A calibration method for the piezoelectric coefficient of a piezoelectric sensor based on a short rod model

Abstract

The present invention discloses a method for calibrating the piezoelectric coefficient of a piezoelectric sensor based on a short-rod model. The method comprises: establishing a contact dynamics model; obtaining a combination of the piezoelectric coefficient and the anvil micro-displacement coefficient based on the contact dynamics model; and obtaining a final piezoelectric coefficient based on the combination of the piezoelectric coefficient and the anvil micro-displacement coefficient, combined with the Young's modulus of a glass ball. This method can resolve the problem of a piezoelectric sensor's actual piezoelectric coefficient potentially differing from the factory-calibrated piezoelectric coefficient, ensuring that the piezoelectric coefficient is consistent with the actual value.

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 the piezoelectric coefficient of a piezoelectric sensor based on a short rod model. Background Art

[0002] In the 1990s, the Ultra fast load cell (hereinafter referred to as 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 relatively expensive, and the verticality and centering degree during construction are very high, 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 was selected ( Figure 2 ) replaces UFCL. Piezoelectric sensor is a sensor based on the piezoelectric effect. It is a self-generating and electromechanical conversion sensor. Its sensitive element is made of piezoelectric material. When the piezoelectric material is subjected to force, an electric charge is generated on the surface. This charge is amplified and the impedance is converted by the charge amplifier and the measurement circuit to become an electrical output proportional to the external force. Piezoelectric sensors are used to measure non-electrical physical quantities that convert force and energy into electricity. In conjunction with the short-bar dynamic model and calibration method, it can partially replace the UFLC with the Hopkinson bar as the core component. It has a simple configuration and easy operation, providing a new fracture energy testing method for the application of modern crushing models, especially the Tavares model. Although the piezoelectric sensor has been calibrated at the factory, it will be affected by subsequent reprocessing, such as the material and thickness of the anvil and base, so it needs to be calibrated again after installation.

[0004] The impact force-time curve of a piezoelectric sensor is very important for fracture energy testing. That is, the force must be accurate, and the corresponding time is also important. This involves the integral and quadratic integral of the two. Currently, the following methods are available for sensor calibration:

[0005] The working principle of the drop hammer impact force generator 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, and the dynamic force sensor is calibrated by reproducing the impact acceleration. During the impact of the device, the effective mass that collides with the dynamic force sensor and the peak impact acceleration reproduced by the laser interferometer or the impact acceleration standard set are used. However, this method requires instruments such as a laser interferometer, which is inconvenient to operate and needs to be sent to a special inspection agency. In addition, the micro-displacement of the anvil is difficult to measure and difficult to observe, requiring a specific model 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 further 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 is obtained.

[0014] Optionally, the contact dynamics model is:

[0015]

[0016]

[0017] Among them, v0 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 start 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, ρr is the density of the rod, A r is the cross-sectional area of ​​the rod, C r is the propagation velocity of stress wave in the rod, τ is the auxiliary integral variable, C1 is the degree of displacement of the end face of the anvil according to the stress wave transmission law, 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 a piezoelectric coefficient and anvil micro-displacement coefficient is obtained.

[0021] By performing 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, obtaining the final piezoelectric coefficient based on the combination of the piezoelectric coefficient and the anvil micro-displacement coefficient in combination with the Young's modulus of the glass 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, inversely calculate the Young's modulus of the glass to obtain the inversely 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 inversely 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,b Composite stiffness in the Hertz contact model, Y p is the Young's modulus after back-calculation, kp is the stiffness of the glass ball, and v is the Poisson's ratio of 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 uses the new device to establish a short rod model to correct the piezoelectric coefficient of the piezoelectric sensor, thereby achieving the purpose of making the piezoelectric coefficient consistent with the actual one. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0035] Figure 1 Schematic diagram of the structure and testing principle of the 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 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 This is a flow chart of a method for calibrating 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 of the embodiments in this 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 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.

[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 material of the sensor anvil and steel ball, the initial Young's modulus of the anvil and steel ball is obtained.

[0051] Furthermore, the contact dynamics model is:

[0052]

[0053] Among them, v0 is the initial velocity of the steel ball when it contacts the particle, τ is the auxiliary integral variable, and 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, C1 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 in the figure, the impact force-time curve is obtained by hitting the sensor anvil with a regular small steel ball at different heights. The curve is compared with the curve obtained by the theoretical model to verify 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, a micro-displacement occurs 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, the calculation should be based on steel-steel impact.

[0060] ② The model should be one of the following: a steel ball hitting a plane (no displacement of the end face) or a steel ball hitting a long rod (the end face moves 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 no-displacement model should be the theoretical maximum, while the stress-wave displacement model should be the theoretical minimum. The contact times for the two models are almost identical, so a compromise between the first two models is achieved by adding a coefficient to the displacement term of the anvil end face in the ball-on-long-rod model, resulting in the "ball-on-short-rod model."

[0063] Furthermore, based on the contact dynamics model, the combination of the piezoelectric coefficient and the 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 face of the anvil is determined. The schematic diagram of the displacement of the anvil is shown as follows: Figure 5 、 Figure 6 As shown in the figure, C1 directly represents the degree of displacement of the anvil's end face according to the laws of stress wave transmission. When C1 = 0, there is no displacement, representing the ball-impacting-plane model. When C1 = 1, the displacement is maximum, representing the ball-impacting-long-rod model. This coefficient can be understood as the proportion of displacement reduced by the anvil's end face due to stress wave reflection. As can be seen from the figure, as microdisplacement increases, that is, as C1 increases, the impact curve height decreases and the duration slightly prolongs. Therefore, different C1 coefficients should be adapted to the appropriate piezoelectric coefficient.

[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 the piezoelectric coefficient and the anvil micro-displacement coefficient to obtain the test results;

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

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

[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 Young's modulus after backcalculation. Based on the initial Young's modulus and the backcalculated 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 force 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, with corresponding coefficients of 310N / V and 250N / V.

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

[0085] From the two models, we can see that the piezoelectric coefficient is tentatively set at 280N / V. Using a small steel ball to impact the sensor at different heights, the resulting impact force-time is compared with the two theoretical models, and we can conclude that:

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

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

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

[0089] Then, theoretical calculations are performed under different C1s at 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. No impact force curve was recorded, only the fracture conditions were recorded for statistical purposes. It was finally determined that the standard residuals of 295 N / V and 310 N / 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's Young's modulus is between 60 GPa and 70 GPa. Based on the fracture probability residuals above, the coefficient should be between 295 N / V and 310 N / V. The calculated stiffness falls within this range (as shown in Table 3). Ultimately, 295 N / V is selected.

[0097] Table 3

[0098]

[0099] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection 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; 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, inversely calculate the Young's modulus of the glass to obtain the inversely calculated Young's modulus; Obtain the final piezoelectric coefficient based on the initial Young's modulus and the back-calculated Young's modulus; 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, the Young's modulus is compared with the actual Young's modulus to obtain a final piezoelectric coefficient; 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, obtaining the initial Young's modulus of the anvil and the steel ball; The contact dynamics model is: Among them, v0 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 start of contact, F(t) is the impact force, u a is the displacement of the anvil, ρ is the density of the anvil, A is the area of ​​the anvil, 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 velocity of stress wave in the rod, τ is the auxiliary integral variable, C1 is the degree of displacement of the end face of the anvil according to the stress wave transmission law, V a is the velocity of the end face; Based on the contact dynamics model, the combination of the piezoelectric coefficient and the 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 a piezoelectric coefficient and anvil micro-displacement coefficient is obtained; 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 back-calculation, k p is the stiffness of the glass ball, and v is the Poisson's ratio of stiffness.

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