A flow-induced vibration based magnetic coupling piezoelectric energy harvesting system

Abstract

This invention discloses a magnetically coupled piezoelectric energy harvesting system based on flow-induced vibration. The basic structure consists of a variable cross-section cantilever beam, double-layer MFC piezoelectric sheets, a permanent magnet, and a flow-blocking fluid with a slit and an arc-shaped opening on one side. The root of the cantilever beam is fixed to a base, and a permanent magnet is installed at the free end, creating magnetic repulsion between the two magnets. Piezoelectric sheets are attached to the root of the cantilever beam to form a composite stiffness distribution. The two piezoelectric sheets are symmetrically placed on the upper and lower sides of the cantilever beam, connected to an external load resistor R, forming a closed circuit. The flow-blocking fluid is installed horizontally in the direction of the current at the free end of the cantilever beam. This invention, by optimizing the flow-blocking fluid structure and magnetic coupling mechanism, constructs a multi-field coupling theoretical model of flow-solid-electric-magnetic fields, solving the problems of low piezoelectric energy harvesting efficiency and narrow operating bandwidth in underwater low-frequency vibration environments, and achieving efficient energy capture and conversion.

Description

Technical Field

[0001] This invention relates to the fields of piezoelectric energy harvesting, fluid-induced vibration and multi-field coupling technology, and particularly to a magnetically coupled piezoelectric energy harvesting system based on fluid-induced vibration. Background Technology

[0002] With the development of the Internet of Things (IoT) and underwater wireless sensor networks, the demand for distributed self-powered underwater low-power devices is becoming increasingly urgent. Traditional batteries suffer from limited lifespan, difficulty in replacement, and environmental pollution, making them unsuitable for long-term underwater operation. Piezoelectric energy harvesting technology can convert clean energy sources such as flow-induced vibrations into electrical energy, enabling underwater devices to be self-powered, and has significant application value.

[0003] Piezoelectric energy harvesters have become a research hotspot due to their advantages of simple structure, ease of miniaturization, and high energy density. Traditional cantilever beam piezoelectric energy harvesters have relatively high natural frequencies, resulting in weak response, low harvesting efficiency, and narrow operating bandwidth in low-frequency, high-damped underwater environments. Existing flow-induced vibration energy harvesting devices mostly use conventional cylindrical obstructed fluids, which have large laminar flow regions, weak eddy current forces, and low excitation efficiency. Using magnetic coupling structures alone makes it difficult to fully utilize underwater fluid excitation and achieve synergistic effects between flow field excitation and nonlinear stiffness control, thus limiting the performance of underwater low-frequency energy harvesting. Summary of the Invention

[0004] The purpose of this invention is to solve the problems of poor low-frequency response, low collection efficiency, narrow operating bandwidth, and insufficient excitation in existing underwater piezoelectric energy harvesters. It provides a magnetically coupled piezoelectric energy harvesting system based on flow-induced vibration. By optimizing the fluid resistance structure and the nonlinear stiffness control of magnetic coupling, and combining the multi-field coupling of fluid-solid-electric-magnetic fields, it achieves efficient and wideband collection of underwater low-frequency vibration energy.

[0005] The technical solution adopted in this invention is as follows: S1: Construct a magnetically coupled piezoelectric energy harvester based on flow-induced vibration, including a base, a variable cross-section piezoelectric cantilever beam, an MFC piezoelectric element, a permanent magnet assembly, an optimized flow-blocking system, and an external load circuit. S2: Based on the Euler-Bernoulli beam principle, theoretical modeling and analysis of cantilever beams are carried out. S3: Based on the magnetic dipole model, perform nonlinear magnetic force modeling and analysis. S4: Based on the principle of virtual work, perform electromechanical coupling modeling and analysis.

[0006] Furthermore, the specific process of step S1 is as follows: The variable cross-section piezoelectric cantilever beam is fixed at the base, and the free end is connected in sequence to a permanent magnet assembly and an optimized choke fluid. MFC piezoelectric sheets are symmetrically pasted on the upper and lower surfaces of the cantilever beam and connected in series. The permanent magnet assembly forms a nonlinear magnetic repulsion force, and the optimized choke fluid generates vortex-induced vibration under water flow excitation, driving the cantilever beam and piezoelectric sheets to realize the conversion of mechanical energy into electrical energy.

[0007] The variable cross-section piezoelectric cantilever beam is divided into a piezoelectric segment and a pure substrate segment. The length of the piezoelectric segment is lp, the length of the pure substrate segment is L-lp, and the total length is L. The substrate material of the cantilever beam is an elastic metal or a composite material, and the cross-sectional width is constant along the length direction.

[0008] The MFC piezoelectric sheet has a double-layer structure and is symmetrically arranged on the upper and lower surfaces of the variable cross-section piezoelectric cantilever beam, covering the entire piezoelectric segment. The electrodes of the two piezoelectric sheets are connected in reverse series and connected to an external load resistor R to form a closed power output circuit.

[0009] The permanent magnet assembly consists of two permanent magnets, one fixed to the free end of the cantilever beam and the other fixed to the opposite support. The initial static spacing is d0, and the optimal spacing is 0.03m.

[0010] The optimized flow-blocking type is a cylindrical structure with a slit and an arc opening on one side. The slit runs through the incoming flow direction, and the arc opening is located on the back flow side, which can reduce the volume of the stagnant zone, enhance the vortex intensity and shedding periodicity, and improve the vortex excitation force.

[0011] Furthermore, the specific process of step S2 is as follows: Based on the Euler-Bernoulli beam principle, neglecting shear deformation and rotational inertia, and considering the low-frequency characteristics of underwater eddy-induced vibration, the effects of higher-order modes can be ignored. Only the first-order mode is retained for solving the distributed parameters of the cantilever beam. The lateral vibration displacement can be expressed as: , where βp1 and βs1 are the first-order modal characteristic values ​​of the piezoelectric segment and the substrate segment, respectively, lp is the length of the piezoelectric sheet, and L is the total length of the cantilever beam.

[0012] Using the principle of energy equivalence, the equivalent mass Meq and stiffness Ks of the first-order mode are derived:

[0013] Where ρs and ρp are the densities of the cantilever beam and the piezoelectric sheet, respectively; bs and bp are the widths of the cantilever beam and the piezoelectric sheet, respectively; hs and hp are the thicknesses of the cantilever beam and the piezoelectric sheet, respectively; Mt is the total mass of the magnet; and Ys and Yp are the elastic moduli of the cantilever beam and the piezoelectric sheet, respectively.

[0014] Furthermore, the specific process of step S3 is as follows: Two magnets placed opposite each other at the end of a cantilever beam generate magnetic repulsion. The change in the distance between the magnets as a function of the cantilever beam's deflection can be expressed as:

[0015] Where d0 is the magnet spacing in the static state. Let represent the deflection at the free end of the cantilever beam. Changes in deflection cause changes in magnetic repulsion, introducing nonlinear stiffness characteristics into the system. The magnetic repulsion between the two can be described using a magnetic dipole model, quantifying the impact of the magnetic repulsion potential energy on the system.

[0016] Define the magnetic coupling constant:

[0017] In the formula, μ0 is the free permeability, and M and V are the magnetization and volume of the two magnets, respectively. The magnetic coupling constant reflects the influence of the magnets on the magnetic potential energy.

[0018] Given that the cantilever beam experiences relatively small vibration deflection in underwater environments, it meets the requirements. At the static equilibrium position of the system Taylor expansion of the magnetic potential energy expression:

[0019] Differentiating the magnetomotive force yields the linear magnetic stiffness k. m and third-order nonlinear magnetic stiffness s:

[0020] Where the linear magnetic stiffness k m It demonstrates the softening stiffness effect brought about by magnetic repulsion, effectively reducing the equivalent natural frequency of the system, widening the resonant frequency band of the system, and adapting to the energy harvesting scenario of low-frequency vortex-induced excitation underwater; the third-order nonlinear magnetic stiffness introduces stiffness hardening characteristics, suppresses the divergence phenomenon of the beam under large deflection vibration, and ensures the stability of the system operation.

[0021] Furthermore, the specific process of step S4 is as follows: Based on the principle of virtual work, the electromechanical coupling coefficient Θ is derived. Combined with Kirchhoff's laws, the circuit equation is established. The piezoelectric equivalent capacitance Cp, the output voltage v(t), and the generalized coordinate q(t) satisfy the dynamic coupling relationship.

[0022] By combining the Lagrange equations and the Rayleigh dissipation function, a set of fluid-solid-electromagnetic multi-field coupled dynamic equations is constructed:

[0023] In the formula, c is the system damping coefficient, and f0 is the vortex-induced excitation amplitude.

[0024] When the incoming flow velocity U = 0.7m / s-0.8m / s and the initial spacing between permanent magnets is 0.03m, the system output power reaches its peak value, and the optimal load resistance is determined by the inherent parameters of the system.

[0025] The beneficial effects of this invention are: The optimized flow-blocking structure with slits and a single-sided arc opening significantly enhances vortex-induced lift and improves flow field excitation intensity, making it suitable for underwater low-frequency fluid environments.

[0026] The variable cross-section cantilever beam and double-layer series MFC piezoelectric sheet structure improve electromechanical coupling efficiency, resulting in higher output voltage and making it suitable for underwater self-powered applications.

[0027] Introducing magnetic coupling nonlinear stiffness reduces the system's natural frequency, broadens the operating bandwidth, suppresses large deflection vibration divergence, and improves operational stability.

[0028] A fluid-solid-electric-magnetic multi-field coupling model is constructed to achieve synergistic effects of mechanical vibration, piezoelectric conversion, fluid excitation and magnetic nonlinearity, thereby significantly improving energy harvesting efficiency. Attached Figure Description

[0029] Figure 1 Overall structural diagram of the invention Figure 2 Output power variation curves with load under different magnet spacing Figure 3 Output power versus flow velocity curves under different magnet spacing Figure 4 Comparison curves of output power of different flow-blocking structures Detailed Implementation The present invention will be further described in detail below with reference to specific embodiments.

[0030] This embodiment provides a magnetically coupled piezoelectric energy harvester based on flow-induced vibration. The overall structure includes a base, a variable cross-section piezoelectric cantilever beam, a double-layer MFC piezoelectric sheet, two sets of permanent magnets, a single-sided arc-shaped flow barrier with a slit, and an external load resistor. The root of the cantilever beam is fixed to the base, and the flow barrier is installed at the free end along the water flow direction. The permanent magnet at the end and the fixed permanent magnet on the opposite side have the same pole facing each other.

[0031] The variable cross-section piezoelectric cantilever beam has a total length L and a piezoelectric segment length lp. The segment from the root to lp is the piezoelectric segment, which is covered with a double-layer MFC piezoelectric sheet, while the rest is a pure substrate segment. The cantilever beam has a uniform width, and the piezoelectric segment is thicker than the pure substrate segment, forming a variable cross-section stiffness distribution.

[0032] MFC piezoelectric elements are symmetrically attached to the upper and lower surfaces of the cantilever beam, with the electrodes connected in reverse series. The output terminal is connected to a load resistor R, which converts bending strain energy into electrical energy output.

[0033] The optimized flow obstruction is a cylindrical body with an axial slit and an arc-shaped opening on the back flow side, with a Reynolds number of [missing information]. A stable vortex street is generated, which excites the cantilever beam to vibrate periodically.

[0034] A first-order modal model was established based on Euler-Bernoulli beam theory to obtain the equivalent mass M. eq Equivalent stiffness K s A vortex-induced lift model was established to obtain the generalized excitation force f0sin(ωvt); the magnetic stiffness k was obtained through a magnetic dipole model. m The nonlinear coefficient s is used; the electromechanical coupling coefficient Θ is obtained from the principle of virtual work, and a multi-field coupling equation system is established.

[0035] Simulations were performed using MATLAB, and the results showed that the output power was maximized when the flow velocity was 0.7 m / s-0.8 m / s and the magnet spacing was 0.03 m. The optimized flow resistance significantly improved the power compared to the conventional cylindrical flow. The optimal load resistance remained essentially unchanged, and the impedance matching was stable.

[0036] According to the results of this embodiment, the water flow through the obstructing fluid generates vortex-induced vibration, which drives the cantilever beam to bend and deform. The MFC piezoelectric sheet generates charge due to the positive piezoelectric effect, and outputs voltage through series connection. The magnetic repulsion nonlinear stiffness adjusts the resonance characteristics and broadens the operating frequency band, thereby realizing efficient underwater low-frequency energy harvesting.

Claims

1. A magnetically coupled piezoelectric energy harvesting system based on flow-induced vibration, characterized in that, It includes the following steps: S1: Construct a magnetically coupled piezoelectric energy harvester based on flow-induced vibration, including a base, a variable cross-section piezoelectric cantilever beam, an MFC piezoelectric sheet, a permanent magnet assembly, an optimized flow-blocking system, and an external load circuit. S2: Based on the Euler-Bernoulli beam principle, theoretical modeling and analysis of cantilever beams are carried out. S3: Based on the magnetic dipole model, perform nonlinear magnetic force modeling and analysis. S4: Based on the principle of virtual work, perform electromechanical coupling modeling and analysis.

2. The energy harvesting system according to claim 1, characterized in that: The variable cross-section piezoelectric cantilever beam is divided into a piezoelectric segment and a pure substrate segment. The length of the piezoelectric segment is lp, the length of the pure substrate segment is L-lp, and the total length is L. The substrate material of the cantilever beam is an elastic metal or a composite material, and the cross-sectional width is constant along the length direction. The MFC piezoelectric sheet has a double-layer structure and is symmetrically arranged on the upper and lower surfaces of the variable cross-section piezoelectric cantilever beam, covering the entire piezoelectric segment. The electrodes of the two piezoelectric sheets are connected in reverse series and connected to an external load resistor R to form a closed circuit to output electrical energy. The permanent magnet assembly consists of two permanent magnets, one fixed to the free end of the cantilever beam and the other fixed to the opposite support. The initial static distance is d0, and experimental verification shows that the optimal distance is 0.03m. The optimized flow-blocking fluid is a cylindrical structure with a slit and an arc opening on one side. The slit runs through the incoming flow direction, which can introduce secondary flow, delay boundary layer separation, and make the vortex core more concentrated. The arc opening is located on the back flow side to reduce the stagnant zone and enhance the vortex intensity and shedding periodicity.

3. The energy harvesting system according to claim 2, characterized in that, The lateral vibration of the cantilever beam is modeled based on Euler-Bernoulli beam theory, retaining only the first-order mode, and the vibration displacement is... And the equivalent mass M of the system is obtained through energy equivalence. eq With equivalent stiffness K s .

4. The energy harvesting system according to claim 2, characterized in that, The permanent magnets generate a nonlinear magnetic repulsion force, introducing a linear magnetic stiffness k. m With the third-order nonlinear magnetic stiffness s, the equivalent stiffness of the system can be adjusted and the resonant frequency band can be broadened, suppressing large deflection vibration divergence and ensuring the stability of the system operation.

5. The energy harvesting system according to claim 2, characterized in that, The system satisfies the fluid-solid-electromagnetic multi-field coupled dynamic equations: In the formula, c is the damping coefficient, Θ is the electromechanical coupling coefficient, and C p f0 is the equivalent capacitance of the piezoelectric element and f0 is the amplitude of the eddy excitation.

6. The energy harvesting system according to any one of claims 1-5, characterized in that, When the incoming flow velocity U is between 0.7m / s and 0.8m / s and the initial spacing between permanent magnets is 0.03m, the output power reaches its peak value, and the optimal load resistance is uniquely determined by the inherent parameters of the system.

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