Quasi-zero stiffness vibration isolation cell based on flexible curved beam, design method and vibration isolator

Abstract

The invention relates to a quasi-zero stiffness vibration isolation cell based on a flexible curved beam, a design method and a vibration isolator. Each cell comprises a first platform, a second platform, two first flexible curved beams and n second flexible curved beams, and n is a positive odd number. The first platform and the second platform are arranged in parallel in a spaced mode, the flexible curved beams are arranged between the two platforms, the n second flexible curved beams are arranged between the two first flexible curved beams arranged in the same direction, one end of each flexible curved beam is in rigid connection with the first platform through a support, and the other end of each flexible curved beam is in rigid connection with the second platform through a support. The mandrels of the flexible curved beams are cubic non-uniform B-spline curves defined by the same control point, the width of the cross section of the second flexible curved beam is twice that of the cross section of the first flexible curved beam, a gap is formed between every two adjacent flexible curved beams, and the flexible curved beams are arranged at an angle of 180 degrees. The cellular structure is simple and compact, most of harmful vibration can be effectively isolated, and yawing moment in the horizontal direction can be mutually offset.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of vibration control, in particular to a quasi-zero stiffness vibration isolation cell based on a flexible curved beam, a design method and a vibration isolator. BACKGROUND

[0002] In the fields of aerospace, precision instruments and equipment, and transportation equipment, low-frequency or even ultra-low-frequency vibrations have a non-negligible impact on the normal operation, working precision and reliability of the equipment, and the comfort of the operators. The traditional approach is that researchers at home and abroad generally use various forms of negative stiffness structures to reduce the stiffness of the system, with the purpose of reducing the natural frequency of the system, so as to achieve a lower initial isolation frequency. However, this approach has the disadvantage of low carrying capacity of the system. Therefore, in order to solve the contradiction between low initial isolation frequency and high carrying capacity, researchers have proposed a vibration isolator based on the concept of quasi-zero stiffness, which has the characteristics of high static and low dynamic stiffness, thereby achieving low initial isolation frequency and high carrying capacity.

[0003] Most single-degree-of-freedom quasi-zero stiffness vibration isolators adopt a structure in which positive stiffness and negative stiffness elastic elements are connected in parallel. The vibration isolator approaches zero stiffness by the principle of mutual cancellation of positive and negative stiffness near the balance position. This is the origin of the concept of quasi-zero stiffness. The vibration isolator developed based on this concept can only approach zero stiffness but cannot achieve zero stiffness. The positive stiffness and negative stiffness elastic elements often need to be connected in the form of a kinematic pair, which brings the problems of assembly precision and friction, making the cost of processing and assembly relatively high. For example, Chinese patent application No. CN110365249A. The main problems of this type of structure are complex structure, large size, low space utilization, and high production cost. In addition, due to the friction problem of the kinematic pair in the mechanism, the working precision and reliability of the quasi-zero stiffness vibration isolation mechanism are affected. SUMMARY

[0004] The first object of the present application is to provide a quasi-zero stiffness vibration isolation cell based on a flexible curved beam, which has a simple and compact structure and can effectively reduce or isolate most harmful vibrations.

[0005] The second object of the present application is to provide a design method for a quasi-zero stiffness vibration isolation cell based on a flexible curved beam. The designed vibration isolation cell has a simple and compact structure and can effectively reduce or isolate most harmful vibrations.

[0006] The third object of the present application is to provide a quasi-zero stiffness vibration isolator based on a flexible curved beam, which has a simple and compact structure and can effectively reduce or isolate most harmful vibrations.

[0007] In order to achieve the above-mentioned purpose, the first aspect of the present application provides a quasi-zero stiffness vibration isolation cell based on flexible curved beams, characterized in that it comprises: a first platform; a second platform, which is arranged in parallel and spaced apart from the first platform; two first flexible curved beams, which are arranged in a spaced apart manner between the first platform and the second platform, and the first ends of the two first flexible curved beams are rigidly connected to the first end of the first platform through a first support, and the second ends are rigidly connected to the second end of the second platform through a second support; n second flexible curved beams, which are arranged between the two first flexible curved beams, wherein n is an odd positive number, one end of each second flexible curved beam is rigidly connected to one end of the first platform through a first support, and the other end is rigidly connected to the other end of the second platform through a second support; the centroid axis of each flexible curved beam is a cubic non-uniform B-spline curve defined by the same control point, and the cross-sectional shape and size of each flexible curved beam remain consistent in the plane perpendicular to the tangent of the centroid axis, the cross-sectional width of the second flexible curved beam is twice that of the first flexible curved beam, there is a gap between the two adjacent flexible curved beams, the gap is equal in width in the length direction of the flexible curved beam, and the local coordinate system of the two adjacent flexible curved beams is arranged by rotating 180° around the line connecting the first platform and the second platform, wherein the X-axis of one flexible curved beam points from its first end to its second end, and the X-axis direction of the other adjacent flexible curved beam is opposite to it.

[0008] Optionally, the outer side surface of the first support located at the opposite ends of the first platform is flush with the plane of the end of the first platform; the outer side surface of the second support located at the opposite ends of the second platform is flush with the plane of the end of the second platform; the outer side surface of the two first flexible curved beams in the spacing direction is flush with the outer side plane of the first platform and the second platform on the same side.

[0009] Optionally, the quasi-zero stiffness vibration isolation cell is integrally formed by additive manufacturing.

[0010] Optionally, the printing material of the quasi-zero stiffness vibration isolation cell is stainless steel or titanium alloy.

[0011] Optionally, the printing material of the quasi-zero stiffness vibration isolation cell is 316L stainless steel.

[0012] Optionally, the span-depth ratio of each flexible curved beam is at least 8.

[0013] Optionally, the gap between the two adjacent flexible curved beams is 0.3mm to 1mm.

[0014] Optionally, the thickness of the flexible curved beam is 0.15mm to 1.2mm, and the cross-sectional width of the second flexible curved beam is at least 2mm.

[0015] In a second aspect, the present application provides a design method for the quasi-zero stiffness vibration isolation cell based on the flexible curved beam in the first aspect, comprising the following steps: (a) determining the overall size of the quasi-zero stiffness vibration isolation cell, the interval distance between the first platform and the second platform, the number of the flexible curved beams, the number and size of the first support and the second support, and the span-to-height ratio of the flexible curved beam, the span and the height of the flexible curved beam according to the space to be arranged and the selected material; (b) establishing a coordinate system: a Cartesian coordinate system is established with the end point of the second support close to the flexible curved beam as the origin, the interval direction between the first platform and the second platform as the Y axis, the interval direction of the two first flexible curved beams as the Z axis, and the direction from the first end to the second end of the first platform as the X axis; (c) defining the centroid axis of the flexible curved beam: defining the centroid axis of the flexible curved beam based on a 3rd order non-uniform B-spline curve, and the number of control points is not less than 6; (d) setting the parameters of the flexible curved beam: including the thickness and width of the second flexible curved beam and the gap between the adjacent two flexible curved beams, wherein the cross-sectional shape and size of the second flexible curved beam are consistent in the plane perpendicular to the tangent of the centroid axis; (e) adjusting the control point parameters: adjusting the Y coordinate deviation parameters of the control points to make the reaction force-displacement curve stiffness of the flexible curved beam near the equilibrium position tend to zero; wherein the value range of is 0.8 to 1.2, =1 is the reference design value, when >1, the positive stiffness is enhanced, and when <1, the negative stiffness is enhanced; (f) dividing the second flexible curved beam: dividing the second flexible curved beam into two first flexible curved beams along the width direction; (g) the two first flexible curved beams are located on both sides, and the second flexible curved beam is arranged between the two first flexible curved beams, and the local coordinate system of the adjacent two flexible curved beams is arranged by rotating 180° around the line connecting the first platform and the second platform, wherein the X axis of one flexible curved beam points from the first end to the second end, and the X axis direction of the adjacent other flexible curved beam is opposite to that of the one flexible curved beam; (h) performing finite element simulation reverse verification.

[0016] In a third aspect, the present application further provides a quasi-zero stiffness vibration isolator based on the flexible curved beam, comprising a plurality of quasi-zero stiffness vibration isolation cells in any one of the first aspect.

[0017] The above technical scheme of the present application has the following advantages: The present application provides a quasi-zero stiffness vibration isolation cell based on flexible curved beams, comprising a first platform, a second platform, two first flexible curved beams and n second flexible curved beams, wherein n is an odd positive number. The first platform and the second platform are arranged in parallel and at intervals, the two first flexible curved beams are arranged in the same direction and at intervals between the first platform and the second platform, and the n second flexible curved beams are arranged between the two first flexible curved beams. One end of each flexible curved beam is rigidly connected to the first platform through a support, and the other end is rigidly connected to the second platform through a support. The centroid axis of each flexible curved beam is a 3rd order non-uniform B-spline curve defined by the same control point, and the cross-sectional shape and size of each flexible curved beam remain consistent in the plane perpendicular to the tangent of the centroid axis. The cross-sectional width of the second flexible curved beam is twice that of the first flexible curved beam. There is a gap between the two adjacent flexible curved beams, and the gap is equal in width in the length direction of the flexible curved beam. The local coordinate system of the two adjacent flexible curved beams is arranged by rotating 180° around the line connecting the first platform and the second platform, wherein the X-axis of one flexible curved beam points from its first end to its second end, and the X-axis direction of the adjacent other flexible curved beam is opposite to that of the one flexible curved beam. Based on the 3rd order non-uniform B-spline curved beam, the friction of the kinematic pair in the vibration isolation mechanism is avoided, the assembly cost of the structure is reduced, and the vibration isolation precision and effect are greatly improved. The vibration isolation cell structure is compact, can effectively isolate most harmful vibrations, can well suppress low-frequency vibrations from a single direction, and the cell structure can mutually offset the yaw moment in the horizontal direction, so that it has good vibration isolation precision.

[0018] The present application provides a design method of the quasi-zero stiffness vibration isolation cell based on flexible curved beams, which can quickly design flexible curved beams with different quasi-zero stiffness ranges, thereby meeting the needs of different vibration isolation frequency bands and vibration isolation loads. BRIEF DESCRIPTION OF DRAWINGS

[0019] The drawings of the present application are provided for illustrative purposes only, and the proportions and quantities of the components in the drawings may not be consistent with the actual product.

[0020] Figure 1 is a front view schematic diagram of a quasi-zero stiffness vibration isolation cell based on flexible curved beams in an embodiment of the present application; Figure 2 is Figure 1 a left view schematic diagram of the quasi-zero stiffness vibration isolation cell in Figure 3 is Figure 1 a perspective view schematic diagram of the quasi-zero stiffness vibration isolation cell in Figure 4 is a yaw moment offset schematic diagram of a quasi-zero stiffness vibration isolation cell based on flexible curved beams in an embodiment of the present application; Figure 5is a schematic diagram of a quasi-zero stiffness vibration isolation cell based on a flexible curved beam in an embodiment of the present application when the load is balanced near the stiffness zero point; Figure 6 is a schematic diagram of the force-displacement relationship of the quasi-zero stiffness vibration isolation cell based on a flexible curved beam in an embodiment of the present application; Figure 7 is Figure 3 a schematic diagram of the deformation and stress distribution of a single flexible curved beam of the quasi-zero stiffness vibration isolation cell shown in Figure 8 is Figure 3 a schematic diagram of the force-displacement curve of the quasi-zero stiffness vibration isolation cell shown in during 100 stress cycles test; Figure 9 is a schematic diagram of the quasi-zero stiffness vibration isolation cell based on a flexible curved beam in an embodiment of the present application Figure 3 is a schematic diagram of the change relationship of the longitudinal stiffness of the quasi-zero stiffness vibration isolation cell with displacement in

[0021] Figure 10 is a schematic diagram of the change relationship of the vibration transmissibility of the quasi-zero stiffness vibration isolation cell with dimensionless excitation frequency in Figure 3 Figure 11 is a schematic diagram of the Cartesian coordinate system of the flexible curved beam of the quasi-zero stiffness vibration isolation cell in an embodiment of the present application; Figure 12 is a schematic diagram of the design region of a flexible curved beam in an embodiment of the present application; Figure 13 is a schematic diagram of the structure of a quasi-zero stiffness vibration isolator based on a flexible curved beam in an embodiment of the present application; Figure 14 is a schematic diagram of the structure of another quasi-zero stiffness vibration isolator based on a flexible curved beam in an embodiment of the present application.

[0022] Figure 15 is a vibration isolation cell in a comparative example.

[0023] In the figure: 1: quasi-zero stiffness vibration isolation cell; 11: first platform; 111: first support; 12: second platform; 121: second support; 13: first flexible curved beam; 14: second flexible curved beam. DETAILED DESCRIPTION

[0024] ​In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0025] As shown in Figures 1-3 , the embodiment of the present application provides a quasi-zero stiffness vibration isolation cell 1 based on a flexible curved beam, which comprises a first platform 11, a second platform 12, two first flexible curved beams 13 and n second flexible curved beams 14, wherein n is an odd positive number, for example, 1, 3, 5, 7, etc. In this embodiment, n is 1, that is, one second flexible curved beam 14. The first platform 11 and the second platform 12 are arranged in parallel and spaced apart. A support is arranged on the opposite side of the first platform 11 and the second platform 12, respectively. The upper support arranged on the first platform 11 is a first support 111, and the support arranged on the second platform 12 is a second support 121. The first support 111 and the second support 121 are mainly used for directly connecting with the flexible curved beam, so that the flexible curved beam has a certain distance from the first platform 11 and the second platform 12, preventing the flexible curved beam from deforming and interfering with the movement of the first platform 11 and the second platform 12, and at the same time, the support has sufficient bending stiffness to ensure the stability of the movement of the curved beam. The number of the first support 111 and the second support 121 can be set according to the number of the flexible curved beam to be connected, which is not limited here.

[0026] As shown in Figure 2 and Figure 3 , the two first flexible curved beams 13 are arranged in spaced apart between the first platform 11 and the second platform 12, and the first end (the right end of the cell) of the two first flexible curved beams 13 is respectively connected with the first end of the first platform 11 through a first support 111, and the second end (the left end of the cell) is connected with the second end of the second platform 12 through a second support 121. A second flexible curved beam 14 is arranged between the two first flexible curved beams 13, and the left end (the direction shown in Figure 1 is taken as the reference) of the second flexible curved beam 14 is connected with the left end of the first platform 11 through the first support 111, and the right end is connected with the other end of the second platform 12 through the second support 121. Figure 1 Figure 1

[0027] ​​The centroid axis of the first flexible curved beam 13 and the second flexible curved beam 14 is a cubic non-uniform B-spline curve defined by the same control points, and the cross-sectional shape and size of each flexible curved beam remains consistent in the plane perpendicular to the tangent of the centroid axis, i.e. each flexible curved beam is an equal cross-section curved panel itself. The cross-sectional width of the second flexible curved beam 14 is twice that of the first flexible curved beam 13, and any two adjacent flexible curved beams have a gap to prevent motion interference. The gap is equal in width in the length direction of the flexible curved beam (any cross-section of the gap in the length direction of the flexible curved beam is the same), and the local coordinate system of the two adjacent flexible curved beams (here, the "local coordinate system" emphasizes that the coordinate system is a local coordinate system of the cell (the coordinate system of the flexible curved beam itself), rather than the coordinate system of the cell) is arranged 180° around the line connecting the first platform and the second platform, with the X-axis of one flexible curved beam pointing from the first end to the second end, and the X-axis of the adjacent flexible curved beam pointing in the opposite direction. Referring to Figure 11 As shown, the origin of the coordinate system of each flexible curved beam in the vibration isolation cell is located on the contact surface between the second support 121 and the flexible curved beam, the coordinate axes corresponding to the coordinate systems of different flexible curved beams are parallel to each other, and the x-coordinate axes of adjacent curved beams are 180°. The following example is used to further understand the concept of the 180° arrangement of adjacent flexible curved beams. For example, define one end of the flexible curved beam as the first end and the other end as the second end. Referring to Figure 1 As shown, the first end of one of the two adjacent flexible curved beams is located at the left end and the second end is located at the right end, and the first end of the other flexible curved beam is located at the right end and the second end is located at the left end.

[0028] In use, the first platform 11 of the quasi-zero stiffness vibration isolation cell 1 is fixed to the object to be isolated, and the second platform 12 is fixed to the vibration source. Referring to Figure 5As shown in the figure, m is the equivalent mass of the object to be isolated, c is the damping coefficient, k is the equivalent stiffness of the quasi-zero stiffness vibration isolation cell 1, and x is the displacement response of the object to be isolated; its isolation mechanism is that the vibration source gives a harmonic response excitation, which is filtered through the flexible curved beam of the quasi-zero stiffness vibration isolation cell 1, and the excitation force is transmitted to the object to be isolated, that is, an input cosine wave is output after attenuation, which is still a cosine wave, only the phase has changed. The vibration isolation cell structure is compact, can effectively isolate most harmful vibrations, can well suppress low-frequency vibrations from one direction, and the cell structure can mutually offset the horizontal yaw moment, so that it has good vibration isolation precision. Compared with the traditional quasi-zero stiffness vibration isolation mechanism composed of positive and negative stiffness elastic elements in parallel, the curved beam based on the third non-uniform B-spline in the embodiment not only avoids the friction of the kinematic pair in the vibration isolation mechanism, but also reduces the assembly cost of the structure, greatly improving the vibration isolation precision and effect. In essence, the curved beam in the embodiment also generates quasi-zero stiffness by parallel connection of positive and negative stiffness elastic elements, the convex curve part of the cubic curve is responsible for generating negative stiffness characteristics, and the concave curve part of the cubic curve is responsible for generating positive stiffness characteristics. The positive and negative stiffness cancel each other out to achieve the quasi-zero stiffness characteristic.

[0029] The quasi-zero stiffness vibration isolation cell 1 in the embodiment adopts the positive odd root second flexible curved beam 14 in order to offset the yaw moment. When n is an odd number, the curved beam group is arranged in a central symmetry, the yaw moment vectors are summed to zero, and only in this way can the vibration isolation cell generate a reaction force-displacement curve with quasi-zero stiffness characteristics. Referring to Figure 4 As shown in the figure, during use, the whole cell can be regarded as two symmetrical units, unit one generates a clockwise yaw moment, and unit two generates a counterclockwise yaw moment, and the yaw moments generated by the two units cancel each other out. If the cell includes an even number of second flexible curved beams 14, a yaw moment will be generated. In one example, referring to Figure 15 As shown in the figure, the cell includes two second flexible curved beams, and the cell is divided into three units from the structure. The counterclockwise yaw moment generated by unit one can be offset by the clockwise yaw moment generated by unit two, and the counterclockwise yaw moment generated by unit three has no object to offset. Therefore, the cell with two second flexible curved beams exhibits a yaw moment as a whole, which is not conducive to the working precision of the vibration isolator.

[0030] In one example, the first platform 11 and the second platform 12 are the same size, and the widths of the first support 111 and the second support 121 are the same as the widths of the connected flexible curved beams.

[0031] In one example, referring to Figure 1 and Figure 3 As shown in the figures, the outer side surface of the first support 111 at the left end of the first platform 11 is connected to the first flexible curved beam 12 at the left end of the first platform 11, and the outer side surface of the first support 111 at the right end of the first platform 11 is connected to the second flexible curved beam 13 at the right end of the first platform 11. Figure 1The left side of the left first support and the right side of the right first support are respectively flush with the left end plane and the right side plane of the first platform 11 along the length direction. Similarly, the outer side of the second support 121 at the opposite ends of the second platform is flush with the plane of the left and right ends of the second platform 12. See Figure 2 The outer side of the two first flexible curved beams 13 in the spacing direction Figure 2 The left side of the left first flexible curved beam 13 and the right side of the right first flexible curved beam 13 are flush with the outer side of the first platform 11 and the second platform 12 on the side, and neither the flexible curved beam nor the support exceeds the first platform and the second platform, which is more regular as a whole, facilitating arrangement.

[0032] The quasi-zero stiffness vibration isolation cell in the embodiment is integrally formed by additive manufacturing. The printing material of the quasi-zero stiffness vibration isolation cell 1 can be selected as required, such as stainless steel, titanium alloy, plastic or resin that meets the requirements (generally considering Young's modulus, Poisson's ratio, yield strength). In a specific embodiment, the quasi-zero stiffness vibration isolation cell 1 is made of 316L stainless steel powder and integrally formed by laser selective melting (Selective Laser Melting, SLM) additive manufacturing. The device used is a BLT-S200 printer. The printing parameters are set as follows: laser power: 150W~250W, scanning speed: 700mm / s~1200mm / s, scanning interval 0.06~0.1mm, layer thickness 0.02~0.05mm. The printing is carried out along the vertical direction of the cell (according to the clockwise rotation of the cell by 90°) during printing. According to the process requirements of additive manufacturing, the support located above during processing needs to be provided with a printing transition slope to provide printing support. The angle between the printing transition slope and the horizontal plane (the direction during processing) is 30°~50°, and the preferred angle is 45°. Figure 1 The orientation of the cell is rotated clockwise by 90°) during printing. According to the process requirements of additive manufacturing, the support located above during processing needs to be provided with a printing transition slope to provide printing support. The angle between the printing transition slope and the horizontal plane (the direction during processing) is 30°~50°, and the preferred angle is 45°.

[0033] Compared with the vibration isolation cell made of resin or plastic, the vibration isolation cell made of stainless steel has greater carrying capacity under the condition of the same volume.

[0034] In an example, the gap between the two adjacent flexible curved beams is 0.3mm to 1mm, for example, 0.3mm, 0.4mm, 0.45mm, 0.5mm, 0.52mm, 0.56mm, 0.7mm, 0.8mm, 0.9mm, 1mm, etc., so as to prevent the adjacent two flexible curved beams from interfering with each other and to minimize the overall size of the cell. It should be noted that the size of the gap between the adjacent flexible curved beams only needs to meet the condition that the adjacent flexible curved beams do not interfere with each other, and can be set as required on this basis.

[0035] In order to make the flexible curved beam have better stability, preferably, in the embodiment, the span-height ratio (L / H) of the flexible curved beam single beam is at least 8 (L is the span, and H is the height). In a specific example, when the flexible thickness is 0.2 mm, the height H is 3 mm, and the span L is 27 mm. In another example, when the height H is 5 mm, the span L is 40 mm under the condition of meeting the vibration isolation requirement. The smaller the span is, the better. Figure 12

[0036] In an example, the thickness of the flexible curved beam is 0.15-1.0 mm, for example, 0.16 mm, 18 mm, 0.2 mm, 0.25 mm, 0.3 mm, 0.4 mm, 0.5 mm, 0.6 mm, 0.7 mm, 0.8 mm, 0.9 mm, 1.0 mm, etc.

[0037] In order to ensure the stability of the vibration isolation cell structure, in an example, the width of the second flexible curved beam is at least 2 mm, and the width of the first flexible curved beam 13 is at least 1 mm.

[0038] In an example, Figure 1 The second flexible curved beam of the quasi-zero stiffness vibration isolation cell in FIG. 8 has a span (length) L=28 mm, a height H=3 mm, a width b=4 mm, and a thickness t=0.19 mm.

[0039] Figure 6 FIG. 8 shows the force-displacement curve of the quasi-zero stiffness vibration isolation cell in FIG. 8. It can be seen from the figure that the force-displacement curve of the vibration isolation cell has the quasi-zero stiffness characteristic (approximate platform section), and the load corresponding to the quasi-zero stiffness platform can also be determined. Figure 1

[0040] FIG. 8 shows the finite element simulation deformation schematic diagram of the single curved beam of the quasi-zero stiffness vibration isolation cell in FIG. 8. The figure shows the surface stress distribution state of the curved beam from the initial position to the maximum deformation position. By comparing the maximum surface stress with the safe yield strength of the material (316L stainless steel), it can be known that the geometric design of the curved beam meets the requirements. Figure 7 Figure 1 FIG. 8 shows the force-displacement curve of the quasi-zero stiffness vibration isolation cell in FIG. 8. It can be seen from the figure that the force-displacement curve of the vibration isolation cell has the quasi-zero stiffness characteristic (approximate platform section), and the load corresponding to the quasi-zero stiffness platform can also be determined.

[0041] Figure 8 Figure 1 FIG. 8 shows the force-displacement curve of the quasi-zero stiffness vibration isolation cell in FIG. 8. It can be seen from the figure that the force-displacement curve of the vibration isolation cell has the quasi-zero stiffness characteristic (approximate platform section), and the load corresponding to the quasi-zero stiffness platform can also be determined.

[0042] Figure 9 FIG. 8 shows the force-displacement curve of the quasi-zero stiffness vibration isolation cell in FIG. 8. It can be seen from the figure that the force-displacement curve of the vibration isolation cell has the quasi-zero stiffness characteristic (approximate platform section), and the load corresponding to the quasi-zero stiffness platform can also be determined. Figure 1 Figure 6 ​​​​The first derivative curve of the shown reaction force-displacement curve, through which it can be seen that the minimum stiffness is very close to zero stiffness, i.e. the quasi-zero stiffness characteristic of the cell is verified.

[0043] The following provides a calculation method of the vibration isolation performance of the quasi-zero stiffness vibration isolation cell based on a flexible curved beam, and verifies the vibration isolation performance thereof: The vibration isolation performance of the vibration isolation cell introduced in the embodiments of the present application is calculated as follows. In order to approach the actual vibration situation, the structural damping caused by the intermolecular friction of the metal when large deformation occurs is considered, so the damping term is added in the vibration differential equation of the cell, and a simple harmonic excitation disturbance is added, so that the vibration isolation cell vibrates near the equilibrium position. Finally, the motion differential equation of the quasi-zero stiffness vibration isolation cell under simple harmonic excitation is expressed by the duffing equation containing the third order nonlinear term: (1) Wherein, m is the mass of the vibration isolation object, c is the damping coefficient, is the third order coefficient of the fitted force-displacement near the equilibrium position, is the amplitude of the simple harmonic excitation force, is the excitation frequency.

[0044] For the convenience of analysis and calculation, the coefficients in the motion differential equation (1) are normalized, thereby introducing the following parameters: (2) The normalized parameters in equation (2) are brought into equation (1) to simplify: (3) The harmonic balance method is used to solve the nonlinear differential equation problem, and the corresponding period is set as: (4) Substitute equation (4) into equation (3) and eliminate the response phase, to obtain the amplitude-frequency characteristic equation of the vibration isolation cell: (5) Wherein, A is the amplitude of the vibration displacement response.

[0045] Substitute equation (4) into the damping force term and the nonlinear elastic force term in equation (3), to calculate the amplitude of the force transmitted to the support under excitation vibration: (6) The force transmissibility is one of the important indicators for evaluating the vibration isolation effect of the cell, and the definition is the ratio of the amplitude of the force transmitted to the foundation to the amplitude of the excitation force, so: (7) According to Figure 1The normalized excitation amplitude , damping ratio =0.04, nonlinear term coefficient , the force transmissibility curve of the vibration isolation cell shown in Figure 10 .

[0046] As can be seen from the force transmissibility curve shown in Figure 10 , the excitation force amplitude transmitted by the quasi-zero stiffness vibration isolation cell is reduced by more than 95% when the excitation force frequency is greater than 3.6Hz, which shows that the quasi-zero stiffness vibration isolation cell in this embodiment has good low-frequency vibration isolation performance, and can realize low-frequency vibration isolation and also meet the demand of high-frequency vibration isolation.

[0047] The embodiment also provides a design method of a quasi-zero stiffness vibration isolation cell based on a flexible curved beam, comprising the following steps: (a) determining the overall size of the quasi-zero stiffness vibration isolation cell, the interval distance between the first platform and the second platform, the number of the flexible curved beams, the number and size of the first support and the second support, and the span-to-height ratio, the span and the height of the flexible curved beams according to the selected material and the space to be arranged. When selecting the material, the Young's modulus, the Poisson's ratio and the yield strength properties of the material are generally considered. A load shared by a vibration isolation cell is determined according to the target vibration isolation object, and then a span-to-height ratio is determined. After the span-to-height ratio is determined, the span and the height of the curved beam are selected according to the limitation of the vibration isolation cell arrangement space. The span and the height do not need to be too large, and just need to meet the needs, so that the cell arrangement space and the manufacturing cost are saved. The number of the first support and the second support is determined according to the number of the flexible curved beams, and each flexible curved beam corresponds to a first support and a second support. The support is mainly arranged to ensure that the flexible curved beam does not collide with the first platform and the second platform when the flexible curved beam is deformed. At the same time, the support is designed to have a certain thickness to ensure sufficient bending stiffness, so that the support is always perpendicular to the first platform and the second platform when the curved beam is deformed.

[0048] (b) establishing a coordinate system: a Cartesian coordinate system is established with the end point of the second support close to the flexible curved beam as the origin, the interval direction between the first platform and the second platform as the Y axis, the interval direction between the two first flexible curved beams as the Z axis, and the direction from the first end of the first platform to the second end as the X axis (see Figure 11 ).

[0049] (c) defining the flexible curved beam centroid axis: the flexible curved beam centroid axis is defined based on a cubic non-uniform B-spline curve, and the number of control points is not less than 6.

[0050] (d) Setting the parameters of the flexible curved beam: This includes the thickness and width of the second flexible curved beam and the gap between two adjacent flexible curved beams. The cross-sectional shape and dimensions of the second flexible curved beam remain consistent in a plane perpendicular to the centroidal axis tangent. When selecting the thickness of the flexible curved beam, start with the minimum thickness that the additive manufacturing equipment can produce. Of course, if the thickness of the flexible curved beam is too small, the load-bearing capacity of the cell will be small, so the thickness can be appropriately increased. The greater the length and height of the curved beam, the thicker the flexible curved beam can be. After selecting the geometric parameters of the length, height, and thickness of the curved beam, the final step is to select the width of the curved beam. The width of the curved beam only affects the vertical translation of the reaction-displacement curve of a single cell, and does not change the trend of the force-displacement curve. Therefore, by flexibly adjusting the width of the curved beam, the single cell can meet the predetermined load requirements.

[0051] (e) Adjusting control point parameters: By adjusting the Y-axis coordinate deviation parameters of the control points This causes the stiffness of the reaction force-displacement curve of the flexible curved beam to approach zero near the equilibrium position; in The value ranges from 0.8 to 1.2. =1 is the baseline design value, when When >1, the positive stiffness increases, when When the value is less than 1, the negative stiffness increases.

[0052] (f) Dividing the second flexible curved beam: The first flexible curved beam is obtained by uniformly dividing the designed second flexible curved beam along the width direction. It is worth noting that the division here mainly refers to the fact that the first flexible curved beam and the designed second flexible curved beam have the same parameters except for the width, and the width satisfies that the width of the first flexible curved beam is half of the width of the second flexible curved beam.

[0053] (h) Two first flexible curved beams are located on both sides, and a second flexible curved beam is set between the two first flexible curved beams. The local coordinate system of the two adjacent flexible curved beams is rotated 180° around the line perpendicular to the connection between the first platform and the second platform. The X-axis of one flexible curved beam points from its first end to its second end, and the X-axis of the other adjacent flexible curved beam is opposite to it. Finite element simulation reverse verification is performed to confirm whether the maximum surface stress of the vibration isolation cell exceeds the yield strength of the material within the specified deformation range, whether the force-displacement curve of the cell has quasi-zero stiffness characteristics, and whether the quasi-zero stiffness plateau force of the force-displacement curve meets the requirements. If all these requirements are met, a qualified vibration isolation cell is designed.

[0054] See one example. Figure 12 As shown, the projection of the flexible curved beam's outline onto the xoy plane, i.e., the curved beam's outline within a rectangular design region of length L and height H, is constrained to a certain extent. Figure 12two end points between which are shown in the rectangular region along the diagonal direction. The profile line of the flexible curved beam is a 4-order 3-degree non-uniform B-spline curve, and the shape of the curve is determined by 6 control points, in which the control points are recorded as P0, P1, P2, P3, P4 and P5 from left to right, and the coordinate expression of the curved beam profile curve satisfies the following formula definition: Figure 12 Given parameters: 1) n+1 control points (i=0,1,…,n) 2) Curve order k=4, degree k-1=3 (8) Wherein, is the definition domain of the node vector, is the left boundary of the node vector, and is the right boundary of the node vector.

[0055] The curve is approximated by constructing a polynomial function (8), wherein is called a k-order (k-1-degree) B-spline Bernstein basis function, which is defined by a De Boor-Cox recursive formula: (9) In the recursive formula, it is agreed that .

[0056] With the basis function and the coordinates of each control point, the coordinates of each point on the B-spline curve can be calculated according to different variable u values. The length of the node interval in the definition domain is calculated according to the Hartly-Judd method as follows: (10) Therefore, the node value is (11) In order to ensure that the k-1-degree spline curve can pass through the first and last two control points, the node vector and must be k-fold nodes, so the node vector after the k-fold node is (wherein n+k=9), and the k-fold nodes at the left and right ends have no effect on the polynomial function in formula (8). In addition, the node vector obtained by the Hartly-Judd method is non-uniform, and the overall curved beam profile line is smoothly connected by n-k+2 segments of k-1-degree polynomial curves. Therefore, the above is the 3-degree non-uniform B-spline flexible curved beam introduced in the embodiment of the application.

[0057] In an example, the centroid axis curve of the flexible curved beam is adjusted by and In order to ensure that the minimum stiffness of the flexible curved beam in the quasi-zero stiffness interval in the embodiment of the application is close enough to 0, so that the vibration isolator has good vibration isolation performance, a parameter​ Used to optimize curve shape, used to represent and The y-coordinate deviation between the two control points; changing this parameter will only affect... and The local shape of the curve near the two control points. By controlling the magnitude of this parameter, the minimum stiffness of the reaction force-displacement curve of the curved beam can be made sufficiently close to 0. The value range is [0.8, 1.2], and the initial value is 1. A value greater than 1 indicates that the difference in the y-coordinate between the two control points is increasing, and the curved beam is showing a positive stiffness trend. A value less than 1 indicates that the difference in the y-coordinates between the two control points decreases, and the curved beam exhibits a negative stiffness trend.

[0058] According to the curved beam design method provided in this embodiment, flexible curved beams with different quasi-zero stiffness ranges can be designed quickly to meet the requirements of different vibration isolation frequency bands and vibration isolation loads, and even achieve lower initial vibration isolation frequencies. In addition, the quasi-zero stiffness vibration isolation cell structure is compact, has no kinematic pairs, and requires no assembly; that is, the design serves the vibration isolation function and manufacturing method.

[0059] Depending on the application scenario, a single quasi-zero stiffness isolation cell can serve as a quasi-zero stiffness isolator to achieve vibration isolation. Of course, in one example, see... Figure 13 and Figure 14 As shown, a quasi-zero stiffness vibration isolator can be composed of multiple quasi-zero stiffness vibration isolating cells 1 arranged periodically. These multiple quasi-zero stiffness vibration isolating cells 1 can be arranged as a single, periodic unit, or adjacent quasi-zero stiffness vibration isolating cells 1 can share a common platform. For example, two quasi-zero stiffness vibration isolating cells 1 arranged in multiple layers share a single platform (serving as both the second platform of the upper quasi-zero stiffness vibration isolating cell 1 and the first platform of the lower quasi-zero stiffness vibration isolating cell 1). For two quasi-zero stiffness vibration isolating cells 1 arranged in multiple columns within the same layer, the first platform of both quasi-zero stiffness vibration isolating cells 1 is a single unit, and the second platform is also a single unit.

[0060] Of course, in some examples, multiple quasi-zero stiffness isolation cells 1 can also be used in combination (not directly connected).

[0061] In other examples, a quasi-zero stiffness isolator can be composed of multiple quasi-zero stiffness isolator cells 1 arranged in a trapezoidal shape.

[0062] It should be noted that the above examples are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that not every example contains only one independent technical solution, and in the absence of solution conflicts, various technical features mentioned in each example can be combined in any manner to form other embodiments that can be understood by those skilled in the art.

[0063] In addition, the terms "first", "second", "third" are only for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0064] In addition, the technical solutions described in the foregoing examples are modified or some technical features are replaced equivalently without departing from the scope of the present application, and the essence of the corresponding technical solutions does not deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A quasi-zero stiffness vibration isolation cell based on a flexible curved beam, characterized in that, include: First platform; The second platform is set parallel and spaced apart from the first platform; Two first flexible curved beams are spaced apart between the first platform and the second platform, and the first ends of the two first flexible curved beams are rigidly connected to the first end of the first platform through a first support, and the second ends of the two beams are rigidly connected to the second end of the second platform through a second support. n second flexible curved beams are arranged between two first flexible curved beams, where n is a positive odd number. Each second flexible curved beam is rigidly connected at one end to one end of the first platform through a first support, and at the other end to the other end of the second platform through a second support. The centroidal axis of each flexible curved beam is a cubic non-uniform B-spline curve defined by the same control point, and the cross-sectional shape and size of each flexible curved beam are consistent in a plane perpendicular to the tangent of the centroidal axis. The cross-sectional width of the second flexible curved beam is twice the cross-sectional width of the first flexible curved beam. There is a gap between two adjacent flexible curved beams, and the gap is of equal width along the length of the flexible curved beam. The local coordinate system of two adjacent flexible curved beams is arranged by rotating 180° around the line perpendicular to the connection between the first platform and the second platform. The X-axis of one flexible curved beam points from its first end to its second end, and the X-axis of the adjacent flexible curved beam is in the opposite direction.

2. The quasi-zero stiffness vibration isolation cell according to claim 1, characterized in that: The outer surfaces of the first supports located at opposite ends of the first platform are flush with the plane at the end of the first platform. The outer surfaces of the second supports located at opposite ends of the second platform are flush with the plane at the end of the second platform. The outer surfaces of the two first flexible curved beams in the spacing direction are flush with the outer planes of the first and second platforms on the same side.

3. The quasi-zero stiffness vibration isolation cell according to claim 1, characterized in that: The quasi-zero stiffness vibration isolation cell is integrally formed using additive manufacturing.

4. The quasi-zero stiffness vibration isolation cell according to claim 3, characterized in that: The printing material for the quasi-zero stiffness vibration isolation cell is stainless steel or titanium alloy.

5. The quasi-zero stiffness vibration isolation cell according to claim 4, characterized in that: The quasi-zero stiffness vibration isolation cell is printed using 316L stainless steel.

6. The quasi-zero stiffness vibration isolation cell according to claim 5, characterized in that: The span-to-depth ratio of each flexible curved beam is at least 8.

7. The quasi-zero stiffness vibration isolation cell according to claim 6, characterized in that: The thickness of the flexible curved beam is 0.15 mm to 1.2 mm, and the cross-sectional width of the second flexible curved beam is at least 2 mm.

8. The quasi-zero stiffness vibration isolation cell according to claim 5, characterized in that: The gap between two adjacent flexible curved beams is 0.3mm to 1mm.

9. A design method for a quasi-zero stiffness vibration isolation cell based on a flexible curved beam as described in claim 1, characterized in that, Includes the following steps: The overall dimensions of the quasi-zero stiffness isolation cell, the spacing between the first and second platforms, the number of flexible curved beams, the number and dimensions of the first and second supports, the span-to-depth ratio, the span and height of the flexible curved beams are determined based on the space to be arranged and the selected materials. Establish a coordinate system: Establish a Cartesian coordinate system with the end of the second support near the flexible curved beam as the origin. The spacing between the first platform and the second platform is the Y-axis, the spacing between the two first flexible curved beams is the Z-axis, and the direction from the first end to the second end of the first platform is the X-axis. Define the centroidal axis of the flexible curved beam: Define the centroidal axis of the flexible curved beam based on a cubic non-uniform B-spline curve, with no less than 6 control points; Set the parameters of the flexible curved beam: including the thickness and width of the second flexible curved beam and the gap between two adjacent flexible curved beams, wherein the cross-sectional shape and size of the second flexible curved beam remain consistent in a plane perpendicular to the centroidal axis tangent; Adjusting control point parameters: This is done by adjusting the Y-axis coordinate deviation parameter of the control points. This causes the stiffness of the reaction force-displacement curve of the flexible curved beam to approach zero near the equilibrium position; in The value ranges from 0.8 to 1.

2. =1 is the baseline design value, when When >1, the positive stiffness increases, when When the value is less than 1, the negative stiffness increases; Divide the second flexible curved beam: Divide the second flexible curved beam evenly along the width direction to form two first flexible curved beams; Two first flexible curved beams are located on both sides, and a second flexible curved beam is set between the two first flexible curved beams. The local coordinate system of the two adjacent flexible curved beams is rotated 180° around the line perpendicular to the connection between the first platform and the second platform. The X-axis of one flexible curved beam points from its first end to its second end, and the X-axis of the adjacent flexible curved beam is in the opposite direction. Reverse verification using finite element simulation was performed.

10. A quasi-zero stiffness vibration isolator based on a flexible curved beam, characterized in that: It includes multiple quasi-zero stiffness vibration isolation cells as described in claims 1 to 8.

Images