B: buoyancy of the towed body; x b ,y b ,z b : The coordinates of the center of buoyancy of the towed body; (3) Calculation of tow cable tension and torque Simplifying the towline as a rigid body, the transformation matrix between the towline coordinate system and the global coordinate system is: The global tension of the towline is expressed according to the towline coordinate system as: α: streamer yaw angle; γ: towline pitch angle; T: towline tension; L c : Length of tow cable T x ,T y ,T z : Tension in the global coordinate system; Substitute the global tension of the tow cable into the external force of the tow cable to achieve the coupling of the tow cable; x t ,y t ,z t : Drag point coordinates; According to the law of rigid body motion, the tow cable motion equation is obtained: Combining the towed body six-degree-of-freedom motion equation (1), Euler motion equation (3), and tow cable motion equation (12) form a set of ordinary differential equations with 12 variables: Where X = [u, v, w, p, q, r, φ, θ, ψ, T, α, γ]; S2. Input parameters Using the above dynamic model, input the mother ship speed V, cable length L c , seawater density r and parameters related to towed body length, mass, weight, buoyancy, coordinates, and hydrodynamic coefficients; S3. Calculate the equilibrium state In the state of equilibrium point motion, that is, steady-state motion, undisturbed motion X0, all unknown quantities have time derivatives of zero, angular velocity is zero, and the towed body is generally symmetrical, the lateral velocity v is zero, the heel angle φ, the yaw angle ψ are zero, and the tow cable yaw angle α is zero; the unknown quantities are u, w, θ, T, γ, and the corresponding description equations are external forces X, Z, and the external torque M is zero. The longitudinal and vertical velocity relationships of the tow cable equation are as follows: The solution result is recorded as u0, w0, θ0, T0, γ0, and the undisturbed motion state is obtained: X0 = [u0, 0, w0, 0, 0, 0, θ0, 0, T0, 0, γ0]; S4. Calculate parameter matrix Divide the motion X into perturbation motion Unperturbed motion X0, then Substituting X into equation (13), where X0 is the known motion, we obtain The perturbed motion equation is sorted out to obtain the parameter matrices A and B; S5. Calculate eigenvalues Solve for the inverse matrix A of matrix A -1 , and multiply it with the B matrix to obtain the matrix C = A -1 B, calculate the eigenvalue λ and eigenvector of matrix C According to the definition of eigenvalue and eigenvector We get |C-λI|=0, convert it into characteristic determinant, and use Jacobi iteration method to solve the eigenvalue and eigenvector; S6. Determine towing stability If the real parts of all eigenvalues ​​are less than zero, the system is stable, that is, the perturbation motion tends to zero as time increases.

2. The method for calculating the towing stability of an underwater towing system according to claim 1, characterized in that: Step S3 specifically includes the following steps: S3.

1. Determine the motion parameters of the equilibrium point; S3.2, determine that the unknown variables of the unperturbed motion X0 are 5, namely u, w, θ, T, γ, and the rest of the variables of the perturbed motion are 0; S3.3, determine the equation of motion of the equilibrium point; S3.

4. Solve the equation to obtain the values ​​of the undisturbed motion variables u0, w0, θ0, T0, γ0, and summarize them to form the undisturbed motion state: X0 = [u0, 0, w0, 0, 0, 0, θ0, 0, T0, 0, γ0].

3. The method for calculating the towing stability of an underwater towing system according to claim 2, characterized in that: Step S6 specifically includes the following steps: S6.

1. Determine all calculated eigenvalues ​​and eigenvectors; S6.

2. Judge based on eigenvalues: if the eigenvalue is a complex number and the real part is negative, it is a damped oscillation mode; if the eigenvalue is a complex number and the real part is positive, it is a divergent oscillation mode; if the eigenvalue is a positive real number, it diverges directly, and if the eigenvalue is a negative real number, it attenuates directly. When the real parts of all eigenvalues ​​are negative, the system is stable; S6.

3. The motion parameter with the largest deviation from the equilibrium point in the eigenvector corresponding to the eigenvalue is the main vibration mode. The motion equation and design parameters related to the motion parameter are analyzed through the vibration mode. S6.

4. Change the relevant design parameters to scan and optimize the calculation. The smaller the negative real part of the eigenvalue, the better the stability.

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