A design method of graphene resonant acceleration sensor with indirect sensitive structure

Abstract

The application provides a design method of a graphene resonant acceleration sensor with an indirect sensitive structure. The graphene material with micro size and high performance is introduced into the structural design and preparation process of the sensor, which is of great significance for the further development of the resonant acceleration sensor, and at present, due to the high difficulty in processing and transferring of the graphene film, the research on the graphene film as a direct sensitive element of acceleration is limited. In view of the problem, the application provides an indirect sensitive structure, converts the acceleration into pressure change, and uses a resonant probe with the graphene film as a sensitive element to sense the pressure, and indirectly senses the size of the acceleration through the change of the graphene resonant frequency. The method avoids directly adding mass on the graphene film, thereby improving the working stability of the sensor and reducing the preparation difficulty.

Description

Technical Field

[0001] This invention relates to the field of acceleration sensors, and more particularly to the research on a design method for a graphene resonant acceleration sensor with an indirect sensing structure. Background Technology

[0002] As a core component in the field of inertial measurement, accelerometers have received extensive research and attention. With the maturation of research, their application areas have expanded continuously, from military fields such as detection and guidance to civilian fields such as biomedicine and intelligent detection. This widespread application has further spurred performance development, with accelerometers gradually becoming smaller and more miniaturized, placing higher demands on their precision, sensitivity, and stability. Among numerous sensing mechanisms, resonant accelerometers stand out due to their unique and superior performance, including quasi-digital signal output, strong anti-interference capability, good stability, and wide dynamic measurement range, becoming a rapidly developing field in recent years.

[0003] Introducing graphene, a material with miniaturized size and high performance, into the structural design and fabrication of sensors is of great significance for the further development of resonant accelerometers. However, current research on its use as a direct acceleration sensing element is limited due to the high difficulty in processing and transferring graphene films. To address this issue, this invention proposes an indirect sensing structure that converts acceleration into pressure changes and uses a resonant probe with a graphene film as the sensing element to sense this pressure. The magnitude of acceleration is indirectly sensed through changes in the graphene resonant frequency. This method avoids directly adding mass to the graphene film, thereby improving the sensor's operational stability and reducing fabrication difficulty. Summary of the Invention

[0004] The purpose of this invention is to propose a design method for a graphene resonant accelerometer with an indirect sensing structure, providing a theoretical basis for the design of resonant accelerometers.

[0005] To achieve the above objectives, this invention proposes a design method for a graphene resonant accelerometer with an indirect sensing structure, which specifically includes the following steps.

[0006] In one embodiment of the present invention, the accelerometer structure consists of two parts: an indirect sensing structure and a graphene resonant probe. The indirect sensing structure converts the acceleration acting on the sensor into inertial force by adding mass, and further causes the sensitive film to deflect, resulting in a change in pressure within the sealed cavity. The graphene resonant probe, together with a single-mode optical fiber and a graphene film suspended on the end face of the ferrule, forms a FP interference cavity, reflecting the vibration of the graphene in the change of interference intensity, and thus acquiring the change in the graphene resonant frequency caused by the pressure change within the sealed cavity, ultimately realizing the conversion between acceleration and resonant frequency.

[0007] The fabrication of an accelerometer first requires the preparation of a graphene resonant probe, which mainly involves two steps: graphene film transfer and determination of the FP cavity length. A wet transfer method is used to transfer the graphene film to the ceramic ferrule end face. Specifically, commercially available 10-layer copper-based graphene is cut into 1cm x 1cm squares and immersed in a 5% FeCl3 solution for at least 6 hours until the copper substrate is completely removed. Then, the FeCl3 solution is repeatedly diluted with deionized water until it becomes transparent to remove any residual FeCl3. Finally, the purified graphene film is subjected to van der Waals forces... Under the action of the fiber, the accelerometer is transferred to the end face of the ceramic ferrule. Next, the FP cavity length is determined by cutting the end face of the uncoated single-mode fiber flat with a fiber cleaver and inserting it from the tail end of the ceramic ferrule. The length of the FP cavity formed between the fiber end face and the graphene film is displayed in real time by a spectrometer. Epoxy glue is used to fix the connection between the tail end of the ceramic ferrule and the single-mode fiber to determine the final FP cavity length. Finally, the graphene resonant probe, sensitive film, and additional mass are sequentially bonded to the shell with epoxy glue to form a sealed cavity, completing the fabrication of the accelerometer.

[0008] The working principle of an accelerometer is as follows:

[0009] When vertical acceleration is applied to the sensor, the added mass can convert it into inertial force:

[0010] F = ma

[0011] In the formula: F, m, and a are the magnitudes of inertial force, added mass, and acceleration, respectively. Furthermore, this can cause a normal phase displacement in the sensitive thin film.

[0012]

[0013] In the formula: W is the normal phase shift of the sensitive thin film, μ, r s E s H and H represent the Poisson's ratio, radius, elastic modulus, and thickness of the sensitive membrane, respectively. Furthermore, the change in pressure within the sealed cavity caused by this change can be calculated as follows:

[0014]

[0015] In the formula: Δp is the pressure change inside the sealed cavity, P0 and P1 are the pressures inside the sealed cavity before and after the deformation of the sensitive membrane, ρ is the air density, R is the Clapeyron constant, T is the ambient temperature, M is the molar mass of air, V0 and V1 are the gas volumes inside the sealed cavity before and after the deformation of the sensitive membrane, and V0=πr s 2 h, where h is the height of the sealed cavity, V1 = πr s 2 (hW), then the pressure change within the cavity can be further expressed as:

[0016]

[0017] As can be seen from equations (2) and (4), a larger additional mass, a thinner and more deformable sensitive film, and a sealed cavity with a larger diameter and a smaller height can be selected to obtain greater acceleration sensitivity. At the same time, considering that the volume of the accelerometer should not be too large and the stability of the sensitive film during operation should be ensured, a copper block with a mass of 800g is selected as the additional mass, a nitrile diaphragm with a thickness of 0.1mm is selected as the sensitive film, and a stainless steel shell with a radius of 5cm and a height of 8cm is selected as the outer shell.

[0018] Furthermore, because the graphene film is airtight, pressure changes within the sealed cavity can lead to inconsistencies in pressure inside and outside the FP interferometer cavity, causing the graphene film to deflect and deform, resulting in changes in film tension.

[0019]

[0020] In the formula: S p Let v represent the tension change of the graphene film caused by pressure, v, r, E, and t be the Poisson's ratio, radius, elastic modulus, and thickness of the graphene film, respectively, and w be the deflection deformation at the center of the graphene film. When the tension change of the film caused by pressure is much greater than the tension value caused by the prestress of the film, the relationship between the total tension of the film and the pressure change can be approximately obtained:

[0021]

[0022] In the formula: S represents the total tension of the film. Since the graphene film is peripherally fixed, according to the circular film theory, the relationship between the resonant frequency of the graphene film and the total tension of the film can be expressed as:

[0023]

[0024] In the formula: f is the resonant frequency of the graphene film. Combining equations (5) to (7), we can obtain the relationship between the resonant frequency of the graphene film and the pressure change as follows:

[0025]

[0026] Thus, the sensor can convert the applied acceleration into a change in the resonant frequency of the graphene film.

[0027] Instruction manual attached Figure 4 The relationship between the probe's resonant frequency and pressure was demonstrated. A univariate linear fitting revealed a probe resonant frequency-pressure sensitivity of 1.39 Hz / Pa, proving the probe's high sensitivity to pressure. Simultaneously, the curve's linearity was 0.9944, further highlighting the probe's excellent pressure sensitivity. Furthermore, the appendix to the instruction manual... Figure 5 As can be seen, when the vacuum level increased from 0 psi to 9 psi, the probe's quality factor increased from 5.342 to 9.062, indicating a significant improvement in resonance quality. This is because as the vacuum level increases, the in-plane stress of the graphene film gradually increases, making the film more taut. This makes it more stable during vibration and less susceptible to external interference. Simultaneously, the reduction in air volume decreases the gas damping experienced by the graphene film during vibration, thereby reducing energy loss. Furthermore, it can be observed that the increase in quality factor only becomes significant when the vacuum level exceeds 2 psi. This is because at lower vacuum levels, air damping remains relatively large and its change is not significant, resulting in a minimal change in the quality factor. However, at higher vacuum levels, the influence of air damping on the film's vibration decreases significantly, leading to a substantial increase in the quality factor. Although the quality factor of the graphene resonant probe did not undergo a qualitative change due to the reduction in air damping only on one side of the film, it still provides direction for further improvements in probe performance.

[0028] Further testing of acceleration sensitivity was conducted. The rotational speed of the single-axis turntable was adjusted, and the applied acceleration was gradually increased from 0g to 2.5g in increments of 0.5g. The obtained sensor resonant frequency change curve is shown in the attached instruction manual. Figure 6 As shown in the figure, the resonant frequency of the sensor output increases from 0.351MHz to 0.3605MHz with increasing acceleration. Furthermore, fitting the linear portion of the graph yields an acceleration sensitivity of 3575Hz / g and a linearity of 0.9788. Meanwhile, the results also show a dead zone within the 0–1g acceleration measurement range. Therefore, to further determine the precise range of the dead zone, the acceleration increment was reduced to 0.1g, and the test was repeated within the 0.4–1g range. The results are shown in the attached manual. Figure 7As shown, the more precise dead zone location is 0.6g. Ideally, the dead zone of the accelerometer should depend solely on the lock-in amplifier's resolution of adjusting the excitation light frequency. For the lock-in amplifier used in this invention, this value is 1μHz, corresponding to an acceleration resolution of 2.5×10⁻⁶. -10 The experimental results showed a dead zone value much higher than the ideal state, which may be due to the high pressure dead zone value of the resonant probe. Therefore, further experiments determined that the pressure dead zone position of the graphene resonant probe is approximately 0.1 psi, that is, below 689.4 Pa, and the corresponding acceleration dead zone position is below 0.75 g, which is exactly consistent with the experimental test results of acceleration sensitivity. Attached Figure Description

[0029] Figure 1 This is a flowchart illustrating a design method for a graphene resonant accelerometer with an indirect sensing structure according to an embodiment of the present invention.

[0030] Figure 2 This is a structural diagram of the accelerometer sensor according to an embodiment of the present invention;

[0031] Figure 3 This is a flowchart illustrating the fabrication process of the accelerometer sensor according to an embodiment of the present invention;

[0032] Figure 4 This illustrates the relationship between the resonant frequency and pressure in an embodiment of the present invention.

[0033] Figure 5 This illustrates the relationship between the quality factor and pressure in an embodiment of the present invention.

[0034] Figure 6 These are the acceleration sensitivity test results of an embodiment of the present invention;

[0035] Figure 7 The results are the dead zone test results of an embodiment of the present invention. Detailed Implementation

[0036] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar meanings throughout. The embodiments described below are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0037] This invention relates to the design of resonant accelerometers and proposes a design method for a graphene resonant accelerometer with an indirect sensing structure.

[0038] To provide a clearer understanding of the invention, a brief description is provided below. The invention comprises two basic steps: Step 1, structural design of the accelerometer; Step 2, fabrication of the accelerometer.

[0039] Specifically, Figure 1 The diagram shows a flowchart of a design method for a graphene resonant accelerometer with an indirect sensing structure according to an embodiment of the present invention, including the following steps:

[0040] Step S101, structural design of the accelerometer.

[0041] In one embodiment of the present invention, a structural diagram of the acceleration sensor is shown in the appendix to the specification. Figure 2 As shown, it mainly consists of two parts: an indirect sensing structure and a graphene resonant probe. The indirect sensing structure converts the acceleration acting on the sensor into inertial force by adding mass, which further causes the sensitive film to deflect and deform, resulting in a change in pressure within the sealed cavity. The graphene resonant probe, on the other hand, forms a FP interference cavity with a single-mode optical fiber and a graphene film suspended on the end face of the ferrule. It reflects the vibration of the graphene in the change of interference intensity, and then collects the change in the graphene resonant frequency caused by the pressure change within the sealed cavity, ultimately realizing the conversion between acceleration and resonant frequency.

[0042] Step S102, fabrication of the accelerometer.

[0043] In one embodiment of the present invention, the fabrication flowchart of the accelerometer is shown in the appendix to the specification. Figure 3 As shown. First, the graphene resonant probe needs to be fabricated, mainly in two steps: graphene film transfer and determination of the FP cavity length. A wet transfer method is used to transfer the graphene film to the ceramic ferrule end face. The specific process is as follows: Commercially available 10-layer copper-based graphene is cut into 1cm × 1cm squares and immersed in a 5% FeCl3 solution for more than 6 hours. After the copper substrate is completely removed, the FeCl3 solution is repeatedly diluted with deionized water until it becomes transparent to remove residual FeCl3. Finally, the pure graphene film is transferred under the action of van der Waals forces. The fiber is transferred to the end face of the ceramic ferrule. Next, the FP cavity length is determined by cutting the end face of the uncoated single-mode fiber flat with a fiber cleaver and inserting it into the ceramic ferrule. The length of the FP cavity formed between the fiber end face and the graphene film is displayed in real time by a spectrometer. Epoxy adhesive is used to fix the connection between the ceramic ferrule and the single-mode fiber to determine the final FP cavity length. Finally, the graphene resonant probe, sensitive film, and additional mass are sequentially bonded to the shell with epoxy adhesive to form a sealed cavity, completing the fabrication of the accelerometer.

[0044] The working principle of an accelerometer is as follows:

[0045] When vertical acceleration is applied to the sensor, the added mass can convert it into inertial force:

[0046] F = ma (1)

[0047] In the formula: F, m, and a are the magnitudes of inertial force, added mass, and acceleration, respectively. Furthermore, this can cause a normal phase displacement in the sensitive thin film.

[0048]

[0049] In the formula: W is the normal phase shift of the sensitive thin film, μ, r s E s H and H represent the Poisson's ratio, radius, elastic modulus, and thickness of the sensitive membrane, respectively. Furthermore, the change in pressure within the sealed cavity caused by this change can be calculated as follows:

[0050]

[0051] In the formula: Δp is the pressure change inside the sealed cavity, P0 and P1 are the pressures inside the sealed cavity before and after the deformation of the sensitive membrane, ρ is the air density, R is the Clapeyron constant, T is the ambient temperature, M is the molar mass of air, V0 and V1 are the gas volumes inside the sealed cavity before and after the deformation of the sensitive membrane, and V0=πr s 2 h, where h is the height of the sealed cavity, V1 = πr s 2 (hW), then the pressure change within the cavity can be further expressed as:

[0052]

[0053] As can be seen from equations (2) and (4), a larger additional mass, a thinner and more deformable sensitive film, and a sealed cavity with a larger diameter and a smaller height can be selected to obtain greater acceleration sensitivity. At the same time, considering that the volume of the accelerometer should not be too large and the stability of the sensitive film during operation should be ensured, a copper block with a mass of 800g is selected as the additional mass, a nitrile diaphragm with a thickness of 0.1mm is selected as the sensitive film, and a stainless steel shell with a radius of 5cm and a height of 8cm is selected as the outer shell.

[0054] Furthermore, because the graphene film is airtight, pressure changes within the sealed cavity can lead to inconsistencies in pressure inside and outside the FP interferometer cavity, causing the graphene film to deflect and deform, resulting in changes in film tension.

[0055]

[0056] In the formula: S pLet v represent the tension change of the graphene film caused by pressure, v, r, E, and t be the Poisson's ratio, radius, elastic modulus, and thickness of the graphene film, respectively, and w be the deflection deformation at the center of the graphene film. When the tension change of the film caused by pressure is much greater than the tension value caused by the prestress of the film, the relationship between the total tension of the film and the pressure change can be approximately obtained:

[0057]

[0058] In the formula: S represents the total tension of the film. Since the graphene film is peripherally fixed, according to the circular film theory, the relationship between the resonant frequency of the graphene film and the total tension of the film can be expressed as:

[0059]

[0060] In the formula: f is the resonant frequency of the graphene film. Combining equations (5) to (7), we can obtain the relationship between the resonant frequency of the graphene film and the pressure change as follows:

[0061]

[0062] Therefore, according to equations (4) and (8), the sensor can convert the applied acceleration into a change in the resonant frequency of the graphene film.

[0063] Instruction manual attached Figure 4 The relationship between the probe's resonant frequency and pressure was demonstrated. A univariate linear fitting revealed a probe resonant frequency-pressure sensitivity of 1.39 Hz / Pa, proving the probe's high sensitivity to pressure. Simultaneously, the curve's linearity was 0.9944, further highlighting the probe's excellent pressure sensitivity. Furthermore, the appendix to the instruction manual... Figure 5 As can be seen, when the vacuum level increased from 0 psi to 9 psi, the probe's quality factor increased from 5.342 to 9.062, indicating a significant improvement in resonance quality. This is because as the vacuum level increases, the in-plane stress of the graphene film gradually increases, making the film more taut. This makes it more stable during vibration and less susceptible to external interference. Simultaneously, the reduction in air volume decreases the gas damping experienced by the graphene film during vibration, thereby reducing energy loss. Furthermore, it can be observed that the increase in quality factor only becomes significant when the vacuum level exceeds 2 psi. This is because at lower vacuum levels, air damping remains relatively large and its change is not significant, resulting in a minimal change in the quality factor. However, at higher vacuum levels, the influence of air damping on the film's vibration decreases significantly, leading to a substantial increase in the quality factor. Although the quality factor of the graphene resonant probe did not undergo a qualitative change due to the reduction in air damping only on one side of the film, it still provides direction for further improvements in probe performance.

[0064] Further testing of acceleration sensitivity was conducted. The rotational speed of the single-axis turntable was adjusted, and the applied acceleration was gradually increased from 0g to 2.5g in increments of 0.5g. The obtained sensor resonant frequency change curve is shown in the attached instruction manual. Figure 6 As shown in the figure, the resonant frequency of the sensor output increases from 0.351MHz to 0.3605MHz with increasing acceleration. Furthermore, fitting the linear portion of the graph yields an acceleration sensitivity of 3575Hz / g and a linearity of 0.9788. Meanwhile, the results also show a dead zone within the 0–1g acceleration measurement range. Therefore, to further determine the precise range of the dead zone, the acceleration increment was reduced to 0.1g, and the test was repeated within the 0.4–1g range. The results are shown in the attached manual. Figure 7 As shown, the more precise dead zone location is 0.6g. Ideally, the dead zone of the accelerometer should depend solely on the lock-in amplifier's resolution of adjusting the excitation light frequency. For the lock-in amplifier used in this invention, this value is 1μHz, corresponding to an acceleration resolution of 2.5×10⁻⁶. -10 The experimental results showed a dead zone value much higher than the ideal state, which may be due to the high pressure dead zone value of the resonant probe. Therefore, further experiments determined that the pressure dead zone position of the graphene resonant probe is approximately 0.1 psi, that is, below 689.4 Pa, and the corresponding acceleration dead zone position is below 0.75 g, which is exactly consistent with the experimental test results of acceleration sensitivity.

[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. These modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A design method for a graphene resonant accelerometer with an indirect sensing structure, characterized in that: The accelerometer sensor consists of two parts: an indirect sensing structure and a graphene resonant probe. The indirect sensing structure converts the acceleration acting on the sensor into inertial force by adding mass, which further causes the sensitive film to deflect and deform, resulting in a change in pressure within the sealed cavity. The graphene resonant probe, on the other hand, forms a FP interference cavity with a single-mode optical fiber and a graphene film suspended on the end face of the ferrule. It reflects the vibration of the graphene in the change of interference intensity, and then collects the change in the graphene resonant frequency caused by the pressure change within the sealed cavity, ultimately realizing the conversion between acceleration and resonant frequency. The fabrication of an accelerometer first requires the preparation of a graphene resonant probe, which mainly involves two steps: graphene film transfer and determination of the FP cavity length. A wet transfer method is used to transfer the graphene film to the ceramic ferrule end face. Specifically, commercially available 10-layer copper-based graphene is cut into 1cm x 1cm squares and immersed in a 5% FeCl3 solution for at least 6 hours until the copper substrate is completely removed. Then, the FeCl3 solution is repeatedly diluted with deionized water until it becomes transparent to remove any residual FeCl3. Finally, the purified graphene film is subjected to van der Waals forces... Under the action of the fiber, the accelerometer is transferred to the end face of the ceramic ferrule. Next, the FP cavity length is determined by cutting the end face of the uncoated single-mode fiber flat with a fiber cleaver and inserting it from the tail end of the ceramic ferrule. The length of the FP cavity formed between the fiber end face and the graphene film is displayed in real time by a spectrometer. Epoxy glue is used to fix the connection between the tail end of the ceramic ferrule and the single-mode fiber to determine the final FP cavity length. Finally, the graphene resonant probe, sensitive film, and additional mass are sequentially bonded to the shell with epoxy glue to form a sealed cavity, completing the fabrication of the accelerometer. The working principle of an accelerometer is as follows: When vertical acceleration is applied to the sensor, the added mass can convert it into inertial force: F = ma (1) In the formula: F, m, and a are the magnitudes of inertial force, added mass, and acceleration, respectively. Furthermore, this can cause a normal phase displacement in the sensitive thin film. In the formula: W is the normal phase shift of the sensitive thin film, μ, r s E s H and H represent the Poisson's ratio, radius, elastic modulus, and thickness of the sensitive membrane, respectively. Furthermore, the change in pressure within the sealed cavity caused by this change can be calculated as follows: In the formula: Δp is the pressure change inside the sealed cavity, P0 and P1 are the pressures inside the sealed cavity before and after the deformation of the sensitive membrane, ρ is the air density, R is the Clapeyron constant, T is the ambient temperature, M is the molar mass of air, V0 and V1 are the gas volumes inside the sealed cavity before and after the deformation of the sensitive membrane, and V0=πr s 2 h, where h is the height of the sealed cavity, V1 = πr s 2 (hW), then the pressure change within the cavity can be further expressed as: As can be seen from equations (2) and (4), a larger additional mass, a thinner and more deformable sensitive film, and a sealed cavity with a larger diameter and a smaller height can be selected to obtain greater acceleration sensitivity. At the same time, considering that the volume of the accelerometer should not be too large and the stability of the sensitive film during operation should be ensured, a copper block with a mass of 800g is selected as the additional mass, a nitrile diaphragm with a thickness of 0.1mm is selected as the sensitive film, and a stainless steel shell with a radius of 5cm and a height of 8cm is selected as the outer shell. Furthermore, because the graphene film is airtight, pressure changes within the sealed cavity can lead to inconsistencies in pressure inside and outside the FP interferometer cavity, causing the graphene film to deflect and deform, resulting in changes in film tension. In the formula: S p Let v represent the tension change of the graphene film caused by pressure, v, r, E, and t be the Poisson's ratio, radius, elastic modulus, and thickness of the graphene film, respectively, and w be the deflection deformation at the center of the graphene film. When the tension change of the film caused by pressure is much greater than the tension value caused by the prestress of the film, the relationship between the total tension of the film and the pressure change can be approximately obtained: In the formula: S represents the total tension of the film. Since the graphene film is peripherally fixed, according to the circular film theory, the relationship between the resonant frequency of the graphene film and the total tension of the film can be expressed as: In the formula: f is the resonant frequency of the graphene film. Combining equations (5) to (7), we can obtain the relationship between the resonant frequency of the graphene film and the pressure change as follows: Therefore, according to equations (4) and (8), the sensor can convert the applied acceleration into a change in the resonant frequency of the graphene film.

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