A method and apparatus for broadband collection of friction-induced stick-slip vibrations

Abstract

The application discloses a method and a device for collecting friction-induced stick-slip vibration in a wide frequency band. The method can effectively convert low-frequency friction-induced stick-slip vibration into electric energy by using the principle of friction electrification through the relative movement between a moving slider and a fixed wall. The moving slider is located on an elastic clamping beam. By applying clamping force on both ends of the clamping beam, the potential energy inside the beam is changed, forming a single-stable and double-stable nonlinear structure. This design not only overcomes the problem of weak response and narrow frequency band of traditional energy oscillators under low-frequency vibration, but also adjusts the potential energy according to the strength and frequency of stick-slip vibration, so as to adapt to the change of vibration environment and effectively convert the low-frequency stick-slip vibration energy induced by friction. The application can enhance the response of the energy oscillator under low-frequency vibration and improve the energy conversion efficiency of the friction-induced stick-slip vibration. The application provides a new technical solution for efficient utilization of low-frequency friction-induced energy.

Description

Technical Field

[0001] This invention relates to the field of friction-induced stick-slip vibration monitoring, and in particular to a method and apparatus for collecting friction-induced stick-slip vibration over a wide bandwidth. Background Technology

[0002] Friction-induced stick-slip vibration is a typical self-excited vibration commonly found in various mechanical systems, such as cutting systems, windshield wipers, and vehicle base brakes—dry friction systems with low relative sliding speeds. Particularly during train braking, when the train speed approaches a complete stop, the vehicle exhibits noticeable fluttering behavior accompanied by low-frequency creeping groaning noise, severely impacting passenger comfort. Furthermore, practical engineering applications have shown that this fluttering behavior can lead to problems such as brake pad chipping, seriously endangering train safety. Although this vibration is harmful and difficult to completely eliminate, it possesses considerable energy that can be converted into electrical energy using energy harvesting technology. The harvested electrical energy can power miniature sensors installed on the braking interface, enabling passive monitoring of the interface's health status.

[0003] Existing technologies primarily rely on piezoelectric materials or electromagnetic induction devices to convert vibrational energy into electrical energy. However, piezoelectric materials have low response efficiency to low-frequency vibrations (such as the 0.1-100Hz vibration during train braking creep) and are prone to performance degradation due to mechanical fatigue. Electromagnetic devices require precise alignment and continuous relative motion, making them unsuitable for the complex multi-degree-of-freedom vibration environment of the braking interface. Triboelectric nanogenerators, as an emerging technology, possess better low-frequency response capabilities and are well-suited for low-frequency vibration excitation such as friction-induced stick-slip vibration. However, methods and devices for broadband collection of friction-induced stick-slip vibration still have certain shortcomings in terms of energy conversion efficiency and adaptability. In traditional methods, the energy oscillator has a weak response under low-frequency vibration conditions, resulting in limited energy collection from friction-induced stick-slip vibration. Furthermore, these methods have narrow operating bandwidths, failing to cover a wide range of vibration frequencies, making them difficult to effectively adapt to different vibration environments. In addition, existing devices cannot dynamically adjust their potential energy according to the intensity and frequency changes of stick-slip vibration, resulting in low energy conversion efficiency under different vibration conditions and difficulty in effectively utilizing external vibration energy. This fixed potential energy characteristic limits the device's adaptability, leading to a decrease in energy conversion efficiency during low-frequency stick-slip vibrations, thus affecting the stability and practicality of energy harvesting. Therefore, improving low-frequency response, broadening the operating frequency band, and achieving adaptive potential energy adjustment to more efficiently convert friction-induced stick-slip vibration energy remain pressing issues in this field.

[0004] Therefore, this application proposes a broadband method and apparatus for collecting friction-induced stick-slip vibrations, aiming to effectively collect the vibration energy caused by stick-slip vibrations and use a high-efficiency nano-triboelectric generator as an energy conversion medium to convert the mutual motion between the friction interfaces into electrical energy. Summary of the Invention

[0005] In order to overcome the shortcomings and deficiencies of the existing technology, the present invention provides a method and apparatus for collecting friction-induced stick-slip vibrations in a wideband.

[0006] In a first aspect, the technical solution adopted by the present invention is a method for collecting friction-induced stick-slip vibrations in a wideband manner, the method comprising: Step S1: Design a variable steady-state vibration structure with adjustable potential energy based on the principle of instability of slender beams under pressure. The vibration structure includes an elastic beam vibration main structure, one end of which is fixed and clamped on the base, and the other end is subjected to longitudinal pressure by a nut to adjust the internal potential energy of the elastic beam and change its vibration characteristics. There is a pair of sliders in the middle part of the elastic beam, and the end face of the sliders contacts the wall to form two pairs of friction pairs. Construct the initial dynamic motion equation of the elastic beam. Step S2: Set up a triboelectric nanogenerator on the friction pair to convert the mutual motion between the friction pair into electrical energy. The triboelectric nanogenerator consists of two copper foil electrodes and a polytetrafluoroethylene (PTFE) film placed between the two copper foil electrodes. This design utilizes Maxwell's displacement current principle to generate electron transfer, which can achieve the purpose of converting the mutual motion between the friction pair into electrical energy. Step S3: Based on the structure designed in steps S1 and S2, derive the potential energy function and kinetic energy function of the elastic beam, and construct the dynamic equation of motion of the elastic beam according to the Lagrange equation. Step S4: Model the frictional force between the friction pairs in step S1 according to Coulomb's law of friction and construct the frictional force equation; Step S5: Construct the electrodynamic equations of the triboelectric nanogenerator from step S2 based on Kirchhoff's laws; Step S6: Combining steps S3, S4, and S5, the electromechanical coupling control equations for the entire energy harvesting system are derived. Step S7: Solve the motion and output voltage of the system using the electromechanical coupling control equations in step S6, optimize the key parameters in the design, compare the energy output performance between monostable and multistable states, and achieve adaptive adjustment of different steady-state structures according to different vibration environments to achieve the optimal output of the system.

[0007] Furthermore, the initial dynamic equation of motion for the elastic beam, for a compressed elastic beam structure, has an internal potential energy function divided into two parts: one part is the strain energy generated by the beam's elongation along its length, and the other part is the strain energy generated by the elastic beam's bending deformation. The two parts are superimposed to produce the total elastic potential energy. The elastic strain expressions for the two parts are as follows:

[0008] in, This refers to the strain energy generated when the beam elongates along its length. The strain energy generated by the bending deformation of an elastic beam. Let be the first derivative of the lateral displacement of a point on the elastic beam with respect to the coordinates. Let z be the first derivative of the longitudinal displacement of a point on the elastic beam with respect to the coordinates, and z be the distance from a point on the elastic beam to its neutral layer. Let be the second derivative of the lateral displacement of a point on the elastic beam with respect to the coordinates. Let be the second derivative of the longitudinal displacement of a point on the elastic beam with respect to the coordinates.

[0009] The total potential energy function of the system is calculated, and its expression is:

[0010] in, Represents the potential energy function. Let be the elastic modulus of the elastic beam. Represents a volumetric infinitesimal element.

[0011] Furthermore, the potential energy function and kinetic energy function of the elastic beam are expressed as follows: ; in, Represents the kinetic energy of an elastic beam. For the density of the elastic beam, Let be the cross-sectional area of ​​the elastic beam. Let the length of the elastic beam be _____. For external excitation displacement, The first derivative of the external stimulus with respect to time. Let be the first derivative of the lateral displacement of the elastic beam with respect to time. Let the first derivative of the longitudinal displacement of the elastic beam with respect to time be denoted as . Dirac symbol, For the mass of the slider, Let the coordinates of the elastic beam be along its length. Let be a length infinitesimal element on the elastic beam; Due to the non-extensibility of the beam, the longitudinal and lateral displacements have the following relationship:

[0012] in, For the magnitude of the preload, Let be a point on the elastic beam, which is a small element.

[0013] The lateral displacement of the clamping beam is updated as a series of orthogonal mode shapes multiplied by the time coordinate, expressed as:

[0014] in, Represents time-dependent modal coordinates. The mode shape representing an elastic beam; Define the Lagrange:

[0015] in, Represents the Lagrange quantity. As the kinetic energy of the system, This represents the potential energy of the system.

[0016] Furthermore, the dynamic equations of motion for the elastic beam constructed based on the Lagrange equations are expressed as follows:

[0017] The expressions for each coefficient are as follows:

[0018] in, This represents the second derivative of the modal coordinates with respect to time. This represents the first derivative of the modal coordinates with respect to time. For the second derivative of the external stimulus with respect to time, The damping coefficient is... Let the moment of inertia of the elastic beam be... This represents the first derivative of the mode function with respect to the coordinates at a point on the mode shape function. It represents the second derivative of the mode function with respect to the coordinates at a certain point.

[0019] Furthermore, the equation for friction is expressed as follows: ; in, Represents kinetic friction. and These are the coefficients of kinetic friction between the slider and the metal film and the dielectric material, respectively. The normal contact force between the slider and the wall surface is applied by the compression spring inside the slider. The height of the slider. and The initial position of the slider represents the length of the slider overlapping the dielectric film patch and the length of the slider overlapping the metal electrode at the initial moment of excitation. Represents the symbolic function. This represents the relative sliding speed between the slider and the wall; Assumption , ,So and The following relationship exists between them:

[0020] in, and Representing the position coefficient, without loss of generality, considering the adhesive state during the friction process, the condition for adhesion to occur is:

[0021] in, For maximum static friction, To determine the absolute value of static friction, the following principle applies: ; in, and Here, represents the coefficient of static friction between the slider and the metal film and the dielectric film, respectively, and the magnitude of the static friction force under adhesive conditions. for:

[0022] Furthermore, the electrodynamic equation of the triboelectric nanogenerator simplifies the triboelectric nanogenerator to a first-order lumped-parameter circuit of an ideal voltage source and a capacitor in series. According to Kirchhoff's laws, the electrodynamic equation can be obtained as follows:

[0023] in, This is the voltage across the external resistor. The charge transferred between the two electrodes. The equivalent capacitance of the triboelectric nanogenerator. This is the open-circuit voltage of the circuit; The expressions for equivalent capacitance and open-circuit voltage are:

[0024] in, The surface triboelectric charge density, The thickness of the dielectric material, and These are the vacuum permittivity and the relative permittivity, respectively. The length of the slider; According to Ohm's law, the voltage across the external resistor is: The equivalent circuit differential equation of TEH is:

[0025] in, This refers to the value of the external resistor.

[0026] Secondly, the technical solution adopted by the present invention is a broadband device for collecting friction-induced stick-slip vibrations. The device includes a main vibration elastic beam structure, one end of which is clamped to a fixed end, and the other end of which is clamped to a movable support block and held in place by the clamping block.

[0027] The movable end has a preload nut that can apply a preload force P, compressing the elastic beam from a free state to a monostable and bistable state. The elastic beam has a slider cavity in the middle, and in the internal cross-section of the slider cavity, there are sliders on both the left and right sides of the main vibrating elastic beam structure that can move along the cavity.

[0028] The sliders have a hollow internal structure with compression springs inside, which provide spring force to press the left and right sliders against the left and right side walls respectively. A PTFE film is adhered to the surface of the sliders; correspondingly, copper foil is present at the upper end of the wall surface, and a PTFE film is present at the lower end.

[0029] The PTFE film on the slider and the copper foil on the sidewall together form a triboelectric nanogenerator.

[0030] Beneficial effects: This invention proposes a method and apparatus for wideband collection of friction-induced stick-slip vibrations. By utilizing the principle of triboelectric charging through the relative motion between a moving slider and a fixed wall, the invention effectively converts low-frequency friction-induced stick-slip vibrations into electrical energy. Simultaneously, the moving slider rests on an elastic clamping beam. By applying clamping forces at both ends of the beam, the potential energy within the beam is altered, forming a monostable and bistable nonlinear structure. This design not only overcomes the problems of weak response and narrow bandwidth of traditional energy oscillators under low-frequency vibrations but also adjusts its own potential energy according to the intensity and frequency changes of the stick-slip vibration to adapt to changes in the vibration environment, effectively converting the energy of friction-induced low-frequency stick-slip vibrations. This invention enhances the response of the energy oscillator under low-frequency vibration conditions, improving the energy conversion efficiency for friction-induced stick-slip vibrations. Furthermore, this method broadens the operating bandwidth, enabling the device to adapt to vibration environments within different frequency ranges and improving the stability of energy collection. In addition, the device can dynamically adjust its own potential energy according to the intensity and frequency changes of the stick-slip vibration, thereby optimizing the vibration energy conversion process and maintaining high energy collection efficiency under different operating conditions. This adaptive adjustment mechanism effectively improves the applicability of the device in complex vibration environments and provides a new technical solution for the efficient utilization of low-frequency friction-induced energy. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the overall steps of the method of the present invention; Figure 2 This is a three-dimensional structural diagram of the device of the present invention; Figure 3 This is a cross-sectional view of the inside of the slider cavity of the present invention; Figure 4 This is a diagram showing the static equilibrium point and elastic potential energy of the elastic beam of the present invention as a function of preload. Figure 5 This is a graph showing the output voltage and corresponding slider vibration displacement under 3Hz excitation according to the present invention. Figure 6 This is a graph showing the variation trend of slider vibration amplitude and output voltage amplitude with vibration frequency in the bistable mode of the present invention; Figure 7 This is a graph showing the relationship between the amplitude and frequency of the slider vibration in the linear system of the present invention. Detailed Implementation

[0032] It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other. The following describes the application in further detail with reference to the accompanying drawings and specific embodiments.

[0033] This invention utilizes the Maxwell displacement current effect of a triboelectric nanogenerator at a dry friction interface to convert the energy of friction-induced stick-slip vibrations into electrical energy. Simultaneously, to overcome the shortcomings of traditional energy harvesters, such as narrow operating bandwidth and poor adaptability, this invention proposes a method and device for harvesting friction-induced stick-slip vibrations with adjustable potential energy over a wide bandwidth. This method alters the internal potential energy of a clamping beam by adjusting the preload applied to both ends, allowing it to form a monostable or bistable vibration structure depending on the magnitude of the preload. The advantage is that it can adapt to different vibration environments by adjusting the frequency and intensity of the stick-slip vibrations, achieving an adaptive energy conversion effect.

[0034] like Figure 1 As shown, a method for collecting friction-induced stick-slip vibrations over a wide bandwidth includes: Step S1: Design a variable steady-state vibration structure with adjustable potential energy based on the principle of instability of slender beams under pressure. The vibration structure includes an elastic beam vibration main structure, one end of which is fixed and clamped on the base, and the other end is subjected to longitudinal pressure by a nut to adjust the internal potential energy of the elastic beam and change its vibration characteristics. There is a pair of sliders in the middle part of the elastic beam, and the end face of the sliders contacts the wall to form two pairs of friction pairs. Construct the initial dynamic motion equation of the elastic beam. Specifically, utilizing the principle of compressive instability in slender beams, a variable steady-state vibration structure with adjustable potential energy is designed. This structure includes an elastic beam as the main vibration structure, with one end fixed to a base and the other end subjected to longitudinal pressure via a nut, thereby adjusting the internal potential energy of the elastic beam and altering its vibration characteristics. This design allows the elastic beam to form monostable or multistable vibration modes under different stress conditions, improving the adaptability of energy harvesting. Furthermore, a pair of sliders are arranged in the middle of the elastic beam, with their end faces contacting the wall surface, forming two pairs of friction pairs, causing the beam's vibration to be affected by friction at the slider end faces. This structural design lays the foundation for vibration energy harvesting and, by constructing the initial dynamic equations of motion for the elastic beam, provides a basis for subsequent mathematical modeling.

[0035] Step S2: Set up a triboelectric nanogenerator on the friction pair to convert the mutual motion between the friction pair into electrical energy. The triboelectric nanogenerator consists of two copper foil electrodes and a polytetrafluoroethylene (PTFE) film placed between the two copper foil electrodes. This design utilizes Maxwell's displacement current principle to generate electron transfer, which can achieve the purpose of converting the mutual motion between the friction pair into electrical energy. Specifically, a triboelectric nanogenerator is integrated at the location of the friction pair to convert the relative motion between the friction pairs into electrical energy. The triboelectric nanogenerator mainly consists of two copper foil electrodes and a polytetrafluoroethylene (PTFE) film placed between the two copper foil electrodes. When the vibrating structure undergoes periodic motion, the friction pair between the slider and the wall surface experiences relative displacement through contact and separation, thereby generating charge transfer between the copper foil electrodes and forming a voltage output. This energy conversion mechanism can effectively harvest the energy of friction-induced stick-slip vibrations and provide a stable electrical energy output, enabling the system to not only have mechanical vibration conversion capabilities but also achieve efficient electrical energy harvesting.

[0036] Step S3: Based on the structure designed in steps S1 and S2, derive the potential energy function and kinetic energy function of the elastic beam, and construct the dynamic equation of motion of the elastic beam according to the Lagrange equation. Specifically, based on the structural design in steps S1 and S2, the potential energy function and kinetic energy function of the elastic beam are derived, and the dynamic equations of motion for the elastic beam are constructed according to the Lagrange equations. The Lagrange equations can describe the energy balance of the system. By analyzing the motion of the elastic beam under different initial potential energies and force conditions, a mathematical model is established. This process not only reflects the steady-state characteristics of the structure but also provides a foundation for subsequent electromechanical coupling modeling. By constructing these dynamic equations, the response characteristics of the vibration system can be studied in depth, and its energy harvesting efficiency can be further optimized.

[0037] Step S4: Model the frictional force between the friction pairs in step S1 according to Coulomb's law of friction and construct the frictional force equation; Specifically, based on Coulomb's law of friction, the frictional force of the friction pair in step S1 is modeled, and a frictional force equation is constructed. Coulomb's law of friction states that the magnitude of the frictional force is related to the normal force of the contact surface and the coefficient of friction. In this system, the friction between the slider and the wall directly affects the vibration behavior of the elastic beam; therefore, it is necessary to accurately describe the changing characteristics of the frictional force. Frictional force modeling can not only reveal the influence of the friction pair on the system's vibration modes but also provide a mathematical expression for frictional energy consumption for subsequent electromechanical coupling analysis.

[0038] Step S5: Construct the electrodynamic equations of the triboelectric nanogenerator from step S2 based on Kirchhoff's laws; Specifically, based on Kirchhoff's laws, an electrodynamic equation for the triboelectric nanogenerator is constructed to describe the charge accumulation and transport processes during energy conversion. Kirchhoff's laws, including the current law (KCL) and voltage law (KVL), are used to analyze the circuit characteristics of the triboelectric nanogenerator. During its motion, the triboelectric nanogenerator generates charge transfer, forming a dynamic electric field; therefore, the electrodynamic equation needs to be combined to describe the charge accumulation, dissipation, and voltage output characteristics. This modeling process can predict voltage variations under different vibration conditions, laying the foundation for optimizing the system's energy output.

[0039] Step S6: Combining steps S3, S4, and S5, the electromechanical coupling control equations for the entire energy harvesting system are derived. Specifically, by integrating steps S3 (vibration structure dynamics), S4 (friction equation), and S5 (electrodynamic equation), the electromechanical coupling control equation for the entire energy harvesting system is derived. This equation combines the motion equation of the elastic beam, the characteristics of friction, and the charge accumulation behavior of the triboelectric nanogenerator to form a complete energy conversion model. This electromechanical coupling equation can describe the overall dynamic characteristics of the system and reveal the specific mechanism of mechanical energy conversion into electrical energy, providing a theoretical basis for optimizing the design and regulation strategies of the energy harvesting system.

[0040] Step S7: Solve the motion and output voltage of the system using the electromechanical coupling control equations in step S6, optimize the key parameters in the design, compare the energy output performance between monostable and multistable states, and achieve adaptive adjustment of different steady-state structures according to different vibration environments to achieve the optimal output of the system.

[0041] Specifically, the electromechanical coupling control equations in step S6 are used to solve for the system's motion behavior and output voltage, and key parameters are optimized. Numerical simulations are used to analyze the impact of different steady states (monostable and multistable) on energy output, comparing energy harvesting performance under different operating conditions. Furthermore, the system can adaptively adjust its steady-state structure according to different vibration environments to optimize energy output, ensuring efficient operation under various conditions. Finally, experimental verification and parameter optimization ensure that the system achieves optimal energy harvesting performance under complex vibration environments.

[0042] Furthermore, the initial dynamic equations of motion for an elastic beam under compression show that the internal potential energy function is divided into two parts: one part is the strain energy generated by the beam's elongation along its length, and the other part is the strain energy generated by the beam's bending deformation. The superposition of these two parts produces the total elastic potential energy. The elastic strain expressions for the two parts are as follows:

[0043] in, This refers to the strain energy generated when the beam elongates along its length. The strain energy generated by the bending deformation of an elastic beam. Let be the first derivative of the lateral displacement of a point on the elastic beam with respect to the coordinates. Let be the first derivative of the longitudinal displacement of a point on the elastic beam with respect to the coordinates. Let be the distance from a point on the elastic beam to its neutral layer. Let be the second derivative of the lateral displacement of a point on the elastic beam with respect to the coordinates. Let be the second derivative of the longitudinal displacement of a point on the elastic beam with respect to the coordinates.

[0044] The total potential energy function of the system is calculated, and its expression is:

[0045] in, Let E represent the potential energy function, and E be the elastic modulus of the elastic beam. Represents a volumetric infinitesimal element.

[0046] Furthermore, the potential energy function and kinetic energy function of the elastic beam are expressed as follows:

[0047] in, Represents the kinetic energy of an elastic beam. For the density of the elastic beam, Let be the cross-sectional area of ​​the elastic beam. Let the length of the elastic beam be _____. For external excitation displacement, The first derivative of the external stimulus with respect to time. Let be the first derivative of the lateral displacement of the elastic beam with respect to time. Let the first derivative of the longitudinal displacement of the elastic beam with respect to time be denoted as . Dirac symbol, For the mass of the slider, Let the coordinates of the elastic beam be along its length. Let be a length infinitesimal element on the elastic beam; Due to the non-extensibility of the beam, the longitudinal and lateral displacements have the following relationship:

[0048] in, For the magnitude of the preload, Let be a point on the elastic beam, which is a small element.

[0049] The lateral displacement of the clamping beam is updated as a series of orthogonal mode shapes multiplied by the time coordinate, expressed as:

[0050] in, Represents time-dependent modal coordinates. The mode shape representing an elastic beam; Define the Lagrange:

[0051] in, Represents the Lagrange quantity. As the kinetic energy of the system, This represents the potential energy of the system.

[0052] Furthermore, based on the Lagrange equations, the dynamic equations of motion for the elastic beam are constructed, and the expression is:

[0053] The expressions for each coefficient are as follows:

[0054] in, This represents the second derivative of the modal coordinates with respect to time. This represents the first derivative of the modal coordinates with respect to time. For the second derivative of the external stimulus with respect to time, The damping coefficient is... Let the moment of inertia of the elastic beam be... This represents the first derivative of the mode function with respect to the coordinates at a point on the mode shape function. It represents the second derivative of the mode function with respect to the coordinates at a certain point.

[0055] Furthermore, the equation for friction is expressed as follows:

[0056] in, Represents kinetic friction. and These are the coefficients of kinetic friction between the slider and the metal film and the dielectric material, respectively. The normal contact force between the slider and the wall surface is applied by the compression spring inside the slider. The height of the slider. and The initial position of the slider represents the length of the slider overlapping the dielectric film patch and the length of the slider overlapping the metal electrode at the initial moment of excitation. Represents the symbolic function. This represents the relative sliding speed between the slider and the wall; Assumption , ,So and The following relationship exists between them:

[0057] in, and Representing the position coefficient, without loss of generality, considering the adhesive state during the friction process, the condition for adhesion to occur is:

[0058] in, For maximum static friction, To determine the absolute value of static friction, the following principle applies: ; in, and Here, represents the coefficient of static friction between the slider and the metal film and the dielectric film, respectively, and the magnitude of the static friction force under adhesive conditions. for:

[0059] Furthermore, the electrodynamic equation of the triboelectric nanogenerator simplifies the triboelectric nanogenerator to a first-order lumped-parameter circuit of an ideal voltage source and a capacitor in series. According to Kirchhoff's laws, the electrodynamic equation can be obtained as follows:

[0060] in, This is the voltage across the external resistor. The charge transferred between the two electrodes. The equivalent capacitance of the triboelectric nanogenerator. This is the open-circuit voltage of the circuit; The expressions for equivalent capacitance and open-circuit voltage are:

[0061] in, The surface triboelectric charge density, The thickness of the dielectric material, and These are the vacuum permittivity and the relative permittivity, respectively. The length of the slider; According to Ohm's law, the voltage across the external resistor is: The equivalent circuit differential equation of TEH is:

[0062] in, This refers to the value of the external resistor.

[0063] like Figure 2 and Figure 3 As shown, a broadband device for collecting friction-induced stick-slip vibration is disclosed. This device is used to implement a method for collecting friction-induced stick-slip vibration in a broadband manner. The device includes a main vibrating elastic beam structure 6 with a length of 80 mm, a width of 20 mm, a thickness of 0.2 mm, and made of stainless steel. One end of the main vibrating elastic beam structure 6 is clamped on a fixed end 1, and the other end is clamped on a movable support block 10 and held in place by a clamping block 7.

[0064] A preload nut 8 is located on the movable end side, which can apply a preload force P to compress the elastic beam from a free state to a monostable and bistable structure. There is a slider cavity 3 in the middle of the elastic beam. The height and width of the slider cavity are 20mm. The internal cross-section of the slider cavity shows that there are sliders 12 and 13 on the left and right sides of the main vibrating elastic beam structure 6, which can move along the cavity.

[0065] The slider has a hollow internal structure containing compression springs 15 and 16. The stiffness of the springs can be changed according to the required friction force. Their function is to provide spring force to press the left and right sliders against the left and right side walls 2 and 9 respectively. PTFE films 11 and 14 are adhered to the slider surface. Correspondingly, there is copper foil 4 at the upper end of the wall surface and PTFE film 5 at the lower end.

[0066] The PTFE film on the slider and the copper foil on the sidewall together form a triboelectric nanogenerator.

[0067] When the entire structure is subjected to external excitation, relative displacement will occur between the slider and the wall due to inertial force. In particular, when the external excitation frequency is low, the relative motion speed of the slider is low. Due to the difference between the dynamic and static friction coefficients between the slider and the wall, the slider will generate stick-slip vibration relative to the wall. The relative displacement caused by this vibration will generate Maxwell displacement current inside the nano-triboelectric generator, thereby converting the stick-slip vibration energy into electrical energy.

[0068] like Figure 4The figure shows the static equilibrium point and elastic potential energy of the elastic beam in this embodiment as a function of preload. It can be observed that when the preload is small, the elastic beam has only one static equilibrium point, indicating that the system is monostable. When the preload exceeds a certain critical point, the system suddenly has two critical points, indicating that the system becomes a bistable system. From the potential energy function under different preloads, it can be seen that when the preload is less than the critical value, the potential energy decreases as the preload increases. When the preload exceeds the critical value, the shape of the potential energy function changes; the origin changes from the lowest potential energy point to a local highest point, and symmetrical potential wells are formed on both sides. Moreover, the depth of the potential wells increases with further increases in preload. The vibration behavior of the elastic beam can be changed by adjusting the magnitude of the preload.

[0069] Figure 5 The figure shows the voltage signal generated by the triboelectric nanogenerator and the vibration displacement signal of the slider under external excitation of 3Hz. It can be seen from the figure that the slider produces obvious stick-slip vibration. When the slider is in the sticky state, its vibration displacement remains constant, and its output voltage is zero. Only when the slider is in the sliding state is its output voltage non-zero, which proves that the device can effectively collect stick-slip vibration energy.

[0070] Figure 6 The figure shows the changes in slider vibration amplitude and output voltage amplitude with vibration frequency. Figure 7 The figure shows the amplitude-frequency curve of the linear vibration energy harvester. It can be observed that the voltage amplitude and vibration amplitude of this energy harvester initially increase with increasing frequency. When the frequency exceeds a certain critical value, the vibration and voltage suddenly disappear. Its effective frequency bandwidth can reach 17Hz, which is much larger than the effective frequency bandwidth of the linear system, approximately 2Hz.

[0071] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," "link," and "fix" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0072] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various equivalent changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for collecting friction-induced stick-slip vibrations over a wide bandwidth, characterized in that... The method includes: Step S1: Design a variable steady-state vibration structure with adjustable potential energy based on the principle of instability of a slender beam under pressure. The vibration structure includes an elastic beam vibration main structure, one end of which is fixed and clamped on the base, and the other end is subjected to longitudinal pressure by a nut to adjust the internal potential energy of the elastic beam and change its vibration characteristics. There is a pair of sliders in the middle part of the elastic beam. The sliders have a hollow structure inside and contain compression springs to provide spring force to press the left and right sliders against the left and right side walls respectively. The end face of the slider contacts the left and right side walls to form two pairs of friction pairs. Construct the initial dynamic motion equation of the elastic beam. Step S2: Set up a triboelectric nanogenerator on the friction pair to convert the mutual motion between the friction pairs into electrical energy. The triboelectric nanogenerator consists of two copper foil electrodes and a polytetrafluoroethylene film placed between the two copper foil electrodes. Step S3: Based on the structure designed in steps S1 and S2, derive the potential energy function and kinetic energy function of the elastic beam, and construct the dynamic equation of motion of the elastic beam according to the Lagrange equation. Step S4: Model the frictional force between the friction pairs in step S1 according to Coulomb's law of friction and construct the frictional force equation; Step S5: Construct the electrodynamic equations of the triboelectric nanogenerator from step S2 based on Kirchhoff's laws; Step S6: Combining steps S3, S4, and S5, the electromechanical coupling control equations for the entire energy harvesting system are derived. Step S7: Solve the motion and output voltage of the system using the electromechanical coupling control equations in step S6, optimize the key parameters in the design, compare the energy output performance between monostable and multistable states, and achieve adaptive adjustment of different steady-state structures according to different vibration environments to achieve the optimal output of the system.

2. The method for collecting friction-induced stick-slip vibrations in a broadband manner as described in claim 1, characterized in that, The initial dynamic equation of motion for the elastic beam, for a compressed elastic beam structure, is divided into two parts: one part is the strain energy generated by the beam's elongation along its length, and the other part is the strain energy generated by the beam's bending deformation. The two parts are superimposed to produce the total elastic potential energy. The expressions for the elastic strain of the two parts are as follows: in, This refers to the strain energy generated when the beam elongates along its length. The strain energy generated by the bending deformation of an elastic beam. Let be the first derivative of the lateral displacement of a point on the elastic beam with respect to the coordinates. Let be the first derivative of the longitudinal displacement of a point on the elastic beam with respect to the coordinates. Let be the distance from a point on the elastic beam to its neutral layer. Let be the second derivative of the lateral displacement of a point on the elastic beam with respect to the coordinates. Let be the second derivative of the longitudinal displacement of a point on the elastic beam with respect to the coordinates. The total potential energy function of the system is calculated, and its expression is: in, Represents the potential energy function. Let be the elastic modulus of the elastic beam. Represents a volumetric infinitesimal element.

3. The method for collecting friction-induced stick-slip vibrations in a broadband manner as described in claim 2, characterized in that, The kinetic energy function is expressed as follows: in, Represents the kinetic energy function. For the density of the elastic beam, Let be the cross-sectional area of ​​the elastic beam. Let the length of the elastic beam be _____. For external excitation displacement, The first derivative of the external stimulus with respect to time. Let be the first derivative of the lateral displacement of the elastic beam with respect to time. Let the first derivative of the longitudinal displacement of the elastic beam with respect to time be denoted as . Dirac symbol, For the mass of the slider, Let the coordinates of the elastic beam be along its length. Let be a length infinitesimal element on the elastic beam; Due to the non-extensibility of the beam, the longitudinal and lateral displacements have the following relationship: in, For the magnitude of the preload, Let be a infinitesimal element at a point on the elastic beam; The lateral displacement of the clamping beam is updated as a series of orthogonal mode shapes multiplied by the time coordinate, expressed as: in, Represents time-dependent modal coordinates. The mode shape representing an elastic beam; Define the Lagrange: in, Represents the Lagrange quantity. This represents the potential energy function.

4. The method for collecting friction-induced stick-slip vibrations in a broadband manner as described in claim 3, characterized in that, The dynamic equations of motion for the elastic beam, constructed based on the Lagrange equations, are expressed as follows: The expressions for each coefficient are as follows: in, This represents the second derivative of the modal coordinates with respect to time. This represents the first derivative of the modal coordinates with respect to time. For the second derivative of the external stimulus with respect to time, The damping coefficient is... Let the moment of inertia of the elastic beam be... This represents the first derivative of the mode function with respect to the coordinates at a point on the mode shape function. It represents the second derivative of the mode function with respect to the coordinates at a certain point.

5. The method for collecting friction-induced stick-slip vibrations in a broadband manner as described in claim 4, characterized in that, The equation for friction force is expressed as follows: ； in, Represents kinetic friction. and These are the coefficients of kinetic friction between the slider and the metal film and the dielectric material, respectively. The normal contact force between the slider and the wall surface is applied by the compression spring inside the slider. The height of the slider. and The initial position of the slider represents the length of the slider overlapping the dielectric film patch and the length of the slider overlapping the metal electrode at the initial moment of excitation. Represents the symbolic function. This represents the relative sliding speed between the slider and the wall; Assumption , ,So and The following relationship exists between them: in, and Representing the position coefficient, without loss of generality, considering the adhesive state during the friction process, the condition for adhesion to occur is: in, For maximum static friction, To determine the absolute value of static friction, the following principle applies: in, and Here, represents the coefficient of static friction between the slider and the metal film and the dielectric film, respectively, and the magnitude of the static friction force under adhesive conditions. for:

6. The method for collecting friction-induced stick-slip vibrations in a broadband manner as described in claim 5, characterized in that, The electrodynamic equation of the triboelectric nanogenerator simplifies the triboelectric nanogenerator to a first-order lumped-parameter circuit of an ideal voltage source and a capacitor in series. According to Kirchhoff's laws, the electrodynamic equation can be obtained as follows: ； in, This is the voltage across the external resistor. The charge transferred between the two electrodes. The equivalent capacitance of the triboelectric nanogenerator. This is the open-circuit voltage of the circuit; The expressions for equivalent capacitance and open-circuit voltage are: in, The surface triboelectric charge density, The thickness of the dielectric material, and These are the vacuum permittivity and the relative permittivity, respectively. The length of the slider; According to Ohm's law, the voltage across the external resistor is: The equivalent circuit differential equation of TEH is: in, This refers to the value of the external resistor.

7. A broadband device for collecting friction-induced stick-slip vibrations, characterized in that, The device is used to implement the broadband collection of friction-induced stick-slip vibration as described in claim 1, comprising: a main vibration elastic beam structure (6), one end of the main vibration elastic beam structure (6) being clamped on a fixed end (1), and the other end of the main vibration elastic beam structure (6) being clamped on a movable support block (10) and clamped by a clamping block (7); There is a preload nut (8) on the movable end side, which can load the preload force P to compress the elastic beam from the free state to the monostable and bistable structure. There is a slider cavity (3) in the middle of the elastic beam. The internal cross-section of the slider cavity shows that the main vibration elastic beam structure (6) has a slider (12) and (13) on each side for moving along the cavity. The slider surface is covered with PTFE films (11) and (14), and correspondingly, the upper end of the wall surface has copper foil (4) and the lower end has PTFE film (5). The PTFE film on the slider and the copper foil on the sidewall together form a triboelectric nanogenerator.

Images