Method for verifying piezoelectric coefficient of piezoelectric sensor based on short rod model

Abstract

The invention discloses a verification method for a piezoelectric coefficient of a piezoelectric sensor based on a short rod model. The verification method comprises the following steps: establishing a contact dynamical model; based on the contact dynamical model, obtaining a combination of a piezoelectric coefficient and a cutting board micro-displacement coefficient; and based on the combination of the piezoelectric coefficient and the micro-displacement coefficient of the cutting board, the final piezoelectric coefficient is obtained by combining the Young modulus of the glass ball. According to the invention, the problem that the actual piezoelectric coefficient of the piezoelectric sensor is possibly different from the piezoelectric coefficient calibrated at a factory can be solved, so that the piezoelectric coefficient is consistent with the actual piezoelectric coefficient.

Description

Technical Field

[0001] The invention belongs to the technical field of mineral processing engineering equipment, and in particular relates to a method for calibrating a piezoelectric coefficient of a piezoelectric sensor based on a short rod model. Background Art

[0002] In the 1990s, the Ultra fast load cell (UFLC) was developed. Figure 1 ), but it has only been built in research institutions in certain regions and has been slow to be promoted. The main reason is that the Hopkinson bar device is expensive, and the verticality and centering degree are very high during construction, which makes it difficult to apply.

[0003] In order to make the configuration simple and easy to operate, a new device with a piezoelectric sensor as the core component is selected ( Figure 2 ) replaces UFCL. Piezoelectric sensor is a sensor based on piezoelectric effect. It is a self-generating and electromechanical conversion sensor. Its sensitive element is made of piezoelectric material. When piezoelectric material is subjected to force, charge is generated on the surface. After the charge is amplified and the impedance is transformed by the charge amplifier and the measurement circuit, it becomes an electrical output proportional to the external force. Piezoelectric sensors are used to measure non-electrical physical quantities that can be converted into electricity. With the short rod dynamic model and calibration method, it can partially replace the UFLC with the Hopkinson rod as the core component, and the configuration is simple and easy to operate, providing a new fracture energy test method for the application of modern crushing models, especially the Tavares model. Although the piezoelectric sensor has been calibrated at the original factory, it will be affected by subsequent processing, such as the material and thickness of the cutting board and the base, so it needs to be calibrated again after installation.

[0004] The impact force-time curve of the piezoelectric sensor is very important for the fracture energy test, that is, the force must be accurate, and the corresponding time is also important, which involves the integral and quadratic integral of the two. Currently, there are the following methods to calibrate the sensor:

[0005] The working principle of the drop hammer impact force generating device is as follows: a rigid mass block falls freely from a certain height in the vertical direction and collides with the dynamic force sensor installed on the base. The impact motion generated during the collision is converted into an impact force excitation by the mass block and transmitted to the dynamic force sensor. Figure 3As shown. The working principle of the impact force calibration device is based on Newton's second law. The dynamic force sensor is calibrated by reproducing the impact acceleration. During the impact of the device, the peak impact acceleration is reproduced by the laser interferometer or the impact acceleration standard set based on the effective mass that collides with the dynamic force sensor. However, this method requires instruments such as laser interferometers, which are inconvenient to operate and need to be sent to a special inspection agency. In addition, the micro-displacement measurement of the anvil is difficult and difficult to observe, and a specific model is required to infer. Therefore, a model that can reflect the contact dynamics in a collision and a simple method that can be tested on a new device are needed. Summary of the invention

[0006] In order to solve the above technical problems, the present invention proposes a calibration method for the piezoelectric coefficient of a piezoelectric sensor based on a short rod model, which can solve the problem that the actual piezoelectric coefficient of the piezoelectric sensor may be different from the piezoelectric coefficient calibrated at the factory, so that the piezoelectric coefficient is consistent with the actual one.

[0007] To achieve the above object, the present invention provides a method for calibrating the piezoelectric coefficient of a piezoelectric sensor based on a short rod model, comprising:

[0008] Establish contact dynamics model;

[0009] Based on the contact dynamics model, a combination of a piezoelectric coefficient and anvil micro-displacement coefficient is obtained;

[0010] Based on the combination of the piezoelectric coefficient and the anvil micro-displacement coefficient, the final piezoelectric coefficient is obtained in combination with the fracture probability and the Young's modulus of the glass.

[0011] Optionally, before establishing the contact dynamics model, the following steps are also included:

[0012] Get the sensor anvil material and steel ball material;

[0013] Based on the material of the sensor anvil and the material of the steel ball, the initial Young's modulus of the anvil and the steel ball are obtained.

[0014] Optionally, the contact dynamics model is:

[0015]

[0016]

[0017] Among them, v 0 is the initial velocity of the steel ball when it contacts the particle, g is the acceleration due to gravity, m b is the mass of the steel ball, t is the time from the beginning of contact, F(t) is the impact force, u a is the displacement of the anvil, ρ is its density, A is its area, C a is the propagation speed of stress wave, ur is the displacement of the rod end, ρ r is the density of the rod, A r is the cross-sectional area of ​​the rod, C r is the propagation speed of stress wave in the rod, τ is the auxiliary integral variable, C 1 is the displacement of the end face of the anvil according to the law of stress wave transmission, V a is the velocity of the end face, and α is the deformation of the end face.

[0018] Optionally, based on the contact dynamics model, obtaining a combination of a piezoelectric coefficient and anvil micro-displacement coefficient includes:

[0019] Based on the contact dynamics model, an impact force-time curve is obtained;

[0020] Based on the impact force-time curve, a combination of piezoelectric coefficient and anvil micro-displacement coefficient is obtained.

[0021] By carrying out drop hammer tests, the fracture probability of ore particles under different impact energies was obtained. Based on this, the values ​​tested under different combinations were compared and the combination with the smallest standard residual was selected.

[0022] Optionally, based on the combination of the piezoelectric coefficient and the anvil micro-displacement coefficient, combined with the glass Young's modulus, obtaining the final piezoelectric coefficient includes:

[0023] Performing a fracture energy test on the glass ball based on the combination of the piezoelectric coefficient and the anvil micro-displacement coefficient to obtain a test result;

[0024] Based on the test results, back-calculate the Young's modulus of the glass to obtain the back-calculated Young's modulus;

[0025] Based on the initial Young's modulus and the back-calculated Young's modulus, a final piezoelectric coefficient is obtained.

[0026] Optionally, the method for obtaining the back-calculated Young's modulus is:

[0027]

[0028]

[0029] Y p =k p ×(1-ν 2 )

[0030] Among them, F c is the breaking force, E c is the fracture energy, d p is the geometric mean particle size, α c is the shape variable, K e is the contact stiffness, k a,bComposite stiffness in the Hertz contact model, Y p is the Young's modulus after backcalculation, k p is the stiffness of the glass ball, and v is the Poisson's ratio of the stiffness.

[0031] Based on the initial Young's modulus and the back-calculated Young's modulus, obtaining the final piezoelectric coefficient includes:

[0032] Compared with the prior art, the present invention has the following advantages and technical effects:

[0033] The present invention is based on establishing an adaptive contact dynamics model. Through a new device with a piezoelectric sensor as the core component, the piezoelectric coefficient can be determined based on existing experimental materials by comparing actual data with theoretical data. The present invention achieves the purpose of making the piezoelectric coefficient consistent with the actual by using the new device to correct the piezoelectric coefficient of the piezoelectric sensor by establishing a short rod model. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0035] Figure 1 Schematic diagram of the structure and test principle of UFLC according to an embodiment of the present invention;

[0036] Figure 2 A simplified structural diagram of a new test device according to an embodiment of the present invention;

[0037] Figure 3 Schematic diagram of a drop hammer type impact force generating device according to an embodiment of the present invention;

[0038] Figure 4 A structural diagram of a piezoelectric sensor according to an embodiment of the present invention;

[0039] Figure 5 Schematic diagram corresponding to different micro-displacement degrees under the short rod model of an embodiment of the present invention;

[0040] Figure 6 The specific fracture energy distribution diagram of different particle sizes tested by the device of the present invention and UFLC;

[0041] Figure 7 The present invention is a flowchart of a method for verifying the piezoelectric coefficient of a piezoelectric sensor based on a short rod model according to an embodiment of the present invention. DETAILED DESCRIPTION

[0042] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0043] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0044] The present invention proposes a method for calibrating the piezoelectric coefficient of a piezoelectric sensor based on a short rod model. Figure 7 As shown, specifically including:

[0045] Establish contact dynamics model;

[0046] Based on the contact dynamics model, the combination of piezoelectric coefficient and anvil micro-displacement coefficient is obtained;

[0047] Based on the combination of piezoelectric coefficient and anvil micro-displacement coefficient, the final piezoelectric coefficient is obtained by combining the fracture probability with the Young's modulus of the glass.

[0048] Furthermore, before establishing the contact dynamics model, the following steps are also included:

[0049] Get the sensor anvil material and steel ball material;

[0050] Based on the sensor anvil material and steel ball material, the initial Young's modulus of the anvil and steel ball are obtained.

[0051] Furthermore, the contact dynamics model is:

[0052]

[0053] Among them, v 0 is the initial velocity of the steel ball when it contacts the particle, τ is the auxiliary integral variable, u r is the displacement of the rod end, ρ r is the density of the rod, A r is the cross-sectional area of ​​the rod, C r is the propagation speed of stress wave in the rod, C 1 is the displacement of the end face of the anvil according to the stress wave transmission law ( Figure 5 );

[0054] Specifically, the structure of the piezoelectric sensor is as follows Figure 4 As shown, the impact force-time curve is obtained by using a regular small steel ball to hit the sensor anvil at different heights, and compared with the curve obtained by the theoretical model for verification, so as to determine the piezoelectric coefficient range and the collision model of the steel ball;

[0055] (1) Steel ball impact plane model:

[0056] Assume that the anvil is a completely rigid body, that is, the micro-displacement is 0.

[0057] (2) Steel ball hits the long rod:

[0058] When the stress wave is reflected back, a micro displacement is generated on the front face. By comparing the measured values ​​with the theoretical values ​​of the three collision models, we can draw the following conclusions:

[0059] ① When the steel ball contacts the sensor, it should be calculated as steel-steel impact.

[0060] ② The model should be one of the following: a steel ball hitting a plane (with no end displacement) and a steel ball hitting a long rod (with the end moving according to the stress wave transmission law), or a combination of these.

[0061] ③ The collision model can be a short stick model, which is more flexible and convenient for calibration

[0062] The non-displacement model should be the theoretical maximum value, while the stress wave displacement model should be the theoretical minimum value. The contact time of the two models is almost the same. The first two models are compromised, and a coefficient is added to the displacement term of the end face of the anvil in the small ball hitting the long rod model to form the "small ball hitting the short rod model".

[0063] Furthermore, based on the contact dynamics model, the combination of piezoelectric coefficient and anvil micro-displacement coefficient is obtained, including:

[0064] Based on the contact dynamics model, the impact force-time curve is obtained;

[0065] Based on the impact force-time curve, the combination of piezoelectric coefficient and anvil micro-displacement coefficient is obtained.

[0066] Specifically, based on the above results, the degree of displacement of the end surface of the anvil is determined. The schematic diagram of the displacement of the anvil is shown in Figure 5 , Figure 6 As shown; among them C 1 The direct meaning of is the degree of displacement of the end face of the anvil according to the law of stress wave transmission. 1 = 0, there is no displacement, that is, the ball hits the plane model. When C 1 = 1, the displacement is the largest, which is the model of a small ball hitting a long rod. This coefficient can be understood as the proportion of the displacement reduced by the stress wave reflection on the end face of the anvil. It can be seen from the figure that as the micro displacement increases, that is, C 1 As the impact curve height decreases, the time is slightly prolonged. 1 The coefficients should be adapted to the appropriate piezoelectric coefficients.

[0067] Based on the fracture probability of ore particles under different impact energies, the piezoelectric coefficient is preliminarily determined;

[0068] Furthermore, based on the combination of the piezoelectric coefficient and the anvil micro-displacement coefficient, combined with the glass Young's modulus, the final piezoelectric coefficient is obtained, including:

[0069] The fracture energy of the glass ball is tested based on the combination of piezoelectric coefficient and anvil micro-displacement coefficient to obtain the test results;

[0070] Based on the test results, Young's modulus of the glass is back-calculated to obtain the back-calculated Young's modulus;

[0071] Based on the initial Young's modulus and the back-calculated Young's modulus, the final piezoelectric coefficient is obtained.

[0072] Furthermore, the method for obtaining the back-calculated Young's modulus is:

[0073]

[0074] Y p =k p ×(1-ν 2 )

[0075] Among them, F c is the breaking force, E c is the fracture energy, d p is the geometric mean particle size, α c is the shape variable, K e is the contact stiffness, k a,b Composite stiffness in the Hertz contact model, Y p is the back-calculated Young's modulus. Based on the initial Young's modulus and the back-calculated Young's modulus, the final piezoelectric coefficient is obtained including:

[0076] Example

[0077] Step 1: Based on Table 1, determine the material of the impact sensor anvil and the steel ball used for impact

[0078] Based on the material, the Young's modulus and Poisson's ratio of the anvil and steel ball are determined. For example, the Young's modulus of the anvil and steel ball used in the experiment are both 206 GPa, and the Poisson's ratio is 0.3.

[0079] Table 1

[0080]

[0081] Step 2: Establish an adaptive contact dynamics model

[0082] The no-displacement model should be the theoretical maximum value, and the stress wave displacement model should be the theoretical minimum value.

[0083] The contact times of the two are almost the same, and the corresponding coefficients are 310N / V and 250N / V.

[0084] Step 3: Compare the actual measurements with the two models

[0085] From the two models, we can know that the piezoelectric coefficient is temporarily set at 280N / V. A small steel ball is used to impact the sensor at different heights. The impact force-time obtained is compared with the two theoretical models, and we can draw the following conclusions:

[0086] (1) The actual contact time and theoretical measured contact time basically coincide, so the calculation using steel-steel impact is correct.

[0087] (2) The contact model should be one of the following: steel ball hitting a flat surface (no displacement of the end surface) or steel ball hitting a long rod (the end surface moves according to the law of stress wave transmission), or a combination of these. Figure 6 , 7 (shown)

[0088] Step 4: Estimate different combinations of piezoelectric coefficients and anvil micro-displacement coefficients

[0089] Then, theoretical calculations are performed under different C1s under the same piezoelectric coefficient and compared with the actual image to determine the piezoelectric coefficient corresponding to C1.

[0090] Step 5: Preliminary determination of the piezoelectric coefficient by performing a drop hammer test

[0091] The fracture probability of ore particles under different impact energies was obtained. Based on this, the values ​​tested under different combinations were compared and the combination with the smallest standard residual was selected.

[0092] The drop hammer test used materials with a narrow particle size range, with no less than 50 particles in each group. The impact force curve was not recorded, and only the fracture conditions were recorded for statistical purposes. It was finally determined that the standard residuals of 295N / V and 310N / V were the smallest, as shown in Table 2.

[0093] Table 2

[0094]

[0095] Step 7: Inverse calculation of glass Young's modulus to complete verification

[0096] For example, if the material is soda-lime glass, the manufacturer determines that its Young's modulus is between 60 GPa and 70 GPa. From the above fracture probability residual, it can be seen that the coefficient is selected between 295 N / V and 310 N / V. The inversely calculated stiffness is within this range (as shown in Table 3). Finally, 295 N / V is selected.

[0097] Table 3

[0098]

[0099] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A method for calibrating the piezoelectric coefficient of a piezoelectric sensor based on a short rod model, characterized in that: include: Establish contact dynamics model; Based on the contact dynamics model, a combination of a piezoelectric coefficient and anvil micro-displacement coefficient is obtained; Based on the combination of the piezoelectric coefficient and the anvil micro-displacement coefficient, the final piezoelectric coefficient is obtained by combining the fracture probability of the ore particles under different impact energies and the Young's modulus of the glass ball.

2. According to the method for verifying the piezoelectric coefficient of a piezoelectric sensor based on a short rod model according to claim 1, it is characterized in that: Before establishing the contact dynamics model, the following steps are also included: Get the sensor anvil material and steel ball material; Based on the material of the sensor anvil and the material of the steel ball, the initial Young's modulus of the anvil and the steel ball are obtained.

3. The method for verifying the piezoelectric coefficient of a piezoelectric sensor based on a short rod model according to claim 1 is characterized in that: The contact dynamics model is: Where v0 is the initial velocity of the steel ball when it contacts the particle, g is the gravitational acceleration, m b is the mass of the steel ball, t is the time from the beginning of contact, F(t) is the impact force, u a is the displacement of the anvil, ρ is its density, A is its area, C a is the propagation speed of stress wave, u r is the displacement of the rod end, ρ r is the density of the rod, A r is the cross-sectional area of ​​the rod, C r is the propagation speed of stress wave in the rod, τ is the auxiliary integral variable, C1 is the displacement degree of the end face of the anvil according to the law of stress wave transmission, V a is the velocity of the end face, and α is the deformation of the end face.

4. The method for verifying the piezoelectric coefficient of a piezoelectric sensor based on a short rod model according to claim 1 is characterized in that: Based on the contact dynamics model, the combination of piezoelectric coefficient and anvil micro-displacement coefficient is obtained including: Based on the contact dynamics model, an impact force-time curve is obtained; Based on the impact force-time curve, a combination of piezoelectric coefficient and anvil micro-displacement coefficient is obtained.

5. The method for verifying the piezoelectric coefficient of a piezoelectric sensor based on a short rod model according to claim 2 is characterized in that: Based on the combination of the piezoelectric coefficient and the anvil micro-displacement coefficient, combined with the fracture probability and the Young's modulus of the glass, the final piezoelectric coefficient is obtained, including: Based on the fracture probability of ore particles under different impact energies, the piezoelectric coefficient is preliminarily determined; Performing a fracture energy test on the glass ball based on the combination of the piezoelectric coefficient and the anvil micro-displacement coefficient to obtain a test result; Based on the test results, back-calculate the Young's modulus of the glass to obtain the back-calculated Young's modulus; Based on the initial Young's modulus and the back-calculated Young's modulus, a final piezoelectric coefficient is obtained.

6. The method for verifying the piezoelectric coefficient of a piezoelectric sensor based on a short rod model according to claim 5 is characterized in that: The method for obtaining the back-calculated Young's modulus is: Y p =k p ×(1-n 2 ) Among them, F c is the breaking force, E c is the fracture energy, d p is the geometric mean particle size, α c is the shape variable, K e is the contact stiffness, k a,b Composite stiffness in the Hertz contact model, Y p is the Young's modulus after backcalculation, k p is the stiffness of the glass ball, and v is the Poisson's ratio of the stiffness.

7. The method for verifying the piezoelectric coefficient of a piezoelectric sensor based on a short rod model according to claim 5, characterized in that: Based on the initial Young's modulus and the back-calculated Young's modulus, obtaining the final piezoelectric coefficient includes: Based on the initial Young's modulus and the back-calculated Young's modulus, they are compared with the actual Young's modulus to obtain the final piezoelectric coefficient.

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