A method for controlling landing gear vibration frequency

Abstract

The present application belongs to the field of aircraft vibration control design and is a method for controlling the vibration frequency of a landing gear. The method avoids the problem of coupling between the external excitation frequency and the landing gear vibration modal frequency during the taxiing phase by comparing the relative deviation between the landing gear vibration modal frequency and the external excitation frequency. The method first determines the landing gear vibration modal frequency by performing a landing gear simulation or a landing gear test, and then determines the external excitation frequency of the landing gear. If the relative deviation between the landing gear vibration modal frequency and the external excitation frequency is not less than 6%, the problem of coupling between the external excitation frequency and the landing gear vibration modal frequency will not occur, thereby avoiding resonance of the landing gear. The method can be used to solve the problem of coupling between the external excitation frequency and the landing gear vibration modal frequency during the take-off and landing taxiing phases, avoid post-investigation and processing of landing gear resonance failures, and provide guidance for the dynamic design of the landing gear.

Description

Technical Field

[0001] The present invention relates to the field of aircraft vibration control design, and in particular to a method for controlling the vibration frequency of a landing gear. Background Art

[0002] Improper landing gear design can cause abnormal vibration during takeoff and landing. During the rollout phase, the wheel speed of the landing gear constantly fluctuates. Road surface unevenness or tire eccentricity, for example, act as a sweeping frequency excitation on the wheel. At a certain taxiing speed, if the excitation frequency approaches the landing gear vibration modal frequency, resonance can easily occur, leading to abnormalities during takeoff and landing.

[0003] Therefore, how to reasonably design the vibration characteristics of the landing gear so that its vibration modal frequency avoids the external excitation frequency is a technical problem that needs to be solved in the field of landing gear design. Summary of the Invention

[0004] The purpose of the present application is to provide a method for controlling the vibration frequency of a landing gear, so as to solve the problem in the prior art that the vibration modal frequency of the landing gear is difficult to avoid the excitation frequency.

[0005] The technical solution of the present application is: a method for controlling the vibration frequency of a landing gear, comprising: performing a landing gear simulation or a landing gear test to determine the vibration modal frequency of the landing gear; determining the external excitation frequency of the landing gear; calculating the relative deviation between the vibration modal frequency of the landing gear and the external excitation frequency, and checking whether the relative deviation values are both no less than 6%. If so, the landing gear design requirements are met; if not, the landing gear is redesigned until the requirements are met.

[0006] Preferably, the method for performing the landing gear simulation or landing gear test comprises: setting the landing gear to a fully extended state; obtaining the heading first-order bending modal frequency f h , lateral first-order bending mode frequency f c and the first-order torsional mode frequency f n The method for obtaining the modal frequency is: modeling the landing gear through finite element software and calculating the vibration modal frequency of the landing gear; or testing the vibration modal frequency of the landing gear through a full-aircraft ground resonance test.

[0007] Preferably, a theoretical analysis method is used to calculate the external excitation frequency of the landing gear. The specific method is: obtain the aircraft performance report, record the front wheel speed V corresponding to the aircraft takeoff phase TO and takeoff run distance L TO , front wheel touchdown speed V during landing phase LD and landing roll distance L LDThe external excitation caused by tire extrusion deformation or eccentricity during wheel rolling is set as unbalanced induced excitation, the aircraft taxiing speed is set to increase or decrease linearly with take-off time or landing time, and the external excitation frequency is determined by the calculation theory of centrifugal force with unbalanced rotating body.

[0008] Preferably, the rotation angle of the unbalanced rotating body is:

[0009]

[0010] Where ω is the circular frequency, ω0 is the initial rotation angular velocity; t is time; α is the angular acceleration; the relationship between the external excitation frequency f and the circular frequency ω is:

[0011]

[0012] Preferably, the calculation formula for the relative deviation between the landing gear vibration modal frequency and the external excitation frequency is:

[0013]

[0014] Where err i,j is the landing gear vibration modal frequency f j With external excitation frequency f i relative deviation.

[0015] The present invention discloses a method for controlling landing gear vibration frequency. This method avoids the problem of coupling between the external excitation frequency and the landing gear vibration modal frequency during the taxiing phase by comparing the relative deviation between the landing gear vibration modal frequency and the external excitation frequency. The method first determines the landing gear vibration modal frequency through a landing gear simulation or landing gear test, and then determines the external excitation frequency of the landing gear. If the relative deviation between the landing gear vibration modal frequency and the external excitation frequency is no less than 6%, the problem of coupling between the external excitation frequency and the landing gear vibration modal frequency will not occur, thus preventing the landing gear from resonating. This method can be used to resolve the problem of coupling between the external excitation frequency and the landing gear vibration modal frequency during the takeoff and landing phases, avoid post-investigation and treatment of landing gear resonance failures, and provide guidance for the dynamic design of landing gear. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions provided by this application, the following is a brief introduction to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments of this application.

[0017] Figure 1 This is a schematic diagram of the change of wheel speed with taxiing time in this application;

[0018] Figure 2 This is a schematic diagram of the structure of the rotating body with unbalanced mass in this application;

[0019] Figure 3 This is a schematic diagram of the overall process of this application. DETAILED DESCRIPTION

[0020] In order to make the purpose, technical solutions and advantages of the implementation of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below in conjunction with the drawings in the embodiments of this application.

[0021] A method for controlling the vibration frequency of a landing gear, such as Figure 3 As shown, the following steps are included:

[0022] Step S100, performing landing gear simulation or landing gear test to determine the vibration modal frequency of the landing gear;

[0023] Preferably, the method for performing landing gear simulation or landing gear test includes:

[0024] 1) Set the landing gear to fully extended position;

[0025] 2) Get the first-order bending mode frequency f h , lateral first-order bending mode frequency f c and the first-order torsional mode frequency f n ;

[0026] 3) The modal frequencies are obtained by modeling the landing gear using finite element software and calculating the vibration modal frequencies of the landing gear; or by testing the vibration modal frequencies of the landing gear through a full-aircraft ground resonance test.

[0027] like Figure 1 、 Figure 2 As shown, step S200, determining the external excitation frequency of the landing gear;

[0028] This application uses a theoretical analysis method to determine the external excitation frequency. The specific method is as follows:

[0029] 1) Obtain the aircraft performance report and record the nose wheel speed V corresponding to the aircraft's takeoff phase TO and takeoff run distance L TO , front wheel touchdown speed V during landing phase LD and landing roll distance L LD ;

[0030] 2) The external excitation caused by tire extrusion deformation or eccentricity during wheel rolling is assumed to be the unbalance-induced excitation. The aircraft's taxiing speed is assumed to increase or decrease linearly with takeoff time or landing time. The external excitation frequency is determined using the calculation theory of the centrifugal force of an unbalanced rotating body.

[0031] The specific calculation method of the external excitation frequency is:

[0032] The rotation angle of the unbalanced rotating body is:

[0033]

[0034] Where: ω is the circular frequency, ω0 is the initial rotation angular velocity (unit: rad / s); t is the time (unit: s); α is the angular acceleration (unit: rad / s 2 ); Formula (1) implies that the initial eccentricity angle is zero.

[0035] The formula for calculating normal force is:

[0036] F n =mω 2 r=m(ω0+αt) 2 r (2)

[0037] The tangential force calculation formula is:

[0038]

[0039] By triangulating the normal force and tangential force, the x-direction force can be obtained as:

[0040]

[0041] The y-force is:

[0042]

[0043] From equations (4) and (5), we can see that the excitation force conforms to the following form:

[0044] F(t)=Asinθ+Bcosθ (6)

[0045] According to the auxiliary angle formula of trigonometric function, we can get:

[0046]

[0047] Comparing equations (4), (5) and (7), we can see that the expression of the circular frequency of the excitation force is as follows:

[0048]

[0049] In formula (8), the expressions of the three key parameters are as follows:

[0050] The initial rotation angular velocity ω0 is:

[0051]

[0052] The angular acceleration α is:

[0053]

[0054] The duration (or end time) T corresponding to time t is:

[0055]

[0056] The relationship between the external excitation frequency f and the circular frequency ω is as follows:

[0057]

[0058] It can be seen from formula (12) that the external excitation frequency f changes linearly with time. During the takeoff roll phase, f increases with the increase of t, which is equivalent to the positive stroke frequency sweep; during the landing roll phase, f decreases with the increase of t, which is equivalent to the negative stroke frequency sweep.

[0059] Since the excitation force is the largest at the moment of takeoff and landing, and the landing gear state undergoes a sudden change, resonance problems are more likely to occur. Therefore, this patent only focuses on the frequencies at these two moments, which are recorded as the excitation frequency f1 at the moment of takeoff and the excitation frequency f2 at the moment of landing. The expression obtained according to equations (9) to (12) is:

[0060]

[0061]

[0062] Where: r is the tire radius.

[0063] Step S300 , calculating the relative deviation between the landing gear vibration modal frequency and the external excitation frequency, and checking whether the relative deviation values are all not less than 6%. If so, the landing gear design requirements are met; if not, the landing gear is redesigned until the requirements are met.

[0064] In order to make the landing gear vibration mode frequency (f h 、f c and f n ) To "reasonably avoid" external excitation frequencies (f1 and f2), it is necessary to formulate effective frequency control criteria. The frequency control criteria are formulated below.

[0065] Use formula (15) to calculate the relative deviation between the landing gear vibration modal frequency and the external excitation frequency, and check whether the relative deviation values are not less than 6%. If so, the design requirements are met; if not, the landing gear system needs to be redesigned, and steps 1 to 3 need to be repeated until the design requirements are met.

[0066]

[0067] Where: err i,j is the landing gear vibration modal frequency f j (respectively take f h 、f cand f n ) and external excitation frequency f i (respectively take the relative deviation of f1 and f2).

[0068] The theoretical basis for using 6% as the quantitative criterion for the relative deviation between the landing gear vibration modal frequency and the external excitation frequency is as follows:

[0069] The vibration response equation of a single degree of freedom under simple harmonic excitation force is:

[0070]

[0071] Where: m is mass; c is damping; k is stiffness; F is the amplitude of the exciting force, and ω is the circular frequency of the exciting force.

[0072] Assume the response displacement expression is:

[0073] x=A[cos(ωt)+isin(ωt)] (17)

[0074] The corresponding response speed and acceleration expressions are:

[0075]

[0076]

[0077] Substituting equations (17) to (19) into equation (16), we can obtain:

[0078] -mAω 2 +icAω+kA=F (20)

[0079] The displacement transfer function is thus:

[0080]

[0081] make:

[0082]

[0083] Then formula (21) can be transformed into:

[0084]

[0085] From formula (25), we can know that the expression of the transfer function amplitude of displacement relative to exciting force is:

[0086]

[0087] Correspondingly, the expression for the transfer function amplitude of velocity and acceleration relative to the exciting force is:

[0088]

[0089]

[0090] Acceleration is more convenient in actual vibration response testing. Therefore, the following first discusses the frequency design criteria using the acceleration transfer function as an example.

[0091] By definition, resonance refers to the situation where a physical system vibrates with a larger amplitude at specific frequencies than at other frequencies. These specific frequencies are called resonant frequencies.

[0092] From formula (28), we can know that the extreme value condition of the amplitude of the vibration acceleration transfer function of the single degree of freedom system is:

[0093]

[0094] Arranging formula (29) shows that the acceleration transfer function amplitude is maximum when the frequency ratio γ and the damping ratio ζ meet the following conditions:

[0095]

[0096] It can be seen from formula (30) that the resonant frequency is approximately equal to the natural frequency of the system only when the damping ratio is very small.

[0097] Substituting equation (30) into equation (28), the amplitude of the acceleration transfer function at resonance is obtained as follows:

[0098]

[0099] Combined with the definition of half-power bandwidth, it is considered that the transfer function amplitude is reduced to the resonance amplitude A When the frequency is reduced by 3dB, it leaves the resonance region. Therefore, the transfer function amplitude corresponding to the critical frequency of the non-resonance region (equivalent to the half-power frequency point) is:

[0100]

[0101] The critical frequency of the non-resonant region corresponding to B can be solved by equations (28) and (32). The solution process is as follows:

[0102]

[0103] make:

[0104]

[0105] Then formula (33) can be transformed into a quadratic equation:

[0106] ay 2 +by+1=0 (35)

[0107] Solving this quadratic equation yields:

[0108]

[0109] Substituting equation (34) into equation (36) yields the expression for the critical frequency ratio γ in the non-resonant region:

[0110]

[0111] Similarly, for the displacement and velocity transfer function amplitudes, the expressions for the critical frequency ratio γ in the non-resonance region are:

[0112]

[0113] The common damping ratio range for aircraft structures is ζ = 0.01 to 0.05 (reference AIAA 2007-2061). Substituting this into equations (37) to (39) yields the corresponding critical frequency ratio range in the non-resonant region. The specific values are shown in Tables 1 to 3. The table also lists the percentage deviations of γ1 and γ2 relative to 1. It can be seen that |γ1-1| and |γ2-1| increase approximately linearly with ζ. When ζ = 0.05, the frequency ratio deviation percentage reaches its maximum value, and the maximum frequency ratio deviation percentage is always less than 6%. Therefore, to be conservative, the recommended frequency control criterion is: the relative deviation between the landing gear vibration modal frequency and the external excitation frequency should be no less than 6%.

[0114] Table 1 Calculation results of critical frequency ratio in non-resonance region (based on displacement transfer function)

[0115] Serial number ζ <![CDATA[γ1]]> <![CDATA[γ2]]> <![CDATA[|γ1-1|]]> <![CDATA[|γ2-1|]]> 1 0.01 0.9898 1.0099 1.02％ 0.99％ 2 0.02 0.9794 1.0194 2.06％ 1.94％ 3 0.03 0.9686 1.0287 3.14％ 2.87％ 4 0.04 0.9575 1.0377 4.25％ 3.77％ 5 0.05 0.9461 1.0464 5.39％ 4.64％

[0116] Table 2 Calculation results of critical frequency ratio in non-resonance region (based on velocity transfer function)

[0117] Serial number ζ <![CDATA[γ1]]> <![CDATA[γ2]]> <![CDATA[|γ1-1|]]> <![CDATA[|γ2-1|]]> Serial number 1 0.01 0.9900 1.0100 1.00％ 1.00％ 1 2 0.02 0.9802 1.0202 1.98％ 2.02％ 2 3 0.03 0.9704 1.0304 2.96％ 3.04％ 3 4 0.04 0.9608 1.0408 3.92％ 4.08％ 4 5 0.05 0.9512 1.0512 4.88％ 5.12％ 5

[0118] Table 3 Calculation results of critical frequency ratio in non-resonance region (based on acceleration transfer function)

[0119] Serial number ζ <![CDATA[γ1]]> <![CDATA[γ2]]> <![CDATA[|γ1-1|]]> <![CDATA[|γ2-1|]]> 1 0.01 0.9902 1.0103 0.98％ 1.03％ 2 0.02 0.9810 1.0210 1.90％ 2.10％ 3 0.03 0.9721 1.0324 2.79％ 3.24％ 4 0.04 0.9637 1.0444 3.63％ 4.44％ 5 0.05 0.9557 1.0570 4.43％ 5.70％

[0120] The present application avoids the problem of coupling between the external excitation frequency and the landing gear vibration modal frequency during the taxiing phase by comparing the relative deviation between the landing gear vibration modal frequency and the external excitation frequency. By first performing a landing gear simulation or landing gear test to determine the landing gear vibration modal frequency, and then determining the external excitation frequency of the landing gear, if the relative deviation between the landing gear vibration modal frequency and the external excitation frequency is not less than 6%, the problem of coupling between the external excitation frequency and the landing gear vibration modal frequency will not occur, thereby avoiding resonance of the landing gear.

[0121] This method has a simple and clear concept and a sufficient theoretical basis. Compared with the existing technology, the established external excitation frequency prediction method has a sufficient theoretical basis, and the quantitative indicators of the landing gear vibration modal frequency and the external excitation deviation are more reasonable and more operational. It can be used to solve the problem of coupling between the external excitation frequency and the landing gear vibration modal frequency during the take-off and landing phases, avoid the subsequent investigation and treatment of landing gear resonance failures, and provide guidance for the dynamic design of the landing gear.

[0122] As a specific implementation method, vibration frequency control design was carried out for two types of landing gear (referred to as Case 1 and Case 2 respectively), as follows:

[0123] Case 1:

[0124] Step 1: Determine the vibration modal frequencies of the landing gear.

[0125] The vibration modal frequencies of the landing gear were obtained by the full-aircraft ground resonance test, as shown in Table 4.

[0126] Table 4 Landing gear vibration modal frequencies

[0127]

[0128] Step 2: Determine the external excitation frequency.

[0129] Table 5 shows the parameter values required to calculate the external excitation frequency.

[0130] Table 5 Parameter values required to calculate external excitation frequency

[0131] Serial number Parameter naming symbol Numerical 1 Front wheel lift speed <![CDATA[V TO ]]> 60.8m / s 2 Front wheel ground contact speed <![CDATA[V LD ]]> 59.6m / s 3 Tire radius r 0.460m

[0132] According to equations (13) and (14), the external excitation frequencies f1 and f2 can be calculated:

[0133] f1=21.0Hz、f2=20.6Hz

[0134] Step 3: Calculate the relative deviation between the landing gear vibration modal frequency and the external excitation frequency.

[0135] The relative deviation between the landing gear vibration modal frequency and the external excitation frequency is calculated according to formula (15). Among them, the first-order torsional frequency of the landing gear is closest to the external excitation frequencies f1 and f2, and their relative deviations are:

[0136] err 1,n =3.33%, err 2,n =1.46%

[0137] It can be seen that the relative deviation between the landing gear vibration modal frequency and the external excitation frequency is less than 6%, which does not meet the frequency control criterion and is likely to cause resonance problems.

[0138] During actual use, this type of landing gear experienced resonance problems and had to be redesigned.

[0139] Case 2:

[0140] Step 1: Determine the vibration modal frequencies of the landing gear.

[0141] The vibration modal frequencies of the landing gear were obtained by the full-aircraft ground resonance test, see Table 6.

[0142] Table 6 Landing gear vibration modal frequencies

[0143]

[0144] Step 2: Determine the external excitation frequency.

[0145] Table 7 shows the parameter values required to calculate the external excitation frequency.

[0146] Table 7 Parameter values required to calculate external excitation frequency

[0147] Serial number Parameter naming symbol Numerical 1 Front wheel lift speed <![CDATA[V TO ]]> 57.2m / s 2 Front wheel ground contact speed <![CDATA[V LD ]]> 54.4m / s 3 Tire radius r 0.254m

[0148] According to equations (13) and (14), the external excitation frequencies f1 and f2 can be calculated:

[0149] f1=35.8Hz、f2=34.1Hz

[0150] Step 3: Calculate the relative deviation between the landing gear vibration modal frequency and the external excitation frequency.

[0151] The relative deviation between the landing gear vibration modal frequency and the external excitation frequency is calculated according to formula (15). Among them, the first-order bending frequency of the landing gear is closest to the external excitation frequencies f1 and f2, and their relative deviations are:

[0152] err 1,n =26.8%, err 2,n =23.2%

[0153] It can be seen that the relative deviation between the landing gear vibration modal frequency and the external excitation frequency is greater than 6%, which meets the frequency control criterion and does not cause resonance problems.

[0154] During actual use, this type of landing gear has never experienced any resonance problems.

[0155] Comparing the analysis results of the above two cases, it can be seen that this patent is feasible and effective.

[0156] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for controlling the vibration frequency of a landing gear, characterized in that: include: Conduct landing gear simulation or landing gear test to determine the vibration modal frequency of the landing gear; Determine the external excitation frequency of the landing gear; Calculate the relative deviation between the landing gear vibration modal frequency and the external excitation frequency, and check whether the relative deviation values are all not less than 6%. If so, the landing gear design requirements are met; if not, redesign the landing gear until the requirements are met; The theoretical analysis method is used to calculate the external excitation frequency of the landing gear. The specific method is: Obtain the aircraft performance report and record the nose wheel speed V corresponding to the aircraft takeoff phase TO and takeoff run distance L TO , front wheel touchdown speed V during landing phase LD and landing roll distance L LD ; The external excitation caused by tire extrusion deformation or eccentricity during wheel rolling is set as unbalance-induced excitation. The aircraft's taxiing speed is set to increase or decrease linearly with takeoff time or landing time. The external excitation frequency is determined by the calculation theory of centrifugal force with an unbalanced rotating body.

2. The method for controlling landing gear vibration frequency according to claim 1, wherein: The method for performing the landing gear simulation or landing gear test includes: Set the landing gear to full extension; Get the heading first-order bending mode frequency f h , lateral first-order bending mode frequency f c and the first-order torsional mode frequency f n ; The modal frequencies can be obtained by modeling the landing gear using finite element software and calculating the vibration modal frequencies of the landing gear; or by testing the vibration modal frequencies of the landing gear using a full-aircraft ground resonance test.

3. The method for controlling landing gear vibration frequency according to claim 1, wherein: The rotation angle of the unbalanced rotating body is: Where ω is the circular frequency, ω0 is the initial rotation angular velocity; t is the time; α is the angular acceleration; The relationship between the external excitation frequency f and the circular frequency ω is:

4. The method for controlling landing gear vibration frequency according to claim 1, wherein: The calculation formula for the relative deviation between the landing gear vibration modal frequency and the external excitation frequency is: Where err i,j is the landing gear vibration modal frequency f j With external excitation frequency f i relative deviation.

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