A method for calculating shipboard resonance based on an assisted landing device

Abstract

The application discloses a shipboard resonance calculation method based on an auxiliary landing device, which comprises the following steps: analyzing a shipboard resonance space dynamic model based on the auxiliary landing device, and establishing a body motion equation of six motion degrees of freedom; in the rotor part of the shipboard resonance space dynamic model, only one degree of freedom of flapping is considered for each blade, and a rotor motion equation represented by two degrees of freedom is formed; a state equation for shipboard resonance calculation based on the auxiliary landing device is obtained based on the body motion equation and the rotor motion equation, and eigenvalues of the state equation for shipboard resonance calculation based on the auxiliary landing device are solved by calculating each dynamic parameter of the shipboard resonance space dynamic model, so that the stability of shipboard resonance based on the auxiliary landing device is determined.

Description

Technical Field

[0001] This invention relates to, but is not limited to, the field of helicopter dynamics technology, and specifically to a method for calculating ship deck resonance based on an auxiliary landing device. Background Technology

[0002] Helicopter ground resonance is a dynamic instability problem caused by the coupling of the rotor and the fuselage; it is a self-excited vibration. When helicopters operate on a ship's deck, "ship deck resonance" may occur, and this problem must be considered for shipborne helicopters. The mechanism of "ship deck resonance" is the same as that of "ground resonance," except that it occurs on a ship's deck.

[0003] When helicopters need to land on a ship's deck using an auxiliary landing system, in addition to considering the ship's motion parameters, the impact of the auxiliary landing system on the stability of the rotor-aircraft coupling must also be taken into account. As early as the 1950s, relevant fields abroad conducted in-depth research on this mechanism and developed related theoretical methods. However, the ship deck resonance analysis module in CAMRAD software, limited by its versatility requirements, is complex to use and computationally inefficient, and it does not consider the influence of the auxiliary landing system. Summary of the Invention

[0004] The purpose of this invention is to solve the above-mentioned problems. This invention provides a method for calculating ship deck resonance based on an auxiliary landing device, which addresses the limitations, complexity, low computational efficiency, and lack of consideration for the influence of the auxiliary landing device on ship deck resonance in existing ship deck resonance analysis methods when shipborne helicopters land on the ship deck via an auxiliary landing device.

[0005] The technical solution of the present invention:

[0006] This invention provides a method for calculating ship deck resonance based on an auxiliary landing device, comprising:

[0007] A shipboard resonance spatial dynamic model based on an auxiliary landing device is used for analysis. Six degrees of freedom are considered for the fuselage portion of the model, and equations of motion for the fuselage with six degrees of freedom are established. For the rotor portion of the model, only one degree of freedom (pivot) is considered for each blade, and after multi-blade coordinate transformation, rotor motion equations are formed using two degrees of freedom. Based on the fuselage and rotor motion equations, a state equation for calculating shipboard resonance based on the auxiliary landing device is obtained. By calculating the dynamic parameters of the shipboard resonance spatial dynamic model, the eigenvalues ​​of the state equation for shipboard resonance based on the auxiliary landing device are solved, thereby determining the stability of shipboard resonance based on the auxiliary landing device.

[0008] Optionally, the ship deck resonance calculation method based on the auxiliary landing device described above specifically includes:

[0009] Step 1: Based on the balance relationship of the six degrees of freedom of motion in the body part of the ship deck resonance spatial dynamic model, establish the body motion equation based on the ship deck resonance calculation of the auxiliary landing device;

[0010] Step 2: Based on the torque balance relationship, and using multi-blade coordinate transformation, establish the rotor motion equation based on the ship surface resonance calculation of the auxiliary landing device;

[0011] Step 3: Convert the airframe motion equations and rotor motion equations into state equations for ship surface resonance calculations based on the auxiliary landing device;

[0012] Step 4: Obtain the dynamic parameters required as input variables in the ship deck resonance space dynamic model through measurement;

[0013] Step 5: Calculate the main landing gear load and tail landing gear load by analyzing the motion balance relationship between the ship and the landing gear, and then obtain the stiffness coefficient of the auxiliary landing device required in the ship deck resonance space dynamic model, the stiffness coefficient and damping coefficient of the main landing gear, and the stiffness coefficient and damping coefficient of the tail landing gear.

[0014] Step 6: Based on the obtained dynamic parameters, obtain the coefficient matrices [M], [K] and [C] of the motion equation, and then obtain the coefficient matrices [A] and [B] of the state equation calculated based on the ship surface resonance of the auxiliary landing device;

[0015] Step 7: By solving the eigenvalues ​​of the state equation calculated based on the ship deck resonance of the auxiliary landing device, the stability of the ship deck resonance based on the auxiliary landing device is determined.

[0016] Optionally, in the ship deck resonance calculation method based on the auxiliary landing device described above, step 1 includes:

[0017] Based on the balance relationships of three forces and three moments in the fuselage of the ship deck resonance spatial dynamic model, six equilibrium motion equations for the fuselage based on the ship deck resonance calculation of the auxiliary landing device are established, including: equilibrium motion equations for directional force and directional moment, equilibrium motion equations for lateral force and lateral moment, and equilibrium motion equations for vertical force and vertical moment.

[0018] Optionally, in the ship deck resonance calculation method based on the auxiliary landing device described above, the rotor motion equation established in step 2 is:

[0019]

[0020]

[0021] Optionally, in the ship deck resonance calculation method based on the auxiliary landing device described above, step 3 includes:

[0022] Step 31: Based on matrix theory, the equations of motion for the airframe and the rotor are simplified into the following expressions:

[0023]

[0024] Step 32, let Where I is the identity matrix, the expression in step 31 simplifies to the state equation used for ship surface resonance calculation based on the auxiliary landing device:

[0025]

[0026] Optionally, in the ship deck resonance calculation method based on the auxiliary landing device described above, step 5 includes:

[0027] Step 51: Based on the kinematic balance relationship between the ship and the landing gear, establish the kinematic balance equations of the landing gear, including: the balance equation of the vertical force of the landing gear, the balance equation of the lateral moment of the landing gear, and the balance equation of the yaw moment of the landing gear.

[0028] Step 52: Obtain the taillift load by solving the kinematic equilibrium equation of the landing gear in Step 51;

[0029] Step 53: Obtain the main lifting load by solving the motion equilibrium equation of the landing gear in step 51. The main lifting load includes the left main lifting load and the right main lifting load.

[0030] Step 54: Based on the calculated main landing load, obtain the stiffness coefficient of the auxiliary landing device, the stiffness coefficient and damping coefficient of the main landing device, and the stiffness coefficient and damping coefficient of the tail landing device required for the ship deck resonance calculation based on the auxiliary landing device.

[0031] Optionally, in the ship deck resonance calculation method based on the auxiliary landing device described above, step 7 includes:

[0032] Step 71: Set the calculation range for rotor speed Ω, and solve the eigenvalues ​​of the state equation; where the real part of the eigenvalue is σ. i The modal damping, represented by the imaginary part ω, is derived from the ship's deck resonance spatial dynamic model based on the auxiliary landing device. i This indicates the frequency of the ship's deck resonance spatial dynamic model based on the auxiliary landing device;

[0033] Step 72: Determine the stability of the system based on the real part of the eigenvalue: If the real part of the eigenvalue is less than zero, the system is stable at the set rotor speed; if the real part of the eigenvalue is greater than zero, the system is unstable.

[0034] This invention also provides a computer-readable storage medium, including: a memory and a processor;

[0035] The memory is configured to store executable instructions;

[0036] The processor is configured to implement the ship deck resonance calculation method based on the auxiliary landing device as described above when executing the executable instructions stored in the memory.

[0037] The beneficial effects of this invention are:

[0038] This invention provides a method for calculating shipboard resonance based on an auxiliary landing device. It employs a spatial dynamic model of shipboard resonance based on the auxiliary landing device for analysis. For the fuselage portion of the model, six degrees of freedom are considered, and six degrees of freedom equations for the fuselage motion are established. For the rotor portion, only one degree of freedom (pivot) is considered for each blade, resulting in a rotor motion equation expressed through two degrees of freedom after multi-blade coordinate transformation. Based on the fuselage and rotor motion equations, a state equation for calculating shipboard resonance based on the auxiliary landing device is obtained. By calculating the dynamic parameters of the spatial dynamic model, the eigenvalues ​​of the state equation for shipboard resonance based on the auxiliary landing device are solved, thereby determining the stability of the shipboard resonance. This invention, combined with engineering practice, establishes a method for calculating shipboard resonance based on an auxiliary landing device through theoretical derivation. This method has good versatility, is easy to understand, and the parameters required for calculation can be obtained through measurement or calculation. The calculation and analysis conclusions can be used to guide model design, possessing significant engineering application value. Attached Figure Description

[0039] The accompanying drawings are provided to further understand the technical solutions of the present invention and constitute a part of the specification. They are used together with the embodiments of this application to explain the technical solutions of the present invention and do not constitute a limitation on the technical solutions of the present invention.

[0040] Figure 1 This is a schematic diagram of the fuselage portion in the ship deck resonance spatial dynamic model based on the auxiliary landing device used in the embodiments of the present invention;

[0041] Figure 2 This is a schematic diagram of the rotor section in the ship deck resonance spatial dynamic model based on the auxiliary landing device used in the embodiments of the present invention;

[0042] Figure 3 Example diagrams are provided to illustrate the calculation results obtained by the ship deck resonance calculation method based on the auxiliary landing device in this embodiment of the invention. Detailed Implementation

[0043] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0044] As explained in the background section, existing ship deck resonance analysis methods for helicopters landing on the ship deck using auxiliary landing gear must consider not only the ship's motion parameters but also the impact of the auxiliary landing gear on the stability of the rotor-aircraft coupling. However, existing ship deck analysis methods, such as the ship deck resonance analysis module in CAMRAD software, are limited by the requirement for versatility, are complex to use, have low computational efficiency, and do not consider the influence of auxiliary landing gear.

[0045] In addition, after the ground resonance of the Yan'an-2 helicopter designed by my country, major scientific research institutions have conducted in-depth research on the mechanism and analysis method of ground resonance, but it is basically at the theoretical level and has not involved practical engineering applications. The research on the ship deck resonance of the auxiliary landing device is even more negligible, and a ship deck resonance calculation method based on the auxiliary landing device that can be applied to engineering practice has not yet been formed.

[0046] To address the aforementioned problems, embodiments of the present invention provide a method for calculating ship deck resonance based on an auxiliary landing device.

[0047] The present invention provides the following specific embodiments, which can be combined with each other. For the same or similar concepts or processes, they may not be described again in some embodiments.

[0048] The ship deck resonance calculation method based on an auxiliary landing device provided in this invention adopts a spatial dynamic model, which includes two parts: the fuselage and the rotor. Figure 1 The diagram shown is a schematic representation of the fuselage portion in the shipboard resonance spatial dynamic model based on an assisted landing device used in an embodiment of the present invention. Figure 2 The diagram shown is a schematic representation of the rotor section in the ship deck resonance spatial dynamic model based on an auxiliary landing device used in an embodiment of the present invention. In ship deck resonance analysis, as... Figure 1 As shown, the machine body is considered to have six degrees of freedom of motion, namely three translational directions and three rotational directions (i.e., three force directions and three torque directions); as Figure 2 As shown, for the rotor section, only one degree of freedom is considered for wobbling per blade. After multi-blade coordinate transformation, it can be represented by two degrees of freedom. In summary, the spatial dynamic model used in the ship deck resonance calculation method based on the auxiliary landing device provided in this embodiment of the invention considers a total of eight degrees of freedom.

[0049] The specific implementation method of the ship deck resonance calculation method is described below. The ship deck resonance calculation method based on the auxiliary landing device provided in this embodiment of the invention includes the following steps:

[0050] Step 1: Based on the balance relationship of the three forces and the balance relationship of the three moments in the fuselage of the ship's deck resonance spatial dynamic model, establish the fuselage motion equation based on the ship's deck resonance calculation using the auxiliary landing device.

[0051] In this step, the equilibrium equation of motion for the heading force is:

[0052]

[0053] The equilibrium equation of motion for the heading moment is:

[0054]

[0055] The equilibrium equations for the lateral forces are:

[0056]

[0057] The equilibrium equation of motion for the lateral moment is:

[0058]

[0059] The equation of motion for the vertical force equilibrium is:

[0060]

[0061] The equilibrium equation for the vertical moment is:

[0062]

[0063] Step 2: Based on the torque balance relationship, and using multi-blade coordinate transformation, establish the rotor motion equation based on the ship surface resonance calculation of the auxiliary landing device.

[0064] The rotor motion equations established in this step are as follows:

[0065]

[0066]

[0067] Step 3: Using matrix theory, the equations of motion of the aircraft and the rotor are converted into state equations that can be used for ship surface resonance calculations based on the auxiliary landing device.

[0068] The conversion methods for this step include:

[0069] Based on matrix theory, the equations of motion for the airframe and the rotor can be simplified into the following general form:

[0070]

[0071] make If I is the identity matrix, then the above general form of the equation simplifies to a state equation that can be used for ship surface resonance calculations based on auxiliary landing devices:

[0072]

[0073] The physical meanings of all parameters in the above equations and expressions are shown in Table 1.

[0074] Table 1

[0075]

[0076]

[0077]

[0078]

[0079] Step 4: Obtain the dynamic parameters required as input variables in the ship deck resonance space dynamic model by measurement; these dynamic parameters as input variables include the dynamic parameters numbered 1-29 in Table 1 above.

[0080] Step 5: Calculate the main landing gear load and tail landing gear load by analyzing the motion balance between the ship and the landing gear. Then, obtain the stiffness coefficient of the auxiliary landing device required in the ship deck resonance space dynamic model, the stiffness coefficient and damping coefficient of the main landing gear, and the stiffness coefficient and damping coefficient of the tail landing gear, as shown in the dynamic parameters of serial numbers 30-50 in Table 1 above.

[0081] The calculation method in this step is explained in detail below, including the following specific steps:

[0082] (a) Based on the kinematic balance relationship between the ship and the landing gear, establish the kinematic balance equations for the landing gear, including: the balance equations for the vertical forces of the landing gear, the balance equations for the lateral moments of the landing gear, and the balance equations for the yaw moments of the landing gear.

[0083] The equilibrium equations for the vertical forces of the landing gear are as follows:

[0084] GCos(b jx Cos(b) jy )-T-PN-P ML -P MR +Ma z +P YU =0;

[0085] The equilibrium equation for the lateral moment of the landing gear is as follows:

[0086]

[0087] The equilibrium equation for the landing gear yaw moment is as follows:

[0088] (P ML -P MR )Y M +I X ε x +Ma y Z M -GSin(b jx )Z M =0;

[0089] (b) The tail-end load is obtained by solving the equation:

[0090]

[0091] (c) The main lifting load is obtained by solving the equations. The main lifting load includes the left main lifting load and the right main lifting load:

[0092]

[0093] The meanings of all physical parameters in the formula are shown in Table 2.

[0094] (d) Based on the calculated main landing load, obtain the stiffness coefficient of the auxiliary landing device, the stiffness coefficient and damping coefficient of the main landing device, and the stiffness coefficient and damping coefficient of the tail landing device required for the ship deck resonance calculation based on the auxiliary landing device; as shown in the dynamic parameters of serial numbers 30-50 in Table 1.

[0095] The meanings of the physical parameters in the above formulas are shown in Table 2 below:

[0096] Table 2

[0097] Serial Number symbol Physical meaning 1 G Total weight, N 2 T Lift, N 3 <![CDATA[I y ]]> <![CDATA[Mass moment of inertia of the whole machine about the y-axis, kgm 2 > 4 <![CDATA[X YUM ]]> The X-axis distance from the aircraft's center of gravity to the grab point of the auxiliary landing gear, in meters. 5 <![CDATA[P MR ]]> Right main load, N 6 <![CDATA[P ML ]]> Left main starter load, N 7 <![CDATA[P N ]]> Tail lift load, N 8 <![CDATA[P YU ]]> Auxiliary landing gear payload, N 9 <![CDATA[a x ]]> <![CDATA[X - acceleration of the helicopter's center of gravity caused by the ship's rolling at the landing point, m / s 2 > 10 <![CDATA[a y ]]> <![CDATA[Y - acceleration of the helicopter's center of gravity caused by the ship's roll at the landing point, m / s 2 > 11 <![CDATA[a z ]]> <![CDATA[Z - acceleration caused by the ship's roll of the helicopter's center of gravity at the landing site, m / s 2 > 12 <![CDATA[b jx ]]> Ship roll angle, rad 13 <![CDATA[b jy ]]> Ship pitch angle, rad 14 <![CDATA[ε X ]]> <![CDATA[Roll angular acceleration of ship, rad / s 2 > 15 <![CDATA[ε Y ]]> <![CDATA[Ship pitch angular acceleration, rad / s 2 >

[0098] Step 6: Based on the obtained dynamic parameters, obtain the coefficient matrices [M], [K] and [C] of the motion equation, and then obtain the coefficient matrix of the state equation calculated based on the ship deck resonance of the auxiliary landing device.

[0099] The coefficient matrices [M], [K], and [C] are respectively:

[0100]

[0101] In the formula:

[0102] M 11 =MM 17 =km ye cosγ

[0103] M22 = I y M 27 = km ye (zH cosγ + xH sinγ)

[0104] M 33 = M M 38 = km ye

[0105] M 44 = I x M 46 = I xz M 48 = km ye zH

[0106] M 55 = M M 57 = km ye sinγ

[0107] M 64 = I xz M 66 = I z M 68 = km ye xH

[0108]

[0109]

[0110]

[0111] Wherein:

[0112] K 1,1 = K XMR + K XML + K XN + K YUX

[0113] K 1,2 = K XMR z M + K XML z M + K XN z N + K YUX z YU

[0114] K 1,6 = K XMR y M - K XML y M + K YUX y YU

[0115] K 2,1 =K 1,2

[0116]

[0117] K 2,4 =K ZMR y M x M -K ZML y M x M +K YUZ y YU x YU

[0118] K 2,5 =K ZMR x M +K ZML x M -K ZN x N +K YUZ x YU -(K ZMR z M +K ZML z M +K ZN z N +K YUZ z YU )sinα

[0119] K 2,6 =K XMR y M z M -K XML y M z M +K YUX y YU z YU

[0120] K 3,3 =K YMR +K YML +K YN +K YUY

[0121] K 3,4 =-(K YMR z M +K YML z M +K YN z N +K YUY z YU )

[0122] K 3,6 =KYMR x M +K YML x M -K YN x N +K YUY x YU

[0123] K 4,2 =K 2,4

[0124] K 4,3 =K 3,4

[0125]

[0126] K 4,5 =K ZMR y M -K ZML y M +K YUZ y YU

[0127] K 4,6 =K YN x N z N -K YMR x M z M -K YML x M z M -K YUY x YU z YU

[0128] K 5,2 =K ZMR x M +K ZML x M -K ZN x N +K YUZ x YU

[0129] K 5,4 =K 4,5

[0130] K 5,5 =K ZMR +K ZML +K ZN +K YUZ

[0131] K 6,1 =K 1,6

[0132] K6,2 = K 2,6

[0133] K 6,3 = K 3,6

[0134] K 6,4 = K 4,6

[0135]

[0136] K 7,7 = K cj + l cj S cj Ω 2 - I cj Ω 2

[0137] K 7,8 = C cj Ω

[0138] K 8,7 = - K 7,8

[0139] K 8,8 = K 7,7

[0140]

[0141] Where:

[0142] C 1,1 = C XMR + C XML + C XN [[ID=]69]

[0143] C 1,2 = C XMR z M + C XML z M + C XN z N ed]]

[0144] C 1,6 = C XMR y M - C XML y M

[0145] C 2,1 = C 1,2

[0146]

[0147] C 2,4 = C ZMR xM y M -C ZML x M y M

[0148] C 2,5 =C ZMR x M +C ZML x M -C ZN x N

[0149] C 2,6 =C XMR z M y M -C XML z M y M

[0150] C 3,3 =C YMR +C YML +C YN

[0151] C 3,4 =-(C YMR z M +C YML z M +C YN z N )

[0152] C 3,6 =C YMR x M +C YML x M -C YN x N

[0153] C 4,2 =C 2,4

[0154] C 4,3 =C 3,4

[0155]

[0156] C 4,5 =C ZMR y M -C ZML y M

[0157] C 4,6 =C YN x N z N -CYMR x M z M -C YML x M z M

[0158] C 5,2 =C 2,5

[0159] C 5,4 =C 4,5

[0160] C 5,5 =C ZMR +C ZML +C ZN

[0161] C 6,1 =C 1,6

[0162] C 6,2 =C 2,6

[0163] C 6,3 =C 3,6

[0164] C 6,4 =C 4,6

[0165]

[0166] C 7,7 =C cj

[0167] C 7,8 =2I cj Ω

[0168] C 8,7 =-C 7,8

[0169] C 8,8 =C 7,7

[0170] Based on the coefficient matrices [M], [K] and [C] obtained above, the coefficient matrices [A] and [B] in the state equation for ship deck resonance calculation based on the auxiliary landing device are calculated.

[0171] Step 7: Calculate the ship surface resonance based on the auxiliary landing device using eigenvalues. Specifically, set the calculation range for the rotor speed Ω, solve the state equation using eigenvalues, and obtain a series of eigenvalues ​​σ. i +jω i (i = 1, 2, ..., 8), the real part of the eigenvalue σ iThe modal damping, represented by the imaginary part ω, is derived from the ship's deck resonance spatial dynamic model based on the auxiliary landing device. i This represents the frequency of the ship's deck resonance spatial dynamic model based on the auxiliary landing device. The stability of the system is determined by the real part of the eigenvalues: if the real part of the eigenvalue is less than zero, the system is stable at the set rotor speed; if the real part of the eigenvalue is greater than zero, the system is unstable. Thus, a continuous damping curve varying with rotor speed can be obtained. Based on the sign of this curve, the unstable region of ship deck resonance or the critical stable speed can be determined.

[0172] The method for calculating shipboard resonance based on an auxiliary landing device provided in this invention uses a shipboard resonance spatial dynamic model based on the auxiliary landing device for analysis. In the fuselage part of the model, six degrees of freedom are considered, and a six-degree-of-freedom equation of motion is established. In the rotor part, only one degree of freedom (pivot) is considered for each blade, and after multi-blade coordinate transformation, a rotor motion equation expressed by two degrees of freedom is formed. Based on the fuselage and rotor motion equations, a state equation for calculating shipboard resonance based on the auxiliary landing device is obtained. By calculating the dynamic parameters of the shipboard resonance spatial dynamic model, the eigenvalues ​​of the state equation for shipboard resonance calculation based on the auxiliary landing device are solved, thereby determining the stability of shipboard resonance based on the auxiliary landing device. This invention, combined with engineering practice, establishes a method for calculating shipboard resonance based on an auxiliary landing device through theoretical derivation. This method has good versatility, is easy to understand, and the parameters required for calculation can be obtained through measurement or calculation. The calculation and analysis conclusions can be used to guide model design and have significant engineering application value.

[0173] The following example, assuming a specific sea condition, will be used to further illustrate the invention based on the auxiliary landing device:

[0174] Example 1

[0175] This embodiment 1 provides a ship deck resonance spatial dynamic model and dynamic stability calculation method based on an auxiliary landing device, including the following steps:

[0176] Step 1: Based on the balance relationships of the three forces and three moments in the fuselage of the ship's deck resonance spatial dynamic model, establish the fuselage motion equations for ship deck resonance calculation based on the auxiliary landing device:

[0177] Equilibrium equations for heading force:

[0178]

[0179] Equilibrium equations for lateral moments:

[0180]

[0181] Equilibrium equations for lateral forces:

[0182]

[0183] Equilibrium equations for the heading moment:

[0184]

[0185] Equilibrium equations for vertical forces:

[0186]

[0187] The equilibrium equation for the vertical moment is:

[0188]

[0189] Step 2: Based on the torque balance relationship, and using multi-blade coordinate transformation, establish the rotor motion equations based on ship surface resonance calculation using the auxiliary landing device:

[0190]

[0191]

[0192] Step 3: Using matrix theory, the equations of motion of the aircraft and the rotor can be used as state equations for calculating the ship surface resonance based on the auxiliary landing device.

[0193] Based on matrix theory, the equations of motion for the airframe and the rotor can be simplified into the following general forms:

[0194]

[0195] make If I is the identity matrix, then equation (9) simplifies to a state equation that can be used for ship surface resonance calculations based on auxiliary landing devices:

[0196]

[0197] Step 4: Obtain the dynamic parameters (such as the dynamic parameters 1-29 in Table 1) that are required as input variables in the ship deck resonance space dynamic model through measurement.

[0198] Step 5: Calculate the main landing gear load and tail landing gear load by analyzing the motion balance between the ship and the landing gear. Then, obtain the stiffness coefficient of the auxiliary landing device required in the ship deck resonance space dynamic model, the stiffness coefficient and damping coefficient of the main landing gear, and the stiffness coefficient and damping coefficient of the tail landing gear (as shown in the dynamic parameters of serial numbers 30-50 in Table 1).

[0199] (a) Based on the kinematic balance relationship between the ship and the landing gear, establish the kinematic balance equations for the landing gear, including:

[0200] The equilibrium equations for the vertical forces on the landing gear are as follows:

[0201] GCos(b jx Cos(b) jy )-T-PN-P ML -P MR +Ma z +P YU =0; (11)

[0202] The equilibrium equation for the lateral moment of the landing gear is as follows:

[0203]

[0204] The equilibrium equation for the landing gear yaw moment is as follows:

[0205] (P ML -P MR )Y M +I X ε x +Ma y Z M -GSin(b jx )Z M =0; (13)

[0206] (b) The tail-end load is obtained by solving the equation:

[0207]

[0208] (c) The main lifting load is obtained by solving the equations. The main lifting load includes the left main lifting load and the right main lifting load:

[0209]

[0210] The meanings of all physical parameters in the formula are shown in Table 2.

[0211] (d) Based on the calculated main landing load, obtain the stiffness coefficient, main landing stiffness coefficient, damping coefficient, and tail landing stiffness coefficient and damping coefficient of the auxiliary landing device required for the ship deck resonance calculation based on the auxiliary landing device (dynamic parameters in Table 1, serial numbers 30-50).

[0212] Step 6: Based on the obtained dynamic parameters, obtain the coefficient matrices [M], [K], and [C] of the motion equations, and then obtain the coefficient matrix of the state equations calculated based on the ship deck resonance of the auxiliary landing device:

[0213]

[0214]

[0215]

[0216] Based on the coefficient matrices [M], [K] and [C] obtained above, the [A] and [B] matrices in the state equation for ship deck resonance calculation based on the auxiliary landing device are calculated.

[0217] Step 7: Calculate the ship deck resonance based on the auxiliary landing device using eigenvalues. Specifically, set the calculation range for the rotor speed Ω, solve the state equation using eigenvalues, and obtain a series of eigenvalues ​​σ. i +jω i (i = 1, 2, ..., 8), the real part of the eigenvalue σ i The modal damping, represented by the imaginary part ω, is derived from the ship's deck resonance spatial dynamic model based on the auxiliary landing device. i This represents the frequency of the ship's deck resonance spatial dynamic model based on the auxiliary landing device. The stability of the system is determined by the real part of the eigenvalues: if the real part of the eigenvalue is less than zero, the system is stable at the set rotor speed; if the real part of the eigenvalue is greater than zero, the system is unstable. Thus, a continuous damping curve varying with rotor speed can be obtained. Based on the sign of this curve, the unstable region of ship deck resonance or the critical stable speed can be determined. Figure 3 This is an example diagram showing the calculation results obtained using the ship deck resonance calculation method based on the auxiliary landing device according to an embodiment of the present invention. These results can be used to analyze the damping margin and speed margin of ship deck resonance, and ultimately determine whether there is a risk of ship deck resonance. Figure 3 Analysis shows that the speed range is 271 r / min to 295 r / min, the speed margin is 5.04%, and the damping ratio is 0.55%.

[0218] While the embodiments disclosed in this invention are as described above, they are merely illustrative of the embodiments to facilitate understanding of the invention and are not intended to limit the invention. Any person skilled in the art to which this invention pertains may make any modifications and variations in the form and details of the implementation without departing from the spirit and scope disclosed herein; however, the scope of patent protection for this invention shall still be determined by the scope defined in the appended claims.

Claims

1. A method for calculating ship deck resonance based on an auxiliary landing device, characterized in that, include: Step 1: Based on the balance relationship of the six degrees of freedom of motion in the body part of the ship deck resonance spatial dynamic model, establish the body motion equation based on the ship deck resonance calculation of the auxiliary landing device; Step 2: Based on the torque balance relationship, and using multi-blade coordinate transformation, establish the rotor motion equation based on the ship surface resonance calculation of the auxiliary landing device; Step 3: Convert the airframe motion equations and rotor motion equations into state equations for ship surface resonance calculations based on the auxiliary landing device; Step 4: Obtain the dynamic parameters required as input variables in the ship deck resonance space dynamic model through measurement; Step 5: Calculate the main landing gear load and tail landing gear load by analyzing the motion balance relationship between the ship and the landing gear, and then obtain the stiffness coefficient of the auxiliary landing device required in the ship deck resonance space dynamic model, the stiffness coefficient and damping coefficient of the main landing gear, and the stiffness coefficient and damping coefficient of the tail landing gear. Step 6: Based on the obtained dynamic parameters, obtain the coefficient matrix of the equation of motion. , and This allows us to obtain the coefficient matrix of the state equation for ship deck resonance calculation based on the auxiliary landing device. and ; Step 7: By solving the eigenvalues ​​of the state equation calculated based on the ship deck resonance of the auxiliary landing device, the stability of the ship deck resonance based on the auxiliary landing device is determined. Step 1 includes: Based on the balance relationships of three forces and three moments in the body of the ship's deck resonance spatial dynamic model, six equilibrium motion equations for the body based on the ship's deck resonance calculation using the auxiliary landing device are established. These equations include: equilibrium motion equations for directional force and directional moment, equilibrium motion equations for lateral force and lateral moment, and equilibrium motion equations for vertical force and vertical moment. The rotor motion equation established in step 2 is as follows: ； 。 2. The method for calculating ship deck resonance based on an auxiliary landing device according to claim 1, characterized in that, Step 3 includes: Step 31: Based on matrix theory, the equations of motion for the airframe and the rotor are simplified into the following expressions: ； Step 32, let , Where I is the identity matrix, the expression in step 31 simplifies to obtain the state equation for calculating ship surface resonance based on the auxiliary landing device: 。 3. The method for calculating ship deck resonance based on an auxiliary landing device according to claim 2, characterized in that, Step 5 includes: Step 51: Based on the kinematic balance relationship between the ship and the landing gear, establish the kinematic balance equations of the landing gear, including: the balance equation of the vertical force of the landing gear, the balance equation of the lateral moment of the landing gear, and the balance equation of the yaw moment of the landing gear. Step 52: Obtain the taillift load by solving the kinematic equilibrium equation of the landing gear in Step 51; Step 53: Obtain the main lifting load by solving the motion equilibrium equation of the landing gear in step 51. The main lifting load includes the left main lifting load and the right main lifting load. Step 54: Based on the calculated main landing load, obtain the stiffness coefficient of the auxiliary landing device, the stiffness coefficient and damping coefficient of the main landing device, and the stiffness coefficient and damping coefficient of the tail landing device required for the ship deck resonance calculation based on the auxiliary landing device.

4. The method for calculating ship deck resonance based on an auxiliary landing device according to claim 3, characterized in that, Step 7 includes: Step 71, Set the rotor speed The computational range is used to solve the eigenvalues ​​of the state equations; where the real part of the eigenvalues ​​is... The imaginary part represents the modal damping of the ship's deck resonance spatial dynamic model based on the auxiliary landing device. This indicates the frequency of the ship's deck resonance spatial dynamic model based on the auxiliary landing device; Step 72: Determine the stability of the system based on the real part of the eigenvalue: If the real part of the eigenvalue is less than zero, the system is stable at the set rotor speed; if the real part of the eigenvalue is greater than zero, the system is unstable.

5. A computer-readable storage medium, characterized in that, include: Memory and processor; The memory is configured to store executable instructions; The processor is configured to implement the ship deck resonance calculation method based on any one of claims 1 to 4 when executing the executable instructions stored in the memory.

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