An erosion modeling method based on particle size classification collection and quantitative characterization of breakage rate

Abstract

The application relates to the technical field of erosion modeling, and discloses an erosion modeling method based on particle grading collection and quantitative characterization of a breaking rate. The method comprises the following steps: acquiring initial physical state data and initial particle size distribution of a test piece; performing a gas-solid two-phase flow erosion experiment; acquiring sectional mass data and total particle size distribution after erosion by using a three-stage grading collection device; calculating the specific surface area increment; calculating the particle breaking energy consumption based on the von Rittinger breaking theory, dividing the initial total kinetic energy into target material damage energy consumption, particle rebound kinetic energy and breaking energy consumption, and calculating a theoretical erosion rate; constructing an initial erosion rate prediction model to obtain a predicted erosion rate; calculating the deviation of the predicted erosion rate and the theoretical erosion rate; using the recursive least square method in combination with a sliding window and a variable forgetting factor to online identify and optimize a breaking correction coefficient, and generating an erosion correction model adapted to the current working condition; and the application improves the physical authenticity and prediction accuracy of erosion damage evaluation.

Description

Technical Field

[0001] This application relates to the field of erosion modeling technology, and in particular to an erosion modeling method based on particle classification collection and quantitative characterization of breakage rate. Background Technology

[0002] Gas-solid two-phase flow erosion is one of the main forms of damage to aero-engine compressor blades in dusty environments. Repeated impacts of high-speed particles on the blade surface lead to material loss, profile changes, and coating peeling, severely affecting engine performance and service life. To assess erosion damage, various erosion experimental devices and predictive models have been developed both domestically and internationally. Existing experimental devices typically include modules such as a high-pressure gas source, particle delivery, an acceleration nozzle, and specimen clamping. They can control operating parameters such as erosion angle and velocity, and use surface mass loss and morphological changes of the specimen as damage evaluation indicators.

[0003] However, existing technologies have the following shortcomings: First, the experimental devices do not effectively collect and classify the eroded particles. The impacted particles are splashed, scattered, or mixed with impurities, making it impossible to obtain pure particle samples suitable for analysis, resulting in a lack of data support for particle breakage mechanism research. Second, a systematic comparative analysis method for particle size distribution before and after erosion has not yet been established in the industry, making it impossible to quantitatively characterize key parameters such as particle breakage rate and particle size shift, and making it difficult to establish a quantitative relationship between breakage behavior and erosion damage. Third, existing erosion prediction models are generally based on the simplified assumption that "particles are rigid, non-breakable media," ignoring the energy consumption of particle breakage during impact and its contribution to erosion damage, leading to conservative model predictions and significant deviations from actual working conditions. Furthermore, traditional model parameters are fixed and cannot adapt to differences in breakage characteristics under different particle batches and varying working conditions, limiting their engineering applicability.

[0004] Therefore, there is an urgent need to develop a method for systematically acquiring particle breakage data, quantitatively characterizing the degree of breakage, and establishing an erosion modeling method that takes into account the breakage effect, in order to overcome the shortcomings of existing technologies. Summary of the Invention

[0005] To address the aforementioned technical issues, this application provides an erosion modeling method based on particle classification and quantitative characterization of breakage rate. By classifying and recovering particles before and after erosion and analyzing particle size, the method quantitatively characterizes particle breakage parameters and constructs an erosion prediction model that includes a breakage correction coefficient. This method is applicable to the erosion-resistant structural design, damage assessment, and service life prediction of key components such as aero-engine compressor blades and gas turbine blades.

[0006] In a first aspect, this application provides an erosion modeling method based on particle classification and quantitative characterization of breakage rate, the method comprising: Step S1: Obtain the initial physical state data of the test piece and calibrate the particles used for erosion to obtain the initial particle size distribution. Step S2: Perform a gas-solid two-phase flow erosion experiment on the test piece. After the experiment, use a collection device with a multi-stage structure to obtain segmented mass data of different particle size ranges and the total particle size distribution after erosion, and calculate the specific surface area increment before and after erosion. Step S3: Calculate the energy consumption of particle crushing based on the crushing theory. According to the law of conservation of energy, the initial total kinetic energy of the particle impacting the test piece is divided into the energy consumption of target material damage, the kinetic energy of particle rebound and the energy consumption of particle crushing. The theoretical erosion rate is calculated in combination with the initial physical state data. Step S4: Determine the coefficients to be calibrated by fitting experimental data under non-fracture conditions, and construct an initial erosion rate prediction model based on the specific surface area increment and the coefficients to be calibrated to obtain the predicted erosion rate. Step S5: Calculate the deviation between the predicted erosion rate and the theoretical erosion rate, use the recursive least squares method for online parameter identification, and combine the sliding window and variable forgetting factor mechanism to optimize the initial erosion rate prediction model and generate an erosion correction model adapted to the current working conditions.

[0007] Compared with the prior art, the beneficial effects of the present invention are at least as follows: First, by designing a collection device with a three-level classification structure, efficient classification and recovery of fine particles, mainstream broken particles, and unbroken large-diameter particles of all particle sizes is achieved. Combined with hydroponic dispersion and image particle size analysis, the specific surface area increment, particle breakage rate, and particle size peak offset can be accurately calculated, thereby overcoming the hardware and method defects of traditional erosion experiments that cannot obtain pure particle samples after breakage and cannot quantitatively characterize the degree of breakage.

[0008] Secondly, this application converts the specific surface area increment into particle crushing energy consumption based on the von Rittinger crushing theory, and establishes the physical relationship between the initial total kinetic energy and the energy consumption of target material damage, particle rebound kinetic energy and crushing energy consumption according to the law of conservation of energy. The theoretical erosion rate is derived, and a semi-empirical prediction model containing a reference constant and multiple crushing correction coefficients is constructed. The initial values ​​of each coefficient are determined by step-by-step fitting under no-crushing and crushing conditions, so that the prediction model can quantitatively reflect the enhancing effect of crushing behavior on erosion damage, significantly improving the physical reality and prediction accuracy of the model.

[0009] Finally, this application employs recursive least squares to identify the breakage correction coefficient online, combined with a sliding window and variable forgetting factor mechanism, enabling the model to dynamically adjust its parameters according to the deviation of each experiment, track changes in particle batches or working conditions in a timely manner, and always maintain optimal adaptability to the current working conditions. This overcomes the shortcomings of traditional models with fixed parameters and inability to adapt to changes in working conditions, endows the erosion prediction model with continuous self-evolution capability, and greatly improves its engineering practicality and long-term prediction robustness. Attached Figure Description

[0010] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is a flowchart of an erosion modeling method based on particle classification collection and quantitative characterization of breakage rate in an embodiment of this application; Figure 2 This is a schematic diagram of the overall structure of the erosion test system according to an embodiment of this application; Figure 3 This is a partial structural diagram of the specimen workbench according to an embodiment of this application; Figure 4 This is a cumulative curve of particle size distribution before and after erosion in an embodiment of this application; Figure 2 In the middle: 101—Gas cylinder group, 102—Gas exhaust, 103—Nitrogen pressure valve, 104—Control valve, 110—Nitrogen cylinder, 111—Nitrogen valve, 112—Powder tray, 113—Powder tank, 114—Control component, 120—Spray gun body, 121—Three-coordinate electronic control moving unit, 122—Rotating disk, 123—Powder pipe, 124—Electrical control unit, 125—Powder needle, 126—Venturi tube, 300—Metal soundproof chamber, 320—Side dust collector, 321—Lower dust collection drawer, 322—Scientific vacuum cleaner, 400—PLC integrated control system, 200—Angle scale, 202—Free-rotating vise, 203—Test piece, 204—Vertical fixed surface, 205—Horizontal working surface, 206—Acrylic protective buckle cover; Figure 3 In the middle: 120—spray gun body, 200—angle scale, 201—angle pointer, 202—free-rotating vise, 203—test piece, 204—vertical fixed surface, 205—horizontal working surface, 206—acrylic protective buckle cover, 210—base plate, 302—support rod. Detailed Implementation

[0012] This application provides an erosion modeling method based on particle classification collection and quantitative characterization of breakage rate. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0013] For ease of understanding, the specific process of the embodiments of this application is described below. The core concept of this method is as follows: by designing an erosion experimental device with multi-level hierarchical collection function, the particle size distribution changes before and after erosion are obtained. Based on this, characteristic parameters such as particle breakage rate, peak particle size shift, and specific surface area increment are quantitatively characterized. These breakage characteristic parameters are then introduced into the erosion prediction model. Simultaneously, based on the law of conservation of energy, a physical relationship between breakage energy consumption and target material damage is established. Finally, through online parameter identification and model adaptive update mechanisms, an erosion correction model that can reflect the particle breakage effect under different working conditions is generated. This method consists of five sequentially executed steps. Please refer to [link to relevant documentation]. Figure 1 An erosion modeling method based on particle classification collection and quantitative characterization of breakage rate in this application embodiment includes: Step S1: Obtain the initial physical state data of the test piece and calibrate the particles used for erosion to obtain the initial particle size distribution.

[0014] Step S1 includes: acquiring the initial physical state data of the test piece, including the surface hardness of the test piece; taking an un-eroded original particle sample; performing hydroponic dispersion treatment on the original particle sample; using an image particle size analysis device to detect the dispersed original particle sample; and directly obtaining the initial particle size distribution function before erosion.

[0015] Specifically, the initial physical state data of the test specimen is first obtained, and the particles used for erosion are calibrated to obtain the initial particle size distribution. The test specimen is typically made of aero-engine compressor blade material, such as TC4 titanium alloy plate, whose surface needs to be polished to uniformly roughen the surface. The initial physical state data mainly refers to the surface hardness of the test specimen, which reflects the material's ability to resist plastic deformation and erosion damage and can be directly measured using a surface hardness tester. For erosion particles, silica particles are selected in this embodiment, with a particle size range controlled between 5 micrometers and 150 micrometers. Uneroded raw particle samples are taken and first subjected to hydroponic dispersion treatment, i.e., the particles are uniformly dispersed in a liquid medium to avoid agglomeration. Then, image particle size analysis equipment, such as a laser particle size analyzer or dynamic image analyzer, is used to detect the dispersed particles, directly obtaining the initial particle size distribution function before erosion, denoted as . ,in Let be the probability density function (volume frequency distribution), satisfying d is the particle size. and These represent the lower and upper limits of the particle size detection range, respectively. This initial particle size distribution function serves as the basic reference curve for subsequent calculations of characteristic parameters such as specific surface area increment and particle breakage rate.

[0016] After obtaining the initial particle size distribution function, in order to further quantitatively characterize the fragmentation behavior of particles during the erosion process and establish the energy correlation between the degree of fragmentation and the damage to the target material, it is necessary to conduct gas-solid two-phase flow erosion experiments and perform graded recovery and particle size analysis on the eroded particles, i.e., proceed to step S2.

[0017] Step S2: Perform a gas-solid two-phase flow erosion experiment on the test specimen. After the experiment, use a collection device with a multi-stage structure to obtain segmented mass data of different particle size ranges and the total particle size distribution after erosion, and calculate the specific surface area increment before and after erosion.

[0018] In step S2, a multi-stage collection device is used to obtain segmented mass data for different particle size ranges. This includes: activating a negative pressure collection mechanism located on the side to capture fine particles in a suspended state, generating first segmented mass data; activating a directional micro-negative pressure collection mechanism located inside a sealed protective structure to guide and collect mainstream broken particles, generating second segmented mass data; using a gravity settling collection mechanism located at the bottom to collect unbroken large-diameter particles falling under gravity, generating third segmented mass data; and summarizing the first, second, and third segmented mass data to obtain segmented mass data for different particle size ranges.

[0019] Specifically, a gas-solid two-phase flow erosion experiment is performed on the test specimen, such as... Figure 2The diagram shown is a schematic representation of the overall structure of the erosion testing system used in this application. In the diagram, 101 represents the gas cylinder group, 102 represents the gas outlet, 103 represents the nitrogen pressure valve, 104 represents the control valve, 110 represents the nitrogen cylinder, 111 represents the nitrogen valve, 112 represents the powder tray, 113 represents the powder tank, 114 represents the control component, 120 represents the spray gun body, 121 represents the three-coordinate electronically controlled moving unit, 122 represents the rotary disk, 123 represents the powder tube, 124 represents the electronic control unit, 125 represents the powder needle, 126 represents the venturi tube, and 203 represents the test... The components are: 204 (vertical fixed surface), 205 (horizontal working surface), 206 (acrylic protective cover), 202 (free-rotating vise), 200 (angle scale), 300 (metal soundproof chamber), 320 (side dust collector), 321 (lower dust collection drawer), 322 (scientific vacuum cleaner), and 400 (PLC integrated control system). This system consists of a high-pressure air supply, quantitative particle conveying, integrated electrical control, a multi-condition erosion control console, and a multi-level collaborative particle collection device, all housed within a sealed protective structure.

[0020] Furthermore, such as Figure 3 The diagram shows a partial structural schematic of the test piece workbench. In the diagram, 203 represents the test piece, 204 represents the vertical fixed surface, 206 represents the acrylic protective cover, 201 represents the angle pointer, 120 represents the spray gun body, 302 represents the support rod, 200 represents the angle scale, 202 represents the free-rotating vise, 210 represents the base plate, and 205 represents the horizontal working surface. This workbench uses the free-rotating vise 202 to achieve dual-position switching of the test piece between the horizontal working surface 205 and the vertical fixed surface 204. The angle scale 200, in conjunction with the angle pointer 201, can read the erosion angle with an adjustment accuracy of 0.1 degrees. The support rod 302 is used to fix the spray gun body 120, and the base plate 210 is a rigid support structure.

[0021] Before the experiment, the TC4 titanium alloy specimen 203 was fixed to the specimen workbench using a free-rotating vise 202. Depending on the experimental requirements, either a horizontal working surface 205 or a vertical fixed surface 204 was selected. The erosion angle was adjusted to the target value with an accuracy of 0.1 degrees using an angle scale 200 and the rotation mechanism of the free-rotating vise. The PLC integrated control system 400 was activated, controlling the gas cylinder group 101 to provide a high-pressure gas source, which was adjusted to the set pressure via a nitrogen pressure valve 103 and a control valve 104. Simultaneously, the nitrogen cylinder 110 provided auxiliary gas to the powder tank 113 via a nitrogen valve 111, driving the powder tray 112 to rotate. The powder needle 125 quantitatively extracted particles from the powder tank, transported them through the powder tube 123 to the rotating disk 122, and then into the spray gun body 120. After being uniformly mixed with the mainstream high-speed airflow within the venturi tube 126, the particles were ejected from the spray gun body 120 at a set speed v and erosion angle θ, impacting the surface of the specimen 203. During the experiment, the three-coordinate electronically controlled moving unit 121 can control the spatial position of the spray gun, the electronically controlled unit 124 monitors various parameters in real time, and the high-speed camera equipment can capture the transient process of particle impact and crushing through the reserved interface.

[0022] After the erosion experiment, to obtain segmented mass data for different particle size ranges and the total particle size distribution after erosion, a multi-stage collection device needs to be activated. First, the side dust collector 320 is activated. This side dust collector 320 is connected to the side wall of the metal soundproof chamber 300, and its inlet is equipped with an annular anti-backflow air curtain. It uses negative pressure suction to capture suspended fine particles with a particle size ≤5μm, generating the first segmented mass data. Next, the research vacuum cleaner 322 is activated. This vacuum cleaner is sealed to the dust collection hole on the side wall of the inner acrylic protective cover 206. By controlling the vacuum cleaner's flow rate, a directional micro-negative pressure field is formed within the acrylic chamber, guiding and collecting the mainstream broken particles with a particle size between 5μm and 50μm, generating the second segmented mass data. Simultaneously, using the lower dust collection drawer 321 located at the bottom of the metal soundproof chamber 300, unbroken large-diameter particles (particle size >50μm) falling under gravity are collected by natural gravity settling, generating the third segmented mass data. By summing up the quality data of the first, second, and third segments, we obtain segmented quality data that reflects the particle distribution at different degrees of breakage.

[0023] Step S2, calculating the specific surface area increase before and after erosion, includes: obtaining particle samples corresponding to segmented mass data of different particle size ranges; performing hydroponic dispersion treatment on each segment of particles after graded recovery; detecting the dispersed particles using an image particle size analysis device; obtaining the segmented particle size distribution function corresponding to each segment; and weighting and merging the segmented particle size distribution functions according to the proportions of the first segment mass data, the second segment mass data, and the third segment mass data to obtain the total particle size distribution function after erosion. The increase in specific surface area before and after particle erosion is calculated based on the first formula. The first formula is: ,in Particle density, and These represent the lower and upper limits of the particle size detection range, respectively, where d is the particle size. V represents the total surface area added after the particles are broken, and V is the total volume of the particles. This is the initial particle size distribution function before erosion.

[0024] Specifically, after obtaining the mass data for the first, second, and third segments, the increase in specific surface area needs to be further calculated to quantitatively determine the degree of particle fragmentation caused by erosion. Particle samples collected from each of the three segments are subjected to hydroponic dispersion treatment to ensure uniform dispersion in the liquid medium and prevent agglomeration. Then, image particle size analysis equipment, such as a laser particle size analyzer, is used to detect the particles after each dispersion treatment, obtaining the segmental particle size distribution function corresponding to each segment. Since the proportion of particles in each segment in the total particles is different, the three distribution functions cannot be simply added together. Instead, a weighted merging of the three segmental particle size distribution functions should be performed, using the proportion of each segment's mass data as a weight. This weighted merging process is essentially a normalization process, ensuring that the integral of the merged distribution function over the entire particle size range equals 1, thus obtaining the total particle size distribution function that represents all eroded particles, denoted as . Initial grain size distribution function before erosion It has already been obtained in step S1.

[0025] like Figure 4 The figure shows the cumulative particle size distribution curves before and after erosion in this embodiment. The horizontal axis represents particle size (micrometers), and the vertical axis represents the cumulative percentage (%). The blue solid line represents the initial cumulative particle size distribution curve before erosion, and the red dashed line represents the total cumulative particle size distribution curve after erosion. As can be seen from the figure, the two curves do not completely overlap: within the smaller particle size range, the cumulative percentage values ​​are relatively close; however, when the particle size increases to a certain range, the cumulative percentage after erosion becomes significantly higher than the cumulative percentage before erosion. This change in distribution pattern indicates that the erosion process causes a structural adjustment in the particle size distribution, with a relative increase in the cumulative proportion of the larger particle size range. This directly reflects the fragmentation behavior of the particles during impact with the target material, which leads to the reconstruction of the particle size distribution.

[0026] Based on the initial grain size distribution function before erosion and the total particle size distribution function after erosion Calculate the specific surface area increment according to the following integral relationship. The increase in specific surface area is equal to the integral over the particle size d, with the lower limit of integration being the minimum value within the particle size detection range. The upper limit is the maximum value. The integrand is and The difference multiplied by the particle density The reciprocal of the integral is multiplied by six and divided by the particle size d. The physical meaning of this integral is: converting the change in the number of particles within each particle size range before and after erosion into a change in surface area, then dividing by the total particle volume V, yields the increased surface area per unit volume of particles. This represents the total surface area added after particle breakage, which is the total surface area after erosion minus the total surface area before erosion. This increase in specific surface area directly reflects the severity of particle breakage: the more severe the breakage, the more small particles are generated, the larger the newly added surface area, and thus the more energy is consumed in the breakage. This provides a quantitative basis for subsequent calculation of particle breakage energy consumption based on von Rittinger's breakage theory.

[0027] Through the weighted merging particle size analysis of the three-stage collected particles and the integral calculation of the specific surface area increment, the present invention realizes the reconstruction of the full particle size distribution after erosion and the accurate quantification of the degree of fragmentation. It overcomes the shortcomings of traditional methods that cannot reflect the details of fragmentation based solely on the average particle size, and provides high-fidelity input characteristic parameters for subsequent calculation of fragmentation energy consumption and correction of erosion models.

[0028] Step S3: Calculate the energy consumption of particle crushing based on the crushing theory. According to the law of conservation of energy, the initial total kinetic energy of the particle impacting the test piece is divided into the energy consumption of target material damage, the kinetic energy of particle rebound and the energy consumption of particle crushing. The theoretical erosion rate is calculated in combination with the initial physical state data.

[0029] Step S3, which calculates the energy consumption of particle crushing based on crushing theory, includes: applying von Rittinger theory to establish a direct proportional mathematical relationship between crushing energy consumption and the increase in particle surface area. ,in, This indicates the energy consumption of particle crushing. This represents the crushing energy constant extracted in advance through calibration under no-crushing conditions. This represents the total surface area added after the particles are broken.

[0030] Specifically, step S2 obtained the specific surface area increment and segmented mass data after particle breakage. However, these data only describe the geometric characteristics of the breakage and have not yet established a direct link with the energy distribution during the erosion process. In order to reveal the contribution of particle breakage to erosion damage from a physical mechanism perspective, it is necessary to quantitatively express the energy conversion relationship during particle impact based on breakage theory, and calculate the theoretical erosion rate accordingly, i.e., proceed to step S3.

[0031] In step S3, the energy consumption of particle crushing is first calculated based on crushing theory. This application adopts the von Richter crushing theory, which states that the energy consumed by solid materials during crushing is directly proportional to the increase in surface area. For particles in the erosion process, after impacting the wall, the particles break apart, and the originally intact particles split into multiple smaller particles, significantly increasing the total surface area. The energy corresponding to this increased surface area is the energy consumption of particle crushing. Therefore, a direct proportional mathematical relationship is established between crushing energy consumption and the increase in particle surface area: Particle crushing energy consumption Equals the crushing energy constant K multiplied by the total surface area added after particle crushing. .in, The specific surface area increment was obtained in step S2 by multiplying the total particle volume. The breakage energy constant K is an inherent parameter related to the particle material and needs to be pre-calibrated through experiments under non-breakage conditions. At extremely low impact energy (i.e., when particles do not break), the extremely low impact energy refers to the particle impact velocity being below the critical velocity at which visible breakage occurs. This critical velocity is determined through preliminary experiments: under the same erosion conditions, the particle impact velocity is gradually increased from low to high. After each experiment, the peak shift of the particle size distribution curve before and after erosion is measured. When the peak shift first exceeds three times the measurement accuracy of the particle size analysis equipment, the corresponding velocity is the critical velocity. When calibrating the breakage energy constant K, 50% of this critical velocity is taken as the calibration velocity to ensure that the particles only undergo elastic deformation without breakage. At this point, all input energy is converted into particle deformation energy. The K value is obtained by measuring the ratio of this energy to the increased particle surface area (estimated from the change in surface roughness). This calibration process is performed only once, and the same K value is used for all subsequent conditions. This step converts the geometric surface area increment into energy loss due to breakage, providing a crucial input for establishing the subsequent energy conservation equation.

[0032] In step S3, the initial total kinetic energy of the particles impacting the test piece is divided into energy dissipation due to target damage, particle rebound kinetic energy, and particle breakage energy dissipation. This includes: calculating the initial total kinetic energy of the particles impacting the surface of the test piece based on the input total mass of the particles and the initial velocity of the particle impact; calculating the particle rebound kinetic energy by combining the particle rebound velocity obtained from the high-speed camera equipment and introducing the mass-weighted average recovery coefficient; and establishing an energy conservation equation to ensure that the initial total kinetic energy of the particles impacting the wall is... Converted into energy dissipation due to target damage Energy consumption of particle crushing With particle rebound kinetic energy That is, it satisfies the second formula: By subtracting the energy consumed by particle breakage and the kinetic energy of particle rebound from the initial total kinetic energy, the energy consumed by target material damage can be derived in reverse.

[0033] Specifically, after calculating the energy consumption of particle breakage in step S3, it is necessary to further divide the initial total kinetic energy of the particles impacting the test specimen according to the energy destination. When a particle impacts the surface of the specimen with an initial velocity v, its initial total kinetic energy is given by half of the product of the total mass of the input particles and the square of the initial impact velocity. This initial total kinetic energy is not entirely used to remove the specimen material, but is divided into three destinations: a portion of the energy is used to cause the particles to break themselves, which is the particle breakage energy consumption calculated above. Another portion of the energy is carried away from the specimen surface by the broken particles in the form of kinetic energy, which is called particle rebound kinetic energy. The remaining energy is used to cause plastic deformation, micro-cutting, and material peeling on the specimen surface; this is called target damage energy consumption. To obtain the kinetic energy of particle rebound, this application employs a high-speed camera to capture the particle impact and rebound process. The high-speed camera is fixedly installed through a multi-functional equipment hole pre-reserved on the specimen worktable, with the lens aimed at the specimen surface, continuously capturing the particle's trajectory at a sufficiently high frame rate. Image analysis of the captured continuous images allows tracking the incident trajectory of the same particle before impact and its rebound trajectory after impact, thereby measuring the particle's rebound velocity. Considering that particles may break after each impact, producing multiple fragments of different sizes, and that the rebound velocities of each fragment are not identical, this application introduces a mass-weighted average coefficient of restitution to comprehensively characterize the overall rebound kinetic energy. The coefficient of restitution is defined as the ratio of the particle's rebound velocity to its impact velocity, reflecting the degree of kinetic energy loss during the collision. In the case of particle breakage, multiple fragments are produced after impact, each with a different coefficient of restitution. The mass-weighted average coefficient of restitution refers to the weighted average of the coefficients of restitution of all fragments according to the proportion of each fragment's mass to the total mass of all fragments, thus obtaining an equivalent coefficient of restitution that can represent the overall rebound behavior. Based on the equivalent recovery coefficient and the total mass of all fragments (i.e., the total mass of the rebounding particles, which is equal to the total mass of the original particles), the kinetic energy of the rebounding particles can be calculated. The specific calculation method is as follows: multiply the square of the equivalent restoration coefficient by the square of the total mass of the particle and the square of the impact velocity, and then multiply by one half. The result is the particle rebound kinetic energy.

[0034] After establishing quantitative expressions for the initial total kinetic energy, particle breakage energy consumption, and particle rebound kinetic energy, this application establishes the following energy conservation equation based on the law of conservation of energy: The initial total kinetic energy Ek,i of the particle impacting the wall is equal to the energy consumption of the target material damage. Energy consumption of particle crushing With particle rebound kinetic energy The sum of the three. The physical meaning of this equation is: the initial kinetic energy cannot be created or destroyed out of thin air; it must be transformed into the three forms of energy mentioned above. Because the initial total kinetic energy... Energy consumption of particle crushing and particle rebound kinetic energy All of these can be directly measured or calculated experimentally. Therefore, the energy consumption for target damage can be derived by subtracting the energy consumed by particle breakage and the kinetic energy of particle rebound from the initial total kinetic energy. This reverse derivation process avoids the difficulty of directly measuring the energy consumption of the target material, because energy dissipation inside the target material, such as plastic deformation and thermal effects, is difficult to obtain quantitatively through external means. Through step S3, the energy distribution relationship between particle breakage behavior and target material damage is clearly expressed by physical laws, providing a benchmark value that conforms to the law of energy conservation for the subsequent calculation of the theoretical erosion rate.

[0035] Step S3 involves calculating the theoretical erosion rate, including: calculating the theoretical erosion rate based on the third formula according to the energy conservation principle. The third formula is: ,in, For energy conversion efficiency, The total mass of the particles. The surface hardness of the test piece.

[0036] Specifically, the energy dissipation due to target damage is obtained. Next, it needs to be converted into the erosion rate index commonly used in engineering so that it can be compared with the output of subsequent prediction models. The erosion rate is usually defined as the mass loss of the target material under the impact of a unit mass of particles; it is a dimensionless ratio. According to the law of conservation of energy, the energy consumed by target material damage... There is a direct proportional relationship between the energy absorbed by the target and the erosion rate E: the more energy absorbed by the target, the more severe the material removal. However, the process of converting energy into mass loss is not entirely direct. It is limited by the energy dissipation mechanisms inside the material, such as heat and residual stress. The energy actually used to remove the material is only a part of the energy consumed by the target damage.

[0037] Therefore, this application introduces energy conversion efficiency. This indicates the proportion of energy absorbed by the target material that is actually used for material removal; simultaneously, the ease of material removal is related to the surface hardness of the test piece. Closely related, the higher the hardness, the greater the energy required to remove a unit mass of material. Based on this, the theoretical erosion rate is calculated as follows: The theoretical erosion rate E equals the initial total kinetic energy. Subtract particle rebound kinetic energy Subtract the energy consumed in particle crushing Then, divide by the energy conversion efficiency η and the total mass of the particles. and the surface hardness of the test piece The product of these three data points, summed with the mass data from the first, second, and third segments, yields the total mass of the particles involved in this erosion experiment, denoted as [missing information]. Among them, the molecular part ( This refers to the energy dissipated due to target damage. The total mass of particles in the denominator Surface hardness was obtained by weighing with a high-precision electronic balance before the experiment. The energy conversion efficiency η is obtained through hardness testing. It is an empirical parameter that needs to be calibrated by back-calculation using a benchmark experiment under non-fracture conditions. This involves selecting erosion conditions where particle breakage does not occur, measuring the actual mass loss rate, and substituting it into the above formula to solve for the η value. This value is considered a constant under the same target material and particle system. The theoretical erosion rate calculated using this formula is a "true value" directly derived from the law of conservation of energy and experimental data (initial kinetic energy, rebound kinetic energy, and breakage energy consumption). It is unaffected by any empirical model assumptions and can therefore serve as a benchmark for measuring the accuracy of the prediction model in subsequent steps. Thus, step S3 completes the physical mapping from the geometric characteristics of particle breakage to energy distribution and then to the theoretical erosion rate.

[0038] Through the quantitative calculations based on von Rittinger theory and the law of conservation of energy, this invention successfully links particle breakage behavior and erosion damage directly at the energy level, providing a theoretical erosion rate benchmark that does not rely on empirical assumptions, and laying a physical foundation for the adaptive correction of subsequent prediction models.

[0039] Step S4: Determine the calibration coefficients by fitting experimental data under non-fracture conditions, and construct an initial erosion rate prediction model based on the specific surface area increment and the calibration coefficients to obtain the predicted erosion rate.

[0040] In step S4, the calibration coefficient is determined by fitting experimental data under non-fracture conditions. This includes: determining the initial value of the reference constant C related to the material of the test piece and the particle material by fitting experimental data under non-fracture conditions; and determining the first fracture correction coefficient by fitting multiple erosion test data under fracture conditions, with the goal of minimizing the sum of squares of the deviations between the theoretical erosion rate and the predicted erosion rate. Second breakage correction coefficient Third breakage correction coefficient and the fourth breakage correction factor The initial value.

[0041] Specifically, step S3 yields a theoretical erosion rate based on the law of conservation of energy. This theoretical erosion rate depends on experimentally measured rebound kinetic energy and breakage energy consumption. While accurate, it is complex to operate and not readily applicable in engineering. Therefore, it is necessary to construct a simple initial erosion rate prediction model that relies on only a few measurable input parameters. The undetermined coefficients in the model are then determined through fitting experimental data, enabling it to approximate the theoretical erosion rate under common operating conditions. This leads to step S4.

[0042] In step S4, the initial value of the reference constant C related to the material of the test piece and the particle material is first determined by fitting experimental data under non-fracture conditions. Non-fracture conditions refer to selecting extremely low particle impact velocities (ensuring no visible particle breakage) for the erosion experiment. At this point, the particle breakage rate... Zero, specific surface area increment Zero, peak particle size offset The value is zero, so the prediction model is simplified to include only the baseline constant C and the target material hardness. Particle shape factor erosion angle function Particle impact velocity v and its exponent n, particle density and velocity recovery coefficient The basic form.

[0043] Multiple experiments were conducted at different speeds or angles under non-fracture conditions to measure the actual erosion rate, i.e. the theoretical erosion rate. Since the theoretical erosion rate can be directly calculated by energy conservation under non-fracture conditions, the initial value of the reference constant C was obtained by fitting the least squares method with the goal of minimizing the sum of squares of the deviations between the actual erosion rate and the model prediction value. This reference constant C comprehensively reflects the intrinsic erosion characteristics of the combination of target material and particle material and is the basis for all subsequent predictions.

[0044] After obtaining the baseline constant C, the first breakage correction coefficient needs to be determined by fitting multiple erosion test data under breakage conditions. Second breakage correction coefficient Third breakage correction coefficient and the fourth breakage correction factor The initial value. The "fractured condition" refers to normal erosion conditions, where particles break to varying degrees, and the breakage correction term in the model is activated. Multiple sets of erosion experiments were conducted under different velocities, angles, particle batches, or particle size distributions. For each set of experiments, the corresponding theoretical erosion rate (as the target value) and particle breakage rate were obtained through steps S2 and S3. Specific surface area increment Particle size peak offset Fracture characteristic parameters are identified. These parameters are then substituted into the initial erosion rate prediction model, the specific form of which will be given in subsequent steps. The model aims to minimize the sum of squared deviations between the theoretical erosion rate and the model-predicted erosion rate, and is simultaneously fitted using a multivariate nonlinear least squares method. , , , The initial value. Wherein, the first breakage correction coefficient. Second breakage correction coefficient Located in the molecular part, these are used to adjust the positive enhancing effect of particle breakage rate and specific surface area increase on erosion rate; the third breakage correction coefficient and the fourth breakage correction factor Located in the denominator, Used to adjust the correction of the kinetic energy loss term by the particle breakage rate. Used to adjust the peak particle size offset The amplification factor of the effect. All four coefficients are dimensionless, and their initial values ​​are typically between 0 and 1, with specific values ​​depending on the experimental data. Through the above fitting process, the initial erosion rate prediction model has the ability to approximate the theoretical erosion rate under fractured conditions, providing a good starting point for subsequent online parameter identification.

[0045] By adopting a step-by-step fitting strategy of calibrating the benchmark constant under no-crushing conditions and calibrating the crushing correction coefficient under crushing conditions, this invention solves the problem that traditional erosion models have fixed parameters and cannot adapt to changes in particle crushing behavior. This makes the initial prediction model have a high prediction benchmark under different crushing degrees, laying the parameter foundation for subsequent online adaptive updates.

[0046] In step S4, obtaining the predicted erosion rate includes: performing particle size analysis on the particles collected at each stage to obtain the particle size distribution after erosion, and calculating the particle breakage rate. Particle size peak offset Construct an initial erosion rate prediction model: ,in, To predict the erosion rate, The surface hardness of the test piece. For particle shape factor, For the erosion angle, This is a function of the erosion angle. Particle impact velocity, For speed index, The velocity recovery coefficient, Particle density, For particle breakage rate, This represents the peak particle size offset. This represents the increase in specific surface area.

[0047] Specifically, after determining the initial values ​​of the baseline constant C and the first to fourth breakage correction coefficients in step S4, it is necessary to further calculate the particle breakage characteristic parameters using the particle size distribution data after erosion, and construct an initial erosion rate prediction model accordingly to obtain the predicted erosion rate. Specifically, firstly, particle size analysis is performed on the segmented particle samples obtained in step S2 through the three-stage collection device. That is, hydroponic dispersion processing and image particle size analysis are performed on the particles corresponding to the mass data of the first, second, and third segments respectively to obtain the particle size distribution function of each segment. Then, the particle size distribution function after erosion is obtained by weighting and merging according to the proportion of each segment's mass to the total mass. Based on this total particle size distribution function and the initial particle size distribution function before erosion obtained in step S1, the particle breakage rate can be calculated. and particle size peak offset The particle breakage rate is defined as the proportion of the mass of particles smaller than the initial average particle size after erosion to the total mass of particles after erosion. It reflects the overall degree of particle breakage. The initial average particle size refers to the volume average particle size of the initial particle size distribution before erosion. The specific calculation method is as follows: [The initial particle size distribution function is then used]. Multiply by the particle size d and integrate over the entire particle size range; the particle size peak offset is defined as the difference between the particle size corresponding to the peak of the particle size distribution after erosion and the peak particle size before erosion. When this value is negative, it indicates that the crushing has led to the overall refinement of the particles, and the larger the absolute value, the more severe the crushing.

[0048] After obtaining the aforementioned fracture characteristic parameters, an initial erosion rate prediction model was constructed. This model is a semi-empirical, semi-theoretical expression. Its core idea is to introduce a fracture correction factor to reflect the enhancing effect of particle fracture on erosion damage, based on the traditional non-fracture erosion model. The model's input parameters include: the surface hardness of the test piece. (Measured by a hardness tester), particle shape factor (Spherical particles are represented as 1, irregular particles are calibrated experimentally), erosion angle θ and its erosion angle function f(θ), particle impact velocity. and the velocity exponent n (calibrated experimentally, usually taking a value of 2 to 3), and the velocity restitution coefficient. (Measured by high-speed camera) Particle density (Inherent material properties) and the particle breakage rate calculated in step S2 and this step. Specific surface area increment and particle size peak offset The model output is the predicted erosion rate E. The calibration method for the velocity exponent n is as follows: under non-fracture conditions, keeping other parameters constant, measure the erosion rate at at least three different impact velocities. After taking the logarithm of the erosion rate and velocity, perform a linear fit. The resulting slope is the velocity exponent n, and the goodness of fit should be greater than 0.95. The erosion angle function f(θ) can be calibrated through non-fracture erosion experiments at different angles. It is usually fitted using a piecewise polynomial or sine function, and the specific parameters are determined by experimental data.

[0049] The specific operational relationship of the model is as follows: the predicted erosion rate is equal to a fraction, where the numerator is composed of the product of a reference constant, a negative exponential term of the target hardness, a particle shape factor, an erosion angle function, a power term of the particle impact velocity, and two correction factors related to the breakage characteristics. The denominator is composed of the particle density multiplied by a bracketed expression containing a velocity recovery coefficient and breakage-related correction terms. By substituting the parameter values ​​obtained or calculated in steps S1 to S4 into this fraction and performing a division operation, the predicted erosion rate can be output. According to the above model, the predicted erosion rate will increase with the increase of particle breakage rate, specific surface area increment, and peak particle size offset, which is consistent with physical facts: particle breakage produces more sharp-edged new surfaces, enhancing the cutting action, while the broken fine particles are more likely to embed into the target surface, causing additional damage.

[0050] By constructing an initial erosion rate prediction model that includes three independent crushing characteristic parameters—fracture rate, specific surface area increment, and peak particle size shift—this invention directly embeds the contribution of particle crushing behavior to erosion damage into the prediction framework in analytical form. This allows the model to quantitatively reflect the erosion rate changes under different crushing degrees, significantly improving the physical transparency and operational adaptability of traditional empirical models. By introducing particle crushing rate, specific surface area increment, and peak particle size shift as independent correction factors, the initial erosion rate prediction model constructed in this invention can quantitatively describe the enhancing effect of crushing behavior on erosion damage, overcoming the physical limitation of traditional models that ignore crushing, and providing a reasonable and interpretable parameterization basis for subsequent online adaptive updates.

[0051] Step S5: Calculate the deviation between the predicted erosion rate and the theoretical erosion rate, use the recursive least squares method for online parameter identification, and combine the sliding window and variable forgetting factor mechanism to optimize the initial erosion rate prediction model and generate an erosion correction model adapted to the current working conditions.

[0052] Step S5 includes: calculating the deviation between the predicted erosion rate and the theoretical erosion rate after each erosion experiment; using the recursive least squares method to dynamically adjust the breakage correction coefficient in the initial erosion rate prediction model with the goal of minimizing the sum of squares of the deviations, so that the initial erosion rate prediction model can learn the breakage characteristics of the current particle batch and working conditions; setting a sliding window, discarding the oldest data when new experimental data enters the window, and re-identifying the breakage correction coefficient based on the data in the window; introducing a variable forgetting factor, automatically reducing the variable forgetting factor when the deviation of multiple consecutive experiments exceeds a preset threshold, so as to accelerate the model's adaptation speed to new working conditions; and outputting the initial erosion rate prediction model after the above online parameter identification and model adaptive update as the erosion correction model.

[0053] Specifically, step S4 yields an initial erosion rate prediction model and a predicted erosion rate. However, the initial value of the breakage correction coefficient in this model is obtained based on fitting data from a limited batch of experiments, and cannot adapt in real time to the differences in breakage characteristics caused by different particle batches or changes in working conditions. To maintain the model's continuous optimal fit to the current working conditions, it is necessary to adjust the model parameters online using data from each new experiment, enabling the model to have self-learning capabilities, i.e., proceeding to step S5.

[0054] In step S5, after each erosion experiment, the deviation between the predicted erosion rate output in step S4 and the theoretical erosion rate obtained in step S3 based on energy conservation is calculated. This deviation reflects the prediction error of the current model for the experimental conditions. To eliminate this error, the four breakage correction coefficients in the initial erosion rate prediction model are dynamically adjusted using the recursive least squares method. The recursive least squares method is a recursive parameter estimation algorithm. Its core idea is: for each new set of experimental data, including the breakage characteristic parameters and the corresponding theoretical erosion rate of this experiment, the current model parameters are corrected using this data to minimize the sum of squared deviations between the model prediction and the theoretical value. Unlike the one-time batch least squares method, the recursive least squares method does not need to save all historical data; it only needs to retain the previous parameter estimate and covariance matrix for recursive updates, resulting in high computational efficiency and making it very suitable for online applications. Specifically, in this application, after each experiment, the particle breakage rate obtained in this experiment is... Specific surface area increment Particle size peak offset The theoretical erosion rate is used as a new sample and input into the recursive least squares algorithm. The algorithm will automatically calculate the adjustment amount of the current crushing correction coefficient and update its value, so that the model can gradually learn the actual crushing characteristics of the current particle batch and working conditions.

[0055] Since erosion experiments may be conducted under different particle batches, environmental conditions, or equipment states, early experimental data may no longer represent the current operating conditions. Indefinitely retaining all historical data would reduce the model's response speed to changes in operating conditions. Therefore, this application introduces a sliding window mechanism based on the recursive least squares method: a fixed-length sliding window is set to retain data from the most recent N experiments, where N is typically an integer between 10 and 20. When data from a new experiment enters the window, the window automatically discards the oldest experimental data and then re-identifies the recursive least squares parameters based only on the data retained within the window. In this way, the model only remembers the statistical characteristics of the most recent N experiments, gradually forgetting outdated information, thus enabling it to promptly track the slow drift of particle properties or operating conditions.

[0056] Furthermore, in practical applications, operating conditions may change abruptly, such as replacing particles from completely different batches or suddenly altering the erosion velocity range. In such cases, the prediction error may exceed the preset threshold multiple times consecutively. To accelerate the model's adaptation to abrupt changes in operating conditions, this application introduces a variable forgetting factor mechanism based on the sliding window. The forgetting factor is a parameter in the recursive least squares method, ranging from 0 to 1. It determines the weight of historical data: the closer the forgetting factor is to 1, the greater the influence of retaining historical data, and the smoother the model update; the smaller the forgetting factor, the faster historical data is forgotten, and the more sensitive the model is to recent data. This application sets a default forgetting factor under normal operating conditions, such as 0.95, and sets an error threshold, such as a relative error exceeding 20%. The number of consecutive experiments, M, can be preset according to the severity of the change in operating conditions. In this embodiment, M=3. When the relative error of M consecutive experiments exceeds 20%, it is determined that a sudden change in operating conditions has occurred, and the value of the forgetting factor is immediately reduced, such as to 0.8, so that the model quickly abandons the old data and prioritizes the adaptation to the new data. After the prediction bias falls back below the threshold and remains stable for several consecutive cycles, the forgetting factor is gradually restored to its default value. Through the coordinated operation of the sliding window and the variable forgetting factor, the model can remain stable under normal operating conditions and respond quickly to sudden changes in operating conditions.

[0057] The initial erosion rate prediction model, after online parameter identification and adaptive model updating, is output as the final erosion correction model. This erosion correction model not only retains the physical framework of the initial model but also maintains optimal adaptability to the current particle batch and operating conditions through continuous self-learning, significantly improving the model's engineering practicality and prediction accuracy.

[0058] By combining online parameter identification using recursive least squares with a sliding window and variable forgetting factor mechanism, this invention achieves the dynamic self-evolution capability of the erosion prediction model, overcoming the shortcomings of traditional models with fixed parameters and inability to adapt to changes in working conditions, enabling the model to maintain high-precision prediction over a long period of time in practical engineering applications.

[0059] In summary, the erosion modeling method proposed in this application, based on particle classification collection and quantitative characterization of breakage rate, achieves efficient recovery of fine, bulk, and large-diameter particles after erosion and segmented quality data acquisition through the design of a collection device with a three-level classification structure. Based on hydroponic dispersion and image particle size analysis, the total particle size distribution after erosion is obtained through weighted merging, and the specific surface area increment is calculated by integration. Then, the particle breakage energy consumption is obtained based on the von Rittinger breakage theory. On this basis, an energy conservation equation including initial kinetic energy, rebound kinetic energy, and breakage energy consumption is established to derive the theoretical erosion rate. An initial erosion rate prediction model is constructed with a reference constant and four breakage correction coefficients as its core, and the initial values ​​of each coefficient are determined by step-by-step fitting under both breakage-free and breakage-affected conditions. Finally, the breakage correction coefficients are identified online using the recursive least squares method, and the model is adaptively updated by combining a sliding window and a variable forgetting factor to generate an erosion correction model adapted to the current operating conditions. This method overcomes the shortcomings of traditional erosion experiments, such as the inability to recover broken particles, the inability to quantitatively characterize the degree of breakage, and the neglect of breakage effects in prediction models, and significantly improves the physical authenticity of erosion damage assessment and the accuracy of engineering prediction.

[0060] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0061] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0062] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. An erosion modeling method based on particle classification and quantitative characterization of breakage rate, characterized in that, The method includes: Step S1: Obtain the initial physical state data of the test piece, including the surface hardness of the test piece, and calibrate the particles used for erosion to obtain the initial particle size distribution. Step S2: Perform a gas-solid two-phase flow erosion experiment on the test piece. After the experiment, use a collection device with a multi-stage structure to obtain segmented mass data of different particle size ranges and the total particle size distribution after erosion, and calculate the specific surface area increment before and after erosion. Step S3: Calculate the energy consumption of particle crushing based on the crushing theory. According to the law of conservation of energy, the initial total kinetic energy of the particle impacting the test piece is divided into the energy consumption of target material damage, the kinetic energy of particle rebound and the energy consumption of particle crushing. The theoretical erosion rate is calculated in combination with the initial physical state data. In step S3, the initial total kinetic energy of the particles impacting the test piece is divided into energy dissipation due to target damage, particle rebound kinetic energy, and energy dissipation due to particle breakage. This includes: calculating the initial total kinetic energy of the particles impacting the surface of the test piece based on the input total mass of the particles and the initial velocity of the particle impact; calculating the particle rebound kinetic energy by combining the particle rebound velocity obtained from the high-speed camera equipment and introducing a mass-weighted average recovery coefficient; and establishing an energy conservation equation to ensure that the initial total kinetic energy of the particles impacting the wall is... Converted into energy dissipation due to target damage Energy consumption of particle crushing With particle rebound kinetic energy That is, it satisfies the second formula: Subtracting the energy consumed by particle breakage and the kinetic energy of particle rebound from the initial total kinetic energy, the energy consumed by target material damage is derived in reverse; step S3 calculates the theoretical erosion rate, including: calculating the theoretical erosion rate based on the third formula according to the energy conservation relationship. The third formula is: ,in, For energy conversion efficiency, The total mass of the particles. The surface hardness of the test piece; Step S4: Determine the calibration coefficients by fitting experimental data under non-fracture conditions. Construct an initial erosion rate prediction model based on the specific surface area increment and the calibration coefficients to obtain the predicted erosion rate. Obtaining the predicted erosion rate in Step S4 includes: performing particle size analysis on the particles collected at each stage to obtain the particle size distribution after erosion, and calculating the particle breakage rate. Particle size peak offset Construct an initial erosion rate prediction model: ,in, To predict the erosion rate, The surface hardness of the test piece. For particle shape factor, For the erosion angle, This is a function of the erosion angle. Particle impact velocity, For speed index, The velocity recovery coefficient, Particle density, For particle breakage rate, This represents the peak particle size offset. This represents the increase in specific surface area. Step S5: Calculate the deviation between the predicted erosion rate and the theoretical erosion rate, use the recursive least squares method for online parameter identification, and combine the sliding window and variable forgetting factor mechanism to optimize the initial erosion rate prediction model and generate an erosion correction model adapted to the current working conditions.

2. The erosion modeling method based on particle classification collection and quantitative characterization of breakage rate according to claim 1, characterized in that, Step S1 includes: The initial physical state data of the test specimen is obtained. Uneroded original particle samples are taken and hydroponic dispersion treatment is performed on the original particle samples. The original particle samples after dispersion treatment are detected by image particle size analysis equipment to directly obtain the initial particle size distribution function before erosion.

3. The erosion modeling method based on particle classification collection and quantitative characterization of breakage rate according to claim 1, characterized in that, Step S2 employs a multi-stage collection device to acquire segmented mass data for different particle size ranges, including: The negative pressure collection mechanism located on the side is activated to capture fine particles in a suspended state and generate the first segment of mass data; The directional micro-negative pressure collection mechanism, located inside the sealed protective structure, is activated to guide and collect the main broken particles, generating the second segment mass data. Using a gravity settling collection mechanism located at the bottom, unbroken large-diameter particles falling under gravity are collected to generate third-segment mass data. By summing the first segment quality data, the second segment quality data, and the third segment quality data, segment quality data for different particle size ranges are obtained.

4. The erosion modeling method based on particle classification collection and quantitative characterization of breakage rate according to claim 1, characterized in that, Step S2, which calculates the increase in specific surface area before and after erosion, includes: Obtain particle samples corresponding to the segmented mass data of different particle size ranges, and perform hydroponic dispersion treatment on each segment of particles after graded recovery; The dispersed particles were detected using an image particle size analysis device, and the particle size distribution function corresponding to each segment was obtained. The particle size distribution functions of each segment were then weighted and merged according to the proportions of the mass data of the first, second, and third segments to obtain the overall particle size distribution function after erosion. ; The increase in specific surface area before and after particle erosion is calculated based on the first formula. The first formula is: ,in Particle density, and These represent the lower and upper limits of the particle size detection range, respectively, where d is the particle size. V represents the total surface area added after the particles are broken, and V is the total volume of the particles. This is the initial particle size distribution function before erosion.

5. The erosion modeling method based on particle classification collection and quantitative characterization of breakage rate according to claim 1, characterized in that, Step S3, which calculates the energy consumption of particle crushing based on crushing theory, includes: Applying von Rittinger's theory, a direct proportional mathematical relationship is established between crushing energy consumption and the increase in particle surface area: ,in, This indicates the energy consumption of particle crushing. This represents the crushing energy constant extracted in advance through calibration under no-crushing conditions. This represents the total surface area added after the particles are broken.

6. The erosion modeling method based on particle classification and quantitative characterization of breakage rate according to claim 1, characterized in that, Step S4 involves determining the calibration coefficients by fitting experimental data under non-crushing conditions, including: The initial values ​​of the reference constant C related to the material of the test specimen and the particle material were determined by fitting experimental data under non-fracture conditions. The first fracture correction coefficient was determined by fitting multiple erosion test data under fracture conditions, with the objective of minimizing the sum of squared deviations between the theoretical and predicted erosion rates. Second breakage correction coefficient Third breakage correction coefficient and the fourth breakage correction factor The initial value.

7. The erosion modeling method based on particle classification and quantitative characterization of breakage rate according to claim 1, characterized in that, Step S5 includes: After each erosion experiment, the deviation between the predicted erosion rate and the theoretical erosion rate is calculated; The recursive least squares method is used to dynamically adjust the crushing correction coefficient in the initial erosion rate prediction model with the goal of minimizing the sum of squares of the deviations, so that the initial erosion rate prediction model can learn the crushing characteristics of the current particle batch and working conditions. Set up a sliding window, discard the oldest data when new experimental data enters the window, and re-identify the fragmentation correction coefficient based on the data in the window; A variable forgetting factor is introduced, which is automatically reduced when the deviation of multiple consecutive experiments exceeds a preset threshold, so as to accelerate the model's adaptation speed to new working conditions. The initial erosion rate prediction model, after the above online parameter identification and model adaptive update, is output as the erosion correction model.

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