A dynamic stability analysis method for the suspension system of a large ship lift

Abstract

The present invention provides a method for analyzing the dynamic stability of a large ship lift suspension system, comprising: establishing a simplified physical model of the fluid-solid coupling dynamics of the four-hanging-point ship lift tether suspension system; constructing, based on the simplified physical model and using the analytical Lagrangian equations, a seven-degree-of-freedom fluid-solid coupling dynamics equation for water sloshing, main hoist rotation, and rigid plane motion of the tether; converting the seven-degree-of-freedom fluid-solid coupling dynamics equation into a damped five-degree-of-freedom second-order ordinary differential linear equation for water sloshing, tether pitch, and torsional vibration of the synchronous shaft system through variable transformation and the injection of Rayleigh damping into the synchronous shaft torsional vibration system; converting the damped five-degree-of-freedom second-order ordinary differential linear equation into a ten-variable first-order state equation; calculating the eigenvalues ​​of the first-order state equation; and calculating the stability safety factor based on the eigenvalues. The present invention can easily and conveniently determine the dynamic stability of a large ship lift suspension system.

Description

Technical Field

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

[0002] As a navigational facility at a water conservancy hub, counterbalanced ship lifts offer advantages over locks in terms of water conservation, time savings, and adaptability to high water heads. However, they currently lag behind locks in terms of throughput capacity. Therefore, the scaling of ship lifts is a key path to further development of this navigational facility at water conservancy hubs. This is crucial for comprehensively addressing the navigational challenges faced by large-tonnage vessels at high-lift water conservancy hubs and improving the ship lift's capacity.

[0003] The fully balanced wire rope winch vertical ship lift is safe, economical and easy to maintain. The suspension system of the fully balanced wire rope winch vertical ship lift includes the ship carriage and the water inside, the suspension wire rope and the main hoist (large ship lifts refer to those that require 8 winch hoisting mechanisms due to the long length of the ship carriage, such as Figure 2 and Figure 3 As shown). Because the ship compartment of a fully balanced wire rope winch-type vertical ship lift is a water container during vertical lifting operation, and a flexible support method is used for the suspension of the lifting wire rope, the swaying of the water in the ship compartment causes changes in the force and deformation of the lifting wire rope and the main hoist synchronous shaft. Since the lifting wire rope only accounts for a small portion of the total wire ropes suspending the ship compartment, the remaining suspension wire ropes are gravity-balancing ropes and do not play a supporting role for the ship compartment during the lifting and lowering operation of the ship compartment. When the overall layout of the ship lift suspension system is unreasonable, the disturbance of the water will cause dynamic instability of the ship lift suspension system, which manifests itself in the tilting of the ship compartment and huge deformation or even fracture of the synchronous shaft system. Therefore, the stability of the suspension system of a large fully balanced wire rope winch-type vertical ship lift is an important issue that should be considered in the overall layout of this type of ship lift.

[0004] The suspension system of a large, fully balanced, wire rope winch-type vertical ship lift is characterized by its limited, large ship compartment size. The main hoist typically utilizes eight winches, meaning each hoisting point is driven by two winches. These winches drive a large number of hoisting wire ropes (hereafter referred to as hoist ropes) with a wide distribution length. A simplified physical model modeling approach, where all wire ropes in a single hoisting point are simplified as a single spring and the two independent hoisting mechanisms in the same hoisting point are simplified as a single thin-walled rigid ring, fails to reflect the structural characteristics of large ship lifts, such as the large number and wide distribution of hoisting wire ropes in a single hoisting point, and the deployment of two winches in the same main hoisting point. Summary of the Invention

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

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

[0007] Step 1: Establish a simplified physical model of the four-hanging-point fluid-structure interaction dynamics of the ship lift's cabin suspension system that reflects the characteristics of a large fully balanced wire rope winch ship lift;

[0008] Step 2: Based on the constructed simplified physical model of the four-hanging-point fluid-solid coupling dynamics of the ship lift's trolley suspension system, and according to the analytical mechanics Lagrangian equations, a 7-degree-of-freedom fluid-solid coupling dynamics equation for water sloshing, main hoist rotation, and trolley rigid plane motion is constructed;

[0009] Step 3: The 7-DOF fluid-structure coupling dynamics equation is converted into a damped 5-DOF second-order ordinary differential linear equation for water sloshing, trolley tilt, and torsional vibration of the synchronous shaft system by variable transformation and injection of Rayleigh damping into the synchronous shaft torsional vibration system;

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

[0011] Step 5: Using 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 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.

[0013] Furthermore, the simplified physical model of the four-hanging-point fluid-solid coupling dynamics of the ship lift cabin suspension system established in step one includes the ship cabin, the water inside the cabin, the suspension wire rope and the main hoist. The ship cabin is simplified to a rigid body performing planar motion, the water inside the cabin is a fluid that satisfies the Hausner sway assumption, the suspension wire rope is simplified to four linear springs that satisfy Hooke's law according to the distribution of the hanging point area, and the main hoist is simplified to four thin-walled rigid rotating bodies connected by three-section synchronous shafts. The moment of inertia of each thin-walled rigid rotating body around its own axis is converted to one-fourth of the moment of inertia of all rotating parts of the main hoist around their own axis to the moment of inertia of the winch output shaft.

[0014] Furthermore, step 2 specifically includes:

[0015] 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:

[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);

[0035] Where, are the rotation angles of the four thin-walled rigid rotating bodies representing the eight winches of the main hoist; α is the longitudinal inclination angle of the ship-carrying compartment; y is the vertical displacement of the ship-carrying compartment; θ0 is the sway angle of the free surface of the water in the compartment; R is the drum radius, a is the longitudinal center distance between the two lifting points of the main hoist, and b is the center distance between the two winches in one lifting point area. is the vertical displacement of the center of mass of the cabin, C s1 C is the torsional stiffness of the synchronous shaft between the two hoists in the same lifting point area converted to twice the value of the main hoist output shaft based on the energy equivalence principle. s2 The torsional stiffness of the synchronous shaft between the adjacent hoists in the two lifting point areas on the same side of the main hoist is converted to twice the value of the main hoist output shaft based on the energy equivalence principle, J h One quarter of the total moment of inertia of all rotating parts of the main hoist relative to the low-speed shaft; k r k is one quarter of the sum of the tensile stiffness of all the hoisting ropes of the ship engine when the ship carriage is at the lowest navigable position; r 、 C s1 and C s2 Calculate according to the following formula:

[0036] (8);

[0037] (9);

[0038] (10);

[0039] In formulas (8) to (10), n r is the total number of wire ropes wound on the main hoist drum; E r is the elastic modulus of the wire rope, A r is the cross-sectional area of ​​the wire rope, H is the maximum hanging height of the hoist rope for hanging the ship support, 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 synchronous shaft system speed to the drum speed;

[0040] 3) Integrate the mathematical models of the first subsystem and the second subsystem to construct the 7-DOF fluid-solid coupling dynamics equation:

[0041] (11-a);

[0042] (11-b);

[0043] (11-c);

[0044] (11-d);

[0045] (11-e);

[0046] (11-f);

[0047] (11-g).

[0048] Furthermore, step three specifically includes: through variable transformation , , , The 7-DOF fluid-structure coupling dynamic equation is converted into a 5-DOF coupled vibration linear differential equation that describes the mutual coupling of water sloshing, tether box pitch, and synchronous shaft torsional vibration of the large ship lift suspension system. Based on the torsional vibration theory of mechanical systems, Rayleigh damping is injected into the main hoist torsional vibration system, forming the following damped 5-DOF second-order differential linear equation for water sloshing, tether box pitch, and synchronous shaft torsional vibration of the main hoist:

[0049] (12-a);

[0050] (12-b);

[0051] (12-c);

[0052] (12-d);

[0053] (12-e);

[0054] Where, d s1 and d s2 are the Rayleigh damping coefficients of the synchronous shaft between the two hoists in the same lifting point area and the synchronous shaft between the adjacent hoists in the two lifting point areas on the same side of the main hoist; ζ is the damping ratio of the torsional vibration of the synchronous shaft system.

[0055] Further, d s1 and d s2 Calculate according to the following formula:

[0056] (13-a);

[0057] (13-b).

[0058] Furthermore, the value of ζ is 0.008.

[0059] Furthermore, in step 4, the damped 5-DOF second-order ordinary differential linear equation is converted into the following 10-variable first-order state equation:

[0060] (14);

[0061] Where x=(x1, x2, x3, x4, x5, x6, x7, x8, x9, x 10 )

[0062] (15);

[0063] The relevant element a of the state matrix M in formula (15) i The expression for (i=1~13) is as follows:

[0064] (16-a);

[0065] (16-b);

[0066] (16-c);

[0067] (16-d);

[0068] (16-e);

[0069] (16-f);

[0070] (16-g);

[0071] (16-h);

[0072] (16-i);

[0073] (16-j);

[0074] (16-k);

[0075] (16-l);

[0076] (16-m).

[0077] Furthermore, in step five, the state matrix expression and the calculation formula of each element of the 10-variable first-order state equation are derived to calculate the eigenvalue of the state matrix; when the real part of all the eigenvalues ​​of the state equation is negative, the ship lift suspension system is dynamically stable; when the real part of any eigenvalue is greater than zero, the system is unstable.

[0078] Furthermore, step six specifically includes:

[0079] 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 winch hoisting mechanism in the same lifting point area to a n and b n , for each pair of a n and b n When the ratio of the difference between the two center distance values ​​and the larger center distance value in the two calculations is less than or equal to the preset value, and the real part of the eigenvalue of the two calculated state matrices changes the positive and negative signs, 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 ;

[0080] 2) Define the design value a of the longitudinal center distance of the main hoist of the ship lift and the critical value a of the longitudinal center distance of the main hoist of the large ship lift suspension system c The ratio is the safety factor, which is used to evaluate the safety margin of dynamic stability of the suspension system of large ship lifts:

[0081] (17).

[0082] Furthermore, the preset threshold is 0.05%.

[0083] The present invention is based on a simplified physical model of the dynamics of a four-point ship lift suspension system. On this basis, a 7-degree-of-freedom motion differential equation is established to describe the mutual coupling of the rotation of the main hoist of the large ship lift suspension system, the plane rigid body motion of the ship support box and the water body swaying. Through variable transformation, it is converted into a 5-degree-of-freedom undamped coupled linear vibration equation to describe the water body swaying, the longitudinal tilt of the ship support box 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 to make the 5 degrees of freedom; then the spectral stabilization method of the stability theory of constant coefficient differential equations 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

[0084] Figure 1 This is a four-point lifting model diagram for dynamic stability analysis of the suspension system of a large ship lift.

[0085] Figure 2It is a longitudinal section of the suspension system of a large fully balanced wire rope winch type vertical ship lift.

[0086] Figure 3 It is the main hoist plane layout of a large fully balanced wire rope winch type vertical ship lift.

[0087] Figure 4 The present invention provides a flowchart of a method for dynamic stability analysis of a large ship lift suspension system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0088] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0089] See also Figure 4 The embodiment of the present invention provides a method for dynamic stability analysis of a large ship lift suspension system, comprising the following steps:

[0090] Step 1: Establish a simplified physical model of the four-hanging-point fluid-structure interaction dynamics of the ship lift's cabin suspension system that reflects the characteristics of a large fully balanced wire rope winch ship lift;

[0091] Step 2: Based on the constructed simplified physical model of the four-hanging-point fluid-solid coupling dynamics of the ship lift's trolley suspension system, and according to the analytical mechanics Lagrangian equations, a 7-degree-of-freedom fluid-solid coupling dynamics equation for water sloshing, main hoist rotation, and trolley rigid plane motion is constructed;

[0092] Step 3: The 7-DOF fluid-structure coupling dynamics equation is converted into a damped 5-DOF second-order ordinary differential linear equation for water sloshing, trolley tilt, and torsional vibration of the synchronous shaft system by variable transformation and injection of Rayleigh damping into the synchronous shaft torsional vibration system;

[0093] Step 4: convert the damped 5-degree-of-freedom second-order ordinary differential linear equation into a 10-variable first-order state equation;

[0094] Step 5: Using commercial software MATLAB, perform numerical calculations on the eigenvalues ​​of the 10-variable first-order state equation. Specifically, derive the state matrix expression and the calculation formulas for each element of the 10-variable first-order state equation to obtain 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. When the real part of any eigenvalue is greater than zero, the system is unstable.

[0095] 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.

[0096] 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.

[0097] 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:

[0098] 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:

[0099] Using the Hausner assumption, the fluid-solid coupling dynamic equation of the ship support and the water body is established

[0100] (1)

[0101] 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:

[0102] (2)

[0103] 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.

[0104] The vertical force of water on the ship support box and the overturning moment around the center of mass are:

[0105] (3)

[0106] (4)

[0107] 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. 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, the following formulas are used to calculate the dynamic moment and static moment of the water body on the ship support box.

[0108] (5)

[0109] (6)

[0110] Where ρ = 1t / m 3 is the density of the water body, and B is the maximum water width of the ship compartment.

[0111] 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:

[0112] (7-a)

[0113] (7-b)

[0114] (7-c)

[0115] (7-d)

[0116] (7-e)

[0117] (7-f)

[0118] Where, are the rotation angles of the four thin-walled rigid rotating bodies representing the eight winches of the main hoist; α is the longitudinal inclination angle of the ship support compartment; y is the vertical displacement of the ship support compartment; θ0 is the sway angle of the free surface of the water in the compartment; R is the drum radius, a is the longitudinal center distance between the two lifting points of the main hoist (usually referred to as the longitudinal lifting point center distance), and b is the center distance between the two winches in one lifting point area. is the vertical displacement of the center of mass of the cabin, C s1 C is the torsional stiffness of the synchronous shaft (hereinafter referred to as shaft section 1) between the two hoists in the same lifting point area, which is converted to the value of the main hoist output shaft based on the energy equivalence principle. s2 The torsional stiffness of the synchronous shaft (hereinafter referred to as shaft section 2) between the two adjacent hoists in the same side (left or right) of the main hoist is converted to twice the value of the main hoist output shaft based on the energy equivalence principle, J h One quarter of the total moment of inertia of all rotating parts of the main hoist relative to the low-speed shaft (drum shaft); k r It is one quarter of the sum of the tensile stiffness of all the hoisting ropes of the ship lift when the ship support compartment is at the lowest navigable position. r 、 C s1 and C s2 Calculate according to the following formula:

[0119] (8)

[0120] (9)

[0121] (10)

[0122] In formulas (8) to (10), n r is the total number of wire ropes wound on the main hoist drum; E r is the elastic modulus of the wire rope, A r is the cross-sectional area of ​​the wire rope, H is the maximum hanging height of the hoist rope for hanging the ship support, 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 synchronous shaft system speed to the drum speed;

[0123] 3) Integrate the mathematical models of the above two subsystems to construct the differential equation of motion of the large ship lift suspension system (7-degree-of-freedom fluid-solid coupling dynamic equation).

[0124] (11-a)

[0125] (11-b)

[0126] (11-c)

[0127] (11-d)

[0128] (11-e)

[0129] (11-f)

[0130] (11-g)

[0131] In step 3, through variable transformation , , , The 7-DOF fluid-structure coupling dynamic equation described in Equation (11) is transformed into a 5-DOF coupled vibration linear differential equation describing the coupling of water sloshing, tether box pitch, and synchronous shaft torsional vibration in the large ship lift suspension system. Based on the torsional vibration theory of mechanical systems, Rayleigh damping is injected into the main hoist torsional vibration system, forming the following damped 5-DOF second-order differential linear equation for water sloshing, tether box pitch, and synchronous shaft torsional vibration of the main hoist:

[0132] (12-a)

[0133] (12-b)

[0134] (12-c)

[0135] (12-d)

[0136] (12-e)

[0137] Where, d s1 and d s2 are the Rayleigh damping coefficients of the synchronous shaft system segment 1 and segment 2, respectively, and are calculated according to the following formula:

[0138] (13-a)

[0139] (13-b)

[0140] ζ is the damping ratio of the synchronous shaft system's torsional vibration. Based on mechanical vibration theory and for safety reasons, it is set to 0.008.

[0141] In step 4, the damped 5-DOF second-order ordinary differential linear equation (12) is converted into the following 10-variable first-order state equation:

[0142] (14)

[0143] Where x=(x1, x2, x3, x4, x5, x6, x7, x8, x9, x 10 )

[0144] (15)

[0145] The relevant element a of the state matrix M in formula (15) i The expression for (i=1~13) is as follows:

[0146] (16-a)

[0147] (16-b)

[0148] (16-c)

[0149] (16-d)

[0150] (16-e)

[0151] (16-f)

[0152] (16-g)

[0153] (16-h)

[0154] (16-i)

[0155] (16-j)

[0156] (16-k)

[0157] (16-1)

[0158] (16-m)

[0159] In step 5, the relevant parameters are substituted into Equation (16) to obtain the numerical values ​​of the above elements, and the eigenvalues ​​of the matrix M described by Equation (15) are calculated. The dynamic stability of the ship lift suspension system can be determined based on the sign of the real part of the eigenvalue. If the real part of all 10 eigenvalues ​​is less than zero, the system is stable; if the real part of any of the 10 eigenvalues ​​is greater than zero, the system is unstable.

[0160] When calculating, you can use the commercial software MATLAB to perform programming calculations, and its execution statement is:

[0161] 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 0a6 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 10 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];

[0162] d=eig(M).

[0163] Step 6: The specific implementation steps are as follows:

[0164] 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 winch hoisting mechanism in the same lifting point area to a n and b n (ie ratio b n / a n remains unchanged during the reduction process), for each pair of a n and b n When the ratio of the difference between the two center distance values ​​and the larger center distance value in the two calculations is less than or equal to the preset threshold (for example, 0.05%), and the real part of the eigenvalue of the two calculated state matrices changes the positive or negative sign, 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 .

[0165] 2) Define the design value a of the longitudinal center distance of the main hoist of the ship lift and the critical value a of the longitudinal center distance of the main hoist of the large ship lift suspension system c The ratio is the safety factor, which is used to evaluate the safety margin of dynamic stability of the suspension system of large ship lifts:

[0166] (17)

[0167] Let's take a specific example to illustrate: Among the fully balanced wire rope winch vertical ship lifts currently in operation, only the 2×500t ship lift at the Shuikou Hydropower Station on the Minjiang River in Fujian Province and the 2×500t ship lift at the Tingzikou Hydropower Station on the Jialing River have large ship lift cabins. However, the main hoist of the Shuikou ship lift has only one winch hoisting mechanism per lifting point, which is the same as the layout of the main hoists of other medium-sized ship lifts in China. However, the main hoist of the Tingzikou ship lift has two winches per lifting point, such as Figure 3 As shown. Therefore, the embodiment of the present invention uses the Tingzikou ship lift as an example to illustrate the calculation steps. The maximum water area length of the Tingzikou ship lift's ship lift compartment is 128m×12.4m×2.5m (length×width×water depth). The total number of suspension wire ropes in the ship lift compartment is 200, of 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 four-point suspension system of the Tingzikou ship lift, the 16 steel ropes wound on the four drums of the two winch hoisting mechanisms at the same longitudinal position on both sides of the centerline of the engine room ship support compartment are simplified to a single spring; correspondingly, all the rotating parts of the two winch hoisting mechanisms are equivalent to thin-walled circular rings with a radius of 2m (the center radius of the drum rope groove).

[0168] 1. Basic input parameters

[0169] Table 1 Basic technical parameters

[0170]

[0171] 2. Calculate intermediate parameters

[0172] According to formula (2), (5), (6) and formula (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.

[0173] Table 2 Intermediate parameter values

[0174]

[0175] 3. Calculate the unknown elements of the state matrix

[0176] Calculate the unknown element value a of the state equation according to formula (12-a)~(12-m) i (i=1~13).

[0177] Table 3 Calculated unknown element values

[0178]

[0179] 4. Calculate the eigenvalues ​​of the state matrix

[0180] The eigenvalues ​​of the state matrix are calculated using MATLAB commercial computing software. The following two commands can be used to obtain the eigenvalues ​​of the state matrix:

[0181] 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 01 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 00 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 00.76825 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 -0.01495 0 -0.01495 0];

[0182] d=eig(M)

[0183] The first command is to assign values ​​to the state matrix, and the second command is to find the eigenvalues ​​of the state matrix.

[0184] After entering the above command, MATLAB executes the command and gives the following five pairs of eigenvalues:

[0185] −0.18633±28.399i, −0.20261±25.326i, −0.14635±11.026i, −0.0046837±4.9674i, −2.4522×10 -7 ±0.11363i

[0186] Where i is a unit complex number. The real parts of all the above complex numbers are negative, indicating that the Tingzikou ship lift's suspension system is dynamically stable. This is consistent with the current stable state of the ship lift's lifting operation.

[0187] 5. Suspension system dynamic stability margin assessment

[0188] In the calculation formulas (12-a) to (12-m) for the unknown elements of the state matrix, the longitudinal center distance a of the main hoist and the longitudinal spacing b between the two winches in the same hoisting area are set to be smaller than the original design values, while maintaining the original design ratio b / a = 0.3032. Other parameters remain unchanged and the eigenvalues ​​of the state matrix M are calculated. By continuously reducing the values ​​of a and b and repeatedly calculating the eigenvalues ​​of the state matrix M using MATLAB programming, it is found that when a = 23.73m and b = 7.174m, the eigenvalue of the state matrix is:

[0189] −0.3088±47.168i,−0.33617±42.02i,−0.2494±17.657i,−0.000095548±1.8621i,−4.0441×10 -7 ±0.0034477i,

[0190] The real parts of the above eigenvalues ​​are all less than 0, indicating that the ship lift suspension system is stable at this time.

[0191] When a=23.72m, b=7.170m, the eigenvalue of the state matrix is:

[0192] −0.30886±47.178i, −0.33624±42.028i, −0.24944±17.660i, −0.000095406±1.8613i, −0.00069255,0.00069174.

[0193] The last two eigenvalues ​​mentioned above are real numbers, one of which is greater than zero, indicating that the ship lift suspension system is unstable.

[0194] 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 ship lift suspension system. The dynamic stability safety factor of the ship lift suspension system is:

[0195]

[0196] Since the dynamic instability of the ship lift suspension system is primarily caused by the longitudinal instability of the ship support, the minimum safety factor here can be taken as 2.2, as specified in the "Ship Lift Design Code" (GB51177-2016). The above calculations show that the dynamic stability safety factor (2.78) of the Tingzikou ship lift suspension system is greater than the minimum safety factor of 2.2. Therefore, the ship lift suspension system is dynamically stable. This is consistent with the current stable operation of the Tingzikou ship lift.

[0197] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A dynamic stability analysis method for a large ship lift suspension system, characterized in that: The steps include: Step 1: Establish a simplified physical model of the four-hanging-point fluid-structure interaction dynamics of the ship lift's cabin suspension system that reflects the characteristics of a large fully balanced wire rope winch ship lift; Step 2: Based on the constructed simplified physical model of the four-hanging-point fluid-solid coupling dynamics of the ship lift's trolley suspension system, and according to the analytical mechanics Lagrangian equations, a 7-degree-of-freedom fluid-solid coupling dynamics equation for water sloshing, main hoist rotation, and trolley rigid plane motion is constructed; Step 3: The 7-DOF fluid-structure coupling dynamics equation is converted into a damped 5-DOF second-order ordinary differential linear equation for water sloshing, trolley tilt, and torsional vibration of the synchronous shaft system by variable transformation and injection of Rayleigh damping into the synchronous shaft torsional vibration system; Step 4: convert the damped 5-degree-of-freedom second-order ordinary differential linear equation into a 10-variable first-order state equation; Step 5: Using 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 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. Step six 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 : Simultaneously reduce the longitudinal center distance a of the main hoist and the center distance b of the winch hoisting mechanism in the same lifting point area to a n and b n , for each pair of a n and b n Calculate the eigenvalues ​​of the state matrix; When the ratio of the difference between the two center distance values ​​and the larger center distance value in the two calculations is less than or equal to the preset threshold, and the real part of the eigenvalue of the state matrix of the two calculations changes the positive and negative signs, the larger center distance is defined as the critical value a of the longitudinal center distance of the main hoist of the ship lift suspension system. c ; 2) Define the design value a of the longitudinal center distance of the main hoist of the ship lift and the critical value a of the longitudinal center distance of the main hoist of the large ship lift suspension system c The ratio is the safety factor, which is used to evaluate the safety margin of dynamic stability of the suspension system of large ship lifts: (17)。 2. The dynamic stability analysis method for a large ship lift suspension system according to claim 1, characterized in that: The simplified physical model of the four-hanging-point fluid-solid coupling dynamics of the ship lift cabin suspension system established in step 1 includes the ship cabin, the water inside the cabin, the suspension wire rope and the main hoist. The ship cabin is simplified to a rigid body performing planar motion, the water inside the cabin is a fluid that satisfies the Hausner sway assumption, the suspension wire rope is simplified to four linear springs that satisfy Hooke's law according to the distribution of the hanging point area, and the main hoist is simplified to four thin-walled rigid rotating bodies connected by three-section synchronous shafts. The moment of inertia of each thin-walled rigid rotating body around its own axis is converted to one-fourth of the moment of inertia of all rotating parts of the main hoist around their own axis and is converted to the moment of inertia of the winch output shaft.

3. The dynamic stability analysis method for a large ship lift suspension system according to claim 1, characterized in that: Step 2 specifically includes: 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: Using the Hausner assumption, the fluid-solid coupling dynamic equation of the ship support box and the water body is established: (1)； 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: (2)； 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; The vertical force of water on the ship support box and the overturning moment around the center of mass are: (3)； (4)； 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: (5)； (6)； Where ρ = 1t / m 3 is the density of the water body, B is the maximum water width of the ship compartment; 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: (7-a)； (7-b)； (7-c)； (7-d)； (7-e)； (7-f)； Where, are the rotation angles of the four thin-walled rigid rotating bodies representing the eight winches of the main hoist; α is the longitudinal inclination angle of the ship support compartment; y is the vertical displacement of the ship support compartment; θ0 is the sway angle of the free surface of the water in the compartment; R is the drum radius, a is the longitudinal center distance between the two lifting points of the main hoist, and b is the center distance between the two winches in a lifting point area; is the vertical displacement of the center of mass of the cabin, C s1 C is the torsional stiffness of the synchronous shaft between the two hoists in the same lifting point area converted to twice the value of the main hoist output shaft based on the energy equivalence principle. s2 The torsional stiffness of the synchronous shaft between the adjacent hoists in the two lifting point areas on the same side of the main hoist is converted to twice the value of the main hoist output shaft based on the energy equivalence principle, J h One quarter of the total moment of inertia of all rotating parts of the main hoist relative to the low-speed shaft; k r k is one quarter of the sum of the tensile stiffness of all the hoisting ropes of the ship engine when the ship carriage is at the lowest navigable position; r 、 C s1 and C s2 Calculate according to the following formula: (8)； (9)； (10)； In formulas (8) to (10), n r is the total number of wire ropes wound on the main hoist drum; E r is the elastic modulus of the wire rope, A r is the cross-sectional area of ​​the wire rope, H is the maximum hanging height of the hoisting rope for hanging the ship support, 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 synchronous shaft system speed to the drum speed; 3) Integrate the mathematical models of the first subsystem and the second subsystem to construct the 7-DOF fluid-solid coupling dynamics equation: (11-a)； (11-b)； (11-c)； (11-d)； (11-e)； (11-f)； (11-g)。 4. The dynamic stability analysis method for a large ship lift suspension system according to claim 3, characterized in that: Step 3 specifically includes: through variable transformation , , , The 7-DOF fluid-structure coupling dynamic equation is converted into a 5-DOF coupled vibration linear differential equation that describes the mutual coupling of water sloshing, tether box pitch, and synchronous shaft torsional vibration of the large ship lift suspension system. Based on the torsional vibration theory of mechanical systems, Rayleigh damping is injected into the main hoist torsional vibration system, forming the following damped 5-DOF second-order differential linear equation for water sloshing, tether box pitch, and synchronous shaft torsional vibration 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 shaft between the two hoists in the same lifting point area and the synchronous shaft between the adjacent hoists in the two lifting point areas on the same side of the main hoist; ζ is the damping ratio of the torsional vibration of the synchronous shaft system.

5. The dynamic stability analysis method of a large ship lift suspension system according to claim 4, characterized in that: d s1 and d s2 Calculate according to the following formula: (13-a)； (13-b)。 6. The dynamic stability analysis method for a large ship lift suspension system according to claim 4, characterized in that: The value of ζ is 0.

008.

7. The dynamic stability analysis method for a large ship lift suspension system according to claim 4, characterized in that: In step 4, the damped 5-DOF second-order ordinary differential linear equation is converted into the following 10-variable first-order state equation: (14)； Where x=(x1, x2, x3, x4, x5, x6, x7, x8, x9, x 10 ) (15)； The relevant element a of the state matrix M in formula (15) i The expression 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)； Where i=1~13.

8. The dynamic stability analysis method of a large ship lift suspension system according to claim 1 or 7, characterized in that: In step five, the state matrix expression and the calculation formula of each element of the 10-variable first-order state equation are derived to obtain the eigenvalues ​​of the state matrix; when the real part of all the eigenvalues ​​of the state equation is negative, the ship lift suspension system is dynamically stable; when the real part of any eigenvalue is greater than zero, the system is unstable.

9. The dynamic stability analysis method for a large ship lift suspension system according to claim 1, characterized in that: The preset threshold is 0.05%.

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