A semi-mill liner plate design method based on agent model and multi-objective optimization
By using a proxy model and multi-objective optimization method, the design of the semi-autogenous mill liner was optimized, which solved the problem of multi-objective conflict in traditional design, and achieved synergistic optimization of liner life and grinding efficiency, thus improving design efficiency and effectiveness.
Patent Information
- Application Number
- CN202610332481.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-18
- Publication Date
- 2026-06-02
Smart Images
Figure CN122133509A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of mineral processing engineering technology, and in particular to a design method for semi-autogenous mill liners based on surrogate models and multi-objective optimization. Background Technology
[0002] A semi-autogenous mill (SAM) is a large-scale engineering equipment used in mineral processing and crushing. Large volumes of ore are lifted to a high position inside the mill by the liners, then fall, where they are crushed into smaller particles under their own weight and the impact of other ores and abrasives, achieving the purpose of crushing. During this process, the SAM liners bear the responsibility of lifting the ore and abrasives, and also withstand most of the impact from the ore and abrasives, protecting the mill from damage. Under the combined action of friction and impact, the SAM liners wear down and gradually thin, the interface shape of the lifting bars changes, and the ability of the liners to lift ore and abrasives is weakened. Timely maintenance and replacement are necessary to ensure the stable grinding efficiency of the SAM. The SAM needs to be stopped during liner replacement, and frequent shutdowns can significantly impact production efficiency. Therefore, improving liner life is crucial for improving production efficiency. Currently, besides changing the liner material, adjusting the liner structural parameters is the main way to improve liner life.
[0003] In terms of structural parameter optimization, existing technologies mainly employ the following approaches: One approach involves establishing a mechanical model to analyze specific physical phenomena and then optimizing a single structural parameter. For example, some studies have established a mechanical model of particle clamping phenomena to analyze the influence of the liner lifting strip angle on the critical clamping force, thereby determining the optimal angle parameter of the liner. This type of method primarily focuses on single-objective optimization of specific physical phenomena, falling under the category of single-factor analysis. It is difficult to comprehensively consider the interaction between multiple structural parameters and their synergistic impact on multiple performance indicators.
[0004] Another technical approach is to simulate the liner wear process using discrete element method (DEM) simulation and adjust the liner thickness based on the wear distribution. For example, some methods use DEM simulation to obtain the liner's wear volume along the axial and radial directions, and then redistribute the liner volume in each region based on the wear amount to achieve an equal-life design for the liner. While these methods consider the spatial distribution characteristics of wear, their design is based on a single simulation result, lacking explicit modeling of the mapping relationship between structural parameters and performance indicators, and also unable to handle the conflicts and trade-offs between multiple optimization objectives.
[0005] However, the structural parameters of the cylinder liner are complex and diverse. Adjusting these parameters not only affects the liner's lifespan but also its lifting capacity and the overall energy consumption of the semi-autogenous mill. Traditional single-objective optimization methods or empirical trial-and-error methods struggle to find the optimal balance between multiple conflicting objectives and fail to adequately consider the coupling effects of multiple parameters. Consequently, the design results often rely on the accumulated experience of engineers, resulting in long optimization cycles and low efficiency.
[0006] Therefore, there is an urgent need for a semi-autogenous mill cylinder liner optimization design method that can comprehensively consider multiple structural parameters and multiple performance indicators, and effectively handle the conflicting relationships between objectives, so as to achieve synergistic optimization of liner life, grinding efficiency and manufacturing cost. Summary of the Invention
[0007] The purpose of this invention is to provide a semi-autogenous mill liner design method based on surrogate model and multi-objective optimization to solve the problems mentioned in the background art.
[0008] To achieve the above objectives, this invention provides a semi-autogenous mill liner design method based on a surrogate model and multi-objective optimization, comprising the following steps: S1. Determine multiple target parameters for liner structure optimization, including liner life index, grinding efficiency index, and manufacturing cost index; simultaneously, select multiple geometric structural parameters of the liner as optimization factors, and determine the value range of each optimization factor. S2. Using experimental design method, sample points are generated within the range of the values, and corresponding discrete element simulation models are established based on the sample points. When establishing the discrete element simulation model, only the geometric structure parameters that serve as optimization factors are changed, while other non-optimized geometric structure parameters and all simulation running parameters are set to the same value. The response values of the multiple target parameters under each sample point are obtained through discrete element simulation calculation. S3. Based on the sample points and their corresponding response values, construct a proxy model to describe the nonlinear mapping relationship between the optimization factor and the target parameter. After constructing the proxy model, perform an accuracy test on the proxy model. If the test result does not meet the preset accuracy requirements, update the proxy model by adjusting the proxy model type, adding sample points, or correcting the model parameters until the accuracy requirements are met. S4. Using the surrogate model as the fitness function, construct a multi-objective optimization mathematical model with the primary optimization objective as the optimization function and the secondary optimization objective as the constraint condition, and use a multi-objective evolutionary algorithm to iteratively optimize the surrogate model to obtain a set of Pareto optimal solutions that satisfy the constraint conditions; S5. Select a set of structural parameters from the Pareto optimal solution set, and construct a three-dimensional model of the semi-autogenous mill cylinder liner based on the selected structural parameters.
[0009] Preferably, the liner life index in S1 is calculated using the following formula, which quantifies the liner life: ; in, For the lifespan of the liner, For the allowable wear coefficient, For the total volume of the liner, The wear volume of the liner is obtained based on the Archard Wear model; Grinding efficiency is quantified using ore collision energy, and the calculation formula is as follows: ; in, For ore collision energy, For the first The collision energy of individual particles. For the first The relative collision velocity of each particle. The total number of particles; Manufacturing cost indicators are measured by the total volume of the liner. Quantify it.
[0010] Preferably, the optimization factors selected in S1 include the lifting strip face angle, the thickness of the lifting surface liner substrate, the thickness of the non-lifting surface liner substrate, the total height of the liner, and the width of the top surface of the lifting strip.
[0011] Preferably, the simulation operation parameters in S2 include the semi-autogenous mill speed, overall filling rate, ore filling rate, steel ball filling rate, as well as the mechanical properties and contact parameters of the ore, steel balls, and liner materials.
[0012] Preferably, the surrogate model in S3 is a response surface model, and the mathematical expression of the surrogate model is in quadratic polynomial form, as follows: ; in, For the constructed approximate function, for Dimensional independent design variables, To optimize the number of factors, These are constant coefficients. The coefficients of a first-order polynomial, and These are the coefficients of a quadratic polynomial.
[0013] Preferably, the main optimization objective of S4 is to maximize the liner life. The overall liner life is determined by the side with the shorter life between the lifting side and the non-lifting side, as shown in the following mathematical expression: ; The secondary optimization objective is to minimize the manufacturing cost of the liner, which is determined by the total volume of the liner. Quantification, the mathematical expression is as follows: ; in, For the allowable wear coefficient, To increase the volume of the lining substrate, For the non-lifting surface liner substrate volume, To increase the wear of the lining plate substrate, This refers to the wear amount of the non-lifting surface liner substrate. This is the time coefficient.
[0014] Preferably, the constraints in S4 include: ; ; in, The particle collision energy that the optimized liner can generate. The particle collision energy of the original liner. The optimized liner is subjected to particle collision energy. This represents the particle collision energy experienced by the original liner. The formula for calculating the collision energy of particles on the liner is: ; in, The impact energy received by the liner plate For the mass of the colliding particles, This represents the relative collision velocity.
[0015] Preferably, the multi-objective evolutionary algorithm in S4 is the NSGA-II algorithm.
[0016] Preferably, it also includes S6, performing discrete element simulation verification based on the three-dimensional model constructed in S5, and comparing the changes in the life index, grinding efficiency index and manufacturing cost index of the liner before and after optimization.
[0017] Therefore, the semi-autogenous mill liner design method based on surrogate model and multi-objective optimization described above has the following beneficial effects: (1) This invention addresses the multi-objective conflict problem in the design of semi-autogenous mill cylinder liners by combining a surrogate model with a multi-objective optimization algorithm, which can simultaneously optimize multiple conflicting performance indicators. By constructing a Pareto optimal solution set, a set of balanced solutions is provided for designers to choose from, and the optimal design scheme can be flexibly selected according to actual needs, overcoming the shortcomings of traditional single-factor analysis or empirical trial and error methods that are difficult to take into account multiple performance indicators.
[0018] (2) This invention employs surrogate model techniques such as response surface methodology to construct an explicit mathematical relationship between optimization factors and target parameters based on a finite number of discrete element simulations, thus avoiding the need for repeated, time-consuming discrete element simulations during the optimization iteration process. The surrogate model can accurately reflect the nonlinear mapping relationship and interaction between optimization factors and target parameters, significantly improving optimization efficiency while ensuring computational accuracy.
[0019] (3) This invention uses variance analysis to test the goodness of fit of the surrogate model to ensure that the model accuracy meets the requirements; after optimization, a verification step is set to verify the actual effect of the optimization scheme through discrete element simulation. The results of the embodiments show that the liner life optimized by the method of this invention is 20.19% higher than that of the original liner, while the grinding efficiency and liner stress meet the preset constraints, proving the effectiveness and reliability of this invention.
[0020] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description
[0021] Figure 1 This is a flowchart of a semi-autogenous mill liner design method based on surrogate model and multi-objective optimization according to the present invention. Figure 2 This is a cross-sectional view of the semi-autogenous grinding mill cylinder liner according to an embodiment of the present invention; Figure 3 This is the initial cylindrical liner model of an embodiment of the present invention; Figure 4 This is a Pareto front diagram for multi-objective optimization in an embodiment of the present invention. Detailed Implementation
[0022] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely illustrates selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.
[0023] Example like Figure 1 As shown, this invention provides a semi-autogenous mill liner design method based on a surrogate model and multi-objective optimization, comprising the following steps: S1. Based on the actual production needs of the semi-autogenous mill, determine multiple target parameters for liner structure optimization. These multiple target parameters include liner life index, grinding efficiency index, and manufacturing cost index. The optimization objective of this embodiment is to improve liner life and reduce manufacturing cost while ensuring grinding efficiency. At the same time, select multiple geometric structural parameters of the liner as optimization factors and determine the value range of each optimization factor. The liner life index is quantified by the liner life, and the calculation formula is as follows: ; in, For the lifespan of the liner, The allowable wear coefficient is determined based on the liner material and safety requirements. For the total volume of the liner, This is the liner wear volume obtained based on the Archard Wear model; this formula reflects that the overall liner life is determined by the area that wears the fastest (i.e., has the shortest life).
[0024] Grinding efficiency is quantified using ore collision energy, and the calculation formula is as follows: ; in, For ore collision energy, For the first The collision energy of individual particles. For the first The relative collision velocity of each particle. The total number of particles; the greater the ore collision energy, the stronger the impact between particles, and the better the grinding effect.
[0025] Manufacturing cost indicators are measured by the total volume of the liner. Quantification is carried out; given a fixed liner material, the liner volume is directly proportional to the manufacturing cost.
[0026] In addition, to ensure that the optimized liner is not damaged by excessive force, the collision energy of particles on the liner also needs to be considered, and its calculation formula is as follows: ; in, The impact energy received by the liner plate For the mass of the colliding particles, This represents the relative collision velocity.
[0027] like Figure 2 As shown, the cross-sectional structural parameters of the semi-autogenous grinding mill cylinder liner mainly include the lifting bar face angle θ, the liner substrate thickness h, the liner height L, and the lifting bar top surface width W. These parameters all affect the aforementioned target parameters, and therefore, these structural parameters are used as optimization factors. Among them: The lifting bar face angle θ is the angle between the working surface of the lifting bar and the vertical line, which affects the lifting height and drop position of the ore and abrasive. Based on existing research results and production practice, the design range of the lifting bar face angle θ is selected to be between 20° and 40°.
[0028] The thickness h of the liner substrate is the vertical distance from the top surface to the bottom surface of the substrate. During the operation of the semi-autogenous grinding mill, the cylinder rotates unidirectionally. The side of the lifting bar that lifts the particles is the lifting surface, and the opposite side is the non-lifting surface. The side of the liner substrate that shares the same surface as the lifting surface is the lifting surface side, and the side that shares the same surface as the non-lifting surface is the non-lifting surface side. The lifting surface side experiences greater wear and impact, therefore it needs to be designed separately from the non-lifting surface side. Based on existing research and production practice, the thickness h of the liner substrate on the lifting surface is determined... Non-lifting liner substrate thickness Each of these factors is used as an optimization factor, with a design range between 50mm and 130mm.
[0029] The liner height L is the vertical distance from the bottom surface of the liner substrate to the top surface of the lifting bar. The difference between L and the liner substrate thickness is the lifting bar height. The lifting bar height affects the liner's ability to lift ore and abrasive, changing the height and angle of the impact point. Based on existing research and production practice, the design range for the liner height is set between 210mm and 360mm.
[0030] The width W of the top surface of the lifting bar affects the lifting volume of the liner, thus altering the liner's lifting capacity for ore and abrasive. Based on existing research and production practice, the design range for the lifting bar width is between 100mm and 200mm.
[0031] In summary, this embodiment selects five optimization factors: lifting strip angle θ, lifting surface liner substrate thickness, etc. Non-lifting surface liner substrate thickness Liner height L, lifting bar top surface width W.
[0032] S2. Using experimental design methods, sample points are generated within the specified value range, and corresponding discrete element simulation models are established based on the sample points. When establishing the discrete element simulation model, only the geometric structure parameters used as optimization factors are changed, while other non-optimized geometric structure parameters and all simulation operation parameters are set to the same value. The response values of the multiple target parameters at each sample point are obtained through discrete element simulation calculation.
[0033] The Box-Behnken design (BBD) method from the response surface methodology was used for experimental design. This method can effectively estimate the primary effect, secondary effect, and interaction between factors with a small number of trials, providing the necessary sample points for subsequent construction of surrogate models.
[0034] The five optimization factors mentioned above are represented by A, B, C, D and E respectively, and three levels are set as shown in Table 1. Among them, -1, 0 and 1 correspond to the low, medium and high levels of each optimization factor respectively.
[0035] Table 1 Levels of BBD Response Variables
[0036] Based on the BBD design, 46 experimental schemes were generated, as shown in Table 2. Table 2 lists the combination of encoding levels for each optimization factor in the 46 experimental schemes. These combinations cover the key sample points in the design space and will serve as input conditions for subsequent discrete element simulations. These 46 experimental schemes cover the key sample points in the design space and can provide sufficient training data for the construction of subsequent surrogate models.
[0037] Table 2 BBD Experimental Design
[0038] To reduce computational costs, a cylindrical slice model is used for discrete element simulation, such as... Figure 3 As shown, the slice thickness was set to 500 mm (more than three times the maximum particle diameter to ensure the rationality of the simulation). When establishing the discrete element simulation model, only the geometric structure parameters used as optimization factors were changed, while other non-optimized geometric structure parameters and all simulation running parameters were set to the same value to ensure the comparability of simulation results.
[0039] The various material mechanical properties and contact parameters required for simulation were obtained through experimental determination, as shown in Table 3 (taking the relevant parameters of a certain type of semi-autogenous mill as an example). These parameters define the physical properties of the ore, steel balls, and liner materials, as well as their contact behavior, and are the basis for the discrete element simulation to accurately simulate actual working conditions.
[0040] Table 3 Mechanical property parameters of ore, steel balls and lining plates
[0041] When the semi-autogenous mill is running normally, the rotation speed is 10.6 rpm and the overall filling rate is 28%, of which steel balls account for 11% and ore accounts for 17%. The ratio of steel balls to ore media is shown in Table 4. This table defines the types, sizes and corresponding total masses of particles to be generated in the simulation, ensuring that the media distribution in the simulation is consistent with the actual working conditions.
[0042] Table 4 Medium Quality
[0043] The semi-autogenous mill speed, overall filling rate, ore filling rate, and steel ball filling rate set above, along with the material properties, contact parameters, and media ratios listed in Tables 3 and 4, together constitute all the operating parameters for this discrete element simulation. All 46 experimental schemes were conducted under these same simulation operating parameters to ensure the comparability of results for each sample point.
[0044] Discrete element simulation was performed according to the 46 test schemes shown in Table 2 to obtain the total volume of the liner at each sample point. Increase the volume of the lining substrate. Non-lifting surface liner substrate volume , increase bar volume And increase the wear of the surface liner substrate within a set time. Non-lifting surface liner substrate wear amount Impact energy of the lining plate Ore collision energy The simulation results, along with the semi-autogenous mill speed, overall filling rate, ore filling rate, steel ball filling rate, and the mechanical properties and contact parameters of the ore, steel balls, and liner materials listed in Table 3, constitute all the operating parameters for this discrete element simulation. All 46 experimental schemes were conducted under the same simulation operating parameters to ensure the comparability of results for each sample point.
[0045] The experimental data are shown in Table 5. Each set of data in Table 5 corresponds to the simulation output of a certain experimental scheme in Table 2. These data will be used as training samples for the subsequent construction of the surrogate model.
[0046] Table 5 Experimental Data
[0047] S3. Based on the sample points and their corresponding response values, construct a surrogate model to describe the nonlinear mapping relationship between the optimization factors and the target parameters. Based on the 46 sets of experimental data shown in Table 5, a quadratic polynomial response surface model is used to construct the mapping relationship between each target parameter and the optimization factors. Specifically, the optimization factors (A, B, C, D, E) in Table 2 are used as input variables, and the response quantities in Table 5 are used as input variables. , , , , , , , Using these variables as output variables, a surrogate model is constructed through multivariate regression fitting. The surrogate model is a response surface model, and its mathematical expression is in quadratic polynomial form, as follows: ; in, For the constructed approximate function, for Dimensional independent design variables, To optimize the number of factors, These are constant coefficients. The coefficients of a first-order polynomial, and The coefficients are quadratic polynomials. Characterizing the second-order effects of design variables, This model characterizes the interaction effects between different design variables. It can fit nonlinear relationships well and explicitly express the mathematical relationship between inputs and outputs, providing a fitness function for rapid computation in subsequent optimization.
[0048] The results shown in Table 5 were fitted with a quadratic polynomial to construct regression equations between each simulation result and different structural parameters.
[0049] Total volume of lining plate The regression equation is: ; Increase the volume of the lining plate substrate The regression equation is: ; Non-lifting surface liner substrate volume The regression equation is: ; Increase bar volume The regression equation is: ; Increase the wear of the surface liner substrate The regression equation is: ; Non-lifting surface liner substrate wear The regression equation is: ; Impact energy of the liner The regression equation is: ; Ore collision energy The regression equation is: ; Analysis of variance was performed on the above regression equations, and the results showed that all the regression models had good goodness of fit, and the R-squared values of each surrogate model were [missing data]. 2 The values are all greater than 0.9, indicating that the model has good fitting accuracy and can accurately reflect the nonlinear mapping relationship between the optimization factor and the target parameter. If the goodness of fit of a surrogate model does not meet the preset accuracy requirement, the surrogate model is updated by increasing the number of sample points, introducing higher-order terms, or using a hybrid model until the accuracy requirement is met.
[0050] Thus, based on the experimental schemes designed in Tables 1 and 2, the simulation parameters set in Tables 3 and 4, and the simulation results data in Table 5, surrogate models that can be used for subsequent multi-objective optimization have been successfully constructed. These surrogate models will serve as the fitness functions for multi-objective optimization in S4, enabling rapid calculation of response values at any design point.
[0051] S4. Using the surrogate model as the fitness function, construct a multi-objective optimization mathematical model with the primary optimization objective as the optimization function and the secondary optimization objective as the constraint condition, and use a multi-objective evolutionary algorithm to iteratively optimize the surrogate model to obtain a set of Pareto optimal solutions that satisfy the constraint conditions.
[0052] Based on the optimization objective of "increasing the service life of the liner and reducing manufacturing costs while ensuring grinding efficiency," two optimization goals are determined: The primary optimization objective is to maximize the liner life. Considering that the overall liner life is determined by the shorter life of the lifting side and the non-lifting side (i.e., the weakest link determines the overall life), a min function is used to characterize the overall life, and the mathematical expression is as follows: ; in, The allowable wear coefficient is set at 0.8 in this embodiment based on the liner material and safety requirements. To increase the volume of the lining substrate, For the non-lifting surface liner substrate volume, To increase the wear of the lining plate substrate, This refers to the wear amount of the non-lifting surface liner substrate. The time coefficient is used to convert the wear amount within the simulation time into the daily wear amount (in this embodiment, the wear data of 28 sets of liners over 24 seconds is converted into the daily wear amount of a single liner, which is taken as 128.57). This formula calculates the lifespan of both sides separately and takes the smaller value as the measure of the overall lifespan. The optimization algorithm will pursue this minimum value as large as possible, that is, maximize the lifespan of the weak side.
[0053] The secondary optimization objective is to minimize the manufacturing cost of the liner, which is determined by the total volume of the liner. Quantification, the mathematical expression is as follows: .
[0054] To ensure that the optimized liner does not reduce grinding efficiency or become damaged due to excessive stress, the following constraints are set: ; ; in, The particle collision energy that the optimized liner can generate. The particle collision energy of the original liner. The optimized liner is subjected to particle collision energy. This represents the particle collision energy experienced by the original liner.
[0055] The surrogate model constructed in step S3 is used as the fitness function, that is, the fitness function corresponding to any design point is quickly calculated through the surrogate model. , , , , , , Equivalent, thus obtaining , The constraints were defined. Using MATLAB software, the NSGA-II algorithm was employed to iteratively optimize the aforementioned multi-objective optimization mathematical model. The NSGA-II algorithm is an elite strategy genetic algorithm based on non-dominated sorting, suitable for low-dimensional multi-objective optimization problems. The algorithm parameters were set as follows: population size of 100, maximum number of iterations of 200, crossover probability of 0.9, and mutation probability of 0.1.
[0056] Through iterative calculations, a set of Pareto optimal solutions satisfying the constraints is obtained. The Pareto front is as follows: Figure 4 As shown in the figure, the horizontal axis represents the liner lifetime (first objective), and the vertical axis represents the liner volume (second objective). The figure reveals a clear conflict between lifetime and volume—an increase in lifetime is usually accompanied by an increase in volume, which validates the necessity of multi-objective optimization.
[0057] Based on the focus of this optimization (improving service life), a set of solutions with a similar volume to the original liner and a significantly improved service life was selected as the final design scheme. The optimized structural parameters are shown in Table 6. Table 6 lists a set of parameter values selected from the Pareto optimal solution obtained through multi-objective optimization. These parameters are the basis for the optimized liner structure design.
[0058] Table 6. Liner structure parameters after genetic algorithm optimization
[0059] Rounding the above parameters, we obtain the actual manufacturable structural parameters: lifting strip face angle θ = 28°, lifting face liner substrate thickness. =105mm, thickness of non-lifting surface liner base plate =100mm, total height of liner L=270m, width of lifting bar W=110mm.
[0060] S5. Select a set of structural parameters from the Pareto optimal solution set, and construct a three-dimensional model of the semi-autogenous grinding mill cylinder liner based on the partially rounded structural parameters selected in S4. This model is used to manufacture the liner with optimized structural parameters. The three-dimensional model constructed in this step can be directly used to guide the actual production and manufacturing of the liner.
[0061] S6. Based on the three-dimensional model constructed in S5, use EDEM software to perform discrete element simulation verification. The simulation parameters are kept consistent with those in S2. Based on the simulation results, apply the life formula again to calculate the life of the optimized liner and compare the changes in the life index, grinding efficiency index, and manufacturing cost index of the liner before and after optimization.
[0062] The calculation results show that the lifespan of the original liner is expected to be 213 days, while the lifespan of the optimized liner is expected to be 256 days, an increase of 20.19%. At the same time, the verification simulation shows that the ore collision energy of the optimized liner is no lower than that of the original liner, and the collision energy experienced by the liner is no higher than that of the original liner, thus meeting the preset constraints.
[0063] Therefore, the present invention adopts the above-mentioned semi-autogenous mill liner design method based on surrogate model and multi-objective optimization, which can effectively realize multi-objective collaborative optimization of semi-autogenous mill cylinder liner, significantly extend the service life of the liner while ensuring grinding efficiency, and control the manufacturing cost without significantly increasing it.
[0064] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.
Claims
1. A semi-autogenous mill liner design method based on surrogate model and multi-objective optimization, characterized in that, Includes the following steps: S1. Determine multiple target parameters for liner structure optimization, including liner life index, grinding efficiency index, and manufacturing cost index; simultaneously, select multiple geometric structural parameters of the liner as optimization factors, and determine the value range of each optimization factor. S2. Using experimental design method, sample points are generated within the range of the values, and corresponding discrete element simulation models are established based on the sample points. When establishing the discrete element simulation model, only the geometric structure parameters that serve as optimization factors are changed, while other non-optimized geometric structure parameters and all simulation running parameters are set to the same value. The response values of the multiple target parameters under each sample point are obtained through discrete element simulation calculation. S3. Based on the sample points and their corresponding response values, construct a proxy model to describe the nonlinear mapping relationship between the optimization factor and the target parameter. After constructing the proxy model, perform an accuracy test on the proxy model. If the test result does not meet the preset accuracy requirements, update the proxy model by adjusting the proxy model type, adding sample points, or correcting the model parameters until the accuracy requirements are met. S4. Using the surrogate model as the fitness function, construct a multi-objective optimization mathematical model with the primary optimization objective as the optimization function and the secondary optimization objective as the constraint condition, and use a multi-objective evolutionary algorithm to iteratively optimize the surrogate model to obtain a set of Pareto optimal solutions that satisfy the constraint conditions; S5. Select a set of structural parameters from the Pareto optimal solution set, and construct a three-dimensional model of the semi-autogenous mill cylinder liner based on the selected structural parameters.
2. The semi-autogenous mill liner design method based on surrogate model and multi-objective optimization according to claim 1, characterized in that, The liner life index in S1 is calculated using the following formula, which quantifies the liner life: ； in, For the lifespan of the liner, For the allowable wear coefficient, For the total volume of the liner, The wear volume of the liner is obtained based on the Archard Wear model; Grinding efficiency is quantified using ore collision energy, and the calculation formula is as follows: ； in, For ore collision energy, For the first The collision energy of individual particles. For the first The relative collision velocity of each particle. The total number of particles; Manufacturing cost indicators are measured by the total volume of the liner. Quantify it.
3. The semi-autogenous mill liner design method based on surrogate model and multi-objective optimization according to claim 1, characterized in that: The optimization factors selected in S1 include the lifting strip face angle, the thickness of the lifting face liner substrate, the thickness of the non-lifting face liner substrate, the total height of the liner, and the width of the lifting strip top surface.
4. The semi-autogenous mill liner design method based on surrogate model and multi-objective optimization according to claim 1, characterized in that: The simulation parameters in S2 include the semi-autogenous mill speed, overall filling rate, ore filling rate, steel ball filling rate, as well as the mechanical properties and contact parameters of the ore, steel balls, and liner materials.
5. The semi-autogenous mill liner design method based on surrogate model and multi-objective optimization according to claim 1, characterized in that: The surrogate model in S3 is a response surface model, and its mathematical expression is in quadratic polynomial form, as follows: ； in, For the constructed approximate function, for Dimensional independent design variables, To optimize the number of factors, These are constant coefficients. The coefficients of a first-order polynomial, and These are the coefficients of a quadratic polynomial.
6. The semi-autogenous mill liner design method based on surrogate model and multi-objective optimization according to claim 1, characterized in that, The main optimization objective of S4 is to maximize the liner life. The overall liner life is determined by the shorter life of the lifting side and the non-lifting side, as shown in the following mathematical expression: ； The secondary optimization objective is to minimize the manufacturing cost of the liner, which is determined by the total volume of the liner. Quantification, the mathematical expression is as follows: ； in, For the allowable wear coefficient, To increase the volume of the lining substrate, For the non-lifting surface liner substrate volume, To increase the wear of the lining plate substrate, This refers to the wear amount of the non-lifting surface liner substrate. This is the time coefficient.
7. The semi-autogenous mill liner design method based on surrogate model and multi-objective optimization according to claim 5, characterized in that, The constraints in S4 include: ； ； in, The particle collision energy that the optimized liner can generate. The particle collision energy of the original liner. The optimized liner is subjected to particle collision energy. This represents the particle collision energy experienced by the original liner. The formula for calculating the collision energy of particles on the liner is: ； in, The impact energy received by the liner plate For the mass of the colliding particles, This represents the relative collision velocity.
8. The semi-autogenous mill liner design method based on surrogate model and multi-objective optimization according to claim 1, characterized in that: The multi-objective evolutionary algorithm in S4 is the NSGA-II algorithm.
9. The semi-autogenous mill liner design method based on surrogate model and multi-objective optimization according to claim 1, characterized in that: It also includes S6, and discrete element simulation verification based on the three-dimensional model constructed from S5, comparing the changes in the life index, grinding efficiency index and manufacturing cost index of the liner before and after optimization.