A time and frequency domain hybrid analysis method for ground resonance analysis when a sway bar fails

Abstract

The application relates to a time domain and frequency domain mixed analysis method for ground resonance analysis when a pendulum damper fails. The method comprises the following steps: establishing a blade swing motion equation, obtaining a hub dynamics equation, combining the hub dynamics equation, applying external excitation to the blade swing motion equation to excite the response of a rotor swing back mode, removing the excitation, converting the response of the blade swing motion equation to a fixed coordinate system to obtain the attenuation response of the rotor swing back mode, performing fast Fourier transform on the attenuation response of the rotor swing back mode to obtain a response curve in the frequency domain, comparing and analyzing the frequency change of the rotor swing back mode before and after a single pendulum damper fails at a rated rotating speed, and identifying the damping of the rotor swing back mode by using a moving rectangular window method to judge the stability of the rotor swing back mode. Therefore, the result accuracy of the time domain and frequency domain mixed analysis for ground resonance when the pendulum damper fails is improved.

Description

Technical Field

[0001] The present application relates to the technical field of helicopter dynamics, and specifically provides a time-domain and frequency-domain hybrid analysis method for ground resonance analysis when a shimmy damper fails. Background Art

[0002] During helicopter flight, the shimmy damper is subjected to cyclical loads and experiences significant temperature fluctuations. Failure can occur after exceeding its service life. This makes it difficult to ensure the exact same dynamic characteristics of each rotor blade. In this case, multi-blade coordinate transformation is no longer applicable. Therefore, dynamic equations must be established using the degrees of freedom of each blade and the aircraft's motion to analyze the ground resonance of the helicopter when the shimmy damper fails.

[0003] The eigenvalue analysis method is based on the assumption that The analysis assumes that the phase difference between the blades is fixed. However, in reality, the phase difference between the blades is not necessarily fixed when the rotor begins to rotate. Only when it reaches steady state can the phase difference remain consistent. In addition, the results of eigenvalue analysis can only indicate whether the coupled system has converged, but cannot show the time required to reach convergence or the amplitude of the response during the convergence process. The time history and amplitude are also important factors in analyzing aeroelastic stability. Even if the system is converged, if the response amplitude is too large or the vibration duration is too long, it will cause damage to the system. Therefore, the eigenvalue analysis method is not complete in practical applications, resulting in poor accuracy of the results of the hybrid time-domain and frequency-domain analysis of ground resonance when the damper fails. Summary of the Invention

[0004] In response to the above-mentioned deficiencies in the prior art, the purpose of this application is to propose a time domain and frequency domain hybrid analysis method for ground resonance analysis when the shimmy damper fails, which is used to analyze the stability of the rotor shimmy retreat mode. At the same time, the attenuation response of the rotor shimmy retreat mode is subjected to a fast Fourier transform to obtain a frequency domain response curve, thereby realizing the analysis of the frequency spectrum of the rotor shimmy retreat mode. By stimulating the response of the rotor shimmy retreat mode, the amplitude of the blade in the time domain can also be analyzed.

[0005] To achieve the above objectives, the technical solutions adopted in this application are as follows:

[0006] A hybrid time-domain and frequency-domain analysis method for analyzing ground resonance when a shimmy damper fails, the method comprising:

[0007] S1. Establish a shimmy damper model with a linear spring and damper in parallel. Based on the shimmy damper model, perform dynamic modeling of the helicopter blades in a rotating coordinate system. Set the shimmy damping of the first blade to zero, balance the torque about the vertical hinge, and establish the shimmy motion equations for each blade.

[0008] S2, analyzing the helicopter body dynamics characteristics, and making equivalent processing to the hub center to obtain equivalent results, obtaining the hub dynamics equation according to the equivalent results and the force generated by each piece of blade;

[0009] S3, combining the hub dynamics equation, applying external excitation to each piece of blade oscillation equation, the excitation frequency is the first order oscillation natural frequency of the blade, which excites the response of the rotor oscillation back mode, removes the excitation, converts the response of each piece of blade oscillation equation to the fixed coordinate system to obtain the attenuation response of the rotor oscillation back mode, and carries out fast Fourier transform on the attenuation response of the rotor oscillation back mode to obtain the response curve in frequency domain, and compares and analyzes the frequency change of the rotor oscillation back mode before and after the failure of a single anti-swing device under rated speed according to the response curve in frequency domain.

[0010] S4, using the moving rectangular window method to identify the damping of the rotor oscillation back mode for the attenuation response of the rotor oscillation back mode, and judging the stability of the rotor oscillation back mode according to the damping of the rotor oscillation back mode.

[0011] In one embodiment, the expression of the blade oscillation equation is:

[0012]

[0013] wherein, and are the static moment and inertia moment of each piece of blade respectively, is the oscillation hinge extension amount, is the kth piece of blade oscillation angle, is the azimuth angle of the kth piece of blade, is the rotor speed, is the oscillation angular velocity, is the oscillation angular acceleration, is the anti-swing device damping, is the anti-swing device stiffness, is the hub longitudinal acceleration, is the hub longitudinal acceleration.

[0014] In one embodiment, S2 includes:

[0015] analyzing the transverse dynamics characteristics of the helicopter body to obtain the natural frequency and roll mode of the body without damping roll mode;

[0016] analyzing the longitudinal dynamics characteristics of the helicopter body to obtain the natural frequency and pitch mode of the body without damping pitch mode;

[0017] According to the vibration frequency and mode of the body, based on the principle that the maximum kinetic energy and potential energy and dissipated energy of the body when it vibrates at its natural frequency are equal to the equivalent system, according to the natural frequency of the undamped roll mode of the body, the roll mode, the natural frequency of the pitch mode and the pitch mode, the equivalent results of the roll mode and the pitch mode of the body are obtained by equivalent processing at the hub center.

[0018] According to the equivalent results of the roll mode and the pitch mode of the body and the force generated by each blade, the hub dynamics equation is obtained.

[0019] In one embodiment, the analysis of the helicopter body lateral dynamics characteristics obtains the natural frequency of the undamped roll mode of the body and the roll mode, which comprises:

[0020] The lateral dynamics characteristics of the body are analyzed by force balance and moment balance , and the lateral dynamics equation is obtained:

[0021]

[0022]

[0023] wherein, is the freedom of the body around the x axis through the center of mass, is the mass of the body, is the lateral acceleration of the body, is the angular acceleration of the helicopter around axis, is the lateral velocity of the body, is the angular velocity of the helicopter around axis, is the vertical damping of the main landing gear, is the lateral displacement of the body, is the total lateral damping of the landing gear, is the vertical damping of the main landing gear, is the lateral resultant force of the body, is the moment of the helicopter around axis, is the moment of inertia of the body around the longitudinal axis, is the vertical distance from the center of gravity of the helicopter to the ground, is the total lateral stiffness of the landing gear, is the vertical stiffness of the main landing gear, is the gravity received by the helicopter, is the horizontal distance between the main landing gear and the front landing gear;

[0024] The natural frequency of the undamped roll mode of the body is obtained by solving .

[0025]

[0026] wherein, , , , , , is the vertical distance from the center of gravity of the helicopter to the ground, is the total lateral stiffness of the landing gear, is the vertical stiffness of the main landing gear, is the gravitational force experienced by the helicopter, is the mass of the helicopter, is the horizontal distance between the main landing gear and the front landing gear, is the moment of inertia of the airframe about the longitudinal axis, is the natural frequency of the roll mode of the airframe, is the lateral stiffness of one of the main landing gear, is the lateral stiffness of the front landing gear, is the lateral stiffness of the other main landing gear;

[0027] Substituting the natural frequency of the undamped roll mode of the airframe into the lateral dynamics equation, the roll mode is obtained as:

[0028]

[0029] wherein, is the natural frequency of the roll mode of the airframe, is the roll mode.

[0030] In one embodiment, the analyzing the longitudinal dynamics of the airframe of the helicopter to obtain the natural frequency of the undamped pitch mode of the airframe and the pitch mode comprises:

[0031] Analyzing the longitudinal dynamics of the airframe from the equilibrium of forces and the equilibrium of moments to obtain the longitudinal dynamics equation:

[0032]

[0033]

[0034] wherein, is the degree of freedom of the airframe about the y-axis through the center of mass, is the resultant lateral force of the airframe, is the resultant moment of the helicopter about the x-axis, is the longitudinal acceleration of the airframe, is the longitudinal velocity of the airframe, is the longitudinal displacement of the body, is the angular velocity of the helicopter about the axis of rotation, is the angular velocity of the helicopter about the axis of rotation, is the longitudinal damping of the landing gear, is the vertical damping of the main landing gear, is the vertical damping of the main landing gear, is the vertical damping of the front landing gear, is the total longitudinal stiffness of the landing gear, is the moment of inertia of the body about the lateral axis, is the horizontal distance between the front landing gear and the center of gravity, is the horizontal distance between the main landing gear and the center of gravity;

[0035] is the solution of the equation , the natural frequency of the undamped pitch mode of the body is:

[0036]

[0037] wherein, , , , , is the vertical stiffness of the front landing gear, is the horizontal distance between the front landing gear and the center of gravity, is the horizontal distance between the main landing gear and the center of gravity, is the moment of inertia of the body about the lateral axis, is the natural frequency of the pitch mode;

[0038] Substituting the natural frequency of the undamped pitch mode of the body into the longitudinal dynamics equation, the pitch mode is obtained as:

[0039]

[0040] wherein, is the pitch mode, is the natural frequency of the pitch mode.

[0041] In one embodiment, the expression of the equivalent result of the roll mode of the body is:

[0042]

[0043]

[0044]

[0045] wherein, is the lateral equivalent mass of the hub, vertical distance from the center of gravity of the airframe to the center of the hub, longitudinal stiffness of the landing gear equivalent to the center of the hub, natural frequency of the pitch mode, longitudinal damping of the landing gear equivalent to the center of the hub.

[0046] In one embodiment, the expression of the equivalent result of the pitch mode of the airframe is:

[0047]

[0048]

[0049]

[0050] wherein, longitudinal equivalent mass of the hub, longitudinal stiffness of the landing gear equivalent to the center of the hub, longitudinal damping of the landing gear equivalent to the center of the hub.

[0051] In one embodiment, the hub dynamics equation is:

[0052]

[0053] wherein, longitudinal velocity of the hub, longitudinal displacement of the hub, lateral velocity of the hub, lateral displacement of the hub, mass of the blade.

[0054] In one embodiment, the S3 comprises:

[0055] S31: applying an external excitation to each piece of blade vibration equation, the excitation frequency is the first-order blade vibration natural frequency, exciting the response of the rotor vibration back mode, solving the hub dynamics equation and the blade vibration equation after applying external excitation to each piece by using Runge-Kutta method, obtaining the blade vibration response, removing the excitation, transforming the blade vibration response multi-blade coordinate to the fixed coordinate system to obtain the decay response of the rotor vibration back mode, performing fast Fourier transform on the decay response of the rotor vibration back mode to obtain the response curve in the frequency domain, and comparing and analyzing the frequency change of the rotor vibration back mode before and after the failure of a single anti-hunt device at the rated speed according to the response curve in the frequency domain.

[0056] In one embodiment, the S4 comprises:

[0057] performing fast Fourier transform on the decay response of the rotor lag mode, determining the amplitude of the fast Fourier transform, performing linear fitting on the natural logarithm curve of the amplitude of the fast Fourier transform, and obtaining the damping of the rotor lag mode;

[0058] determining the stability of the rotor lag mode according to whether the damping of the rotor lag mode is greater than 0.

[0059] The beneficial effects of the present application are as follows:

[0060] The ground resonance analysis time and frequency domain hybrid analysis method when the above-described lag damper fails, by establishing a lag damper model of a linear spring and damper in parallel, performing dynamic modeling on the rotor coordinate system of the blades of the helicopter according to the lag damper model, and making the first blade lag damping 0, balancing the moment around the vertical hinge, establishing the lag motion equation of each blade, analyzing the dynamic characteristics of the helicopter body, and obtaining the equivalent result by equivalent processing to the center of the hub, obtaining the hub dynamic equation according to the equivalent result and the force generated by each blade, combining the hub dynamic equation, and applying external excitation to the lag motion equation of each blade, the excitation frequency is the first-order lag natural frequency of the blade to excite the response of the rotor lag mode, removing the excitation, and converting the response of the lag motion equation of each blade to the fixed coordinate system to obtain the decay response of the rotor lag mode, performing fast Fourier transform on the decay response of the rotor lag mode to obtain the response curve in the frequency domain, and comparing and analyzing the frequency change of the rotor lag mode before and after the failure of a single lag damper at the rated speed according to the response curve in the frequency domain, using the moving rectangular window method to identify the damping of the rotor lag mode, and judging the stability of the rotor lag mode according to the damping of the rotor lag mode. Thus, by performing fast Fourier transform on the decay response of the rotor lag mode to obtain the response curve in the frequency domain, the frequency spectrum of the rotor lag mode is analyzed, the amplitude of the blade in the time domain and the decay speed can also be analyzed by exciting the response of the rotor lag mode, and the ground resonance when the lag damper fails is analyzed in the time domain and the frequency domain. In the time domain, the time required to reach convergence and the amplitude of the response in the convergence process are displayed. In the frequency domain, in addition to analyzing the lag damping, an additional peak value in the frequency spectrum when the lag damper fails can also be found, thereby improving the result accuracy of the time and frequency domain hybrid analysis of the ground resonance when the lag damper fails. BRIEF DESCRIPTION OF DRAWINGS

[0061] Figure 1 The flowchart of the ground resonance analysis time and frequency domain hybrid analysis method when the lag damper fails in an embodiment of the present application;

[0062] Figure 2 The first Blade geometry model;

[0063] Figure 3 A YOZ plane geometric model of a helicopter in one embodiment of the present application;

[0064] Figure 4 The XOZ plane geometric model of a helicopter in one embodiment of the present application;

[0065] FIG5(a) and FIG5(b) are schematic diagrams showing the time variation curves of the blade shimmy response when the blade is subjected to a cosine excitation of the first-order shimmy fallback frequency and the blade shimmy free decay response after the excitation is removed, when the shimmy damper fails and when the shimmy damper does not fail in one embodiment;

[0066] Figure 6 FIG1 is a schematic diagram of a frequency domain response curve of a shimmy damper failure in one embodiment;

[0067] Figure 7 FIG. 1 is a graph showing how the damping of a rotor shimmy backward mode varies with rotor speed when the shimmy damper fails in one embodiment. DETAILED DESCRIPTION

[0068] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0069] In one embodiment, a hybrid time-domain and frequency-domain analysis method for analyzing ground resonance when a shimmy damper fails is provided. This method is described using a terminal as an example, and includes the following steps:

[0070] Step S1, refer to Figure 1 As shown in the figure, a shimmy damper model with a linear spring and damper in parallel is established. Based on the shimmy damper model, the helicopter blades are dynamically modeled in the rotating coordinate system. The shimmy damping of the first blade is set to 0, the moment balance is taken around the vertical hinge, and the shimmy motion equation of each blade is established.

[0071] The number of blades can be determined according to the actual situation of the helicopter, such as 4 blades.

[0072] In one embodiment, Figure 2 Shown The blade geometry model and the blade swing motion equation are expressed as:

[0073]

[0074] in, and are the static moment and inertia moment of each blade, is the flapwise extension of the oscillating hinge, is the kth flap oscillation angle, is the azimuth angle of the kth flap, is the rotor speed, is the oscillation angular velocity, is the oscillation angular acceleration, is the damping of the anti-flutter device, is the stiffness of the anti-flutter device, is the hub longitudinal acceleration, is the hub longitudinal acceleration.

[0075] Step S2, analyzing the helicopter body dynamics characteristics, and making equivalent processing to the hub center to obtain equivalent results, obtaining the hub dynamics equation according to the equivalent results and the forces generated by each flap.

[0076] In one embodiment, S2 includes:

[0077] analyzing the helicopter body lateral dynamics characteristics, obtaining the natural frequency and roll mode of the body undamped roll mode; analyzing the helicopter body longitudinal dynamics characteristics, obtaining the natural frequency and pitch mode of the body undamped pitch mode; according to the vibration frequency and mode of the body, based on the principle that the maximum kinetic energy and potential energy of the body when vibrating at its natural frequency and the dissipated energy are equal to the equivalent system, according to the natural frequency and roll mode of the body undamped roll mode, the natural frequency and pitch mode of the pitch mode, the body is equivalent at the hub center. The equivalent results of the roll mode and the equivalent results of the pitch mode of the body are obtained; according to the equivalent results of the roll mode and the equivalent results of the pitch mode of the body and the forces generated by each flap, the hub dynamics equation is obtained.

[0078] In one embodiment, analyzing the helicopter body lateral dynamics characteristics, obtaining the natural frequency and roll mode of the body undamped roll mode, includes:

[0079] analyzing the body lateral dynamics characteristics, such as Figure 3 the physical model of the body YOZ plane, the force balance and the moment balance , the lateral dynamics equation is obtained:

[0080]

[0081]

[0082] wherein, is the freedom of the body around the x axis through the center of mass, the mass of the body, the lateral acceleration of the body, is the helicopter around axial angular acceleration, is the lateral velocity of the fuselage, is the angular velocity of the helicopter around axial angular velocity, is the vertical damping of the main landing gear, is the lateral displacement of the fuselage, is the total lateral damping of the landing gear, is the vertical damping of the main landing gear, is the lateral resultant force of the fuselage, is the moment of the helicopter around axial moment, is the moment of inertia of the fuselage around the longitudinal axis, is the vertical distance from the center of gravity of the helicopter to the ground, is the total lateral stiffness of the landing gear, is the vertical stiffness of the main landing gear, is the gravity force on the helicopter, is the horizontal distance between the main landing gear and the front landing gear;

[0083] The natural frequency of the undamped lateral roll mode of the fuselage is obtained by solving the equation:

[0084]

[0085] where, , , , , , is the vertical distance from the center of gravity of the helicopter to the ground, is the total lateral stiffness of the landing gear, is the vertical stiffness of the main landing gear, is the gravity force on the helicopter, is the mass of the helicopter, is the horizontal distance between the main landing gear and the front landing gear, is the moment of inertia of the fuselage around the longitudinal axis, is the natural frequency of the lateral roll mode of the fuselage, is the lateral stiffness of one of the main landing gears, is the lateral stiffness of the front landing gear, is the lateral stiffness of the other main landing gear;

[0086] Substituting the natural frequency of the undamped lateral roll mode of the fuselage into the lateral dynamics equation, the lateral roll mode is obtained as:

[0087]

[0088] where, ​is the natural frequency of the body roll mode, is the roll mode.

[0089] In one embodiment, the longitudinal dynamics of the helicopter body are analyzed to obtain the natural frequency of the undamped pitch mode of the body and the pitch mode, including:

[0090] The longitudinal dynamics of the body are analyzed, such as Figure 4 The physical model of the body XOZ plane is obtained from the force balance and the moment balance The longitudinal dynamics equation is obtained:

[0091]

[0092]

[0093] wherein, is the degree of freedom of the body around the y axis through the center of mass, is the body lateral force, is the helicopter body moment around the axis, is the body longitudinal acceleration, is the body longitudinal velocity, is the body longitudinal displacement, is the helicopter body angular velocity around the axis, is the helicopter body angular velocity around the axis, is the landing gear longitudinal damping, is the main landing gear vertical damping, is the main landing gear vertical damping, is the front landing gear vertical damping, is the total landing gear longitudinal stiffness, is the body moment of inertia around the lateral axis, is the horizontal distance of the front landing gear from the center of mass, is the horizontal distance of the main landing gear from the center of mass;

[0094] The natural frequency of the undamped pitch mode of the body is obtained from

[0095]

[0096] wherein, , , , , is the front landing gear vertical stiffness, is the horizontal distance of the front landing gear from the center of mass, ​is the horizontal distance between the main landing gears and the center of gravity, is the moment of inertia of the fuselage about the lateral axis, is the natural frequency of the pitch mode;

[0097] Substituting the natural frequency of the undamped pitch mode of the fuselage into the longitudinal dynamics equation, the pitch mode is obtained as:

[0098]

[0099] where, is the pitch mode, is the natural frequency of the pitch mode.

[0100] In one example, according to the vibration frequency and mode shape of the fuselage, the fuselage is equivalent at the hub center according to the principle that the maximum kinetic energy and potential energy and dissipated energy of the fuselage when it vibrates at its natural frequency are equal to those of the equivalent system, and the equivalent mass, equivalent stiffness, and equivalent damping of the fuselage are obtained. In this way, the fuselage vibration system is simplified to an equivalent mass-stiffness-damping system at the hub center in the plane of rotation of the rotor. In one embodiment, the expression of the equivalent result of the roll mode of the fuselage is:

[0101]

[0102]

[0103]

[0104] where, is the lateral equivalent mass of the hub, is the vertical distance from the center of gravity of the fuselage to the hub center, is the longitudinal stiffness of the landing gear equivalent to the hub center, is the natural frequency of the pitch mode, is the longitudinal damping of the landing gear equivalent to the hub center, is the lateral damping of one of the main landing gears, is the lateral damping of the front landing gear, is the lateral damping of the other main landing gear.

[0105] In one embodiment, the expression of the equivalent result of the pitch mode of the fuselage is:

[0106]

[0107]

[0108]

[0109] where, ​a longitudinal equivalent mass of the hub, a longitudinal equivalent stiffness of the landing gear at the hub center, a longitudinal equivalent damping of the landing gear at the hub center, a longitudinal damping of one of the main landing gears, a longitudinal damping of the front landing gear, a longitudinal damping of the other main landing gear.

[0110] In one embodiment, the hub dynamics equation is:

[0111]

[0112] wherein, a longitudinal velocity of the hub, a longitudinal displacement of the hub, a lateral velocity of the hub, a lateral displacement of the hub, a blade mass.

[0113] Step S3, in combination with the hub dynamics equation, an external excitation is applied to each piece of the blade vibration equation, the excitation frequency is the first order vibration natural frequency of the blade, the response of the rotor vibration back-off mode is excited, the excitation is removed, the response of each piece of the blade vibration equation is converted to the fixed coordinate system to obtain the attenuation response of the rotor vibration back-off mode, the attenuation response of the rotor vibration back-off mode is subjected to fast Fourier transform to obtain the response curve in the frequency domain, and the frequency change of the rotor vibration back-off mode before and after the failure of a single sway damper at the rated speed is compared and analyzed according to the response curve in the frequency domain.

[0114] In one embodiment, S3 comprises:

[0115] S31: an external excitation is applied to each piece of the blade vibration equation, the excitation frequency is the first order vibration natural frequency of the blade, the response of the rotor vibration back-off mode is excited, the Runge-Kutta method is used to solve the hub dynamics equation and the blade vibration equation of each piece after the external excitation is applied, the blade vibration response is obtained, the excitation is removed, the multi-blade coordinate transformation of the blade vibration response is converted to the fixed coordinate system to obtain the attenuation response of the rotor vibration back-off mode, the attenuation response of the rotor vibration back-off mode is subjected to fast Fourier transform to obtain the response curve in the frequency domain, and the frequency change of the rotor vibration back-off mode before and after the failure of a single sway damper at the rated speed is compared and analyzed according to the response curve in the frequency domain.

[0116] In one embodiment, an external excitation is applied to each piece of the blade vibration equation, wherein the external excitation load acting on the kth piece of the blade vibration equation is:

[0117] ​

[0118] wherein, is the amplitude of the external excitation load, is the frequency of the first-order flapping mode of the blade, is the external excitation load, is time, is the number of blade pieces, is the blade number.

[0119] The Runge-Kutta method is used to solve the blade hub dynamics equation and the blade flapping motion equation after each piece of the blade is subjected to the external excitation, and the blade vibration response is obtained. The expression of the Runge-Kutta method is as follows:

[0120]

[0121]

[0122] wherein, is the time step, is the current iteration result, is the last iteration result, is the solution object, is the time variable.

[0123] After the excitation is removed, the multi-blade coordinate transformation is performed on the blade flapping response of each piece to determine the decay response of the rotor flapping back mode .

[0124] .

[0125] The fast Fourier transform is performed on the decay response of the rotor flapping back mode, and the response curve in the frequency domain is obtained, as shown in Figure 6 , which is used for comparative analysis of the change of the rotor flapping back mode frequency before and after the failure of a single lag damper at a constant rotating speed.

[0126] In step S4, the moving rectangular window method is used to identify the damping of the rotor flapping back mode according to the decay response of the rotor flapping back mode, and the stability of the rotor flapping back mode is determined according to the damping of the rotor flapping back mode.

[0127] In one embodiment, S4 includes:

[0128] The finite Fourier transform is performed on the decay response of the rotor flapping back mode, the amplitude of the finite Fourier transform is determined, the natural logarithmic curve of the amplitude of the finite Fourier transform is linearly fitted, and the damping of the rotor flapping back mode is obtained; and the stability of the rotor flapping back mode is determined according to whether the damping of the rotor flapping back mode is greater than 0.

[0129] In one example, when the rotor backward shimmy mode response reaches a steady state under the action of an external excitation load, the external excitation load is removed and the blade free response is analyzed to obtain the attenuation response of the rotor backward shimmy mode. Then, the moving rectangular window method is used to identify the damping of the rotor backward shimmy mode from the attenuation response. First, Perform a finite Fourier transform and determine the magnitude of the finite Fourier transform :

[0130]

[0131]

[0132]

[0133] The natural logarithm of is:

[0134]

[0135] in, is the cosine transform of the decay response of the rotor flap backward mode, is the period of the decay response of the rotor flapping backward mode, is the initial value of the time integral, is the frequency of the rotor flap backward mode attenuation response, is a constant, is the sine transform of the rotor flap backward mode attenuation response, is the damping ratio, is the frequency of the rotor flap backward mode attenuation response, is the frequency of the fluctuation term, is the phase of the wave term.

[0136] Follow The change relationship is a slope A linear fit is performed on the curve, along with a fluctuation term at twice the analysis frequency. The slope of the resulting line is the damping of the rotor shimmy mode. Repeating steps S3 and S4 with varying speeds reveals the damping of the rotor shimmy mode as it varies with speed.

[0137] In one example, the time-varying curve of the blade oscillation amplitude generated according to the blade vibration response in the case where the damper connected with the blade 1 fails and the damper connected with the blade 2 works normally is shown in FIG. 5(a) and FIG. 5(b). FIG. 5(a) is a time-varying curve of the blade oscillation amplitude when the rotor is excited. As can be seen from the figure, the oscillation amplitude of the blade whose damper fails (blade 1) is greater than that of the blade whose damper does not fail (blade 2). FIG. 5(b) is a time-varying curve of the free decay oscillation amplitude of the blade after the excitation is removed. As can be seen from the figure, the decay speed of the blade whose damper fails (blade 1) is much smaller than that of the blade whose damper does not fail (blade 2).

[0138] Figure 6 The response curve in the frequency domain generated when the rotor speed is 280 rpm after the single damper fails is given. The frequency at the peak in the low-frequency region is , and the frequency at the peak in the high-frequency region is These two frequencies are exactly the modal frequencies of the backward and forward oscillation modes, and there is only a single mode when the damper works normally. It is difficult to obtain the two modal frequencies after the damper fails by using the Floquet theory.

[0139] Figure 7 The method of the present application is used to analyze the rule of the damping of the backward oscillation mode of the rotor with the change of the speed when one damper fails. Generally, the modal damping analyzed by using the Floquet theory is more accurate, Figure 7 It is shown that the results of the method of the present application and the Floquet theory are consistent, which proves the accuracy of the method of the present application.

[0140] The time domain and frequency domain mixed analysis method for ground resonance analysis when the above-mentioned pendulum damper fails, by establishing a pendulum damper model of a linear spring and damper in parallel, according to the pendulum damper model, performing dynamic modeling on the blades of the helicopter in the rotating coordinate system, and making the first blade pendulum damping 0, balancing the moment around the vertical hinge, establishing the pendulum motion equation of each blade, analyzing the dynamic characteristics of the helicopter body, and performing equivalent processing to the center of the hub to obtain the equivalent result, according to the equivalent result and the pendulum motion equation of each blade, obtaining the hub dynamic equation, combining the hub dynamic equation, applying external excitation to the pendulum motion equation of each blade, the excitation frequency is the first-order pendulum natural frequency of the blade to excite the response of the rotor pendulum after-retreating mode, removing the excitation, converting the response of the pendulum motion equation of each blade to the fixed coordinate system to obtain the attenuation response of the rotor pendulum after-retreating mode, performing fast Fourier transform on the attenuation response of the rotor pendulum after-retreating mode to obtain the response curve in the frequency domain, and according to the response curve in the frequency domain, comparing and analyzing the frequency change of the rotor pendulum after-retreating mode before and after the failure of a single pendulum damper at the rated speed, using the moving rectangular window method to identify the damping of the rotor pendulum after-retreating mode, and judging the stability of the rotor pendulum after-retreating mode according to the damping of the rotor pendulum after-retreating mode. Thus, by performing fast Fourier transform on the attenuation response of the rotor pendulum after-retreating mode to obtain the response curve in the frequency domain, the frequency spectrum of the rotor pendulum after-retreating mode is analyzed, the amplitude of the blade in the time domain and the speed of attenuation can also be analyzed by exciting the response of the rotor pendulum after-retreating mode, and the ground resonance of the helicopter when the pendulum damper fails is analyzed in the time domain and the frequency domain. In the time domain, the time required to reach convergence and the amplitude of the response in the convergence process are displayed. In the frequency domain, in addition to analyzing the damping of the pendulum after-retreating mode, an additional peak value in the frequency spectrum when the pendulum damper fails can also be found, thereby improving the accuracy of the results of the time domain and frequency domain mixed analysis of the ground resonance when the pendulum damper fails.

[0141] It should be understood that, although Figure 1 The steps in the flowchart of the method are displayed in sequence according to the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, the execution of these steps is not strictly limited in sequence, and these steps can be executed in other orders. Moreover, Figure 1 At least part of the steps in the method can include multiple sub-steps or multiple stages, which are not necessarily executed at the same time, but can be executed at different times, and the execution order of these sub-steps or stages is not necessarily sequential, but can be executed alternately or alternately with at least part of other steps or sub-steps or stages of other steps.

[0142] Any combination of the technical features in the above embodiments can be made, and for the sake of brevity, not all possible combinations are described above, however, as long as the combination of the technical features does not exist in contradiction, it shall be considered within the scope of the present disclosure.

[0143] The above embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it shall not be understood as a limitation on the patent scope of the present application. It shall be pointed out that, for ordinary skilled persons in the art, several modifications and improvements can be made without departing from the concept of the present application, and these shall be within the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the appended claims.

Claims

1. A time and frequency domain hybrid analysis method for ground resonance analysis in case of failure of a sway-bar, characterized in that, The method comprises: S1, a linear spring and damper parallel pendulum damper model is established, the dynamics of the blades of the helicopter in the rotating coordinate system is modeled according to the pendulum damper model, the first piece of blade vibration damping is 0, the moment balance around the vertical hinge is balanced, the vibration equation of each piece of blade is established; S2, the dynamic characteristics of the helicopter body are analyzed, the equivalent processing is carried out on the hub center to obtain the equivalent results, the hub dynamics equation is obtained according to the equivalent results and the force generated by each piece of blade; S3, the hub dynamics equation is combined to apply external excitation to each piece of blade vibration equation, the excitation frequency is the first order blade vibration natural frequency to excite the response of the rotor vibration back-off mode, the excitation is removed, the response of each piece of blade vibration equation is converted to the fixed coordinate system to obtain the attenuation response of the rotor vibration back-off mode, the attenuation response of the rotor vibration back-off mode is subjected to fast Fourier transform to obtain the response curve in the frequency domain, and the frequency change of the rotor vibration back-off mode before and after the failure of a single pendulum damper under the rated speed is compared and analyzed according to the response curve in the frequency domain; S4, the moving rectangular window method is used to identify the damping of the rotor vibration back-off mode, and the stability of the rotor vibration back-off mode is judged according to the damping of the rotor vibration back-off mode; The expression of the blade vibration equation is: ； wherein, and are the moment of inertia and the moment of inertia of each blade respectively, is the flapwise extension of the hinge, is the flapwise angle of the kth blade, is the azimuth angle of the kth blade, is the rotor speed, is the flapwise angular velocity, is the flapwise angular acceleration, is the damping of the pitch control, is the stiffness of the pitch control, is the longitudinal acceleration of the hub, is the longitudinal acceleration of the hub; S2 comprises: The lateral dynamic characteristics of the helicopter body are analyzed, the natural frequency and roll mode of the body without damping are obtained; The longitudinal dynamic characteristics of the helicopter body are analyzed, the natural frequency and pitch mode of the body without damping are obtained; According to the vibration frequency and mode of the body, based on the principle that the maximum kinetic energy and potential energy of the body when vibrating at its natural frequency and the dissipated energy are equal to the equivalent system, the equivalent results of the roll mode and the pitch mode of the body are obtained according to the natural frequency, the roll mode, the natural frequency and the pitch mode of the body without damping; The hub dynamics equation is obtained according to the equivalent results of the roll mode and the pitch mode of the body and the force generated by each piece of blade.

2. The method of claim 1, wherein, The lateral dynamic characteristics of the helicopter body are analyzed, the natural frequency and roll mode of the body without damping are obtained, which comprises: The lateral dynamic characteristics of the vehicle are analyzed by force balance and moment balance , and lateral dynamic equations are obtained. ， ； in, is the degree of freedom of the body around the x-axis passing through the center of mass, Body mass, The lateral acceleration of the aircraft, For helicopters to circle Angular acceleration of the axis, is the lateral velocity of the aircraft, For helicopters to circle Angular velocity of the shaft, For the vertical damping of the main landing gear, is the lateral displacement of the body, is the total lateral damping of the landing gear, For the vertical damping of the main landing gear, is the lateral force of the body, For helicopters to circle Resultant moment of the shaft, is the moment of inertia of the body around the longitudinal axis, is the vertical distance from the helicopter's center of gravity to the ground, is the total lateral stiffness of the landing gear, is the vertical stiffness of the main landing gear, is the gravity acting on the helicopter, is the horizontal distance between the main landing gear and the nose landing gear; From , the natural frequency of the undamped roll mode of the body is found to be: ； wherein, , , , , , is the vertical distance from the center of gravity of the helicopter to the ground, is the total lateral stiffness of the landing gear, is the vertical stiffness of the main landing gear, is the weight force to which the helicopter is subjected, is the mass of the helicopter, is the horizontal distance between the main landing gear and the front landing gear, is the moment of inertia of the fuselage about the longitudinal axis, is the natural frequency of the lateral roll mode of the fuselage, is the lateral stiffness of one of the main landing gears, is the lateral stiffness of the front landing gear, is the lateral stiffness of the other main landing gear; The natural frequency of the body without damping roll mode is substituted into the lateral dynamic equation to obtain the roll mode: ； wherein, is the body roll mode natural frequency, is the roll mode.

3. The method of claim 2, wherein, The longitudinal dynamic characteristics of the helicopter body are analyzed, the natural frequency and pitch mode of the body without damping are obtained, which comprises: The longitudinal dynamics characteristics of the vehicle are analyzed by force and moment balance and the longitudinal dynamics equation is obtained​ ； ； wherein, is the degree of freedom of the body about the y-axis through the center of mass, is the lateral force of the body, is the moment of the helicopter about the x-axis, is the longitudinal acceleration of the body, is the longitudinal velocity of the body, is the longitudinal displacement of the body, is the moment of the helicopter about the y-axis, is the moment of the helicopter about the z-axis, is the longitudinal suspension damping, is the vertical suspension damping of the main landing gear, is the vertical suspension damping of the main landing gear, is the vertical suspension damping of the front landing gear, is the total longitudinal suspension stiffness, is the moment of inertia of the body about the lateral axis, is the horizontal distance of the front landing gear from the center of gravity, is the horizontal distance of the main landing gear from the center of gravity; From , the natural frequency of the undamped pitch mode of the body is found to be: ； wherein, , , , , is the front landing gear vertical stiffness, is the front landing gear horizontal distance from the center of gravity, is the main landing gear horizontal distance from the center of gravity, is the moment of inertia of the airframe about the lateral axis, is the natural frequency of the pitch mode; The natural frequency of the body without damping pitch mode is substituted into the longitudinal dynamic equation to obtain the pitch mode: ； wherein is the pitch mode, is the natural frequency of the pitch mode.

4. The method of claim 3, wherein, The expression of the equivalent results of the roll mode of the body is: ； ； ； wherein, Mhub is the hub lateral equivalent mass, h is the vertical distance from the body center of gravity to the hub center, Khub is the landing gear equivalent to the hub center longitudinal stiffness, ωpitch is the pitch mode natural frequency, Chub is the landing gear equivalent to the hub center longitudinal damping.

5. The method of claim 4, wherein, The expression of the equivalent results of the pitch mode of the body is: ， ， ； wherein, Mhub is the longitudinal equivalent mass of the hub, Khub is the longitudinal stiffness of the landing gear equivalent to the hub center, Chub is the longitudinal damping of the landing gear equivalent to the hub center.

6. The method of claim 5, wherein, The hub dynamics equation is: ； wherein, is the hub longitudinal velocity, is the hub longitudinal displacement, is the hub lateral velocity, is the hub lateral displacement, is the blade mass.

7. The method of claim 1, wherein, S3 comprises: S31: applying an external excitation to each piece of blade oscillation equation, the excitation frequency is the first order blade oscillation natural frequency, exciting the response of the rotor oscillation backward mode, solving the hub dynamics equation and the blade oscillation equation after applying the external excitation to each piece by using Runge-Kutta method, obtaining the blade vibration response, removing the excitation, transforming the blade vibration response multi-blade coordinate to the fixed coordinate system to obtain the attenuation response of the rotor oscillation backward mode, performing fast Fourier transform on the attenuation response of the rotor oscillation backward mode to obtain the response curve in the frequency domain, and comparing and analyzing the frequency change of the rotor oscillation backward mode before and after the failure of a single anti-hunting device at the rated speed according to the response curve in the frequency domain.

8. The method of claim 1, wherein, The S4 comprises: performing finite Fourier transform on the attenuation response of the rotor oscillation backward mode, determining the amplitude of the finite Fourier transform, performing linear fitting on the natural logarithmic curve of the amplitude of the finite Fourier transform to obtain the damping of the rotor oscillation backward mode; determining the stability of the rotor oscillation backward mode according to whether the damping of the rotor oscillation backward mode is greater than 0. determining the stability of the rotor oscillation backward mode according to whether the damping of the rotor oscillation backward mode is greater than 0.

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