Friction coefficient estimation method and program

Abstract

The purpose of the present disclosure is to provide a novel means for appropriately setting a coefficient of friction when simulating the behavior of particles.　In one aspect, the present disclosure encompasses the following invention.　A method for estimating a first friction coefficient and a second friction coefficient, wherein: the first friction coefficient and the second friction coefficient are coefficients of friction for simulating motion of at least one type of powder inside a rotating drum at least on the basis of a discrete element method (DEM); the first friction coefficient is the coefficient of friction between the powders; and the second friction coefficient is the coefficient of friction between the powder and the inner wall of the rotating drum. The method includes: a step for acquiring at least a first measured value, wherein the first measured value is an actually measured value when the powder is moved in the rotating drum under a first condition; a step for creating first input data at least on the basis of the first condition and the first measured value; and a step for executing a first simulation at least on the basis of the first input data.

Description

Friction coefficient estimation method and program

[0001] The present disclosure relates to a method and a program for estimating a friction coefficient.

[0002] The discrete element method (DEM) is known as a method for simulating particle behavior. In this method, particles are first considered as elements such as spheres. Next, contact and / or sliding between each element is calculated. Then, the movement of each element at each time is tracked.

[0003] For example, the behavior of particles in a rotating vessel can be predicted based on DEM. Patent Document 1 discloses the following invention: a method for predicting the operating power of an inner and outer cylinder reciprocating ball mill, which comprises simulating the motion of balls in an inner and outer cylinder reciprocating ball mill when finely grinding powder using the inner and outer cylinder reciprocating ball mill by a discrete element method using a viscoelastic dynamics model, calculating the collision energy E of all balls, and calculating the operating power Y of the inner and outer cylinder reciprocating ball mill based on the collision energy E of the balls.

[0004] Japanese Patent Application Publication No. 11-253828

[0005] When simulating particle behavior based on DEM, it is necessary to set initial parameters. If these parameters are set inappropriately, simulation results that differ from actual behavior will occur. The parameters that need to be set include the friction coefficient between particle walls and the friction coefficient between particles. The present disclosure aims to provide a new means for appropriately or efficiently setting these friction coefficients when simulating particle behavior.

[0006] In relation to the above object, one aspect of the present disclosure includes the following invention: (Invention 1) A method for estimating a first friction coefficient and a second friction coefficient, wherein the first friction coefficient and the second friction coefficient are friction coefficients for simulating the movement of at least one type of powder inside a rotating drum based at least on a discrete element method (DEM), the first friction coefficient is a friction coefficient between powder particles, and the second friction coefficient is a friction coefficient between the powder and an inner wall of the rotating drum, the method including: a step of acquiring at least a first measured value, wherein the first measured value is a measured value when the powder is moved inside the rotating drum under first conditions; a step of creating first input data based at least on the first conditions and the first measured value; and a step of performing a first simulation based at least on the first input data. (Invention 2) A method for estimating a first friction coefficient and a second friction coefficient, wherein the first friction coefficient and the second friction coefficient are friction coefficients for simulating the movement of at least one type of powder inside a rotating drum based at least on a discrete element method (DEM), the first friction coefficient is a friction coefficient between powder particles, and the second friction coefficient is a friction coefficient between the powder and an inner wall of the rotating drum, the method comprising: a step of acquiring at least a first measured value, wherein the first measured value is a measured value when the powder is moved inside the rotating drum under first conditions; a step of creating first input data based at least on the first conditions and the first measured value; and a step of performing a first simulation based at least on the first input data, wherein the step of creating the first input data comprises creating a first changed condition based at least on the first condition, and the step of performing the first simulation comprises simulating at least on the first input data based at least on the first changed condition. The first modified condition is compared with the first condition in that the following parameters are the same: particle diameter to drum diameter ratio; Froude number; packing rate; particle density. The particle diameter under the first modified condition is larger than the particle diameter under the first condition.(Invention 3) The method of Invention 2, wherein the first measured value includes a rise ratio or an angle of repose of the powder while the rotating drum is rotating. (Invention 4) A method of estimating a first friction coefficient and a second friction coefficient, wherein the first friction coefficient and the second friction coefficient are friction coefficients for simulating the movement of at least one type of powder inside a rotating drum based at least on a discrete element method (DEM), the first friction coefficient is a friction coefficient between powder particles, and the second friction coefficient is a friction coefficient between the powder and an inner wall of the rotating drum, the method comprising: a step of acquiring at least a first measured value, wherein the first measured value is an actual measurement value when the powder is moved inside the rotating drum under first conditions; and a step of creating first input data based at least on the first conditions and the first measured value, wherein the step of creating the first input data includes obtaining a candidate first friction coefficient and a candidate second friction coefficient based on at least one of a database and a trained model. (Invention 5) The method of Invention 4, wherein the trained model includes at least the following terms (a) to (b) as objective variables, and further wherein the trained model includes one or more of the following terms (c) to (h) and / or parameter terms derived from (c) to (h) as explanatory variables: (a) first friction coefficient (b) second friction coefficient (c) particle diameter (d) drum diameter (e) Froude number (f) packing fraction (g) particle density (h) rise ratio or angle of repose. (Invention 6) The method of Invention 4 or 5, further comprising: a step of acquiring at least second actual measurement values, wherein the second actual measurement values ​​are actual measurement values ​​obtained when the powder is moved in the rotating drum under second conditions; and wherein the step of creating first input data includes creating the first input data further based on the second conditions and the second actual measurement values.(Invention 7) A method for estimating a first friction coefficient and a second friction coefficient, wherein the first friction coefficient and the second friction coefficient are friction coefficients for simulating the movement of at least one type of powder inside a rotating drum based at least on a discrete element method (DEM), the first friction coefficient is a friction coefficient between powder particles, and the second friction coefficient is a friction coefficient between the powder and an inner wall of the rotating drum, the method comprising: a step of acquiring at least a first measured value and a second measured value, wherein the first measured value is a measured value when the powder is moved inside the rotating drum under first conditions, and the second measured value is a measured value when the powder is moved inside the rotating drum under second conditions different from the first conditions; a step of performing a first simulation based at least on the first conditions; and a step of performing a second simulation based at least on the second conditions. The method of claim 7, wherein the first condition is a rotation speed of the drum and the second condition is a rotation speed of the powder.(Invention 10) A method according to any one of Inventions 7 to 9, wherein the step of creating first input data includes creating a first change condition based at least on the first condition, the step of creating second input data includes creating a second change condition based at least on the second condition, the step of performing the first simulation includes simulating at least based on the first input data based at least on the first change condition, and the step of performing the second simulation includes simulating at least based on the second input data based at least on the second change condition, wherein the first change condition is consistent with the first condition in the following parameters: ratio of particle diameter to drum diameter, Froude number, packing rate, and particle density, and the second change condition is consistent with the second condition in the following parameters: ratio of particle diameter to drum diameter, Froude number, packing rate, and particle density, the particle diameter under the first change condition is larger than the particle diameter under the first condition, and the particle diameter under the second change condition is larger than the particle diameter under the second condition. (Invention 11) A method according to any one of Inventions 1 to 10, wherein the powder includes a medium, the step of acquiring at least a first actual measurement value includes acquiring an actual measurement value when the medium and a second powder are moved in the rotating drum in a state in which they coexist, the step of performing the first simulation includes performing the first simulation under conditions in which the second powder is not included, the first friction coefficient is a friction coefficient between the media when the second powder coexists, and the second friction coefficient is a friction coefficient between the media and the inner wall of the rotating drum when the second powder coexists, in the step of acquiring at least a first actual measurement value, a particle diameter of the media is larger than a particle diameter of the second powder, and in the step of acquiring at least a first actual measurement value, the number of the media is smaller than the number of the second powder. (Invention 12) A program for executing the method according to any one of Inventions 1 to 11.

[0007] In one aspect, the invention creates input data based on actual measurements of the friction coefficient when the friction coefficient is measured in a rotating drum, and then performs a simulation based on the input data. This allows for a friction coefficient that matches the actual measurements.

[0008] 1 shows an apparatus of a system of the present disclosure in one embodiment; 2 shows the configuration of a system of the present disclosure in one embodiment; 3 shows the concepts of angle of repose and rise ratio; 4 shows the configuration of a database of the present disclosure in one embodiment; 5 shows the configuration of a database of the present disclosure in one embodiment; 6 shows the configuration of a database of the present disclosure in one embodiment;

[0009] Specific embodiments for carrying out the present invention will be described below. The following description is intended to facilitate understanding of the invention and is not intended to limit the scope of the present invention.

[0010] 1. Overview In one embodiment, the present disclosure relates to a method and program for estimating a friction coefficient.

[0011] The technical field to which the present invention is applicable is not particularly limited, and the present invention can be applied to any technical field in which the behavior of particles is simulated, provided that the environment in which the particles behave is inside a rotating drum.

[0012] The size of the particles is not particularly limited, and the method and program of the present disclosure can be applied to particles of any size. For example, the size of the particles may be on the order of meters, millimeters, micrometers, or nanometers. In one embodiment, the particles of the present disclosure are powders. The type of particles is also not limited, and the method and program of the present disclosure may simulate the behavior of one type of particle or two or more types of particles. The number of particles is also not particularly limited. In one embodiment, the terms "particles" and "powder" used herein are used interchangeably. In one embodiment, the terms "particles" and "powder" used herein may or may not include media. The media has the function of crushing other particles introduced into the rotating drum and / or the function of promoting the mixing of these particles. Therefore, in certain embodiments, a simulation is performed to predict the state in which the particles to be crushed and / or stirred and the media coexist within the rotating drum.

[0013] The simulating algorithm is based at least on the discrete element method (DEM).

[0014] 2. Environment for Executing the Program The environment for executing the program and method is not particularly limited, and a typical information processing device (also referred to as a computing device) can be used. The information processing device (100) can typically include a processor (110), a memory (120), a non-transitory storage medium (130), and a communication module (140), as shown in FIG. 1.

[0015] Examples of the information processing device (100) include, but are not limited to, a server, a personal computer, a tablet terminal, a smartphone, a smart watch, smart glasses, etc.

[0016] The program is stored in a non-transitory storage medium (130, for example, HDD, SSD, etc.), loaded into a memory (120, for example, RAM, etc.) as needed, and executed by a processor (110, for example, CPU, etc.). If necessary, the program can connect to a network through a communication module (140) to send and receive information.

[0017] In one embodiment, the program may be installed as application software on one information processing device (100) and executed by the information processing device (100).

[0018] In another embodiment, the number of information processing devices (100) is not limited to one, and multiple information processing devices (100) may be used as needed. In this case, the functions of the program may be distributed among the multiple information processing devices (100).

[0019] Alternatively, as shown in Fig. 2, a system (200) may be configured in which a server (210) and a terminal (220) are interconnected via a network. In the system (200), the terminal (220) may receive input from a user and transmit at least a portion of the received input to the server (210). The server (210) may receive input information transmitted from the terminal (220), process the information, and transmit a portion of the output to the terminal (220). The terminal (220) may then receive output information transmitted from the server (210) and display it on the terminal (220).

[0020] Therefore, in another aspect, the present disclosure also relates to an information processing device including the program of the present disclosure, and a system including the information processing device. In yet another aspect, the present disclosure relates to a terminal and / or a server constituting the system of the present disclosure. The internal configuration of the terminal and the server may be the same as that of the information processing device shown in FIG. 1. In yet another aspect, the present disclosure relates to a computer-readable non-transitory storage medium (e.g., HDD, SSD, flash memory, optical disk, etc.) storing a program.

[0021] 3. Method for Estimating Friction Coefficient In one embodiment, the present disclosure relates to a method for estimating a friction coefficient. More specifically, the present disclosure relates to a method for estimating a first friction coefficient and a second friction coefficient. The first friction coefficient and the second friction coefficient are friction coefficients for simulating the movement of at least one type of powder inside a rotating drum based at least on a discrete element method (DEM). The first friction coefficient is a friction coefficient between powder particles, and the second friction coefficient is a friction coefficient between the powder and the inner wall of the rotating drum.

[0022] The method includes the steps of: acquiring at least a first actual measurement value, where the first actual measurement value is an actual measurement value when powder is moved in a rotating drum under a first condition; generating first input data based at least on the first condition and the first actual measurement value; and performing a first simulation based at least on the first input data.

[0023] As described above, various measured values ​​are obtained by actually moving powder inside a rotating drum. Then, to search for a friction coefficient that matches the measured value, first input data is created (e.g., a friction coefficient is set), and a first simulation is performed. If the result of the first simulation is close to the measured value, this means that the friction coefficient is sufficiently appropriate to be applied to the simulation. On the other hand, if the result of the first simulation is not close to the measured value, a different friction coefficient may be set and further simulation may be performed. Alternatively, the friction coefficient may be estimated by another means, and the first simulation may be performed to confirm whether the estimated friction coefficient is appropriate.

[0024] In this specification, the term "approximate" means that the difference between two values ​​is 10% or less, preferably 8% or less, and more preferably 5% or less, based on the value with the smaller absolute value. For example, if there are two values ​​"21" and "20", the difference between them is 1. If the value with the smaller absolute value is used as the reference, then 1 / 20 = 5%. Therefore, in this specification, the two values ​​are treated as being approximate.

[0025] Furthermore, in this specification, the term "match" means that the difference between two values ​​is 3% or less, preferably 1% or less, and more preferably 0.5% or less, based on the value with the smaller absolute value. For example, if there are two values ​​"101" and "100", the difference between them is 1. If the value with the smaller absolute value is used as the reference, then 1 / 100 = 1%. Therefore, in this specification, the two values ​​are treated as matching.

[0026] If a plurality of similar or identical values ​​are found and it is necessary to select which one to use, the value with the smallest difference may be used.

[0027] The first measured value described above, the second measured value described below, and other measured values ​​are not particularly limited, but may include, for example, the rise ratio or angle of repose of the powder when the rotating drum is rotating.

[0028] The angle of repose refers to the angle of the gradient formed by the powder as the rotating drum rotates (see Figure 3).

[0029] The rise ratio means the ratio of the height H of the powder lifted when the rotary drum is rotating to the diameter D of the drum.

[0030] For example, the increase ratio may be a value expressed by the following formula (see FIG. 3): η=H / D

[0031] The first condition described above, the second condition described below, and other conditions for rotating the rotating drum are not particularly limited, and may include, for example, any one or more of the following conditions: the inner dimensions of the rotating drum (e.g., drum diameter), the inner depth of the rotating drum, the volume of the rotating drum, particle diameter, Froude number, rotation speed, filling rate, density of a particle per particle, mass of a particle per particle, volume of a particle per particle, number of particles, and a parameter based on any two or more of these (e.g., ratio of particle diameter to drum diameter, etc.).

[0032] The above conditions are all conditions that can be known in advance, or can be known by other measurement means (for example, particle size).

[0033] The numerical values ​​of each condition item may be directly input by the user through an information processing device, or may be derived from information input by the user through the information processing device. For example, if information on the inner dimensions of the rotating drum is available, the volume inside the rotating drum can be derived. Alternatively, if information on the composition of particles is available, the particle density per particle can be derived by referring to another database, etc.

[0034] The above-described method may be used as a preliminary method for performing simulations to examine various conditions for moving particles inside a rotating drum. For example, if there are many types of conditions to be examined, it would be time-consuming to try all of them by actually rotating the rotating drum. Therefore, it is more efficient to perform simulations in advance for the conditions to be examined and then actually rotate the rotating drum only for those conditions that produce good results. However, performing such a simulation requires inputting the friction coefficient.

[0035] Therefore, by using the method described above, we first obtain actual measurements by actually rotating the drum, and then run a simulation to confirm the friction coefficient that matches the actual measurements. This allows us to run a simulation under the conditions we want to consider.

[0036] In the following sections, further specific embodiments (first embodiment, second embodiment, third embodiment, fourth embodiment, etc.) based on the above embodiment will be described. Note that, to reiterate, the scope of the present invention is not limited to the further specific embodiments, and also includes combinations of these embodiments.

[0037] 4. First Embodiment By performing the first simulation as described above, it is possible to estimate the friction coefficient, or to confirm whether a friction coefficient estimated by another means is appropriate. However, depending on the simulation conditions, the calculation load may be large (for example, when the number of particles to be calculated is large, or when the particles to be calculated are small, etc.). Furthermore, when the calculation load is large, it may take a long time to obtain the results of the first simulation. The method according to the first embodiment can reduce the calculation load.

[0038] The method according to the first embodiment includes the following steps: acquiring at least a first actual measurement value, where the first actual measurement value is an actual measurement value obtained when powder is moved in a rotating drum under a first condition; generating first input data based at least on the first condition and the first actual measurement value; and performing a first simulation based at least on the first input data.

[0039] Here, the step of creating the first input data includes creating a first change condition based at least on the first condition, and further, the step of performing the first simulation includes performing a simulation based at least on the first input data based at least on the first change condition.

[0040] The first modified condition is the same as the first condition in terms of the following parameters: particle diameter to drum diameter ratio, Froude number, filling rate, and particle density.

[0041] The particle diameter under the first modified condition is larger than the particle diameter under the first condition.

[0042] In the above method, the calculation load can be reduced by performing a simulation under modified conditions (first modified conditions) in which the particle diameter is increased, rather than under the conditions (first conditions) under which the actual measured values ​​were obtained.

[0043] In a DEM-based simulation, the time step must be set to perform the simulation appropriately. The smaller the time step, the greater the calculation load, and the larger the time step, the smaller the calculation load. However, in a DEM-based simulation, there are constraints regarding stability, and in order to satisfy these constraints, the time step must satisfy the following condition: Δt<2π / Ω×(m / K). 1 / 2 Δt: Time step m: Mass of particle K: Spring constant of particle Ω: For example, 5 to 20

[0044] For example, if the particle diameter is doubled, the mass will increase by eight times, so the upper limit of the time step will be 2.8 times. Therefore, increasing the particle diameter will increase the time step. And, increasing the time step will reduce the calculation load.

[0045] However, simply increasing the particle size when performing a simulation may result in simulation results that differ from the behavior of actual particles. To reduce this, the inventors discovered that by increasing the particle size under the condition that the following parameters are consistent, it is possible to maintain the reproducibility of the simulation: - Ratio of particle size to drum diameter - Froude number - Filling rate - Particle density

[0046] The particle size is the size corresponding to the diameter or radius of a particle. In the DEM-based simulation method, particles are treated as spheres. Therefore, once the initial parameters of the simulation are determined, the particle diameter can be obtained.

[0047] The drum diameter is the diameter or radius of the rotating drum. The cross section of the rotating drum is circular. The rotating drum rotates around the center of the circle, moving the particles inside the drum.

[0048] The Froude number is a dimensionless number that represents the ratio of centrifugal force to gravity. When the drum is rotated, the behavior of particles varies depending on the speed. For example, if the rotation speed is increased extremely, centrifugal force becomes dominant, and the particles inside the drum adhere to the inner wall of the drum while rotating. On the other hand, when the rotation speed is below a certain level, gravity becomes dominant, and the particles inside the drum rise to a certain height and then fall.

[0049] Typically, the Froude number can be expressed by the following formula: F r =ω 2 R / g=ω 2 D / (2g)

[0050] ω: rotation speed of the rotating drum (rad / sec) R: radius of the rotating drum (m) D: diameter of the rotating drum (m) g: gravitational acceleration (m / s 2 )

[0051] The packing ratio is the ratio of the volume of the particles divided by the volume inside the drum. The volume of the particles may be the apparent packing volume (including the interstitial spaces between the particles) or the sum of the volumes of the individual particles. An example of the latter is when the volume inside the drum is 1000 cm. 3 , the volume of each particle is 0.1 cm 3 If the number of particles is 500, the filling rate is 5% (0.1 x 500 / 1000 = 0.05).

[0052] Typically, the filling factor can be expressed by the following formula: φ=4V p / (πTD 2 ) = V p / (πTR 2 ) V p : Apparent filling volume (m 3 ) T: Depth of the rotating drum (m) D: Diameter of the rotating drum (m)

[0053] Particle density is the ratio of mass to volume in a single particle.

[0054] The technique in the first embodiment is particularly useful in powder simulations. Powder generally has a small particle diameter. Therefore, the mass tends to be small accordingly. When the mass is small, the time step tends to be small as described above, and the calculation load tends to be large. However, by using the method described above to perform a simulation while maintaining reproducibility under conditions where the powder particles are large, the calculation load can be reduced.

[0055] 5. Second Embodiment By executing the first simulation as described above, it is possible to estimate the friction coefficient, or to confirm whether the friction coefficient estimated by another means is appropriate. It is desirable that the estimated friction coefficient be highly accurate.

[0056] In view of this objective, the method according to the second embodiment includes the following steps: obtaining at least a first actual measurement value and a second actual measurement value, wherein the first actual measurement value is an actual measurement value obtained when the powder is moved in the rotating drum under a first condition, and the second actual measurement value is an actual measurement value obtained when the powder is moved in the rotating drum under a second condition different from the first condition; performing a first simulation based at least on the first condition; and performing a second simulation based at least on the second condition.

[0057] Here, the steps of performing a first simulation and performing a second simulation are repeated until the value obtained as a result of performing each simulation falls within a range of approximate values ​​based at least on the first actual measurement value and the second actual measurement value.

[0058] In a further preferred embodiment, at least the rotation speed of the drum may be different between the first condition and the second condition. In a further preferred embodiment, only the rotation speed of the drum may be different between the first condition and the second condition (i.e., the other conditions may be the same).

[0059] As described above, the rotation speed of the drum and the Froude number can be expressed by a specific relationship. In a more preferred embodiment, the rotation speed of the drum under the first condition and the second condition is such that the Froude number is 10. -5 ~10 -1If the drum rotation speed is within this range, the rise ratio and / or angle of repose can be measured.

[0060] The advantage of using two actual measurements is as follows: when only one actual measurement is used, if a simulation is performed under the same or similar conditions as those under which the actual measurement was obtained, it is highly likely that the results will be close to the actual particle behavior. However, if a simulation is performed under conditions that are significantly different from those under which the actual measurement was obtained, the results may differ from the actual particle behavior.

[0061] Another advantage is that if only one measured value is used, there may be multiple candidate friction coefficients. In particular, the friction coefficients to be determined include at least two types: a first friction coefficient and a second friction coefficient. Therefore, while a combination of the first and second friction coefficients (F1A, F2A) may produce simulation results that match the measured values ​​under the first condition, a combination of the first and second friction coefficients (F1B, F2B) may also produce simulation results that match the measured values ​​under the first condition. In such cases, using the measured values ​​under the second condition makes it possible to verify which candidate combination is correct.

[0062] In this way, by using two actual measured values, the reliability of the obtained friction coefficient can be improved.

[0063] In addition to the first and second conditions, the simulation may be performed by obtaining actual measurements for a third or more conditions. However, from the viewpoint of efficiently determining the friction coefficient, it is preferable to consider only two types of conditions.

[0064] While it is possible to uniquely estimate the first and second friction coefficients independently based on two or more actual measurement values ​​as in this embodiment, in other embodiments it is also possible to estimate the average value of the first and second friction coefficients based on a single actual measurement value. In this case, the first and second friction coefficients are treated as being equal. In other words, the first and second friction coefficients are estimated in these other embodiments as well.

[0065] 6. Third Embodiment By performing the first simulation as described above, it is possible to estimate the friction coefficient, or to confirm whether a friction coefficient estimated by another means is appropriate. However, it would be useful to have a means for more quickly obtaining candidate friction coefficients. The method according to the third embodiment makes it possible to quickly obtain candidate friction coefficients.

[0066] The method according to the third embodiment includes the steps of: obtaining at least a first actual measurement value, where the first actual measurement value is an actual measurement value obtained when the powder is moved in the rotating drum under a first condition; and generating first input data based at least on the first condition and the first actual measurement value.

[0067] Here, the step of creating the first input data includes obtaining a candidate first friction coefficient and a candidate second friction coefficient based on at least one of a database and a trained model.

[0068] In a further preferred embodiment, the method according to the third embodiment may further include a step of performing a first simulation based at least on the first input data, thereby confirming whether the candidate first friction coefficient and the candidate second friction coefficient are appropriate.

[0069] 6-1. Use of Database When using a database, the database may include one or more of the following items or related items (Figure 4): particle diameter, drum diameter, Froude number, packing rate, particle density, rise ratio, angle of repose, inter-particle friction coefficient, inter-particle wall friction coefficient (friction coefficient between a particle and the inner wall of the drum), etc. The term "related item" refers to the following types of items: (1) items necessary to derive the target item; and (2) items derived from the target item.

[0070] In the former case, the database may include the items "drum diameter" and "lift height" instead of or in addition to the above-mentioned item "rise ratio". In the latter case, the database may include the item "ratio of particle diameter to drum diameter" instead of or in addition to the above-mentioned item "particle diameter" and item "drum diameter". The items "drum diameter" and "lift height" can be considered as items related to the item "rise ratio". The item "ratio of particle diameter to drum diameter" can be considered as an item related to the items "particle diameter" and "drum diameter".

[0071] Preferably, the items included in the database are ratios rather than values ​​obtained by physical measurement. The reason for this is that items based on ratios are versatile, even when the physical dimensions of a drum or the like change. For example, compared to a pattern in which the drum diameter and particle diameter are provided separately, the ratio of particle diameter to drum diameter is treated the same whether it is 100 / 1 or 10 / 0.1, so the efficiency of storing and searching database data is good (though if the drum diameter and particle diameter were provided separately, two lines of data would be required).

[0072] The items included in the database may include ratios between different conditions. For example, the database may include a ratio between an item related to a first condition and an item related to a second condition. For example, as shown in FIG. 5, the database may include the ratio of the Froude number under a first condition (e.g., a condition in which the drum is rotated at a high speed) to a second condition (e.g., a condition in which the drum is rotated at a slower speed than the speed under the first condition). The same applies to the rise ratio.

[0073] Furthermore, a ratio that combines a plurality of items may be used. For example, as shown in Fig. 6, a ratio that combines the Froude number and the climb ratio, and also combines an item related to the first condition and an item related to the second condition may be used.

[0074] When a database is used, a program may query the database to obtain the inter-particle friction coefficient and the inter-particle wall friction coefficient (or the average value of these). In this case, items other than the inter-particle friction coefficient and the inter-particle wall friction coefficient in the database may be set as query conditions. In the query process, the condition values ​​do not need to match exactly, and data with high similarity may be obtained.

[0075] 6-2. Use of Trained Models A trained model may be used instead of or in addition to a database. The trained model may be produced by training the above-described database as training data. The type of trained model is not particularly limited, but includes one or more selected from the following or a combination thereof: a multiple regression analysis model, a support vector regression (SVR) method, a partial least squares (PLS) method, a neural network method, a random forest method, or a decision tree method. The neural network is not limited, but includes, for example, one or more selected from the following or a combination thereof: a CNN, a GAN, a DNN, a LSTM, an RNN, etc. The multiple regression analysis model may be based on linear regression or nonlinear regression. Preferably, the multiple regression analysis model may be based on nonlinear regression. The trained model may be a model based at least on ensemble learning using multiple models (e.g., a model based on a random forest method using multiple decision tree-based models).

[0076] The trained model includes explanatory variables and response variables. The response variables include the inter-particle friction coefficient and the inter-particle wall friction coefficient (or their average values). The explanatory variables may include one or more of the following items or items related thereto: particle diameter, drum diameter, Froude number, packing ratio, particle density, rise ratio, angle of repose, etc.

[0077] 6-2-1. Example 1 Based on a Linear Multiple Regression Analysis Model Below, an example based on a linear multiple regression analysis model is shown.

[0078] Two types of linear multiple regression analysis models are prepared. f = a1D + a2F r +a3φ+a4ρ+a5H+a6W f (Formula 1-1) W f = b1D + b2F r +b3φ+b4ρ+b5H+b6P f (Formula 1-2)

[0079] P f : Coefficient of friction between particles W f : Coefficient of friction between particle walls D: Ratio of particle diameter to drum diameter F r : Froude number φ: Filling rate (vol%) ρ: Particle density (kg / m 3 ) H: Rise ratio a n : Coefficient (n is a positive integer) b n : coefficient (n is a positive integer)

[0080] At the stage of obtaining the actual measurement values, D and F r , φ, ρ, H, etc. are already obtained. In addition, when the trained model is produced, each coefficient a n and b n The value of is also obtained. This learning model can be produced by learning using the database shown in FIG. 4 as training data, for example.

[0081] (a) For example, using the parameters of the first condition (for example, the condition when the drum is rotated at a low speed) and an arbitrary coefficient of friction between particle walls W, P f (b) Calculated P f and the parameters of the second condition (for example, the condition when the drum is rotated at a higher speed than the rotation speed of the first condition) are substituted to obtain W f Calculate (c) W and Wf (d) If they do not match (the definition of "match" is as above), f (e) If there is a match, the process ends.

[0082] By performing the above steps (a) to (e), it is possible to calculate the inter-particle friction coefficient and the inter-particle wall friction coefficient. f The above steps (a) to (e) may be performed while comparing the above (in this case, for example, in step (a), the parameters of the first condition and an arbitrary inter-particle friction coefficient P are used to calculate W f (The calculation is based on the following.)

[0083] 6-2-2. Example 2 Based on a Linear Multiple Regression Analysis Model Another example based on a linear multiple regression analysis model is shown below.

[0084] Two types of linear multiple regression analysis models are prepared. f = a1D + a2F r '+a3φ+a4ρ+a5H' (Formula 2-1) W f = b1D + b2F r '+b3φ+b4ρ+b5H' (Formula 2-2)

[0085] P f : Coefficient of friction between particles W f : Coefficient of friction between particle walls D: Ratio of particle diameter to drum diameter F r ': ratio of the Froude number under the first condition to the Froude number under the second condition φ: packing ratio (vol%) ρ: particle density (kg / m 3 ) H': Ratio of the increase ratio under the first condition to the increase ratio under the second condition a n : Coefficient (n is a positive integer) b n : coefficient (n is a positive integer)

[0086] The above example assumes that only the rotation speed of the drum is different. Therefore, the parameters other than the Froude number and the rise ratio are the same between the first and second conditions. n and b nThe learning model for calculating the value of can be produced by learning using the database shown in FIG. 5 as training data, for example.

[0087] Once the measured values ​​for the first condition and the second condition are obtained, all parameters are determined. Therefore, by substituting the parameters into the above-mentioned formulas 2-1 and 2-2, the inter-particle friction coefficient and the inter-particle wall friction coefficient can be calculated.

[0088] 6-2-3. Example 3 Based on a Linear Multiple Regression Analysis Model Hereinafter, yet another example based on a linear multiple regression analysis model will be described.

[0089] Two types of linear multiple regression analysis models are prepared. f =a1D+a2α+a3φ+a4ρ (Formula 3-1) W f =b1D+b2α+b3φ+b4ρ (Formula 3-2)

[0090] P f : Coefficient of friction between particles W f : Coefficient of friction between particle walls D: Ratio of particle diameter to drum diameter α: (H1-H2) / (F r1 -F r2 ) F r1 : Froude number under the first condition F r2 : Froude number under the second condition H1: Rise ratio under the first condition H2: Rise ratio under the second condition φ: Filling ratio (vol%) ρ: Particle density (kg / m 3 ) a n : Coefficient (n is a positive integer) b n : Coefficient (n is a positive integer)

[0091] The above example assumes that only the rotation speed of the drum is different. Therefore, the parameters other than the Froude number and the rise ratio are the same between the first and second conditions. n and b n The learning model for calculating the value of can be produced by learning using the database shown in FIG. 6 as training data, for example.

[0092] Once the measured values ​​for the first condition and the second condition are obtained, all parameters are determined. Therefore, by substituting the parameters into the above formulas 3-1 and 3-2, the inter-particle friction coefficient and the inter-particle wall friction coefficient can be calculated.

[0093] 6-2-4. Example 4 Based on a Linear Multiple Regression Analysis Model Hereinafter, yet another example based on a linear multiple regression analysis model will be described.

[0094] One type of linear multiple regression analysis model is prepared. AVG(P f , W f ) = a1D + a2F r +a3φ+a4ρ+a5H (formula 4-1)

[0095] P f : Coefficient of friction between particles W f : Coefficient of friction between particle walls AVG(P f , W f ): Average value of inter-particle friction coefficient and inter-particle wall friction coefficient D: Ratio of particle diameter to drum diameter F r : Froude number φ: Filling rate (vol%) ρ: Particle density (kg / m 3 ) H: Rise ratio a n : coefficient (n is a positive integer)

[0096] At the stage of obtaining the actual measurement values, D and F r , φ, ρ, H, etc. are already obtained. In addition, when the trained model is produced, each coefficient a n The values ​​of D and F are also obtained. r By substituting the values ​​of φ, ρ, H, etc., the average values ​​of the inter-particle friction coefficient and inter-particle wall friction coefficient can be obtained.

[0097] 6-2-5. Example Based on Random Forest Model Instead of the above-described multiple regression analysis, a random forest model may be used to calculate the inter-particle friction coefficient and the inter-particle wall friction coefficient. The explanatory variables used in the random forest model may be the same as the explanatory variables described above in "6-2-1. Example 1 Based on a Linear Multiple Regression Analysis Model" to "6-2-4. Example 4 Based on a Linear Multiple Regression Analysis Model," or additional variables may be added.

[0098] There are no particular limitations on the hyperparameters in the random forest model (such as the number of decision trees, the maximum depth of each decision tree, and the number of features used for division), and these can be set appropriately by a person skilled in the art.

[0099] Calculation of the inter-particle friction coefficient and inter-particle wall friction coefficient based on the random forest model can achieve a relatively high accuracy, for example, a relatively high correlation coefficient (between the model-predicted value and the actual measured value).

[0100] 7. Fourth Embodiment In addition to or instead of the above-described embodiments, in another embodiment, the powder includes a media.

[0101] Generally, a specific simulation can be performed to predict the state in which media crush other particles in a rotating drum. In this case, it is theoretically possible to calculate both the movement of the media and the movement of the other particles to be crushed. However, compared to the size and number of media, the size of the particles to be crushed is small, and the number of particles to be crushed is large. This causes a heavy calculation load when performing the simulation. The method of the fourth embodiment can contribute to the problem of reducing the calculation load when performing the simulation.

[0102] For example, another embodiment relates to a method for predicting how media will pulverize other particles in a rotating drum, and this method may be a modified version of any of the methods described above in "3. Method for estimating friction coefficient" to "6. Third embodiment."

[0103] As a specific example, first, the powder includes a media and a second powder to be crushed and / or stirred. Actual measurements are obtained when both are moved within a rotating drum. Specific examples of the actual measurements may be values ​​described in the above-mentioned method (e.g., angle of repose, etc.). First input data can be created based at least on the actual measurements (and the first condition), and a first simulation can be performed based on the first input data. Here, the first simulation is performed under conditions that do not include the second powder. For example, the first simulation is performed under conditions where only the media is present within the rotating drum. This reduces the computational load that would otherwise be incurred due to the presence of the second powder. The first and second friction coefficients can then be estimated based on the results of the first simulation with the reduced computational load.

[0104] The measured values ​​that form the basis of the first simulation are those obtained under conditions in which the media and the second powder are present. Therefore, despite the simulation results being obtained under conditions in which the second powder is not present, the estimated first and second friction coefficients are values ​​that reflect or are close to the presence of the second powder. In other words, the first friction coefficient corresponds to the friction coefficient between the media when the second powder is present. The second friction coefficient corresponds to the friction coefficient between the media and the inner wall of the rotating drum when the second powder is present. To further explain, in one example, a large amount of second powder much smaller than the media may be present on the surface of the media. In this situation, the first and second friction coefficients of the media are different from those when the second powder is not present on the surface of the media. Typically, the presence of the second powder on the surface tends to make the media less slippery. In the method according to the fourth embodiment, although the simulation is performed under conditions in which the second powder is not present, it is ultimately possible to estimate two types of friction coefficients of the media even under conditions in which the second powder is present.

[0105] After estimating the first and second coefficients of friction of the media, a further simulation may be performed based on the estimated values. The further simulation may be performed under different conditions than the first simulation. This allows predictions to be made by simulating under various conditions without conducting multiple experiments.

[0106] Therefore, the method may further include performing a simulation under conditions different from those of the first simulation. In a further embodiment, after performing the simulation under the different conditions, a numerical value related to the motion of the media under the different conditions may be obtained. The numerical value related to the motion of the media may include, for example, any one or more of the following: media position, number of collisions, and speed. In a further embodiment, the method may include calculating collision energy based at least on the numerical value related to the motion of the media. The collision energy may be calculated, for example, based on the following formula: Here, E w : Collision energy N c : Number of collisions m * : Converted mass V r : Relative velocity at the time of collision

[0107] The collision energy has a significant effect on the state of the second powder to be pulverized (for example, the size of the second powder after being pulverized using media in the rotating drum). In other words, by calculating the collision energy as described above, the state of the second powder when the pulverization conditions (for example, the rotation speed of the drum and the amount of media filled) are changed can be estimated by simulation alone, without conducting experiments.

[0108] 1. Obtaining actual measurements Particles were packed into a drum and rotated under the following conditions.

[0109]

[0110] Then, the increase ratio was obtained as an actual measurement value under each of Condition 1 and Condition 2.

[0111] 2. Running the simulation (simulation under conditions with larger particle diameter) Next, the conditions of Condition 1 were changed. Specifically, the initial particle diameter was changed to 5 mm. After that, in accordance with the changed particle diameter, the rotation speed and drum diameter were changed so that the following items were the same as those in Condition 1. - Ratio of particle diameter to drum diameter - Froude number - Filling rate - Particle density

[0112] Condition 1 after the change is as follows:

[0113] Under the above-mentioned modified conditions, a particle simulation based on DEM was performed by varying the inter-particle friction coefficient and the inter-particle wall friction coefficient between 0.01 and 0.08.

[0114] As a result, the increase ratio was found to be close to the actual measured value when the following combinations were used.

[0115]

[0116] Therefore, a simulation was performed for these two combinations in the same manner as for condition 1, but with condition 2 changed.

[0117]

[0118] The results of a simulation performed under the friction coefficients listed in Combinations 1 and 2 (i.e., the friction coefficients listed in Table 3) are shown.

[0119]

[0120] Therefore, the condition of combination 1 resulted in a result closer to the increase ratio of the actually measured value. Therefore, the inter-particle friction coefficient and inter-particle wall friction coefficient of combination 1 can be used as the estimated friction coefficient.

[0121] 3. Calculation of friction coefficient based on random forest method Data for the following combinations of explanatory variables and objective variables were prepared.

[0122] Objective variable P f : Coefficient of friction between particles W f : friction coefficient between particle walls

[0123] Explanatory variable D: Ratio of particle diameter to drum diameter F r ': Froude number ratio f: injection rate (vol%) r: particle density (kg / m 3 ) H: Rise ratio (h / D)

[0124] A learning model based on the random forest method was constructed using a specific environment (Python, scikit-learn). The hyperparameters were set as follows: n_estimators: 100, max_depth: 10, max_features: sqrt, min_samples_split: 2.

[0125] Test data was input into the constructed model to obtain the inter-particle friction coefficient and the inter-particle wall friction coefficient. The correlation coefficient between the correct values ​​in the test data and the values ​​output from the model was examined. f (Interparticle friction coefficient): 0.92 W f (friction coefficient between particle walls): 0.97

[0126] It was shown that a high correlation coefficient can be achieved by using an appropriate trained model.

[0127] Specific embodiments of the invention have been described above. The above embodiments are merely illustrative examples, and the present invention is not limited to these embodiments. For example, technical features disclosed in one of the above embodiments may be applied to other embodiments. Furthermore, unless otherwise specified, for a particular method, the order of some steps may be interchanged, and additional steps may be added between two specific steps. The scope of the present invention is defined by the claims.

Claims

1. A method for estimating a first friction coefficient and a second friction coefficient, wherein the first friction coefficient and the second friction coefficient are friction coefficients for simulating the movement of at least one type of powder inside a rotating drum based at least on a discrete element method (DEM), the first friction coefficient being a friction coefficient between powder particles, and the second friction coefficient being a friction coefficient between the powder and an inner wall of the rotating drum, the method comprising: a step of acquiring at least a first measured value, wherein the first measured value is an actual measured value when the powder is moved inside the rotating drum under first conditions; a step of creating first input data based at least on the first conditions and the first measured value; and a step of performing a first simulation based at least on the first input data.

2. A method for estimating a first friction coefficient and a second friction coefficient, wherein the first friction coefficient and the second friction coefficient are friction coefficients for simulating the movement of at least one type of powder inside a rotating drum based at least on a discrete element method (DEM), the first friction coefficient being a friction coefficient between powder particles, and the second friction coefficient being a friction coefficient between the powder and the inner wall of the rotating drum, the method comprising: a step of acquiring at least a first measured value, wherein the first measured value is an actual measured value when the powder is moved inside the rotating drum under first conditions; a step of creating first input data based at least on the first conditions and the first measured value; and a step of performing a first simulation based at least on the first input data; the step of creating the first input data comprises creating a first changed condition based at least on the first condition, and the step of performing the first simulation comprises simulating at least on the first input data based at least on the first changed condition. The first modified condition is compared with the first condition in that the following parameters are the same: ratio of particle diameter to drum diameter; Froude number; packing rate; and particle density. The particle diameter under the first modified condition is larger than the particle diameter under the first condition.

3. The method of claim 2, wherein said first measured value comprises the rise rate or angle of repose of the powder as said rotating drum rotates.

4. A method for estimating a first friction coefficient and a second friction coefficient, wherein the first friction coefficient and the second friction coefficient are friction coefficients for simulating the movement of at least one type of powder inside a rotating drum based at least on a discrete element method (DEM), the first friction coefficient is a friction coefficient between powder particles, and the second friction coefficient is a friction coefficient between the powder and the inner wall of the rotating drum, the method comprising: a step of acquiring at least a first measured value, wherein the first measured value is an actual measured value when the powder is moved inside the rotating drum under first conditions; and a step of creating first input data based at least on the first conditions and the first measured value; and the step of creating the first input data comprises obtaining a candidate first friction coefficient and a candidate second friction coefficient based on at least one of a database and a trained model.

5. The method of claim 4, wherein the trained model includes at least the following terms (a) to (b) as objective variables, and further includes one or more of the following terms (c) to (h) and / or parameter terms derived from (c) to (h) as explanatory variables: (a) first friction coefficient, (b) second friction coefficient, (c) particle diameter, (d) drum diameter, (e) Froude number, (f) packing rate, (g) particle density, and (h) rise ratio or angle of repose.

6. The method of claim 4 or 5, further comprising: a step of acquiring at least a second actual measurement value, wherein the second actual measurement value is an actual measurement value obtained when the powder is moved in the rotating drum under second conditions; and a step of creating first input data comprising creating first input data further based on the second conditions and the second actual measurement value.

7. A method for estimating a first friction coefficient and a second friction coefficient, wherein the first friction coefficient and the second friction coefficient are friction coefficients for simulating the movement of at least one type of powder inside a rotating drum based at least on a discrete element method (DEM), the first friction coefficient being a friction coefficient between powder particles, and the second friction coefficient being a friction coefficient between the powder and the inner wall of the rotating drum, the method comprising: a step of acquiring at least a first measured value and a second measured value, wherein the first measured value is a measured value when the powder is moved inside the rotating drum under first conditions, and the second measured value is a measured value when the powder is moved inside the rotating drum under second conditions different from the first conditions; a step of performing a first simulation based at least on the first conditions; and a step of performing a second simulation based at least on the second conditions. The steps of performing the first simulation and performing the second simulation are repeated until a value resulting from each simulation run is within a range of approximations based at least on the first actual measurement and the second actual measurement.

8. The method of claim 7, wherein at least the rotational speed of the drum is different between the first condition and the second condition.

9. The method of claim 7 or 8, wherein the first and second measured values ​​include the rise ratio or angle of repose of the powder when the rotating drum is rotating.

10. A method according to any one of claims 7 to 9, wherein the step of creating first input data includes creating first modified conditions based at least on the first conditions; the step of creating second input data includes creating second modified conditions based at least on the second conditions; the step of performing a first simulation includes simulating based at least on the first input data based at least on the first modified conditions; the step of performing a second simulation includes simulating based at least on the second input data based at least on the second modified conditions; the first modified conditions are matched with the first conditions in the following parameters: ratio of particle diameter to drum diameter, Froude number, packing rate, and particle density; and the second modified conditions are matched with the second conditions in the following parameters: ratio of particle diameter to drum diameter, Froude number, packing rate, and particle density. The particle diameter under the first modified conditions is larger than the particle diameter under the first conditions, and the particle diameter under the second modified conditions is larger than the particle diameter under the second conditions.

11. A method according to any one of claims 1 to 10, wherein the powder includes a media, the step of acquiring at least a first actual measurement value comprises acquiring an actual measurement value when the media and a second powder are moved in the rotating drum in a state in which they coexist, the step of performing the first simulation comprises performing the first simulation under conditions in which the second powder is not included, the first friction coefficient is the friction coefficient between the media when the second powder coexists, and the second friction coefficient is the friction coefficient between the media and the inner wall of the rotating drum when the second powder coexists, the particle diameter of the media in the step of acquiring at least a first actual measurement value is larger than the particle diameter of the second powder, and the number of the media in the step of acquiring at least a first actual measurement value is smaller than the number of the second powder.

12. A program for executing the method according to any one of claims 1 to 11.

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