A method for testing dynamic damage-fracture characteristics of mining ceramic balls

Abstract

The application discloses a kind of mining ceramic ball dynamic damage-fracture characteristic test method, belongs to the field of mineral processing and grinding medium performance test field, comprising: first, based on the three-body series contact model of hertz contact theory is established, the deformation energy distribution coefficient of ceramic ball is solved, and the macroscopic collision energy is uniformly converted into the deformation energy actually absorbed by ceramic ball;Then, the fracture energy dataset is obtained by single dynamic collision test and the fracture energy distribution parameter is fitted;Finally, through low-energy repeated collision test, the damage accumulation coefficient is obtained by inversion according to Tavares damage accumulation model.The application takes the deformation energy actually absorbed by ceramic ball as the unified energy scale, realizes the comprehensive characterization of fracture energy distribution and long-term fatigue degradation behavior, and provides reliable basic mechanical parameters for ceramic ball performance evaluation and discrete element simulation prediction.

Description

Technical Field

[0001] This invention belongs to the field of mineral processing and grinding media performance testing, and particularly relates to a method for testing the dynamic damage-fracture characteristics of mining ceramic balls. Background Technology

[0002] Mining ceramic balls have gained increasing attention in the fine grinding of iron ore, non-ferrous metal ores, and non-metallic minerals due to their advantages such as high hardness, good wear resistance, and minimal contamination of the slurry. Compared to traditional grinding media such as steel balls, ceramic balls have a lower wear rate, effectively reducing grinding media consumption costs. However, ceramic materials are typically brittle, and whether damage accumulation and fracture will occur under long-term, high-frequency impacts in large ball mills has always been a significant factor restricting the large-scale application of mining ceramic balls. Currently, the performance evaluation of mining ceramic balls mainly uses static or quasi-static mechanical indicators such as uniaxial compressive strength, Vickers hardness, and impact toughness. These indicators can reflect the basic mechanical properties of the ceramic material itself, but they are difficult to characterize the dynamic damage evolution and fracture behavior of ceramic balls after hundreds of thousands or even millions of repeated impacts in a ball mill, nor can they obtain parameters describing the strength dispersion and fatigue damage characteristics of the ceramic ball group. Therefore, existing evaluation methods cannot accurately reflect the service performance of mining ceramic balls under actual grinding conditions, nor can they provide a unified basis for comparing the performance of ceramic balls from different manufacturers, with different materials, and with different specifications. In recent years, the Tavares crushing model has been successfully applied to the dynamic fracture characterization of ore particles. This model uses fracture energy distribution to describe the strength dispersion of the particle population and uses a damage accumulation model to describe the fatigue damage process of particles under subcritical repeated collision conditions, providing a relatively complete theoretical framework for the study of particle crushing behavior.

[0003] However, the Tavares crushing model primarily studies natural ore particles and has not yet established a corresponding dynamic characterization method for high-stiffness grinding media such as mining ceramic balls. The stiffness of ore particles is much lower than that of steel punches and anvils; during collision, most deformation occurs at the contact point between the ore particles and the punch. Therefore, using the total collision energy as the energy input can yield relatively accurate fracture energy parameters. However, mining ceramic balls have a much higher elastic modulus and contact stiffness than steel. In the three-body collision system of "steel punch—ceramic ball—steel anvil," the input energy is not entirely absorbed by the ceramic ball but is redistributed among the punch, ceramic ball, and anvil according to the contact flexibility of each contact unit. The deformation energy actually absorbed by the ceramic ball only accounts for a portion of the total deformation energy of the collision system. If the total collision energy is directly used as the energy input, the actual deformation energy borne by the ceramic ball will be severely overestimated, leading to significantly higher fracture energy parameters. Furthermore, the actual working conditions of ceramic balls in ball mills are mainly collisions between ceramic balls, which differ significantly from the contact conditions and energy distribution relationships of the "steel-ceramic ball-steel" three-body collision system in PFLC tests. This further exacerbates the discrepancy between laboratory test results and actual service performance. Simultaneously, existing technologies lack a unified method for calculating deformation energy when applying the Tavares fracture energy distribution model and damage accumulation model to ceramic ball systems. They also lack a systematic dynamic damage-fracture characteristic characterization process tailored to the high stiffness of ceramic balls. This means that fracture parameters obtained in the laboratory cannot be directly used for accurate prediction of ceramic ball fragmentation behavior in discrete element simulations, becoming a key technical bottleneck restricting the scientific selection of mining ceramic balls and their engineering application in large ball mills. Summary of the Invention

[0004] To solve the above-mentioned technical problems, the present invention provides a method for testing the dynamic damage-fracture characteristics of mining ceramic balls, comprising: A three-body collision contact model consisting of a punch, a mining ceramic ball, and an anvil is established, and the deformation energy distribution coefficient of the ceramic ball in the collision system is determined based on Hertzian contact theory. A single dynamic collision test was conducted on the ceramic ball using a collision load testing device to obtain the force-time signal during the collision process. The force-time signal was converted into a force-displacement relationship. The total deformation energy of the collision system was obtained by integrating the force-displacement curve. The total deformation energy of the collision system was converted into the actual deformation energy absorbed by the ceramic ball according to the deformation energy distribution coefficient, and the fracture energy of the ceramic ball was obtained. The above single dynamic collision test was repeated on multiple ceramic balls of the same specification to obtain a fracture energy dataset. The fracture energy distribution parameters of the ceramic balls of that specification were obtained by fitting the fracture energy dataset. Multiple repeated collision tests were conducted on the ceramic ball with a fixed deformation energy lower than the fracture energy distribution characteristic value of the ceramic ball of this specification. The fracture of the ceramic ball under different cumulative collision numbers was recorded. The damage accumulation coefficient of the ceramic ball of this specification was obtained by inverting the relationship between the cumulative fracture probability and the number of collisions.

[0005] Optionally, the deformation energy distribution coefficient is determined in the following manner: Obtain the elastic modulus and Poisson's ratio of the materials of the punch, ceramic ball and anvil, and calculate the elastic compliance of each material; determine the contact stiffness of the two Hertzian contacts based on the contact geometry between the punch and the ceramic ball, and between the ceramic ball and the anvil, and the composite compliance. Under the condition of three-body series contact, with the constraint that the same instantaneous force is transmitted at the two contact points, the elastic energy stored at the contact point between the ceramic ball and the punch and the contact point between the ceramic ball and the anvil are calculated respectively. The ratio of the sum of the elastic energies at the two points to the total deformation energy of the collision system is used as the deformation energy distribution coefficient.

[0006] Optionally, the fracture energy distribution parameters are obtained by fitting the fracture energy dataset with a log-normal distribution model with an upper intercept. The fracture energy distribution parameters include the median fracture energy, the discrete standard deviation of the distribution, and the maximum fracture energy. In the fitting, the cumulative fracture probability is determined according to the ratio of the cumulative distribution function of the log-normal distribution to the cumulative distribution function at the upper intercept.

[0007] Optionally, the damage accumulation coefficient is obtained by inversion in the following manner: The deformation energy absorbed by the ceramic ball in each repeated collision is used as the damage loading energy level. The current fracture energy of the ceramic ball is set, and the current fracture energy is higher than the deformation energy of a single collision is used as a constraint. The damage variables generated by a single collision are calculated based on the damage accumulation model. After each collision, the current fracture energy of the ceramic ball is updated. When the updated fracture energy is lower than or equal to the deformation energy of a single collision, it is determined that the collision caused the ceramic ball to fracture. Using the experimentally determined values ​​of fracture probability under different cumulative collision counts as the target, the damage accumulation coefficient is inverted and optimized until the model calculation value and the experimentally determined value reach the preset fitting accuracy.

[0008] Optionally, the damage variable generated by the single collision is obtained by solving for the following implicit relationship: The damage variable depends on the ratio of the deformation energy of a single collision to the current fracture energy before the collision, as well as the damage accumulation coefficient, and the product of the damage variable and a factor minus the damage variable is equal to the damage accumulation coefficient raised to the power of the ratio.

[0009] Optionally, the collision load testing device is a piezoelectric rapid load testing device, and the force-time signal is acquired by a piezoelectric collision force sensor; When converting the force-time signal into a force-displacement relationship, the maximum deformation corresponding to the initiation of the main crack is identified based on the contact mechanics model, and this maximum deformation is used as the upper limit of the force-displacement curve integral.

[0010] Optionally, the punch and the anvil are made of the same material, and the deformation energy distribution coefficient is determined jointly based on the material flexibility of the ceramic ball and the material flexibility of the punch and the anvil, specifically: The material flexibility of the ceramic ball is multiplied by two and then divided by the sum of the material flexibility of the punch, the material flexibility of the ceramic ball multiplied by two, and the material flexibility of the anvil.

[0011] Optionally, in the three-body collision contact model, the contact between the punch and the ceramic ball and the contact between the ceramic ball and the anvil are both Hertzian contacts; The impact energy carried by the punch is distributed at the punch-ceramic ball contact and ceramic ball-anvil contact according to the contact flexibility of each contact unit. The deformation energy distribution coefficient is the proportion of the sum of elastic energy stored by the ceramic ball participating in both contacts to the total deformation energy of the collision system.

[0012] On the other hand, the present invention also provides an electronic device including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0013] On the other hand, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0014] Compared with the prior art, the present invention has the following advantages and technical effects: This invention establishes a unified conversion method for deformation energy of high-stiffness ceramic spheres. By constructing a three-body series contact model and solving for the deformation energy distribution coefficient based on Hertzian contact theory, it eliminates the energy evaluation bias caused by differences in material stiffness between different collision systems. This ensures that laboratory test results accurately reflect the actual deformation energy borne by the ceramic spheres, solving the problem of severely overestimating fracture energy parameters due to the direct evaluation of total collision energy in traditional methods. Furthermore, this invention applies the Tavares fracture energy distribution model and damage accumulation model to mining ceramic spheres. Through single-collision fracture energy testing, it obtains fracture energy distribution parameters, including the median fracture energy and the standard deviation of the distribution, achieving quantitative characterization of the discrete strength of the ceramic sphere population. The damage accumulation coefficient is obtained through inversion using low-energy repeated collision tests, filling the gap in testing methods for fatigue degradation behavior of ceramic spheres under subcritical repeated collision conditions. The complete parameter system established by this invention, covering "deformation energy conversion - fracture energy distribution - damage accumulation", can directly provide fracture criterion input parameters under a unified energy scale for discrete element simulation. It solves the technical problem that laboratory testing and simulation prediction cannot be connected due to the mismatch of energy scales, and provides reliable basic mechanical parameters for the selection of mining ceramic balls and the prediction of ball breakage risk in large ball mills. Attached Figure Description

[0015] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of a method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a three-body series contact model according to an embodiment of the present invention; Figure 3 The collision curve of a φ20 ceramic ball in an embodiment of the present invention; Figure 4 The deformation energy is obtained from the force and deformation curves corresponding to the embodiments of the present invention; Figure 5 This is a fracture energy distribution diagram showing the cumulative fracture energy distribution curves of different sizes of mining ceramic balls according to an embodiment of the present invention; Figure 6 This is a specific fracture energy distribution diagram showing the cumulative fracture energy distribution curves of different sizes of mining ceramic balls according to an embodiment of the present invention. Figure 7 The specific fracture energy distribution evolution condition diagram of the φ25 ceramic ball in the embodiment of the present invention: absorbed specific deformation energy 1000J / kg, γ=7.8; Figure 8 The cumulative damage and fracture probability curve of the φ25 ceramic ball under different γ values ​​is shown in the embodiment of the present invention: the absorbed specific deformation energy is 1000 J / kg. Detailed Implementation

[0016] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0017] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0018] Example 1 like Figure 1 As shown, this embodiment provides a method for testing the dynamic damage-fracture characteristics of mining ceramic balls, including: The Tavares fracture model has two core concepts: fracture energy and stressing energy.

[0019] Fracture energy is the maximum elastic strain energy stored in a particle from the moment of contact to the moment of initiation of the main crack; it is the critical energy required for initial fracture. Essentially, it reflects a material's ability to resist impact damage. For a single-particle collision process, the change in impact load over time forms a force-time curve, which can be further analyzed using contact mechanics to obtain a force-displacement curve.

[0020] ; In the formula, E is the fracture energy; F is the impact force; and αc is the maximum deformation of the particle when the main fracture occurs. This parameter differs from the traditional compressive strength; it not only considers the ultimate load but also comprehensively reflects the elastic response and crack propagation behavior of the material, making it more suitable for evaluating the impact resistance of brittle materials.

[0021] Deformation energy refers to the elastic strain energy that a ceramic ball actually absorbs and uses for deformation in a single collision. Its magnitude depends on the collision conditions, energy distribution, and the medium environment, and is an event attribute.

[0022] The relationship between the two can be summarized as follows: when the deformation energy is greater than or equal to the fracture energy, the sphere fractures; when the deformation energy is less than the fracture energy, the sphere may not break immediately, but damage accumulation may occur. At the instant of fracture, the deformation energy is numerically equal to the fracture energy, but the two concepts are different—the former is the "actual absorbed amount," while the latter is the "critical threshold." The fracture energy test in this study essentially measures the critical deformation energy that the ceramic sphere withstands at the instant of fracture; while the normal impact energy obtained from discrete element simulation needs to be converted through contact mechanics to obtain the actual deformation energy, and then compared with the fracture energy using a unified dimension.

[0023] The main components of the Tavares fragmentation model include: (1) Fracture energy distribution model; The fracture energy of ore particles is not a fixed value, but follows a certain probability distribution. Tavares proposed that the fracture energy can be described by a log-normal distribution with an upper intercept, and its cumulative fracture probability can be described by a log-normal distribution with an upper intercept. ; ; In the formula, P ( E ) is the particle's deformation energy E The probability of fracture below; E 50 The median fracture energy corresponding to a 50% probability of fracture. σ The standard deviation of the distribution is used to characterize the dispersion of particle group strength. E 50 The larger the particle, the stronger its overall impact resistance. σ The larger the value, the wider the distribution. E max The maximum fracture energy is the cutoff value of the distribution.

[0024] (2) Damage accumulation model; When the single deformation energy of a particle is lower than its critical fracture energy, it will not break immediately, but irreversible microcracks and residual damage will be generated inside. With repeated collisions, these damages will gradually accumulate, the effective stiffness of the particle will continue to decrease, and its ability to resist subsequent collisions will be weakened accordingly.

[0025] The model uses a continuous damage mechanics framework to describe this process. For a single loading process, the particle reaches its maximum deformation after being loaded. α c Before fracture, the accumulated damage from the collision is: ; In the formula: γ The damage accumulation coefficient is a parameter describing the rate of damage relative to the deformation process of particles under stress. γ When the size is large, the material exhibits brittle fracture. γ Even when the deformation is small, D It will also show a significant increase, exhibiting gradual cumulative damage. When the particles fracture, they no longer possess any stiffness. D Set to 1. Specify the deformation energy. E k,i Next i Damage from the secondary collision D i* as follows: ; It should be noted that in the above formula E k,i All of these are specific deformation energy absorbed by ore particles.

[0026] (3) Energy distribution model: Local deformation is caused by the local deformation of the two colliding bodies at the point of contact. and Together they form a whole.

[0027] ; The local deformation of the collider is related to the material of the collider; that is, the larger the composite elastic modulus E*1, the smaller the local deformation.

[0028] ; ; The deformation energy of a collision is the integral of the contact force over the deformation. Since the force is continuous and consistent, the deformation energy of colliding body 1 is... E 1. Relationship with total deformation energy E as follows.

[0029] ; For collider 1, the energy distribution coefficient e is: ; This invention addresses the lack of a dynamic impact performance evaluation method for mining ceramic balls by proposing a dynamic damage-fracture characteristic characterization method for mining ceramic balls based on dynamic impact tests, contact mechanics energy distribution theory, and the Tavares fracture model. This method uses the actual stressing energy absorbed by the ceramic ball as a unified energy scale. It obtains the fracture energy distribution through numerous impact tests, acquires damage accumulation parameters through subcritical repeated impact tests, and ultimately establishes a parameter system for the dynamic damage-fracture characteristics of mining ceramic balls.

[0030] (1) A method for calculating deformation energy based on a three-body series contact model; Mining ceramic balls possess high elastic modulus and low deformation, and their collision process differs significantly from that of natural ores. In the three-body collision system of "steel punch-ceramic ball-steel anvil," the input collision energy is redistributed among the contact units, with only a portion stored within the ceramic ball as elastic strain energy. Therefore, directly evaluating its fracture performance based on collision energy will overestimate the actual deformation energy it bears. Furthermore, the material contact conditions in the PFLC test system differ from those in the actual "ceramic ball-ceramic ball" working condition in a ball mill, resulting in differences in the actual energy absorbed by the ceramic ball under the same collision energy. Therefore, before characterizing the dynamic fracture characteristics of ceramic balls, it is necessary to establish a method for calculating deformation energy to achieve a unified energy scale across different collision systems.

[0031] like Figure 2 As shown, let the drop hammer, ceramic ball, and anvil be denoted as h (Hammer), b (Ball), and a (Anvil), respectively. The three-body system contains two Hertz contacts in series: drop hammer-ceramic ball and ceramic ball-anvil. The following calculations are for the elastic strain energy distribution at maximum compression, i.e., the stressing energy of the ceramic ball, not the final damage dissipation energy.

[0032] (1) Elastic flexibility of each material Define material compliance term : ; in, E i For Young's modulus, ν i Poisson's ratio, E i * represents material stiffness; i = h,b,a They represent a drop hammer, a ceramic ball, and a cutting board, respectively.

[0033] The combined compliance of the upper and lower contacts is: ; ; Corresponding Hertz contact coefficient: ; ; In the formula, R u ∗ 、R l * Let be the equivalent radius of curvature for the upper and lower contact surfaces. The plane and radius are... R b When ceramic balls come into contact: ; (2) Deformation and energy storage at two contacts; When three bodies are connected in series and loaded, the same instantaneous force F is transmitted between the upper and lower contact points: ; ; The elastic energies stored in the upper and lower contacts are as follows: ; Total system deformation energy: ; (3) Energy distribution within each contact; In the contact (upper contact) between the punch and the ceramic ball: ; ; In the contact (upper contact) between the ceramic ball and the cutting board: ; ; Therefore, the total energy storage of the ceramic spheres is: ; It can be seen that the energy distribution coefficients of the three-body system are as follows: ; in, This refers to the proportion of this portion of energy to the total deformation energy of the entire system. Let be the deformation energy of colliding body i.

[0034] and: ; (4) The simplified result when both the top and bottom are steel is: If both the drop hammer and the anvil are made of steel (referred to as 's'), and the contact geometry is identical on both sides, then: ; ; Then we have: ; ; The ceramic ball participates in both upper and lower contact simultaneously, therefore it cannot be simply described as three independent springs pressing... C h :C b :C a The allocation may underestimate the energy storage capacity of ceramic spheres.

[0035] The technical effect of this embodiment is as follows: (1) A unified conversion method for deformation energy of high-stiffness ceramic spheres was established, improving the physical authenticity and engineering applicability of dynamic fracture test results. Considering that the PFLC test uses a three-body collision system of "steel punch—ceramic sphere—steel anvil," while actual grinding conditions mainly involve differences in collisions between ceramic spheres, this invention introduces a three-body series contact model. Based on Hertzian contact theory, an energy distribution relationship is established, uniformly converting the macroscopic collision energy under any collision system into the actual deformation energy absorbed by the ceramic sphere. Taking the collision of a typical high-alumina ceramic sphere (E=350 GPa) with steel (E=210 GPa) as an example, the deformation energy distribution coefficient of the ceramic sphere in the three-body system is 38.6%, meaning that its actual absorbed deformation energy is only 38.6% of the total deformation energy of the system. (2) A method for testing and characterizing the dynamic fracture characteristics of mining ceramic balls was established. Based on impact fracture testing such as the PFLC device, this invention introduces the Tavares fracture energy distribution model and damage accumulation model, and establishes a complete method from single impact fracture energy testing to low-energy repeated impact damage accumulation testing, which can systematically obtain the fracture energy distribution (including the median fracture energy E). 50 The system incorporates dynamic mechanical parameters such as distribution parameter σ, size effect law, and damage accumulation coefficient γ, enabling a comprehensive characterization of the strength dispersion and long-term fatigue deterioration behavior of ceramic ball groups. This overcomes the shortcomings of existing technologies that rely on static indicators and cannot reflect the impact resistance and fatigue resistance under actual grinding conditions.

[0036] (3) This invention provides directly input basic fracture mechanics parameters for the application of ceramic balls in large ball mills and the prediction of ball breakage risks. The fracture energy distribution and damage accumulation coefficient obtained by this invention have clear physical meaning and a unified energy scale, and can be used as direct input parameters for the fracture criterion of ceramic balls in discrete element simulation. This solves the technical problem that traditional methods cannot connect laboratory testing with simulation prediction due to energy scale mismatch, and provides a reliable data foundation for the selection of mining ceramic balls, the formulation of replenishment systems, and the engineering application of large mills.

[0037] On the other hand, this embodiment also provides an electronic device, including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0038] On the other hand, this embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0039] Example 2 This embodiment provides a method for testing the dynamic damage-fracture characteristics of mining ceramic balls, including: If steel is takenE s = 210 GPa, ν s = 0.30, then we have: ; High-alumina ceramics E c = 350 GPa, ν c = 0.22: ; The proportion of energy received by the ceramic ball is: ; In subsequent fracture characteristic tests, the total deformation energy of the three-body contact system of the drop hammer-ceramic ball-anvil should be calculated first, and then multiplied by the deformation energy distribution coefficient of the ceramic ball. The result is the actual deformation energy (stressing energy) borne by the ceramic ball, which is used as the energy input for subsequent damage accumulation and fracture analysis.

[0040] (2) Test method for fracture energy of ceramic spheres; The distribution coefficient of deformation energy actually absorbed by the ceramic sphere is obtained. η b Subsequently, dynamic impact tests on single ceramic spheres were conducted using a PFLC (Power-Time Collision Chromatography) device. The specific process involved first obtaining the impact curve (force-time relationship, requiring identification of the fracture point), and then... The calculation formula yields the deformation curve (force-deformation relationship), such as Figure 3 and Figure 4 As shown, the total deformation energy during the collision is obtained by integration, and then multiplied by the energy distribution coefficient. η b Then the maximum deformation energy of the ceramic sphere before fracture was obtained. E For ceramic balls of the same specification, at least 30 samples should be tested. The specific procedure is as follows: The fracture energy of ceramic spheres was determined using a piezoelectric rapid load testing device (PFLC), equipped with a large-range sensor of 150 kN and a heavy-duty 4 kg impact head. The testing device mainly consists of a guide rail, a punch, an anvil, a piezoelectric impact force sensor, a high-speed signal acquisition card, and a computer. During the test, a single ceramic sphere is placed in the center of the anvil, and the punch falls freely along the guide rail, colliding head-on with the sample. The sensor records the impact load signal in real time. Using a contact mechanics model, the force-time curve is integrated to transform into a force-displacement relationship, and the maximum deformation corresponding to the initiation of the main crack is identified. α The formula is as follows: ; In the formula, u bLet be the displacement of the anvil, in μm; V 0 represents the initial velocity of the steel ball when it contacts the particle, in m / s; g The acceleration due to gravity is 9.8 m / s². 2 ; m b For the mass of the collision head, g ; t The time from the start of contact, in μs; E m It is the fracture energy, mJ; F ( t () represents the collision force, in N; ρ a The density of the cutting board is kg / m³. 3 ; A a Let m be the area of ​​the cutting board. 2 C1 directly represents the degree of displacement of the anvil end face according to the stress wave transmission law.

[0041] However, it must be noted that unlike the Tavares crushing model, which primarily deals with medium-hardness ore particles, the ceramic ball has very high stiffness, exceeding that of the punch and anvil. Therefore, not all the impact energy carried by the falling hammer or impactor is applied to the ceramic ball. In the PFLC test, the "steel punch-ceramic ball-steel anvil" constitutes a three-body collision system. The impact energy is redistributed among these three components. What truly drives the propagation and fracture of cracks within the ceramic ball is the deformation energy, not the total deformation energy. Therefore, the total deformation energy must be multiplied by an energy distribution factor. η b .

[0042] (3) Test method for fracture energy distribution of mining ceramic balls; In this embodiment, both "fracture energy" and "deformation energy" are expressed in Joules (J), representing the absolute value of the elastic strain energy actually absorbed and used for deformation during the collision of a single ceramic sphere. Fracture energy (E) is the maximum elastic strain energy stored in the ceramic sphere from the moment of contact until the initiation of the main crack, i.e., the critical energy required for initial fracture; deformation energy is the elastic strain energy actually absorbed by the ceramic sphere in a single collision. Both are equal in value at the instant of fracture, and both are in Joules (J). The former is an inherent property of the material, while the latter is the actual amount absorbed under specific collision conditions.

[0043] However, ceramic spheres of different sizes exhibit significant differences in mass. When comparing absolute fracture energy (J), larger spheres, due to their greater mass and higher absolute deformation energy, will inevitably have higher fracture energy than smaller spheres. However, this difference does not necessarily reflect the material's inherent impact resistance. To eliminate the influence of mass and achieve a lateral comparison of impact resistance performance between ceramic spheres of different sizes, this embodiment introduces the concepts of "specific fracture energy" and "specific deformation energy," both measured in J / kg, representing the energy value per unit mass.

[0044] Because ceramic spheres inevitably contain pores, inclusions, grain boundary defects, and residual stress, the fracture energy between different particles is not a fixed value but follows a certain probability distribution. Tavares proposed that the fracture energy of brittle particles can be described by a log-normal distribution, and its cumulative fracture probability can be described by a log-normal distribution with an upper intercept. ; ; In the formula, P ( E ) is the particle's deformation energy E The probability of fracture below; E 50 The median fracture energy corresponding to a 50% probability of fracture. σ is a distribution parameter used to characterize the dispersion of particle group intensity. E 50 The larger the particle, the stronger its overall impact resistance. σ The larger the value, the wider the distribution. E max This represents the maximum fracture energy, i.e., the maximum cutoff value of the distribution.

[0045] like Figure 5 and Figure 6 As shown, for ceramic balls, the fracture energy distribution is more significant in engineering than a single strength value because the media in industrial mills are subjected to random collisions rather than ideal single loading, and service safety is a probabilistic issue.

[0046] (4) Test method for cumulative damage characteristics of mining ceramic balls: The conversion relationship between specific fracture energy and fracture energy is: specific fracture energy = fracture energy ÷ ceramic ball mass. Correspondingly, the specific deformation energy absorbed by the ceramic ball in a single collision = the actual deformation energy absorbed by the ceramic ball ÷ the ceramic ball mass. In the fracture energy distribution test, the specific fracture energy distribution curve can be obtained by dividing the fracture energy dataset (unit J) obtained in step (3) by the corresponding ceramic ball mass (unit kg). This distribution facilitates the direct comparison of the impact resistance between ceramic balls of different specifications. In the damage accumulation test, the "significantly lower than the median fracture energy E" selected in step (4) 50The "fixed deformation energy" is also converted into specific deformation energy (unit J / kg) according to the mass, and then applied as a uniform damage loading energy level to ceramic balls of different specifications. For example, in the embodiment, 1000J / kg is used as the damage loading energy level for φ25 ceramic balls.

[0047] Testing the fracture energy of a single impact is insufficient to reflect the long-term service performance of mining ceramic balls; further research is needed to determine the damage accumulation patterns of the ceramic balls.

[0048] This invention still employs low-energy multiple impact tests, essentially functioning as a small-scale drop-weight device (PFLC could be continued, but the sensors need not be activated; it would be purely for drop-weight applications). First, based on the three-body series contact model established in the first part, the impact energy of the drop hammer is converted into the actual stressing energy absorbed by the ceramic sphere, and a value significantly lower than the median fracture energy of a ceramic sphere of corresponding specifications is selected. E 50 The fixed deformation energy is used as the damage loading energy level, so that a single collision is unlikely to directly cause the ceramic ball to break.

[0049] Subsequently, a single ceramic sphere was continuously subjected to a collision load with the same deformation energy, and the test was stopped according to a preset number of collisions (e.g., 10, 20, 50). The fracture probability after reaching different numbers of collisions was statistically analyzed. Through a large number of repeated tests, the variation law of the fracture energy distribution and cumulative fracture probability of the ceramic sphere under different cumulative collision numbers can be obtained.

[0050] According to the Tavares damage accumulation model, the current fracture energy of the ceramic ball is E n-1 The deformation energy corresponding to a single collision is E k And satisfy: ; Therefore, this collision will not cause immediate fracture, but rather a certain degree of damage. The damage variable D satisfies the implicit damage equation proposed by Tavares: ; in D For single-collision damage variables; γ This is the damage accumulation coefficient; E k This represents the deformation energy corresponding to a single collision. E n-1 Let be the fracture energy before the collision. Since the above equation is an implicit equation, it can be solved using the bisection method, Newton's iteration method, or other numerical algorithms.

[0051] After obtaining the damage variable, the fracture energy of the ceramic ball gradually decreases. When a certain collision satisfies... At that time, it was assumed that the collision caused the ceramic ball to fracture. Further, using the fracture probability of different collision numbers measured experimentally as the target value, the damage accumulation coefficient γ was inverted and optimized to achieve the best fit between the model calculation results and the experimental results. After fitting, the damage accumulation coefficient of the corresponding specification of mining ceramic ball can be obtained. Figure 7 and Figure 8 As shown.

[0052] Analysis of ceramic ball impact fracture results: The dynamic impact resistance of ceramic spheres can be characterized by both fracture energy distribution and damage accumulation parameters. The median fracture energies of 20, 25, and 30 mm ceramic spheres are 3.4, 4.8, and 7.4 J, respectively (equivalent to at least 8.8 J, 12.4 J, and 19.3 J in hammer and anvil impact energies, respectively; that is, dividing the fracture energy by the coefficient ηb gives the minimum impact energy required for fracture). This indicates that the ceramic spheres of this specification used in the test are quite robust, and the high damage coefficients of 7.60–8.05 indicate that the ceramic spheres have strong resistance to low-energy repeated impacts.

[0053] Besides its function as an indicator: Discrete element method (DEM) simulation can serve as an important tool for predicting the fragmentation behavior of ceramic balls within a mill. The key lies in the input parameter being the fracture energy distribution corresponding to the ceramic ball's own material, rather than the fracture-inducing collision energy under a specific collision system. This is because the collision energy output by simulation software is the macroscopic collision energy of the two-ball system, which cannot automatically remove the distribution coefficient to restore the actual deformation energy absorbed by the ball. Directly using the collision energy as the criterion would severely underestimate the impact resistance of the ceramic ball, leading to distorted fragmentation rate predictions. Therefore, the true fracture energy distribution of the ceramic ball obtained using this method is a necessary input for DEM and represents the core value of the distribution coefficient in engineering applications.

[0054] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for testing the dynamic damage-fracture characteristics of mining ceramic balls, characterized in that, include: A three-body collision contact model consisting of a punch, a mining ceramic ball, and an anvil is established, and the deformation energy distribution coefficient of the ceramic ball in the collision system is determined based on Hertzian contact theory. A single dynamic collision test was conducted on the ceramic ball using a collision load testing device to obtain the force-time signal during the collision process. The force-time signal was converted into a force-displacement relationship. The total deformation energy of the collision system was obtained by integrating the force-displacement curve. The total deformation energy of the collision system was converted into the actual deformation energy absorbed by the ceramic ball according to the deformation energy distribution coefficient, and the fracture energy of the ceramic ball was obtained. The above single dynamic collision test was repeated on multiple ceramic balls of the same specification to obtain a fracture energy dataset. The fracture energy distribution parameters of the ceramic balls of that specification were obtained by fitting the fracture energy dataset. Multiple repeated collision tests were conducted on the ceramic ball with a fixed deformation energy lower than the fracture energy distribution characteristic value of the ceramic ball of this specification. The fracture of the ceramic ball under different cumulative collision numbers was recorded. The damage accumulation coefficient of the ceramic ball of this specification was obtained by inverting the relationship between the cumulative fracture probability and the number of collisions.

2. The method according to claim 1, characterized in that, The deformation energy distribution coefficient is determined in the following manner: Obtain the elastic modulus and Poisson's ratio of the materials of the punch, ceramic ball and anvil, and calculate the elastic compliance of each material; determine the contact stiffness of the two Hertzian contacts based on the contact geometry between the punch and the ceramic ball, and between the ceramic ball and the anvil, and the composite compliance. Under the condition of three-body series contact, with the constraint that the same instantaneous force is transmitted at the two contact points, the elastic energy stored at the contact point between the ceramic ball and the punch and the contact point between the ceramic ball and the anvil are calculated respectively. The ratio of the sum of the elastic energies at the two points to the total deformation energy of the collision system is used as the deformation energy distribution coefficient.

3. The method according to claim 1, characterized in that, The fracture energy distribution parameters are obtained by fitting the fracture energy dataset with a log-normal distribution model with an upper intercept. The fracture energy distribution parameters include the median fracture energy, the discrete standard deviation of the distribution, and the maximum fracture energy. In the fitting, the cumulative fracture probability is determined according to the ratio of the cumulative distribution function of the log-normal distribution to the cumulative distribution function at the upper intercept.

4. The method according to claim 1, characterized in that, The damage accumulation coefficient is obtained by inversion in the following manner: The deformation energy absorbed by the ceramic ball in each repeated collision is used as the damage loading energy level. The current fracture energy of the ceramic ball is set, and the current fracture energy is higher than the deformation energy of a single collision is used as a constraint. The damage variables generated by a single collision are calculated based on the damage accumulation model. After each collision, the current fracture energy of the ceramic ball is updated. When the updated fracture energy is lower than or equal to the deformation energy of a single collision, it is determined that the collision caused the ceramic ball to fracture. Using the experimentally determined values ​​of fracture probability under different cumulative collision counts as the target, the damage accumulation coefficient is inverted and optimized until the model calculation value and the experimentally determined value reach the preset fitting accuracy.

5. The method according to claim 1, characterized in that, The damage variable generated by a single collision is obtained by solving the following implicit relation: The damage variable depends on the ratio of the deformation energy of a single collision to the current fracture energy before the collision, as well as the damage accumulation coefficient, and the product of the damage variable and a factor minus the damage variable is equal to the damage accumulation coefficient raised to the power of the ratio.

6. The method according to claim 1, characterized in that, The collision load testing device is a piezoelectric rapid load testing device, and the force-time signal is acquired by a piezoelectric collision force sensor; When converting the force-time signal into a force-displacement relationship, the maximum deformation corresponding to the initiation of the main crack is identified based on the contact mechanics model, and this maximum deformation is used as the upper limit of the force-displacement curve integral.

7. The method according to claim 1, characterized in that, The punch and the anvil are made of the same material. The deformation energy distribution coefficient is determined based on the material flexibility of the ceramic ball and the material flexibility of the punch and the anvil, specifically: The material flexibility of the ceramic ball is multiplied by two and then divided by the sum of the material flexibility of the punch, the material flexibility of the ceramic ball multiplied by two, and the material flexibility of the anvil.

8. The method according to claim 1, characterized in that, In the three-body collision contact model, the contact between the punch and the ceramic ball, and the contact between the ceramic ball and the anvil, are both Hertzian contacts; The impact energy carried by the punch is distributed at the punch-ceramic ball contact and ceramic ball-anvil contact according to the contact flexibility of each contact unit. The deformation energy distribution coefficient is the proportion of the sum of elastic energy stored by the ceramic ball participating in both contacts to the total deformation energy of the collision system.

9. An electronic device comprising a memory, a processor, and a computing program stored in the memory and executable on the processor, characterized in that, When the processor executes the computing program, it implements the method of any one of claims 1-8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1-8.

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