Pre-stress controllable piezoelectric bimorph deformation wing based on flexible hinge parallel and method

Abstract

The application discloses a pre-pressure controllable piezoelectric bimorph deformation wing based on a flexible hinge parallel connection and a method. The deformation wing mainly comprises four layers of piezoelectric composite bimorphs fixed at a leading edge, the two sides of the four layers of bimorphs are short and the middle is long, and the four layers of bimorphs are connected in parallel through four interlayer connecting rib structures; the third group of interlayer connecting rib structures are provided with protruding shafts at positions corresponding to the two sides of the rotation shafts of the uppermost and lowermost piezoelectric composite bimorphs, bearings and prefabricated clamping groove bearing sleeves are sleeved on the protruding shafts, polymer spiral winding actuators fixed at the leading edge are sleeved on the bearing sleeves to load and unload axial pressure; one of the two middle layers of longer bimorphs is fixedly connected with a trailing edge, and the other layer can slide in a prefabricated slot at a tail edge; finally, upper and lower skins are fixed with upper and lower sides of a large end of the leading edge, four groups of ribs and upper and lower sides of a large end of the trailing edge in sequence. The application can greatly improve the output power of the pre-compressed piezoelectric bimorph deformation wing and prolong the service life of the piezoelectric bimorph deformation wing.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of high-power piezoelectric actuation. Specifically, it relates to a pre-compression controllable piezoelectric bimorph deformation wing based on flexible hinge parallel connection and a method. BACKGROUND

[0002] Pre-compression piezoelectric composite bimorphs can directly produce large bending deformation and have a large working frequency band, so they are expected to be used as a new generation of micro air vehicle continuous deformation wing actuators. However, long-term loading of axial pressure will cause the initial bending of the bimorphs due to the material itself and the processing and manufacturing to further increase, eventually leading to the breakage of the piezoelectric bimorphs. On the other hand, the output force of a single layer of pre-compression piezoelectric composite bimorphs is not large enough, and the internal space of the deformation wing is very small, but the existing interlayer parallel connection can only connect three layers of bimorph actuators at most, which limits the output force of the deformation wing. Therefore, how to further increase the output force of the pre-compression piezoelectric composite bimorph deformation wing in the small internal space of the deformation wing and improve the working life is a technical problem that needs to be solved at present. SUMMARY

[0003] In order to improve the output force and actuation displacement of the existing piezoelectric bimorph actuator, the purpose of the present application is to provide a pre-compression controllable piezoelectric bimorph deformation wing based on flexible hinge parallel connection and a method, in order to further increase the output force of the pre-compression piezoelectric composite bimorph deformation wing in the small internal space of the deformation wing and improve the working life, so as to further move towards the engineering direction.

[0004] In order to achieve the above-mentioned purpose, the present application uses a group of flexible rolling contact hinges to connect the wing rib structure between layers to correlate the transverse actuation of four layers of piezoelectric composite bimorphs at certain lengths. The main part of the flexible rolling contact hinge of the flexible rolling contact hinge interlayer connecting wing rib structure can make the rolling of each hinge disc with unchanged radial distance, so as to correlate the transverse movement of the four layers of piezoelectric composite bimorphs, and decouple the rotation of each layer of bimorph section around the neutral axis. Since the flexible rolling contact hinge structure is more compact than the existing interlayer parallel connection structure, more layers of piezoelectric bimorphs can be connected in parallel, thereby increasing the output force of the deformation wing. On the other hand, the present application controls the temperature of the polymer spiral winding actuator by power supply, realizes the function of loading axial pressure on the bimorph during work and unloading axial pressure during non-work, and improves the working life of the pre-compression piezoelectric bimorph deformation wing.

[0005] The present application specifically adopts the following technical solutions:

[0006] In a first aspect, the present application provides a pre-pressure controllable piezoelectric bimorph deformation wing based on a flexible hinge parallel mechanism, which comprises a leading edge, a trailing edge, a skin, a polymer spiral winding actuator, and upper, middle upper, middle lower and lower piezoelectric composite bimorphs arranged in sequence from top to bottom; the four piezoelectric composite bimorphs have the same width and their fixed ends are fixed to the leading edge, the lengths of the middle upper and middle lower piezoelectric composite bimorphs are greater than those of the upper and lower piezoelectric composite bimorphs, and the four piezoelectric composite bimorphs are mirror symmetric about the center plane of the deformation wing as a whole; the trailing edge is horizontally provided with an upper pre-prepared groove and a lower pre-prepared groove, the free end of the middle upper piezoelectric composite bimorph is inserted into the upper pre-prepared groove of the trailing edge and fixed, and the free end of the middle lower piezoelectric composite bimorph is inserted into the lower pre-prepared groove of the trailing edge and forms a sliding fit;

[0007] The four piezoelectric composite bimorphs are connected through four interlayer connecting rib structures with flexible rolling contact hinges to form a fit, which are first, second, third and fourth interlayer connecting rib structures from the leading edge to the trailing edge; the upper and lower piezoelectric composite bimorphs pass through the first, second and third interlayer connecting rib structures in sequence, while the middle upper and middle lower piezoelectric composite bimorphs pass through all the four interlayer connecting rib structures from the leading edge to the trailing edge in sequence;

[0008] Any Mth interlayer connecting rib structure takes two ribs as the skeleton, the two ribs are fixed on the inner surface of the skin wrapped outside the morphing wing in the form of roots opposite, and the roots of the two ribs on the same side are flexibly connected by a group of flexible rolling contact hinge structures; each group of flexible rolling contact hinge structures includes 2 half-round connecting discs, N-2 first full-round connecting discs, N-1 second full-round connecting discs and N adapter shafts, the diameter of the second full-round connecting disc is smaller than that of the first full-round connecting disc, the diameters of the half-round connecting disc and the first full-round connecting disc are consistent, wherein N is the number of piezoelectric composite bimorphs passing through the Mth interlayer connecting rib structure; the plane ends of the two half-round connecting discs are respectively fixedly connected to the roots of the two ribs, the N-2 first full-round connecting discs and the N-1 second full-round connecting discs are alternately arranged between the curved ends of the two half-round connecting discs, and the second full-round connecting disc is adjacent to the half-round connecting disc; a flexible connecting belt is arranged between any two adjacent connecting discs, one end of the flexible connecting belt is fixedly wrapped on one of the adjacent connecting discs through one side belt surface, the other end of the flexible connecting belt is fixedly wrapped on the other adjacent connecting disc through the other side belt surface, and the two adjacent connecting discs always keep the edges abutting under the connection of the flexible connecting belt and can roll relative to each other with the radial distance unchanged; all the half-round connecting discs and the first full-round connecting discs are respectively fixedly connected to one adapter shaft; each side flexible rolling contact hinge structure of the Mth interlayer connecting rib structure is fixedly connected to the same side of the N piezoelectric composite bimorphs passing through the Mth interlayer connecting rib structure through the N adapter shafts, so that the piezoelectric composite bimorphs are actuated in parallel; M is one, two, three or four;

[0009] The third interlayer connecting rib structure is provided with an extending shaft at the positions corresponding to the upper piezoelectric composite bimorph and the lower piezoelectric composite bimorph on the left and right sides, a bearing is sleeved on each of the four extending shafts, a prefabricated clamping groove bearing sleeve is sleeved on each bearing, a prefabricated clamping groove is opened on the outer wall of each prefabricated clamping groove bearing sleeve in the circumferential direction, and a polymer spiral winding type actuator is sleeved on each prefabricated clamping groove, and one end of each polymer spiral winding type actuator is fixed to the leading edge. The four piezoelectric composite bimorphs are subjected to axial pressure by the four polymer spiral winding type actuators on both sides.

[0010] As a preferred embodiment of the first aspect, the first interlayer connecting rib structure has two groups of flexible rolling contact hinge structures, each group of flexible rolling contact hinge structures has 2 half-round connecting discs, 2 first full-round connecting discs, 3 second full-round connecting discs and 4 adapter shafts, the 2 first full-round connecting discs are arranged between the 2 half-round connecting discs, the adjacent half-round connecting disc and the first full-round connecting disc are connected by the 1 second full-round connecting disc, and the adjacent two first full-round connecting discs are also connected by the 1 second full-round connecting disc; the spacing of the 4 adapter shafts is the same as the spacing of the four piezoelectric composite bimorphs.

[0011] As a preferred embodiment of the first aspect, the second interlayer connecting rib structure is identical in structure to the first interlayer connecting rib structure, except that the second rib height in the second interlayer connecting rib structure is smaller than the first rib height in the first interlayer connecting rib structure.

[0012] As a preferred embodiment of the first aspect, the third interlayer connecting rib structure is identical in structure to the second interlayer connecting rib structure, except that the third rib height in the third interlayer connecting rib structure is smaller than the second rib height in the second interlayer connecting rib structure.

[0013] As a preferred embodiment of the first aspect, there are two groups of flexible rolling contact hinge structures in the fourth interlayer connecting rib structure, each group of flexible rolling contact hinge structures having 2 half-round connecting plates, 1 second full-round connecting plate, and 2 adapter shafts, the 2 half-round connecting plates being connected by the 1 second full-round connecting plate; the 4 adapter shafts have the same spacing as the four-layer piezoelectric composite bimorph.

[0014] As a preferred embodiment of the first aspect, the prefabricated card slot bearing sleeve is axially sleeved on the bearing in an interference fit, and the bearing is a micro bearing.

[0015] As a preferred embodiment of the first aspect, the four-layer piezoelectric composite bimorph is composed of an intermediate layer and upper and lower piezoelectric composite materials attached to the upper and lower surfaces of the intermediate layer, respectively, the intermediate layer having two sides provided with protruding lugs for connecting and fixing with the adapter shafts, and each adapter shaft being fixedly connected with the corresponding protruding lug by a bolt and nut.

[0016] As a preferred embodiment of the first aspect, the polymer spiral-wound actuator is a torsional geometry formed by continuously twisting the polymer fiber material and the heat-conducting metal wire into a curled spiral shape while maintaining tension; and a certain length of the polymer fiber material and the heat-conducting metal wire at both ends of the polymer spiral-wound actuator is not spiral-wound, the polymer fiber material at one end forming a loop to be sleeved on the prefabricated card slot bearing sleeve, the polymer fiber material at the other end being fixed to the leading edge, and the heat-conducting metal wires at both ends being used for connecting an external power source; preferably, a thermistor is embedded in the polymer spiral-wound actuator for monitoring the temperature of the polymer spiral-wound actuator.

[0017] In a second aspect, the present application provides an actuation method for a flexible-hinge-parallel-based pre-stress controllable piezoelectric bimorph deformation wing, which employs any of the solutions of the first aspect, and the method comprises:

[0018] In the actuation working state, voltages are applied to the upper piezoelectric composite bimorph, the middle-upper piezoelectric composite bimorph, the middle-lower piezoelectric composite bimorph and the lower piezoelectric composite bimorph in the morphing wing respectively, wherein the upper piezoelectric composite of the four-layer piezoelectric bimorph is applied with a voltage of the same polarity and the same amplitude, the lower piezoelectric composite of the four-layer piezoelectric bimorph is applied with a voltage of the opposite polarity and the same amplitude, so that the four-layer piezoelectric bimorph bends synchronously in the same direction; during the bending of the four-layer piezoelectric bimorph, the lateral deformation force is transmitted to the upper and lower skins and the trailing edge through the flexible rolling contact hinge structure of the four interlayer connecting rib structures, while the cross sections of the four-layer piezoelectric bimorph are kept independent of each other, so that the skins fixed on the four interlayer connecting rib structures are elongated or shortened, and the trailing edge is deflected with the free end of the middle two piezoelectric bimorphs, so that the morphing wing surface is continuously and smoothly deformed; when it is needed to increase the overall deformation amplitude of the morphing wing, the polymer spiral winding actuator in the bearing sleeve is further applied with a power voltage, so that the polymer spiral winding actuator is heated and shrinks, the shrinkage force is transmitted to the four-layer piezoelectric bimorph through the third interlayer connecting rib structure, so that the piezoelectric composite bimorph is subjected to axial pre-pressure, and the bending deformation is increased.

[0019] In the non-actuation working state, the voltages applied to the four-layer piezoelectric composite bimorph and the polymer spiral winding actuator are removed, so that the morphing wing is in a non-deformed state.

[0020] As a preferred embodiment of the second aspect, the total axial pressure applied by the four polymer spiral winding actuators to all piezoelectric composite bimorphs should be less than the total first-order axial buckling force of all piezoelectric composite bimorphs.

[0021] Compared with the prior art, the present application has the following advantages:

[0022] The present application adopts a more compact flexible rolling contact hinge interlayer connecting rib structure, so that the number of parallel piezoelectric bimorphs in a narrow space is further increased, the output force is increased, and the output power is increased; by applying or unloading the power voltage to the polymer spiral winding actuator, the polymer spiral winding actuator is heated and shrinks or returns to the original length, the loading and unloading of the axial pre-pressure of the four-layer piezoelectric bimorph are controlled, and the service life of the pre-compressed piezoelectric bimorph morphing wing is prolonged. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 is an axonometric view of the pre-pressure controllable piezoelectric bimorph morphing wing based on flexible hinge parallelism of the present application;

[0024] Figure 2 is the parts explosion diagram of the flexible hinge-based parallel pre-pressure controllable piezoelectric bimorph deformed wing of the present application;

[0025] Figure 3 is the schematic diagram of the first flexible rolling contact hinge interlayer connecting rib structure;

[0026] Figure 4 is the schematic diagram of the second flexible rolling contact hinge interlayer connecting rib structure;

[0027] Figure 5 is the schematic diagram of the third flexible rolling contact hinge interlayer connecting rib structure;

[0028] Figure 6 is the schematic diagram of the fourth flexible rolling contact hinge interlayer connecting rib structure;

[0029] Figure 7 is the deformation schematic diagram of the second flexible rolling contact hinge interlayer connecting structure;

[0030] Figure 8 is the structural schematic diagram of the polymer spiral winding actuator;

[0031] Figure 9 is the side view of the flexible hinge-based parallel pre-pressure controllable piezoelectric bimorph deformed wing of the present application before deformation.

[0032] Figure 10 is the side view of the flexible hinge-based parallel pre-pressure controllable piezoelectric bimorph deformed wing of the present application after deformation.

[0033] In the figure, 1 is the leading edge, 2 is the first interlayer connecting rib structure, 21 is the first rib, 22 is the second whole round connecting disc, 23 is the first whole round connecting disc, 24 is the flexible connecting belt, 25 is the half round connecting disc, 26 is the adapter shaft, 3 is the second interlayer connecting rib structure, 31 is the second rib, 4 is the micro bearing, 5 is the pre-made clamping groove bearing sleeve, 6 is the third interlayer connecting rib structure, 61 is the third rib, 62 is the extended shaft, 7 is the fourth interlayer connecting rib structure, 71 is the fourth rib, 8 is the trailing edge, 81 is the upper pre-made groove of the trailing edge, 82 is the lower pre-made groove of the trailing edge, 9 is the polymer spiral winding type actuator, 91 is the polymer fiber material, 92 is the thermistor, 93 is the heat-conducting metal wire, 94 is the wire clamping aluminum sleeve, 10 is the bolt and nut, 11 is the skin, 12 is the upper layer piezoelectric composite bimorph, 13 is the middle upper layer piezoelectric composite bimorph, 14 is the middle lower layer piezoelectric composite bimorph, and 15 is the lower layer piezoelectric composite bimorph. DETAILED DESCRIPTION

[0034] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. Technical features in the various embodiments of the present invention can be combined accordingly without mutual conflict.

[0035] In the description of this invention, it should be understood that when an element is considered to be "connected" to another element, it can be a direct connection to the other element or an indirect connection, i.e., there is an intermediate element. Conversely, when an element is said to be "directly" connected to another element, there is no intermediate element.

[0036] In the description of this invention, it should be understood that the terms "first" and "second" are used only for descriptive purposes and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first" and "second" may explicitly or implicitly include at least one of those features.

[0037] like Figures 1-6 As shown, in a preferred embodiment of the present invention, a pre-pressure controllable piezoelectric bicrystalline deformable wing based on parallel flexible hinges is provided. Its main components include a leading edge 1, a trailing edge 8, a skin 11, a polymer helical actuator 9, and four parallel piezoelectric composite bicrystalline layers. The four piezoelectric composite bicrystalline layers are arranged at intervals in the vertical direction, from top to bottom as an upper piezoelectric composite bicrystalline layer 12, a middle-upper piezoelectric composite bicrystalline layer 13, a middle-lower piezoelectric composite bicrystalline layer 14, and a lower piezoelectric composite bicrystalline layer 15. One end of each piezoelectric composite bicrystalline layer is fixed to the vertical plane of the leading edge 1. For ease of description, the end of the piezoelectric composite bicrystalline layer fixed to the leading edge 1 is referred to as the fixed end, and the other end as the free end.

[0038] like Figure 1 and 2As shown, each piezoelectric composite bimorph is a three-layer structure, and the middle layer is located in the middle. The upper and lower surfaces of the middle layer are attached with the upper piezoelectric composite and the lower piezoelectric composite, respectively. The actuation principle of the piezoelectric composite bimorph is prior art, and its specific model is not limited, and a corresponding commercially available product can be used to realize it. Each piezoelectric composite bimorph can be regarded as a cantilever beam actuator. Since the airfoil of the morphing wing is symmetric, the width, thickness and material of the four-layer piezoelectric composite bimorph cantilever beam actuators are the same, only the length is different. The lengths of the middle two piezoelectric composite bimorphs, i.e. the middle upper piezoelectric composite bimorph 13 and the middle lower piezoelectric composite bimorph 14, are the same, and the lengths of the other two piezoelectric composite bimorphs, i.e. the upper piezoelectric composite bimorph 12 and the lower piezoelectric composite bimorph 15, are also the same. The lengths of the middle two piezoelectric composite bimorphs are greater than the lengths of the other two piezoelectric composite bimorphs. The four-layer piezoelectric composite bimorph is mirror symmetric about the center plane of the morphing wing.

[0039] The wing surface between the leading edge 1 and the trailing edge 8 is covered with a skin 11. One end of the skin 11 on the upper and lower sides is fixed to the upper and lower ends of the plane of the leading edge 1, respectively, and the other end of the skin 11 is fixed to the upper and lower ends of the trailing edge 4. The middle of the skin 11 is bonded to each rib of the four interlayer connecting rib structures, thereby realizing the continuous smooth transition of the morphing wing skin surface.

[0040] Two prefabricated grooves are horizontally provided on the vertical plane of the trailing edge 8, which are the upper prefabricated groove 81 and the lower prefabricated groove 82. The free end of the middle upper piezoelectric composite bimorph 13 is inserted into the upper prefabricated groove 81 of the trailing edge 8 for fixation, and the free end of the middle lower piezoelectric composite bimorph 14 is inserted into the lower prefabricated groove 82 of the trailing edge 8. However, in order to ensure the smooth realization of the deflection function of the morphing wing, the free end of the middle lower piezoelectric composite bimorph 14 is not completely fixed with the lower prefabricated groove 82, and the two constitute a sliding fit, i.e. the free end of the middle lower piezoelectric composite bimorph 14 can perform extension and translation in the lower prefabricated groove 82. In this way, the trailing edge 8 can be freely deflected with the middle upper piezoelectric composite bimorph 13 to maintain the smooth transition of the trailing edge and the skin, and at the same time, the support of the transverse bending force of the middle lower piezoelectric composite bimorph 14 is obtained.

[0041] The four interlayer connecting rib structures are arranged inside the skin 11 and are sequentially the first interlayer connecting rib structure 2, the second interlayer connecting rib structure 3, the third interlayer connecting rib structure 6 and the fourth interlayer connecting rib structure 7 from the leading edge 1 to the trailing edge 8. Since the lengths of the four-layer piezoelectric composite bimorphs are different, the middle two layers are shorter, and the upper and lower layers are longer, the upper piezoelectric composite bimorph 12 and the lower piezoelectric composite bimorph 15 pass through the first three interlayer connecting rib structures from the leading edge to the trailing edge, that is, sequentially through the first interlayer connecting rib structure 2, the second interlayer connecting rib structure 3 and the third interlayer connecting rib structure 6; the middle upper piezoelectric composite bimorph 13 and the middle lower piezoelectric composite bimorph 14 pass through the four interlayer connecting rib structures from the leading edge to the trailing edge, that is, sequentially through the first interlayer connecting rib structure 2, the second interlayer connecting rib structure 3, the third interlayer connecting rib structure 6 and the fourth interlayer connecting rib structure 7. Therefore, the first interlayer connecting rib structure 2, the second interlayer connecting rib structure 3 and the third interlayer connecting rib structure 6 each pass through the four-layer piezoelectric composite bimorphs, and the fourth interlayer connecting rib structure 7 only passes through two piezoelectric composite bimorphs.

[0042] In the present application, all interlayer connecting rib structures and each layer of piezoelectric composite bimorphs need to be fixed and connected with the protruding lug 121 at each position in the length direction of the middle layer of each piezoelectric composite bimorph through the adapter shaft 26 and the bolt and nut 10, thereby transmitting the transverse bending force of each piezoelectric composite bimorph to each rib and skin 3.

[0043] Specifically, each group of interlayer connecting rib structures needs to correlate the transverse actuation of the four-layer piezoelectric composite bimorph at a certain length, and the flexible rolling contact hinge structure of the main part of the interlayer connecting rib structure can make each hinge disc roll with each other with a constant radial distance, thereby correlating the transverse movement of the four-layer piezoelectric bimorph, and decoupling the rotation of each layer bimorph section around the neutral axis. The four interlayer connecting rib structures have basically the same structure, in order not to lose generality, the first interlayer connecting rib structure 2, the second interlayer connecting rib structure 3, the third interlayer connecting rib structure 6 and the fourth interlayer connecting rib structure 7 will be generalized as the Mth interlayer connecting rib structure, so M can be one, two, three or four in turn.

[0044] For any Mth interlayer connecting rib structure, it takes two ribs as the skeleton, both of which are fixed on the inner surface of the skin 11 wrapped outside the morphing wing. Each rib is formed by splicing three rib rods into a concave shape, and the ends of the two vertical rib rods are the rib roots. The two ribs of the Mth interlayer connecting rib structure are fixed in the form of opposite roots, and the upper and lower skins 11 are attached to the horizontal rib rod surface of the ribs. The roots of the two ribs on the same side are flexibly connected by a group of flexible rolling contact hinge structures, so the roots on both sides are flexibly connected by two groups of flexible rolling contact hinge structures respectively. Each group of flexible rolling contact hinge structures includes 2 half-round connecting discs 25, N-2 first full-round connecting discs 23, N-1 second full-round connecting discs 22 and N adapter shafts 26, where N is the number of piezoelectric composite bimorphs passing through the Mth interlayer connecting rib structure. The diameter of the second full-round connecting disc 22 is smaller than that of the first full-round connecting disc 23, the first full-round connecting disc 23 is a large connecting disc, and the second full-round connecting disc 22 is a small connecting disc to reduce the occupied space. The diameters of the half-round connecting disc 25 and the first full-round connecting disc 23 are consistent. For the first interlayer connecting rib structure 2, the second interlayer connecting rib structure 3, the third interlayer connecting rib structure 6 and the fourth interlayer connecting rib structure 7, N is 4, 4, 4 and 2 respectively. In the Mth interlayer connecting rib structure, the half-round connecting disc 25 is a half-round connecting disc, the diameter side of the half circle is a flat end, and the other side is a curved end. The flat ends of the two half-round connecting discs 25 are fixedly connected to the roots of the two ribs on the side where they are located, and the N-2 first full-round connecting discs 23 and the N-1 second full-round connecting discs 22 are alternately arranged between the curved ends of the two half-round connecting discs 25, and the second full-round connecting disc 22 adjacent to the half-round connecting disc 25. Flexible connecting bands 24 are provided between any two adjacent connecting discs, which are flexible connecting band bodies with two ends in the length direction and two side band surfaces in the thickness direction. Two adjacent connecting discs are referred to as connecting disc A and connecting disc B, one end of the flexible connecting band 24 is fixedly connected to one of the adjacent connecting discs A and wrapped by one side band surface, and the other end of the flexible connecting band 24 is fixedly connected to the other adjacent connecting disc B and wrapped by the other side band surface. The connecting disc A and the connecting disc B always keep the edges abutting under the connection of the flexible connecting band 24, and the connecting disc A and the connecting disc B actually bear the force indirectly through the flexible connecting band 24 clamped in the middle at the abutting position. The two adjacent connecting discs A and B can rotate around the adjacent connecting disc axis with a relatively constant radial distance between them. In addition, the total number of half-round connecting discs 25 and first full-round connecting discs 23 in each flexible rolling contact hinge structure is N, and the total number of adapter shafts 26 is also N, so all half-round connecting discs 25 and first full-round connecting discs 23 correspond to one adapter shaft 26 fixedly connected to each of them.Each side flexible rolling contact hinge structure of the Mth inter-laminar connecting rib structure is fixedly connected with the same side of the N piezoelectric composite bimorphs passing through the Mth inter-laminar connecting rib structure through N adapter shafts 26, so that each piezoelectric composite bimorph is actuated in parallel. It should be noted that the so-called "same side" here refers to the side of the N piezoelectric composite bimorphs located on the same side of the flexible rolling contact hinge structure. In order to facilitate connection, the two sides of the middle layer of each piezoelectric composite bimorph can be respectively provided with an extended ear 121 for fixed connection with the adapter shaft 26, and each adapter shaft 26 and the corresponding extended ear 121 are fixedly connected by a bolt and nut 10.

[0045] It should be noted that since the above-mentioned N value is different for different M values, the assembly forms of the first inter-laminar connecting rib structure 2, the second inter-laminar connecting rib structure 3 and the third inter-laminar connecting rib structure 6 are basically the same, but for the fourth inter-laminar connecting rib structure 7, there is no second whole circular connecting disc 22. Based on the above general structure description of the four inter-laminar connecting rib structures, the specific structure forms of each of the four will be further described below in combination with the drawings. In order to distinguish, the ribs in the first inter-laminar connecting rib structure 2, the second inter-laminar connecting rib structure 3 and the third inter-laminar connecting rib structure 6 are respectively called the first rib 21, the second rib 31, the third rib 61 and the fourth rib 71.

[0046] As shown in Figure 3 The first inter-laminar connecting rib structure 2 has a total of two first ribs 21 and two groups of flexible rolling contact hinge structures, each group of flexible rolling contact hinge structures has 2 half circular connecting discs 25, 2 first whole circular connecting discs 23, 3 second whole circular connecting discs 22 and 4 adapter shafts 26, the 2 first whole circular connecting discs 23 are arranged between the 2 half circular connecting discs 25, the adjacent half circular connecting disc 25 and the first whole circular connecting disc 23 are connected by the 1 second whole circular connecting disc 22, and the adjacent two first whole circular connecting discs 23 are also connected by the 1 second whole circular connecting disc 22. The spacing of the 4 adapter shafts 26 is the same as the spacing of the four piezoelectric composite bimorphs. The two first ribs 21 are fixedly connected to the inner side of the skin 11 away from the side of the piezoelectric bimorphs. The entire first inter-laminar connecting rib structure 2 is fixedly connected to the 8 extended ears 121 on the four piezoelectric composite bimorphs by the 8 adapter shafts 26 and the bolt and nut 10.

[0047] As shown in Figure 4As shown in FIG. 6, the second interlayer connecting rib structure 3 has the same structure as the first interlayer connecting rib structure 2, and also has two second ribs 31 and two groups of flexible rolling contact hinge structures, each group of flexible rolling contact hinge structures having 2 half-round connecting discs 25, 2 first full-round connecting discs 23, 3 second full-round connecting discs 22 and 4 adapter shafts 26. The difference between the second interlayer connecting rib structure 3 and the first interlayer connecting rib structure 2 is that the height of the second rib 31 in the second interlayer connecting rib structure 3 is less than the height of the first rib 21 in the first interlayer connecting rib structure 2, so as to meet the curvature requirement of the airfoil surface.

[0048] As shown in FIG. 6, the second interlayer connecting rib structure 3 has the same structure as the first interlayer connecting rib structure 2, and also has two second ribs 31 and two groups of flexible rolling contact hinge structures, each group of flexible rolling contact hinge structures having 2 half-round connecting discs 25, 2 first full-round connecting discs 23, 3 second full-round connecting discs 22 and 4 adapter shafts 26. The difference between the second interlayer connecting rib structure 3 and the first interlayer connecting rib structure 2 is that the height of the second rib 31 in the second interlayer connecting rib structure 3 is less than the height of the first rib 21 in the first interlayer connecting rib structure 2, so as to meet the curvature requirement of the airfoil surface. Figure 5 As shown in FIG. 6, the second interlayer connecting rib structure 3 has the same structure as the first interlayer connecting rib structure 2, and also has two second ribs 31 and two groups of flexible rolling contact hinge structures, each group of flexible rolling contact hinge structures having 2 half-round connecting discs 25, 2 first full-round connecting discs 23, 3 second full-round connecting discs 22 and 4 adapter shafts 26. The difference between the second interlayer connecting rib structure 3 and the first interlayer connecting rib structure 2 is that the height of the second rib 31 in the second interlayer connecting rib structure 3 is less than the height of the first rib 21 in the first interlayer connecting rib structure 2, so as to meet the curvature requirement of the airfoil surface.

[0049] Figure 6 As shown in FIG. 6, the second interlayer connecting rib structure 3 has the same structure as the first interlayer connecting rib structure 2, and also has two second ribs 31 and two groups of flexible rolling contact hinge structures, each group of flexible rolling contact hinge structures having 2 half-round connecting discs 25, 2 first full-round connecting discs 23, 3 second full-round connecting discs 22 and 4 adapter shafts 26. The difference between the second interlayer connecting rib structure 3 and the first interlayer connecting rib structure 2 is that the height of the second rib 31 in the second interlayer connecting rib structure 3 is less than the height of the first rib 21 in the first interlayer connecting rib structure 2, so as to meet the curvature requirement of the airfoil surface.

[0050] Each group of interlayer connecting rib structures can be made by three-dimensional printing. The use of the present application as an interlayer parallel structure can ensure that the airfoil surface deforms, not only enabling the associated bending movement of each layer of piezoelectric composite bimorph, transmitting transverse bending force and decoupling the rotation of each layer of bimorph around the neutral axis, but also increasing the number of parallel piezoelectric composite bimorphs compared with existing multi-layer parallel structures, thereby further improving the output power of the piezoelectric composite bimorph deformation wing.

[0051] As shown in FIG. 6, the second interlayer connecting rib structure 3 has the same structure as the first interlayer connecting rib structure 2, and also has two second ribs 31 and two groups of flexible rolling contact hinge structures, each group of flexible rolling contact hinge structures having 2 half-round connecting discs 25, 2 first full-round connecting discs 23, 3 second full-round connecting discs 22 and 4 adapter shafts 26. The difference between the second interlayer connecting rib structure 3 and the first interlayer connecting rib structure 2 is that the height of the second rib 31 in the second interlayer connecting rib structure 3 is less than the height of the first rib 21 in the first interlayer connecting rib structure 2, so as to meet the curvature requirement of the airfoil surface. Figure 7 ​As shown, in the present application, the flexible freedom in the interlayer connecting rib structure is mainly realized by the connection of the flexible connecting belts 24. The second whole-circle connecting disc 22 in the interlayer connecting rib structure needs to be connected with the first whole-circle connecting disc 23 and the half-circle connecting disc 25 through the flexible connecting belts 24, so that the flexible rolling connecting discs are not separated radially, and only the adjacent connecting discs are allowed to roll around the central axis of each other. The first whole-circle connecting disc 23 and the half-circle connecting disc 25 are fixedly connected with the protruding tabs 121 of the intermediate layer of the piezoelectric composite bimorph through the adapter shafts 26, so as to associate the transverse movement of each layer of piezoelectric composite bimorph, and decouple the rotation of the cross section of each layer of bimorph around the neutral axis, so as to further increase the number of parallel layers while increasing the flexibility of bending deformation, and improve the output force of the deformation wing.

[0052] In addition, in order to further improve the bending deformation degree, the polymer spiral winding actuator 9 is arranged to apply an axial force to each piezoelectric composite bimorph in the present application. As shown, Figure 5 As shown, the third interlayer connecting rib structure 6 is provided with protruding shafts 62 on the left and right sides corresponding to the positions of the upper piezoelectric composite bimorph 12 and the lower piezoelectric composite bimorph 15. The protruding shafts 62 can be arranged outside the half-circle connecting disc 25. Four bearings 5 are respectively sleeved on the four protruding shafts 62. Considering the limitation of installation space, the bearings 5 can be micro bearings. A prefabricated clamping groove bearing sleeve 4 is sleeved on each bearing 5. Considering the reliability of installation, the prefabricated clamping groove bearing sleeve 4 is axially sleeved on the bearing 5 in an interference fit. A prefabricated clamping groove 41 is formed on the outer wall of each prefabricated clamping groove bearing sleeve 4 in a circumferential direction. A polymer spiral winding actuator 9 is sleeved on each prefabricated clamping groove 41, and one end of the polymer spiral winding actuator 9 is fixed to the leading edge 1. The four piezoelectric composite bimorphs are loaded and unloaded by the four polymer spiral winding actuators 9 on both sides. Whether the axial pressure needs to be applied can be adjusted according to the working state.

[0053] As shown, Figure 8As shown, in an embodiment of the present application, a specific form of the polymer spiral-wound actuator 9 is provided. The manufacturing method of the polymer spiral-wound actuator 9 is as follows: the polymer fiber material 91 and the heat-conducting metal wire 93 are continuously twisted into a twisted geometric structure in a state of maintaining tension, and during the twisting process, a certain length of the polymer fiber material 91 and the heat-conducting metal wire 93 at both ends of the polymer spiral-wound actuator 9 are reserved without being spiral-wound. The polymer fiber material 91 reserved at one end forms a loop that is sleeved on the preformed slot bearing sleeve 4, and the polymer fiber material 91 reserved at the other end is fixed to the leading edge 1. The heat-conducting metal wires 93 reserved at both ends are used to connect external power sources. In order to facilitate temperature control and thus adjust the shrinkage force, a thermistor 92 is embedded in the polymer spiral-wound actuator 9 for monitoring the temperature of the polymer spiral-wound actuator 9. In operation, the polymer spiral-wound actuator 9 is heated by connecting the heat-conducting metal wires 93 to an external power source, so as to apply axial pressure to the four-layer piezoelectric composite bimorph in operation and unload the axial pressure in non-operation. The temperature of the polymer spiral-wound actuator 9 is monitored by the thermistor 92, so as to ensure that the axial pressure amplitude is within a suitable range, thereby increasing the working life of the pre-compressed piezoelectric composite bimorph deformed wing.

[0054] In operation of the pre-pressure controllable piezoelectric composite bimorph deformed wing based on the flexible hinge parallel connection, the four-layer piezoelectric composite bimorph cantilever beam actuator needs to bend in the same direction, so the upper piezoelectric composite material of the upper piezoelectric composite bimorph 12, the middle and lower piezoelectric composite bimorph 13, the middle and lower piezoelectric composite bimorph 14, and the lower piezoelectric composite bimorph 15 needs to be connected to the same polarity and same amplitude voltage, and the lower piezoelectric composite material of the four-layer piezoelectric composite bimorph needs to be connected to the opposite polarity and same amplitude voltage.

[0055] Based on the above-described pre-pressure controllable piezoelectric bimorph deformed wing based on the flexible hinge parallel connection, the present application further provides an actuation method of a self-adaptive flexible deformed wing, and the specific process is as follows:

[0056] In the actuation state, the upper piezoelectric composite bimorph 12, the middle upper piezoelectric composite bimorph 13, the middle lower piezoelectric composite bimorph 14 and the lower piezoelectric composite bimorph 15 in the morphing wing are respectively applied with voltages, wherein the upper piezoelectric composite of the four-layer piezoelectric composite bimorph is applied with a voltage of the same polarity and the same amplitude, and the lower piezoelectric composite of the four-layer piezoelectric composite bimorph is applied with a voltage of the opposite polarity and the same amplitude, so that the four-layer piezoelectric composite bimorphs bend in the same direction. In the bending process, the four-layer piezoelectric composite bimorphs transmit the transverse deformation force to the upper and lower skins 11 and the trailing edge 8 through the flexible rolling contact hinge structure of the four sets of interlayer connecting rib structures, and decouple the rotation of the four-layer piezoelectric composite bimorph cross section around the neutral axis, that is, the cross sections of the four-layer piezoelectric composite bimorphs rotate independently of each other, so that the skin 11 fixed on the four interlayer connecting rib structures is elongated or shortened, and the trailing edge 8 is deflected with the free end of the middle two piezoelectric composite bimorphs, so that the morphing wing surface is continuously and smoothly deformed. In order to increase the overall deflection amplitude of the morphing wing, a power voltage is applied to the polymer spiral winding actuator 9 fixed at one end of the leading edge 1 and sleeved into the bearing sleeve 4, so that the polymer spiral winding actuator 9 is heated and shrunk, the shrinkage force is transmitted to the four-layer piezoelectric composite bimorph through the third interlayer connecting rib structure 6, and the piezoelectric composite bimorph is in an axially pre-stressed state, thereby generating greater bending deformation. It should be noted that the axial pressure caused by the temperature applied to the polymer spiral winding actuator 9 needs to be less than the total first-order axial buckling force of the four-layer piezoelectric composite bimorph, so as to prevent the piezoelectric composite bimorph from being damaged.

[0057] In the non-actuation state, the voltages applied to the four-layer piezoelectric composite bimorph and the polymer spiral winding actuator 9 are removed, so that the morphing wing is in a non-deformed state.

[0058] The side views of the flexible hinge parallel pre-stress controllable piezoelectric bimorph morphing wing before and after deformation are shown in Figure 9 and Figure 10 .

[0059] In summary, the four-layer piezoelectric composite bimorph actuator is connected in parallel by the flexible rolling contact hinge interlayer connecting structure, and the axial pressure is controlled by the polymer spiral winding actuator, so as to improve the output power and service life of the piezoelectric actuator in the narrow space of the morphing wing, and further promote the engineering of the piezoelectric actuator. In the present application, piezoelectric materials can be piezoelectric fiber composites or piezoelectric ceramic materials.

[0060] The above-described embodiments are only the preferred ones of the present application, and are not intended to limit the present application. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present application. Therefore, any technical solutions obtained by equivalent replacement or equivalent transformation shall fall within the protection scope of the present application.

Claims

1. A pre-stress controllable piezoelectric bimorph deformed wing based on flexible hinge parallel, characterized by: The morphing wing comprises a leading edge (1), a trailing edge (8), a skin (11), a polymer helical winding actuator (9), and upper piezoelectric composite bimorphs (12), middle upper piezoelectric composite bimorphs (13), middle lower piezoelectric composite bimorphs (14) and lower piezoelectric composite bimorphs (15) arranged in sequence from top to bottom; the four piezoelectric composite bimorphs have the same width and are fixed to the leading edge (1), the lengths of the middle upper piezoelectric composite bimorphs (13) and the middle lower piezoelectric composite bimorphs (14) are greater than the lengths of the upper piezoelectric composite bimorphs (12) and the lower piezoelectric composite bimorphs (15), and the four piezoelectric composite bimorphs are mirror symmetric about the center plane of the morphing wing; the trailing edge (8) is horizontally provided with an upper pre-prepared slot (81) and a lower pre-prepared slot (82), the free ends of the middle upper piezoelectric composite bimorphs (13) are inserted into the upper pre-prepared slot (81) of the trailing edge (8) and fixed, and the free ends of the middle lower piezoelectric composite bimorphs (14) are inserted into the lower pre-prepared slot (82) of the trailing edge (8) and form a sliding fit; The four piezoelectric composite bimorphs are connected through four interlayer connecting rib structures with flexible rolling contact hinges, and the interlayer connecting rib structures are sequentially a first interlayer connecting rib structure (2), a second interlayer connecting rib structure (3), a third interlayer connecting rib structure (6) and a fourth interlayer connecting rib structure (7) from the leading edge (1) to the trailing edge (8); the upper piezoelectric composite bimorphs (12) and the lower piezoelectric composite bimorphs (15) sequentially pass through the first interlayer connecting rib structure (2), the second interlayer connecting rib structure (3) and the third interlayer connecting rib structure (6), and the middle upper piezoelectric composite bimorphs (13) and the middle lower piezoelectric composite bimorphs (14) sequentially pass through all the four interlayer connecting rib structures from the leading edge to the trailing edge; Any Mth interlayer connecting rib structure takes two ribs as the framework, the two ribs are fixed in the inner surface of the skin (11) wrapped outside the morphing wing in the form of roots opposite, and the roots of the two ribs on the same side are flexibly connected by a group of flexible rolling contact hinge structures; each group of flexible rolling contact hinge structures includes 2 half-round connecting discs (25), N-2 first full-round connecting discs (23), N-1 second full-round connecting discs (22) and N adapter shafts (26), the diameter of the second full-round connecting disc (22) is smaller than that of the first full-round connecting disc (23), the diameter of the half-round connecting disc (25) and the first full-round connecting disc (23) is consistent, wherein N is the number of piezoelectric composite bimorphs passing through the Mth interlayer connecting rib structure; the plane end of the two half-round connecting discs (25) is fixedly connected to the roots of the two ribs respectively, the N-2 first full-round connecting discs (23) and the N-1 second full-round connecting discs (22) are alternately arranged between the curved end of the two half-round connecting discs (25), and the second full-round connecting disc (22) is adjacent to the half-round connecting disc (25); a flexible connecting belt (24) is arranged between any two adjacent connecting discs, one end of the flexible connecting belt (24) is fixedly connected to one of the adjacent connecting discs and wrapped thereon through one side belt surface, the other end of the flexible connecting belt (24) is fixedly connected to the other adjacent connecting disc and wrapped thereon through the other side belt surface, the two adjacent connecting discs always keep the edges abutting under the connection of the flexible connecting belt (24) and can roll relative to each other with the radial distance unchanged; one adapter shaft (26) is fixedly connected to all the half-round connecting discs (25) and the first full-round connecting discs (23); each side flexible rolling contact hinge structure of the Mth interlayer connecting rib structure is fixedly connected to the same side of the N piezoelectric composite bimorphs passing through the Mth interlayer connecting rib structure through the N adapter shafts (26), so that the piezoelectric composite bimorphs are actuated in parallel; M is one, two, three or four; The third interlayer connecting rib structure (6) is provided with an extension shaft (62) at the positions corresponding to the upper piezoelectric composite bimorph (12) and the lower piezoelectric composite bimorph (15) on the left and right sides, a bearing (5) is sleeved on each of the four extension shafts (62), a prefabricated clamping groove bearing sleeve (4) is sleeved on each bearing (5), a prefabricated clamping groove (41) is formed on the outer wall of each prefabricated clamping groove bearing sleeve (4) in the circumferential direction, and a polymer spiral winding actuator (9) with one end fixed to the leading edge (1) is sleeved on each prefabricated clamping groove (41).

2. The pre-stress controllable piezoelectric bimorph deformed wing based on the flexible hinge parallel mechanism according to claim 1, characterized in that: The first interlayer connecting rib structure (2) has two groups of flexible rolling contact hinge structures, each group of the flexible rolling contact hinge structure has two semicircular connecting discs (25), two first whole circular connecting discs (23), three second whole circular connecting discs (22) and four adapter shafts (26), the two first whole circular connecting discs (23) are arranged between the two semicircular connecting discs (25), the adjacent semicircular connecting disc (25) and the first whole circular connecting disc (23) are connected through the second whole circular connecting disc (22), and the adjacent two first whole circular connecting discs (23) are also connected through the second whole circular connecting disc (22); the interval of the four adapter shafts (26) is the same as the interval of the four-layer piezoelectric composite bimorph.

3. A pre-stress controllable piezoelectric bimorph deformed wing based on the flexible hinge parallel mechanism according to claim 2, characterized in that: The second interlayer connecting rib structure (3) has the same structure as the first interlayer connecting rib structure (2), and the only difference is that the height of the second rib (31) in the second interlayer connecting rib structure (3) is less than the height of the first rib (21) in the first interlayer connecting rib structure (2).

4. The pre-stress controllable piezoelectric bimorph deformed wing based on the flexible hinge parallel mechanism according to claim 3, characterized in that: The third interlayer connecting rib structure (6) has the same structure as the second interlayer connecting rib structure (3), and the only difference is that the height of the third rib (61) in the third interlayer connecting rib structure (6) is less than the height of the second rib (31) in the second interlayer connecting rib structure (3).

5. The pre-stress controllable piezoelectric bimorph deformed wing based on the flexible hinge parallel mechanism according to claim 1, characterized in that: The fourth interlayer connecting rib structure (7) has two groups of flexible rolling contact hinge structures, each group of the flexible rolling contact hinge structure has two semicircular connecting discs (25), one second whole circular connecting disc (22) and two adapter shafts (26), the two semicircular connecting discs (25) are connected through the second whole circular connecting disc (22); the interval of the four adapter shafts (26) is the same as the interval of the four-layer piezoelectric composite bimorph.

6. The pre-stress controllable piezoelectric bimorph deformed wing based on the flexible hinge parallel mechanism according to claim 1, characterized in that: The prefabricated card slot bearing sleeve (4) is axially sleeved on the bearing (5) in an interference fit manner, and the bearing (5) is a micro bearing.

7. The pre-stress controllable piezoelectric bimorph deformed wing based on the flexible hinge parallel mechanism according to claim 1, characterized in that: The four-layer piezoelectric composite bimorph is composed of an intermediate layer and upper and lower piezoelectric composite materials attached to the upper and lower surfaces of the intermediate layer, respectively. The intermediate layer is provided with an extension tab (121) on each side for connecting and fixing with the adapter shaft (26), and each adapter shaft (26) and the corresponding extension tab (121) are fixedly connected through a bolt and nut (10).

8. The pre-stress controllable piezoelectric bimorph morphing wing based on the flexure-kinematics parallel mechanism according to claim 1, characterized in that: The polymer spiral winding type actuator (9) is a torsional geometric structure formed by continuously twisting the polymer fiber material (91) and the heat-conducting metal wire (93) to a curled spiral shape under tension; and a certain length of the polymer fiber material (91) and the heat-conducting metal wire (93) are reserved at both ends of the polymer spiral winding type actuator (9) without spiral winding, the polymer fiber material (91) reserved at one end forms a sleeve ring sleeved on the prefabricated card slot bearing sleeve (4), the polymer fiber material (91) reserved at the other end is fixed to the leading edge (1), and the heat-conducting metal wires (93) reserved at both ends are used for connecting external power supply.

9. The pre-stress controllable piezoelectric bimorph morphing wing based on the flexure-kinematics parallel mechanism according to claim 1, characterized in that: The polymer spiral winding actuator (9) is embedded with a thermistor (92) for monitoring the temperature of the polymer spiral winding actuator (9).

10. An actuating method of the piezoelectric bimorph deformation wing based on the flexible hinge parallel mechanism with controllable pre-pressure according to any one of claims 1-9, characterized in that: Comprise: In the actuation state, the upper piezoelectric composite bimorph (12), the middle upper piezoelectric composite bimorph (13), the middle lower piezoelectric composite bimorph (14) and the lower piezoelectric composite bimorph (15) in the deformed wing are respectively applied with voltages, wherein the upper piezoelectric composite of the four-layer piezoelectric composite bimorph is applied with a voltage of the same polarity and the same amplitude, the lower piezoelectric composite of the four-layer piezoelectric composite bimorph is applied with a voltage of the opposite polarity and the same amplitude, so that the four-layer piezoelectric bimorphs bend synchronously in the same direction; during the bending of the four-layer piezoelectric composite bimorphs, the transverse deformation force is transmitted to the upper and lower skins (11) and the trailing edge (8) through the flexible rolling contact hinge structure in the four interlayer connecting rib structures, while the cross sections of the four-layer piezoelectric composite bimorphs are kept independent of each other, so that the skin (11) fixed on the four interlayer connecting rib structures is deformed by elongation or shortening with the four interlayer connecting rib structures, and the trailing edge (8) is deflected with the free ends of the middle two-layer piezoelectric bimorphs, so that the deformed wing surface is continuously and smoothly deformed as a whole; when it is needed to increase the overall deformation amplitude of the deformed wing, the polymer spiral winding actuator (9) wrapped in the bearing sleeve (4) is further applied with a power voltage, so that the polymer spiral winding actuator (9) is heated and shrinks, the shrinkage force is transmitted to the four-layer piezoelectric composite bimorphs through the third interlayer connecting rib structure (6), so that each layer of piezoelectric composite bimorph is under axial pre-stress, thereby increasing the bending deformation; In the non-actuation state, the voltages applied to the four-layer piezoelectric composite bimorphs and the polymer spiral winding actuator (9) are removed, so that the deformed wing is in a non-deformed state as a whole.

11. The actuation method of claim 10, wherein: The total axial pressure applied by the four polymer spiral winding actuators (9) to all piezoelectric composite bimorphs should be less than the total first-order axial buckling force of all piezoelectric composite bimorphs.

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