Topology optimization method and system for compliant mechanisms with complete hinge features

Abstract

The present invention relates to a method and system for topological optimization of a compliant mechanism with complete hinge features. The method comprises: defining volume constraints and intersection area constraints of a rounded corner flexible hinge mechanism, and defining non-intersecting regions and intersecting regions of basic components; designing an initial topological description function based on the design parameters of the basic components, and adjusting the initial topological description function to obtain a required topological description function for the intersection region of the basic components; establishing an optimization model based on the volume constraints, intersection area constraints, and required topological description function, performing finite element analysis on the optimization model, and calculating sensitivity information of the topological optimization problem of the rounded corner flexible hinge mechanism, and obtaining a topological map containing complete flexible hinge features based on the sensitivity information. Through this application, the problem of the flexible hinge region in the rounded corner flexible hinge mechanism being covered by other basic components, resulting in incomplete flexible hinge features, is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of topology optimization, and in particular to a topology optimization method and system for a compliant mechanism with complete hinge features. Background Art

[0002] Flexure hinge mechanisms utilize the elastic deformation of flexible hinges to transmit and convert motion and force, and are classified as centralized compliant mechanisms. Compared to traditional rigid mechanisms, compliant mechanisms offer advantages such as integrated processing, assembly-free and lubrication-free operation, and ease of miniaturization. These advantages have led to their widespread application in a wide range of fields, including modern traditional systems, microelectronics manufacturing, micro-electromechanical systems, and precision positioning.

[0003] The performance of a flexible hinge mechanism primarily depends on the flexible hinge itself, so designing a complete flexible hinge can improve the overall performance of the rounded flexible hinge mechanism. Currently, a flexible hinge mechanism topology optimization method and system, published as CN116757051A, uses only notched hinges, omitting most hinge types. Furthermore, only the integrated design of the hinge and mechanism is considered. As a result, the optimization results reveal that most hinges are missing, resulting in a more or less incomplete flexible hinge. Summary of the Invention

[0004] Based on this, the purpose of the present invention is to provide a topology optimization method and system for a compliant mechanism with complete hinge features to address the deficiencies in the prior art.

[0005] To achieve the above objectives, the present invention provides a topology optimization method for a compliant mechanism with complete hinge features, the method comprising:

[0006] Defining volume constraints and intersection area constraints of the rounded corner flexible hinge mechanism, and defining non-intersecting areas and intersecting areas of basic components, wherein the basic components are rods of the rounded corner flexible hinge mechanism;

[0007] Designing an initial topological description function of the basic component based on the design parameters of the basic component, and adjusting the initial topological description function based on important parameters of the rounded flexible hinge mechanism to obtain a required topological description function of the intersection area of ​​the basic component;

[0008] An optimization model is established based on the volume constraint, the intersection area constraint and the required topological description function, a finite element analysis is performed on the optimization model, and the sensitivity information of the topological optimization problem of the rounded flexible hinge mechanism is calculated. Based on the sensitivity information, a topological map containing complete flexible hinge features is obtained.

[0009] The beneficial effects of the present invention are: by defining the volume constraints and intersection area constraints of the rounded flexible hinge mechanism, and defining the intersecting areas and non-intersecting areas of the basic components, the initial topological description function of the basic components is designed based on the design parameters of the basic components, and then the initial topological description function is adjusted based on the important parameters of the basic components to obtain the required topological description function of the intersection area of ​​the basic components, and then an optimization model with the maximum output displacement as the objective function is established based on the volume constraints, intersection area constraints and required topological description functions. By performing finite element analysis on the optimization model and calculating the sensitivity information of the topological optimization problem of the rounded flexible hinge mechanism, the sensitivity information can be used to obtain a topological map containing a complete flexible hinge. Different from the existing technology, this method solves the problem that the flexible hinge area in the rounded flexible hinge mechanism is covered by other basic components, resulting in incomplete flexible hinge features.

[0010] Furthermore, the step of establishing an optimization model based on the volume constraint, the intersection area constraint and the required topological description function includes:

[0011] Taking the geometric characteristic parameters of the basic components as design variables, based on the volume constraint and the intersection area constraint, and according to the area coverage of the rounded flexible hinge mechanism, a required basic component is screened out from the plurality of basic components;

[0012] An intersection area constraint is imposed on the non-intersecting regions requiring basic components to establish an optimization model with the maximum output displacement as the objective function.

[0013] Furthermore, the expression for the area coverage of the rounded flexible hinge mechanism is as follows:

[0014]

[0015] in, represents the area coverage of the rounded flexible hinge mechanism, Indicates the The hinge area of ​​a basic component occupies the area of ​​the entire design domain and is expressed as follows:

[0016]

[0017] in, express The basic components The hinge region of the unit The topological description function values ​​on the four nodes of represents the Heaviside function, Indicates the The intersection area of ​​the hinge area and the sum of the areas occupied by other components in the basic component.

[0018] Furthermore, the expression of the optimization model is as follows:

[0019]

[0020] in, No. A vector of all design variables of a basic component; =1,…,N; represents the output displacement of the mechanism; Represents the virtual load acting in the output displacement direction; Indicated by virtual load The resulting displacement vector; represents the load applied in the input direction; Indicates the load acting in the input direction The resulting node displacement vector; represents the global stiffness matrix; represents the area occupied by the solid material in the design domain; Indicates the The area occupied by each of the basic components in the design domain; Indicates the number of components in the design domain; Indicates the upper limit of the available volume of solid materials; represents an adaptive relaxation coefficient, ; It is expressed as the intersection area aggregation function; T represents the vector transpose sign; dV represents the volume element; U represents the summation formula; P represents the vector composed of design variables.

[0021] Furthermore, the step of calculating the sensitivity information of the topology optimization problem of the rounded flexible hinge mechanism includes:

[0022] Calculating the sensitivity of the topology optimization problem of the fillet flexure hinge mechanism by deriving component design parameters;

[0023] The expression of the sensitivity of the objective function to the design variables of the basic components is as follows:

[0024]

[0025] represents the output displacement of the mechanism; Indicated by virtual load The resulting displacement vector; T represents the vector transpose sign; K represents the overall stiffness matrix; represents partial derivative; representing design variables of the basic components; Indicates the load acting in the input direction The resulting nodal displacement vectors; through the equilibrium equations The node displacement vector can be obtained , we get:

[0026]

[0027] in, , , then the expression of the sensitivity of the output displacement to the design variable is as follows:

[0028]

[0029] Overall stiffness matrix versus design variables The sensitivity is as follows:

[0030]

[0031] in, represents the elastic modulus of the material, represents the Heaviside function; c represents the penalty coefficient; Represents the topological description function value of node j in unit e The function value after filtering; e represents the unit; j represents the number of unit nodes; Represents the topological description function value = 1, ..., 4, the element stiffness matrix corresponding to element e, and NE represents the total number of elements in the design domain; then the output displacement is obtained for the design variable The expression for the sensitivity of is as follows:

[0032]

[0033] Volume constraint function for design variables The expression for the sensitivity of is as follows:

[0034]

[0035] Where V represents the volume constraint function, Represents the total number of elements in the design domain;

[0036] The expression of the partial derivative of the intersection area constraint function with respect to the design variable is as follows:

[0037]

[0038] in, represents the intersection area aggregation function, NC represents the number of components in the design domain, represents the area of ​​the intersection, =1× ,when hour, , the partial derivative of the design variable is 0, when , then the expression of the sensitivity information of the topology optimization problem of the rounded flexible hinge mechanism is as follows:

[0039]

[0040] Among them, T ijk Represents the topological description function value of the intersection area of ​​the non-intersecting area of ​​the i-th basic component and the sum of the areas occupied by other basic components at the four nodes of unit e.

[0041] Furthermore, the expression of the topological description function is as follows:

[0042]

[0043] in,

[0044]

[0045] Indicates the The topological description function of the non-intersecting region of the basic components, Indicates that except for When there are three basic components, the topological description function of the area occupied by other components is Indicates that a topological description function is needed, Indicates quantity, Indicates the number of components in the design domain;

[0046] The expression for the area of ​​the intersection region is as follows:

[0047]

[0048] in, represents the area of ​​the intersection, represents the Heaviside function, Presentation Component The intersection area of ​​the non-intersecting area and the sum of the areas occupied by other components in the unit The topological description function values ​​on the four nodes of ;

[0049] All areas that violate the intersection constraint are aggregated using the intersection area aggregation function, where the expression of the intersection area aggregation function is as follows:

[0050]

[0051] in,

[0052]

[0053] =1×

[0054] in, represents the intersection area aggregation function, It represents the intersection area of ​​the hinge of the i-th basic component with other basic components.

[0055] Furthermore, the expression of the initial topology description function is as follows:

[0056]

[0057]

[0058] in, Represents the coordinates of the center point of a single basic component in the local coordinate system; Indicates the The basic components in half length in direction; represents an even number; Indicates the The coordinates of the center point of each basic component in the global coordinate system; Indicates the The inclination angle of the local coordinate system of each basic component relative to the global coordinate system; represents the width function of the basic component; represents the initial topology description function;

[0059] The expression of the width function is as follows:

[0060]

[0061] in,

[0062]

[0063] in, Represents the width function, variable 、 、 All said The thickness parameter, L represents the half length of the basic component, represents the half length of the straight beam, and Both indicate rounded corners.

[0064] Furthermore, the method further comprises:

[0065] The intersection area of ​​the intersecting area of ​​each basic component and the non-intersecting area of ​​other basic components is defined as 0.

[0066] To achieve the above objectives, the present invention further provides a topology optimization system for a compliant mechanism with complete hinge features, which is used to implement the above-mentioned topology optimization method for a compliant mechanism with complete hinge features. The system comprises:

[0067] A definition module, used to define volume constraints and intersection area constraints of the rounded corner flexible hinge mechanism, and to define non-intersecting areas and intersecting areas of basic components, wherein the basic components are rods of the rounded corner flexible hinge mechanism;

[0068] an adjustment module, configured to design an initial topological description function of the basic component based on the design parameters of the basic component, and adjust the initial topological description function based on important parameters of the rounded flexible hinge mechanism to obtain a required topological description function of the intersection area of ​​the basic component;

[0069] An establishment and calculation module is used to establish an optimization model based on the volume constraint, the intersection area constraint and the required topological description function, perform finite element analysis on the optimization model, and calculate the sensitivity information of the topological optimization problem of the rounded flexible hinge mechanism, and obtain a topological map containing complete flexible hinge features based on the sensitivity information.

[0070] Furthermore, the establishment and calculation module includes:

[0071] a screening unit, configured to screen out required basic components from the plurality of basic components based on the volume constraint and the intersection area constraint, using the geometric characteristic parameters of the basic components as design variables, and according to the area coverage of the rounded flexible hinge mechanism;

[0072] A unit is established for applying an intersection area constraint to the non-intersecting area requiring the basic component, so as to establish an optimization model with the maximum output displacement as the objective function. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 Flowchart of a topology optimization method for a compliant mechanism with complete hinge features in one embodiment of the present invention;

[0074] Figure 2 is a schematic structural diagram of basic components in one embodiment of the present invention;

[0075] Figure 3 is a schematic diagram of intersecting areas and non-intersecting areas of basic components in one embodiment of the present invention;

[0076] Figure 4is a schematic diagram of the intersection area between basic components in one embodiment of the present invention;

[0077] Figure 5 Schematic diagram of the design domain, applied loads and boundary conditions of the compliant gripper in the second embodiment of the present invention;

[0078] Figure 6 Schematic diagram of the initial layout of the compliant gripper in the second embodiment of the present invention;

[0079] Figure 7 is a schematic diagram of the topological result of the compliant gripper in the second embodiment of the present invention;

[0080] Figure 8 is a schematic diagram of the iterative results of the compliant gripper in the second embodiment of the present invention;

[0081] Figure 9 is a schematic diagram of the optimization result of the compliant gripper in the second embodiment of the present invention;

[0082] Figure 10 4 is a structural block diagram of a topology optimization system for a compliant mechanism with complete hinge features in three embodiments of the present invention.

[0083] The following specific embodiments will further illustrate the present invention in conjunction with the above-mentioned drawings. DETAILED DESCRIPTION

[0084] In order to make the purpose, technical solutions and advantages of this application more clearly understood, the present application is described and illustrated below in conjunction with the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely used to explain this application and are not intended to limit this application. Based on the embodiments provided in this application, all other embodiments obtained by those of ordinary skill in the art without making any creative efforts are within the scope of protection of this application.

[0085] Obviously, the drawings described below are merely examples or embodiments of the present application. Those skilled in the art can, without inventive effort, apply the present application to other similar scenarios based on these drawings. Furthermore, it is also understood that, although the effort involved in such a development process may be complex and lengthy, for those skilled in the art related to the content disclosed in this application, changes in design, manufacturing, or production based on the technical content disclosed in this application are merely conventional technical means and should not be construed as an insufficiency of the content disclosed in this application.

[0086] References to "embodiments" in this application mean that a particular feature, structure, or characteristic described in connection with the embodiment may be included in at least one embodiment of the application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor does it refer to independent or alternative embodiments that are mutually exclusive of other embodiments. It is understood, both explicitly and implicitly, by those skilled in the art that the embodiments described in this application may be combined with other embodiments unless there is a conflict.

[0087] Unless otherwise defined, technical or scientific terms used herein shall have the ordinary meaning as understood by persons of ordinary skill in the art to which this application belongs. The terms "a," "an," "an," "the," and similar expressions used herein do not denote quantitative limitations and may refer to either the singular or the plural. The terms "comprise," "include," "have," and any variations thereof, used herein, are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or apparatus comprising a series of steps or modules (units) is not limited to the listed steps or units but may also include steps or units not listed, or may include other steps or units inherent to the process, method, product, or apparatus. The terms "connected," "connected," "coupled," and similar expressions used herein are not limited to physical or mechanical connections but may include electrical connections, whether direct or indirect. As used herein, "plurality" means two or more. "And / or" describes an association between associated objects, indicating that three possible relationships exist. For example, "A and / or B" may mean: A exists alone; A and B exist simultaneously; or B exists alone. The character " / " generally indicates that the objects before and after are in an "or" relationship. The terms "first", "second", "third", etc. involved in this application are only used to distinguish similar objects and do not represent a specific order for the objects.

[0088] Example 1

[0089] See also Figures 1-4 , is a topology optimization method for a compliant mechanism with complete hinge features in the first embodiment of the present invention, such as Figure 1 As shown, the method includes the following steps:

[0090] Step S101, defining volume constraints and intersection area constraints of a rounded corner flexible hinge mechanism, and defining non-intersecting regions and intersecting regions of basic components, wherein the basic components are rods of the rounded corner flexible hinge mechanism;

[0091] Among them, first define the important parameters of the rounded corner flexible hinge mechanism and the design parameters of the basic components. Specifically, the important parameters of the rounded corner flexible hinge mechanism include the design domain, boundary conditions, load capacity, virtual spring stiffness of the input and output ends, volume constraint and intersection area constraint. The design parameters of the basic components include the output value of the design variable, the range of change of the design variable, the non-intersecting area and the intersecting area. It should be noted that, if Figure 2 As shown, the reference is to the global coordinate system oxy and the local coordinate system o k x k y k A schematic diagram of the basic components described below.

[0092] Step S102: designing an initial topology description function of the basic component based on the design parameters of the basic component, and adjusting the initial topology description function based on important parameters of the rounded flexible hinge mechanism to obtain a required topology description function of the intersection area of ​​the basic component;

[0093] Among them, based on the design parameters, the initial topological description function of the basic component is described by a two-dimensional superellipse, and the initial topological description function is adjusted based on the important parameters to obtain the required topological description function of the intersection area of ​​the basic component. It should be noted that the intersection area of ​​the basic component is the overlapping part between one of the basic components and the other basic components.

[0094] Specifically, the expression of the initial topology description function is as follows:

[0095]

[0096]

[0097] in, Represents the coordinates of the center point of a single basic component in the local coordinate system; Indicates the The basic components in half length in direction; Represents an even number, usually 6; Indicates the The coordinates of the center point of each basic component in the global coordinate system; Indicates the The inclination angle of the local coordinate system of each basic component relative to the global coordinate system; represents the width function of the basic component; represents the initial topology description function;

[0098] The expression of the width function is as follows:

[0099]

[0100] in,

[0101]

[0102] in, Represents the width function, variable 、 、 All said The thickness parameter, L represents the half length of the basic component, represents the half length of the straight beam, and Both indicate rounded corners.

[0103] Furthermore, the expression of the topological description function is as follows:

[0104]

[0105] in,

[0106]

[0107] Indicates the The topological description function of the non-intersecting region of the basic components, Indicates that except for When there are three basic components, the topological description function of the area occupied by other components is Indicates that a topological description function is needed, Indicates quantity, Indicates the number of components in the design domain;

[0108] The expression for the area of ​​the intersection region is as follows:

[0109]

[0110] in, Indicates the The intersection area of ​​the hinge area and the sum of the areas occupied by other components in each basic component, represents the Heaviside function, Presentation Component The intersection area of ​​the non-intersecting area and the sum of the areas occupied by other components in the unit The topological description function values ​​on the four nodes of ;

[0111] All areas that violate the intersection constraint are aggregated using the intersection area aggregation function, where the expression of the intersection area aggregation function is as follows:

[0112]

[0113] in,

[0114]

[0115] =1×

[0116] in, represents the intersection area aggregation function, It represents the intersection area of ​​the hinge of the i-th basic component with other basic components.

[0117] Step S103: establishing an optimization model based on the volume constraint, the intersection area constraint, and the required topological description function, performing finite element analysis on the optimization model, and calculating the sensitivity information of the topological optimization problem of the rounded flexible hinge mechanism, and obtaining a topological map containing complete flexible hinge features based on the sensitivity information.

[0118] Furthermore, the step of establishing an optimization model based on the volume constraint, the intersection area constraint and the required topological description function includes:

[0119] Taking the geometric characteristic parameters of the basic components as design variables, based on the volume constraint and the intersection area constraint, and according to the area coverage of the rounded flexible hinge mechanism, a required basic component is screened out from the plurality of basic components;

[0120] An intersection area constraint is imposed on the non-intersecting regions requiring basic components to establish an optimization model with the maximum output displacement as the objective function.

[0121] Among them, based on the movable deformable component method, the geometric characteristic parameters of the basic components are used as design variables. Under the volume constraint and the intersection area constraint, the basic components that need to be subject to intersection constraints are found according to the area coverage rate of the rounded flexible hinge mechanism, and the intersection constraint is imposed on the hinge part (non-intersecting area) in the basic component, and an optimization model with the maximum output displacement of the mechanism as the objective function is established.

[0122] It should be noted that the optimization model is subjected to finite element analysis, and the sensitivity information of the topological optimization problem of the rounded flexible hinge mechanism is calculated. Based on the sensitivity information, the optimization model is iteratively optimized, and the design variables are updated to obtain a topological diagram containing complete flexible hinge features.

[0123] Through the above steps, the rod containing the rounded flexible hinge mechanism is used as the basic component, the important parameters of the rounded flexible hinge mechanism are defined, and the design parameters of the basic component are defined. Based on the design parameters and through a two-dimensional superellipse, the initial topology description function of the basic component is described. Then, based on the important parameters, the initial topology description function is adjusted to obtain the required topology description function of the intersection area of ​​the basic component. Then, the geometric characteristic parameters of the basic component are used as design variables. Based on the required topology description function and through a movable deformable component, an optimization model with the maximum output displacement as the objective function is established. By performing finite element analysis on the optimization model and calculating the sensitivity information of the topology optimization problem of the rounded flexible hinge mechanism, the optimization model is iteratively optimized using the sensitivity information, and the design variables are updated to obtain a topology map containing a complete flexible hinge. Different from the existing technology, this method solves the problem that the flexible hinge area in the rounded flexible hinge mechanism is covered by other basic components, resulting in incomplete flexible hinge features.

[0124] Furthermore, the expression for the area coverage of the rounded flexible hinge mechanism is as follows:

[0125]

[0126] in, represents the area coverage of the rounded flexible hinge mechanism, Indicates the The hinge area of ​​a basic component occupies the area of ​​the entire design domain and is expressed as follows:

[0127]

[0128] in, express The basic components The hinge region of the unit The topological description function values ​​on the four nodes of represents the Heaviside function, Indicates the The intersection area of ​​the hinge area and the sum of the areas occupied by other components in the basic component.

[0129] Furthermore, the expression of the optimization model is as follows:

[0130]

[0131] in, Indicates that A vector of all design variables of a basic component; =1,…,N; represents the output displacement of the mechanism; Indicates the virtual load acting in the output displacement direction; Indicated by virtual load The resulting displacement vector; represents the load applied in the input direction; Indicates the load acting in the input direction The resulting node displacement vector; represents the global stiffness matrix; represents the area occupied by the solid material in the design domain; Indicates the The area occupied by each of the basic components in the design domain; Indicates the number of components in the design domain; Indicates the upper limit of the available volume of solid materials; represents an adaptive relaxation coefficient, ; It is expressed as the intersection area aggregation function; T represents the vector transpose sign; dV represents the volume element; U represents the summation formula; P represents the vector composed of design variables.

[0132] Furthermore, the step of defining the intersection area constraint of the rounded flexible hinge mechanism includes: first, defining the basic component as two parts: a non-intersection area (hinge part) and an intersection area, and defining the intersection area of ​​the i-th basic component as The non-intersecting area is , similarly, define the intersection area of ​​the jth basic component as , the non-intersecting area is , define the intersection area of ​​the non-intersecting area of ​​each basic component and the intersecting area of ​​other basic components to be 0, that is, to ensure that: .

[0133] Furthermore, the step of performing finite element analysis on the optimization model includes:

[0134] The design domain is meshed by a meshing method to obtain a plurality of mesh units;

[0135] Performing finite element analysis on the optimized model by using a substitute material model method;

[0136] A mathematical relationship is established between the topological description function value at the unit node and the stiffness of the mesh unit to obtain the functional expression of the unit elastic modulus. Specifically, when the values ​​of the topological description function at the four nodes of the mesh unit are known, the functional expression of the unit elastic modulus is as follows:

[0137]

[0138] in, Display unit The elastic modulus of the material, represents the elastic modulus of the material, represents the Heaviside function, Indicates that the jth basic component is in the grid cell The topological description function values ​​on the four nodes of is the penalty coefficient, the value is 2;

[0139] The Heaviside function Using its regularized form Instead, its regularized form is expressed as follows:

[0140]

[0141] in, Represents a regularization parameter, which is used to control the regularization amplitude. is a small positive number, which is used to ensure the non-singularity of the global stiffness matrix. Represents a function variable.

[0142] Calculate the The specific expression of the stiffness matrix of each element is:

[0143]

[0144] in, Indicates the The stiffness matrix of each element, Describe the function value for the topology =1,…,4, the element stiffness matrix corresponding to element e is .

[0145] Furthermore, the step of calculating the sensitivity information of the topology optimization problem of the rounded flexible hinge mechanism includes:

[0146] Calculating the sensitivity of the topology optimization problem of the fillet flexure hinge mechanism by deriving component design parameters;

[0147] The expression of the sensitivity of the objective function to the design variables of the basic components is as follows:

[0148]

[0149] Represents the output displacement of the mechanism; T represents the vector transpose sign; K represents the overall stiffness matrix; represents partial derivative; Represent the design variables of the basic components; by balancing the equations The node displacement vector can be obtained , we get:

[0150]

[0151] Since the applied load is constant, the effect of constant load F on the design variables is The partial derivative of , and then by , then the expression of the sensitivity of the output displacement to the design variable is as follows:

[0152]

[0153] Overall stiffness matrix versus design variables The sensitivity is as follows:

[0154]

[0155] in, represents the elastic modulus of the material, represents the Heaviside function; c represents the penalty coefficient; Represents the topological description function value of node j in unit e The function value after filtering; e represents the unit; j represents the number of unit nodes; Represents the topological description function value = 1, ..., 4, the element stiffness matrix corresponding to element e, and NE represents the total number of elements in the design domain; In order to enhance the versatility of the code, the finite difference method is used here to calculate , then the output displacement is obtained for the design variable The expression for the sensitivity of is as follows:

[0156]

[0157] Volume constraint function for design variables The expression for the sensitivity of is as follows:

[0158]

[0159] Where V represents the volume constraint function, Represents the total number of elements in the design domain;

[0160] The expression of the partial derivative of the intersection area constraint function with respect to the design variable is as follows:

[0161]

[0162] in, represents the intersection area aggregation function, NC represents the number of components in the design domain, Indicates the The intersection area of ​​the hinge area and the sum of the areas occupied by other components in each basic component, =1× ,when hour, , that is, in actual calculation, the basic components are judged in pairs. If , indicating that the two basic components do not intersect, then the intersection area constraint is invalid, so the partial derivative of the design variable is 0. , indicating that the two basic components intersect, the expression of the sensitivity information of the topology optimization problem of the fillet flexible hinge mechanism is as follows:

[0163]

[0164] Among them, T ijk Represents the topological description function value of the intersection area of ​​the non-intersecting area of ​​the i-th basic component and the sum of the areas occupied by other basic components at the four nodes of unit e.

[0165] Example 2

[0166] In order to further verify the effectiveness of the topology optimization method of a compliant mechanism with complete hinge features of the present invention, this embodiment uses a compliant clamp as an example to verify the present invention.

[0167] Since the compliant gripper is symmetrical, the lower half is taken for design. The design domain, loads and boundary conditions of the compliant gripper are as follows: Figure 5 As shown, the initial layout of the compliant gripper is as follows Figure 6 As shown in the figure, (a) represents a compliant gripper without contour lines, and (b) represents a compliant gripper with contour lines. The volume fraction of the solid material of the compliant gripper is set to 0.3, the size of the design domain is set to 1 cm × 2 cm, the size of the notch is 0.25 cm × 0.5 cm, and a 160 × 80 finite element grid is used for discretization. The spring constant at the input end of the structure is , the applied force is , the spring constant added at the output end is , let the spring constants at the input and output be .

[0168] The topological results, iteration results and optimization results in this embodiment are as follows: Figure 7 、 Figure 8 、 Figure 9 As shown, the complete hinge structure in the flexible hinge can be clearly seen from the figure, so the topology optimization method of the compliant mechanism with a complete hinge of the present invention is effective.

[0169] Example 3

[0170] See also Figure 10 , which is a structural block diagram of a topology optimization system for a compliant mechanism with complete hinge features in the third embodiment of the present invention, as shown in FIG. Figure 10 As shown, the system includes:

[0171] A definition module, used to define volume constraints and intersection area constraints of the rounded corner flexible hinge mechanism, and to define non-intersecting areas and intersecting areas of basic components, wherein the basic components are rods of the rounded corner flexible hinge mechanism;

[0172] an adjustment module, configured to design an initial topological description function of the basic component based on the design parameters of the basic component, and adjust the initial topological description function based on important parameters of the rounded flexible hinge mechanism to obtain a required topological description function of the intersection area of ​​the basic component;

[0173] An establishment and calculation module is used to establish an optimization model based on the volume constraint, the intersection area constraint and the required topological description function, perform finite element analysis on the optimization model, and calculate the sensitivity information of the topological optimization problem of the rounded flexible hinge mechanism, and obtain a topological map containing complete flexible hinge features based on the sensitivity information.

[0174] In the specific implementation, by defining the volume constraint and intersection area constraint of the rounded flexible hinge mechanism, and defining the intersecting area and non-intersecting area of ​​the basic components, the initial topological description function of the basic components is designed based on the design parameters of the basic components, and then the initial topological description function is adjusted based on the important parameters of the basic components to obtain the required topological description function of the intersection area of ​​the basic components. Then, based on the volume constraint, the intersection area constraint and the required topological description function, an optimization model with the maximum output displacement as the objective function is established. By performing finite element analysis on the optimization model and calculating the sensitivity information of the topological optimization problem of the rounded flexible hinge mechanism, the sensitivity information can be used to obtain a topological map containing a complete flexible hinge. Different from the existing technology, this method solves the problem that the flexible hinge area in the rounded flexible hinge mechanism is covered by other basic components, resulting in incomplete flexible hinge features.

[0175] Furthermore, the establishment and calculation module includes:

[0176] a screening unit, configured to screen out required basic components from the plurality of basic components based on the volume constraint and the intersection area constraint, using the geometric characteristic parameters of the basic components as design variables, and according to the area coverage of the rounded flexible hinge mechanism;

[0177] A unit is established for applying an intersection area constraint to the non-intersecting area requiring the basic component, so as to establish an optimization model with the maximum output displacement as the objective function.

[0178] Furthermore, the expression for the area coverage of the rounded flexible hinge mechanism is as follows:

[0179]

[0180] in, represents the area coverage of the rounded flexible hinge mechanism, Indicates the The hinge area of ​​a basic component occupies the area of ​​the entire design domain and is expressed as follows:

[0181]

[0182] in, express The basic components The hinge region of the unit The topological description function values ​​on the four nodes of represents the Heaviside function, Indicates the The intersection area of ​​the hinge area and the sum of the areas occupied by other components in the basic component.

[0183] Furthermore, the expression of the optimization model is as follows:

[0184]

[0185] in, Indicates that A vector of all design variables of a basic component; =1,…,N; represents the output displacement of the mechanism; Indicates the virtual load acting in the output displacement direction; Indicated by virtual load The resulting displacement vector; represents the load applied in the input direction; Indicates the load acting in the input direction The resulting node displacement vector; represents the global stiffness matrix; represents the area occupied by the solid material in the design domain; Indicates the The area occupied by each of the basic components in the design domain; Indicates the number of components in the design domain; Indicates the upper limit of the available volume of solid materials; represents an adaptive relaxation coefficient, ; It is expressed as the intersection area aggregation function; T represents the vector transpose sign; dV represents the volume element; U represents the summation formula; P represents the vector composed of design variables.

[0186] Furthermore, the expression of the initial topology description function is as follows:

[0187]

[0188]

[0189] in, Represents the coordinates of the center point of a single basic component in the local coordinate system; Indicates the The basic components in half length in direction; represents an even number; Indicates the The coordinates of the center point of each basic component in the global coordinate system; Indicates the The inclination angle of the local coordinate system of each basic component relative to the global coordinate system; represents the width function of the basic component; represents the initial topology description function;

[0190] The expression of the width function is as follows:

[0191]

[0192] in,

[0193]

[0194] in, Represents the width function, variable 、 、 All said The thickness parameter, L represents the half length of the basic component, represents the half length of the straight beam, and Both indicate rounded corners.

[0195] Furthermore, the expression of the topological description function is as follows:

[0196]

[0197] in,

[0198]

[0199] Indicates the The topological description function of the non-intersecting region of the basic components, Indicates that except for When there are three basic components, the topological description function of the area occupied by other components is Indicates that a topological description function is needed, Indicates quantity, Indicates the number of components in the design domain;

[0200] The expression for the area of ​​the intersection region is as follows:

[0201]

[0202] in, represents the area of ​​the intersection, represents the Heaviside function, Presentation Component The intersection area of ​​the non-intersecting area and the sum of the areas occupied by other components in the unit The topological description function values ​​on the four nodes of ;

[0203] All areas that violate the intersection constraint are aggregated using the intersection area aggregation function, where the expression of the intersection area aggregation function is as follows:

[0204]

[0205] in,

[0206]

[0207] =1×

[0208] in, represents the intersection area aggregation function, It represents the intersection area of ​​the hinge of the i-th basic component with other basic components.

[0209] Furthermore, the establishment and calculation module is used to:

[0210] Calculating the sensitivity of the topology optimization problem of the fillet flexure hinge mechanism by deriving component design parameters;

[0211] The expression of the sensitivity of the objective function to the design variables of the basic components is as follows:

[0212]

[0213] represents the output displacement of the mechanism; K represents the overall stiffness matrix; represents partial derivative; Represent the design variables of the basic components; by balancing the equations The node displacement vector can be obtained , we get:

[0214]

[0215] in, , , then the expression of the sensitivity of the output displacement to the design variable is as follows:

[0216]

[0217] Overall stiffness matrix versus design variables The sensitivity is as follows:

[0218]

[0219] in, represents the elastic modulus of the material, represents the Heaviside function; c represents the penalty coefficient; Represents the topological description function value of node j in unit e The function value after filtering; e represents the unit; j represents the number of unit nodes; Represents the topological description function value = 1, ..., 4, the element stiffness matrix corresponding to element e, and NE represents the total number of elements in the design domain; then the output displacement is obtained for the design variable The expression for the sensitivity of is as follows:

[0220]

[0221] Volume constraint function for design variables The expression for the sensitivity of is as follows:

[0222]

[0223] Where V represents the volume constraint function, Represents the total number of elements in the design domain;

[0224] The expression of the partial derivative of the intersection area constraint function with respect to the design variable is as follows:

[0225]

[0226] in, represents the intersection area aggregation function, NC represents the number of components in the design domain, Indicates the The intersection area of ​​the hinge area and the sum of the areas occupied by other components in each basic component, =1× ,when hour, , that is, in actual calculation, the basic components are judged in pairs. If , indicating that the two basic components do not intersect, then the intersection area constraint is invalid, so the partial derivative of the design variable is 0. , indicating that the two basic components intersect, the expression of the sensitivity information of the topology optimization problem of the fillet flexible hinge mechanism is as follows:

[0227]

[0228] Among them, T ijk Represents the topological description function value of the intersection area of ​​the non-intersecting area of ​​the i-th basic component and the sum of the areas occupied by other basic components at the four nodes of unit e.

[0229] Furthermore, the definition module is also used to:

[0230] The intersection area of ​​the intersecting area of ​​each basic component and the non-intersecting area of ​​other basic components is defined as 0.

[0231] Example 4

[0232] The fourth embodiment of the present invention is based on the same inventive concept. The present invention proposes a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the steps of the topology optimization method of a flexible mechanism with complete hinge features of the above embodiment.

[0233] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, "computer-readable medium" can be any device that stores, communicates, propagates, or transmits a program for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0234] More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or more wires (electronic devices), a portable computer disk cartridge (magnetic devices), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium and then editing, interpreting, or processing it in another suitable manner as necessary, and then storing it in a computer memory.

[0235] The memory may include a large-capacity memory for data or instructions. By way of example, and not limitation, the memory may include a hard disk drive (HDD), a floppy disk drive, a solid-state drive (SSD), flash memory, an optical disk, a magneto-optical disk, a magnetic tape, or a Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, the memory may include removable or non-removable (or fixed) media. Where appropriate, the memory may be internal or external to the data processing device. In a specific embodiment, the memory is non-volatile memory. In a specific embodiment, the memory includes read-only memory (ROM) and random access memory (RAM). Where appropriate, the ROM may be a mask-programmed ROM, a programmable ROM (PROM), an erasable PROM (EPROM), an electrically erasable PROM (EEPROM), an electrically alterable ROM (EAROM) or a flash memory (FLASH), or a combination of two or more of these. Under appropriate circumstances, the RAM can be a static random access memory (SRAM) or a dynamic random access memory (DRAM), where the DRAM can be a fast page mode dynamic random access memory (FPMDRAM), an extended data out dynamic random access memory (EDODRAM), a synchronous dynamic random access memory (SDRAM), etc.

[0236] Example 5

[0237] The fifth embodiment of the present invention is based on the same inventive concept. The present invention proposes a terminal, which includes: a processor and a memory; the processor and the memory communicate with each other; the memory is used to store instructions; the processor is used to execute the instructions in the memory, and execute the topology optimization method of the flexible mechanism with complete hinge characteristics of the above embodiment.

[0238] It should be understood that various components of the present invention may be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods may be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof may be used: a discrete logic circuit having logic gate circuits for implementing logic functions on data signals, an application-specific integrated circuit having suitable combinational logic gate circuits, a programmable gate array (PGA), a field-programmable gate array (FPGA), etc.

[0239] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0240] Under the premise that no conflict occurs, those skilled in the art may freely combine and superimpose the above-mentioned additional technical features.

[0241] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A topology optimization method for a compliant mechanism with complete hinge features, characterized in that: The method comprises: Defining volume constraints and intersection area constraints of the rounded corner flexible hinge mechanism, and defining non-intersecting areas and intersecting areas of basic components, wherein the basic components are rods of the rounded corner flexible hinge mechanism; Designing an initial topological description function of the basic component based on the design parameters of the basic component, and adjusting the initial topological description function based on important parameters of the rounded flexible hinge mechanism to obtain a required topological description function of the intersection area of ​​the basic component; An optimization model is established based on the volume constraint, the intersection area constraint, and the required topological description function, a finite element analysis is performed on the optimization model, and sensitivity information of the topological optimization problem of the rounded flexure hinge mechanism is calculated, and a topological map containing complete flexure hinge features is obtained based on the sensitivity information; The step of establishing an optimization model based on the volume constraint, the intersection area constraint and the required topology description function comprises: Taking the geometric characteristic parameters of the basic components as design variables, based on the volume constraint and the intersection area constraint, and according to the area coverage of the rounded flexible hinge mechanism, a required basic component is screened out from the plurality of basic components; Applying an intersection area constraint to the non-intersecting regions requiring basic components to establish an optimization model with a maximum output displacement as an objective function; The expression of the topological description function is as follows: in, Indicates the The topological description function of the non-intersecting region of the basic components, Indicates that except for When there are three basic components, the topological description function of the area occupied by other components is Indicates that a topological description function is needed, Indicates quantity, Indicates the number of components in the design domain; The expression for the area of ​​the intersection region is as follows: in, represents the area of ​​the intersection, represents the Heaviside function, Presentation Component The intersection area of ​​the non-intersecting area and the sum of the areas occupied by other components in the unit The topological description function values ​​on the four nodes of ; All areas that violate the intersection constraint are aggregated using the intersection area aggregation function, where the expression of the intersection area aggregation function is as follows: in, =1× in, represents the intersection area aggregation function, It represents the intersection area of ​​the hinge of the i-th basic component with other basic components.

2. The topology optimization method for a compliant mechanism with complete hinge features according to claim 1, characterized in that: The expression of the area coverage of the rounded flexible hinge mechanism is as follows: in, represents the area coverage of the rounded flexible hinge mechanism, Indicates the The hinge area of ​​a basic component occupies the area of ​​the entire design domain and is expressed as follows: in, express The basic components The hinge region of the unit The topological description function values ​​on the four nodes of represents the Heaviside function, Indicates the The intersection area of ​​the hinge area and the sum of the areas occupied by other components in the basic component.

3. The topology optimization method for a compliant mechanism with complete hinge features according to claim 1, characterized in that: The expression of the optimization model is as follows: in, Indicates that A vector of all design variables of a basic component; =1,…,N; represents the output displacement of the mechanism; Indicates the virtual load acting in the output displacement direction; Indicated by virtual load The resulting displacement vector; represents the load applied in the input direction; Indicates the load acting in the input direction The resulting node displacement vector; represents the global stiffness matrix; represents the area occupied by the solid material in the design domain; Indicates the The area occupied by each of the basic components in the design domain; Indicates the number of components in the design domain; Indicates the upper limit of the available volume of solid materials; represents an adaptive relaxation coefficient, ; It is expressed as the intersection area aggregation function; T represents the vector transpose sign; dV represents the volume element; U represents the summation formula; P represents the vector composed of design variables.

4. The topology optimization method for a compliant mechanism with complete hinge features according to claim 1, characterized in that: The step of calculating the sensitivity information of the topology optimization problem of the rounded flexure hinge mechanism includes: Calculating the sensitivity of the topology optimization problem of the fillet flexure hinge mechanism by deriving component design parameters; The expression of the sensitivity of the objective function to the design variables of the basic components is as follows: represents the output displacement of the mechanism; Indicated by virtual load The resulting displacement vector; T represents the vector transpose sign; K represents the overall stiffness matrix; represents partial derivative; representing design variables of the basic components; Indicates the load acting in the input direction The resulting nodal displacement vectors; through the equilibrium equations The node displacement vector can be obtained , we get: in, , , then the expression of the sensitivity of the output displacement to the design variable is as follows: Overall stiffness matrix versus design variables The sensitivity is as follows: in, represents the elastic modulus of the material, represents the Heaviside function; c represents the penalty coefficient; Represents the topological description function value of node j in unit e The function value after filtering; e represents the unit; j represents the number of unit nodes; Represents the topological description function value = 1, ..., 4, the element stiffness matrix corresponding to element e, and NE represents the total number of elements in the design domain; then the output displacement is obtained for the design variable The expression for the sensitivity of is as follows: Volume constraint function for design variables The expression for the sensitivity of is as follows: Where V represents the volume constraint function, Represents the total number of elements in the design domain; The expression of the partial derivative of the intersection area constraint function with respect to the design variable is as follows: in, represents the intersection area aggregation function, NC represents the number of components in the design domain, represents the area of ​​the intersection, =1× ,when hour, , the partial derivative of the design variable is 0, when , then the expression of the sensitivity information of the topology optimization problem of the rounded flexible hinge mechanism is as follows: Among them, T ijk Represents the topological description function value of the intersection area of ​​the non-intersecting area of ​​the i-th basic component and the sum of the areas occupied by other basic components at the four nodes of unit e.

5. The topology optimization method for a compliant mechanism with complete hinge features according to claim 1, characterized in that: The expression of the initial topology description function is as follows: in, Represents the coordinates of the center point of a single basic component in the local coordinate system; Indicates the The basic components in half length in direction; represents an even number; Indicates the The coordinates of the center point of each basic component in the global coordinate system; Indicates the The inclination angle of the local coordinate system of each basic component relative to the global coordinate system; represents the width function of the basic component; represents the initial topology description function; The expression of the width function is as follows: in, in, Represents the width function, variable 、 、 All said The thickness parameter, L represents the half length of the basic component, represents the half length of the straight beam, and Both indicate rounded corners.

6. The topology optimization method for a compliant mechanism with complete hinge features according to claim 1, characterized in that: The method further comprises: The intersection area of ​​the intersecting area of ​​each basic component and the non-intersecting area of ​​other basic components is defined as 0.

7. A topology optimization system for a compliant mechanism with complete hinge features, used to implement the topology optimization method for a compliant mechanism with complete hinge features as claimed in any one of claims 1 to 6, characterized in that: The system comprises: A definition module, used to define volume constraints and intersection area constraints of the rounded corner flexible hinge mechanism, and to define non-intersecting areas and intersecting areas of basic components, wherein the basic components are rods of the rounded corner flexible hinge mechanism; an adjustment module, configured to design an initial topological description function of the basic component based on the design parameters of the basic component, and adjust the initial topological description function based on important parameters of the rounded flexible hinge mechanism to obtain a required topological description function of the intersection area of ​​the basic component; an establishment and calculation module for establishing an optimization model based on the volume constraint, the intersection area constraint, and the required topological description function, performing finite element analysis on the optimization model, and calculating sensitivity information of the topological optimization problem of the rounded flexure hinge mechanism, and obtaining a topological map containing complete flexure hinge features based on the sensitivity information; The establishment and calculation module includes: a screening unit, configured to screen out required basic components from the plurality of basic components based on the volume constraint and the intersection area constraint, using the geometric characteristic parameters of the basic components as design variables, and according to the area coverage of the rounded flexible hinge mechanism; Establishing a unit for applying an intersection area constraint to the non-intersecting area requiring the basic component to establish an optimization model with the maximum output displacement as the objective function; The expression of the topological description function is as follows: in, Indicates the The topological description function of the non-intersecting region of the basic components, Indicates that except for When there are three basic components, the topological description function of the area occupied by other components is Indicates that a topological description function is needed, Indicates quantity, Indicates the number of components in the design domain; The expression for the area of ​​the intersection region is as follows: in, represents the area of ​​the intersection, represents the Heaviside function, Presentation Component The intersection area of ​​the non-intersecting area and the sum of the areas occupied by other components in the unit The topological description function values ​​on the four nodes of ; All areas that violate the intersection constraint are aggregated using the intersection area aggregation function, where the expression of the intersection area aggregation function is as follows: in, =1× in, represents the intersection area aggregation function, It represents the intersection area of ​​the hinge of the i-th basic component with other basic components.

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