CN113295321A - Embedded runner type micro-cantilever sensor and detection method - Google Patents

Embedded runner type micro-cantilever sensor and detection method Download PDF

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CN113295321A
CN113295321A CN202110582375.3A CN202110582375A CN113295321A CN 113295321 A CN113295321 A CN 113295321A CN 202110582375 A CN202110582375 A CN 202110582375A CN 113295321 A CN113295321 A CN 113295321A
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CN113295321B (en
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郝秀春
何山
李虹霞
李鑫
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Jiangsu University
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    • G01LMEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L9/00Measuring steady of quasi-steady pressure of fluid or fluent solid material by electric or magnetic pressure-sensitive elements; Transmitting or indicating the displacement of mechanical pressure-sensitive elements, used to measure the steady or quasi-steady pressure of a fluid or fluent solid material, by electric or magnetic means
    • G01L9/12Measuring steady of quasi-steady pressure of fluid or fluent solid material by electric or magnetic pressure-sensitive elements; Transmitting or indicating the displacement of mechanical pressure-sensitive elements, used to measure the steady or quasi-steady pressure of a fluid or fluent solid material, by electric or magnetic means by making use of variations in capacitance, i.e. electric circuits therefor

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Abstract

The invention provides an embedded runner type micro-cantilever sensor and a detection method, and relates to the field of MEMS. Different from the traditional embedded channel type micro-cantilever beam, the embedded elongated flow channel is required to be arranged at a position close to the upper surface of the cantilever beam, is far away from the neutral surface of the beam and spans the area with the most obvious strain, so that the flow resistance of the flow channel is ensured to be remarkably changed when the cantilever beam deforms. Meanwhile, fluid with constant volume flow rate in the micro flow channel passes through the micro flow channel, and pressure difference between the upstream and the downstream of the flow channel is measured through the pressure sensor when the cantilever beam deforms, so that the load borne by the cantilever beam can be calculated. According to the invention, the deformation quantity of the cantilever beam is firstly converted into the flow resistance deformation quantity through the embedded flow channel, so that the changed pressure difference is formed at the upstream and the downstream of the fluid, and finally the changed pressure difference is converted into the electrical quantity through the pressure sensor, so that the inherent defect of the traditional cantilever beam detection method when a sensor sensitive structure is arranged on the surface of the cantilever beam is avoided, and the stability and the reliability of the micro-cantilever beam sensor are improved.

Description

Embedded runner type micro-cantilever sensor and detection method
Technical Field
The invention mainly relates to the field of micro-electro-mechanical systems, in particular to a micro-channel embedded cantilever beam sensor and a detection method.
Background
The micro-electro-mechanical system is increasingly widely applied in production and life because of the advantages of miniaturization, integration and the like, and a plurality of micro-sensors with good performance and high reliability are derived. The cantilever structure, as the simplest microstructure, can detect extremely small displacements or mass changes, which makes micro-cantilevers a common choice for high-precision and high-sensitivity sensors.
The object to be measured and the micro-cantilever are fixed together in a certain way, which can cause the bending of the micro-cantilever or the change of the resonance frequency, and then the change of the micro-cantilever is read out by an optical or electrical method, such as a common light beam deflection method, a piezoresistive method, a piezoelectric method, a capacitance method and the like.
In patent CN109696185A, a bionic micro-cantilever structure is disclosed, in which piezoresistors are arranged on the cantilever and a wheatstone bridge is formed by electrode leads. A cantilever beam structure for hypersensitive sensing of micro information is designed based on a stress amplification mechanism of a special structure of a tarsal bone joint of a scorpion, but inherent defects of additional cantilever beam bending and resistance value change caused by current generated in a signal reading process of a piezoresistive method are not compensated, and the piezoresistive method cannot be applied to a liquid environment. A lever type cantilever beam flow rate detecting device is disclosed in patent CN 112326993A. Based on the traditional electrical and mechanical principles, the lever is driven by fluid to rotate so as to change the stress distribution in the cantilever beam, so that the resonance frequency of the cantilever beam is changed, and the device has the characteristic of high flow velocity detection sensitivity. However, the design also highlights a significant disadvantage of a piezoelectric method, namely static detection cannot be achieved independently, when static quantities such as mass and the like are detected, vibration needs to be applied to the cantilever beam through a vibration source, and other problems are easily caused by an additional structure. Patent CN110307919A discloses a high-sensitivity wide-range capacitive force sensor and a method for manufacturing the same, wherein two different force sensitive quantities are adopted, and the magnitudes of a plurality of variable-pitch capacitance responses are used, so that although the range of the sensor is increased, the problem of nonlinearity of the capacitive sensor cannot be solved, and the electromagnetic interference shielding with the structure is difficult to implement. In patent CN 108801468A, a micro-cantilever array optical readout imaging system and method are disclosed, in which an optical readout lens group is replaced by a small hole array to realize optical readout, so as to reduce the system volume and cost, and the installation and debugging are simple, but the optical deflection method is greatly affected by the surrounding environment, the noise of a signal processing circuit is also one of the important factors affecting the measurement accuracy, and the optical device is often very large in volume.
Disclosure of Invention
In order to overcome the defects of the prior art, a novel cantilever beam detection method is provided, and an embedded flow channel type micro-cantilever beam sensor is invented, wherein the embedded flow channel type micro-cantilever beam sensor comprises a micro-cantilever beam (110), a fluid inlet (100), a fluid outlet (102) and an embedded elongated flow channel (101); the elongated flow channel is internally provided with fluid which has constant volume flow rate and laminar flow motion.
Optionally, the embedded elongated flow channel (101) needs to be close to the upper surface of the cantilever beam and far away from the neutral surface of the cantilever beam; the embedded elongated flow channel (101) simultaneously spans the junction of the fixed end and the movable end of the cantilever beam.
Optionally, the flow channel of the embedded flow channel (101) near the fluid outlet (100) and the fluid outlet (102) respectively passes through a section of cylindrical cavity (131).
Optionally, the thin layer (132) above the columnar cavity (131) is used as a pressure sensing film, and the pressure sensing film is respectively used for forming a pressure sensor (200) for detecting the fluid pressure upstream and downstream of the flow channel.
Optionally, the pressure sensor (200) is a capacitive pressure sensor.
The detection technical scheme of the invention is as follows: the flow resistance change of the embedded elongated flow channel (101) caused by the deformation of the cantilever beam (110) converts the load change of the cantilever beam into the upstream and downstream pressure difference change of the flow channel, and then the pressure sensor (200) detects the pressure difference change. Wherein when the concentrated load F is applied to the tail end of the embedded channel type cantilever beam sensor, the pressure difference between the upstream and the downstream of the micro-channel is
Figure BDA0003085567460000021
Wherein QvIs the volume flow rate of the fluid in the flow channel, and is a fixed value, C is the friction coefficient, mu is the hydrodynamic viscosity, y is the distance between the core of the micro-channel and the flow neutral surface, L is the length of the cantilever beam, L is the length of the flow channel, A is the cross-sectional area of the micro-channel, DHHydraulic diameter of the flow channel, E elastic modulus of the cantilever beam, IZThe inertia moment of the cross section of the cantilever beam to the z axis, N is in the shape of a micro channelThe number of variable segments is an even number.
Compared with the traditional piezoresistive micro-cantilever beam, the piezoresistive micro-cantilever beam has certain similarity, the piezoresistor originally arranged at the deformation part of the cantilever beam is replaced by the embedded slender flow channel, the current is replaced by the fluid with constant volume flow rate in the flow channel, and the voltage to be measured is changed into the pressure difference between the upstream and the downstream of the micro-flow channel detected by the pressure sensor. Compared with the traditional electrical detection method, the method avoids adding extra structures on the surface of the cantilever beam, such as doping to obtain resistance or depositing piezoelectric materials; on the contrary, the flow channel serving as a sensitive structure is arranged inside the cantilever beam, so that the flow channel is prevented from falling off easily like a piezoelectric material, the stability and the service life of the sensor are further improved, and the interference of an external environment can be greatly avoided. In addition, the temperature stability of the liquid is higher than that of a semiconductor material, heat is not generated during working, even if the pressure sensor part adopts a piezoresistive pressure sensor, extra heat is generated during working and can be taken away by fluid, and the fluid also plays a role in stabilizing the temperature of the sensor.
Therefore, the invention has better linearity when detecting the stress of the sensor, can improve the sensitivity of the sensor by increasing the length of the flow channel and further increasing the flow resistance, and effectively avoids the defects that the piezoresistive method is greatly influenced by the temperature and cannot be applied to the liquid environment. Compared with other common detection methods, the stability and the anti-interference capability of the structure are improved.
Drawings
FIG. 1 is a structural diagram of the embedded runner cantilever beam, and FIG. 1(a) is a structural plan view; FIG. 1(b) is a sectional view taken along line A-A;
FIG. 2 is a schematic diagram of the detection principle;
FIG. 3 is a schematic diagram of a variable pole pitch capacitive pressure sensor used in an embodiment;
FIG. 4 is a functional block diagram of an integrated sensor detection system in an embodiment;
FIG. 5 is a general flow chart of software of the detection system in the embodiment.
Detailed Description
The working principle and the detection method of the invention are explained by the corresponding calculation formula in the following with the accompanying drawings.
An embedded channel type micro-cantilever sensor is shown in figure 1 and comprises a micro-cantilever (110), a fluid inlet (100), a fluid outlet (102) and an embedded elongated channel (101); the fluid which has constant volume flow rate and laminar flow motion passes through the elongated flow channel; the embedded elongated flow channel (101) needs to be close to the upper surface of the cantilever beam, is far away from the neutral surface of the cantilever beam, and simultaneously spans the junction of the fixed end and the movable end of the cantilever beam; micro channels near a fluid inlet (100) and a fluid outlet (102) at the fixed end of the cantilever beam respectively pass through a section of columnar cavity (131), and a thin layer (132) on the upper side of the cavity is used as a pressure sensing film for manufacturing a pressure sensor so as to respectively detect the hydraulic pressure of fluid flowing out from the upstream and the downstream; the pressure sensor is a variable-pole-distance capacitive pressure sensor and structurally comprises a sensitive layer which is integrated at the fixed end of a cantilever beam and used as a movable pole plate, a columnar pressure cavity which is communicated with a flow channel inside the fixed end, a lower electrode (133) which is positioned at the position of a pressure sensing film on the upper surface of the cantilever beam, a substrate (135) which is used as a fixed pole plate of the capacitance sensor, and an upper electrode (134) which is fixed on the substrate.
The method comprises the following steps:
step 1, converting the load change of the cantilever beam into the upstream and downstream pressure difference change of the flow channel through the flow resistance change of the elongated flow channel (101) caused by the deformation of the cantilever beam (110), and calculating the pressure difference generated by the fluid inlet (100) and the fluid outlet (102) to be
Figure BDA0003085567460000041
Wherein
Figure BDA0003085567460000042
Wherein Q isvIs the volume flow rate of the fluid, C is the coefficient of friction, μ is the hydrodynamic viscosity, L is the length of the channel, A is the cross-sectional area of the microchannel, DHIs the hydraulic diameter of the flow channel; the volume flow velocity Qv of the elongated flow channel (101) is obtained according to the Poiseul's law;
step 2, neglecting the change of the cross section area when the cantilever beam is bent, and solving the change of the cross section area when the cantilever beam is deformedVariation of flow resistance of elongated flow passage (101)
Figure BDA0003085567460000043
Δ L is a channel length variation of the elongated flow channel (101);
step 3, calculating the relation between the channel length variation Delta L of the elongated flow channel (101) and the initial length L;
step 4, only analyzing the deformation condition of the cantilever beam when the tail end of the cantilever beam is subjected to concentrated load to explain the principle, and calculating the bending moment on the beam at the moment as M-F (l-x); x is the distance from the infinitesimal to the fixed end of the cantilever beam, F is the concentrated load applied to the tail end of the cantilever beam, and l is the length of the cantilever beam;
step 5, by taking the amount obtained in the step 2-4 into consideration that the stress of the beam is not equal everywhere, obtaining the relation between the channel length variation quantity delta L of the elongated flow channel (101) and the concentrated load value F and the relation between the flow resistance R and the concentrated load value F, further obtaining the linear relation between the flow resistance variation quantity delta R and the concentrated load value F, and when the channel length L (L < L) is increased, the flow resistance variation quantity is increased, namely the sensitivity of the sensor is increased; when L is reduced, the sensitivity coefficient Delta R/R is increased;
step 6, adopting a capacitance type pressure sensor to detect the pressure of the fluid, directly using a thin layer (132) on the side close to the upper surface of the columnar cavity (131) as a pressure sensing film serving as a sensitive structure as the embedded channel is integrally close to the upper surface, and arranging an electrode (133) on the pressure sensing film; the fixed pole plate needs to additionally increase a substrate (135) at the fixed end of the cantilever beam and place another electrode (134) at the upper side; when the fluid has pressure, the pressure generated at the lower side of the thin layer (132) can cause the pressure sensing film to generate obvious deformation, so that the polar distance between the pressure sensing film and the upper electrode (134) is changed, and the change of the capacitance of the miniature capacitive pressure sensor (200) is further changed;
step 7, the calculated pressure P is the resultant force of the hydraulic pressure and the pressure of the dielectric layer position on the pressure sensing film acting on the pressure sensing film together, and the difference of the pressure values measured by the pressure sensors is equal to the pressure difference delta P only when the pressures of the dielectric layer positions of the two capacitance sensors are equal; the dielectric layer is connected to the outside by arranging an air outlet hole on one side of the substrate (135), so that the pressure of the two capacitance sensors at the position is always equal to the atmospheric pressure, and meanwhile, the fixed pole plate can lead out the electrode so as to be connected with a lead.
The following describes the specific implementation of the method of the present invention:
the invention uses the embedded channel as a sensitive structure to detect the deformation of the sensor, and the principle of the invention is explained by combining the slender flow channel shown in figure 2. The left and right sides of the flow channel in fig. 2(a) are fixedly constrained, and a section of elongated flow channel is arranged in the middle, when a certain flow rate of fluid flows through the long straight channel, a pressure difference is generated between the upstream and the downstream of the long straight channel, and the value can be calculated by the following formula:
Figure BDA0003085567460000051
where Δ P is the pressure difference between the upstream pressure P1 and the downstream pressure P2, QvIs the volume flow rate of the fluid, C is the coefficient of friction, μ is the hydrodynamic viscosity, L is the length of the channel, A is the cross-sectional area of the microchannel, DHIs the hydraulic diameter of the flow channel. It can be readily seen from equation (1) that a large pressure differential can develop between the upstream and downstream flow paths of the elongate flow passage.
If an external force is applied to the position of the elongated flow path at this time, the flow path is deformed as shown in fig. 2(b), and if the volumetric flow rate Qv is maintained, the cross-sectional area a decreases as the length L of the intermediate elongated flow path (101) increases, and thus the pressure difference Δ P increases.
According to the poisson law:
Qv=ΔP/R (2)
wherein R is the flow resistance, and the unit is Pa.s.m-3In conjunction with equation (1), it can be seen that for the elongated flow channel in the figure, the flow resistance is calculated as:
Figure BDA0003085567460000052
it can therefore be understood that a flow channel deformation leads to an increase in flow resistance and thus to an increase in the pressure difference upstream and downstream of the fluid. The structure is similar to the working principle of a piezoresistor, so that the structure is suitable for various stress strain detections like a piezoresistor method, and the effect of the structure in the MEMS is far better than that in the macroscopic environment because the flow resistance is inversely proportional to the fourth power of the cross section area of a flow channel.
In this embodiment, because the neutral plane is not stressed nor deformed when the cantilever beam is deformed, the embedded microfluidic (101) channel needs to be far from the neutral plane, as close to the surface as possible, and should be placed where the deformation is most significant.
For the elongated flow channel of fig. 1, ignoring the change in cross-sectional area when the cantilever beam is bent, the change in flow resistance when deformed is:
Figure BDA0003085567460000061
wherein the relationship between the channel length variation and the initial length of the elongated flow channel (101) is as follows:
ΔL=εL (5)
epsilon is the positive strain of the section of the beam, if the interface of the embedded flow channel is very small, the influence of the flow channel and the fluid on the measurement mechanical parameters is neglected, and the stress definition comprises the following steps:
Figure BDA0003085567460000062
wherein sigma is the positive strain of the section of beam, y is the distance between the strain position and the neutral plane, M is the bending moment applied to the beam, and IZIs the moment of inertia of the beam to the z-axis.
In this embodiment, only the deformation condition of the cantilever beam when the end of the cantilever beam is subjected to concentrated load is analyzed to illustrate the principle, and then the bending moment on the beam at this time is:
M=F(l-x) (7)
x is the distance from the infinitesimal to the fixed end of the cantilever beam, F is the concentrated load applied to the tail end of the cantilever beam, and l is the length of the cantilever beam.
From equations 4 to 7, considering that the stress of the beam is not equal everywhere, the total deformation amount (length change amount) is related to the concentrated load value by:
Figure BDA0003085567460000063
therefore, the relationship of the flow resistance to the concentrated load F is:
Figure BDA0003085567460000064
as can be seen from formula 9, the flow resistance variation and the concentrated load value are in a linear relationship; and when the channel length L (L < L) is increased, the flow resistance variation is increased, namely the sensitivity of the sensor is increased; when L is reduced, the sensitivity coefficient Delta R/R is increased; the piezoresistive sensor is the same as the piezoresistive sensor and conforms to the common principle. In the formula 9, only the flow resistance variation of a single-section channel is calculated, and since there is an inlet and an outlet of fluid in practice, at least two sections of micro channels are required to form a section of U-shaped micro channel, and in practice, the channel is designed to be serpentine in order to increase the output.
In the embodiment, the pressure of the fluid is detected by using a capacitive pressure sensor as shown in fig. 3. The cylindrical pressure sensing cavity (i.e. the cylindrical cavity (131)) of the capacitive pressure sensor can be manufactured together with the elongated flow channel (101) by the same process. Because the embedded channel is wholly close to the upper surface, a thin layer (132) on the upper surface side of the pressure sensing cavity (131) can be directly used as a pressure sensing film to serve as a sensitive structure, and an electrode (133) is arranged on the pressure sensing film; the fixed pole plate needs to additionally add a substrate (135) at the fixed end of the cantilever beam and place another electrode (134) at the upper side. When the fluid has pressure, the pressure generated at the lower side of the pressure sensing film (i.e. the thin layer (132)) can cause the pressure sensing film to generate obvious deformation, so that the polar distance between the pressure sensing film and the upper electrode (134) is changed, and the capacitance of the miniature capacitive pressure sensor (200) is changed.
In this embodiment, a variable-pitch capacitive sensor with a circular plate is adopted, and the capacitance value calculation formula is as follows:
Figure BDA0003085567460000071
in the formula of0Is a vacuum dielectric constant of ∈rDielectric constant of air relative to vacuum, delta0The initial pole pitch of the capacitor plates, a is the radius of the plates, D is the bending stiffness of the pressure-sensitive film material, and P is the pressure applied to the pressure-sensitive film.
The pressure P calculated by the equation (10) is a resultant force of the hydraulic pressure acting on the pressure sensing film together with the pressure at the position of the dielectric layer on the pressure sensing film, and the difference between the pressure values measured by the pressure sensors is equal to the pressure difference Δ P only when the pressures at the positions of the dielectric layers of the two capacitance sensors are equal. In the embodiment, the dielectric layer is connected to the outside by arranging an air outlet hole on one side of the substrate (135), so that the pressure of the two capacitance sensors at the position is always equal to the atmospheric pressure, and meanwhile, the fixed polar plate can lead out the electrode so as to be connected with a lead.
The capacitance value can be detected by a dedicated weak capacitance signal detection chip, such as AD7746 or PCap 01. The capacitance value of the micro capacitor is about tens of pF, and a PCap01 capacitance digital conversion chip is recommended to be selected, the chip can simultaneously measure 4 capacitors in a drift mode, and when the basic capacitance is 10pF, the measurement speed of 5Hz can be kept to be measured with the resolution of 6aF, so that the design requirement is met. The PCap01 is placed on the same package substrate as the MEMS sensor, which is connected to the sensing circuitry by wire bonding.
The PCap01 chip is provided with a 48-bit signal processing unit inside, and the obtained measurement data is sent to the output port of the chip, and the data can be output through a Serial Peripheral Interface (SPI) serial communication mode. The PCap01 is used for calculating a capacitance value by charging and discharging a measured capacitor, recording the charging and discharging time of the measured capacitor and the time required by the reference capacitor to be charged and discharged through the same resistor, outputting an unsigned fixed point number with a 3-bit integer 21-bit decimal number, and calculating the value of the measured capacitor through the following formula:
Figure BDA0003085567460000081
in the formula CMEMSIs the measured capacitance, CDROIs the numerical ratio of the readings, CREFIs the value of the reference capacitance.
The output of the PCap01 needs to be read by a single chip microcomputer and can be sent to an upper computer for further processing, recording and displaying after primary processing, an STM32 single chip microcomputer can be selected as a main control chip to control the PCap01, the whole circuit is extremely simple to build, and the whole block diagram of the measurement and control circuit system is shown in FIG. 4.
STM32 sends the data to upper computer LabVIEW again and handles, passes through serial ports between singlechip and the upper computer and connects, adopts general asynchronous transceiver transmitter (UART). LabVIEW mainly realizes the function of a serial port through VISA, and a program flow chart is shown in figure 5, the serial port is initialized and set according to parameters in a program of a single chip microcomputer, a character string read to a buffer area is converted into a byte array, a frame head can be searched through searching a one-dimensional array, data of each channel in a shift array are recombined in sequence according to a found index and combined into a character string, a text attribute node of the character string is utilized to extract capacitance ratio, and a capacitance value C is calculated according to a formula (11)m. And then, the hydraulic pressure P of the position corresponding to the capacitor can be calculated according to a formula (10), the flow resistance R of the embedded flow channel and the variation quantity delta R of the flow resistance relative to the initial value are calculated according to a formula (2), and finally, the load F applied to the tail end of the cantilever beam is calculated according to a formula (9).
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example," or "some examples" or the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims (5)

1. An embedded channel type micro-cantilever sensor is characterized by comprising a micro-cantilever (110), a fluid inlet (100), a fluid outlet (102) and an embedded slender channel (101); the embedded slender flow channel is internally provided with fluid which has constant volume flow rate and laminar flow motion and passes through the embedded slender flow channel; the flow channels of the embedded flow channel (101) near the fluid inlet (100) and the fluid outlet (102) respectively pass through a section of cylindrical cavity (131).
2. The micro-cantilever with embedded flow channel as claimed in claim 1, wherein the embedded elongated flow channel (101) is required to be close to the upper surface of the cantilever and far away from the neutral surface of the cantilever; the embedded elongated flow channel (101) simultaneously spans the junction of the fixed end and the movable end of the cantilever beam.
3. The micro-cantilever with embedded flow channel as claimed in claim 1, wherein the thin layer (132) above the cylindrical cavity (131) is used as a pressure sensing film to form a pressure sensor (200) for detecting the fluid pressure upstream and downstream of the flow channel.
4. The micro-cantilever according to claim 3, wherein the pressure sensor (200) is a capacitive pressure sensor.
5. The method for detecting the deformation of the embedded runner type micro-cantilever sensor is characterized in that the deformation of the cantilever (110) is caused by the embedded slender partThe flow resistance of the flow channel (101) changes, the load change of the cantilever beam is converted into the pressure difference change between the upstream and the downstream of the flow channel, and the pressure sensor (200) detects the pressure difference change. Wherein when the concentrated load F is applied to the tail end of the embedded channel type cantilever beam sensor, the pressure difference between the upstream and the downstream of the micro-channel is
Figure FDA0003085567450000011
Wherein QvIs the volume flow rate of the fluid in the flow channel, and is a fixed value, C is the friction coefficient, mu is the hydrodynamic viscosity, y is the distance between the core of the micro-channel and the flow neutral surface, L is the length of the cantilever beam, L is the length of the flow channel, A is the cross-sectional area of the micro-channel, DHHydraulic diameter of the flow channel, E elastic modulus of the cantilever beam, IZThe cantilever beam cross section is to the moment of inertia of z axle, and N is the quantity of miniflow channel deformation section, is an even number.
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