CN115649437B

CN115649437B - Design method of distributed flexibility type flapping wing aircraft and flapping wing driving mechanism

Info

Publication number: CN115649437B
Application number: CN202211432775.7A
Authority: CN
Inventors: 张弘志; 孙中超; 宣建林; 宋笔锋; 杨晓君; 汪亮; 稂鑫雨; 张明昊
Original assignee: Northwestern Polytechnical University
Current assignee: Northwestern Polytechnical University
Priority date: 2022-11-16
Filing date: 2022-11-16
Publication date: 2024-05-03
Anticipated expiration: 2042-11-16
Also published as: CN115649437A

Abstract

The invention discloses a distributed flexibility type ornithopter and a design method of a ornithopter driving mechanism, and belongs to the technical field of ornithopters. The distributed compliance type flapping wing driving mechanism comprises a flapping wing driving mechanism mounting frame, a piezoelectric bimorph driver and a distributed compliance type transmission chain, wherein the piezoelectric bimorph driver and the distributed compliance type transmission chain are arranged on the flapping wing driving mechanism mounting frame; the distributed flexibility type transmission chain comprises a pair of vertical elastic pieces and a transverse elastic piece, and the fixed end of the piezoelectric bimorph driver is fixed at the rear end of the distributed flexibility type transmission chain; simplifying the piezoelectric bimorph driver into an equivalent single-degree-of-freedom second-order linear vibration system; b. the distributed flexibility type transmission chain is simplified into an equivalent multi-rigid-body torsion spring system; c. solving aerodynamic resistance and moment of the flapping wing; d. assembling a model; e. establishing a forced vibration equation set; f. taking an objective function of the optimization problem; g. optimizing design. It has long service life and high flying efficiency.

Description

Design method of distributed flexibility type flapping wing aircraft and flapping wing driving mechanism

Technical Field

The invention relates to the technical field of flapping wing aircrafts.

Background

The flapping wing driving mechanism is a power system of the bionic flapping wing aircraft, and the configuration scheme and the dynamic performance of the driving mechanism have important influence on the flight capacity of the flapping wing aircraft. The traditional flapping wing driving mechanisms all adopt a configuration scheme of combining a rigid connecting rod and a friction type kinematic pair, and are widely applied to large-scale and centimeter-level flapping wing aircrafts. However, when the size of the ornithopter is reduced to millimeter level, the rigid connecting rod-friction kinematic pair type ornithopter driving mechanism has various problems of reduced component strength, severe wear of kinematic pairs, difficult lifting of the movement frequency and the like. Therefore, people have to search for other new mechanism configurations.

A carbon fiber rigid thin plate type slider-rocker flapping wing driving mechanism formed by integrally connecting polyimide film flexible hinges is developed by Wood team of Harvard university and is used for equipping coin-sized 'Robobee' and 'HMF' series micro piezoelectric flapping wing aircrafts, and the movement frequency of the miniature piezoelectric flapping wing aircrafts can reach more than 100 Hz. However, in the high-frequency motion process, the flexible hinge position of the concentrated flexible flapping wing driving mechanism has obvious stress concentration phenomenon, so that the service life of the concentrated flexible hinge driving mechanism is greatly shortened. The flexible supporting rod is utilized by the university of Wuhan technology to design a space four-bar mechanism, so that the number of components and kinematic pairs in a transmission chain is reduced, the weight reduction effect is achieved, meanwhile, the energy consumption of a prime mover can be saved by means of the resonance characteristic of the flexible components, but the mechanism still cannot avoid the use of friction kinematic pairs, and is not suitable for high-frequency motion.

In order for the flapping wing drive mechanism to meet the expected performance requirements, researchers have also sought to explore rational optimization design methods. For the traditional flapping wing driving mechanism with a rigid connecting rod-friction kinematic pair and concentrated flexibility, researchers often independently model and optimize a prime motor, a transmission chain and a flapping wing, and the influence of power coupling effect among all components on the overall performance of the driving mechanism cannot be estimated. Researchers continue to explore a number of modeling and design methodologies suitable for multi-component coupling analysis. The Shanghai university has established a piezoelectric-polysome coupling dynamics model for a centralized flexibility type slider rocker flapping wing mechanism driven by a piezoelectric bimorph by utilizing a finite element method so as to accurately solve the flapping angle of a flapping wing under the action of an electric field of the piezoelectric bimorph, but the method has the defect of higher calculation cost and is not suitable for analysis of a more complex system. Takashi et al in Toyota central research laboratory set up a "piezoelectric single-chip-folding spring-flapping wing" multisystem coupled vibration model for a piezoelectric direct-drive type insect-simulated flapping wing driving mechanism capable of being folded back and forth, and the model can rapidly calculate the resonant frequency of the driving mechanism and the maximum motion amplitude of the flapping wing under the condition of considering the mass effect, the elastic effect and the damping effect of each component at the same time, but the model still cannot accurately predict the change rule of the motion parameters of the mechanism along with the excitation voltage. In addition, the optimization of the performance of the flapping wing driving mechanism by researchers at present only focuses on the improvement of the flapping wing movement frequency and movement amplitude, and other important performance indexes such as the whole machine weight, the whole machine volume, the energy conversion efficiency and the like of the mechanism are not comprehensively considered, so that most of the designed flapping wing driving mechanism is difficult to realize the installed flight.

Disclosure of Invention

The invention aims to solve the technical problem of providing a design method of a distributed flexibility type flapping wing aircraft and a flapping wing driving mechanism, and the design method has the characteristics of long service life, high flight efficiency and the like. And provides a corresponding overall comprehensive performance optimization design method.

In order to solve the technical problems, the invention adopts the following technical scheme:

A distributed flexibility type flapping wing aircraft comprises a fuselage, a flight control system, a flapping wing driving mechanism and a pair of flapping wings, wherein the flapping wing driving mechanism is a distributed flexibility type flapping wing driving mechanism and comprises a flapping wing driving mechanism mounting frame, a piezoelectric bimorph driver and a distributed flexibility type transmission chain, wherein the piezoelectric bimorph driver and the distributed flexibility type transmission chain are arranged on the flapping wing driving mechanism mounting frame;

The distribution compliance type transmission chain is a bilateral symmetry structure, and it includes a pair of vertical shell fragment and a horizontal shell fragment, and a pair of vertical shell fragment is left side shell fragment and right side shell fragment respectively, and left side shell fragment and right side shell fragment bilateral symmetry set up, and their connection structure is: the method comprises the steps of firstly, symmetrically pre-bending and deforming the upper end part of a left elastic piece and the upper end part of a right elastic piece outwards respectively, upwards pre-bending and deforming the left end part of a transverse elastic piece and the right end part of the transverse elastic piece respectively, then fixedly bonding the left end part of the transverse elastic piece and the upper end part of the left elastic piece together, and fixedly bonding the right end part of the transverse elastic piece and the upper end part of the right elastic piece together, so that a distributed flexible transmission chain with pre-stress is formed; the distributed flexibility type transmission chain is provided with two flapping arms and a flapping transmission part, the two flapping arms are a left flapping arm and a right flapping arm respectively, a left flapping arm supporting part is formed at the junction of the left elastic piece and the transverse elastic piece, and a left flapping arm is formed at the connection part of the left elastic piece at the outer end of the left flapping arm supporting part and the transverse elastic piece; the junction of the right elastic piece and the transverse elastic piece forms a right flapping arm supporting part, and the connection part of the right elastic piece and the transverse elastic piece at the outer end of the right flapping arm supporting part forms a right flapping arm; the left side flapping arm and the right side flapping arm incline upwards from the inner end to the outer end under the action of the pre-stress elasticity of the distributed flexible transmission chain, so that the distributed flexible transmission chain forms a bilateral symmetry structure; a flapping transmission part is formed at the middle part of the transverse elastic sheet;

The pair of flapping wings are symmetrically arranged on the left flapping arm and the right flapping arm respectively;

The fixed end of the piezoelectric bimorph driver is fixed at the rear end of the distributed soft type transmission chain, and the free end of the piezoelectric bimorph driver is fixedly connected with the flapping transmission part of the distributed soft type transmission chain;

the piezoelectric bimorph driver drives the flapping transmission part to vibrate up and down through the free end of the piezoelectric bimorph driver, and under the action of the pre-stress elasticity, the distribution flexibility type transmission chain drives the left flapping arm and the right flapping arm to do the same-frequency same-amplitude flapping motion, so that the pair of flapping wings are driven to do the flapping motion to generate lifting force.

The invention is further improved in that:

In the distributed flexibility type transmission chain, a flapping transmission part of a transverse elastic piece is a transverse elastic piece large rigidity section, the parts of the transverse elastic pieces, which are positioned at two sides of the flapping transmission part, are transverse elastic piece small rigidity sections, and the rigidity of the transverse elastic piece large rigidity sections is larger than that of the transverse elastic piece small rigidity sections, wherein the transverse elastic piece small rigidity sections positioned at the left side of the flapping transmission part are transverse elastic piece left side small rigidity sections, and the transverse elastic piece small rigidity sections positioned at the right side of the flapping transmission part are transverse elastic piece right side small rigidity sections;

The lower parts of the left side spring plate and the right side spring plate are vertical spring plate large rigidity sections, the upper parts of the left side flapping arm and the right side flapping arm are vertical spring plate small rigidity sections, and the rigidity of the vertical spring plate large rigidity sections is larger than that of the vertical spring plate small rigidity sections; the vertical spring piece large rigidity section of the left spring piece is a left spring piece large rigidity section, the vertical spring piece small rigidity section of the left spring piece is a left spring piece small rigidity section, the vertical spring piece large rigidity section of the right spring piece is a right spring piece large rigidity section, and the vertical spring piece small rigidity section of the right spring piece is a right spring piece small rigidity section; the lower parts of the left elastic piece large rigidity section and the right elastic piece large rigidity section are respectively fixed on the flapping wing driving mechanism mounting frame through a transmission chain fixing plate so as to enable the flapping transmission part to keep the vertical direction when vibrating.

The two flapping arms are connected with the flapping wings through a hinged connection structure; the hinge type connecting structure comprises a flapping arm connecting sheet, a pre-bending angle adjusting flexible hinge, a flapping wing connecting sheet and a passive torsion flexible hinge; the flapping arm connecting sheet is connected with the flapping wing connecting sheet through a pre-bending angle adjusting flexible hinge, the flapping wing connecting sheet is connected with the flapping wing through a passive torsion flexible hinge, the flapping arm connecting sheet is fixedly bonded with the flapping arm, the angle of the pre-bending angle adjusting flexible hinge enables the flapping wing to be kept in a horizontal state when in a static state, and when the flapping arm performs flapping motion, the flapping wing performs passive torsion motion around the front edge of the passive torsion flexible hinge under the combined action of aerodynamic force and self inertia force.

The flapping wing driving mechanism mounting frame is made of a woven carbon fiber laminated plate material, the bending part of the flapping wing driving mechanism mounting frame is connected by a flexible bending film in the middle layer of the woven carbon fiber laminated plate to form a folding seam, and the folding seam of the woven carbon fiber laminated plate and the butt seam of the woven carbon fiber laminated plate are glued and fixed, so that the flapping wing driving mechanism mounting frame forms an integrated structure; the left side shell fragment, right side shell fragment and horizontal shell fragment are by the mutual lamination bonding of three-layer width polypropylene sheet metal constitution, and wherein the thickness of outside two-layer polypropylene sheet metal is the same, and its rigidity's size is realized through the thickness size of intermediate layer polypropylene sheet metal.

The flapping arm connecting sheet and the flapping wing connecting sheet are made of carbon fiber laminated plates, and the pre-bending angle adjusting flexible hinge and the passive torsion flexible hinge are made of polyimide.

A design method of a distributed flexibility type flapping wing driving mechanism comprises the following steps:

a. According to the principle of a centralized mass method, the piezoelectric bimorph driver is simplified into an equivalent single-degree-of-freedom second-order linear vibration system which simultaneously comprises an equivalent mass block M _act,e, an equivalent linear damping C _act,e, an equivalent linear spring K _act,e and an equivalent piezoelectric driving force F _p; the equivalent mass M _act,e is connected to the ground by a mobile pair in the vertical direction: the equivalent linear spring K _act,e and the equivalent linear damping C _act,e are mutually connected in parallel along the vertical direction, the upper ends of the equivalent linear spring K _act,e and the equivalent linear damping C _act,e are fixedly connected with the equivalent mass block M _act,e, and the lower ends of the equivalent linear spring K _act,e and the equivalent linear damping C _act,e are fixedly connected with the ground; the equivalent piezoelectric driving force F _p acts on the equivalent mass block M _act,e along the vertical direction, and in the linear range, the equivalent piezoelectric driving force F _p is in direct proportion to the electric field strength E _V along the thickness direction of the piezoelectric ceramic plate;

Namely: f _p＝λ_pE_V

Wherein: lambda _p is the force-electric proportionality coefficient; e _V is a function of the piezoelectric bimorph drive voltage U and the drive frequency f _elec; defining the displacement of the equivalent mass M _act,e along the vertical direction as an equivalent linear displacement output x _act of the piezoelectric bimorph driver;

b. The distributed flexibility type transmission chain is simplified into an equivalent multi-rigid-body torsion spring system formed by connecting a plurality of sections of rigid connecting rods and torsion springs according to the theory of 1R and 2R pseudo rigid body models of the large-deformation flexible beams, and then:

a) In the transverse spring plate, the flapping transmission part is equivalent to a connecting rod l ₁₁;

in the left small stiffness section of the transverse elastic piece, a left flapping arm supporting part supports the transverse elastic piece, a torsion spring K ₁₁ is equivalent to a part between the left end of the flapping transmission part and the left flapping arm supporting part, and the left flapping arm supporting part is equivalent to a torsion spring K ₁₃; the equivalent of the left end of the flapping transmission part and the torsion spring K ₁₁ is a connecting rod l ₁₂, the equivalent of the part between the torsion spring K ₁₃ and the torsion spring K ₁₁ is a connecting rod l ₁₄, and the equivalent of the left flapping arm part is a connecting rod l ₁₆; the fixed connection of the flapping transmission part and the small rigidity section at the left side of the transverse elastic sheet is equivalent to a fixed pair between a connecting rod l ₁₁ and a connecting rod l ₁₂;

In the right small rigidity section of the transverse elastic sheet, the parts corresponding to the torsion springs K ₁₁, K ₁₃, the connecting rod l ₁₂, the connecting rod l ₁₄ and the connecting rod l ₁₆ are respectively equivalent to the torsion springs K ₁₂, K ₁₄, the connecting rod l ₁₃, the connecting rod l ₁₅ and the connecting rod l ₁₇; the fixed connection of the flapping transmission part and the small rigidity section on the right side of the transverse elastic sheet is equivalent to a fixed pair between a connecting rod l ₁₁ and a connecting rod l ₁₃;

b) In the left spring plate;

In the left elastic piece large-rigidity section, the part of the left elastic piece large-rigidity section which is fixedly connected with the flapping wing driving mechanism mounting frame through a transmission chain fixing plate so as to keep the vertical direction is equivalent to a connecting rod l ₂₁, the upper part adjacent to the connecting rod l ₂₁ is equivalent to a torsion spring K ₂₁, and the part above the torsion spring K ₂₁ is equivalent to a connecting rod l ₂₂;

In the small-rigidity section of the left elastic piece, the supporting part of the left flapping arm is equivalent to a torsion spring K ₂₃; the part between the torsion spring K ₂₃ and the connecting rod l ₂₂ is equivalent to the torsion spring K ₂₂, the part below the torsion spring K ₂₂ is equivalent to the connecting rod l ₂₃, the part between the torsion spring K ₂₂ and the torsion spring K ₂₃ is equivalent to the connecting rod l ₂₄, and the part of the left flapping arm is equivalent to the connecting rod l ₂₅; the fixed connection between the left elastic piece large rigidity section and the left elastic piece small rigidity section is equivalent to a fixed pair between a connecting rod l ₂₂ and a connecting rod l ₂₃;

In the right elastic sheet, the parts corresponding to the connecting rod l ₂₁, the torsion spring K ₂₁, the connecting rod l ₂₂, the torsion spring K ₂₂, the torsion spring K ₂₃, the connecting rod l ₂₃, the connecting rod l ₂₄ and the connecting rod l ₂₅ are respectively equivalent to the connecting rod l ₃₁, the torsion spring K ₃₁, the connecting rod l ₃₂, the torsion spring K ₃₂, the torsion spring K ₃₃, the connecting rod l ₃₃, the connecting rod l ₃₄ and the connecting rod l ₃₅; the fixed connection between the right elastic piece large rigidity section and the right elastic piece small rigidity section is equivalent to a fixed pair between a connecting rod l ₃₂ and a connecting rod l ₃₃;

The left side flapping arm is equivalent to the tangent fixedly connection of the connecting rod l ₂₅ and the connecting rod l ₁₆; the right side flapping arm is equivalent to the tangent fixedly connection of the connecting rod l ₃₅ and the connecting rod l ₁₇; the Y-shaped connecting structure in the flexible transmission chain is simulated and distributed; and a connecting rod l ₂₁ and a connecting rod l ₃₁ which are fixedly connected with the installation frame of the flapping wing driving mechanism in the vertical direction are kept, so that the distributed flexibility type transmission chain forms an equivalent multi-rigid-body torsion spring system in a shape of a door;

c. According to the principle of equivalent conversion between the distributed load and the concentrated load, the aerodynamic load applied to the flapping wing along the flapping plane in the motion process is equivalent to the concentrated aerodynamic resistance F _wing acting on the pressure center of the flapping wing; the centralized aerodynamic drag F _wing is positioned in the flapping plane of the flapping wing, is vertical to the spanwise direction of the flapping wing, and is opposite to the movement direction of the flapping wing; obtaining aerodynamic damping coefficients of the flapping wing at different positions and in different motion states by means of slice integration according to the principle of phyllin And the distance l _aero between the centre of pressure and the root axis; the mass characteristics of the flapping wing are simulated by using a rigid rod l _wing, wherein the mass m _wing of the rigid rod is equal to the real mass of the flapping wing, the moment of inertia J _wing of the rigid rod l _wing relative to the wing root axis is equal to the real moment of inertia of the flapping wing relative to the wing root axis, and therefore an equivalent 'mass-moment of inertia-pneumatic damping' system of the flapping wing is established; wherein the expression of the equivalent concentrated aerodynamic drag force F _wing of the flapping wing and the aerodynamic damping moment M _wing formed at the root of the flapping wing is as follows:

M_wing＝F_wing·l_aero

Wherein: θ _wing is the flapping angle of the flapping wing, The flapping angular velocity of the flapping wing; pneumatic damping coefficient/>Is the flapping angle theta _wing and the flapping angular velocity/>, of the flapping wingIs a function of (2);

d. According to the actual position relation of each component in the distributed flexibility type flapping wing driving mechanism, an equivalent single-degree-of-freedom second-order linear vibration system of the piezoelectric bimorph driver, an equivalent multi-rigid-torsion spring system of a distributed flexibility type transmission chain and an equivalent mass-moment of inertia-pneumatic damping system of a flapping wing are subjected to model assembly, and an equivalent mass block M _act,e in the equivalent single-degree-of-freedom second-order vibration system of the piezoelectric bimorph driver is fixedly connected with a connecting rod l ₁₁ in the equivalent multi-rigid-torsion spring system of the distributed flexibility type transmission chain; the wing roots of the flapping wings in the pair of flapping wings equivalent 'mass-moment of inertia-pneumatic damping' systems are respectively fixedly connected with a connecting rod l ₁₆, a connecting rod l ₂₅, a connecting rod l ₁₇ and a connecting rod l ₃₅ in the distributed flexibility type transmission chain equivalent 'multi-rigid body-torsion spring' system, the included angle between the root of the left flapping wing and the connecting rod l ₁₆ is theta _s, and the included angle between the root of the right flapping wing and the connecting rod l ₁₇ is theta _s, so that the equivalent 'mass-moment of inertia-spring-damping' system of the distributed flexibility type flapping wing driving mechanism can be built;

e. The following three independent motion parameters in the equivalent mass-moment of inertia-spring-damping system of the split-distribution flexibility type flapping wing driving mechanism are defined as generalized displacement: equivalent linear displacement output x _act of the piezoelectric bimorph driver, rotation angle theta ₁₁ of torsion spring K ₁₁ and rotation angle theta ₁₃ of torsion spring K ₁₃; a generalized displacement vector q= [ x _act θ₁₁ θ₁₃]^T ] is defined accordingly; defining a system generalized external force vector corresponding to the generalized displacement as: f= [ F _p 0 0]^T; defining bilateral symmetry motion constraints of the system as: θ ₁₁＝θ₁₂、θ₁₃＝θ₁₄; q and F are substituted into a Lagrangian equation of a second type, and a three-degree-of-freedom second-order system forced vibration equation set of a piezoelectric-structure-flow field coupling complete machine dynamics model of the distributed flexibility type flapping wing driving mechanism is established as follows:

Wherein: m is a system generalized mass matrix, C is a system generalized damping matrix, and K is a system generalized stiffness matrix;

The input excitation of the 'piezoelectric-structure-flow field' coupling complete machine dynamics model of the distributed flexibility type flapping wing driving mechanism is the driving voltage U of the piezoelectric bimorph driver, the output response is the flapping angle theta _wing＝θ₁₁+θ₁₃-θ_s of the flapping wing, and the second-order ordinary differential equation set is solved through the numerical value Obtaining steady state response function, flapping angular velocity/>, of flapping angle theta _wing of flapping wingA relationship among the steady state response function of the piezoelectric bimorph driver, the flutter period T _flap, the flutter frequency f _flap, and the driving voltage U of the piezoelectric bimorph driver;

f. The objective function of the overall comprehensive performance optimization problem of the distributed flexibility type flapping wing driving mechanism is as follows: average aerodynamic lift of a pair of flapping wings The overall energy conversion efficiency eta of the distributed flexibility type flapping wing driving mechanism and the overall mass m _tota l of the distributed flexibility type flapping wing driving mechanism;

Average aerodynamic lift of a pair of flapping wings Obtained by phyllin theory, the expression is as follows:

Wherein: ρ _air is the air density, R is the half-span length of the flapping wing, c (R) is the transformation function of the flapping wing chord length in the span direction, The average lift coefficient of the flapping wing in one flapping period is shown;

The whole energy conversion efficiency eta of the distributed flexibility type flapping wing driving mechanism can be obtained through a flapping wing pneumatic induction power formula of a hovering type flapping wing aircraft and an equivalent circuit model theory of a piezoelectric bimorph, and the expression is as follows:

Wherein: p _lift is the induced power of the flapping wings, P _elec is the electric power of the piezoelectric bimorph driver, U _eff is the effective value of the driving voltage U of the piezoelectric bimorph driver, and Z _eff is the equivalent impedance of the piezoelectric bimorph driver;

The optimal design variables are as follows: a shape parameter of a distributed compliance drive chain comprising: the length, thickness and width of the big rigidity section of horizontal shell fragment, the length, thickness and width of the little rigidity section of horizontal shell fragment, the length, thickness and width of the big rigidity section of vertical shell fragment, the length, thickness and width of the little rigidity section of vertical shell fragment, the shape parameter of piezoelectricity bimorph driver, it includes: the thickness t ₁ of the piezoelectric ceramic layer and the thickness t ₂ of the middle layer of the piezoelectric bimorph driver, the thickness t ₃ of the extension section, the width w ₂ of the fixed end and the width w ₁ of the free end of the piezoelectric bimorph driver, the length L ₂ of the driving section and the length L ₁ of the extension section of the piezoelectric bimorph driver, and the driving voltage U of the piezoelectric bimorph;

determining optimization constraint conditions according to design requirements: the height, width and span upper limit of the distributed flexibility type flapping wing driving mechanism and the upper limit of the driving voltage U of the piezoelectric bimorph driver;

g. for average aerodynamic lift of a pair of flapping wings Energy conversion efficiency eta of distributed compliance type flapping wing driving mechanism and inverse/>, of mass of distributed compliance type flapping wing driving mechanismThe three objective functions introduce corresponding weight coefficients and are linearly combined to form a unified objective function, and the expression is as follows:

Wherein: a ₁,a₂ and a ₃ are weight coefficients, and a ₁+a₂+a₃ =1; s is a unified objective function, and the minimum value is reached in the optimization process;

The weight coefficient is selected as follows: ① If the aircraft is expected to have stronger loading capacity and maneuvering performance, a ₁;② is increased, if the aircraft is expected to have stronger cruising ability, a ₂;③ is increased, if the aircraft is expected to realize a structure lightweight design so as to carry more effective load, a ₁ and a ₃ are increased at the same time;

And carrying out optimization solution on the design variables by adopting a constraint optimization algorithm, and obtaining the optimal design point of the distributed flexibility type flapping wing driving mechanism in a feasible domain.

The beneficial effects of adopting above-mentioned technical scheme to produce lie in:

The invention adopts the distributed flexibility type flapping wing driving mechanism, works by virtue of large-scale elastic deformation of the flexible component in the distributed flexibility type transmission chain, and has the advantages that the friction and abrasion problems of the traditional kinematic pair are avoided, and the stress concentration phenomenon of the component can be effectively relieved, so that the problems of short service life and low driving efficiency of the adopted rigid connecting rod-hinge type flapping wing driving mechanism at present can be effectively improved, and the service life of the adopted rigid connecting rod-hinge type flapping wing driving mechanism can be prolonged; meanwhile, the resonance characteristics between the flexible component, the piezoelectric bimorph driver and the flapping wings are utilized, so that the integral driving efficiency of the mechanism can be remarkably improved.

Aiming at the characteristic that the mechanism has strong power coupling effect among all components in the motion process, a complete machine comprehensive performance optimization design method is provided so as to rapidly and accurately calculate the dynamic response characteristic of the mechanism, and simultaneously, the comprehensive optimization can be carried out on various performance indexes of the mechanism.

Drawings

FIG. 1 is a schematic structural view of a distributed compliance ornithopter;

FIG. 2 is a cross-sectional view of FIG. 1;

FIG. 3 is a schematic illustration of the distributed compliance ornithopter drive mechanism of FIG. 1;

FIG. 4 is a schematic illustration of the configuration of the distributed compliance drive train of FIG. 3;

FIG. 5 is a schematic illustration of an actuation arm and hinge connection;

FIG. 6 is a schematic diagram of shape parameters of a piezoelectric bimorph actuator;

FIG. 7 is a schematic diagram of shape parameters of a piezoelectric bimorph actuator;

FIG. 8 is an equivalent "single degree of freedom second order linear vibration" system for a piezoelectric bimorph actuator;

FIG. 9 is a schematic diagram of an equivalent "multiple rigid-torsion spring" system of transverse spring plates in a distributed compliance drive train;

FIG. 10 is a schematic diagram of an equivalent "multiple rigid-torsion spring" system of left hand spring plates in a distributed compliance drive train;

FIG. 11 is a schematic diagram of an overall equivalent "multiple rigid-torsion spring" system for a distributed compliance drive train;

FIG. 12 is a flapping-wing equivalent "mass-moment of inertia-pneumatic damping" system;

FIG. 13 is a schematic diagram of an equivalent "mass-moment of inertia-spring-damper" system for a distributed compliance ornithopter drive mechanism;

FIG. 14 is a schematic diagram of parameters of the included angle between the root of the flapping wing and the connecting rod l ₁₇.

In the drawings: 1. a body; 2. flapping wings; 3. a flapping wing driving mechanism mounting frame; 4. a piezoelectric bimorph driver; 5. a left spring plate; 6. a right spring plate; 7. a transverse spring plate; 8. a flapping transmission part; 9. a left side flapping arm; 10. a right side flapping arm; 11. a drive chain fixing plate; 12. a flutter arm connecting sheet; 13. the flexible hinge is adjusted by the pre-bending angle; 14. the flapping wing is connected with the plate; 15. passively twisting the flexible hinge;

The azimuth description in the application takes the azimuth of the distributed flexible type ornithopter as the reference, the flight direction of the distributed flexible type ornithopter is the front, and the upper part is the upper part of the flight state of the distributed flexible type ornithopter.

Detailed Description

The invention will be described in further detail with reference to the drawings and the specific embodiments.

Standard parts used in the invention can be purchased from the market, special-shaped parts can be customized according to the description of the specification and the drawings, and the specific connection modes of the parts adopt conventional means such as mature bolts, rivets, welding, pasting and the like in the prior art, and the detailed description is omitted.

Referring to fig. 1 to 5, the embodiment comprises a fuselage 1, a flight control system, a flapping wing driving mechanism and a pair of flapping wings 2, wherein the flapping wing driving mechanism is a distributed compliance type flapping wing driving mechanism, and comprises a flapping wing driving mechanism mounting frame 3, a piezoelectric bimorph driver 4 arranged on the flapping wing driving mechanism mounting frame 3 and a distributed compliance type transmission chain;

The distribution compliance type transmission chain is a bilateral symmetry structure, and comprises a pair of vertical shrapnel and a transverse shrapnel 7, wherein the pair of vertical shrapnels are respectively a left shrapnel 5 and a right shrapnel 6, the left shrapnel 5 and the right shrapnel 6 are symmetrically arranged in a left-right opposite direction, and the connection structure is as follows: the upper end part of the left elastic piece 5 and the upper end part of the right elastic piece 6 are symmetrically and respectively deformed in an outward pre-bending way, the left end part of the transverse elastic piece 7 and the right end part of the transverse elastic piece are respectively deformed in an upward pre-bending way, then the left end part of the transverse elastic piece 7 and the upper end part of the left elastic piece 5 are fixedly bonded together, and the right end part of the transverse elastic piece 7 and the upper end part of the right elastic piece 6 are fixedly bonded together, so that a transmission chain with the distribution flexibility of the pre-stress force is formed; the distributed flexibility type transmission chain is provided with two flapping arms and a flapping transmission part 8, wherein the two flapping arms are a left flapping arm 9 and a right flapping arm 10 respectively, a left flapping arm supporting part is formed at the intersection of the left elastic piece 5 and the transverse elastic piece 7, and a left flapping arm 9 is formed at the connection part of the left elastic piece 5 at the outer end of the left flapping arm supporting part and the transverse elastic piece 7; the junction of the right elastic piece 6 and the transverse elastic piece 7 forms a right flapping arm supporting part, and the connection part of the right elastic piece 6 and the transverse elastic piece 7 at the outer end of the right flapping arm supporting part forms a right flapping arm 10; the left side flapping arm 9 and the right side flapping arm 10 incline upwards from the inner end to the outer end under the action of the pre-stress elasticity of the distributed flexible transmission chain, so that the distributed flexible transmission chain forms a bilateral symmetry structure; the middle part of the transverse spring plate 7 forms a flapping transmission part 8;

a pair of flapping wings 2 are symmetrically arranged on a left flapping arm 9 and a right flapping arm 10 respectively;

The fixed end of the piezoelectric bimorph driver 4 is fixed at the rear end of the distributed soft type transmission chain, and the free end of the piezoelectric bimorph driver is fixedly connected with the flapping transmission part 8 of the distributed soft type transmission chain;

The piezoelectric bimorph driver 4 drives the flapping transmission part 8 to vibrate up and down through the free end of the piezoelectric bimorph driver, and under the action of pre-stress elasticity, the distributed flexibility transmission chain drives the left flapping arm 9 and the right flapping arm 10 to do the same-frequency and same-amplitude flapping motion, so that the pair of flapping wings 2 are driven to do the flapping motion to generate lifting force.

The invention is further improved in that:

In the distributed flexibility type transmission chain, a flapping transmission part 8 of a transverse elastic sheet 7 is a transverse elastic sheet large rigidity section, the parts of the transverse elastic sheet 7 positioned at two sides of the flapping transmission part 8 are transverse elastic sheet small rigidity sections, and the rigidity of the transverse elastic sheet large rigidity section is larger than that of the transverse elastic sheet small rigidity section, wherein the transverse elastic sheet small rigidity section positioned at the left side of the flapping transmission part 8 is a transverse elastic sheet left side small rigidity section, and the transverse elastic sheet small rigidity section positioned at the right side of the flapping transmission part 8 is a transverse elastic sheet right side small rigidity section;

The lower parts of the left elastic piece 5 and the right elastic piece 6 are vertical elastic piece large rigidity sections, the upper parts of the left flapping arm 9 and the right flapping arm 10 are vertical elastic piece small rigidity sections, and the rigidity of the vertical elastic piece large rigidity sections is larger than that of the vertical elastic piece small rigidity sections; the vertical spring piece large rigidity section of the left spring piece 5 is a left spring piece large rigidity section, the vertical spring piece small rigidity section of the left spring piece 5 is a left spring piece small rigidity section, the vertical spring piece large rigidity section of the right spring piece 6 is a right spring piece large rigidity section, and the vertical spring piece small rigidity section of the right spring piece 6 is a right spring piece small rigidity section; the lower parts of the left elastic piece large rigidity section and the right elastic piece large rigidity section are respectively fixed on the flapping wing driving mechanism mounting frame 3 through a transmission chain fixing plate 11 so as to keep the flapping transmission part 8 in the vertical direction when vibrating.

The two flapping arms are connected with the flapping wing 2 through a hinged connection structure; the hinge type connecting structure comprises a flapping arm connecting sheet 12, a pre-bending angle adjusting flexible hinge 13, a flapping wing connecting sheet 14 and a passive torsion flexible hinge 15; the flapping arm connecting sheet 12 is connected with the flapping wing connecting sheet 14 through a pre-bending angle adjusting flexible hinge 13, the flapping wing connecting sheet 14 is connected with the flapping wing 2 through a passive torsion flexible hinge 15, the flapping arm connecting sheet 12 is fixedly bonded with the flapping arm, the angle of the pre-bending angle adjusting flexible hinge 13 enables the flapping wing 2 to be kept in a horizontal state when in a static state, and when the flapping arm performs flapping motion, the flapping wing 2 performs passive torsion motion around the front edge of the passive torsion flexible hinge 15 under the combined action of aerodynamic force and self inertia force.

The flapping wing driving mechanism mounting frame 3 is made of a woven carbon fiber laminated plate material, the bending part of the flapping wing driving mechanism mounting frame 3 is connected by a flexible bending film in the middle layer of the woven carbon fiber laminated plate to form a folding joint, and the folding joint of the woven carbon fiber laminated plate and the butt joint of the woven carbon fiber laminated plate are glued and fixed, so that the flapping wing driving mechanism mounting frame 3 forms an integrated structure; the left elastic sheet 5, the right elastic sheet 6 and the transverse elastic sheet 7 are formed by mutually laminating and bonding three polypropylene sheets with the same width, wherein the thicknesses of the two polypropylene sheets at the outer side are the same, and the rigidity is realized by the thickness of the polypropylene sheet at the middle layer.

The flapping arm connecting sheet 12 and the flapping wing connecting sheet 14 are made of carbon fiber laminated plates, and the pre-bending angle adjusting flexible hinge 13 and the passive torsion flexible hinge 15 are made of polyimide.

Referring to fig. 6-13, a design method of a distributed compliance type flapping wing driving mechanism comprises the following steps:

a. According to the principle of a centralized mass method, the piezoelectric bimorph driver 4 is simplified into an equivalent single-degree-of-freedom second-order linear vibration system which simultaneously comprises an equivalent mass block M _act,e, an equivalent linear damping C _act,e, an equivalent linear spring K _act,e and an equivalent piezoelectric driving force F _p; connecting the equivalent mass M _act,e with the ground through a moving pair along the vertical direction; the equivalent linear spring K _act,e and the equivalent linear damping C _act,e are mutually connected in parallel along the vertical direction, the upper ends of the equivalent linear spring K _act,e and the equivalent linear damping C _act,e are fixedly connected with the equivalent mass block M _act,e, and the lower ends of the equivalent linear spring K _act,e and the equivalent linear damping C _act,e are fixedly connected with the ground; the equivalent piezoelectric driving force F _p acts on the equivalent mass block M _act,e along the vertical direction, and in the linear range, the equivalent piezoelectric driving force F _p is in direct proportion to the electric field strength E _V along the thickness direction of the piezoelectric ceramic plate;

Namely: f _p＝λ_pE_V

Wherein: lambda _p is the force-electricity proportionality coefficient, and can be determined according to a mechanical-electrical coupling model of the piezoelectric ceramic material; e _V is a function of the piezoelectric bimorph driving voltage U and the driving frequency f _elec, and can be determined according to the equivalent circuit model theory of the piezoelectric bimorph; the displacement of the equivalent mass M _act,e along the vertical direction is defined as an equivalent linear displacement output x _act of the piezoelectric bimorph driver 4; the mass M _act,e of the equivalent mass M _act,e of the equivalent single-degree-of-freedom second-order linear vibration system and the rigidity K _act,e of the equivalent linear spring K _act,e are determined by the damping value C _act,e of the equivalent linear damping C _act,e through the width w ₂ of the fixed end, the width w ₁ of the free end, the length L ₂ of the driving end, the length L ₁ of the extension section, the thickness t ₁ of the piezoelectric ceramic layer, the thickness t ₂ of the middle layer and the thickness t ₃ of the extension section of the piezoelectric bimorph driver 4, and the specific expression is as follows:

m_act,e＝m_act·M(w_r,l_r,d_r)

Wherein: m _act is the true mass of the piezoelectric bimorph actuator, M (w _r,l_r,d_r) is the equivalent mass factor of the piezoelectric bimorph actuator 4, l _r is the length factor of the piezoelectric bimorph actuator 4, d _r is the thickness factor of the piezoelectric bimorph actuator 4, w _n is the nominal width of the piezoelectric bimorph actuator 4, w _r is the width factor of the piezoelectric bimorph actuator 4, w (x) is the width variation function of the piezoelectric bimorph actuator 4, As a function of the change in linear velocity along the length direction due to bending of the piezoelectric bimorph actuator 4,/>For the end speed of the piezoelectric bimorph driver 4, C ₄₄ is the bending flexibility coefficient of the piezoelectric bimorph cantilever beam, G _K(w_r,l_r) is the equivalent stiffness factor of the piezoelectric bimorph driver 4, and ζ is the equivalent damping ratio of the piezoelectric bimorph driver 4 (determined by experiment); wherein the method comprises the steps of m_act、M(w_r,l_r,d_r)、l_r、d_r、w_n、w_r、w(x)、/>G _K(w_r,l_r) is as follows:

wherein: ρ ₁ is the density of the piezoelectric ceramic, ρ ₂ is the density of the carbon fiber, and ρ ₃ is the density of the glass fiber.

The piezoelectric bimorph driver 4 adopts a configuration scheme with equal strength along the length direction, and the fixed end width w ₂, the free end width w ₁, the driving end length L ₂ and the extension length L ₁ should satisfy the following relation:

a) In the transverse spring 7, the flapping transmission part 8 is equivalent to a connecting rod l ₁₁;

In the left small rigidity section of the transverse elastic piece, a left flapping arm supporting part supports the transverse elastic piece 7, a torsion spring K ₁₁ is equivalent to a part between the left end of the flapping transmission part 8 and the left flapping arm supporting part, and the left flapping arm supporting part is equivalent to a torsion spring K ₁₃; the left end of the flapping transmission part 8 is equivalent to a connecting rod l ₁₂, the part between the torsional spring K ₁₃ and the torsional spring K ₁₁ is equivalent to a connecting rod l ₁₄, and the part of the left flapping arm 9 is equivalent to a connecting rod l ₁₆; the fixed connection of the flapping transmission part 8 and the small rigidity section at the left side of the transverse elastic sheet is equivalent to a fixed pair between a connecting rod l ₁₁ and a connecting rod l ₁₂;

In the right small rigidity section of the transverse elastic sheet, the parts corresponding to the torsion springs K ₁₁, K ₁₃, the connecting rod l ₁₂, the connecting rod l ₁₄ and the connecting rod l ₁₆ are respectively equivalent to the torsion springs K ₁₂, K ₁₄, the connecting rod l ₁₃, the connecting rod l ₁₅ and the connecting rod l ₁₇; the fixed connection of the flapping transmission part 8 and the small rigidity section on the right side of the transverse elastic sheet is equivalent to a fixed pair between a connecting rod l ₁₁ and a connecting rod l ₁₃;

the length of the connecting rod l ₁₁ is equal to the large-rigidity section of the transverse elastic piece, the connecting rod l ₁₂, the connecting rod l ₁₃, the connecting rod l ₁₄, the connecting rod l ₁₅ and the connecting rod l ₁₆, the length of the connecting rod l ₁₇ is determined by the 2R pseudo-rigid theory through the length of the small-rigidity section on the left side of the transverse elastic piece 7 and the small-rigidity section on the right side of the transverse elastic piece, the rigidity of the torsion springs K ₁₁, the torsion springs K ₁₂ and the torsion springs K ₁₃ is determined by the 2R pseudo-rigid theory through the section moment of inertia and the length of the small-rigidity section on the left side of the transverse elastic piece and the small-rigidity section on the right side of the transverse elastic piece; the specific expression is as follows:

s₁₁＝L_a

s₁₂＝s₁₃＝0.1L_b

s₁₄＝s₁₅＝0.44L_b

s₁₆＝s₁₇＝0.46L_b

Wherein: l _a is the length of a large-rigidity section of the transverse elastic sheet, L _b is the length of a small-rigidity section on the left side and the right side of the transverse elastic sheet, E _K is the Young modulus of a polypropylene material, I _b is the section moment of inertia of the small-rigidity section on the left side and the right side of the transverse elastic sheet, s ₁₁、s₁₂、s₁₃、s₁₄、s₁₅、s₁₆、s₁₇ respectively corresponds to the lengths of a connecting rod L ₁₁, a connecting rod L ₁₂, a connecting rod L ₁₃, a connecting rod L ₁₄, a connecting rod L ₁₅, a connecting rod L ₁₆ and a connecting rod L ₁₇, and K ₁₁、k₁₂、k₁₃、k₁₄ respectively corresponds to the rigidities of a torsion spring K ₁₁, a torsion spring K ₁₂, a torsion spring K ₁₃ and a torsion spring K ₁₄.

B) In the left spring 5;

In the left elastic piece large rigidity section, the part of the left elastic piece large rigidity section which is fixedly connected with the flapping wing driving mechanism mounting frame 3 through the transmission chain fixing plate 11 so as to keep the vertical direction is equivalent to a connecting rod l ₂₁, the part which is close to the upper part of the connecting rod l ₂₁ is equivalent to a torsion spring K ₂₁, and the part which is positioned above the torsion spring K ₂₁ is equivalent to a connecting rod l ₂₂;

In the small-rigidity section of the left elastic piece, the supporting part of the left flapping arm is equivalent to a torsion spring K ₂₃; the part between the torsion spring K ₂₃ and the connecting rod l ₂₂ is equivalent to the torsion spring K ₂₂, the part below the torsion spring K ₂₂ is equivalent to the connecting rod l ₂₃, the part between the torsion spring K ₂₂ and the torsion spring K ₂₃ is equivalent to the connecting rod l ₂₄, and the part of the left flapping arm 9 is equivalent to the connecting rod l ₂₅; the fixed connection between the left elastic piece large rigidity section and the left elastic piece small rigidity section is equivalent to a fixed pair between a connecting rod l ₂₂ and a connecting rod l ₂₃;

The length of the connecting rod l ₂₁ and the length of the connecting rod l ₂₂ are determined by the 1R pseudo-rigid body theory through the length of the left elastic sheet large-rigidity section, and the rigidity of the torsion spring K ₂₁ is determined by the 1R pseudo-rigid body theory through the section moment of inertia and the length of the left elastic sheet large-rigidity section; the length of the connecting rod l ₂₃, the connecting rod l ₂₄ and the connecting rod l ₂₅ is determined by the 2R pseudo-rigid body theory from the length of the small stiffness section of the left elastic sheet, the stiffness of the torsion spring K ₂₂ and the torsion spring K ₂₃ is determined by the 2R pseudo-rigid body theory from the section moment of inertia and the length of the small stiffness section of the left elastic sheet; the specific expression is as follows:

s₂₁＝0.2L_c

s₂₂＝0.8L_c

s₂₃＝0.1L_d

s₂₄＝0.44L_d

s₂₅＝0.46L_d

Wherein: l _c is the length of the left elastic piece large rigidity section, L _d is the length of the left elastic piece small rigidity section, I _c is the cross-sectional moment of inertia of the left elastic piece large rigidity section, I _d is the cross-sectional moment of inertia of the left elastic piece small rigidity section, s ₂₁、s₂₂、s₂₃、s₂₄、s₂₅ is respectively corresponding to the lengths of a connecting rod L ₂₁, a connecting rod L ₂₂, a connecting rod L ₂₃, a connecting rod L ₂₄ and a connecting rod L ₂₅, and K ₂₁、k₂₂、k₂₃ is respectively corresponding to the rigidities of a torsion spring K ₂₁, a torsion spring K ₂₂ and a torsion spring K ₂₃.

In the right elastic sheet 6, the parts corresponding to the connecting rod l ₂₁, the torsion spring K ₂₁, the connecting rod l ₂₂, the torsion spring K ₂₂, the torsion spring K ₂₃, the connecting rod l ₂₃, the connecting rod l ₂₄ and the connecting rod l ₂₅ are respectively equivalent to the connecting rod l ₃₁, the torsion spring K ₃₁, the connecting rod l ₃₂, the torsion spring K ₃₂, the torsion spring K ₃₃, the connecting rod l ₃₃, the connecting rod l ₃₄ and the connecting rod l ₃₅; the fixed connection between the right elastic piece large rigidity section and the right elastic piece small rigidity section is equivalent to a fixed pair between a connecting rod l ₃₂ and a connecting rod l ₃₃;

The length of the connecting rod l ₃₁ and the length of the connecting rod l ₃₂ are determined by the 1R pseudo-rigid body theory through the length of the large-rigidity section of the right elastic sheet, and the rigidity of the torsion spring K ₃₁ is determined by the 1R pseudo-rigid body theory through the section moment of inertia and the length of the large-rigidity section of the right elastic sheet; the length of the connecting rod l ₃₃, the connecting rod l ₃₄ and the connecting rod l ₃₅ is determined by the 2R pseudo-rigid body theory from the length of the small stiffness section of the right elastic sheet, the stiffness of the torsion spring K ₃₂ and the torsion spring K ₃₃ is determined by the 2R pseudo-rigid body theory from the section moment of inertia and the length of the small stiffness section of the right elastic sheet; the specific expression is as follows:

s₃₁＝0.2L_e

s₃₂＝0.8L_e

s₃₃＝0.1L_f

s₃₄＝0.44L_f

s₃₅＝0.46L_f

Wherein: l _e is the length of the large-rigidity section of the right elastic sheet, L _f is the length of the small-rigidity section of the right elastic sheet, I _e is the cross-sectional moment of inertia of the large-rigidity section of the right elastic sheet, I _f is the cross-sectional moment of inertia of the small-rigidity section of the right elastic sheet, s ₃₁、s₃₂、s₃₃、s₃₄、s₃₅ respectively corresponds to the lengths of a connecting rod L ₃₁, a connecting rod L ₃₂, a connecting rod L ₃₃, a connecting rod L ₃₄ and a connecting rod L ₃₅, and K ₃₁、k₃₂、k₃₃ respectively corresponds to the rigidities of a torsion spring K ₃₁, a torsion spring K ₃₂ and a torsion spring K ₃₃.

The geometric parameters of the left spring and the right spring are identical, so the following relation exists:

L_c＝L_e

L_d＝L_f

I_c＝I_e

I_d＝I_f

The left side flapping arm 9 is equivalent to the tangent fixedly connection of the connecting rod l ₂₅ and the connecting rod l ₁₆; the right side flapping arm 10 is equivalent to the tangent fixedly connection of a connecting rod l ₃₅ and a connecting rod l ₁₇; the Y-shaped connecting structure in the flexible transmission chain is simulated and distributed; and a connecting rod l ₂₁ and a connecting rod l ₃₁ which are fixedly connected with the installation frame 3 of the flapping wing driving mechanism in the vertical direction are kept, so that the distributed flexible transmission chain forms a whole equivalent multi-rigid-body torsion spring system in a shape of a door;

c. According to the principle of equivalent conversion between the distributed load and the concentrated load, the aerodynamic load applied to the flapping wing 2 along the flapping plane in the motion process is equivalent to the concentrated aerodynamic resistance F _wing acting on the pressure center of the flapping wing; the centralized aerodynamic drag F _wing is positioned in the flapping plane of the flapping wing, is vertical to the spanwise direction of the flapping wing, and is opposite to the movement direction of the flapping wing; according to the principle of leaf element, the aerodynamic damping coefficient of the flapping wing 2 in different positions and motion states is obtained by means of slice integration And the distance l _aero between the centre of pressure and the root axis; the mass characteristics of the flapping wing 2 are simulated by using a rigid rod l _wing, wherein the mass m _wing of the rigid rod l _wing is equal to the real mass of the flapping wing 2, the moment of inertia J _wing of the rigid rod relative to the wing root axis is equal to the real moment of inertia of the flapping wing 2 relative to the wing root axis, and an equivalent 'mass-moment of inertia-pneumatic damping' system of the flapping wing 2 is established; wherein the expression of the equivalent concentrated aerodynamic drag force F _wing of the flapping wing 2 and the aerodynamic damping moment M _wing formed at the root of the flapping wing 2 is as follows:

M_wing＝F_wing·l_aero

Wherein: θ _wing is the flapping angle of the flapping wing 2, Aerodynamic damping coefficient for flapping angular velocity of flapping wing 2Is the flapping angle theta _wing and the flapping angular velocity/>, of the flapping wing 2And also the geometry of the flapping wings, can be determined by performing aerodynamic experiments;

d. According to the actual position relation of each component in the distributed flexibility type flapping wing driving mechanism, an equivalent multi-rigid-torsion spring system of a single-degree-of-freedom second-order linear vibration system and an equivalent mass-moment-inertia-pneumatic damping system of a distributed flexibility type transmission chain are subjected to model assembly, and an equivalent mass block M _act,e in the equivalent single-degree-of-freedom second-order vibration system of a piezoelectric bimorph driver 4 is fixedly connected with a connecting rod l ₁₁ in the equivalent multi-rigid-torsion spring system of the distributed flexibility type transmission chain; the root of the flapping wing 2 in the equivalent 'mass-moment of inertia-pneumatic damping' system of the pair of flapping wings 2 is fixedly connected with a connecting rod l ₁₆, a connecting rod l ₂₅, a connecting rod l ₁₇ and a connecting rod l ₃₅ in the equivalent 'multi-rigid-body-torsion spring' system of the distributed soft type transmission chain respectively, the included angle between the root of the left flapping wing and the connecting rod l ₁₆ is theta _s, and the included angle between the root of the right flapping wing and the connecting rod l ₁₇ is theta _s, so that the equivalent 'mass-moment of inertia-spring-damping' system of the distributed soft type flapping wing driving mechanism can be built;

e. The following three independent motion parameters in the equivalent mass-moment of inertia-spring-damping system of the split-distribution flexibility type flapping wing driving mechanism are defined as generalized displacement: equivalent linear displacement output x _act of the piezoelectric bimorph actuator 4, rotation angle theta ₁₁ of torsion spring K ₁₁, rotation angle theta ₁₃ of torsion spring K ₁₃; a generalized displacement vector q= [ x _act θ₁₁ θ₁₃]^T ] is defined accordingly; defining a system generalized external force vector corresponding to the generalized displacement as: f= [ F _p 0 0]^T; defining bilateral symmetry motion constraints of the system as: θ ₁₁＝θ₁₂、θ₁₃＝θ₁₄; q and F are substituted into a Lagrangian equation of a second type, and a three-degree-of-freedom second-order system forced vibration equation set of a piezoelectric-structure-flow field coupling complete machine dynamics model of the distributed flexibility type flapping wing driving mechanism is established as follows:

The input excitation of the 'piezoelectric-structure-flow field' coupling complete machine dynamics model of the distributed flexibility type flapping wing driving mechanism is the driving voltage U of the piezoelectric bimorph driver 4, the output response is the flapping angle theta _wing＝θ₁₁+θ₁₃-θ_s of the flapping wing 2, and a second-order ordinary differential equation set is solved through a numerical value Obtaining steady state response function, flapping angular velocity/>, of flapping angle theta _wing of flapping wing 2A relation among the steady-state response function of the piezoelectric bimorph driver 4, the flutter period T _flap, the flutter frequency f _flap, and the driving voltage U;

f. the objective function of the overall comprehensive performance optimization problem of the distributed flexibility type flapping wing driving mechanism is as follows: average aerodynamic lift of a pair of flapping wings 2 The overall energy conversion efficiency eta of the distributed flexibility type flapping wing driving mechanism and the overall mass m _tot_al of the distributed flexibility type flapping wing driving mechanism;

Wherein: ρ _air is the air density, R is the half-span length of the flapping wing 2, c (R) is the transformation function of the flapping wing 2 chord length in the spanwise direction; The average lift coefficient of the flapping wing 2 in a flapping period can be determined according to the geometry of the flapping wing and the passive torsion angle around the front edge of the flapping wing, wherein the passive torsion angle of the flapping wing around the front edge of the flapping wing can be determined by experimental observation;

the whole energy conversion efficiency eta of the distributed flexibility type flapping wing driving mechanism can be obtained through a flapping wing pneumatic induction power formula and a piezoelectric bimorph equivalent circuit model theory, and the expression is as follows:

The whole machine mass m _tota l of the distributed flexibility type flapping wing driving mechanism is determined by the shape parameters of a distributed flexibility type transmission chain, the material density, the shape parameters of a piezoelectric bimorph driver, the density of a piezoelectric ceramic material, the density of a carbon fiber material and the density of a glass fiber material;

The optimal design variables are as follows: a shape parameter of a distributed compliance drive chain comprising: the length, thickness and width of the large rigidity section of the horizontal spring plate, the length, thickness and width of the small rigidity section of the horizontal spring plate, the length, thickness and width of the large rigidity section of the vertical spring plate, the length, thickness and width of the small rigidity section of the vertical spring plate, and the shape parameters of the piezoelectric bimorph driver 4, which comprises: the thickness t ₁ of the piezoelectric ceramic layer of the piezoelectric bimorph driver 4, the thickness t ₂ of the middle layer, the thickness t ₃ of the extension section, the width w ₂ of the fixed end and the width w ₁ of the free end of the piezoelectric bimorph driver 4, the length L ₂ of the driving section of the piezoelectric bimorph driver 4, the length L ₁ of the extension section and the driving voltage U of the piezoelectric bimorph;

determining optimization constraint conditions according to design requirements: the height, width and span upper limit of the distributed flexibility type flapping wing driving mechanism and the upper limit of the piezoelectric bimorph driving voltage U;

g. For average aerodynamic lift of a pair of flapping wings 2 Energy conversion efficiency eta of distributed compliance type flapping wing driving mechanism and inverse/>, of mass of distributed compliance type flapping wing driving mechanismThe three objective functions introduce corresponding weight coefficients and are linearly combined to form a unified objective function, and the expression is as follows:

Claims

1. A distributed compliance type ornithopter comprising a fuselage (1), a flight control system, a flapping wing driving mechanism and a pair of flapping wings (2), characterized in that: the flapping wing driving mechanism is a distributed flexibility type flapping wing driving mechanism and comprises a flapping wing driving mechanism mounting frame (3), a piezoelectric bimorph driver (4) arranged on the flapping wing driving mechanism mounting frame (3) and a distributed flexibility type transmission chain;

The utility model provides a distribution compliance type drive chain is bilateral symmetry structure, and it includes a pair of vertical shell fragment and a horizontal shell fragment (7), a pair of vertical shell fragment is left side shell fragment (5) and right side shell fragment (6) respectively, left side shell fragment (5) with bilateral symmetry sets up about right side shell fragment (6), and their connection structure is: the method comprises the steps of firstly symmetrically pre-bending and deforming the upper end part of a left elastic piece (5) and the upper end part of a right elastic piece (6) outwards respectively, pre-bending and deforming the left end part of a transverse elastic piece (7) and the right end part of the transverse elastic piece upwards respectively, then fixedly bonding the left end part of the transverse elastic piece (7) and the upper end part of the left elastic piece (5), and fixedly bonding the right end part of the transverse elastic piece (7) and the upper end part of the right elastic piece (6) together, so that the distributed soft transmission chain with pre-stress force is formed; the distributed flexibility type transmission chain is provided with two flapping arms and a flapping transmission part (8), the two flapping arms are a left flapping arm (9) and a right flapping arm (10) respectively, a left flapping arm supporting part is formed at the intersection of the left elastic piece (5) and the transverse elastic piece (7), and the left flapping arm (9) is formed at the connection part of the left elastic piece (5) at the outer end of the left flapping arm supporting part and the transverse elastic piece (7); a right-side flapping arm supporting part is formed at the intersection of the right-side elastic piece (6) and the transverse elastic piece (7), and a right-side flapping arm (10) is formed at the connection part of the right-side elastic piece (6) and the transverse elastic piece (7) at the outer end of the right-side flapping arm supporting part; the left side flapping arm (9) and the right side flapping arm (10) incline upwards from the inner end to the outer end under the action of the pre-stress elasticity of the distributed soft transmission chain, so that the distributed soft transmission chain forms a bilateral symmetry structure; the middle part of the transverse elastic sheet (7) forms the flapping transmission part (8);

In the distributed flexibility type transmission chain, the flapping transmission part (8) of the transverse elastic piece (7) is a transverse elastic piece large rigidity section, the parts of the transverse elastic piece (7) positioned at two sides of the flapping transmission part (8) are transverse elastic piece small rigidity sections, and the rigidity of the transverse elastic piece large rigidity section is larger than that of the transverse elastic piece small rigidity section, wherein the transverse elastic piece small rigidity section positioned at the left side of the flapping transmission part (8) is a transverse elastic piece left side small rigidity section, and the transverse elastic piece small rigidity section positioned at the right side of the flapping transmission part (8) is a transverse elastic piece right side small rigidity section;

The lower parts of the left elastic piece (5) and the right elastic piece (6) are vertical elastic piece large rigidity sections, the upper parts of the left flapping arm (9) and the right flapping arm (10) are vertical elastic piece small rigidity sections, and the rigidity of the vertical elastic piece large rigidity sections is larger than that of the vertical elastic piece small rigidity sections; the vertical spring piece high-rigidity section of the left spring piece (5) is a left spring piece high-rigidity section, the vertical spring piece low-rigidity section of the left spring piece (5) is a left spring piece low-rigidity section, the vertical spring piece high-rigidity section of the right spring piece (6) is a right spring piece high-rigidity section, and the vertical spring piece low-rigidity section of the right spring piece (6) is a right spring piece low-rigidity section; the lower part of the left elastic piece large rigidity section and the lower part of the right elastic piece large rigidity section are respectively fixed on the flapping wing driving mechanism mounting frame (3) through a transmission chain fixing plate (11) so as to keep the flapping transmission part (8) in a vertical direction when vibrating;

the pair of flapping wings (2) are symmetrically arranged on the left flapping arm (9) and the right flapping arm (10) respectively;

The fixed end of the piezoelectric bimorph driver (4) is fixed at the rear end of the distributed soft type transmission chain, and the free end of the piezoelectric bimorph driver is fixedly connected with a flapping transmission part (8) of the distributed soft type transmission chain;

The piezoelectric bimorph driver (4) drives the flapping transmission part (8) to vibrate up and down through the free end of the piezoelectric bimorph driver, under the action of the pre-stress elasticity, the distributed flexibility type transmission chain drives the left side flapping arm (9) and the right side flapping arm (10) to do the same-frequency same-amplitude flapping motion, so that a pair of flapping wings (2) are driven to do the flapping motion to generate lifting force.

2. A distributed compliance ornithopter according to claim 1, wherein: the two flapping arms are connected with the flapping wings (2) through a hinged connection structure; the hinge type connecting structure comprises a flapping arm connecting sheet (12), a pre-bending angle adjusting flexible hinge (13), a flapping wing connecting sheet (14) and a passive torsion flexible hinge (15); the flapping arm connecting piece (12) is connected with the flapping wing connecting plate (14) through the pre-bending angle adjusting flexible hinge (13), the flapping wing connecting plate (14) is connected with the flapping wing (2) through the passive torsion flexible hinge (15), the flapping arm connecting piece (12) is fixedly bonded with the flapping arm, the angle of the pre-bending angle adjusting flexible hinge (13) enables the flapping wing (2) to be in a horizontal state when in a static state, and when the flapping arm performs flapping motion, the flapping wing (2) performs passive torsion motion around the front edge of the passive torsion flexible hinge (15) under the combined action of aerodynamic force and self inertia force.

3. A distributed compliance ornithopter according to claim 1, wherein: the flapping wing driving mechanism mounting frame (3) is made of a woven carbon fiber laminated plate material, the bending part of the flapping wing driving mechanism mounting frame (3) is connected by a flexible bending film of an intermediate layer of the woven carbon fiber laminated plate to form a folding seam, and the folding seam of the woven carbon fiber laminated plate and the butt seam of the woven carbon fiber laminated plate are glued and fixed, so that the flapping wing driving mechanism mounting frame (3) forms an integrated structure; the left elastic sheet (5), the right elastic sheet (6) and the transverse elastic sheet (7) are formed by mutually laminating and bonding three polypropylene sheets with the same width, wherein the thicknesses of the two polypropylene sheets at the outer side are the same, and the rigidity is realized through the thickness of the polypropylene sheet at the middle layer.

4. A distributed compliance ornithopter according to claim 2, wherein: the flapping arm connecting sheet (12) and the flapping wing connecting sheet (14) are made of carbon fiber laminated plates, and the pre-bending angle adjusting flexible hinge (13) and the passive torsion flexible hinge (15) are made of polyimide.

5. The design method of the distributed flexibility type flapping wing driving mechanism comprises a flapping wing driving mechanism mounting frame (3), a piezoelectric bimorph driver (4) arranged on the flapping wing driving mechanism mounting frame (3) and a distributed flexibility type transmission chain;

the design method of the distributed flexibility type flapping wing driving mechanism is characterized by comprising the following steps of:

a. According to the principle of a centralized mass method, the piezoelectric bimorph driver (4) is simplified into an equivalent single-degree-of-freedom second-order linear vibration system which simultaneously comprises an equivalent mass block M _act,e, an equivalent linear damping C _act,e, an equivalent linear spring K _act,e and an equivalent piezoelectric driving force F _p; the equivalent mass M _act,e is connected to the ground by a mobile pair in the vertical direction: the equivalent linear spring K _act,e and the equivalent linear damping C _act,e are mutually connected in parallel along the vertical direction, the upper ends of the equivalent linear spring K _act,e and the equivalent linear damping C _act,e are fixedly connected with the equivalent mass block M _act,e, and the lower ends of the equivalent linear spring K _act,e and the equivalent linear damping C _act,e are fixedly connected with the ground; the equivalent piezoelectric driving force F _p acts on the equivalent mass block M _act,e along the vertical direction, and in the linear range, the equivalent piezoelectric driving force F _p is in direct proportion to the electric field strength E _V along the thickness direction of the piezoelectric ceramic plate;

Namely: f _p＝λ_pE_V

Wherein: lambda _p is the force-electric proportionality coefficient; e _V is a function of the piezoelectric bimorph drive voltage U and the drive frequency f _elec; defining the displacement of the equivalent mass M _act,e along the vertical direction as an equivalent linear displacement output x _act of the piezoelectric bimorph driver (4);

b. The distributed flexibility type transmission chain is simplified into an equivalent multi-rigid-body torsion spring system formed by connecting a plurality of sections of rigid connecting rods and torsion springs according to the theory of 1R and 2R pseudo rigid body models of large-deformation flexible beams, and then:

a) In the transverse elastic sheet (7), the flapping transmission part (8) is equivalent to a connecting rod l ₁₁;

In the small-rigidity section at the left side of the transverse elastic piece, the left-side flapping arm supporting part supports the transverse elastic piece (7), a torsion spring K ₁₁ is equivalent at a position between the left end of the flapping transmission part (8) and the left-side flapping arm supporting part, and the left-side flapping arm supporting part is equivalent to a torsion spring K ₁₃; the left end of the flapping transmission part (8) is equivalent to a connecting rod l ₁₂ with the torsion spring K ₁₁, the part between the torsion spring K ₁₃ and the torsion spring K ₁₁ is equivalent to a connecting rod l ₁₄, and the part of the left flapping arm (9) is equivalent to a connecting rod l ₁₆; the fixed connection of the flapping transmission part (8) and the small rigidity section at the left side of the transverse elastic piece is equivalent to a fixed pair between a connecting rod l ₁₁ and a connecting rod l ₁₂;

In the small rigidity section on the right side of the transverse elastic piece, the parts corresponding to the torsion spring K ₁₁, the torsion spring K ₁₃, the connecting rod l ₁₂ and the connecting rod l ₁₄ and the connecting rod l ₁₆ are respectively equivalent to the torsion spring K ₁₂, the torsion spring K ₁₄, the connecting rod l ₁₃, the connecting rod l ₁₅ and the connecting rod l ₁₇; the fixed connection of the flapping transmission part (8) and the small rigidity section on the right side of the transverse elastic piece is equivalent to a fixed pair between a connecting rod l ₁₁ and a connecting rod l ₁₃;

b) In the left spring piece (5);

In the left elastic piece large-rigidity section, the part of the left elastic piece large-rigidity section which is fixedly connected with the flapping wing driving mechanism mounting frame (3) through the transmission chain fixing plate (11) so as to keep the vertical direction is equivalent to a connecting rod l ₂₁, the part which is close to the upper part of the connecting rod l ₂₁ is equivalent to a torsion spring K ₂₁, and the part which is positioned above the torsion spring K ₂₁ is equivalent to a connecting rod l ₂₂;

In the left elastic piece small rigidity section, the left flapping arm supporting part is equivalent to a torsion spring K ₂₃; the part between the torsion spring K ₂₃ and the connecting rod l ₂₂ is equivalent to a torsion spring K ₂₂, the part below the torsion spring K ₂₂ is equivalent to a connecting rod l ₂₃, the part between the torsion spring K ₂₂ and the torsion spring K ₂₃ is equivalent to a connecting rod l ₂₄, and the part of the left flapping arm (9) is equivalent to a connecting rod l ₂₅; the fixed connection between the left elastic piece large rigidity section and the left elastic piece small rigidity section is equivalent to a fixed pair between a connecting rod l ₂₂ and a connecting rod l ₂₃;

In the right elastic sheet (6), the parts corresponding to the connecting rod l ₂₁, the torsion spring K ₂₁, the connecting rod l ₂₂, the torsion spring K ₂₂, the torsion spring K ₂₃, the connecting rod l ₂₃, the connecting rod l ₂₄ and the connecting rod l ₂₅ are respectively equivalent to a connecting rod l ₃₁, a torsion spring K ₃₁, a connecting rod l ₃₂, a torsion spring K ₃₂, a torsion spring K ₃₃, a connecting rod l ₃₃, a connecting rod l ₃₄ and a connecting rod l ₃₅; the fixed connection between the right elastic piece large rigidity section and the right elastic piece small rigidity section is equivalent to a fixed pair between a connecting rod l ₃₂ and a connecting rod l ₃₃;

The left side flapping arm (9) is equivalent to the tangent fixedly connection of the connecting rod l ₂₅ and the connecting rod l ₁₆; equivalent the right side flapping arm (10) to the tangent fixedly connection of the connecting rod l ₃₅ and the connecting rod l ₁₇; so as to simulate a herringbone connection structure in the distributed soft transmission chain; the connecting rod l ₂₁ and the connecting rod l ₃₁ which are fixedly connected with the flapping wing driving mechanism mounting frame (3) in the vertical direction are kept, so that the distributed flexibility type transmission chain forms an equivalent multi-rigid-body torsion spring system in a shape of a door;

c. According to the principle of equivalent conversion between distributed load and concentrated load, the aerodynamic load along the flapping plane borne by the flapping wing (2) in the motion process is equivalent to the concentrated aerodynamic resistance F _wing acting on the pressure center of the flapping wing; the centralized aerodynamic drag F _wing is positioned in the flapping plane of the flapping wing, is perpendicular to the spanwise direction of the flapping wing, and is opposite to the movement direction of the flapping wing; according to the principle of leaf element, the aerodynamic damping coefficient of the flapping wing (2) in different positions and motion states is obtained by means of slice integration And the distance l _aero between the centre of pressure and the root axis; simulating the mass characteristics of the flapping wing (2) by using a rigid rod l _wing, wherein the mass m _wing of the rigid rod l _wing is equal to the real mass of the flapping wing (2), and the moment of inertia J _wing of the rigid rod relative to the wing root axis is equal to the real moment of inertia of the flapping wing (2) relative to the wing root axis, so as to establish an equivalent 'mass-moment of inertia-pneumatic damping' system of the flapping wing (2); wherein the expression of the equivalent concentrated aerodynamic drag force F _wing of the flapping wing (2) and the aerodynamic damping moment M _wing formed at the root of the flapping wing (2) is as follows:

M_wing＝F_wing·l_aero

Wherein: theta _wing is the flapping angle of the flapping wing (2), Is the flapping angular velocity of the flapping wing (2); pneumatic damping coefficientIs the flapping angle theta _wing and the flapping angular velocity/>, of the flapping wingIs a function of (2);

d. According to the actual position relation of each component in the distributed flexibility type flapping wing driving mechanism, the equivalent single-degree-of-freedom second-order linear vibration system of the piezoelectric bimorph driver (4) is subjected to model assembly, the equivalent 'mass-moment of inertia-pneumatic damping' system of the distributed flexibility type transmission chain is subjected to model assembly, and an equivalent mass M _act,e in the equivalent single-degree-of-freedom second-order vibration system of the piezoelectric bimorph driver (4) is fixedly connected with a connecting rod l ₁₁ in the equivalent 'multi-rigid-body-torsion spring' system of the distributed flexibility type transmission chain; the wing root of the flapping wing (2) in the pair of flapping wing equivalent 'mass-moment of inertia-pneumatic damping' systems is respectively fixedly connected with the connecting rod l ₁₆, the connecting rod l ₂₅ and the connecting rod l ₁₇ in the distributed compliance transmission chain equivalent 'multi-rigid body-torsion spring' system, the included angle between the root of the left flapping wing and the connecting rod l ₁₆ is theta _s, and the included angle between the root of the right flapping wing and the connecting rod l ₁₇ is theta _s, so that the equivalent 'mass-moment of inertia-spring-damping' system of the distributed compliance flapping wing driving mechanism can be built;

e. The following three independent motion parameters in the equivalent mass-moment of inertia-spring-damping system of the distributed flexibility type flapping wing driving mechanism are taken to be defined as generalized displacement: an equivalent linear displacement output x _act of the piezoelectric bimorph driver (4), a rotation angle theta ₁₁ of the torsion spring K ₁₁ and a rotation angle theta ₁₃ of the torsion spring K ₁₃; a generalized displacement vector q= [ x _act θ₁₁θ₁₃]^T ] is defined accordingly; defining a system generalized external force vector corresponding to the generalized displacement as: f= [ F _p 0 0]^T; defining bilateral symmetry motion constraints of the system as: θ ₁₁＝θ₁₂、θ₁₃＝θ₁₄; q and F are substituted into a second Lagrangian equation, and a three-degree-of-freedom second-order system forced vibration equation set of a piezoelectric-structure-flow field coupling complete machine dynamics model of the distributed flexibility type flapping wing driving mechanism is established as follows:

The input excitation of the piezoelectric-structure-flow field coupling complete machine dynamics model of the distributed flexibility type flapping wing driving mechanism is the driving voltage U of the piezoelectric bimorph driver (4), the output response is the flapping angle theta _wing＝θ₁₁+θ₁₃-θ_s of the flapping wing (2), and a second-order ordinary differential equation set is solved through a numerical value Obtaining a steady state response function and a flapping angular velocity/>, of a flapping angle theta _wing of the flapping wingA relation between a steady state response function of the piezoelectric bimorph driver (4), a flutter period T _flap, a flutter frequency f _flap and a driving voltage U of the piezoelectric bimorph driver;

f. the objective function of the overall comprehensive performance optimization problem of the distributed flexibility type flapping wing driving mechanism is three as follows: average aerodynamic lift of a pair of said flapping wings (2) The overall energy conversion efficiency eta of the distributed flexibility type flapping wing driving mechanism is equal to the overall mass m _total of the distributed flexibility type flapping wing driving mechanism;

Average aerodynamic lift of a pair of said flapping wings Obtained by phyllin theory, the expression is as follows:

Wherein: ρ _air is the air density, R is the half-span length of the flapping wing (2), c (R) is the transformation function of the chord length of the flapping wing (2) in the span direction, An average lift coefficient for the flapping wing (2) in one flapping cycle;

the whole energy conversion efficiency eta of the distributed flexibility type flapping wing driving mechanism is obtained through a flapping wing pneumatic induction power formula of a hovering type flapping wing aircraft and an equivalent circuit model theory of a piezoelectric bimorph, and the expression is as follows:

Wherein: p _lift is the induction power of the flapping wing, P _elec is the electric power of the piezoelectric bimorph driver, U _eff is the effective value of the driving voltage U of the piezoelectric bimorph driver, and Z _eff is the equivalent impedance of the piezoelectric bimorph driver;

The optimal design variables are as follows: shape parameters of the distributed compliance drive train, comprising: the length, thickness and width of the big rigidity section of horizontal shell fragment, the length, thickness and width of the little rigidity section of horizontal shell fragment, the length, thickness and width of the big rigidity section of vertical shell fragment, the length, thickness and width of the little rigidity section of vertical shell fragment, the shape parameter of piezoelectricity bimorph driver (4), it includes: the thickness t ₁ of the piezoelectric ceramic layer, the thickness t ₂ of the middle layer and the thickness t ₃ of the extension section of the piezoelectric bimorph driver (4), the width w ₂ of the fixed end and the width w ₁ of the free end of the piezoelectric bimorph driver (4), the length L ₂ of the driving section and the length L ₁ of the extension section of the piezoelectric bimorph driver (4), and the driving voltage U of the piezoelectric bimorph;

Determining optimization constraint conditions according to design requirements: the height, width and span upper limit of the distributed flexibility type flapping wing driving mechanism and the upper limit of the driving voltage U of the piezoelectric bimorph driver (4);

g. Is the average aerodynamic lift of a pair of said flapping wings (2) Energy conversion efficiency eta of the distributed compliance type flapping wing driving mechanism and inverse/>, of mass of the distributed compliance type flapping wing driving mechanismThe three objective functions introduce corresponding weight coefficients and are linearly combined to form a unified objective function, and the expression is as follows: