A fluid-structure interaction model for a biomimetic robotic fish based on MFC materials

Abstract

This invention discloses a fluid-structure interaction (FSI) model for a biomimetic robotic fish based on MFC materials, comprising: a biomimetic robotic fish structural dynamics model, a biomimetic robotic fish fluid model, and a FSI module. The biomimetic robotic fish structural dynamics model simulates the deformation of the biomimetic robotic fish to obtain structural displacement data. The biomimetic robotic fish fluid model simulates the motion of the fluid surrounding the biomimetic robotic fish to obtain fluid pressure data. The FSI module inputs the structural displacement data as boundary conditions into the biomimetic robotic fish fluid model and the fluid pressure data as loads into the biomimetic robotic fish structural dynamics model, performing iterative calculations until the biomimetic robotic fish structural dynamics model and the biomimetic robotic fish fluid model reach an equilibrium state. This FSI model helps optimize the biomimetic robotic fish structural model and improve the swimming efficiency of the biomimetic robotic fish.

Description

Technical Field

[0001] This invention relates to the field of underwater robot technology, and more specifically to a fluid-structure interaction model of a biomimetic robotic fish based on MFC material. Background Technology

[0002] Currently, fish propulsion modes are categorized into two types: body-tail fin mode and central fin-pair fin mode. The central fin-pair fin propulsion mode is slow and inefficient, failing to meet the driving requirements of underwater robots. Therefore, biomimetic robotic fish primarily focus on the body-tail fin mode. The body-tail fin propulsion mode mainly utilizes the undulation of the fish's body or the swaying of its tail fin to propel the water around its body diagonally backward, using the reaction force of the water to generate forward thrust.

[0003] Marco Fiber Composites (MFCs) are composites of piezoelectric fibers and a resin matrix through specific ratios, spatial distributions, and interconnections, combining the advantages of traditional piezoelectric polymers with those of resin matrices. Due to the protective effect of the resin matrix, MFCs exhibit significant improvements in strength and brittleness compared to traditional piezoelectric polymers. The significantly altered ratio and spatial distribution of the composite material with the resin matrix greatly enhances its flexibility and piezoelectric properties. MFCs can achieve complete piezoelectric controlled deformation and offer advantages such as lightweight and high efficiency.

[0004] Therefore, how to optimize the design and performance of biomimetic robotic fish based on piezoelectric fiber composites (MFC) is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of the above problems, the present invention provides a fluid-structure interaction model of a biomimetic robotic fish based on MFC material, so as to at least solve some of the technical problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] This invention provides a fluid-structure interaction model for a biomimetic robotic fish based on MFC materials, comprising: a biomimetic robotic fish structural dynamics model, a biomimetic robotic fish fluid model, and a fluid-structure interaction module; wherein:

[0008] The biomimetic robotic fish structure dynamic model is used to simulate the deformation of the biomimetic robotic fish and obtain structural displacement data.

[0009] The biomimetic robotic fish fluid model is used to simulate the movement of fluid around the biomimetic robotic fish and obtain fluid pressure data.

[0010] The fluid-structure interaction module is used to input the displacement data of the structure as boundary conditions into the fluid model of the biomimetic robotic fish, and input the fluid pressure data as loads into the dynamic model of the biomimetic robotic fish structure, and perform iterative calculations until the dynamic model of the biomimetic robotic fish structure and the fluid model of the biomimetic robotic fish reach an equilibrium state.

[0011] Furthermore, the steps for constructing the biomimetic robotic fish structure dynamic model include:

[0012] Design a biomimetic robotic fish based on MFC materials;

[0013] Modal analysis was performed on the bionic robotic fish to obtain the first-order mode shape and the first-order mode frequency of the driving voltage signal in the body-tail fin propulsion mode.

[0014] Based on the first-order mode shape and first-order mode frequency, the external forces and torques experienced by the biomimetic robotic fish during steady-state swimming motion are obtained through dynamic analysis and fluid dynamics.

[0015] A dynamic model of the biomimetic robotic fish structure is constructed based on the external forces and torques.

[0016] Furthermore, the main body of the biomimetic robotic fish is composed of two MFC flat panels sandwiching a CFRP substrate.

[0017] The two MFC plates are symmetrically distributed and are subjected to sinusoidal driving voltage signals with the same frequency but opposite phase. While one MFC plate shrinks, the other MFC plate stretches, causing the CFRP substrate in the middle to undergo periodic bending deformation.

[0018] Furthermore, the head of the biomimetic robotic fish is fixed with a weight to limit lateral displacement of the head.

[0019] Furthermore, the biomimetic robotic fish structure dynamic model is expressed as follows:

[0020]

[0021] Where m represents the mass of the simulated robotic fish; F(t) represents the swimming acceleration of the simulated robotic fish; F(t) represents the external force acting on the simulated robotic fish; I c (t) represents the instantaneous rotational inertia of the simulated robotic fish relative to its center of mass; ω represents the rate of change of the instantaneous moment of inertia over time. c (t) represents the control angular velocity of the simulated robotic fish; M represents the control angular acceleration of the simulated robotic fish. c (t) represents the external torque acting on the simulated robotic fish.

[0022] Furthermore, the construction steps of the biomimetic robotic fish fluid model include:

[0023] Define the computational domain for the fluid;

[0024] The Navier-Stokes equations are used to describe the fluid motion in the fluid computational domain, and boundary conditions are considered to construct a biomimetic robotic fish fluid model.

[0025] Based on the biomimetic robotic fish fluid model, a dynamic mesh model is used to handle moving or deforming objects in the fluid computation domain.

[0026] Furthermore, the biomimetic robotic fish fluid model is represented as follows:

[0027]

[0028] Where ρ represents fluid density; V represents fluid velocity; V x V y and V z These represent the components of fluid velocity along the x, y, and z axes, respectively; P represents fluid pressure; μ represents the dynamic viscosity of the fluid; F x F y F z These represent the pressure components on the x, y, and z axes, respectively.

[0029] Furthermore, the use of a dynamic mesh model to handle moving or deforming objects in the fluid computational domain includes:

[0030] Based on the object's current boundary position, velocity and its increment, and time increment, determine the object's boundary position at the next moment;

[0031] The mesh is adjusted and modified in the region near the boundary of the object, and the region with severe distortion is re-divided.

[0032] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a fluid-structure interaction model for a biomimetic robotic fish based on MFC materials, which has the following beneficial effects:

[0033] The fluid-structure interaction model provided by this invention helps to optimize the structural model of the biomimetic robotic fish and improve its swimming efficiency.

[0034] This invention improves computational efficiency and reduces computational complexity by refining the calculation method of the fluid-structure interaction model.

[0035] This invention applies a dynamic mesh model to fluid-structure interaction analysis of the MFC robotic fish. Each step re-meshes the mesh based on the previous calculation data to ensure the accuracy of fluid-structure interaction calculations.

[0036] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0038] Figure 1 This is a schematic diagram of the fluid-structure interaction model provided in an embodiment of the present invention.

[0039] Figure 2 This is a schematic diagram of the biomimetic robotic fish model provided in an embodiment of the present invention.

[0040] Figure 3 This is a schematic diagram of the coordinate system of the biomimetic robotic fish provided in an embodiment of the present invention.

[0041] Figure 4 This is a schematic diagram of the fluid domain boundary conditions for the biomimetic robotic fish provided in an embodiment of the present invention.

[0042] Figure 5 This is a schematic diagram of the fluid computational domain grid model of the biomimetic robotic fish provided in an embodiment of the present invention.

[0043] Figure 6 This is a schematic diagram of the pressure cloud map for fluid-structure coupling analysis of the biomimetic robotic fish provided in an embodiment of the present invention. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] See Figure 1 As shown, this embodiment of the invention discloses a fluid-structure interaction model for a biomimetic robotic fish based on MFC materials, including: a biomimetic robotic fish structural dynamics model, a biomimetic robotic fish fluid model, and a fluid-structure interaction module; wherein:

[0046] A biomimetic robotic fish structure dynamics model is used to simulate the deformation of the biomimetic robotic fish and obtain structural displacement data.

[0047] A biomimetic robotic fish fluid model is used to simulate the movement of fluid around a biomimetic robotic fish and obtain fluid pressure data.

[0048] The fluid-structure interaction module is used to input structural displacement data as boundary conditions into the biomimetic robotic fish fluid model and fluid pressure data as loads into the biomimetic robotic fish structural dynamic model for iterative calculations until the biomimetic robotic fish structural dynamic model and the biomimetic robotic fish fluid model reach an equilibrium state.

[0049] Next, each of the above parts will be explained in detail.

[0050] 1. Dynamic model of the biomimetic robotic fish structure

[0051] The steps involved in constructing the dynamic model of this biomimetic robotic fish structure include:

[0052] (1) Design a biomimetic robotic fish based on MFC materials;

[0053] The biomimetic robotic fish consists of three parts: a actuator, a substrate, and an adhesive layer. The actuator comprises two MFC (Metal-Fiber Composite) plates, and the substrate is made of CFRP (Chemical Reinforced Polymer) carbon fiber sheet, with the CFRP substrate sandwiched between the two MFC plates. The actuator is connected to the substrate via the adhesive layer. The deformation of the actuator is transmitted to the substrate through the adhesive layer, controlling the bending or torsional deformation of the substrate. The MFC material selected is model M-8528-P1, with the central CFRP sheet having a thickness of 0.2 mm. Other structural parameters of the biomimetic robotic fish are shown in Table 1. The biomimetic robotic fish model is shown below. Figure 2 As shown.

[0054] Table 1: Structural Parameters of the Robotic Fish Model

[0055] name parameter Body length (mm) 167 Maximum body height (mm) 55 Caudal fin height (mm) 50 Body thickness (mm) CFRP0.2 MFC dimensions (mm) 112×40 Activity area dimensions (mm) 85×28

[0056] The robotic fish has two symmetrically distributed MFC (Metal-Fiber Chromium Fusion) plates, each subjected to a sinusoidal drive voltage signal with the same frequency but opposite phase. As one MFC contracts, the other stretches, causing the CFRP (Crystal Reinforced Plastic) substrate in between to undergo periodic bending deformation. Adding a weight to the head of the robotic fish limits its lateral displacement, increases the lateral deformation of the tail, enhances the water jet propulsion effect, and increases propulsion.

[0057] (2) Modal analysis was performed on the biomimetic robotic fish to obtain the first-order mode shape and the first-order mode frequency of the driving voltage signal in the body-tail fin propulsion mode; specifically:

[0058] Modal analysis is a numerical analysis method for calculating the vibration characteristics of a biomimetic robotic fish structure. The dynamic equation for the undamped modal analysis of MFC is expressed as:

[0059] [M]{x″}+[C]{x'}+[K]{x}={0}

[0060] Where M represents the mass matrix of the biomimetic robotic fish structure; C represents the damping matrix of the biomimetic robotic fish structure; K represents the stiffness matrix of the biomimetic robotic fish structure; and x represents the displacement vector of the biomimetic robotic fish.

[0061] The free vibration of the biomimetic robotic fish structure is a simple harmonic motion, and the displacement is a sinusoidal function, i.e., x = x sin(ωt). Substituting into the above equation, we get:

[0062] ([K]-ω 2 [M]){x}={0}

[0063] In the formula, the eigenvalue ω i The corresponding feature vector {x} i Natural frequency The corresponding mode shape.

[0064] Modal analysis was performed on the robotic fish structure to obtain the first four vibration modes. The calculated bending mode frequencies of the robotic fish are shown in Table 2.

[0065] Table 2 Calculation results of the bending modal frequencies of the robotic fish

[0066]

[0067] The biomimetic robotic fish adopts a tuna-like propulsion mode from the body-tail fin model. This means the front of the body maintains minimal deformation, while the lateral movement of the tail fin propels the surrounding fluid backward, generating forward thrust. The first-order mode shape maintains no lateral displacement at the fixed end, with minimal lateral displacement in the front half of the body along its length and greater lateral displacement at the free tail end. This conforms to the tuna-like fish propulsion method, therefore the biomimetic robotic fish's mode shape approximates a first-order mode shape, and the frequency of the driving voltage signal is also near the first-order mode frequency.

[0068] (3) Based on the first-order mode shape and first-order mode frequency, the external forces and torques experienced by the biomimetic robotic fish during steady-state swimming are obtained through dynamic analysis and fluid dynamics; specifically:

[0069] Establish a fish coordinate system at the center of the biomimetic robotic fish's head. b x b y b Establish a centroid coordinate system with the center of mass of the robotic fish as the origin. c x c y c The oxy coordinate system, in contrast, is the inertial coordinate system. The coordinate system of the robotic fish is defined as follows: Figure 3 As shown.

[0070] During its motion, the biomimetic robotic fish is subjected to independent external and internal forces (torques). The external forces (torques) determine the macroscopic motion of the biomimetic robotic fish in the inertial coordinate system oxy, while the internal forces (torques), such as the mass of the biomimetic robotic fish, determine its own deformation. The motion includes the translation and rotation of the robotic fish, and the resulting velocities include the translational velocity and rotational velocity with respect to the center-of-mass coordinate system.

[0071] (4) A dynamic model of the biomimetic robotic fish structure is constructed based on external forces and external torques. This model is expressed as follows:

[0072]

[0073] Where m represents the mass of the simulated robotic fish; F(t) represents the swimming acceleration of the simulated robotic fish; F(t) represents the external force acting on the simulated robotic fish; I c (t) represents the instantaneous rotational inertia of the simulated robotic fish relative to its center of mass; ω represents the rate of change of the instantaneous moment of inertia over time. c (t) represents the control angular velocity of the simulated robotic fish; M represents the control angular acceleration of the simulated robotic fish. c (t) represents the external torque acting on the simulated robotic fish.

[0074] 2. Bionic robotic fish fluid model

[0075] The construction steps of this biomimetic robotic fish fluid model include:

[0076] (1) Determine the fluid computational domain;

[0077] In this embodiment of the invention, the fluid computation domain in the fluid-structure interaction analysis of the biomimetic robotic fish is designed as a cuboid with dimensions of 590×133×440mm, and the robotic fish structural model is located in the center of the fluid computation domain.

[0078] (2) The Navier-Stokes equations are used to describe the fluid motion in the computational domain, and boundary conditions are considered to construct a biomimetic robotic fish fluid model; specifically:

[0079] The Navier-Stokes equations are the equations of motion describing the conservation of momentum in viscous incompressible fluids. The equations for incompressible viscous fluids in the MFC robotic fish are expressed as follows:

[0080]

[0081] Where ρ represents fluid density; V represents fluid velocity; V x V y and V zThese represent the components of fluid velocity along the x, y, and z axes, respectively; P represents fluid pressure; μ represents the dynamic viscosity of the fluid; F x F y F z These represent the pressure components on the x, y, and z axes, respectively.

[0082] Due to the large deformation and nonlinear characteristics of the robotic fish structure, the Navier-Stokes equations are used for fluid domain calculations to more comprehensively reflect the coupling properties. The boundary conditions of the robotic fish's fluid domain are as follows: Figure 4 As shown.

[0083] (3) Based on the biomimetic robotic fish fluid model, a dynamic mesh model is used to handle moving or deforming objects in the fluid computation domain.

[0084] When the computational boundary is a motion problem or when objects within the computational domain are moving or deformed, a dynamic mesh model is required. The mesh distribution at the moving boundary moves with the boundary. Based on the current boundary position, velocity, and its increment, along with the time increment, the boundary position at the next moment is determined. The mesh is adjusted and modified in regions near the boundary position, and severely distorted regions are re-meshed to eliminate distorted mesh elements caused by boundary movement. A fluid computational domain mesh model is shown below. Figure 5 As shown.

[0085] 3. Fluid-structure interaction module

[0086] In the transient analysis of the robotic fish, the solid domain and the fluid domain have their own meshes and boundary conditions, and data exchange occurs at the interface. In each computational step, the fluid domain solver obtains data from itself and the previous step's computation results from the solid domain, and substitutes it into the new step's computation; the solid domain solver does the same.

[0087] To determine the hydrodynamic performance of the robotic fish, we analyze its forward propulsion during movement. The length of the robotic fish represents the x-axis, and its tail fin swings along the z-axis. We need to calculate the fluid pressure along the x-axis, which is obtained by integrating the fluid pressure and viscous pressure.

[0088]

[0089] Where dA represents the infinitesimal surface element of the robotic fish structure; This represents the direction vector of the unit surface element dA along the x-axis. This represents the i-th normal vector of surface element dA; Indicates fluid pressure; This represents the viscosity-stress tensor along the x-axis.

[0090] Fluid pressure, as one of the coupling data at the interface, plays a significant role in the propulsion process of the biomimetic robotic fish. Different frequencies and amplitudes of the driving signal result in different deformation effects in the robotic fish, leading to varying fluid pressures in the fluid-structure interaction analysis. The biomimetic robotic fish operates by propelling fluid backward through the swinging of its tail fin, utilizing the reaction force of the fluid on the tail fin to generate forward propulsion. The pressure of the fluid domain surrounding the robotic fish structure determines the magnitude of the reaction force, directly affecting the propulsion effect. Figure 6 This represents the fluid pressure cloud map generated when the driving voltage signal is a 3Hz sine wave. During the bending deformation of the robotic fish, the fluid flow near the robotic fish structure is significantly disturbed, and the fluid pressure is affected by the deformation, velocity, and velocity increment of the robotic fish.

[0091] The fluid pressure is highest in absolute value around the robotic fish structure, increasing closer to the body. In the flow region further away from the structure, the pressure does not change significantly during deformation. The peak fluid pressure occurs near the tail of the robotic fish. Comparing pressure contour maps at different times, the pressure in the surrounding fluid computational domain reaches its maximum value when the tail fin deformation reaches its peak. The tail fin swings along the z-axis, resulting in a significant pressure difference along the z-axis on both sides of the robotic fish. The propulsion effect of the biomimetic robotic fish can be represented by the sum of the fluid pressures over one cycle; higher pressure generates greater thrust and better propulsion.

[0092] It is evident that a well-constructed fluid-structure interaction model helps to obtain the optimal driving voltage amplitude and frequency, thereby optimizing the design and performance of the biomimetic robotic fish.

[0093] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0094] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A fluid-structure interaction model for a biomimetic robotic fish based on MFC materials, characterized in that, include: The biomimetic robotic fish structure dynamics model, the biomimetic robotic fish fluid model, and the fluid-structure interaction module; among which: The biomimetic robotic fish structure dynamic model is used to simulate the deformation of the biomimetic robotic fish and obtain structural displacement data. The biomimetic robotic fish fluid model is used to simulate the movement of fluid around the biomimetic robotic fish and obtain fluid pressure data. The fluid-structure interaction module is used to input the displacement data of the structure as boundary conditions into the fluid model of the bionic robotic fish, and input the fluid pressure data as loads into the dynamic model of the bionic robotic fish structure, and perform iterative calculations until the dynamic model of the bionic robotic fish structure and the fluid model of the bionic robotic fish reach an equilibrium state. The biomimetic robotic fish fluid model is represented as follows: Where ρ represents fluid density; V represents fluid velocity; V x V y and V z These represent the components of fluid velocity along the x, y, and z axes, respectively; P represents fluid pressure; μ represents the dynamic viscosity of the fluid; F x F y F z These represent the pressure components on the x, y, and z axes, respectively.

2. The fluid-structure interaction model of a biomimetic robotic fish based on MFC material according to claim 1, characterized in that, The steps for constructing the biomimetic robotic fish structure dynamic model include: Design a biomimetic robotic fish based on MFC materials; Modal analysis was performed on the bionic robotic fish to obtain the first-order mode shape and the first-order mode frequency of the driving voltage signal in the body-tail fin propulsion mode. Based on the first-order mode shape and first-order mode frequency, the external forces and torques experienced by the biomimetic robotic fish during steady-state swimming motion are obtained through dynamic analysis and fluid dynamics. A dynamic model of the biomimetic robotic fish structure is constructed based on the external forces and torques.

3. The fluid-structure interaction model of a biomimetic robotic fish based on MFC material according to claim 2, characterized in that, The main body of the biomimetic robotic fish consists of two MFC flat panels sandwiching a CFRP substrate. The two MFC plates are symmetrically distributed and are subjected to sinusoidal driving voltage signals with the same frequency but opposite phase. While one MFC plate shrinks, the other MFC plate stretches, causing the CFRP substrate in the middle to undergo periodic bending deformation.

4. The fluid-structure interaction model of a biomimetic robotic fish based on MFC material according to claim 2, characterized in that, The head of the biomimetic robotic fish is fixed with a weight to limit lateral displacement of the head.

5. The fluid-structure interaction model of a biomimetic robotic fish based on MFC material according to claim 2, characterized in that, The biomimetic robotic fish structure dynamic model is represented as follows: Where m represents the mass of the simulated robotic fish; F(t) represents the swimming acceleration of the simulated robotic fish; F(t) represents the external force acting on the simulated robotic fish; I c (t) represents the instantaneous rotational inertia of the simulated robotic fish relative to its center of mass; ω represents the rate of change of the instantaneous moment of inertia over time. c (t) represents the control angular velocity of the simulated robotic fish; M represents the control angular acceleration of the simulated robotic fish. c (t) represents the external torque acting on the simulated robotic fish.

6. The fluid-structure interaction model of a biomimetic robotic fish based on MFC materials according to claim 1, characterized in that, The construction steps of the biomimetic robotic fish fluid model include: Define the computational domain for the fluid; The Navier-Stokes equations are used to describe the fluid motion in the fluid computational domain, and boundary conditions are considered to construct a biomimetic robotic fish fluid model. Based on the biomimetic robotic fish fluid model, a dynamic mesh model is used to handle moving or deforming objects in the fluid computation domain.

7. The fluid-structure interaction model of a biomimetic robotic fish based on MFC material according to claim 6, characterized in that, The method of using a dynamic mesh model to handle moving or deforming objects in the fluid computational domain includes: Based on the object's current boundary position, velocity and its increment, and time increment, determine the object's boundary position at the next moment; The mesh is adjusted and modified in the region near the boundary of the object, and the region with severe distortion is re-divided.

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