CN105740575A - Flapping wing analysis and design based on fluctuation propelling theory - Google Patents

Abstract

The invention relates to flapping wing analysis and design based on the fluctuation propelling theory. Firstly, based on the fluctuation propelling theory, root causes influencing the aerodynamic efficiency of a flapping wing are analyzed, and propelling waves are defined to express the propelling effect generated by the flapping wing, so that it is found that the nature of aerodynamic efficiency is the ratio of the flying speed to the wave speed of the propelling waves, in other words, the aerodynamic efficiency is related to the ratio of the flying speed to the wave speed of the propelling waves, and thus a method for carrying out forward design on the aerodynamic efficiency of the flapping wing is found. The flapping wing design method based on the fluctuation propelling theory comprises the following steps that firstly, on the condition that joint propelling force meets the propelling force requirement, the maximum torsion angle alpha max and the flapping frequency f of the flapping wing are calculated according to the aerodynamic efficiency and the propelling force requirement, and then the target working point of the flapping wing is designed; secondly, according to a twist rigidity model and aerodynamic force, the wing face rigidity kr matched with the target working point obtained in the first step is obtained; thirdly, the flapping wing is designed according to the wing face rigidity kr obtained in the second step.

Description

The flapping wing analysis theoretical based on undulatory propulsion and design

Technical field

The present invention relates to aerospace field, and particularly relate to a kind of flapping wing analysis theoretical based on undulatory propulsion and method for designing.

Background technology

Birds are evolved by reptile, and its forearm has torsional freedom, observe the forearm finding birds and can reverse with main motion generating period of swatting in flapping flight process, and research proves that this torsion is the key factor that flapping wing produces thrust.

Different sayings is there is in this flapping wing twist motion in field.Some scholars think that the aerodynamic moment acting on aerofoil makes aerofoil produce to reverse, and namely passively reverse, and only just can produce control power by active twist when maneuvering flight.Other scholars think that birds adjust little brachiostrophosis rule to reach high pneumatic efficiency all consciously at whole flight course.In recent years, this torsion rule was by extensive discussions, and wherein professor Send makes outstanding contributions.He calculates maximum propulsive efficiency point based on the method for quasi-steady aerodynamic force, and devises SmartBird and be verified.But, the essential mechanism that birds aerofoil reverses is undistinct, and active twist compares whether passive torsion can have higher pneumatic efficiency, remains without clear and definite answer.Meanwhile, in the prior art but without a kind of forward design method instructing flapping-wing aircraft to design based on the gentle power demand of pneumatic efficiency.

Summary of the invention

In order to solve above-mentioned deficiency of the prior art, the present invention is primarily based on undulatory propulsion theory, analyze the basic reason affecting flapping wing pneumatic efficiency, and define " translatory wave " to express the propelling effect that flapping wing produces, thus finding that the essence of pneumatic efficiency is the ratio of flight speed and " translatory wave " velocity of wave, namely the size of pneumatic efficiency is relevant to the ratio of flight speed Yu " translatory wave " velocity of wave, and have found a kind of method that flapping wing pneumatic efficiency is carried out Top-Down Design accordingly.

In an embodiment of the present invention, the flapping wing method for designing theoretical based on undulatory propulsion comprises the steps: first step, when closing thrust and meeting thrust requirements, calculates the maximum twist angle α of flapping wing according to pneumatic efficiency and thrust requirements_maxWith frequency f of fluttering, and then design flapping wing target operation points；Second step, according to twisting rigidity model and aerodynamic force, obtains the aerofoil rigidity k matched with this target operation points obtained in described first step_r；Third step, utilizes the aerofoil rigidity k tried to achieve in described second step_rCarry out the design of described flapping wing.

Wherein, this conjunction thrust and pneumatic efficiency can be calculated acquisition by following formula:

$F_{flap-thrust}=2\·{\∫}_0^{\frac{b}{2}}({\mathrm{\πF}}_0/b)(\frac{1}{{\mathrm{\η}}_{Thrust}}-1){\mathrm{\α}}_{max}{\left(r\right)}^{2}dr$

${\mathrm{\η}}_{Thrust}=\frac{u_0}{2\mathrm{\π}f\frac{h_0}{{\mathrm{\α}}_{max}}}$

Wherein, F₀For dynamic pressure, b is that the span is long, and r is the span-wise length of infinitesimal, u₀For far-end speed of incoming flow, h₀For swatting amplitude.

Wherein, this twisting rigidity model is represented by following formula, and this aerodynamic force is tried to achieve by formula (12):

τ_y(t)=F_N(t)·y_cop

τ_y(t)=k_r·(α_P-α₀)

Wherein, τ_yT () is moment, F_NT () is aerodynamic force, y_copFor the distance of pressure heart distance torsional axis, k_rFor stiffness coefficient, i.e. described aerofoil rigidity, α_pFor current time motion torsion angle, α₀The meansigma methods of motion torsion angle is swatted for the cycle.

Wherein, adopt EPP foam as the base material of flapping wing, on described EPP foam, smear latex subsequently, and stickup carbon beam forms described flapping wing below aerofoil.

Wherein, for the aerofoil rigidity k obtained in described second step_r, by the applying amount of latex and the quantity of the described carbon beam pasted below aerofoil and the arranged direction smeared on described EPP foam, reach required aerofoil rigidity k_r。

The flapping wing aerofoil with deformability is modeled by the present invention, obtains the limit slew range that desirable passive torsion aerofoil can reach, it has been found that through the aerofoil of rigidity Design, by passively reversing the equally possible efficient operating point reaching SmartBird.

By above-mentioned solution, present invention achieves following beneficial effect: namely, the present invention adopts a kind of Passive deformation modeling pattern by changing aerofoil rigidity, it is achieved thereby that active twist effect, and reach the high pneumatic efficiency of active twist by designing aerofoil rigidity, it is to avoid to the light-weighted technology requirement of actuator height frequency range.

Accompanying drawing explanation

Fig. 1 is 2D flapping wing illustraton of model.

Fig. 2 is 3D flapping wing illustraton of model.

Fig. 3 is variation rigidity schematic diagram.

Fig. 4 is thrust and relationship between efficiency figure.

As shown in the figure, in order to enable clearly to realize the structure of embodiments of the invention, it is labelled with specific structure and device in the drawings, but it is only for signal needs, it is not intended to limit the invention in this ad hoc structure, device and environment, according to specific needs, these devices and environment can be adjusted or revise by those of ordinary skill in the art, and adjusting or revising of carrying out still includes in the scope of appended claims.

Detailed description of the invention

Below in conjunction with the drawings and specific embodiments, a kind of flapping wing method for designing theoretical based on undulatory propulsion provided by the invention is described in detail.Here doing to illustrate, in order to make embodiment more detailed, the following examples are best, preferred embodiment, may be used without other alternative for some known technologies those skilled in the art and are carried out simultaneously；And accompanying drawing part is merely to describe embodiment more specifically, and it is not intended as the present invention is carried out concrete restriction.

Before carrying out the flapping wing method for designing of the present invention, first the basic acts of flapping flight be analyzed by the present invention.The basic acts of the flapping flight of such as birds etc. can be split as the twist motion swatting motion and forearm around shoulder joint, and this approximate fractionation have ignored the jackknife action in cruise process.

Those skilled in that art generally believe that swatting motion substantially conforms to sinusoidal rule with twist motion, and both phase angles differ 90 °.In order to disassemble analysis flapping wing pneumatic principle, the present invention is by the abstract beating campaign up and down for level of flapping motion around the reciprocating rotary that shoulder is the center of circle, and thinks that the action swatted up and down is full symmetric, and its motor process is as shown in Figure 1.When flapping motion arrives peak or during minimum point, torsion angle exactly zero；When flapping wing is upwards swatted by minimum point, first torsion angle increases from zero, reaches maximum, hereafter reduce near middle position, and when swatting peak, torsion angle is decreased to again zero；Process of swatting downwards is similar, and torsion angle first reduces, and reaches minima near middle position, the back to zero when minimum point.

Consider the motor process shown in Fig. 1, obtain describing a series of equations of flapping wing translation and twist motion:

Z (t)=h₀sin(ωt)

X (t)=u₀t

α_p(t)=α_maxcos(ωt)

${\mathrm{tan\α}}_H\left(t\right)=\frac{\stackrel{\·}{z}\left(t\right)}{\stackrel{\·}{x}\left(t\right)}=\frac{h_0\·\mathrm{\ω}\·cos\left(\mathrm{\ω}t\right)}{u_0}$

${\mathrm{\α}}_H\left(t\right)=arctan\left(\frac{h_0\·\mathrm{\ω}\·cos\left(\mathrm{\ω}t\right)}{u_0}\right)$

α (t)=α_P(t)-α_H(t)

${\mathrm{\α}}_{Hmax}=arctan\left(\frac{h_0\·\mathrm{\ω}}{u_0}\right)$

$F_L\left(t\right)=\frac{1}{2}{\mathrm{\ρv}}^{2}S\·2\mathrm{\π}\·\mathrm{\α}\left(t\right)$

$F_N\left(t\right)=\frac{F_L\left(t\right)}{cos\mathrm{\α}\left(t\right)}$

F_Thrust(t)=F_N(t)sinα_P(t)(1)

F_Lift(t)=F_N(t)cosα_P(t)

In Serial Prescription formula (1), the physical meaning of each parameter is as shown in the table:

Table 1: the physical meaning of each parameter in Serial Prescription formula (1)

h0	Swat amplitude	α(t)	The instantaneous angle of attack
				ω=2 π f	Swat angular frequency	αHmax	Transient flow angle maximum
z(t)	Vertical motion	ρ	Gas density
				x(t)	Propulsion	v	Instantaneous speed of incoming flow
u0	Far-end speed of incoming flow	S	Wing area
				αmax	Maximum twist angle	FN(t)	Aerodynamic force
αp(t)	The angle of pitch	FThrust(t)	Thrust
				αH(t)	Transient flow angle	FLift(t)	Lift

Average thrust in one cycle, the average mechanical output of input, the power of average thrust output and efficiency can be expressed as:

$<F_{Thrust}>=\frac{1}{T}{\&Integral;}_{t_0}^{t_0+T}{F}_{Thrust}\left(t\right)dt$

$<P_x>=\frac{1}{T}{\&Integral;}_{t_0}^{t_0+T}{F}_{Thrust}\left(t\right)\&CenterDot;u_{0}dt---\left(2\right)$

$<P_h>=\frac{1}{T}{\&Integral;}_{t_0}^{t_0+T}{F}_{Lift}\left(t\right)\&CenterDot;\stackrel{\&CenterDot;}{z}\left(t\right)dt$

${\mathrm{\&eta;}}_{Thrust}=\frac{<P_x>}{<P_h>}$

In formula, t₀For any time, T is flutter cycle.

Owing to Serial Prescription formula (2) is difficult to resolve, the relation of wherein variable and aerodynamic force output is also unintelligible, also cannot obtain analytic solutions.But, when angle is little, it can be assumed that for following Serial Prescription formula (3).Needing exist for illustrating, when flapping flight, angle is little, and therefore following supposition is also entirely in this area reasonably.

sinα≈α

cosα≈1

tanα≈α(3)

v≈u₀

F_N≈F_L

Based on assumed above, then Serial Prescription formula (2) can be simplified, such that it is able to obtain the analytic solutions of a cycle internal efficiency and average thrust:

< F_Thrust>=π F₀·α_max ²·(ω^*λ-1)

${\mathrm{\&eta;}}_{Thrust}=\frac{<P_x>}{<P_h>}=\frac{1}{{\mathrm{\&omega;}}^{*}\mathrm{\&lambda;}}=\frac{u_0}{2\mathrm{\&pi;}f\frac{h_0}{{\mathrm{\&alpha;}}_{max}}}---\left(4\right)$

In formula, F₀For dynamic pressure,ω^*For intermediate variable.

In above Serial Prescription formula (4), the expression formula of efficiency represents flight speed u₀Ratio with additionally certain speed.In order to be best understood from the meaning of this ratio, a kind of Generalized Wave of definition characterizes propulsion efficiency produced by flapping wing, is called translatory wave, and this certain speed other is translatory wave velocity of wave.Now efficiency may be considered the ratio of flight speed and translatory wave velocity of wave.Definition translatory wave wavelength X and velocity of wave here:

$\mathrm{\&lambda;}=2\mathrm{\&pi;}\frac{h_0}{{\mathrm{\&alpha;}}_{max}}---\left(5\right)$

V_w=λ f

Being may certify that by the efficiency expression formula in Serial Prescription formula (4), when translatory wave velocity of wave is equal to flight speed, the pneumatic efficiency of flapping wing is close to 100%, but is now nearly free from thrust.When translatory wave velocity of wave is more than flight speed, flapping wing starts to produce thrust, but pneumatic efficiency declines again therewith.

When flapping-wing aircraft is designed, it is desirable to pneumatic efficiency is more high more good, but, as the above analysis, during pneumatic efficiency 100%, do not produce thrust, so, can not using this point as operating point, it is necessary to consider thrust and pneumatic efficiency to select operating point.

If first devising the pneumatic efficiency of flapping wing, other affects the flapping wing parameter of thrust so that thrust meets design envelope curve to need co-design afterwards.Usually, some geometric parameters of flapping-wing aircraft are referred to the birds that nature is concrete, and variable is just defined as maximum twist angle α_maxWith frequency f of fluttering.

Serial Prescription formula (4) is arranged, it is possible to obtain:

$<F_{Thrust}>=\left({\mathrm{\&pi;F}}_0\right)(\frac{1}{{\mathrm{\&eta;}}_{Thrust}}-1){{\mathrm{\&alpha;}}_{\max }}^2---\left(6\right)$

${\mathrm{\&eta;}}_{Thrust}=\frac{u_0}{2\mathrm{\&pi;}f\frac{h_0}{{\mathrm{\&alpha;}}_{max}}}$

By Serial Prescription formula (6) it can be seen that average thrust < F_Thrust> along with maximum twist angle α_maxIncrease and quickly increase.Need exist for illustrating, if α_maxIncrease and make η_ThrustAlso increasing, then F will decline, unless now change is swatted frequency and made efficiency improve constantly, under the limit, efficiency is 1, and now thrust is 0.So, in order to ensure thrust requirements, efficiency is limited in here, is merely illustrative one mentality of designing of explanation, namely ensures thrust with torsion angle, use frequency guaranteed efficiency.Therefore, if guaranteed efficiency η_ThrustConstant, frequency f of fluttering will increase, and this not only results in the decline of mechanical efficiency, and can improve the requirement to whole flapping wing actuating unit.Therefore, in the present invention, it is preferred to pass through to design maximum twist angle α_maxMeet minimum thrust requirements, carry out guaranteed efficiency η with minimum frequency f simultaneously_Thrust。

The swatting up and down of flapping wing can cause the deformation of flexible aerofoil.In the present invention, the Passive deformation of aerofoil is analyzed, and by changing aerofoil rigidity, so that passively twisting up to the effect of active twist, thus mates best operating point.

In order to this plastic deformation is resolved, done herein and analyzed the change that have ignored aerofoil camber, it is believed that the aerofoil of rigidity is connected with spar by torsion spring, when aerofoil is subject to Aerodynamic force action, can whole be rotated around spar.Aerofoil rigidity is flexibly connected with aerofoil and spar and considers by this simplified model, obtains a mixing stiffness coefficient, and flapping wing design can be played good directive function by its result, and in the art, this simplification is considered as rational.

If ignoring the viscous friction of air-flow and aerofoil, then aerodynamic force should just be perpendicular to aerofoil with joint efforts.Using the leading edge of aerofoil as reference position, utilizing foline method to obtain the infinitesimal moment to spar on aerofoil, integration obtains resultant couple, thus solving pressure heart position:

$\begin{array}{c}{\mathrm{\&tau;}}_{N,y}\left(t\right)={\&Integral;}_{r=0}^b\left(c_m\left(r\right)\&CenterDot;\frac{\mathrm{\&rho;}}{2}c\left(r\right){\&lsqb;\stackrel{\&CenterDot;}{z}\left(t\right)\&rsqb;}^2{C}_L\left(\mathrm{\&alpha;}\left(t\right)\right)\right)dr\\ =\frac{\mathrm{\&rho;}}{2}{\&lsqb;\stackrel{\&CenterDot;}{z}\left(t\right)\&rsqb;}^2{C}_L\left(\mathrm{\&alpha;}\left(t\right)\right){\&Integral;}_{r=0}^b\left(c_m\left(r\right)\&CenterDot;c\left(r\right)\right)dr\end{array}---\left(7\right)$

In formula (7), ρ is atmospheric density, and b is that the span is long, C_L(α (t)) is the lift coefficient under α (t) angle of attack, c_mR () is the distance of each infinitesimal of aerofoil Yu spar.

Especially, for rectangle aerofoil, have: c_m(r)=c/2, c (r)=c, it is possible to find y_cop=c_mR ()=c/2, can obtain in conjunction with twisting rigidity model:

τ_y(t)=F_N(t)·y_cop(8)

τ_y(t)=k_r·(α_P-α₀)

In Serial Prescription formula (8), k_rFor stiffness coefficient, α₀The meansigma methods of motion torsion angle is swatted for the cycle.

Simultaneous formula (7) and formula (8), it can be deduced that maximum twist angle α_maxExpression formula:

${\mathrm{\&alpha;}}_{max}=\frac{arctan\left(\frac{h_0\mathrm{\&omega;}}{u_0}\right)}{+\frac{k_r}{F_{0}c\mathrm{\&pi;}}}=\frac{{\mathrm{\&alpha;}}_{Hmax}}{1+\frac{k_r}{F_0\&CenterDot;c\&CenterDot;\mathrm{\&pi;}}}---\left(9\right)$

When aerofoil rigidity is from completely flexible to perfect rigidity, k_r∈ [0 ,+∞], maximum twist angle α_max∈[0,α_Hmax].Owing to when translatory wave speed is more than flight speed, flapping wing just can produce thrust, so maximum twist angle α_max∈[0,α_Hmax] permanent establishment, i.e. any α that flapping wing can be made to produce thrust_maxCan by passively reversing realization.According to formula (9), the aerofoil rigidity k needed can be obtained_r。

Above-mentioned analysis is based on the aerofoil fluttered up and down with reverse, and is promoted by the aerofoil that this model is swatted to reality around shoulder joint at this.Here adopt foline method that the aerofoil swatted around shoulder joint splits into infinitesimal, get, along exhibition vector product, the conjunction thrust that these infinitesimals produce.

$F_{flap-thrust}=2\&CenterDot;{\&Integral;}_0^{\frac{b}{2}}({\mathrm{\&pi;F}}_0/b)(\frac{1}{{\mathrm{\&eta;}}_{Thrust}}-1){\mathrm{\&alpha;}}_{max}{\left(r\right)}^{2}dr---\left(10\right)$

${\mathrm{\&eta;}}_{Thrust}=\frac{u_0}{2\mathrm{\&pi;}f\frac{h_0}{{\mathrm{\&alpha;}}_{max}}}$

Owing to wing root is connected with fuselage, and wing tip flexibility is maximum, therefore the α to each position is opened up on edge_maxR () angle of attack is slightly increased by fuselage guide vane.If being approximately considered α_maxR () with spanwise linear change, then formula (10) can abbreviation be:

$F_{flap-thrust}=({\mathrm{\&pi;F}}_0/b)(\frac{1}{{\mathrm{\&eta;}}_{Thrust}}-1)\&CenterDot;2{\&Integral;}_0^{\frac{b}{2}}{\left(\frac{2r}{b}{\mathrm{\&alpha;}}_{max}\right)}^{2}dr=\frac{1}{3}{F}_{Thrust}---\left(11\right)$

Aerofoil normal force maximum moment be flapping wing upper flutter or under flutter through middle position, there is the maximum moment swatting speed, same in order to be generalized to the three-dimensional flapping motion swatted around shoulder joint, it is engraved in spanwise when normal force is maximum and is integrated, obtain the aerodynamic force making aerofoil reverse:

$F_{N-max}={\&Integral;}_0^{\frac{b}{2}}\frac{1}{2}\mathrm{\&rho;}{\left({\stackrel{\&CenterDot;}{z}}_{max}\right)}^{2}c\&CenterDot;2\mathrm{\&pi;}\&CenterDot;{\mathrm{\&alpha;}}_{P\max }dr---\left(12\right)$

Based on the above-mentioned analysis to pneumatic efficiency and aerodynamic force and each physical parameter, the invention provides a kind of forward design method carrying out flapping wing design based on the gentle power demand of pneumatic efficiency, comprise the steps:

Step 1, when closing thrust and meeting thrust requirements (that is, according to closing thrust), calculates maximum twist angle α according to pneumatic efficiency and thrust requirements_maxWith frequency f of fluttering, so that it is determined that target operation points, i.e. maximum twist angle α_max, flutter frequency f and flight speed.

In a preferred embodiment of the invention, this conjunction thrust and pneumatic efficiency can be calculated acquisition by formula (10).

Step 2, according to twisting rigidity model and aerodynamic force, obtains the aerofoil rigidity k matched with this target operation points obtained in step 1_r。

In a preferred embodiment of the invention, this twisting rigidity model can be represented by above formula (8), and this aerodynamic force can be tried to achieve by above formula (12).

Step 3, utilizes the aerofoil rigidity k tried to achieve in step 2_rCarry out flapping wing design.

The design of the flapping wing of flapping-wing aircraft is carried out, as shown in Figure 3 based on the said method of the present invention.In a preferred embodiment of the invention, the flapping wing of this flapping-wing aircraft initially with the EPP foam base material as flapping wing, can be smeared latex, and stickup carbon beam form flapping wing below aerofoil subsequently on EPP foam.Wherein, in a preferred embodiment of the invention, for the aerofoil rigidity k obtained in step 2_r, the quantity of the carbon beam forming time rib and the arranged direction pasted below the applying amount of latex smeared on EPP foam and aerofoil can be passed through, reach required aerofoil rigidity.

Fig. 4 illustrates the relation of thrust and pneumatic efficiency, is labelled with the target operation points of model machine simultaneously.

Additionally, based on above-mentioned steps, we devise a frame flapping wing proof machine.Contrast with active twist sized flap wings system in order to convenient, the flapping wing model machine overall construction design that the present invention introduces is similar to SmartBird, it is different in that and some parameter of flapping wing has been redesigned, utilize forward rigidity Design to mate proposed target operation points, avoid the active twist mechanism that SmartBird adopts, adopt passive torsional mode to reach similar flight index.Model machine parameter is as follows:

Geometric parameter: the span is 2m, wing area 0.5m², weight 400g, the wing is stroke 0.4m slightly up and down.

Aerodynamic parameter: pneumatic efficiency 78%, flight speed 4.8m/s, average thrust 0.7N.

Design parameter: 32 ° of aerofoil maximum twist angle, frequency 2.89Hz of fluttering, aerofoil rigidity 0.52Nm/rad.

The present invention contains any replacement, amendment, equivalent method and scheme made in the spirit and scope of the present invention.Understand thoroughly to make the public that the present invention to be had, present invention below preferred embodiment describes in detail concrete details, and does not have the description of these details can also understand the present invention completely for a person skilled in the art.It addition, in order to avoid the essence of the present invention is caused unnecessary obscuring, do not describe well-known method, process, flow process, element and circuit etc. in detail.

One of ordinary skill in the art will appreciate that all or part of step realizing in above-described embodiment method can be by the hardware that program carrys out instruction relevant and completes, this program can be stored in computer read/write memory medium, as: ROM/RAM, magnetic disc, CD etc..

The above is only the preferred embodiment of the present invention; it should be pointed out that, for those skilled in the art, under the premise without departing from the principles of the invention; can also making some improvements and modifications, these improvements and modifications also should be regarded as protection scope of the present invention.

Claims (5)

1., based on the flapping wing method for designing that undulatory propulsion is theoretical, comprise the steps:

First step, when the conjunction thrust of the aerofoil of described flapping wing meets thrust requirements, calculates the maximum twist angle α of flapping wing according to pneumatic efficiency and thrust requirements_maxWith frequency f of fluttering, thus designing the target operation points of flapping wing；

Second step, according to twisting rigidity model and aerodynamic force, obtains the aerofoil rigidity k matched with the described target operation points obtained in described first step_r；

Third step, utilizes the aerofoil rigidity k tried to achieve in described second step_rCarry out the design of described flapping wing.

2. method according to claim 1, it is characterised in that:

Described conjunction thrust is expressed from the next and tries to achieve:

$F_{flap-thrust}=2\&CenterDot;{\&Integral;}_0^{\frac{b}{2}}({\mathrm{\&pi;F}}_0/b)(\frac{1}{{\mathrm{\&eta;}}_{Thrust}}-1){\mathrm{\&alpha;}}_{max}{\left(r\right)}^{2}dr$

And, described pneumatic efficiency is expressed from the next and tries to achieve:

${\mathrm{\&eta;}}_{Thrust}=\frac{u_0}{2\mathrm{\&pi;}f\frac{h_0}{{\mathrm{\&alpha;}}_{max}}}$

Wherein, F₀For dynamic pressure, b is that the span is long, and r is span-wise length infinitesimal, u₀For far-end speed of incoming flow, h₀For swatting amplitude, F_flap-thrustFor closing thrust, η_ThrustFor pneumatic efficiency.

3. method according to claim 1, it is characterised in that: described twisting rigidity model is represented by following formula (1),

$\begin{array}{c}{\mathrm{\&tau;}}_y\left(t\right)=F_N\left(t\right)\&CenterDot;y_{\mathrm{cop}}\\ {\mathrm{\&tau;}}_y\left(t\right)=k_r\&CenterDot;({\mathrm{\&alpha;}}_P-{\mathrm{\&alpha;}}_0)\end{array}---\left(1\right)$

Wherein, τ_yT () is moment；F_NT () is aerodynamic force；y_copDistance for pressure heart distance torsional axis；k_rFor stiffness coefficient, i.e. described aerofoil rigidity；α_pMotion torsion angle for current time；α₀The meansigma methods of motion torsion angle is swatted for the cycle；

And, described aerodynamic force is tried to achieve by formula (2):

$F_{N-max}={\&Integral;}_0^{\frac{b}{2}}\frac{1}{2}\mathrm{\&rho;}{\left({\stackrel{\&CenterDot;}{z}}_{max}\right)}^{2}c\&CenterDot;2\mathrm{\&pi;}\&CenterDot;{\mathrm{\&alpha;}}_{Pmax}dr---\left(2\right)$

Wherein, ρ is gas density,For maximum speed of swatting, α_PmaxFor maximum motion torsion angle, c is aerofoil chord length, and r is span-wise length infinitesimal, F_N-maxFor aerodynamic force.

4. the method according to any one of claim 1-3, it is characterised in that: adopt EPP foam as the base material of flapping wing, on described EPP foam, smear latex subsequently, and stickup carbon beam forms described flapping wing below aerofoil.

5. method according to claim 4, it is characterised in that: for the aerofoil rigidity k obtained in described second step_r, by the applying amount of latex and the quantity of the described carbon beam pasted below aerofoil and the arranged direction smeared on described EPP foam, reach required aerofoil rigidity k_r。