A method for calibrating ore cumulative damage constant based on single-axis compression and drop ball impact test

Abstract

The application discloses a kind of ore cumulative damage constant calibration method based on single-axis compression and drop ball impact test, belong to the technical field of damage condition in ore crushing process.It includes the following steps: first, obtain the fracture energy of ore particles by uniaxial compression test, and construct the cumulative probability distribution function of fracture energy;Subsequently, convert the fracture energy into specific fracture energy, and establish a crushing probability model based on lognormal distribution;Further, obtain the crushing probability data under different impact times through drop ball impact test;On this basis, introduce the cumulative damage evolution model, establish the crushing probability prediction model under multiple impact actions, and realize the inversion calibration of cumulative damage constant by minimizing the standard residual between predicted value and test value.The application can quantitatively describe the damage accumulation process of ore under repeated impact, improve the accuracy of crushing model, and provide a theoretical basis for ore crushing mechanism research and equipment optimization.

Description

Technical Field

[0001] This invention relates to the technical field of damage during ore crushing, and in particular to a method for calibrating the cumulative damage constant of ore based on uniaxial compression and falling ball impact tests. Background Technology

[0002] Mineral crushing is a crucial step in mineral processing engineering, accounting for 50% to 70% of the total energy consumption in mineral beneficiation. The ore crushing process is essentially a process in which internal defects continuously expand under the action of external forces, eventually leading to fracture. However, due to the complex structure of ore and the difficulty in directly observing the crushing process, its mechanism remains unclear.

[0003] In existing technologies, uniaxial compression tests are typically used to obtain the strength and fracture energy parameters of ore, or drop hammer impact tests are used to determine the breakage probability under a single impact condition for parameter calibration of the breakage model. However, these methods are mainly based on single loading conditions and fail to reflect the damage accumulation behavior of ore under multiple impacts or compressions during actual breakage. Therefore, it is necessary to provide a new method to quantitatively describe the damage evolution of ore under repeated loading, thereby improving the accuracy and engineering applicability of the breakage model. Summary of the Invention

[0004] The purpose of this invention is to solve the above problems and provide a method for calibrating the cumulative damage constant of ore based on uniaxial compression and falling ball impact tests, to determine the cumulative damage characteristics of ore under repeated impacts, so as to better study the fracture situation of defective ore during the crushing process.

[0005] The technical solution of this invention is: A method for calibrating the cumulative damage constant of ore based on uniaxial compression and falling ball impact tests includes the following steps: a. Perform uniaxial compression tests on single-particle ore samples, record the displacement-force curves, and calculate the fracture energy of each particle by integration; b. Arrange the obtained fracture energies in ascending order, and use the order statistic method to calculate the cumulative breakage probability, thereby obtaining the cumulative breakage probability distribution of the fracture energy of the ore particles; c. Convert the fracture energy into mass ratio fracture energy, and use the log-normal distribution function to establish a model of the relationship between the cumulative crushing probability of ore and mass ratio fracture energy, so as to obtain the median mass ratio fracture energy and distribution parameters; d. Repeated impact tests were conducted on single-particle ore samples using a falling ball impact test device. Under constant impact energy conditions, the particle breakage was recorded for each number of impacts, and the breakage probability curve was obtained. e. Establish a cumulative damage evolution model based on the number of impacts to describe the damage accumulation process of particles under multiple impacts, and construct a breakage probability prediction model. f. By comparing the predicted breakage probability with the experimental breakage probability, a standard residual function is constructed, and the optimal cumulative damage constant is determined by minimizing the residual.

[0006] Preferably, the sample (single-particle ore sample) in step a has a particle size of -16 to +13.2 mm. A representative sample of 30 particles is taken, and the displacement-force curve of each sample is integrated separately to obtain the fracture energy of the 30 particles.

[0007] Preferably, in step b, the obtained fracture energies are arranged in ascending order, and then a serial number is assigned to the sorted observations. i , i =1, 2, ..., N, where N is the total number of valid tests performed. The cumulative fragmentation probability distribution of particle fracture energy is calculated by the following formula: .

[0008] Preferably, in step c, the fracture energy obtained in step a is divided by its respective mass to obtain the mass-to-fracture energy of the ore. The relationship model between the cumulative ore breakage probability and the mass-to-fracture energy is established by the log-normal distribution function, and the fitting formula is as follows: in, The median fracture energy, For distribution parameters, The fracture energy is the ratio of ore mass to fracture energy.

[0009] Preferably, the sample (single-particle ore sample) in step d has a particle size of -16 to +13.2 mm, and 30 representative particles are taken, with a fixed specific impact energy of 63 J / kg. If a particle loses at least 10% of its original weight during the impact, then the particle is considered broken.

[0010] Preferably, in step e, the formula for predicting the particle breakage probability curve used in the breakage probability prediction model is as follows: in For the first n The specific crushing energy absorbed during a single impact, expressed in J / kg; for n - The specific crushing energy absorbed during the first impact, expressed in J / kg; For particles to absorb more crushing energy Damage below; This refers to a specific impact energy, expressed in J / kg. The cumulative damage constant is dimensionless.

[0011] Preferably, in step f, the optimal cumulative damage constant is determined by formula (5): in For the firsti The probability of fracture under a number of impacts, expressed in % The probability of breakage is obtained from the simulation, expressed in percent.

[0012] The beneficial effects of this invention are: this invention can calibrate the cumulative damage constant of ore particles, determine the cumulative damage characteristics of ore under repeated impact, and thus better study the fracture situation of defective ore during the crushing process. Attached Figure Description

[0013] Figure 1 This is the uniaxial pressure testing device used in this invention. At this time, cracks appear in the ore sample, which is judged as fracture. Figure 2 This is a displacement-force curve of copper ore particles under quasi-static crushing in a uniaxial pressure testing machine according to the present invention. Figure 3 This is a distribution diagram of the crushing probability and crushing specific energy of copper ore with a sample particle size of -16 to +13.2 mm according to the present invention; Figure 4 This is a graph showing the probability of copper ore breakage based on prediction and testing according to the present invention. Figure 5 This is a displacement-force curve of phosphate rock particles under quasi-static crushing in a uniaxial pressure testing machine according to the present invention. Figure 6 This is a distribution diagram of the crushing probability and crushing specific energy of phosphate rock with a sample particle size of -16 to +13.2 mm according to the present invention; Figure 7 This is a graph showing the probability of phosphate rock breakage based on prediction and testing according to the present invention. Detailed Implementation

[0014] Example 1: A method for calibrating the cumulative damage constant of ore based on uniaxial compression and falling ball impact tests, comprising the following steps: a. Quasi-static crushing of single-particle ore samples was carried out using a uniaxial compression testing machine. This method was applied to single-particle copper ore. The displacement-force curve of the particles was integrated separately to obtain the fracture energy of 30 particles. The sample particle size in step a was -16 to +13.2 mm. A representative sample of 30 particles was selected. b. Arrange the fracture energies of each particle obtained in step a in ascending order, and use the order statistics method to calculate the cumulative breakage probability to obtain the cumulative breakage probability distribution of the fracture energy of the ore particles. Specifically, the obtained fracture energies are sorted in ascending order, and then a sequence number is assigned to the sorted observations. i , i =1, 2, ..., N, where N is the total number of valid tests performed. The cumulative fragmentation probability distribution of particle fracture energy is calculated by the following formula: .

[0015] c. Convert the fracture energy into mass ratio fracture energy, and use the log-normal distribution function to establish a model of the relationship between the cumulative crushing probability of ore and mass ratio fracture energy, so as to obtain the median mass ratio fracture energy and distribution parameters; Specifically, the fracture energy obtained in step a is divided by the respective masses to obtain the mass-to-fracture energy of the ore. The relationship between the cumulative probability of ore breakage and the mass-to-fracture energy is established using a log-normal distribution function, and the fitting formula is as follows: in, The median fracture energy, For distribution parameters, The fracture energy is the ratio of ore mass to fracture energy.

[0016] d. Repeated impact tests were conducted on single-particle ore samples using a falling ball impact test device. The sample particle size was -16 to +13.2 mm. Thirty representative particles were selected. Under constant impact energy conditions, the number of impacts required for the ore to break was recorded to obtain the test breakage probability curve. The fixed impact energy was 63 J / kg. e. Establish a cumulative damage evolution model based on the number of impacts to describe the damage accumulation process of particles under multiple impacts, and construct a breakage probability prediction model; specifically... In step e, the formula for predicting the particle breakage probability curve used in the breakage probability prediction model is as follows: .in For the first n The specific crushing energy absorbed during a single impact, expressed in J / kg; for n - The specific crushing energy absorbed during the first impact, expressed in J / kg; For particles to absorb more crushing energy Damage below; This refers to a specific impact energy, expressed in J / kg.

[0017] f. By comparing the predicted breakage probability with the experimental breakage probability curves, a standard residual function is constructed, the standard residual under different cumulative damage coefficient values ​​is calculated, and the optimal cumulative damage constant is determined by minimizing the residual.

[0018] Through calculation and comparison, the minimum total standard residual was found to be 2.676, and the optimal cumulative damage coefficient was 3.88.

[0019] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for calibrating the cumulative damage constant of ore based on uniaxial compression and falling ball impact tests, comprising the following steps: a. Perform uniaxial compression tests on single-particle ore samples, record the displacement-force curves, and calculate the fracture energy of each particle by integration; b. Arrange the obtained fracture energies in ascending order, and use the order statistic method to calculate the cumulative breakage probability, thereby obtaining the cumulative breakage probability distribution of the fracture energy of the ore particles; c. Convert the fracture energy into mass ratio fracture energy, and use the log-normal distribution function to establish a model of the relationship between the cumulative crushing probability of ore and mass ratio fracture energy, so as to obtain the median mass ratio fracture energy and distribution parameters; d. Repeated impact tests were conducted on single-particle ore samples using a falling ball impact test device. Under constant impact energy conditions, the particle breakage was recorded for each number of impacts, and the breakage probability curve was obtained. e. Establish a cumulative damage evolution model based on the number of impacts to describe the damage accumulation process of particles under multiple impacts, and construct a breakage probability prediction model. f. By comparing the predicted breakage probability with the experimental breakage probability, a standard residual function is constructed, and the optimal cumulative damage constant is determined by minimizing the residual.

2. The method for calibrating the cumulative damage constant of ore based on uniaxial compression and falling ball impact tests according to claim 1, characterized in that: In step a, the particle size of the single ore sample is -16 to +13.2 mm, and 30 particles are selected. The displacement-force curve of each sample is integrated separately to obtain the fracture energy of the 30 particles.

3. The method for calibrating the cumulative damage constant of ore based on uniaxial compression and falling ball impact tests according to claim 1, characterized in that: In step b, the obtained fracture energies are sorted in ascending order, and then a serial number is assigned to the sorted observations. i , i =1, 2, ..., N, where N is the total number of valid tests performed. The cumulative fragmentation probability distribution of particle fracture energy is calculated by the following formula: .

4. The method for calibrating the cumulative damage constant of ore based on uniaxial compression and falling ball impact tests according to claim 1, characterized in that: In step c, the fracture energy obtained in step a is divided by its respective mass to obtain the mass-to-fracture energy of the ore. The relationship between the cumulative probability of ore breakage and the mass-to-fracture energy is established by the log-normal distribution function, and the fitting formula is as follows: in, The median fracture energy, For distribution parameters, The fracture energy is the ratio of ore mass to fracture energy.

5. The method for calibrating the cumulative damage constant of ore based on uniaxial compression and falling ball impact tests according to claim 1, characterized in that: In step d, the particle size of the single ore sample is -16 to +13.2 mm. 30 particles are selected, and the impact energy is fixed at 63 J / kg. If a particle loses at least 10% of its original weight during the impact, then the particle is considered broken.

6. The method for calibrating the cumulative damage constant of ore based on uniaxial compression and falling ball impact tests according to claim 1, characterized in that: In step e, the formula for predicting the particle breakage probability curve used in the breakage probability prediction model is as follows: in For the first n The specific crushing energy absorbed during a single impact, expressed in J / kg; for n - The specific crushing energy absorbed during the first impact, expressed in J / kg; For particles to absorb more crushing energy Damage below; This refers to a specific impact energy, expressed in J / kg. This represents the cumulative damage constant.

7. The method for calibrating the cumulative damage constant of ore based on uniaxial compression and falling ball impact tests according to claim 1, characterized in that: In step f, the optimal cumulative damage constant is determined using formula (5): in For the first i The probability of fracture under a number of impacts, expressed in % The breakage probability is obtained from the simulation, expressed in percent.

Images