A distributed flexibility flapping wing drive mechanism and its design method

Abstract

The present invention discloses a distributed flexibility flapping wing drive mechanism and its design method, belonging to the technical field of flapping wing aircraft. The distributed flexibility flapping wing drive mechanism includes a flapping wing drive mechanism mounting frame, a piezoelectric bimorph driver and a distributed flexibility transmission chain arranged on the flapping wing drive mechanism mounting frame; the distributed flexibility transmission chain includes a pair of vertical elastic sheets and a horizontal elastic sheet, and the distributed flexibility transmission chain has two flapping arms and a flapping transmission part; the fixed end of the piezoelectric bimorph driver is fixed at the rear end of the distributed flexibility transmission chain; the method includes a. simplifying the piezoelectric bimorph driver into an equivalent single-degree-of-freedom second-order linear vibration system; b. simplifying the distributed flexibility transmission chain into an equivalent "multi-rigid body - torsion spring" system; c. obtaining the aerodynamic drag and moment of the flapping wing; d. performing model assembly; e. establishing a forced vibration equation set; f. taking the objective function of the optimization problem; g. optimizing the design. It has the characteristics of long working life and high flight efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of flapping-wing aircrafts. Background Art

[0002] The flapping-wing drive mechanism is the power system of a bionic flapping-wing aircraft. Its configuration scheme and dynamic performance have an important impact on the flight ability of the flapping-wing aircraft. Traditional flapping-wing drive mechanisms all adopt a configuration scheme combining rigid connecting rods and friction-type kinematic pairs, and have been widely used in large-scale and centimeter-scale flapping-wing aircrafts. However, when the size of the flapping-wing aircraft is reduced to the millimeter level, this type of "rigid connecting rod - friction kinematic pair" flapping-wing drive mechanism will have various problems such as a decrease in component strength, severe wear of kinematic pairs, and difficulty in increasing the movement frequency. Therefore, people have to continue to explore other new mechanism configuration schemes.

[0003] The Wood team at Harvard University developed a carbon fiber rigid thin plate slider-rocker flapping-wing drive mechanism integrally connected by polyimide film flexible hinges, which is used to equip coin-sized "Robobee" and "HMF" series of micro piezoelectric flapping-wing aircrafts, and its movement frequency can reach more than 100 Hz. However, during the high-frequency movement process of this type of concentrated flexibility flapping-wing drive mechanism, obvious stress concentration phenomena will occur at the positions of the flexible hinges, thus greatly shortening its service life. Wuhan University of Science and Technology designed a spatial four-bar mechanism using flexible support rods, thereby reducing the number of components and kinematic pairs in the transmission chain, achieving a weight reduction effect, and at the same time, the energy consumption of the prime mover can be saved by relying on the resonance characteristics of the flexible components. However, this mechanism still cannot avoid the use of friction-type kinematic pairs, so it is not suitable for high-frequency movement either.

[0004] To enable the flapping wing drive mechanism to meet the expected performance requirements, researchers still need to explore reasonable optimization design methods. For traditional "rigid link - friction kinematic pair" and concentrated flexibility type flapping wing drive mechanisms, researchers often independently model and optimize the prime mover, transmission chain, and flapping wing, and cannot evaluate the influence of the dynamic coupling effect between components on the overall performance of the drive mechanism. Therefore, researchers have continued to explore a large number of modeling and design methods applicable to multi-component coupling analysis. Shanghai Jiao Tong University once used the finite element method to establish a piezoelectric - multi-body coupling dynamics model for a concentrated flexibility type slider-crank flapping wing mechanism driven by a piezoelectric bimorph, in order to accurately solve the flapping angle reached by the flapping wing under the electric field of the piezoelectric bimorph. However, this method has the disadvantage of high computational cost and is not suitable for the analysis of more complex systems. Takashi et al. from Toyota Central R&D Labs in Japan established a "piezoelectric single crystal - folding spring - flapping wing" multi-system coupling vibration model for a piezoelectric direct drive insect-like flapping wing drive mechanism that can be folded back and forth passively. Under the condition of simultaneously considering the mass effect, elastic effect, and damping effect of each component, this model can quickly calculate the resonance frequency of the drive mechanism and the maximum movement amplitude of the flapping wing. However, this model still cannot accurately predict the variation law of the motion parameters of the mechanism with the excitation voltage. In addition, currently, researchers' optimization of the performance of the flapping wing drive mechanism only focuses on improving the flapping frequency and movement amplitude of the flapping wing, and does not comprehensively consider other important performance indicators such as the overall weight, overall volume, and energy conversion efficiency of the mechanism, resulting in most of the designed flapping wing drive mechanisms being difficult to achieve installed flight. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a distributed flexibility type flapping wing drive mechanism and its design method, which have the characteristics of long working life and high flight efficiency, and propose a corresponding overall machine comprehensive performance optimization design method.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A distributed flexibility type flapping wing drive mechanism, comprising a flapping wing drive mechanism mounting frame, a piezoelectric bimorph driver, and a distributed flexibility type transmission chain arranged on the flapping wing drive mechanism mounting frame;

[0008] The distributed flexibility type transmission chain has a left-right symmetrical structure, which includes a pair of vertical elastic sheets and a horizontal elastic sheet. The pair of vertical elastic sheets are respectively a left elastic sheet and a right elastic sheet, and the left elastic sheet and the right elastic sheet are symmetrically arranged facing each other left and right. Their connection structure is as follows: First, the upper end parts of the left elastic sheet and the right elastic sheet are symmetrically pre-bent outward respectively, and the left end part and the right end part of the horizontal elastic sheet are pre-bent upward respectively. Then, the left end part of the horizontal elastic sheet is fixedly bonded to the upper end part of the left elastic sheet, and the right end part of the horizontal elastic sheet is fixedly bonded to the upper end part of the right elastic sheet, thereby forming a distributed flexibility type transmission chain with prestress elasticity; The distributed flexibility type transmission chain has two flapping arms and a flapping transmission part. The two flapping arms are respectively a left flapping arm and a right flapping arm. The intersection of the left elastic sheet and the horizontal elastic sheet forms a left flapping arm support part, and the connection part of the left elastic sheet and the horizontal elastic sheet at the outer end of the left flapping arm support part forms the left flapping arm; The intersection of the right elastic sheet and the horizontal elastic sheet forms a right flapping arm support part, and the connection part of the right elastic sheet and the horizontal elastic sheet at the outer end of the right flapping arm support part forms the right flapping arm; The left flapping arm and the right flapping arm are inclined upward from the inner end to the outer end under the action of the prestress elasticity of the distributed flexibility type transmission chain, so that the distributed flexibility type transmission chain forms a left-right symmetrical structure; The middle part of the horizontal elastic sheet forms the flapping transmission part;

[0009] The fixed end of the piezoelectric bimorph driver is fixed at the rear end of the distributed flexibility type transmission chain, and its free end is fixedly connected to the flapping transmission part of the distributed flexibility type transmission chain;

[0010] The piezoelectric bimorph driver drives the flapping transmission part to vibrate up and down through its free end. Under the action of the prestress elasticity, the distributed flexibility type transmission chain drives the left flapping arm and the right flapping arm to perform flapping movements with the same frequency and the same amplitude.

[0011] The further improvement of the present invention lies in:

[0012] In the distributed flexibility type transmission chain, the flapping transmission part of the horizontal elastic sheet is a large stiffness section of the horizontal elastic sheet, and the parts of the horizontal elastic sheet on both sides of the flapping transmission part are small stiffness sections of the horizontal elastic sheet. The stiffness of the large stiffness section of the horizontal elastic sheet is greater than the stiffness of the small stiffness section of the horizontal elastic sheet. Among them, the small stiffness section of the horizontal elastic sheet on the left side of the flapping transmission part is the left small stiffness section of the horizontal elastic sheet, and the small stiffness section of the horizontal elastic sheet on the right side of the flapping transmission part is the right small stiffness section of the horizontal elastic sheet;

[0013] The lower parts of the left and right elastic pieces are the large-stiffness sections of the vertical elastic pieces, and the upper parts of the left and right flapping arms are the small-stiffness sections of the vertical elastic pieces. The stiffness of the large-stiffness section of the vertical elastic piece is greater than that of the small-stiffness section of the vertical elastic piece. Among them, the large-stiffness section of the vertical elastic piece of the left elastic piece is the large-stiffness section of the left elastic piece, the small-stiffness section of the vertical elastic piece of the left elastic piece is the small-stiffness section of the left elastic piece, the large-stiffness section of the vertical elastic piece of the right elastic piece is the large-stiffness section of the right elastic piece, and the small-stiffness section of the vertical elastic piece of the right elastic piece is the small-stiffness section of the right elastic piece. The lower parts of the large-stiffness section of the left elastic piece and the large-stiffness section of the right elastic piece are respectively fixed on the flapping wing drive mechanism mounting bracket through the drive chain fixing plate, so as to keep it vertical when the flapping transmission part vibrates.

[0014] The flapping wing drive mechanism mounting bracket is made of woven carbon fiber laminate material. The bent part of the flapping wing drive mechanism mounting bracket is connected by a flexible bending film in the middle layer of the woven carbon fiber laminate to form a folding seam, and glue is applied and fixed at the folding seam of the woven carbon fiber laminate and the butt joint seam of the woven carbon fiber laminate, so that the flapping wing drive mechanism mounting bracket forms an integrated structure. The left elastic piece, the right elastic piece and the transverse elastic piece are all composed of three polypropylene thin plates with the same width laminated and bonded to each other. Among them, the thicknesses of the two outer polypropylene thin plates are the same, and the magnitude of its stiffness is realized by the thickness of the polypropylene thin plate in the middle layer.

[0015] A design method for a distributed flexibility flapping wing drive mechanism includes the following steps:

[0016] a. According to the principle of the lumped mass method, the piezoelectric bimorph actuator is simplified into an equivalent single-degree-of-freedom second-order linear vibration system that simultaneously contains 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 block M act,e is connected to 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 connected in parallel with each other along the vertical direction, and their upper ends are both fixedly connected to the equivalent mass block M act,e , and their lower ends are both fixedly connected to the ground; the equivalent piezoelectric driving force F p acts on the equivalent mass block M act,e along the vertical direction. Within the linear range, the equivalent piezoelectric driving force F p is proportional to the electric field strength E V along the thickness direction of the piezoelectric ceramic sheet;

[0017] That is: F p = λ p E V

[0018] Where: λp is the force-electricity proportionality coefficient; E V is the function of the driving voltage U and driving frequency f of the piezoelectric bimorph; elec Defining the displacement of the equivalent mass block M act,e in the vertical direction as the equivalent linear displacement output x of the piezoelectric bimorph driver act ;

[0019] b. The distributed flexibility type transmission chain is simplified into an equivalent "multi-rigid body - torsion spring" system composed of multiple rigid connecting rods and torsion springs according to the 1R and 2R pseudo-rigid body model theories of large deformation flexible beams, then:

[0020] a). In the transverse elastic sheet, the flapping transmission part is equivalent to the connecting rod l 11 ;

[0021] In the small stiffness section on the left side of the transverse elastic sheet, the left flapping arm support part forms a support for the transverse elastic sheet, and the part between the left end of the flapping transmission part and the left flapping arm support part is equivalent to the torsion spring K 11 , and the left flapping arm support part is equivalent to the torsion spring K 13 ; The left end of the flapping transmission part and the torsion spring K 11 are equivalent to the connecting rod l 12 , and the torsion spring K 13 and the torsion spring K 11 are equivalent to the connecting rod l 14 , and the left flapping arm part is equivalent to the connecting rod l 16 ; The fixed connection between the flapping transmission part and the small stiffness section on the left side of the transverse elastic sheet is equivalent to the fixed pair between the connecting rod l 11 and the connecting rod l 12 ;

[0022] In the small stiffness section on the right side of the transverse elastic sheet, the parts corresponding to the torsion spring K 11 , the torsion spring K 13 , the connecting rod l 12 , the connecting rod l 14 , 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 , the connecting rod l 17 ; The fixed connection between the flapping transmission part and the small stiffness section on the right side of the transverse elastic sheet is equivalent to the fixed pair between the connecting rod l 11 and the connecting rod l 13 ;

[0023] b). In the left elastic sheet;

[0024] In the large stiffness section of the left elastic piece, the part of the large stiffness section of the left elastic piece in the vertical direction is kept equivalent to a connecting rod l by fixedly connecting the transmission chain fixing plate with the flapping wing drive mechanism mounting bracket. 21 , adjacent to the connecting rod l 21 , the upper part is equivalent to a torsion spring K 21 , located above the torsion spring K 21 , the above part is equivalent to a connecting rod l 22 ;

[0025] In the small stiffness section of the left elastic piece, the left flapping arm support part is equivalent to a torsion spring K 23 ; between the torsion spring K 23 and the connecting rod l 22 , the part is equivalent to a torsion spring K 22 , below the torsion spring K 22 , the part is equivalent to a connecting rod l 23 , between the torsion spring K 22 and the torsion spring K 23 , the part is equivalent to a connecting rod l 24 , the left flapping arm part is equivalent to a connecting rod l 25 ; the fixed connection between the large stiffness section and the small stiffness section of the left elastic piece is equivalent to a fixed pair between the connecting rod l 22 and the connecting rod l 23 ;

[0026] In the right elastic piece, 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 , 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 , the connecting rod l 35 ; the fixed connection between the large stiffness section and the small stiffness section of the right elastic piece is equivalent to a fixed pair between the connecting rod l 32 and the connecting rod l 33 ;

[0027] The left flapping arm is equivalently fixedly connected in a tangential manner to the connecting rod l 25 and the connecting rod l 16 ; the right flapping arm is equivalently fixedly connected in a tangential manner to the connecting rod l 35 and the connecting rod l 17Tangential fixed connection; thus simulating the "herringbone" connection structure in the distributed flexibility drive chain; and the connecting rod l that remains fixedly connected to the flapping wing drive mechanism mounting bracket in the vertical direction 21 and the connecting rod l 31 , so that the distributed flexibility drive chain forms an equivalent "multi-rigid body - torsion spring" system in the shape of a "gate";

[0028] c. According to the equivalent conversion principle between distributed loads and concentrated loads, the aerodynamic load acting on the flapping wing along the flapping plane during movement is equivalent to a concentrated aerodynamic drag F acting on its center of pressure wing ; The concentrated aerodynamic drag F wing is located in the flapping plane of the flapping wing, perpendicular to the spanwise direction of the flapping wing, and opposite to the movement direction of the flapping wing; According to the "blade element theory", the aerodynamic damping coefficient of the flapping wing at different positions and movement states is obtained by strip integration and the distance l between the center of pressure and the wing root axis aero ; Using the rigid rod l wing to simulate the mass characteristics of the flapping wing, where the mass m of the rigid rod wing is equal to the true mass of the flapping wing, and the moment of inertia J of the rigid rod l wing relative to the wing root axis is equal to the true moment of inertia of the flapping wing relative to the wing root axis, thus establishing an equivalent "mass - moment of inertia - aerodynamic damping" system for the flapping wing; Among them, the equivalent concentrated aerodynamic drag F of the flapping wing wing and the aerodynamic damping moment M wing formed at the wing root of the flapping wing are expressed as follows: wing The expressions of

[0029]

[0030] M wing = F wing ·l aero

[0031] In the formula: θ wing is the flapping angle of the flapping wing, is the flapping angular velocity of the flapping wing; The aerodynamic damping coefficient is a function of the flapping angle θ wing of the flapping wing and the flapping angular velocity ;

[0032] d. According to the actual positional relationship of each component in the distributed flexibility flapping wing drive mechanism, model assembly is carried out on the equivalent single-degree-of-freedom second-order linear vibration system of the piezoelectric bimorph actuator, the equivalent "multi-rigid body - torsion spring" system of the distributed flexibility drive chain, and the equivalent "mass - moment of inertia - aerodynamic damping" system of the flapping wing. The equivalent mass block M in the equivalent single-degree-of-freedom second-order vibration system of the piezoelectric bimorph actuatoract,e The connecting rod l in the equivalent "multi-rigid body - torsion spring" system of the distributed flexibility type drive chain 11 is fixedly connected; the root parts of the flapping wings in the equivalent "mass - moment of inertia - aerodynamic damping" system of a pair of flapping wings are respectively fixedly connected with the connecting rod l in the equivalent "multi-rigid body - torsion spring" system of the distributed flexibility type drive chain 16 and the connecting rod l 25 and the connecting rod l 17 and the connecting rod l 35 are fixedly connected. The angle between the root of the left flapping wing and the connecting rod l 16 is θ s and the angle between the root of the right flapping wing and the connecting rod l 17 is θ s Thus, an equivalent "mass - moment of inertia - spring - damping" system of the distributed flexibility type flapping wing drive mechanism can be built;

[0033] e. Take the following three independent motion parameters in the equivalent "mass - moment of inertia - spring - damping" system of the distributed flexibility type flapping wing drive mechanism as the generalized displacements: the equivalent linear displacement output x of the piezoelectric bimorph actuator act , the rotation angle θ of the torsion spring K 11 , and the rotation angle θ of the torsion spring K 11 ; accordingly, define the generalized displacement vector q = [x 13 θ 13 θ act 11 ; define the generalized external force vector of the system corresponding to the generalized displacement as: F = [F 13 0 0] T ; define the left - right symmetry motion constraint of the system as: θ p = θ T , θ 11 = θ 12 ; substitute q and F into the second - type Lagrange equation to establish the following forced vibration equations of the three - degree - of - freedom second - order system of the "piezoelectric - structure - fluid field" coupled overall dynamics model of the distributed flexibility type flapping wing drive mechanism:

[0034]

[0035] In the formula: M is the generalized mass matrix of the system, C is the generalized damping matrix of the system, and K is the generalized stiffness matrix of the system;

[0036] The input excitation of the "piezoelectric - structure - fluid field" coupled overall dynamics model of the distributed flexibility type flapping wing drive mechanism is the driving voltage U of the piezoelectric bimorph actuator, and the output response is the flapping angle θ of the flapping wing 13 14 = θ wing 11 + θ 13 ​​​-θ s , the flapping angle θ of the flapping wing is obtained by numerically solving the second-order ordinary differential equation system to obtain the steady-state response function of the flapping angle θ, the flapping angular velocity wing of the steady-state response function, and the flapping period T of the steady-state response function, the flapping frequency f flap ; flap and the relationship between the driving voltage U of the piezoelectric bimorph actuator;

[0037] f. The objective functions for optimizing the overall performance of the distributed compliance flapping wing drive mechanism are the following three: the average aerodynamic lift of a pair of flapping wings the overall energy conversion efficiency η of the distributed compliance flapping wing drive mechanism, and the overall mass m of the distributed compliance flapping wing drive mechanism total ;

[0038] The average aerodynamic lift of a pair of flapping wings is obtained through the blade element theory, and its expression is as follows:

[0039]

[0040] where: ρ air is the air density, R is the semi-span of the flapping wing, c(r) is the transformation function of the flapping wing chord length in the wingspan direction, is the average lift coefficient of the flapping wing in one flapping period;

[0041] The overall energy conversion efficiency η of the distributed compliance flapping wing drive mechanism can be obtained through the aerodynamic induced power formula of the flapping wing of the hovering flapping wing aircraft and the equivalent circuit model theory of the piezoelectric bimorph, and its expression is as follows:

[0042]

[0043] where: P lift is the induced power of the flapping wing, P elec is the electrical power of the piezoelectric bimorph actuator, U eff is the effective value of the driving voltage U of the piezoelectric bimorph actuator, and Z eff is the equivalent impedance of the piezoelectric bimorph actuator;

[0044] The optimized design variables are: the shape parameters of the distributed flexibility type drive chain, which include: the length, thickness and width of the large stiffness section of the lateral elastic sheet, the length, thickness and width of the small stiffness section of the lateral elastic sheet, the length, thickness and width of the large stiffness section of the vertical elastic sheet, the length, thickness and width of the small stiffness section of the vertical elastic sheet, the shape parameters of the piezoelectric bimorph actuator, which include: the thickness t1 of the piezoelectric ceramic layer and the thickness t2 of the intermediate layer of the piezoelectric bimorph actuator, the thickness t3 of the extension section, the width w2 of the fixed end and the width w1 of the free end of the piezoelectric bimorph actuator, the drive section length L2 and the extension section length L1 of the piezoelectric bimorph actuator, and the drive voltage U of the piezoelectric bimorph actuator;

[0045] Determine the optimization constraints according to the design requirements: the height, width and upper limit of the wingspan of the distributed flexibility type flapping wing drive mechanism and the upper limit of the drive voltage U of the piezoelectric bimorph actuator;

[0046] g. is the average aerodynamic lift of a pair of flapping wings The energy conversion efficiency η of the distributed flexibility type flapping wing drive mechanism and the reciprocal of the mass of the distributed flexibility type flapping wing drive mechanism Introduce corresponding weight coefficients for the three objective functions and perform a linear combination on them to form a unified objective function, and its expression is as follows:

[0047]

[0048] In the formula: a1, a2 and a3 are weight coefficients, and a1 + a2 + a3 = 1; S is the unified objective function, and make it reach the minimum value during the optimization process;

[0049] The selection principles of the weight coefficients are as follows: ① If it is desired that the aircraft has stronger load-carrying capacity and maneuverability, then increase a1; ② If it is desired that the aircraft has stronger endurance, then increase a2; ③ If it is desired that the aircraft realizes a lightweight structural design to facilitate carrying more payloads, then increase both a1 and a3 at the same time;

[0050] Use the constrained optimization algorithm to optimize and solve the design variables, and obtain the optimal design point of the distributed flexibility type flapping wing drive mechanism within the feasible region.

[0051] The beneficial effects produced by adopting the above technical solutions are as follows:

[0052] By adopting a distributed flexibility flapping wing drive mechanism, the present invention operates relying on the large-scale elastic deformation of flexible components in the distributed flexibility transmission chain. It neither has the friction and wear problems of traditional kinematic pairs nor can effectively relieve the stress concentration phenomenon of components. Therefore, it can effectively improve the problems of short service life and low drive efficiency of the currently adopted "rigid connecting rod - hinge type" flapping wing drive mechanism, and can extend its service life. At the same time, by utilizing the resonance characteristics between the flexible components, the piezoelectric bimorph driver, and the flapping wing, the drive efficiency of the overall mechanism can be significantly improved.

[0053] In view of the characteristic that the mechanism has a strong dynamic coupling effect among components during the movement process, an overall machine comprehensive performance optimization design method is proposed to quickly and accurately calculate the dynamic response characteristics of the mechanism, and at the same time, comprehensive optimization of its various performance indicators can also be carried out. Brief Description of the Drawings

[0054] Figure 1 is a schematic structural diagram of a distributed flexibility flapping wing aircraft;

[0055] Figure 2 is Figure 1 a sectional view of

[0056] Figure 3 is Figure 1 a schematic structural diagram of the distributed flexibility flapping wing drive mechanism in

[0057] Figure 4 is Figure 3 a schematic structural diagram of the distributed flexibility transmission chain in

[0058] Figure 5 is a schematic diagram of the connection structure between the flapping arm and the hinge;

[0059] Figure 6 is a schematic diagram of the shape parameters of the piezoelectric bimorph driver;

[0060] Figure 7 is a schematic diagram of the shape parameters of the piezoelectric bimorph driver;

[0061] Figure 8 is the equivalent "single-degree-of-freedom second-order linear vibration" system of the piezoelectric bimorph driver;

[0062] Figure 9 is a schematic diagram of the equivalent "multi-rigid body - torsion spring" system of the transverse elastic sheet in the distributed flexibility transmission chain;

[0063] Figure 10 is a schematic diagram of the equivalent "multi-rigid body - torsion spring" system of the left elastic sheet in the distributed flexibility transmission chain;

[0064] Figure 11It is a schematic diagram of the overall equivalent "multi-rigid body - torsion spring" system of the distributed flexibility drive chain;

[0065] Figure 12 It is an equivalent "mass - moment of inertia - aerodynamic damping" system of the flapping wing;

[0066] Figure 13 It is a schematic diagram of the equivalent "mass - moment of inertia - spring - damping" system of the distributed flexibility flapping wing drive mechanism;

[0067] Figure 14 It is the angle parameter schematic diagram between the root of the flapping wing and the connecting rod l 17 and.

[0068] In the attached drawings: 1. fuselage; 2. flapping wing; 3. flapping wing drive mechanism mounting bracket; 4. piezoelectric bimorph driver; 5. left shrapnel; 6. right shrapnel; 7. transverse shrapnel; 8. flapping transmission part; 9. left flapping arm; 10. right flapping arm; 11. drive chain fixing plate; 12. flapping arm connecting piece; 13. pre-bending angle adjustment flexible hinge; 14. flapping wing connecting plate; 15. passive torsion flexible hinge;

[0069] In this application, the orientation description is based on the orientation of the distributed flexibility flapping wing aircraft. The flying direction of the distributed flexibility flapping wing aircraft is the front, and the upper part is the upper part of the flying state of the distributed flexibility flapping wing aircraft. Detailed implementation mode

[0070] The present invention will be further described in detail below in conjunction with the attached drawings and specific embodiments.

[0071] For the convenience of description, the distributed flexibility flapping wing aircraft is taken as an example for detailed introduction.

[0072] The standard parts used in the present invention can all be purchased from the market. The special-shaped parts can be customized according to the records of the specification and the attached drawings. The specific connection methods of each part all adopt conventional means such as bolts, rivets, welding, and pasting in the prior art, and will not be elaborated here.

[0073] See Figures 1 to 5 , this embodiment includes a fuselage 1, a flight control system, a flapping wing drive mechanism, and a pair of flapping wings 2. The flapping wing drive mechanism is a distributed flexibility flapping wing drive mechanism, which includes a flapping wing drive mechanism mounting bracket 3 and a piezoelectric bimorph driver 4 and a distributed flexibility drive chain arranged on the flapping wing drive mechanism mounting bracket 3;

[0074] The distributed flexibility type transmission chain has a left - right symmetric structure, which includes a pair of vertical elastic pieces and a transverse elastic piece 7. The pair of vertical elastic pieces are respectively a left - hand elastic piece 5 and a right - hand elastic piece 6. The left - hand elastic piece 5 and the right - hand elastic piece 6 are symmetrically arranged facing each other left - and - right. Their connection structure is as follows: First, the upper - end parts of the left - hand elastic piece 5 and the right - hand elastic piece 6 are symmetrically pre - bent outward respectively, and the left - end part and the right - end part of the transverse elastic piece 7 are pre - bent upward respectively. Then, the left - end part of the transverse elastic piece 7 is fixedly bonded to the upper - end part of the left - hand elastic piece 5, and the right - end part of the transverse elastic piece 7 is fixedly bonded to the upper - end part of the right - hand elastic piece 6, thus forming a distributed flexibility type transmission chain with prestress elastic force. The distributed flexibility type transmission chain has two flapping arms and a flapping transmission part 8. The two flapping arms are respectively a left - hand flapping arm 9 and a right - hand flapping arm 10. The intersection of the left - hand elastic piece 5 and the transverse elastic piece 7 forms a left - hand flapping - arm support part, and the connecting part of the left - hand elastic piece 5 and the transverse elastic piece 7 at the outer end of the left - hand flapping - arm support part forms the left - hand flapping arm 9. The intersection of the right - hand elastic piece 6 and the transverse elastic piece 7 forms a right - hand flapping - arm support part, and the connecting part of the right - hand elastic piece 6 and the transverse elastic piece 7 at the outer end of the right - hand flapping - arm support part forms the right - hand flapping arm 10. The left - hand flapping arm 9 and the right - hand flapping arm 10 are inclined upward from the inner end to the outer end under the action of the prestress elastic force of the distributed flexibility type transmission chain, so that the distributed flexibility type transmission chain forms a left - right symmetric structure. The middle part of the transverse elastic piece 7 forms the flapping transmission part 8;

[0075] A pair of flapping wings 2 are symmetrically installed on the left - hand flapping arm 9 and the right - hand flapping arm 10 respectively;

[0076] The fixed end of the piezoelectric bimorph actuator 4 is fixed at the rear end of the distributed flexibility type transmission chain, and its free end is fixedly connected to the flapping transmission part 8 of the distributed flexibility type transmission chain;

[0077] The piezoelectric bimorph actuator 4 drives the flapping transmission part 8 to vibrate up and down through its free end. Under the action of the prestress elastic force, the distributed flexibility type transmission chain drives the left - hand flapping arm 9 and the right - hand flapping arm 10 to perform flapping motions with the same frequency and amplitude, thereby driving a pair of flapping wings 2 to perform flapping motions to generate lift force.

[0078] The further improvement of the present invention lies in:

[0079] In the distributed flexibility type transmission chain, the flapping transmission part 8 of the transverse elastic piece 7 is a large - stiffness section of the transverse elastic piece, and the parts of the transverse elastic piece 7 on both sides of the flapping transmission part 8 are small - stiffness sections of the transverse elastic piece. The stiffness of the large - stiffness section of the transverse elastic piece is greater than that of the small - stiffness section of the transverse elastic piece. Among them, the small - stiffness section of the transverse elastic piece on the left side of the flapping transmission part 8 is the left - hand small - stiffness section of the transverse elastic piece, and the small - stiffness section of the transverse elastic piece on the right side of the flapping transmission part 8 is the right - hand small - stiffness section of the transverse elastic piece;

[0080] The lower parts of the left shrapnel 5 and the right shrapnel 6 are the large stiffness sections of the vertical shrapnel, and the upper parts of the left flapping arm 9 and the right flapping arm 10 are the small stiffness sections of the vertical shrapnel. The stiffness of the large stiffness section of the vertical shrapnel is greater than that of the small stiffness section of the vertical shrapnel. Among them, the large stiffness section of the vertical shrapnel of the left shrapnel 5 is the large stiffness section of the left shrapnel, the small stiffness section of the vertical shrapnel of the left shrapnel 5 is the small stiffness section of the left shrapnel, the large stiffness section of the vertical shrapnel of the right shrapnel 6 is the large stiffness section of the right shrapnel, and the small stiffness section of the vertical shrapnel of the right shrapnel 6 is the small stiffness section of the right shrapnel. The lower parts of the large stiffness section of the left shrapnel and the large stiffness section of the right shrapnel are respectively fixed on the flapping wing drive mechanism mounting bracket 3 through the drive chain fixing plate 11, so as to keep them vertical when the flapping transmission part 8 vibrates.

[0081] The two flapping arms are connected to the flapping wing 2 through a hinge connection structure. The hinge connection structure includes a flapping arm connection piece 12, a pre-bending angle adjustment flexible hinge 13, a flapping wing connection plate piece 14 and a passive torsion flexible hinge 15. The flapping arm connection piece 12 is connected to the flapping wing connection plate piece 14 through the pre-bending angle adjustment flexible hinge 13, and the flapping wing connection plate piece 14 is connected to the flapping wing 2 through the passive torsion flexible hinge 15. The flapping arm connection piece 12 is fixedly bonded to the flapping arm. The angle of the pre-bending angle adjustment flexible hinge 13 keeps the flapping wing 2 in a horizontal state when it is stationary. When the flapping arm makes a flapping motion, under the combined action of aerodynamic force and its own inertia force, the flapping wing 2 realizes a passive torsion motion around the leading edge of the passive torsion flexible hinge 15.

[0082] The flapping wing drive mechanism mounting bracket 3 is made of woven carbon fiber laminate material. The bent part of the flapping wing drive mechanism mounting bracket 3 is connected by a flexible bending film in the middle layer of the woven carbon fiber laminate to form a folding seam, and glue is applied and fixed at the folding seam of the woven carbon fiber laminate and the butt joint seam of the woven carbon fiber laminate, so that the flapping wing drive mechanism mounting bracket 3 forms an integrated structure. The left shrapnel 5, the right shrapnel 6 and the transverse shrapnel 7 are all composed of three layers of polypropylene thin plates with the same width laminated and bonded to each other. Among them, the thicknesses of the two outer layers of polypropylene thin plates are the same, and the magnitude of its stiffness is realized by the thickness of the middle layer of polypropylene thin plate.

[0083] The flapping arm connection piece 12 and the flapping wing connection plate piece 14 are both made of carbon fiber laminate material, and the pre-bending angle adjustment flexible hinge 13 and the passive torsion flexible hinge 15 are both made of polyimide.

[0084] See Figures 6 to 13 , a design method for a distributed flexibility flapping wing drive mechanism, includes the following steps:

[0085] a. According to the principle of the lumped mass method, the piezoelectric bimorph actuator 4 is simplified to a model that simultaneously contains an equivalent mass block M act,e , an equivalent linear damping Cact,e , equivalent linear spring K act,e and equivalent piezoelectric driving force F p of an equivalent single-degree-of-freedom second-order linear vibration system; the equivalent mass block M act,e is connected to the ground through a moving pair along the vertical direction; the equivalent linear spring K act,e and the equivalent linear damper C act,e are connected in parallel with each other along the vertical direction, and their upper ends are both fixedly connected to the equivalent mass block M act,e , and their lower ends are both fixedly connected to the ground; the equivalent piezoelectric driving force F p acts on the equivalent mass block M act,e along the vertical direction. Within the linear range, the equivalent piezoelectric driving force F p is proportional to the electric field strength E V in the thickness direction of the piezoelectric ceramic sheet;

[0086] That is: F p =λ p E V

[0087] In the formula: λ p is the force-electricity proportionality coefficient, which can be determined according to the mechanical-electric coupling model of the piezoelectric ceramic material; E V is a function of the driving voltage U and driving frequency f elec of the piezoelectric bimorph, and can be determined according to the equivalent circuit model theory of the piezoelectric bimorph; the displacement of the equivalent mass block M act,e along the vertical direction is defined as the equivalent linear displacement output x act of the piezoelectric bimorph driver 4; the mass m act,e of the equivalent mass block M act,e of the equivalent single-degree-of-freedom second-order linear vibration system, the stiffness k act,e of the equivalent linear spring K act,e , and the damping value c act,e of the equivalent linear damper C act,e are determined by the fixed-end width w2, free-end width w1, driving-end length L2, extension-section length L1, thickness t1 of the piezoelectric ceramic layer, intermediate-layer thickness t2, and extension-section thickness t3 of the piezoelectric bimorph driver 4. The specific expressions are as follows:

[0088] m act,e =m act ·M(w r ,l r ,d r )

[0089]

[0090]

[0091] In the formula: mact 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, is the variation function of the linear velocity along the length direction of the piezoelectric bimorph actuator 4 due to bending, is the end velocity of the piezoelectric bimorph actuator 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 actuator 4, ξ is the equivalent damping ratio of the piezoelectric bimorph actuator 4 (measured by experiment); where 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 ) are expressed as follows:

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101] Where: ρ1 is the density of the piezoelectric ceramic, ρ2 is the density of the carbon fiber, and ρ3 is the density of the glass fiber.

[0102] The piezoelectric bimorph actuator 4 adopts a constant strength configuration along the length direction. The width w2 of its fixed end, the width w1 of its free end, the length L2 of its driving end, and the length L1 of its extension section should satisfy the following relational expressions:

[0103]

[0104] b. The distributed compliance transmission chain is simplified into an equivalent "multi-rigid body - torsion spring" system composed of multiple rigid connecting rods and torsion springs according to the 1R and 2R pseudo-rigid body model theories of large deformation flexible beams. Then:

[0105] a). In the lateral elastic sheet 7, the flapping transmission part 8 is equivalent to the connecting rod l 11 ;

[0106] In the small stiffness section on the left side of the lateral elastic sheet, the left flapping arm support part forms a support for the lateral elastic sheet 7. The part between the left end of the flapping transmission part 8 and the left flapping arm support part is equivalent to the torsion spring K 11 , and the left flapping arm support part is equivalent to the torsion spring K 13 ; The left end of the flapping transmission part 8 and the torsion spring K 11 are equivalent to the connecting rod l 12 , the torsion spring K 13 and the torsion spring K 11 are equivalent to the connecting rod l 14 , the left flapping arm 9 is equivalent to the connecting rod l 16 ; The fixed connection between the flapping transmission part 8 and the small stiffness section on the left side of the lateral elastic sheet is equivalent to the fixed pair between the connecting rod l 11 and the connecting rod l 12 ;

[0107] In the small stiffness section on the right side of the lateral elastic sheet, the parts corresponding to the torsion spring K 11 , the torsion spring K 13 , the connecting rod l 12 , the connecting rod l 14 , 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 , the connecting rod l 17 ; The fixed connection between the flapping transmission part 8 and the small stiffness section on the right side of the lateral elastic sheet is equivalent to the fixed pair between the connecting rod l 11 and the connecting rod l 13 ;

[0108] Among them, the length of the connecting rod l 11 is equal to the length of the large stiffness section of the lateral elastic sheet, and the connecting rod l12 , connecting rod l 13 , connecting rod l 14 , connecting rod l 15 , connecting rod l 16 , connecting rod l 17 The length of is determined by the lengths of the small stiffness segments on the left and right sides of the lateral spring plate 7 of the lateral spring plate through the 2R pseudo-rigid body theory. Torsion spring K 11 , torsion spring K 12 , torsion spring K 13 , torsion spring K 14 The stiffness of is determined by the moment of inertia and length of the cross-section of the small stiffness segments on the left and right sides of the lateral spring plate through the 2R pseudo-rigid body theory; the specific expression is as follows:

[0109] s 11 = L a

[0110] s 12 = s 13 = 0.1L b

[0111] s 14 = s 15 = 0.44L b

[0112] s 16 = s 17 = 0.46L b

[0113]

[0114]

[0115] In the formula: L a is the length of the large stiffness segment of the lateral spring plate, L b is the length of the small stiffness segments on the left and right sides of the lateral spring plate, E K is the Young's modulus of the polypropylene material, I b is the moment of inertia of the cross-section of the small stiffness segments on the left and right sides of the lateral spring plate, s 11 , s 12 , s 13 , s 14 , s 15 , s 16 , s 17 correspond to the lengths of the connecting rod l 11 , connecting rod l 12 , connecting rod l 13 , connecting rod l 14 , connecting rod l 15 , connecting rod l 16 , connecting rod l 17 , the length of, k11 、k 12 、k 13 、k 14 correspond to torsion springs K 11 、torsion springs K 12 、torsion springs K 13 、torsion springs K 14 respectively.

[0116] b). In the left elastic sheet 5;

[0117] In the large stiffness section of the left elastic sheet, the part of the large stiffness section of the left elastic sheet in the vertical direction is equivalent to a connecting rod l by fixing the transmission chain fixing plate 11 to the flapping wing driving mechanism mounting bracket 3 21 , adjacent to the connecting rod l 21 The upper part is equivalent to a torsion spring K 21 , located above the torsion spring K 21 The above part is equivalent to a connecting rod l 22 ;

[0118] In the small stiffness section of the left elastic sheet, the left flapping arm support part is equivalent to a torsion spring K 23 ; Between the torsion spring K 23 and the connecting rod l 22 The part is equivalent to a torsion spring K 22 , below the torsion spring K 22 The part is equivalent to a connecting rod l 23 , between the torsion spring K 22 and the torsion spring K 23 The part between is equivalent to a connecting rod l 24 , the left flapping arm 9 part is equivalent to a connecting rod l 25 ; The fixed connection between the large stiffness section and the small stiffness section of the left elastic sheet is equivalent to a fixed pair between the connecting rod l 22 and the connecting rod l 23 ;

[0119] Among them, the length of the connecting rod l 21 , the connecting rod l 22 is determined by the length of the large stiffness section of the left elastic sheet through the 1R pseudo-rigid body theory, and the stiffness of the torsion spring K 21 is determined by the sectional moment of inertia and length of the large stiffness section of the left elastic sheet through the 1R pseudo-rigid body theory; the connecting rod l 23 , the connecting rod l 24 , the connecting rod l 25 The length is determined by the length of the small stiffness section of the left elastic sheet through the 2R pseudo-rigid body theory, and the torsion spring K 22 , the torsion spring K 23 The stiffness is determined by the sectional moment of inertia and length of the small stiffness section of the left elastic sheet through the 2R pseudo-rigid body theory; the specific expressions are as follows:

[0120] s 21 = 0.2Lc

[0121] s 22 = 0.8L c

[0122]

[0123] s 23 = 0.1L d

[0124] s 24 = 0.44L d

[0125] s 25 = 0.46L d

[0126]

[0127]

[0128] Where: L c is the length of the large stiffness section of the left elastic piece, L d is the length of the small stiffness section of the left elastic piece, I c is the moment of inertia of the cross-section of the large stiffness section of the left elastic piece, I d is the moment of inertia of the cross-section of the small stiffness section of the left elastic piece, s 21 、s 22 、s 23 、s 24 、s 25 correspond to the lengths of the connecting rods l 21 、the connecting rods l 22 、the connecting rods l 23 、the connecting rods l 24 、the connecting rods l 25 respectively, and k 21 、k 22 、k 23 correspond to the stiffnesses of the torsion springs K 21 、the torsion springs K 22 、the torsion springs K 23 respectively.

[0129] In the right elastic piece 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 , the connecting rod l 25 are respectively equivalent to the connecting rod l 31 , the torsion spring K 31 , the connecting rod l32 , torsion spring K 32 , torsion spring K 33 , connecting rod l 33 , connecting rod l 34 , connecting rod l 35 ; The fixed connection between the large stiffness section and the small stiffness section of the right elastic sheet is equivalent to the connecting rod l 32 and the connecting rod l 33 between the fixed pairs;

[0130] Among them, the connecting rod l 31 , the connecting rod l 32 's length is determined by the length of the large stiffness section of the right elastic sheet through the 1R pseudo-rigid body theory, and the stiffness of the torsion spring K 31 is determined by the section moment of inertia and length of the large stiffness section of the right elastic sheet through the 1R pseudo-rigid body theory; the connecting rod l 33 , the connecting rod l 34 , the connecting rod l 35 's length is determined by the length of the small stiffness section of the right elastic sheet through the 2R pseudo-rigid body theory, and the stiffness of the torsion spring K 32 , the torsion spring K 33 is determined by the section moment of inertia and length of the small stiffness section of the right elastic sheet through the 2R pseudo-rigid body theory; the specific expressions are as follows:

[0131] s 31 = 0.2L e

[0132] s 32 = 0.8L e

[0133]

[0134] s 33 = 0.1L f

[0135] s 34 = 0.44L f

[0136] s 35 = 0.46L f

[0137]

[0138]

[0139] In the formula: L e is the length of the large stiffness section of the right elastic sheet, L f is the length of the small stiffness section of the right elastic sheet, I e is the section moment of inertia of the large stiffness section of the right elastic sheet, I fis the moment of inertia of the cross-section of the small stiffness section of the right elastic sheet, s 31 , s 32 , s 33 , s 34 , s 35 correspond to the lengths of the connecting rods l 31 , connecting rod l 32 , connecting rod l 33 , connecting rod l 34 , connecting rod l 35 respectively; k 31 , k 32 , k 33 correspond to the stiffnesses of the torsion springs K 31 , torsion spring K 32 , torsion spring K 33 respectively.

[0140] The geometric shape parameters of the left elastic sheet and the right elastic sheet are exactly the same. Therefore, the following relational expressions exist:

[0141] L c = L e

[0142] L d = L f

[0143] I c = I e

[0144] I d = I f

[0145] The left flapping arm 9 is equivalently regarded as the tangential fixed connection of the connecting rods l 25 and the connecting rod l 16 ; the right flapping arm 10 is equivalently regarded as the tangential fixed connection of the connecting rods l 35 and the connecting rod l 17 ; thus simulating the "herringbone" connection structure in the distributed flexibility transmission chain; and the connecting rods l 21 and the connecting rod l 31 that are fixedly connected to the flapping wing drive mechanism mounting bracket 3 in the vertical direction, so that the distributed flexibility transmission chain forms an overall equivalent "multi-rigid body - torsion spring" system in the shape of a "gate";

[0146] c. According to the equivalent conversion principle between distributed loads and concentrated loads, the aerodynamic load acting on the flapping wing 2 in the flapping plane during movement is equivalently regarded as a concentrated aerodynamic drag F wing acting on its pressure center; the concentrated aerodynamic drag F wingIt is located within the flapping plane of the flapping wing, perpendicular to the spanwise direction of the flapping wing, and opposite to the movement direction of the flapping wing; according to the "blade element theory", the aerodynamic damping coefficient of the flapping wing 2 at different positions and motion states is obtained by strip integration. and the distance l between the center of pressure and the wing root axis aero ; using the rigid rod l wing to simulate the mass characteristics of the flapping wing 2, where the mass m wing of the rigid rod l wing is equal to the true 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 true moment of inertia of the flapping wing 2 relative to the wing root axis, thereby establishing an equivalent "mass - moment of inertia - aerodynamic damping" system for the flapping wing 2; where the equivalent concentrated aerodynamic resistance F wing of the flapping wing 2 and the aerodynamic damping moment M wing formed at the wing root of the flapping wing 2 are expressed as follows:

[0147]

[0148] M wing = F wing ·l aero

[0149] In the formula: θ wing is the flapping angle of the flapping wing 2, is the flapping angular velocity of the flapping wing 2, and the aerodynamic damping coefficient is a function of the flapping angle θ wing of the flapping wing 2 and the flapping angular velocity , and is also related to the geometric shape of the flapping wing, and can be determined by conducting aerodynamic experiments;

[0150] d. According to the actual positional relationship of each component in the distributed flexibility type flapping wing drive mechanism, for a single - degree - of - freedom second - order linear vibration system, the equivalent "multi - rigid - body - torsion spring" system of the distributed flexibility type transmission chain, and the equivalent "mass - moment of inertia - aerodynamic damping" system of the flapping wing, model assembly is carried out. The equivalent mass block M act,e in the equivalent single - degree - of - freedom second - order vibration system of the piezoelectric bimorph actuator 4 is fixedly connected to the connecting rod l 11 in the equivalent "multi - rigid - body - torsion spring" system of the distributed flexibility type transmission chain; the root parts of the equivalent "mass - moment of inertia - aerodynamic damping" systems of a pair of flapping wings 2 are respectively fixedly connected to the connecting rod l 16 , the connecting rod l 25 , the connecting rod l 17 , the connecting rod l 35 in the equivalent "multi - rigid - body - torsion spring" system of the distributed flexibility type transmission chain. The angle between the root of the left flapping wing and the connecting rod l 16 is θs The angle between the root of the right flapping wing and the connecting rod l 17 is θ s Thus, an equivalent "mass - moment of inertia - spring - damper" system of the distributed flexibility flapping wing drive mechanism can be established;

[0151] e. Define the following three independent motion parameters in the equivalent "mass - moment of inertia - spring - damper" system of the distributed flexibility flapping wing drive mechanism as the generalized displacements: the equivalent linear displacement output x of the piezoelectric bimorph actuator 4 act , the torsion spring K 11 's rotation angle θ 11 , the torsion spring K 13 's rotation angle θ 13 ; Accordingly, define the generalized displacement vector q = [x act θ 11 θ 13 T ; Define the system generalized external force vector corresponding to the generalized displacement as: F = [F p 0 0] T ; Define the left - right symmetry motion constraint of the system as: θ 11 = θ 12 , θ 13 = θ 14 ; Substitute q and F into the second - type Lagrange equation to establish the forced vibration equations of the three - degree - of - freedom second - order system of the "piezoelectric - structure - flow field" coupled whole - machine dynamics model of the distributed flexibility flapping wing drive mechanism as follows:

[0152]

[0153] In the formula: M is the system generalized mass matrix, C is the system generalized damping matrix, and K is the system generalized stiffness matrix;

[0154] The input excitation of the "piezoelectric - structure - flow field" coupled whole - machine dynamics model of the distributed flexibility flapping wing drive mechanism is the driving voltage U of the piezoelectric bimorph actuator 4, and the output response is the flapping angle θ of the flapping wing 2 wing = θ 11 + θ 13 - θ s , and by numerically solving the second - order ordinary differential equations obtain the steady - state response function of the flapping angle θ of the flapping wing 2 wing , the steady - state response function of the flapping angular velocity , the flapping period T flap , the flapping frequency f flap and the relationship between the driving voltage U of the piezoelectric bimorph actuator 4;

[0155] ​f. The objective functions for optimizing the overall performance of the distributed flexibility flapping-wing drive mechanism are the following three: the average aerodynamic lift of a pair of flapping wings 2 The overall energy conversion efficiency η of the distributed flexibility flapping-wing drive mechanism, and the overall mass m of the distributed flexibility flapping-wing drive mechanism total ;

[0156] The average aerodynamic lift of a pair of flapping wings is obtained through the blade element theory, and its expression is as follows:

[0157]

[0158] In the formula: ρ air is the air density, R is the semi-span of the flapping wing 2, and c(r) is the transformation function of the chord length of the flapping wing 2 in the wingspan direction; is the average lift coefficient of the flapping wing 2 in a flapping cycle, which can be determined according to the geometric shape of the flapping wing and the passive torsion angle around its leading edge. The passive torsion angle of the flapping wing around its leading edge can be determined by experimental observation;

[0159] The overall energy conversion efficiency η of the distributed flexibility flapping-wing drive mechanism can be obtained through the aerodynamic induced power formula of the flapping wing and the equivalent circuit model theory of the piezoelectric bimorph, and its expression is as follows:

[0160]

[0161] In the formula: P lift is the induced power of the flapping wing, P elec is the electric power of the piezoelectric bimorph actuator, U eff is the effective value of the driving voltage U of the piezoelectric bimorph actuator, and Z eff is the equivalent impedance of the piezoelectric bimorph actuator;

[0162] The overall mass m of the distributed flexibility flapping-wing drive mechanism total is determined by the shape parameters of the distributed flexibility transmission chain, the material density, the shape parameters of the piezoelectric bimorph actuator, the piezoelectric ceramic material density, the carbon fiber material density, and the glass fiber material density;

[0163] The optimized design variables are: the shape parameters of the distributed compliance flapping drive chain, which include: the length, thickness, and width of the large stiffness section of the lateral elastic sheet, the length, thickness, and width of the small stiffness section of the lateral elastic sheet, the length, thickness, and width of the large stiffness section of the vertical elastic sheet, the length, thickness, and width of the small stiffness section of the vertical elastic sheet, and the shape parameters of the piezoelectric bimorph actuator 4, which include: the thickness t1 of the piezoelectric ceramic layer and the thickness t2 of the intermediate layer of the piezoelectric bimorph actuator 4, the thickness t3 of the extension section, the width w2 of the fixed end and the width w1 of the free end of the piezoelectric bimorph actuator 4, the driving section length L2 and the extension section length L1 of the piezoelectric bimorph actuator 4, and the driving voltage U of the piezoelectric bimorph actuator;

[0164] Determine the optimization constraints according to the design requirements: the height, width, and upper limit of the wingspan of the distributed compliance flapping drive mechanism and the upper limit of the driving voltage U of the piezoelectric bimorph actuator;

[0165] g is the average aerodynamic lift of a pair of flapping wings 2 The energy conversion efficiency η of the distributed compliance flapping drive mechanism and the reciprocal of the mass of the distributed compliance flapping drive mechanism Introduce corresponding weight coefficients to the three objective functions and perform a linear combination on them to form a unified objective function, and its expression is as follows:

[0166]

[0167] In the formula: a1, a2, and a3 are weight coefficients, and a1 + a2 + a3 = 1; S is the unified objective function, and it is made to reach the minimum value during the optimization process;

[0168] The selection principles of the weight coefficients are as follows: ① If it is desired that the aircraft has stronger load-carrying capacity and maneuverability, then increase a1; ② If it is desired that the aircraft has stronger endurance, then increase a2; ③ If it is desired that the aircraft realizes a lightweight structural design to facilitate carrying more payloads, then increase both a1 and a3 simultaneously;

[0169] Use the constrained optimization algorithm to optimize and solve the design variables, and obtain the optimal design point of the distributed compliance flapping drive mechanism within the feasible region.

Claims

1. A distributed flexibility flapping wing drive mechanism, characterized in that: The distributed flexibility flapping wing drive mechanism includes a flapping wing drive mechanism mounting bracket (3), a piezoelectric bimorph driver (4) and a distributed flexibility transmission chain arranged on the flapping wing drive mechanism mounting bracket (3); The distributed flexibility transmission chain is a left-right symmetric structure, which includes a pair of vertical elastic sheets and a horizontal elastic sheet (7). The pair of vertical elastic sheets are respectively a left elastic sheet (5) and a right elastic sheet (6). The left elastic sheet (5) and the right elastic sheet (6) are symmetrically arranged facing each other left and right. Their connection structure is as follows: First, the upper end parts of the left elastic sheet (5) and the right elastic sheet (6) are symmetrically pre-bent outward, and the left end part and the right end part of the horizontal elastic sheet (7) are pre-bent upward respectively. Then, the left end part of the horizontal elastic sheet (7) is fixedly bonded to the upper end part of the left elastic sheet (5), and the right end part of the horizontal elastic sheet (7) is fixedly bonded to the upper end part of the right elastic sheet (6), so as to form the distributed flexibility transmission chain with prestress elasticity. The distributed flexibility transmission chain has two flapping arms and a flapping transmission part (8). The two flapping arms are respectively a left flapping arm (9) and a right flapping arm (10). The intersection of the left elastic sheet (5) and the horizontal elastic sheet (7) forms a left flapping arm support part. The connection part of the left elastic sheet (5) and the horizontal elastic sheet (7) at the outer end of the left flapping arm support part forms the left flapping arm (9). The intersection of the right elastic sheet (6) and the horizontal elastic sheet (7) forms a right flapping arm support part. The connection part of the right elastic sheet (6) and the horizontal elastic sheet (7) at the outer end of the right flapping arm support part forms the right flapping arm (10). The left flapping arm (9) and the right flapping arm (10) are inclined upward from the inner end to the outer end under the action of the prestress elasticity of the distributed flexibility transmission chain, so that the distributed flexibility transmission chain forms a left-right symmetric structure. The middle part of the horizontal elastic sheet (7) forms the flapping transmission part (8); In the distributed flexibility transmission chain, the flapping transmission part (8) of the horizontal elastic sheet (7) is a large stiffness section of the horizontal elastic sheet. The parts of the horizontal elastic sheet (7) on both sides of the flapping transmission part (8) are small stiffness sections of the horizontal elastic sheet. The stiffness of the large stiffness section of the horizontal elastic sheet is greater than that of the small stiffness section of the horizontal elastic sheet. Among them, the small stiffness section of the horizontal elastic sheet on the left side of the flapping transmission part (8) is the left small stiffness section of the horizontal elastic sheet, and the small stiffness section of the horizontal elastic sheet on the right side of the flapping transmission part (8) is the right small stiffness section of the horizontal elastic sheet; The lower parts of the left elastic sheet (5) and the right elastic sheet (6) are vertical elastic sheet large stiffness segments, the upper parts of the left flapping arm (9) and the right flapping arm (10) are vertical elastic sheet small stiffness segments, and the stiffness of the vertical elastic sheet large stiffness segment is greater than that of the vertical elastic sheet small stiffness segment; wherein, the vertical elastic sheet large stiffness segment of the left elastic sheet (5) is the left elastic sheet large stiffness segment, the vertical elastic sheet small stiffness segment of the left elastic sheet (5) is the left elastic sheet small stiffness segment, the vertical elastic sheet large stiffness segment of the right elastic sheet (6) is the right elastic sheet large stiffness segment, and the vertical elastic sheet small stiffness segment of the right elastic sheet (6) is the right elastic sheet small stiffness segment; the lower parts of the left elastic sheet large stiffness segment and the right elastic sheet large stiffness segment are respectively fixed on the flapping wing drive mechanism mounting frame (3) through the drive chain fixing plate (11) so as to keep them in the vertical direction when the flapping drive part (8) vibrates; The fixed end of the piezoelectric bimorph driver (4) is fixed at the rear end of the distributed compliance drive chain, and its free end is fixedly connected with the flapping drive part (8) of the distributed compliance drive chain; The piezoelectric bimorph driver (4) drives the flapping drive part (8) to vibrate up and down through its free end. Under the action of the prestress force, the distributed compliance drive chain drives the left flapping arm (9) and the right flapping arm (10) to perform flapping motions with the same frequency and amplitude.

2. The distributed flexibility flapping wing drive mechanism according to claim 1, characterized in that: The flapping wing drive mechanism mounting frame (3) is made of woven carbon fiber laminate material. The bent part of the flapping wing drive mechanism mounting frame (3) is connected by a flexible bending film in the middle layer of the woven carbon fiber laminate to form a folding seam, and glue is applied and fixed at the folding seam and the butt joint seam of the woven carbon fiber laminate, so that the flapping wing drive 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 all composed of three polypropylene thin plates with the same width laminated and bonded to each other, wherein the thicknesses of the two outer polypropylene thin plates are the same, and the magnitude of their stiffness is realized by the thickness of the middle polypropylene thin plate.

3. A design method for the distributed flexibility flapping wing drive mechanism according to any one of claims 1 to 2, characterized in that, The method includes the following steps: a. According to the principle of lumped mass method, the piezoelectric bimorph actuator (4) is simplified into an equivalent single-degree-of-freedom second-order linear vibration system that simultaneously includes 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 block M act,e is connected to the ground through a moving pair in the vertical direction: the equivalent linear spring K act,e and the equivalent linear damping C act,e are connected in parallel with each other in the vertical direction, and their upper ends are fixedly connected to the equivalent mass block M act,e , and their lower ends are fixedly connected to the ground; the equivalent piezoelectric driving force F p acts on the equivalent mass block M act,e in the vertical direction. Within the linear range, the equivalent piezoelectric driving force F p is proportional to the electric field strength E V in the thickness direction of the piezoelectric ceramic sheet; That is: F p = λ p E V where: λ p is the force-electricity proportionality coefficient; E V is a function of the driving voltage U and driving frequency f of the piezoelectric bimorph elec ; the displacement of the equivalent mass block M act,e in the vertical direction is defined as the equivalent linear displacement output x of the piezoelectric bimorph driver (4) act ; b. The distributed compliance drive chain is simplified into an equivalent "multi-rigid body - torsion spring" system composed of multiple rigid connecting rods and torsion springs according to the 1R and 2R pseudo-rigid body model theory of large deformation flexible beams, then: a). In the lateral elastic sheet (7), the flapping transmission part (8) is equivalent to a connecting rod l 11 ; In the small stiffness section on the left side of the transverse elastic piece, the left flapping arm support portion forms a support for the transverse elastic piece (7), and the portion between the left end of the flapping transmission portion (8) and the left flapping arm support portion is equivalent to a torsion spring K 11 , the left flapping arm support portion is equivalent to a torsion spring K 13 ; the left end of the flapping transmission portion (8) and the torsion spring K 11 are equivalent to a connecting rod l 12 , the torsion spring K 13 and the torsion spring K 11 are equivalent to a connecting rod l 14 , the left flapping arm (9) is equivalent to a connecting rod l 16 ; the fixed connection between the flapping transmission portion (8) and the small stiffness section on 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 stiffness section on the right side of the lateral elastic piece, it is related to the torsion spring K 11 , the torsion spring K 13 , the connecting rod l 12 , the connecting rod l 14 , the connecting rod l 16 The corresponding parts are respectively equivalent to the torsion spring K 12 , the torsion spring K 14 , the connecting rod l 13 , the connecting rod l 15 , the connecting rod l 17 ; The fixed connection between the flapping transmission part (8) and the small stiffness section on the right side of the lateral elastic piece is equivalent to the fixed pair between the connecting rod l 11 and the connecting rod l 13 ; b). In the left elastic sheet (5); In the large stiffness section of the left elastic piece, the part of the large stiffness section of the left elastic piece in the vertical direction is equivalent to a connecting rod l by fixedly connecting the transmission chain fixing plate (11) with the flapping wing driving mechanism mounting frame (3). 21 , adjacent to the connecting rod l 21 , the upper part is equivalent to a torsion spring K 21 , located above the torsion spring K 21 , the above part is equivalent to a connecting rod l 22 ; In the small stiffness section of the left elastic piece, the left flapping arm support part is equivalent to a torsion spring K 23 ; Between the torsion spring K 23 and the connecting rod l 22 , the part is equivalent to a torsion spring K 22 , and the part below the torsion spring K 22 is equivalent to the connecting rod l 23 . Between the torsion spring K 22 and the torsion spring K 23 , the part is equivalent to the connecting rod l 24 . The part of the left flapping arm (9) is equivalent to the connecting rod l 25 ; The fixed connection between the large stiffness section and the small stiffness section of the left elastic piece is equivalent to the fixed pair between the connecting rod l 22 and the connecting rod l 23 . In the right elastic piece (6), the part 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 , the connecting rod l 25 is 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 , the connecting rod l 35 ; the fixed connection between the large stiffness section and the small stiffness section of the right elastic piece is equivalent to the fixed pair between the connecting rod l 32 and the connecting rod l 33 . Equivalent the left flapping arm (9) to the connecting rod l 25 and the connecting rod l 16 are tangentially fixed; Equivalent the right flapping arm (10) to the connecting rod l 35 and the connecting rod l 17 are tangentially fixed; Thus simulate the "V"-shaped connection structure in the distributed compliance drive chain; And keep the connecting rod l 21 vertically fixed to the flapping wing drive mechanism mounting bracket (3) and the connecting rod l 31 , so that the distributed compliance drive chain forms a "door"-shaped equivalent "multi-rigid body - torsion spring" system; c. According to the equivalent conversion principle between distributed load and concentrated load, the aerodynamic load acting on the flapping wing (2) along the flapping plane during movement is equivalent to a concentrated aerodynamic drag force F acting on its pressure center. wing ; The concentrated aerodynamic drag force F wing is located within the flapping plane of the flapping wing, perpendicular to the spanwise direction of the flapping wing, and opposite to the movement direction of the flapping wing; According to the "blade element theory", the aerodynamic damping coefficient of the flapping wing (2) at different positions and movement states is obtained by strip integration. and the distance l between the pressure center and the wing root axis. aero ; Use the rigid rod l wing to simulate the mass characteristics of the flapping wing (2), where the mass m wing of the rigid rod is equal to the actual 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 actual moment of inertia of the flapping wing (2) relative to the wing root axis, so as to establish an equivalent "mass - moment of inertia - aerodynamic damping" system of the flapping wing (2); Among them, the equivalent concentrated aerodynamic drag force F wing of the flapping wing (2) and the aerodynamic damping moment M wing formed at the wing root of the flapping wing (2) wing are expressed as follows:​ M wing = F wing · l aero Where: θ wing is the flapping angle of the flapping wing (2), and is the flapping angular velocity of the flapping wing (2); The aerodynamic damping coefficient is a function of the flapping angle θ wing of the flapping wing and the flapping angular velocity ; d. According to the actual positional relationships of the components in the distributed compliance flapping wing drive mechanism, model assembly is carried out on the equivalent single-degree-of-freedom second-order linear vibration system of the piezoelectric bimorph actuator (4), the equivalent "multi-rigid body - torsion spring" system of the distributed compliance transmission chain, and the equivalent "mass - moment of inertia - aerodynamic damping" system of the flapping wing. The equivalent mass block M in the equivalent single-degree-of-freedom second-order vibration system of the piezoelectric bimorph actuator (4) act,e is fixedly connected to the connecting rod l in the equivalent "multi-rigid body - torsion spring" system of the distributed compliance transmission chain 11 ; the root parts of the flapping wings (2) in a pair of the equivalent "mass - moment of inertia - aerodynamic damping" systems of the flapping wings are respectively fixedly connected to the connecting rod l 16 in the equivalent "multi-rigid body - torsion spring" system of the distributed compliance transmission chain, the connecting rod l 25 in the equivalent "multi-rigid body - torsion spring" system of the distributed compliance transmission chain, the connecting rod l 17 in the equivalent "multi-rigid body - torsion spring" system of the distributed compliance transmission chain, the connecting rod l 35 in the equivalent "multi-rigid body - torsion spring" system of the distributed compliance transmission chain. The included angle between the root of the left flapping wing and the connecting rod l 16 is θ s , and the included angle between the root of the right flapping wing and the connecting rod l 17 is θ s , so that the equivalent "mass - moment of inertia - spring - damping" system of the distributed compliance flapping wing drive mechanism can be built; e. Define the following three independent motion parameters in the equivalent "mass - moment of inertia - spring - damper" system of the distributed flexibility flapping wing drive mechanism as generalized displacements: the equivalent linear displacement output x of the piezoelectric bimorph actuator (4) act , the rotation angle θ of the torsion spring K 11 , the rotation angle θ of the torsion spring K 11 ; accordingly, define the generalized displacement vector q = [x 13 , the rotation angle θ of the torsion spring K 13 ; thus, define the generalized displacement vector q = [x act θ 11 θ 13 T ; define the system generalized external force vector corresponding to the generalized displacement as: F = [F p 0 0] T ; define the left - right symmetry motion constraint of the system as: θ 11 = θ 12 , θ 13 = θ 14 ; substitute q and F into the second - kind Lagrange equation to establish the following forced vibration equations of the three - degree - of - freedom second - order system of the "piezo - structure - flow field" coupled whole - machine dynamics model of the distributed flexibility flapping wing drive mechanism​ Where: M is the system generalized mass matrix, C is the system generalized damping matrix, and K is the system generalized stiffness matrix; The input excitation of the "piezoelectric - structure - flow field" coupled whole - machine dynamics model of the distributed flexibility flapping - wing drive mechanism is the driving voltage U of the piezoelectric bimorph actuator (4), and the output response is the flapping angle θ of the flapping wing (2). wing = θ 11 + θ 13 - θ s , by numerically solving the second - order ordinary differential equation system to obtain the steady - state response function of the flapping angle θ of the flapping wing wing , the steady - state response function of the flapping angular velocity , the flapping period T flap , the flapping frequency f flap and the relationship between them and the driving voltage U of the piezoelectric bimorph actuator (4); f. The objective functions for optimizing the overall comprehensive performance of the distributed flexibility flapping wing drive mechanism are the following three: the average aerodynamic lift of a pair of the flapping wings (2) the overall energy conversion efficiency η of the distributed flexibility flapping wing drive mechanism, and the overall mass m of the distributed flexibility flapping wing drive mechanism total ; The average aerodynamic lift of a pair of the flapping wings is obtained by the blade element theory, and its expression is as follows: Where: ρ air is the air density, R is the semi-span of the flapping wing (2), and c(r) is the transformation function of the chord length of the flapping wing (2) in the wingspan direction, is the average lift coefficient of the flapping wing (2) in one flapping cycle; The overall energy conversion efficiency η of the distributed compliance flapping wing drive mechanism is obtained through the flapping wing aerodynamic induced power formula of the hovering flapping wing aircraft and the equivalent circuit model theory of the piezoelectric bimorph, and its expression is as follows: Where: P lift is the induced power of the flapping wing, and P elec is the electrical power of the piezoelectric bimorph actuator, U eff is the effective value of the driving voltage U of the piezoelectric bimorph actuator, and Z eff is the equivalent impedance of the piezoelectric bimorph actuator; The optimized design variables are: the shape parameters of the distributed compliance flapping drive chain, which include: the length, thickness and width of the large stiffness section of the lateral elastic sheet, the length, thickness and width of the small stiffness section of the lateral elastic sheet, the length, thickness and width of the large stiffness section of the vertical elastic sheet, the length, thickness and width of the small stiffness section of the vertical elastic sheet, the shape parameters of the piezoelectric bimorph actuator (4), which include: the thickness t1 of the piezoelectric ceramic layer and the thickness t2 of the intermediate layer of the piezoelectric bimorph actuator (4), the thickness t3 of the extension section, the width w2 of the fixed end and the width w1 of the free end of the piezoelectric bimorph actuator (4), the driving section length L2 and the extension section length L1 of the piezoelectric bimorph actuator (4), and the driving voltage U of the piezoelectric bimorph actuator; Determine the optimization constraint conditions according to the design requirements: the height, width and upper limit of the wingspan of the distributed compliance flapping drive mechanism and the upper limit of the driving voltage U of the piezoelectric bimorph actuator (4); g. The average aerodynamic lift of a pair of the flapping wings (2) The energy conversion efficiency η of the distributed flexibility flapping wing drive mechanism and the reciprocal of the mass of the distributed flexibility flapping wing drive mechanism Corresponding weight coefficients are introduced for the three objective functions and linearly combined to form a unified objective function, and its expression is as follows: Where: a1, a2 and a3 are weight coefficients, and a1 + a2 + a3 = 1; S is the unified objective function, and it is minimized during the optimization process; The selection principles of the weight coefficients are as follows: ① If it is desired that the aircraft has stronger load-carrying capacity and maneuverability, then increase a1; ② If it is desired that the aircraft has stronger endurance, then increase a2; ③ If it is desired that the aircraft realizes a lightweight structure design to facilitate carrying more payloads, then increase both a1 and a3 simultaneously; Use the constrained optimization algorithm to optimize and solve the design variables, and obtain the optimal design point of the distributed compliance flapping drive mechanism within the feasible region.

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