Rapid reverse design method for torsional quasi-zero stiffness vibration isolator based on curved beam

Abstract

The invention belongs to the technical field of vibration suppression, and particularly relates to a rapid reverse design method for a torsional quasi-zero stiffness vibration isolator based on a curved beam. The method specifically comprises the steps that an inner ring and an outer ring of the vibration isolator are simplified into rigid bodies, a multi-control-point curve is used for representing a curved beam, and a head control point and a tail control point are fixed to the rigid bodies of the inner ring and the outer ring; setting boundary conditions at two ends of the curved beam; curved beam shape-torque data acquisition: applying angular displacement to the inner end of the curved beam model, and acquiring corresponding torque values of different curved beam shapes under equal-interval angular displacement by adjusting the positions and weights of multiple control points; constructing a network model, and performing network model training by using the data set; the trained network model is combined with a heuristic algorithm, geometric parameters of the curved beam are obtained through the heuristic algorithm and input into the network model, a corresponding torque value is obtained, adaptability evaluation is conducted through the heuristic algorithm, and the optimal curved beam shape is obtained through circulating and returning.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of vibration suppression, and particularly relates to a fast reverse design method of a torsional quasi-zero stiffness vibration isolator based on a curved beam. BACKGROUND

[0002] Vibration is widespread in various engineering fields, but its adverse effects cannot be ignored. Harmful vibration can lead to reduced processing precision, prevent precision equipment from functioning normally, accelerate structural fatigue, and even cause serious failure and damage. Vibration isolation technology, as a classic and reliable vibration control method, can effectively block the propagation of vibration and provide necessary static support by adding flexible vibration isolation devices between the vibration source and the protected object, and has been widely applied in industries, aerospace, and precision manufacturing. Torsional vibration isolators are mainly used in work scenes where input torque fluctuates. Fluctuating torque when driving the output load will cause periodic fluctuations in output torque and rotational speed. The introduction of a torsional vibration isolator can effectively attenuate the fluctuation of input torque and minimize the fluctuation of output angular velocity, thereby improving the smoothness of the power transmission system.

[0003] Linear vibration isolators are difficult to have low stiffness while having large carrying capacity. Nonlinear vibration isolators with quasi-zero stiffness characteristics have gradually become a research hotspot in the field of vibration control due to their high static and low dynamic stiffness characteristics. Quasi-zero stiffness vibration isolators achieve significant low-frequency vibration isolation performance without losing load capacity by designing structures with dynamic stiffness close to zero. The main quasi-zero stiffness vibration isolators are mainly achieved by precise combination of negative stiffness elements and positive stiffness elements. The principle is to offset the stiffness of linear elements through negative stiffness mechanism, reducing dynamic stiffness without reducing load capacity. Typical negative stiffness elements include inclined springs, buckling structures, cam roller mechanisms, and scissors-like structures. In addition, innovative designs based on magnetic elements, hydraulic and pneumatic structures, and bionic structures have also made significant progress in recent years.

[0004] Currently, quasi-zero stiffness vibration isolators are mainly used to isolate axial vibration, while torsional quasi-zero stiffness vibration isolators are less studied. Researchers have proposed torsional quasi-zero stiffness vibration isolators with cam roller spring mechanisms and vibration isolators using magnetic mechanisms. In recent years, the development of deep learning technology has provided a new tool and approach for structural design. As an important branch of artificial intelligence, deep learning models can quickly capture the complex mapping relationship between structure parameters and performance by training large-scale data sets. The introduction of deep learning technology into quasi-zero stiffness structure design can not only greatly improve design efficiency, but also quickly generate optimized design schemes that meet specific requirements for different application scenarios. This method can effectively avoid excessive reliance on experience in traditional design, and achieve more accurate and efficient vibration isolator design.

[0005] However, the existing torsional quasi-zero stiffness vibration isolation structure design is mostly based on the design principle of parallel connection of positive and negative stiffness, and the structure is complex and has many components. The vibration isolator needs to go through a complex assembly process, and there may be assembly gaps between components, which leads to unstable performance. In addition, these designs are often large in size and not compact, making it difficult to meet the needs of modern industry for integration and efficiency. SUMMARY

[0006] To solve the above problems, the present application provides a fast reverse design method for a torsional quasi-zero stiffness vibration isolator based on a curved beam, which combines deep learning and optimization algorithms to achieve the unification of low-frequency torsional vibration isolation and load capacity, and provides a more compact and efficient vibration isolation solution.

[0007] The technical scheme of the present application is as follows:

[0008] A fast reverse design method for a torsional quasi-zero stiffness vibration isolator based on a curved beam, the specific process is as follows:

[0009] Curved beam modeling: the inner ring and the outer ring of the vibration isolator are simplified as rigid bodies, and the curved beam is represented by multiple control points, and the first and last control points are fixed to the inner ring and the outer ring rigid bodies by rigid connection; boundary conditions are set at both ends of the curved beam: the outer end is a fully constrained boundary, and the inner end can have angular displacement;

[0010] Curved beam shape-torque data collection: by applying angular displacement to the inner end of the curved beam model, the positions and weights of the multiple control points are adjusted to collect the corresponding torque values of different curved beam shapes under equal interval angular displacement, and a curved beam shape-torque data set is obtained;

[0011] Network model construction and training: the input of the network model is the geometric parameters of the curved beam, and the output of the model is the torque value, and the network model is trained using the data set;

[0012] Curved beam reverse design: the trained network model is combined with a heuristic algorithm, the geometric parameters of the curved beam are obtained using the heuristic algorithm and input into the network model, the corresponding torque value is obtained, and the adaptability is evaluated using the heuristic algorithm, and the optimal curved beam shape is obtained through repeated cycles.

[0013] Optionally, after obtaining the curved beam shape-torque data set, a self-intersection detection algorithm and a curvature radius calculation algorithm are used to eliminate unfeasible curved beam geometric parameters to obtain feasible curved beam geometric parameters.

[0014] Optionally, the present application takes the feasible curved beam geometric parameters as input, continuously loads angular displacement on the inner end, and calculates the angular displacement-torque nonlinear curve using the finite element method, and takes equal interval N torque values on the nonlinear curve as output data.

[0015] Optionally, the finite element model of the application adopts isotropic elastic constitutive, and the loading adopts displacement control, and the maximum applied torsion angle is 1 rad.

[0016] Optionally, the network model of the application comprises an input layer, an output layer and a plurality of hidden layers, the input of the input layer is the geometric parameters of the curved beam, including the positions of the control points except the first and last control points and the weights of all the control points, and the output layer comprises N nodes, corresponding to N torque values selected at equal intervals on the non-linear curve of the output rotation angle-torque.

[0017] Optionally, the inner end of the application can be angularly displaced in the clockwise direction, and the angular displacement continuously loaded on the inner end is the angular displacement in the clockwise direction.

[0018] Optionally, the heuristic algorithm of the application is an improved real-coded genetic algorithm (IRGA), IRGA is used as a searcher to randomly generate an initial population, a fitness function is used to evaluate the quality of individuals, the population is continuously iteratively evolved through tournament selection, directional crossover and directional mutation operations, the fitness values of all individuals are calculated, and the individuals with excellent performance enter the next generation until the termination condition is met.

[0019] Optionally, the curved beam of the application is represented by a non-uniform rational B-spline curve with multiple control points, or represented by a cubic spline curve, or represented by a B-spline curve.

[0020] Optionally, the network model of the application is a deep neural network, a convolutional neural network or a recurrent neural network.

[0021] Optionally, the optimal curved beam structure obtained in the reverse design process of the curved beam of the application is assembled into a quasi-zero stiffness vibration isolator in series / parallel.

[0022] Beneficial effects:

[0023] First, the application uses a single-element curved beam structure to achieve torsional quasi-zero stiffness, which is simpler and more compact in structure than the combination of positive and negative stiffness elements of the traditional quasi-zero stiffness vibration isolator, and has small volume and light weight.

[0024] Second, in the repeated iteration process of the improved real-coded genetic algorithm, the neural network model is used to quickly predict the torque-rotation angle curve, instead of finite element calculation, which avoids complex modeling process and lengthy calculation time.

[0025] Third, the application is easy to combine multiple curved beam units to realize modular construction of diversified quasi-zero stiffness behavior, and can meet the vibration isolation requirements under different load conditions. It has broad application potential in multi-working-condition vibration isolation or structure function customization. BRIEF DESCRIPTION OF DRAWINGS

[0026] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description only constitute some embodiments of the present application, and all other drawings obtained by those skilled in the art without creative effort based on these drawings also belong to the protection scope of the present application.

[0027] Figure 1 A three-dimensional schematic diagram of a torsional quasi-zero stiffness vibration isolator based on a curved beam;

[0028] Figure 2 A parameterized schematic diagram of a curved beam shape;

[0029] Figure 3 A schematic diagram of a deep neural network structure;

[0030] Figure 4 A flowchart of the optimization design of a torsional quasi-zero stiffness curved beam;

[0031] Figure 5 A schematic diagram of an optimized torsional quasi-zero stiffness curved beam of an example;

[0032] Figure 6 A torque-angle curve of a curved beam with a torsional quasi-zero stiffness characteristic, which is a neural network (DNN) prediction result, a finite element calculation (FEM) verification result and an optimization target point, respectively;

[0033] Figure 7 A torque-angle curve of a torsional quasi-zero stiffness vibration isolator composed of a plurality of parallel curved beams;

[0034] Figure 8 A schematic diagram of a structure of a torsional quasi-zero stiffness vibration isolator in series;

[0035] Figure 9 Torque-angle curves of a single torsional quasi-zero stiffness vibration isolator and two vibration isolators in series. DETAILED DESCRIPTION

[0036] The embodiments of the present application will be described in detail below with reference to the drawings.

[0037] It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict, and all other embodiments obtained by those skilled in the art without creative effort based on the embodiments in the present disclosure also belong to the protection scope of the present disclosure.

[0038] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on this disclosure, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement an apparatus and / or practice a method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this apparatus and / or practice this method.

[0039] like Figure 1 As shown, the vibration isolator designed in this application can be divided into three main parts: the outer ring, the inner ring, and the curved beam. Under the action of torque, the main deformation of the structure occurs in the curved beam. This is because its stiffness is much lower than that of the rings at both ends. Therefore, in static deformation analysis, the rings at both ends can be simplified as rigid bodies, and the mechanical behavior of the curved beam can be focused on. Based on this, this application proposes a rapid reverse design method for a torsional quasi-zero stiffness vibration isolator based on a curved beam, which includes the following parts:

[0040] Curved beam modeling: The inner and outer rings of the isolator are simplified as rigid bodies. A multi-control point NURBS curve is used to represent the curved beam, with the first and last control points fixed on the inner and outer rings. Boundary conditions are set at both ends of the curved beam: the outer end is a fully constrained boundary, while the inner end allows angular displacement.

[0041] Curved beam shape-torque data collection: By applying angular displacement to the inner end of the curved beam model and adjusting the positions and weights of multiple control points, the torque values ​​corresponding to different curved beam shapes under equally spaced angular displacements are collected to obtain a curved beam shape-torque dataset;

[0042] Network model construction and training: The input of the network model is the geometric parameters of the curved beam, and the output of the model is the torque value. The network model is trained using the data set;

[0043] Curved beam reverse design: Combine the trained network model with the heuristic algorithm, use the heuristic algorithm to obtain the geometric parameters of the curved beam and input them into the network model to obtain the corresponding torque value. Then use the heuristic algorithm to perform adaptability evaluation, and through repeated cycles, obtain the optimal curved beam shape.

[0044] The following is a detailed description of each step in the implementation of the above process:

[0045] Curved beam modeling: the inner ring and the outer ring of the vibration isolator are simplified as rigid bodies, the curved beam is described by NURBS curve with multiple control points, and the first and last control points are fixed on the inner ring and the outer ring rigid bodies; different boundary conditions are applied at both ends of the curved beam: the outer end is a fully constrained boundary, and the inner end is applied with clockwise angular displacement; the specific process of this step is:

[0046] The curved beam in the vibration isolator is simplified as an axis curve of the neutral layer for geometric and mechanical analysis in combination with its boundary conditions and geometric characteristics. As shown in Figure 2 To realize parameterized modeling, the curved beam is described by NURBS curve with 6 control points (P1-P6), wherein the first and last control points are fixed at the middle positions of the inner and outer circular arcs of the fan-shaped design boundary, the weights associated with all control points and the control point coordinates in the design region are adjustable for controlling the overall shape of the curved beam; this simplification strategy preserves the geometric characteristics of the curved beam, ignores the thickness effect, and converts the three-dimensional continuous mechanical problem into a two-dimensional curve parameterization problem, and the three-dimensional curved beam structure can be reconstructed by means of the planar curve. Different boundary conditions are applied at both ends of the curved beam: the outer end is a fully constrained boundary (restricting all translational and rotational degrees of freedom), and the inner end is applied with clockwise angular displacement.

[0047] Curved beam shape-torque data collection: by applying clockwise angular displacement to the inner end of the curved beam model, the corresponding torque values under different curved beam shapes and equal interval angular displacements are collected by adjusting the positions and weights of the control points. The specific process of this step is:

[0048] First, in order to realize efficient prediction of the nonlinear torsional response of the curved beam structure, the present application constructs a data set with the positions and weights of the control points of the curved beam as input and the corresponding torque values under preset equal interval angular displacement as output. By adjusting the control points and weights, an infinite number of curved beam shapes can be generated. However, randomly generated NURBS curves may have self-intersection and excessive curvature problems, and self-intersection point detection algorithm and curvature radius calculation algorithm are used to screen out unfeasible design schemes.

[0049] Secondly, the feasible NURBS parameters are created to generate the geometry and discretize the shell elements (a type of finite element mesh used to simulate thin-walled structures, which ignores the stress distribution in the thickness direction of the structure and only retains the mid-surface behavior compared to three-dimensional solid elements, which can significantly reduce the computational degrees of freedom and effectively capture the deformation characteristics, especially suitable for nonlinear mechanical analysis of thin-walled curved beams and other structures), and the nonlinear torsional response is obtained by the finite element method (FEM). Since the shape of the curved beam is determined by 14 independent variables, this leads to an extremely broad design space. To address this challenge, an automated method is used to randomly generate several different and physically feasible curved beam geometry parameters as input, and the corresponding nonlinear torsional response is calculated using the finite element method, taking 40 equally spaced torque values as output data, which constitutes the data set for training the deep learning model. Among them, the finite element model uses isotropic elastic constitutive relation, displacement control is used for loading, and the maximum applied torsional angle is 1 rad. It is worth noting that the dimensionless torque-rotation response curve is independent of material parameters and structural dimensions, and the method has universality and adaptability under different scales and material conditions.

[0050] The parameterization of the curved beam shape in this embodiment is realized by a non-uniform rational B-spline (NURBS) curve, which can also be replaced by a cubic spline, a B-spline, or other simple spline curves.

[0051] Network model construction and training: In order to establish the mapping relationship between the curved beam geometry parameters and the torsional response, a DNN model that is easy to train is designed as a multi-output regressor. As shown in Figure 3 The DNN model is composed of an input layer, an output layer, and several hidden layers, where the input layer contains 14 nodes corresponding to 14 variables - 8 coordinate values (including the x and y coordinates of 4 intermediate control points (a total of 8 variables), and 6 weight parameters of 6 control points. It should be noted that the first and last two control points of the curved beam (i.e. the starting point and the ending point) are used to connect the rigid support structure, and their positions remain fixed in the design, so they are not involved in optimization, and only the four intermediate control points are adjusted as variables. ) and 6 weights; the output layer contains 40 nodes corresponding to 40 equally spaced torque values on the torque-rotation curve.

[0052] From the dataset, 80% of the data were randomly selected as the training set; the remaining 20% of the data were not involved in the training as the test set. Z-Score normalization method was used to normalize the data in the input layer, and the rectified linear unit (ReLU) was selected as the activation function. The root mean square error (RMSE) was selected as the loss function. Batch normalization layers were added between the fully connected layers and the activation functions, and dropout layers were added to the last two layers to enhance the generalization ability. After weighing the training time and prediction accuracy, the DNN architecture of 512x512x512x256x256 was determined, the Adam optimizer was used, the batch size was set to 256, the initial learning rate was 0.01, and the learning rate was reduced by 10 times after every 40 epochs.

[0053] In this embodiment, the deep neural network DNN can also be replaced by a more complex convolutional neural network or a recurrent neural network.

[0054] Inverse design of curved beam: The trained network model DNN is combined with the improved real-coded genetic algorithm (IRGA), the DNN is used as a predictor to output the corresponding force-displacement response curve, and the IRG is used as a searcher to finally obtain the optimal curved beam shape design. The specific process of this step is as follows:

[0055] The trained DNN can quickly and accurately determine the nonlinear mechanical response of a curved beam with any complex irregular shape. As shown in Figure 4 To realize the on-demand customization of the proposed torsional quasi-zero stiffness vibration isolator in performance, the trained DNN model is combined with the improved real-coded genetic algorithm (IRGA) to construct a systematic inverse design framework. The DNN, as a highly efficient surrogate model, replaces the traditional finite element method in the optimization iteration process, thereby significantly accelerating the inverse design process. The IRGA adopts a real number coding strategy, which is particularly suitable for continuous variable optimization problems, effectively overcoming the limitations of traditional binary-coded genetic algorithms. Unlike conventional genetic algorithms that rely on random mutation and crossover, the IRGA introduces a directional genetic operator that can intelligently utilize the gradient information of the objective function to strategically guide the search process towards the more optimal regions in the design space, thereby significantly improving the convergence speed and the quality of the solution. In addition, this algorithm has lower sensitivity to the selection of the initial population and stronger robustness, enabling faster convergence to superior solutions. Specifically, the DNN model is combined with the IRGA to optimize the 14 design parameters of the curved beam. The DNN is used as a predictor to output the corresponding force-displacement response curve, and the IRGA is used as a searcher to randomly generate the initial population. The fitness function is used to evaluate the quality of the individuals, and the population is continuously iterated and evolved through tournament selection, directional crossover, and directional mutation operations. The fitness values of all individuals are calculated, and the superior individuals enter the new generation until the termination condition is met, such asFigures 5-6 The improved real number coding genetic algorithm of the iteration process in the embodiment can be replaced by other heuristic algorithms such as a particle swarm algorithm, a simulated annealing algorithm, an ant colony algorithm, and the like.

[0056] As shown in Figures 7-9 The nonlinear torque-angle response of a single curved beam structure can be precisely controlled by a reverse design method based on geometric configuration. On this basis, the modular construction of diversified quasi-zero stiffness behavior is realized by systematic combination of multiple curved beam units. Such curved beam structures have high programmability, and their mechanical responses can be programmed and controlled at the structure level through spatial configuration. In parallel combination, multiple curved beam units share the external load, significantly enhancing the load-carrying capacity of the platform region of the overall structure. The force-angle curve of the parallel curved beam forms a superposition effect in the platform region, which is suitable for scenarios with high load demand under small torsional deformation. The series structure effectively extends the angle range of the quasi-zero stiffness interval by distributing the total angle to each sub-module, enhancing the structure's ability to maintain low stiffness characteristics in the large deformation domain, which is beneficial to improve the vibration isolation adaptability of the system under large excitation. Further, by connecting multiple quasi-zero stiffness modules with different target load characteristics in series, a multi-platform torque-angle response curve can be constructed, which can meet the vibration isolation requirements under different load conditions. It has broad application potential in multi-working condition vibration isolation or structure function customization.

[0057] The method has high flexibility, greatly improves the design efficiency with the help of deep learning, and the torsional isolator based on the curved beam structure has small size, light weight, and significantly improved space utilization. Compared with the torsional isolator based on parallel positive and negative stiffness elements, the structure complexity is greatly reduced while achieving wideband low-frequency vibration isolation.

[0058] To sum up, the above is only a preferred embodiment of the present application, and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A fast reverse design method for a torsional quasi-zero stiffness isolator based on a curved beam, characterized in that: The specific process is: Curved beam modeling: The inner and outer rings of the isolator are simplified as rigid bodies. A multi-control point curve is used to represent the curved beam, with the first and last control points fixed on the inner and outer rings. Boundary conditions are set at both ends of the curved beam: the outer end is a fully constrained boundary, while the inner end is allowed to undergo angular displacement. Curved beam shape-torque data collection: By applying angular displacement to the inner end of the curved beam model and adjusting the positions and weights of multiple control points, the torque values ​​corresponding to different curved beam shapes under equally spaced angular displacements are collected to obtain a curved beam shape-torque dataset; Network model construction and training: The input of the network model is the geometric parameters of the curved beam, and the output of the model is the torque value. The network model is trained using the data set; Curved beam reverse design: Combine the trained network model with the heuristic algorithm, use the heuristic algorithm to obtain the geometric parameters of the curved beam and input them into the network model to obtain the corresponding torque value. Then use the heuristic algorithm to perform adaptability evaluation, and through repeated cycles, obtain the optimal curved beam shape.

2. The rapid inverse design method for a torsional quasi-zero stiffness isolator based on a curved beam according to claim 1 is characterized in that: After obtaining the curved beam shape-torque data set, the self-intersection point detection algorithm and the curvature radius calculation algorithm are used to eliminate infeasible curved beam geometric parameters and obtain feasible curved beam geometric parameters.

3. The rapid inverse design method for a torsional quasi-zero stiffness isolator based on a curved beam according to claim 2 is characterized in that: The feasible curved beam geometric parameters are used as input, the inner end is continuously loaded with angular displacement, and the finite element method is used to calculate the angle-torque nonlinear curve, and N torque values ​​at equal intervals are taken on the nonlinear curve as output data.

4. The rapid inverse design method for a torsional quasi-zero stiffness isolator based on a curved beam according to claim 3 is characterized in that: The finite element model adopts an isotropic elastic constitutive model, the loading adopts displacement control, and the maximum applied torsion angle is 1 rad.

5. The rapid inverse design method for a torsional quasi-zero stiffness isolator based on a curved beam according to claim 3 is characterized in that: The network model includes an input layer, an output layer and several hidden layers. The input of the input layer is the geometric parameters of the curved beam, including the positions of the remaining control points except the first and last control points and the weights of all control points. The output layer includes N nodes, corresponding to N torque values ​​selected at equal intervals on the output angle-torque nonlinear curve.

6. The rapid inverse design method for a torsional quasi-zero stiffness isolator based on a curved beam according to claim 3 is characterized in that: The inner end can undergo angular displacement in a clockwise direction, and the angular displacement of the inner end when continuously loaded is an angular displacement in a clockwise direction.

7. The rapid inverse design method for a torsional quasi-zero stiffness isolator based on a curved beam according to claim 1 is characterized in that: The heuristic algorithm is an improved real-coded genetic algorithm (IRGA). IRGA is used as a searcher to randomly generate an initial population. The fitness function is used to evaluate the quality of individuals. The population evolves iteratively through tournament selection, directional crossover, and directional mutation operations. The fitness values ​​of all individuals are calculated, and individuals with outstanding performance enter the new generation until the termination condition is met.

8. The rapid inverse design method for a torsional quasi-zero stiffness isolator based on a curved beam according to claim 1 is characterized in that: The curved beam is represented by a non-uniform rational B-spline curve with multiple control points, a cubic spline curve, or a sampled B-spline curve.

9. The rapid inverse design method for a torsional quasi-zero stiffness isolator based on a curved beam according to claim 1 is characterized in that: The network model is: a deep neural network, a convolutional neural network or a recurrent neural network.

10. The rapid inverse design method for a torsional quasi-zero stiffness isolator based on a curved beam according to claim 1 is characterized in that: The optimal curved beam structure obtained during the reverse design of the curved beam is assembled into a quasi-zero stiffness vibration isolator by series / parallel curved beam structures.

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