A method for experimentally measuring the coefficient of restitution of non-spherical particles

Abstract

The application discloses a kind of experimental measurement methods of non-spherical particle energy recovery coefficient, it is characterized in that, including the following steps: 1) establish the flat plate model of particle-wall collision working condition;2) establish non-spherical particle model and carry out DEM simulation;3) according to the motion parameter of non-spherical particle after collision, combined with free fall motion, the landing point of particle is calculated, and the random landing point distribution of non-spherical particle after collision with wall is quantified using probability density function;4) design several non-spherical particle models to carry out the above simulation and calculation, obtain the energy recovery coefficient and random landing point distribution of several different non-spherical particles;5) build artificial neural network training model, use Python tool to establish the nonlinear fitting relationship between random landing point distribution and energy recovery coefficient by artificial neural network, construct non-spherical particle energy recovery coefficient prediction model;The application has important significance to the research of particle-wall collision field.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of computer simulation technology and experiment, and particularly relates to a method for measuring energy restitution coefficient of non-spherical particles. BACKGROUND

[0002] In the study of the collision process between particles and wall, the restitution coefficient is an important parameter. Different restitution coefficient definition methods have different descriptions on the kinematics and dynamics characteristics of particles in the collision process, and there are also differences in applicable occasions and calculation difficulty. Among the three restitution coefficients defined according to velocity, momentum and energy, the existing research results show that the energy restitution coefficient based on energy loss is the most accurate and most widely applicable, but in the experimental process, the measurement of energy loss is very difficult, especially for non-spherical particles.

[0003] With the rapid development of the computer industry, the simulation efficiency and calculation accuracy of engineering software are also gradually improved, and simulation research is gradually paid attention to by people. Through software simulation of the corresponding working condition, more experimental data that are difficult to measure can be obtained, and these data make the energy loss can be counted, and then the energy restitution coefficient can be calculated.

[0004] At present, there is still no method for obtaining the energy restitution coefficient from simple experimental measurement. However, based on the simulation data of engineering software, the relationship between experimental parameters and physical parameters can be established by artificial neural network technology, and then the energy restitution coefficient of non-spherical particles can be calculated based on simple experimental measurement, which is a new method. SUMMARY

[0005] The present application explores the blank field of experimental measurement of energy restitution coefficient, and proposes a method for measuring the energy restitution coefficient of non-spherical particles based on DEM and artificial neural network.

[0006] The technical scheme of the present application is as follows:

[0007] 1) A simple particle-wall collision working condition flat plate model is established by using a three-dimensional modeling software, and the model is imported into a DEM (Discrete Element Method) simulation software.

[0008] 2) A non-spherical particle model is established and DEM simulation is performed, and the particle motion data obtained by simulation are calculated according to the calculation formula of the energy restitution coefficient definition:

[0009]

[0010]

[0011]

[0012] wherein, E1 is the total energy of the particle before collision, E2 is the total energy of the particle after collision, E K1 , E R1 , E P1 are the translational kinetic energy, rotational kinetic energy and potential energy of the particle before collision, respectively, E K2 , E R2 , E P2 are the translational kinetic energy, rotational kinetic energy and potential energy of the particle after collision, respectively, and E energy_loss is the energy loss of the particle during the collision.

[0013] 3) According to the motion parameters of the non-spherical particle after collision, combined with the free fall motion, the falling point of the particle is calculated, and the probability density function method is used to quantify the random falling point distribution of the non-spherical particle after collision with the wall.

[0014] 4) A plurality of non-spherical particle models are designed to perform the above simulation and calculation, and a large number of energy recovery coefficients and random falling point distributions of different non-spherical particles are obtained.

[0015] 5) A complete artificial neural network training model is built by using a third-party tool Python; a nonlinear fitting relationship between the random falling point distribution and the energy recovery coefficient is established by using the Python tool through the artificial neural network, and a non-spherical particle energy recovery coefficient prediction model is constructed.

[0016] 6) According to the simulation working condition, an experimental device is built, an experiment is performed, a curve formed by the falling point distribution of the particle is shot, the obtained curve is converted into a discrete point form, and the energy recovery coefficient of the target experimental particle is calculated according to the prediction model obtained in step 5).

[0017] Further, step 5) is as follows:

[0018] 5.1) Select ReLU function as the activation function of the artificial neural network training, wherein the number of neurons is greater than the number of input parameters, and the learning rate is selected in the range of 0-1;

[0019] 5.2) The artificial neural network training structure is continuously debugged, the loss function value is reduced, and the performance of the neural network structure is repeatedly trained several times, and the neural network structure with the best performance is selected to construct the model;

[0020] 5.3) The particle falling point distribution obtained by DEM simulation calculation is input, and the particle energy recovery coefficient is output, the performance of the artificial neural network structure is debugged, and the particle energy recovery coefficient prediction model is fitted and constructed.

[0021] Further, the experimental device in step 6) comprises a particle dropping funnel, a flat plate arranged at a predetermined height below the particle dropping funnel, and a particle dropping collecting device, wherein the flat plate is adjustable in inclination angle, and the particle dropping collecting device comprises a plurality of partitions arranged equidistantly in a horizontal direction, and the experimental device is limited between two vertically parallel glass plates with a distance of 10-20 equivalent diameters of the non-spherical particles.

[0022] The working principle of the present application is that an artificial neural network is combined with a DEM simulation method to construct an experimental measurement method of the energy restitution coefficient, and the detailed particle motion information of the non-spherical particle collision process is obtained by the DEM method to calculate the energy restitution coefficient, because the size of the energy restitution coefficient will affect the random dropping distribution of the non-spherical particles, therefore, the data of the particle random dropping distribution and the energy restitution coefficient can be trained by the artificial neural network to obtain a prediction model with the dropping distribution as input and the energy restitution coefficient as output; and the dropping distribution obtained by a simple dropping experiment can be used to calculate the energy restitution coefficient of the actual non-spherical particles according to the prediction model.

[0023] The mainstream restitution coefficient is currently defined as the velocity restitution coefficient, and the reason for its wide application is the easy measurement of velocity in experiments rather than the accuracy and universality of the definition itself. Existing research has shown that the energy restitution coefficient is the most accurate and universal restitution coefficient definition, but due to the difficulty of measuring energy loss in experiments, the development and application of the energy restitution coefficient have been greatly limited. To explore the experimental measurement method of the energy restitution coefficient, the present application proposes a DEM method combined with artificial neural network technology, the energy restitution coefficient is calculated by the DEM method, and the random distribution of the particle dropping point is obtained. The particle dropping point distribution is affected by the size of the energy restitution coefficient, that is, the particle dropping point distribution contains the information of the particle energy restitution coefficient. The artificial neural network technology is adopted, the random dropping point distribution is taken as input, and the particle energy restitution coefficient is taken as output, the relationship between the two is mined according to a large amount of simulation data, and an artificial neural network prediction model of the particle energy restitution coefficient is constructed. Through this model, the measurement of energy loss is converted into the measurement of particle dropping point distribution, and the particle dropping point distribution obtained by simple measurement in the experiment can be substituted into the artificial neural network model to obtain the particle energy restitution coefficient. At the same time, the collision experiment device requires low, and the particle dropping point distribution statistical calculation is convenient, which is a simple measurement method of the particle energy restitution coefficient, and has important significance for the research in the field of particle-wall collision.

[0024] The beneficial effects of the present application are: the method for calculating the particle energy recovery coefficient by means of the DEM method and the artificial neural network technology through the fast and efficient collision experiment of the particle landing point distribution, the measurement problem of energy loss is converted into the measurement problem of the particle landing point distribution, a new idea and method for experimentally measuring the energy recovery coefficient are provided, and the experimental device is easy to build, and the target parameter measurement is clear and simple. BRIEF DESCRIPTION OF DRAWINGS

[0025] Figure 1 is a structural schematic diagram of the experimental device of the present application;

[0026] Figure 2 is a schematic diagram of the simulated collision process designed by the present application;

[0027] Figure 3 is a schematic diagram of the particle random landing point distribution quantified by the probability density function of the present application;

[0028] Figure 4 is a schematic diagram of the principle and structure of the artificial neural network;

[0029] Figure 5 is a schematic diagram of the number of hidden layers of the artificial neural network structure used by the present application;

[0030] Figure 6 is a schematic diagram of the number of neurons of the artificial neural network structure used by the present application;

[0031] Figure 7 is a schematic diagram of the learning rate of the artificial neural network structure used by the present application;

[0032] Figure 8 is a comparison diagram of the predicted value of the energy recovery coefficient prediction model constructed by the present application and the target value of the DEM simulation. DETAILED DESCRIPTION

[0033] The technical solutions of the present application will be further described below with reference to the drawings,

[0034] An experimental measurement method of the energy recovery coefficient of non-spherical particles, comprising the following steps:

[0035] 1) Establish a flat plate model of particle-wall collision working condition, and import the model into the DEM simulation software;(The flat plate model is an extension of the wall, the wall is a plane, and the simplest three-dimensional angle is to make a cuboid, simply speaking, it is a cuboid wood block.)

[0036] 2) Establish a non-spherical particle model and perform DEM simulation, and calculate the particle motion data obtained by simulation according to the calculation formula defined by the energy recovery coefficient:

[0037]

[0038]

[0039]

[0040] Where E1 is the total energy of the particles before the collision, E2 is the total energy of the particles after the collision, and E... K1 E R1 E P1 These are the translational kinetic energy, rotational kinetic energy, and potential energy of the particle before the collision, E. K2 E R2 E P2 These represent the translational kinetic energy, rotational kinetic energy, and potential energy of the particle after the collision, E. energy_loss This refers to the energy loss of particles during the collision process;

[0041] 3) Based on the motion parameters of the non-spherical particles after the collision, and combined with the calculation of the particle's landing point using free fall motion, the probability density function is used to quantify the random landing point distribution of the non-spherical particles after colliding with the wall, such as... Figure 3 As shown;

[0042] 4) Design several non-spherical particle models to perform the above simulations and calculations, and obtain the energy recovery coefficients and random drop point distributions of several different non-spherical particles;

[0043] 5) Build an artificial neural network training model, such as Figure 4 As shown, a nonlinear fitting relationship between random drop point distribution and energy recovery coefficient is established using Python tools through artificial neural networks, thereby constructing a prediction model for the energy recovery coefficient of non-spherical particles.

[0044] 5.1) The ReLU function is selected as the activation function for training the artificial neural network, where the number of neurons is greater than the number of input parameters, and the learning rate is set within the range of 0 to 1; Figure 5 The number of hidden layers has been determined to be 2. Figure 6 The number of neurons was determined to be 50. Figure 7 The learning rate was set at 0.2.

[0045] 5.2) Continuously adjust the training structure of the artificial neural network, reduce the loss function value, repeat the training multiple times, and select the neural network structure with the best performance to build the model;

[0046] 5.3) Using the particle impact point distribution obtained from DEM simulation as input and the particle energy recovery coefficient as output, the optimal performance artificial neural network structure obtained through debugging is used to fit and construct a particle energy recovery coefficient prediction model.

[0047] 6) Based on the simulated working conditions, build an experimental device and conduct experiments. By photographing the curve formed by the distribution of particle landing points, convert the obtained curve into discrete point form, and calculate the energy recovery coefficient of the target experimental particle according to the prediction model obtained in step 5).

[0048] like Figures 1-2 The experimental setup shown includes a funnel for particle discharge, a plate, and a particle discharge collection device. The plate is positioned at a predetermined height below the particle discharge funnel, and the tilt angle of the plate is adjustable. The particle discharge collection device includes several partitions arranged at equal intervals along the horizontal direction. The entire experimental setup is confined between two vertically parallel glass plates, with the distance between the glass plates being 10 to 20 times the equivalent diameter of the non-spherical particle.

[0049] Experimental procedure: The target experimental particles were placed into the feeding funnel and fell into the particle collection device after collision. The curve formed by the distribution of particle landing points was photographed.

[0050] Example:

[0051] Step 1: Create a flat plate model of the particle collision condition using 3D modeling software and import it into DEM simulation software.

[0052] Step 2: Model the non-spherical particles and set the corresponding physical property parameters.

[0053] Step 3: Simulate the particle-wall collision process, output the particle motion information data required during the collision process, and use Python to programmatically calculate the energy recovery coefficient of the particles according to the energy recovery coefficient definition formula.

[0054] Step 4: Based on the velocity and position information of the particles at the end of the collision, Python is used to programmatically calculate the distribution of the particle landing points on the two-dimensional plane according to the free fall motion formula.

[0055] Step 5: Design a large number of different non-spherical particles to perform simulation calculations in steps 2-4, so as to obtain a large amount of data on particle energy recovery coefficients and impact point distributions, including particles of various shapes.

[0056] Step 6: Select the ReLU function as the activation function for training the artificial neural network, ensuring that the number of neurons is greater than the number of input parameters, and set the learning rate to a value between 0 and 1. Continuously adjust the neural network training structure, reduce the loss function value, repeat the training multiple times, and select the neural network structure with the best performance to build the model.

[0057] Step 7: Using the particle impact point distribution obtained from DEM simulation as input and the particle energy recovery coefficient as output, a particle energy recovery coefficient prediction model is constructed by fitting the best-performing neural network structure obtained through debugging.

[0058] Step 8: Build an experimental device with the same working condition as the simulation, make the target experimental particles fall into the particle dropping collection device after collision, shoot the curve formed by the particle dropping point distribution, convert the curve into discrete point form and input into the obtained prediction model, and the energy recovery coefficient of the target experimental particles can be calculated.

[0059] As Figure 8 shown, the prediction value of the energy recovery coefficient prediction model constructed by the application is compared with the target value of the DEM simulation, and the model MSE error is only 0.0097.

Claims

1. An experimental method for measuring the energy recovery coefficient of non-spherical particles, characterized in that, Includes the following steps: 1) Establish a plate model of particle-wall collision and import the model into DEM simulation software; 2) Establish a non-spherical particle model and perform DEM simulation. Calculate the particle motion data obtained from the simulation using the formula defined by the energy recovery coefficient: Where E1 is the total energy of the particles before the collision, E2 is the total energy of the particles after the collision, and E... K1 E R1 E P1 These are the translational kinetic energy, rotational kinetic energy, and potential energy of the particle before the collision, E. K2 E R2 E P2 These represent the translational kinetic energy, rotational kinetic energy, and potential energy of the particle after the collision, E. energy_loss This refers to the energy loss of particles during the collision process; 3) Based on the motion data of non-spherical particles after the collision, the landing point of the particles is calculated by combining the free fall motion, and the probability density function is used to quantify the random landing point distribution of non-spherical particles after colliding with the wall. 4) Design several non-spherical particle models to perform the above simulations and calculations, and obtain the energy recovery coefficients and random drop point distributions of several different non-spherical particles; 5) Build an artificial neural network training model, and use Python tools to establish a nonlinear fitting relationship between random drop point distribution and energy recovery coefficient through artificial neural network, and construct a prediction model for energy recovery coefficient of non-spherical particles; 6) Based on the simulated working conditions, build an experimental setup and conduct the experiment. By photographing the curve formed by the distribution of non-spherical particle landing points, convert the obtained curve into discrete point form, and calculate the energy recovery coefficient of the target experimental particle according to the prediction model obtained in step 5).

2. The experimental measurement method for the energy recovery coefficient of non-spherical particles according to claim 1, characterized in that, Step 5) is as follows: 5.1) The ReLU function is selected as the activation function for training the artificial neural network, where the number of neurons is greater than the number of input parameters, and the learning rate is taken in the range of 0 to 1; 5.2) Continuously adjust the training structure of the artificial neural network, reduce the loss function value, repeat the training multiple times, and select the neural network structure with the best performance to build the model; 5.3) Using the particle impact point distribution obtained from DEM simulation as input and the particle energy recovery coefficient as output, the optimal performance artificial neural network structure obtained through debugging is used to fit and construct a particle energy recovery coefficient prediction model.

3. The experimental measurement method for the energy recovery coefficient of non-spherical particles according to claim 1, characterized in that, The experimental apparatus in step 6) includes a hopper for particle discharge, a plate, and a particle discharge collection device. The plate is positioned at a predetermined height below the particle discharge hopper, and the tilt angle of the plate is adjustable. The particle discharge collection device includes several partitions arranged at equal intervals along the horizontal direction. The entire experimental apparatus is confined between two vertical parallel glass plates, with the distance between the glass plates being 10 to 20 times the equivalent diameter of the non-spherical particles.

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