WO2022095962A1 - 一种弹性参数大范围连续可调的齿轮力学超材料 - Google Patents

一种弹性参数大范围连续可调的齿轮力学超材料 Download PDF

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WO2022095962A1
WO2022095962A1 PCT/CN2021/129010 CN2021129010W WO2022095962A1 WO 2022095962 A1 WO2022095962 A1 WO 2022095962A1 CN 2021129010 W CN2021129010 W CN 2021129010W WO 2022095962 A1 WO2022095962 A1 WO 2022095962A1
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gear
gears
metamaterial
meshing
mechanics
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PCT/CN2021/129010
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English (en)
French (fr)
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方鑫
温激鸿
郁殿龙
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国防科技大学
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Priority to US17/759,098 priority Critical patent/US12007013B2/en
Publication of WO2022095962A1 publication Critical patent/WO2022095962A1/zh

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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
    • F16H—GEARING
    • F16H57/00—General details of gearing
    • F16H57/0018—Shaft assemblies for gearings
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • 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
    • F16H—GEARING
    • F16H1/00—Toothed gearings for conveying rotary motion
    • F16H1/02—Toothed gearings for conveying rotary motion without gears having orbital motion
    • F16H1/20—Toothed gearings for conveying rotary motion without gears having orbital motion involving more than two intermeshing members
    • F16H1/22—Toothed gearings for conveying rotary motion without gears having orbital motion involving more than two intermeshing members with a plurality of driving or driven shafts; with arrangements for dividing torque between two or more intermediate shafts
    • 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
    • F16H—GEARING
    • F16H1/00—Toothed gearings for conveying rotary motion
    • F16H1/28—Toothed gearings for conveying rotary motion with gears having orbital motion
    • 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
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/17—Toothed wheels
    • 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
    • F16H—GEARING
    • F16H57/00—General details of gearing
    • F16H57/0018—Shaft assemblies for gearings
    • F16H57/0037—Special features of coaxial shafts, e.g. relative support thereof
    • 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
    • F16H—GEARING
    • F16H57/00—General details of gearing
    • F16H2057/0056—Mounting parts arranged in special position or by special sequence, e.g. for keeping particular parts in his position during assembly
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation

Definitions

  • the invention relates to the field of mechanics and mechanical engineering, in particular to a gear mechanics metamaterial with adjustable elastic parameters in a wide range.
  • the core of the fourth industrial revolution is intelligent structures and equipment, such as adaptive aircraft, adaptive control systems, intelligent connectors, intelligent vibration and noise control, and so on.
  • the intelligence of the equipment requires that the units and materials of the manufacturing equipment are intelligently adjustable.
  • Mechanical materials with adjustable elastic properties can provide basic support for the design and preparation of smart devices.
  • traditional piezoelectric materials and shape memory alloy materials are difficult to produce large-scale elastic tuning. The design of new smart materials presents many challenges.
  • Mechanical metamaterials refer to artificial materials with extraordinary mechanical properties, which can produce properties such as low density, high modulus, negative Poisson's ratio, and chirality.
  • Typical structures include two-dimensional honeycomb structures, three-dimensional lattice structures, folded structures, and chiral structures.
  • Mechanical metamaterials provide important structural design solutions for industrial systems such as aerospace, ships, high-speed rail, and automobiles.
  • Reconfigurable mechanical metamaterials refer to mechanical metamaterials that can change their geometry under the action of external stimuli (such as compressive force). Changes in geometry can lead to essential changes in mechanical properties, such as elastic modulus, shear modulus, deformation mode, damping, and anisotropy can abruptly change from one value to another.
  • the invention provides a gear mechanics metamaterial with a wide range of elastic parameters continuously adjustable, which is used to overcome the defects of narrow elastic parameter adjustment range, few stable states and low regulation robustness in the existing reconfigurable mechanical metamaterial design technology.
  • the present invention provides a gear mechanics metamaterial whose elastic parameters are continuously adjustable in a wide range, including a gear array, a frame and a connecting shaft;
  • the gear array is composed of mechanical metamaterial cells periodically along the x and y directions.
  • the cell is formed by the arrangement of multiple gears, and adjacent gears are meshed with each other;
  • the gear includes a central hole and two centrally symmetrical special-shaped holes, the special-shaped hole and the outer wall of the gear
  • the thickness of the cantilever increases or decreases uniformly;
  • the connecting shaft is arranged in the central hole of the gear, and the gear array is connected with the frame through the connecting shaft.
  • the meshing modes of two adjacent gears include positive polarity meshing and negative polarity meshing; the thickness of the cantilever at the meshing points of two adjacent gears is positive polarity meshing when one gradually increases and the other gradually decreases. Negative polarity meshing occurs when the thickness of the cantilever at the meshing point increases or decreases simultaneously.
  • the two center-symmetric special-shaped holes on the gear are separated by a cantilever beam on the same horizontal line, and there is an angle difference between the cantilever beams of the two gears meshing with each other, and the angle difference is 0 to 180 degrees.
  • the rigidity of the frame is less than the minimum rigidity formed by the meshing of the gears.
  • the frame is an elastic frame, and the elastic frame is formed by periodic extension of thin-walled rings, and a thick-walled ring with a through hole is provided at the connection point of two adjacent thin-walled rings;
  • the through hole of the ring is sleeved on the connecting shaft, and the gear is connected with the through hole of the thick-walled ring through the connecting shaft.
  • each of the mechanical metamaterial cells is composed of 4 gears that mesh with each other, and the 4 gears are arranged in a 2 ⁇ 2 array.
  • This structure can be used as a gear mechanics metamaterial for tuning Young's modulus, damping, and anisotropy parameters.
  • two adjacent gears are connected in a positive-polarity meshing manner or a negative-polarity meshing manner, and the installation angle of each other gear is the same as the installation front and back sides (the same gear has both front and back sides).
  • each of the mechanical metamaterial cells is composed of 7 gears that mesh with each other, the gears are arranged in a 3 ⁇ 3 array, and the positions of the middle row or both sides of the column are vacated for a gear position to form a defect state.
  • the cavity formed by every three gears is provided with an insert which forms a conformal and coordinated contact with the three gears. This structure can be used as a gear mechanics metamaterial for regulating shear modulus.
  • the insert is a cross-shaped insert, and the four ends of the cross-shaped insert are concave arcs that match the arc of the gear; the ends of the cross-shaped insert are Two symmetrical elastic arms extend outward from the top.
  • a gear mechanics metamaterial with continuously adjustable elastic parameters in a large range includes a gear array, a frame and a connecting shaft, and the gear array is periodically extended along the x and y directions by the mechanical metamaterial cell.
  • the unit cell is composed of a plurality of gears arranged, adjacent gears are meshed with each other, and the arrangement is designed according to the elastic parameters to be adjusted;
  • the gears include a center hole and two center-symmetric special-shaped holes, so The thickness of the cantilever between the special-shaped hole and the outer wall of the gear increases or decreases uniformly;
  • the connecting shaft is arranged in the central hole of the gear, and the gear array is connected to the frame through the connecting shaft.
  • the present invention provides a gear mechanics metamaterial whose elastic parameters are continuously adjustable in a large range.
  • the meshing modes of two adjacent gears include positive polarity meshing and negative polarity meshing; the thickness of the cantilever at the meshing point of the adjacent two gears is one When the thickness of the cantilever at the meshing point of two adjacent gears increases or decreases at the same time, it is a negative polarity meshing.
  • the two center-symmetric special-shaped holes on the gear are separated by a cantilever beam on the same horizontal line, and there is an angle difference between the cantilever beams of the two gears meshing with each other, and the angle difference is 0-180 degrees.
  • the gear mechanics metamaterial provided by the present invention has a wide range of continuously adjustable elastic parameters, and uses the porous structure of the gear to realize wide range continuous adjustment of Young's modulus, shear modulus and damping.
  • Young's modulus When adjusting Young's modulus, a tight fit is used between the gears, and each internal gear meshes with 4 adjacent gears. Young's modulus, damping and anisotropy parameters can be adjusted simultaneously.
  • the damping of the mechanical metamaterial is derived from the slip between the gear teeth, and the damping effect increases with the increase of Young's modulus, which is used to achieve high stiffness and high damping characteristics.
  • a cavity is reserved for every other gear in the array, so that some of the gears only mesh with 2 adjacent gears, and are placed in the cavity left by every 3 gear meshes. insert.
  • the structure that modulates the shear modulus can also realize the simultaneous regulation of Young's modulus.
  • the mechanical metamaterial provided by the present invention directly uses gear meshing and rotation to achieve a large-scale continuous adjustment of Young's modulus, shear modulus, damping, anisotropy, and non-reciprocity, and achieves high structural reliability and weight. Robustness of structural operation, high stiffness, high strength, high damping, high achievability, and easy manufacturing.
  • Fig. 1a is a top view of a single gear according to a preferred embodiment of the present invention, and the special-shaped hole of the gear has a shape similar to a Taiji diagram, referred to as a Taiji gear;
  • Fig. 1b is a perspective structural view of a single gear according to a preferred embodiment of the present invention.
  • FIG. 2 is a schematic diagram of two gears in positive polarity meshing in a preferred embodiment of the present invention, and the angle difference between the two gears is 3 degrees.
  • FIG. 3 is a schematic diagram of the negative polarity meshing of two gears in a preferred embodiment of the present invention, and the angle difference between the two gears is 15 degrees.
  • FIG. 4 is a structural diagram of a gear mechanics metamaterial for adjusting Young’s modulus, damping and anisotropy parameters according to a preferred embodiment of the present invention, which is composed of 5 ⁇ 5 gears, the meshing mode is positive polarity, and the angle difference is 3 degrees ;
  • FIG. 5 is a schematic diagram of the arrangement of the gears in the x-direction and the y-direction.
  • FIG. 8 is a graph showing the variation of the damping parameter ⁇ with the gear rotation angle ⁇ in the preferred embodiment, which corresponds to the meshing mode and the angle difference marked in FIG. 6 .
  • Figure 9 is a schematic diagram of the cellular structure of mechanical metamaterials used to control Young's modulus and non-reciprocity parameters.
  • FIG. 10 is a structural diagram of an implant in the middle of every three gears in FIG. 9 , and each implant is in the shape of a cross.
  • FIG. 11 is a structural diagram of a mechanical metamaterial composed of the cells shown in FIG. 9 .
  • Figure 12 is the variation curve of the shear modulus G with the gear rotation angle ⁇ in the preferred embodiment; in the legend, G + and G - represent the shear obtained when the application direction of the shear stress ⁇ is positive and negative, respectively modulus.
  • the basic unit of the gear mechanics metamaterial proposed by the present invention is a single porous gear, preferably designed with a spur gear, as shown in Figure 1a and Figure 1b (wherein Figure 1a is a top view of a single gear in a preferred embodiment of the present invention, Fig. 1b is a perspective structural view of a single gear of a preferred embodiment of the present invention).
  • the inside of the gear 100 contains a center-symmetric hole structure.
  • each gear 100 includes a center hole 101 and two center-symmetric special-shaped holes 102 .
  • the shape of the special-shaped hole is similar to the "Tai Chi diagram", which may be referred to as a Tai Chi gear.
  • Two center-symmetric cantilever arms 103 are formed between the special-shaped hole 102 and the outer wall of the gear, and the thickness of the cantilever arms 103 increases or decreases uniformly with the angle (ie, changes smoothly).
  • the influence of the gear teeth on the bending stiffness of the cantilever 103 can be reduced by increasing the number of gear teeth.
  • the spiral directions of the front and back of the "Tai Chi Diagram"-shaped gear are opposite.
  • a gear mechanics metamaterial whose elastic parameters are continuously adjustable in a large range, including a gear array, a frame 300 and a connecting shaft 200;
  • the gear array is formed by the periodic extension of mechanical metamaterial cells along the x-direction and the y-direction;
  • the cell is formed by arranging a plurality of gears 100, the arrangement of the gears 100 is designed according to the elastic parameters to be adjusted, and the adjacent gears mesh with each other;
  • the gear 100 includes a central hole 101 and two centrally symmetrical
  • the special-shaped hole 102 the thickness of the cantilever 103 between the special-shaped hole 102 and the outer wall of the gear increases or decreases uniformly;
  • the connecting shaft 200 is arranged in the central hole 101 of the gear, and the gear array passes through the connecting shaft 200 Connect to frame 300.
  • the anisotropy parameter value is defined as the ratio of the Young's moduli in the x-direction and the y-direction when the rotation angle ⁇ is given, that is, E x /E y .
  • the non-reciprocal parameter value is defined as the ratio of the amount of shear deformation produced by the application of positive shear stress ⁇ + and negative shear stress ⁇ ⁇ for a given rotation angle ⁇ and shear stress ⁇ .
  • the meshing modes of two adjacent gears include positive polarity meshing and negative polarity meshing.
  • the thickness of the cantilever 103 at the meshing point of two adjacent gears gradually increases, and the other gradually decreases (that is, the spiral directions of the two “Tai Chi”-shaped gears are opposite), it is positive polarity meshing, and two adjacent gears mesh.
  • the thickness of the cantilever 103 at the point increases or decreases at the same time (that is, the spiral directions of the two "Tai Chi diagram" shaped gears are opposite)
  • the meshing is negative.
  • Figure 2 when the spiral directions of the two gears are opposite, it is called positive meshing.
  • the two gears have the same spiral direction, it is called negative meshing.
  • the two centrally symmetric special-shaped holes 102 on the gear are separated by a cantilever beam 104 on the same horizontal line, and there is an angle difference between the cantilever beams 104 of the two gears meshing with each other, and the range of the angle difference is 0-180 Spend.
  • the angular difference between the local figure coordinates is 3 degrees and 15 degrees, respectively.
  • the stiffness of the frame 300 is much less than the minimum stiffness created by gear meshing.
  • the frame 300 is an elastic frame, the elastic frame is periodically extended by thin-walled rings 301 , and a thick-walled wall with a through hole is provided at the connection point of two adjacent thin-walled rings 301 in the longitudinal direction. Ring 302 ; the through hole of the thick-walled ring 302 is sleeved on the connecting shaft 200 .
  • the joints of two adjacent thin-walled rings 301 are welded together.
  • Both sides of the gear array are connected with an elastic frame through a connecting shaft 200 .
  • the gears are connected as a whole through the connecting shaft 200 and the elastic frame.
  • the stiffness k arm of a single cantilever is defined as the ratio of the applied force to the amount of deformation when a radial force is applied between the gear center hole and the cantilever point, so the k arm cantilever thickness is closely related, while the cantilever thickness varies smoothly with the rotation angle ⁇ , Thus k arm ( ⁇ ) is a smooth function.
  • K p K arm ( ⁇ ) is defined.
  • the damping coefficient ⁇ is positively related to E y .
  • the adjustment of K arm ( ⁇ ) can be realized by changing the rotation angle of the gear, and then the adjustment of Young's modulus, damping and anisotropy parameters can be realized.
  • k arm1 and k arm2 depend on the meshing polarity (positive or negative) of the two gears and the angle difference ⁇ , the regulation range and change process curve of the parameters during the rotation can be controlled by changing the meshing polarity and the angle difference.
  • the gear mechanics metamaterial for adjusting Young's modulus, damping and anisotropy is shown in Figure 4, including a gear array, a frame and a connecting shaft; the gear array is composed of mechanical metamaterial cells It is periodically extended along the x-direction and the y-direction; each of the mechanical metamaterial cells is composed of 4 gears that mesh with each other, and the 4 gears are arranged in a 2 ⁇ 2 array.
  • the gear array is a tight fit, with each internal gear meshing with 4 adjacent gears.
  • the two adjacent gears are connected in a positive-polarity meshing manner or a negative-polarity meshing manner, and the angle difference between the two adjacent gears (in the x-direction and along the y-direction) is the same.
  • the same gear has positive and negative sides, and the installation front and back sides of two adjacent gears are also the same.
  • the gears in the layout of the gear array are installed in the same way for every other gear, as shown in Figure 5, that is, in the horizontal direction (or vertical direction) of the gear array top)
  • the installation polarity and installation angle of every other gear are the same.
  • the invention provides the equivalent Young's modulus control characteristics of the gear mechanics metamaterial tested theoretically and experimentally.
  • the control characteristic curve of the Young's modulus of the mechanical metamaterial with the meshing property of adjacent gears being positive polarity and the angle difference is 3 degrees with the rotation angle ⁇ is shown in Figure 6.
  • the Young's modulus in a single direction can be smooth and continuous Control 80 times.
  • the Young's modulus control characteristics of the mechanical metamaterial whose meshing property of adjacent gears is negative and the angle difference is 15 degrees is shown in Fig. 7, and its Young's modulus can be smoothly and continuously controlled by 38 times.
  • the damping of the mechanical metamaterial is derived from the slip between the gear teeth, and the damping effect increases with the increase of Young's modulus, which is used to achieve high stiffness and high damping characteristics.
  • the damping ratio of the mechanics with positive meshing polarity and 3-degree angle difference obtained through finite element simulation and experimental testing is shown in Figure 8, and its damping coefficient ⁇ can be adjusted within the range of 0-0.18.
  • the gear mechanics metamaterial design scheme proposed by the present invention is shown in Figures 9 to 11, including a gear array, a frame and a connecting shaft; the gear array is periodically extended along the x and y directions by the mechanical metamaterial cells.
  • Each of the mechanical metamaterial cells is composed of 7 gears meshing with each other, the gears are arranged in a 3 ⁇ 3 array, and the position of one gear in the middle row or on both sides of the column is vacated to form a defect In the state, the cavity formed by every three gears is provided with an insert which forms conformal coordinated contact with the three gears.
  • the insert is a cross-shaped insert 400, and the four ends of the cross-shaped insert 400 are concave arcs 401 matching the arcs of the gears, and the concave arcs 401 forms a conformal coordinated contact with the gear.
  • Defective gears eliminate shear self-locking, and the cross-shaped insert increases the coupling of the gear array in the diagonal direction, so that the shear stress is mainly borne by the gears on the diagonal, so that the shear mold can be adjusted.
  • Continuous smooth regulation of quantity Preferably, as shown in FIG. 10 , two symmetrical elastic arms 402 extend outward from the end of the cross-shaped insert, which are used to reduce the rotational resistance during the rotation of the gear and prevent the cross-shaped insert from turning the gear Stuck. Because the gear is not axisymmetric structure, the stiffness in the two diagonal directions is different.
  • the stiffnesses in the two diagonal directions provided by the gears are:
  • K d1 ( ⁇ ) K p ( ⁇ -45°)k cr /2[K p ( ⁇ -45°)+k cr ]
  • K d2 ( ⁇ ) K p ( ⁇ +45°)k cr /2[K p ( ⁇ +45°)+k cr ]
  • Nonreciprocal quantities are defined as ratios due to phase difference
  • the invented gear mechanics metamaterial for regulating shear modulus has non-reciprocal shear deformation behavior, that is, the shear deformation depends on the direction of the applied shear stress, and the non-reciprocal quantity can also be synchronously and smoothly regulated.
  • the present invention completes the finite element simulation and theoretical test of the shear modulus regulation characteristics, and the results are shown in FIG. 12 .
  • the shear modulus in the examples is smoothly adjusted continuously by a factor of 107.

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Abstract

本发明公开一种弹性参数大范围连续可调的齿轮力学超材料，包括齿轮阵列、框架和连接轴；所述齿轮阵列由力学超材料元胞沿x方向和y方向周期性延拓而成；所述元胞由多个齿轮排列构成，相邻齿轮之间相互啮合；所述齿轮包括一个中心孔和两个中心对称的异形孔，所述异形孔与齿轮外壁之间的悬臂的厚度均匀增大或减小；所述连接轴设置在所述齿轮的中心孔中，所述齿轮阵列通过连接轴与框架连接。本发明提供的力学超材料的等效杨氏模量、剪切模量、阻尼、各向异性等弹性参数都与啮合点悬臂的厚度密切相关，通过旋转超材料中的任意一个齿轮就能旋转超材料中所有齿轮，从而改变啮合点的悬臂厚度，实现对力学超材料弹性参数的光滑连续调控。

Description

一种弹性参数大范围连续可调的齿轮力学超材料 技术领域
本发明涉及力学与机械工程领域，具体是一种弹性参数大范围可调的齿轮力学超材料。
背景技术
当前，第四次工业革命已经到来，第四次工业革命的核心为智能结构与设备，比如自适应飞行器、自适应控制系统、智能连接器、智能振动噪声控制等等。设备的智能化要求制造设备的单元和材料智能可调。弹性特性(包括杨氏模量、剪切模量、变形模式)可调的力学材料能为智能设备的设计制备提供基础支撑。然而，传统的压电材料和形状记忆合金材料难以产生大范围弹性调节。新型智能材料设计存在诸多挑战。
力学超材料是指具有超常力学特性的人工材料，可以产生低密度高模量、负泊松比、手性等特性。典型结构有二维蜂窝结构、三维点阵结构、折叠结构、手性结构。力学超材料为航空航天、船舶、高铁、汽车等工业系统提供了重要的结构设计方案。可重构力学超材料是指能在外部刺激(如压缩力)作用下改变几何形状的力学超材料。几何形状的变化会导致力学属性的本质变化，如弹性模量、剪切模量、变形模式、阻尼、各向异性可从一个值突变到另外一个值。弹性特性的完美调节不仅需要大的参数调节范围，还需要密集的稳定调节状态。然而，当前设计的可重构力学超材料只能产生极少的稳定的重构状态，难以实现具有较大工程应用价值的智能材料设计。大范围连续可调的智能材料设计需要新设计方案。
发明内容
本发明提供了一种弹性参数大范围连续可调的齿轮力学超材料，用于克服现有可重构力学超材料设计技术中弹性参数调节范围窄、稳定状态少、调控健壮性低等缺陷。
为实现上述目的，本发明提供一种弹性参数大范围连续可调的齿轮力学超材料，包括齿轮阵列、框架和连接轴；所述齿轮阵列由力学超材料元胞沿x方向和y方向周期性延拓而成；所述元胞由多个齿轮排列构成，相 邻齿轮之间相互啮合；所述齿轮包括一个中心孔和两个中心对称的异形孔，所述异形孔与齿轮外壁之间的悬臂的厚度均匀增大或减小；所述连接轴设置在所述齿轮的中心孔中，所述齿轮阵列通过连接轴与框架连接。
进一步的，相邻两个齿轮的啮合方式包括正极性啮合和负极性啮合；相邻两个齿轮啮合点处的悬臂厚度一个逐渐增大另一个逐渐减小时为正极性啮合，相邻两个齿轮啮合点处的悬臂厚度同时增大或者减小时为负极性啮合。
进一步的，所述齿轮上两个中心对称的异形孔之间通过在同一水平线上的悬梁隔开，相互啮合的两个齿轮的悬梁之间有角度差，所述角度差为0至180度。
进一步的，所述框架的刚度小于齿轮啮合形成的最小刚度。
进一步的，所述框架为弹性框架，所述弹性框架由薄壁圆环周期性延拓而成，相邻两个薄壁圆环的连接点处设有带通孔的厚壁圆环；所述厚壁圆环的通孔套设在连接轴上，所述齿轮通过连接轴与所述厚壁圆环的通孔连接。
进一步的，每个所述力学超材料元胞由4个相互啮合的齿轮构成，4个齿轮按2×2的阵列排布。这种结构可作为用于调控杨氏模量、阻尼、各向异性参数的齿轮力学超材料。
进一步的，相邻两个齿轮按照正极性啮合方式或负极性啮合方式连接，每间隔一个齿轮的安装角度和安装正反面(同一个齿轮有正反两面)相同。
进一步的，每个所述力学超材料元胞由7个相互啮合的齿轮构成，齿轮按3×3的阵列排布，中间一排或列两侧的位置均空出一个齿轮的位置形成缺陷态，每三个齿轮形成的空穴中设有与三个齿轮形成共形协调接触的置入物。这种结构可作为用于调控剪切模量的齿轮力学超材料。
进一步的，所述置入物为十字架形置入物，所述十字架形置入物的四个端部为与齿轮的弧形相匹配的内凹圆弧；所述十字架形置入物的端部向外延伸出两个对称的弹性臂。
进一步的，相邻两个齿轮采用正极性啮合。
本发明具有以下有益效果：
1、本发明提供的一种弹性参数大范围连续可调的齿轮力学超材料，包括齿轮阵列、框架和连接轴，所述齿轮阵列由力学超材料元胞沿x方向和y方向周期性延拓而成；所述元胞由多个齿轮排列构成，相邻齿轮之间相互啮合，排布方式根据需调控的弹性参数设计；所述齿轮包括一个中心孔和两个中心对称的异形孔，所述异形孔与齿轮外壁之间的悬臂的厚度均匀增大或减小；所述连接轴设置在所述齿轮的中心孔中，所述齿轮阵列通过连接轴与框架连接。通过旋转超材料中的任意一个齿轮就能旋转超材料中所有齿轮。当在齿轮上施加压缩载荷时，轮齿接触会将载荷传递给齿轮悬臂，并使悬臂产生弯曲变形。变形的刚度与啮合点两侧的悬臂厚度密切相关。因每个齿轮上的悬臂厚度光滑变化(即均匀变化)，通过旋转齿轮即可调节变形刚度，从而实现对杨氏模量、剪切模量、阻尼、各向异性、非互异性参数的调控。通过旋转超材料中的任意一个齿轮就能旋转超材料中所有齿轮，从而改变啮合点的悬臂厚度，实现对超材料弹性参数的光滑连续调控。
2、本发明提供的一种弹性参数大范围连续可调的齿轮力学超材料，相邻两个齿轮的啮合方式包括正极性啮合和负极性啮合；相邻两个齿轮啮合点处的悬臂厚度一个逐渐增大另一个逐渐减小时为正极性啮合，相邻两个齿轮啮合点处的悬臂厚度同时增大或者减小时为负极性啮合。所述齿轮上两个中心对称的异形孔之间通过在同一水平线上的悬梁隔开，相互啮合的两个齿轮的悬梁之间有角度差，所述角度差为0-180度。通过改变齿轮之间的啮合方式和角度差能控制旋转过程中参数的调控范围和变化过程曲线。
3、本发明提供的一种弹性参数大范围连续可调的齿轮力学超材料运用齿轮的多孔结构实现杨氏模量、剪切模量和阻尼的大范围连续调节。调节杨氏模量时，齿轮之间采用紧配合，每个内部齿轮与4个相邻齿轮啮合。杨氏模量、阻尼和各向异性参数可同步调节。所述力学超材料的阻尼来源于轮齿之间的滑移，阻尼效应随着杨氏模量的增加而增加，用于实现高刚度高阻尼特性。调节剪切模量和非互异性参数时，阵列中每隔一个齿轮预留一个空穴，使部分齿轮仅与2个相邻齿轮啮合，且在每3个齿轮啮合留 下的空穴中放置嵌入物。调节剪切模量的结构也可实现对杨氏模量的同步调控。
4、本发明提供的力学超材料直接应用齿轮啮合和旋转实现杨氏模量、剪切模量、阻尼、各向异性、非互异性的大范围连续调节，实现较高的结构可靠性、重构操作的健壮性，同时也实现了高刚度、高强度、高阻尼，可实现性强，易于制造。
除了上面所描述的目的、特征和优点之外，本发明还有其它的目的、特征和优点。下面将参照图，对本发明作进一步详细的说明。
附图说明
为了更清楚地说明本发明实施例中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图示出的结构获得其他的附图。在附图中：
图1a是本发明优选实施例的单个齿轮的俯视图，所述齿轮的异形孔具有类似太极图的形状，简称太极齿轮；
图1b是本发明优选实施例的单个齿轮的立体结构图。
图2是本发明优选实施例中两个齿轮正极性啮合的示意图，两个齿轮的角度差为3度。
图3是本发明优选实施例中两个齿轮负极性啮合的示意图，两个齿轮的角度差为15度。
图4是本发明优选实施例的用于调控杨氏模量、阻尼和各向异性参数的齿轮力学超材料结构图，由5×5个齿轮构成，啮合方式为正极性，角度差为3度；
图5是齿轮在x方向和y方向的排布方式示意图。
图6是优选实施例中y方向的杨氏模量E y随着齿轮旋转角度θ的变化曲线；图中标注P +(β＝3°)表示力学超材料中的齿轮是按照正极性方式啮合的，且角度差为3度。
图7是优选实施例中通过有限元仿真方法计算的y方向的杨氏模量Ey随着齿轮旋转角度θ的变化曲线；图中标注P -(β＝15°)表示力学超材 料中的齿轮是按照负极性方式啮合的，且角度差为15度。
图8是优选实施例中阻尼参数η随着齿轮旋转角度θ的变化曲线，此图对应图6中所标注的啮合方式和角度差。
图9是用于调控杨氏模量和非互异性参数的力学超材料元胞结构示意图。
图10是图9中每3个齿轮中间部位的置入物结构图，每个置入物为十字架形状。
图11为由图9所示元胞构成的力学超材料结构图。
图12为优选实施例中剪切模量G随着齿轮旋转角度θ的变化曲线；图注中G +和G -分别表示剪切应力τ的施加方向为正向和负向时得到的剪切模量。
其中，100、齿轮，101、中心孔，102、异形孔，103、悬臂，104、悬梁，200、连接轴，300、框架，301、薄壁圆环，302、厚壁圆环，400、十字架形置入物，401、内凹圆弧，402、弹性臂。
具体实施方式
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明的一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。
本发明提出的齿轮力学超材料的基本单元为单个多孔齿轮，优选地，采用直齿轮来设计，如图1a和图1b所示(其中，图1a是本发明优选实施例的单个齿轮的俯视图，图1b是本发明优选实施例的单个齿轮的立体结构图)。齿轮100内部含有中心对称的孔结构，优选地，每个齿轮100包含一个中心孔101和两个中心对称的异形孔102。优选地，异形孔形状与“太极图”类似，可简称太极齿轮。异形孔102与齿轮外壁之间形成了两个中心对称的悬臂103，悬臂103的厚度随着角度均匀增大或减小(即光滑变化)。当齿轮模数确定时，通过增加齿轮齿数可降低轮齿对悬臂103弯曲刚度的影响。优选地，“太极图”形状的齿轮的正面和反面的图形螺旋方向相反。
一种弹性参数大范围连续可调的齿轮力学超材料，包括齿轮阵列、框架300和连接轴200；所述齿轮阵列由力学超材料元胞沿x方向和y方向周期性延拓而成；所述元胞由多个齿轮100排列构成，齿轮100的排布方式根据需调控的弹性参数设计而成，相邻齿轮之间相互啮合；所述齿轮100包括一个中心孔101和两个中心对称的异形孔102，所述异形孔102与齿轮外壁之间的悬臂103的厚度均匀增大或减小；所述连接轴200设置在所述齿轮的中心孔101中，所述齿轮阵列通过连接轴200与框架300连接。
通过旋转超材料中的任意一个齿轮就能旋转超材料中所有齿轮。当在齿轮上施加压缩载荷时，轮齿接触会将载荷传递给齿轮悬臂103，并使悬臂103产生弯曲变形。变形的刚度与啮合点两侧的悬臂103厚度密切相关。因每个齿轮上的悬臂103的厚度光滑变化，通过旋转齿轮即可调节变形刚度，从而实现对杨氏模量、剪切模量、阻尼、各向异性、非互异性参数的调控。通过旋转超材料中的任意一个齿轮就能旋转超材料中所有齿轮，从而改变啮合点的悬臂103厚度，实现对超材料弹性参数的光滑连续调控。
所述各向异性参数值定义为给定旋转角度θ时，x方向与y方向的杨氏模量的比值，即E x/E y。所述非互异性参数值定义为给定旋转角度θ和剪切应力τ时，施加正向剪切应力τ +与负向剪切应力τ -产生的剪切变形量的比值。
相邻两个齿轮的啮合方式包括正极性啮合和负极性啮合。相邻两个齿轮啮合点处的悬臂103厚度一个逐渐增大另一个逐渐减小(即两个“太极图”形状的齿轮的图形螺旋方向相反)时为正极性啮合，相邻两个齿轮啮合点处的悬臂103厚度同时增大或者减小时(即两个“太极图”形状的齿轮的图形螺旋方向相反)为负极性啮合。如图2所示，两个齿轮的图形螺旋方向相反时称为正极性啮合。如图3所示，两个齿轮的图形螺旋方向相同时称为负极性啮合。所述齿轮上两个中心对称的异形孔102之间通过在同一水平线上的悬梁104隔开，相互啮合的两个齿轮的悬梁104之间有角度差，所述角度差的范围为0-180度。例如，图2和图3所示的两个齿轮啮合时局部图形坐标之间的角度差分别为3度和15度。通过齿轮传递， 旋转力学超材料中的任意一个齿轮即可旋转所有其他齿轮。两个啮合齿轮的旋转方向相反，分别为θ和-θ。
所述框架300的刚度远小于齿轮啮合形成的最小刚度。在一个具体实施方式中，所述框架300为弹性框架，所述弹性框架由薄壁圆环301周期性延拓而成，纵向相邻两个薄壁圆环301的连接点处设有带通孔的厚壁圆环302；所述厚壁圆环302的通孔套设在连接轴200上。横向相邻的两个薄壁圆环301连接处焊接在一起。所述齿轮阵列两面均通过连接轴200连接有弹性框架。所述齿轮通过连接轴200以及弹性框架将所有的齿轮连接为一个整体。
当在齿轮上施加压缩载荷时，轮齿接触会将载荷传递给齿轮悬臂，并使悬臂产生弯曲变形。将单个悬臂的刚度k arm定义为在齿轮中心孔和悬臂点之间施加径向力时作用力与变形量的比值，因此k arm悬臂厚度密切相关，而悬臂厚度随着旋转角度θ光滑变化，从而k arm(θ)为光滑函数。一对啮合的悬臂形成的总刚度为k arm＝k arm1k arm2/(k arm1+k arm2)，其中k arm1和k arm2分别为啮合点两侧的两个悬臂的刚度，从而K arm(θ)也为光滑函数。当施加的载荷较大使接触非线性效应不再显著时，定义K p＝K arm(θ)。所述齿轮力学超材料在y方向的等效杨氏模量为E y＝K p/B+E f，其中B为齿轮的宽度，E f为连接齿轮的框架的等效杨氏模量。阻尼系数η与E y正相关。x方向的杨氏模量E x与y方向的杨氏模量之间的关系为E x(θ)＝E y(θ+90°)，各向异性参数值定义为E x/E y。根据这些理论可知，可通过改变齿轮的旋转角实现对K arm(θ)的调节，进而实现对杨氏模量、阻尼和各向异性参数的调节。因k arm1和k arm2取决于两个齿轮的啮合极性(正极或负极)以及角度差β，因此可通过改变啮合极性和角度差控制旋转过程中参数的调控范围和变化过程曲线。
在一个具体实施例中，用于调节杨氏模量、阻尼和各向异性的齿轮力学超材料如图4所示，包括齿轮阵列、框架和连接轴；所述齿轮阵列由力学超材料元胞沿x方向和y方向周期性延拓而成；每个所述力学超材料元胞由4个相互啮合的齿轮构成，4个齿轮按2×2的阵列排布。所述齿轮阵列为紧密配合，每个内部齿轮与4个相邻齿轮啮合。相邻两个齿轮按照 正极性啮合方式或负极性啮合方式连接，相邻两个齿轮(沿x方向以及沿y方向)的角度差相同。同一个齿轮有正反两面,相邻两个齿轮安装正反面也相同。为了使整个超材料的极性和相邻齿轮的角度差保持一致，齿轮阵列的布局中每间隔一个齿轮的齿轮安装方法相同，如图5所示，即齿轮阵列中水平方向上(或垂直方向上)每间隔一个齿轮的安装极性和安装角度相同。
本发明提供了理论与实验测试的齿轮力学超材料的等效杨氏模量调控特性。相邻齿轮啮合属性为正极性、角度差为3度的力学超材料的杨氏模量随着旋转角度θ变化的调控特性曲线如图6所示，其单个方向的杨氏模量可以光滑连续调控80倍。相邻齿轮啮合属性为负极性、角度差为15度的力学超材料的杨氏模量调控特性如图7所示，其杨氏模量可以光滑连续调控38倍。此外，由于x方向与y方向的杨氏模量之间具有90度相位差E x(θ)＝E y(θ+90°)，E x与E y同步变化，所以各向异性参数值E x/E y也随着齿轮旋转角度θ变化，从而实现了各向异性的调控。
所述力学超材料的阻尼来源于轮齿之间的滑移，阻尼效应随着杨氏模量的增加而增加，用于实现高刚度高阻尼特性。本实施例通过有限元仿真和实验测试得到啮合极性为正、角度差为3度的力学的阻尼比如图8所示，其阻尼系数η可在0-0.18范围内调节。
以上实施例虽然也能调控剪切模量，但是由于剪切自锁的存在，其对剪切模量的调控幅度较小。为了实现对剪切模量和互异性的大范围光滑调节，需要去掉一些齿轮并增加对角线方向的耦合。为此，本发明提出的齿轮力学超材料设计方案如图9-图11所示，包括齿轮阵列、框架和连接轴；所述齿轮阵列由力学超材料元胞沿x方向和y方向周期性延拓而成；每个所述力学超材料元胞由7个相互啮合的齿轮构成，齿轮按3×3的阵列排布，中间一排或列两侧的位置均空出一个齿轮的位置形成缺陷态，每三个齿轮形成的空穴中设有与三个齿轮形成共形协调接触的置入物。优选的，所述置入物为十字架形置入物400，所述十字架形置入物400的四个端部为与齿轮的弧形相匹配的内凹圆弧401，所述内凹圆弧401与齿轮形成共形协调接触。形成缺陷态的齿轮消除了剪切自锁，十字架形置入物增加了 齿轮阵列在对角线方向的耦合，使剪切应力主要由对角线上的齿轮承担，从而可实现对剪切模量的连续光滑调控。优选地，如图10所示，所述十字架形置入物的端部向外延伸出两个对称的弹性臂402，用于降低齿轮旋转过程中的旋转阻力，防止十字架形置入物将齿轮卡死。因齿轮不是轴对称结构，导致两个对角线方向的刚度不同。优选的，调控剪切模量时齿轮啮合全部为正极性，啮合角度差β根据所需调控的范围设定。为增加调控范围，优选的，本实施例中设定β＝3°。
根据这一设计，由齿轮提供的两个对角线方向的刚度分别为:
K d1(θ)＝K p(θ-45°)k cr/2[K p(θ-45°)+k cr]
K d2(θ)＝K p(θ+45°)k cr/2[K p(θ+45°)+k cr]
其中，k cr是十字架形置入物在对角线方向的刚度。因此，正向的剪切模量为
Figure PCTCN2021129010-appb-000001
负向的剪切模量为
Figure PCTCN2021129010-appb-000002
所以，正向和逆向剪切模量之间具有90度相位差
Figure PCTCN2021129010-appb-000003
由这些理论可知，可以改变旋转角度实现对正向和逆向剪切模量
Figure PCTCN2021129010-appb-000004
和
Figure PCTCN2021129010-appb-000005
的连续光滑调控。
非互易量定义为比值
Figure PCTCN2021129010-appb-000006
因相位差关系
Figure PCTCN2021129010-appb-000007
所发明调控剪切模量的齿轮力学超材料具有非互易的剪切变形行为，即剪切变形取决于施加的切应力的方向，且非互易量也可以同步光滑调控。
本发明完成了剪切模量调控特性的有限元仿真与理论测试，结果如图12所示。实施例中的剪切模量被光滑连续调节107倍。
以上所述仅为本发明的优选实施例，并非因此限制本发明的专利范围，凡是在本发明的发明构思下，利用本发明说明书及附图内容所作的等效结构变换，或直接/间接运用在其他相关的技术领域均包括在本发明的专利保护范围内。

Claims (10)

  1. 一种弹性参数大范围连续可调的齿轮力学超材料，其特征在于，包括齿轮阵列、框架和连接轴；所述齿轮阵列由力学超材料元胞沿x方向和y方向周期性延拓而成；所述元胞由多个齿轮排列构成，相邻齿轮之间相互啮合；所述齿轮包括一个中心孔和两个中心对称的异形孔，所述异形孔与齿轮外壁之间的悬臂的厚度均匀增大或减小；所述连接轴设置在所述齿轮的中心孔中，所述齿轮阵列通过连接轴与框架连接。
  2. 权利要求1所述的一种弹性参数大范围连续可调的齿轮力学超材料，其特征在于，相邻两个齿轮的啮合方式包括正极性啮合和负极性啮合；相邻两个齿轮啮合点处的悬臂厚度一个逐渐增大另一个逐渐减小时为正极性啮合，相邻两个齿轮啮合点处的悬臂厚度同时增大或者减小时为负极性啮合。
  3. 根据权利要求1所述的一种弹性参数大范围连续可调的齿轮力学超材料，其特征在于，所述齿轮上两个中心对称的异形孔之间通过在同一水平线上的悬梁隔开，相互啮合的两个齿轮的悬梁之间有角度差，所述角度差为0至180度。
  4. 根据权利要求1任一所述的一种弹性参数大范围连续可调的齿轮力学超材料，其特征在于，所述框架的刚度小于齿轮啮合形成的最小刚度。
  5. 根据权利要求1所述的一种弹性参数大范围连续可调的齿轮力学超材料，其特征在于，所述框架为弹性框架，所述弹性框架由薄壁圆环周期性延拓而成，相邻两个薄壁圆环的连接点处设有带通孔的厚壁圆环；所述厚壁圆环的通孔套设在连接轴上，所述齿轮通过连接轴与所述厚壁圆环的通孔连接。
  6. 根据权利要求1-5任一所述的一种弹性参数大范围连续可调的齿轮力学超材料，其特征在于，每个所述力学超材料元胞由4个相互啮合的齿轮构成，4个齿轮按2×2的阵列排布。
  7. 根据权利要求6所述的一种弹性参数大范围连续可调的齿轮力学超材料，其特征在于，相邻两个齿轮按照正极性啮合方式或负极性啮合方式连接，每间隔一个齿轮的安装角度和安装正反面相同。
  8. 根据权利要求1-5任一所述的一种弹性参数大范围连续可调的齿轮力学超材料，其特征在于，每个所述力学超材料元胞由7个相互啮合的齿轮构成，齿轮按3×3的阵列排布，中间一排或列两侧的位置均空出一个齿轮的位置形成缺陷态，每三个齿轮形成的空穴中设有与三个齿轮形成共形协调接触的置入物。
  9. 根据权利要求8所述的一种弹性参数大范围连续可调的齿轮力学超材料，其特征在于，所述置入物为十字架形置入物，所述十字架形置入物的四个端部为与齿轮的弧形相匹配的内凹圆弧；所述十字架形置入物的端部向外延伸出两个对称的弹性臂。
  10. 根据权利要求8所述的一种弹性参数大范围连续可调的齿轮力学超材料，其特征在于，相邻两个齿轮采用正极性啮合。
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US20030015051A1 (en) * 2001-07-23 2003-01-23 Asahi Kogaku Kogyo Kabushiki Kaisha Gear mechanism with an idler gear, a gear mechanism with a device for eliminating backlash between gears, and a motor driving mechanism
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