Establishment method and application of ground resonance nonlinear analysis model

Abstract

The invention relates to an establishment method and application of a ground resonance nonlinear analysis model, and belongs to the technical field of analysis model establishment methods and application. In order to overcome the defect that an accurate ground resonance analysis conclusion cannot be obtained due to the fact that nonlinear mechanical characteristics of a rotor wing shimmy damper and a machine body damper are not considered in the prior art, the invention provides an establishment method of a ground resonance nonlinear analysis model. According to the method, the influence of the nonlinear factor of the blade shimmy damper and the nonlinear non-proportional damping of the body damper can be considered, and an accurate resonance analysis result is obtained. The method comprises the following steps: S1, selecting a blade shimmy damper model, calculating the acting force of a blade shimmy damper, and determining a blade shimmy motion equation; s2, calculating equivalent parameters of an aircraft body equivalent to a propeller hub center on the skid-type undercarriage under different responses, inputting longitudinal and transverse displacements and speeds of the propeller hub center, and determining an aircraft body motion equation; and S3, determining a ground resonance nonlinear analysis model.

Description

Technical Field

[0001] The invention relates to a method for establishing a ground resonance nonlinear analysis model and its application, in particular to a method for establishing a ground resonance nonlinear analysis model of a skid-type helicopter and its application, belonging to the technical field of analysis model establishment methods and their applications. Background Art

[0002] At present, there are many studies on the ground resonance of wheeled landing gear helicopters, but there are few studies on the ground resonance of skid-type landing gear helicopters. Narramore et al. analyzed the ground resonance stability of Bell429 skid-type helicopter at room temperature (16°) and low temperature (-39°). The results showed that the helicopter had sufficient modal damping at all operating speeds in a wide temperature range, indicating that the helicopter had good ground resonance stability. The study also found that low temperature would increase the natural frequency of blade shimmy, and the coupling speed of the rotor shimmy retreat mode and the body motion mode would increase, which would reduce the ground resonance stability.

[0003] Walden et al. conducted a ground resonance test on the RQ-8A unmanned skid helicopter with the harpoon grid moored. The finite element method is generally used to analyze the dynamic characteristics of the skid helicopter ground resonance. Sharf et al. used ANSYS software to establish a finite element model of the skid landing gear. The obtained airframe mass, stiffness and damping parameters were used to calculate the ground resonance instability zone through a mathematical model, and the software was used to perform rotor / airframe uncoupled modal analysis. The results showed that increasing the height of the landing gear helps to alleviate the ground resonance instability of the helicopter. Xu Min et al. proposed a method to obtain the airframe motion characteristic parameters through the finite element method and to perform ground resonance stability analysis of the skid helicopter based on the eigenvalue method. Yu Renye et al. used a plane model to analyze the damping required for the ground resonance airframe of the skid helicopter.

[0004] The above studies rarely take into account the influence of nonlinear factors on ground resonance, but there are many nonlinear factors in skid-type helicopters, among which the rotor blade damper and the fuselage damper have a greater impact on ground resonance. When conducting preliminary design of helicopter ground resonance, these nonlinear components are often equivalently linearized, but when conducting ground resonance verification analysis, the nonlinear mechanical characteristics of the rotor damper and the fuselage damper must be considered, otherwise it is impossible to draw a more accurate ground resonance analysis conclusion.

[0005] The ground resonance of a skid-type helicopter can be simply described as a dynamic instability phenomenon caused by the coupling between the rigid body motion supported on the elastic landing gear and the rotor motion, which at least includes the rotor shimmy and the horizontal motion of the body at the center of the hub. The blade damper and the body damper are both nonlinear, and the body damper constitutes a non-proportional damping of the body motion. Therefore, it is essentially a self-excited vibration stability problem of a nonlinear multi-degree-of-freedom system with rigid-flexible coupling, rotor-body coupling, and non-proportional damping. Summary of the invention

[0006] The purpose of the present invention is to solve the deficiency that the prior art fails to consider the nonlinear mechanical characteristics of the rotor shimmy damper and the fuselage damper, resulting in the inability to draw accurate ground resonance analysis conclusions, and proposes a method for establishing and applying a ground resonance nonlinear analysis model, which can take into account the influence of the nonlinear factors of the blade shimmy damper and the nonlinear non-proportional damping of the fuselage damper, so as to obtain more accurate ground resonance analysis results of a skid-type helicopter.

[0007] In order to solve the above problems, the present application is implemented through the following technical solutions:

[0008] A method for establishing a ground resonance nonlinear analysis model is characterized in that it includes the following steps:

[0009] S1. Determine the rotor blade swing motion equation:

[0010] Select the blade shimmy damper model, calculate the blade shimmy damper force, and determine the blade shimmy motion equation;

[0011] Preferably, the step S1 specifically comprises selecting a nonlinear viscoelastic damper model or a nonlinear hydraulic damper model as a blade shimmy damper model, inputting blade shimmy damper model parameters and an initial response of blade shimmy vibration to calculate the blade shimmy damper force, and determining the blade shimmy vibration motion equation according to the blade shimmy damper force;

[0012] Preferably, the blade damper model parameters are determined by the selected damper model, and different selected damper models require different parameters;

[0013] The blade shimmy initial response includes an initial shimmy angle and a shimmy angular velocity;

[0014] According to the selected damper model and the initial response of blade shimmy, the Runge-Kutta method is used to iteratively solve the blade shimmy damper force;

[0015] Preferably, the nonlinear viscoelastic damper model is:

[0016] is the displacement s and velocity of the damper The relevant restoring force is: i is the i-th order elastic force coefficient, N k is the elastic force order, c is the damping force coefficient, z is the sliding restoring force, k s is the sliding linear stiffness, z s is the slip limit restoring force, is the sliding limit displacement, the required parameters are: k i 、N k , z, k s 、z s ;

[0017] Preferably, the nonlinear hydraulic damper model is:

[0018] Where: m v is the valve core mass, c v , k v are the valve core motion damping and stiffness, respectively, v A is the displacement of the valve core relative to the valve seat, v is the valve core pressure area, P L =P1-P2 is the piston load pressure, C v0 is the constant flow coefficient of the valve port, γ v is the fitting parameter of the valve port flow coefficient to the valve core displacement, d v is the inner diameter of the valve seat, α v is the semi-cone angle of the valve core, F0 is the pre-pressure of the constant pressure valve, ρ o is the oil density, β o is the bulk elastic modulus of the oil, V o is the volume of the hydraulic cylinder, A p is the piston pressure area, s is the piston displacement, C d is the piston damping hole flow coefficient, A d is the cross-sectional area of ​​the piston damping hole, F 活 is the force on the piston, the required parameter is P L , A p ;

[0019] Preferably, the blade swing vibration equation is:

[0020]

[0021] I b and S b are the inertia moment and static moment of the blade to the flap hinge, e is the overhang of the flap hinge, k b0 and c b0 are the shimmy stiffness and damping without considering the effect of blade shimmy damper, Ω is the rotor speed, ζ k is the swing angle of the kth blade, y kis the azimuth angle of the kth blade, s k is the displacement of the viscoelastic damper of the kth blade, and F is the force acting on the viscoelastic damper or the force F of the nonlinear hydraulic damper 活 ;

[0022] S2. Determine the body motion equation

[0023] Add the airframe damper model to the airframe model on the skid-type landing gear, calculate the equivalent linear damping of the airframe damper under different responses, include it in the finite element analysis model on the skid-type landing gear, calculate the equivalent parameters of the airframe equivalent to the hub center on the skid-type landing gear under different responses, input the longitudinal and lateral displacements and velocities of the hub center, and determine the airframe motion equation;

[0024] Preferably, in step S2, a nonlinear hydraulic damper model is selected as the machine body damper model, parameters of the machine body damper model are input, and the equivalent linear damping of the machine body damper under different responses is calculated;

[0025] The equivalent linear damping is determined based on the fact that the energy consumed by the actual system and the equivalent linear system in one vibration cycle is equal. Specifically, the excitation amplitude of the damper is s a , the excitation frequency is ω, then its motion is:

[0026] s=s a sinωt, period of motion

[0027] The energy W absorbed by the nonlinear damper during one cycle of motion is:

[0028] Where: is the force generated by the damper, calculated by its dynamic model;

[0029] The energy absorbed by the equivalent linear system during one cycle of motion is: By Mode The equivalent linear damping of the damper is obtained as:

[0030]

[0031] Calculate the equivalent parameters of the fuselage equivalent to the hub center on the skid landing gear with different responses. The specific steps are as follows:

[0032] The hub center motion and damper motion have the following relationship: Where: c x and c y are the equivalent damping of the longitudinal and lateral motion of the hub center, v hx and v hyare the longitudinal and lateral velocity amplitudes of the hub center, c e is the equivalent damping of the body damper, v d is the velocity amplitude of the body damper;

[0033] The relationship between the hub center velocity amplitude and the body damper velocity amplitude is:

[0034] According to the above formula, input v hx and v hy , we get v d , according to the equivalent damping-velocity curve C of the body damper e =f e (v d ), calculate the equivalent damping of the airframe damper, and according to the airframe modal equivalent damping-damper damping curve c x =f x (C e ) and c y =f y (C e ) to obtain the equivalent damping of the body.

[0035] The equivalent mass and equivalent stiffness of the airframe are calculated as follows:

[0036] The natural frequency of the airframe modal can be directly obtained by finite element software, and the specific calculation of its instantaneous center position, equivalent mass and equivalent stiffness is as follows:

[0037] Where: j = 1-4 represents the longitudinal, pitch, roll and lateral modes respectively, z is the instantaneous center position of the airframe modal, a positive value indicates that it is above the center of gravity, and a negative value indicates that it is below the center of gravity, x and φ are the translational momentum and rotational momentum of the center of gravity under the airframe modal respectively, m is the modal equivalent mass of the airframe, I = [I y I y I x I x ] is the body inertia moment, m f is the body mass, z h is the height from the center of the hub to the center of gravity of the fuselage, k is the equivalent modal stiffness of the fuselage, ω is the modal natural frequency of the fuselage, and this natural frequency is the natural frequency of the system without damping.

[0038] Preferably, the body motion equation is:

[0039]

[0040] Where: S b is the static moment of the blade to the flap hinge, m b is the blade mass, Ω is the rotor speed, N b is the number of blades, ζ kis the swing angle of the kth blade, y k is the azimuth angle of the kth blade, x h and h are the longitudinal and lateral displacements of the hub center, m x 、c x and k x are the mass, damping and stiffness of the longitudinal motion from the airframe to the hub center, m y 、c y and k y They are respectively the mass, damping and stiffness of the lateral motion from the airframe equivalent to the center of the hub.

[0041] S3. Determine the ground resonance nonlinear analysis model

[0042] The blade vibration motion equation in step S1 is combined with the body motion equation in step S2 to form a ground resonance nonlinear analysis model.

[0043]

[0044] Another technical solution adopted by the present invention is: an application of the ground resonance nonlinear analysis model established by the above method in the nonlinear time domain simulation analysis of ground resonance vibration stability.

[0045] An application of a ground resonance nonlinear analysis model includes time domain response analysis and modal damping analysis, wherein the time domain response analysis includes the following steps:

[0046] A. Exciting the modal response of the body

[0047] The hub center is excited longitudinally and transversely respectively to excite the steady-state response of the required airframe mode. Then, the damper velocity amplitude is calculated according to the hub center motion and compared with the velocity amplitude used to determine the damper damping, i.e., the theoretical value.

[0048] Preferably, the body damper takes equivalent damping at different speed amplitudes to determine the excitation frequency, and uses an excitation force amplitude calculation formula to determine the excitation force amplitude at the hub center;

[0049] The calculation formula of the exciting force amplitude is: v d is the velocity amplitude of the body damper;

[0050] B. Identification of airframe modal damping

[0051] After the body modal steady-state response in step A is completed, the transient response is subjected to modal damping identification after the excitation is cancelled, and the attenuation law of the transient response is determined according to the change of the modal damping in the time domain;

[0052] Get the transient response envelope of the airframe modal

[0053] Where: ωx(t) and ωy(t) are the longitudinal and transverse vibration frequencies of the hub center respectively;

[0054] After obtaining the transient response envelope of the airframe modal, the modal damping is calculated as follows:

[0055]

[0056] Preferably, the larger the amplitude of the damper axial velocity in the steady-state response, the more delayed the change of the body modal damping in the transient response part.

[0057] The method proposed in the present invention is based on a ground resonance equivalent plane model of a helicopter, and adopts a nonlinear dynamic model of a hydraulic damper or a viscoelastic damper to take into account the influence of the nonlinearity of the shimmy damper in the blade shimmy motion. Combined with the influence of the damper nonlinearity on the inherent modal characteristics of the body, the influence of the nonlinear non-proportional damping of the body damper is taken into account in the body motion.

[0058] The present invention establishes a simple and effective helicopter ground resonance equivalent plane model based on the characteristics of the skid landing gear elastic structure and the connection mode of the fuselage damper. The model not only takes into account the nonlinearity of the blade damper and the fuselage damper, but also considers the influence of the non-proportional damping formed by the fuselage damper on the inherent characteristics of the fuselage. The model can be used for the verification and analysis of the ground resonance stability of the skid helicopter.

[0059] The established nonlinear analysis model of ground resonance of a skid-type helicopter is used to carry out time-domain simulation of dynamic response and modal damping analysis of a certain type of skid-type helicopter, further illustrating the feasibility of the established nonlinear model as a verification and analysis model for ground resonance of a skid-type helicopter. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 : Flowchart of the present invention;

[0061] Figure 2 :Component diagram of nonlinear analysis model of ground resonance of skid-type helicopter;

[0062] Figure 3 : Aircraft equivalent parameter calculation process;

[0063] Figure 4 : Change of damper velocity amplitude;

[0064] Figure 5 : Longitudinal excitation, the velocity amplitude v of the excited damper d =Time domain response diagram when 2mm / s;

[0065] Figure 6 : Longitudinal excitation, the velocity amplitude v of the excited damperd =Time domain response diagram when 5mm / s;

[0066] Figure 7 : Longitudinal excitation, the velocity amplitude v of the excited damper d =Time domain response diagram when 50mm / s;

[0067] Figure 8 : Longitudinal excitation, the velocity amplitude v of the excited damper d =Time domain response diagram when 100mm / s;

[0068] Fig. 9 : Transverse excitation, the velocity amplitude v of the excited damper d =Time domain response diagram when 2mm / s;

[0069] Fig.10 : Transverse excitation, the velocity amplitude v of the excited damper d =Time domain response diagram when 5mm / s;

[0070] Fig.11 : Transverse excitation, the velocity amplitude v of the excited damper d =Time domain response diagram when 50mm / s;

[0071] Fig.12 : Transverse excitation, the velocity amplitude v of the excited damper d =Time domain response diagram when 100mm / s;

[0072] Fig.13 : The curve of the airframe modal damping ratio changing with the speed of the improved damper;

[0073] Fig.14 : longitudinal modal damping of the airframe under different velocity amplitudes of the damper;

[0074] Fig.15 : Transverse modal damping of the airframe at different velocity amplitudes of the damper.

[0075] illustrate: Fig.13 Middle: (a) valve not open; (b) valve open. DETAILED DESCRIPTION

[0076] The following is a specific implementation of the present invention with reference to the accompanying drawings to further illustrate the composition of the present invention.

[0077] Example 1. Figure 1 A method for establishing a ground resonance nonlinear analysis model is shown, comprising the following steps:

[0078] S1. Determine the rotor blade swing motion equation:

[0079] Select the blade shimmy damper model, calculate the blade shimmy damper force, and determine the blade shimmy motion equation;

[0080] Wherein, the step S1 specifically includes selecting a nonlinear viscoelastic damper model or a nonlinear hydraulic damper model as a blade shimmy damper model, inputting blade shimmy damper model parameters and a blade shimmy initial response to calculate a blade shimmy damper force, and determining a blade shimmy motion equation according to the blade shimmy damper force;

[0081] The parameters of the blade damper model are determined by the selected damper model. Different damper models are selected, and different parameters are required.

[0082] The blade shimmy initial response includes an initial shimmy angle and a shimmy angular velocity;

[0083] According to the selected damper model and the initial response of blade shimmy, the Runge-Kutta method is used to iteratively solve the blade shimmy damper force;

[0084] Wherein, the nonlinear viscoelastic damper model is:

[0085] is the displacement s and velocity of the damper The relevant restoring force is: i is the i-th order elastic force coefficient, N k is the elastic force order, c is the damping force coefficient, z is the sliding restoring force, k s is the sliding linear stiffness, z s is the slip limit restoring force, is the sliding limit displacement, the required parameters are: k i 、N k , z, k s 、z s ;

[0086] Wherein, the blade swing vibration equation is:

[0087]

[0088] I b and S b are the inertia moment and static moment of the blade to the flap hinge, e is the overhang of the flap hinge, k b0 and c b0 are the shimmy stiffness and damping without considering the effect of the blade shimmy damper, Ω is the rotor speed, ζ k is the swing angle of the kth blade, y k is the azimuth angle of the kth blade, s k is the displacement of the viscoelastic damper of the kth blade, and F is the force acting on the viscoelastic damper;

[0089] S2. Determine the body motion equation

[0090] Add the airframe damper model to the airframe model on the skid-type landing gear, calculate the equivalent linear damping of the airframe damper under different responses, include it in the finite element analysis model on the skid-type landing gear, calculate the equivalent parameters of the airframe equivalent to the hub center on the skid-type landing gear under different responses, input the longitudinal and lateral displacements and velocities of the hub center, and determine the airframe motion equation;

[0091] Wherein, in the step S2, a nonlinear hydraulic damper model is selected as the machine body damper model, the machine body damper model parameters are input, and the equivalent linear damping of the machine body damper under different responses is calculated;

[0092] The equivalent linear damping is determined based on the fact that the energy consumed by the actual system and the equivalent linear system in one vibration cycle is equal, as follows: The excitation amplitude of the damper is s a , the excitation frequency is ω, then its motion is:

[0093] s=s a sinωt, period of motion

[0094] The energy W absorbed by the nonlinear damper during one cycle of motion is:

[0095] Where: is the force generated by the damper, calculated by its dynamic model;

[0096] The energy absorbed by the equivalent linear system during one cycle of motion is:

[0097] By Mode The equivalent linear damping of the damper is obtained as:

[0098]

[0099] Calculate the equivalent parameters of the fuselage equivalent to the hub center on the skid landing gear with different responses. The specific steps are as follows:

[0100] The hub center motion and damper motion have the following relationship:

[0101] Where: c x and c y are the equivalent damping of the longitudinal and lateral motion of the hub center, v hx and v hy are the longitudinal and lateral velocity amplitudes of the hub center, c e is the equivalent damping of the body damper, v dis the velocity amplitude of the body damper;

[0102] The relationship between the hub center velocity amplitude and the body damper velocity amplitude is:

[0103] According to the above formula, input v hx and v hy , we get v d ,

[0104] According to the equivalent damping-speed curve C of the body damper e =f e (v d ), calculate the equivalent damping of the airframe damper, and according to the airframe modal equivalent damping-damper damping curve c x =f x (C e ) and c y =f y (C e ) to obtain the equivalent damping of the body.

[0105] The equivalent mass and equivalent stiffness of the airframe are calculated as follows:

[0106] The natural frequency of the airframe modal can be directly obtained by finite element software, and the specific calculation of its instantaneous center position, equivalent mass and equivalent stiffness is as follows:

[0107] Where: j = 1-4 represents the longitudinal, pitch, roll and lateral modes respectively, z is the instantaneous center position of the airframe modal, a positive value indicates that it is above the center of gravity, and a negative value indicates that it is below the center of gravity, x and φ are the translational momentum and rotational momentum of the center of gravity under the airframe modal respectively, m is the modal equivalent mass of the airframe, I = [I y I y I x I x ] is the body inertia moment, m f is the body mass, z h is the height from the hub center to the center of gravity of the fuselage, k is the equivalent modal stiffness of the fuselage, ω is the natural frequency of the fuselage modal, which is the natural frequency of the system without damping;

[0108] Among them, the body motion equation is:

[0109]

[0110] , where: S b is the static moment of the blade to the flap hinge, m b is the blade mass, Ω is the rotor speed, N b is the number of blades, ζ k is the swing angle of the kth blade, y kis the azimuth angle of the kth blade, x h and h are the longitudinal and lateral displacements of the hub center, m x 、c x and k x are the mass, damping and stiffness of the longitudinal motion from the airframe to the hub center, m y 、c y and k y They are respectively the mass, damping and stiffness of the lateral motion from the airframe equivalent to the center of the hub.

[0111] S3. Determine the ground resonance nonlinear analysis model

[0112] The blade vibration motion equation in step S1 is combined with the body motion equation in step S2 to form a ground resonance nonlinear analysis model.

[0113]

[0114] Embodiment 2. The method for establishing a ground resonance nonlinear analysis model in this embodiment is basically the same as that in Embodiment 1, except that: the nonlinear hydraulic damper model is selected as the blade damper model in step S1.

[0115] The nonlinear hydraulic damper model is:

[0116]

[0117] Where: m v is the valve core mass, c v , k v are the valve core motion damping and stiffness, respectively, v A is the displacement of the valve core relative to the valve seat, v is the valve core pressure area, P L =P1-P2 is the piston load pressure, C v0 is the constant flow coefficient of the valve port, γ v is the fitting parameter of the valve port flow coefficient to the valve core displacement, d v is the inner diameter of the valve seat, α v is the semi-cone angle of the valve core, F0 is the pre-pressure of the constant pressure valve, ρ o is the oil density, β o is the bulk elastic modulus of the oil, V o is the volume of the hydraulic cylinder, A p is the piston pressure area, s is the piston displacement, C d is the piston damping hole flow coefficient, A d is the cross-sectional area of ​​the piston damping hole, F 活 is the force on the piston, the required parameter is P L , A p ;

[0118] The blade swing vibration equation is:

[0119]

[0120] I b and S b are the inertia moment and static moment of the blade to the flap hinge, e is the overhang of the flap hinge, k b0 and c b0 are the shimmy stiffness and damping without considering the effect of the blade shimmy damper, Ω is the rotor speed, ζ k is the swing angle of the kth blade, y k is the azimuth angle of the kth blade, s k is the displacement of the kth blade viscoelastic damper, and F is the force F acting on the nonlinear hydraulic damper 活 .

[0121] Embodiment 3: Application of the ground resonance nonlinear analysis model established by the above method in the nonlinear time-domain simulation analysis of the ground resonance stability of a skid-type helicopter.

[0122] An application of a ground resonance nonlinear analysis model includes time domain response analysis and modal damping analysis, wherein the time domain response analysis includes the following steps:

[0123] A. Exciting the modal response of the body

[0124] The hub center is excited longitudinally and transversely respectively to excite the steady-state response of the required airframe mode. Then, the damper velocity amplitude is calculated according to the hub center motion and compared with the velocity amplitude used to determine the damper damping, i.e., the theoretical value.

[0125] Among them, the equivalent damping of the airframe damper under different speed amplitudes is used to determine the excitation frequency, and the excitation force amplitude calculation formula is used to determine the excitation force amplitude at the hub center;

[0126] The calculation formula of the exciting force amplitude is:

[0127] v d is the velocity amplitude of the body damper;

[0128] The experimental results are as follows Figure 4 As shown, in order to compare and analyze the influence of rotor-airframe coupling, the results when the rotor-airframe is not coupled are also shown in the figure. The simulated airframe damper velocity amplitude is consistent with the initially selected velocity amplitude, i.e., the theoretical value, in most cases, which shows the feasibility of using the above formula to determine the exciting force amplitude.

[0129] B. Identification of airframe modal damping

[0130] After the body modal steady-state response in step A is completed, the transient response is subjected to modal damping identification after the excitation is cancelled, and the attenuation law of the transient response is determined according to the change of the modal damping in the time domain;

[0131] Get the transient response envelope of the airframe modal

[0132] Where: ωx(t) and ωy(t) are the longitudinal and transverse vibration frequencies of the hub center respectively;

[0133] After obtaining the transient response envelope of the airframe modal, the modal damping is calculated as follows:

[0134]

[0135] Among them, the larger the amplitude of the damper axial velocity in the steady-state response, the more delayed the change of the body modal damping in the transient response part.

[0136] Example 4: Experimental results verify the application of a ground resonance nonlinear analysis model established by the above method in the nonlinear time-domain simulation analysis of the ground resonance stability of a skid-type helicopter.

[0137] Select the two cases before the valve of the airframe damper is opened, vd = 2mm / s and vd = 5mm / s, and the two cases after the valve is opened, vd = 50mm / s and vd = 100mm / s, respectively, and perform longitudinal and transverse vibration on the hub center for 10s. After the steady-state response of the corresponding mode is excited, the excitation is cancelled. The responses are as follows: Figure 5-Figure 12 As shown in the figure, (a) is the displacement of the damper; (b) is the hub center speed. Since the velocity amplitude of the airframe damper has a greater influence on its equivalent damping, and the displacement amplitude of the blade damper has a greater influence on its complex modulus, and the blade swing angle and the damper displacement give the same information, the hub center gives a velocity response, while the blade only gives the displacement response of its damper. The displacement responses of the dampers of each blade differ only in phase difference, so only the displacement response of the first damper is given.

[0138] Depend on Figure 5 (a) It can be seen that when the hub center is longitudinally excited, the blade shimmy is not a single-frequency vibration. The steady-state response of the blade damper is Fourier transformed, and the two frequencies are 4.44Hz and 7.47Hz respectively. The rotor speed is 358rpm (5.97Hz), and the hub center longitudinal excitation frequency (airframe longitudinal displacement modal frequency) is 1.52Hz. It can be seen that the two vibration frequencies are Ω-ωx and Ω+ωx respectively, that is, the blade shimmy caused by the body movement. Similar phenomena also exist in the other three cases of longitudinal excitation and the four cases of lateral excitation. It is just that due to the different excitation frequencies in different cases, the blade shimmy frequency caused by the body movement will also be different. Figure 5 (b) It can be seen that after the excitation is removed, the transient response begins to decay. After a period of time, there is still a small longitudinal vibration at the center of the hub. This is because the equivalent damping of the body damper is close to 0 at a small speed amplitude, and the response decays very slowly at this time.

[0139] and Figure 5 By comparing the results in (b), we can see that Figure 6 (b) The longitudinal velocity response at the center of the hub decays more slowly in the initial stage. Analysis shows that when the velocity amplitude of the body damper is 2 mm / s, its equivalent damping is 413.21 Ns / mm, and when the velocity amplitude is 5 mm / s, its equivalent damping is 1009.8 Ns / mm. When the damping of the body damper is 1009.8 Ns / mm, the longitudinal modal damping of the body is smaller, but as the response decays, its longitudinal modal damping will change. The specific change trend can be seen from the subsequent modal damping analysis.

[0140] When the velocity amplitude of the damper is 50 mm / s, its equivalent damping is 178.29 Ns / mm, and when the velocity amplitude is 100 mm / s, its equivalent damping is 93.33 Ns / mm. Although its equivalent damping is reduced, it is different from the previous two cases. The reduction of equivalent damping at this time will reduce the longitudinal modal damping of the body. In theory, Figure 7 Compared with the results in (b), Figure 8 The longitudinal velocity response of the hub center in (b) should decay more slowly in the initial stage, but after comparison, it seems that Figure 8 In (b), the longitudinal velocity response at the hub center decays faster. Analysis shows that this is caused by the change in the magnitude relationship of the longitudinal modal damping ratio of the airframe in the two cases during the attenuation process.

[0141] The above results fully demonstrate that when the body damper is nonlinear and its damping constitutes non-proportional damping to the system, the influence of the body damper on the body modal response becomes complicated. At different stages, changes in the velocity amplitude of the body damper will cause different changes in its equivalent damping, and changes in its equivalent damping will also cause different changes in the body modal damping.

[0142] Depend on Figure 9-12 It can be seen that the influence of different velocity amplitudes of the airframe damper on the lateral modal response of the airframe is similar to that on the longitudinal modal response, but it is obvious that the lateral modal response of the airframe decays faster. Analysis shows that the damping ratio of the lateral motion mode of the airframe is larger.

[0143] In addition, due to the small number of transient response vibration cycles, it is not possible to clearly observe the different transient response attenuation and its change trend in the time domain under different axial velocity amplitudes of the excitation damper. It is necessary to further identify and analyze the modal damping of the transient response.

[0144] After stimulating a certain order modal response of the skid-type helicopter rotor-body coupling system, the modal damping identification is performed on its transient response. The dynamic stability of the system can be judged according to the size of the modal damping. The change of the modal damping in the time domain can also be observed, and the attenuation law of the transient response can be explained.

[0145] In order to better analyze the airframe modal damping of the ground resonance of the skid-type helicopter, the relationship between the airframe modal damping ratio of the improved airframe damper and the axial velocity of the airframe damper is expressed as follows: Fig.13 shown.

[0146] The modal damping of the airframe under the central excitation of the hub is identified, and its variation with time is obtained as follows: Fig.14 , Fig.15 shown.

[0147] Depend on Fig.14 , Fig.15 It can be seen that due to the nonlinearity of the damping of the body damper and its influence on the non-proportional damping of the system, the longitudinal and transverse modal damping of the body changes with the attenuation of the transient response, and its change basically follows Fig.13 The airframe modal damping ratio changes with the decreasing trend of the damper axial velocity amplitude, because the response of the airframe damper is attenuated when the system is stable. In addition, the larger the damper axial velocity amplitude is during steady-state response, the more delayed the airframe modal damping change in the transient response part.

[0148] Depend on Fig.14 , Fig.15 It can also be seen that when the body modal response decays to approach 0, the axial velocity of the body damper will also approach 0, resulting in very small damping provided by the damper. Since other structural damping is not considered, the body modal damping will also present a very small value.

[0149] It should be noted that due to the rapid attenuation of the transient response, especially the lateral modal response of the body, the number of vibration cycles in the attenuation stage is small, which makes the change curve of the identified modal damping in the time domain not smooth, which may have a certain impact on the damping identification accuracy.

[0150] Finally, it should be noted that the above are only preferred embodiments of the present application and are not intended to limit the present application. Although the present application has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments or to replace some of the technical features therein by equivalents. For example, in the present application, if the storage stress type of the radar seeker is different from the temperature, humidity, vibration and light, such as temperature cycle, salt spray, dust, impact, etc., it can be directly replaced. The specific method is the same. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. A method for establishing a ground resonance nonlinear analysis model, characterized in that: The following steps are involved: S1. Determine the rotor blade swing motion equation: Select the blade shimmy damper model, calculate the blade shimmy damper force, and determine the blade shimmy motion equation; S2. Determine the body motion equation Add the airframe damper model to the airframe model on the skid-type landing gear, calculate the equivalent linear damping of the airframe damper under different responses, include it in the finite element analysis model on the skid-type landing gear, calculate the equivalent parameters of the airframe equivalent to the hub center on the skid-type landing gear under different responses, input the longitudinal and lateral displacements and velocities of the hub center, and determine the airframe motion equation; S3. Determine the ground resonance nonlinear analysis model The blade vibration motion equation in step S1 is combined with the body motion equation in step S2 to form a ground resonance nonlinear analysis model.

2. The method for establishing a ground resonance nonlinear analysis model according to claim 1, characterized in that: The step S1 specifically includes selecting a nonlinear viscoelastic damper model or a nonlinear hydraulic damper model as a blade shimmy damper model, inputting blade shimmy damper model parameters and blade shimmy initial response to calculate blade shimmy damper force, and determining the blade shimmy motion equation according to the blade shimmy damper force.

3. The method for establishing a ground resonance nonlinear analysis model according to claim 1 or 2, characterized in that: The parameters of the blade damper model are determined by the selected damper model. Different damper models are selected, and different parameters are required. The blade shimmy initial response includes an initial shimmy angle and a shimmy angular velocity; According to the selected damper model and the initial response of blade shimmy, the Runge-Kutta method is used to iteratively solve the blade shimmy damper force.

4. The method for establishing a ground resonance nonlinear analysis model according to claim 3, characterized in that: The nonlinear viscoelastic damper model is: is the displacement s and velocity of the damper Resilience Where: k i is the i-th order elastic force coefficient, N k is the elastic force order, c is the damping force coefficient, z is the sliding restoring force, k s is the sliding linear stiffness, z s is the slip limit restoring force, is the sliding limit displacement, the required parameters are: k i 、N k , z, k s 、z s ; The nonlinear hydraulic damper model is: Where: m v is the valve core mass, c v , k v are the valve core motion damping and stiffness, respectively, v A is the displacement of the valve core relative to the valve seat, v is the valve core pressure area, P L =P1-P2 is the piston load pressure, C v0 is the constant flow coefficient of the valve port, γ v is the fitting parameter of the valve port flow coefficient to the valve core displacement, d v is the inner diameter of the valve seat, α v is the semi-cone angle of the valve core, F0 is the pre-pressure of the constant pressure valve, ρ o is the oil density, β o is the bulk elastic modulus of the oil, V o is the volume of the hydraulic cylinder, A p is the piston pressure area, s is the piston displacement, C d is the piston damping hole flow coefficient, A d is the cross-sectional area of ​​the piston damping hole, F 活 is the force on the piston, the required parameter is P L , A p .

5. The method for establishing a ground resonance nonlinear analysis model according to claim 3, characterized in that: The blade swing vibration equation is: I b and S b are the inertia moment and static moment of the blade to the flap hinge, e is the overhang of the flap hinge, k b0 and c b0 are the shimmy stiffness and damping without considering the effect of blade shimmy damper, Ω is the rotor speed, ζ k is the swing angle of the kth blade, y k is the azimuth angle of the kth blade, s k is the displacement of the viscoelastic damper of the kth blade, and F is the force acting on the viscoelastic damper or the force F of the nonlinear hydraulic damper 活 .

6. The method for establishing a ground resonance nonlinear analysis model according to claim 1 or 2, characterized in that: In the step S2, a nonlinear hydraulic damper model is selected as the machine body damper model, parameters of the machine body damper model are input, and the equivalent linear damping of the machine body damper under different responses is calculated; The equivalent linear damping is determined based on the energy consumed by the actual system and the equivalent linear system in one vibration cycle. The specific steps are as follows; The excitation amplitude of the damper is s a , the excitation frequency is ω, then its motion is: s=s a sinωt, Movement cycle The energy W absorbed by the nonlinear damper during one cycle of motion is: Where: is the force generated by the damper, calculated by its dynamic model; The energy absorbed by the equivalent linear system during one cycle of motion is: By Mode The equivalent linear damping of the damper is obtained as: Calculate the equivalent parameters of the fuselage equivalent to the hub center on the skid landing gear with different responses. The specific steps are as follows: The hub center motion and damper motion have the following relationship: Where: c x and c y are the equivalent damping of the longitudinal and lateral motion of the hub center, v hx and v hy are the longitudinal and lateral velocity amplitudes of the hub center, c e is the equivalent damping of the body damper, v d is the velocity amplitude of the body damper; The relationship between the hub center velocity amplitude and the body damper velocity amplitude is: According to the above formula, input v hx and v hy , we get v d , According to the equivalent damping-speed curve C of the body damper e =f e (v d ), calculate the equivalent damping of the airframe damper, and according to the airframe modal equivalent damping-damper damping curve c x =f x (C e ) and c y =f y (C e ) to obtain the equivalent damping of the body. The equivalent mass and equivalent stiffness of the airframe are calculated as follows: The natural frequency of the airframe modal can be directly obtained by finite element software, and the specific calculation of its instantaneous center position, equivalent mass and equivalent stiffness is as follows: Where: j = 1-4 represents the longitudinal, pitch, roll and lateral modes respectively, z is the instantaneous center position of the airframe modal, a positive value indicates that it is above the center of gravity, and a negative value indicates that it is below the center of gravity, x and φ are the translational momentum and rotational momentum of the center of gravity under the airframe modal respectively, m is the modal equivalent mass of the airframe, I = [I y I y I x I x ] is the body inertia moment, m f is the body mass, z h is the height from the center of the hub to the center of gravity of the fuselage, k is the equivalent modal stiffness of the fuselage, ω is the modal natural frequency of the fuselage, and this natural frequency is the natural frequency of the system without damping.

7. The method for establishing a ground resonance nonlinear analysis model according to claim 1 or 2, characterized in that: The body motion equation is: ， Where: S b is the static moment of the blade to the flap hinge, m b is the blade mass, Ω is the rotor speed, N b is the number of blades, ζ k is the swing angle of the kth blade, y k is the azimuth angle of the kth blade, x h and h are the longitudinal and lateral displacements of the hub center, m x 、c x and k x are the mass, damping and stiffness of the longitudinal motion from the airframe to the hub center, m y 、c y and k y They are respectively the mass, damping and stiffness of the lateral motion from the airframe equivalent to the center of the hub.

8. An application of the ground resonance nonlinear analysis model established by the above method in the nonlinear time domain simulation analysis of the ground resonance stability of a skid-type helicopter.

9. An application of a ground resonance nonlinear analysis model, characterized in that: It includes time domain response analysis and modal damping analysis, wherein the time domain response analysis includes the following steps: A. Exciting the modal response of the body The hub center is excited longitudinally and transversely respectively to excite the steady-state response of the required airframe mode. Then, the damper velocity amplitude is calculated according to the hub center motion and compared with the velocity amplitude used to determine the damper damping, i.e., the theoretical value. B. Identification of airframe modal damping After the body modal steady-state response in step A is completed, the transient response is subjected to modal damping identification after the excitation is cancelled, and the attenuation law of the transient response is determined according to the change of the modal damping in the time domain.

10. The application of a ground resonance nonlinear analysis model according to claim 9, characterized in that: The equivalent damping of the airframe damper at different speed amplitudes is used to determine the excitation frequency, and the excitation force amplitude calculation formula is used to determine the excitation force amplitude at the hub center; The calculation formula of the exciting force amplitude is: v d is the velocity amplitude of the body damper; The larger the amplitude of the damper axial velocity in steady-state response, the more delayed the change of the body modal damping in the transient response part.

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