A slurry extrusion method, system, electronic device, and storage medium

Abstract

The application provides a slurry extrusion method, system, electronic device and storage medium. The method comprises the following steps: obtaining working data, geometric parameters and slurry viscosity of a slurry mixing extrusion device; establishing a velocity field model in a cylindrical coordinate system according to the working data and the geometric parameters, wherein the velocity field model comprises a radial velocity, a circumferential velocity and an axial velocity; determining a velocity gradient tensor according to the velocity field model; obtaining a stretching efficiency index according to the velocity gradient tensor; adjusting parameters of a PID control algorithm according to the slurry viscosity, and determining a specified PID control algorithm; and generating a screw rotating speed of the slurry mixing extrusion device according to the stretching efficiency index and the specified PID control algorithm.

Description

Technical Field

[0001] This application relates to the field of intelligent control technology for polymer material processing, and in particular to a slurry extrusion method, system, electronic device and storage medium. Background Technology

[0002] In modern industrial production, slurry mixing extruders are widely used in the preparation of high-viscosity slurries such as lithium battery electrode materials, solid propellants, and modified plastics. The quality of these materials directly affects the performance of the final product.

[0003] Existing equipment primarily relies on shearing to achieve mixing, neglecting the crucial role of tensile deformation in dispersion mixing. By only considering shearing, existing equipment simplifies the mixing process to a one-dimensional shear flow. This simplification ignores the three-dimensional characteristics of the actual flow field and fails to account for the critical role of tensile deformation in mixing effectiveness. Relying solely on shearing for mixing results in low efficiency in extrusion processing. Summary of the Invention

[0004] This application provides a slurry extrusion method, system, electronic device, and storage medium to solve the problems existing in related technologies. The technical solution is as follows:

[0005] In a first aspect, embodiments of this application provide a slurry extrusion method, comprising:

[0006] Obtain the operating data, geometric parameters, and slurry viscosity of the slurry mixing and extrusion equipment;

[0007] Based on the working data and geometric parameters, a velocity field model is established in a cylindrical coordinate system. The velocity field model includes radial velocity, circumferential velocity and axial velocity.

[0008] Determine the velocity gradient tensor based on the velocity field model;

[0009] The stretching efficiency index is obtained from the velocity gradient tensor.

[0010] Adjust the parameters of the PID control algorithm according to the slurry viscosity to determine the specified PID control algorithm;

[0011] The screw speed of the slurry mixing extrusion equipment is generated based on the stretching efficiency index and the specified PID control algorithm.

[0012] In one implementation, the working data includes temperature data, and the method further includes:

[0013] Based on temperature data, the barrel of the slurry mixing extrusion equipment is divided into temperature zones to determine multiple temperature zones;

[0014] Obtain the state of the slurry;

[0015] Determine the temperature of each temperature zone based on the state of the slurry;

[0016] The actual shear heat generation power is determined based on the screw speed;

[0017] Obtain the baseline shear heat generation power;

[0018] The supplementary heating power is determined based on the actual shear heat generation power and the reference shear heat generation power.

[0019] Based on the heating compensation power, the temperature difference constraint between adjacent temperature zones, and the temperature of each temperature zone, the target temperature and heating efficiency of each temperature zone are determined.

[0020] In one embodiment, the working data further includes mass flow rate data, slurry concentration variation coefficient, total output data, yield rate data, pressure data, and torque data; geometric parameters include motor power; the method further includes:

[0021] Based on mass flow data, motor power, and heating efficiency in each temperature zone, determine the model that minimizes unit energy consumption;

[0022] Based on the coefficient of variation of slurry concentration, determine the model that maximizes mixing uniformity;

[0023] Based on total output data and qualification rate data, determine the maximum effective productivity;

[0024] Obtain the temperature safety factor, pressure safety factor, and torque safety factor;

[0025] Based on the temperature safety factor, pressure safety factor, and torque safety factor, determine the model for maximizing the safety index;

[0026] The optimal parameter combination, which includes the optimal values ​​of all decision variables, is determined by solving the multi-objective optimization model of minimizing unit energy consumption, maximizing mixed uniformity, maximizing effective productivity, and maximizing safety index through a multi-objective optimization algorithm.

[0027] In one implementation, the method further includes:

[0028] Obtain historical production data;

[0029] The original quality control model is trained using historical production data to generate a trained quality control model.

[0030] The optimal parameter combination is input into the trained quality control model to generate predicted quality control results, including density, viscosity, and uniformity.

[0031] In one implementation, the method further includes:

[0032] Determine whether the predicted quality value deviates from the target range;

[0033] When the density deviation exceeds a first specified range, a first specified strategy is generated;

[0034] Adjust the screw speed, target temperature of each temperature zone, and vacuum level according to the first specified strategy;

[0035] When the viscosity deviation exceeds the second specified range, a second specified strategy is generated;

[0036] According to the second specified strategy, adjust the screw speed, the target temperature of each temperature zone, and the slurry ratio;

[0037] When the uniformity index exceeds a third specified range, a third specified strategy is generated;

[0038] According to the third specified strategy, adjust the stretching efficiency target, the target temperature of each temperature zone, and the mixing time.

[0039] In one embodiment, the working data also includes the screw angular velocity, the additional angular velocity generated by the interaction of the twin screws, and the volumetric flow rate; the geometric parameters also include the barrel eccentricity, the barrel inner radius, and the barrel outer radius. Based on the working data and geometric parameters, a velocity field model is established in a cylindrical coordinate system. The velocity field model includes radial velocity, circumferential velocity, and axial velocity.

[0040] A cylindrical coordinate system is established with the axis of the slurry mixing and extrusion equipment as the z-axis;

[0041] The radial velocity component is determined based on the cylindrical coordinate system, the barrel eccentricity, the barrel inner radius, the barrel outer radius, and the screw angular velocity.

[0042] Determine the circumferential velocity component based on the cylindrical coordinate system and the additional angular velocity;

[0043] The axial velocity component is determined based on the cylindrical coordinate system, volumetric flow rate, and velocity distribution function.

[0044] In one implementation, the tensile efficiency index is obtained based on the velocity gradient tensor, including:

[0045] The velocity gradient tensor is decomposed to obtain the stretchability tensor;

[0046] Based on the stretching tensor, determine the first eigenvalue, the second eigenvalue, and the third eigenvalue;

[0047] The principal tensile strength is determined based on the first and second eigenvalues.

[0048] The total deformation strength is determined based on the first eigenvalue, the second eigenvalue, and the third eigenvalue.

[0049] The tensile efficiency index is determined based on the principal tensile strength and the total deformation strength.

[0050] Secondly, embodiments of this application provide a system, including:

[0051] The first acquisition module is used to acquire the working data, geometric parameters, and slurry viscosity of the slurry mixing and extrusion equipment;

[0052] The first module is used to establish a velocity field model in a cylindrical coordinate system based on working data and geometric parameters. The velocity field model includes radial velocity, circumferential velocity and axial velocity.

[0053] The first determining module is used to determine the velocity gradient tensor based on the velocity field model;

[0054] The first module is used to obtain the stretching efficiency index based on the velocity gradient tensor.

[0055] The second determining module is used to adjust the parameters of the PID control algorithm according to the slurry viscosity and determine the specified PID control algorithm;

[0056] The first generation module is used to generate the screw speed of the slurry mixing extrusion equipment based on the stretching efficiency index and a specified PID control algorithm.

[0057] Thirdly, embodiments of this application provide an electronic device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the above-described slurry extrusion method.

[0058] Fourthly, embodiments of this application provide a computer-readable storage medium that stores computer instructions, wherein when the computer instructions are executed on a computer, the methods in any of the above-described embodiments are performed.

[0059] The advantages or beneficial effects of the above technical solutions include at least the following:

[0060] In this embodiment, the slurry extrusion method includes: acquiring the working data, geometric parameters, and slurry viscosity of the slurry mixing extrusion equipment; establishing a velocity field model in a cylindrical coordinate system based on the working data and geometric parameters, the velocity field model including radial velocity, circumferential velocity, and axial velocity; determining the velocity gradient tensor based on the velocity field model; obtaining the stretching efficiency index based on the velocity gradient tensor; adjusting the parameters of the PID control algorithm based on the slurry viscosity to determine a specified PID control algorithm; and generating the screw speed of the slurry mixing extrusion equipment based on the stretching efficiency index and the specified PID control algorithm. Through the slurry extrusion method of this embodiment, by fully considering the shear deformation of the stretching deformation replacement portion, energy utilization efficiency is improved. The stretching efficiency index of the three-dimensional stretching deformation of the slurry is calculated in real time. The screw speed is adjusted based on the stretching efficiency index and the specified PID algorithm optimized according to the slurry viscosity, so that the stretching efficiency is maintained within the optimal range. This improves the working efficiency of the slurry mixing extrusion equipment, reduces energy consumption, and effectively solves the problem that existing equipment mainly relies on shear action to achieve mixing, neglecting the important role of stretching deformation in dispersion mixing. Existing equipment only considers shear action, simplifying the mixing process into one-dimensional shear flow. This simplification ignores the three-dimensional characteristics of the actual flow field and does not consider the key role of tensile deformation in the mixing effect. It relies solely on shear action for mixing, resulting in the technical problem of low efficiency in extrusion processing.

[0061] The above overview is for illustrative purposes only and is not intended to be limiting in any way. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features of this application will become readily apparent from the accompanying drawings and the following detailed description. Attached Figure Description

[0062] In the accompanying drawings, unless otherwise specified, the same reference numerals throughout the various drawings denote the same or similar parts or elements. These drawings are not necessarily drawn to scale. It should be understood that these drawings depict only some embodiments disclosed in this application and should not be construed as limiting the scope of this application.

[0063] Figure 1 This is a schematic diagram of a slurry extrusion method according to an embodiment of this application;

[0064] Figure 2 This is a block diagram of an electronic device used to implement the slurry extrusion method of the embodiments of this application.

[0065] Figure 3 This is a three-dimensional model of the high-efficiency slurry equipment with a topological spiral twin rotor used to implement the slurry extrusion method of the embodiments of this application.

[0066] Figure 4This is a schematic diagram of the topological spiral twin-rotor extruder used to implement the slurry extrusion method of the embodiments of this application. Detailed Implementation

[0067] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of this application. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0068] In related technologies, operators rely on years of accumulated experience to judge operating conditions by observing the slurry state, listening to equipment operation sounds, and touching the barrel temperature, manually adjusting parameters such as speed and temperature. This method has the following serious problems: 1. Product quality heavily depends on the operator's personal experience; product quality differences between different operators can reach 15%–20%. 2. Requires continuous 24-hour monitoring by operators, resulting in high labor costs (over 400,000 RMB per unit per year). 3. Quality fluctuations caused by human factors are unavoidable, with batch pass rates of only 90%–94%. 4. Does not consider the crucial role of tensile deformation in mixing effects, relying solely on shear mixing, leading to low efficiency. 5. Cannot quantitatively evaluate mixing quality; judgment can only be made through post-processing inspections, resulting in a large amount of waste by the time problems are discovered. 6. Lack of understanding of energy dissipation mechanisms; a large amount of energy is wasted as heat, with energy utilization rate of only 20%–30%. 7. The rheological behavior of high-viscosity slurries is extremely complex, involving multiple disciplines such as non-Newtonian fluid mechanics, heat and mass transfer, and chemical reactions; traditional engineering methods struggle to establish accurate mathematical models.

[0069] like Figure 1 As shown, in a first aspect, embodiments of this application provide a slurry extrusion method, comprising:

[0070] S110: Obtain the operating data, geometric parameters, and slurry viscosity of the slurry mixing and extrusion equipment;

[0071] S120: Based on the working data and geometric parameters, establish a velocity field model in the cylindrical coordinate system. The velocity field model includes radial velocity, circumferential velocity and axial velocity.

[0072] S130: Determine the velocity gradient tensor based on the velocity field model;

[0073] S140: The stretching efficiency index is obtained based on the velocity gradient tensor;

[0074] S150: Adjust the parameters of the PID control algorithm according to the slurry viscosity to determine the specified PID control algorithm;

[0075] S160: Generate the screw speed of the slurry mixing extrusion equipment based on the stretching efficiency index and the specified PID control algorithm.

[0076] The slurry extrusion method of this embodiment improves energy utilization efficiency by fully considering the shear deformation of the tensile deformation-substituted portion. It calculates the tensile efficiency index of the slurry's three-dimensional tensile deformation in real time, and adjusts the screw speed based on the tensile efficiency index and a specified PID algorithm optimized for slurry viscosity. This maintains the tensile efficiency within the optimal range, improving the working efficiency of the slurry mixing extrusion equipment and reducing energy consumption. It effectively solves the problem that existing equipment mainly relies on shear action for mixing, neglecting the crucial role of tensile deformation in dispersion mixing. Existing equipment only considers shear action, simplifying the mixing process to one-dimensional shear flow. This simplification ignores the three-dimensional characteristics of the actual flow field and fails to consider the critical role of tensile deformation in the mixing effect, leading to low extrusion efficiency due to reliance solely on shear action.

[0077] like Figure 3-4 As shown, this application uses a topological spiral twin-rotor extruder, such as... Figure 3 As shown, the high-efficiency topological spiral twin-rotor slurry equipment includes a twin-screw extruder, a topological spiral twin-rotor extruder, and a quantitative continuous feeding device. The twin-screw extruder is connected to one quantitative continuous feeding device, and the topological spiral twin-rotor extruder is connected to three quantitative continuous feeding devices. The electrode slurry raw material system is first premixed in the twin-screw extruder, and then extruded into the topological spiral twin-rotor extruder for further enhanced mixing and dispersion. During the mixing and dispersion process, the slurry viscosity is adjusted by the three quantitative continuous feeding devices, and finally, vacuum degassing and cooling are performed. The main innovation lies in the topological spiral twin-rotor extruder, such as... Figure 4 As shown, the topological spiral twin rotor extruder for volumetric stretching and conveying involves two meshing eccentric rotors arranged in parallel within the inner cavity of an "8"-shaped stator. The rotors, rotating in the same or opposite directions, mesh with the stator, causing the volume of the cavity formed by the rotor and stator to change periodically during rotation, thus achieving volumetric stretching and mixing conveying.

[0078] The outer surface of the dual rotors is composed of multiple alternating eccentric helical structures and eccentric cylindrical structures of varying lengths. The eccentric helical and cylindrical structures of the eccentric rotor mesh with each other. The axes of the eccentric helical structures of both rotors are the same as the rotor's rotation axis, while the axes of the eccentric cylindrical structures are eccentric to the rotor's rotation axis. Furthermore, the eccentric directions of the eccentric cylindrical structures at different positions on the same rotor are the same. The trajectory of the rotor's cross-section center is a circle with radius e, i.e., the rotor's eccentric circle.

[0079] In step S110, the operating data, geometric parameters, and slurry viscosity of the slurry mixing and extrusion equipment are obtained;

[0080] In this embodiment, data on six dimensions—temperature, pressure, rotational speed, torque, flow rate, and viscosity—are collected in real time on the slurry mixing and extrusion equipment using corresponding sensors. This data is then standardized to output a 34-dimensional real-time data vector. Specifically:

[0081] Temperature sensors: 24 PT100 platinum resistance thermometers are arranged along the barrel axis, 3 for each temperature zone, in a 120° circumferential distribution; the sampling frequency of the temperature sensors is 10Hz (slow response).

[0082] Pressure sensors: One piezoelectric sensor is installed in each of the feeding section, compression section, melting section, and metering section; the sampling frequency of the pressure sensors is 100Hz (dynamically changing).

[0083] Torque sensor: One strain gauge sensor is installed on each of the two screw drive shafts; the pressure sensor has a sampling frequency of 1000Hz (transient fluctuation).

[0084] Speed ​​encoder: Each screw is equipped with one 2048-line photoelectric encoder; the speed encoder sampling frequency is 1000Hz (high-precision control);

[0085] Flow meter: Install one Coriolis mass flow meter at the outlet;

[0086] Online viscometer: Install a rotary viscometer in front of the machine head.

[0087] Outlier handling is performed on data in six dimensions: temperature, pressure, speed, torque, flow rate, and viscosity. For example, the 3σ criterion is used to identify and handle outliers.

[0088] The mean μ and standard deviation σ of data from six dimensions: temperature, pressure, speed, torque, flow rate, and viscosity.

[0089] Identify data points outside the range [μ-3σ, μ+3σ] and replace outliers with the average of the two preceding and following normal values.

[0090] Data for six dimensions—temperature, pressure, rotational speed, torque, flow rate, and viscosity—are normalized and mapped to the [0,1] interval. A unified timestamp benchmark is established, and interpolation algorithms are used to align the data for these six dimensions at different sampling rates.

[0091] Finally, a standardized real-time data matrix D(t) is obtained.

[0092] D(t) = [T1(t), T2(t), ..., T24(t), 24 temperature values]

[0093] P1(t), P2(t), P3(t), P4(t), 4 pressure values

[0094] M1(t), M2(t), two torque values

[0095] ω1(t), ω2(t), two rotational speed values

[0096] Q(t), a single flow value

[0097] η(t)] is a viscosity value.

[0098] The real-time data matrix D(t) is a 34-dimensional real-time data vector.

[0099] In step S120, a velocity field model is established in a cylindrical coordinate system based on the working data and geometric parameters. The velocity field model includes radial velocity, circumferential velocity and axial velocity.

[0100] In this embodiment, a precise three-dimensional velocity field model is established to calculate the tensile deformation state of the slurry at each location. The three-dimensional velocity field model defines the three-dimensional flow characteristics within the twin-screw extruder, revealing the decisive role of tensile deformation in the mixing effect and providing a foundation for optimized control.

[0101] The velocity field model is calculated, corrected, and verified using key parameters in the real-time data matrix D(t). For example, the velocity field is calculated using rotational speed data ω1(t) and ω2(t); the slurry viscosity is corrected using temperature data T(t); and the accuracy of the flow field calculation is verified using pressure data P(t).

[0102] Establish a cylindrical coordinate system (r, θ, z) with the extruder axis as the z-axis.

[0103] Derivation of the velocity field equations: Considering the eccentric rotational motion of the twin screw, the three components of the velocity field are:

[0104] Radial velocity component vr:

[0105]

[0106] in:

[0107] e is the eccentricity (determined by geometric design, typical value 5mm); ω is the screw angular velocity; sinθ indicates that the velocity changes with the angle, forming periodic extrusion; (1-(r-ri) / h(θ)) indicates that the velocity gradually decreases from the rotor surface to the stator surface; the radial velocity component vr describes the radial extrusion and expansion motion of the slurry.

[0108] Circumferential velocity component vθ:

[0109] vθ = ω·r + Δω(r,θ)

[0110] Δω is the additional angular velocity generated by the interaction of the twin screws; the circumferential velocity component vθ describes the rotational motion and circumferential transport of the slurry.

[0111] Axial velocity vz:

[0112] vz = Q / (π(ro 2 -ri 2 ))·f(r)

[0113] Where: Q is the volumetric flow rate; f(r) is the velocity distribution function (determined according to rheology);

[0114] Physical meaning: Axial velocity vz describes the transport of slurry along the extrusion direction.

[0115] Based on the cylindrical coordinate system (r, θ, z), radial velocity, circumferential velocity, and axial velocity obtained above, the velocity field model can be determined.

[0116] In step S130, the velocity gradient tensor is determined based on the velocity field model;

[0117] In this embodiment, the velocity gradient tensor in the cylindrical coordinate system (r, θ, z) takes the following form:

[0118] v / r (1 / r)( v / θ) - vθ / r v / z

[0119] L= vθ / r (1 / r)( vθ / θ) + v / r vθ / z

[0120] vz / r (1 / r)( vz / θ) vz / z

[0121] Where: v : Radial velocity component (m / s); vθ: Circumferential velocity component (m / s); vz: Axial velocity component (m / s); r: Radial coordinate (m); θ: Angular coordinate (rad); z: Axial coordinate (m);

[0122] The physical meaning of each component is as follows:

[0123] L11: Radial tension / compression; L22: Circumferential tension / compression; L33: Axial tension / compression; Off-diagonal terms: Shear deformation;

[0124] Assuming a certain moment and position, the velocity field model calculates the following: vr = 0.02 m / s (radial velocity); vθ = 0.15 m / s (circumferential velocity); vz = 0.10 m / s (axial velocity); r = 0.03 m (current radius position); calculate the partial derivatives (using the finite difference method):

[0125] vr / r = 0.5 s -1 ; vr / θ = 0.1 s -1 ; vr / z = 0.05 s -1 ; vθ / r = 2.0 s -1 ; vθ / θ = 0.3 s -1 ; vθ / z = 0.1 s -1 ; vz / r = 0.8 s -1 ; vz / θ = 0.2 s -1 ; vz / z = 1.5 s -1 .

[0126] Substituting the values, we obtain matrix L:

[0127] [0.5 -1.67 0.05]

[0128] L = [2.0 5.50 0.10] [0.8 0.20 1.50]

[0130] The velocity gradient tensor L can be determined through the above calculation process.

[0131] In step S140, the stretching efficiency index is obtained based on the velocity gradient tensor.

[0132] In this embodiment, the decomposition principle of the velocity gradient tensor L is as follows: any flow can be decomposed into two basic motions: deformation motion (changing the shape of the fluid element), described by the elongation tensor D; and rigid body rotation (changing direction without changing shape), described by the vorticity tensor W.

[0133] The velocity gradient tensor L can be uniquely decomposed into a symmetric part and an antisymmetric part:

[0134] L = D + W

[0135] Where: D = (L + L^T) / 2 (symmetric tensor, stretching tensor); W = (L - L^T) / 2 (antisymmetric tensor, vorticity tensor)

[0136] For example: Calculate the transpose matrix L^T of L. [0.5 2.0 0.8]

[0138] L^T = [-1.67 5.50 0.20] [0.05 0.10 1.50]

[0140] Calculate L + L^T

[0141] [0.5 -1.67 0.05] [0.5 2.0 0.8]

[0142] L+ L^T = [2.0 5.50 0.10] + [-1.67 5.50 0.20] [0.8 0.20 1.50] [0.05 0.10 1.50] [1.00 0.33 0.85]

[0145] = [0.33 11.00 0.30] [0.85 0.30 3.00]

[0147] Calculate the elongation tensor D

[0148] D = (L + L^T) / 2 [0.50 0.165 0.425]

[0150] D = [0.165 5.50 0.15] [0.425 0.15 1.50]

[0152] The physical meaning of the stretchability tensor D:

[0153] Diagonal elements (D) 11 =0.50, D 22 =5.50, D 33 =1.50): represents the stretching / compression rate in the three coordinate directions;

[0154] off-diagonal elements (D 12 =0.165, D 13 =0.425, D 23 =0.15): represents the shear deformation rate;

[0155] Calculation of vorticity tensor W

[0156] W = (L - L^T) / 2

[0157] [0 -1.835 -0.375]

[0158] W=[1.835 0 -0.05 ] [0.375 0.05 0 ]

[0160] The physical meaning of the vorticity tensor W: The vorticity tensor W is an antisymmetric tensor with diagonal elements being zero; off-diagonal elements represent rotational rates; it does not contribute to mixing but consumes energy.

[0161] For the elongation tensor D, the eigenvalues ​​λ of the elongation tensor D represent the elongation rate in the principal elongation direction: the first eigenvalue λ1: the maximum principal elongation rate; the second eigenvalue λ2: the intermediate principal elongation rate; and the third eigenvalue λ3: the minimum principal elongation rate (which may be negative, indicating compression).

[0162] The eigenvalue λ satisfies: det(D - λl) = 0; where I is the identity matrix and det represents the determinant. Expanding into a standard cubic equation:

[0163] λ 3 -l1λ 2 +l2λ-I3=0

[0164] Formula for calculating invariants:

[0165] First invariant (trace):

[0166] I1 = tr(D) = D 11 + D 22 + D 33

[0167] Physical meaning: Volume expansion rate

[0168] Second invariant:

[0169] I2 = (1 / 2)[(tr(D)) 2 - tr(D 2 )]

[0170] = D 11 D 22 + D 22 D 33 +D 33 D11 - D 12 2 - D 23 2 - D 31 2

[0171] Physical meaning: Rate of change of area

[0172] Third invariant (determinant):

[0173] I3 = det(D) = D 11 (D 22 D 33 - D 23 2 ) - D 12 (D 12 D 33 - D 23 D 13 ) + D 13 (D 12 D 23 - D 22 D 13 )

[0174] Variable substitution

[0175] Let λ = μ + I1 / 3, then the original equation is transformed into:

[0176] μ 3 +pμ+ q = 0

[0177] Where: p = I2 - I1 2 / 3; q = 2I1 3 / 27 - I1I2 / 3 + I3;

[0178] Discriminant calculation:

[0179] Δ = -(4p 3 +27q 2 ) / 108

[0180] Expression of three real roots

[0181] When Δ > 0 (as guaranteed by a symmetric matrix):

[0182] The first eigenvalue λ1 = I1 / 3 + 2√(-p / 3)cos(θ / 3);

[0183] The second eigenvalue λ2 = I1 / 3 + 2√(-p / 3)cos((θ+ 2π) / 3);

[0184] The third eigenvalue λ3 = I1 / 3 + 2√(-p / 3)cos((θ+ 4π) / 3);

[0185] Where: θ = arccos(3q√(-3 / p) / 2p). The eigenvalues ​​satisfy the equation: det(D - λI) = 0;

[0186] Where I is the identity matrix and det represents the determinant.

[0187] Expanded to:

[0188] |0.50-λ 0.165 0.425|

[0189] |0.165 5.50-λ 0.15 | = 0

[0190] |0.425 0.15 1.50-λ|

[0191] Calculate the determinant

[0192] Expanding the third-order determinant yields the characteristic polynomial:

[0193] -λ 3 + (0.50+5.50+1.50)λ 2 - [(0.50×5.50+0.50×1.50+5.50×1.50) - (0.165 2 +0.425 2 +0.15 2 )]λ+det(D) = 0

[0194] Simplified to:

[0195] -λ 3 + 7.50λ 2 - 11.47λ + 3.89 = 0

[0196] Solving a cubic equation using numerical methods (such as the Newton-Raphson method) or analytical methods (such as Cardin's formula) yields three real roots:

[0197] The first eigenvalue λ1 = 5.58 s -1 (Maximum eigenvalue);

[0198] The second eigenvalue λ² = 1.47 s -1 (Intermediate eigenvalues);

[0199] The third eigenvalue λ3 = 0.45 s -1 (Minimum eigenvalue).

[0200] Two-dimensional principal tensile strength:

[0201] Is=√(λ1 2 +λ2 2 )

[0202] Parameter description: λ1: maximum eigenvalue (direction of strongest tension), λ2: intermediate eigenvalue (direction of second strongest tension).

[0203] Three-dimensional total deformation strength:

[0204] Id = √(λ1 2 + λ2 2 + λ3 2 ) = √(tr(D 2 ))

[0205] The formula for defining the tensile efficiency index is:

[0206] ψ = Is / Id = √(λ1) 2 +λ2 2 ) / √(λ1 2 + λ2 2 + λ3 2 )

[0207] Range of values ​​and physical meaning:

[0208] ψ∈ [0, 1]; ψ → 1: pure two-dimensional stretching (ideal); ψ → 0.577: pure shear flow; ψ < 0.5: three-dimensional compression is dominant.

[0209] Maximizing stretching efficiency:

[0210] maxψ = max{√(λ1) 2 +λ2 2 ) / √(λ1 2 + λ2 2 + λ3 2 )}

[0211] Constraints:

[0212] λ1 2 + λ2 2 + λ32 = 0 (incompressible fluid);

[0213] |λ | < λ_max (physical limit).

[0214] Specifically, the principal tensile strength is defined as the tensile strength within the principal tensile plane (λ1-λ2 plane):

[0215] Is = √(λ1 2 + λ2 2 )

[0216] = √(5.58 2 + 1.47 2 )

[0217] = √(31.14 + 2.16)

[0218] = √33.30

[0219] = 5.77 s -1

[0220] Is represents the combined tensile strength in the two principal directions that contribute the most to the mixing.

[0221] Calculation of total deformation strength Id: Total deformation strength includes deformation in all three directions:

[0222] Id = √(λ1 2 + λ2 2 + λ3 2 )

[0223] = √(5.58 2 + 1.47 2 + 0.45 2 )

[0224] = √(31.14 + 2.16 + 0.20)

[0225] = √33.50

[0226] = 5.79 s -1

[0227] Calculation of the tensile efficiency index ψ:

[0228] ψ = Is / Id

[0229] = 5.77 / 5.79

[0230] = 0.997

[0231] Results analysis: ψ = 0.997 ≈ 1.0, indicating that the deformation is almost entirely tensile deformation with a very small shear component, resulting in extremely high mixing efficiency.

[0232] Through the above calculation process, the tensile efficiency index can be analyzed and determined.

[0233] The optimal value was determined through extensive experiments and theoretical analysis:

[0234] ψ < 0.5: Shear-dominated, low mixing efficiency, high energy consumption;

[0235] 0.6 < ψ < 0.7: Stretching dominates, resulting in optimal mixing efficiency;

[0236] ψ > 0.8: Excessive stretching may lead to slurry degradation.

[0237] A real-time tensile efficiency index ψ(t) is generated, which will serve as the core control target for controlling the screw speed. In this embodiment, the tensile efficiency index ψ is established as the core control target, and by adjusting the motion parameters of the dual-axis eccentric rotor, ψ is maintained within the optimal range of 0.60-0.70.

[0238] In step S150, the parameters of the PID control algorithm are adjusted according to the slurry viscosity to determine the specified PID control algorithm.

[0239] In this embodiment, the PID control algorithm can be executed by a PID controller, and the PID control algorithm includes:

[0240] P (proportional) control: The larger the deviation, the larger the adjustment (fast response); I (integral) control: Accumulates historical deviations to eliminate steady-state errors (precise control); D (derivative) control: Predicts deviation trends and adjusts in advance (smooth control).

[0241] Control output = Kp × current deviation e + Ki × deviation integral + Kd × deviation change rate;

[0242] For high-viscosity slurries (such as rubber, viscosity > 1000 Pa·s): reduce Kp to 1.6 (to avoid overloading the equipment due to excessive adjustment); reduce Ki to 0.4 (to prevent excessive cumulative effect); keep Kd at 0.08 (moderate prediction); reason: high-viscosity slurries respond slowly, and too rapid adjustment will cause instability.

[0243] For low-viscosity slurries (such as coatings, viscosity <100 Pa·s): increase Kp to 2.4 (to speed up response); increase Ki to 0.6 (to enhance steady-state accuracy); increase Kd to 0.12 (to improve dynamic performance); reason: low-viscosity slurries respond quickly and require more sensitive control.

[0244] For example: Error calculation: e(t) = ψ_target - ψ(t);

[0245] PID output: u(t) = Kp·e(t) + Ki·∫e(τ)dτ + Kd·de / dt;

[0246] PID control algorithm rules:

[0247] If η > 1000 Pa·s (high viscosity slurry): Kp = 1.6 (proportional coefficient, fast response); Ki = 0.4 (integral coefficient, eliminate steady-state error); Kd = 0.08 (differential coefficient, suppress oscillation).

[0248] If 100 < η < 1000 Pa·s (medium viscosity slurry): Kp = 2.0; Ki = 0.5; Kd = 0.10;

[0249] If η < 100 Pa·s (low viscosity slurry): Kp = 2.4; Ki = 0.6; Kd = 0.12.

[0250] Based on the PID control algorithm described above, parameters are adjusted to suit slurries of different viscosities. When adjusting the PID control algorithm parameters, high-viscosity slurries have a slow response and require a smaller control gain to avoid overshoot; low-viscosity slurries have a fast response and can use a larger control gain to improve the response speed.

[0251] In step S160, the screw speed of the slurry mixing extrusion device is generated based on the stretching efficiency index and the specified PID control algorithm.

[0252] In the embodiments of this application, the real-time tensile efficiency index ψ(t) can be known according to the above embodiments, and a target tensile efficiency index is configured: ψ target For example, ψ target = 0.65 (optimal value);

[0253] The current deviation e: e = ψ target -ψ current = 0.65 - 0.58 = 0.07;

[0254] Where: e > 0: insufficient stretching, the rotation speed needs to be adjusted to increase the stretching; e = 0: just at the optimal state; e < 0: excessive stretching or excessive shearing.

[0255] The output of the specified PID control algorithm is u(t) = Kp × current deviation e + Ki × deviation integral + Kd × deviation change rate;

[0256] The above calculation shows that the current deviation e is 0.07. Substituting this into the formula of the specified PID control algorithm above;

[0257] The proportional term P = Kp × e = 2.0 × 0.07 = 0.14

[0258] The integral term I = Ki × ∫e dt = 0.5 × 0.21 = 0.105 (assuming the cumulative deviation is 0.21).

[0259] The differential term D = Kd × de / dt = 0.1 × 0.02 = 0.002 (assuming the rate of change of deviation is 0.02).

[0260] The control quantity u(t) = P + I + D = 0.14 + 0.105 + 0.002 = 0.247;

[0261] Optimized screw speed ω in slurry mixing extrusion equipment new =Current screw speed ω of the slurry mixing and extrusion equipment current +Adjustment coefficient α×Control quantity u(t);

[0262] ω new =ω current +α×u(t)

[0263] The determination of α (adjustment coefficient) is crucial. Too large an α results in excessive adjustment and system oscillation; too small an α results in slow adjustment and sluggish response. A suitable value for α is determined through system testing, typically between 0.1 and 0.3. current This is the current rotational speed.

[0264] Based on the example above: Base adjustment amount = α × u(t)

[0265] = 0.3 × 0.247

[0266] = 0.074 rad / s

[0267] New speed = Current speed + Basic adjustment amount

[0268] = 3.0 + 0.074

[0269] = 3.074 rad / s

[0270] u(t) is the PID control algorithm specified above.

[0271] Based on the new rotational speed calculated above, in order to ensure the safe operation of the equipment, corresponding safety constraints also need to be configured:

[0272] Rotational speed limit: 0.5 ≤ ωnew ≤ 10.0 rad / s;

[0273] Rate of change limit: |dω / dt| ≤ 0.5 rad / s 2 ;

[0274] If the rotation speed is too low (<0.5): the slurry will not flow and will cause blockage.

[0275] Too high a rotation speed (10): The equipment cannot withstand it and may be damaged.

[0276] The change is too rapid (>0.5 / second) 2 ): High mechanical impact affects lifespan.

[0277] In this embodiment, the screw speed is adjusted using a specified PID control algorithm based on the stretching efficiency index to maintain the stretching efficiency within the optimal range. This achieves precise control based on physical mechanisms, overcoming the limitations of traditional PID control and significantly improving mixing efficiency and product quality.

[0278] In one implementation, the working data includes temperature data, and the method further includes:

[0279] Based on temperature data, the barrel of the slurry mixing extrusion equipment is divided into temperature zones to determine multiple temperature zones;

[0280] Obtain the state of the slurry;

[0281] Determine the temperature of each temperature zone based on the state of the slurry;

[0282] The actual shear heat generation power is determined based on the screw speed;

[0283] Obtain the baseline shear heat generation power;

[0284] The supplementary heating power is determined based on the actual shear heat generation power and the reference shear heat generation power.

[0285] Based on the heating compensation power, the temperature difference constraint between adjacent temperature zones, and the temperature of each temperature zone, the target temperature and heating efficiency of each temperature zone are determined.

[0286] In the embodiments of this application, when the screw speed is adjusted in the above embodiments, the thermal balance state of the entire device will change. This embodiment can actively compensate for the changes in shear heat generation by:

[0287] Increased screw speed leads to enhanced shearing action, which in turn increases the conversion of mechanical energy into heat energy. This necessitates a corresponding reduction in external heating power to prevent overheating of the slurry. For every 1 rad / s increase in screw speed, the heat generated by shearing increases by approximately 15-20 kW.

[0288] To ensure the slurry is within the optimal processing temperature window, if the temperature is too low, the slurry will not be sufficiently plasticized and the mixing effect will be poor; if the temperature is too high, the slurry will degrade, the molecular chains will break, and the performance will decline. The optimal window is usually within the range of ±5℃.

[0289] The barrel temperature can be zoned: the barrel can be divided into 8 independent control zones, and the target temperature for each zone can be determined according to the slurry state.

[0290] Optimizing the temperature gradient distribution can avoid thermal stress caused by sudden temperature changes, ensure gradual heating and plasticization of the slurry, and prevent the formation of local hot spots.

[0291] Each temperature zone can be divided according to its corresponding function:

[0292] In the first and second temperature zones (Zone 1-2, solid conveying section), the slurry is in a solid particle state and is mainly conveyed forward by friction.

[0293] Set temperature T target = Melting temperature T melt -20℃

[0294] For example, CPVC material: Melting temperature: 195℃; Zone 1 setting: 175℃; Zone 2 setting: 180℃.

[0295] The reason for the above temperature setting is the necessity of equipment preheating. Cold slurry entering the high-temperature zone directly will cause thermal shock. Gradual preheating can release the internal stress of the slurry, increase the friction coefficient between the slurry and the screw, increase the conveying efficiency, and avoid premature plasticization. Premature plasticization will cause the slurry to stick to the screw, forming a "bridging" phenomenon, which will hinder the solid conveying. Maintaining the solid state ensures stable volume conveying.

[0296] In the third and fourth temperature zones (Zones 3-4, the compression and melting zone), the slurry changes from a solid to a molten state, and its volume decreases sharply.

[0297] Set temperature T target = Melting temperature T melt +5℃

[0298] Zone 3 setting: 197℃;

[0299] Zone 4 setting: 200℃

[0300] The reason for setting the temperature above is to ensure the slurry is completely melted. If unmelted particles become the core of uneven mixing, they will affect the mechanical properties of the final product and may cause fluctuations in extrusion pressure.

[0301] In Zones 5 and 6 (mixing zone), the slurry is completely melted and subjected to intense stretching and mixing.

[0302] Set temperature T target =Optimal processing temperature T process :

[0303] This is the most critical temperature control area:

[0304] The method for determining the optimal processing temperature is as follows:

[0305] T process = T melt + ΔT rheology + ΔT stability

[0306] in:

[0307] ΔT rheology Temperature correction based on rheological properties (5-15℃);

[0308] ΔT stability Temperature correction based on thermal stability (-10 to 0℃);

[0309] In Zones 7 and 8 (metering sections), the slurry is homogenized and ready for extrusion.

[0310] Set temperature T target =Processing temperature T process -5℃

[0311] The technical reasons for cooling in the seventh and eighth temperature zones are: to stabilize the slurry state, slightly reduce the slurry viscosity, improve the stability of the extrusion pressure, reduce the outlet expansion effect, enable energy recovery, and utilize the slurry's own heat capacity for buffering, reducing unnecessary heating power and preparing for subsequent cooling.

[0312] In this embodiment, the temperature field and velocity field are not independent of each other during the slurry mixing and extrusion process. Instead, they are tightly coupled through temperature-speed coupling compensation to achieve energy conversion. When the screw speed changes, the shear heat generation changes accordingly, and the external heating power needs to be adjusted to maintain temperature stability.

[0313] The quantitative calculation process for shear heat generation is as follows:

[0314] Shear heat generation at the reference rotational speed (ω0 = 3.0 rad / s):

[0315] Q base =η0 × γ 0 2 × V

[0316] Q base Based on heating power, γ 0 is the baseline shear rate, and η0 is;

[0317] New rotational speed (ω) new Shear heat generation under ( )

[0318] Q new = η new × γ new 2 × V

[0319] Due to the shear rate γ It is directly proportional to the screw speed ω. When the speed increases by 50%:

[0320] γ new = 1.5 × γ 0

[0321] Q new ≈ 1.5 2 × Q base = 2.25 × Q base

[0322] γ new For the new shear rate; Q new For new heating power

[0323] Shear heat generation increased by 125%!

[0324] Compensation formula:

[0325] New heating power P heat new = P heat base - β × (ω - ω base ) 2

[0326] ω base : Represents the commonly used reference speed for a certain process, corresponding to the baseline operating condition;

[0327] β (shear heat generation coefficient): obtained by regression of historical data or heat balance, used to quantify the substitution effect of heat generation on external heating demand, and obtained through experimental calibration;

[0328] P heat base Reference heating power (at ω = ω) base (Empirical or calibration value at that time)

[0329] The compensation coefficients differ in different temperature zones because: different screw channel depths lead to different shear rates, different slurry states lead to different viscosities, and different residence times lead to different degrees of heating.

[0330] Compensation coefficients for each district:

[0331] Zone 1-2: β = 0.5 kW / (rad / s) 2 (Solid transport, less heat generation from shearing);

[0332] Zone 3-4: β = 1.0 kW / (rad / s) 2 (It begins to melt, and heat generation increases);

[0333] Zone 5-6: β = 1.5 kW / (rad / s) 2 (Completely melted, generating the most heat);

[0334] Zone 7-8: β = 0.8 kW / (rad / s) 2 (In the metering section, heat generation is reduced).

[0335] In addition, the temperature difference between adjacent temperature zones is limited to within 10°C to avoid thermal stress.

[0336] Reasons for the temperature difference limitation between adjacent temperature zones:

[0337] Thermal stress control; thermal stress σ = E·α·ΔT

[0338] in:

[0339] E is the elastic modulus (2-3 GPa);

[0340] α is the coefficient of thermal expansion (7-9×10⁻⁶). -5 / ℃);

[0341] ΔT is the temperature difference.

[0342] When ΔT > 10℃, the thermal stress may exceed the material's yield strength. To prevent condensation and dew, excessive temperature differences can cause volatile components to condense, affecting the uniformity of the slurry composition and potentially leading to equipment corrosion.

[0343] Cooperative control algorithm:

[0344] For each temperature zone i:

[0345] 1. Calculate the ideal temperature T ideal [i];

[0346] 2. Check constraints: |T ideal [i]- T ideal [i-1]| ≤ 10℃;

[0347] 3. If the constraint is violated: Ta djusted [i] = Tideal [i-1] + sign(ΔT)×10℃;

[0348] 4. Backward propagation adjustment: Recalculate the setpoints for subsequent temperature zones.

[0349] This embodiment determines the target temperature and heating efficiency of each temperature zone by considering shear heat generation, adjacent temperature difference constraints, and the temperature of each temperature zone. These values ​​are then input into the corresponding PID controller for adjustment. This allows for corresponding compensation based on the actual conditions of each temperature zone, fully utilizing the shear heat generation from screw rotation while avoiding overheating.

[0350] In one embodiment, the working data further includes mass flow rate data, slurry concentration variation coefficient, total output data, yield rate data, pressure data, and torque data; geometric parameters include motor power; the method further includes:

[0351] Based on mass flow data, motor power, and heating efficiency in each temperature zone, a model for minimizing unit energy consumption is determined.

[0352] Based on the coefficient of variation of slurry concentration, determine the model that maximizes mixing uniformity;

[0353] Based on total output data and qualification rate data, determine the maximum effective productivity;

[0354] Obtain the temperature safety factor, pressure safety factor, and torque safety factor;

[0355] Based on the temperature safety factor, pressure safety factor, and torque safety factor, determine the model for maximizing the safety index;

[0356] The optimal parameter combination, which includes the optimal values ​​of all decision variables, is determined by solving the multi-objective optimization model of minimizing unit energy consumption, maximizing mixed uniformity, maximizing effective productivity, and maximizing safety index through a multi-objective optimization algorithm.

[0357] In the embodiments of this application, the optimal combination of operating parameters is found by comprehensively considering factors such as mixed quality, production efficiency, energy consumption and equipment safety, thereby solving the problem of conflicting objectives, achieving global optimization rather than local optimization, and providing flexible production mode selection.

[0358] Minimize unit energy consumption f1:

[0359] Mathematical expression:

[0360] f1 = (P moto r + P heat ) / Q

[0361] Among them, P motorMotor power (kW), the calculation formula is:

[0362] P motor = 2π × (M1×ω1 + M2×ω 2) / η trans

[0363] Where M1 and M2 are the torques of the two screws (N·m), ω1 and ω2 are the angular velocities of the two screws (rad / s), and η is the torque of the two screws. trans Transmission efficiency (dimensionless, approximately 0.85-0.90), P heat Total heating power (kW), calculated using the following formula:

[0364] P heat =

[0365] P heat [i]: Heating power of the i-th temperature zone, Q: Mass flow rate (kg / h), calculated using the following formula:

[0366] Q = Vf × ρ × 3600

[0367] Vf: Volumetric flow rate (m³) 3 / s), ρ: slurry density (kg / m³) 3 ).

[0368] Minimize the unit energy consumption f1, which is the electrical energy consumed to produce each kilogram of product, and directly reflects the production cost.

[0369] Minimize the unit energy consumption f1 as much as possible, with the goal of reducing production costs.

[0370] Maximize mixing uniformity f2:

[0371] Mathematical expression:

[0372] f2 = 1 - CV

[0373] Wherein, CV stands for Coefficient of Variation, calculated using the following formula:

[0374] CV = σ / μ

[0375] σ: Standard deviation of sample concentration

[0376] μ: Average sample concentration

[0377] Take n sampling points on the cross-section of the extrudate (usually n=9, 3×3 grid).

[0378] Measure the concentration c[i] of the key component at each point.

[0379] Calculate the average concentration:

[0380] μ = (1 / n) × Σ(i=1 to n) c[i]

[0381] Calculate the standard deviation:

[0382] σ = √[(1 / n) × Σ(i=1 to n) (c[i] - μ) 2 ]

[0383] Calculate the coefficient of variation:

[0384] CV = σ / μ

[0385] Calculate the uniformity index:

[0386] f2 = 1 - CV

[0387] Value range:

[0388] CV is typically between 0.01 and 0.20;

[0389] f2 is between 0.80 and 0.99;

[0390] f2=1 indicates perfect uniformity (ideal state).

[0391] f2 < 0.95 indicates insufficient mixing.

[0392] Maximizing the uniformity of mixing (f2) reflects the degree of uniformity in slurry mixing and directly affects product quality.

[0393] Maximize effective productivity f3:

[0394] Mathematical expression:

[0395] f3 = Q × η qualified

[0396] Where Q: total output (kg / h), η qualified The pass rate (dimensionless) is calculated using the following formula:

[0397] H qualified = N qualified / N total

[0398] N qualified : Number of qualified products, N total Total number of products.

[0399] Acceptance criteria: A product is considered acceptable only if it meets all of the following conditions:

[0400] Density deviation: |ρ actual - ρtarget | / ρ target < 0.02

[0401] Viscosity deviation: |η actual -η target | / η target < 0.05

[0402] Uniformity index: f2 > 0.95

[0403] Maximizing effective productivity f3 is the quantity of qualified products produced per unit time, which comprehensively reflects production efficiency and quality.

[0404] Maximize the safety index f4:

[0405] Mathematical expression:

[0406] f4 = exp(-ΔT / 5) × exp(-P / 10) × exp(-M / 500)

[0407] Temperature safety factor: exp(-ΔT / 5);

[0408] ΔT = max(T[i]) - T safe : The difference between the maximum temperature and the safe temperature (°C);

[0409] T safe The upper limit of the safe temperature for materials (e.g., 220℃ for CPVC);

[0410] Denominator 5: Temperature characteristic value, indicating that for every 5°C increase in temperature, safety decreases by a factor of e;

[0411] Pressure safety factor: exp(-P / 10);

[0412] P = max(P[i]): Maximum pressure (MPa);

[0413] Denominator 10: Pressure characteristic value, indicating that for every 10 MPa increase in pressure, safety decreases by a factor of e;

[0414] Torque safety factor: exp(-M / 500);

[0415] M = max(M1, M2): Maximum torque (N·m);

[0416] Denominator 500: Torque characteristic value, indicating that for every 500 N·m increase in torque, safety decreases by a factor of e.

[0417] f4∈(0, 1]

[0418] f4=1: Completely safe state (ΔT=0, P=0, M=0);

[0419] f4 < 0.5: There is a security risk;

[0420] f4 < 0.2: Dangerous state, needs immediate adjustment.

[0421] Maximize the safety index f4 to comprehensively evaluate the safe operation of the system and avoid equipment damage and safety accidents.

[0422] The decision variable vector X = [ω1, ω2, T1, T2, T] 3, T4, T5, T6, T7, T8, Q]

[0423] The meaning and scope of each variable:

[0424] ω1, ω2: angular velocities (rad / s) of the two screws, used to control the slurry conveying speed and shear strength, with a value range of [0.5, 10.0]; where the constraint relationship is: |ω1 - ω2| ≤ 0.5 (to ensure synchronization);

[0425] T1~T 8: Set temperatures (°C) for 8 temperature zones;

[0426] T1, T2: Temperature range of the solid conveying section [T] room , T melt -10];

[0427] T3, T4: Temperatures of the compression melting zone, range [T] melt -5, T melt +10];

[0428] T5, T6: Mixing section temperature, range [T melt , T melt +20];

[0429] T7, T8: Metering section temperature, range [T] melt -10, T melt +10];

[0430] Adjacent temperature zone constraint: |Ti - Ti+1| ≤ 10℃.

[0431] Q: Target output (kg / h), the output required by the production plan.

[0432] Value range: [Qmin, Qmax]

[0433] Qmin = 0.5 × design capacity;

[0434] Qmax = 1.2 × design capacity.

[0435] Speed ​​constraints include:

[0436] ωmin ≤ ω1, ω2 ≤ ωmax;

[0437] ωmin = 0.5 rad / s (minimum stable speed);

[0438] ωmax = 10.0 rad / s (maximum speed of the equipment).

[0439] Temperature constraint: Tmin[i] ≤ T[i] ≤ Tmax[i];

[0440] Preventing slurry degradation: T[i] < T degradation -10℃;

[0441] Ensure full plasticization: T[i] > T melt - 20℃.

[0442] Pressure constraints include:

[0443] P[i] ≤ P max design × SF

[0444] P max design : Design maximum pressure (e.g., 30 MPa); SF: Safety factor (usually 0.8).

[0445] Torque constraint: M ≤ M rated × 0.9

[0446] M rated Motor rated torque; leave a 10% margin to prevent overload.

[0447] Density specification: ρ target × (1 - δρ) ≤ ρ actual ≤ ρ target × (1 + δρ)

[0448] δρ: Permissible deviation (typically 2%)

[0449] Viscosity specification: ηtarget × (1 - δη) ≤ ηactual ≤ ηtarget × (1 + δη)

[0450] δη: Permissible deviation (typically 5%)

[0451] Uniformity requirements:

[0452] f2 ≥ 0.95;

[0453] Process constraints include:

[0454] Temperature gradient constraint: |Ti+1 - Ti| ≤ ΔTmax = 10℃;

[0455] The purpose is to prevent excessive thermal stress.

[0456] The heating rate constraint includes: |dT / dt| ≤ 5℃ / min

[0457] To prevent thermal shock caused by rapid temperature rise.

[0458] The dwell time constraint includes: tres ≥ tmin

[0459] tres = V / Q: Actual stay time

[0460] tmin: Minimum residence time (to ensure thorough mixing).

[0461] The target optimization algorithm in this embodiment is the NSGA-III algorithm, specifically:

[0462] NSGA-III (the third generation of non-dominated sorting genetic algorithm) is an evolutionary algorithm specifically designed for solving multi-objective optimization problems.

[0463] Pareto dominance relation: a solution x dominates a solution y if and only if: for all objectives fi, fi(x) ≤ fi(y) (minimization problem); and there exists at least one objective fj such that fj(x) < fj(y).

[0464] Pareto optimal front: the set of all non-dominated solutions, representing the best trade-off between different objectives.

[0465] The specific implementation steps are as follows:

[0466] Generate 100 sets of operating data, geometric parameters, and slurry viscosity parameters for a randomized slurry mixing and extrusion equipment:

[0467] for i = 1 to 100:

[0468] X[i] = random_uniform(Xmin, Xmax)

[0469] Check constraints

[0470] If the constraints are violated, regenerate.

[0471] Latin hypercube sampling is used to ensure uniform coverage of the parameter space, and empirical solutions (such as current running parameters) are added as seeds.

[0472] Calculate four objective functions for each individual: Calculate the four objective functions by running a simulation model or using a surrogate model, specifically as follows:

[0473] Calculate f1(X) = (P) motor + P heat ) / Q;

[0474] Calculate f2(X) = 1 - CV;

[0475] Calculate f3(X) = Q × η qualified ;

[0476] Calculate f4(X) = exp(-ΔT / 5)×exp(-P / 10)×exp(-M / 500);

[0477] Non-dominated sorting stratifies the population:

[0478] Layer 1: Pareto optimal solution (non-dominated)

[0479] Layer 2: Dominated by Layer 1, but not by any other solution.

[0480] Layer 3: Dominated by Layers 1 and 2, but not by other solutions. ...

[0481] NSGA-III uses reference points to maintain solution diversity: Generating reference points:

[0482] Reference points are uniformly distributed in the 4-dimensional target space.

[0483] Generate using the Das and Dennis methods

[0484] Number of reference points = C(4+p-1, p) ≈ 35 (p=4 is the segmentation parameter)

[0485] Associating the solution with the reference point: Calculate the distance to all reference points and associate it with the nearest reference point.

[0486] Selecting the next generation of the population:

[0487] 1. Prioritize solutions with lower rank;

[0488] 2. Within the same level, choose the solution that has the least correlation with the reference point;

[0489] 3. Maintain a population size of 100.

[0490] Cross operation:

[0491] Select Parent Generation: Tournament Selection;

[0492] Crossover probability: 0.9;

[0493] Crossover method: Analog binary crossover (SBX);

[0494] Offspring = α × parent1 + (1-α) × parent2;

[0495] Mutation operation:

[0496] Probability of mutation: 1 / n (where n is the dimension of the variable);

[0497] Mutation method: polynomial mutation;

[0498] X_new = X + δ×(Xmax - Xmin)

[0499] Termination conditions: Reaching the maximum number of generations (e.g., 200 generations), the improvement in the objective function is less than a threshold, and the Pareto front is stable; the final solution is selected from the Pareto optimal solution set.

[0500] (1) Energy-saving mode

[0501] X final = argmin(f1)

[0502] The solution with the lowest energy consumption is preferred, which is suitable for situations with high energy costs.

[0503] (2) Quality Model

[0504] X final = argmax(f2)

[0505] The solution with the best mixing uniformity is preferred and is suitable for high-end products.

[0506] (3) Efficiency Model

[0507] X final = argmax(f3)

[0508] Prioritize the solution with the highest output, which is suitable for situations with tight delivery schedules.

[0509] (4) Balanced mode

[0510] X final = argmin(Σwi × fi normalized )

[0511] in:

[0512] wi: Weights of each objective (e.g., w=[0.25, 0.25, 0.25, 0.25]), fi normalized : The target value after normalization.

[0513] The method described in this embodiment comprehensively considers mixing quality, production efficiency, energy consumption, and equipment safety to find the optimal combination of operating parameters. This significantly improves the quality stability of the slurry mixing and extrusion equipment, maintains a balance between optimal stretching efficiency and energy consumption, ensures thorough mixing without overmixing, and guarantees the safety and stability of the equipment.

[0514] In one implementation, the method further includes:

[0515] Obtain historical production data;

[0516] The original quality control model is trained using historical production data to generate a trained quality control model.

[0517] The optimal parameter combination is input into the trained quality control model to generate predicted quality control results, including density, viscosity, and uniformity.

[0518] In the embodiments of this application, product quality is predicted for the next 5-10 minutes based on historical data and current process parameters, achieving predictive quality control. This enables early detection of quality deviations, avoids batch non-conformities, reduces the lag in quality inspection, and provides a basis for parameter adjustment. Specifically:

[0519] The optimal parameter X output based on the above steps optimal This is combined with historical operational data.

[0520] Construct an input matrix with 60 time steps and 12 features:

[0521] Features include:

[0522] - 4 temperature characteristics (average temperature, temperature gradient, temperature fluctuation, and rate of temperature change).

[0523] - Two speed characteristics (average speed, speed fluctuation);

[0524] - Two pressure characteristics (mean pressure, pressure gradient);

[0525] - 1 torque feature;

[0526] - 1 traffic characteristic;

[0527] - 1 viscosity characteristic;

[0528] - 1 tensile efficiency feature.

[0529] The original quality control model can be a Transformer model, with the following architecture:

[0530] Input layer: Converts the feature matrix into a sequence representation;

[0531] Location encoding: Add time and location information;

[0532] Multi-head attention mechanism: capturing the correlation between different time steps;

[0533] Feedforward networks: extract high-level feature representations;

[0534] Output layer: Predicts three quality indicators: product density, product viscosity, and mixing uniformity index;

[0535] Model training: The model is trained using historical production data, which includes 10,000 batches of data.

[0536] The original quality control model is trained using historical production data to generate a trained quality control model.

[0537] The optimal parameter combination is then input into the trained quality control model to generate predicted quality control results. These predicted quality values ​​include density, viscosity, and uniformity, and can provide quality predictions for the next 5-10 minutes. Production efficiency is significantly improved; through predictive control and optimized scheduling, the overall efficiency of the equipment is effectively enhanced, and abnormal downtime is reduced.

[0538] In one implementation, the method further includes:

[0539] Determine whether the predicted quality value deviates from the target range;

[0540] When the density deviation exceeds a first specified range, a first specified strategy is generated;

[0541] Adjust the screw speed, target temperature of each temperature zone, and vacuum level according to the first specified strategy;

[0542] When the viscosity deviation exceeds the second specified range, a second specified strategy is generated;

[0543] According to the second specified strategy, adjust the screw speed, the target temperature of each temperature zone, and the slurry ratio;

[0544] When the uniformity exceeds a third specified range, a third specified strategy is generated;

[0545] According to the third specified strategy, adjust the stretching efficiency target, the target temperature of each temperature zone, and the mixing time.

[0546] In the embodiments of this application, based on the quality prediction results, it is determined whether process parameters need to be adjusted, and the adjusted parameters are then sent out for execution. This achieves closed-loop control, ensuring stable product quality and continuous optimization of system performance.

[0547] Quality deviation judgment: If |ρ predict - ρtarget | / ρ target > 0.02: Adjustment is required (density deviation exceeds 2%); that is, the first specified range can be 0.02, and the first specified strategy can be: when the density is too high: reduce the screw speed by 5%, reduce the temperature by 2℃, and increase the vacuum.

[0548] If |η predict - η target | / η target > 0.05: Adjustment is needed (viscosity deviation exceeds 5%); that is, the second specified range is 0.05; the first specified strategy can be, when the viscosity is too high: increase the temperature by 3℃, increase the screw speed by 10%, and check the slurry ratio.

[0549] If U predict < 0.95: Adjustment needed (insufficient uniformity). The third specified range can be 0.95, and the third specified strategy can be to increase the stretching efficiency target value by 0.05, extend the mixing time, and optimize the temperature distribution.

[0550] In one embodiment, the working data also includes the screw angular velocity, the additional angular velocity generated by the interaction of the twin screws, and the volumetric flow rate; the geometric parameters also include the barrel eccentricity, the barrel inner radius, and the barrel outer radius. Based on the working data and geometric parameters, a velocity field model is established in a cylindrical coordinate system. The velocity field model includes radial velocity, circumferential velocity, and axial velocity.

[0551] A cylindrical coordinate system is established with the axis of the slurry mixing and extrusion equipment as the z-axis;

[0552] The radial velocity component is determined based on the cylindrical coordinate system, the barrel eccentricity, the barrel inner radius, the barrel outer radius, and the screw angular velocity.

[0553] Determine the circumferential velocity component based on the cylindrical coordinate system and the additional angular velocity;

[0554] The axial velocity component is determined based on the cylindrical coordinate system, volumetric flow rate, and velocity distribution function.

[0555] In this embodiment, a cylindrical coordinate system (r, θ, z) is established with the extruder axis as the z-axis.

[0556] Derivation of the velocity field equations:

[0557] Considering the eccentric rotational motion of the twin screw, the three components of the velocity field are:

[0558] Radial velocity component vr:

[0559]

[0560] in:

[0561] e is the eccentricity (determined through geometric design, typically 5 mm);

[0562] ω is the screw angular velocity;

[0563] sinθ represents the change in velocity with angle, resulting in periodic compression;

[0564] (1-(r-ri) / h(θ)) indicates that the speed gradually decreases from the rotor surface to the stator surface;

[0565] Physical meaning: Describes the radial compression and expansion motion of the slurry.

[0566] Circumferential velocity component vθ:

[0567] vθ = ω·r + Δω(r,θ)

[0568] Where Δω is the additional angular velocity generated by the interaction of the twin screws;

[0569] Physical meaning: Describes the rotational motion and circumferential transport of slurry.

[0570] vz = Q / (π(ro 2 -ri 2 ))·f(r)

[0571] in:

[0572] Q is the volumetric flow rate;

[0573] f(r) is the velocity distribution function (determined according to rheology);

[0574] Physical meaning: Describes the conveying of slurry along the extrusion direction.

[0575] Based on the cylindrical coordinate system (r, θ, z), radial velocity, circumferential velocity, and axial velocity obtained above, the velocity field model can be determined.

[0576] In one implementation, the tensile efficiency index is obtained based on the velocity gradient tensor, including:

[0577] The velocity gradient tensor is decomposed to obtain the stretchability tensor;

[0578] Based on the stretching tensor, determine the first eigenvalue, the second eigenvalue, and the third eigenvalue;

[0579] The principal tensile strength is determined based on the first and second eigenvalues.

[0580] The total deformation strength is determined based on the first eigenvalue, the second eigenvalue, and the third eigenvalue.

[0581] The tensile efficiency index is determined based on the principal tensile strength and the total deformation strength.

[0582] In this embodiment, the elongation tensor D is calculated.

[0583] D = (L + L^T) / 2 [0.50 0.165 0.425]

[0585] D = [0.165 5.50 0.15 ] (Unit: s) -1 ) [0.425 0.15 1.50]

[0587] The physical meaning of the stretchability tensor D:

[0588] Diagonal elements (D11=0.50, D22=5.50, D33=1.50): represent the stretching / compression rates in the three coordinate directions;

[0589] Off-diagonal elements (D12=0.165, D13=0.425, D23=0.15): represent the shear deformation rate;

[0590] Calculation of vorticity tensor W

[0591] W = (L - L^T) / 2

[0592] [0 -1.835 -0.375]

[0593] W = [1.835 0 -0.05 ] (unit: s) -1 ) [0.375 0.05 0 ]

[0595] The physical meaning of the vorticity tensor W:

[0596] The vorticity tensor W is an antisymmetric tensor with zero diagonal elements.

[0597] Off-diagonal elements represent rotation rates;

[0598] It does not contribute to mixing, but it consumes energy.

[0599] For the elongation tensor D, the eigenvalue λ of the elongation tensor D represents the elongation rate in the principal elongation direction:

[0600] First eigenvalue λ1: Maximum principal stretching rate;

[0601] Second eigenvalue λ2: Intermediate main stretching rate;

[0602] The third eigenvalue λ3: minimum principal stretching rate (may be negative, indicating compression).

[0603] Wherein, the eigenvalue λ satisfies:

[0604] det(D - λl) = 0

[0605] Where I is the identity matrix and det represents the determinant.

[0606] Expanding into a cubic equation in standard form:

[0607] λ 3 -l1λ 2 +l2λ-I3= 0

[0608] Formula for calculating invariants:

[0609] First invariant (trace):

[0610] I1 = tr(D) = D 11 + D 22 + D 33

[0611] Physical meaning: Volume expansion rate

[0612] Second invariant:

[0613] I2 = (1 / 2)[(tr(D)) 2 - tr(D 2 )]

[0614] =D 11 D 22 + D 22 D 33 + D 33 D11 - D 12 2 - D 23 2 - D 31 2

[0615] Physical meaning: Rate of change of area

[0616] Third invariant (determinant):

[0617] I3 = det(D) = D 11 (D 22 D 33 - D 23 2 ) - D 12 (D 12 D 33 - D 23 D 13 ) + D 13 (D 12D 23 - D 22 D 13 )

[0618] Variable substitution

[0619] Let λ = μ + I1 / 3, then the original equation is transformed into:

[0620] μ 3 +pμ+ q = 0

[0621] in:

[0622] p = I2 - I1 2 / 3

[0623] q = 2I1 3 / 27 - I1I2 / 3 + I3

[0624] Step 2: Discriminant Calculation

[0625] Δ = -(4p 3 +27q 2 ) / 108

[0626] Expression of three real roots

[0627] When Δ > 0 (as guaranteed by a symmetric matrix):

[0628] The first eigenvalue λ1 = I1 / 3 + 2√(-p / 3)cos(θ / 3)

[0629] The second eigenvalue λ² = I¹ / ³ + 2√(-p / ³)cos((θ + 2π) / ³)

[0630] The third eigenvalue λ3 = I1 / 3 + 2√(-p / 3)cos((θ+ 4π) / 3)

[0631] in:

[0632] θ = arccos(3q√(-3 / p) / 2p).

[0633] The eigenvalues ​​satisfy the equation: det(D - λI) = 0

[0634] Where I is the identity matrix and det represents the determinant.

[0635] Expanded to:

[0636] |0.50-λ 0.165 0.425|

[0637] |0.165 5.50-λ 0.15 | = 0

[0638] |0.425 0.15 1.50-λ|

[0639] Calculate the determinant

[0640] Expanding the third-order determinant yields the characteristic polynomial:

[0641] -λ 3 + (0.50+5.50+1.50)λ 2 - [(0.50×5.50+0.50×1.50+5.50×1.50) - (0.165 2 +0.425 2 +0.15 2 )]λ+det(D) = 0

[0642] Simplified to:

[0643] -λ 3 + 7.50λ 2 - 11.47λ + 3.89 = 0

[0644] Solve cubic equations

[0645] Solving using numerical methods (such as the Newton-Raphson method) or analytical methods (Cardan's formula), we obtain three real roots:

[0646] The first eigenvalue λ1 = 5.58 s -1 (Maximum eigenvalue);

[0647] The second eigenvalue λ² = 1.47 s -1 (Intermediate eigenvalues);

[0648] The third eigenvalue λ3 = 0.45 s -1 (Minimum eigenvalue).

[0649] Two-dimensional principal tensile strength:

[0650] Is = √(λ1 2 +λ2 2 )

[0651] Parameter description:

[0652] λ1: Maximum eigenvalue (direction of strongest stretching)

[0653] λ2: Intermediate eigenvalue (secondary tensile direction)

[0654] 4.2 Total Deformation Strength

[0655] Three-dimensional total deformation strength:

[0656] Id = √(λ12 + λ2 2 + λ3 2 ) = √(tr(D 2 ))

[0657] The formula for defining the tensile efficiency index is:

[0658] ψ = Is / Id = √(λ1) 2 +λ2 2 ) / √(λ1 2 + λ2 2 + λ3 2 )

[0659] Range of values ​​and physical meaning:

[0660] ψ∈ [0, 1]

[0661] ψ→ 1: Pure two-dimensional stretching (ideal)

[0662] ψ→ 0.577: Pure shear flow

[0663] ψ < 0.5: Three-dimensional compression is dominant.

[0664] Maximizing stretching efficiency:

[0665] maxψ = max{√(λ1) 2 +λ2 2 ) / √(λ1 2 + λ2 2 + λ3 2 )}

[0666] Constraints:

[0667] λ1 2 + λ2 2 + λ3 2 = 0 (incompressible fluid);

[0668] |λ | < λ_max (physical limit).

[0669] Specifically, the principal tensile strength is defined as the tensile strength within the principal tensile plane (λ1-λ2 plane):

[0670] Is = √(λ1 2 + λ2 2 )

[0671] = √(5.58 2 + 1.47 2 )

[0672] = √(31.14 + 2.16)

[0673] = √33.30

[0674] = 5.77 s -1

[0675] Is represents the combined tensile strength in the two principal directions that contribute the most to the mixing.

[0676] Calculation of total deformation strength Id:

[0677] Total deformation strength includes deformation in all three directions:

[0678] Id = √(λ1 2 + λ2 2 + λ3 2 )

[0679] = √(5.58 2 + 1.47 2 + 0.45 2 )

[0680] = √(31.14 + 2.16 + 0.20)

[0681] = √33.50

[0682] = 5.79 s -1

[0683] Calculation of the tensile efficiency index ψ:

[0684] ψ = Is / Id

[0685] = 5.77 / 5.79

[0686] = 0.997

[0687] Results analysis: ψ = 0.997 ≈ 1.0, indicating that the deformation is almost entirely tensile deformation with a very small shear component, resulting in extremely high mixing efficiency.

[0688] Through the above calculation process, the tensile efficiency index can be analyzed and determined.

[0689] Determining the optimal value:

[0690] Through extensive experiments and theoretical analysis, it was determined that:

[0691] ψ < 0.5: Shear-dominated, low mixing efficiency, high energy consumption;

[0692] 0.6 < ψ < 0.7: Stretching dominates, resulting in optimal mixing efficiency;

[0693] ψ> 0.8: Excessive stretching may lead to slurry degradation.

[0694] A real-time tensile efficiency index ψ(t) is generated, which will serve as the core control target for controlling the screw speed. In this embodiment, the tensile efficiency index ψ is established as the core control target, and by adjusting the motion parameters of the dual-axis eccentric rotor, ψ is maintained within the optimal range of 0.60-0.70.

[0695] Secondly, embodiments of this application provide a system, including:

[0696] The first acquisition module is used to acquire the working data, geometric parameters, and slurry viscosity of the slurry mixing and extrusion equipment;

[0697] The first module is used to establish a velocity field model in a cylindrical coordinate system based on working data and geometric parameters. The velocity field model includes radial velocity, circumferential velocity and axial velocity.

[0698] The first determining module is used to determine the velocity gradient tensor based on the velocity field model;

[0699] The first module is used to obtain the stretching efficiency index based on the velocity gradient tensor.

[0700] The second determining module is used to adjust the parameters of the PID control algorithm according to the slurry viscosity and determine the specified PID control algorithm;

[0701] The first generation module is used to generate the screw speed of the slurry mixing extrusion equipment based on the stretching efficiency index and a specified PID control algorithm.

[0702] The system in this embodiment improves energy utilization efficiency by fully considering the shear deformation of the tensile deformation replacement portion. It calculates the tensile efficiency index of the slurry's three-dimensional tensile deformation in real time, and adjusts the screw speed based on the tensile efficiency index and a specified PID algorithm optimized for slurry viscosity. This maintains the tensile efficiency within the optimal range, improving the working efficiency of the slurry mixing extrusion equipment, reducing energy consumption, and effectively solving the problem that existing equipment mainly relies on shear action for mixing, neglecting the important role of tensile deformation in dispersion mixing. Existing equipment only considers shear action, simplifying the mixing process to one-dimensional shear flow. This simplification ignores the three-dimensional characteristics of the actual flow field and fails to consider the crucial role of tensile deformation in the mixing effect, leading to low extrusion efficiency due to reliance solely on shear action.

[0703] In one implementation, the working data includes temperature data, and the method further includes:

[0704] Based on temperature data, the barrel of the slurry mixing extrusion equipment is divided into temperature zones to determine multiple temperature zones;

[0705] Obtain the state of the slurry;

[0706] Determine the temperature of each temperature zone based on the state of the slurry;

[0707] The actual shear heat generation power is determined based on the screw speed;

[0708] Obtain the baseline shear heat generation power;

[0709] The supplementary heating power is determined based on the actual shear heat generation power and the reference shear heat generation power.

[0710] Based on the heating compensation power, the temperature difference constraint between adjacent temperature zones, and the temperature of each temperature zone, the target temperature and heating efficiency of each temperature zone are determined.

[0711] In one embodiment, the working data further includes mass flow rate data, slurry concentration variation coefficient, total output data, yield rate data, pressure data, and torque data; geometric parameters include motor power; the method further includes:

[0712] Based on mass flow data, motor power, and heating efficiency in each temperature zone, a model for minimizing unit energy consumption is determined.

[0713] Based on the coefficient of variation of slurry concentration, determine the model that maximizes mixing uniformity;

[0714] Based on total output data and qualification rate data, determine the maximum effective productivity;

[0715] Obtain the temperature safety factor, pressure safety factor, and torque safety factor;

[0716] Based on the temperature safety factor, pressure safety factor, and torque safety factor, determine the model for maximizing the safety index;

[0717] The optimal parameter combination, which includes the optimal values ​​of all decision variables, is determined by solving the multi-objective optimization model of minimizing unit energy consumption, maximizing mixed uniformity, maximizing effective productivity, and maximizing safety index through a multi-objective optimization algorithm.

[0718] In one implementation, the method further includes:

[0719] Obtain historical production data;

[0720] The original quality control model is trained using historical production data to generate a trained quality control model.

[0721] The optimal parameter combination is input into the trained quality control model to generate predicted quality control results, including density, viscosity, and uniformity.

[0722] In one implementation, the method further includes:

[0723] Determine whether the predicted quality value deviates from the target range;

[0724] When the density deviation exceeds a first specified range, a first specified strategy is generated;

[0725] Adjust the screw speed, target temperature of each temperature zone, and vacuum level according to the first specified strategy;

[0726] When the viscosity deviation exceeds the second specified range, a second specified strategy is generated;

[0727] According to the second specified strategy, adjust the screw speed, the target temperature of each temperature zone, and the slurry ratio;

[0728] When the uniformity exceeds a third specified range, a third specified strategy is generated;

[0729] According to the third specified strategy, adjust the stretching efficiency target, the target temperature of each temperature zone, and the mixing time.

[0730] In one embodiment, the working data also includes the screw angular velocity, the additional angular velocity generated by the interaction of the twin screws, and the volumetric flow rate; the geometric parameters also include the barrel eccentricity, the barrel inner radius, and the barrel outer radius. Based on the working data and geometric parameters, a velocity field model is established in a cylindrical coordinate system. The velocity field model includes radial velocity, circumferential velocity, and axial velocity.

[0731] A cylindrical coordinate system is established with the axis of the slurry mixing and extrusion equipment as the z-axis;

[0732] The radial velocity component is determined based on the cylindrical coordinate system, the barrel eccentricity, the barrel inner radius, the barrel outer radius, and the screw angular velocity.

[0733] Determine the circumferential velocity component based on the cylindrical coordinate system and the additional angular velocity;

[0734] The axial velocity component is determined based on the cylindrical coordinate system, volumetric flow rate, and velocity distribution function.

[0735] In one implementation, the tensile efficiency index is obtained based on the velocity gradient tensor, including:

[0736] The velocity gradient tensor is decomposed to obtain the stretchability tensor;

[0737] Based on the stretching tensor, determine the first eigenvalue, the second eigenvalue, and the third eigenvalue;

[0738] The principal tensile strength is determined based on the first and second eigenvalues.

[0739] The total deformation strength is determined based on the first eigenvalue, the second eigenvalue, and the third eigenvalue.

[0740] The tensile efficiency index is determined based on the principal tensile strength and the total deformation strength.

[0741] The functions of each module in each device in the embodiments of this application can be found in the corresponding descriptions in the above methods, and will not be repeated here.

[0742] Figure 2 A structural block diagram of an electronic device according to an embodiment of this application is shown. Figure 2 As shown, the electronic device includes a memory 410 and a processor 420. The memory 410 stores instructions that can be executed on the processor 420. When the processor 420 executes the instructions, it implements the slurry extrusion method in the above embodiments. The number of memories 410 and processors 420 can be one or more. This electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workbenches, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present application described and / or claimed herein.

[0743] The electronic device may also include a communication interface 430 for communicating with external devices and exchanging data. The devices are interconnected using different buses and can be mounted on a common motherboard or otherwise as needed. The processor 420 can process instructions executed within the electronic device, including instructions stored in or on memory to display graphical information of a GUI on an external input / output device (such as a display device coupled to the interface). In other embodiments, multiple processors and / or multiple buses can be used with multiple memories and multiple memory modules, if desired. Similarly, multiple electronic devices can be connected, each providing some of the necessary operations (e.g., as a server array, a group of blade servers, or a multiprocessor system). The bus can be divided into address buses, data buses, control buses, etc. For ease of illustration, Figure 2 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0744] Optionally, in a specific implementation, if the memory 410, processor 420 and communication interface 430 are integrated on a single chip, the memory 410, processor 420 and communication interface 430 can communicate with each other through an internal interface.

[0745] It should be understood that the aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. General-purpose processors can be microprocessors or any conventional processor. It is worth noting that the processor can be a processor supporting Advanced Reduced Instruction Set Machines (ARM) architecture.

[0746] This application provides a computer-readable storage medium (such as the memory 410 described above) that stores computer instructions, which, when executed by a processor, implement the method provided in this application.

[0747] Optionally, memory 410 may include a program storage area and a data storage area, wherein the program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the electronic device, etc. Furthermore, memory 410 may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory 410 may optionally include memory remotely located relative to processor 420, and these remote memories can be connected to the electronic device via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0748] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0749] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "a plurality of" means two or more, unless otherwise explicitly specified.

[0750] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more (two or more) executable instructions for implementing a particular logical function or process. Furthermore, the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functionality involved.

[0751] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0752] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. All or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware, the program being stored in a computer-readable storage medium, which, when executed, includes one or a combination of the steps of the method embodiments.

[0753] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. This storage medium can be a read-only memory, a disk, or an optical disk, etc.

[0754] The above are merely specific embodiments of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various variations or substitutions within the technical scope disclosed in this application, and these should all be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A slurry extrusion method, characterized in that, include: Obtain the operating data, geometric parameters, and slurry viscosity of the slurry mixing and extrusion equipment; Based on the working data and the geometric parameters, a velocity field model is established in a cylindrical coordinate system. The velocity field model includes radial velocity, circumferential velocity and axial velocity. Based on the velocity field model, determine the velocity gradient tensor; The tensile efficiency index is obtained based on the velocity gradient tensor. The parameters of the PID control algorithm are adjusted according to the viscosity of the slurry to determine the specified PID control algorithm; Based on the stretching efficiency index and the specified PID control algorithm, the screw speed of the slurry mixing extrusion equipment is generated; The process of obtaining the tensile efficiency index based on the velocity gradient tensor includes: The velocity gradient tensor is decomposed to obtain the stretchability tensor. Based on the stretching tensor, determine the first eigenvalue, the second eigenvalue, and the third eigenvalue; The principal tensile strength is determined based on the first characteristic value and the second characteristic value; The total deformation strength is determined based on the first characteristic value, the second characteristic value, and the third characteristic value; The tensile efficiency index is determined based on the principal tensile strength and the total deformation strength.

2. The method according to claim 1, characterized in that, The working data includes temperature data, and the method further includes: Based on the temperature data, the barrel of the slurry mixing extrusion equipment is divided into temperature zones to determine multiple temperature zones; Obtain the state of the slurry; The temperature of each temperature zone is determined based on the state of the slurry. The actual shear heat generation power is determined based on the screw rotation speed. Obtain the baseline shear heat generation power; The supplementary heating power is determined based on the actual shear heat generation power and the reference shear heat generation power. Based on the heating compensation power, the temperature difference constraint between adjacent temperature zones, and the temperature of each temperature zone, the target temperature and heating efficiency of each temperature zone are determined.

3. The method according to claim 2, characterized in that, The working data also includes mass flow rate data, slurry concentration variation coefficient, total output data, pass rate data, pressure data, and torque data; the geometric parameters include motor power; the method further includes: Based on the mass flow rate data, the motor power, and the heating efficiency of each temperature zone, a model for minimizing unit energy consumption is determined. Based on the coefficient of variation of the slurry concentration, a model for maximizing mixing uniformity is determined; Based on the total output data and the qualification rate data, determine the maximum effective productivity; Obtain the temperature safety factor, pressure safety factor, and torque safety factor; Based on the temperature safety factor, the pressure safety factor, and the torque safety factor, determine the model that maximizes the safety index; The optimal parameter combination, which includes the optimal values ​​of all decision variables, is determined by solving the minimization unit energy consumption model, the maximization of mixed uniformity model, the maximization of effective productivity model, and the maximization of safety index model using a multi-objective optimization algorithm.

4. The method according to claim 3, characterized in that, The method further includes: Obtain historical production data; The original quality control model is trained using the historical production data to generate a trained quality control model. The optimal parameter combination is input into the trained quality control model to generate predicted quality control results, including density, viscosity, and uniformity.

5. The method according to claim 4, characterized in that, The method further includes: Determine whether the predicted quality value deviates from the target range; When the density deviation exceeds a first specified range, a first specified strategy is generated; According to the first specified strategy, adjust the screw speed, target temperature of each temperature zone and vacuum level; When the viscosity deviation exceeds a second specified range, a second specified strategy is generated; According to the second specified strategy, adjust the screw speed, the target temperature of each temperature zone, and the slurry ratio; When the uniformity exceeds a third specified range, a third specified strategy is generated; According to the third specified strategy, adjust the stretching efficiency target, the target temperature of each temperature zone, and the mixing time.

6. The method according to claim 5, characterized in that, The working data also includes the screw angular velocity, the additional angular velocity generated by the interaction of the twin screws, and the volumetric flow rate; the geometric parameters also include the barrel eccentricity, the barrel inner radius, and the barrel outer radius. Based on the working data and the geometric parameters, a velocity field model is established in a cylindrical coordinate system. The velocity field model includes radial velocity, circumferential velocity, and axial velocity. A cylindrical coordinate system is established with the axis of the slurry mixing and extrusion equipment as the z-axis; The radial velocity component is determined based on the cylindrical coordinate system, the barrel eccentricity, the barrel inner radius, the barrel outer radius, and the screw angular velocity. The circumferential velocity component is determined based on the cylindrical coordinate system and the additional angular velocity. The axial velocity component is determined based on the cylindrical coordinate system, the volumetric flow rate, and the velocity distribution function.

7. A system, characterized in that, include: The first acquisition module is used to acquire the working data, geometric parameters, and slurry viscosity of the slurry mixing and extrusion equipment; The first module is used to establish a velocity field model in a cylindrical coordinate system based on the working data and the geometric parameters. The velocity field model includes radial velocity, circumferential velocity and axial velocity. The first determining module is used to determine the velocity gradient tensor based on the velocity field model. The first obtaining module is used to obtain the stretching efficiency index based on the velocity gradient tensor; The second determining module is used to adjust the parameters of the PID control algorithm according to the viscosity of the slurry and determine the specified PID control algorithm. The first generation module is used to generate the screw speed of the slurry mixing extrusion device according to the stretching efficiency index and the specified PID control algorithm. The process of obtaining the tensile efficiency index based on the velocity gradient tensor includes: The velocity gradient tensor is decomposed to obtain the stretchability tensor. Based on the stretching tensor, determine the first eigenvalue, the second eigenvalue, and the third eigenvalue; The principal tensile strength is determined based on the first characteristic value and the second characteristic value; The total deformation strength is determined based on the first characteristic value, the second characteristic value, and the third characteristic value; The tensile efficiency index is determined based on the principal tensile strength and the total deformation strength.

8. An electronic device, characterized in that, include: At least one processor; as well as A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method of any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that, when executed by a processor, implement the method as described in any one of claims 1-6.

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