A Modeling Method for a Cantilever-Type Magneto-Mechano-Electric Hybrid Energy Harvester

Abstract

The present invention discloses a modeling method for a cantilever - type magnetic - machine - electric hybrid energy harvester, which includes an energy harvester, a magnetic - machine - electric cantilever - type theoretical model with a magnetic mass block, an analysis of the electromagnetic force and magnetostrictive force of the tip permanent magnet, and a modal analysis of the magnetic - machine - electric energy harvester with a magnetic mass block. A distributed linear theoretical model of the energy harvester is established and derived, and the multi - field coupling relationship, the collection efficiency of magnetic field energy, partial piezoelectric coverage mode, the influence of the bias magnetic field on the output effect of the material, etc. of this model are analyzed; the energy harvester is composed of a single - layer piezoelectric material, a magnetostrictive beam, a fixed end, a permanent magnet, a tip magnetic mass block, and a load resistor. The permanent magnet and the tip magnetic mass block are placed with the same polarization direction to provide the bias magnetic field required for the normal operation of the magnetostrictive material. The tip magnetic mass block is used to control the vibration frequency and output power and collect the low - frequency magnetic field around the collecting wire.

Description

Technical Field

[0001] The present invention relates to the field of magneto-mechanical-electrical hybrid energy harvesters, and particularly to a modeling method for a cantilever beam type magneto-mechanical-electrical hybrid energy harvester. Background Art

[0002] Hybrid energy harvesting technology, that is, harvesting various energies in nature, such as electromagnetic energy, vibration energy, thermal energy, light energy, etc.; is mainly used to solve the drawbacks of traditional power supply methods and achieve self-power supply of devices. There is a large amount of electromagnetic energy around power transmission lines. Therefore, energy harvesting based on AC cables has always been a research hotspot for institutions and scholars. The energy harvested by power transmission can supply power to some micro sensors in the form of electrical energy. The energy harvester using the piezoelectric effect is one of the most promising candidate technologies. Secondly, there are also electromagnetic, electrostatic, and piezoelectric energy harvesters. Among the four vibration power generation technologies, each has its application scenarios, advantages and disadvantages. Therefore, it is necessary to study and analyze a composite energy harvester that combines the above energy harvesting technologies.

[0003] In 2016, Li Zhihong et al. designed a new type of rod-shaped piezoelectric-electromagnetic composite energy harvester. By establishing a mathematical model for the composite energy harvester, expressions for voltage, current, and output power were derived. Then, numerical simulations were conducted on the output power characteristics of the composite energy harvester, and the internal resistance value of the piezoelectric sheet and other parameter conditions were set. By comparing and analyzing the composite energy harvester model with single piezoelectric or electromagnetic energy harvester models, the output power was theoretically increased by 38.2% and 4.74%. In 2018, Xueping Xu et al. proposed a hybrid energy harvesting method based on a magnetostrictive-piezoelectric composite vibrating partially covered cantilever beam, studied the influence of the phase difference between harmonic vibration and alternating magnetic field on the performance of the energy harvester at the same frequency, and respectively tested the energy harvesting performance of Galfenol alloy and nickel alloy. It was demonstrated that a bias magnetic field could stably improve the output performance of the composite device, but the optimal solution of the device was not studied with the bias magnetic field as a variable. In 2017, Oskar Z. Olszewski et al. reported a low-frequency vibration magneto-electric energy harvester, which was a cantilever beam structure composed of piezoelectric materials, permanent magnet materials, etc., and could harvest energy from a wire carrying an alternating current load. When approaching the alternating current-carrying wire, the magnet was coupled with the alternating magnetic field of the wire, causing the cantilever to vibrate and generate electricity. This device used microelectromechanical system technology and could obtain an average power output of 1.5 μW when using the optimal load. In 2020, Rammohan Sriramdas et al. designed a magneto-mechanical-electric (MME) harvester that could harvest energy from an extremely low-frequency magnetic field. The MME harvester consisted of a composite cantilever composed of piezoelectric and magnetostrictive materials and a permanent magnet tip mass, which absorbed the alternating magnetic field, resonated at a fixed frequency, and proposed a theoretical method that could maintain the resonance frequency during any period. Compared with the traditional structure, the power generation performance of the distributed MME harvester was increased by 280%. However, hybrid excitation, bias magnetic field were not considered, and a detailed theoretical model analysis of the device was not given. Summary of the Invention

[0004] To solve the above problems, the object of the present invention is to provide a modeling method for a cantilever beam type magneto-mechanical-electric composite hybrid energy harvester. Taking the magnetostrictive / piezoelectric / permanent magnet cantilever beam type hybrid energy harvester as the research object, through mathematical modeling, analysis and comparison, finite element simulation, etc., a distributed linear theoretical model of the energy harvester is established and derived, and the multi-field coupling relationship of the model, the energy harvesting efficiency of the magnetic field energy, the partial piezoelectric coverage mode, the influence of the bias magnetic field on the output effect of the material, etc. are discussed.

[0005] To achieve the above object, the modeling method for a cantilever beam type magneto-mechanical-electric composite hybrid energy harvester provided by the present invention is realized as follows:

[0006] A modeling method for a cantilever - type magneto - mechano - electro - hybrid energy harvester, including an energy harvester, a magneto - mechano - electro cantilever - type theoretical model with a magnetic mass block, an analysis of the electromagnetic force and magnetostrictive force of the tip permanent magnet, and a modal analysis of the magneto - mechano - electro energy harvester with a magnetic mass block. The energy harvester includes a single - layer piezoelectric material, a magnetostrictive beam, a fixed end, a permanent magnet, a tip magnetic mass block, and a load resistor. The single - layer piezoelectric material covers the single - layer magnetostrictive material in a partially - covering form. The left end of the single - layer magnetostrictive material is installed on the fixed end, and the right end is fixed on the base. The permanent magnet and the tip magnetic mass block are placed with the same polarization direction to provide the bias magnetic field required for the normal operation of the magnetostrictive material. The tip magnetic mass block is attached to the top of the beam, used to control the vibration frequency and output power, and collect the low - frequency magnetic field around the collecting wire. The magnetostrictive beam is made of a single - layer magnetostrictive material, and the load resistor represents the load on the single - layer piezoelectric material.

[0007] The modeling scheme of the magneto - mechano - electro cantilever - type theoretical model is as follows:

[0008] Let the thickness and length of the magnetostrictive beam be h m and Lm (Lm = L1 + L2), the thickness, length, and width of the single - layer piezoelectric material be hp, lp (lp = L1), and b respectively. The magnetostrictive beam is modeled using the Euler - Bernoulli beam assumption, ignoring the viscous air damping coefficient. The governing equation of motion can be written as:

[0009]

[0010] where M(x, t) is the internal bending moment of the beam, v(x, t) represents the relative displacement of the beam cross - section in the magnetostrictive beam; m is the mass per unit length; f(t) is the force generated by the tip magnetic mass block, where:

[0011]

[0012] where T M and T P are the stresses on the magnetostrictive beam and the single - layer piezoelectric material. At this time, the constitutive equations of the single - layer piezoelectric material and the magnetostrictive beam are introduced;

[0013]

[0014]

[0015] D = e 31 S p + ε 33 E

[0016] where E m and E S are the Young's moduli of the magnetostrictive beam and the single - layer piezoelectric material respectively, sm and s p are the strains of the magnetostrictive beam and the single-layer piezoelectric material, H and E represent the magnetic field strength and the electric field strength respectively, where the voltage V = Ehp. Substituting Equation (3) into Equation (2), we can obtain:

[0017]

[0018] where H(x) and EI are the Heaviside function and the corresponding equivalent stiffness of the cantilever beam. Substituting Equation (4) into (1), the motion equilibrium equation of the magnetostrictive beam can be obtained:

[0019]

[0020] δ(x) is the Dirac δ function; m is the mass per unit length; is the piezoelectric coupling coefficient, η is the magnetic field coupling coefficient; V(t) and H(t) are the voltage on the single-layer piezoelectric material and the magnetic field on the magnetostrictive beam. These parameters are determined by the geometric and material properties of the magnetostrictive beam, where:

[0021] m = (ρ m h m l m + ρ s h s l s )

[0022]

[0023]

[0024] m, b, l, η, h m , ρ, E, respectively represent the mass per unit length, width, length, piezoelectric coupling coefficient, piezomagnetic coupling coefficient, thickness, density, Young's modulus, and neutral layer position of the magnetostrictive beam.

[0025] The analysis scheme of the electromagnetic force and magnetostrictive force of the tip magnetic mass block of the present invention is as follows:

[0026] In the alternating magnetic field collector, the force directly acts on the magnet. For the magneto-mechanical-electrical cantilever beam type theoretical model with a magnetic mass block, since the left end is fixed, only the force on the tip magnetic mass block under the external magnetic field needs to be considered. The force directly acts on the tip magnetic mass block. The force acting on the tip magnetic mass block in the magnetic field is proportional to the integral of the magnetic field gradient over the volume of the magnet. There is:

[0027]

[0028] Where Fx and Fy are the forces exerted by the wire on the magnet in the x and y directions respectively; Br is the remanent flux density of the tip magnetic mass; V is the volume of the magnet; Hy is the vertical component of the magnetic field. According to the Biot-Savart law, the magnetic field around a single current-carrying wire is described by the following formula:

[0029]

[0030] In the formula, i is the current, ex and ey are the unit vectors in the x and y directions respectively. Using equation (7), F y is expressed as:

[0031]

[0032] Among them, only considering the main acting direction of the magnet, that is, the vertical force component F y , the external force f(t) on the right side of equation 6 can be obtained as:

[0033] f(t) = f m (t) + f a (t) (10)

[0034] Among them, f m (t) is the electromagnetic force received by the tip magnetic mass, and f a (t) is the mechanical excitation providing acceleration excitation. According to equation 9, the electromagnetic force received by the tip permanent magnet can be obtained, and substituting it into 6, the control equation of the beam can be obtained as:.

[0035]

[0036] Among them: h Mt is the height of the tip magnetic mass, Br is the remanent flux density of the tip magnetic mass, and lx is the horizontal distance from the left side of the magneto-mechanical-electrical energy harvester to the wire.

[0037] The modal analysis scheme of the magneto-mechanical-electrical energy harvester with a magnetic mass is as follows:

[0038] Using modal analysis, the relative displacement along the magnetostrictive beam is expressed as the sum of the products of the mode shape function and the modal coordinates, as follows:

[0039]

[0040] Among them, r represents the rth vibration mode. Substituting (12) into (11) and integrating over the length of the magnetostrictive beam, and using the orthogonality of the beam, we can obtain:

[0041]

[0042] Among them,

[0043]

[0044]

[0045]

[0046]

[0047] Let \(i(t)\) be the current in the wire, with the inward direction being positive, and \(a(t)\) be the acceleration excitation provided to the energy harvester. \(\omega_r\) is the resonance frequency in the \(r\)-th vibration mode. r is the resonance frequency in the \(r\)-th vibration mode.

[0048] Applying Kirchhoff's first law to the equivalent circuit of the magneto-mechanical-electrical energy harvester, we get:

[0049]

[0050] where \(R\) l represents the sum of the internal resistance of the energy harvesting circuit and the external load resistance, and \(C\) P corresponds to the internal capacitance of a single-layer piezoelectric material:

[0051]

[0052] where the current in the piezoelectric layer can be expressed by the following formula:

[0053]

[0054] From Equation (2.12), we get:

[0055]

[0056] Combining Equation (18) with Equations (15) and (17), we can obtain the frequency-domain response of the output voltage:

[0057]

[0058] The time responses of the output power and voltage are determined by solving the equations of motion. Then, the energy harvesting device is modeled as a mass-spring-damper system to evaluate the damping coefficient of the output circuit. Finally, the finite element method is used to verify the output voltage.

[0059] The scheme of the present invention for verifying the output voltage using the finite element method is as follows: In all analyses and finite element analyses, the geometric and material properties of the energy harvesting device are shown in Tables 1.1 and 1.2 respectively:

[0060] Table 1.1 Material Dimensions

[0061]

[0062] Table 1.2 Material Parameters

[0063]

[0064]

[0065] For this model, the tentative current passing through the wire is 10 A, and the permanent residual magnetic flux is 1.2 T. The force nephogram at various positions around the wire is obtained by the analytical method. The wire is located at x = 0 and y = 0. Considering the influence of the magnetic field generated by the current at different positions on the permanent magnet, the tip magnetic mass block, and the magnetostrictive beam, take L x = 20 mm, L y = 15 mm. The force on the permanent magnet is approximately 10 mN. When determining the geometric dimensions and material parameters, first set the input excitation. Under the conditions of an acceleration excitation of 0.1 g and an excitation current of 10 A, the load resistance is 1 kΩ. It can be solved by the Runge - Kutta algorithm. When the first - order resonance frequency of the magneto - mechanical - electrical composite material terminal voltage is obtained, the maximum output voltage is about 2.2 V, and the output power can reach 0.5 mW. Set the acceleration excitation to zero. When there is only current excitation, the time - domain diagram of the single - excitation voltage output can be obtained. Under the condition of single - current excitation, the output voltage can reach about 1.1 V. After adding the acceleration excitation, the voltage output increases by 50%. The frequency - domain response shows that as the acceleration excitation increases, the output also increases. When the acceleration excitation is zero, the output voltage drops from 22 V to 11 V, and the output voltage decreases by about 50%. The output power drops from 0.52 mW to 0.13 mW, a decrease of about 75%.

[0066] The research plan for the influence of hybrid excitation in the present invention is as follows: The magneto - mechanical - electrical composite hybrid energy harvester material can detect the alternating magnetic field generated by the wire current, and set the acceleration excitation in the solid mechanics - body load. The results of the analytical integration based on the motion control equation are verified by the finite - element analysis method. The coil with a current of 10 A passing through it is simulated by the finite - element method to obtain the internal magnetic - field distribution of the model. The vibrations and magnetic excitations at different frequencies are calculated. Combining the output voltage, there is a slight decrease in the output, and the first - order resonance frequency decreases slightly. If the energy harvester is in the hybrid excitation with the excitation frequency near the first natural frequency, the maximum stress range in the structure is much smaller than the yield stress of the single - layer piezoelectric material and the magnetostrictive beam, and only reaches the maximum value of 2.55×10 5 N / m 2, where, when there is only electromagnetic excitation, that is, when the wire coil current input in the model is 10 A, the potential difference between the upper and lower layers of the single-layer piezoelectric material can reach about 1 V, and the voltage is slightly lower than the analytical solution. When mixed excitation is input, that is, when acceleration excitation and current excitation act together, the frequency response of the voltage of the piezoelectric layer can be obtained. It can be seen that the total voltage output is about 2.2 V, the resonance frequency shifts slightly to the right, and the first-order resonance frequency can reach 51 HZ. Compared with the single-excitation input of the same material, the voltage output of the mixed excitation is greatly improved.

[0067] Since the present invention takes the magnetostrictive / piezoelectric / permanent magnet cantilever hybrid energy harvester as the research object, through mathematical modeling, analysis and comparison, finite element simulation, etc., a distributed linear theoretical model of the energy harvester is established and deduced, and the multi-field coupling relationship of the model, the energy collection efficiency of the magnetic field energy, the partial piezoelectric coverage mode, the influence of the bias magnetic field on the output effect of the material, etc. are analyzed, so as to obtain the following beneficial effects:

[0068] 1. In the AC magnetic field harvester, the force directly acts on the magnet. Since the left end of the magneto-mechanical-electrical cantilever beam type theoretical model with a magnetic mass block is fixed, only the force on the tip magnetic mass block under the external magnetic field needs to be considered. In the traditional mode, the force is applied by the inertial force, and the inertial force comes from the applied acceleration. In the AC magnetic field harvester, the force directly acts on the tip magnetic mass block, and the tip magnetic mass block also plays the role of mass.

[0069] 2. The contributions provided by the magnetostrictive layer and the permanent magnet account for a large proportion. Compared with the traditional non-magnetic mass electric energy harvester, the magneto-mechanical-electrical composite energy harvester can collect energy more effectively.

[0070] 3. Compared with the single-excitation input of the same material, the voltage output of the mixed excitation is greatly improved. Description of the Drawings

[0071] Figure 1 It is a schematic structural diagram of the energy harvester of a cantilever beam type magneto-mechanical-electrical composite hybrid energy harvester modeling method of the present invention;

[0072] Figure 2 It is an equivalent circuit diagram of the magneto-mechanical-electrical energy harvester of a cantilever beam type magneto-mechanical-electrical composite hybrid energy harvester modeling method of the present invention;

[0073] Figure 3 It is a force cloud diagram of the permanent magnet at different positions of the wire of a cantilever beam type magneto-mechanical-electrical composite hybrid energy harvester modeling method of the present invention;

[0074] Figure 4 It is a relative position diagram of the wire and the transducer of a cantilever beam type magneto-mechanical-electrical composite hybrid energy harvester modeling method of the present invention;

[0075] Figure 5 Output voltage time-domain diagram of the energy harvester for the modeling method of a cantilever beam type magnetic-mechanical-electrical hybrid energy harvester of the present invention;

[0076] Figure 6 Output power time-domain diagram of the energy harvester for the modeling method of a cantilever beam type magnetic-mechanical-electrical hybrid energy harvester of the present invention;

[0077] Figure 7 Single-excitation output voltage time-domain diagram of the energy harvester for the modeling method of a cantilever beam type magnetic-mechanical-electrical hybrid energy harvester of the present invention;

[0078] Figure 8 Output voltage frequency-domain diagram of the energy harvester for the modeling method of a cantilever beam type magnetic-mechanical-electrical hybrid energy harvester of the present invention;

[0079] Figure 9 Output power frequency-domain diagram of the energy harvester for the modeling method of a cantilever beam type magnetic-mechanical-electrical hybrid energy harvester of the present invention;

[0080] Figure 10 Influence diagram of the phase angle difference between the acceleration excitation and the current excitation on the hybrid output of the energy harvester for the modeling method of a cantilever beam type magnetic-mechanical-electrical hybrid energy harvester of the present invention;

[0081] Figure 11 Stress diagram of the energy harvester for the modeling method of a cantilever beam type magnetic-mechanical-electrical hybrid energy harvester of the present invention;

[0082] Figure 12 Voltage diagram of the energy harvester for the modeling method of a cantilever beam type magnetic-mechanical-electrical hybrid energy harvester of the present invention;

[0083] Figure 13 Numerical and analytical comparison diagram of the voltage-frequency response of the hybrid excitation of the energy harvester for the modeling method of a cantilever beam type magnetic-mechanical-electrical hybrid energy harvester of the present invention;

[0084] Figure 14 Numerical and analytical comparison diagram of the power-frequency response of the energy harvester for the modeling method of a cantilever beam type magnetic-mechanical-electrical hybrid energy harvester of the present invention;

[0085] Figure 15 Schematic diagram of the force on the permanent magnet around the wire of the energy harvester for the modeling method of a cantilever beam type magnetic-mechanical-electrical hybrid energy harvester of the present invention.

[0086] Description of main component symbols.

[0087]

[0088] Detailed implementation manners

[0089] The present invention will be further described in detail below in conjunction with embodiments and with reference to the accompanying drawings.

[0090] Please refer to Figures 1 to 14 Shown is a modeling method for a cantilever magneto - mechanical - electrical hybrid energy harvester in the present invention, including an energy harvester, a magneto - mechanical - electrical cantilever beam theoretical model with a magnetic mass block, an analysis of the electromagnetic force and magnetostrictive force of the tip permanent magnet, and a modal analysis of the magneto - mechanical - electrical energy harvester with a magnetic mass block.

[0091] As Figure 1 Shown, the energy harvester includes a single - layer piezoelectric material 1, a magnetostrictive beam 2, a fixed end 3, a permanent magnet 4, a tip magnetic mass block 5, and a load resistor 6. The single - layer piezoelectric material 1 covers the single - layer magnetostrictive material in a partially covering form. The left end of the single - layer magnetostrictive material is installed on the fixed end 3, and the right end is fixed on the base 7. The permanent magnet 4 and the tip magnetic mass block 5 are placed with the same polarization direction to provide the bias magnetic field required for the normal operation of the magnetostrictive material. The tip magnetic mass block 5 is attached to the top of the beam, used to control the vibration frequency and output power, and collect the low - frequency magnetic field around the collecting wire. The magnetostrictive beam 2 is made of a single - layer magnetostrictive material, and the load resistor 6 represents the load on the single - layer piezoelectric material 1.

[0092] The modeling scheme for the magneto - mechanical - electrical cantilever beam theoretical model with a magnetic mass block is as follows:

[0093] Let the thickness and length of the magnetostrictive beam 2 be h m and L (Lm = L1 + L2). The thickness, length, and width of the single - layer piezoelectric material 1 are hp, lp (hp = L1, lp = L1), and b respectively. The magnetostrictive beam 2 is modeled using the Euler - Bernoulli beam hypothesis, ignoring the viscous air damping coefficient, and the governing equation of motion can be written as:

[0094]

[0095] where M(x, t) is the internal bending moment of the beam, v(x, t) represents the relative displacement of the beam cross - section in the magnetostrictive beam 2; m is the mass per unit length; f(t) is the force generated by the tip magnetic mass block 5, where:

[0096]

[0097] where T M and T Pis the stress on the magnetostrictive beam 2 and the single-layer piezoelectric material 1. At this time, the constitutive equations of the single-layer piezoelectric material 1 and the magnetostrictive beam 2 are introduced;

[0098]

[0099]

[0100] D = e 31 S p + ε 33 E

[0101] where E m and E S are the Young's moduli of the magnetostrictive beam 2 and the single-layer piezoelectric material 1 respectively, s m and s p are the strains of the magnetostrictive beam 2 and the single-layer piezoelectric material 1, H and E represent the magnetic field intensity and the electric field intensity respectively, where the voltage V = Ehp. Substituting Equation (3) into Equation (2) gives:

[0102]

[0103] where H(x) and EI are the Heaviside function of the cantilever beam and the corresponding equivalent stiffness. Substituting Equation (4) into (1), the motion equilibrium equation of the magnetostrictive beam 2 can be obtained:

[0104]

[0105] δ(x) is the Dirac δ function; m is the mass per unit length; is the piezoelectric coupling coefficient, η is the magnetic field coupling coefficient; V(t) and H(t) are the voltage on the single-layer piezoelectric material 1 and the magnetic field on the magnetostrictive beam 2, and these parameters are determined by the geometric and material properties of the magnetostrictive beam 2, where:

[0106] m = (ρ m h m l m + ρ s h s l s )

[0107]

[0108]

[0109] m, b, l, η, h m , ρ, E, represent the mass per unit length, width, length, piezoelectric coupling coefficient, piezomagnetic coupling coefficient, thickness, density, Young's modulus, and neutral layer position of the magnetostrictive beam 2 respectively.

[0110] The analysis scheme of the electromagnetic force and magnetostrictive force of the tip magnetic mass 5 of the present invention is as follows:

[0111] In the alternating magnetic field collector, the force directly acts on the magnet. Since the left end of the magneto-mechanical-electrical cantilever beam type theoretical model with a magnetic mass is fixed, only the force on the tip magnetic mass 5 under the external magnetic field needs to be considered. In the traditional mode, the force is applied by the inertial force, and the inertial force comes from the applied acceleration. In the alternating magnetic field collector, the force directly acts on the tip magnetic mass 5, and the tip magnetic mass 5 also plays the role of mass. The force acting on the tip magnetic mass 5 in the magnetic field is proportional to the integral of the magnetic field gradient over the volume of the magnet, and there is:

[0112]

[0113] Where Fx and Fy are the forces acting on the magnet by the wire in the x and y directions respectively; Br is the remanent magnetic flux density of the tip magnetic mass 5, with the unit of Tesla; V is the volume of the magnet; Hy is the vertical component of the magnetic field. According to the Biot-Savart law, the magnetic field around a single current-carrying wire is described by the following formula:

[0114]

[0115] In the formula, i is the current, ex and ey are the unit vectors in the x and y directions respectively. Using equation (7), F y is expressed as:

[0116]

[0117] Among them, only considering the main acting direction of the magnet, that is, the vertical force component F y , the external force f(t) on the right side of equation 6 can be obtained as:

[0118] f(t) = f m (t) + f a (t) (10)

[0119] Among them, f m (t) is the electromagnetic force received by the tip magnetic mass 5, and f a (t) is the mechanical excitation providing the acceleration excitation. According to equation 9, the electromagnetic force received by the tip permanent magnet can be obtained, and substituting it into 6, the control equation of the beam is:.

[0120]

[0121] Among them: h Mtis the height of the tip magnetic mass 5, Br is the remanent magnetic flux density of the tip magnetic mass 5, and lx is the horizontal distance from the left side of the magneto-mechanical-electric energy harvester to the wire.

[0122] The modal analysis scheme of the magneto-mechanical-electric energy harvester with a magnetic mass is as follows:

[0123] Using modal analysis, the relative displacement along the magnetostrictive beam 2 is expressed as the sum of the products of the mode shape function and the modal coordinates, as shown below:

[0124]

[0125] where r represents the r-th vibration mode. Substituting (12) into (11) and integrating over the length of the magnetostrictive beam 2, and using the orthogonality of the beam, we can obtain:

[0126]

[0127] where

[0128]

[0129]

[0130]

[0131]

[0132] i(t) is the current in the wire, with the direction into the page being positive, a(t) is the acceleration excitation provided to the energy harvester, and ω r is the resonance frequency in the r-th vibration mode.

[0133] Applying Kirchhoff's first law to the equivalent circuit of the magneto-mechanical-electric energy harvester, we can obtain:

[0134]

[0135] where R l represents the sum of the internal resistance of the energy collection circuit and the external load resistance 6, and C P corresponds to the internal capacitance of the single-layer piezoelectric material 1:

[0136]

[0137] where the current of the piezoelectric layer can be expressed by the following formula:

[0138]

[0139] Through equation (2.12), we can obtain:

[0140]

[0141] Combining (18) with (15) and (17) yields the frequency domain response of the output voltage:

[0142]

[0143] The time response of the output power and voltage is determined by solving the equations of motion. The energy harvesting device is then modeled as a system of mass, springs, and dampers to evaluate the damping coefficient of the output circuit. Finally, the output voltage is verified using the finite element method.

[0144] The present invention uses the finite element method to verify the output voltage scheme as follows: In all analyses and finite element analysis, the geometric and material properties of the energy harvesting device are shown in Tables 1.1 and 1.2 respectively:

[0145] Table 1.1 Material dimensions

[0146]

[0147] Table 1.2 Material parameters

[0148]

[0149]

[0150] For this model, the conductor current is temporarily set to 10A and the permanent residual magnetic flux is 1.2T. The force cloud diagram around the conductor is obtained by analytical method. Figure 3 As shown in the force cloud diagram of the permanent magnet at different positions of the wire, the wire position is x=0 and y=0, and it can be obtained that Figure 15 The corresponding force cloud diagram of the wire at different positions is about 0-5mm away from the wire, and the maximum force can reach 60mN. Considering the influence of the magnetic field generated by the current at different positions on the permanent magnet, the tip magnetic mass block 5 and the magnetostrictive beam 2, Lx = 20mm, Ly = 15mm, the force on the permanent magnet is about 10mN, and the relative position of the wire and the transducer is as follows Figure 4 When determining the geometric dimensions and material parameters, first set the input excitation. Under the conditions of acceleration excitation of 0.1g, excitation current of 10A, and load resistance 6 of 1kΩ, the Runge-Kutta algorithm can be used to solve the maximum output voltage of the magneto-mechanical-electrical composite material at the first-order resonance frequency, which is 2.2V, and the output power can reach 0.5mW, as shown in the figure. Figure 6As shown. When the acceleration excitation is set to zero and there is only current excitation, a time-domain diagram of the single-excitation voltage output can be obtained. Under the condition of single current excitation, the output voltage can reach about 1.1V. It can be seen that the excitation does not change the resonance frequency of the device. After adding the acceleration excitation, the voltage output increases by 50%. The frequency-domain response shows that as the acceleration excitation increases, the output also increases. When the acceleration excitation is zero, the output voltage drops from 22V to 11V, and the output voltage decreases by about 50%. The output power drops from 0.52mW to 0.13mW, a decrease of about 75%. It can be seen that the contribution provided by the current excitation (i.e., the contribution provided by the magnetostrictive layer and the permanent magnet) accounts for a large proportion. Compared with the traditional non-magnetic mass block electrical energy harvester, the magneto-mechanical-electrical composite energy harvester can collect energy more effectively.

[0151] The scheme for studying the influence of hybrid excitation in the present invention is as follows: To study the influence of hybrid excitation, in addition to the amplitude of the input signal having an impact on the output, since the input signal is a sine signal, the phase angle of the input excitation also has a certain influence on the output. The finite element method divides the research object into several units, uses the mechanical equilibrium conditions and continuous boundary conditions, and then integrates the small units into a whole. The finite element method describes the details of the object in detail, which is difficult to achieve by other methods. The magneto-mechanical-electrical composite hybrid energy harvester material can detect the alternating magnetic field generated by the wire current and set the acceleration excitation in the solid mechanics - body load. The results based on the analytical integration of the motion control equation are verified by the finite element analysis method. The coil with a current of 10A is simulated by the finite element method to obtain the internal magnetic field distribution of the model, and the vibration and magnetic excitation at different frequencies are calculated. Combining the output voltage, there is a slight decrease in the output voltage and a slight decrease in the first-order resonance frequency. If the energy harvester is in the hybrid excitation when the excitation frequency is near the first natural frequency, the maximum stress range in the structure is much smaller than the yield stress of the single-layer piezoelectric material 1 and the magnetostrictive beam 2, and only reaches the maximum value of 2.55×10 5 N / m2. Among them, when there is only electromagnetic excitation, that is, when the wire coil current in the model is 10A, the potential difference between the upper and lower layers of the single-layer piezoelectric material 1 can reach about 1V, and the voltage is slightly lower than the analytical solution. When the input is hybrid excitation, that is, when the acceleration excitation and the current excitation act together, the frequency response of the voltage of the piezoelectric layer can be obtained. It can be seen that the total voltage output is about 2.2V, the resonance frequency shifts slightly to the right, and the first-order resonance frequency can reach 51HZ. Compared with the single-excitation input of the same material, the voltage output of the hybrid excitation is greatly improved.

[0152] The working principle and process of the present invention are as follows:

[0153] Taking the magnetostrictive / piezoelectric / permanent magnet cantilever hybrid energy harvester as the research object, through mathematical modeling, analysis and comparison, finite element simulation, etc., a distributed linear theoretical model of the energy harvester is established and derived, and the multi-field coupling relationship, the harvesting efficiency of magnetic field energy, partial piezoelectric coverage mode, the influence of bias magnetic field on the output effect of the material, etc. of this model are analyzed; in the alternating magnetic field harvester, the force acts directly on the magnet, and for the magneto-mechanical-electrical cantilever theoretical model with a magnetic mass block, since the left end is fixed, only the force on the tip magnetic mass block 5 under the external magnetic field needs to be considered, and the force acts directly on the tip magnetic mass block 5; the time response of the output power and voltage is determined by solving the motion equation, and then the energy harvesting device is modeled as a mass, spring and damper system to evaluate the damping coefficient of the output circuit. Finally, the finite element method will be used to verify the output voltage.

Claims

1. A modeling method for a cantilever beam type magnetic-machine-electric hybrid energy harvester, characterized in that: It includes an energy harvester, a magneto-mechano-electric cantilever beam theoretical model with a magnetic mass block, an analysis of the electromagnetic force and magnetostrictive force of the tip permanent magnet, and a modal analysis of the magneto-mechano-electric energy harvester with a magnetic mass block. The energy harvester includes a single-layer piezoelectric material, a magnetostrictive beam, a fixed end, a permanent magnet, a tip magnetic mass block, and a load resistor. The single-layer piezoelectric material covers the single-layer magnetostrictive material in a partially covered form. The left end of the single-layer magnetostrictive material is mounted on the fixed end, and the right end is fixed on the base. The permanent magnet and the tip magnetic mass block are placed with the same polarization direction to provide the bias magnetic field required for the normal operation of the magnetostrictive material. The tip magnetic mass block is attached to the top of the beam to control the vibration frequency and output power and collect the low-frequency magnetic field around the collecting wire. The magnetostrictive beam is made of a single-layer magnetostrictive material, and the load resistor represents the load on the single-layer piezoelectric material.

2. The modeling method of the cantilever magneto-mechano-electric hybrid energy harvester according to claim 1, wherein: The modeling scheme of the magneto-mechano-electric cantilever beam theoretical model with a magnetic mass block is as follows: Let the thickness and length of the magnetostrictive beam be h m and L, where L = L1 + L2; the thickness, length, and width of the single-layer piezoelectric material are respectively , , b, where = L1; the magnetostrictive beam is modeled using the Euler-Bernoulli beam assumption, ignoring the viscous air damping coefficient, and the governing equation of motion is written as: （1） Among them, is the internal bending moment of the beam, represents the relative displacement of the beam cross-section in the magnetostrictive beam; is the mass per unit length; is the force generated by the tip magnetic mass block, where: （2） wherein and are the stresses on the magnetostrictive beam and the single-layer piezoelectric material. At this time, the constitutive equations of the single-layer piezoelectric material and the magnetostrictive beam are introduced; （3） Wherein, and are the Young's moduli of the magnetostrictive beam and the single-layer piezoelectric material, respectively, and are the strains of the magnetostrictive beam and the single-layer piezoelectric material, and represent the magnetic field strength and the electric field strength, respectively, where the voltage V = Ehp. Substituting Equation (3) into Equation (2), we get: （4） Among them, and are the Heaviside function of the cantilever beam and the corresponding equivalent stiffness. Substituting Equation (4) into (1), the motion equilibrium equation of the magnetostrictive beam is obtained: （5） is the Dirac delta function; is the mass per unit length; θ is the piezoelectric coupling coefficient, and η is the magnetic field coupling coefficient; and are the voltage on the single-layer piezoelectric material and the magnetic field on the magnetostrictive beam, and these parameters are determined by the geometric and material properties of the magnetostrictive beam, where: （6） , , , , , , , , respectively represent the mass per unit length, width, length, piezoelectric coupling coefficient, piezomagnetic coupling coefficient, thickness, density, Young's modulus, and neutral layer position of the magnetostrictive beam.

3. The modeling method of the cantilever magneto-mechanical-electrical hybrid energy harvester according to claim 1, characterized in that: The analysis scheme of the electromagnetic force and magnetostrictive force of the tip magnetic mass block is as follows: In the alternating magnetic field harvester, the force directly acts on the magnet. Since the left end of the magneto-mechano-electric cantilever beam theoretical model with a magnetic mass block is fixed, only the force on the tip magnetic mass block under the external magnetic field needs to be considered. The force directly acts on the tip magnetic mass block. The force acting on the tip magnetic mass block in the magnetic field is proportional to the integral of the magnetic field gradient over the volume of the magnet. There is: （7） where and are the forces exerted by the wire on the magnet in the x and y directions, respectively; is the remanent flux density of the tip magnetic mass; is the volume of the magnet; Hy is the vertical component of the magnetic field. According to the Biot-Savart law, the magnetic field around a single current-carrying wire is described by the following equation: （8） In the formula, is the current, and are respectively and unit vectors in the directions. Using Equation (7), is expressed as: （9） Among them, only the main acting direction of the magnet, that is, the vertical force component, is considered , and the external force on the right side of Equation 6 is obtained as follows: （10） Among them, is the electromagnetic force on the tip magnetic mass, is the mechanical excitation that provides acceleration excitation. The electromagnetic force on the tip permanent magnet is obtained according to Equation 9 and substituted into Equation 6 to obtain the control equation of the beam as follows: （11） Wherein: , , is the height of the tip magnetic mass, is the remanent magnetic flux density of the tip magnetic mass, is the horizontal distance from the left side of the magneto-mechanical-electrical energy harvester to the wire.

4. The modeling method of the cantilever magneto-mechanical-electrical hybrid energy harvester according to claim 1, characterized in that: The modal analysis scheme of the magneto-mechano-electric energy harvester is as follows: Using modal analysis, the relative displacement along the magnetostrictive beam is expressed as the sum of the products of the mode shape function and the modal coordinates, as shown below: （12） Among them, represents the th vibration mode. Substitute (12) into (11) and integrate along the length of the magnetostrictive beam. Using the orthogonality of the beam, we get: （13） Where, （14） $I$ is the current in the wire, with the direction into the page being positive, $a$ is the acceleration excitation provided to the energy harvesting device, which is the resonant frequency in the $n$-th vibration mode, $f_n$ is the resonant frequency in the $n$-th vibration mode; Applying Kirchhoff's first law to the equivalent circuit of the magneto-mechano-electric energy harvester, we get: （15） wherein represents the sum of the internal resistance of the energy harvesting circuit and the external load resistance, corresponding to the internal capacitance of the single-layer piezoelectric material: （16） Where, the current of the piezoelectric layer is expressed by the following formula: （17） From equation (2.12), we get: （18） Combining equation (18) with equations (15) and (17) gives the frequency-domain response of the output voltage: （19） The time response of the output power and voltage is determined by solving the motion equation. Then, the energy harvesting device is modeled as a mass, spring, and damper system to evaluate the damping coefficient of the output circuit. Finally, the output voltage will be verified using the finite element method.

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