Compliant mechanism topological optimization method and system with complete hinge features

Abstract

The invention relates to a compliant mechanism topological optimization method and system with complete hinge features, and the method comprises the steps: defining the volume constraint and intersection area constraint of a rounded-corner flexible hinge mechanism, and defining the non-intersection region and the intersection region of a basic assembly; designing an initial topology description function based on the design parameters of the basic components, and adjusting the initial topology description function to obtain a required topology description function of an intersection region of the basic components; the method comprises the following steps: establishing an optimization model based on volume constraint, intersection area constraint and a required topology description function, carrying out finite element analysis on the optimization model, calculating sensitivity information of a topological optimization problem of the fillet flexible hinge mechanism, and obtaining a topological graph containing complete flexible hinge features based on the sensitivity information. Through the application, the problem that the flexible hinge region in the fillet flexible hinge mechanism is covered by other basic components, resulting in incomplete features of the finally obtained flexible hinge is solved.

Description

Technical Field

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

[0002] A flexible hinge mechanism uses the elastic deformation of a flexible hinge to complete the transmission and conversion of motion and force, and belongs to a centralized compliant mechanism. Compared with traditional rigid mechanisms, compliant mechanisms have the advantages of integrated processing, no assembly required, no lubrication required, and easy miniaturization. Based on these advantages, compliant mechanisms are widely used in many fields such as modern traditional systems, the manufacturing of microelectronic devices, microelectromechanical systems, and precision positioning.

[0003] The performance of a flexible hinge mechanism mainly depends on the flexible hinge part. Therefore, designing a complete flexible hinge can improve the overall performance of the fillet flexible hinge mechanism. Currently, in a topology optimization method and system for a flexible hinge mechanism with the publication number CN116757051A, since only notch-type hinges are used for the flexible hinge, most hinge types are not covered, and only the integrated design of the hinge and the mechanism is considered, resulting in the situation that most hinges are covered in the optimization result, and the finally obtained flexible hinge is more or less incomplete. 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 characteristics to solve the deficiencies in the prior art.

[0005] To achieve the above purpose, the present invention provides a topology optimization method for a compliant mechanism with complete hinge characteristics, and the method includes: Defining the volume constraint and the intersection area constraint of the fillet flexible hinge mechanism, and defining the non-intersecting area and the intersecting area of the basic components, where the basic components are the rods of the fillet flexible hinge mechanism; Designing an initial topology description function of the basic components based on the design parameters of the basic components, and adjusting the initial topology description function based on the important parameters of the fillet flexible hinge mechanism to obtain the required topology description function of the intersecting area of the basic components; Establishing an optimization model based on the volume constraint, the intersection area constraint, and the required topology description function, performing finite element analysis on the optimization model, and calculating the sensitivity information of the topology optimization problem of the fillet flexible hinge mechanism, and obtaining a topology graph containing complete flexible hinge characteristics based on the sensitivity information.

[0006] The beneficial effects of the present invention are as follows: By defining the volume constraint and the intersection area constraint of the fillet flexible hinge mechanism, and defining the intersectable region and non-intersectable region of the basic components, an 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 region of the basic components. Then, an optimization model with the maximum output displacement as the objective function is established based on the volume constraint, the intersection area constraint, and the required topological description function. By performing finite element analysis on the optimization model and calculating the sensitivity information of the topological optimization problem of the fillet flexible hinge mechanism, a topological graph containing a complete flexible hinge can be obtained using the sensitivity information. Different from the prior art, the problem that the flexible hinge region in the fillet flexible hinge mechanism is covered by other basic components, resulting in an incomplete flexible hinge feature in the end, is solved.

[0007] Further, the step of establishing the optimization model based on the volume constraint, the intersection area constraint, and the required topological description function includes: Taking the geometric feature parameters of the basic components as design variables, based on the volume constraint and the intersection area constraint, and screening out the required basic components from multiple basic components according to the area coverage rate of the fillet flexible hinge mechanism; Applying the intersection area constraint to the non-intersectable region of the required basic components to establish an optimization model with the maximum output displacement as the objective function.

[0008] Further, the expression of the area coverage rate of the fillet flexible hinge mechanism is as follows:

[0009] Among them, represents the area coverage rate of the fillet flexible hinge mechanism, represents the area occupied by the hinge region of the -th basic component in the entire design domain, and the expression is as follows:

[0010] Among them, represents when the topological description function values of the hinge region of the basic component at the four nodes of the unit , represents the Heaviside function, represents the intersection area of the hinge region of the -th basic component with the sum of the regions occupied by other components.

[0011] Further, the expression of the optimization model is as follows:

[0012] wherein, the vector composed of all design variables of the th basic component; represents the output displacement of the mechanism; represents the virtual load acting in the direction of the output displacement; represents the displacement vector generated by the virtual load ; represents the load applied in the input direction; represents the nodal displacement vector generated by the load acting in the input direction; represents the global stiffness matrix; represents the region occupied by the solid material in the design domain; represents the th region occupied by the th basic component in the design domain; represents the upper limit of the available volume of the solid material; represents an adaptive relaxation coefficient, ; represents the intersection area condensation function; T represents the vector transpose symbol; dV represents the volume element; U represents the summation formula; P represents the vector composed of design variables.

[0013] Furthermore, the steps of calculating the sensitivity information of the topology optimization problem of the fillet flexible hinge mechanism include: calculating the sensitivity of the topology optimization problem of the fillet flexible hinge mechanism by deriving the component design parameters; The expression of the sensitivity of the objective function to the design variables of the basic component is as follows:

[0014] represents the output displacement of the mechanism; represents the displacement vector generated by the virtual load ; T represents the vector transpose symbol; K represents the global stiffness matrix; represents the partial derivative; represents the design variable of the basic component; represents the nodal displacement vector generated by the load acting in the input direction; through the equilibrium equation the nodal displacement vector can be obtained, then:

[0015] Among them, , , the expression of the sensitivity of the output displacement to the design variable is as follows:

[0016] The sensitivity of the global stiffness matrix to the design variable is as follows:

[0017] Among them, represents the elastic modulus of the material, represents the Heaviside function; c represents the penalty coefficient; represents the value of the topological description function of node j in element e The filtered function value; e represents the element; j represents the number of element nodes; represents the value of the topological description function = 1,..., 4, the element stiffness matrix corresponding to element e, and ; NE represents the total number of elements in the design domain; then the expression of the sensitivity of the output displacement to the design variable is as follows:

[0018] The expression of the sensitivity of the volume constraint function to the design variable is as follows:

[0019] Among them, 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:

[0020] Among them, represents the intersection area condensation function, NC represents the number of components in the design domain, represents the area of the intersection region, = 1 × , when , , the partial derivative with respect to the design variable is 0, when , then the expression of the sensitivity information of the topological optimization problem of the filleted flexible hinge mechanism is as follows:

[0021] Among them, T ijkDenote the topological description function values of the intersection region between the non - overlapping region of the \(i\) - th basic component and the total region occupied by other basic components at the four nodes of element \(e\).

[0022] Furthermore, the expression of the required topological description function is as follows:

[0023] Where,

[0024] Denote the - th topological description function of the non - overlapping region of the basic component, Denote the topological description function of the region occupied by other components except the - th basic component, Denote the required topological description function, Denote the quantity, Denote the number of components in the design domain; The expression of the intersection region area is as follows:

[0025] Where, Denote the intersection region area, Denote the Heaviside function, Denote the component 's topological description function values of the intersection region between the non - overlapping region and the total region occupied by other components at the four nodes of element ; Condense all the areas violating the intersection constraints through the intersection area condensation function. Where, the expression of the intersection area condensation function is as follows:

[0026] Where,

[0027] =1×

[0028] Where, Denote the intersection area condensation function, Denote the intersection area between the hinge of the \(i\) - th basic component and other basic components.

[0029] Furthermore, the expression of the initial topological description function is as follows:

[0030]

[0031] Among them, represents the coordinates of the center point of a single basic component in the local coordinate system; represents the th basic component in the direction of the half length; represents an even number; represents the th basic component in the global coordinate system of the center point coordinates; represents the th basic component of the local coordinate system relative to the global coordinate system of the inclination angle; represents the width function of the basic component; represents the initial topological description function; The expression of the width function is as follows:

[0032] Among them,

[0033] Among them, represents the width function, the variable , , all represent thickness parameter, L represents the half length of the basic component, represents the half length of the straight beam, and both represent the rounded part.

[0034] Furthermore, the method further includes: Defining the intersection area of the intersectable region of each of the basic components and the non-intersectable region of the other basic components as 0.

[0035] In order to achieve the above object, the present invention also provides a compliant mechanism topology optimization system with complete hinge features for implementing the compliant mechanism topology optimization method with complete hinge features described above. The system includes: A definition module for defining the volume constraint and the intersection area constraint of the fillet flexible hinge mechanism, and defining the non-intersectable region and the intersectable region of the basic components, where the basic components are the rods of the fillet flexible hinge mechanism; An adjustment module for designing the initial topological description function of the basic components based on the design parameters of the basic components, and adjusting the initial topological description function based on the important parameters of the fillet flexible hinge mechanism to obtain the required topological description function of the intersection region of the basic components; A building and calculating module is used to establish an optimization model based on the volume constraint, the intersection area constraint, and the topological description function required, perform finite element analysis on the optimization model, calculate sensitivity information of the topological optimization problem of the fillet flexible hinge mechanism, and obtain a topological graph containing complete flexible hinge characteristics based on the sensitivity information.

[0036] Furthermore, the building and calculating module includes: A screening unit is used to use the geometric feature parameters of the basic components as design variables, based on the volume constraint and the intersection area constraint, and screen out the required basic components from multiple basic components according to the area coverage rate of the fillet flexible hinge mechanism. A building unit is used to impose an intersection area constraint on the non-intersecting regions of the required basic components to establish an optimization model with the maximum output displacement as the objective function. Description of the Drawings

[0037] Figure 1 It is a flowchart of a compliant mechanism topological optimization method with complete hinge characteristics in an embodiment of the present invention; Figure 2 It is a schematic structural diagram of basic components in an embodiment of the present invention; Figure 3 It is a schematic diagram of the intersecting regions and non-intersecting regions of basic components in an embodiment of the present invention; Figure 4 It is a schematic diagram of the intersection regions between basic components in an embodiment of the present invention; Figure 5 It is a schematic diagram of the design domain, applied load, and boundary conditions of a compliant gripper in a second embodiment of the present invention; Figure 6 It is a schematic diagram of the initial layout of a compliant gripper in a second embodiment of the present invention; Figure 7 It is a schematic diagram of the topological result of a compliant gripper in a second embodiment of the present invention; Figure 8 It is a schematic diagram of the iterative result of a compliant gripper in a second embodiment of the present invention; Figure 9 It is a schematic diagram of the optimized result of a compliant gripper in a second embodiment of the present invention; Figure 10 It is a structural block diagram of a compliant mechanism topological optimization system with complete hinge characteristics in a third embodiment of the present invention.

[0038] The following specific embodiments will further illustrate the present invention in conjunction with the above drawings. Specific Embodiments

[0039] In order to make the objectives, technical solutions and advantages of the present application clearer and more understandable, the present application will be described and explained below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application. Based on the embodiments provided in the present application, all other embodiments obtained by those of ordinary skill in the art without making creative efforts fall within the scope of protection of the present application.

[0040] Obviously, the accompanying drawings in the following description are only some examples or embodiments of the present application. For those of ordinary skill in the art, the present application can also be applied to other similar scenarios based on these drawings without making creative efforts. In addition, it can also be understood that although the efforts made in such a development process may be complex and time-consuming, for those of ordinary skill in the art related to the content disclosed in the present application, some design, manufacturing or production changes based on the technical content disclosed in the present application are only conventional technical means and should not be understood as insufficient disclosure of the content of the present application.

[0041] Referring to "embodiments" in the present application means that the specific features, structures or characteristics described in connection with the embodiments can be included in at least one embodiment of the present application. The phrase appears at various positions in the specification and does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. Those of ordinary skill in the art understand explicitly and implicitly that the embodiments described in the present application can be combined with other embodiments without conflict.

[0042] Unless otherwise defined, the technical terms or scientific terms involved in this application shall have the ordinary meanings understood by those with ordinary skills in the technical field to which this application pertains. The words such as "a", "an", "one", "the" and the like involved in this application do not indicate a limitation in quantity and may represent singular or plural. The terms "comprising", "including", "having" and any variations thereof involved in this application are intended to cover non-exclusive inclusion; for example, a process, method, system, product or device comprising a series of steps or modules (units) is not limited to the listed steps or units, but may further include steps or units not listed, or may further include other steps or units inherent to these processes, methods, products or devices. The words such as "connected", "coupled" and the like involved in this application are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The "plurality" involved in this application means two or more. "And / or" describes the association relationship of associated objects and indicates that three relationships may exist. For example, "A and / or B" may represent: A exists alone, A and B exist simultaneously, and B exists alone. The character " / " generally indicates an "or" relationship between the associated objects before and after. The terms "first", "second", "third" and the like involved in this application are only used to distinguish similar objects and do not represent a specific order for the objects.

[0043] Embodiment 1 Please refer to Figures 1-4 , which is a compliant mechanism topology optimization method with complete hinge characteristics in the first embodiment of the present invention. As Figure 1 shown, the method includes the following steps: Step S101, defining the volume constraint and the intersection area constraint of the fillet flexible hinge mechanism, and defining the non-intersecting area and the intersecting area of the basic components, where the basic components are the rods of the fillet flexible hinge mechanism; Among them, first define the important parameters of the fillet flexible hinge mechanism and define the design parameters of the basic components. Specifically, the important parameters of the fillet flexible hinge mechanism include the design domain, boundary conditions, load quantity, virtual spring stiffness at the input end and the output end, volume constraint and intersection area constraint. The design parameters of the basic components include the output value of the design variable, the change range of the design variable, the non-intersecting area and the intersecting area. It should be noted that, as Figure 2 shown, it is a schematic diagram of the basic components under the reference global coordinate system oxy and the local coordinate system o k x k y k below.

[0044] Step S102: Design the 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 the important parameters of the fillet flexible hinge mechanism to obtain the required topological description function of the intersection region of the basic component; Among them, based on the design parameters, the initial topological description function of the basic component is described by a two-dimensional super-ellipse, and the initial topological description function is adjusted based on the important parameters to obtain the required topological description function of the intersection region of the basic component. It should be noted that the intersection region of the basic component is the overlapping part of one basic component and other basic components.

[0045] Specifically, the expression of the initial topological description function is as follows:

[0046]

[0047] Among them, represents the coordinates of the center point of a single basic component in the local coordinate system; represents the th basic component in the direction of the semi-length; represents an even number, usually taking 6; represents the th basic component in the global coordinate system of the center point coordinates; represents the th basic component of the local coordinate system relative to the global coordinate system of the inclination angle; represents the width function of the basic component; represents the initial topological description function; The expression of the width function is as follows:

[0048] Among them,

[0049] Among them, represents the width function, the variable , , all represent thickness parameter, L represents the semi-length of the basic component, represents the semi-length of the straight beam, and both represent the fillet part.

[0050] Furthermore, the expression of the required topological description function is as follows:

[0051] Among them,

[0052] represents the topological description function of the non - intersecting region of the th basic component, represents the topological description function of the region occupied by other components except the th basic component, represents the topological description function required, represents the quantity, represents the number of components in the design domain; The expression for the intersection region area is as follows:

[0053] Among them, represents the intersection region area between the hinge region of the th basic component and the total area of the regions occupied by other components, represents the Heaviside function, represents the component of the topological description function values at the four nodes of the unit for the intersection region between the non - intersecting region of and the total area of the regions occupied by other components; All areas violating the intersection constraints are condensed through the intersection area condensation function, where the expression of the intersection area condensation function is as follows:

[0054] Among them,

[0055] = 1×

[0056] Among them, represents the intersection area condensation function, represents the intersection area between the hinge of the

[0057] Step S103: Based on the volume constraint, the intersection area constraint, and the topological description function required, establish an optimization model, perform finite - element analysis on the optimization model, and calculate the sensitivity information of the topological optimization problem of the filleted flexible hinge mechanism. Based on the sensitivity information, obtain a topological graph containing the complete flexible hinge characteristics.

[0058] Further, the steps of establishing an optimization model based on the volume constraint, the intersection area constraint, and the required topological description function include: Taking the geometric feature parameters of the basic components as design variables, based on the volume constraint and the intersection area constraint, and screening out the required basic components from multiple basic components according to the area coverage rate of the fillet flexible hinge mechanism; Applying the intersection area constraint to the non-intersecting regions of the required basic components to establish an optimization model with the maximum output displacement as the objective function.

[0059] Among them, based on the movable deformable component method, taking the geometric feature parameters of the basic components as design variables, under the volume constraint and the intersection area constraint, according to the area coverage rate of the fillet flexible hinge mechanism, find out the basic components that need to apply the intersection constraint, apply the intersection constraint to the hinge part (non-intersecting region) of this basic component, and establish an optimization model with the maximum output displacement of the mechanism as the objective function.

[0060] It should be noted that perform finite element analysis on the optimization model, calculate the sensitivity information of the topological optimization problem of the fillet flexible hinge mechanism, and based on the sensitivity information, perform iterative optimization on the optimization model, update the design variables, and obtain a topological graph containing complete flexible hinge features.

[0061] Through the above steps, taking the rod member containing the fillet flexible hinge mechanism as the basic component, defining the important parameters of the fillet flexible hinge mechanism, and defining the design parameters of the basic component, based on the design parameters and using the two-dimensional super-ellipse to describe the initial topological description function of the basic component, then adjusting the initial topological description function based on the important parameters to obtain the required topological description function of the intersection region of the basic component, and then taking the geometric feature parameters of the basic component as design variables, based on this required topological description function, and establishing an optimization model with the maximum output displacement as the objective function through the movable deformable component, by performing finite element analysis on the optimization model, calculating the sensitivity information of the topological optimization problem of the fillet flexible hinge mechanism, and using the sensitivity information to perform iterative optimization on the optimization model, updating the design variables, to obtain a topological graph containing complete flexible hinges, which is different from the prior art and solves the problem that the flexible hinge region in the fillet flexible hinge mechanism is covered by other basic components, resulting in incomplete flexible hinge features finally obtained.

[0062] Further, the expression of the area coverage rate of the fillet flexible hinge mechanism is as follows:

[0063] Among them, represents the area coverage rate of the fillet flexible hinge mechanism, represents the The hinge region of a basic component occupies the area of the entire design domain, and the expression is as follows:

[0064] where, represents the topological description function values of the hinge region of the basic component at the four nodes of the unit ; represents the Heaviside function, represents the -th basic component, and

[0065] Further, the expression of the optimization model is as follows:

[0066] where, represents the vector composed of all design variables of the -th basic component; = 1,..., N; represents the output displacement of the mechanism; represents the virtual load acting in the direction of the output displacement; represents the displacement vector generated by the virtual load ; represents the load applied in the input direction; represents the nodal displacement vector generated by the load acting in the input direction; represents the global stiffness matrix; represents the region occupied by the solid material in the design domain; represents the -th basic component in the design domain; represents the number of components in the design domain; represents the upper limit of the available volume of the solid material; represents an adaptive relaxation coefficient, ; represents the intersection area condensation function; T represents the vector transpose symbol; dV represents the volume element; U represents the summation formula; P represents the vector composed of design variables.

[0067] Further, the steps of defining the intersection area constraint of the fillet flexible hinge mechanism include: First, define the basic component as two parts, the non-intersecting region (hinge part) and the intersecting region, and define the intersecting region of the -th basic component as , and the non-intersecting region as Similarly, define the intersectable region of the j-th basic component as , and the non-intersectable region as . Define the intersection area between the non-intersectable regions of each of the basic components and the intersectable regions of the other basic components as 0, that is, ensure: .

[0068] Furthermore, the steps for performing finite element analysis on the optimization model include: Perform mesh division on the design domain through a mesh division method to obtain multiple mesh elements; Perform finite element analysis on the optimization model through a surrogate material model method; Establish a mathematical relationship between the topological description function values at the unit nodes and the stiffness of the mesh elements to obtain a function expression for the unit elastic modulus. Specifically, when the values of the topological description functions at the four nodes of the known mesh element are given, the function expression for the unit elastic modulus is as follows:

[0069] where, represents the material elastic modulus of element , represents the material elastic modulus, represents the Heaviside function, represents the values of the topological description functions at the four nodes of the j-th basic component in the mesh element , and the exponent is the penalty coefficient, with a value of 2; Replace the Heaviside function with its regularization form , and its regularization form is expressed as follows:

[0070] where, represents a regularization parameter, whose role is to control the regularization amplitude, is a very small positive number, whose purpose is to ensure the non-singularity of the global stiffness matrix, represents the function variable.

[0071] The specific expression for calculating the stiffness matrix of the -th element is:

[0072] where, represents the stiffness matrix of the -th element, is the value of the topological description function When \(i = 1,\cdots,4\), the element stiffness matrix corresponding to element \(e\) and there is .

[0073] Furthermore, the step of calculating the sensitivity information of the topology optimization problem of the fillet flexible hinge mechanism includes: Calculating the sensitivity of the topology optimization problem of the fillet flexible hinge mechanism by differentiating the component design parameters; The expression of the sensitivity of the objective function to the design variables of the basic component is as follows:

[0074] \(\mathbf{u}\) represents the output displacement of the mechanism; \(T\) represents the vector transpose symbol; \(K\) represents the global stiffness matrix; \(\frac{\partial}{\partial}\) represents the partial derivative; \(\mathbf{x}\) represents the design variables of the basic component; Through the equilibrium equation The nodal displacement vector \(\mathbf{u}\) can be obtained , then we get:

[0075] Among them, because the applied load is constant, the partial derivative of the constant load \(F\) with respect to the design variable \(\frac{\partial F}{\partial x}\) , and then from , then the expression of the sensitivity of the output displacement to the design variable is as follows:

[0076] The sensitivity of the global stiffness matrix to the design variable \(\mathbf{x}\) is as follows:

[0077] Among them, \(E\) represents the material elastic modulus, \(H\) represents the Heaviside function; \(c\) represents the penalty coefficient; \(q_{ej}\) represents the value of the topology description function of node \(j\) in element \(e\) The filtered function value; \(e\) represents the element; \(j\) represents the number of element nodes; \(q_{e}\) represents the value of the topology description function When \(i = 1,\cdots,4\), the element stiffness matrix corresponding to element \(e\), and ; \(NE\) represents the total number of elements in the design domain; To enhance the generality of the code, the finite difference method is used here to calculate , then the expression of the sensitivity of the output displacement to the design variable \(\mathbf{x}\) is as follows:

[0078] The expression for the sensitivity of the volume constraint function with respect to the design variables is as follows:

[0079] where V represents the volume constraint function, represents the total number of elements in the design domain; The expression for the partial derivative of the intersection area constraint function with respect to the design variables is as follows:

[0080] where represents the intersection area aggregation function, NC represents the number of components in the design domain, represents the th intersection area between the hinge region and the total area occupied by other components in the = 1 × when at that time, that is, in actual calculation, pairwise judgment is made for basic components in sequence. If , it indicates that the two basic components do not intersect, then the intersection area constraint is invalid, so the partial derivative with respect to the design variables is 0. When , it indicates that the two basic components intersect, then the expression for the sensitivity information of the topology optimization problem of the fillet flexible hinge mechanism is as follows:

[0081] where T ijk represents the topological description function values at the four nodes of element e for the intersection area between the non - intersectable region of the

[0082] Example 2 To further verify the effectiveness of the topology optimization method for compliant mechanisms with complete hinge characteristics of the present invention, this example verifies the present invention by taking a compliant gripper as an example.

[0083] Due to the symmetry of the compliant gripper, the lower half is taken for design. The design domain, load, and boundary conditions of the compliant gripper are as Figure 5 shown, and the initial layout of the compliant gripper is as Figure 6 shown, where (a) represents the compliant gripper without contour lines, and (b) represents the 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, where the size of the notch part is 0.25 cm × 0.5 cm, and it is discretized using 160 × 80 finite - element meshes. The spring coefficient at the input end of the structure is , and the applied force is , the spring coefficient added at the output end is , let the spring coefficients of the input end and the output end be .

[0084] The topological result, iteration result and optimization result in this embodiment are respectively as Figure 7 , Figure 8 , Figure 9 shown. It can be clearly seen from the figure the complete hinge structure in the flexible hinge. Therefore, the topology optimization method of the compliant mechanism with a complete hinge of the present invention is effective.

[0085] Embodiment III Please refer to Figure 10 , which is the structural block diagram of the topology optimization system of the compliant mechanism with complete hinge features in the third embodiment of the present invention. As Figure 10 shown, the system includes: A definition module for defining the volume constraint and intersection area constraint of the fillet flexible hinge mechanism, and defining the non-intersecting area and intersecting area of the basic components, where the basic components are the rods of the fillet flexible hinge mechanism; An adjustment module for designing an initial topological description function of the basic components based on the design parameters of the basic components, and adjusting the initial topological description function based on the important parameters of the fillet flexible hinge mechanism to obtain the required topological description function of the intersecting area of the basic components; A building and calculation module for building 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 topology optimization problem of the fillet flexible hinge mechanism, and obtaining a topological graph containing complete flexible hinge features based on the sensitivity information.

[0086] In specific implementation, by defining the volume constraint and intersection area constraint of the fillet flexible hinge mechanism, and defining the intersecting area and non-intersecting area of the basic components, designing an initial topological description function of the basic components based on the design parameters of the basic components, and then adjusting the initial topological description function based on the important parameters of the basic components to obtain the required topological description function of the intersecting area of the basic components, and then building an optimization model with the maximum output displacement as the objective function based on the volume constraint, intersection area constraint and required topological description function, performing finite element analysis on the optimization model, and calculating the sensitivity information of the topology optimization problem of the fillet flexible hinge mechanism, so as to be able to obtain a topological graph containing a complete flexible hinge using the sensitivity information, which is different from the prior art and solves the problem that the flexible hinge area in the fillet flexible hinge mechanism is covered by other basic components, resulting in incomplete flexible hinge features finally obtained.

[0087] Further, the building and calculation module includes: A screening unit, which uses the geometric feature parameters of the basic components as design variables, and based on the volume constraint and the intersection area constraint, and screens out the required basic components from a plurality of the basic components according to the area coverage rate of the fillet flexible hinge mechanism; An establishment unit, which applies an intersection area constraint to the non-intersecting area of the required basic components to establish an optimization model with the maximum output displacement as the objective function.

[0088] Furthermore, the expression of the area coverage rate of the fillet flexible hinge mechanism is as follows:

[0089] Among them, represents the area coverage rate of the fillet flexible hinge mechanism, represents the area occupied by the hinge area of the th basic component in the entire design domain, and the expression is as follows:

[0090] Among them, represents when the basic component the topological description function values of the hinge area of at the four nodes of the unit, represents the Heaviside function, represents the th basic component, the intersection area of the hinge area and the sum of the areas occupied by other components.

[0091] Furthermore, the expression of the optimization model is as follows:

[0092] Among them, represents the vector composed of all design variables of the th basic component; = 1,..., N; represents the output displacement of the mechanism; represents the virtual load acting in the output displacement direction; represents the displacement vector generated by the virtual load ; represents the load applied in the input direction; represents the load acting in the input direction generates the nodal displacement vector; represents the global stiffness matrix; represents the area occupied by the solid material in the design domain; represents the The area occupied by one of the basic components in the design domain; Indicates the number of components in the design domain; Represents the upper limit of the available volume of the solid material; Represents an adaptive relaxation coefficient, ; Represents the intersection area aggregation function; T represents the vector transpose symbol; dV represents the volume element; U represents the summation formula; P represents the vector composed of design variables.

[0093] Furthermore, the expression of the initial topology description function is as follows:

[0094]

[0095] Among them, Represents the coordinates of the center point of a single basic component in the local coordinate system; Represents the th basic component in direction of the semi-length; Represents an even number; Represents the th basic component in the global coordinate system of the center point coordinates; Represents the th basic component of the local coordinate system relative to the global coordinate system of the inclination angle; Represents the width function of the basic component; Represents the initial topology description function; The expression of the width function is as follows:

[0096] Among them,

[0097] Among them, Represents the width function, the variable 、 、 All represent thickness parameter, L represents the semi-length of the basic component, Represents the semi-length of the straight beam, And Both represent the rounded part.

[0098] Furthermore, the expression of the required topology description function is as follows:

[0099] Among them,

[0100] Represents the topological description function of the non - overlapping region of the th basic component, Represents the topological description function of the region occupied by other components except the th basic component, Represents the topological description function required, Represents the quantity, Represents the number of components in the design domain; The expression of the intersection area is as follows:

[0101] Among them, Represents the intersection area, Represents the Heaviside function, Represents the component The topological description function values at the four nodes of the intersection region between the non - overlapping region of and the total region occupied by other components in the unit ; All the areas violating the intersection constraints are condensed through the intersection area condensation function. Among them, the expression of the intersection area condensation function is as follows:

[0102] Among them,

[0103] =1×

[0104] Among them, Represents the intersection area condensation function, Represents the intersection area between the hinge of the i - th basic component and other basic components.

[0105] Furthermore, the establishment and calculation module is used for: Calculating the sensitivity of the topological optimization problem of the fillet flexible hinge mechanism by taking the derivative of the component design parameters; The expression of the sensitivity of the objective function to the design variables of the basic component is as follows:

[0106] Represents the output displacement of the mechanism; K represents the overall stiffness matrix; Represents the partial derivative; Represents the design variable of the basic component; Through the equilibrium equation The nodal displacement vector can be obtained , then we get:

[0107] Among them, , , then the expression of the sensitivity of the output displacement to the design variable is as follows:

[0108] The sensitivity of the global stiffness matrix to the design variable is as follows:

[0109] Among them, represents the elastic modulus of the material, represents the Heaviside function; c represents the penalty coefficient; represents the value of the topological description function of node j in element e The filtered function value; e represents the element; j represents the number of nodes in the element; represents the value of the topological description function = 1,..., 4, the element stiffness matrix corresponding to element e, and ; NE represents the total number of elements in the design domain; then we get the expression of the sensitivity of the output displacement to the design variable as follows:

[0110] The expression of the sensitivity of the volume constraint function to the design variable is as follows:

[0111] Among them, 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:

[0112] Among them, represents the intersection area condensation function, NC represents the number of components in the design domain, represents the th intersection area between the hinge area of the basic component and the total area occupied by other components, = 1 × when , , that is, in actual calculation, judge two basic components in turn. If , indicating that the two basic components do not intersect, then the intersection area constraint is invalid, so the partial derivative with respect to the design variable is 0. When , indicating that the two basic components intersect, then the expression of the sensitivity information of the topological optimization problem of the fillet flexure hinge mechanism is as follows:

[0113] where T ijk represents the topological description function values of the intersection region of the non-intersecting region of the i-th basic component and the total region occupied by other basic components at the four nodes of the element e.

[0114] Furthermore, the defining module is further configured to: define the intersection area of the intersecting region of each of the basic components and the non-intersecting regions of the other basic components to be 0.

[0115] Embodiment 4 In the fourth embodiment of the present invention, based on the same inventive concept, a computer-readable storage medium proposed by the present invention stores a computer program, and when the computer program is executed by a processor, it implements the steps of the compliant mechanism topological optimization method with complete hinge characteristics in the above embodiment. The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a definite sequence list of executable instructions for implementing logical functions, and can be specifically implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other systems that can fetch instructions from the instruction execution system, apparatus, or device and execute the instructions), or in combination with these instruction execution systems, apparatus, or devices. For the purposes of this specification, a "computer-readable medium" can be any device that contains, communicates, propagates, or transports a program for use by or in connection with an instruction execution system, apparatus, or device. More specific examples (non-exhaustive list) of computer-readable media include the following: an electrical connection part (electronic device) having one or more wirings, a portable computer disk cartridge (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other media, then editing, interpreting, or otherwise processing it as appropriate, and then storing it in a computer memory.

[0116] Among them, the memory may include a mass storage 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), a 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. In a suitable case, the memory may include removable or non-removable (or fixed) media. In a suitable case, the memory may be internal or external to the data processing device. In a particular embodiment, the memory is a non-volatile memory. In a particular embodiment, the memory includes a read-only memory (ROM) and a random access memory (RAM). In a suitable case, 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, or a combination of two or more of these. In a suitable case, the RAM may be a static random access memory (SRAM) or a dynamic random access memory (DRAM), where the DRAM may be a fast page mode dynamic random access memory (FPMDRAM), an extended date out dynamic random access memory (EDODRAM), a synchronous dynamic random access memory (SDRAM), etc.

[0117] Embodiment Five In the fifth embodiment of the present invention, based on the same inventive concept, a terminal proposed by the present invention 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 compliant mechanism topology optimization method with complete hinge characteristics in the above embodiment.

[0118] It should be understood that each part of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above embodiment, multiple steps or methods can be implemented by software or firmware stored in the memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, any one or a combination of the following technologies well known in the art can be used: discrete logic circuits having logic gate circuits for implementing logic functions on data signals, application specific integrated circuits having appropriate combinational logic gate circuits, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc.

[0119] In the description of this specification, the description with reference to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0120] On the premise of no conflict, those skilled in the art can freely combine and superimpose the above additional technical features.

[0121] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A topology optimization method for compliant mechanisms with complete hinge characteristics, characterized in that, The method includes: Defining the volume constraint and the intersection area constraint of the fillet flexible hinge mechanism, and defining the non-intersecting area and the intersecting area of the basic components, where the basic components are the rods of the fillet flexible hinge mechanism; Designing an initial topological description function of the basic components based on the design parameters of the basic components, and adjusting the initial topological description function based on the important parameters of the fillet flexible hinge mechanism to obtain the required topological description function of the intersecting area of the basic components; 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 fillet flexible hinge mechanism, and obtaining a topological graph containing complete flexible hinge features based on the sensitivity information.

2. The compliant mechanism topology optimization method with complete hinge features according to claim 1, wherein The step of establishing an optimization model based on the volume constraint, the intersection area constraint, and the required topological description function includes: Taking the geometric feature parameters of the basic components as design variables, screening out the required basic components from multiple basic components based on the volume constraint and the intersection area constraint, and according to the area coverage rate of the fillet flexible hinge mechanism; Applying the intersection area constraint to the non-intersecting area of the required basic components to establish an optimization model with the maximum output displacement as the objective function.

3. The compliant mechanism topology optimization method with complete hinge features according to claim 2, characterized in that, The expression of the area coverage rate of the fillet flexible hinge mechanism is as follows: Among them, represents the area coverage rate of the fillet flexible hinge mechanism, represents the area of the hinge region of the th basic component occupying the entire design domain, and the expression is as follows: Among them, represents the topological description function value of the hinge region of the basic component at the four nodes of the unit . represents the Heaviside function, represents the intersection area of the hinge region and the total area occupied by other components in the 4. The compliant mechanism topology optimization method with complete hinge features according to claim 1, characterized in that The expression of the optimization model is as follows: Among them, denotes the vector composed of all design variables of the th basic component; = 1, …, N; denotes the output displacement of the mechanism; denotes the virtual load acting in the direction of the output displacement; denotes the displacement vector generated by the virtual load ; denotes the load applied in the input direction; denotes the nodal displacement vector generated by the load acting in the input direction; denotes the global stiffness matrix; denotes the region occupied by the solid material in the design domain; denotes the th region occupied by the th basic component in the design domain; denotes the upper limit of the available volume of the solid material; denotes an adaptive relaxation coefficient, ; denotes the intersection area condensation function; T denotes the vector transpose symbol; dV denotes the volume element; U denotes the summation formula; P denotes the vector composed of design variables.

5. The compliant mechanism topology optimization method with complete hinge features according to claim 1, characterized in that The step of calculating the sensitivity information of the topological optimization problem of the fillet flexible hinge mechanism includes: Calculating the sensitivity of the topological optimization problem of the fillet flexible hinge mechanism by deriving the component design parameters; The expression of the sensitivity of the objective function to the design variables of the basic components is as follows: Denote the output displacement of the mechanism; Denote the displacement vector generated by the virtual load ; T denotes the vector transpose symbol; K denotes the global stiffness matrix; Denote the partial derivative; Denote the design variable of the basic component; Denote the nodal displacement vector generated by the load acting in the input direction ; The nodal displacement vector can be obtained through the equilibrium equation ; then we get: ​ Among them, , then the expression of the sensitivity of the output displacement to the design variables is as follows: The sensitivity of the global stiffness matrix with respect to the design variables is as follows: Among them, represents the elastic modulus of the material, represents the Heaviside function; c represents the penalty coefficient; represents the value of the topological description function of node j in element e the filtered function value; e represents the element; j represents the number of element nodes; represents the value of the topological description function is the element stiffness matrix corresponding to element e when = 1, …, 4, and ; NE represents the total number of elements in the design domain; then the expression of the sensitivity of the output displacement to the design variable is as follows: The expression of the sensitivity of the volume constraint function with respect to the design variable 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 variables is as follows: Among them, represents the intersection area aggregation function, NC represents the number of components in the design domain, represents the area of the intersection region, = 1 × When then the partial derivative with respect to the design variable is 0. When the expression of the sensitivity information of the topology optimization problem of the fillet flexible hinge mechanism is as follows: Among them, T ijk represents the topological description function values of the intersection region between the non-intersecting region of the i-th basic component and the total region occupied by other basic components at the four nodes of the element e.

6. The topology optimization method of the compliant mechanism with complete hinge features according to claim 1, characterized in that, The expression of the required topological description function is as follows: Where, Indicates The topological description function of the non-intersecting regions of the basic components is Indicates that except for When there are 1 basic component, it is the topological description function of the area occupied by other components. Indicates that a topological description function is needed. Indicates quantity, Represents the number of components in the design domain; The expression of the intersection area is as follows: Among them, represents the area of the intersection region, represents the Heaviside function, represents the component the topological description function values of the intersection region between the non-intersecting region of and the total area occupied by other components at the four nodes of the unit ; Condensing all the areas violating the intersection constraint through the intersection area condensation function, where the expression of the intersection area condensation function is as follows: Where, =1× Among them, represents the intersection area aggregation function, represents the intersection area between the hinge of the i-th basic component and other basic components.

7. The compliant mechanism topology optimization method with complete hinge features according to claim 1, characterized in that The expression of the initial topological description function is as follows: Among them, represents the coordinates of the center point of a single basic component in the local coordinate system; represents the th basic component in the direction of the half length; represents an even number; represents the th basic component in the global coordinate system of the center point coordinates; represents the th basic component of the local coordinate system relative to the global coordinate system of the inclination angle; represents the width function of the basic component; represents the initial topology description function; The expression of the width function is as follows: Where, Among them, represents the width function, and the variable , , all represent the thickness parameter of, L represents the half length of the basic component, represents the half length of the straight beam, and both represent the rounded corner part.

8. The compliant mechanism topology optimization method with complete hinge features according to claim 1, characterized in that The method further includes: Defining that the intersection area of the intersecting area of each basic component and the non-intersecting area of other basic components is 0.

9. A compliant mechanism topology optimization system with complete hinge features for implementing the compliant mechanism topology optimization method with complete hinge features according to any one of claims 1-8, characterized in that, The system includes: A defining module, configured to define the volume constraint and the intersection area constraint of the fillet flexible hinge mechanism, and define the non-intersecting area and the intersecting area of the basic components, where the basic components are the rods of the fillet flexible hinge mechanism; An adjusting module, configured to design an initial topological description function of the basic components based on the design parameters of the basic components, and adjust the initial topological description function based on the important parameters of the fillet flexible hinge mechanism to obtain the required topological description function of the intersecting area of the basic components; A establishing and calculating 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, calculate the sensitivity information of the topological optimization problem of the fillet flexible hinge mechanism, and obtain a topological graph containing complete flexible hinge features based on the sensitivity information.

10. The compliant mechanism topology optimization system with complete hinge features according to claim 9, characterized in that, The establishing and calculating module includes: A screening unit is used to use the geometric feature parameters of the basic components as design variables, based on the volume constraint and the intersection area constraint, and screen out the required basic components from multiple basic components according to the area coverage rate of the fillet flexible hinge mechanism. A establishing unit is used to impose an intersection area constraint on the non-intersecting regions of the required basic components to establish an optimization model with the maximum output displacement as the objective function.

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