CN115649437A - Distributed flexibility type flapping wing aircraft and design method of flapping wing driving mechanism - Google Patents
Distributed flexibility type flapping wing aircraft and design method of flapping wing driving mechanism Download PDFInfo
- Publication number
- CN115649437A CN115649437A CN202211432775.7A CN202211432775A CN115649437A CN 115649437 A CN115649437 A CN 115649437A CN 202211432775 A CN202211432775 A CN 202211432775A CN 115649437 A CN115649437 A CN 115649437A
- Authority
- CN
- China
- Prior art keywords
- flapping
- equivalent
- connecting rod
- flapping wing
- wing
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 230000007246 mechanism Effects 0.000 title claims abstract description 107
- 238000000034 method Methods 0.000 title claims abstract description 29
- 238000013461 design Methods 0.000 title claims abstract description 26
- 230000005540 biological transmission Effects 0.000 claims abstract description 106
- 238000005457 optimization Methods 0.000 claims abstract description 20
- 238000013016 damping Methods 0.000 claims description 39
- 239000012634 fragment Substances 0.000 claims description 29
- 230000006870 function Effects 0.000 claims description 26
- 238000005452 bending Methods 0.000 claims description 20
- 238000006073 displacement reaction Methods 0.000 claims description 20
- 229920000049 Carbon (fiber) Polymers 0.000 claims description 18
- 239000004917 carbon fiber Substances 0.000 claims description 18
- VNWKTOKETHGBQD-UHFFFAOYSA-N methane Chemical compound C VNWKTOKETHGBQD-UHFFFAOYSA-N 0.000 claims description 18
- 239000004743 Polypropylene Substances 0.000 claims description 10
- 230000009471 action Effects 0.000 claims description 10
- 238000006243 chemical reaction Methods 0.000 claims description 10
- -1 polypropylene Polymers 0.000 claims description 10
- 229920001155 polypropylene Polymers 0.000 claims description 10
- 230000008878 coupling Effects 0.000 claims description 9
- 238000010168 coupling process Methods 0.000 claims description 9
- 238000005859 coupling reaction Methods 0.000 claims description 9
- 239000011159 matrix material Substances 0.000 claims description 9
- 239000000919 ceramic Substances 0.000 claims description 8
- 230000008569 process Effects 0.000 claims description 8
- 230000002146 bilateral effect Effects 0.000 claims description 6
- 238000005316 response function Methods 0.000 claims description 6
- 230000009466 transformation Effects 0.000 claims description 6
- 230000005684 electric field Effects 0.000 claims description 4
- 230000005284 excitation Effects 0.000 claims description 4
- 229920001721 polyimide Polymers 0.000 claims description 4
- 230000004044 response Effects 0.000 claims description 4
- RZVHIXYEVGDQDX-UHFFFAOYSA-N 9,10-anthraquinone Chemical compound C1=CC=C2C(=O)C3=CC=CC=C3C(=O)C2=C1 RZVHIXYEVGDQDX-UHFFFAOYSA-N 0.000 claims description 3
- KFLQGJQSLUYUBF-WOJBJXKFSA-N Phyllanthin Chemical compound C([C@H](COC)[C@@H](COC)CC=1C=C(OC)C(OC)=CC=1)C1=CC=C(OC)C(OC)=C1 KFLQGJQSLUYUBF-WOJBJXKFSA-N 0.000 claims description 3
- KFLQGJQSLUYUBF-PMACEKPBSA-N Phyllanthin Natural products C([C@@H](COC)[C@H](COC)CC=1C=C(OC)C(OC)=CC=1)C1=CC=C(OC)C(OC)=C1 KFLQGJQSLUYUBF-PMACEKPBSA-N 0.000 claims description 3
- 239000004642 Polyimide Substances 0.000 claims description 3
- 238000010030 laminating Methods 0.000 claims description 3
- 230000003068 static effect Effects 0.000 claims description 3
- 239000000463 material Substances 0.000 description 6
- 230000000694 effects Effects 0.000 description 4
- LFQSCWFLJHTTHZ-UHFFFAOYSA-N Ethanol Chemical compound CCO LFQSCWFLJHTTHZ-UHFFFAOYSA-N 0.000 description 2
- 238000005299 abrasion Methods 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 2
- 229910010293 ceramic material Inorganic materials 0.000 description 2
- 230000001808 coupling effect Effects 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
- 239000003365 glass fiber Substances 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 230000005489 elastic deformation Effects 0.000 description 1
- 238000005265 energy consumption Methods 0.000 description 1
- 239000004744 fabric Substances 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 239000011664 nicotinic acid Substances 0.000 description 1
- 230000002035 prolonged effect Effects 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 238000012827 research and development Methods 0.000 description 1
- 238000003466 welding Methods 0.000 description 1
- 239000002023 wood Substances 0.000 description 1
Images
Landscapes
- Toys (AREA)
Abstract
The invention discloses a distributed flexibility type flapping wing aircraft and a design method of a flapping wing driving mechanism, and belongs to the technical field of flapping wing aircraft. A distributed flexibility type flapping wing aircraft is characterized in that a distributed flexibility type flapping wing driving mechanism comprises a flapping wing driving mechanism mounting rack, 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 rack; the distributed flexibility type transmission chain comprises a pair of vertical elastic sheets and a transverse elastic sheet, and the fixed end of the piezoelectric bimorph driver is fixed at the rear end of the distributed flexibility type transmission chain; simplifying a 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 the model; e. establishing a forced vibration equation set; f. taking an objective function of an optimization problem; g. and (5) optimizing and designing. It has long service life, flight characteristics such as efficient.
Description
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 flapping wing driving mechanism have important influence on the flight capability of the flapping wing aircraft. The traditional flapping wing driving mechanism adopts a configuration scheme that a rigid connecting rod is combined with a friction type motion pair, and is widely applied to large-scale and centimeter-scale flapping wing aircrafts. However, when the size of the flapping wing air vehicle is reduced to millimeter magnitude, the rigid connecting rod-friction kinematic pair type flapping wing driving mechanism has various problems of component strength reduction, severe abrasion of kinematic pairs, difficulty in increasing the motion frequency and the like. Therefore, people have to continuously search for other novel mechanism configuration schemes.
A carbon fiber rigid thin plate type sliding block-rocker flapping wing driving mechanism formed by integrally connecting polyimide film flexible hinges is developed by a Wood group of Harvard university and is used for being equipped with coin-sized Robobe and HMF series miniature piezoelectric flapping wing aircrafts, and the motion frequency of the miniature piezoelectric flapping wing aircraft can reach more than 100 Hz. However, in the high-frequency motion process of the concentrated flexibility type flapping wing driving mechanism, the obvious stress concentration phenomenon occurs at the position of the flexible hinge, so that the service life of the concentrated flexibility type flapping wing driving mechanism is greatly shortened. Wuhan science and technology university has utilized flexible bracing piece to design a space four-bar linkage to reduced the figure of component and kinematic pair in the driving chain, played and subtract heavy effect, also can save the energy consumption of prime mover with the help of the resonance characteristic of flexible component simultaneously, but this mechanism still can't avoid the use of friction formula kinematic pair, therefore also is not suitable for doing the high frequency motion.
In order to meet the expected performance requirements of the flapping-wing driving mechanism, researchers also need to explore a reasonable optimization design method. For the traditional rigid connecting rod-friction kinematic pair type and centralized flexibility type flapping wing driving mechanism, researchers often model and optimize a prime motor, a transmission chain and a flapping wing independently, and cannot evaluate the influence of the power coupling effect among all components on the overall performance of the driving mechanism. Researchers continue to explore a large number of modeling and design methodologies suitable for multi-component coupling analysis. A finite element method is used by Shanghai university of transportation to establish a piezoelectric-multi-body coupling dynamic model for a piezoelectric bimorph-driven centralized flexibility type sliding block rocker flapping wing mechanism so as to accurately solve the flapping angle of the flapping wing under the action of an electric field of a piezoelectric bimorph, but the method has the defect of high calculation cost and is not suitable for analysis of a more complex system. Takashi et al of the Central research and development laboratory of Toyota, japan establishes a piezoelectric direct-drive insect-imitating flapping wing driving mechanism capable of being folded back and forth passively, and establishes a piezoelectric single chip-folding spring-flapping wing multi-system coupling vibration model, and the model can quickly calculate the resonance frequency of the driving mechanism and the maximum motion amplitude of the flapping wing under the condition of simultaneously considering the mass effect, the elastic effect and the damping effect of each component, but the model still cannot accurately predict the change rule of the motion parameters of the mechanism along with the excitation voltage. In addition, at present, researchers only focus on the improvement of the motion frequency and the motion amplitude of the flapping wing aiming at the optimization of the performance of the flapping wing driving mechanism, 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 designed flapping wing driving mechanisms are difficult to achieve installed flight.
Disclosure of Invention
The invention aims to solve the technical problem of providing a distributed flexibility type flapping wing aircraft and a design method of a flapping wing driving mechanism, and the distributed flexibility type flapping wing aircraft has the characteristics of long service life, high flying efficiency and the like. And provides a corresponding overall performance optimization design method.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a distributed flexibility type flapping wing aircraft comprises an aircraft body, 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 mounting frame of the flapping wing driving mechanism, 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 mounting frame of the flapping wing driving mechanism;
the distribution compliance formula driving chain is 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 the symmetry sets up about left side shell fragment and the right side shell fragment in opposite directions, and their connection structure is: firstly, the upper end part of a left spring plate and the upper end part of a right spring plate are respectively and symmetrically pre-bent and deformed outwards, the left end part and the right end part of a transverse spring plate are respectively and pre-bent and deformed upwards, then the left end part of the transverse spring plate and the upper end part of the left spring plate are fixedly bonded together, and the right end part of the transverse spring plate and the upper end part of the right spring plate are fixedly bonded together, so that a distribution flexibility type transmission chain with pre-stress elasticity is formed; the distributed flexibility type transmission chain is provided with two flapping arms and a flapping transmission part, wherein the two flapping arms are respectively a left flapping arm and a right flapping arm, a left flapping arm supporting part is formed at the intersection of a left elastic sheet and a transverse elastic sheet, and a left elastic sheet at the outer end of the left flapping arm supporting part is connected with the transverse elastic sheet to form a left flapping arm; the intersection of the right elastic sheet and the transverse elastic sheet forms a right flapping arm supporting part, and the connecting part of the right elastic sheet and the transverse elastic sheet at the outer end of the right flapping arm supporting part forms a right flapping arm; the left flapping arm and the right flapping arm are inclined upwards 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 bilateral symmetry structure; the middle part of the transverse elastic sheet forms a flapping transmission part;
the pair of flapping wings are respectively and symmetrically arranged on the left side flapping arm and the right side flapping arm;
the fixed end of the piezoelectric bimorph driver is fixed at the rear end of the distributed flexibility type transmission chain, and the free end of the piezoelectric bimorph driver is fixedly connected with the flapping transmission part of the distributed flexibility 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 the distributed flexibility type transmission chains drive the left side flapping arm and the right side flapping arm to do same-frequency and same-amplitude flapping motion under the action of the pre-stress elastic force, so that the pair of flapping wings are driven to do the flapping motion to generate the lift force.
The invention further improves that:
in the distributed flexibility type transmission chain, a flapping transmission part of a transverse elastic sheet is a transverse elastic sheet large rigidity section, the parts of the transverse elastic sheet positioned at two sides of the flapping transmission part are transverse elastic sheet small rigidity sections, the rigidity of the transverse elastic sheet large rigidity section is greater 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 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 is a transverse elastic sheet right side small rigidity section;
the lower parts of the left spring plate and the right spring plate are vertical spring plate large rigidity sections, the upper parts of the left flapping arm and the right flapping arm are vertical spring plate small rigidity sections, and the rigidity of the vertical spring plate large rigidity sections is greater than that of the vertical spring plate small rigidity sections; the large rigidity section of the vertical elastic sheet of the left elastic sheet is a large rigidity section of the left elastic sheet, the small rigidity section of the vertical elastic sheet of the left elastic sheet is a small rigidity section of the left elastic sheet, the large rigidity section of the vertical elastic sheet of the right elastic sheet is a large rigidity section of the right elastic sheet, and the small rigidity section of the vertical elastic sheet of the right elastic sheet is a small rigidity section of the right elastic sheet; the lower part of the large rigidity section of the left spring plate and the lower part of the large rigidity section of the right spring plate are respectively fixed on the mounting frame of the flapping wing driving mechanism through a transmission chain fixing plate so as to keep the flapping transmission part in a vertical direction when vibrating.
The two flapping arms are connected with the flapping wings through a hinge type connecting 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 piece is connected with the flapping wing connecting plate piece through a pre-bending angle adjusting flexible hinge, the flapping wing connecting plate piece is connected with the flapping wing through a passive torsion flexible hinge, the flapping arm connecting piece 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 the flapping wing is 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 inertial force.
The mounting frame of the flapping wing driving mechanism is made of a woven carbon fiber laminated plate material, the bending parts of the mounting frame of the flapping wing driving mechanism are connected by a flexible bending film in the middle layer of the woven carbon fiber laminated plate to form folding seams, and the folding seams of the woven carbon fiber laminated plate and the butt seams of the woven carbon fiber laminated plate are glued and fixed, so that the mounting frame of the flapping wing driving mechanism forms an integrated structure; the left spring plate, the right spring plate and the transverse spring plate are formed by mutually laminating and bonding three polypropylene thin plates with the same width, wherein the two polypropylene thin plates on the outer side have the same thickness, and the rigidity is realized by the thickness of the polypropylene thin plate on the middle layer.
The flapping arm connecting sheet and the flapping wing connecting plate are both made of carbon fiber laminated plates, and the pre-bending angle adjusting flexible hinge and the passive torsion flexible hinge are both 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 the concentrated mass method, the piezoelectric bimorph driver is simplified into a piezoelectric bimorph driver simultaneously containing equivalent mass blocks M act,e Equivalent linear damping C act,e Equivalent linear spring K act,e And equivalent piezoelectric driving force F p The equivalent single-degree-of-freedom second-order linear vibration system; the equivalent mass M is displaced by a pair of vertical displacements act,e And (3) connecting with the ground: equivalent linear spring K act,e Equivalent linear damping C act,e Are connected in parallel with each other along the vertical direction, and the upper ends of the equivalent mass blocks M are connected with the equivalent mass blocks M act,e The lower ends of the fixed connection bodies are fixedly connected with the ground; equivalent piezoelectric driving force F p Acting on equivalent mass M in vertical direction act,e In the linear range, the equivalent piezoelectric driving force F p And the electric field intensity E along the thickness direction of the piezoelectric ceramic sheet V Is in direct proportion;
namely: f p ＝λ p E V
In the formula: lambda [ alpha ] p Is the force-to-electricity proportionality coefficient; e V Then is the piezoelectric bimorph drive voltage U and the drive frequency f elec A function of (a); equivalent mass block M act,e Displacement in the vertical directionDefined as the equivalent linear displacement output x of a piezoelectric bimorph actuator act ；
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 1R and 2R pseudo-rigid-body model theory of the large-deformation flexible beam, and then:
a) In the transverse elastic sheet, the flapping transmission part is equivalent to a connecting rod l 11 ；
In the small rigidity section at the left side of the transverse elastic sheet, the left side flapping arm supporting part supports the transverse elastic sheet, and the part between the left end of the flapping transmission part and the left side flapping arm supporting part is equivalent to a torsion spring K 11 The left flapping arm support part is equivalent to a torsion spring K 13 (ii) a Left end of flapping transmission part and torsional spring K 11 Equivalent to connecting rod l 12 Torsion spring K 13 And torsion spring K 11 The middle part is equivalent to a connecting rod l 14 The left flapping arm position is equivalent to a connecting rod l 16 (ii) a The fixed connection between the flapping transmission part and the small rigidity section at the left side of the transverse elastic sheet is equivalent to a connecting rod l 11 And a connecting rod l 12 A fixed pair therebetween;
in the small rigidity section at the right side of the transverse elastic sheet, the transverse elastic sheet is connected with a torsion spring K 11 Torsion spring K 13 Connecting rod l 12 Connecting rod l 14 Connecting rod l 16 The corresponding parts are respectively equivalent to torsion springs K 12 Torsion spring K 14 Connecting rod l 13 Connecting rod l 15 Connecting rod l 17 (ii) a The fixed connection between the flapping transmission part and the small rigidity section at the right side of the transverse elastic sheet is equivalent to a connecting rod l 11 And a connecting rod l 13 A fixed pair therebetween;
b) In the left spring plate;
in the large rigidity section of the left spring plate, the part of the large rigidity section of the left spring plate fixedly connected with the mounting rack of the flapping wing driving mechanism through the transmission chain fixing plate to keep the vertical direction is equivalent to a connecting rod l 21 Next to the connecting rod l 21 Is equivalent to a torsion spring K 21 In the torsion spring K 21 The above parts are equivalent to a connecting rod l 22 ；
In the small rigidity section of the left elastic sheet, the supporting part of the left flapping arm is equivalent to a torsion spring K 23 (ii) a In the torsion spring K 23 And a connecting rod l 22 The part between is equivalent to a torsion spring K 22 Torsion spring K 22 The following parts are equivalent to a connecting rod l 23 Torsional spring K 22 And torsion spring K 23 The middle part is equivalent to a connecting rod l 24 The left flapping arm position is equivalent to a connecting rod l 25 (ii) a The fixed connection between the large rigidity section of the left spring plate and the small rigidity section of the left spring plate is equivalent to a connecting rod l 22 And a connecting rod l 23 A fixed pair therebetween;
in the right spring plate, with link l 21 Torsion spring K 21 Connecting rod l 22 Torsion spring K 22 Torsion spring K 23 Connecting rod l 23 Connecting rod l 24 Connecting rod l 25 The corresponding parts are respectively equivalent to connecting rods l 31 Torsion spring K 31 Connecting rod l 32 Torsion spring K 32 Torsion spring K 33 Connecting rod l 33 Connecting rod l 34 Connecting rod l 35 (ii) a The fixed connection between the large rigidity section of the right spring plate and the small rigidity section of the right spring plate is equivalent to a connecting rod l 32 And a connecting rod l 33 A fixed pair between;
the left flapping arm is equivalent to a connecting rod l 25 And a connecting rod l 16 The tangent of the two-way pipe is fixedly connected; the right side flapping arm is equivalent to a connecting rod l 35 And a connecting rod l 17 The tangent of the two-way pipe is fixedly connected; the herringbone connecting structure in the distribution flexibility type transmission chain is simulated; and a connecting rod l fixedly connected with the mounting rack of the flapping wing driving mechanism in the vertical direction 21 And a connecting rod 31 So that the distributed flexibility type transmission chain forms an equivalent multi-rigid-torsion spring system in a shape like a Chinese character 'men';
c. according to the principle of equivalent transformation between distributed load and concentrated load, the aerodynamic load along the flapping plane borne by the flapping wing in the moving process is equivalent to the concentrated aerodynamic resistance F acting on the pressure center of the flapping wing wing (ii) a Concentrated aerodynamic drag F wing The flapping wing is positioned in a flapping plane of the flapping wing, is vertical to the unfolding direction of the flapping wing and is opposite to the moving direction of the flapping wing; according to the 'phyllotaxis' method, the aerodynamic damping coefficient of the flapping wing at different positions and in different motion states is obtained through a strip integral mode
And the distance l between the center of pressure and the root axis aero (ii) a Using rigid rods l wing Simulating the mass characteristic of a flapping wing, in which the mass m of the rigid rod wing Rigid rod l equal to the true mass of the flapping wing wing Moment of inertia J about the wing root axis wing The actual moment of inertia of the flapping wing relative to the wing root axis is equal, so that an equivalent mass-moment of inertia-aerodynamic damping system of the flapping wing is established; wherein the equivalent concentrated aerodynamic drag F of the flapping wings wing And the aerodynamic damping moment M formed at the wing root of the flapping wing wing The expression of (a) is as follows:
M wing ＝F wing ·l aero
in the formula: theta wing Is the flapping angle of the flapping wing,
the flapping angular velocity of the flapping wing; coefficient of aerodynamic damping
Is the flapping angle theta of the flapping wing wing And angular velocity of flapping
A function of (a);
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 a piezoelectric bimorph driver, an equivalent multi-rigid-torsion spring system of a distributed flexibility type transmission chain and an equivalent mass-rotational inertia-pneumatic damping system of a flapping wing are subjected to model assembly, and an equivalent mass block M in the equivalent single-degree-of-freedom second-order vibration system of the piezoelectric bimorph driver is subjected to model assembly act,e And is divided intoConnecting rod in equivalent 'multi-rigid-torsional spring' system of cloth flexibility type transmission chain 11 Carrying out fixed connection; the root parts of the flapping wings in a pair of flapping wing equivalent 'mass-rotational inertia-pneumatic damping' systems are respectively connected with a connecting rod l in a distributed flexibility type transmission chain equivalent 'multi-rigid-body-torsion spring' system 16 Connecting rod l 25 Connecting rod l 17 Connecting rod l 35 Fixedly connected with the root of the left flapping wing and the connecting rod l 16 The included angle between is theta s The root of the right flapping wing and the connecting rod l 17 The included angle between is theta s Thereby an equivalent mass-rotational inertia-spring-damping system of the distributed flexibility type flapping wing driving mechanism can be built;
e. the following three independent motion parameters in an equivalent 'mass-rotational inertia-spring-damping' system of a distributed flexibility type flapping wing driving mechanism are taken to be defined as generalized displacement: equivalent linear displacement output x of piezoelectric bimorph driver act Torsion spring K 11 Angle of rotation theta 11 Torsion spring K 13 Angle of rotation theta 13 (ii) a Accordingly, a generalized displacement vector q = [ x ] is defined act θ 11 θ 13 ] T (ii) a Defining the system generalized external force vector corresponding to the generalized displacement as: f = [ F = p 0 0] T (ii) a The left-right symmetric motion constraint of the system is defined as: theta 11 ＝θ 12 、θ 13 ＝θ 14 (ii) a Substituting q and F into a second Lagrange equation, and establishing a three-degree-of-freedom second-order system forced vibration equation set of a piezoelectric-structure-flow field coupling complete machine dynamic model of the distributed flexibility type flapping wing driving mechanism as follows:
in the formula: 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' coupled complete machine dynamics model of the distributed flexibility type flapping wing driving mechanism is the driving voltage U of the piezoelectric bimorph driver, and the output response isFlapping angle theta of flapping wing wing ＝θ 11 +θ 13 -θ s By numerically solving a system of second order ordinary differential equations
Obtaining the flapping angle theta of the flapping wing wing Steady state response function, flapping angular velocity
Steady state response function, flapping period T flap Flapping frequency f flap The relation with 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 of the distributed flexibility type flapping wing driving mechanism tota l；
Average aerodynamic lift of a pair of flapping wings
Obtained by the theory of phyllanthin, the expression of which is as follows:
in the formula: rho air R is the half span length of the flapping wing, c (R) is a function of the transformation of the length of the flapping wing chord in the span direction,
the average lift coefficient of the flapping wings in a flapping period is obtained;
the whole energy conversion efficiency eta of the distributed flexibility type flapping wing driving mechanism can be obtained through the flapping wing pneumatic induced power formula of the hovering type flapping wing aircraft and the equivalent circuit model theory of the piezoelectric bimorph, and the expression is as follows:
in the formula: p lift Is the induced power of the flapping wing, P elec Electric power for piezoelectric bimorph actuators, U eff Effective value, Z, of the driving voltage U of the piezoelectric bimorph driver eff Is the equivalent impedance of the piezoelectric bimorph driver;
the optimization design variables are: a shape parameter of a distributed compliance drive chain, comprising: the length of the big rigidity section of horizontal shell fragment, thickness and width, the length of the little rigidity section of horizontal shell fragment, thickness and width, the length of the big rigidity section of vertical shell fragment, thickness and width, the length of the little rigidity section of vertical shell fragment, thickness and width, the shape parameter of piezoelectricity bimorph driver, it includes: thickness t of piezoelectric ceramic layer of piezoelectric bimorph driver 1 And the thickness t of the intermediate layer 2 Thickness t of the extension 3 Width w of fixed end of piezoelectric bimorph driver 2 And a free end width w 1 Length L of driving section of piezoelectric bimorph driver 2 Length L of extension segment 1 Driving voltage U by piezoelectric bimorph;
determining an optimization constraint condition according to design requirements: distributing the upper limit of the height, the width and the wingspan of the flexibility type flapping wing driving mechanism and the upper limit of the driving voltage U of the piezoelectric bimorph driver;
g. is the average aerodynamic lift of a pair of flapping wings
Energy conversion efficiency eta of distributed flexibility type flapping wing driving mechanism and reciprocal of mass of distributed flexibility type flapping wing driving mechanism
The three objective functions introduce corresponding weight coefficients and are linearly combined to form a unified objective function, and the expression of the unified objective function is as follows:
in the formula: a is 1 ，a 2 And a 3 Is a weight coefficient, and a 1 +a 2 +a 3 =1; s is a uniform objective function, and the minimum value is reached in the optimization process;
the weight coefficient is selected according to the following principle: (1) if it is desired that the aircraft possess greater load carrying capacity and maneuverability, a is increased 1 (ii) a (2) If the aircraft is expected to have stronger endurance, a is increased 2 (ii) a (3) If it is desired that the aircraft be designed to be structurally light so as to carry more payload, then a is increased simultaneously 1 And a 3 ；
And (4) optimizing and solving the design variables by adopting a constraint optimization algorithm, and acquiring the optimal design point of the distributed flexibility type flapping wing driving mechanism in a feasible region.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in:
the flapping wing driving mechanism works by means of large-scale elastic deformation of the flexible component in the distributed flexibility type transmission chain by adopting the distributed flexibility type flapping wing driving mechanism, so that the problem of friction and abrasion of the traditional kinematic pair is solved, and the stress concentration phenomenon of the component can be effectively relieved, therefore, the problems of short service life and low driving efficiency of the existing 'rigid connecting rod-hinge' flapping wing driving mechanism can be effectively solved, and the service life of the flapping wing driving mechanism can be prolonged; meanwhile, the resonance characteristics among the flexible component, the piezoelectric bimorph driver and the flapping wings are utilized, so that the driving efficiency of the whole mechanism can be obviously improved.
Aiming at the characteristic that the mechanism has a strong dynamic coupling effect among components in the motion process, the overall comprehensive performance optimization design method is provided to quickly and accurately calculate the dynamic response characteristics of the mechanism and comprehensively optimize the performance indexes of multiple aspects 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 structural view of the distributed compliance flapping wing drive mechanism of FIG. 1;
FIG. 4 is a schematic diagram of the structure of the distributed compliance drive train of FIG. 3;
FIG. 5 is a schematic view of a flapping arm and hinge connection;
FIG. 6 is a shape parameter schematic of a piezoelectric bimorph actuator;
FIG. 7 is a shape parameter schematic of a piezoelectric bimorph actuator;
FIG. 8 is an equivalent "single degree of freedom second order linear vibration" system of a piezoelectric bimorph actuator;
FIG. 9 is a schematic view of an equivalent "multi-rigid-torsion spring" system of transverse springs in a distributed compliance type transmission chain;
FIG. 10 is a schematic diagram of an equivalent "multi-rigid-torsion spring" system for the left spring plate in a distributed compliance type transmission chain;
FIG. 11 is a schematic view of an overall equivalent "multi-rigid-body-torsion spring" system of a distributed compliance type transmission chain;
FIG. 12 is an equivalent "mass-moment of inertia-aerodynamic damping" system for a flapping wing;
FIG. 13 is a schematic view of an equivalent "mass-moment of inertia-spring-damping" system of a distributed compliance flapping wing drive;
FIG. 14 shows the root of the flapping wing and the connecting rod l 17 The included angle parameter between them is shown schematically.
In the drawings: 1. a body; 2. flapping wings; 3. a mounting rack of the flapping wing driving mechanism; 4. a piezoelectric bimorph driver; 5. a left spring plate; 6. a right spring plate; 7. a transverse elastic sheet; 8. a flapping transmission part; 9. a left flapping arm; 10. the arm is swung to the right side; 11. a transmission chain fixing plate; 12. a flapping arm connecting sheet; 13. a flexible hinge is adjusted by a pre-bending angle; 14. the flapping wing is connected with the plate; 15. a passive torsion flexible hinge;
the direction description in this application is based on the direction of distributing the flexibility formula flapping wing aircraft, and the direction of distributing the flexibility formula flapping wing aircraft flight is the place ahead, and the top is the top of distributing the flexibility formula flapping wing aircraft flight state.
Detailed Description
The invention will be described in further detail below with reference to the figures and specific examples.
The standard parts used in the invention can be purchased from the market, the special-shaped parts can be customized according to the description and the description of the attached drawings, and the specific connection mode of each part adopts the conventional means of mature bolts, rivets, welding, sticking and the like in the prior art, and the detailed description is not repeated.
Referring to fig. 1 to 5, the embodiment includes 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 flexibility type flapping wing driving mechanism, and includes a mounting frame 3 of the flapping wing driving mechanism, a piezoelectric bimorph driver 4 arranged on the mounting frame 3 of the flapping wing driving mechanism, and a distributed flexibility type transmission chain;
the distribution compliance formula driving chain is bilateral symmetry structure, and it includes a pair of vertical shell fragment and a horizontal shell fragment 7, and a pair of vertical shell fragment is left side shell fragment 5 and right side shell fragment 6 respectively, and left side shell fragment 5 and right side shell fragment 6 left and right sides symmetry in opposite directions set up, and their connection structure is: firstly, the upper end part of a left spring plate 5 and the upper end part of a right spring plate 6 are respectively and symmetrically pre-bent and deformed outwards, the left end part and the right end part of a transverse spring plate 7 are respectively and pre-bent and deformed upwards, then the left end part of the transverse spring plate 7 is fixedly bonded with the upper end part of the left spring plate 5, and the right end part of the transverse spring plate 7 is fixedly bonded with the upper end part of the right spring plate 6, so that a distribution flexibility type transmission chain with pre-stress elasticity 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 respectively a left flapping arm 9 and a right flapping arm 10, a left flapping arm supporting part is formed at the intersection of a left spring sheet 5 and a transverse spring sheet 7, and a left flapping arm 9 is formed at the connecting part of the left spring sheet 5 and the transverse spring sheet 7 at the outer end of the left flapping arm supporting part; a right flapping arm supporting part is formed at the intersection of the right elastic sheet 6 and the transverse elastic sheet 7, and a right flapping arm 10 is formed at the connecting part of the right elastic sheet 6 and the transverse elastic sheet 7 at the outer end of the right flapping arm supporting part; the left flapping arm 9 and the right flapping arm 10 incline upwards 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 bilateral symmetry structure; the middle part of the transverse elastic sheet 7 forms a flapping transmission part 8;
the pair of flapping wings 2 are respectively and symmetrically arranged on the left side flapping arm 9 and the right side flapping arm 10;
the fixed end of the piezoelectric bimorph driver 4 is fixed at the rear end of the distributed flexibility type transmission chain, and the free end of the piezoelectric bimorph driver is fixedly connected with the flapping transmission part 8 of the distributed flexibility 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 the distributed flexible transmission chains drive the left flapping arm 9 and the right flapping arm 10 to perform same-frequency and same-amplitude flapping motion under the action of the pre-stress elastic force, so that the pair of flapping wings 2 are driven to perform flapping motion to generate lift force.
The invention further improves 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, which are positioned at two sides of the flapping transmission part 8, are transverse elastic sheet small rigidity sections, the rigidity of the transverse elastic sheet large rigidity section is greater 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 spring 5 and the right spring 6 are vertical spring large-rigidity sections, the upper parts of the left flapping arm 9 and the right flapping arm 10 are vertical spring small-rigidity sections, and the rigidity of the vertical spring large-rigidity sections is greater than that of the vertical spring small-rigidity sections; the large vertical spring plate stiffness section of the left spring plate 5 is a large left spring plate stiffness section, the small vertical spring plate stiffness section of the left spring plate 5 is a small left spring plate stiffness section, the large vertical spring plate stiffness section of the right spring plate 6 is a large right spring plate stiffness section, and the small vertical spring plate stiffness section of the right spring plate 6 is a small right spring plate stiffness section; the lower part of the large rigidity section of the left spring plate and the lower part of the large rigidity section of the right spring plate are respectively fixed on the mounting rack 3 of the flapping wing driving mechanism through a transmission chain fixing plate 11, so that the flapping transmission part 8 keeps a vertical direction when vibrating.
The two flapping arms are connected with the flapping wings 2 through a hinge type connecting 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 a 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 does flapping motion, the flapping wing 2 realizes passive torsion motion around the front edge of the passive torsion flexible hinge 15 under the combined action of aerodynamic force and self inertial force.
The mounting frame 3 of the flapping wing driving mechanism is made of a woven carbon fiber laminated plate material, the bending parts of the mounting frame 3 of the flapping wing driving mechanism are connected by a flexible bending film in the middle layer of the woven carbon fiber laminated plate to form folding seams, and the folding seams of the woven carbon fiber laminated plate and the butt seams of the woven carbon fiber laminated plate are glued and fixed, so that the mounting frame 3 of the flapping wing driving mechanism forms an integrated structure; the left spring plate 5, the right spring plate 6 and the transverse spring plate 7 are formed by mutually laminating and bonding three polypropylene thin plates with the same width, wherein the two polypropylene thin plates on the outer side have the same thickness, and the rigidity is realized by the thickness of the polypropylene thin plate on the middle layer.
The flapping arm connecting sheet 12 and the flapping wing connecting plate 14 are both made of carbon fiber laminated plates, and the pre-bending angle adjusting flexible hinge 13 and the passive torsion flexible hinge 15 are both made of polyimide.
Referring to fig. 6 to 13, a design method of a distributed flexibility type flapping wing driving mechanism comprises the following steps:
a. according to the principle of the lumped mass method, the piezoelectric bimorph driver 4 is simplified into a piezoelectric bimorph driver with an equivalent mass M act,e Equivalent linear damping C act,e Equivalent linear spring K act,e And equivalent piezoelectric driving force F p Equivalent single freedom ofA linear vibration system of degree second order; the equivalent mass M is moved by a pair of vertical moving members act,e Is connected with the ground; equivalent linear spring K act,e Equivalent linear damping C act,e Are connected in parallel with each other along the vertical direction, and the upper ends of the equivalent mass blocks M are connected with the equivalent mass blocks M act,e The lower ends of the fixed connection bodies are fixedly connected with the ground; equivalent piezoelectric driving force F p Acting on equivalent mass M in vertical direction act,e In the linear range, the equivalent piezoelectric driving force F p And the electric field intensity E along the thickness direction of the piezoelectric ceramic sheet V Is in direct proportion;
namely: f p ＝λ p E V
In the formula: lambda [ alpha ] p The force-electricity proportionality coefficient can be determined according to an electromechanical coupling model of the piezoelectric ceramic material; e V Then is the piezoelectric bimorph drive voltage U and the drive frequency f elec The function of (2) can be determined according to an equivalent circuit model theory of the piezoelectric bimorph; equivalent mass block M act,e The displacement in the vertical direction is defined as the equivalent linear displacement output x of the piezoelectric bimorph actuator 4 act (ii) a Equivalent mass block M of equivalent single-degree-of-freedom second-order linear vibration system act,e Mass m of act,e Equivalent linear spring K act,e Stiffness k of act,e Equivalent linear damping C act,e Damping value c of act,e Width w of fixed end of piezoelectric bimorph driver 4 2 Width w of free end 1 Length L of drive end 2 Length L of extension 1 Thickness t of piezoelectric ceramic layer 1 Thickness t of intermediate layer 2 Thickness t of the extension 3 Determining that the specific expression is as follows:
m act,e ＝m act ·M(w r ,l r ,d r )
in the formula: m is act True mass of piezoelectric bimorph actuator, M (w) r ,l r ,d r ) Is the equivalent quality factor, l, of the piezoelectric bimorph actuator 4 r Is the length factor of the piezoelectric bimorph actuator 4, d r Is the thickness factor, w, of the piezoelectric bimorph actuator 4 n Nominal width, w, of the piezoelectric bimorph actuator 4 r Is the width factor of the piezoelectric bimorph actuator 4, w (x) is a function of the width variation of the piezoelectric bimorph actuator 4,
as a function of the linear velocity of the piezoelectric bimorph actuator 4 in the longitudinal direction due to bending,
end velocity, C, of the piezoelectric bimorph actuator 4 44 Is the flexural compliance coefficient, G, of a piezoelectric bimorph cantilever K (w r ,l r ) Is the equivalent stiffness factor of the piezoelectric bimorph actuator 4, and xi is the equivalent damping ratio of the piezoelectric bimorph actuator 4 (determined by experiments); wherein m is act 、M(w r ,l r ,d r )、l r 、d r 、w n 、w r 、w(x)、
G K (w r ,l r ) The expression of (a) is as follows:
in the formula: rho 1 Is the density of the piezoelectric ceramic, ρ 2 Is the density of the carbon fiber, p 3 Is the density of the glass fibers.
The piezoelectric bimorph driver 4 adopts a configuration scheme with equal strength along the length direction, and the width w of the fixed end of the piezoelectric bimorph driver 2 Width w of free end 1 Length L of drive end 2 Length L of extension 1 The following relationships should be satisfied:
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 1R and 2R pseudo-rigid-body model theory of the large-deformation flexible beam, and then:
a) In the transverse spring 7, the flapping transmission part 8 is equivalent to be connectedRod l 11 ；
In the small rigidity section at the left side of the transverse elastic sheet, the supporting part of the left flapping arm supports the transverse elastic sheet 7, and the part between the left end of the flapping transmission part 8 and the supporting part of the left flapping arm is equivalent to a torsion spring K 11 The left flapping arm support part is equivalent to a torsion spring K 13 (ii) a The left end of the flapping transmission part 8 and a torsion spring K 11 Equivalent to connecting rod l 12 Torsion spring K 13 And torsion spring K 11 The middle part is equivalent to a connecting rod l 14 The part 9 of the left flapping arm is equivalent to a connecting rod l 16 (ii) a The fixed connection between the flapping transmission part 8 and the small rigidity section at the left side of the transverse elastic sheet is equivalent to a connecting rod l 11 And a connecting rod l 12 A fixed pair therebetween;
in the small rigidity section at the right side of the transverse elastic sheet, the transverse elastic sheet is connected with a torsion spring K 11 Torsion spring K 13 Connecting rod l 12 Connecting rod l 14 Connecting rod l 16 The corresponding parts are respectively equivalent to torsion springs K 12 Torsion spring K 14 Connecting rod l 13 Connecting rod l 15 Connecting rod l 17 (ii) a The fixed connection between the flapping transmission part 8 and the small rigidity section at the right side of the transverse elastic sheet is equivalent to a connecting rod l 11 And a connecting rod l 13 A fixed pair therebetween;
wherein, the connecting rod l 11 The length of the connecting rod is equal to the large rigidity section of the transverse elastic sheet, and the 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 the spring is determined by the length of the small rigidity section at the left side of the transverse elastic sheet 7 and the length of the small rigidity section at the right side of the transverse elastic sheet through the 2R pseudo rigid body theory, and the torsion spring K 11 Torsion spring K 12 Torsion spring K 13 Torsional spring K 14 The rigidity of the elastic sheet is determined by the section inertia moment and the length of the small rigidity section on the left side of the transverse elastic sheet and the small rigidity section on the right side of the transverse elastic sheet through a 2R pseudo rigid body theory; the specific expression is as follows:
s 11 ＝L a
s 12 ＝s 13 ＝0.1L b
s 14 ＝s 15 ＝0.44L b
s 16 ＝s 17 ＝0.46L b
in the formula: l is a Is the length of the large rigidity section of the transverse elastic sheet, L b The length of the small rigidity sections at the left and right sides of the transverse elastic sheet, E K Is the Young's modulus of a polypropylene material, I b Is the section inertia moment s of the small rigidity sections at the left and right sides of the transverse elastic sheet 11 、s 12 、s 13 、s 14 、s 15 、s 16 、s 17 Respectively correspond to a connecting rod l 11 Connecting rod l 12 Connecting rod 13 Connecting rod l 14 Connecting rod l 15 Connecting rod l 16 Connecting rod l 17 Length of (k) 11 、k 12 、k 13 、k 14 Respectively correspond to a torsional spring K 11 Torsion spring K 12 Torsion spring K 13 Torsion spring K 14 The rigidity of (2).
b) In the left spring plate 5;
in the large rigidity section of the left spring plate, the part of the large rigidity section of the left spring plate fixedly connected with the mounting rack 3 of the flapping wing driving mechanism through the transmission chain fixing plate 11 to keep the vertical direction is equivalent to a connecting rod l 21 Next to the connecting rod l 21 Is equivalent to a torsion spring K 21 In the torsion spring K 21 The above parts are equivalent to a connecting rod l 22 ；
In the small rigidity section of the left elastic sheet, the supporting part of the left flapping arm is equivalent to a torsion spring K 23 (ii) a In the torsion spring K 23 And a connecting rod l 22 The part between is equivalent to a torsion spring K 22 Torsion spring K 22 The following parts are equivalent to a connecting rod l 23 Torsion spring K 22 And torsion spring K 23 The middle part is equivalent to a connecting rod l 24 The part 9 of the left flapping arm is equivalent to a connecting rod l 25 (ii) a The left spring plate is largeThe fixed connection between the rigidity section and the small rigidity section of the left spring plate is equivalent to a connecting rod l 22 And a connecting rod l 23 A fixed pair therebetween;
wherein, the connecting rod l 21 Connecting rod l 22 The length of the spring is determined by the length of the large rigidity section of the left spring plate through the 1R pseudo rigid body theory, and the torsion spring K 21 The rigidity of the left spring plate is determined by the section inertia moment and the length of the large rigidity section of the left spring plate through a 1R pseudo rigid body theory; connecting rod 23 Connecting rod l 24 Connecting rod l 25 The length of the spring is determined by the length of the small rigidity section of the left spring plate through the 2R pseudo rigid body theory, and the torsion spring K 22 Torsion spring K 23 The rigidity of the left spring plate is determined by the section inertia moment and the length of the small rigidity section of the left spring plate through a 2R pseudo rigid body theory; the specific expression is as follows:
s 21 ＝0.2L c
s 22 ＝0.8L c
s 23 ＝0.1L d
s 24 ＝0.44L d
s 25 ＝0.46L d
in the formula: l is a radical of an alcohol c Is the length of the large rigidity section of the left spring plate, L d Is the length of the small rigidity section of the left spring plate, I c Is the section moment of inertia, I, of the large-rigidity section of the left spring plate d Is the section moment of inertia, s, of the small stiffness section of the left spring plate 21 、s 22 、s 23 、s 24 、s 25 Respectively correspond to a connecting rod l 21 Connecting rod l 22 To, connectRod l 23 Connecting rod l 24 Connecting rod l 25 Length of (k) 21 、k 22 、k 23 Respectively correspond to a torsional spring K 21 Torsion spring K 22 Torsion spring K 23 The rigidity of (2).
In the right spring 6, with link l 21 Torsion spring K 21 Connecting rod l 22 Torsional spring K 22 Torsion spring K 23 Connecting rod l 23 Connecting rod l 24 Connecting rod l 25 The corresponding parts are respectively equivalent to connecting rods l 31 Torsion spring K 31 Connecting rod l 32 Torsion spring K 32 Torsion spring K 33 Connecting rod l 33 Connecting rod l 34 Connecting rod l 35 (ii) a The fixed connection between the large rigidity section of the right spring plate and the small rigidity section of the right spring plate is equivalent to a connecting rod l 32 And a connecting rod l 33 A fixed pair therebetween;
wherein, the connecting rod l 31 Connecting rod l 32 The length of the spring is determined by the length of the large rigidity section of the right spring plate through the 1R pseudo rigid body theory, and the torsion spring K 31 The rigidity of the right elastic sheet is determined by the section inertia moment and the length of the large rigidity section of the right elastic sheet through a 1R pseudo rigid body theory; connecting rod 33 Connecting rod l 34 Connecting rod l 35 The length of the torsion spring K is determined by the length of the small rigidity section of the right spring plate through the 2R pseudo rigid body theory 32 Torsion spring K 33 The rigidity of the spring plate is determined by the section inertia moment and the length of the small rigidity section of the right spring plate through a 2R pseudo rigid body theory; the specific expression is as follows:
s 31 ＝0.2L e
s 32 ＝0.8L e
s 33 ＝0.1L f
s 34 ＝0.44L f
s 35 ＝0.46L f
in the formula: l is a radical of an alcohol e Length of the large rigidity section of the right spring plate, L f Is the length of the small rigidity section of the right spring plate, I e Is the section moment of inertia, I, of the large rigidity section of the right spring plate f Is the section moment of inertia, s, of the small stiffness section of the right spring plate 31 、s 32 、s 33 、s 34 、s 35 Respectively correspond to a connecting rod l 31 Connecting rod l 32 Connecting rod l 33 Connecting rod l 34 Connecting rod l 35 Length of (k) 31 、k 32 、k 33 Respectively correspond to a torsional spring K 31 Torsion spring K 32 Torsion spring K 33 The rigidity of (2).
The geometric parameters of the left spring plate and the right spring plate are completely the same, so that the following relation exists:
L c ＝L e
L d ＝L f
I c ＝I e
I d ＝I f
the left flapping arm 9 is equivalent to a connecting rod l 25 And a connecting rod l 16 The tangent of the two-way pipe is fixedly connected; the right flapping arm 10 is equivalent to a connecting rod l 35 And a connecting rod l 17 The tangent of the two-way pipe is fixedly connected; the herringbone connecting structure in the distribution flexibility type transmission chain is simulated; and a connecting rod l fixedly connected with the mounting rack 3 of the flapping wing driving mechanism in the vertical direction 21 And a connecting rod 31 So that the distributed flexibility type transmission chain forms a door-shaped overall equivalent multi-rigid-body torsion spring system;
c. according to the principle of equivalent transformation between distributed load and concentrated load, the aerodynamic load along the flapping plane borne by the flapping wing 2 in the moving process is equivalent to the concentrated aerodynamic resistance F acting on the pressure center of the flapping wing wing (ii) a Centralizing qiDynamic resistance F wing The flapping wing is positioned in a flapping plane of the flapping wing, is vertical to the unfolding direction of the flapping wing and is opposite to the moving direction of the flapping wing; according to the 'phyllotaxis' method, the aerodynamic damping coefficient of the flapping wing 2 at different positions and in different motion states is obtained through the strip integral method
And the distance l between the center of pressure and the root axis aero (ii) a Using rigid rods l wing Simulating the mass characteristics of the flapping wing 2, in which the rigid rod l wing Mass m of wing The moment of inertia J of the rigid bar with respect to the root axis, equal to the true mass of the flapping wing 2 wing The actual moment of inertia of the flapping wing 2 relative to the wing root axis is equal, so that an equivalent mass-moment of inertia-aerodynamic damping system of the flapping wing 2 is established; wherein the equivalent concentrated aerodynamic drag F of the flapping wings 2 wing And its aerodynamic damping moment M formed at the root of the flapping wing 2 wing The expression of (a) is as follows:
M wing ＝F wing ·l aero
in the formula: theta wing Is the flapping angle of the flapping wing 2,
is the flapping angular velocity and aerodynamic damping coefficient of the flapping wing 2
Is the flapping angle theta of the flapping wing 2 wing And angular speed of flapping
The function of (a) is also related to the geometry of the flapping wing, and can be determined by carrying out aerodynamic experiments;
d. based on the actual position of each component in the distributed flexibility type flapping wing driving mechanismThe system carries out model assembly on a single-freedom-degree second-order linear vibration system, an equivalent multi-rigid-body torsion spring system of a distributed flexibility type transmission chain and an equivalent mass-rotational inertia-pneumatic damping system of a flapping wing, and an equivalent mass block M in an equivalent single-freedom-degree second-order vibration system of a piezoelectric bimorph driver 4 act,e Connecting rod l in multi-rigid-body torsional spring system equivalent to distributed flexibility type transmission chain 11 Carrying out fixed connection; the root parts of the flapping wings 2 in an equivalent 'mass-rotational inertia-pneumatic damping' system of a pair of flapping wings 2 are respectively connected with a connecting rod l in an equivalent 'multi-rigid-torsion spring' system of a distributed flexibility type transmission chain 16 Connecting rod l 25 Connecting rod l 17 Connecting rod l 35 Fixedly connected with the root of the left flapping wing and the connecting rod l 16 The included angle between is theta s The root of the right flapping wing and the connecting rod l 17 The included angle between is theta s Thereby an equivalent mass-rotational inertia-spring-damping system of the distributed flexibility type flapping wing driving mechanism can be built;
e. the following three independent motion parameters in an equivalent 'mass-rotational inertia-spring-damping' system of a distributed flexibility type flapping wing driving mechanism are taken to be defined as generalized displacement: equivalent linear displacement output x of piezoelectric bimorph driver 4 act Torsion spring K 11 Angle of rotation theta of 11 Torsion spring K 13 Angle of rotation theta 13 (ii) a Accordingly, a generalized displacement vector q = [ x ] is defined act θ 11 θ 13 ] T (ii) a Defining the system generalized external force vector corresponding to the generalized displacement as: f = [ F = p 0 0] T (ii) a The left-right symmetric motion constraint of the system is defined as: theta 11 ＝θ 12 、θ 13 ＝θ 14 (ii) a Substituting q and F into a second Lagrange equation, and establishing a three-degree-of-freedom second-order system forced vibration equation set of a piezoelectric-structure-flow field coupling complete machine dynamic model of the distributed flexibility type flapping wing driving mechanism as follows:
in the formula: 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 'piezoelectricity-structure-flow field' coupling complete machine dynamic model of the distributed flexibility type flapping wing driving mechanism is the driving voltage U of the piezoelectric bimorph driver 4, and the output response is the flapping angle theta of the flapping wing 2 wing ＝θ 11 +θ 13 -θ s By numerically solving a system of second order ordinary differential equations
Obtaining the flapping angle theta of the flapping wing 2 wing Steady state response function, flapping angular velocity
Steady state response function, flapping period T flap Flutter frequency f flap The relationship with the drive voltage U of the piezoelectric bimorph driver 4;
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 of the distributed flexibility type flapping wing driving mechanism to t al ；
Average aerodynamic lift of a pair of flapping wings
Obtained by the theory of phyllanthin, the expression of which is as follows:
in the formula: rho air The air density is shown, R is the half span length of the flapping wing 2, and c (R) is a transformation function of the chord length of the flapping wing 2 in the span direction;
the average lift coefficient of the flapping wing 2 in a flapping cycle can be determined according to the geometric shape of the flapping wing and the passive torsion angle around the leading edge of the flapping wing, wherein the passive torsion angle of the flapping wing around the leading edge of the flapping wing can be determined by means of experimental observation;
the whole energy conversion efficiency eta of the distributed flexibility type flapping wing driving mechanism can be obtained by a flapping wing pneumatic induced power formula and an equivalent circuit model theory of a piezoelectric bimorph, and the expression is as follows:
in the formula: p lift Induced power, P, of the flapping wing elec Electric power for piezoelectric bimorph actuators, U eff Effective value of driving voltage U, Z for piezoelectric bimorph driver eff Is the equivalent impedance of the piezoelectric bimorph driver;
overall mass m of distributed flexibility type flapping wing driving mechanism tota The shape parameters of the distribution flexibility type transmission chain, the material density, the shape parameters of the piezoelectric bimorph driver, the density of the piezoelectric ceramic material, the density of the carbon fiber material and the density of the glass fiber material are determined;
the optimization design variables are as follows: a shape parameter of a distributed compliance drive chain, comprising: the length of the big rigidity section of horizontal shell fragment, thickness and width, the length of the little rigidity section of horizontal shell fragment, thickness and width, the length of the big rigidity section of vertical shell fragment, thickness and width, the length of the little rigidity section of vertical shell fragment, thickness and width, the shape parameter of piezoelectricity bimorph driver 4, it includes: thickness t of piezoelectric ceramic layer of piezoelectric bimorph actuator 4 1 And the thickness t of the intermediate layer 2 Thickness t of the extension 3 Width w of fixed end of piezoelectric bimorph driver 4 2 And a free end width w 1 Length L of driving section of piezoelectric bimorph driver 4 2 Length L of extension segment 1 Driving voltage U by piezoelectric bimorph;
determining an optimization constraint condition according to design requirements: distributing the upper limit of the height, the width and the wingspan of the flexibility type flapping wing driving mechanism and the upper limit of the piezoelectric bimorph driving voltage U;
g. is the average aerodynamic lift of a pair of flapping wings 2
Energy conversion efficiency eta of distributed flexibility type flapping wing driving mechanism and reciprocal of mass of distributed flexibility type flapping wing driving mechanism
Corresponding weight coefficients are introduced into the three objective functions and are linearly combined to form a unified objective function, and the expression of the unified objective function is as follows:
in the formula: a is 1 ，a 2 And a 3 Is a weight coefficient, and a 1 +a 2 +a 3 =1; s is a uniform objective function, and the minimum value is reached in the optimization process;
the weight coefficient is selected according to the following principle: (1) if it is desired that the aircraft possess greater load carrying capacity and maneuverability, a is increased 1 (ii) a (2) If it is desired that the aircraft have a greater endurance, a is increased 2 (ii) a (3) If it is desired that the aircraft achieve a structurally light design in order to carry more payload, then a is increased at the same time 1 And a 3 ；
And (4) optimizing and solving the design variables by adopting a constraint optimization algorithm, and acquiring the optimal design point of the distributed flexibility type flapping wing driving mechanism in a feasible region.
Claims (6)
1. The utility model provides a distribution compliance formula flapping wing aircraft, includes fuselage (1), flight control system, flapping wing actuating mechanism and a pair of flapping wing (2), its 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 rack (3), a piezoelectric bimorph driver (4) and a distributed flexibility type transmission chain, wherein the piezoelectric bimorph driver (4) is arranged on the flapping wing driving mechanism mounting rack (3);
the distribution compliance formula driving chain is bilateral symmetry structure, and it includes a pair of vertical shell fragment and a horizontal shell fragment (7), and is 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 right side shell fragment (6) are controlled and are set up in opposite directions, and their connection structure is: firstly, the upper end part of the left spring plate (5) and the upper end part of the right spring plate (6) are respectively and symmetrically pre-bent and deformed outwards, the left end part and the right end part of the transverse spring plate (7) are respectively and pre-bent and deformed upwards, then the left end part of the transverse spring plate (7) and the upper end part of the left spring plate (5) are fixedly bonded together, and the right end part of the transverse spring plate (7) and the upper end part of the right spring plate (6) are fixedly bonded together, so that the distribution flexibility type transmission chain with pre-stress elasticity 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 respectively a left flapping arm (9) and a right flapping arm (10), a left flapping arm supporting part is formed at the intersection of the left spring sheet (5) and the transverse spring sheet (7), and the connecting part of the left spring sheet (5) and the transverse spring sheet (7) at the outer end of the left flapping arm supporting part forms the left flapping arm (9); a right flapping arm supporting part is formed at the intersection of the right elastic sheet (6) and the transverse elastic sheet (7), and the right flapping arm (10) is formed at the connecting part of the right elastic sheet (6) at the outer end of the right flapping arm supporting part and the transverse elastic sheet (7); the left flapping arm (9) and the right flapping arm (10) are inclined upwards 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 bilateral symmetry structure; the middle part of the transverse elastic sheet (7) forms the flapping transmission part (8);
the pair of flapping wings (2) are respectively and symmetrically arranged on the left side flapping arm (9) and the right side flapping arm (10);
the fixed end of the piezoelectric bimorph driver (4) is fixed at the rear end of the distributed flexibility type transmission chain, and the free end of the piezoelectric bimorph driver is fixedly connected with the flapping transmission part (8) of the distributed flexibility 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 the pre-stress elastic force, the distributed flexibility type transmission chain drives the left side flapping arm (9) and the right side flapping arm (10) to do same-frequency and same-amplitude flapping motion, so that the pair of flapping wings (2) are driven to do flapping motion to generate lift force.
2. The distributed compliance ornithopter of claim 1, wherein: in the distributed flexibility type transmission chain, the flapping transmission part (8) of the 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, the rigidity of the transverse elastic sheet large rigidity section is greater 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 spring piece (5) and the right spring piece (6) are vertical spring piece large rigidity sections, the upper parts of the left flapping arm (9) and the right flapping arm (10) are vertical spring piece small rigidity sections, and the rigidity of the vertical spring piece large rigidity sections is greater than that of the vertical spring piece small rigidity sections; the large vertical spring piece stiffness section of the left spring piece (5) is a large left spring piece stiffness section, the small vertical spring piece stiffness section of the left spring piece (5) is a small left spring piece stiffness section, the large vertical spring piece stiffness section of the right spring piece (6) is a large right spring piece stiffness section, and the small vertical spring piece stiffness section of the right spring piece (6) is a small right spring piece stiffness section; the lower part of the large rigidity section of the left spring plate and the lower part of the large rigidity section of the right spring plate 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 driving part (8) in a vertical direction when vibrating.
3. The distributed compliance ornithopter of claim 1, wherein: the two flapping arms are connected with the flapping wing (2) through a hinge type connecting structure; the hinge type connecting structure comprises a flapping arm connecting piece (12), a pre-bending angle adjusting flexible hinge (13), a flapping wing connecting plate piece (14) and a passive torsion flexible hinge (15); the flapping arm connecting plate (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 plate (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 does flapping motion, the flapping wing (2) can wind the front edge of the passive torsion flexible hinge (15) to do passive torsion motion under the combined action of aerodynamic force and self inertial force.
4. The distributed compliance ornithopter of claim 2, wherein: the flapping wing driving mechanism mounting frame (3) is made of woven carbon fiber laminated plates, the bending positions of the flapping wing driving mechanism mounting frame (3) are connected through flexible bending films in the middle layers of the woven carbon fiber laminated plates to form folding seams, and the folding seams of the woven carbon fiber laminated plates and the butt seams of the woven carbon fiber laminated plates are glued and fixed, so that the flapping wing driving mechanism mounting frame (3) forms an integrated structure; the left spring plate (5), the right spring plate (6) and the transverse spring plate (7) are formed by mutually laminating and bonding three polypropylene thin plates with the same width, wherein the two polypropylene thin plates on the outer side have the same thickness, and the rigidity is realized by the thickness of the polypropylene thin plate on the middle layer.
5. The distributed compliance ornithopter of claim 3, wherein: the flapping arm connecting sheet (12) and the flapping wing connecting plate sheet (14) are both made of carbon fiber laminated plates, and the pre-bending angle adjusting flexible hinge (13) and the passive torsion flexible hinge (15) are both made of polyimide.
6. A design method of a flapping wing driving mechanism with distributed flexibility is characterized by comprising the following steps:
a. according to the principle of a concentrated mass method, the piezoelectric bimorph driver (4) is simplified into a piezoelectric bimorph driver with an equivalent mass M act,e Equivalent linear damping C act,e Equivalent linear spring K act,e And equivalent piezoelectric driving force F p The equivalent single-degree-of-freedom second-order linear vibration system; the equivalent mass M is displaced by a pair of vertical displacements act,e And (3) connecting with the ground: equivalent linear spring K act,e Equivalent linear damping C act,e Are connected in parallel with each other along the vertical direction, and the upper ends of the two are all connected with an equivalent mass block M act,e The lower ends of the fixed connection bodies are fixedly connected with the ground; equivalent piezoelectric driving force F p Acting on equivalent mass M in vertical direction act,e In the linear range, the equivalent piezoelectric driving force F p And the electric field intensity E along the thickness direction of the piezoelectric ceramic sheet V Is in direct proportion;
namely: f p ＝λ p E V
In the formula: lambda [ alpha ] p Is the force-electric proportionality coefficient; e V Then is the piezoelectric bimorph drive voltage U and the drive frequency f elec A function of (a); equivalent mass block M act,e The displacement along the vertical direction is defined as the equivalent linear displacement output x of the piezoelectric bimorph driver (4) act ；
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 1R and 2R pseudo-rigid-body model theory of the large-deformation flexible beam, 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 sheet, the supporting part of the left flapping arm supports the transverse elastic sheet (7), and the part between the left end of the flapping transmission part (8) and the supporting part of the left flapping arm is equivalent toTorsional spring K 11 The left flapping arm supporting part is equivalent to a torsion spring K 13 (ii) a The left end of the flapping transmission part (8) and the torsion spring K 11 Equivalent to connecting rod l 12 Said torsion spring K 13 And the torsion spring K 11 The middle part is equivalent to a connecting rod l 14 The part of the left flapping arm (9) is equivalent to a connecting rod l 16 (ii) a The fixed connection between the flapping transmission part (8) and the small rigidity section at the left side of the transverse elastic sheet is equivalent to a connecting rod l 11 And a connecting rod l 12 A fixed pair therebetween;
in the small rigidity section at the right side of the transverse elastic sheet, the torsion spring K is connected with the transverse elastic sheet 11 Said torsion spring K 13 Said connecting rod l 12 Said connecting rod l 14 Said connecting rod l 16 The corresponding parts are respectively equivalent to torsion springs K 12 Torsion spring K 14 Connecting rod l 13 Connecting rod l 15 Connecting rod l 17 (ii) a The fixed connection between the flapping transmission part (8) and the small rigidity section at the right side of the transverse elastic sheet is equivalent to a connecting rod l 11 And a connecting rod l 13 A fixed pair therebetween;
b) In the left spring plate (5);
in the large rigidity section of the left spring plate, the transmission chain fixing plate (11) is fixedly connected with the mounting rack (3) of the flapping wing driving mechanism to keep the large rigidity section of the left spring plate in the vertical direction equivalent to a connecting rod l 21 Next to the connecting rod l 21 Is equivalent to a torsion spring K 21 Is located in the torsion spring K 21 The above parts are equivalent to a connecting rod l 22 ；
In the small rigidity section of the left elastic sheet, the supporting part of the left flapping arm is equivalent to a torsion spring K 23 (ii) a In the torsion spring K 23 And the connecting rod l 22 The part between is equivalent to a torsion spring K 22 Said torsion spring K 22 The following parts are equivalent to a connecting rod l 23 Said torsion spring K 22 With the torsion spring K 23 The middle part is equivalent to a connecting rod l 24 The part of the left flapping arm (9) is equivalent to a connecting rod l 25 (ii) a The fixed connection between the large rigidity section of the left spring plate and the small rigidity section of the left spring plate is equivalent to a connecting rodl 22 And a connecting rod l 23 A fixed pair therebetween;
in the right spring (6), the connecting rod l 21 Said torsion spring K 21 Said connecting rod l 22 Said torsion spring K 22 Said torsion spring K 23 Said connecting rod l 23 Said connecting rod l 24 Said connecting rod l 25 The corresponding parts are respectively equivalent to connecting rods l 31 Torsion spring K 31 Connecting rod l 32 Torsion spring K 32 Torsion spring K 33 Connecting rod l 33 Connecting rod l 34 Connecting rod l 35 (ii) a The fixed connection between the large rigidity section of the right spring plate and the small rigidity section of the right spring plate is equivalent to a connecting rod l 32 And a connecting rod l 33 A fixed pair therebetween;
equating the left flapping arm (9) to the connecting rod l 25 With said connecting rod l 16 The tangent of the two-way pipe is fixedly connected; equating the right flapping arm (10) to the connecting rod l 35 And the connecting rod l 17 The tangent of the two-way pipe is fixedly connected; simulating a herringbone connecting structure in the distributed flexibility type transmission chain; and the connecting rod l fixedly connected with the mounting rack (3) of the flapping wing driving mechanism in the vertical direction 21 And the connecting rod l 31 So that the distributed flexibility type transmission chain forms an equivalent multi-rigid-torsional spring system in a shape like a Chinese character 'men';
c. according to the principle of equivalent transformation between distributed load and concentrated load, the aerodynamic load along the flapping plane borne by the flapping wing (2) in the moving process is equivalent to the concentrated aerodynamic resistance F acting on the pressure center of the flapping wing wing (ii) a Said central aerodynamic resistance F wing The flapping wing is positioned in a flapping plane of the flapping wing, is vertical to the unfolding direction of the flapping wing, and is opposite to the moving direction of the flapping wing; according to the 'phyllotaxis' method, the aerodynamic damping coefficient of the flapping wing (2) at different positions and in different motion states is obtained through the strip integral method
And the distance l between the center of pressure and the root axis aero (ii) a By using rigidityRod l wing Simulating the mass characteristics of the flapping wing (2), wherein the rigid rod l wing Mass m of wing The moment of inertia J of the rigid rod relative to the root axis of the flapping wing (2) is equal to the true mass of the flapping wing wing The actual moment of inertia of the flapping wing (2) relative to the wing root axis is equal, so that an equivalent mass-moment of inertia-aerodynamic damping system of the flapping wing (2) is established; wherein the equivalent concentrated aerodynamic drag F of the flapping wing (2) wing And the aerodynamic damping moment M formed at the wing root of the flapping wing (2) wing The expression of (c) is as follows:
M wing ＝F wing ·l aero
in the formula: theta wing Is the flapping angle of the flapping wing (2),
is the flapping angular velocity of the flapping wing (2); coefficient of aerodynamic damping
Is the flapping angle theta of the flapping wing wing And angular speed of flapping
A function of (a);
d. according to the actual position relation of each component in the distributed flexibility type flapping wing driving mechanism, carrying out model assembly on the equivalent single-degree-of-freedom second-order linear vibration system of the piezoelectric bimorph driver (4), the equivalent multi-rigid-torsion spring system of the distributed flexibility type transmission chain and the equivalent mass-rotational inertia-pneumatic damping system of the flapping wing, and carrying out model assembly on an equivalent mass block M in the equivalent single-degree-of-freedom second-order vibration system of the piezoelectric bimorph driver (4) act,e Equivalent multi-rigid-body torsional spring system of distributed flexibility type transmission chainThe connecting rod l in 11 Carrying out fixed connection; respectively connecting the root part of the flapping wing (2) in a pair of flapping wing equivalent 'mass-rotational inertia-pneumatic damping' systems with the connecting rod l in the distributed flexibility type transmission chain equivalent 'multi-rigid-torsion spring' system 16 Said connecting rod l 25 Said connecting rod l 17 Said connecting rod l 35 Fixedly connected, the root of the left flapping wing is connected with the connecting rod l 16 The included angle between is theta s The root of the right flapping wing and the connecting rod l 17 The included angle between is theta s So as to build an equivalent mass-rotational inertia-spring-damping system of the distributed flexibility type flapping wing driving mechanism;
e. the following three independent motion parameters in an equivalent 'mass-rotational inertia-spring-damping' system of the distributed flexibility type flapping wing driving mechanism are taken and defined as generalized displacement: the equivalent linear displacement output x of the piezoelectric bimorph driver (4) act Said torsion spring K 11 Angle of rotation theta 11 Said torsion spring K 13 Angle of rotation theta 13 (ii) a Accordingly, a generalized displacement vector q = [ x ] is defined act θ 11 θ 13 ] T (ii) a Defining the system generalized external force vector corresponding to the generalized displacement as: f = [ F = p 0 0] T (ii) a The left-right symmetric motion constraint of the system is defined as: theta 11 ＝θ 12 、θ 13 ＝θ 14 (ii) a Substituting q and F into a second Lagrange equation, and establishing 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 as follows:
in the formula: m is a system generalized mass matrix, C is a system generalized damping matrix and K is a system generalized stiffness matrix;
"piezoelectricity-structure-flow field" coupling complete machine dynamics model of distribution flexibility formula flapping wing actuating mechanismThe input excitation is the driving voltage U of the piezoelectric bimorph driver (4), and the output response is the flapping angle theta of the flapping wing (2) wing ＝θ 11 +θ 13 -θ s By numerically solving a system of second order ordinary differential equations
Obtaining the flapping angle theta of the flapping wing wing Steady state response function, flapping angular velocity
Steady state response function, flapping period T flap Flapping frequency f flap A relation with a drive voltage U of the piezoelectric bimorph driver (4);
f. the objective function of the overall comprehensive performance optimization problem of the distributed flexibility type flapping wing driving mechanism is as follows: a pair of said flapping wings (2) having a mean aerodynamic lift
The whole energy conversion efficiency eta of the distributed flexibility type flapping wing driving mechanism and the whole mass m of the distributed flexibility type flapping wing driving mechanism total ；
A pair of said flapping wings
Obtained by the theory of phyllanthin, the expression of which is as follows:
in the formula: rho air R is the half span length of the flapping wing (2) for the air density, c (R) is the transformation function of the chord length of the flapping wing (2) in the wingspan direction,
for said flapping wing(2) The average lift coefficient over a flapping cycle;
the whole energy conversion efficiency eta of the distributed flexibility type flapping wing driving mechanism is obtained through a flapping wing aerodynamic induced power formula of a hovering flapping wing aircraft and an equivalent circuit model theory of a piezoelectric bimorph, and the expression is as follows:
in the formula: p lift Is the induced power of the flapping wing, P elec Electric power for the piezoelectric bimorph driver, U eff Is the effective value, Z, of the driving voltage U of the piezoelectric bimorph driver eff Is the equivalent impedance of the piezoelectric bimorph driver;
the optimization design variables are: shape parameters of the distributed compliance drive chain, comprising: the length, the thickness and the width of the large rigidity section of the transverse elastic sheet, the length, the thickness and the width of the small rigidity section of the transverse elastic sheet, the length, the thickness and the width of the large rigidity section of the vertical elastic sheet, the length, the thickness and the width of the small rigidity section of the vertical elastic sheet, and the shape parameters of the piezoelectric bimorph driver (4) comprise: the thickness t of the piezoelectric ceramic layer of the piezoelectric bimorph actuator (4) 1 And the thickness t of the intermediate layer 2 Thickness t of the extension 3 Width w of fixed end of the piezoelectric bimorph driver (4) 2 And a free end width w 1 The length L of the driving section of the piezoelectric bimorph driver (4) 2 And the length L of the extension segment 1 The piezoelectric bimorph drives a voltage U;
determining an optimization constraint condition according to design requirements: the upper limit of the height, the width and the wingspan of the distributed-flexibility flapping wing driving mechanism and the upper limit of the driving voltage U of the piezoelectric bimorph driver (4) are set;
g. is the average aerodynamic lift of a pair of the flapping wings (2)
Said distributionEnergy conversion efficiency eta of flexibility type flapping wing driving mechanism and reciprocal of mass of distribution flexibility type flapping wing driving mechanism
The three objective functions introduce corresponding weight coefficients and are linearly combined to form a unified objective function, and the expression of the unified objective function is as follows:
in the formula: a is 1 ，a 2 And a 3 Is a weight coefficient, and a 1 +a 2 +a 3 =1; s is a uniform objective function, and the minimum value is reached in the optimization process;
the weight coefficient is selected according to the following principle: (1) if it is desired that the aircraft possess greater load carrying capacity and maneuverability, a is increased 1 (ii) a (2) If it is desired that the aircraft have a greater endurance, a is increased 2 (ii) a (3) If it is desired that the aircraft achieve a structurally light design in order to carry more payload, then a is increased at the same time 1 And a 3 ；
And optimizing and solving the design variables by adopting a constraint optimization algorithm, and acquiring the optimal design point of the distributed flexibility type flapping wing driving mechanism in a feasible region.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211432775.7A CN115649437B (en) | 2022-11-16 | 2022-11-16 | Design method of distributed flexibility type flapping wing aircraft and flapping wing driving mechanism |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211432775.7A CN115649437B (en) | 2022-11-16 | 2022-11-16 | Design method of distributed flexibility type flapping wing aircraft and flapping wing driving mechanism |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN115649437A true CN115649437A (en) | 2023-01-31 |
| CN115649437B CN115649437B (en) | 2024-05-03 |
Family
ID=85021229
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211432775.7A Active CN115649437B (en) | 2022-11-16 | 2022-11-16 | Design method of distributed flexibility type flapping wing aircraft and flapping wing driving mechanism |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115649437B (en) |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103708033A (en) * | 2013-12-23 | 2014-04-09 | 上海交通大学 | Double piezoelectric actuators type micro flapping wing aircraft based on soft hinges |
| US20150307191A1 (en) * | 2014-04-28 | 2015-10-29 | Daedalus Flight Systems, LLC | Flapping wing aerial vehicles |
| CN105217031A (en) * | 2015-10-29 | 2016-01-06 | 西北工业大学 | A kind of micro air vehicle with flapping-wing based on fans drive |
| CN106081104A (en) * | 2016-07-20 | 2016-11-09 | 上海交通大学 | A kind of insecticide yardstick Piezoelectric Driving flapping-wing MAV |
-
2022
- 2022-11-16 CN CN202211432775.7A patent/CN115649437B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103708033A (en) * | 2013-12-23 | 2014-04-09 | 上海交通大学 | Double piezoelectric actuators type micro flapping wing aircraft based on soft hinges |
| US20150307191A1 (en) * | 2014-04-28 | 2015-10-29 | Daedalus Flight Systems, LLC | Flapping wing aerial vehicles |
| CN105217031A (en) * | 2015-10-29 | 2016-01-06 | 西北工业大学 | A kind of micro air vehicle with flapping-wing based on fans drive |
| CN106081104A (en) * | 2016-07-20 | 2016-11-09 | 上海交通大学 | A kind of insecticide yardstick Piezoelectric Driving flapping-wing MAV |
Non-Patent Citations (1)
| Title |
|---|
| 王姝歆;陈国平;周建华;颜景平;: "压电双晶片驱动的仿生柔性扑翼机构研究", 光学精密工程, no. 04, 25 August 2006 (2006-08-25) * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN115649437B (en) | 2024-05-03 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108945430B (en) | Bionic flapping-folding-active torsion hybrid-driven flapping wing aircraft | |
| CN103395493B (en) | Piezoelectric ceramic flapping-wing-type robot | |
| CN102338690B (en) | Three-freedom-degree flapping-wing comprehensive experiment platform | |
| CN108945431A (en) | The imitative birds of flapping-wing aircraft and the folding wing of bat | |
| CN111688911B (en) | Deformation wing device based on four-corner star-shaped scissor mechanism and rib plates with variable lengths | |
| CN115892465A (en) | Distributed flexibility type flapping wing driving mechanism and design method thereof | |
| CN106275388A (en) | A kind of based on planar linkage closed-loop element containing hinge deformable trailing edge mechanism again | |
| CN108750104B (en) | Flapping wing aircraft with self-adaptive and actively twisted wings | |
| CN111688913B (en) | Dual-drive wing with variable span length and up-down dihedral angle | |
| CN105217031A (en) | A kind of micro air vehicle with flapping-wing based on fans drive | |
| CN211996141U (en) | Bionic flapping wing aircraft with self-adaptive attack angle | |
| CN202075115U (en) | Three degrees of freedom flapping wing integrated experiment platform | |
| CN209814271U (en) | Four-degree-of-freedom flapping wing aircraft device | |
| CN109911197B (en) | Four-degree-of-freedom ornithopter device | |
| CN115649437A (en) | Distributed flexibility type flapping wing aircraft and design method of flapping wing driving mechanism | |
| CN113415409A (en) | Non-control surface aircraft wing with variable camber | |
| CN116461691A (en) | Airfoil continuous deformation mechanism based on slide bar-flexible truss-skin | |
| Liu et al. | Liftoff of a motor-driven flapping wing rotorcraft with mechanically decoupled wings | |
| CN216374999U (en) | Copying ornithopter | |
| CN115837977A (en) | Flapping folding movement mechanism for flapping wing aircraft | |
| CN113799981B (en) | Flapping wing device for dragonfly-imitating flapping wing aircraft | |
| CN115432154A (en) | Variable-stiffness simulated bat flexible flapping wing propulsion device with span-chord-direction movement function | |
| CN113859528A (en) | Dragonfly-like flapping wing aircraft | |
| Swain et al. | Effect of wing flexibility on the aerodynamic performance of a robotic dragonfly | |
| CN112319800A (en) | Bionic flapping wing aircraft imitating butterfly wing |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |