CN102494193B - Hoop for airplane hydraulic pipeline and design method thereof - Google Patents

Abstract

The invention discloses a hoop for an airplane hydraulic pipeline and a design method thereof. The method comprises the steps of 1 establishing a vibration equation model of the hoop and the hydraulic pipeline and obtaining vibration isolation transmissibility; 2 according to the flight profile of an airplane, obtaining a target function and determining and optimizing damping ratio xi of parameters; and 3 determining materials used by the hoop for the airplane hydraulic pipeline according to optimized damping ratio, and designing a hoop structure. The hoop comprises fastening bolts, spring gaskets, an upper metal rubber pad block, an upper anti-lock brake system (ABS) plastic hoop block, a lower ABS plastic hoop block and a lower metal rubber pad block. The lower ABS plastic hoop block is internally embedded in the lower metal rubber pad block, the upper ABS plastic hoop block is internally embedded in the upper metal rubber pad block, and the airplane hydraulic pipeline is located between the lower metal rubber pad block and the upper metal rubber pad block. Two fastening bolts penetrate through the upper ABS plastic hoop block and the lower ABS plastic hoop block, and the spring gaskets are arranged between the two fastening bolts and the upper ABS plastic hoop block. The vibration isolation rate weighted sum corresponding to excitation source frequency points determined by the flight profile of the airplane serves as a basis of parameters for designing the hoop, and the hoop is designed according to the basis of the parameters.

Description

A kind of aircraft hydraulic tubing clip and design method thereof

Technical field

The invention belongs to plane hydraulic system dither pipeline vibration damping field, be specifically related to a kind of aircraft hydraulic tubing clip and design method thereof.

Background technique

Because the output of the flow of aircraft hydraulic pumps source pulsed, the aircraft hydraulic tubing can be subjected to the pulsatile impact of fluid, and excessive vibratory impulse can cause pipeline breaking to cause aircraft crash, and therefore carrying out Vibration Absorption Designing for the aircraft pipeline is problem demanding prompt solution.At the beginning of the new architecture design, except selecting to meet the supporting structure material and pipeline material of static strength and fatigue strength requirement, also to carry out necessary test and adjustment to pipe-line system, make the natural frequency of pipe-line system avoid the fluid pulsation frequency, the pulsation of getting rid of fluid causes the possibility of pipe-line system fatigue ruption.Since the aircraft hydraulic fluid have high pressure, at a high speed, the big characteristics of pulsation, if the solid coupled vibrations of the stream of pulsation of liquid-transport pipe-line inner fluid and solid pipeline does not take place, the amplitude of pressure fluctuation after but pressure pulsation or resonance strengthen is excessive, make the pressure pulsation that acts on the tube wall surpass the allowable stress limit of pipeline material, even surpassed the yield stress limit of pipeline material, then will cause breaking of tube wall at short notice.

The pipeline clip was all adopted experience design in the past, and too much stressed the design of clip rigidity, but ignored two factors: 1) present generation aircraft oil hydraulic pump rotating speed is higher, and pairing vibrating source frequency values is higher; 2) because pipeline is a kind of beam structure, pipeline is full of fluid simultaneously, therefore the natural frequency of liquid-filling pipe is difficult to reach more than 2.5 times of vibrating source frequency, sometimes even less than the vibrating source frequency, when the resonance of pipeline does not take place at that time easily for pipeline clip design, therefore selecting appropriate vibration damping rigidity and damping and reducing clip weight is to design the important evidence of clip.

The more employing of present domestic aircraft adds the metal clip of rubber washer, as shown in Figure 1, what aircraft adopted at present is the clamping stirrup of HB3-25-2002 band pad, clip is made up of peripheral clip piece (band) and rubber sheet gasket, clip piece (band) generally adopts the 1Cr18Ni9 material, and rubber is nitrile rubber.

This kind structure clip has possessed certain rigid and damping and amortization, and rubber can the absorption portion pipe vibration, but has following defective:

1) rubber material non-refractory, easily aging, long-time pipe vibration can cause rubber material to lose efficacy, cause clip to support and have fretting wear, along with the development of fretting wear, support stiffness descends gradually, thereby the natural frequency of pipeline is reduced gradually, when the pipeline natural frequency that reduces and pressure pulsation frequency near or when overlapping, the vibration that stream is coupled admittedly takes place, cause the inefficacy of pipe-line system equally.

2) the aircraft clip hoop piece (band) that impales fixation outward adopts metallic material to have very high rigidity, but because the clip quantity of an airplane is very many, one of design objective of aircraft is as much as possible to alleviate quality, and too much metallic material clip can bring extra weight.

Summary of the invention

The objective of the invention is in order to address the above problem, a kind of aircraft hydraulic tubing clip and design method thereof are proposed, at first confirm the weight of each Frequency point of vibrating source according to the aircraft flight section, obtain objective function according to weight than the vibration isolation rate of calculating clip, clip damping ratio parameter is optimized, choose suitable material by the optimal damper rate that obtains, design a kind of novel composite structure clip, make it on aircraft hydraulic pressure dither pipeline, bring into play the weakening effect with high damping, light weight.

A kind of aircraft hydraulic tubing design method of clip comprises following step:

Step 1: set up clip and hydraulic tubing vibration equation model, obtain vibration transmissibility;

Set up the clip model, aircraft hydraulic pressure liquid-filling pipe is lumped mass piece m, and k is a clip rigidity, and c is the clip damping constant, and the excitation force that the pulsation of fluid produces in the aircraft hydraulic tubing is F (t), and it is x (t) that pipeline is subjected to the vibratory impulse displacement, F _b(t) expression is delivered to the power on the aircraft base rack;

Set up the model sport equation:

$m\stackrel{\·\·}{x}\left(t\right)+c\stackrel{\·}{x}\left(t\right)+\mathrm{kx}\left(t\right)=F\left(t\right)---\left(1\right)$

If act on aircraft hydraulic tubing excitation force and displacement be:

F(t)＝Fe ^iωt (2)

x(t)＝Xe ^iωt (3)

Wherein, ω is a pipeline vibrating source vibration frequency, and F, X are the constants of being determined by initial conditions; In formula (2), (3) substitution formula (1):

-ω ²mXe ^iωt+iωcXe ^iωt+kXe ^iωt＝Fe ^iωt (4)

$X=\frac{F}{k-{\mathrm{\ω}}^{2}m+\mathrm{i\ωc}}---\left(5\right)$

The power that is delivered on the aircraft base rack is F _b(t):

$F_b\left(t\right)=c\stackrel{\·}{x}\left(t\right)+\mathrm{kx}\left(t\right)---\left(6\right)$

In formula (3) substitution (6), can get:

$F_b\left(t\right)=k{\mathrm{Xe}}^{\mathrm{i\ωt}}+\mathrm{i\ωc}{\mathrm{Xe}}^{\mathrm{i\ωt}}=\frac{k+\mathrm{i\ωc}}{k-{\mathrm{\ω}}^{2}m+\mathrm{i\ωc}}{\mathrm{Fe}}^{\mathrm{i\ωt}}$ (7)

$=\frac{1+\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000118671070000032.png,HDA0000118671070000041.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&xi;}(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)}{1+\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000118671070000032.png,HDA0000118671070000041.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&xi;}(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)-{(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)}^2}{\mathrm{Fe}}^{\mathrm{i\&omega;t}}$

Wherein, ω _nBe the natural frequency of liquid-filling pipe,

ξ is the damping ratio of liquid-filling pipe,

Be delivered to the F on the aircraft base rack _b(t) ratio of absolute value is called vibration transmissibility T and between the F (t);

Then the aircraft hydraulic tubing through the vibration transmissibility T of clip is:

$T=\left|\frac{F_b\left(t\right)}{F\left(t\right)}\right|=\sqrt{\frac{1+{\left[2\mathrm{\&xi;}(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)\right]}^2}{{[1-{(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)}^2]}^2+{\left[2\mathrm{\&xi;}(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)\right]}^2}}---\left(8\right)$

Step 2: according to the aircraft flight section, draw objective function, determine parameters optimization ξ;

According to the aircraft flight section, obtain the time scale of aircraft hydraulic pumps under different rotating speeds, the aircraft hydraulic pumps rotating speed is corresponding one by one with the vibrating source frequency, the time scale difference that different frequency is occupied, set the weight ratio of different frequency point, be brought in the formula (8) with the different frequency point and obtain different vibration transmissibilities, each transmissibility is obtained weighted sum T with weight than distributing _F, as the formula (9):

T _F＝a ₁T(ω ₁)+a ₂T(ω ₂)+…a _iT(ω _i)+…+a _mT(ω _m) (9)

Wherein, ω _iFrequency for aircraft hydraulic pumps different rotating speeds correspondence; a _iBe the occupied percentage of time of aircraft hydraulic pumps different rotating speeds; The objective function of formula (9) for optimizing, wherein, ω _nIt is determined value; ξ is a damping ratio, Be the value relevant with rigidity, therefore change the clip material, optimize its damping ratio and make formula (9) value reduce to minimum with the clip damping;

Step 3, determine the material of aircraft hydraulic tubing according to the damping ratio of optimizing, the design yoke configurations with clip;

Damping ratio ξ by step 2 obtains consults relevant handbook, selects the material of aircraft hydraulic tubing with clip, the design yoke configurations;

A kind of aircraft hydraulic tubing clip comprises clamping bolt, compression spring, goes up the metal-rubber cushion block, goes up ABS plastic clip piece, following ABS plastic clip piece and following metal-rubber cushion block;

Following ABS plastic clip piece is embedded in down the metal-rubber cushion block, last ABS plastic clip piece is embedded in the metal-rubber cushion block, the aircraft hydraulic tubing is down between metal-rubber cushion block and the last metal-rubber cushion block, two clamping bolts pass ABS plastic clip piece and following ABS plastic clip piece, and clip is fixed on the airframe stand; Be provided with compression spring between clamping bolt and the last ABS plastic clip piece.

The invention has the advantages that:

(1) having proposed first with the pairing vibration isolation rate of the vibrating source Frequency point weighted sum that the aircraft flight section is determined is the foundation of design clip parameter, this kind method experience design method than before has more sufficient theoretical foundation, can be used as a kind of universal method and under the coupling of multi-frequency operating mode, use, and designed the light-duty clip of a kind of high damping at certain type according to this;

(2) novel clip possesses the high damping characteristic, and the metal-rubber of employing not only has higher damping and amortization as the more original rubber of damping material, and simultaneously itself has high temperature resistant and difficult advantage such as aging as a kind of metallic material;

(3) the peripheral part that is connected with the aircraft stand of novel clip has been selected ABS plastic, and more original metal clip piece (band) not only quality significantly reduces, and its intensity, rigidity enough guarantee fixing tube simultaneously;

(4) novel clip has been done deep excavation on the selection theoretical foundation, and, metal rubber material is embedded in the peripheral clip piece according to the novel yoke configurations of material behavior design, guaranteed the positional stability of damping material, new structure technology is easy to realize simultaneously, is convenient to produce in batches.

Description of drawings

Fig. 1 is the structural representation of clip in the background technique;

Fig. 2 is a method flow diagram of the present invention;

Fig. 3 is clip of the present invention and hydraulic tubing model schematic representation;

Fig. 4 is certain model aircraft flight profile, mission profile of the present invention;

Fig. 5 is clip damping ratio of the present invention and vibration isolation rate variation relation;

Fig. 6 be the metal-rubber used among the present invention and General Purpose Rubber material lag loop relatively;

Fig. 7 is clip of the present invention and piping erection reduced graph;

Fig. 8 is the tomograph of clip of the present invention;

Fig. 9 is the two-dimensional structure figure of clip of the present invention.

Among the figure:

1-clamping bolt 2-compression spring 3-goes up the metal-rubber cushion block

Metal-rubber cushion block under the ABS plastic clip piece 6-under the last ABS plastic clip of the 4-piece 5-

7-aircraft hydraulic tubing 8-airframe stand

Embodiment

The present invention is described in further detail below in conjunction with drawings and Examples.

The present invention is the design method of a kind of aircraft hydraulic tubing with clip, and flow process comprises following step as shown in Figure 2:

Step 1: set up clip and hydraulic tubing vibration equation model, obtain vibration transmissibility.

Set up the clip model, as shown in Figure 3, aircraft hydraulic pressure liquid-filling pipe is lumped mass piece m, and k is a clip rigidity, and c is the clip damping constant, and the excitation force that the pulsation of fluid produces in the aircraft hydraulic tubing is F (t), and it is x (t) that pipeline is subjected to the vibratory impulse displacement, F _b(t) expression is delivered to the power on the aircraft base rack.

Set up the model sport equation:

$m\stackrel{\&CenterDot;\&CenterDot;}{x}\left(t\right)+c\stackrel{\&CenterDot;}{x}\left(t\right)+\mathrm{kx}\left(t\right)=F\left(t\right)---\left(10\right)$

If act on aircraft hydraulic tubing excitation force and displacement be:

F(t)＝Fe ^iωt (11)

x(t)＝Xe ^iωt (12)

Wherein, ω is a pipeline vibrating source vibration frequency, and F, X are the constants of being determined by initial conditions.In formula (11), (12) substitution formula (10):

-ω ²mXe ^iωt+iωcXe ^iωt+kXe ^iωt＝Fe ^iωt (13)

$X=\frac{F}{k-{\mathrm{\&omega;}}^{2}m+\mathrm{i\&omega;c}}---\left(14\right)$

The power that is delivered on the aircraft base rack is F _b(t):

$F_b\left(t\right)=c\stackrel{\&CenterDot;}{x}\left(t\right)+\mathrm{kx}\left(t\right)---\left(15\right)$

In formula (12) substitution (15), can get:

$F_b\left(t\right)=k{\mathrm{Xe}}^{\mathrm{i\&omega;t}}+\mathrm{i\&omega;c}{\mathrm{Xe}}^{\mathrm{i\&omega;t}}=\frac{k+\mathrm{i\&omega;c}}{k-{\mathrm{\&omega;}}^{2}m+\mathrm{i\&omega;c}}{\mathrm{Fe}}^{\mathrm{i\&omega;t}}$ (16)

$=\frac{1+\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000118671070000032.png,HDA0000118671070000041.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&xi;}(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)}{1+\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000118671070000032.png,HDA0000118671070000041.png"\; state="\{\{state\}\}">i</figure-callout>}2\mathrm{\&xi;}(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)-{(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)}^2}{\mathrm{Fe}}^{\mathrm{i\&omega;t}}$

Wherein, ω _nBe the natural frequency of liquid-filling pipe,

ξ is the damping ratio of liquid-filling pipe,

Be delivered to the F on the aircraft base rack _b(t) ratio of absolute value is called vibration transmissibility T and between the F (t).

Then the aircraft hydraulic tubing through the vibration transmissibility T of clip is:

$T=\left|\frac{F_b\left(t\right)}{F\left(t\right)}\right|=\sqrt{\frac{1+{\left[2\mathrm{\&xi;}(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)\right]}^2}{{[1-{(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)}^2]}^2+{\left[2\mathrm{\&xi;}(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)\right]}^2}}---\left(17\right)$

Step 2: according to the aircraft flight section, draw objective function, determine parameters optimization ξ.

According to the aircraft flight section, obtain the time scale of aircraft hydraulic pumps under different rotating speeds, because the aircraft hydraulic pumps rotating speed is corresponding one by one with the vibrating source frequency, the time scale difference that different frequency is occupied, set the weight ratio of different frequency point according to this, be brought in the formula (17) with the different frequency point and obtain different vibration transmissibilities, each transmissibility is obtained weighted sum T with weight than distributing _F, as the formula (18).

T _F＝a ₁T(ω ₁)+a ₂T(ω ₂)+…a _iT(ω _i)+…+a _mT(ω _m) (18)

Wherein, ω _iFrequency for aircraft hydraulic pumps different rotating speeds correspondence; a _iBe the occupied percentage of time of aircraft hydraulic pumps different rotating speeds.Formula (18) has been reacted the effectiveness in vibration suppression of clip, is the objective function of optimizing, in the formula (18), and ω _nIt is determined value; ξ is a damping ratio,

Therefore be the value relevant with rigidity with the clip damping, changing its damping ratio of clip optimization of material, that formula (18) value is reduced to is minimum, just makes effectiveness in vibration suppression the best of clip at the rotating speed of different oil hydraulic pumps.

For example:

As shown in Figure 4, be certain model aircraft flight profile, mission profile.By flight profile, mission profile, aircraft hydraulic pumps time scale under full rotating speed is that time scale is that time scale is 8% under 63%, the 65% full rotating speed under 29%, the 80% full rotating speed (cruising speed).Therefore can make the weighted sum of vibration isolation rate under three kinds of flight operating modes drop to minimum by damping and the rigidity of adjusting clip.Optimum parameters is ξ;

Objective function is:

T _F＝0.29T ₁(ω ₁)+0.63T ₂(ω ₂)+0.08T ₃(ω ₃) (19)

By differentiate can get its minimum value, the damping ratio ξ after being optimized simultaneously to formula (19).

Obtain optimum clip damping parameter by an example emulation, one section typical liquid-filling pipe natural frequency of aircraft is 440Hz, the aircraft hydraulic pumps source is 600Hz at full rotating speed lower frequency, frequency under 80% rotating speed is 480Hz, frequency under 65% rotating speed is 390Hz, the substitution formula is calculated in (19), obtains the minimum value of ξ in 0～5 interval, as shown in Figure 5.

As can be seen from Figure 5, when ξ hour, when just clip rigidity was excessive, vibration isolation rate T value was bigger, can't play the vibration isolation effect substantially, when ξ=0.5716, it is 0.9845 that vibration isolation rate T obtains minimum value, when ξ＞0.5716, vibration isolation rate T is increase gradually again.Less by the damping ratio ξ that calculates common clip in the past, generally near 0.25, therefore need to adjust the clip material its damping ratio ξ is being chosen near the optimum value.

Step 3, determine that the aircraft hydraulic tubing is with the material of clip, design yoke configurations.

Damping ratio ξ by step 2 obtains consults relevant handbook, selects the material of aircraft hydraulic tubing with clip, the design yoke configurations.

By consulting relevant handbook, and through detailed calculated, in step 2 gave an actual example, the peripheral fixed structure material of clip of the present invention adopted high strength ABS (acrylonitrile-butadiene-styrene (ABS) plastics) plastics, damping pad employing metal rubber material.

The foundation of selecting is: 1) the damping pad rubber material non-refractory of existing clip, easily aging, long-time pipe vibration can cause rubber material to lose efficacy, therefore to select high damping and exotic material damping material as pipeline, metal-rubber is wound in reticular structure by the wire of 1Cr18Ni9 material, and extrusion modling.Fig. 6 be itself and General Purpose Rubber material lag loop relatively, it is big more that lag loop surrounds area, illustrate that its dissipation performance is strong more, its dry friction damping characteristics is better than rubber damping, metallic material is high temperature resistant difficult aging simultaneously, so metal rubber material is more suitable for as vibration damping equipment than rubber damper.

2) the 1Cr18Ni9 metallic material density that adopted of the peripheral fixed block of existing clip (band) is about 7.9g/cm ³, and the ABS density of material only has 1.04g/cm ³, its density only is 13.2% of 1Cr18Ni9, can use for a long time in-40 ℃～100 ℃ scopes, its tension hardness is 48MPa simultaneously, and flexural strength is 65MPa, therefore enough can be used as the peripheral clip piece of pipeline, and the clip quality is had significantly reduce, rigidity is significantly less than metallic material.Be approximately 0.56 by calculating the novel yoke configurations damping ratio that is adopted, near optimum value.

The present invention has at first determined that according to the aircraft flight section each Frequency point of vibrating source occupies the percentage of time, setting the pairing vibration isolation rate of each Frequency point weighted sum is objective function, obtain the objective function minimum value by adjusting the clip damping ratio, obtained optimum clip parameter simultaneously, and by this selection of parameter suitable material choose foundation as new clip, selected at last metal-rubber piece is as damping material, and ABS plastic is as the peripheral immobilization material of clip, and designed the structure of novel clip.

A kind of aircraft hydraulic tubing clip as Fig. 7, Fig. 8, shown in Figure 9, comprises clamping bolt 1, compression spring 2, goes up metal-rubber cushion block 3, goes up ABS plastic clip piece 4, following ABS plastic clip piece 5 and following metal-rubber cushion block 6.

Following ABS plastic clip piece 5 is embedded in down metal-rubber cushion block 6, last ABS plastic clip piece 4 is embedded in metal-rubber cushion block 3, aircraft hydraulic tubing 7 is down between metal-rubber cushion block 6 and the last metal-rubber cushion block 3, two clamping bolts 1 pass ABS plastic clip piece 4 and following ABS plastic clip piece 5, and clip is fixed on the airframe stand 8.Be provided with compression spring 2 between clamping bolt 1 and the last ABS plastic clip piece 4.

As shown in Figure 7, aircraft hydraulic tubing 7 concerns with the mounting point of clip, from figure, can just find out, ABS plastic clip piece and airframe stand 8 connect firmly, mainly play the solid Zhi Zuoyong of aircraft hydraulic tubing 7, last metal-rubber cushion block 3, following metal-rubber cushion block 6 are nested in the plastics clip, play the weakening effect of pipeline.

As shown in Figure 9, last ABS plastic clip piece 4, following ABS plastic clip piece 5 make metal-rubber cushion block 3 at the groove that leaves d=1～2mm respectively, metal-rubber cushion block 6 is nested in the clip piece down, and the part that last metal-rubber cushion block 3, following metal-rubber cushion block 6 are stayed clip piece outside is 2～3mm; When aircraft hydraulic tubing 7 was positioned at clip, top structure and bottom structure left the w=1mm gap, step up aircraft hydraulic tubing 7 with clamping bolt 1.

Claims (1)

1. the design method of an aircraft hydraulic tubing usefulness clip is characterized in that, comprises following step:

Step 1: set up clip and hydraulic tubing vibration equation model, obtain vibration transmissibility;

Set up the clip model, aircraft hydraulic pressure liquid-filling pipe is lumped mass piece m, and k is a clip rigidity, and c is the clip damping constant, and the excitation force that the pulsation of fluid produces in the aircraft hydraulic tubing is F (t), and it is x (t) that pipeline is subjected to the vibratory impulse displacement, F _b(t) expression is delivered to the power on the aircraft base rack;

Set up the model sport equation:

$m\stackrel{\&CenterDot;\&CenterDot;}{x}\left(t\right)+c\stackrel{\&CenterDot;}{x}\left(t\right)+\mathrm{kx}\left(t\right)=F\left(t\right)---\left(1\right)$

If act on aircraft hydraulic tubing excitation force and displacement be:

F(t)＝Fe ^iωt （2）

x(t)＝Xe ^iωt （3）

Wherein, ω is a pipeline vibrating source vibration frequency, and F, X are the constants of being determined by initial conditions; In formula (2), (3) substitution formula (1):

-ω ²mXe ^iωt+iωcXe ^iωt+kXe ^iωt＝Fe ^iωt （4）

$X=\frac{F}{k-{\mathrm{\&omega;}}^{2}m+\mathrm{i\&omega;c}}---\left(5\right)$

The power that is delivered on the aircraft base rack is F _b(t):

$F_b\left(t\right)=c\stackrel{\&CenterDot;}{x}\left(t\right)+\mathrm{kx}\left(t\right)---\left(6\right)$

In formula (3) substitution (6), can get:

$F_b\left(t\right)=\mathrm{kX}{e}^{\mathrm{i\&omega;t}}+\mathrm{i\&omega;cX}{e}^{\mathrm{i\&omega;t}}=\frac{k+\mathrm{i\&omega;c}}{k-{\mathrm{\&omega;}}^{2}m+\mathrm{i\&omega;c}}F{e}^{\mathrm{i\&omega;t}}$

（7）

$=\frac{1+i2\mathrm{\&xi;}(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)}{1+i2\mathrm{\&xi;}(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)-{(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)}^2}F{e}^{\mathrm{i\&omega;t}}$

Wherein, ω _nBe the natural frequency of liquid-filling pipe,

ξ is the damping ratio of liquid-filling pipe,

Be delivered to the F on the aircraft base rack _b(t) ratio of absolute value is called vibration transmissibility T and between the F (t);

Then the aircraft hydraulic tubing through the vibration transmissibility T of clip is:

$T=\left|\frac{F_b\left(t\right)}{F\left(t\right)}\right|=\sqrt{\frac{1+{\left[2\mathrm{\&xi;}(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)\right]}^2}{{[1-{(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)}^2]}^2+{\left[2\mathrm{\&xi;}(\mathrm{\&omega;}/{\mathrm{\&omega;}}_n)\right]}^2}}---\left(8\right)$

Step 2: according to the aircraft flight section, draw objective function, determine parameters optimization ξ;

According to the aircraft flight section, obtain the time scale of aircraft hydraulic pumps under different rotating speeds, the aircraft hydraulic pumps rotating speed is corresponding one by one with the vibrating source frequency, the time scale difference that different frequency is occupied, set the weight ratio of different frequency point, be brought in the formula (8) with the different frequency point and obtain different vibration transmissibilities, each transmissibility is obtained weighted sum T with weight than distributing _F, as the formula (9);

T _F＝a ₁T(ω ₁)+a ₂T(ω ₂)+···a _iT(ω _i)+···+a _mT(ω _m) （9）

Wherein, ω _iFrequency for aircraft hydraulic pumps different rotating speeds correspondence; a _iBe the occupied percentage of time of aircraft hydraulic pumps different rotating speeds; The objective function of formula (9) for optimizing, wherein, ω _nIt is determined value; ξ is a damping ratio,

Be the value relevant with rigidity, therefore change the clip material, optimize its damping ratio and make formula (9) value reduce to minimum with the clip damping;

Step 3, determine the material of aircraft hydraulic tubing according to the damping ratio of optimizing, the design yoke configurations with clip;

Damping ratio ξ by step 2 obtains consults relevant handbook, selects the material of aircraft hydraulic tubing with clip, the design yoke configurations.

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