Method for obtaining amplitude characteristic parameters of piezoelectric pressure sensor

Abstract

The application discloses a method for acquiring amplitude characteristic parameters of a piezoelectric pressure sensor, and belongs to the field of pressure sensor measurement and calibration. The acquisition method fully utilizes the data of measurement points near the amplitude of a half-sine pressure pulse, and simulates the pulse amplitude excitation of a repeated calibration experiment by using the excitation points near the pulse amplitude, so that the influence of poor repeatability of an existing half-sine pressure pulse generating device on the repeatability calculation result of a calibrated pressure sensor can be effectively overcome.

Description

Technical Field

[0001] This invention relates to the field of pressure sensor metrology and calibration technology, and more specifically, to a method for obtaining amplitude characteristic parameters of a piezoelectric pressure sensor. Background Technology

[0002] Piezoelectric pressure sensors possess excellent dynamic characteristics and are widely used in testing artillery chamber pressure, blast shock waves, and shock wave pressure within confined containers. To ensure the dynamic testing accuracy of piezoelectric pressure sensors, they require regular calibration.

[0003] Because piezoelectric pressure sensors exhibit charge leakage under static pressure, static calibration cannot accurately obtain their sensitivity, linearity, and repeatability. Therefore, quasi-static calibration methods are commonly used internationally to obtain the amplitude characteristic parameters of piezoelectric pressure sensors, including sensitivity, linearity, and repeatability. Quasi-static calibration refers to using a pressure pulse generator to produce a pressure pulse similar to a half-sine wave as the pressure source. The width of this pressure pulse is between 1 ms and 12 ms, and its effective bandwidth is within the range of 1 kHz, far lower than the natural frequency of the piezoelectric pressure sensor (typically several hundred kHz).

[0004] Currently, the quasi-static calibration methods for obtaining the amplitude characteristics of piezoelectric pressure sensors can be divided into three main categories based on the different installation and reference pressure monitoring methods: (1) Direct comparison calibration method: This method directly selects a high-precision pressure sensor as the standard sensor and uses the measured pressure pulse amplitude of the standard sensor as the "true value"; (2) Absolute calibration method: One method uses a high-precision force sensor installed on the hammer head to measure the force value, and then predicts the "true value" of the pressure using a model of the relationship between the impact force and the pressure inside the pressure cylinder; the other method uses an acceleration sensor installed on the piston rod or a laser interferometer vertically above the hammer to measure the piston rod acceleration, and then combines the mathematical model of the impact acceleration and the pressure inside the pressure cylinder from the beginning to the end of the impact on the piston rod to realize the monitoring of the pressure pulse amplitude inside the pressure cylinder and make a calibration. The pressure "true value" is determined by: (1) measuring the optical path change in the pressure cylinder using a laser interferometer, and then using a mathematical model between the optical path and the pressure to predict the pulse pressure "true value"; (2) monitoring the displacement change of the piston rod during the impact process using a high-speed camera, and then using a mathematical model between the displacement and the pressure in the pressure cylinder to predict the pressure "true value"; (3) indirect comparison quasi-static calibration method: This method first establishes an empirical model between the typical structural parameters of the drop hammer hydraulic calibration device and the peak pressure in the pressure cylinder, then removes the reference pressure sensor, and uses the prediction result of the model as the pressure "true value"; or first establishes a prediction model of the reference pressure curve, and then substitutes the output voltage response curve of the pressure measurement system to be calibrated and its first and second derivatives into the model for calculation, and the amplitude of the calculated reference pressure curve is used as the "true value". To obtain the amplitude characteristic parameters of a piezoelectric pressure sensor, several pressure calibration points are typically selected evenly within the range of the piezoelectric pressure sensor. Multiple repeated experiments are conducted at each calibration point to obtain a dataset consisting of the excitation pressure amplitude and response voltage amplitude of the piezoelectric pressure sensor. Then, a linear fitting method is used to obtain the sensitivity of the piezoelectric pressure sensor, and a calculation model for nonlinearity and repeatability is provided with reference to JJG 860-2015, the calibration procedure for pressure sensors (static).

[0005] However, commonly used semi-sinusoidal pressure pulse generators mainly include: falling weight hydraulic calibration devices, pendulum hydraulic calibration devices, and gas pulse pressure generators. These devices primarily generate pressure pulses by having a heavy hammer strike a piston rod assembly, compressing the pressure-transmitting medium within the pressure-generating cylinder and causing it to rebound. The repeatability of these devices is generally poor, resulting in a significant overestimation of the repeatability of the calculated piezoelectric pressure sensor.

[0006] To address this issue, the book "Examples of Uncertainty Evaluation in Pressure Measurement" proposes two methods: first, constructing the working equation and sensitivity of a piezoelectric pressure sensor; then, using this working equation to obtain correction values ​​for the voltage response of the pressure sensor under calibration in multiple repeated experiments; and finally, calculating repeatability based on the corrected voltage response values. Additionally, the paper "Method for Obtaining Working Characteristic Parameters and Studying Low-Frequency Characteristics of a Quasi-Static Shock Wave Pressure Measurement System" proposes two approaches: first, uniformly selecting several pressure calibration points within the range of the pressure sensor under calibration; then, conducting multiple rounds of repeated experiments from low to high pressure calibration points; establishing the working equation for each round of calibration experiments; and finally, uniformly selecting several new pressure detection points within the full-scale range of the pressure sensor under calibration, substituting them into the working equations constructed in each round of calibration experiments, and obtaining the standard deviation at each new pressure detection point. Finally, referring to JJG 860-2015, the Verification Procedure for Pressure Sensors (Static), a calculation model for repeatability is provided. Both of these methods require first constructing the working linear equation of the piezoelectric pressure sensor under calibration before evaluating its repeatability.

[0007] Furthermore, the patent "A Method for Obtaining Operating Characteristic Parameters of a Piezoelectric Pressure Sensor for Quasi-Static Calibration" (Patent No.: ZL 202110629880.9) utilizes the rising and falling edges of a half-sine pressure pulse to simulate the continuous pressurization and depressurization operations of static calibration, thereby evaluating the sensitivity, linearity, repeatability, and hysteresis parameters of the piezoelectric pressure sensor. However, the operating characteristic parameters obtained by this method are not the amplitude response characteristic parameters of the piezoelectric pressure sensor. Although this method can maintain good consistency in selecting the pulse excitation point, inconsistencies in the pulse excitation amplitude will directly lead to significant differences in the voltage response value corresponding to the same pulse excitation point, resulting in poor repeatability calculation results for the piezoelectric pressure sensor. Summary of the Invention

[0008] 1. The technical problem that the invention aims to solve

[0009] To address the aforementioned problems, this invention provides a method for obtaining amplitude characteristic parameters of a piezoelectric pressure sensor. This method fully utilizes measurement point data near the amplitude of a half-sine pressure pulse and uses excitation points near the pulse amplitude to simulate the pulse amplitude excitation of a repeated calibration experiment.

[0010] 2. Technical Solution

[0011] To achieve the above objectives, the technical solution provided by the present invention is as follows:

[0012] The present invention discloses a method for obtaining amplitude characteristic parameters of a piezoelectric pressure sensor, comprising the following steps:

[0013] Step 1: Select n pressure calibration points evenly across the full range of the pressure sensor being calibrated, and conduct one calibration experiment at each pressure calibration point.

[0014] Step 2: Taking the calibration experimental data of the i-th pressure calibration point as an example, select z pressure measurement points near the amplitude of the reference pressure curve detected by the standard pressure sensor as excitation. Assume that these z pressure measurement points are p i1 ,p i2 ,...,p il ,...,p iz Simultaneously, the response point data corresponding to these z pressure measurement points are obtained from the output curve detected by the calibrated pressure sensor. Let these z response point data be y... i1 ,y i2 ,...,y il ,...,y iz ;

[0015] Step 3: Obtain the average value of the response data corresponding to z pressure measurement points and z calibrated pressure sensors, respectively;

[0016]

[0017]

[0018] p il This is the l-th data point among z measurement points selected from the vicinity of the reference pressure curve amplitude;

[0019] y il This refers to the l-th data point among z measurement points selected from the vicinity of the amplitude of the output curve of the pressure sensor being calibrated;

[0020] Step 4: Repeat steps 2 and 3 to obtain the average values ​​of z excitation points near the amplitude of the other n-1 pressure calibration points and the average values ​​of z corresponding responses of the calibrated pressure sensor. At this point, we have obtained the dataset of average excitation point values ​​obtained from one calibration experiment at each of the n pressure calibration points. Data set of average response points of the calibrated pressure sensor

[0021] Step 5: Process the dataset and Perform linear fitting to obtain the working linear equation and sensitivity k of the calibrated pressure sensor;

[0022] y = kp + b (3)

[0023] Where b is the zero-point output of the pressure sensor being calibrated;

[0024] Step Six: Obtain the full-scale output value of the pressure sensor being calibrated. The full-scale output value y of the pressure sensor being calibrated... FS Calculate according to formula (4):

[0025] y FS =|k(p max -p min (4)

[0026] Step 7: Substitute the dataset into equation (4) to calculate the predicted values. Dataset {y′1,y′2,...,y′ i-1 ,y′ i ,...,y′ n}

[0027] Calculate using equation (5) and y′ i The absolute value of the difference Δy i A residual dataset {Δy1,Δy2,...,Δy} can be obtained. i-1 ,Δy i ,...,Δy n}; where the maximum value of the n residuals is denoted as Δy. max .

[0028]

[0029] The linearity ε of the calibrated pressure sensor is calculated using formula (6). r :

[0030]

[0031] Step 8: Calculate the standard deviation s of each calibration point according to formula (7). i .

[0032]

[0033] Calculate the standard deviation s of the calibrated pressure sensor over the entire measurement range using formula (8):

[0034]

[0035] The repeatability ε of the calibrated pressure sensor is calculated using formula (9). r :

[0036]

[0037] Furthermore, in step one, the number of pressure detection points n ≥ 5.

[0038] Furthermore, in step two, the number of pressure measurement points z ≥ 3.

[0039] Furthermore, in step five, the linear fitting method can be the least squares method, the tangent method, or the endpoint translation method.

[0040] Furthermore, in step one, the reference pressure curve can also be indirectly obtained by combining the acceleration curve monitored by a high-precision force sensor, a high-precision accelerometer, or a laser velocity interferometer with a mathematical model of the relationship between acceleration and pressure inside the pressure-generating cylinder.

[0041] Furthermore, in step one, the reference pressure curve can also be indirectly obtained by combining the piston rod displacement change curve monitored by the high-speed camera with a mathematical model of the relationship between displacement and pressure in the pressure-generating cylinder.

[0042] 3. Beneficial effects

[0043] Compared with the prior art, the technical solution provided by this invention has the following advantages:

[0044] (1) This invention utilizes measurement points in the region near the amplitude of a half-sine pressure pulse to simulate a repeated calibration experiment, which can effectively overcome the influence of poor repeatability of existing half-sine pressure pulse generators on the repeatability calculation results of the calibrated pressure sensor.

[0045] (2) The repeatability acquisition method of the piezoelectric pressure sensor based on the present invention does not require prior acquisition of the working linear equation of the pressure sensor being calibrated.

[0046] (3) The present invention has high utilization rate of calibration data in the region near the pulse amplitude, high calibration efficiency, and low time cost for calibration. Attached Figure Description

[0047] Figure 1 This is a schematic diagram illustrating the working principle of a drop hammer hydraulic calibration device, as described in an embodiment of the present invention.

[0048] Figure 2 This is a schematic diagram of the data curve obtained from the first calibration of the pressure sensor being calibrated at the second pressure calibration point.

[0049] Figure 3 This is a magnified schematic diagram of the curve near the amplitude of the data curve measured during the first calibration at the second pressure calibration point of the pressure sensor being calibrated.

[0050] In the attached diagram: 1-Pressure sensor to be calibrated, 2-Standard pressure sensor, 3-Pressure cylinder, 4-Flag, 5-Piston rod assembly, 6-Pressure transmission medium;

[0051] 7 - Voltage response curve of the calibrated pressure sensor; 8 - Reference pressure curve output by the standard pressure sensor;

[0052] 9 - Voltage response curve of the calibrated pressure sensor; 10 - Reference pressure curve output by the standard pressure sensor. Detailed Implementation

[0053] To further understand the content of this invention, a detailed description of the invention will be provided in conjunction with the accompanying drawings.

[0054] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0055] The present invention will be further described below with reference to embodiments.

[0056] Example

[0057] Combination Figure 1 , Figure 2 and Figure 3 This invention provides a method for obtaining amplitude characteristic parameters of a piezoelectric pressure sensor based on excitation-response data near the pulse amplitude, comprising the following steps:

[0058] Step 1: This invention uses Figure 1 The drop hammer hydraulic calibration device shown is used as a pressure source. A 113B24 piezoelectric pressure sensor manufactured by a PCB company is used as the pressure sensor to be calibrated 1. The pressure sensor to be calibrated 1 and the standard pressure sensor 2 are symmetrically installed at the same height on the wall of the pressure cylinder 3. The process of the weight 4 falling freely and hitting the piston rod assembly 5 to squeeze the pressure transmission medium 6 and rebound can generate a pressure pulse similar to a half sine wave in the pressure cylinder.

[0059] Eight pressure calibration points were evenly selected across the entire range of the pressure sensor 1 being calibrated. These eight pressure points are as follows: A calibration experiment was performed at each pressure calibration point. Figure 2 Curve 7 shows the data curves obtained from the first calibration of the pressure sensor 1 under calibration at the second pressure calibration point (1.78 MPa). Curve 8 is the voltage response curve detected by the pressure sensor 1 under calibration. Curve 8 is the reference pressure curve measured by the standard pressure sensor 2.

[0060] Step Two: Taking the calibration test data from the second pressure calibration point (1.78 MPa) as an example, from... Figure 2 A magnified view of a portion of the pulse amplitude, such as... Figure 3 As shown. Curve 9 is the voltage response curve of the pressure sensor 1 being calibrated, and curve 10 is the reference pressure curve output by the standard pressure sensor 2. Figure 3 As can be seen, the reference pressure excitation points near the amplitude are very close. The locally magnified curve formed by these excitation points approximates a horizontal line, at which point the differences between the pressure excitation points can be ignored. Therefore, the excitation near the amplitude can be used to approximate the repeated calibration experiment under this amplitude condition.

[0061] Four pressure measurement points were selected near the amplitude of the reference pressure curve at the second pressure calibration point (1.78 MPa) as excitation. These four pressure measurement points were 1.7823 MPa, 1.7822 MPa, 1.7823 MPa, and 1.7823 MPa, respectively. Simultaneously, the response point data corresponding to these four pressure measurement points were obtained from the output curve detected by the calibrated pressure sensor. These four response point data were 1.3198 V, 1.3197 V, 1.3198 V, and 1.3197 V, respectively.

[0062] Step 3: Obtain the average value of the response data corresponding to the 4 pressure measurement points and the 4 calibrated pressure sensors respectively;

[0063]

[0064]

[0065] Step 4: Repeat steps 2 and 3 to obtain the average value of the four excitation points near the amplitude of the other seven pressure detection points and the average value of the four corresponding voltage responses of the calibrated pressure sensor 1.

[0066] At this point, we can obtain the average dataset of excitation points obtained from one calibration experiment at each of the eight pressure calibration points.

[0067] The dataset of average response points of the calibrated pressure sensor 1

[0068] Step 5: Perform least squares fitting on the dataset of the average excitation point values ​​obtained from one calibration experiment at each of the 8 pressure calibration points and the dataset of the average response point values ​​of the pressure sensor 1 being calibrated, and obtain the working straight line equation of the pressure sensor 1 being calibrated.

[0069] y = 0.7374p + 0.0044 (12)

[0070] The sensitivity of the pressure sensor 1 being calibrated is 0.7374 V / MPa; the zero-point output of the pressure sensor 1 being calibrated is 0.0044 V.

[0071] Step Six: Obtain the full-scale output value of the pressure sensor 1 being calibrated. Take p... max =6.94918MPa and p min =0MPa, the full-scale output value y of the pressure sensor 1 being calibrated FS Calculate according to formula (13):

[0072] y FS =|k(p max -p min )|=|0.7374×(6.94918-0)|=5.1243(13)

[0073] Step 7: Obtain the average dataset of excitation points by performing one calibration experiment at each of the 8 pressure calibration points.

[0074] Substituting these values ​​into equation (12) respectively, we obtain the predicted value dataset {y1′,y2′,...,y i ′ -1 ,y i ′,...,y8′}={0.00435V,1.31858V,1.90298V,2.78638V,3.22146V,4.15778V,4.77472V,5.12859V};

[0075] Calculate using equation (14) and y i The absolute value of the difference Δy i This yields a residual dataset {0.00435V, 0.00117V, 0.00180V, 0.0026V, 0.00389V, 0.00045V, 0.00289V, 0.00176V}. The maximum value of the eight residual data points in this dataset is Δy. max =0.00435V;

[0076]

[0077] The linearity ε of the calibrated pressure sensor 1 is calculated according to formula (15). l :

[0078]

[0079] Step 8: Calculate the standard deviation s of each calibration point according to formula (16). i This yields a standard deviation dataset as follows: {0V, 0.00006V, 0.00013V, 0.00019V, 0.00015V, 0.0001V, 0.0001V, 0.0001V};

[0080]

[0081] Calculate the standard deviation s of the calibrated pressure sensor 1 over the entire measurement range using formula (17):

[0082]

[0083] The repeatability ε of the calibrated pressure sensor 1 is calculated using formula (18). r :

[0084]

[0085] The present invention and its embodiments have been described above illustratively. This description is not restrictive and is merely one embodiment of the present invention, and is not actually limited thereto. Therefore, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the present invention, such designs should fall within the protection scope of the present invention.

Claims

1. A method for obtaining amplitude characteristic parameters of a piezoelectric pressure sensor, characterized in that: Includes the following steps: Step 1: Select uniformly across the full range of the pressure sensor being calibrated. n There are 1 pressure calibration point, and a calibration experiment is carried out at each pressure calibration point; Step Two: Using the first i Taking the calibration test data at one pressure calibration point as an example, the amplitude of the reference pressure curve detected by the standard pressure sensor is selected near the calibration test data. z Using pressure measurement points as excitation, and simultaneously acquiring this from the output curve detected by the calibrated pressure sensor. z Response point data corresponding to each pressure measurement point; Step 3: Obtain separately z Each pressure measurement point and z The average value of the response data corresponding to each calibrated pressure sensor; Step 4: Repeat steps 2 and 3 to obtain the others. n -1 pressure checkpoint amplitude z The average value of each excitation point and the calibrated pressure sensor z The average value of each corresponding response; thus, we can obtain n The dataset of average excitation points obtained by performing one calibration experiment at each pressure calibration point, and the dataset of average response points of the calibrated pressure sensor; Step 5: Perform linear fitting on the dataset obtained in Step 4 to obtain the working linear equation and sensitivity of the calibrated pressure sensor. k ; Step Six: Obtain the full-scale output value of the pressure sensor being calibrated, and calculate the full-scale output value of the pressure sensor being calibrated. ; Step 7: Calculate the predicted value dataset and calculate the linearity of the calibrated pressure sensor. ; Step 8: Calculate the standard deviation of each calibration point. ; Calculate the standard deviation of the calibrated pressure sensor over the entire measurement range. ; Calculate the repeatability of the calibrated pressure sensor .

2. The method for obtaining amplitude characteristic parameters of a piezoelectric pressure sensor according to claim 1, characterized in that: In step two, assume that the z pressure measurement points are respectively p i1, p i2,..., p il,..., p iz The z response points are respectively y i1, y i2,..., y il,..., y iz ; In step three, the average values ​​of the response data corresponding to z pressure measurement points and z calibrated pressure sensors are obtained respectively according to the following formulas; (1) (2) This is the l-th data point among z measurement points selected from the vicinity of the reference pressure curve amplitude; This is the l-th data point among z measurement points selected from the range of the output curve amplitude of the pressure sensor being calibrated.

3. The method for obtaining amplitude characteristic parameters of a piezoelectric pressure sensor according to claim 2, characterized in that: In step four, the average value of the excitation points obtained from one calibration experiment at each of the n pressure calibration points is: The average data set of the corresponding response points of the calibrated pressure sensor is as follows: ; In step five, the dataset is processed. and Perform linear fitting to obtain the operating linear equation and sensitivity of the calibrated pressure sensor. k ; (3) in, b It is the zero-point output of the pressure sensor being calibrated.

4. The method for obtaining amplitude characteristic parameters of a piezoelectric pressure sensor according to claim 3, characterized in that: In step six, the full-scale output value of the pressure sensor being calibrated is... Calculate according to formula (4): (4)。 5. The method for obtaining amplitude characteristic parameters of a piezoelectric pressure sensor according to claim 4, characterized in that: In step seven, the dataset is substituted into equation (4) to calculate the predicted dataset. ; Calculate using equation (5) and The absolute value of the difference Obtain a residual dataset The maximum value of the n residuals is denoted as . ; (5)。 6. The method for obtaining amplitude characteristic parameters of a piezoelectric pressure sensor according to claim 5, characterized in that: In step seven, the linearity of the pressure sensor being calibrated is calculated according to formula (6). : (6)。 7. The method for obtaining amplitude characteristic parameters of a piezoelectric pressure sensor according to claim 6, characterized in that: In step eight: calculate the standard deviation of each calibration point according to formula (7). ; (7) Calculate the standard deviation of the calibrated pressure sensor over the entire measurement range using formula (8). : (8) The repeatability of the calibrated pressure sensor is calculated using formula (9). : (9)。 8. A method for obtaining amplitude characteristic parameters of a piezoelectric pressure sensor according to any one of claims 1-7, characterized in that: In step one, the number of pressure detection points n ≥ 5.

9. A method for obtaining amplitude characteristic parameters of a piezoelectric pressure sensor according to any one of claims 1-7, characterized in that: In step two, the number of pressure measurement points z ≥3.

10. A method for obtaining amplitude characteristic parameters of a piezoelectric pressure sensor according to any one of claims 1-7, characterized in that: In step five, the linear fitting method is either the least squares method, the tangent method, or the endpoint translation method.

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