Design method of variable elastic modulus metamaterial

Abstract

The invention discloses a design method of a variable elastic modulus metamaterial with gear step extension fused with continuous non-polarity. Based on the composition relation of all parts of the gear and the superposition mode of the rigidity of the gear, the relation between the overall rigidity of the gear and the main rigidity of a gear structure and the contact rigidity of gear rings and gear teeth is deduced. And further based on the relationship, constructing a variable elastic modulus control equation and a variable elastic modulus control equation of the gear unit, designing gear pairs with the same diameter, gear pairs with different diameters and elliptical non-circular gear pairs, and assembling the gear pairs into the metamaterial through an array. According to the method, the elastic modulus of the metamaterial can be continuously and accurately adjusted within a certain range with continuous nonpolar adjustability, meanwhile, the change rate of the performance of the elastic modulus can be made to be slower under the specific working condition, namely, the change period of the whole performance is prolonged, and meanwhile, the constraint condition for avoiding interference is solved; and when the working condition change is aggravated, the elastic modulus performance adjustable range adaptive change of the material can be met.

Description

Technical Field

[0001] The present invention relates to the field of metamaterial design, and particularly to a method for designing a metamaterial with variable elastic modulus. Background Art

[0002] Metamaterials are artificial composite materials or composite structures with extraordinary, abnormal, adjustable, and programmable physical properties that natural materials do not possess. The design concept is to break through the limitations of certain apparent natural laws through reasonable structural design without violating the basic physical theorems, and artificially obtain new substances and new materials with extraordinary and abnormal physical properties that are completely different from those in nature.

[0003] The concept of metamaterials originally originated in the field of electromagnetic waves, referring to controlling the propagation characteristics of electromagnetic waves through precisely designed microstructures. These structures can often achieve electromagnetic characteristics that traditional materials cannot reach, such as negative refractive index, zero electromagnetic response, ultra-high conductivity, etc. In recent years, with the continuous in-depth research, the concept of metamaterials has gradually expanded to the mechanical field, and the research on mechanical metamaterials has begun to rise and develop rapidly.

[0004] Mechanical metamaterials have excellent performance, but there are still deficiencies in the existing design. It is mainly reflected in the following aspects: the existing metamaterial design can only adapt to specific working environments. Once the working conditions change, the performance will not match the working conditions, and then the material design will fail.

[0005] The fundamental reason for this problem is that once the material structure is determined, the mechanical properties of the material are also determined and cannot be adaptively changed with the working conditions, especially unable to achieve continuous and precise adjustment of the material properties.

[0006] Patent for invention "Gear mechanical metamaterial with continuously adjustable elastic parameters in a large range" (Patent No. 202011220745.0) designed a gear metamaterial that can achieve changes in elastic modulus, but it still has the following problems:

[0007] (1) After the structure of the gear metamaterial is determined, the change period of its elastic modulus is determined. If, under specific working conditions, a slower (smoother) change rate of the required elastic modulus performance is needed, that is, the change period of the entire performance is expected to increase, then this design cannot meet the requirements.

[0008] (2) Although the elastic modulus of the gear metamaterial can vary between a minimum value and a maximum value, and the performance of the metamaterial can meet the adaptive adjustment of the working conditions, the adjustable range is relatively limited. If the amplitude of the change in working conditions increases and may exceed the adaptive adjustable range of the elastic modulus performance of this design material, then this design may fail at this time. Summary of the Invention

[0009] The technical problem to be solved by the present invention is to provide a design method for a metamaterial with variable elastic modulus, which has the advantages of slow performance change rate and wide adjustable range.

[0010] To solve the above technical problem, the present invention provides a design method for a metamaterial with variable elastic modulus, comprising the following steps:

[0011] Step 1) Based on the structural composition and the principle of stiffness superposition, construct a basic unit of a gear metamaterial with continuously adjustable variable elastic modulus based on the same gear unit, that is, the first gear pair;

[0012] Step 2) Based on the speed shifting principle, construct a performance shifting method to perform stepwise expansion on the first gear pair;

[0013] Expand the performance of the gear metamaterial with performance gears. For the purpose of making the change rate of the elastic modulus more stable, stepwise adjust the change period of the elastic modulus of the gear metamaterial through gear units with different diameters to obtain a basic unit of the periodically adjusted gear metamaterial, that is, the second gear pair;

[0014] Expand the performance of the gear metamaterial with performance gears. For the purpose of making a leapfrog adjustment of the adjustable range of the elastic modulus, use elliptical non-circular gears as gear units to adjust the extreme values of the elastic modulus of the gear metamaterial at the minimum and maximum values to obtain a basic unit of the extreme value adjusted gear metamaterial, that is, the third gear pair;

[0015] Step 3) Assemble the first gear pair, the second gear pair and the third gear pair on two gear shafts and satisfy that only one pair of gear pairs is meshing at the same time to form a basic unit of the gear pair;

[0016] Step 4) Arrange the basic units of the gear pair in an array meshing pattern, and a metamaterial with variable elastic modulus with gear step expansion property fusion continuous non-polarity can be obtained.

[0017] Further, in step 1), based on the composition relationship of each part of the gear unit and the superposition method of gear stiffness, deduce the relationship between the overall stiffness of the gear unit and the main body stiffness of the gear structure of the gear unit and the contact stiffness of the teeth of the gear ring of the gear unit. Based on the above relationship, construct a control equation for variable elastic modulus of the gear unit;

[0018] Based on the control equation for variable elastic modulus of the gear unit, design the main body of the gear structure of the gear unit;

[0019] Select the number of teeth and modulus to establish a finite element model of the overall structure of two gear units, set the contact relationship between the gears, construct and characterize the load and boundary conditions of the gear metamaterial, obtain the deformation of the gear unit through finite element calculation, and convert this deformation into elastic modulus;

[0020] Select the structural design parameters of the gear structure body of the gear unit as variables, take the maximum and minimum values of the required elastic modulus as the objectives, and obtain the overall structural design of the gear unit within the specified elastic modulus change range through repeated iteration. At the same time, the elastic modulus of the corresponding basic unit of the gear metamaterial is also obtained.

[0021] Furthermore, the control equation is:

[0022]

[0023] In the formula, K G is the overall stiffness of the gear unit, K M is the stiffness of the gear structure body, K R is the contact stiffness of the teeth of the gear ring, γ is the rotation angle of the gear unit, F is the load force, U is the deformation of the gear unit in the direction of the load force, and E~K G (γ) is the proportional relationship between the elastic modulus E and the overall stiffness.

[0024] Furthermore, the elastic modulus E is calculated by the following formula:

[0025]

[0026] In the formula, S is the acting area of the force, L y is the initial length of the center distance between two gear units, and dy is the deformation of the gear unit.

[0027] Furthermore, when designing the gear structure body of the gear unit, part of the gear structure body is hollowed out.

[0028] Furthermore, in step 2), with the center distance of the first gear pair unchanged, the same gear unit in the first gear pair is changed into two gear units with different diameters, and the diameter ratio of the two gear units with different diameters is less than the limit value a to obtain the second gear pair.

[0029] Furthermore, the limit value a is solved by the following formula:

[0030] We get

[0031] In the formula, r 1 is the radius of the gear unit with a smaller diameter, ar 1 is the radius of the gear unit with a larger diameter, ar 1 +r 1 is the center distance after the meshing of the two gear units in the second gear pair, is the distance between the center points of the gear units on the diagonal line after the second gear pair is arrayed.

[0032] Further, in step 2), the third gear pair adopts elliptical non-circular gears of the third to sixth order, and the tooth profile structure of the gear teeth is obtained through the design principle of the elliptical non-circular gear pair.

[0033] Specifically, with the center distance of the first gear pair unchanged, the module and the number of teeth are selected. According to the selected order of the elliptical non-circular gears and based on the existing design principle of the elliptical non-circular gear pair, the tooth profile structure of the gear teeth under the condition of a fixed center distance is obtained, and a three-dimensional structure is constructed.

[0034] Based on the control equation of the variable elastic modulus of the gear unit, the main body of the gear structure of the gear unit of the third gear pair is designed, and the main body part of the gear structure is hollowed out.

[0035] A finite element model of the third gear pair is established, the contact relationship between the gears is set, the load and boundary conditions of the third gear pair are constructed and characterized, the deformation of the main body of the gear structure is obtained through finite element calculation, and this deformation is converted into the elastic modulus of the basic unit of the gear metamaterial. Through repeated calculations, the corresponding elastic modulus of the basic unit of the gear metamaterial is obtained.

[0036] Select the structural design parameters of the main body of the gear structure of the gear unit, take them as variables, take the maximum and minimum values of the required elastic modulus as the objectives, and through repeated iterations, obtain the overall gear structure design within the specified elastic modulus change range and the corresponding elastic modulus of the basic unit of the gear metamaterial.

[0037] Further, an elastic connecting piece is arranged between adjacent gear shafts.

[0038] Advantages of the present invention:

[0039] The present invention realizes continuous and precise adjustment of the elastic modulus of the metamaterial within a certain range with continuous non-polarity. At the same time, with the step-by-step expansion of the gear position, the performance of the metamaterial is expanded, which can meet the requirements under specific working conditions, making the change rate of the elastic modulus performance slower (more stable), that is, the change period of the entire performance is increased; it can also meet the adaptability change of the adjustable range of the elastic modulus performance of the material when the working conditions change intensively. Description of the drawings

[0040] Figure 1 It is the overall gear structure of the present invention and the corresponding structural components;

[0041] Figure 2 It is a schematic diagram of the structure of the first gear pair formed by matching two equal-circle gear units in the present invention;

[0042] Figure 3 It is the structural design parameters of the equal-circle gear unit of the present invention;

[0043] Figure 4 It is the curve graph of the periodic change of the elastic modulus of the first gear pair of the present invention;

[0044] Figure 5 This is a schematic structural diagram of the equal - circle gears 2x2 array of the present invention;

[0045] Figure 6 This is a schematic structural diagram of the second gear pair formed by the cooperation of the large and small gear units of the present invention;

[0046] Figure 7 This is a curve graph of the periodic change of the elastic modulus of the second gear pair of the present invention;

[0047] Figure 8 This is a schematic diagram of the 2x2 - form array of the second gear pair of the present invention;

[0048] Figure 9 This is a schematic structural diagram of the third gear pair formed by meshing two fourth - order elliptical gears of the present invention;

[0049] Figure 10 This is a curve graph of the periodic change of the elastic modulus of the third gear pair of the present invention;

[0050] Figure 11 This is a schematic diagram of the performance gear position principle of the gear metamaterial of the present invention;

[0051] Figure 12 This is a schematic diagram showing the 4x4 array structure of the gear metamaterial of the present invention. Detailed implementation manners

[0052] The following further explains the present invention in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the cited embodiments do not limit the present invention.

[0053] An embodiment of the variable - elastic - modulus metamaterial design method of the present invention includes the following steps:

[0054] First, based on the structural composition and the stiffness superposition principle, construct a gear metamaterial with continuously adjustable variable elastic modulus based on the same gear unit, that is, the first gear pair;

[0055] Specifically, based on the composition relationship of each part of the gear unit and the superposition method of gear stiffness, deduce the relationship between the overall stiffness of the gear unit and the stiffness of the gear structure main body of the gear unit and the contact stiffness of the teeth of the gear ring of the gear unit. Further, based on this relationship, construct the control equation of the variable elastic modulus of the gear unit.

[0056] Based on the composition relationship of the gear structure main body and the teeth of the gear ring of the gear unit, construct the overall stiffness of the gear unit. Based on the superposition method of gear stiffness, the following relationship exists between the overall stiffness of the gear unit and the stiffness of each part:

[0057] 1 / K G= 1 / K M + 1 / K R (1)

[0058] where K G denotes the overall stiffness of the gear unit, and K M denotes the stiffness of the main body of the gear structure of the gear unit, and K R is the contact stiffness of the teeth of the gear ring of the gear unit.

[0059] Now, define the rotation angle of the gear unit as γ. It can be seen that the contact stiffness K R remains unchanged and does not change with the change of the angle γ. However, the stiffness K M of the main body of the gear structure is characterized by the load and the deformation under the load as:

[0060] K M = F / U (2)

[0061] In the formula, F is the load force and U is the deformation of the gear unit in the direction of the load force.

[0062] Assume that the direction of the load force F applied to the gear unit is fixed. When the gear is under the action of the same load F, if the deformations obtained at different positions corresponding to different γ are different, that is, U changes with γ, U can be written as U(γ). Substitute it into equations (1) and (2), and combine with the proportional relationship between the elastic modulus E and the overall stiffness, that is, E ~ K G (γ), we can get:

[0063]

[0064] From this analysis, it can be concluded that at different angles γ, if U(γ) changes, the overall stiffness K G (γ) of the gear unit is also different. K G (γ) will change with the change of the angle γ. By realizing the precise control of the rotation angle γ of the gear pair, the precise control of K G (γ) can be achieved. And because the rotation angle of the gear pair is continuous, K G (γ) will also change continuously with the angle γ, thus realizing the continuous and stepless precise adjustment of the elastic modulus E of the gear unit. Equation (3) is the control equation for the variable elastic modulus of the gear unit.

[0065] The overall structure of the gear can be divided into the main body part of the gear structure and the part of the teeth of the gear ring. Referring to Figure 1 as shown, according to the description in the above process, based on the composition relationship of each part of the gear, the overall stiffness of the gear unit is constructed as shown in equation (1), and further the control equation for the variable elastic modulus of the gear unit shown in equation (3) can be obtained.

[0066] According to the control equation, i.e., the design principle of variable elastic modulus of the gear unit, the main body of the gear structure of the gear unit can be designed so that U(γ) changes with the rotation angle γ, and the stiffness K of the main body of the gear structure M will change. According to Equation (3), the stiffness K of the main body of the gear structure M After the change, it can directly affect the overall stiffness K G (γ), that is, it also changes accordingly. Thus, the purpose of changing the overall stiffness as the rotation angle γ changes can be achieved by designing the main body of the gear structure.

[0067] Generally, in order to reduce the weight, the main body part of the gear structure is hollowed out; and for the convenience of design, the hollowed-out main body structure is usually designed as a centrosymmetric structure. According to this design principle, the main body of the gear structure is designed, such as Figure 1 the main body of the gear structure shown in the lower right corner. When the main body part of this structure rotates around its axis, there is a situation where the structure does not coincide with the current angle after the rotation angle, so that U(γ) can change at different angles γ.

[0068] Select the number of teeth 48 and the module 1.5 mm, and design the tooth ring gear of this gear as Figure 1 shown in the upper right corner. Further, a finite element model of the overall structure of the gear pair is established, such as Figure 2 shown. In the figure, the gear pair is composed of two gear units of equal size. The green structural member is an elastic connecting member with a fixed center distance, that is, the connecting and fixing member between the two gear shafts corresponding to the two gear units. Since the elastic connecting member has a very small stiffness compared with the gear unit, therefore, Figure 2 as shown, the overall stiffness is still determined by the gear unit.

[0069] Set Figure 2 the contact relationship between the gears shown in, construct and characterize the load and boundary conditions of the basic unit of the gear metamaterial, set the center of the upper gear unit as the load application position, Figure 2 the load F shown in is vertically downward, and the center of the lower gear unit is treated as a fixed boundary. The deformation of the gear structure is obtained through finite element calculation. Define the deformation of the center of the upper gear unit relative to the center of the lower gear unit as dy, then the stiffness of the gear pair can be defined as:

[0070]

[0071] Convert this deformation into the elastic modulus of a pair of gear pairs of the gear metamaterial. According to the relationship between the elastic modulus E, stress σ y and strain ε y , it can be obtained that:

[0072]

[0073] Where S is the area of ​​force action, L is y is the initial length of the center distance between the two gears. y All are known quantities. According to formula (6), the deformation definition dy can be converted into the elastic modulus E.

[0074] Assuming that the gear rotates clockwise, with the vertical direction as the reference, the angle the gear rotates is defined as γ, such as Figure 2 As shown, by repeated calculations, the corresponding deformation dy at different rotation angles γ and the corresponding elastic modulus of the gear metamaterial basic unit can be obtained.

[0075] The structural design parameters of the gear structure of the gear unit are selected as variables x1, x2, x3, and x4. The required elastic modulus maximum value 30Gpa and minimum value 5Gpa are set as targets. With the help of optimization calculation, the overall structural design of the gear unit in the specified elastic modulus variation range can be obtained through repeated iterations, and the corresponding elastic modulus under different rotation angles γ can be obtained, such as Figure 4 As shown, the blue solid line represents the elastic modulus E, and the orange dotted line represents the deformation dy. The elastic modulus adjustment range meets the requirements, the elastic modulus decreases at 0°-90°, and the elastic modulus increases at 90° to 180°. Based on the above gear unit, a first gear pair, i.e., the first gear metamaterial basic unit, can be obtained. The elastic modulus of the first gear metamaterial basic unit can be continuously adjusted within the range of 0°-180°. And the change period of its elastic modulus is 180°.

[0076] The gear metamaterial can be obtained by arraying the first gear pair obtained above, such as Figure 5 As shown in the figure, a 2x2 array structure is shown. Moreover, under this structure, the gear metamaterial is composed of gear units with the same diameter.

[0077] Since the elastic modulus of the gear metamaterial formed by the first gear pair array varies between 0°-180°, and the extreme value range of the elastic modulus is also determined, in actual use conditions, when the rate of change of the elastic modulus performance needs to be more stable, or the amplitude of the working condition change is aggravated, and exceeds the elastic modulus performance adaptability adjustable range of the designed material, the gear metamaterial cannot be used, resulting in failure of the gear metamaterial. In addition, when designing the above structure, due to the limitation of the structural morphology, the performance after adjustment will not change in a step-like manner, so it cannot meet the needs of various working conditions at the same time.

[0078] Therefore, it is extremely important to simultaneously meet the requirements under various working conditions through gear metamaterials. Based on the speed shifting principle, a performance shifting method is constructed: without changing the center distance between two gear shafts, different gears on one shaft are meshed with different gears on the other shaft. Different gear pairs are meshed to form different gear metamaterial structures, which can achieve performance shifting. And after performance shifting, the change of the performance of the gear metamaterial is discontinuous, that is, stepwise. And when different gear pairs are meshed, gear metamaterials with continuously adjustable elastic modulus as shown in the meshing of the previous gear pair can be formed. The performance shifting method is combined with the method of continuously adjustable elastic modulus when different gear pairs are meshed, realizing a gear metamaterial design method with stepped expansion and continuous stepless adjustment of variable elastic modulus. This design method is based on the first gear pair composed of gear units with the same diameter as described above.

[0079] Specifically, to expand the performance of the gear metamaterial with performance gears, the change period of the elastic modulus of the gear metamaterial is adjusted to make the change rate of the elastic modulus performance slower (smoother), that is, the change period of the whole performance is increased. For example, the change period of the elastic modulus of the previous gear metamaterial is 180°, and it is desired to change the change period of its elastic modulus to 360°. Under the same conditions, changing the diameter of the gear can change the change period of the elastic modulus of the gear metamaterial composed of gear units.

[0080] Without changing the original center distance, the original gears with the same diameter are changed to two gear units with one large and one small diameter meshed. Here, the diameter ratio of the large and small gears is set to 2, as Figure 6 shown. Based on the small gear unit, since the small gear unit needs to rotate more turns to complete a cycle of the change of the elastic modulus of the gear metamaterial, the change period of the whole performance is increased. According to the symmetry of the variable elastic modulus structure part in the gear unit, it can be analyzed that the change period of its elastic modulus becomes 360°. Through simulation, the change curve of its elastic modulus within 360 degrees is Figure 7 , and the elastic modulus change range is 6.5 - 37.1 GPa.

[0081] When the diameter difference between the two gears is larger, the increase degree of the change period of the whole performance is more obvious. But after the gear array forms the gear metamaterial, it is necessary to avoid interference of the gears on the diagonal of the array. Assume the radius of the small gear unit is r 1 , the radius of the large gear unit is ar 1 , and the center distance between the two meshing gears is ar 1 + r 1 .

[0082] The connecting line of the gear center points on the diagonal of the gear metamaterial after the array, the connecting line of the center distances of the meshing gears on the horizontal line of the array, and the connecting line of the centers of the meshing gears on the vertical line of the array form an isosceles right triangle. The former is the hypotenuse of the right triangle, and the latter two are the two right sides of the right triangle, as Figure 8 shown.

[0083] According to the relationship between the hypotenuse and the right side of an isosceles triangle, the distance of the connecting line of the gear center points on the diagonal of the array is If there is no interference phenomenon after the gear array, the distance of the connecting line of the gear center points on the diagonal of the array should be greater than 2 times the radius of the large gear, that is, as shown in Equation (4) It can be obtained that a < 2.414. That is, the second gear pair can be obtained.

[0084] To expand the performance of the gear metamaterial in terms of performance gears, the extreme value of the elastic modulus of the gear metamaterial can also be adjusted to increase the performance robustness of the metamaterial to meet the requirements and adapt to more working conditions, changing the relatively limited adjustable range of the elastic model of the original gear metamaterial.

[0085] Since the above first and second gear pairs are both circular gear units, the extreme values of their elastic moduli do not change significantly, which are 5 GPa - 30 GPa and 6.5 GPa - 37.1 GPa respectively. Considering the limitation of the same center distance, the comprehensive complexity and design space, a 4th-order elliptical non-circular gear pair is selected to form the third gear pair in combination. With the existing fixed center distance, a module of 1.5 mm and a number of teeth of 44 are selected. According to the selected order of the elliptical non-circular gear, based on the existing design principle of the elliptical non-circular gear pair, its eccentricity can be obtained as 0.1296, and the 4th-order elliptical pitch curve is 35.2 mm. A 3D model of it is constructed, as Figure 9 shown, which are two meshing 4th-order elliptical non-circular gears under the existing center distance.

[0086] Based on the variable elastic modulus control equation of the gear unit, the variable elastic modulus structure part of the gear unit is designed. Generally, in order to reduce the weight, the main structure part is hollowed out; and for the convenience of design, the hollowed-out main structure is usually designed as a centrally symmetric structure. The hollowed-out structure is as Figure 9 shown.

[0087] Similar to the calculation process of the aforementioned equal circular gears, a finite element model of the overall structure of the third gear pair is further established, the same contact relationship between the two gears is set, and the load and boundary conditions of the gear metamaterial basic unit are constructed and characterized. The load is still applied to the center of the upper gear unit, and the load direction is vertically downward. The center of the lower gear unit is treated as a fixed boundary. The deformation of the third gear pair is obtained by finite element calculation. Similar to the calculation process of the aforementioned gear, this deformation can be converted into the elastic modulus of the gear metamaterial basic unit with the help of formulas (5)-(6). Repeated calculations can obtain the elastic modulus of the gear metamaterial basic unit (third gear pair) corresponding to different rotation angles γ.

[0088] The structural design parameters of the gear structure of the gear unit are selected as variables, and the required elastic modulus maximum value 80GPa and minimum value 20GPa are taken as targets. With the help of optimization calculation, the gear unit structure design with a specified elastic modulus variation range can be obtained through repeated iterations, and the corresponding elastic modulus of the gear metamaterial basic unit under different rotation angles γ can be obtained, such as Figure 10 shown.

[0089] Through the above steps, three gear pairs can be designed, namely the first gear pair, the second gear pair and the third gear pair. Take one gear from each gear pair and assemble them together in the form of a common gear shaft, and take the remaining gears and assemble them together in the form of a common gear shaft. During assembly, by setting and adjusting the axial distance of the gears, when a certain gear pair is in meshing, other gear pairs will not be in meshing, such as Figure 11 shown.

[0090] exist Figure 11 middle, Figure 11 (a) shows the state display of performance gear 1, at this time, a pair of gear units with equal diameters are in contact. Move the right gear shaft upward to make a pair of circular gears with unequal radii contact and mesh, realizing the switch from performance gear 1 to performance gear 2. Figure 11 Then move the right gear shaft downward to make the fourth-order elliptical non-circular gear engage and switch from performance gear 2 to performance gear 3, as shown in (b). Figure 11 As shown in (c), the gear shifting of the multi-speed adjustable mechanical metamaterial based on the gear unit is completed by moving the gear shaft back and forth.

[0091] Due to the meshing of different gear pairs, different gear metamaterial structures are formed, thus achieving performance shifting. And after the performance shifting, the change in the properties of the gear metamaterial is discontinuous, i.e., stepwise. Moreover, when different gear pairs are meshing, a metamaterial structure with continuously adjustable elastic modulus as shown in the gear pair meshing can be formed. By integrating the performance shifting method with the method of continuously adjustable elastic modulus when different gear pairs are meshing, a design method of variable elastic modulus metamaterial with stepwise topology fusion and continuous non-polar modulation is realized.

[0092] By arraying the above structure, a variable elastic modulus metamaterial with stepwise topology fusion and continuous non-polar modulation can be obtained. As Figure 12 shown, it is a 4x4 array structure. Elastic connectors with relatively low stiffness are arranged between the gear shafts to fix and support the gear shafts. Since the stiffness of the elastic connectors is much smaller than that of the gear pairs, it can be ignored, and the stiffness of the gear metamaterial is still determined by the stiffness of the gear pairs.

[0093] The above-described embodiments are merely preferred embodiments given to fully illustrate the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are within the protection scope of the present invention.

Claims

1. A method for designing a variable elastic modulus metamaterial, characterized in that: The following steps are involved: Step 1) Based on the structural composition and stiffness superposition principle, a gear metamaterial basic unit with continuously adjustable variable elastic modulus based on the same gear unit, i.e., the first gear pair, is constructed; Step 2) Based on the speed shifting principle, a performance shifting method is constructed to perform step expansion on the first gear pair; The performance of the gear metamaterial is expanded with the performance gear, and the rate of change of the elastic modulus is made more stable. The change period of the elastic modulus of the gear metamaterial is adjusted in steps through gear units with different diameters, and the basic unit of the gear metamaterial with period adjustment, i.e., the second gear pair, is obtained. The performance of gear metamaterials is expanded with performance gears, and the adjustable range of elastic modulus is adjusted in a leapfrog manner. The minimum and maximum values ​​are adjusted to the extreme values ​​of the elastic modulus of gear metamaterials by using elliptical non-circular gears as gear units, and the basic unit of extreme value adjustment gear metamaterials, i.e., the third gear pair, is obtained. Step 3) Assembling the first gear pair, the second gear pair and the third gear pair on two gear shafts and ensuring that only one pair of gear pairs is meshed at the same time, to form a gear pair basic unit; Step 4) The gear pair basic units are arranged in a meshing array to obtain a variable elastic modulus metamaterial that combines gear step extension with continuous stepless tunability.

2. The method for designing a variable elastic modulus metamaterial according to claim 1, wherein: In step 1), based on the composition relationship of the various parts of the gear unit and the superposition method of the gear stiffness, the relationship between the overall stiffness of the gear unit and the main stiffness of the gear structure of the gear unit and the contact stiffness of the gear ring teeth of the gear unit is derived, and the variable elastic modulus control equation of the gear unit is constructed based on the above relationship; Based on the variable elastic modulus control equation of the gear unit, the gear structure of the gear unit is designed; The number of teeth and the module are selected to establish the finite element model of the overall structure of the two gear units, the contact relationship between the gears is set, the load and boundary conditions of the gear metamaterial are constructed and characterized, the deformation of the gear unit is obtained through finite element calculation, and this deformation is converted into elastic modulus; The structural design parameters of the gear structure body of the gear unit are selected as variables, and the required maximum and minimum values ​​of the elastic modulus are taken as targets. Through repeated iterations, the overall structural design of the gear unit in the specified elastic modulus variation range is obtained, and the elastic modulus of the corresponding gear metamaterial basic unit is also obtained.

3. The method for designing a variable elastic modulus metamaterial according to claim 2, wherein: The governing equation is: In the formula, K G is the overall stiffness of the gear unit, K M is the stiffness of the gear structure, K R is the contact stiffness of the gear ring teeth, γ is the rotation angle of the gear unit, F is the load force, U is the deformation of the gear unit in the direction of the load force, E~K G (γ) is the proportional relationship between the elastic modulus E and the overall stiffness.

4. The method for designing a variable elastic modulus metamaterial according to claim 3, wherein: The elastic modulus E is calculated by the following formula: Where S is the area of ​​force action, L is y is the initial length of the center distance between the two gear units, and dy is the deformation of the gear unit.

5. The method for designing a variable elastic modulus metamaterial according to claim 2, wherein: When designing the gear structure body of the gear unit, the gear structure body is partially hollowed out.

6. The method for designing a variable elastic modulus metamaterial according to claim 1, wherein: In step 2), while the center distance of the first gear pair remains unchanged, the same gear unit in the first gear pair is changed into two gear units with a larger diameter and a smaller diameter, and the diameter ratio of the two gear units with a larger diameter and a smaller diameter is less than the specified value a, to obtain a second gear pair.

7. The method for designing a metamaterial with a variable elastic modulus according to claim 1, wherein: The limit value a is solved using the following formula: have to In the formula, r1 is the radius of the gear unit with a smaller diameter, ar1 is the radius of the gear unit with a larger diameter, and ar1+r1 is the center distance between the two gear units in the second gear pair after meshing. It is the distance between the center points of the gear units on the diagonal line behind the second gear pair array.

8. The method for designing a variable elastic modulus metamaterial according to claim 1, wherein: In step 2), the third gear pair adopts a third-order to sixth-order elliptical non-circular gear, and the gear tooth profile structure is obtained by the design principle of the elliptical non-circular gear pair; Specifically, when the center distance of the first gear pair remains unchanged, the module and the number of teeth are selected, and according to the selected order of the elliptical non-circular gear and based on the existing design principle of the elliptical non-circular gear pair, the gear tooth profile structure with the center distance fixed is obtained, and a three-dimensional structure is constructed; Based on the variable elastic modulus control equation of the gear unit, the gear structure main body of the gear unit of the third gear pair is designed, and the main part of the gear structure is hollowed out; Establish a finite element model of the third gear pair, set the contact relationship between the gears, construct and characterize the load and boundary conditions of the third gear pair, obtain the deformation of the gear structure body through finite element calculation, and convert this deformation into the elastic modulus of the gear metamaterial basic unit. Repeat the calculation to obtain the corresponding elastic modulus of the gear metamaterial basic unit; The structural design parameters of the gear structure body of the gear unit are selected as variables, and the required maximum and minimum values ​​of the elastic modulus are taken as targets. Through repeated iterations, the overall structural design of the gear in the specified elastic modulus variation range and the corresponding elastic modulus of the gear metamaterial basic unit are obtained.

9. The method for designing a variable elastic modulus metamaterial according to claim 1, wherein: An elastic connecting piece is arranged between adjacent gear shafts.

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