A method for analyzing electromechanical coupling of triboelectric nanogenerators

Abstract

The present invention discloses a method for analyzing the electromechanical coupling of a triboelectric nanogenerator, comprising the following steps: installing two triboelectric nanogenerators on a test bench so that the two generators can make contact and separate, performing mechanical and electrical tests on the two generators, and obtaining a relationship diagram between force and displacement and voltage output data; establishing bond graph models of the two triboelectric nanogenerators when in contact and separated, respectively, and deriving a system state equation; obtaining corresponding specific parameter values ​​in the bond graph model through experimental data, substituting the values ​​into the state equation to solve the mathematical model, and converting the bond graph model into a corresponding block diagram; establishing a simulation model by combining the mathematical model and the block diagram, obtaining simulated voltage data, and comparing the simulated voltage data with the voltage output data to verify the validity of the bond graph model; and analyzing different parameters of the bond graph model to obtain the influence of the different parameters on the output performance of the triboelectric nanogenerator. The present invention can simply analyze the working mechanism of the generator.

Description

Technical Field

[0001] The present invention relates to the field of nano energy technology, in particular to a method for analyzing electromechanical coupling of a triboelectric nanogenerator. Background Art

[0002] Since its invention by Academician Wang Zhonglin and his team in 2012, triboelectric nanogenerators have achieved remarkable development and application in the fields of energy and sensing. The core principle of triboelectric nanogenerator technology is the coupling of contact electrification and electrostatic induction. Contact electrification, commonly known as triboelectricity, has been documented as far back as 2,600 years ago, yet a scientific explanation for it remains elusive. This is due to the complex mechanism of contact electrification, involving the coupling of multiple physical quantities, including force, electricity, magnetism, and dielectric polarization. Not only is the theory complex, but actual experimental control of performance is often unsatisfactory and time-consuming.

[0003] With the advancement of science and technology, various engineering systems are becoming increasingly complex, driven by both structural complexity and the coupling of multiple physical quantities. The current equivalent circuit model for a triboelectric nanogenerator (TGN) is a series connection of an ideal voltage source and a capacitor. This model only accounts for the circuit elements involved in the TGN's operation and cannot fully describe its mechanism. Relying solely on mathematical models to describe the TGN's operation is not only extremely complex but often difficult to solve due to the coupling of multiple physical quantities. Summary of the Invention

[0004] The purpose of this section is to summarize some aspects of the embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the abstract and title of this application to avoid obscuring the purpose of this section, the abstract and the title of the invention, and such simplifications or omissions should not be used to limit the scope of the present invention.

[0005] In view of the above-mentioned and / or existing problems in the difficult-to-solve working mechanism of the existing friction nanogenerator, the present invention is proposed.

[0006] Therefore, the problem to be solved by the present invention is that the model for studying the working mechanism of the friction nanogenerator in the prior art is too complex and difficult to solve. The present invention provides a method for analyzing the electromechanical coupling of the friction nanogenerator, which can easily analyze the working mechanism of the friction nanogenerator.

[0007] In order to solve the above technical problems, the present invention provides the following technical solutions: a method for analyzing the electromechanical coupling of a triboelectric nanogenerator, comprising the following steps:

[0008] Two triboelectric nanogenerators were mounted on a test bench, allowing them to move in and out of contact. Mechanical and electrical tests were then conducted on them. During the tests, the two triboelectric nanogenerators moved in and out of contact, generating a force-displacement relationship diagram and voltage output data.

[0009] The bond graph models of the two triboelectric nanogenerators in contact and separation were established, and the system state equation was derived.

[0010] The bond graph model is converted into a corresponding block diagram, and a dynamic simulation model of the triboelectric nanogenerator is established by combining the block diagram with actual operating conditions.

[0011] The specific parameter values ​​corresponding to the bond graph model are obtained through experimental data, substituted into the dynamic simulation model, and the voltage data in the simulation experiment is obtained. The voltage data in the simulation experiment is compared with the voltage output data obtained from the actual experiment to verify the validity of the bond graph model.

[0012] The different parameters of the bond graph model are analyzed to obtain the effects of different parameters on the output performance of the friction nanogenerator.

[0013] As a further improvement of the present invention, the bond graph model of two triboelectric nanogenerators in contact is: Let the system state variable X = [p2 q5 q9] T , input variable U = [Se1];

[0014] The characteristic equations of each energy storage element are as follows:

[0015]

[0016] The characteristic equations of each resistive element are as follows:

[0017]

[0018] From the causal relationship and the direction of power flow The flow equation and potential equation are as follows:

[0019]

[0020] Among them, f2=f3=f4, e4=e5=e6=e7, f7=f8=f9;

[0021] Se1 is the potential input mechanical force of the friction nanogenerator during contact, I2 is the energy stored in the friction nanogenerator before contact (m1 is the mass of the friction nanogenerator, p2 is the momentum of the friction nanogenerator), R3 is the energy consumed by the friction nanogenerator to overcome the air resistance before contact, C5 represents the energy stored in the elastic deformation of the surfaces of the two friction nanogenerators at the moment of contact, R6 is the energy consumed by plastic deformation, sound waves and inertial energy generated at the moment of contact, e6 is the unified potential variable force of the R6 part of the energy, R8 is the energy consumed by contact discharge at the moment of contact, C9 is the contact charge generated at the moment of contact, e3 is the potential variable force of air resistance, e4 is the potential variable of bond No. 4 in the bond graph model, e5 is the potential variable force of elastic deformation energy storage, e7 and f7 are the potential variable and flow variable of bond No. 7 in the contact bond graph model, respectively, indicating the direction of energy flow, e8 is the potential variable voltage for contact discharge, f2 is the flow variable velocity of energy storage in the friction nanogenerator, f3 is the flow variable velocity of air resistance, f4 is the flow variable of bond No. 4 in the bond graph model, f8 is the flow variable current for contact discharge, f9 is the flow variable current for contact charge, k2 is the elastic coefficient in the process of recovering elastic deformation, q11 is the generalized displacement in the process of recovering elastic deformation, p12 is the generalized momentum of the friction nanogenerator in the separation process, are the first-order derivatives of state variables p2, q5, and q9, respectively.

[0022] As a further improvement of the present invention, the system state equation during contact is:

[0023]

[0024] Where k1 is the elastic coefficient of elastic deformation, p2, q5, and q9 are the generalized momentum of bonding element 2, the generalized displacement of bonding element 5, and the generalized displacement of bonding element 9, respectively. are the first-order derivatives of state variables p2, q5, and q9, respectively.

[0025] As a further improvement of the present invention, the bond graph model of the two triboelectric nanogenerators when separated is: Let the system state variable X = [q 11 p 12 p 15 q 21 ] T , input variable U=[Sf 10 e 18 ] T ;

[0026] The characteristic equations of each energy storage element are as follows:

[0027]

[0028] The characteristic equations of each resistive element are as follows:

[0029]

[0030] The causal relationship and power flow direction can be written as The flow equation and potential equation are as follows:

[0031]

[0032] e 11 =e 12 =e 13 =e 14 ,f 14 =f 15 =f 16 =f 17 ,e 17 =e 18 =e 19 ,

[0033]

[0034] Sf 10 is the flow input velocity of the TGN system during separation, C 11 is the energy released by the elastic deformation when the two TENG sheets return to their original shape, e 11 and f 11 are the potential variable force and flow variable velocity of the energy released by elastic deformation; I 12 is the kinetic energy consumed in the separation process of the triboelectric nanogenerator, e 12 and f 12 are the potential variable force and flow variable velocity of the energy consumed in the separation process of the triboelectric nanogenerator; R 13 The energy consumed in the separation process to overcome air resistance and offset the inertial force generated in the contact process, e 13 and f 13 The potential variable force and flow variable velocity that consume energy to overcome the electrostatic force during the separation process; e 14 and f 14 are the potential variable and flow variable of bond No. 14 in the bond graph model; I 15 is the energy consumed by the magnetic field excited by the changing electric field during the separation process, e 15 and f 15 is the potential variable voltage and flow variable current of this part of energy; e 17 and f 17 are the potential variable and flow variable of bond No. 17 in the bond graph model, R 16 The energy consumed in overcoming the electrostatic force during the separation process, e 16 and f 16is the potential variable voltage and flow variable current of this part of energy; C 18 The contact electrification charge generated during the contact process is used as input in the separation process. 18 and f 18 are the potential variable voltage and flow variable current of this part of energy respectively; r is the representation of the bond graph model when mechanical energy and electromagnetic energy are converted, which has no energy consumption itself, e 19 and f 19 are the potential variable and flow variable of bond No. 19 in the bond graph model, e 20 and f 20 are the potential variable and flow variable of bond No. 20 in the bond graph model, representing the direction of energy flow, C 21 is the equivalent output capacitance of the triboelectric nanogenerator during separation, e 21 and f 21 are the potential variable voltage and flow variable current of the equivalent output capacitor energy respectively; Se 22 is the equivalent output voltage of the triboelectric nanogenerator during separation process, f 22 is the flow variable current of the output equivalent voltage energy, q 11 、p 12 、p 15 ,q 21 are respectively the generalized displacement of bonding element 11, the generalized momentum of bonding element 12, the generalized momentum of bonding element 15, and the generalized displacement of bonding element 21. are state variables q 11 、p 12 、p 15 ,q 21 The first derivative of .

[0035] As a further improvement of the present invention, the system state equation during separation is,

[0036]

[0037] Compared with the prior art, the present invention has the following advantages: the present invention can intuitively represent the interactions between the various components of the triboelectric nanogenerator system, simplifying the analysis work. By analyzing the different parameters of the bond graph model, the influence of different parameters on the output performance of the triboelectric nanogenerator can be obtained, providing guidance for the design of the triboelectric nanogenerator. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive effort. Among them:

[0039] Figure 1 This is a schematic diagram of the structure of two pairs of friction nanogenerators connected to a leaf spring in the present invention.

[0040] Figure 2 FS dynamometer diagram of the loader without TENG under different experimental conditions (including stroke and frequency).

[0041] Figure 3 FS dynamometer diagram of the loader with TENG under different experimental conditions (including stroke and frequency).

[0042] Figure 4 Bond graph model of the friction nanogenerator in contact.

[0043] Figure 5 Bond graph model of the triboelectric nanogenerator when it is separated.

[0044] Figure 6 The block diagram model corresponding to the bonding diagram of the friction nanogenerator when in contact.

[0045] Figure 7 The block diagram model corresponding to the bonding diagram when the friction nanogenerator is separated.

[0046] Figure 8 Schematic diagram of electrostatic induction at the moment of TENG contact.

[0047] Figure 9 Schematic diagram of electrostatic induction when TENG returns to its initial position after separation.

[0048] Figure 10 A partially enlarged schematic diagram of electrostatic induction when the TENG returns to its initial position after separation.

[0049] Figure 11 This is the dynamic model diagram of Simulink contact simulation.

[0050] Figure 12 This is the output result diagram of Simulink contact simulation.

[0051] Figure 13 Separate simulation dynamic models for Simulink.

[0052] Figure 14 Separate simulation output result diagram for Simulink.

[0053] Figure 15 This is a diagram showing the impact of different contact charge conditions on the output voltage.

[0054] In the picture, 1 is a friction nanogenerator, and 2 is a leaf spring. DETAILED DESCRIPTION

[0055] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0056] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0057] Secondly, the term "one embodiment" or "embodiment" herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in various places throughout this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive of other embodiments.

[0058] Example 1

[0059] Reference Figures 1 to 7 , which is the first embodiment of the present invention, provides a method for analyzing electromechanical coupling of a triboelectric nanogenerator 1, comprising the following steps:

[0060] Two pairs of triboelectric nanogenerators 1 were connected to a leaflet spring 2, which was then mounted on a laboratory bench. A loader (the loader is conventional, and its specific structure is not disclosed in this application) was used to vertically load the leaflet spring 2 downward, causing the pair of triboelectric nanogenerators 1 to move in and out of contact. Mechanical and electrical tests were performed on the springs. During the tests, the pair of triboelectric nanogenerators 1 moved in and out of contact, generating a force-displacement relationship diagram and voltage output data for the triboelectric nanogenerators 1.

[0061] The bond graph models of a pair of triboelectric nanogenerators 1 in contact and separation are established respectively, and the system state equation is derived;

[0062] The bond graph model is converted into a corresponding block diagram, and a dynamic simulation model of the triboelectric nanogenerator 1 is established by combining the block diagram with actual operating conditions;

[0063] The specific parameter values ​​corresponding to the bond graph model are obtained through experimental data, substituted into the dynamic simulation model, and the voltage data in the simulation experiment is obtained. The voltage data in the simulation experiment is compared with the voltage output data obtained from the actual experiment to verify the validity of the bond graph model.

[0064] By analyzing different parameters of the bond graph model, we can obtain the effects of different parameters on the output performance of the friction nanogenerator 1.

[0065] The process of converting the bond graph model into the corresponding block diagram is to draw the block diagram units corresponding to different bond graph elements according to the correspondence between the bond graph and the block diagram in the bond graph theory, draw a flow addition point for each 0-junction, and draw a potential addition point for each 1-junction. Then, according to the equipotential relationship of the 0-junction, connect the same potential variables, according to the equiflow relationship of the 1-junction, connect the same flow variables, and according to the energy flow of the bond graph, connect different block diagram units from the system input to the system output. In this way, the block diagram model corresponding to the bond graph is established.

[0066] The bonding graph model of two triboelectric nanogenerators 1 in contact is:

[0067] Let the system state variable X = [p2 q5 q9] T , input variable U = [Se1];

[0068] The characteristic equations of each energy storage element are as follows:

[0069]

[0070] The characteristic equations of each resistive element are as follows:

[0071]

[0072] From the causal relationship and the direction of power flow The flow equation and potential equation are as follows:

[0073]

[0074] Among them, f2=f3=f4, e4=e5=e6=e7, f7=f8=f9;

[0075] Substituting the characteristic equations of the energy storage element and the resistive element into the flow equation and the potential equation, the system state equation is:

[0076]

[0077] The bonding graph model of the two triboelectric nanogenerators 1 when separated is:

[0078] Let the system state variable X=[q11 p 12 p 15 q 21 ] T , input variable U=[Sf 10 e 18 ] T ;

[0079] The characteristic equations of each energy storage element are as follows:

[0080]

[0081] The characteristic equations of each resistive element are as follows:

[0082]

[0083] The causal relationship and power flow direction can be written as The flow equation and potential equation are as follows:

[0084]

[0085] e 11 =e 12 =e 13 =e 14 ,f 14 =f 15 =f 16 =f 17 ,e 17 =e 18 =e 19 ,

[0086]

[0087] Substituting the energy storage element and resistive characteristic equation into the potential equation and flow equation, the system state equation is:

[0088]

[0089] Before the experiment, a friction nanogenerator 1 was prepared first. Two ABS plates were selected as materials. Wires were placed on one side of the two ABS plates, and a copper film was attached to the side with the wires. Then one of the plates was selected and an FEP film was attached to the surface of the copper film to complete the preparation of the friction nanogenerator 1. When the two TENG plates contacted and separated as the leaf spring 2 moved, the copper film surface would lose electrons and the FEP film surface would gain electrons. Under the coupling of friction electrification and electrostatic induction, the friction nanogenerator 1 would collect the energy of the vibration of the leaf spring 2 (the leaf spring 2 is the existing technology. In this embodiment, it is a component for automobile shock absorption) and convert it into electrical energy. The two wires were connected to external electronic devices to realize the power supply function. During the experiment, the two wires were electrically connected to a 6514 electrometer to test the output voltage data. When the loader moved under different conditions, it drove the leaf spring 2 to compress or extend, and the friction nanogenerator 1 underwent similar vertical contact and separation movements.

[0090] After setting the loading and experimental parameters (including stroke and frequency), the loader starts running. The loader itself has a force sensor and a displacement sensor. The computer connected to it can display the force and displacement data. The data generated in the experiment is processed to obtain the FS indicator diagram of the friction nanogenerator 1 during operation. The experimental charge and voltage measuring device is electrically connected to the friction nanogenerator 1. The experimental charge and voltage measuring device outputs the charge and voltage data under the experimental conditions. Based on the experimental data, the values ​​of the corresponding parameters in the system state equation are obtained, thereby calculating the system state variables.

[0091] Example 2

[0092] Reference Figures 8 to 15 , which is the second embodiment of the present invention. This embodiment uses scientific verification to verify that the method in this application can effectively analyze the parameters of the friction nanogenerator 1.

[0093] The charge in the experiment consists of two main components: charge generated by contact electrification and charge transferred by electrostatic induction. In the actual experiment, a 6514 electrometer was used to measure voltage and charge data. Since the input impedance of the 6514 electrometer during these measurements was greater than 200 TΩ, the resistive load characteristics of the triboelectric nanogenerator 1 indicate that the output characteristics closely resemble those of a completely open circuit, indicating no charge transfer. The contact charge generated during contact is converted from the output of the triboelectric nanogenerator 1 to the input contact charge during the separation process when the triboelectric nanogenerator 1 separates due to mechanical motion. This is represented by capacitive elements in the bond diagram.

[0094] In the established bond graph model, GY is the element where energy conversion occurs. The experiment includes the combined action of mechanical force, electric field and magnetic field. This was discovered in the process of establishing the power bond graph model in this application. It was found that the working process of the friction nanogenerator 1 contains three energies, and it can also correspond to the existing theory. Because the two plates are equivalent to the capacitor model, when the distance between the plates changes, the voltage generated between them and the electric field will change. The changing electric field will excite the magnetic field, but the energy of the excited magnetic field is small. Therefore, this application mainly analyzes through electromechanical coupling, but through the transformation of potential variables and flow variables, it is converted into measurable electrical variables.

[0095] Some parameters are selected based on experimental data, while others are determined based on simulation data. In order to clearly describe the electrostatic induction situation of the contact-separation process, the electrostatic field module in Comsol software is used to simulate the electrostatic induction of the actual contact-separation situation of TENG. The actual simulation situation is as follows: Figures 8-10 As shown in the figure, Comsol software was used to simulate electrostatic induction in a triboelectric nanogenerator (TENG). The distance between the two plates during contact was set to 0.01 mm. In reality, the distance between the two plates during contact is zero, and the theoretical contact voltage is also 0 V. After separation and returning to the initial position, the distance between the two plates is 1.2 mm. The voltage at this point is close to the experimental value of 2.377612 V. The simulated output voltage is specifically 2.373322 V, which is within the difference range, thus validating the experimental results. The figure also shows the distribution of electrostatically induced charge at different locations.

[0096] Table 1 Different experimental data obtained under different experimental conditions

[0097]

[0098] Table 2 Parameter information of triboelectric nanogenerator 1

[0099]

[0100] In this embodiment, the experimental data used in the bond graph model are experimental data corresponding to a loader stroke of 15 mm and a frequency of 1.6 Hz. To clearly analyze the contact discharge situation, the friction nanogenerator 1 was first contacted and separated 30 times during the experiment, and the relevant experimental data were adjusted. Under these conditions, the mathematical model parameters corresponding to the power bond graph model are as follows:

[0101] 1) Se1 = 0.380609 (N);

[0102] 2), m1=5.224723e-3(kg), p2=2.612362e-4(N·S);

[0103] 3)、R3=2.83284e-5(N·S / m);

[0104] 4)、k1=1.2675e7(N / m),q5=1.2e-6(m);

[0105] 5)、R6=2.421822(N·S / m);

[0106] 6)、R8=16.317745(Ω);

[0107] 7)、q9=2.473e-9(C),C9=1.0203e-9(F);

[0108] 8)、Sf 10 =0.05(m / s);

[0109] 9)、k2=1.2675e7(N / m),q 11 =1.2e-6(m);

[0110] 10)、m2=4.8312e-3(kg),p 12 =2.4156e-4(N·S);

[0111] 11)、R 13 =4.376792(N·S / m);

[0112] 12)、p 15 =20.881071(J / A),I 15 =5.113732e8(J / A 2 );

[0113] 13)、R 16 =1.505415e9(Ω);

[0114] 14)、e 18 =0.370498(V);

[0115] 15)、r=2.341206e8(Ω);

[0116] 16)、q 21 =2.473e-9(C),C 21 =3.8722e-12(F)。

[0117] The parameters determined in the embodiments of the present invention are as described above. It should be noted that certain parameter values ​​have been simplified without affecting the analysis results. For example, the contact process is actually an accelerated motion, while the separation process is a decelerated motion. For ease of analysis, except for the collision energy generated at the moment of contact, the average velocity of the remaining parameters is taken as 0.05 m / s for parameter calculation. At the moment of contact, mechanical contact can be established in just a few microseconds. At the moment of contact collision, plastic deformation, sound waves, inertial energy, etc. are generated. During the separation process, a portion of energy is required to offset the inertial energy of the contact process, and the output contact charge is the contact charge generated by a single contact-separation process. When calculating the electric field energy and magnetic field energy, since their values ​​are relatively small, the average value is used instead of the integral operation in the actual calculation. For clarity and ease of understanding, some bond graph elements are represented by similar physical quantities in combination with bond graph theory. Finally, the analysis of the equivalent output capacitance and equivalent output voltage requires corresponding calculations to convert them into the capacitance and voltage generated by a single contact-separation process. Substituting all relevant parameters into the state equation, we can obtain the mathematical model of the triboelectric nanogenerator 1 system. However, the validity of this model needs to be verified through relevant simulations.

[0118] In the embodiment of the present invention, the established bond graph model is converted into the corresponding block diagram, and then the equivalent dynamic simulation model can be constructed in the Simulink module in the Matlab software. Corresponding transformations must be made during the conversion of the two block diagrams, because the same bond graph element has energy storage and energy release during the working process. The final constructed Simulink simulation model and the simulation output results are as follows: Figures 11-14 shown.

[0119] Figure 11 This is the dynamic simulation model of the contact bond graph model in the Simulink software. Since no friction charge is generated before contact, the Simulink simulation module is adjusted and a delay module is added to conform to the actual situation. Figure 12 This is an oscillogram of the triboelectric charge output by the contact module. Since there is no triboelectric charge before contact, triboelectric charge is generated at the moment of contact. The error between the output triboelectric charge value and the experimentally measured value of 0.378025e-9C is not much, so the simulation result is acceptable. Figure 13 To separate the dynamic simulation model of the bond graph model in Simulink software, since the input in the bond graph theory only includes potential source and current source, and the input friction charge does not belong to either, the input friction charge is adjusted accordingly and converted into a related potential source, input potential source E18, and the Simulink simulation module is adjusted at the same time; Figure 14The display shows the output equivalent voltage oscillogram of the separation module. To ensure practical significance, a saturation module needs to be added, otherwise the voltage will continue to increase with the simulation time. The saturation value is set to the maximum effective separation distance. Since the positive and negative charges are equal before separation, the voltage is not displayed externally. It is theoretically known that the equivalent circuit model of the friction nanomotor is a series connection of a voltage source and a capacitor, and the output characteristics are linearly related. Figure 15 The output voltage is linear, consistent with actual conditions, and the error between the simulation output and the experimental data, 2.377612 V, is relatively small. Therefore, the simulation results are acceptable. The simulation output data indicates that the error between the simulation data and the experimental data is within the required range, demonstrating that the power bond graph model established in this invention is effective and can accurately reflect the operating mechanism of the triboelectric nanogenerator 1.

[0120] This paper only analyzes several parameters that are relatively independent and have a greater impact on the output. For other parameters with more correlations, the values ​​of the parameters related to them should be confirmed one by one according to the actual materials, structures, operating conditions, etc. of TENG. For example, in the simulation, it was found that Se1, Sf 10 , I2, I 12 Because they have an impact on all other parameters, they are not analyzed separately. 11 It is the storage and release of elastic deformation energy. Since the energy value is relatively small, it is not suitable for q9 and Se. 22 The output voltage has little impact and is not analyzed separately. The simulation of the remaining parameters shows that the contact charge and the maximum effective separation distance are the main factors affecting the output voltage. Figure 15 As shown in FIG, the voltage reaches its maximum value at the position where the maximum effective separation distance is reached. Therefore, if the output performance of the triboelectric nanogenerator 1 is to be improved, efforts should be made to increase both the amount of contact charge generated and the maximum effective separation distance.

[0121] Compared with the existing technology, the present invention can handle systems where multiple energy sources coexist in a unified manner. The model structure is simple and contains a lot of information. Most importantly, it can reveal the interactions and energy conversion relationships between the various components of the system, deepen people's understanding of the working mechanism of the friction nanogenerator 1 system, and that different outputs can be obtained by changing different parameters, providing theoretical guidance for the structural design of the friction nanogenerator 1.

[0122] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for analyzing electromechanical coupling of a triboelectric nanogenerator, characterized by: The following steps are included: Two pieces of triboelectric nanogenerators (1) are mounted on a test bench so that the two pieces of triboelectric nanogenerators can move in contact and separation, and mechanical and electrical tests are performed on the two pieces of triboelectric nanogenerators (1). During the test, the two pieces of triboelectric nanogenerators (1) move in contact and separation, and a relationship diagram between force and displacement and voltage output data of the triboelectric nanogenerators (1) are obtained; The bonding graph models of the two triboelectric nanogenerators (1) when in contact and separation are established, and the system state equation is derived; The bond graph model is converted into a corresponding block diagram, and a dynamic simulation model of the triboelectric nanogenerator (1) is established by combining the block diagram with actual operating conditions; The specific parameter values ​​corresponding to the bond graph model are obtained through experimental data, substituted into the dynamic simulation model, and the voltage data in the simulation experiment is obtained. The voltage data in the simulation experiment is compared with the voltage output data obtained from the actual experiment to verify the validity of the bond graph model. The different parameters of the bond graph model are analyzed to obtain the effects of different parameters on the output performance of the triboelectric nanogenerator (1); The bonding graph model of two triboelectric nanogenerators (1) in contact is: Let the system state variable X = [p2 q5 q9] T , input variable U = [Se1]; The characteristic equations of each energy storage element are as follows: The characteristic equations of each resistive element are as follows: From the causal relationship and the direction of power flow The flow equation and potential equation are as follows: Among them, f2=f3=f4, e4=e5=e6=e7, f7=f8=f9; Se1 is the potential input mechanical force of the friction nanogenerator (1) during the contact process, I2 is the energy stored in the friction nanogenerator (1) before contact (m1 is the mass of the friction nanogenerator (1), p2 is the momentum of the friction nanogenerator (1)), R3 is the energy consumed by the friction nanogenerator (1) to overcome the air resistance before contact, C5 represents the energy stored in the elastic deformation of the surfaces of the two friction nanogenerators (1) at the moment of contact, R6 is the energy consumed by the plastic deformation, sound wave and inertial energy generated at the moment of contact, e6 is the unified potential variable force of the R6 part of the energy, R8 is the energy consumed by the contact discharge at the moment of contact, C9 is the contact charge generated at the moment of contact, e3 is the potential variable force of air resistance, e4 is the potential variable of bond No. 4 in the bond diagram model, e5 is the potential variable force of elastic deformation energy storage, e7 and f7 are the potential variable and flow variable of bond No. 7 in the contact bond diagram model, respectively, indicating the direction of energy flow, e8 is the potential variable voltage of contact discharge, f2 is the flow variable velocity of energy storage in the friction nanogenerator (1), f3 is the flow variable velocity of air resistance, f4 is the flow variable of bond No. 4 in the bond diagram model, f8 is the flow variable current of contact discharge, f9 is the flow variable current of contact charge, k2 is the elastic coefficient in the process of recovering elastic deformation, q11 is the generalized displacement in the process of recovering elastic deformation, p12 is the generalized momentum of the friction nanogenerator (1) in the separation process, are the first-order derivatives of the state variables p2, q5, and q9, respectively; The system state equation at contact is: Where k1 is the elastic coefficient of elastic deformation, p2, q5, and q9 are the generalized momentum of bonding element 2, the generalized displacement of bonding element 5, and the generalized displacement of bonding element 9, respectively. are the first-order derivatives of state variables p2, q5, and q9, respectively.

2. The electromechanical coupling analysis method of a triboelectric nanogenerator according to claim 1, wherein: The bonding graph model of the two triboelectric nanogenerators (1) when separated is: Let the system state variable X=[q 11 p 12 p 15 q 21 ] T , input variable U=[Sf 10 e 18 ] T ; The characteristic equations of each energy storage element are as follows: The characteristic equations of each resistive element are as follows: The causal relationship and power flow direction can be written as The flow equation and potential equation are as follows: e 11 =e 12 =e 13 =e 14 ,f 14 =f 15 =f 16 =f 17 ,e 17 =e 18 =e 19 , Sf 10 is the flow input velocity of the separation process of the triboelectric nanogenerator (1) system, C 11 is the energy released by the elastic deformation when the two TENG sheets return to their original shape, e 11 and f 11 are the potential variable force and flow variable velocity of the energy released by elastic deformation; I 12 is the kinetic energy consumed in the separation process of the triboelectric nanogenerator (1), e 12 and f 12 are the potential variable force and flow variable velocity of the energy consumed in the separation process of the triboelectric nanogenerator (1); R 13 The energy consumed in the separation process to overcome air resistance and offset the inertial force generated in the contact process, e 13 and f 13 The potential variable force and flow variable velocity that consume energy to overcome the electrostatic force during the separation process; e 14 and f 14 are the potential variable and flow variable of bond No. 14 in the bond graph model; I 15 is the energy consumed by the magnetic field excited by the changing electric field during the separation process, e 15 and f 15 is the potential variable voltage and flow variable current of this part of energy; e 17 and f 17 are the potential variable and flow variable of bond No. 17 in the bond graph model, R 16 The energy consumed in overcoming the electrostatic force during the separation process, e 16 and f 16 is the potential variable voltage and flow variable current of this part of energy; C 18 The contact electrification charge generated during the contact process is used as input in the separation process. 18 and f 18 are the potential variable voltage and flow variable current of this part of energy respectively; r is the representation of the bond graph model when mechanical energy and electromagnetic energy are converted, which has no energy consumption itself, e 19 and f 19 are the potential variable and flow variable of bond No. 19 in the bond graph model, e 20 and f 20 are the potential variable and flow variable of bond No. 20 in the bond graph model, representing the direction of energy flow, C 21 is the equivalent output capacitance of the triboelectric nanogenerator (1) during the separation process, e 21 and f 21 are the potential variable voltage and flow variable current of the equivalent output capacitor energy respectively; Se 22 is the equivalent output voltage of the triboelectric nanogenerator (1) during the separation process, f 22 is the flow variable current of the output equivalent voltage energy, q 11 、p 12 、p 15 ,q 21 They are respectively the generalized displacement of bonding element 11, the generalized momentum of bonding element 12, the generalized momentum of bonding element 15, and the generalized displacement of bonding element 21. are state variables q 11 、p 12 、p 15 ,q 21 The first derivative of .

3. The electromechanical coupling analysis method of a triboelectric nanogenerator according to claim 2, wherein: The system state equation during separation is:

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