A semi-analytical calculation method for the static stability of an air-cushion support platform

Abstract

The present invention discloses a semi-analytical calculation method for the static stability of an air-cushion support platform. The method includes: obtaining the parameter information of the air-cushion support platform in the upright floating state; obtaining the parameter information of the air-cushion support platform in the inclined state and constructing a semi-analytical solution model; combining the parameter information of the air-cushion support platform in the upright floating state, solving the semi-analytical solution model, and constructing a semi-analytical calculation model according to the solution result; performing iterative solution processing on the semi-analytical calculation model, and outputting the restoring moment of the air-cushion support platform. By using the present invention, it is possible to solve the static stability of the air-cushion support platform under the condition of large-angle rotation of the air-cushion support platform while considering various extreme situations and improve the solution efficiency. As a semi-analytical calculation method for the static stability of an air-cushion support platform, the present invention can be widely applied to the field of performance calculation of air-cushion support platforms.

Description

Technical Field

[0001] The present invention relates to the field of performance calculation of air-cushion support platforms, and particularly to a semi-analytical calculation method for the static stability of air-cushion support platforms. Background Art

[0002] An air-cushion support platform is an ocean floating platform jointly supported by an air-cushion and a buoyancy chamber for drainage. The air-cushion refers to an enclosed cavity surrounded by the water surface and a sealed wall above the water surface, and the buoyancy chamber refers to an enclosed chamber formed by a rigid structure immersed in water with a certain drainage volume. When the air-cushion support platform floats on the sea surface, static stability is one of the core indicators of its hydrodynamic performance. Insufficient static stability will lead to capsizing accidents of the air-cushion support platform. Therefore, studying the static stability of the air-cushion support platform has very important guiding significance for the structural design of the air-cushion support platform, the drainage volume distribution of the air-cushion and the buoyancy chamber, etc. The existing small-angle stability calculations of ships and ocean platforms mainly use the analytical method for direct calculation. However, the analytical method has a complex theory and the calculation model does not have universality, that is, it is necessary to separately derive and construct calculation models for each configuration scheme of ships and ocean platforms, which is very inconvenient for engineering applications. For large-angle stability, or the stability of ships and ocean platforms with irregular shapes, it is mainly carried out based on numerical simulation methods. However, numerical simulation requires a large amount of computing resources and cannot be widely applied in engineering. Summary of the Invention

[0003] In order to solve the above technical problems, the purpose of the present invention is to provide a semi-analytical calculation method for the static stability of an air-cushion support platform, which can solve the static stability of the air-cushion support platform under the condition of large-angle rotation and considering various extreme situations, and improve its solution efficiency.

[0004] The technical solution adopted by the present invention is: a semi-analytical calculation method for the static stability of an air-cushion support platform, including the following steps:

[0005] Obtain the parameter information of the air-cushion support platform in the upright state;

[0006] Obtain the parameter information of the air-cushion support platform in the inclined state and construct a semi-analytical solution model;

[0007] Combine the parameter information of the air-cushion support platform in the upright state to solve the semi-analytical solution model, and construct a semi-analytical calculation model according to the solution results;

[0008] Perform iterative solution processing on the semi-analytical calculation model and output the restoring moment of the air-cushion support platform.

[0009] Further, the parameter information of the air-cushion support platform includes the liquid level height in the air chamber, the gas volume in the air chamber, and the drainage volume of the air-cushion support platform.

[0010] Further, the step of obtaining the parameter information of the air-cushion support platform in the inclined state and constructing a semi-analytical solution model specifically includes:

[0011] Rotate the air-cushion support platform by a certain angle and calculate the coordinate data of the air-cushion support platform after rotation;

[0012] Based on the coordinate data of the air-cushion support platform after rotation, set variable parameters, where the variable parameters include the shaft height of the air-cushion support platform and the liquid level height in the air chamber in the inclined state;

[0013] Based on the variable parameters, construct the gas volume in the air chamber in the inclined state and its Jacobian matrix, and the drainage volume of the air-cushion support platform in the inclined state and its Jacobian matrix;

[0014] Integrate the gas volume in the air chamber in the inclined state and its Jacobian matrix, and the drainage volume of the air-cushion support platform in the inclined state and its Jacobian matrix to construct a semi-analytical solution model.

[0015] Further, the step of combining the parameter information of the air-cushion support platform in the upright state, solving the semi-analytical solution model, and constructing a semi-analytical calculation model according to the solution results specifically includes:

[0016] According to the static stability condition, combine the drainage volume of the air-cushion support platform in the upright state to calculate the drainage volume of the air-cushion support platform in the inclined state and its Jacobian matrix to obtain a first calculation result;

[0017] According to the ideal gas state condition, combine the gas volume in the air chamber in the upright state to calculate the gas volume in the air chamber in the inclined state and its Jacobian matrix to obtain a second calculation result;

[0018] Combine the variable parameters, the first calculation result, and the second calculation result to construct a semi-analytical calculation model.

[0019] Further, the semi-analytical calculation model is as follows:

[0020]

[0021] In the above formula, J F represents the Jacobian matrix of the non-linear equation system, z1,…,z n represents the liquid level height of the air chamber in the inclined state, z0 represents the shaft height of the air-cushion support platform, F j represents the non-linear equation system composed of the gas volume in the air chamber and the drainage volume of the air-cushion support platform, z k represents the shaft height and the liquid level height of the air-cushion support platform in the inclined state.

[0022] Further, in the calculation process of the drainage volume of the air-cushion support platform and its Jacobian matrix in the tilted state, and the calculation process of the gas volume in the air chamber and its Jacobian matrix in the tilted state, it is specifically considered whether the air chamber on the air-cushion support platform leaks, whether the inner liquid level of the air chamber on the air-cushion support platform intersects with the wet deck, and whether there are intersections between the reference water level and the bottom and top of the buoyancy chamber of the air-cushion support platform. The wet deck is located at the top of the air chamber.

[0023] Further, the step of performing iterative solution processing on the semi-analytical calculation model and outputting the restoring moment of the air-cushion support platform specifically includes:

[0024] Based on a preset iterative algorithm, perform linear processing on the semi-analytical calculation model to obtain the values of the preliminary variable parameters;

[0025] Substitute the values of the preliminary variable parameters into the semi-analytical solution model for iterative calculation until the calculation result meets the preset calculation accuracy, and output the values of the variable parameters;

[0026] Calculate the floating moment and the gravity moment of the air-cushion support platform according to the values of the variable parameters;

[0027] Sum up the floating moment and the gravity moment to obtain the restoring moment of the air-cushion support platform.

[0028] Further, the preset iterative algorithm is as follows:

[0029]

[0030] In the above formula, represents the values of the shaft height and the liquid level height of the air-cushion support platform after the i-th iteration, and F j represents the non-linear equation system composed of the gas volume in the air chamber and the drainage volume of the air-cushion support platform.

[0031] Further, the calculation formula of the restoring moment of the air-cushion support platform is as follows:

[0032] M r = M a + M b + M g

[0033] In the above formula, M r represents the restoring moment received by the air-cushion support platform, M a represents the restoring moment of the air chamber, M b represents the restoring moment of the buoyancy chamber, M g represents the gravity moment of the air-cushion support platform.

[0034] The beneficial effects of the method of the present invention are as follows: By constructing a semi-analytical solution model and a semi-analytical calculation model, the present invention can effectively solve the static stability of an air-cushion support platform under extreme conditions such as wet deck flooding, platform bottom water emergence, and air chamber air leakage at a large inclination angle. By using the semi-analytical calculation method to solve the constructed model, it has the characteristics of fast solution speed and greatly improves the calculation efficiency of static stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a flowchart of the steps of a semi-analytical calculation method for the static stability of an air-cushion support platform according to the present invention;

[0036] Figure 2 is a schematic horizontal cross-sectional view of an air-cushion support platform according to the present invention;

[0037] Figure 3 is a schematic vertical cross-sectional view of an air-cushion support platform in the upright floating state according to the present invention;

[0038] Figure 4 is a schematic vertical cross-sectional view of an air-cushion support platform after tilting by an angle θ, with no water entry at the top wet deck and no water emergence at the bottom surface of the buoyancy chamber;

[0039] Figure 5 is a schematic vertical cross-sectional view of an air-cushion support platform after tilting by an angle θ, with water entry at the top wet deck of the buoyancy chamber, water emergence at the bottom surface, and partial air leakage in some air chambers;

[0040] Reference numerals: 1. Buoyancy chamber; 2. Air chamber; 3. Reference water level; 4. Inner liquid level. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0041] The following further describes the present invention in detail with reference to the drawings and specific embodiments. For the step numbers in the following embodiments, they are only set for the convenience of explanation and illustration, and no limitation is imposed on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0042] Referring to Figure 1 , the present invention provides a semi-analytical calculation method for the static stability of an air-cushion support platform, and the method includes the following steps:

[0043] S1. Obtain the parameter information of the air-cushion support platform in the upright floating state;

[0044] Specifically, referring to Figure 2 , the air-cushion support platform is composed of 1 buoyancy chamber and 8 non-communicating air chambers. The buoyancy chamber refers to a sealed structure enclosed by a solid wall surface and having a certain drainage volume, and the air chamber refers to a closed cavity enclosed by the water surface and the solid wall above the water surface;

[0045] The upright floating state means that the air-cushion support platform floats freely on the water surface vertically and without inclination. Taking the intersection point of the vertical line passing through the center of gravity of the air-cushion support platform in the upright floating state and the reference horizontal plane as the coordinate origin o, taking the upward direction along the vertical line of the center of gravity as the z-axis, and taking the inclination rotation axis direction of the air-cushion support platform as the y-axis direction, a geodetic coordinate system o-xyz is established.

[0046] S11. Obtain the liquid level height in the air chamber in the upright floating state;

[0047] Specifically, referring to Figures 3 to 5 , based on the established geodetic coordinate system o-xyz, let the liquid level height coordinate in the air chamber of the air-cushion support platform in the upright floating state be z ja , j = 1, 2,..., 8. The liquid level height in the air chamber in the upright floating state can be obtained by direct on-site measurement or by calculating the absolute pressure of the gas in the air chamber. The calculation process is as follows:

[0048]

[0049] In the above formula, p a represents the atmospheric pressure, ρ represents the density of water, g represents the acceleration of gravity, j represents the number of air chambers, and j = 1, 2,..., 8.

[0050] S12. Obtain the gas volume in the air chamber in the upright floating state based on the liquid level height in the air chamber in the upright floating state;

[0051] Specifically, according to the obtained liquid level height in the air chamber in the upright floating state, the gas volume in the air chamber in the upright floating state can be calculated. The calculation formula is as follows:

[0052] V ja = S j (z jf - z ja )

[0053] In the above formula, S j represents the horizontal cross-sectional area of the j-th air chamber, and z jf represents the wet deck height coordinate of the j-th air chamber;

[0054] Among them, the calculation formula of z jf is as follows:

[0055] z jf = h jf + z b

[0056] In the above formula, h jf represents the vertical distance between the wet deck of the j-th air chamber and the bottom of the air-cushion support platform, and z b represents the height coordinate of the bottom of the air-cushion support platform.

[0057] S13. Obtain the drainage volume of the air-cushion support platform in the upright floating state;

[0058] Specifically, the calculation formula for the drainage volume of the air-cushion support platform in the upright floating state is as follows:

[0059]

[0060] In the above formula, S b represents the horizontal cross-sectional area of the buoyancy chamber of the air-cushion support platform.

[0061] S2. Obtain the height of the liquid level in the air chamber after rotating by an angle θ;

[0062] S21. Obtain the coordinate expression of the air-cushion support platform after rotating by an angle θ;

[0063] Specifically, based on the coordinate system o-xyz established in S1, the inclination rotation axis of the air-cushion support platform can be written as d = [0, y d , z0] T , where z0 is the height coordinate of the rotation axis, T represents the transpose of the vector, and the air-cushion support platform is inclined by an angle θ, that is, the rotation matrix R for rotating by an angle θ around the inclination rotation axis d can be written as follows:

[0064]

[0065] Furthermore, the coordinate expression of any point on the air-cushion support platform can be obtained. Assuming that the coordinate expression of any point r in the upright floating state is r = [x, y, z] T , after rotating by a certain angle, its coordinate expression can be r' = [x', y', z'] T or r' = R(r - d) + d, and expanding it can obtain the following:

[0066]

[0067] S22. Based on the coordinate system after rotation transformation, calculate and obtain the height of the liquid level in the air chamber after the air-cushion support platform is inclined by an angle θ in the following order;

[0068] Specifically, when the air-cushion support platform rotates around the inclination rotation axis d, the liquid level in the air chamber always remains horizontal. Therefore, the liquid level in the air chamber rotates in the opposite direction relative to the air-cushion support platform, and the rotation axis is located on the inner liquid level and parallel to the y-axis;

[0069] S221. The gas volume in the air chamber does not change, and the liquid level in the air chamber rotates by -θ around the rotation axis parallel to the y-axis on the liquid level;

[0070] Specifically, for the gas volume in the air chamber not to change, the air chamber should meet the following conditions:

[0071]

[0072] That is

[0073]

[0074] In the above formula, x ja is the x - coordinate of the centroid of the liquid surface in the air chamber, and the rotation axis a j passes through the centroid of the liquid surface in the air chamber;

[0075] Furthermore, since the cross - section S j is a regular fan - shaped ring, the analytical calculation formula of x ja is as follows:

[0076]

[0077] In the above formula, R1 and R2 respectively represent the inner radius and the outer radius of the fan - shaped ring air chamber, and α 1j , α 2j respectively represent the starting angle and the ending angle of the fan - shaped ring air chamber;

[0078] Assume that the rotation axis a j of the liquid surface in the j - th air chamber is a = [x ja , y a , z ja T , j = 1, 2, …, 8. According to the characteristic that the liquid surface in the air chamber still fills the cross - section of the air chamber after rotation, the rotation matrix R j of the liquid surface in the air chamber rotating by - θ angle can be written as follows: a It can be written as follows:

[0079]

[0080] At this time, the coordinates w’ of any point w on the liquid surface in the air chamber after rotation can be expressed as follows:

[0081] w’ = R a (w - a j ) + a j

[0082] In the above formula, a j represents the rotation axis of the liquid surface in the j - th air chamber.

[0083] S222. The liquid surface in the air chamber remains stationary relative to the air - cushion support platform and rotates by θ angle together with the air - cushion support platform, forming a state where the air - cushion support platform is inclined by θ angle and the liquid surface in the air chamber remains horizontal;

[0084] ​Specifically, when the liquid level in the j-th air chamber remains stationary relative to the air-cushion support platform and rotates by an angle θ together with the air-cushion support platform, the rotation axis a of the liquid level in the air chamber j coordinates become a' j =[x' ja , y' a , z' ja T , and further expanding a' j gives the following:

[0085] a' j =R(a j -d)+d

[0086] In the above formula, d represents the inclination rotation axis of the air-cushion support platform;

[0087] Further substituting the expressions of a j , R, and d, we get:

[0088]

[0089] Thus, it can be known that after the air-cushion support platform tilts by an angle θ, if the gas volume in the air chamber remains unchanged, the height coordinate of the liquid level in the j-th air chamber is:

[0090] z' ja =(z ja -z0)cosθ - x ja sinθ + z0

[0091] In the above formula, z0 represents the rotation axis height of the air-cushion support platform.

[0092] S223. Due to the change in the gas pressure in the air chamber, the liquid level in the air chamber rises or falls to a new height;

[0093] Specifically, due to the change in the gas draft in the j-th air chamber, the gas pressure changes, which in turn causes the gas volume to change and the liquid level in the air chamber also changes accordingly. Thus, the liquid level height in the air chamber can finally be written as:

[0094] z j =z' ja +(z j -z' ja )

[0095] That is, the liquid level in the j-th air chamber rises by z j -z' ja due to the pressure change, where z j is a variable.

[0096] ​S23. Based on the liquid level height in the air chamber after the air-cushion support platform tilts at an angle θ, judge the relationship between whether the air chamber leaks air and the wet deck of the air chamber, and calculate the gas volume in the air chamber and its Jacobian matrix after the air-cushion support platform tilts at an angle θ;

[0097] Specifically, denote r jf =[x jf , y jf , z jf T as the point with the largest x coordinate on the wet deck of the j-th air chamber in the upright state of the air-cushion support platform, and r jb =[x jb , y jb , z b T as the point with the smallest x coordinate at the bottom opening section of the j-th air chamber in the upright state of the air-cushion support platform. Assume that after the air-cushion platform tilts at an angle θ, the coordinates of point r jf and point r jb become r' jf =[x' jf , y' jf , z' jf T and r' jb =[x' jb , y' jb , z' jb T . The different relationships between the liquid level height z j in the air chamber and the heights z' jf , z' jb of the upper and lower boundary points of the air chamber can be calculated, and their calculation formulas are as follows:

[0098] z' jf =(z jf -z0)cosθ - x jf sinθ + z0

[0099] z' jb =(z b -z0)cosθ - x jb sinθ + z0

[0100] In the above formula, z jf represents the z coordinate of point r jf , z b represents the height coordinate of the bottom of the air-cushion support platform, and z0 represents the height coordinate of the rotating shaft.

[0101] Furthermore, based on the liquid level height z j in the air chamber and the heights z' jf , z' jb ​​​​Calculate the gas volume in the air chamber and the corresponding Jacobian matrix after the air-cushion support platform tilts at an angle θ for different relationships between them.

[0102] S231. It is determined that the liquid level in the j-th air chamber is below the wet deck and has no intersection with the wet deck, and the air chamber is not leaking.

[0103] Specifically, if the liquid level in the j-th air chamber is below the wet deck and has no intersection with the wet deck, and the air chamber is not leaking, that is, the liquid level height in the j-th air chamber is lower than point r′ jf but higher than point r′ jb , and their size relationship is as follows:

[0104] z′ jb ≤z j ≤z′ jf

[0105] That is, this corresponds to the state where the tilt angle θ of the air-cushion support platform is relatively small. The gas volume in the j-th air chamber can be calculated by the analytical method, and its calculation formula is as follows:

[0106]

[0107] Furthermore, the calculation formula of the Jacobian matrix of the gas volume V j in the j-th air chamber is as follows:

[0108]

[0109] In the above formula, S j represents the horizontal cross-sectional area of the j-th air chamber;

[0110] S232. It is determined that the j-th air chamber is not leaking, but the liquid level in the air chamber intersects with the wet deck.

[0111] Specifically, it is determined that the j-th air chamber is not leaking, but the liquid level in the air chamber intersects with the wet deck, that is, the liquid level height in the j-th air chamber is higher than point r′ jf and point r′ jb , and their size relationship formula is as follows:

[0112]

[0113] That is, it corresponds to the state where the tilt angle θ of the air-cushion support platform is relatively large. At this time, the calculation formula of the gas volume in the j-th air chamber is as follows:

[0114]

[0115] In the above formula, represents the step function, and its calculation formula is as follows:

[0116]

[0117] Further discretize the two-dimensional cross-section S j into a series of surface elements Δ(S j ), l = 1, 2, …, L, and then numerically solve. The specific expression of the discretization is as follows: l , l = 1, 2, …, L and then numerically solve. The specific expression of the discretization is as follows:

[0118]

[0119] Furthermore, calculate the Jacobian matrix calculation formula of the gas volume V j in the j-th air chamber, which is specifically as follows:

[0120]

[0121] In the above formula, x j0 represents the intersection line coordinates of the inner liquid surface and the wet deck of the air chamber, and H(x) represents the unit step function, where

[0122]

[0123]

[0124] S233. It is determined that the j-th air chamber leaks air;

[0125] Specifically, when it is determined that the j-th air chamber leaks air, that is, the liquid level height in the j-th air chamber is lower than the point r′ jb , and the size relationship is:

[0126] z j < z′ jb

[0127] At this time, the enclosed gas volume and its Jacobian matrix in the j-th air chamber are both 0, which are specifically as follows:

[0128] V j = 0

[0129]

[0130] where k = 0, 1, 2, …, 8.

[0131] S24. Calculate the drainage volume and its Jacobian matrix after the air-cushion support platform tilts by an angle θ;

[0132] Specifically, since the air-cushion support platform includes a buoyancy chamber and an air chamber, it is necessary to calculate the drainage volume and the Jacobian matrix of the buoyancy chamber and the air chamber after tilting by an angle θ respectively;

[0133] S241. Calculation of the drainage volume of the buoyancy chamber and its Jacobian matrix after the air-cushion support platform is tilted by an angle θ;

[0134] Specifically, the drainage volume of the buoyancy chamber after the air-cushion support platform rotates by an angle θ around the tilt axis d is equivalent to the cross-sectional area z w = [x w , y w , 0] T formed after rotating -θ around the tilt axis d, and the cross-sectional area z' w = [x' w , y' w , z' w T The volume of the buoyancy chamber below the intersection surface with the buoyancy chamber is specifically calculated as follows:

[0135]

[0136] After further simplification, we get Denote r f = [x f , y f , z f T as the point with the largest x-coordinate on the wet deck of the buoyancy chamber in the upright state of the air-cushion support platform, and r b = [x b , y b , z b T as the point with the smallest x-coordinate on the bottom surface of the buoyancy chamber in the upright state of the air-cushion support platform. According to the different relationships between the cross-sectional height z' w and the heights z f , z b of the upper and lower boundary points of the buoyancy chamber, the drainage volume of the buoyancy chamber and its derivative can be solved by classification. Further, the different relationships between the cross-sectional height z' w and the heights z f , z b of the upper and lower boundary points of the buoyancy chamber specifically include the following steps;

[0137] S2411. If there is no water entry on the wet deck at the top of the buoyancy chamber and no water outlet at the bottom, that is, the intersection plane z' w has no intersection with the wet deck z = z f at the top of the buoyancy chamber or the bottom surface z = z b of the buoyancy chamber;

[0138] Specifically, for the intersection plane z' w having no intersection with the wet deck z = z f at the top of the buoyancy chamber or the bottom surface z = z b of the buoyancy chamber, it satisfies the following conditional relationships:

[0139] ​​​

[0140] Then the drainage volume of the buoyancy chamber after the air-cushion support platform tilts by an angle θ can be written as:

[0141]

[0142] Since the horizontal cross-section S b of the buoyancy chamber is a regular circular ring, the corresponding Jacobian matrix calculation formula for the drainage volume V 0b of the buoyancy chamber can be obtained as follows:

[0143]

[0144] S2412. If the wet deck at the top of the buoyancy chamber enters the water or the bottom exits the water, that is, the cross-section z' w intersects with the wet deck at the top of the buoyancy chamber z = z f or the bottom surface of the chamber z = z b ;

[0145] Specifically, for the cross-section z' w intersecting with the wet deck at the top of the buoyancy chamber z = z f or the bottom surface of the chamber z = z b , the following conditional relationship is satisfied:

[0146] z' w (x f , y f ) > z f

[0147] Or

[0148] z' w (x b , y b ) < z b

[0149] Furthermore, the drainage volume of the buoyancy chamber after the air-cushion support platform tilts by an angle θ can be written as follows:

[0150]

[0151] Furthermore, by discretizing the integration region S b and then numerically solving it, the corresponding Jacobian matrix calculation formula for the drainage volume V 0b of the buoyancy chamber can be obtained as follows:

[0152]

[0153] Among them, x f0 and x b0 are defined as follows:

[0154]

[0155] S242. Calculation of the drainage volume of the air chamber and its Jacobian matrix after the air-cushion support platform is tilted by an angle θ;

[0156] Specifically, for calculating the drainage volume of the air chamber after the air-cushion support platform is tilted by an angle θ, it is mainly necessary to consider whether there is air leakage in the air chamber;

[0157] S2421. The j-th air chamber does not leak air;

[0158] Specifically, if the j-th air chamber does not leak air, combining the above steps S231 and S232, the drainage volume V of the j-th air chamber j0a can be obtained by subtracting the air chamber volume V above the reference water level from the gas volume V in the air chamber. j The calculation formula is as follows: jw The calculation formula is as follows:

[0159] V j0a = V j - V jw

[0160] where the gas volume V in the air chamber j = V j (z0, z j ), and the air chamber volume V above the reference water level jw , the solution process of which is similar to that of V j , only need to change the variable z j in V j to 0, that is, V jw = V j (z0, 0). The Jacobian matrix calculation formula of the air chamber volume V above the reference water level jw is specifically as follows:

[0161]

[0162] In summary, the Jacobian matrix calculation formula of the drainage volume V of the j-th air chamber j0a is specifically as follows:

[0163]

[0164] S2422. The j-th air chamber leaks air;

[0165] Specifically, if the j-th air chamber leaks air, combining step S233, the drainage volume V of the j-th air chamber j0a and its Jacobian matrix calculation formula are respectively as follows:

[0166] Vj0a = 0

[0167]

[0168] In summary, the drained volume of the air chambers and the calculation results of its Jacobian matrix after the air cushion support platform is tilted by an angle θ are as follows:

[0169]

[0170]

[0171] S243. Output the drained volume of the air cushion support platform after it is tilted by an angle θ and the calculation results of its Jacobian matrix;

[0172] Specifically, the drained volume V0 of the air cushion support platform after it is tilted by an angle θ can be obtained by adding the total drained volume V of all air chambers 0a and the drained volume V of the buoyancy chamber 0b , that is:

[0173] V0 = V 0a + V 0b

[0174] The Jacobian matrix representation of its volume is as follows:

[0175]

[0176] S3. Combine the parameter information of the air cushion support platform in the upright state, solve the semi-analytical solution model, and construct a semi-analytical calculation model according to the solution results;

[0177] S31. Calculate the Jacobian matrix of the drained volume of the air cushion support platform before and after tilting;

[0178] Specifically, according to the prerequisite conditions for the calculation of static stability, the drained volume of the air cushion support platform remains unchanged before and after tilting, and we can get:

[0179] F0 = V0 - V a = 0

[0180] Therefore, the Jacobian matrix of the drained volume of the air cushion support platform before and after tilting is as follows:

[0181]

[0182] S32. Calculate the Jacobian matrix of the gas state in the air chambers of the air cushion support platform before and after tilting;

[0183] Specifically, if the j-th air chamber does not leak air after the air-cushion support platform tilts by an angle θ, combining the above steps S231 and S232 and according to the ideal gas state equation, the gas state in the air chamber can be obtained as follows:

[0184]

[0185] In the above formula, γ represents the adiabatic index;

[0186] Further determine the Jacobian matrix of the gas state in the air chamber when there is no air leakage in the air chamber as follows:

[0187]

[0188] If the j-th air chamber leaks air after the air-cushion support platform tilts by an angle θ, combining the above step S33 and according to the ideal gas state equation, the gas state in the air chamber can be obtained as follows:

[0189] F j =0

[0190] Further determine the Jacobian matrix of the gas state in the air chamber when there is air leakage in the air chamber as follows:

[0191]

[0192] S33. Based on the Jacobian matrix of the drainage volume of the air-cushion support platform before and after tilting, the Jacobian matrix of the gas state in the air chamber of the air-cushion support platform before and after tilting, the inclination axis height z0 of the air-cushion support platform and the liquid level height z in the air chamber k , construct a semi-analytical calculation model;

[0193] Specifically, first establish a non-linear equation system with the inclination axis height z0 of the air-cushion support platform and the liquid level height z in the air chamber k , k = 1, 2,..., 8 as variables, as follows:

[0194] F j (z0, z1,..., z n ) = 0, j = 0, 1, 2,..., 8

[0195] Based on the established non-linear equation system, its Jacobian matrix, that is, the semi-analytical calculation model, can be obtained, as follows:

[0196]

[0197] S34. Perform iterative solution calculations on the semi-analytical calculation model to obtain the inclination axis height of the air-cushion support platform and the liquid level height in the air chamber after tilting by an angle θ;

[0198] Specifically, first linearize the non-linear equations to obtain linear equations, and the processing process is as follows:

[0199]

[0200] Input the initial guess values of the inclination axis height and the liquid level height in the air chamber Perform iterative solution until the calculation result meets the preset calculation accuracy. The accuracy is generally a relative error less than 1E-4 (0.01%) according to engineering requirements, and output the calculation result. The calculation result is the inclination axis height of the air cushion support platform and the liquid level height in the air chamber after tilting by the angle θ. The specific calculation process is as follows:

[0201]

[0202] In the above formula, δ represents the relative error limit, and further, take 0.01%;

[0203] Then the output inclination axis height of the air cushion support platform and the liquid level height in the air chamber after tilting by the angle θ are:

[0204]

[0205] S4. Calculate the restoring moment acting on the air cushion support platform, and the static stability of the air cushion support platform can be deduced based on the restoring moment;

[0206] Specifically, the restoring moment acting on the air cushion support platform includes the buoyancy moment and the gravity moment. The restoring moment acting on the air cushion support platform includes the restoring moment of the buoyancy chamber and the restoring moment of the air chamber. The calculation formula for the restoring moment acting on the air cushion support platform is as follows:

[0207] M r = M a + M b + M g

[0208] In the above formula, M e represents the restoring moment acting on the air cushion support platform, M a represents the restoring moment of the air chamber, M b represents the restoring moment of the buoyancy chamber, M g represents the gravity moment of the air cushion support platform;

[0209] S41. Calculate the buoyancy moment acting on the buoyancy chamber after the air cushion support platform tilts by the angle θ;

[0210] Specifically, if there is no water entry at the wet deck at the top of the buoyancy chamber and no water outlet at the bottom after the air cushion support platform tilts by the angle θ, then the reference water plane z w = [x w , yw ,0] T The cross-section z' formed after rotating -θ angle around the inclination axis d w =[x' w ,y' w ,z' w T The x and z coordinates of the buoyancy center of the buoyancy tank below the intersection surface with the buoyancy tank can be written as follows:

[0211]

[0212] If the top wet deck of the buoyancy tank enters the water or the bottom exits the water, the reference water level z w =[x w ,y w ,0] T The cross-section z' formed after rotating -θ angle around the inclination axis d w =[x' w ,y' w ,z' w T The x and z coordinates of the buoyancy center of the buoyancy tank below the intersection surface with the buoyancy tank can be written as follows:

[0213]

[0214] Further calculate the x coordinate of the buoyancy center of the buoyancy tank after the air-cushion support platform tilts by θ angle, and its calculation formula is as follows:

[0215] x 0b =x' 0b cosθ+(z' 0b -z0)sinθ

[0216] So the buoyancy moment received by the buoyancy tank after the air-cushion support platform tilts by θ angle is as follows:

[0217] M b =ρgV 0b x 0b

[0218] S42. Calculate the buoyancy moment received by the air chamber after the air-cushion support platform tilts by θ angle;

[0219] Specifically, if the j-th air chamber does not leak air, and the inner liquid level and the reference water level have no intersection line with the wet deck, then the x coordinate of the buoyancy center of the j-th air chamber is as follows:

[0220]

[0221] If the j-th air chamber does not leak air, but the inner liquid level or the reference water level has an intersection line with the wet deck, then the x coordinate of the buoyancy center of the j-th air chamber is specifically as follows: ​​

[0222] x jab = x' jab cosθ + (z' jab - z0)sinθ

[0223] wherein, the calculation formulas of x' jab and z' jab are as follows:

[0224]

[0225]

[0226] If the j-th air chamber leaks, the x coordinate of the center of buoyancy of the j-th air chamber can be denoted as:

[0227] x jab = 0

[0228] In summary, the calculation formula of the buoyancy moment received by the air chamber after the air-cushion support platform tilts by an angle θ is as follows:

[0229]

[0230] S43. Calculate the gravity moment received by the air-cushion support platform after it tilts by an angle θ;

[0231] Specifically, let the weight of the air-cushion support platform be m, and the center-of-gravity coordinates of the air-cushion support platform in the upright state be [0, 0, z g0 T , and the x coordinate of the center of gravity after the air-cushion support platform tilts by an angle θ is as follows:

[0232] x g = (z g0 - z0)sinθ

[0233] Thus, the gravity moment received by the air-cushion support platform after it tilts by an angle θ is as follows:

[0234] M g = -mgx g

[0235] The static stability of a ship or an offshore platform can be characterized by the restoring moment formed by its gravity and buoyancy after the ship or the offshore platform tilts, that is, those skilled in the art should know that the restoring moment represents the static stability when they see it.

[0236] The above has specifically described the preferred embodiments of the present invention, but the present invention is not limited to the described embodiments. Those skilled in the art can also make various equivalent deformations or substitutions without departing from the spirit of the present invention, and these equivalent deformations or substitutions are all included within the scope defined by the claims of this application.​

Claims

1. A semi-analytical calculation method for the static stability of an air-cushion support platform, characterized in that, It includes the following steps: Obtain the parameter information of the air-cushion support platform in the upright floating state; Obtain the parameter information of the air-cushion support platform in the inclined state and construct a semi-analytical solution model; Combine the parameter information of the air-cushion support platform in the upright floating state, solve the semi-analytical solution model, and construct a semi-analytical calculation model according to the solution results; Perform iterative solution processing on the semi-analytical calculation model and output the restoring moment of the air-cushion support platform; The step of obtaining the parameter information of the air-cushion support platform in the inclined state and constructing a semi-analytical solution model specifically includes: Perform a rotation of a certain angle on the air-cushion support platform and calculate the coordinate data of the air-cushion support platform after rotation; Based on the coordinate data of the air-cushion support platform after rotation, set variable parameters, where the variable parameters include the shaft height of the air-cushion support platform and the liquid level height in the air chamber in the inclined state; Based on the variable parameters, construct the gas volume in the air chamber in the inclined state and its Jacobian matrix and the drainage volume of the air-cushion support platform in the inclined state and its Jacobian matrix; Integrate the gas volume in the air chamber in the inclined state and its Jacobian matrix and the drainage volume of the air-cushion support platform in the inclined state and its Jacobian matrix to construct a semi-analytical solution model; The step of combining the parameter information of the air-cushion support platform in the upright floating state, solving the semi-analytical solution model, and constructing a semi-analytical calculation model according to the solution results specifically includes: According to the static stability condition, combine the drainage volume of the air-cushion support platform in the upright floating state to calculate the drainage volume of the air-cushion support platform in the inclined state and its Jacobian matrix, and obtain the first calculation result; According to the ideal gas state condition, combine the gas volume in the air chamber in the upright floating state to calculate the gas volume in the air chamber in the inclined state and its Jacobian matrix, and obtain the second calculation result; Combine the variable parameters, the first calculation result and the second calculation result to construct a semi-analytical calculation model; The semi-analytical calculation model is as follows: In the above formula, J F represents the Jacobian matrix of the nonlinear equations, z1, ..., z n represents the liquid level height of the air chamber in the inclined state, z0 represents the shaft height of the air cushion support platform, F j represents the nonlinear equations composed of the gas volume in the air chamber and the drainage volume of the air cushion support platform, z k represents the shaft height of the air cushion support platform and the liquid level height of the air chamber in the inclined state.

2. The semi-analytical calculation method for the static stability of an air-cushion support platform according to claim 1, characterized in that, The parameter information of the air-cushion support platform includes the liquid level height in the air chamber, the gas volume in the air chamber, and the drainage volume of the air-cushion support platform.

3. The semi-analytical calculation method for the static stability of an air-cushion support platform according to claim 1, characterized in that, The calculation process of the drainage volume of the air-cushion support platform in the inclined state and its Jacobian matrix and the calculation process of the gas volume in the air chamber in the inclined state specifically also consider whether the air chamber on the air-cushion support platform leaks, whether the inner liquid level of the air chamber on the air-cushion support platform intersects with the wet deck, and whether there are intersections between the reference horizontal plane and the bottom and top of the buoyancy chamber of the air-cushion support platform. The wet deck is located at the top of the air chamber.

4. The semi-analytical calculation method for the static stability of an air-cushion support platform according to claim 1, characterized in that, The step of performing iterative solution processing on the semi-analytical calculation model and outputting the restoring moment of the air-cushion support platform specifically includes: Based on a preset iterative algorithm, perform linear processing on the semi-analytical calculation model to obtain the values of the preliminary variable parameters; Substitute the values of the preliminary variable parameters into the semi-analytical solution model for iterative calculation until the calculation results meet the preset calculation accuracy, and output the values of the variable parameters; Calculate the floating moment and the gravity moment of the air-cushion support platform according to the values of the variable parameters; Sum the floating moment and the gravity moment to obtain the restoring moment of the air-cushion support platform.

5. The semi-analytical calculation method for the static stability of an air-cushion support platform according to claim 4, characterized in that, The preset iterative algorithm is as follows: In the formula, represents the values of the shaft height of the air-cushion support platform and the liquid level height of the air chamber after the i-th iteration, and F j represents the non-linear equations composed of the gas volume in the air chamber and the drainage volume of the air-cushion support platform.

6. The semi-analytical calculation method for the static stability of an air-cushion support platform according to claim 4, characterized in that, The calculation formula for the restoring moment of the air-cushion support platform is as follows: M r = M a + M b + M g In the above formula, M r represents the restoring moment acting on the air-cushion support platform, M a represents the restoring moment of the air chamber, M b represents the restoring moment of the buoyancy chamber, M g represents the gravitational moment of the air-cushion support platform.

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