Dynamic stability analysis method for large ship lift suspension system

Abstract

The invention provides a dynamic stability analysis method for a suspension system of a large ship lift. The method comprises the following steps: establishing a four-suspension-point fluid-solid coupling dynamics simplified physical model of the suspension system of a ship lift chamber of the ship lift; on the basis of a simplified physical model, according to an analysis mechanics Lagrange equation, a seven-degree-of-freedom fluid-solid coupling kinetic equation of water body shaking, main elevator rotation and ship reception chamber rigid plane motion is constructed; the seven-degree-of-freedom fluid-solid coupling kinetic equation is converted into a damped five-degree-of-freedom second-order ordinary differential linear differential equation of water body shaking, ship reception chamber trim and synchronous shaft system torsional vibration through variable transformation and Rayleigh damping injection in a synchronous shaft torsional vibration system; converting the damped five-degree-of-freedom second-order ordinary differential linear differential equation into a 10-variable first-order state equation; calculating a characteristic value of the variable first-order state equation; and calculating a stability safety coefficient according to the characteristic value. According to the method, the dynamic stability of the large ship lift suspension system can be simply and conveniently judged.

Description

Technical Field

[0001] The present invention relates to the field of water conservancy and hydropower engineering, and particularly to a method for analyzing the dynamic stability of a suspension system of a large ship lift. Background Art

[0002] As a navigation facility of a water conservancy project, the counterweight ship lift has the advantages of water saving, time saving and adaptability to high water heads compared with a ship lock. However, there is still a gap in throughput compared with a ship lock at present. Therefore, the enlargement of the ship lift is the way for the further development of this navigation type in a water conservancy project, and it is of great significance for comprehensively solving the problem of the navigation of large-tonnage ships in a high-lift water conservancy project and improving the shipping throughput of the ship lift.

[0003] The fully balanced wire rope hoisting vertical ship lift has the advantages of both safety and economy, and is simple and convenient to maintain. The suspension system of the fully balanced wire rope hoisting vertical ship lift includes a ship chamber and the water body inside it, suspension wire ropes and a main hoist (for a large ship lift, specifically a ship lift with a large ship chamber length, the main hoist arrangement needs to adopt 8 hoisting mechanisms, such as Figure 2 and Figure 3 shown). Since the fully balanced wire rope hoisting vertical ship lift is in a vertical lifting and lowering operation condition, the ship chamber is a water-containing container, and a flexible support method using lifting wire ropes is adopted. The sloshing of the water body in the ship chamber causes changes in the forces and deformations of the lifting wire ropes and the main hoist synchronous shaft. Since the lifting wire ropes only account for a small part of all the wire ropes suspending the ship chamber, and the remaining suspension wire ropes are gravity balance ropes, they do not play a supporting role for the ship chamber during the lifting and lowering of the ship chamber. When the overall layout of the ship lift suspension system is unreasonable, the disturbance of the water body will cause the dynamic instability of the ship lift suspension system, and its manifestation forms are the overturning of the ship chamber and the huge deformation or even fracture of the synchronous shaft system. Therefore, the stability of the suspension system of a large fully balanced wire rope hoisting vertical ship lift is an important issue that should be considered in the overall layout of this type of ship lift.

[0004] The characteristics of the suspension system of a large fully balanced wire rope hoisting vertical ship lift are that the limited size of the water area in the ship chamber is large, and the main hoist usually adopts eight hoisting machines, that is, two hoisting machines are used to drive in each hoisting point area of the main hoist, and the number of the driving lifting wire ropes (referred to as lifting ropes) is large and the distribution length is large. If the method of modeling by simplifying all the wire ropes in the same hoisting point area into a single spring and simplifying the two independent hoisting mechanisms in the same hoisting point area of the main hoist into a single thin-walled rigid ring with two hoisting points is adopted, then this simplified physical model cannot reflect the structural characteristics of a large ship lift with a large number and wide distribution of lifting wire ropes in the same hoisting point area and the arrangement of two hoisting mechanisms in the same hoisting point area of the main hoist. Summary of the Invention

[0005] In view of this, the present invention provides a method for analyzing the dynamic stability of a suspension system of a large ship lift, which can simply and conveniently judge the dynamic stability of the suspension system of the large ship lift.

[0006] A method for analyzing the dynamic stability of a suspension system of a large ship lift includes the following steps:

[0007] Step 1: Establish a simplified physical model of the fluid-structure interaction dynamics of the four-hoist-point suspension system of the ship lift cabin that reflects the characteristics of a large fully balanced wire-rope hoisting ship lift. <>

[0008] Step 2: Based on the established simplified physical model of the fluid-structure interaction dynamics of the four-hoist-point suspension system of the ship lift cabin, construct a 7-degree-of-freedom fluid-structure interaction dynamics equation for water body sloshing, main hoist rotation, and rigid plane motion of the ship lift cabin according to the Lagrange equation of analytical mechanics.

[0009] Step 3: Transform the 7-degree-of-freedom fluid-structure interaction dynamics equation through variable transformation and injecting Rayleigh damping into the synchronous shaft torsional vibration system into a damped 5-degree-of-freedom second-order ordinary differential linear differential equation for water body sloshing, longitudinal tilt of the ship lift cabin, and torsional vibration of the synchronous shaft system.

[0010] Step 4: Transform the damped 5-degree-of-freedom second-order ordinary differential linear differential equation into a 10-variable first-order state equation.

[0011] Step 5: Use the commercial software MATLAB to perform programming numerical calculations on the eigenvalues of the 10-variable first-order state equation.

[0012] Step 6: Calculate the dynamic stability safety factor of the ship lift suspension system according to the eigenvalues obtained in Step 5. The dynamic stability safety factor of the ship lift suspension system is used to quantitatively evaluate the margin of the dynamic stability of the suspension system of the large ship lift.

[0013] Furthermore, the simplified physical model of the fluid-structure interaction dynamics of the four-hoist-point suspension system of the ship lift cabin established in Step 1 includes the ship lift cabin, the water body in the cabin, the suspension wire ropes, and the main hoist. The ship lift cabin is simplified as a rigid body performing planar motion, the water body in the cabin is a fluid satisfying the Hausner sloshing assumption, the suspension wire ropes are simplified as four linear springs satisfying Hooke's law according to the distribution in the hoist point area, and the main hoist is simplified as four thin-walled rigid rotating bodies connected by three sections of synchronous shafts. The moment of inertia of each thin-walled rigid rotating body about its own axis is one-fourth of the moment of inertia of all rotating components of the main hoist about their own axes converted to the moment of inertia of the winch output shaft.

[0014] Furthermore, Step 2 specifically includes:

[0015] 1) Construct a mathematical model of the first subsystem for the coupled motion of the water body in the ship lift cabin and the rigid body of the ship lift cabin:

[0016] Using the Hausner assumption, the fluid-solid coupling dynamic equation of the ship support box and the water body is established:

[0017] (1);

[0018] Where θ0 is the sloshing angle of the free surface of the water in the hull when the hull is tilting, α is the tilting angle of the hull, and ω is the w is the first-order natural frequency of water sloshing, which can be calculated as follows:

[0019] (2);

[0020] h is the design water depth of the ship-carrying compartment, L is the maximum water length of the ship-carrying compartment, and g is the acceleration of gravity;

[0021] The vertical force of water on the ship support box and the overturning moment around the center of mass are:

[0022] (3);

[0023] (4);

[0024] Where, P w and M w are the vertical pressure of the water in the ship support chamber on the ship support chamber and the overturning moment around the center of mass, J w and C w In order to characterize the physical parameters of the dynamic moment and static moment of the water body on the ship support box, they are calculated as follows:

[0025] (5)

[0026] (6)

[0027] Where ρ = 1t / m 3 is the density of the water body, B is the maximum water width of the ship compartment;

[0028] 2) Construct the mathematical model of the second subsystem in which the rotation of the main hoist and the plane rigid body motion of the ship support box are coupled:

[0029] (7-a);

[0030] (7-b);

[0031] (7-c);

[0032] (7-d);

[0033] (7-e);

[0034] (7-f); Wherein, are respectively the angles of rotation of four thin-walled rigid rotating bodies representing eight hoists of the main hoist; α is the longitudinal inclination angle of the ship chamber; y is the vertical displacement of the ship chamber; θ0 is the sloshing angle of the free surface of the water in the chamber; R is the drum radius, a is the longitudinal center distance between two suspension points of the main hoist, b is the center distance between two hoists in one suspension point area, is the vertical displacement of the centroid of the ship chamber, C s1 is twice the value of the torsional stiffness of the synchronous shaft between two hoists in the same suspension point area converted to the output shaft of the main hoist according to the energy equivalence principle, C s2 is twice the value of the torsional stiffness of the synchronous shaft between adjacent hoists in two suspension point areas on the same side of the main hoist converted to the output shaft of the main hoist according to the energy equivalence principle, J h is one quarter of the total moment of inertia of all rotating parts of the main hoist relative to the low-speed shaft; k r is one quarter of the sum of the tensile stiffnesses of all the lifting ropes of the ship hoist when the ship chamber is at the lowest navigable position; k r , C s1 and C s2 are respectively calculated according to the following formulas:

[0035] (8);

[0036] (9);

[0037] (10);

[0038] In formulas (8) to (10), n r is the total number of steel wires wound on the drum of the main hoist; E r is the elastic modulus of the steel wire, A r is the cross-sectional area of the steel wire, H is the maximum suspension height of the lifting rope suspending the ship chamber, G is the shear elastic strain of the steel, I s is the polar moment of inertia of the cross-section of a single synchronous shaft, i s is the ratio of the rotational speed of the synchronous shaft system to the rotational speed of the drum;

[0039] 3) Integrate the mathematical model of the first subsystem and the mathematical model of the second subsystem to construct a 7-degree-of-freedom fluid-structure interaction dynamics equation:

[0040] (11-a);

[0041] (11 - b);

[0042] (11 - c);

[0043] (11 - d);

[0044] (11 - e);

[0045] (11 - f);

[0046] (11 - g).

[0047] Further, Step 3 specifically includes: Through variable transformation , , , , transform the 7 - degree - of - freedom fluid - structure interaction dynamics equation into a 5 - degree - of - freedom coupled vibration linear differential equation that describes the coupling of water body sloshing, longitudinal tilt of the ship - carrying chamber, and torsional vibration of the synchronous shaft in the large - scale ship lift suspension system. According to the torsional vibration theory of mechanical systems, Rayleigh damping is injected into the torsional vibration system of the main hoist to form the following damped 5 - degree - of - freedom second - order differential linear differential equation for water body sloshing, longitudinal tilt of the ship - carrying chamber, and torsional vibration of the main hoist synchronous shaft:

[0048] (12 - a);

[0049] (12 - b);

[0050] (12 - c);

[0051] (12 - d);

[0052] (12 - e);

[0053] In the formula, d s1 and d s2 are the Rayleigh damping coefficients of the synchronous shaft between two winches in the same suspension point area and the synchronous shaft between adjacent winches in two suspension point areas on the same side of the main hoist, respectively; ζ is the damping ratio of the torsional vibration of the synchronous shaft system.

[0054] Further, d s1 and d s2 are calculated according to the following formulas respectively:

[0055] (13 - a);

[0056] (13 - b).

[0057] Furthermore, ζ takes the value of 0.008.

[0058] Furthermore, in step four, the damped 5-degree-of-freedom second-order ordinary differential linear differential equation is rewritten in the form of the following 10-variable first-order state equation:

[0059] (14);

[0060] where x = (x1, x2, x3, x4, x5, x6, x7, x8, x9, x 10 )

[0061] (15);

[0062] In equation (15), the expressions for the relevant elements a i (i = 1~13) of the state matrix M are as follows:

[0063] (16-a);

[0064] (16-b);

[0065] (16-c);

[0066] (16-d);

[0067] (16-e);

[0068] (16-f); (16-g);

[0069] (16-h);

[0070] (16-i);

[0071] (16-j);

[0072] (16-k);

[0073] (16-l);

[0074] (16-m).

[0075] Further, in step five, the state matrix expression and the calculation formula for each element of the 10-variable first-order state equation are derived to obtain the eigenvalues of the state matrix. When the real parts of all eigenvalues of the state equation are negative, the suspension system of the ship lift is dynamically stable; when the real part of any eigenvalue is greater than zero, the system is unstable.

[0076] Further, step six specifically includes:

[0077] 1) Define and calculate the critical value a of the longitudinal center distance of the main hoist of the large ship lift suspension system as follows c : Simultaneously reduce the longitudinal center distance a of the main hoist and the center distance b of the hoisting mechanism in the same suspension point area to a n and b n , and calculate the eigenvalues of the state matrix for each pair of a n and b n values. When the ratio of the difference in the center distance values between two calculations to the larger center distance value in the two calculations is less than or equal to the preset value, and the real parts of the eigenvalues of the state matrix change signs during the two calculations, the larger center distance value is defined as the critical value a of the longitudinal center distance of the main hoist of the ship lift suspension system c ;

[0078] 2) Define the ratio of the designed value a of the longitudinal center distance of the main hoist of the ship lift to the critical value a c of the longitudinal center distance of the main hoist of the large ship lift suspension system as the safety factor to evaluate the safety margin of the dynamic stability of the large ship lift suspension system:

[0079] (17).

[0080] Further, the preset threshold is 0.05%.

[0081] Based on the dynamic simplified physical model of the four-suspension-point ship lift suspension system, a 7-degree-of-freedom motion differential equation describing the coupling of the rotation of the main hoist of the large ship lift suspension system, the planar rigid body motion of the ship chamber, and the water body sloshing is established, and through variable transformation, it is transformed into a 5-degree-of-freedom undamped coupled linear vibration equation describing the water body sloshing, the longitudinal tilt of the ship chamber, and the torsional vibration of the synchronous shaft. According to the mechanical vibration theory, Rayleigh damping is injected into the synchronous shaft torsional vibration system, so that the 5 degrees of freedom; then the spectral stability method of the stability theory of ordinary differential equations with constant coefficients is applied, and by calculating the eigenvalues of the state equation and judging the positive and negative signs of the real parts of the eigenvalues, the dynamic stability of the large ship lift suspension system can be simply and conveniently judged. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 is a four-suspension-point model diagram for the dynamic stability analysis of the ship lift suspension system.

[0083] Figure 2It is a longitudinal sectional view of the suspension system of a large fully balanced wire rope hoisting vertical ship lift.

[0084] Figure 3 It is the plane layout of the main hoist of a large fully balanced wire rope hoisting vertical ship lift.

[0085] Figure 4 It is a flowchart of a method for analyzing the dynamic stability of a suspension system of a large ship lift provided by an embodiment of the present invention. Detailed implementation manners

[0086] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some but not all of the embodiments of the present invention. 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.

[0087] Please refer to Figure 4 , an embodiment of the present invention provides a method for analyzing the dynamic stability of a suspension system of a large ship lift, including the following steps:

[0088] Step 1: Establish a simplified physical model of a fluid-structure interaction dynamics of a four-point suspension system of a ship lift car that reflects the characteristics of a large fully balanced wire rope hoisting ship lift;

[0089] Step 2: Based on the established simplified physical model of the fluid-structure interaction dynamics of the four-point suspension system of the ship lift car, construct a 7-degree-of-freedom fluid-structure interaction dynamics equation for water body sloshing, main hoist rotation and rigid plane motion of the ship lift car according to the Lagrange equation of analytical mechanics;

[0090] Step 3: Convert the 7-degree-of-freedom fluid-structure interaction dynamics equation into a damped 5-degree-of-freedom second-order ordinary differential linear differential equation for water body sloshing, longitudinal tilt of the ship lift car and torsional vibration of the synchronous shaft system through variable transformation and injection of Rayleigh damping into the synchronous shaft torsional vibration system;

[0091] Step 4: Convert the damped 5-degree-of-freedom second-order ordinary differential linear differential equation into a 10-variable first-order state equation;

[0092] Step 5: Numerically calculate the eigenvalues of the 10-variable first-order state equation by programming using the commercial software MATLAB; specifically, deduce the state matrix expression and calculation formulas for each element of the 10-variable first-order state equation, and calculate the eigenvalues of the state matrix; when the real parts of all eigenvalues of the state equation are negative, the suspension system of the ship lift is dynamically stable, and when the real part of any eigenvalue is greater than zero, the system is unstable;

[0093] Step 6: Calculate the dynamic stability safety factor of the ship lift suspension system based on the characteristic value obtained in step 5. The dynamic stability safety factor of the ship lift suspension system is used to quantitatively evaluate the margin of dynamic stability of the large ship lift suspension system.

[0094] Aiming at the characteristics of large ship lifts with long ship carriages, many suspension wire ropes, and two winches in each lifting point area of the main hoist, the present invention establishes a simplified physical model of the four-lifting-point fluid-solid coupling dynamics of the ship lift's ship carriage suspension system, including the ship carriage, water inside the carriage, suspension wire ropes, and the main hoist. Figure 1 As shown in the figure. In this simplified physical model, the ship support compartment is simplified to a rigid body moving in a plane, the water inside the compartment is a fluid that satisfies the Hausner sloshing assumption, the suspension wire rope is simplified to four linear springs that satisfy Hooke's law based on the distribution of the suspension points, and the main hoist is simplified to four thin-walled rigid rotating bodies connected by three synchronous shafts. The moment of inertia of each thin-walled rigid rotating body about its own axis is converted to one-quarter of the moment of inertia of all the rotating components of the main hoist about their own axis and then transferred to the winch output shaft. The equivalent stiffness of the synchronous shaft in the simplified physical model is calculated based on the energy equivalence method, which converts the speed reducer's secondary high-speed shaft to the speed reducer's low-speed output shaft.

[0095] In step 2, considering that the large ship lift suspension system is a complex coupling system consisting of a main hoist and synchronous shaft system, a suspension wire rope, a ship support compartment and water in the compartment, and containing multiple coupling subsystems, a mathematical model for the dynamic stability analysis of the system dynamics is constructed based on the simplified physical model of the fluid-solid coupling dynamics of the four-hanging-point ship lift compartment suspension system. The construction of the mathematical model adopts a local-first-overall approach, that is, first construct a mathematical model of the first subsystem in which the water in the ship support compartment and the rigid body motion of the compartment are coupled to each other, and a mathematical model of the second subsystem in which the main hoist rotation and the planar rigid body motion of the ship support compartment are coupled to each other, and then the two subsystem mathematical models are combined to construct an overall mathematical model of the large ship lift suspension system (expressed by a 7-degree-of-freedom fluid-solid coupling dynamics equation) that describes the swaying of the water, the rotation of the main hoist and the planar rigid body motion of the ship support compartment. The specific steps are as follows:

[0096] 1) Construct the mathematical model of the first subsystem of the coupling between the water body of the ship compartment and the rigid body motion of the ship compartment:

[0097] Using the Hausner assumption, the fluid-solid coupling dynamic equation of the ship support and the water body is established

[0098] (1)

[0099] Where θ0 is the sloshing angle of the free surface of the water in the hull when the hull is tilting, α is the tilting angle of the hull, and ω is the w is the first-order natural frequency of water sloshing, which can be calculated as follows:

[0100] (2)

[0101] h is the designed water depth of the ship chamber, L is the maximum water area length of the ship chamber, and g is the acceleration due to gravity.

[0102] The vertical force of the water body on the ship chamber and the overturning moment about the centroid are as follows:

[0103] (3)

[0104] (4)

[0105] In the formula, P w and M w are respectively the vertical pressure of the water body in the ship chamber on the ship chamber and the overturning moment about the centroid. J w and C w are physical parameters characterizing the dynamic moment and static moment of the water body on the ship chamber, and are calculated respectively according to the following formulas

[0106] (5)

[0107] (6)

[0108] In the formula, ρ = 1 t / m 3 is the density of the water body, and B is the maximum water area width of the ship chamber.

[0109] 2) Construct the mathematical model of the second subsystem that couples the rotation of the main hoist and the planar rigid body motion of the ship chamber:

[0110] (7-a)

[0111] (7-b)

[0112] (7-c)

[0113] (7-d)

[0114] (7-e)

[0115] (7-f)

[0116] In the formula, They are the angles of rotation of four thin-walled rigid rotators representing eight hoists of the main hoist respectively; α is the longitudinal inclination angle of the ship chamber; y is the vertical displacement of the ship chamber; θ0 is the sloshing angle of the free surface of the water in the chamber; R is the radius of the drum, a is the longitudinal center distance between two suspension points of the main hoist (usually simply referred to as the longitudinal suspension point center distance), b is the center distance between two hoists in one suspension point area, is the vertical displacement of the centroid of the ship chamber, C s1 is twice the value obtained by converting the torsional stiffness of the synchronous shaft (hereinafter referred to as shaft section 1) between two hoists in the same suspension point area to the output shaft of the main hoist according to the energy equivalence principle, C s2 is twice the value obtained by converting the torsional stiffness of the synchronous shaft (hereinafter referred to as shaft section 2) between adjacent hoists in two suspension point areas on the same side (left or right) of the main hoist to the output shaft of the main hoist according to the energy equivalence principle, J h is one-fourth of the total moment of inertia of all rotating components of the main hoist relative to the low-speed shaft (drum shaft); k r is one-fourth of the sum of the tensile stiffnesses of all lifting ropes of the ship lift when the ship chamber is at the lowest navigable position. k r 、 C s1 and C s2 are calculated respectively according to the following formulas:

[0117] (8)

[0118] (9)

[0119] (10)

[0120] In formulas (8) to (10), n r is the total number of steel wires wound on the drum of the main hoist; E r is the elastic modulus of the steel wire, A r is the cross-sectional area of the steel wire, H is the maximum suspension height of the lifting rope suspending the ship chamber, G is the shear elastic strain of the steel, I s is the polar moment of inertia of the cross-section of a single synchronous shaft, i s is the ratio of the rotational speed of the synchronous shaft system to the rotational speed of the drum;

[0121] 3) Integrate the above two subsystem mathematical models to construct the motion differential equation of the suspension system of the large-scale ship lift (7-degree-of-freedom fluid-structure coupling dynamics equation).

[0122] (11-a)

[0123] (11-b)

[0124] (11-c)

[0125] (11-d)

[0126] (11-e)

[0127] (11-f)

[0128] (11-g)

[0129] In step 3, through variable transformation , , , , the 7-degree-of-freedom fluid-structure interaction dynamics equation described by Equation (11) is transformed into a 5-degree-of-freedom coupled vibration linear differential equation that describes the coupling of water body sloshing, longitudinal tilt of the ship chamber, and torsional vibration of the synchronous shaft in the large ship lift suspension system. According to the torsional vibration theory of mechanical systems, Rayleigh damping is injected into the torsional vibration system of the main hoist to form the following damped 5-degree-of-freedom second-order differential linear differential equation for water body sloshing, longitudinal tilt of the ship chamber, and torsional vibration of the main hoist synchronous shaft:

[0130] (12-a)

[0131] (12-b)

[0132] (12-c)

[0133] (12-d)

[0134] (12-e)

[0135] where d s1 and d s2 are the Rayleigh damping coefficients of shaft section 1 and shaft section 2 of the synchronous shaft system, respectively, and are calculated according to the following formulas:

[0136] (13-a)

[0137] (13-b)

[0138] ζ is the damping ratio of the torsional vibration of the synchronous shaft system. According to the mechanical vibration theory, for safety considerations, it is taken as 0.008.

[0139] In step 4, the damped 5-degree-of-freedom second-order ordinary differential linear differential equation (12) is written in the form of the following 10-variable first-order state equation:

[0140] (14)

[0141] In the formula, x = (x1, x2, x3, x4, x5, x6, x7, x8, x9, x 10 )

[0142] (15)

[0143] For the relevant elements a of the state matrix M in formula (15) i (i = 1 to 13), the expressions are as follows:

[0144] (16 - a)

[0145] (16 - b)

[0146] (16 - c)

[0147] (16 - d)

[0148] (16 - e)

[0149] (16 - f)

[0150] (16 - g)

[0151] (16 - h)

[0152] (16 - i)

[0153] (16 - j)

[0154] (16 - k)

[0155] (16 - l)

[0156] (16 - m)

[0157] In step five, substitute the relevant parameters into formula (16) to obtain the values of the above elements, and calculate the eigenvalues of the matrix M described by formula (15). According to the positive or negative sign of the real part of the eigenvalues, the dynamic stability of the ship lift suspension system can be judged. If the real parts of all 10 eigenvalues are less than zero, the system is stable; if the real part of any one of the 10 eigenvalues is greater than zero, the system is unstable.

[0158] During the calculation, programming calculation can be carried out with the help of the commercial software MATLAB, and its execution statement is:

[0159] M = [0 1 0 0 0 0 0 0 0 0; a1 a2 a3 0 0 0 a4 0 0 0; 0 0 0 1 0 0 0 0 0 0; a5 0 a6 a7 a5 0 a8 0 0 0; 0 0 0 0 0 1 0 0 0 0; 0 0 a3 0 a1 a2 a4 0 0 0; 0 0 0 0 0 0 0 1 0 0; a9 0 a 10 0 a9 0 a 11 0 a 12 0; 0 0 0 0 0 0 0 0 0 1; 0 0 0 0 0 0 a 13 0 a 13 0];

[0160] d = eig(M).

[0161] The specific implementation steps of Step 6 are as follows:

[0162] 1) Define and calculate the critical value a of the longitudinal center distance of the main hoist of the large ship lift suspension system according to the following method c : Simultaneously reduce the longitudinal center distance a of the main hoist and the center distance b of the hoisting mechanism in the same suspension point area to a n and b n (that is, the ratio b n / a n remains unchanged during the reduction process), and calculate the eigenvalues of the state matrix for each pair of a n and b n values. When the difference between the center distance values taken in two calculations and the larger value of the center distance in the two calculations is less than or equal to a preset threshold (for example, 0.05%), and the real parts of the eigenvalues of the state matrix in the two calculations change signs, it is stipulated that the larger value of the center distance is the critical value a of the longitudinal center distance of the main hoist of the ship lift suspension system c .

[0163] 2) Define the ratio of the designed value a of the longitudinal center distance of the main hoist of the ship lift to the critical value a of the longitudinal center distance of the main hoist of the large ship lift suspension system as the safety factor, which is used to evaluate the safety margin of the dynamic stability of the large ship lift suspension system: c

[0164] (17)

[0165] The following is an illustration with a specific example: Among the fully balanced wire rope hoisting type vertical ship lifts that have been built so far, only the 2×500t ship lift at Shuikou Power Station on the Minjiang River in Fujian and the 2×500t ship lift at Tingzikou of the Jialing River Water Control Project have relatively large ship lift compartments. However, for the main hoist of the Shuikou ship lift, there is only one hoisting mechanism at each hanging point area, which is no different from the layout type of the main hoists of other medium-sized ship lifts in China. For the main hoist of the Tingzikou ship lift, two hoisting mechanisms are arranged at each hanging point area, as shown in Figure 3 shown. Therefore, the embodiment of the present invention takes the Tingzikou ship lift as an example to illustrate the calculation steps. The maximum water area length of the ship lift compartment of the Tingzikou ship lift is 128m×12.4m×2.5m (length×width×water depth). The total number of suspension wire ropes of the ship lift compartment is 200, among which 64 are hoisting wire ropes, and the rest are gravity balance ropes. However, only the hoisting wire ropes have an elastic supporting effect on the ship lift compartment during the lifting and lowering operation of the ship lift compartment. The diameter of the wire rope is 66mm, and the calculated cross-sectional area corresponding to the elastic modulus is 2736mm 2 . Therefore, for the dynamic model of the 4-hanging-point suspension system of the Tingzikou ship lift, the 16 wire ropes wound on the 4 drums of the two hoisting mechanisms at the same longitudinal position on both sides of the center line of the machine room ship lift compartment are simplified into one spring; correspondingly, all the rotating parts of the two hoisting mechanisms are equivalent to a thin-walled ring with a radius of 2m (the radius value of the rope groove center of the drum).

[0166] 1. Basic input parameters

[0167] Table 1 Basic technical parameter table

[0168]

[0169] 2. Calculation intermediate parameters

[0170] According to formulas (2), (5), (6), and formulas (9-a) and (9-b), calculate k r , C s1 , C s2 , ω w , J w , C w , d s1 and d s2 and other intermediate parameters.

[0171] Table 2 Intermediate parameter value table

[0172]

[0173] 3. Calculate the unknown elements of the state matrix

[0174] According to formulas (12-a)~(12-m), calculate the unknown element values a i (i = 1~13).

[0175] Table 3 Calculated values of unknown elements

[0176]

[0177] 4. Calculate the eigenvalues of the state matrix

[0178] Use the MATLAB commercial calculation software to calculate the eigenvalues of the state matrix. The eigenvalues of the state matrix can be obtained by using the following two commands:

[0179] M = [0 1 0 0 0 0 0 0 0 0; -654.74 -0.4094 135.53 0 0 0 99.89 0 0 0; 0 0 0 1 0 0 0 0 0 0; 322.26 0 -281.29 -0.26835 322.26 0 237.5 0 0 0; 0 0 0 0 0 1 0 0 0 0; 0 0 135.53 0 -654.74 -0.4094 99.89 0 0 0; 0 0 0 0 0 0 0 1 0 0; 0.49785 0 0.76825 0 0.49785 0 -27.568 0 -3.451 0; 0 0 0 0 0 0 0 0 0 1; 0 0 0 0 0 0 -0.01495 0 -0.01495 0];

[0180] d = eig(M)

[0181] The first command is to assign a value to the state matrix, and the second command is to find the eigenvalues of the state matrix.

[0182] After entering the above commands, MATLAB executes the commands and gives the following 5 pairs of eigenvalues:

[0183] -0.18633 ± 28.399i, -0.20261 ± 25.326i, -0.14635 ± 11.026i, -0.0046837 ± 4.9674i, -2.4522×10 -7 ±0.11363i

[0184] where i is the unit complex number. The real parts of the above complex numbers are all negative, indicating that the suspension system of the Tingzikou ship lift is dynamically stable. This is consistent with the current stable state of the ship lift's lifting and lowering operation.

[0185] 5. Evaluation of the dynamic stability margin of the suspension system

[0186] In the calculation formulas (12-a) to (12-m) of the unknown elements of the state matrix, the longitudinal hoisting point center distance a of the main hoist and the longitudinal spacing b between two winch hoists in the same hoisting point area are respectively taken as values smaller than the original design, and the original design ratio relationship b / a = 0.3032 is maintained, and other parameters remain unchanged, and the eigenvalues of the state matrix M are calculated. By continuously reducing the values of a and b, the eigenvalues of the state matrix M are repeatedly calculated using MATLAB programming. It is found that when a = 23.73m and b = 7.174m, the eigenvalues of the state matrix are:

[0187] −0.3088±47.168i, −0.33617±42.02i, −0.2494±17.657i, −0.000095548±1.8621i, −4.0441×10 -7 ±0.0034477i,

[0188] The real parts of the above eigenvalues are all less than 0, indicating that the suspension system of the ship lift is stable at this time.

[0189] When a = 23.72m and b = 7.170m, the eigenvalues of the state matrix are:

[0190] −0.30886±47.178i, −0.33624±42.028i, −0.24944±17.660i, −0.00009540—6±1.8613i, −0.00069255, 0.00069174.

[0191] The last two of the above eigenvalues are real numbers, and one of them is greater than zero, indicating that the suspension system of the ship lift is unstable at this time.

[0192] The relative difference between the two a values of 23.73 and 23.72 is 0.042%, which is less than 0.05%. Therefore, 23.73 is taken as the critical value of the longitudinal center distance of the main hoist of the suspension system of the ship lift. The dynamic stability safety factor of the suspension system of the ship lift is:

[0193]

[0194] Since the dynamic instability of the suspension system of the ship lift is mainly caused by the longitudinal tilt instability of the ship chamber, the minimum value of the safety factor here can be taken as the minimum value of the longitudinal tilt stability safety factor specified in the "Design Code for Ship Lifts" (GB51177-2016), and its value is 2.2. The above calculations show that the dynamic stability safety factor (2.78) of the suspension system of the Tingzikou Ship Lift is greater than the minimum safety factor of 2.2. Therefore, the suspension system of the ship lift is dynamically stable. This is consistent with the current stable operation state of the Tingzikou Ship Lift.

[0195] As described above, it 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 technical scope disclosed by the present invention should be covered within 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 analyzing the dynamic stability of a suspension system of a large ship lift, characterized in that It includes the following steps: Step 1: Establish a simplified physical model of the fluid-structure interaction dynamics of the four-point suspension system of the ship lift's ship chamber, which reflects the characteristics of a large fully balanced wire rope hoisting ship lift; Step 2: Based on the established simplified physical model of the fluid-structure interaction dynamics of the four-point suspension system of the ship lift's ship chamber, construct a 7-degree-of-freedom fluid-structure interaction dynamics equation for water body sloshing, main hoist rotation, and rigid plane motion of the ship chamber according to the Lagrange equation of analytical mechanics; Step 3: Through variable transformation and injecting Rayleigh damping into the synchronous shaft torsional vibration system, convert the 7-degree-of-freedom fluid-structure interaction dynamics equation into a damped 5-degree-of-freedom second-order ordinary differential linear differential equation for water body sloshing, ship chamber longitudinal tilt, and synchronous shaft system torsional vibration; Step 4: Convert the damped 5-degree-of-freedom second-order ordinary differential linear differential equation into a 10-variable first-order state equation; Step 5: Use the commercial software MATLAB to perform programming numerical calculations on the eigenvalues of the 10-variable first-order state equation; Step 6: Calculate the dynamic stability safety factor of the ship lift suspension system based on the eigenvalues obtained in Step 5. The dynamic stability safety factor of the ship lift suspension system is used to quantitatively evaluate the margin of the dynamic stability of the large ship lift suspension system.

2. The dynamic stability analysis method of the large ship lift suspension system according to claim 1, characterized in that: The simplified physical model of the fluid-structure interaction dynamics of the four-point suspension system of the ship lift's ship chamber established in Step 1 includes the ship chamber, the water body inside the chamber, the suspension wire ropes, and the main hoist. The ship chamber is simplified as a rigid body performing planar motion, the water body inside the chamber is a fluid that satisfies the Hausner sloshing assumption, the suspension wire ropes are simplified as four linear springs that satisfy Hooke's law according to the distribution in the suspension point area, and the main hoist is simplified as four thin-walled rigid rotating bodies connected by three sections of synchronous shafts. The moment of inertia of each thin-walled rigid rotating body about its own axis is one-fourth of the moment of inertia of all the rotating components of the main hoist about their own axes converted to the moment of inertia of the winch output shaft.

3. The dynamic stability analysis method of the suspension system of the large ship lift according to claim 1, characterized in that: Step 2 specifically includes: 1) Construct a mathematical model of the first subsystem that couples the motion of the water body in the ship chamber and the rigid body of the ship chamber: Adopt the Hausner assumption to establish the fluid-structure interaction dynamics equation of the ship chamber and the water body: (1)； In the formula, θ0 is the sloshing angle of the free surface of the water body in the ship chamber during the longitudinal inclination movement of the ship chamber, α is the longitudinal inclination angle of the ship chamber, and ω w is the first-order natural frequency of the water body sloshing, which is calculated according to the following formula: (2)； h is the designed water depth of the ship chamber, L is the maximum water area length of the ship chamber, and g is the acceleration due to gravity; The vertical force of the water body on the ship chamber and the overturning moment about the centroid are: (3)； (4)； where, P w and M w are respectively the vertical pressure of the water body in the ship chamber on the ship chamber and the overturning moment about the centroid of mass, J w and C w are physical parameters characterizing the dynamic moment and static moment of the water body on the ship chamber, and are calculated respectively according to the following formulas: (5)； (6)； where ρ = 1 t / m 3 is the density of the water body, and B is the maximum water area width of the ship carriage; 2) Construct a mathematical model of the second subsystem that couples the rotation of the main hoist and the planar rigid body motion of the ship chamber: (7-a)； (7-b)； (7-c)； (7-d)； (7-e)； (7-f)； In the formula, are respectively the angles of rotation of four thin-walled rigid rotating bodies representing eight hoisting winches of the main hoist; α is the longitudinal inclination angle of the ship chamber; y is the vertical displacement of the ship chamber; θ0 is the sloshing angle of the free surface of the water in the chamber; R is the drum radius, a is the longitudinal center distance between two suspension points of the main hoist, b is the center distance between two winches in one suspension point area, is the vertical displacement of the centroid of the ship chamber, C s1 is twice the value of the torsional stiffness of the synchronous shaft between two winches in the same suspension point area converted to the output shaft of the main hoist according to the energy equivalence principle, C s2 is twice the value of the torsional stiffness of the synchronous shaft between adjacent winches in two suspension point areas on the same side of the main hoist converted to the output shaft of the main hoist according to the energy equivalence principle, J h is one-fourth of the total moment of inertia of all rotating components of the main hoist relative to the low-speed shaft; k r is one-fourth of the sum of the tensile stiffnesses of all lifting ropes of the ship hoist when the ship chamber is at the lowest navigable position; k r 、 C s1 and C s2 are calculated respectively according to the following formulas: (8)； (9)； (10)； In Formulas (8) to (10), n r is the total number of steel ropes wound around the main hoist drum; E r is the elastic modulus of the steel rope, A r is the cross-sectional area of the steel rope, H is the maximum suspension height of the hoisting rope for suspending the ship chamber, G is the shear elastic strain of the steel, I s is the polar moment of inertia of the cross-section of a single synchronous shaft, i s is the ratio of the rotational speed of the synchronous shaft system to the rotational speed of the drum; 3) Integrate the mathematical model of the first subsystem and the mathematical model of the second subsystem to construct a 7-degree-of-freedom fluid-structure interaction dynamics equation: (11-a)； (11-b)； (11-c)； (11-d)； (11-e)； (11-f)； (11-g)。 4. The dynamic stability analysis method of the large ship lift suspension system according to claim 3, characterized in that: Step 3 specifically includes: Through variable transformation , , , , transform the 7-degree-of-freedom fluid-structure interaction dynamics equation into a 5-degree-of-freedom coupled vibration linear differential equation that describes the coupling of water body sloshing, longitudinal tilt of the ship chamber, and torsional vibration of the synchronous shaft in the large ship lift suspension system. According to the torsional vibration theory of mechanical systems, Rayleigh damping is injected into the torsional vibration system of the main hoist to form the following damped 5-degree-of-freedom second-order differential linear differential equation for water body sloshing, longitudinal tilt of the ship chamber, and torsional vibration of the synchronous shaft of the main hoist: (12-a)； (12-b)； (12-c)； (12-d)； (12-e)； where d s1 and d s2 are the Rayleigh damping coefficients of the synchronous shafts between two hoists in the same suspension point area and between adjacent hoists in two suspension point areas on the same side of the main hoist, respectively; ζ is the damping ratio of torsional vibration of the synchronous shaft system.

5. The dynamic stability analysis method of the large ship lift suspension system according to claim 1, characterized in that: d s1 and d s2 are calculated respectively according to the following formulas: (13-a)； (13-b)。 6. The dynamic stability analysis method of the suspension system of a large ship lift as claimed in claim 4, wherein: ζ takes the value of 0.

008.

7. The dynamic stability analysis method of the suspension system of a large ship lift as claimed in claim 4, wherein: In Step 4, convert the damped 5-degree-of-freedom second-order ordinary differential linear differential equation into the following form of a 10-variable first-order state equation: (14)； where \(x=(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x\) 10 ) (15)； The expression of the relevant element a of the state matrix M in Equation (15) i (where i = 1 to 13) is as follows: (16-a)； (16-b)； (16-c)； (16-d)； (16-e)； (16-f)； (16-g)； (16-h)； (16-i)； (16-j)； (16-k)； (16-l)； (16-m)。 8. The dynamic stability analysis method for the large ship lift suspension system according to claim 1 or 7, characterized in that: In Step 5, deduce the state matrix expression and the calculation formula for each element of the 10-variable first-order state equation, and find the eigenvalues of the state matrix; when the real parts of all the eigenvalues of the state equation are negative, the ship lift suspension system is dynamically stable, and when the real part of any eigenvalue is greater than zero, the system is unstable.

9. The dynamic stability analysis method of the large ship lift suspension system according to claim 7, characterized in that: Step 6 specifically includes: 1) Define and calculate the critical value a of the longitudinal center distance of the main hoist of the large ship lift suspension system as follows c : At the same time, reduce the longitudinal center distance a of the main hoist and the center distance b of the winch hoisting mechanism in the same hanging point area to a n and b n , and calculate the eigenvalues of the state matrix for each pair of a n and b n values; when the ratio of the difference in the center distance values between two calculations to the larger center distance value in the two calculations is less than or equal to the preset threshold, and the real part of the eigenvalues of the state matrix changes sign between the two calculations, it is stipulated that the larger center distance value is the critical value a of the longitudinal center distance of the main hoist of the ship lift suspension system c ; 2) Define the ratio of the designed longitudinal center distance a of the main hoist of the ship lift to the critical longitudinal center distance a of the main hoist of the suspension system of the large-scale ship lift as the safety factor, which is used to evaluate the safety margin of the dynamic stability of the suspension system of the large-scale ship lift: c The ratio is used to evaluate the safety margin of the dynamic stability of the suspension system of the large-scale ship lift: (17)。 10. The dynamic stability analysis method of the large ship lift suspension system according to claim 9, characterized in that: The preset threshold is 0.05%.

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