CN115199687B - Multifunctional superstructure with adjustable rigidity and stable state and design method thereof - Google Patents

Multifunctional superstructure with adjustable rigidity and stable state and design method thereof Download PDF

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CN115199687B
CN115199687B CN202211044834.3A CN202211044834A CN115199687B CN 115199687 B CN115199687 B CN 115199687B CN 202211044834 A CN202211044834 A CN 202211044834A CN 115199687 B CN115199687 B CN 115199687B
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kresling
paper folding
folding structure
superstructure
disc
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CN115199687A (en
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李振
康正阳
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Nanjing Tech University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F1/00—Springs
    • F16F1/02—Springs made of steel or other material having low internal friction; Wound, torsion, leaf, cup, ring or the like springs, the material of the spring not being relevant
    • F16F1/025—Springs made of steel or other material having low internal friction; Wound, torsion, leaf, cup, ring or the like springs, the material of the spring not being relevant characterised by having a particular shape
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F1/00—Springs
    • F16F1/36—Springs made of rubber or other material having high internal friction, e.g. thermoplastic elastomers
    • F16F1/371—Springs made of rubber or other material having high internal friction, e.g. thermoplastic elastomers characterised by inserts or auxiliary extension or exterior elements, e.g. for rigidification
    • F16F1/3713—Springs made of rubber or other material having high internal friction, e.g. thermoplastic elastomers characterised by inserts or auxiliary extension or exterior elements, e.g. for rigidification with external elements passively influencing spring stiffness, e.g. rings or hoops
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F1/00—Springs
    • F16F1/36—Springs made of rubber or other material having high internal friction, e.g. thermoplastic elastomers
    • F16F1/373—Springs made of rubber or other material having high internal friction, e.g. thermoplastic elastomers characterised by having a particular shape
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F2228/00—Functional characteristics, e.g. variability, frequency-dependence
    • F16F2228/06—Stiffness
    • F16F2228/066—Variable stiffness
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F2230/00—Purpose; Design features
    • F16F2230/0005—Attachment, e.g. to facilitate mounting onto confer adjustability

Abstract

The invention discloses a multifunctional superstructure with adjustable rigidity and stable state and a design method thereof, and the superstructure comprises a top plate, a bottom plate and a supporting screw rod, wherein an elastic element is arranged between the top plate and the bottom plate, a radian adjusting mechanism is arranged on the top plate, the elastic element comprises an upper Kresling paper folding structure, a lower Kresling paper folding structure, a middle disc, a connecting rod and a thrust bearing, the middle disc is superposed with the central axis of the two Kresling paper folding structures and is positioned between the two Kresling paper folding structures, the top surface of the middle disc is fixedly connected with the bottom of the upper Kresling paper folding structure, the bottom surface of the middle disc is fixedly connected with the top of the lower Kresling paper folding structure, the connecting rod is superposed with the central axis of the middle disc, the thrust bearing is fixedly connected with the middle disc and is fixedly connected with one end of the connecting rod, and the other end of the connecting rod passes through a central circular hole of the radian adjusting mechanism. The invention can freely switch the superstructure between the bistable state mode and the monostable mode of the potential energy traps with different depths, and simultaneously, the rigidity of the steady state position can also be adjusted.

Description

Multifunctional superstructure with adjustable rigidity and stable state and design method thereof
Technical Field
The invention belongs to the technical field of superstructures, and particularly relates to a multifunctional superstructures with adjustable rigidity and stable state and a design method thereof.
Background
In the fields of vibration wave conduction control, vibration isolation, travel switch triggers and the like, the complexity of the engineering environment requires that the mechanical structure device can have strong adaptability, namely the performance of the mechanical structure device has adjustability in a certain range, so that the mechanical structure device is suitable for the complex engineering environment.
However, the performance of conventional mechanical structural devices is usually fixed during design, and performance adjustment is mainly achieved by redesigning the device or replacing structural parts with different performance parameters, which is neither efficient nor economical.
In recent years, research on superstructures similar to Kresling origami is increasing, for example, an invention patent with application number 202210150656.6 discloses a composite anti-explosion structure based on Kresling origami and a design method thereof, and an invention patent with application number 202110930164.4 discloses a longitudinal wave torsional wave transducer inspired by Kresling configuration and a design method thereof, and the following main problems exist in the prior art schemes: when the structural dimensional parameters are all determined, these devices can only control specific impact loads or waves, and lack adaptability to complex engineering environments.
Also as application No. 202110862876.7 discloses a torsional vibration absorber unit and a vibration absorber based on bistable folded paper, wherein the vibration absorber with adjustable suppression frequency is realized by adjusting the stable state of the vibration absorber unit, and different vibration absorber units are matched with different suppression frequencies in a stable state; however, the main problems of the technical scheme are as follows: the steady state number of the vibration absorbers and the number of the vibration absorber units are in a power relation, the steady state relation is complex, and especially the 8-unit vibration absorbers adopted in the embodiment of the technical scheme have 2 in total 8 The relationship between the suppression frequency of the torsional vibration absorber and the corresponding steady state is therefore complex.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to solve the defects in the prior art and provides a multifunctional superstructure with adjustable rigidity and stable state and a design method thereof.
The technical scheme is as follows: the invention discloses a multifunctional superstructure with adjustable rigidity and stable state, which comprises a top plate, a bottom plate and an elastic element, wherein the top plate is provided with a radian adjusting mechanism, and the elastic element is arranged in a rectangular space formed by the top plate and the bottom plate; the radian adjusting mechanism comprises an outer gear ring and a gear disc meshed with the outer gear ring, and a first round hole is formed in the center of the gear disc; the elastic element sequentially comprises an upper Kresling paper folding structure, a middle disc and a lower Kresling paper folding structure from top to bottom, the upper end of the upper Kresling paper folding structure is fixedly connected with the bottom surface of the gear disc, the lower end of the upper Kresling paper folding structure is fixedly connected with the top surface of the center disc, the upper end of the lower Kresling paper folding structure is fixedly connected with the bottom surface of the center disc, and the lower end of the lower Kresling paper folding structure is fixedly connected with the bottom plate; a second round hole is formed in the center of the middle disc, a thrust bearing is connected to the second round hole in an interference fit mode, a connecting rod is connected to the inner ring of the thrust bearing in an interference fit mode, and the other end of the connecting rod upwards penetrates through the first round hole of the gear disc and then extends out of the top plate (capable of being used for being connected with external equipment or instruments); when the initial rotating radian of the elastic element needs to be adjusted, the gear disc is lifted upwards firstly, then the gear disc rotates by a certain radian as required, the gear disc is put down and embedded into the outer gear ring again, at the moment, the internal prestress of the elastic element changes, and when the superstructure deforms again, the external rigidity and the steady-state characteristic of the superstructure also change accordingly.
Further, the upper Kresling paper folding structure and the lower Kresling paper folding structure in the elastic element are integrally bistable structures, the upper Kresling paper folding structure is initially in a first stable state, and the lower Kresling paper folding structure is initially in a second stable state; the top surface and the bottom surface of the upper Kresling paper folding structure and the bottom surface of the lower Kresling paper folding structure are regular polygons, the number of sides of each regular polygon is n, the side length of each regular polygon is P, and the radius of a circumscribed circle of each regular polygon is R; the side surfaces are n parallelograms, the diagonal of which is a valley fold c 0 The long side of the parallelogram is a mountain fold crease b 0 And the shorter side is the side of the regular polygon.
Furthermore, the top plate and the bottom plate are square, the four corresponding vertex angles between the top plate and the bottom plate are respectively connected through the supporting screw rods, a space is provided for the elastic element through the top plate, the bottom plate and the supporting screw rods, and the displacement of the top and the bottom of the elastic element is restrained and controlled.
Further, operating handles (for example, two handles are arranged on one left and one right) are arranged on the gear plate; the outer gear ring is provided with limiting buckles (for example, four limiting buckles can be arranged and uniformly distributed on the outer gear ring) along the circumferential direction of the outer gear ring, one end of each limiting buckle is fixed on the outer gear ring shaft, and the other end of each limiting buckle can freely move to be used for clamping and fixing the gear disc; rotate spacing buckle, upwards mention the toothed disc through the operating handle after it rotates and adjusts initial rotatory radian, adjust after accomplishing again with toothed disc embedding external gear ring, it is fixed with the rotatory playback of spacing buckle.
Further, the central axes of the upper Kresling paper folding structure, the central circular disc, the lower Kresling paper folding structure, the gear disc, the top plate and the bottom plate are superposed.
The invention also discloses a design method of the multifunctional superstructure with adjustable rigidity and stable state, which comprises the following steps:
step (1), setting corresponding parameters of an elastic element, so that the upper Kresling paper folding structure is initially in a first stable state, and the lower Kresling paper folding structure is initially in a second stable state, wherein the specific contents are as follows:
setting the initial height of the second stable state of the Kresling paper folding structure to be L 0 (ii) a The height L of the upper Kresling origami structure at the first steady state 1 The following:
Figure GDA0004110747960000031
wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0004110747960000032
θ 1 ＝2(1-λ)γ,/>
Figure GDA0004110747960000033
θ 2 ＝2λγ，/>
Figure GDA0004110747960000034
θ 1 the relative rotation angle theta of the top surface polygon and the bottom surface polygon when the Kresling paper folding structure is positioned at the first stable state 2 The relative rotation angle between the top surface polygon and the bottom surface polygon when the Kresling paper folding structure is positioned in a second stable state, and gamma is an included angle between a straight line from a center point of the polygon to a certain vertex and a side line of a corresponding polygon; lambda is an angle coefficient;
further calculating to obtain valley fold mark c 0 And mountain fold crease b 0 ：
Figure GDA0004110747960000035
Figure GDA0004110747960000036
At this time, the upper Kresling paper folding structure is in a first stable state, the bottom surface of the upper Kresling paper folding structure is fixed, and downward displacement u and rotation phi are applied to the top surface, namely the upper Kresling paper folding structure reaches a second stable state;
step (2), fixedly connecting the upper end of the upper Kresling paper folding structure in the first stable state with the bottom surface of the gear disc, and fixedly connecting the lower end of the upper Kresling paper folding structure with the top surface of the central disc; the upper end of the Kresling paper folding structure in the second stable state is fixedly connected with the bottom surface of the central disc, the lower end of the Kresling paper folding structure is fixedly connected with the bottom plate, the bottom plate is fully constrained, then the connecting rod is pulled to enable the superstructure to deform, and the change of the elastic potential energy U of the equivalent model along with the displacement of the connecting rod can be obtained according to the following formula:
Figure GDA0004110747960000037
wherein, the corresponding parameter of the upper Kresling paper folding structure is represented by subscript p, and the corresponding parameter of the lower Kresling paper folding structure is represented by subscript s; k is a radical of p And k s Respectively an upper Kresling paper folding structure crease b and a lower Kresling paper folding structure crease b 0 And c 0 Corresponding linear stiffness, b p And c p For Kresling origami construction in the course of deformation b 0 And c 0 Real time length of b s And c s For the following Kresling origami structure in the deformation process b 0 And c 0 The calculation formula of the real-time length is as follows:
Figure GDA0004110747960000038
Figure GDA0004110747960000041
Figure GDA0004110747960000042
Figure GDA0004110747960000043
wherein phi is p And phi s The rotation radians of the gear disc and the middle disc are respectively; h is p And h s The real-time heights of the upper Kresling paper folding structure and the lower Kresling paper folding structure when the superstructure is deformed are respectively set;
then, the force which needs to be applied to the connecting rod when the elastic element deforms is obtained through calculation based on the minimum energy principle, and the calculation formula is as follows:
Figure GDA0004110747960000044
wherein u is s For displacement of the connecting rod in the vertical direction, u s ＝L 1 -h p ：
And (3) adjusting the rotating radian of the elastic element through the radian adjusting mechanism, changing the internal prestress of the elastic element, and changing the overall external characteristic of the superstructure when the connecting rod is pulled to deform the superstructure, so that the external rigidity and the stable characteristic when the superstructure is deformed are changed, and switching between different stable characteristics and different stable rigidities is realized.
Has the advantages that: according to the invention, the elastic element is constructed by utilizing the non-rigid folding characteristic of the Kresling paper folding structure, the external rigidity and the stable state characteristic of the superstructure in the deformation process are changed by adjusting the internal prestress of the elastic element, the switching of different stable state characteristics and different stable state rigidities is realized, and the uneconomical and inefficient rigidity and stable state conversion modes such as part replacement or redesign are avoided.
Drawings
FIG. 1 is a schematic view of the overall structure of the present invention;
FIG. 2 is a schematic view of the top plate outer ring gear and the stopper of the present invention;
FIG. 3 is a schematic view of a gear plate according to the present invention;
FIG. 4 is a schematic view of the assembly of the elastic member of the present invention;
FIG. 5 is a schematic view of the assembly of the intermediate disk, bearing and connecting rod of the present invention;
FIG. 6 is a schematic view of the folds of the Kresling origami structure of the present invention;
FIG. 7 is a three-dimensional schematic view of a Kresling origami structure in a first stable state;
FIG. 8 is a three-dimensional schematic view of the Kresling origami structure in a second stable state;
FIG. 9 is a curve of elastic potential energy according to the adjustment radian φ in the embodiment p A change map of (c);
FIG. 10 is steady state stiffness with adjustment radian φ in an embodiment p A variation diagram of (2).
FIG. 11 is a graph comparing input and output curves of vibration signals in the examples.
Wherein FIG. 9 (a) is bistable and φ p Elastic potential energy equal to 0, bistable and phi in FIG. 9 (b) p Elastic potential energy equal to 0.2, FIG. 9 (c) is bistable and φ p Elastic potential energy equal to 0.4, FIG. 9 (d) is monostable and φ p Elastic potential energy equal to 0.5, FIG. 9 (e) is monostable and φ p Elastic potential energy equal to 0.6; FIG. 10 is the equivalent stiffness of a superstructure in steady state position as a function of φ p Schematic diagram of the variation rule of (1).
The device comprises a top plate 1, an elastic element 2, a bottom plate 3, an outer toothed ring 4, a limiting buckle 5, a gear plate 6, a handle 7, an upper Kresling paper folding structure 8, a middle disc 9, a lower Kresling paper folding structure 10, a connecting rod 11 and a support screw 12.
Detailed Description
The technical solution of the present invention is described in detail below, but the scope of the present invention is not limited to the embodiments.
As shown in fig. 1, the multifunctional superstructure with adjustable rigidity and stable state of the invention comprises a square top plate 1, a square bottom plate 3 and an elastic element 2, wherein four corresponding vertex angles between the top plate 1 and the bottom plate 3 are respectively connected through a support screw 12, the top plate 1 is provided with a radian adjusting mechanism, and the elastic element 2 is arranged in a rectangular space formed by the top plate 1 and the bottom plate 3; the radian adjusting mechanism comprises an outer gear ring 4 and a gear disc 6 meshed with the outer gear ring 4, and a first round hole 6-1 is formed in the center of the gear disc 6; the elastic element 2 sequentially comprises an upper Kresling paper folding structure 8, a middle disc 9 and a lower Kresling paper folding structure 10 from top to bottom, the upper end of the upper Kresling paper folding structure 8 is fixedly connected with the bottom surface of the gear disc 6, the lower end of the upper Kresling paper folding structure 8 is fixedly connected with the top surface of the center disc, the upper end of the lower Kresling paper folding structure 10 is fixedly connected with the bottom surface of the center disc, and the lower end of the lower Kresling paper folding structure 10 is fixedly connected with the bottom plate 3; a second round hole 9-1 is formed in the center of the middle disc 9, a thrust bearing is connected to the second round hole 9-1 in an interference fit manner, a connecting rod 11 is connected to the inner ring of the thrust bearing in an interference fit manner, and the other end of the connecting rod 11 upwards penetrates through a first round hole 6-1 of the gear disc 6 and then extends out of the top plate 1; and the central axes of the upper Kresling paper folding structure 8, the central disc, the lower Kresling paper folding structure 10, the gear disc 6 and the bottom plate 3 are superposed. When the initial rotation radian of the elastic element 2 needs to be adjusted, the gear disc 6 is lifted upwards firstly, then the gear disc rotates for a certain radian as required, then the gear disc 6 is put down and embedded into the outer gear ring 4 again, and at the moment, the internal prestress of the elastic element 2 changes. When the superstructure of the invention is deformed again, the external rigidity and the steady-state property of the superstructure are changed.
To facilitate understanding of the technical solution of the present invention, the structure of Kresling folded paper is now described as follows: the crease design of the Kresling paper folding structure is shown in FIG. 6, wherein the dotted line is the portion to be folded, c 0 Corresponding to a valley fold, b 0 The corresponding crease is a mountain fold, the solid line is a cutting boundary, the shadow part is a part needing to be adhered, the left and right directions of the crease design drawing are connected end to end, and then the three-dimensional Kresling paper folding structure can be obtained, as shown in fig. 7, the upper and lower shadow parts in the crease design drawing are used for fixedly connecting the Kresling paper folding structure and the adjacent parts. The upper Kreling folded paper structure 8 and the lower Kreling folded paper structure 10 can be made of folded paper, PET film, other elastic sheet materials and the like. The bistable structure is used as a vibration isolator, a travel switch trigger and the like, and simultaneously, the stable state potential energy trap of the superstructure is adjustable, which is equivalent to the adjustable performance of the vibration isolator or the trigger, so that the bistable structure has various functions and wide application range.
As shown in fig. 4 to 6, the upper Kresling paper folding structure 8 and the lower Kresling paper folding structure 10 of the elastic element 2 of the present embodiment are integrally bi-stable structures, the upper Kresling paper folding structure 8 is initially in the first stable state, and the lower Kresling paper folding structure is initially in the second stable stateThe paper structure 10 is initially in the second stable state; the top surface and the bottom surface of the upper Kresling paper folding structure 8 and the bottom surface of the lower Kresling paper folding structure 10 are regular polygons, the number of the sides is n, the side length is P, and the radius of a circumscribed circle of each regular polygon is R; the side surfaces are n parallelograms, and the diagonal line of the parallelogram is a valley fold c 0 The long side of the parallelogram is a mountain fold crease b 0 And the shorter side is the side of the regular polygon.
As shown in fig. 2 and 3, the gear plate 6 of the present embodiment is provided with two operating handles 7; four limiting buckles 5 are uniformly arranged on the outer gear ring 4 along the circumferential direction of the outer gear ring, one ends of the limiting buckles 5 are fixed on the ring shaft of the outer gear ring 4, and the other ends of the limiting buckles 5 can freely move to be used for clamping and fixing the gear disc 6; rotate spacing buckle 5, mention toothed disc 6 through operating handle 7 upwards after and rotate it and adjust initial rotatory radian, adjust after accomplishing again with toothed disc 6 embedding outer ring gear 4, it is fixed with the rotatory playback of spacing buckle 5.
The method for designing the superstructure with adjustable rigidity and stable state comprises the following steps:
step (1), setting corresponding parameters of the elastic element 2, so that the upper Kresling paper folding structure 8 is initially in a first stable state, and the lower Kresling paper folding structure 10 is initially in a second stable state, as shown in fig. 6 to 8, specifically:
setting the initial height of the second steady state of the Kresling origami structure 10 to L 0 (ii) a The height L of the upper krescing origami structure 8 in the first stable state 1 The following were used:
Figure GDA0004110747960000061
wherein the content of the first and second substances,
Figure GDA0004110747960000062
θ 1 ＝2(1-λ)γ,/>
Figure GDA0004110747960000063
θ 2 ＝2λγ，/>
Figure GDA0004110747960000064
θ 1 the relative rotation angle theta of the top surface polygon and the bottom surface polygon when the Kresling paper folding structure is positioned at the first stable state 2 The relative rotation angle between the top surface polygon and the bottom surface polygon when the Kresling paper folding structure is positioned at a second stable state is shown, and gamma is the included angle between the straight line from the center point of the polygon to a certain vertex and the side line of the corresponding polygon; λ is an angle coefficient;
further calculating to obtain valley fold mark c 0 And mountain fold crease b 0 ：
Figure GDA0004110747960000071
At this point the upper Kresling paper folding structure 8 is in the first stable state, fixing its bottom surface and applying a downward displacement u and rotation φ to the top surface, even if it reaches the second stable state;
step (2), fixedly connecting the upper end of the upper Kresling paper folding structure 8 in the first stable state with the bottom surface of the gear disc 6, and fixedly connecting the lower end of the upper Kresling paper folding structure with the top surface of the central disc; the upper end of the Kresling paper folding structure 10 in the second stable state is fixedly connected with the bottom surface of the central disc, the lower end of the Kresling paper folding structure is fixedly connected with the bottom plate 3, the bottom plate 3 is fully restrained, then the connecting rod 11 is pulled to enable the superstructure (namely the elastic element 2) of the Kresling paper folding structure to deform, and the change of the elastic potential energy U of the equivalent model along with the displacement of the connecting rod 11 can be obtained according to the following formula:
Figure GDA0004110747960000072
wherein, the parameter of the upper Kresling paper folding structure is represented by subscript p, and the parameter of the lower Kresling paper folding structure is represented by subscript s; k is a radical of p And k s Respectively, upper and lower Kresling paper folding structures 10 creases b 0 And c 0 Corresponding linear stiffness, b p And c p For Kresling origami 8 during deformation 0 And c 0 Real time length of b s And c s Is given by KrEsiling origami structure 10 during deformation b 0 And c 0 The calculation formula of the real-time length is as follows:
Figure GDA0004110747960000073
Figure GDA0004110747960000074
Figure GDA0004110747960000075
Figure GDA0004110747960000076
wherein phi is p And phi s The rotation radians of the gear plate 6 and the middle disk 9 are respectively; when the connecting rod 11 is pulled, the whole superstructure deforms, the heights of the upper Kresling paper folding structure and the lower Kresling paper folding structure change, and h is p And h s The real-time heights of the upper Kresling folded paper structure 8 and the lower Kresling folded paper structure 10 when the superstructure is deformed are respectively set;
then, the force which needs to be applied to the connecting rod 11 when the elastic element 2 deforms is obtained through calculation based on the minimum energy principle, and the calculation formula is as follows:
Figure GDA0004110747960000081
wherein u is s For displacement of the connecting rod 11 in the vertical direction, u s ＝L 1 -h p ：
And (3) adjusting the rotating radian of the elastic element 2 through the radian adjusting mechanism, changing the internal prestress of the elastic element 2, and when the connecting rod 11 is pulled to deform the superstructure, changing the overall external characteristic of the superstructure, further changing the external rigidity and the steady-state characteristic when the superstructure is deformed, so as to realize switching of different steady-state characteristics and different steady-state rigidities.
As shown in FIG. 9, the superstructure of the present invention is bi-stable when the gear plate 6 is adjusted within 0-0.5 radians, as shown in FIGS. 9 (a) -9 (c), and the potential energy well (V) can be changed by adjusting the gear plate 6 at this time b1 、V b2 ) Depth. Technically, as the depth of the potential energy well changes, the load or energy required for steady state switching changes, and at the same time the stiffness of the steady state position changes, as shown by the bistable region in figure 10. Due to the symmetrical bistable characteristic of the superstructure, the equivalent stiffness of two stable positions in the bistable interval is the same.
When the gear wheel 6 is adjusted to 0.5 radians or higher, the superstructure of the present invention is monostable, which is now a non-linear spring, but the stiffness of its steady state position can be continuously changed by adjusting the gear wheel 6 radians, as shown by the monostable region in fig. 10.
The steady state and rigidity adjusting capability are beneficial to adapting the superstructure of the invention to different engineering environments.
Example one
When the superstructure of the invention is used as a travel switch trigger, the bottom plate 3 is fixedly connected with external equipment, and impacts the connecting rod 11 at a certain speed or load, so that the steady state of the superstructure of the invention is changed, and the function of the travel switch trigger is realized.
Different from the traditional travel switch trigger, the superstructure of the invention can change the trigger condition of the steady-state switching of the superstructure by adjusting the initial radian of the top radian adjusting mechanism. Specifically, when phi is shown in FIG. 9 (a) p When equal to 0, V b1 ＝V b2 =1.8J, superstructure should cross energy barrier V b1 Or V b2 Then at least 1.8J of energy needs to be generated to trigger steady state switching of the superstructure. When the engineering environment changes and the sensitivity of the travel switch trigger needs to be improved, the radian adjusting mechanism needs to be adjusted. When phi is p Equal to 0.2, the steady state switching trigger condition of the superstructure of the present invention is reduced to 0.65J as shown in fig. 9 (b). Further, when phi p Equal to 0.4, e.g.Fig. 9 (c) shows that only 0.08J of energy is required to achieve steady state switching. Therefore, the trigger sensitivity of the travel switch trigger based on the superstructure can be changed by adjusting the radian adjusting mechanism, so that the travel switch trigger is suitable for different engineering environments.
Example two
In the embodiment, the superstructure is used as a low-frequency vibration isolator, and the radian adjusting mechanism is adjusted to phi p Equal to 0.5, the superstructure of this embodiment has quasi-zero stiffness, as shown in fig. 9 (d) and fig. 10, and both ends (the connecting rod 11 and the bottom plate 3) of the superstructure of this embodiment are connected to external equipment, so that when low-frequency vibration is generated at one end, the superstructure can absorb most of the vibration energy, and vibration isolation is realized at the other end. As shown in fig. 11, when a low-frequency vibration signal with a frequency of 1Hz and an amplitude of 3mm is input to one end of the superstructure, only a vibration signal with a frequency of 1Hz and an amplitude of 0.3mm is output from the other end of the superstructure, thereby implementing the vibration isolation function.

Claims (6)

1. The utility model provides a multi-functional superstructure of rigidity and steady state adjustable which characterized in that: the device comprises a top plate, a bottom plate and an elastic element, wherein the top plate is provided with a radian adjusting mechanism, and the elastic element is arranged in a rectangular space formed by the top plate and the bottom plate; the radian adjusting mechanism comprises an outer gear ring and a gear disc meshed with the outer gear ring, and a first round hole is formed in the center of the gear disc; the elastic element sequentially comprises an upper Kresling paper folding structure, a middle disc and a lower Kresling paper folding structure from top to bottom, the upper end of the upper Kresling paper folding structure is fixedly connected with the bottom surface of the gear disc, the lower end of the upper Kresling paper folding structure is fixedly connected with the top surface of the center disc, the upper end of the lower Kresling paper folding structure is fixedly connected with the bottom surface of the center disc, and the lower end of the lower Kresling paper folding structure is fixedly connected with the bottom plate; a second round hole is formed in the center of the middle disc, a thrust bearing is connected to the second round hole in an interference fit mode, a connecting rod is connected to the inner ring of the thrust bearing in an interference fit mode, and the other end of the connecting rod upwards penetrates through the first round hole of the gear disc and then extends out of the top plate;
when the initial rotating radian of the elastic element needs to be adjusted, the gear disc is lifted upwards firstly, then the gear disc rotates for a certain radian as required, then the gear disc is put down and embedded into the outer gear ring again, at the moment, the internal prestress of the elastic element changes, and when the superstructure deforms again, the external rigidity and the steady-state characteristic of the superstructure also change accordingly.
2. The adjustable stiffness and steady state multi-functional superstructure according to claim 1, characterized in that: the upper Kresling paper folding structure and the lower Kresling paper folding structure in the elastic element are integrally bistable structures, the upper Kresling paper folding structure is initially in a first stable state, and the lower Kresling paper folding structure is initially in a second stable state;
the top surface and the bottom surface of the upper Kresling paper folding structure and the bottom surface of the lower Kresling paper folding structure are regular polygons, the number of sides of each regular polygon is n, the side length of each regular polygon is P, and the radius of a circumscribed circle of each regular polygon is R; the side surfaces are n parallelograms, and the diagonal line of the parallelogram is a valley fold c 0 The long side of the parallelogram is a mountain fold crease b 0 And the shorter side is the side of the regular polygon.
3. The adjustable stiffness and steady state multi-functional superstructure according to claim 1, characterized in that: the top plate and the bottom plate are square, and the four corresponding vertex angles between the top plate and the bottom plate are respectively connected through supporting screws.
4. The adjustable stiffness and steady state multi-functional superstructure according to claim 1, characterized in that: an operating handle is arranged on the gear disc; the outer gear ring is provided with a limiting buckle along the circumferential direction, one end of the limiting buckle is fixed on the outer gear ring shaft, and the other end of the limiting buckle can freely move and can be used for clamping and fixing the gear disc; rotate spacing buckle, upwards mention the toothed disc through the operating handle after it rotates and adjusts initial rotatory radian, imbed the toothed disc in the outer toothed ring again, it is fixed with the rotatory playback of spacing buckle.
5. The multi-functional superstructure with adjustable stiffness and steady state according to claim 1, characterized in that: the central axes of the upper Kresling paper folding structure, the central circular disc, the lower Kresling paper folding structure, the gear disc, the bottom plate and the top plate are superposed.
6. A design method of multifunctional superstructure with adjustable rigidity and steady state according to any of claims 1 to 5, characterized by that: the method comprises the following steps:
step (1), setting corresponding parameters of an elastic element, so that the upper Kresling paper folding structure is initially in a first stable state, and the lower Kresling paper folding structure is initially in a second stable state, wherein the specific contents are as follows:
setting the initial height of the second stable state of the Kresling paper folding structure to be L 0 (ii) a The height L of the upper Kresling origami structure at the first steady state 1 The following were used:
Figure FDA0004110747950000021
wherein the content of the first and second substances,
Figure FDA0004110747950000022
Figure FDA0004110747950000023
/>
the top surface and the bottom surface of the upper Kresling paper folding structure and the bottom surface of the lower Kresling paper folding structure are regular polygons, the number of the sides of the regular polygons is n, the side length is P, and the radius of a circumscribed circle of each regular polygon is R; the side surfaces are n parallelograms, and the diagonal line of the parallelogram is a valley fold c 0 The long side of the parallelogram is a mountain fold crease b 0 The short side is the side of a regular polygon; theta 1 The relative rotation angle theta of the top surface polygon and the bottom surface polygon when the Kresling paper folding structure is positioned at the first stable state 2 The relative rotation angle between the top surface polygon and the bottom surface polygon when the lower Kresling paper folding structure is positioned at the second stable state is shown, and gamma is the included angle between the straight line from the center point of the polygon to a certain vertex and the side line of the corresponding polygon; lambda is an angle coefficient;
further calculating to obtain valley foldc 0 And mountain fold crease b 0 ：
Figure FDA0004110747950000024
Figure FDA0004110747950000025
At this time, the upper Kresling paper folding structure is in a first stable state, the bottom surface of the upper Kresling paper folding structure is fixed, and downward displacement u and rotation phi are applied to the top surface, namely the upper Kresling paper folding structure reaches a second stable state;
step (2), fixedly connecting the upper end of the upper Kresling paper folding structure in the first stable state with the bottom surface of the gear disc, and fixedly connecting the lower end of the upper Kresling paper folding structure with the top surface of the central disc; the upper end of the Kresling paper folding structure in the second stable state is fixedly connected with the bottom surface of the central disc, the lower end of the Kresling paper folding structure is fixedly connected with the bottom plate, the bottom plate is fully constrained, then the connecting rod is pulled to enable the superstructure to deform, and the change of the elastic potential energy U of the equivalent model along with the displacement of the connecting rod can be obtained according to the following formula:
Figure FDA0004110747950000031
the parameter of the upper Kresling origami structure is denoted by subscript p and the parameter of the lower Kresling origami structure is denoted by subscript s;
k p and k s Respectively an upper Kresling paper folding structure crease b and a lower Kresling paper folding structure crease b 0 And c 0 The linear stiffness corresponding to the position;
b p and c p For Kresling origami construction in the course of deformation b 0 And c 0 The real-time length of (c);
b s and c s For the following Kresling origami structure during deformation b 0 And c 0 The calculation formula of the real-time length is as follows:
Figure FDA0004110747950000032
Figure FDA0004110747950000033
Figure FDA0004110747950000034
Figure FDA0004110747950000035
wherein phi is p And phi s The rotation radians of the gear disc and the middle disc are respectively; h is a total of p And h s The real-time heights of the upper Kresling paper folding structure and the lower Kresling paper folding structure when deformation occurs are respectively set;
then, the force which needs to be applied to the connecting rod when the elastic element deforms is obtained through calculation based on the minimum energy principle, and the calculation formula is as follows:
Figure FDA0004110747950000036
wherein u is s For displacement of the connecting rod in the vertical direction, u s ＝L 1 -h p ；
And (3) adjusting the rotating radian of the elastic element through the radian adjusting mechanism, changing the internal prestress of the elastic element, and changing the overall external characteristic of the superstructure when the elastic element of the superstructure is deformed by pulling the connecting rod, so as to change the external rigidity and the steady-state characteristic when the elastic element of the superstructure is deformed, thereby realizing the switching of different steady-state characteristics and different steady-state rigidities.
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