An agitator ball mill and related design method

Abstract

The application discloses a kind of agitator ball mill and related design method, and the application relates to the technical field of powder grinding equipment, solve the technical problem that high power consumption, low grinding efficiency caused by dead material area of ball mill, the stirring rod rotating with mill is arranged in dead material area, the material in dead material area is forced to stir, eliminate invalid energy consumption, improve the falling frequency and grinding uniformity of material, to realize energy saving and consumption reduction, and combined with digital simulation design method, precise activation of dead material area is realized, a simulation model of ball mill grinding process is established based on discrete element method, the velocity vector field of particles in the cross section of cylinder is monitored, the threshold value is determined adaptively using velocity distribution histogram, the boundary of dead material area is accurately identified, compared with prior art, the positioning method provided by the application has repeatability and quantification characteristics, which provides an objective basis for determining the installation radius, length and number of stirring rods.

Description

Technical Field

[0001] This invention relates to the field of grinding equipment technology, specifically to a stirred ball mill and related design methods. Background Technology

[0002] Ball mills are widely used equipment in material grinding processes. Due to their simple structure and reliable operation, they are used in various industries such as cement, mining, and metallurgy. Taking cement production as an example, the electricity consumption per ton of cement is approximately 20-30 kWh, of which the ball mill accounts for about 10 kWh / t, making it the main energy-consuming link in the production process. The working principle of a ball mill is as follows: the cylinder rotates, and the internal liner lifts the grinding media (steel balls) to a certain height. Subsequently, the grinding media fall or cascade down under gravity, achieving material crushing through impact, compression, and grinding.

[0003] In actual operation, the material movement within the ball mill cylinder is not uniform. Material adjacent to the liners is propelled by friction, rising with the cylinder and participating in the impact crushing process. However, in areas far from the liners, the material lacks sufficient friction and often remains relatively stationary or slides at low speed; this area is known as the dead material zone. Since the filling rate of ball mills is typically 30% or higher, the dead material zone occupies a significant portion of the cylinder volume. Material in the dead material zone hardly participates in the high-energy impact crushing process, resulting in extremely low grinding efficiency and a large amount of wasted electrical energy. To grind the material in the dead material zone more finely, it is often necessary to extend the grinding time or increase the rotation speed, further increasing energy consumption. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a stirred ball mill and related design methods, which solves the problems of high power consumption and low grinding efficiency caused by the presence of dead material zones in ball mills.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solution: a stirring ball mill, comprising a ball mill body and a shell 1, wherein a cylinder is provided inside the shell 1, characterized in that a ball mill liner 2 is installed on the inner wall of the cylinder, and multiple stirring rods 3 are welded and installed on a partition plate 4 located between the feed end and the discharge end inside the cylinder, the stirring rods 3 extend along the axial direction of the cylinder, and the stirring rods 3 are staggered in the circumferential direction of the cylinder; Within the same cross-section of the cylinder, the included angles between adjacent stirring rods are not completely equal, and they are arranged in an alternating pattern of large and small intervals. In the axial direction, the length of the stirring rods is flexibly adjusted according to the size of each compartment.

[0006] A design method for an agitated ball mill, the method specifically includes the following steps: The target ball mill's operating parameters include grinding media filling rate, cylinder rotation speed, design output, feed particle size distribution, and grinding media gradation. A three-dimensional geometric model is established based on the actual geometric dimensions of the ball mill. A simulation model of the grinding process is established based on the discrete element method. The operating parameters are input, the simulation is run, and the velocity vector field of the particles in the cross-section of the cylinder is recorded. Set a speed threshold, mark the continuous area with speed below the threshold as the dead zone, determine the radial position, axial length range and circumferential distribution angle of the dead zone, and thus determine the installation radius of the agitator on the partition plate, the length of the agitator, and the number of agitators that need to be set. Determine the ball mill filling rate, cylinder rotation speed, stirring rod installation radius, number of stirring rods, and stirring rod length; A multi-objective optimization function is established with the objectives of maximizing grinding efficiency and minimizing power consumption per unit product, and constraints are set. A second-order response surface model was constructed using experimental design and response surface methodology. This model was then used as the fitness function of a genetic algorithm to perform multi-objective optimization and obtain the Pareto optimal solution set. Select the final solution from the Pareto optimal solution set, and manufacture and install the stirring rod according to the solution.

[0007] As a further aspect of the present invention, the method for determining the speed threshold is as follows: The tangential velocity values ​​of all particles within the cross-section of the cylinder are statistically analyzed, a velocity distribution histogram is plotted, the local minimum value of the velocity distribution curve is found, and the velocity value corresponding to the local minimum value is used as the dead material zone identification threshold.

[0008] As a further aspect of the present invention, the multi-objective optimization function is: Where X is the design variable vector, The grinding efficiency is E, and the power consumption per unit product is E. and These are the weighting coefficients.

[0009] As a further aspect of the present invention, the design variable vector ,in To improve the filling efficiency of the ball mill , Let n be the rotational speed of the ball mill. The installation radius R of the ball mill stirring rod. Let N be the number of stirring rods. The length of the stirring rod ; Unit product power consumption , where Q is the output.

[0010] As a further aspect of the present invention, the constraints include: Structural constraints , For safety clearance, The inner radius of the cylinder is minus the liner thickness; N must be an integer and within a reasonable range; process constraints: , Performance constraints: .

[0011] As a further aspect of the present invention, the method of constructing a second-order response surface model using experimental design and response surface methodology is as follows: Using a central composite design or Box-Behnken design, M sample points are generated in the five-dimensional design space, with each sample point corresponding to a set of design variables. For each sample point, run a discrete element simulation once and record the corresponding grinding efficiency. Unit power consumption and the volume ratio of dead material area The simulation results were regressed using the least squares method to fit a second-order response surface model: Where y represents E or , For regression coefficients, This is the error term.

[0012] As a further aspect of the present invention, the method for obtaining the Pareto optimal solution set is as follows: The constructed response surface model is used as the fitness function of the genetic algorithm. Population size, crossover probability, and mutation probability are set. The population is sorted into layers according to the two objective function values. The Pareto optimal solution set is found. The tournament selection method is used to select the individuals with the highest Paretofronts and output the Pareto optimal solution set.

[0013] As a further aspect of the present invention, in discrete element simulation, the motion of each particle is described by Newton's equations of motion: Translation equations: Equation of rotation: in, Let i be the mass of particle i. Let be the translational velocity of particle i. and These represent the normal contact force and the tangential contact force between particle i and particle j, respectively. The force exerted by the gas on particle i It is the gravitational acceleration vector. Let be the moment of inertia of the particle. Let be the angular velocity of the particle. Let be the vector pointing from the center of the particle to the contact point. Let be the coefficient of rolling friction affected by particle i.

[0014] As a further aspect of the present invention, the simulation model of the grinding process based on the discrete element method includes: Normal contact force: Tangential force and sliding criterion: Equivalent Young's modulus: Equivalent radius: in For equivalent Young's modulus, For the equivalent radius, The normal overlap is... For equivalent quality, For relative normal velocity, The coefficient of recovery, For equivalent shear modulus, This is the tangential overlap. The relative tangential velocity, The coefficient of sliding friction is and Let be the radii of particles i and j.

[0015] This invention provides a stirred ball mill and related design methods. Compared with the prior art, it has the following advantages: This invention involves welding and installing multiple stirring rods inside the ball mill cylinder, on a partition plate located between the feed end and the discharge end. The stirring rods extend axially along the cylinder, and their ends are not suspended in the air but are supported by the surface of the liner plate on the inner wall of the cylinder. Specifically, the liner plate has protruding structures or reserved support grooves at local locations to support the ends of the stirring rods, preventing them from deforming or breaking due to gravity or material impact during high-speed rotation, thus ensuring the stability of the equipment operation.

[0016] This invention incorporates a stirring rod that rotates with the mill in the dead material zone, forcibly agitating the material there, eliminating ineffective energy consumption, and increasing the material drop frequency and grinding uniformity, thereby achieving energy saving and consumption reduction. Furthermore, it utilizes a digital simulation design method to precisely activate the dead material zone. A simulation model of the ball mill grinding process is established based on the discrete element method. By monitoring the velocity vector field of particles within the cross-section of the cylinder and using a velocity distribution histogram to adaptively determine the threshold, the boundary of the dead material zone is accurately identified. Compared to existing technologies, the positioning method provided by this invention is repeatable and quantifiable, providing an objective basis for determining the installation radius, length, and number of stirring rods.

[0017] This invention incorporates five variables—ball mill filling rate, cylinder rotation speed, stirring rod installation radius, number of stirring rods, and stirring rod length—into the optimization space simultaneously. A second-order polynomial surrogate model is constructed using the response surface methodology, avoiding the need for time-consuming discrete element simulations for each iteration, thus significantly reducing optimization computational costs. Based on this, a genetic algorithm is used for global optimization to obtain the Pareto optimal solution set, achieving an optimal balance between the two mutually constraining objectives of grinding efficiency and unit power consumption. Compared to existing technologies that only optimize steel ball gradation or liner shape, this invention's parameter space search design finds the globally optimal solution rather than a locally optimal one. Attached Figure Description

[0018] Figure 1 This is a front cross-sectional view of the geometric features of the agitated ball mill of the present invention; Figure 2 This is a side cross-sectional view of the geometric features of the agitated ball mill of the present invention; Figure 3 This is a flowchart illustrating the implementation of a design method for a stirred ball mill according to the present invention. The components include: 1. outer shell; 2. ball mill liner; 3. stirring rod; and 4. partition plate. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] First Embodiment Please see Figure 1 and Figure 2 This application provides a stirring ball mill, including a ball mill body and a shell 1. The shell 1 is provided with a cylinder, and a ball mill liner 2 is installed on the inner wall of the cylinder. Inside the cylinder, multiple stirring rods 3 are welded and installed on a partition plate 4 located between the feed end and the discharge end. The stirring rods 3 extend along the axial direction of the cylinder. The root of the stirring rod is welded to the side of the partition plate facing the discharge end or the side facing the feed end. The end of the stirring rod is not suspended, but is supported by the surface of the liner 2 on the inner wall of the cylinder. The liner 2 has a protruding structure or a reserved support groove at a local position. The protruding structure or the reserved support groove is used to support the end of the stirring rod 3 to prevent it from deforming or breaking due to gravity or material impact during high-speed rotation. To avoid excessive motor power fluctuations caused by all stirring rods being subjected to concentrated force at the same time, and to achieve complete coverage of the dead material zone, the stirring rods 3 are arranged in a staggered manner in the circumferential direction. Within the same cross-section of the cylinder, the included angle between adjacent stirring rods is not completely equal, but rather arranged in an alternating pattern of large and small intervals. This disperses the time points at which the stirring rods cut into the material during one rotation. In the axial direction, the length of the stirring rods is flexibly adjusted according to the size of each compartment. To achieve full-cycle coverage of the dead material zone, multiple stirring rods are evenly distributed in the circumferential direction. The specific number and size are controlled according to the specifications and filling rate of the ball mill. In mills with larger diameters, the number and width of the stirring rods can be appropriately increased. This design allows the stirring rods to cut into the dead material zone in stages and segments as the cylinder rotates, throwing and lifting the originally stationary material, making it participate in the collision and grinding with the grinding media, thereby reducing peak power and improving the fluidization effect of the material.

[0021] Second Embodiment Please see Figure 3 As a second embodiment of the present invention, implemented based on the first embodiment, this embodiment provides a design method related to agitated ball mills. The implementation steps of the discrete element simulation positioning method for the dead material zone specifically include: Step 1: Collect the operating parameters of the target ball mill, including grinding media filling rate, cylinder rotation speed, design output, feed particle size distribution, and grinding media gradation. Step 2: Based on the actual assembly dimensions of the ball mill, establish a three-dimensional geometric model. When establishing the cylindrical body geometric model, simplify the shape of the liner to a cylindrical surface with specific lifting bars. Set the cylinder to rotate around the central axis at a constant angular velocity. The grinding media are randomly generated at the bottom of the cylinder according to the set gradation and filling rate. The material particles are generated according to the feed particle size distribution and are initially evenly distributed in the gaps of the grinding media. The simulation time should be at least 10 rotations of the cylinder to ensure that the particle movement reaches dynamic stability. The model includes the inner wall of the cylinder, the shape of the liner, the position of the partition plate, and the grinding media filling space. Step 3: Run a discrete element simulation. At set time steps, record the velocity vector field of all particles on a certain cross-section of the cylinder, and the motion of each particle is described by Newton's equations of motion. Translation equations: Equation of rotation: in, Let i be the mass of particle i. Let be the translational velocity of particle i. and These represent the normal contact force and the tangential contact force between particle i and particle j, respectively. The force exerted by the gas on particle i It is the gravitational acceleration vector. Let be the moment of inertia of the particle. Let be the angular velocity of the particle. Let be the vector pointing from the center of the particle to the contact point. Let be the coefficient of rolling friction affected by particle i; Step 4: Establish a simulation model of the grinding process based on the discrete element method. Input the collected operating parameters into the model, and set the contact parameters between particles and between particles and the cylinder wall, specifically including the coefficient of restitution, the coefficient of sliding friction, and the coefficient of rolling friction. Then, use the nonlinear Hertz contact model to calculate the contact force between particles, and the model expression is as follows: Normal contact force: Tangential force and sliding criterion: Equivalent Young's modulus: Equivalent radius: in For equivalent Young's modulus, For the equivalent radius, The normal overlap is... For equivalent quality, For relative normal velocity, The coefficient of recovery, For equivalent shear modulus, This is the tangential overlap. The relative tangential velocity, The coefficient of sliding friction is and Let be the radii of particles i and j; Step 5: Extract particle velocity data and set a velocity threshold. The velocity threshold is adaptively determined based on the drop velocity distribution of the grinding media: Statistically analyze the tangential velocity values ​​of all particles in the cross-section of the cylinder, create a velocity distribution histogram, find the local minimum value of the velocity distribution curve, use the velocity value corresponding to the local minimum value as the dead material zone identification threshold, mark the continuous area in the cross-section of the cylinder with a velocity lower than the threshold as the dead material zone, and record the radial position, axial length range and circumferential distribution angle of the area. Step 6: Based on the positioning results of the dead material zone, determine the installation radius of the agitator on the partition plate, the length of the agitator, and the number of agitators that need to be installed. The installation radius should ensure that the agitator can cut into the middle of the dead material zone or near the center when rotating.

[0022] Third Embodiment As a third embodiment of the present invention, once the size and output of the ball mill are determined, it is necessary to find the optimal combination of five parameters—filling rate, rotational speed, stirring rod position, number, and size—using a multi-objective optimization method. The specific processing method is as follows: Define the design variable vector ,in To improve the filling efficiency of the ball mill , Let n be the rotational speed of the ball mill. The installation radius R of the ball mill stirring rod. Let N be the number of stirring rods. The length of the stirring rod ; Next, an objective function is established with the constraints of maximizing grinding efficiency and minimizing power consumption. Regarding maximizing grinding efficiency: grinding efficiency... Compared with the specific surface area S or particle size distribution of the product Positive correlation; efficiency model established through simulation or experimental calibration. Regarding minimizing power consumption: the power consumption E per unit product is determined by the motor power P, and Where Q is the output, the objective function is constructed by combining the two. , specific ,in and The weighting coefficients must satisfy the condition that the sum of the two is 1. The optimization process must satisfy physical and technological constraints, including structural constraints. , For safety clearance, The inner radius of the cylinder is calculated by subtracting the liner thickness to prevent the stirring rod from scraping against the liner. N must be an integer and within a reasonable range, for example, 3 ≤ N ≤ 30. Process constraints: , Performance constraints: ; Using a central composite design or Box-Behnken design, M sample points are generated in the five-dimensional design space, with each sample point corresponding to a set of design variables. For each sample point, run a discrete element simulation once and record the corresponding grinding efficiency. Unit power consumption and the volume ratio of dead material area The simulation results were regressed using the least squares method to fit a second-order response surface model: Where y represents E or , For regression coefficients, As an error term, after obtaining the response surface model, 5 to 10 parameter combinations that were not involved in the modeling are randomly selected, and high-precision discrete element simulation is run. The simulation results are compared with the predicted values ​​of the response surface model, and the relative error is calculated. If the relative error of all responses is within 10%, the response surface model is considered reliable; if it exceeds 10%, the number of sample points is increased to 1.5 times the original number, and the model is refitted until the accuracy requirements are met. Next, the constructed response surface model is used as the fitness function of the genetic algorithm. Parameters such as population size, crossover probability, and mutation probability are set. For example, the population size is 150 individuals, the crossover probability is 0.85, and the mutation probability is 0.05. A polynomial mutation operator is used, and the termination condition is: the maximum number of generations reaches 200, or the rate of change of the objective function value of the Pareto front is less than 1% for 20 consecutive generations. Based on the two objective function values, the population is sorted into hierarchical groups to find the Pareto optimal solution set. The tournament selection method is used to select the individuals with higher Pareto fronts. The genetic algorithm ultimately outputs a set of Pareto optimal solutions. Each solution in this set is independent of the two objectives of grinding efficiency and unit power consumption. The user selects a final solution from this set based on the site conditions. For example, if the power cost accounts for a high proportion, the solution with the lowest unit power consumption in the Pareto front is selected. If increasing production is more urgent, the solution with the highest grinding efficiency is selected. If a balance between the two is required, the solution closest to the ideal point can be selected. After selecting the final solution, a complete discrete element simulation is run again with this set of parameters to verify the deviation between the grinding efficiency and power consumption obtained from the simulation and the optimized prediction values. If the deviation is within 5%, the solution is accepted. If the deviation exceeds 5%, the final solution is added as a new sample point to the response surface model for refitting, and the genetic algorithm is run again until the deviation between the predicted value and the simulation value meets the requirements.

[0023] Some of the data in the above formulas are numerical calculations with dimensions removed, and the contents not described in detail in this specification are all prior art known to those skilled in the art.

[0024] The above embodiments are only used to illustrate the technical methods of the present invention and are not intended to limit it. 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 be made to the technical methods of the present invention without departing from the spirit and scope of the technical methods of the present invention.

Claims

1. A stirred ball mill, comprising a ball mill body and a shell 1, wherein a cylindrical body is disposed inside the shell 1, characterized in that, The inner wall of the cylinder is fitted with a ball mill liner 2. Inside the cylinder, multiple stirring rods 3 are welded and installed on the partition plate 4 located between the feed end and the discharge end. The stirring rods 3 extend along the axial direction of the cylinder and are arranged in a staggered manner in the circumferential direction of the cylinder. Within the same cross-section of the cylinder, the included angles between adjacent stirring rods are not completely equal, and they are arranged in an alternating pattern of large and small intervals. In the axial direction, the length of the stirring rods is flexibly adjusted according to the size of each compartment.

2. A design method for a stirred ball mill, used to implement a stirred ball mill according to claim 1, characterized in that, The method specifically includes the following steps: The target ball mill's operating parameters include grinding media filling rate, cylinder rotation speed, design output, feed particle size distribution, and grinding media gradation. A three-dimensional geometric model is established based on the actual geometric dimensions of the ball mill. A simulation model of the grinding process is established based on the discrete element method. The operating parameters are input, the simulation is run, and the velocity vector field of the particles in the cross-section of the cylinder is recorded. Set a speed threshold, mark the continuous area with speed below the threshold as the dead zone, determine the radial position, axial length range and circumferential distribution angle of the dead zone, and thus determine the installation radius of the agitator on the partition plate, the length of the agitator, and the number of agitators that need to be set. Determine the ball mill filling rate, cylinder rotation speed, stirring rod installation radius, number of stirring rods, and stirring rod length; A multi-objective optimization function is established with the objectives of maximizing grinding efficiency and minimizing power consumption per unit product, and constraints are set. A second-order response surface model was constructed using experimental design and response surface methodology. This model was then used as the fitness function of a genetic algorithm to perform multi-objective optimization and obtain the Pareto optimal solution set. Select the final solution from the Pareto optimal solution set, and manufacture and install the stirring rod according to the solution.

3. The design method for a stirred ball mill according to claim 2, characterized in that, The method for determining the speed threshold is as follows: The tangential velocity values ​​of all particles within the cross-section of the cylinder are statistically analyzed, a velocity distribution histogram is plotted, the local minimum value of the velocity distribution curve is found, and the velocity value corresponding to the local minimum value is used as the dead material zone identification threshold.

4. The design method for a stirred ball mill according to claim 2, characterized in that, The multi-objective optimization function is: Where X is the design variable vector, The grinding efficiency is E, and the power consumption per unit product is E. and These are the weighting coefficients.

5. The design method for a stirred ball mill according to claim 4, characterized in that, The design variable vector ,in To improve the filling efficiency of the ball mill , Let n be the rotational speed of the ball mill. The installation radius R of the ball mill stirring rod. Let N be the number of stirring rods. The length of the stirring rod ; Unit product power consumption , where Q is the output.

6. The design method for a stirred ball mill according to claim 2, characterized in that, The constraints include: Structural constraints , For safety clearance, The inner radius of the cylinder is minus the liner thickness; N must be an integer and within a reasonable range; process constraints: , Performance constraints: .

7. The design method for a stirred ball mill according to claim 2, characterized in that, The method of constructing a second-order response surface model using experimental design and response surface methodology is as follows: Using a central composite design or Box-Behnken design, M sample points are generated in the five-dimensional design space, with each sample point corresponding to a set of design variables. For each sample point, run a discrete element simulation once and record the corresponding grinding efficiency. Unit power consumption and the volume ratio of dead material area The simulation results were regressed using the least squares method to fit a second-order response surface model: Where y represents E or , For regression coefficients, This is the error term.

8. The design method for a stirred ball mill according to claim 2, characterized in that, The method for obtaining the Pareto optimal solution set is as follows: The constructed response surface model is used as the fitness function of the genetic algorithm. Population size, crossover probability, and mutation probability are set. The population is sorted into layers according to the two objective function values. The Pareto optimal solution set is found. The tournament selection method is used to select the individuals with the highest Paretofronts and output the Pareto optimal solution set.

9. The design method for a stirred ball mill according to claim 2, characterized in that, In discrete element simulation, the motion of each particle is described by Newton's equations of motion: Translation equations: Equation of rotation: in, Let i be the mass of particle i. Let be the translational velocity of particle i. and These represent the normal contact force and the tangential contact force between particle i and particle j, respectively. The force exerted by the gas on particle i It is the gravitational acceleration vector. Let be the moment of inertia of the particle. Let be the angular velocity of the particle. Let be the vector pointing from the center of the particle to the contact point. Let be the rolling friction coefficient affected by particle i.

10. The design method for a stirred ball mill according to claim 2, characterized in that, The simulation model of the grinding process based on the discrete element method includes: Normal contact force: Tangential force and sliding criterion: Equivalent Young's modulus: Equivalent radius: in For equivalent Young's modulus, For the equivalent radius, The normal overlap is... For equivalent quality, For relative normal velocity, The coefficient of recovery, For equivalent shear modulus, This is the tangential overlap. Relative tangential velocity, The coefficient of sliding friction is and Let be the radii of particles i and j.

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