A rudder blade vibration reduction and shock reduction structure

Abstract

The present invention relates to the technical field of vibration control of rudder blades, and discloses a rudder blade vibration reduction and shock reduction structure. The determination process of the rudder blade vibration reduction and shock reduction structure comprises the following steps: (1) classifying the system damping of the rudder blade; (2) considering the motion of the damping particles in the rudder blade equivalent to a gas-phase flow with a low Reynolds number, and obtaining the equivalent viscous damping of the gas-phase flow system; (3) equivalent friction damping parameters; (4) applying the damping parameters obtained in steps (2) and (3) to the modeling of bending motion and torsional motion; (5) calculating the damping ratio of the rudder blade system under different damping particle configurations; (6) installing the rudder blade: arranging damping particles on the rudder blade based on the best result of the damping ratio simulation in step (5). In the present invention, by calculating the damping ratio of the rudder blade based on the gas-phase flow principle, a system modeling with a similar trend can be obtained, and thus the best rudder blade shock reduction structure can be obtained by simulation theoretical calculation.

Description

Technical Field

[0001] The present invention relates to the technical field of rudder blade vibration control, and in particular to a rudder blade vibration reduction and shock reduction structure based on a gas phase flow-like principle. Background Art

[0002] With the continuous advancement of technology, higher requirements are being placed on aircraft, requiring lighter structures, faster flight speeds, and greater maneuverability. Rudder blade flutter is a factor that must be considered in aircraft design. When an aircraft's flight speed exceeds the critical flutter speed, both its amplitude and the aerodynamic forces within the structure can change dramatically. Component flutter is a major cause of flutter, and since rudder blades are the most important component of an aircraft, research on flutter suppression is crucial. The consequences of aircraft flutter caused by rudder blade flutter can often be severe or even catastrophic.

[0003] Currently, the methods for preparing vibration-damping and shock-reducing structures for rudder blades include, first, adjusting the mass distribution of the rudder blades to minimize the degree of bending-torsion coupling under certain equilibrium conditions; second, changing the stiffness characteristics of the rudder surface. However, adjusting the rudder blades using the above methods results in a decrease in the applicability and stability of the aircraft. Therefore, providing a method for suppressing rudder blade flutter that can utilize the optimal design of the rudder blade structure, suppress rudder blade flutter, and improve the stability of the aircraft is a major technical problem that needs to be solved urgently by those skilled in the art. In existing research, patent CN202010467714.9 discloses a method for suppressing rudder blade flutter. This method uses the finite element-discrete element coupling method to calculate the harmonic response curve of the rudder blade structure and solves the damping ratios of each order of the rudder blade structure under different particle parameters using the half-power method. This method is computationally complex and inefficient. Summary of the Invention

[0004] Therefore, it is necessary to provide a rudder blade vibration reduction and impact reduction structure based on the gas phase flow principle to solve the problems of poor applicability and low stability of the existing rudder blade damping vibration suppression structure.

[0005] To achieve the above object, the present invention provides a rudder blade vibration reduction and impact reduction structure, wherein a cavity is provided in the rudder blade, and the cavity is filled with damping particles.

[0006] The process of determining the vibration reduction and shock reduction structure of the rudder blade includes the following steps:

[0007] (1) Damping classification: The system damping of the rudder blade is divided into rudder blade structural damping, inter-particle collision damping, and friction damping caused by friction between particles and between particles and cavity walls.

[0008] (2) Equivalent viscous damping parameters: The motion of the damping particles in the rudder is equivalent to a gas-like flow with a low Reynolds number. The gas-like flow with a low Reynolds number is modeled to obtain the equivalent viscous damping of the gas-like flow system.

[0009] (3) Equivalent friction damping parameter: Friction damping includes Coulomb friction damping between particles and between particles and cavity wall;

[0010] (4) Rudder blade vibration modeling: The vibration of the rudder blade is equivalent to bending motion and torsional motion, and the bending motion and torsional motion are modeled separately. The equivalent viscous damping parameters and equivalent friction damping parameters obtained in steps (2) and (3) are applied to the modeling of bending motion and torsional motion;

[0011] (5) Damping ratio simulation: In the bending and torsional motion models of the rudder blade, the transient response analysis of the bending and torsional motions is performed respectively to obtain the relationship between time and amplitude. The damping ratios of the bending and torsional motions of the rudder blade system are calculated. The sum of the damping ratios of the bending and torsional motions is the damping ratio of the rudder blade system. The damping ratios of the rudder blade system under different damping particle configurations are calculated, and then the influence trend of different damping particle parameters on the damping ratio of the rudder blade system is obtained.

[0012] (6) Rudder installation: Based on the influence trend of different damping particle configurations on the damping ratio of the rudder system in step (5), configure the optimal damping particle parameters on the rudder system. The damping particle parameters include

[0013] Furthermore, the damping of the rudder blade structure is neglected.

[0014] Furthermore, the viscosity of the gas-phase flow system is equivalent to the effective viscosity generated by the collision between particles.

[0015] Furthermore, the effective viscosity generated by the collision between particles in the gas-phase flow system is analyzed based on the kinetic theory of dense multiphase flow.

[0016] Furthermore, in step (3), when the bending motion and the torsional motion are modeled respectively, the center of mass and the center of rigidity are overlapped.

[0017] Furthermore, the damping ratio can be calculated as follows:

[0018]

[0019] Where ζ is the damping ratio, A is the amplitude of the time-amplitude relationship diagram, and the damping ratio of the bending and torsional motion of the rudder system can be obtained by taking the value of r cycles on the time-amplitude relationship diagram for calculation.

[0020] Furthermore, the damping particle parameters include the particle filling position on the rudder cavity, the filling rate of the particle cavity and the particle size.

[0021] Furthermore, the optimal damping particle parameters determined in step (6) maximize the damping ratio of the rudder blade vibration reduction and shock reduction structure.

[0022] Furthermore, a plurality of cavities are provided on the rudder plate.

[0023] Furthermore, the particle size of the damping particles is 1-2.5 mm.

[0024] Furthermore, the filling rate of the damping particles in the cavity is 70-100%.

[0025] Furthermore, the material of the damping particles in the cavity is iron-based alloy, tungsten-based alloy, ceramic or copper-based alloy.

[0026] The above technical solution has the following beneficial effects:

[0027] In the present invention, the preferred method for modeling the rudder blade vibration reduction and impact reduction structure is based on the gas-phase flow theory, and a modeling method for the damping effect of the damping particles of the rudder blade system is proposed to predict the damping ratio parameters after the particle damping acts on the vibration reduction structure, so as to obtain the best structure for suppressing the rudder blade vibration and reducing the impact force. The gas-phase flow theory is applied to the damping analysis of the particle damper for the rudder blade. The damping in the particle motion process is first split according to different generation categories, and then the rudder blade system is simplified into a two-degree-of-freedom system. Starting from the vibration model of the rudder blade system, the damping ratio of the rudder blade system after the particle damper is applied is obtained. The size of the damping ratio reflects the vibration reduction effect under different particle configuration conditions on the one hand, and provides important simulation parameters for the rudder blade flutter simulation on the other hand.

[0028] The calculated value of the damping ratio of the rudder blade system calculated by the modeling of the present invention is generally consistent with the trend of the actual experimental value of the rudder blade. Compared with the finite element-discrete element coupling method, the calculation amount is less and the efficiency is higher. Therefore, the modeling and calculation method of the damping ratio of the rudder blade system based on the gas-phase flow theory in the present invention is similar to the actual rudder blade system damping ratio change trend. By using the determination process method of the rudder blade vibration reduction and shock reduction structure of the present invention, the staff can perform simulations of various damping rudder blade systems, so as to determine the better rudder blade vibration reduction and shock reduction structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is the mechanical model of the binary rudder.

[0030] Figure 2 This is the time-amplitude relationship diagram of the rudder system after cavity 3 is filled with damping particles.

[0031] Figure 3 A graph of the damping ratio of the particles filling each position.

[0032] Figure 4 This is the time-amplitude relationship diagram of the rudder system with a filling rate of 70%.

[0033] Figure 5 The damping ratio curve under different particle filling rates.

[0034] Figure 6 This is the time-amplitude relationship diagram of the rudder system filled with particles with a diameter of 1 mm.

[0035] Figure 7 The damping ratio curves for different particle sizes.

[0036] Figure 8 The figure shows the fitting comparison curve of the rudder blade damping ratio at different particle filling positions.

[0037] Figure 9 This is a fitting comparison curve of the first two-order damping ratio of the rudder system under different particle filling rates.

[0038] Figure 10 This is a fitting comparison curve of the first two-order damping ratio of the rudder system under different particle sizes. DETAILED DESCRIPTION

[0039] In order to explain the technical content, structural features, achieved objectives and effects of the technical solution in detail, the following is a detailed description in conjunction with specific embodiments and accompanying drawings.

[0040] This embodiment provides a rudder blade vibration reduction and impact reduction structure based on the principle of gas phase flow. The rudder blade is provided with a cavity filled with damping particles.

[0041] The process of determining the vibration reduction and impact reduction structure of the rudder blade specifically includes the following steps:

[0042] (1) Damping classification: The system damping of the rudder blade is divided into rudder blade structural damping, inter-particle collision damping, and friction damping caused by friction between particles and between particles and cavity walls.

[0043] (2) Equivalent viscous damping parameters: The motion of the damping particles in the rudder is equivalent to a low Reynolds number quasi-gas phase flow. The low Reynolds number quasi-gas phase flow is modeled to obtain the equivalent viscous damping of the quasi-gas phase flow system. The specific parameters are as follows:

[0044] Particles are placed in the cavity of the rudder structure. When the rudder is working, the particle concentration in the cavity is high and the vibration is violent. It can be regarded as a gas-like flow with a low Reynolds number. The transfer of momentum between particles can be described by the viscosity and nominal shear stress of the interaction between particles. For a gas-like flow system, the viscosity is: μ sys =μ ppc +μ g Among them, μ sys is the viscosity of the gas-phase flow system, μ ppcis the effective viscosity generated by the collision between particles, μ g is the airflow viscosity. In general, the effective viscosity generated by the collision between particles is much larger than the airflow viscosity. Therefore, the airflow viscosity can be ignored in the modeling process, that is, μ sys ≈μ ppc .

[0045] The effective viscosity generated by interparticle collisions in gas-phase flow systems can be analyzed based on the dynamics theory of dense multiphase flow. The effective viscosity generated by interparticle collisions is expressed as:

[0046]

[0047] Where, e p is the coefficient of restitution of the particle surface, ρ p is the density of the particle, α p is the volume filling rate of particles, d p is the diameter of the particle; χ is the wave specific kinetic energy, For simple harmonic motion, g p In order to reflect the distribution coefficient of particles in the cavity, the particle distribution is measured by the particle volume filling rate. The relationship between the distribution coefficient and the particle volume filling rate is:

[0048]

[0049] Therefore, the viscosity of the gas-phase flow system is:

[0050]

[0051] Where,

[0052] According to the equivalent viscous damping parameter, the corresponding viscous damping force of the gas-phase flow system is obtained as follows:

[0053]

[0054] Where, ρ sys is the gas-phase mixture density, ρ sys =α p ρ p +(1-α p )ρ g , S is the cross-sectional area of ​​the cavity, C d is the damping coefficient, and its expression is:

[0055]

[0056] In the formula, β shows the relationship between the system's equivalent viscous damping parameter and the excitation frequency, β = πd 2 fρsys / μ sys , d is the cavity diameter, and f is the excitation frequency.

[0057] At the same time, the viscous damping force of the gas-phase flow system also satisfies the following formula:

[0058]

[0059] In, c eq is the equivalent viscous damping. Substituting equation (1.5) into equation (1.6) yields:

[0060]

[0061] c eq Arranged into The normalized form of the variable is:

[0062]

[0063] Where, the expressions of c1, c2, and c3 are:

[0064]

[0065] In equations (1.9) to (3.10),

[0066]

[0067] k2=πd 2 ρ sys (1.14)

[0068] In formula (1.12), h is the cavity depth.

[0069] It can be seen from formula (1.8) that the equivalent viscous damping between particles is determined by the velocity amplitude. The equivalent viscous damping value is a multiple power superposition combination of the velocity amplitude, which is reflected in the actual vibration of the gas-phase flow system as a strong nonlinear vibration of the particle system.

[0070] (3) Equivalent friction damping parameters: Friction damping includes the Coulomb friction damping between particles and between particles and cavity walls; the details are as follows:

[0071] In addition to the equivalent viscous damping caused by inter-particle collisions, the damping of the particle system also includes Coulomb friction damping between particles and between particles and the cavity wall. The expression of Coulomb friction damping force is:

[0072]

[0073] Where μ is the coefficient of kinetic friction, F N is the normal force on the particle, and the sign function The expression is:

[0074]

[0075] First, let’s discuss the Coulomb friction damping generated between particles. According to Hertz contact theory, the normal force on the particle can be expressed as:

[0076]

[0077] Where, F Npp is the normal force on the particle, N is the number of particles filled in the cavity, g is the acceleration due to gravity, h p is the stacking height of particles in the cavity.

[0078] At the same time, the Coulomb friction damping force of the gas-phase flow system also satisfies the following formula:

[0079]

[0080] Where c fpp is the equivalent friction damping caused by interparticle friction. Combining equations (1.15) and (1.18), we can obtain:

[0081]

[0082] Where μ pp is the particle kinetic friction coefficient.

[0083] Then, the Coulomb friction damping generated between the particles and the cavity wall is discussed. Since the particle filling rate in the rudder cavity is relatively high, when studying the friction between the particles and the cavity wall, the particle group can be regarded as a whole rather than a discrete individual for force analysis. Therefore, the normal force between the particle and the cavity can be equivalent to the filling mass of the particle, that is:

[0084] F Npw =m p g(1.20)

[0085] Where, F Npw is the normal force between the particle and the cavity, m p is the filling mass of the particles. Combining with formula (1.18), the equivalent friction damping generated by the friction between the particles and the cavity wall can be obtained.

[0086]

[0087] Where μ pw is the coefficient of kinetic friction between the particle and the cavity wall.

[0088] (4) Rudder blade vibration modeling: The vibration of the rudder blade is equivalent to bending motion and torsional motion, and the bending motion and torsional motion are modeled separately. The equivalent viscous damping parameters and equivalent friction damping parameters obtained in steps (2) and (3) are applied to the modeling of bending motion and torsional motion.

[0089] The details are as follows:

[0090] The free vibration motion equation of the two-dimensional rudder blade is established, and the mechanical model of the rudder blade is attached. Figure 1 The rudder blade mechanical model is shown in Table 1.

[0091] Table 1 Basic parameters of the rudder blade mechanical model

[0092] symbol Physical meaning symbol Physical meaning b Rudder blade half chord length <![CDATA[K α ]]> Torsional stiffness coefficient m System equivalent total mass <![CDATA[C α ]]> Torsional damping coefficient G Center of mass <![CDATA[K h ]]> Bending stiffness coefficient E Strong Heart <![CDATA[C h ]]> Bending damping coefficient h Bending motion displacement <![CDATA[x α ]]> The distance between the center of mass and the center of rigidity α Rotation angle of torsional motion around the rigid center <![CDATA[I α ]]> Moment of inertia about the rigid center

[0093] The Lagrange equation is used to establish the free vibration motion equation of the two-dimensional rudder blade. The kinetic energy of the rudder blade system is:

[0094]

[0095] Where r is the distance from the rigid center E, and is positive after the rigid center E; S α is the mass moment of static of the rudder blade, and its expression is S α =mx α ; m is the equivalent total mass of the system, which is m=m p ×L+m t， m t is the mass of the rudder blade.

[0096] The potential energy of the rudder blade system is:

[0097]

[0098] Substituting the kinetic energy and potential energy of the rudder into the Lagrange equation, we get:

[0099]

[0100] Where Q i It is the generalized force of the rudder blade system, and its generalized force is 0 during the free vibration of the rudder blade.

[0101] Arranging the above formula, the free vibration motion equation of the rudder blade is:

[0102]

[0103] The damping of the rudder structure itself is small, so the damping effect is ignored in the above formula. However, after adding particles to the rudder structure, its damping is greatly improved, which is manifested as an increase in bending damping and torsional damping when the rudder moves. At this time, the damping factor cannot be ignored. Therefore, after adding particles to the rudder structure, its motion equation is modified to:

[0104]

[0105] For the rudder blade studied in this invention, its center of mass and center of rigidity are very close. To facilitate subsequent research, the center of mass and center of rigidity are made to coincide with each other during modeling, i.e., x α =0, so S α =mx α = 0, which is equivalent to decoupling Equation (1.26). At this time, Equation (1.26) is transformed into the bending motion equation and the torsional motion equation:

[0106]

[0107] It can be expressed in matrix form as:

[0108]

[0109] Combined with the previous analysis of the damping of the rudder system, the motion equation of the rudder after adding particles can be expressed as:

[0110]

[0111] Where c0 is the structural damping inside the rudder blade. In engineering, the structural damping of the rudder blade is generally ignored, so c0=0; c h,eq is the equivalent viscous damping of bending motion; c h,fpp is the equivalent friction damping between particles in bending motion; c h,fpw is the equivalent friction damping between the bending motion particle and the cavity wall; c α,eq is the equivalent viscous damping of torsional motion; c α,fpp is the equivalent friction damping between torsional motion particles; c α,fpw is the equivalent friction damping between the torsional motion particles and the cavity wall. The calculation formula for the above damping parameters is as follows:

[0112]

[0113] (5) Damping ratio simulation: In the bending and torsional motion models of the rudder blade, the transient response analysis of the bending and torsional motions is performed respectively to obtain the relationship between time and amplitude. The damping ratios of the bending and torsional motions of the rudder blade system are calculated. The sum of the damping ratios of the bending and torsional motions is the damping ratio of the rudder blade system. The damping ratios of the rudder blade system under different damping particle configurations are calculated, and then the influence trend of different damping particle parameters on the damping ratio of the rudder blade system is obtained.

[0114] Specifically as follows: For bending motion, Equation (1.29) can be rewritten as:

[0115]

[0116] Where,

[0117]

[0118] Therefore, the solution of equation (1.36) is: h = asinψ (1.38)

[0119] Where a is the amplitude, ψ is the vibration phase, ψ=ω h t+ψ0, taking the derivative of the above formula, we get:

[0120]

[0121] The derivatives of a and ψ satisfy the following relationship:

[0122]

[0123] Where,

[0124] Substitute equation (1.39) into equation (1.37) and find Substituting into formula (1.40) we get:

[0125]

[0126] Arranging the above formula gives:

[0127]

[0128] Substituting equation (1.43) into equation (1.40) yields:

[0129]

[0130] Where,

[0131] cc h,f =4(c h,fpp +c h,fpw )η h (1.45)

[0132] cc h,0 =πc0ω h η h (1.46)

[0133] cc h,1 =2.88c h,1 ω h 3 / 2 η h (1.47)

[0134] cc h,2 =2.67c h,2 ω h2 η h (1.48)

[0135] cc h,3 =2.50c h,3 ω h 5 / 2 η h (1.49)

[0136] Similarly, according to the above steps, we can get:

[0137]

[0138] Therefore, the transient response of the bending motion equation of the rudder system based on particle damping is:

[0139] h=asin(ω h t+ψ0)(1.51)

[0140] Where ψ0 is a constant.

[0141] Similarly, by modeling the torsional motion of the rudder system according to the above steps, the amplitude ε and speed can also be obtained. The relationship:

[0142]

[0143] Where,

[0144] cc α,f =4(c α,fpp +c α,fpw )η α (1.53)

[0145] cc α,0 =πc0ω α η α (1.54)

[0146] cc α,1 =2.88c α,1 ω α 3 / 2 η α (1.55)

[0147] cc α,2 =2.67c α,2 ω α 2 η α (1.56)

[0148] cc α,3 =2.50c α,3 ω α 5 / 2 η α (1.57)

[0149]

[0150]

[0151] Similarly, according to the above steps, we can get

[0152]

[0153] Therefore, the transient response of the bending motion equation of the rudder system based on particle damping is:

[0154] α=εsin(ω α t+ψ'0)(1.61)

[0155] Equations (1.44) and (1.52) express the relationship between amplitude and velocity. Therefore, the Runge-Kutta method can be used to solve Equations (1.44) and (1.52) to obtain the relationship between time and amplitude. For the rudder system, the damping ratio is less than 0.1, and the damping ratio can be calculated according to the following formula:

[0156]

[0157] Where ζ is the damping ratio, A is the amplitude of the time-amplitude relationship diagram, and the damping ratio of the bending and torsional motion of the rudder system can be obtained by taking the value of r cycles on the time-amplitude relationship diagram for calculation.

[0158] The above process is programmed to perform simulation modal analysis and experimental modal analysis. By inputting the parameters shown in Table 2, the time-amplitude relationship diagram of the rudder system under different particle configurations can be obtained.

[0159] Table 2 Simulation parameters

[0160]

[0161] (6) Rudder blade installation: Based on the influence trend of different damping particle configurations on the damping ratio of the rudder blade system in step (5), the optimal damping particle parameters are configured on the rudder blade system. The damping particle parameters include the particle filling position in the cavity on the rudder blade, the filling rate in the particle cavity, and the particle size.

[0162] 1. Simulation analysis of rudder damping characteristics under various particle parameters

[0163] 1.1. Influence of particle filling position on the damping characteristics of the rudder blade

[0164] While increasing the damping of the rudder blade system, the mass effect of the particles also changes the mass distribution of the rudder blade. Therefore, the position of filling the damping particles is particularly important. If the damping particles are filled in an inappropriate position, the damping will be increased while the static mass effect of the rudder blade will be worsened, which will reduce the critical dynamic pressure of the rudder blade.

[0165] In the designed 12 rudder cavities (such as Figure 2 ) is filled with damping particles of equal mass filling rate, and the damping characteristics of the rudder are calculated. The research will be conducted on cavities No. 1, 3, 4, 6, 7, 9, 10, 11, and 12.

[0166] Taking the case of filling cavity 3 with 80g of 2mm iron alloy particles as an example, the calculation parameters that need to be input are shown in Table 3 below:

[0167] Table 3 Simulation parameter input table

[0168]

[0169] In order to maintain the accuracy of the calculated data, the mass, material, particle size and other related parameters of the particles filled in the calculation are kept consistent, and only the filling position of the particles is changed to calculate the damping ratio of the rudder system. The time-amplitude relationship diagram of the rudder system after the damping particles are filled in cavity 3 is obtained, as shown in the figure below: Figure 2 As shown in the figure, the shaded area is the cavity filled with particles. The calculation results of the damping ratio of each order are shown in Table 4, and the damping ratio curve of the particles filled at each position is plotted as shown in Figure 3 shown

[0170] Table 4. Modal damping ratio before and after filling damping particles at each position

[0171]

[0172] By calculating the modal damping ratio of the rudder system with particles filled at different positions, it is found that when the damping particles are filled at different positions, they also have different effects on the first and second order damping ratios of the rudder system, as follows:

[0173] (1) When the damping particles are placed at different positions, the rudder system exhibits different damping ratios. The farther the particle placement is from the nodal line of the rudder bending moment, the better the effect of the particles on improving the first-order modal damping ratio of the rudder. Therefore, filling the damping particles at positions 1, 3, and 4 is more effective in increasing the first-order damping ratio.

[0174] (2) The farther the filling particles are from the pitch line of the rudder blade torsion, the better the effect of the particles on improving the second-order modal damping ratio of the rudder blade. Therefore, filling damping particles at positions 10 and 12 has a better effect on increasing the second-order damping ratio of the rudder blade system.

[0175] 1.2 Calculation and analysis of rudder damping characteristics with different particle filling rates

[0176] Fill cavity 3 with particles and calculate the effect of the damper's filling rate on the damping effect of the rudder system. Select the damping particle material as iron alloy, the particle size as 2mm, and the particle filling rate as 70%, 75%, 80%, 85%, 90%, 95%, and 100%. Calculate the effect of the damping particles on the rudder's damping ratio at different filling rates. The time-amplitude relationship diagram of the rudder system at a 70% filling rate is shown in the figure below. Figure 4 The calculation results of damping ratio of each order are shown in Table 5, and the damping ratio curves under different particle filling rates are plotted as shown in Figure 5 shown.

[0177] Table 5 Front and rear modal damping ratio of the rudder system under different filling rates

[0178]

[0179] Calculations of the damping ratio at different particle filling rates show that as the filling rate increases within a certain range, the damping ratio of the rudder system also increases. However, after the filling rate exceeds 95%, the damping ratio of the rudder structure begins to decline, and this trend is particularly pronounced for the first-order damping ratio. Therefore, when the particle filling rate is 95%, the first and second order damping ratios of the rudder structure are significantly improved.

[0180] 1.3 Calculation and analysis of the damping characteristics of rudder blades with different particle sizes

[0181] Based on the inherent geometric structure characteristics of the rudder blade, particles with diameters of 1mm, 1.5mm, 2mm, and 2.5mm were selected for calculation. In the calculation, the particle material was selected as iron alloy, the particle damping filling rate was 95%, the filling position of the damping particles was 3, and other parameters remained unchanged. The effect of the damping particles on the damping ratio of the rudder blade was calculated for different particle sizes. The time-amplitude relationship diagram of the rudder blade system with a particle size of 1mm is shown as follows: Figure 6 The calculation results of damping ratio of each order are shown in Table 6, and the damping ratio curves of different particle sizes are plotted as shown in Figure 7 shown

[0182] Table 6 Front and rear modal damping ratio of the rudder system under different particle sizes

[0183]

[0184] As particle size changes, the effect of particles on the rudder system's damping ratio also changes accordingly. When filling the same location with particles of 1mm, 1.5mm, 2mm, and 2.5mm in diameter, the 2mm particle size has the most significant effect on improving the rudder's first- and second-order damping ratios. Therefore, when the particle size is 2mm, the rudder structure has a better effect on improving its first- and second-order damping ratios.

[0185] 2. Experimental analysis of rudder damping characteristics under various particle parameters

[0186] 2.1 Experimental Introduction

[0187] Based on the above analysis results of the optimization calculation of the particle configuration of the aircraft rudder, experiments were conducted on the rudder with different particle filling positions, different particle filling rates, different particle sizes and other parameters. The vibration conditions of each point on the rudder were collected, and the corresponding transfer function was calculated to obtain the damping ratio of the rudder after filling with damping particles.

[0188] By comparing the calculated and experimental values ​​of the damping ratio of the rudder system under different particle parameters, the optimal particle parameter configuration is obtained, thereby verifying the accuracy of the theoretical calculation.

[0189] 2.2 Experimental analysis of rudder damping characteristics at different particle filling positions

[0190] An experimental study on the damping characteristics of the rudder blade under different particle filling positions was carried out. The single position cavities No. 1, No. 3, No. 4, No. 6, No. 7, No. 9, No. 10, No. 11, and No. 12 were studied, and the damping of the rudder blade system after adding damping particles at the corresponding serial number positions was analyzed in turn.

[0191] When particles are filled in each cavity, the first two-order damping ratios of the rudder system at different particle filling positions are summarized according to the experimental results, as shown in Table 7. According to the theoretical modeling calculation and the hammering method, the first and second order damping values ​​of the rudder when filling different positions are obtained, the data obtained by theoretical calculation and experimental calculation are fitted and compared, and a fitting comparison curve is made as shown in Figure 8 shown.

[0192] Table 7 Damping ratio of the rudder structure at different particle filling positions

[0193]

[0194] The comparison curves above, comparing the theoretically calculated damping ratio increase and the experimental damping ratio values, show that the theoretical calculated values ​​for the particle-damped rudder system modeling generally agree with the experimental values. The rudder modeling simulation of the present invention can effectively simulate the effects of different filling positions on the rudder's damping ratio.

[0195] (1) Filling damping particles at different positions has different effects on the damping characteristics of the rudder system;

[0196] (2) Filling damping particles at positions 1, 3, and 4 has the best effect on improving the first-order damping of the rudder blade, while filling damping particles at positions 10 and 12 has the best effect on improving the second-order damping of the rudder blade. That is, the farther the particle filling position is from the bending node line, the better the effect of the particles on improving the first-order damping ratio, and the farther the particles are from the torsion node line, the better the effect of the particles on improving the second-order damping ratio;

[0197] (3) Filling the rudder blade with damping particles at the tip chord position has a better effect on improving the first-order damping of the rudder blade. On the contrary, filling the particles at position 12 of the rudder blade has a poor effect on improving the first-order damping of the rudder blade, and even has a tendency to worsen the damping effect of the rudder blade.

[0198] 2.3 Experimental analysis of rudder damping characteristics with different particle filling rates

[0199] An experimental study on the damping characteristics of the rudder blade under different particle filling rates was carried out. The particle size was 2 mm, the particle material was iron alloy, the filling position was cavity No. 3, and the filling rates were selected as 70%, 75%, 80%, 85%, 90%, 95%, and 100%.

[0200] According to the experimental results, the first two order damping ratios of the rudder system at different particle filling rates are summarized as shown in Table 8. According to the theoretical modeling calculation and hammering method, the first and second order damping values ​​of the rudder at different particle filling rates are obtained. The data obtained by theoretical calculation and experimental calculation are fitted and compared, and a fitting comparison curve is made as shown in Figure 9 shown.

[0201] Table 8 Damping ratio of rudder structure under different particle filling rates

[0202]

[0203] The comparison curves of the theoretical calculated damping ratio increase and the experimental damping ratio values ​​in the figure above show that the theoretical calculated values ​​based on the particle damping rudder system modeling and the experimental values ​​are generally consistent. The rudder modeling simulation of the present invention can well simulate the effect of different damping particle filling rates on the rudder damping ratio. Therefore, the following conclusions can be drawn:

[0204] (1) Different damping particle filling rates have different effects on the damping characteristics of the rudder system;

[0205] (2) As the filling rate increases, the damping ratio of the rudder system also increases. However, when the filling rate exceeds 95%, the damping ratio of the rudder structure begins to decline, and the change in filling rate has a greater impact on the first-order damping ratio than the second-order.

[0206] 2.4 Experimental analysis of rudder damping characteristics with different particle sizes

[0207] An experimental study on the damping characteristics of the rudder blade under different particle sizes was carried out. The filling position was fixed to cavity 3, the filling rate was kept at 95%, the particle material was iron alloy, and the particle sizes were selected as 1mm, 1.5mm, 2mm and 2.5mm.

[0208] According to the experimental results, the first two order damping ratios of the rudder system at different particle sizes are summarized as shown in Table 9. According to the theoretical modeling calculation and hammering method, the first and second order damping values ​​of the rudder at different particle sizes are obtained. The data obtained by theoretical calculation and experimental calculation are fitted and compared, and a fitting comparison curve is made as shown in Figure 10 shown.

[0209] Table 9 Damping ratio of rudder structure under different particle sizes

[0210]

[0211] The comparison curves of the theoretical calculated damping ratio increase and the experimental damping ratio values ​​in the figure above show that the theoretical calculated values ​​based on the particle damping rudder system modeling and the experimental values ​​are generally consistent. The rudder modeling simulation of the present invention can well simulate the effect of different damping particle sizes on the rudder damping ratio. Therefore, the following conclusions can be drawn:

[0212] (1) Different damping particle sizes have different effects on the damping characteristics of the rudder system;

[0213] (2) As the particle size increases, the damping ratio of the rudder system also increases. However, when the particle size exceeds 2 mm, the damping ratio of the rudder structure begins to decrease, and the change in particle size has a greater impact on the first-order damping ratio than the second-order.

[0214] From the above experiments, it can be seen that the simulated damping ratio of the rudder blade vibration reduction and shock reduction structure established based on the airflow-like principle in the present invention is similar to the changing trend of the damping ratio of the actual rudder blade affected by the damping particle parameters. Therefore, technicians can, according to the determination process of the rudder blade vibration reduction and shock reduction structure in the present invention, first simulate and calculate the optimal vibration reduction and shock reduction parameters of the damping particles on the rudder blade, and then apply the optimal damping particle parameters in the actual rudder blade structure.

[0215] It should be noted that, in this document, relational terms such as first and second, etc., are used solely to distinguish one entity or operation from another, and do not necessarily require or imply any actual relationship or order between these entities or operations. Furthermore, the terms "include," "comprise," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or terminal device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or terminal device. Without further limitation, elements defined by the phrase "include..." or "comprising..." do not exclude the presence of additional elements in the process, method, article, or terminal device comprising the elements. Furthermore, in this document, "greater than," "less than," "exceeding," etc., are understood to exclude the number itself; "above," "below," "within," etc., are understood to include the number itself.

[0216] Although the above embodiments have been described, those skilled in the art may make additional changes and modifications to these embodiments once they know the basic creative concepts. Therefore, the above descriptions are merely embodiments of the present invention and do not limit the scope of patent protection of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention's description and drawings, or directly or indirectly applied in other related technical fields, are also included in the scope of patent protection of the present invention.

Claims

1. A rudder blade vibration reduction and impact reduction structure, characterized in that: A cavity is provided in the rudder sheet, and the cavity is filled with damping particles. The process of determining the vibration reduction and shock reduction structure of the rudder blade includes the following steps: (1) Damping classification: The system damping of the rudder blade is divided into rudder blade structural damping, inter-particle collision damping, and friction damping caused by friction between particles and between particles and cavity walls; (2) Equivalent viscous damping parameters: The motion of the damping particles in the rudder is equivalent to a gas-like flow with a low Reynolds number. The gas-like flow with a low Reynolds number is modeled to obtain the equivalent viscous damping of the gas-like flow system. (3) Equivalent friction damping parameter: Friction damping includes Coulomb friction damping between particles and between particles and cavity wall; (4) Rudder blade vibration modeling: The vibration of the rudder blade is equivalent to bending motion and torsional motion, and the bending motion and torsional motion are modeled separately. The equivalent viscous damping parameters and equivalent friction damping parameters obtained in steps (2) and (3) are applied to the modeling of bending motion and torsional motion; (5) Damping ratio simulation: In the bending and torsional motion models of the rudder blade, the transient response analysis of the bending motion and torsional motion is performed respectively to obtain the relationship between time and amplitude. The damping ratio of the bending and torsional motion of the rudder blade system is calculated. The sum of the damping ratios of the bending and torsional motions is the damping ratio of the rudder blade system. The damping ratio of the rudder blade system under different damping particle configurations is calculated, and then the influence trend of different damping particle parameters on the damping ratio of the rudder blade system is obtained. (6) Rudder blade installation: Based on the influence trend of different damping particle configurations on the damping ratio of the rudder blade system in step (5), the optimal damping particle parameters are configured on the rudder blade system.

2. The rudder blade vibration reduction and impact reduction structure according to claim 1, characterized in that: The damping of the rudder blade structure is neglected.

3. The rudder blade vibration reduction and impact reduction structure according to claim 1, characterized in that: The viscosity of a gas-phase flow system is equivalent to the effective viscosity generated by the collision between particles.

4. The rudder blade vibration reduction and impact reduction structure according to claim 1, characterized in that: The effective viscosity generated by the collision between particles in a gas-like flow system is analyzed based on the kinetic theory of dense multiphase flow.

5. The rudder blade vibration reduction and impact reduction structure according to claim 1, characterized in that: In step (3), when modeling bending motion and torsional motion respectively, the center of mass and the center of rigidity are overlapped.

6. The rudder blade vibration reduction and impact reduction structure according to claim 1, characterized in that: The damping ratio can be calculated as follows: Where ζ is the damping ratio, A is the amplitude of the time-amplitude relationship diagram, and the damping ratio of the bending and torsional motion of the rudder system can be obtained by taking the value of r cycles on the time-amplitude relationship diagram for calculation.

7. The rudder blade vibration reduction and impact reduction structure according to claim 1, characterized in that: The damping particle parameters include the particle filling position in the cavity on the rudder plate, the particle filling rate in the cavity and the particle size.

8. The rudder blade vibration reduction and impact reduction structure according to claim 1, characterized in that: The optimal damping particle parameters determined in step (6) maximize the damping ratio of the rudder blade vibration reduction and shock reduction structure.

9. The rudder blade vibration reduction and impact reduction structure according to claim 8, characterized in that: A plurality of cavities are provided on the rudder sheet.

10. The rudder blade vibration reduction and impact reduction structure according to claim 8, characterized in that: The particle size of the damping particles is 1-2.5 mm, the filling rate of the damping particles in the cavity is 70-100%, and the material of the damping particles in the cavity is iron-based alloy, tungsten-based alloy, ceramic or copper-based alloy.

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