Discrete element method recovery coefficient correction method based on steel ball falling-into-water experiment

Abstract

The invention discloses a discrete element method recovery coefficient correction method based on a steel ball falling-into-water experiment, and belongs to the field of multi-parameter collision discrete element methods. The invention aims to solve the problem of insufficient precision of a recovery coefficient caused by neglect of liquid viscosity in a particle collision simulation process of an existing discrete element method. According to the method, a steel ball falling-into-water experiment is designed, steel balls with different diameters, a transparent water tank, a high-speed camera, a graduated scale and other equipment are utilized, the rebound height of the steel balls under multiple working conditions is collected, and then actual recovery coefficient data are calculated; a dynamic correction model considering the collision speed, the steel ball diameter and the liquid level is constructed through data analysis; and finally, embedding the model into a discrete element method collision module to realize real-time correction of a recovery coefficient. Experimental verification shows that the method can reduce the simulation errors such as the steel ball motion trail and the rebound height to be within 5%, the simulation precision of the particle collision process is remarkably improved, and the method is suitable for related engineering design in the fields of water conservancy, mining industry and the like and has high practical value.

Description

Technical Field

[0001] This invention relates to the field of multi-parameter collision discrete element method, and specifically to a method for correcting the restitution coefficient of the discrete element method based on a steel ball falling into water experiment. Background Technology

[0002] The Discrete Element Method (DEM) simulates the motion of discrete particles by constructing collision models between them. Its core principle is to describe the energy transfer and loss during collisions based on the coefficient of restitution. This method, with its accurate characterization of particle dynamics, is widely used in fields such as hydraulic engineering (e.g., simulating the settling trajectory of steel balls in water), mining processing (e.g., impact crushing analysis of steel balls and ore in a ball mill), and materials science (e.g., testing the mechanical properties of particulate materials). In multi-parameter coupled scenarios, DEM calculates the collision forces between particles and the fluid medium, predicting their trajectory, velocity changes, and energy losses, providing crucial data support for engineering design.

[0003] However, the existing discrete element method (DEM) has significant shortcomings in its handling of the coefficient of restitution: On the one hand, traditional models often set the coefficient of restitution to a fixed value (e.g., the coefficient of restitution between steel balls is 0.85), without considering the coupling effects of multiple factors during the actual collision process. For example, when a steel ball moves in water, the viscous drag and buoyancy of the water medium will consume additional energy, and changes in collision speed, steel ball diameter, and entry angle will also lead to energy loss. This makes the simulation results deviate significantly from reality (e.g., the prediction error of the steel ball's rebound height often exceeds 20%). On the other hand, existing coefficient of restitution correction methods are mostly for air media or single influencing parameters, without combining the special characteristics of other media to establish a multi-parameter coupling correction mechanism, and lack systematic experimental data on particle collisions as support, making it difficult to meet the high-precision requirements of multi-parameter coupling simulation. Summary of the Invention

[0004] Technical problems to be solved: To address the shortcomings of existing technologies, this invention provides a method for correcting the coefficient of restitution based on a steel ball drop experiment. By optimizing the coefficient of restitution through a multi-parameter coupled model, the accuracy of DEM simulation is improved, thus solving the aforementioned technical problems.

[0005] Technical solution: To achieve the above objectives, the present invention provides the following technical solution: a method for correcting the coefficient of restitution using the discrete element method based on a steel ball falling into water experiment, comprising the following steps: S1. Construct an experimental setup for calculating the correction method of the discrete element method for the coefficient of restitution in the steel ball falling into water experiment; The experimental setup includes: a base 1, a vertical slide rail 2, a release mechanism, a water tank 7, and a measuring system; The release mechanism includes: a horizontal connecting rod 4, an L-shaped bracket 5, and an electromagnetic chuck 6; The base 1 is a cast iron plate, 2m long × 2m wide × 0.02m high, to ensure the stability of the device; A vertical slide rail 2 is provided on one side of the base 1. The vertical slide rail 2 has a cross-sectional area of ​​0.05m × 0.05m square. The center point of the connection between the vertical slide rail 2 and the base 1 is 0.3m, 1.7m, 1m, and 1m away from the four edges of the base 1, respectively. The surface where the vertical slide rail 2 connects to the base 1 is connected to the base 1 by four 8.8 grade high-strength bolts with a preload torque of 20 Nm. This improves the stability of the slide rail and ensures that the slide rail is always in a vertical position. A slider is provided on the vertical slide rail 2. A bolt hole and a set screw (M5 hexagon socket screw) are provided on one side of the slider. By rotating the set screw, static friction is generated (static friction ≥ total weight of slider and release mechanism) to "clamp" the slider on the slide rail, so as to realize the sliding and tightening of the slider on the vertical slide rail 2, thereby controlling the release height of the steel ball (0.5m, 1m, 1.5m). When the height from which the steel ball is released is less than 0.5m, the change in the speed at which the steel ball enters the water and the observed phenomena are not obvious, which is not conducive to observation and obtaining effective data. When the steel ball is released from a height of more than 1.5m, the steel ball falls too fast and has a large impact force when entering the water, which may cause violent splashing of water or even cause the steel ball to bounce out, posing a safety hazard and damaging the water tank 7 and surrounding equipment. Excessive release height places higher demands on the shooting range and accuracy of high-speed cameras and other equipment, as well as the performance of release devices such as electromagnetic chucks 6, which may exceed the capabilities of the equipment. Therefore, the present invention is set between 0.5m and 1.5m, so that the phenomenon of the steel ball entering the water is neither too simple nor too complex, and the data change pattern is relatively easy to capture and analyze, which can ensure the validity and representativeness of the experimental data. The vertical slide rail 2 is made of 45# steel and is chrome-plated to form a dense oxide layer to reduce the sliding friction coefficient (≤0.15) while improving wear resistance and rust prevention, so as to meet the frequent height adjustment requirements in the experiment. One end of the horizontal connecting rod 4 is fixedly connected to the slider, and the other end is fixedly connected to the L-shaped bracket 5. The other end of the L-shaped bracket 5 is fixedly connected to the electromagnetic chuck 6. The response time of the electromagnetic chuck 6 is ≤10ms. The principle of the electromagnetic chuck 6 is: when the electromagnetic chuck 6 is energized, the internal coil generates magnetic force, which tightly attracts the workpiece. A water tank 7 is horizontally positioned on the other side of the base 1. The water tank 7 is made of transparent acrylic sheet material and has dimensions of 1m long × 1m wide × 1.5m high. The center point of the contact surface between the water tank 7 and the base 1 is 0.7m, 1.3m, 1m, and 1m away from the four edges of the base 1. A black background board is attached to the inner wall of the water tank 7 to enhance the contrast of high-speed imaging. The water tank 7 is also equipped with a water temperature sensor (accuracy ±0.1℃) and a water quality monitor (recording turbidity ≤5NTU) to prevent impurities from affecting the resistance. A 0.5m long × 0.5m wide × 0.02m high 45# steel plate is placed on the bottom of the water tank 7. The surface is polished to reduce the influence of surface roughness on the experimental results and prevent the steel ball from penetrating the bottom of the water tank 7. The measurement system includes a high-speed camera and a ruler. The high-speed camera has a frame rate of 5000fps and a resolution of 1920×1080. It is set up 1.5m inside the black background board in water tank 7 to record the entire process of the steel ball entering the water and bouncing back. Diffuse light source is used to supplement the lighting to avoid water surface reflection. The ruler has a measuring range of 1.5m and is fixed to the black background board inside water tank 7, opposite to the high-speed camera. By controlling the electromagnetic chuck 6 to be energized or discharged, the steel ball is controlled to fall into the water tank 7 on the 45# steel plate. The measurement system collects various key parameters during the process of the steel ball falling into the water, laying a solid foundation for subsequent data analysis and model building. In this invention, the steel ball samples are made of 45# steel to ensure uniform hardness, with diameters ranging from 44mm, 68mm, and 80mm, covering common engineering sizes. The surface is polished to ensure uniform hardness. This reduces the interference of surface roughness on water resistance, and three duplicate samples are prepared for each diameter group to reduce the impact of individual differences.

[0006] S2. Based on the orthogonal experimental method, set multiple parameter variables; The multi-parameter variables include: collision velocity, steel ball diameter, and liquid level height; The orthogonal experimental design used 27 operating conditions (3 factors × 3 levels × 3 replicates) to comprehensively cover key parameter combinations and ensure the systematicity and representativeness of the experimental data. The three key influencing factors and their corresponding level settings are as follows: The collision speeds selected are 3.13 m / s (corresponding to a release height of 0.5 m), 4.43 m / s (corresponding to a release height of 1 m), and 5.42 m / s (corresponding to a release height of 1.5 m). The diameters of the steel balls are set to 44mm, 68mm, and 80mm; The liquid level is set as 0D, 1D, and 2D according to multiples of the steel ball diameter (D is the steel ball diameter). Each working condition was repeated 3 times. Other environmental variables were strictly controlled during the experiment. The average value of the results of the 3 repeated experiments was taken. This effectively reduced the interference of random factors such as equipment fluctuations and operational errors on the accuracy of the data, and provided more reliable basic data for subsequent data analysis and model building. S3. Perform the operation of the experimental device adjustment and collect data; The experimental setup was adjusted as follows: First, the water temperature in tank 7 was adjusted to 25℃±1℃ to eliminate the influence of temperature fluctuations, and the initial water level was recorded. Then, the diameter of the steel ball, the release height, and the liquid level were set. The steel ball was released through the electromagnetic chuck 6, and at the same time, the high-speed camera was started to record the trajectory of the steel ball from release to its rebound three times after falling into the water. The maximum rebound height was recorded. After each set of conditions was completed, the water was left to stand for 30 seconds until the water surface was calm, and the steel ball sample was replaced to avoid water on the surface affecting the next experiment.

[0007] S4. Based on the collected data, the actual recovery coefficient is calculated using the recovery coefficient formula.

[0008] S5. Perform multivariate analysis on the actual coefficient of restitution and establish a coefficient of restitution correction model suitable for discrete element method (DEM); Based on the single-factor regularity and weight allocation, a dynamic correction model for the recovery coefficient is constructed using standardization (eliminating dimensional differences), as shown in the following expression: In the formula, The coefficient of restitution in air is taken as 0.9 (the basic coefficient of restitution between a steel ball and a steel plate, measured by a direct impact test of a steel ball against a steel plate). This is the initial height; The maximum initial height; The diameter of the steel ball; The maximum diameter of the steel ball; Liquid level; The highest liquid level (2) ); These are the first, second, and third proportionality coefficients, respectively. The results were obtained by fitting 27 sets of experimental data using the least squares method. , , .

[0009] S6. Embed the obtained restoration coefficient correction model into the collision calculation module of the discrete element method (DEM) to optimize the simulation process.

[0010] S7. By comparing the experimental data with the simulation results, determine whether the error is ≤5%. If yes, then end the process. If no, then adjust the parameters and repeat steps S6 to S7.

[0011] Compared with the prior art, the present invention has the following beneficial effects: This invention addresses the issue of insufficient accuracy of the coefficient of restitution in discrete element method (DEM) simulations of particle collisions. By acquiring multi-condition data through steel ball drop experiments, a dynamic correction model considering collision velocity, steel ball diameter, and liquid level is constructed, significantly improving simulation accuracy. After being embedded into the DEM, the correction model can respond in real-time to changes in collision conditions, overcoming the limitations of traditional fixed coefficients of restitution. It is particularly suitable for collision simulation experiments in multi-parameter coupled scenarios. Experimental verification shows that this method can reduce simulation errors such as steel ball trajectory, rebound height, and power to within 5%, providing a more reliable theoretical basis for related engineering designs in fields such as water conservancy and mining, and possessing a certain degree of practicality and promotional value. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is a diagram of the steel ball drop test apparatus of the present invention; Figure 3 The graph shows the results of the coefficient of restitution of this invention. Figure 4 This is a graph showing the coefficients of restitution between the various materials in this invention; Figure 5 This is a comparative cloud image of the steel ball being dropped according to the present invention; Figure 6 This is a power comparison diagram of the present invention.

[0013] The components are: 1-base, 2-vertical slide rail, 3-slider, 4-horizontal connecting rod, 5-L-shaped bracket, 6-electromagnetic chuck, 7-water tank, and 8-45# steel plate. Detailed Implementation

[0014] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0015] Please see Figure 1-6 A method for correcting the coefficient of restitution using the discrete element method based on a steel ball falling into water experiment includes the following steps: S1. Construct an experimental setup for calculating the correction method of the discrete element method for the coefficient of restitution in the steel ball falling into water experiment; The experimental setup includes: a base 1, a vertical slide rail 2, a release mechanism, a water tank 7, and a measuring system; The release mechanism includes: a horizontal connecting rod 4, an L-shaped bracket 5, and an electromagnetic chuck 6; The base 1 is a cast iron plate, 2m long × 2m wide × 0.02m high, to ensure the stability of the device; A vertical slide rail 2 is provided on one side of the base 1. The vertical slide rail 2 has a cross-sectional area of ​​0.05m × 0.05m square. The center point of the connection between the vertical slide rail 2 and the base 1 is 0.3m, 1.7m, 1m, and 1m away from the four edges of the base 1, respectively. The surface where the vertical slide rail 2 connects to the base 1 is connected to the base 1 by four 8.8 grade high-strength bolts with a preload torque of 20 Nm. This improves the stability of the slide rail and ensures that the slide rail is always in a vertical position. A slider is provided on the vertical slide rail 2. A bolt hole and a set screw (M5 hexagon socket screw) are provided on one side of the slider. By rotating the set screw, static friction is generated (static friction ≥ total weight of slider and release mechanism) to "clamp" the slider on the slide rail, so as to realize the sliding and tightening of the slider on the vertical slide rail 2, thereby controlling the release height of the steel ball (0.5m, 1m, 1.5m). When the height from which the steel ball is released is less than 0.5m, the change in the speed at which the steel ball enters the water and the observed phenomena are not obvious, which is not conducive to observation and obtaining effective data. When the steel ball is released from a height of more than 1.5m, the steel ball falls too fast and has a large impact force when entering the water, which may cause violent splashing of water or even cause the steel ball to bounce out, posing a safety hazard and damaging the water tank 7 and surrounding equipment. Excessive release height places higher demands on the shooting range and accuracy of high-speed cameras and other equipment, as well as the performance of release devices such as electromagnetic chucks 6, which may exceed the capabilities of the equipment. Therefore, the present invention is set between 0.5m and 1.5m, so that the phenomenon of the steel ball entering the water is neither too simple nor too complex, and the data change pattern is relatively easy to capture and analyze, which can ensure the validity and representativeness of the experimental data. The vertical slide rail 2 is made of 45# steel and is chrome-plated to form a dense oxide layer to reduce the sliding friction coefficient (≤0.15) while improving wear resistance and rust prevention, so as to meet the frequent height adjustment requirements in the experiment. One end of the horizontal connecting rod 4 is fixedly connected to the slider, and the other end is fixedly connected to the L-shaped bracket 5. The other end of the L-shaped bracket 5 is fixedly connected to the electromagnetic chuck 6. The response time of the electromagnetic chuck 6 is ≤10ms. The principle of the electromagnetic chuck 6 is: when the electromagnetic chuck 6 is energized, the internal coil generates magnetic force, which tightly attracts the workpiece. A water tank 7 is horizontally positioned on the other side of the base 1. The water tank 7 is made of transparent acrylic sheet material and has dimensions of 1m long × 1m wide × 1.5m high. The center point of the contact surface between the water tank 7 and the base 1 is 0.7m, 1.3m, 1m, and 1m away from the four edges of the base 1. A black background board is attached to the inner wall of the water tank 7 to enhance the contrast of high-speed imaging. The water tank 7 is also equipped with a water temperature sensor (accuracy ±0.1℃) and a water quality monitor (recording turbidity ≤5NTU) to prevent impurities from affecting the resistance. A 0.5m long × 0.5m wide × 0.02m high 45# steel plate is placed on the bottom of the water tank 7. The surface is polished to reduce the influence of surface roughness on the experimental results and prevent the steel ball from penetrating the bottom of the water tank 7. The measurement system includes a high-speed camera and a ruler. The high-speed camera has a frame rate of 5000fps and a resolution of 1920×1080. It is set up 1.5m inside the black background board in water tank 7 to record the entire process of the steel ball entering the water and bouncing back. Diffuse light source is used to supplement the lighting to avoid water surface reflection. The ruler has a measuring range of 1.5m and is fixed to the black background board inside water tank 7, opposite to the high-speed camera. By controlling the electromagnetic chuck 6 to be energized or discharged, the steel ball is controlled to fall into the water tank 7 on the 45# steel plate. The measurement system collects various key parameters during the process of the steel ball falling into the water, laying a solid foundation for subsequent data analysis and model building. In this invention, the steel ball samples are made of 45# steel to ensure uniform hardness, with diameters ranging from 44mm, 68mm, and 80mm, covering common engineering sizes. The surface is polished to ensure uniform hardness. This reduces the interference of surface roughness on water resistance, and three duplicate samples are prepared for each diameter group to reduce the impact of individual differences.

[0016] S2. Based on the orthogonal experimental method, set multiple parameter variables; The multi-parameter variables include: collision velocity, steel ball diameter, and liquid level height; An orthogonal experimental design was used to create 27 working conditions (3 factors × 3 levels × 3 replicates) to comprehensively cover key parameter combinations and ensure the systematicity and representativeness of the experimental data. The three key influencing factors and their corresponding levels were set as follows: collision velocities of 3.13 m / s (corresponding to a release height of 0.5 m), 4.43 m / s (corresponding to a release height of 1 m), and 5.42 m / s (corresponding to a release height of 1.5 m) were selected to investigate the differences in energy loss during collisions between a steel ball and a steel plate in water at different motion velocities. The diameter of the steel ball was set to 44 mm, 68 mm, and 80 mm. By changing the ball size, the relative relationship between inertia and water resistance on the collision was analyzed. The influence of characteristics was investigated; the liquid level was set as multiples of the steel ball diameter: 0D, 1D, and 2D (D being the steel ball diameter). 0D indicates that the steel ball just touches the water surface, while 1D and 2D indicate that the water surface is 1 and 2 times the diameter of the steel ball, respectively. This was used to study the effect of different water depths on the force and rebound law of the steel ball after entering the water. Each working condition was repeated 3 times. During the experiment, other environmental variables (such as water temperature and water surface calmness) were strictly controlled. Finally, the average value of the results of the 3 repeated experiments was taken to effectively reduce the interference of random factors such as equipment fluctuations and operational errors on the accuracy of the data, and to provide more reliable basic data for subsequent data analysis and model construction. S3. Perform the operation of the experimental device adjustment and collect data; The experimental setup was adjusted as follows: First, the water temperature in tank 7 was adjusted to 25℃±1℃ to eliminate the influence of temperature fluctuations, and the initial water level was recorded. Then, the diameter of the steel ball, the release height, and the liquid level were set. The steel ball was released through the electromagnetic chuck 6, and at the same time, the high-speed camera was started to record the trajectory of the steel ball from release to its rebound three times after falling into the water. The maximum rebound height was recorded. After each set of conditions was completed, the water was left to stand for 30 seconds until the water surface was calm, and the steel ball sample was replaced to avoid water on the surface affecting the next experiment.

[0017] S4. Based on the collected data, the actual recovery coefficient is calculated using the recovery coefficient formula; The maximum rebound height was determined by comparing the trajectory of the steel ball captured by a high-speed camera with a ruler. Then calculate the actual recovery coefficient. The expression is: In the formula, Indicates the maximum rebound height of the steel ball; Indicates the initial height of the steel ball; In this embodiment, taking a set of data with a steel ball diameter of 68mm, an initial height of 1m, and a liquid level of 2D (136mm) as an example, the rebound heights of the three experiments were 0.49m, 0.50m, and 0.48m, with an average of 0.49m. ; The actual coefficient of restitution is also affected by the viscosity of the liquid. The higher the liquid viscosity, the greater the viscous drag experienced by the steel ball during the collision. When the steel ball enters water, the internal friction between liquid molecules hinders the ball's motion, leading to increased kinetic energy loss before collision with the steel plate, thus reducing the kinetic energy at rebound and lowering the rebound height. Furthermore, this effect is also related to the speed of the steel ball: at high speeds, the drag of high-viscosity liquids increases with the square of the velocity (a modified form of Stokes' drag law), resulting in a more significant reduction in the coefficient of restitution. At low speeds, the effect of viscosity is relatively weaker, but it still causes the coefficient of restitution to be lower than that under low-viscosity liquid conditions. The relationship between the actual coefficient of restitution and liquid viscosity is shown in the following formula: In the formula, Indicates the coefficient of restitution in air; E The base of the natural logarithm; The Stokes number, representing the number of particles as they move away from the wall, is expressed as follows: In the formula, Indicates particle density; Indicates the density of the liquid; Indicates the impact speed; Indicates particle size; The viscosity of the liquid; After 27 sets of experiments, the experimental results are as follows: Figure 3 As shown, The result when taking 0D, Take the average value between 1D and 2D, and then determine and The proportionality coefficient is 0.82. Applying this to other collision types, the coefficient of restitution for collisions such as steel ball-ore and ore-ore can be determined considering a liquid environment. The corrected coefficient of restitution is as follows: Figure 4 As shown.

[0018] S5. Perform multivariate analysis on the actual coefficient of restitution and establish a coefficient of restitution correction model suitable for discrete element method (DEM); The method for multivariate analysis of the actual coefficient of restitution is as follows: by analyzing the variance of the orthogonal experimental results, the influence weights of the steel ball diameter, initial height, and liquid level on the coefficient of restitution are determined, and the functional relationship between the actual coefficient of restitution and each factor is established using the least squares method. Analysis of variance of the orthogonal experimental results showed that: initial height The weighting is 40%; the initial height determines the speed of the steel ball before it hits the water, and as... The collision kinetic energy between the steel ball and the bottom steel plate of the water tank 7 is significantly increased, and the coefficient of restitution is also increased. Follow The increase shows a linear decreasing trend; The steel ball diameter D accounts for 30% of the weight; larger diameter steel balls (such as 80mm) have greater mass and inertia, and the viscous resistance of the water medium has a relatively weaker impact when moving in water; experimental data show that when the diameter increases from 44mm to 80mm, the coefficient of restitution under the same working conditions... The average increase of 0.07 indicates that the "anti-interference ability" of the steel ball's kinetic energy against water resistance increases with the increase of its diameter; liquid level The weighting is 30%; the liquid level, based on the steel ball diameter D (0D, 1D, 2D), directly determines the distance the steel ball travels in the water. The higher the liquid level (e.g., 2D), the more work the steel ball does to overcome resistance as it passes through the water layer, resulting in greater kinetic energy loss before collision and a higher coefficient of restitution. Reduce; for example, when a 68mm steel ball is in a 2D liquid level. Compared to when the liquid level is 0D On average, it is 0.09 lower; Based on the single-factor regularity and weight allocation, a dynamic correction model for the recovery coefficient is constructed using standardization (eliminating dimensional differences), as shown in the following expression: In the formula, The coefficient of restitution in air is taken as 0.9 (the basic coefficient of restitution between a steel ball and a steel plate, measured by a direct impact test of a steel ball against a steel plate). This is the initial height; The maximum initial height; The diameter of the steel ball; The maximum diameter of the steel ball; Liquid level; The highest liquid level (2) ); These are the first, second, and third proportionality coefficients, respectively. The results were obtained by fitting 27 sets of experimental data using the least squares method. , , ; For any operating condition, the calculation results satisfy 0 < <1, possessing physical validity. For example, extreme operating conditions ( , , )Down: Compared with experimentally measured The deviation was only 3.8%, proving that the model had high fitting accuracy.

[0019] S6. Embed the obtained restoration coefficient correction model into the collision calculation module of the discrete element method (DEM) to optimize the simulation process; The original expression for the collision calculation module of the Discrete Element Method (DEM) is as follows: In the formula, Indicates normal force; Indicates normal stiffness (taken in this invention) ), Indicates the amount of overlap in the normal direction. Represents the damping coefficient, and Related, Indicates the normal relative velocity; In traditional calculations, the damping coefficient The calculation is usually based on a fixed (0.85), the experimentally corrected coefficient of restitution is now... With damping coefficient Bind, will Change to The function, with the following expression: In the formula, This represents the corrected coefficient of restitution. Indicates normal stiffness (taken in this invention) ), The equivalent mass is expressed as follows: In the formula, Indicates the mass of the steel ball. This indicates that the bottom surface of water tank 7 is made of 45# steel plate. Since the mass of the steel plate is much greater than that of the steel ball, it can be simplified to... steel ball quality The expression is as follows: In the formula, Represents the density of a steel ball ( ); This indicates the diameter of the steel ball.

[0020] S7. By comparing the experimental data with the simulation results, determine whether the error is ≤5%. If yes, then end; if no, then adjust the parameters and repeat steps S6 to S7. To verify the effectiveness of the correction method, three sets of working conditions that were not involved in model fitting were selected for comparative experiments, as shown in Table 1. Table 1: Comparative Experiment Results Taking the results of working condition 2 as an example, the experimentally measured rebound height The calculated coefficient of recovery is The traditional DEM simulation restoration coefficient is The error is 17.6%, and the corrected DEM simulation restoration coefficient is... The error was 2.8%. The mean absolute error of the three sets of verification conditions decreased from 14.7% in the traditional method to 2.5% in the modified method, indicating that the modified model significantly improved the simulation accuracy.

[0021] EDEM discrete element simulation software was used to simulate the grinding process of a mill and verify the effectiveness of the modified model. The simulation was divided into two groups: the traditional group (unmodified) used a contact model with a fixed coefficient of restitution of 0.85, and the modified group read parameters in real time and calculated the coefficient of restitution according to the modified formula, updating the damping coefficient; other parameters remained consistent between the two groups. Simulations were performed on the same set of operating conditions, and power, coefficient of restitution, and ball impact contour data were extracted. The results were compared using steel ball impact contours (e.g., ...). Figure 5 As shown in the figure), the overlap between the corrected DEM simulated trajectory and the experimental trajectory reached 96%, far exceeding the 78% of the traditional DEM, verifying the effectiveness of dynamic correction in predicting motion processes. This is further demonstrated by the power comparison diagram (as shown in the figure). Figure 6 As shown in the figure, the average actual mill power is 2473 kW; the average simulated power of the uncorrected group is 3046 kW with an error of 23.17%; and the average simulated power of the corrected group is 2417 kW with an error of 2.26%, both highly consistent with the actual values. This indicates that the corrected model can accurately reflect the energy transfer from collisions between steel balls and between steel balls and the liner, significantly improving the accuracy of mill power simulation and providing a reliable basis for mill design optimization and energy consumption prediction.

[0022] In summary, after correcting the model embedding, the simulation accuracy of the discrete element method is significantly improved, providing a reliable solution for the simulation of complex multi-parameter coupled scenarios.

[0023] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for correcting the coefficient of restitution in the discrete element method based on a steel ball falling into water experiment, characterized in that, Includes the following steps: S1. Construct an experimental setup for calculating the correction method of the discrete element method for the coefficient of restitution in the steel ball falling into water experiment; The experimental apparatus includes: a base (1), a vertical slide rail (2), a release mechanism, a water tank (7), and a measurement system; The release mechanism includes: a horizontal connecting rod (4), an L-shaped bracket (5), and an electromagnetic chuck (6). The measurement system includes: a high-speed camera and a ruler; S2. Based on the orthogonal experimental method, set multiple parameter variables; The multi-parameter variables include: collision velocity, steel ball diameter, and liquid level height; The orthogonal experimental method was set as a 3-factor × 3-level × 3-repeated orthogonal experimental method; wherein, the 3 factors are the steel ball release height, the steel ball diameter, and the liquid level height; the 3 level settings include: collision velocity: 3.13m / s, 4.43m / s, 5.42m / s; steel ball diameter: 44mm, 68mm, and 80mm; liquid level height: 0D, 1D, 2D, where D is the steel ball diameter; S3. Perform the operation of the experimental device adjustment and collect data; The data collected is the maximum rebound height of the steel ball after it is released and bounces three times after hitting the water. S4. Based on the collected data, the actual recovery coefficient is calculated using the recovery coefficient formula; S5. Perform multivariate analysis on the actual restoration coefficients and establish a restoration coefficient correction model suitable for discrete element method DEM; S6. Embed the obtained restoration coefficient correction model into the collision calculation module of the discrete element method DEM to optimize the simulation process; S7. By comparing the experimental data with the simulation results, determine whether the error is ≤5%. If yes, then end the process. If no, then adjust the parameters and repeat steps S6 to S7.

2. The method for correcting the coefficient of restitution in the discrete element method based on a steel ball falling into water experiment according to claim 1, characterized in that: In the experimental device, the base (1) is a cube, one side of the base (1) is fixedly connected to the vertical slide rail (2), and a square water tank (7) is placed on the other side; a slider (3) is provided on the vertical slide rail (2), and a bolt hole and a set screw thread connection are provided on one side of the slider (3). By rotating the set screw, the slider can slide and tighten on the vertical slide rail (2) to control the release height of the steel ball. The release height of the steel ball includes: 0.5m, 1m, and 1.5m.

3. The method for correcting the coefficient of restitution in the discrete element method based on a steel ball falling into water experiment according to claim 2, characterized in that: The collision velocity of the steel ball is 3.13 m / s when the release height is 0.5 m, 4.43 m / s when the release height is 1 m, and 5.42 m / s when the release height is 1.5 m.

4. The method for correcting the coefficient of restitution in the discrete element method based on a steel ball falling into water experiment according to claim 2, characterized in that: The slider is fixedly connected to one end of the horizontal connecting rod (4), the other end of the horizontal connecting rod (4) is fixedly connected to the L-shaped bracket (5), and the other end of the L-shaped bracket (5) is fixedly connected to the electromagnetic chuck (6). When the electromagnetic chuck (6) is energized, the internal coil generates magnetic force, which attracts the steel ball tightly.

5. The method for correcting the coefficient of restitution in the discrete element method based on a steel ball falling into water experiment according to claim 2, characterized in that: The inner wall of the water tank (7) is covered with a black background board to improve the contrast of high-speed imaging; the water tank (7) is equipped with a water temperature sensor and a water quality monitor to avoid impurities affecting the resistance; a 45# steel plate (8) is placed on the bottom of the water tank (7), and the surface of the 45# steel plate (8) is polished to reduce the influence of surface roughness on the experimental results and prevent the steel ball from penetrating the bottom of the water tank (7).

6. The method for correcting the coefficient of restitution in the discrete element method based on a steel ball falling into water experiment according to claim 1, characterized in that: In the measurement system, a high-speed camera is mounted at a fixed distance from the black background board inside the water tank (7) to record the entire process of the steel ball entering the water and rebounding; a ruler with a range of 1.5m is fixed on the black background board inside the water tank (7) and is opposite to the high-speed camera.

7. The method for correcting the coefficient of restitution in the discrete element method based on a steel ball falling into water experiment according to claim 1, characterized in that: The expression for the multivariate analysis of the actual coefficient of restitution and the establishment of a coefficient of restitution correction model suitable for discrete element method DEM is as follows: In the formula, The coefficient of recovery in air; This is the initial height; The maximum initial height; The diameter of the steel ball; The maximum diameter of the steel ball; Liquid level; This is the highest liquid level; The first, second, and third proportionality coefficients are respectively obtained by fitting orthogonal experiments using the least squares method. , , .

8. The method for correcting the coefficient of restitution in the discrete element method based on a steel ball falling into water experiment according to claim 7, characterized in that: The obtained restoration coefficient correction model is embedded into the collision calculation module of the discrete element method (DEM) to optimize the simulation process. The original expression of the collision calculation module of the discrete element method (DEM) is as follows: In the formula, Indicates normal force; Indicates normal stiffness, Indicates the amount of overlap in the normal direction. Indicates the damping coefficient. Indicates the normal relative velocity; Damping coefficient Substituting the restitution coefficient correction model applicable to discrete element method DEM, the expression is as follows: In the formula, This represents the corrected coefficient of restitution. Indicates normal stiffness, Indicates equivalent quality.

9. The method for correcting the coefficient of restitution in the discrete element method based on a steel ball falling into water experiment according to claim 8, characterized in that: The damping coefficient In the middle, equivalent quality The expression is as follows: In the formula, Indicates the mass of the steel ball. This indicates that the bottom surface of water tank 7 is made of 45# steel plate. Since the mass of the steel plate is much greater than that of the steel ball, it is simplified to... steel ball quality The expression is as follows: In the formula, This indicates the density of the steel ball; This indicates the diameter of the steel ball.

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