A spline curve-based piezoelectric driver amplification mechanism design method, device, medium and product

Abstract

The application discloses a spline curve-based piezoelectric driver amplification mechanism design method, device, medium and product, relates to the technical field of piezoelectric drivers, and comprises the following steps: constructing a parameterized model of a piezoelectric driver amplification mechanism; taking model parameters of the parameterized model as individuals, taking a first maximum output displacement as an individual fitness value, and obtaining optimal model parameters of the parameterized model by using a genetic algorithm; taking the position of a third control point as an individual, taking a second maximum output displacement as an individual fitness value, and obtaining an optimal position of the third control point by using a genetic algorithm; constructing a spline curve by using the optimal model parameters and the optimal position of the third control point, and constructing an optimal parameterized model by taking part of the spline curve as an amplification arm. According to the application, the optimization target and constraint conditions can be adjusted according to working conditions, different design requirements can be met, loss in the amplification energy transmission process is reduced, and the output capacity of the piezoelectric driver under different design requirements is improved.

Description

Technical Field

[0001] This application relates to the field of piezoelectric actuator technology, and in particular to a design method, device, medium and product for a piezoelectric actuator amplification mechanism based on spline curves. Background Technology

[0002] The application of piezoelectric actuators in the aerospace field stems from the need for high precision, rapid response, lightweight design, and adaptability to complex environments. Traditional electromagnetic or hydraulic actuators, due to limitations such as large size, slow response, or susceptibility to electromagnetic interference, struggle to meet the performance requirements of aircraft under complex operating conditions. Piezoelectric actuators, with their nanometer-level positioning accuracy, millisecond-level response speed, and lack of electromagnetic interference, have become a key technology in the aerospace field. For example, in active vibration control, piezoelectric actuators can effectively counteract wing flutter and noise in real time.

[0003] While piezoelectric actuators offer advantages such as high precision and fast response, their inherently small output displacement (typically in the micrometer or submicrometer range) and limited output force restrict their direct application when large strokes (in the millimeter range) are required. The design background of piezoelectric amplification mechanisms is to resolve this contradiction by using mechanical structures or control strategies to convert the minute deformations of piezoelectric materials into larger displacements or force outputs, thereby expanding their application range.

[0004] In most cases, displacement amplification and force output of an actuator cannot be simultaneously achieved. For example, the displacement amplification factor and output force of a flexible hinge lever mechanism are approximately inversely proportional. Excessive geometric amplification design may lead to a sudden drop in driving force, or even fatigue failure due to stress concentration. Similarly, rhomboid displacement amplification actuators also suffer from this problem. Generally speaking, rhomboid displacement amplification actuators have two main structural forms: straight-arm rhomboid structures and curved-arm rhomboid structures. Straight-arm structures are simple in structure and easy to manufacture, but compared to curved-arm structures, their structural form is limited, and their output performance is often fixed once the length and width dimensions are determined. Curved-arm structures, on the other hand, can still achieve actuators with different design requirements by adjusting the curvature of the curved arm after the dimensions are determined. Currently, most curved-arm rhomboid mechanisms are circular curves, and circular curved arms also suffer from limited structural form and a very limited range of structural adjustments. Summary of the Invention

[0005] The purpose of this application is to provide a design method, device, medium and product for a piezoelectric actuator amplification mechanism based on spline curves, which can obtain a piezoelectric actuator that better meets the application requirements through two genetic algorithm optimizations.

[0006] To achieve the above objectives, this application provides the following solution:

[0007] In a first aspect, this application provides a design method for a piezoelectric actuator amplification mechanism based on spline curves, including:

[0008] A parametric model of the piezoelectric actuator amplification mechanism is constructed; the model parameters of the parametric model include: coordinates of point B and coordinates of point C; the coordinates of point B are the coordinates of the upper end of the stacked left mounting end of the piezoelectric actuator amplification mechanism; the coordinates of point C are the coordinates of the left end of the upper output end;

[0009] Using the model parameters of the parameterized model as individuals and the first maximum output displacement as the individual fitness value, the optimal model parameters of the parameterized model are obtained using a genetic algorithm; wherein, the first maximum output displacement is obtained by finite element analysis of the model parameters and material properties of the parameterized model; the optimal model parameters include: the optimal coordinates of point B and the optimal coordinates of point C;

[0010] Using the position of the third control point as an individual and the second maximum output displacement as the individual fitness value, a genetic algorithm is used to obtain the optimal position of the third control point. The second maximum output displacement is obtained through finite element analysis of the parameterized model constructed by the magnifying arm and the material properties. The method for obtaining the magnifying arm includes: constructing a spline curve using the three control points, and using the curve between the first and second control points in the spline curve as the magnifying arm in the parameterized model; the optimal coordinates of point B are the first control point, the optimal coordinates of point C are the second control point, and the position of the third control point is randomly generated.

[0011] Using the optimal model parameters and the optimal position of the third control point, a spline curve is constructed, and the curve between the optimal coordinates of point B and the optimal coordinates of point C in the spline curve is used as an arm to construct the optimal parameterized model.

[0012] Optionally, the construction of the parameterized model of the piezoelectric actuator amplification mechanism specifically includes:

[0013] A rectangular coordinate system is constructed with the geometric center of the piezoelectric actuator amplification mechanism as the origin, the right mounting end of the stack as the x-axis, and the upper output end as the y-axis.

[0014] Define the center position of the left mounting end of the stack as point A, the top end of the left mounting end of the stack as point B, the left end point of the upper output end as point C, and the midpoint of the upper output end as point D.

[0015] Given the coordinates of point A (-x1, 0), point B (-x1, y1), point C (-x2, y2), and point D (0, y2), a set of lines is obtained; the set of lines includes lines AB, BC, and CD.

[0016] The set of lines is mirrored along the x-axis to obtain a copied set of lines;

[0017] The set of copied lines is mirrored along the y-axis to obtain a set of rhomboid lines.

[0018] Assigning length and width attributes (x3, y3) to the set of rhomboid lines, we obtain a parameterized model of the piezoelectric actuator amplification mechanism.

[0019] Optionally, using the model parameters of the parameterized model as individuals and the first maximum output displacement as the individual fitness value, a genetic algorithm is used to obtain the optimal model parameters of the parameterized model, specifically including:

[0020] Constraints are set for the model parameters of the parameterized model; the model parameters include: x1, y1, x2, y2, x3, and y3;

[0021] Set the fitness function to the first maximum output displacement;

[0022] Initialize the population; each individual in the population is a parameter of the model.

[0023] Using each individual, a parametric model is called to generate a simulation model, and finite element analysis is performed on the simulation model to obtain the individual fitness value of each individual;

[0024] After randomly selecting individuals, simulating binary crossover and polynomial mutation, a new generation of population is generated, and the process returns to the step of "using each individual, calling the parameterized model to generate a simulation model, and performing finite element analysis on the simulation model to obtain the individual fitness value of each individual" until the maximum number of iterations is reached or the difference in individual fitness values ​​between the two generations of best individuals is less than a preset threshold, at which point the optimal model parameters are obtained.

[0025] Optionally, using the optimal model parameters and the optimal position of the third control point, a spline curve is constructed, and the curve between the optimal coordinates of point B and the optimal coordinates of point C in the spline curve is used as an arm to construct the optimal parameterized model, specifically including:

[0026] When the optimal model parameters are: optimal B point coordinates (-x10, y10), optimal C point coordinates (-x20, y20), and length and width attributes (x30, y30);

[0027] Using (-x10,0) as the coordinates of point A and (0,y20) as the coordinates of point D, the optimal set of lines is obtained; the optimal set of lines includes lines AB, BC, and CD.

[0028] By using the curve between the optimal coordinates of point B and the optimal coordinates of point C in the spline curve, the straight line BC is replaced to obtain the optimal set of curves;

[0029] The optimal curve set is mirrored along the x-axis to obtain a copied curve set;

[0030] The set of replicated curves is mirrored along the y-axis to obtain the optimal set of diamond curves.

[0031] By assigning length and width attributes (x30, y30) to the optimal rhomboid curve set, the optimal parameterized model of the piezoelectric actuator amplification mechanism is obtained.

[0032] Optionally, the step of using each individual to call the parameterized model to generate a simulation model, and performing finite element analysis on the simulation model to obtain the individual fitness value of each individual specifically includes:

[0033] Each individual is input as a parameter into the parameterized model to obtain the simulation model;

[0034] Based on the simulation model, material properties, analysis steps, boundary conditions, and output parameters are set, and finite element analysis is performed to obtain the individual fitness value of each individual.

[0035] Optionally, using the position of the third control point as an individual and the second maximum output displacement as the individual's fitness value, a genetic algorithm is used to obtain the optimal position of the third control point, specifically including:

[0036] Set constraints on the position of the third control point;

[0037] Set the fitness function to the second maximum output displacement;

[0038] Initialize the population; each individual in the population represents the position of the third control point;

[0039] By combining the optimal coordinates of point B and the optimal coordinates of point C for each individual, a spline curve is constructed;

[0040] The curve between the optimal coordinates of point B and the optimal coordinates of point C in the spline curve is used as the magnifying arm in the parametric model, and a simulation model of the parametric model is constructed to obtain the curved arm simulation model.

[0041] Finite element analysis was performed on the curved arm simulation model to obtain the individual fitness value of each individual.

[0042] After randomly selecting, simulating binary crossover and polynomial mutation of the individuals, a new generation of population is generated, and the process returns to the step of "constructing a spline curve by combining the optimal coordinates of point B and the optimal coordinates of point C with each individual" until the maximum number of iterations is reached or the difference in fitness values ​​between the two generations of best individuals is less than a preset threshold, at which point the optimal position of the third control point is obtained.

[0043] Optionally, constraints are set on the position of the third control point, specifically including:

[0044] When the position of the third control point is (x4, y4), the constraint conditions are (-x10 < x4 < x10; y4 < 0), where (-x10, y10) are the coordinates of the optimal point B.

[0045] In a second aspect, the present application provides a computer device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor executes the computer program to implement the method for designing a piezoelectric actuator amplification mechanism based on a spline curve described in any one of the above.

[0046] In a third aspect, the present application provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the method for designing a piezoelectric actuator amplification mechanism based on a spline curve described in any one of the above.

[0047] In a fourth aspect, the present application provides a computer program product, including a computer program, and when the computer program is executed by a processor, it implements the method for designing a piezoelectric actuator amplification mechanism based on a spline curve described in any one of the above.

[0048] According to the specific embodiments provided by the present application, the following technical effects are disclosed in the present application:

[0049] This application provides a design method, device, medium, and product for a piezoelectric actuator amplification mechanism based on spline curves. The method includes: constructing a parametric model of the piezoelectric actuator amplification mechanism; the model parameters of the parametric model include: coordinates of point B and point C; the coordinates of point B are the coordinates of the upper endpoint of the stacked left mounting end of the piezoelectric actuator amplification mechanism; the coordinates of point C are the coordinates of the left endpoint of the upper output end; using the model parameters of the parametric model as individuals, and the first maximum output displacement as the individual fitness value, the optimal model parameters of the parametric model are obtained using a genetic algorithm; wherein, the first maximum output displacement is obtained by finite element analysis of the model parameters and material properties of the parametric model; the optimal model parameters include: optimal coordinates of point B and optimal coordinates of point C; and using a third control point... The position of the individual is taken as the individual's fitness value, and the optimal position of the third control point is obtained using a genetic algorithm. The second maximum output displacement is obtained by finite element analysis of the parameterized model constructed from the amplification arm and its material properties. The method for obtaining the amplification arm includes: constructing a spline curve using three control points, and using the curve between the first and second control points in the spline curve as the amplification arm in the parameterized model; the optimal B-point coordinates are the first control point, the optimal C-point coordinates are the second control point, and the position of the third control point is randomly generated; using the optimal model parameters and the optimal position of the third control point, a spline curve is constructed, and the curve between the optimal B-point coordinates and the optimal C-point coordinates in the spline curve is used as the amplification arm to construct the optimal parameterized model. This application optimizes the piezoelectric actuator amplification mechanism through two genetic algorithms. First, an optimization algorithm obtains a straight arm structure that meets the constraints of size, output displacement, and output force. Then, based on the straight arm structure, "straight arm → spline curved arm" optimization is performed according to the usage requirements of different working conditions, finally obtaining a piezoelectric actuator that better meets the usage requirements. This design method can adjust and optimize objectives and constraints according to the operating conditions to meet different design requirements, thereby reducing losses in the energy transfer process and improving the output capability of the piezoelectric actuator under different design requirements. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 This is a schematic diagram of a rhomboid piezoelectric actuator amplification mechanism provided in an embodiment of this application.

[0052] Figure 2This is a flowchart illustrating a design method for a piezoelectric actuator amplification mechanism based on spline curves, provided in one embodiment of this application.

[0053] Figure 3 This is a schematic diagram of global dimension parameters and cross-sectional parameters provided for an embodiment of this application.

[0054] Figure 4 This is a schematic diagram of a driver structure provided in an embodiment of this application.

[0055] Figure 5 This is a schematic diagram of a spline curve-based design method provided in an embodiment of this application.

[0056] Figure 6 This is a flowchart illustrating a design method for a piezoelectric actuator amplification mechanism based on spline curves, provided as another embodiment of this application.

[0057] Figure 7 A schematic diagram of the straight arm structure obtained after the first optimization, provided for another embodiment of this application.

[0058] Figure 8 This is a schematic diagram of a spline curve-based articulated arm structure provided for another embodiment of this application.

[0059] Figure 9 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0060] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0061] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0062] In most cases, displacement amplification and force output of an actuator cannot be simultaneously achieved. For example, the displacement amplification factor and output force of a flexible hinge lever mechanism are approximately inversely proportional; excessive geometric amplification may lead to a sudden drop in driving force, or even fatigue failure due to stress concentration. Similarly, rhomboid displacement amplification actuators also suffer from this problem. Generally speaking, rhomboid displacement amplification actuators have roughly two structural forms: a straight-arm rhomboid structure and a curved-arm rhomboid structure, as follows: Figure 1As shown. Straight arms are simple in structure and easy to manufacture, but compared to articulated arms, their structural form is limited; once the length and width are determined, their output performance is also fixed. In contrast, articulated arms, even with fixed dimensions, can still achieve actuators with different design requirements by adjusting the curvature of the arm. Currently, most articulated arm rhomboid mechanisms are circular curves, which also suffer from limited structural form and a very limited range of structural adjustments. Therefore, this application proposes a design method for a piezoelectric actuator amplification mechanism based on spline curves. This method first obtains a straight arm structure that meets the constraints of size, output displacement, and output force through an optimization algorithm. Then, based on the straight arm structure, it performs "straight arm → spline articulated arm" optimization according to the usage requirements of different working conditions, finally obtaining a piezoelectric actuator that better meets the usage requirements.

[0063] In the field of piezoelectric drive technology, the displacement amplification mechanism is the core component for energy transfer, and its performance directly affects the output efficiency of the actuator. Traditional amplification mechanisms (such as levers and flexible hinges) often suffer energy loss and reduce overall efficiency due to friction, material deformation, or unreasonable structural design when amplifying displacement.

[0064] To address these technical challenges, this application constructs a spline curve-based method for describing the geometric shape of amplification mechanisms. By calling parametric modeling scripts, parametric modeling and analysis of the amplification mechanism are performed. This method employs a modular parametric modeling framework, integrating parametric scripts and a finite element simulation platform to establish the correspondence between geometric parameters and performance indicators. Therefore, this design method can adjust and optimize objectives and constraints according to the operating conditions to meet different design requirements, thereby reducing losses during the amplified energy transfer process and improving the output capability of the piezoelectric actuator under different design requirements.

[0065] In one exemplary embodiment, such as Figure 2 As shown, a design method for a piezoelectric actuator amplification mechanism based on spline curves is provided, including the following steps S1 to S4. Wherein:

[0066] S1. Construct a parametric model of the piezoelectric actuator amplification mechanism; the model parameters of the parametric model include: coordinates of point B and coordinates of point C; the coordinates of point B are the coordinates of the upper end of the stacked left mounting end of the piezoelectric actuator amplification mechanism; the coordinates of point C are the coordinates of the left end of the upper output end.

[0067] The construction of a parameterized model for the piezoelectric actuator amplification mechanism specifically includes:

[0068] A rectangular coordinate system is constructed with the geometric center of the piezoelectric actuator amplification mechanism as the origin, the right mounting end of the stack as the x-axis, and the upper output end as the y-axis.

[0069] Define point A as the center of the left mounting end of the stack, point B as the top of the left mounting end of the stack, point C as the left endpoint of the upper output end, and point D as the midpoint of the upper output end.

[0070] Given the coordinates of point A (-x1, 0), point B (-x1, y1), point C (-x2, y2), and point D (0, y2), a set of lines is obtained; the set of lines includes lines AB, BC, and CD.

[0071] The set of lines is mirrored along the x-axis to obtain a copied set of lines.

[0072] The set of copied lines is mirrored along the y-axis to obtain a set of rhomboid lines.

[0073] Assigning length and width attributes (x3, y3) to the rhombic line set yields the parametric model of the piezoelectric actuator amplification mechanism. Here, the length and width attributes refer to the length and width of the cross-section. The previous steps created lines; assigning cross-sectional attributes (length and width attributes) to these lines creates the solid model. This process is similar to that of creating beam elements.

[0074] Specifically, in this embodiment, the parameters of the piezoelectric actuator displacement amplification mechanism are determined as follows:

[0075] For a rhomboid piezoelectric actuator, its amplification mechanism can be divided into three parts: the stacked mounting end, the amplification arm, and the output end (the structure is fixedly connected; the structural form can be referenced). Figure 1 , Figure 1 (This is a front view of the structure). See below. Figure 3 As shown, to parameterize the rhombus amplification mechanism, the 1 / 4 rhombus is divided into four endpoints: A, B, C, and D. AB is the left mounting end of the 1 / 2 stack, BC is the upper left amplification arm, and CD is the upper output end of the 1 / 2 stack. Therefore, parameterizing the coordinates of points A, B, C, and D, as well as the length and width of the cross-section, completes the parameterization of the entire rhombus structure, requiring six parameters: x1, y1, x2, y2, x3, and y3.

[0076] Construct a parametric model of the driver amplification mechanism:

[0077] Using the coordinates of the four endpoints A, B, C, and D (A(-x1,0), B(-x1,y1), C(-x2,y2), D(0,y2), we obtain the lines AB, BC, and CD. Then, we perform a mirror copy based on the axes x=0 and y=0. Finally, we assign the length and width attributes (x3, y3) to the rhombus cross-section to obtain its simulation model.

[0078] S2. Using the model parameters of the parameterized model as individuals and the first maximum output displacement as the individual fitness value, the optimal model parameters of the parameterized model are obtained using a genetic algorithm; wherein, the first maximum output displacement is obtained by finite element analysis of the model parameters and material properties of the parameterized model; the optimal model parameters include: the optimal coordinates of point B and the optimal coordinates of point C.

[0079] The specific steps include:

[0080] Constraints are set for the model parameters of the parameterized model; the model parameters include: x1, y1, x2, y2, x3, and y3.

[0081] Set the fitness function to the first maximum output displacement.

[0082] Initialize the population; each individual in the population is a parameter of the model.

[0083] Using each individual, a parametric model is called to generate a simulation model, and finite element analysis is performed on the simulation model to obtain the individual fitness value of each individual.

[0084] After randomly selecting individuals, simulating binary crossover and polynomial mutation, a new generation of population is generated, and the process returns to the step of "using each individual, calling the parameterized model to generate a simulation model, and performing finite element analysis on the simulation model to obtain the individual fitness value of each individual" until the maximum number of iterations is reached or the difference in individual fitness values ​​between the two generations of best individuals is less than a preset threshold, at which point the optimal model parameters are obtained.

[0085] The output is the obtained optimal model parameters (x10, y10, x20, y20, x30, y30). (This result is a...) Figure 1 (The straight arm structure shown above).

[0086] In this embodiment, parameter optimization is performed using a genetic algorithm. This involves setting constraints, initializing the population, evaluating fitness, performing selection, crossover, mutation, and replacement operations, and setting termination conditions to obtain a set of approximate optimal solutions. The specific process is as follows:

[0087] Six key geometric parameters of the rhombic displacement amplification mechanism were optimized:

[0088] x1: X coordinate of point A / B (determines the length of the magnifying arm);

[0089] y1: Y coordinate of point B (determines the height of the stacked installation end);

[0090] x2: X-coordinate of point C (determines the length of the output terminal);

[0091] y2: Y coordinate of point C / D (determines the height of the magnifying arm);

[0092] x3: Cross-sectional width;

[0093] y3: Cross-sectional height;

[0094] Set constraints: Apply constraints to each parameter, for example, 90≤x1≤130; 7≤y1≤10; 5≤x2≤6; 15≤y2≤30; x3=3, y3=15. (Design according to design requirements).

[0095] Set the fitness function: first maximum output displacement maxU.

[0096] Genetic algorithm optimization process:

[0097] Initialize the population size: for example, generate 50 individuals.

[0098] For each generated individual, the following steps are performed: call the parameterized model to generate a simulation model; perform simulation analysis; calculate the fitness value maxU for each individual.

[0099] Perform selection manipulation (random selection), crossover manipulation (simulated binary crossover), and mutation manipulation (polynomial mutation).

[0100] Generate a new generation of population (the population size is the same as the initial size).

[0101] Repeat the above process.

[0102] Termination condition: The maximum number of iterations is reached or the difference in fitness between the two generations of best individuals is less than 0.001.

[0103] Specifically, the process of using each individual to generate a simulation model by calling a parameterized model, and performing finite element analysis on the simulation model to obtain the individual fitness value for each individual includes:

[0104] Each individual is input as a parameter into the parameterized model to obtain the simulation model; based on the simulation model, material properties, analysis steps, boundary conditions, and output parameters are set, and finite element analysis is performed to obtain the individual fitness value of each individual.

[0105] The specific steps of the finite element analysis in this embodiment include:

[0106] Set material properties, analysis steps, boundary conditions, output parameters, mesh, and perform finite element analysis. See below. Figure 4 As shown, Figure 4 The main body is a piezoelectric actuator, in which the piezoelectric stack is the output element. Its principle is that when energized, it generates a displacement in the x-direction. This displacement is amplified by an external displacement amplification structure and output from the output terminal in the y-direction. This embodiment mainly focuses on the external amplification mechanism; therefore, the piezoelectric stack is simplified to x-direction displacement.

[0107] The input data includes:

[0108] Material properties (steel): Elastic modulus E = 2.1 × 10¹¹ Pa; Poisson's ratio ν = 0.3;

[0109] Density ρ = 7.9 × 10³ (kg / m³) 3 );

[0110] Boundary conditions: The fixed section is completely fixed; input ΔL_left = -0.1mm at the left stacking end; input ΔL_right = +0.1mm at the right stacking end;

[0111] Analysis step settings: Perform static analysis.

[0112] Output: The average value of the y-direction displacement of all nodes on the output plane.

[0113] S3. Using the position of the third control point as an individual and the second maximum output displacement as the individual fitness value, the optimal position of the third control point is obtained using a genetic algorithm; wherein, the second maximum output displacement is obtained by finite element analysis of the parameterized model constructed by the magnifying arm and the material properties; the method for obtaining the magnifying arm includes: constructing a spline curve using three control points, and using the curve between the first and second control points in the spline curve as the magnifying arm in the parameterized model; the coordinates of the optimal B point are the first control point, the coordinates of the optimal C point are the second control point, and the position of the third control point is randomly generated.

[0114] In this embodiment, a parameterized model of the crank arm amplification mechanism is established based on the obtained optimal model parameters. Figure 1 (The curved arm structure shown below).

[0115] Using the optimal model parameters C(x20, y20) and B(x10, y10) as control point 1 (first control point) and control point 2 (second control point), respectively, these two control points are constants. That is, given a fixed length and width of the magnifying arm, the magnification is further increased by changing the third control point of the spline curve, thus transforming the straight line into a curve. For example... Figure 5 As shown, control points 1 and 2 are points C and B mentioned above. The structure of the magnifying arm (spline curve arm) depends on the position of the third control point. The figure illustrates three magnifying arms determined by three different control points 3 (the third control point). (An interpolated spline curve can be obtained by giving a series of control points. The shape of the curve is controlled by these points, and the curve must pass through these control points.)

[0116] The method for establishing the parametric model of the crank arm amplification mechanism is as follows: Delete the straight line BC of the model constructed above, and establish a spline curve with the above three control points. The spline curve is divided into two segments, where the line segment between control point 1 and control point 2 is used as the amplification arm ( Figure 5 the solid line segment part), and the line segment between control point 2 and control point 3 ( Figure 5 the dashed line segment part) is deleted.

[0117] Therefore, the parametric model of the crank arm amplification mechanism is determined by the coordinates (x4, y4) of control point 3, and x4 and y4 are the new optimization parameters for further optimization.

[0118] Set the material properties, analysis steps, boundary conditions, output parameters, mesh division, and perform finite element analysis on the new model in the same way as in step S2. And perform a new round of genetic algorithm optimization in the same way. However, the optimization object in this step is (x4, x5), and the constraints are -x10 < x4 < x10; y4 < 0. The rest is the same. Finally, the final structure is obtained.

[0119] Specifically, taking the position of the third control point as an individual and the second largest output displacement as the individual fitness value, use the genetic algorithm to obtain the optimal position of the third control point, specifically including:

[0120] Set constraint conditions for the position of the third control point. When the position of the third control point is (x4, y4), the constraint conditions are (-x10 < x4 < x10; y4 < 0), where (-x10, y10) is the optimal coordinate of point B.

[0121] Set the fitness function as the second largest output displacement.

[0122] Initialize the population; each individual in the population is the position of the third control point.

[0123] Use each individual to combine the optimal coordinates of point B and the optimal coordinates of point C to construct a spline curve.

[0124] Take the curve between the optimal coordinates of point B and the optimal coordinates of point C in the spline curve as the amplification arm in the parametric model, and construct a simulation model of the parametric model to obtain a crank arm simulation model.

[0125] Perform finite element analysis on the crank arm simulation model to obtain the individual fitness value of each individual.

[0126] After randomly selecting, simulated binary crossover, and polynomial mutation on the individuals, generate a new generation of population, and return to the step of "Use each individual to combine the optimal coordinates of point B and the optimal coordinates of point C to construct a spline curve" until the maximum number of iterations is reached or the difference between the individual fitness values of the two best individuals is less than the preset threshold, and then obtain the optimal position of the third control point.

[0127] This embodiment uses three spline interpolation control points, as follows: Figure 5 The design method for the rhomboid structure of the mid-spline curved arm is shown. The positions of control points 1 and 2 are determined by the optimal coordinates of point B and point C, respectively. Control point 3 is located to the lower right of control points 1 and 2. Adjusting the curved arm structure using this method primarily involves changing the position of control point 3. The figure illustrates how different positions of control point 3 alter the curved arm structure. The amplification mechanism adjusted using this method can achieve functions such as increasing output displacement, improving stiffness, increasing the first-order modal frequency, and increasing blocking force.

[0128] S4. Using the optimal model parameters and the optimal position of the third control point, construct a spline curve, and use the curve between the optimal coordinates of point B and the optimal coordinates of point C in the spline curve as an arm to construct the optimal parameterized model. Specifically, this can be done according to the following steps:

[0129] When the optimal model parameters are: optimal B point coordinates (-x10, y10), optimal C point coordinates (-x20, y20), and length and width attributes (x30, y30);

[0130] Using (-x10,0) as the coordinates of point A and (0,y20) as the coordinates of point D, the optimal set of lines is obtained; the optimal set of lines includes lines AB, BC, and CD.

[0131] By using the curve between the optimal coordinates of point B and the optimal coordinates of point C in the spline curve, the straight line BC is replaced to obtain the optimal set of curves;

[0132] The optimal curve set is mirrored along the x-axis to obtain a copied curve set;

[0133] The set of replicated curves is mirrored along the y-axis to obtain the optimal set of diamond curves.

[0134] By assigning length and width attributes (x30, y30) to the optimal rhomboid curve set, the optimal parameterized model of the piezoelectric actuator amplification mechanism is obtained.

[0135] To address the issue that traditional straight-arm and curved-arm rhomboid amplification mechanisms have limited structural options and cannot adequately meet the demands of complex applications, this embodiment proposes a spline curve-based design method for piezoelectric actuator amplification mechanisms. This method first uses an optimization algorithm to obtain a straight-arm structure that satisfies constraints such as size, output displacement, and output force. Then, based on the straight-arm structure, adjustments are made from straight arm to curved arm according to the specific requirements of different operating conditions. The advantage of this method is that it allows for targeted adjustments to the amplification mechanism of the piezoelectric actuator based on design requirements, and multiple structural forms of the curved-arm rhomboid structure can be designed by simply changing the position of a single control point. Therefore, this method is simple, efficient, and allows the actuator to better adapt to specific application scenarios. For example, if the optimized straight-arm actuator performs well under one condition but poorly under another, and the installation conditions cannot be changed, altering the size to improve performance is not feasible. In this case, changing the straight-arm shape is necessary to improve the actuator's output performance. Therefore, this method holds significant promise in fields such as aerospace.

[0136] In another exemplary embodiment of this application, such as Figure 6 As shown, a design method for a piezoelectric actuator amplification mechanism based on spline curves is provided, which specifically includes the following steps:

[0137] Step 1: Determine the parameters of the piezoelectric actuator displacement amplification mechanism.

[0138] like Figure 3 As shown, in order to parameterize the rhombus-shaped magnifying mechanism, the 1 / 4 rhombus is divided into four endpoints: A, B, C, and D. AB is the left mounting end of the 1 / 2 stack, BC is the upper left magnifying arm, and CD is the upper output end of the 1 / 2 stack. Therefore, the coordinates of the four points A, B, C, and D, as well as the length and width of the cross-section, are parameterized into an array (x1, y1, x2, y2, x3, y3).

[0139] Step 2: Construct a parametric model of the driver amplification mechanism.

[0140] The array (x1,y1,x2,y2,x3,y3) is transformed into coordinates (-x1,0), (-x1,y1), (-x2,y2), and (0,y2) to obtain lines AB, BC, and CD. Then, a mirror copy is performed based on the axes x=0 and y=0. Finally, the length and width attributes (x3, y3) of the rhombus cross section are assigned to obtain the simulation model.

[0141] Step 3: Set material properties, analysis step, boundary conditions, output parameters, mesh, and perform finite element analysis. The structural material properties are set to a density of 7900 kg / m³, a modulus of 210000 MPa, and a Poisson's ratio of 0.3. The analysis unit is a static general-purpose analysis unit. The boundary conditions are: the lower output end is completely fixed, and the left and right fixed ends each input a displacement of 0.1 mm in opposite directions. The mesh uses a structural mesh, and the output parameters are set to displacement output.

[0142] Step 4: Optimize using a genetic algorithm, which involves setting constraints, initializing the population, evaluating fitness, performing selection, crossover, mutation, and replacement operations, and setting termination conditions to obtain a set of near-optimal solutions.

[0143] The constraints are set (in mm): 90≤x1≤130; 7≤y1≤10; 5≤x2≤6; 15≤y2≤30; x3=3, y3=15.

[0144] The population size is set to 20, the fitness is the maximum output displacement, the selection operation is a random uniform function, the crossover operation is a single-point crossover, the mutation operation is achieved by flipping gene loci, the replacement operation is a full replacement, and the termination condition is to terminate after reaching the maximum number of iterations of 50 or when the fitness function improves after more than 15 generations.

[0145] Step 5: Output the solution obtained in Step 4, approximately (128.5, 10, 5, 15, 3, 15). The constructed model is as follows. Figure 7 As shown, the output displacement is 3.76 mm.

[0146] Step 6: Set the endpoints of the magnifying arm as the first two control points (0,15) and (-128.5,10), and the third control point as (-5,5). The final result is as follows. Figure 8 As shown, the output displacement is 3.88, which is an improvement over the output displacement of the straight arm structure with parameters (128.5,10,5,15,3,15).

[0147] This embodiment describes the geometric shape of the rhombic amplification mechanism based on B-spline curves and conducts optimization design according to the design objectives. The spline curves used only have 3 control points, and more complex structural forms can be achieved by adding control points.

[0148] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 9As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operating system and computer programs stored in the non-volatile storage media to run. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network connection. When the computer program is executed by the processor, it implements a design method for a piezoelectric actuator amplification mechanism based on spline curves.

[0149] Those skilled in the art will understand that Figure 9 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0150] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0151] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0152] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0153] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0154] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0155] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0156] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0157] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A design method for a piezoelectric actuator amplification mechanism based on spline curves, characterized in that, include: Construct a parametric model of the piezoelectric actuator amplification mechanism; The model parameters of the parameterized model include: coordinates of point B and coordinates of point C; the coordinates of point B are the coordinates of the upper end of the stacked left mounting end of the piezoelectric actuator amplification mechanism; the coordinates of point C are the coordinates of the left end of the upper output end. Using the model parameters of the parameterized model as individuals and the first maximum output displacement as the individual fitness value, the optimal model parameters of the parameterized model are obtained using a genetic algorithm; wherein, the first maximum output displacement is obtained by finite element analysis of the model parameters and material properties of the parameterized model; the optimal model parameters include: the optimal coordinates of point B and the optimal coordinates of point C; Using the position of the third control point as an individual and the second maximum output displacement as the individual fitness value, a genetic algorithm is used to obtain the optimal position of the third control point. The second maximum output displacement is obtained through finite element analysis of the parameterized model constructed by the magnifying arm and the material properties. The method for obtaining the magnifying arm includes: constructing a spline curve using the three control points, and using the curve between the first and second control points in the spline curve as the magnifying arm in the parameterized model; the optimal coordinates of point B are the first control point, the optimal coordinates of point C are the second control point, and the position of the third control point is randomly generated. Using the optimal model parameters and the optimal position of the third control point, a spline curve is constructed, and the curve between the optimal coordinates of point B and the optimal coordinates of point C in the spline curve is used as an arm to construct the optimal parameterized model.

2. The design method for a piezoelectric actuator amplification mechanism based on spline curves according to claim 1, characterized in that, The parameterized model for constructing the piezoelectric actuator amplification mechanism specifically includes: A rectangular coordinate system is constructed with the geometric center of the piezoelectric actuator amplification mechanism as the origin, the right mounting end of the stack as the x-axis, and the upper output end as the y-axis. Define the center position of the left mounting end of the stack as point A, the top end of the left mounting end of the stack as point B, the left end point of the upper output end as point C, and the midpoint of the upper output end as point D. Given the coordinates of point A (-x1, 0), point B (-x1, y1), point C (-x2, y2), and point D (0, y2), a set of lines is obtained; the set of lines includes lines AB, BC, and CD. The set of lines is mirrored along the x-axis to obtain a copied set of lines; The set of copied lines is mirrored along the y-axis to obtain a set of rhomboid lines. Assigning length and width attributes (x3, y3) to the set of rhomboid lines, we obtain a parameterized model of the piezoelectric actuator amplification mechanism.

3. The design method for a piezoelectric actuator amplification mechanism based on spline curves according to claim 2, characterized in that, Using the model parameters of the parameterized model as individuals and the first maximum output displacement as the individual fitness value, the optimal model parameters of the parameterized model are obtained using a genetic algorithm, specifically including: Constraints are set for the model parameters of the parameterized model; the model parameters include: x1, y1, x2, y2, x3, and y3; Set the fitness function to the first maximum output displacement; Initialize the population; each individual in the population is a parameter of the model. Using each individual, a parametric model is called to generate a simulation model, and finite element analysis is performed on the simulation model to obtain the individual fitness value of each individual; After randomly selecting individuals, simulating binary crossover and polynomial mutation, a new generation of population is generated, and the process returns to the step of "using each individual, calling the parameterized model to generate a simulation model, and performing finite element analysis on the simulation model to obtain the individual fitness value of each individual" until the maximum number of iterations is reached or the difference in individual fitness values ​​between the two generations of best individuals is less than a preset threshold, at which point the optimal model parameters are obtained.

4. The design method for a piezoelectric actuator amplification mechanism based on spline curves according to claim 3, characterized in that, Using the optimal model parameters and the optimal position of the third control point, a spline curve is constructed. The curve between the optimal coordinates of point B and the optimal coordinates of point C is then used as an arm to construct the optimal parameterized model. Specifically, this includes: When the optimal model parameters are: optimal B point coordinates (-x10, y10), optimal C point coordinates (-x20, y20), and length and width attributes (x30, y30); Using (-x10,0) as the coordinates of point A and (0,y20) as the coordinates of point D, the optimal set of lines is obtained; the optimal set of lines includes lines AB, BC, and CD. By using the curve between the optimal coordinates of point B and the optimal coordinates of point C in the spline curve, the straight line BC is replaced to obtain the optimal set of curves; The optimal curve set is mirrored along the x-axis to obtain a copied curve set; The set of replicated curves is mirrored along the y-axis to obtain the optimal set of diamond curves. By assigning length and width attributes (x30, y30) to the optimal rhomboid curve set, the optimal parameterized model of the piezoelectric actuator amplification mechanism is obtained.

5. The design method for a piezoelectric actuator amplification mechanism based on spline curves according to claim 3, characterized in that, The process involves using each individual to generate a simulation model by calling a parametric model, and then performing finite element analysis on the simulation model to obtain the individual fitness value for each individual. Specifically, this includes: Each individual is input as a parameter into the parameterized model to obtain the simulation model; Based on the simulation model, material properties, analysis steps, boundary conditions, and output parameters are set, and finite element analysis is performed to obtain the individual fitness value of each individual.

6. The design method for a piezoelectric actuator amplification mechanism based on spline curves according to claim 1, characterized in that, Using the position of the third control point as an individual and the second maximum output displacement as the individual's fitness value, a genetic algorithm is used to obtain the optimal position of the third control point, specifically including: Set constraints on the position of the third control point; Set the fitness function to the second maximum output displacement; Initialize the population; each individual in the population represents the position of the third control point; By combining the optimal coordinates of point B and the optimal coordinates of point C for each individual, a spline curve is constructed; The curve between the optimal coordinates of point B and the optimal coordinates of point C in the spline curve is used as the magnifying arm in the parametric model, and a simulation model of the parametric model is constructed to obtain the curved arm simulation model. Finite element analysis was performed on the curved arm simulation model to obtain the individual fitness value of each individual. After randomly selecting, simulating binary crossover and polynomial mutation of the individuals, a new generation of population is generated, and the process returns to the step of "constructing a spline curve by combining the optimal coordinates of point B and the optimal coordinates of point C with each individual" until the maximum number of iterations is reached or the difference in fitness values ​​between the two generations of best individuals is less than a preset threshold, at which point the optimal position of the third control point is obtained.

7. The design method for a piezoelectric actuator amplification mechanism based on spline curves according to claim 1, characterized in that, Setting constraints on the position of the third control point specifically includes: When the position of the third control point is (x4, y4), the constraint conditions are (-x10 < x4 < x10; y4 < 0), where (-x10, y10) are the coordinates of the optimal point B.

8. A computer device, comprising: A memory, a processor, and a computer program stored on the memory and capable of running on the processor, characterized in that the processor executes the computer program to implement the design method of the spline curve-based piezoelectric actuator amplification mechanism according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the design method of the spline curve-based piezoelectric actuator amplification mechanism according to any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the design method of the spline curve-based piezoelectric actuator amplification mechanism according to any one of claims 1-7.

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