A sound-solid coupling model of a biomimetic robotic fish based on MFC material

Abstract

The application discloses a kind of based on MFC material's biomimetic robotic fish's sound-solid coupling model, including biomimetic robotic fish main body, biomimetic robotic fish motion control model, MFC material mechanics response model, biomimetic robotic fish modal analysis model and sound-solid coupling analysis model;The application clearly piezoelectric effect and driving mechanism, provide theoretical model for the application of MFC material's biomimetic robotic fish.The application sound-solid coupling calculates the structural behavior of robotic fish under the sound field flow area, propelling mode and deformation response, reduces the difficulty of calculation, further optimizes robotic fish structure.The application combines sound-solid coupling method, mode and transient analysis, predicts the motion state of robotic fish under water, simulates the propulsion movement of biomimetic robotic fish in fluid calculation domain under the driving of sinusoidal voltage.By changing the amplitude and phase difference of MFC driving voltage on left and right sides, straight swimming movement and turning swimming movement of biomimetic robotic fish are realized.

Description

Technical Field

[0001] The present invention relates to the technical field of bionic robotic fish, and more particularly to an acoustic-solid coupling model of a bionic robotic fish based on MFC materials. Background Art

[0002] The ocean covers approximately 71% of the Earth's surface and contains rich biological and mineral resources. Research on the development of marine resources has been included in the nation's long-term plan. Bionic robotic fish are of great significance in ocean exploration. Fish have evolved over millions of years to possess remarkable swimming abilities, enabling them to swim long distances efficiently while maintaining excellent maneuverability. Fish propulsion is by far the most efficient and well-adapted propulsion method in underwater environments. Intelligent materials with functions similar to those of fish muscle tissue are incorporated into the design of bionic robotic fish, acting as actuators to power the robotic fish. Underwater bionic propulsion systems that mimic the appearance and swimming patterns of fish have become powerful tools for the exploration and exploration of marine resources, providing sufficient technical support for exploring complex marine environments. Due to the limitations of traditional propulsion methods, such as large size, high noise, and lack of flexibility, researchers in the field of underwater robotics have shifted their focus to designing small, fast, and flexible robotic fish. MFCs, with their excellent flexibility, large deformation, and strong actuation capabilities, demonstrate significant potential in underwater propulsion. MFC-powered bionic robotic fish can mimic the flexible movements of fish muscles, providing a new approach to the design of bionic actuators.

[0003] Therefore, how to provide an acoustic-solid coupling model of a bionic robotic fish based on MFC materials is an urgent problem that those skilled in the art need to solve. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide an acoustic-solid coupling model of a bionic robotic fish based on MFC materials.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] An acoustic-solid coupling model of a bionic robotic fish based on MFC materials, including a bionic robotic fish body, a bionic robotic fish motion control model, an MFC material mechanical response model, a bionic robotic fish modal analysis model, and an acoustic-solid coupling analysis model;

[0007] The bionic robotic fish body includes two MFC plates and one CFPR plate; wherein the CFPR plate is sandwiched between the two MFC plates;

[0008] The bionic robotic fish motion control model is used to apply an electric field to the two MFC plates to control the bionic robotic fish to move straight, turn left, and turn right;

[0009] The MFC material mechanical response model is used to convert the electric field applied by the bionic robotic fish motion control model into deformation power of the bionic robotic fish;

[0010] The bionic robotic fish modal analysis model is used to predict the vibration shape and modal frequency of the bionic robotic fish bending deformation;

[0011] The acoustic-solid coupling analysis model is used to simulate the structural behavior, propulsion mode and deformation response of the robotic fish based on the predicted vibration mode and modal frequency of the bending deformation of the bionic robotic fish.

[0012] Preferably, the spatial region occupied by the fluid is regarded as the acoustic field region, and the fluid is simulated using acoustic units to construct an acoustic-solid coupling analysis model.

[0013] Preferably, the finite element equation of the acoustic-solid coupling analysis model is as follows:

[0014]

[0015] Where M a ,C a ,K a , A represent the overall mass matrix, damping matrix, stiffness matrix and coupling matrix of the acoustic unit respectively; M S ,C S ,K S represent the overall mass matrix, damping matrix and stiffness matrix of the structure respectively.

[0016] Preferably, in order to simulate the vibration performance of the robotic fish in water, a spherical calculation domain with a diameter of 2000 mm is used as the acoustic-solid coupling calculation domain of the robotic fish; wherein the robotic fish is located in the center.

[0017] Preferably, sinusoidal voltages with the same frequency, amplitude and opposite phases are applied to the two MFC plates respectively to control the bionic robotic fish to move in a straight line.

[0018] Preferably, a first left-turn drive voltage and a second left-turn drive voltage are applied to the left and right MFC plates respectively to control the bionic robotic fish to turn left; wherein, the frequencies of the first left-turn drive voltage and the second left-turn drive voltage are the same and the phases are opposite; and the amplitude of the first left-turn drive voltage is smaller than the amplitude of the second left-turn drive voltage.

[0019] Preferably, the first right-turn drive voltage and the second right-turn drive voltage are applied to the left and right MFC plates respectively to control the bionic robotic fish to turn right; wherein, the frequencies of the first right-turn drive voltage and the second right-turn drive voltage are the same and the phases are opposite; and the amplitude of the first right-turn drive voltage is greater than the amplitude of the second right-turn drive voltage.

[0020] Preferably, the MFC material mechanical response model realizes its conversion function based on the following formula:

[0021]

[0022] Among them, D, σ, E v ,ε respectively represent electric displacement, mechanical stress, electric field intensity and total strain vector; r T ,r S Represent the pressure dielectric constant and pressure strain constant respectively; d represents the piezoelectric strain constant matrix, e represents the piezoelectric pressure constant matrix; s and c represent the material flexibility coefficient matrix and stiffness coefficient matrix respectively; superscript T and S represent the pressure is constant or the strain is constant respectively, and superscript E represents the external applied electric field strength is constant; A area represents the area of ​​the piezoelectric unit; F represents the deformation force of the robotic fish obtained by transformation.

[0023] Preferably, the bionic robotic fish modal analysis model realizes the function of predicting the vibration shape and modal frequency of the bending deformation of the bionic robotic fish based on the robotic fish structural modal finite element equation and the robotic fish fluid finite element equation.

[0024] Preferably, the finite element equation of the robotic fish structure modal is as follows:

[0025]

[0026] Where M S and K S is the structural matrix and stiffness matrix, U represents displacement, F S Represents the external force on the structure, f F represents the pressure vector describing the acoustic-solid coupling, P represents the fluid pressure, R represents the effective area matrix associated with each node on the interface between the robotic fish structure and the fluid, and N S With N F They represent the finite element shape functions of the fish structure and the fluid structure respectively, and n represents the fluid boundary vector;

[0027] The finite element equation of the robotic fish fluid is as follows:

[0028]

[0029] Where M F and K F Denote the mass matrix and stiffness matrix respectively, F F represents the addition of mass, ρ f represents the static density of the fluid.

[0030] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses an acoustic-solid coupling model of a bionic robotic fish based on MFC materials, which can achieve the following beneficial technical effects:

[0031] (1) The present invention clarifies the piezoelectric effect and driving mechanism, and provides a theoretical model for the application of bionic robotic fish made of MFC materials.

[0032] (2) The present invention uses acoustic-solid coupling to calculate the structural behavior, propulsion mode, and deformation response of the robotic fish in the acoustic field, which reduces the calculation difficulty and further optimizes the structure of the robotic fish.

[0033] (3) This invention combines acoustic-solid coupling methods with modal and transient analysis to predict the underwater motion of the robotic fish and simulate the propulsive motion of the bionic robotic fish driven by a sinusoidal voltage within the fluid computational domain. By varying the amplitude and phase difference of the driving voltages of the left and right MFCs, the bionic robotic fish can achieve both straight-line and turning swimming motions. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0035] Figure 1 A bionic robotic fish model provided in an embodiment of the present invention;

[0036] Figure 2 The acoustic-solid coupling calculation domain of the robotic fish provided in an embodiment of the present invention;

[0037] Figure 3 A transient analysis test plane provided in an embodiment of the present invention;

[0038] Figure 4 The tail fin swing amplitude of the robotic fish moving straight ahead provided in an embodiment of the present invention;

[0039] Figure 5 This is the voltage signal for driving the robotic fish to move forward in a straight line provided in an embodiment of the present invention;

[0040] Figure 6 This is the straight-moving motion posture of the robotic fish provided in an embodiment of the present invention;

[0041] Figure 7 The left-turn driving voltage signal of the robotic fish provided in an embodiment of the present invention;

[0042] Figure 8 The left-turning motion posture of the robotic fish provided in an embodiment of the present invention;

[0043] Figure 9 The voltage signal for driving the robotic fish to turn right provided in an embodiment of the present invention;

[0044] Figure 10 This is the right-turning motion posture of the robotic fish provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0046] The embodiment of the present invention discloses an acoustic-solid coupling model of a bionic robotic fish based on MFC materials: (1) The dimensions of the bionic robotic fish

[0047] The main body of the bionic robotic fish is composed of two MFC plates sandwiching a CFRP substrate. The MFC material is model M-8528-P1, and the thickness of the central CFRP plate is 0.2 mm. The other structural parameters of the bionic robotic fish are shown in Table 1. The bionic robotic fish model is shown in Figure 1 shown.

[0048] Table 1 Structural parameters of the robotic fish model

[0049]

[0050]

[0051] (2) Piezoelectric constitutive equation of MFC materials

[0052] The piezoelectric fibers of the MFC material are laid out in the direction of the working surface, polarized along their length, and feature an interdigitated electrode arrangement. This allows the MFC to fully utilize the applied electric field and maximize the inverse piezoelectric effect. Driven by the same external electric field, it produces the greatest mechanical response, thereby enabling the robotic fish to achieve greater driving force and deformation. The MFC piezoelectric actuator was selected as the driving unit for the biomimetic robotic fish. External voltage is used to control the deformation of the MFC actuator, achieving the propulsion mode of tail fin swinging.

[0053] The piezoelectric equation of MFC materials is based on the thermodynamic equation and is divided into d-type and e-type piezoelectric equations. The independent variable is the electric field intensity E. v .

[0054]

[0055] Where D, σ, and E v ,ε respectively represent electric displacement, mechanical stress, electric field intensity and total strain vector. T ,r S represents the pressure dielectric constant and pressure strain constant, respectively. d represents the piezoelectric strain constant matrix, and e represents the piezoelectric pressure constant matrix. s and c represent the material's compliance coefficient matrix and stiffness coefficient matrix, respectively. The superscripts T and S indicate that the pressure is constant or the strain is constant, respectively, and the superscript E indicates that the externally applied electric field strength is constant.

[0056] Convert MFC stress into deformation force of robotic fish.

[0057]

[0058] Where A represents the area of ​​the piezoelectric unit.

[0059] When an external force acts on an MFC, generating a direct piezoelectric effect, positive and negative charges converge on different surfaces of the MFC, generating electric displacement within the MFC. When an external electric field is applied to the MFC, generating an inverse piezoelectric effect, the movement of positive and negative charges within the MFC also generates electric displacement. The MFC piezoelectric strain matrix is ​​expressed as follows.

[0060]

[0061] Where c 11 =c 22 , c 12 =c 21 , c 13 =c 31 =c 23 =c 32 , c 44 =2(c 11 -c 12 ).

[0062] The expression of the MFC stress of the robotic fish is as follows.

[0063]

[0064] Where W pitch is the electrode spacing. Due to the inverse piezoelectric effect, the MFC can generate a large axial force and driving bending moment, causing the robotic fish structure to deform and generate thrust.

[0065] (3) Modal analysis of bionic robotic fish

[0066] To predict the vibration modes and modal frequencies of the model's bending deformation, we first need to perform modal analysis on the acoustic-solid coupling model of the robotic fish and the flow field. The modal finite element equation for the robotic fish structure is as follows.

[0067]

[0068]

[0069] Where M S and K S is the structural matrix and stiffness matrix, U represents displacement, F S Represents the external force on the structure, f F represents the pressure vector describing the acoustic-solid coupling. P represents the fluid pressure, and R represents the effective area matrix associated with each node at the interface between the robotic fish structure and the fluid. N S With N F They represent the finite element shape functions of the fish body structure and the fluid structure respectively, and n represents the fluid boundary vector.

[0070] The finite element equation of the robotic fish fluid is as follows.

[0071]

[0072] Where M F and K F Denote the mass matrix and stiffness matrix respectively, F F represents the addition of mass, ρ f represents the static density of the fluid.

[0073] The coupling between the structure and the flow field is described by boundary pressure. The deformation of the structure is affected by the fluid pressure, and the displacement changes of the structure are transmitted to the fluid domain to simulate the effect of fluid-structure coupling. The acoustic-solid coupling modal frequencies of the robotic fish are shown in Table 2.

[0074] Table 2. Modal frequencies of robotic fish sound-solid coupling

[0075]

[0076] The modal frequencies of the robotic fish in the flow field are significantly lower than those in air, and the frequency difference increases with the modal order. This is primarily due to the presence of hydrostatic pressure, which adds additional mass to the structure and causes the corresponding modal frequencies to decrease. The first- and second-order bending deformations occur at frequencies of 6.13Hz and 29.70Hz, respectively.

[0077] The first-order bending mode occurs at the tail of the robotic fish's caudal fin, where the robot's displacement is greatest. The connection between the caudal fin and the body produces almost no displacement in the z-axis. The rear one-third of the robot's body swings to generate propulsion, while the front two-thirds experience smaller lateral fluctuations, primarily to maintain balance and prevent it from tipping over.

[0078] (4) Bionic robotic fish sound-solid coupling analysis

[0079] Treat the spatial region occupied by the fluid as the acoustic field region, use acoustic units to simulate the fluid, write the acoustic space finite element equation, and then combine it with the structural finite element equation to solve it. The finite element equation for the acoustic-solid coupling analysis of the robotic fish is as follows.

[0080]

[0081] Where M a ,C a ,K a , A represent the overall mass matrix, damping matrix, stiffness matrix and coupling matrix of the acoustic unit respectively; M S ,C S ,K S represent the overall mass matrix, damping matrix and stiffness matrix of the structure respectively.

[0082] In order to simulate the vibration performance of the robotic fish in water, a spherical computational domain with a diameter of 2000 mm is used, with the robotic fish located in the center. The computational domain of the robotic fish acoustic-solid coupling is as follows: Figure 2 shown.

[0083] The robot fish is mainly in the first-order mode during propulsion, so the applied driving frequency is around 6Hz. When the load frequency is 3Hz, the robot fish has better movement and response. The driving voltage has an amplitude between -500V and 1500V, and the frequency is 3Hz. The plane at the end of the tail fin is used as the test plane. Figure 3 As shown in the figure, the tail fin swing amplitude of the robot fish is as follows: Figure 4 shown.

[0084] The displacement of the tail fin tip during a single swing cycle closely resembles a sine wave over time. The swing period is identical to the driving voltage signal, demonstrating the MFC material's strong real-time drive performance. The peak-to-peak swing of the test surface is close to 40mm, approximately one-quarter the overall length of the robotic fish.

[0085] (5) Straight motion control of bionic robotic fish

[0086] In order to achieve the complete motion posture of the bionic robotic fish, the motion control of the robotic fish is analyzed using the acoustic-solid coupling method. When the bionic robotic fish swims straight, the driving voltages on both sides have the same DC bias, the same amplitude, and opposite phases. The driving voltage signal of the robotic fish is as follows: Figure 5 As shown. Using a sinusoidal driving voltage with a frequency of 3Hz, the amplitude of the driving voltage on the left and right sides is maintained, and the driving voltages on both sides are in opposite phases. The bionic robotic fish is symmetrical on both sides, and the peak-to-peak value of the tail fin swing at the end is about 40mm. The propulsion force is obtained by the swing of the tail fin to move forward straight. The straight movement posture of the bionic robotic fish is shown as follows Figure 6 shown.

[0087] (6) Left-turn motion control of the bionic robotic fish

[0088] By changing the driving voltage of the MFC driver, the positive peak value of the left driving voltage is reduced, while the negative peak value remains unchanged. The driving voltage signal of the robot fish turning left is as follows: Figure 7 The driving voltage causes the two MFC actuators to contract in the same way, but the tension of the left MFC actuator is smaller than that of the right MFC actuator. This shifts the balance point of the CFRP substrate to the left, shifting the neutral plane to the left and completing the left turn.

[0089] When the bionic robotic fish turns, the equilibrium position of the tail fin swing is changed by the different degrees of static contraction on both sides. The greater the difference in static contraction on both sides, the greater the offset of the equilibrium position relative to the fish's central axis, and the smaller the turning radius. The turning radius of the robotic fish is controlled by controlling the amplitude difference of the driving voltage on both sides. The greater the amplitude difference, the smaller the turning radius. The left-turning posture of the robotic fish is as follows: Figure 8 shown.

[0090] The fish's tail fin maintains a swing with the same amplitude and period as before near the new equilibrium position, completing the turning action. When the voltage signals of the MFC drivers on both sides have asymmetric waveforms, the z-axis displacement of the tail fin test plane occurs after the load is applied. The tail fin continues to swing in a sinusoidal manner over time, with a frequency maintained at 3Hz, the same as the driving voltage frequency. The positive peak of the sinusoidal voltage signal formed by the tail fin swinging over time decreases, while the reverse peak increases, that is, the equilibrium point of the tail fin swing is offset to the left by about 3mm. The tail fin of the bionic robotic fish maintains a swing with the same frequency near the new equilibrium position, achieving a left-turn propulsion mode.

[0091] (7) Right-turn motion control of bionic robotic fish

[0092] When the robot fish turns right, the driving voltage amplitude on the right side decreases, making the tensile deformation amplitude of the right MFC smaller than that of the left MFC. In the contraction state, the deformation amplitudes of the MFCs on both sides are the same. The driving voltage signal of the robot fish turning right is as follows: Figure 9 The neutral plane of the robot fish is shifted to the right, and the tail fin swings near the right side of the neutral plane, completing the right turn. The right turn posture of the robot fish is shown in Figure 10 shown.

[0093] The sinusoidal voltage signal generated by the tail fin's oscillation changes over time, with the positive peak decreasing and the negative peak increasing. This indicates that the equilibrium point of the tail fin has shifted to the right by about 3 mm. The bionic robotic fish's tail fin maintains the same oscillation frequency near its new equilibrium position, achieving a right-hand propulsion mode.

[0094] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0095] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one 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 present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An acoustic-solid coupling model of a bionic robotic fish based on MFC materials, characterized by: Including the bionic robotic fish main body, bionic robotic fish motion control model, MFC material mechanical response model, bionic robotic fish modal analysis model and acoustic-solid coupling analysis model; The bionic robotic fish body includes two MFC plates and one CFPR plate; wherein the CFPR plate is sandwiched between the two MFC plates; The bionic robotic fish motion control model is used to apply an electric field to the two MFC plates to control the bionic robotic fish to move straight, turn left, and turn right; The MFC material mechanical response model is used to convert the electric field applied by the bionic robotic fish motion control model into deformation power of the bionic robotic fish; The bionic robotic fish modal analysis model is used to predict the vibration shape and modal frequency of the bionic robotic fish bending deformation; The acoustic-solid coupling analysis model is used to simulate the structural behavior, propulsion mode and deformation response of the bionic robotic fish based on the predicted vibration mode and modal frequency of the bending deformation of the bionic robotic fish; The spatial region occupied by the fluid is regarded as the acoustic field region, and the acoustic unit is used to simulate the fluid to construct an acoustic-solid coupling analysis model; The MFC material mechanical response model realizes its conversion function based on the following formula: ； ； ； in, represent the electric displacement, mechanical stress, electric field intensity and total strain vector respectively; denote the pressure dielectric constant and pressure strain constant, respectively; represents the piezoelectric strain constant matrix, e represents the piezoelectric pressure constant matrix; and c represent the flexibility coefficient matrix and stiffness coefficient matrix of the material, respectively; the superscripts T and S represent that the pressure is constant or the strain is constant, respectively; the superscript E represents that the external applied electric field strength is constant; represents the area of ​​the piezoelectric unit; F represents the deformation force of the robotic fish obtained by transformation; The bionic robotic fish modal analysis model realizes the function of predicting the vibration shape and modal frequency of the bending deformation of the bionic robotic fish based on the robotic fish structural modal finite element equation and the robotic fish fluid finite element equation.

2. The acoustic-solid coupling model of a bionic robotic fish based on MFC material according to claim 1, characterized in that: The finite element equation of the acoustic-solid coupling analysis model is as follows: ； Where, Represent the overall mass matrix, damping matrix, stiffness matrix and coupling matrix of the acoustic unit respectively; represent the overall mass matrix, damping matrix and stiffness matrix of the structure respectively.

3. The acoustic-solid coupling model of a bionic robotic fish based on MFC material according to claim 1, characterized in that: In order to simulate the vibration performance of the robotic fish in water, a spherical computational domain with a diameter of 2000 mm is used as the acoustic-solid coupling computational domain of the robotic fish; the robotic fish is located in the center.

4. The acoustic-solid coupling model of a bionic robotic fish based on MFC material according to claim 1, characterized in that: Sinusoidal voltages with the same frequency, amplitude and opposite phase are applied to the two MFC plates to control the bionic robotic fish to move in a straight line.

5. The acoustic-solid coupling model of a bionic robotic fish based on MFC material according to claim 1, characterized in that: A first left-turn drive voltage and a second left-turn drive voltage are applied to the left and right MFC plates, respectively, to control the bionic robotic fish to turn left. The first left-turn drive voltage and the second left-turn drive voltage have the same frequency and opposite phase, and the amplitude of the first left-turn drive voltage is smaller than the amplitude of the second left-turn drive voltage.

6. The acoustic-solid coupling model of a bionic robotic fish based on MFC material according to claim 1, characterized in that: A first right-turn drive voltage and a second right-turn drive voltage are applied to the left and right MFC plates, respectively, to control the bionic robotic fish to turn right. The first right-turn drive voltage and the second right-turn drive voltage have the same frequency and opposite phase, and the amplitude of the first right-turn drive voltage is greater than the amplitude of the second right-turn drive voltage.

7. The acoustic-solid coupling model of a bionic robotic fish based on MFC material according to claim 1, characterized in that: The finite element equation of the robotic fish structure modal is as follows: ； ； Where, and is the structural matrix and stiffness matrix, U represents displacement, Represents the external force on the structure. represents the pressure vector describing the acoustic-solid coupling, P represents the fluid pressure, and R represents the effective area matrix associated with each node at the interface between the robotic fish structure and the fluid. and They represent the finite element shape functions of the fish structure and the fluid structure respectively, and n represents the fluid boundary vector; The finite element equation of the robotic fish fluid is as follows: ； ； Where, and denote the mass matrix and stiffness matrix respectively, An addition that represents mass, represents the static density of the fluid.

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