A method for determining the formula of black masterbatch for chemical fiber filaments to improve the wear of wire guide magnetic parts

Abstract

The invention provides a method for determining a formula of a chemical fiber filament black masterbatch for improving the wear of a guide wire magnet, which belongs to the technical field of chemical fiber filament black masterbatch formula, and comprises the following steps: first, a basic formula is obtained, including a polyester resin, carbon black, a dispersant and a compatibility additive. Then, a mathematical model for formula performance and guide wire wear is established, and parameter fitting is performed through test data. Next, a multi-objective optimization problem is constructed, the goal of which is to optimize the formula performance and minimize the guide wire wear, and an improved particle swarm algorithm is used to solve it. The optimal solution is verified and fine-tuned by actual spinning, and finally the optimal formula of chemical fiber filament black masterbatch that can effectively reduce the guide wire wear is obtained. The method comprehensively considers the raw material ratio, fiber performance and equipment wear, and solves the technical problem that the carbon black in the existing masterbatch will wear the surface of the guide wire magnet when passing through the guide wire magnet during high-speed spinning, and the surface damage of the guide wire magnet will cause hairy wires.

Description

Technical Field

[0001] The invention belongs to the technical field of chemical fiber filament black masterbatch formula, and in particular relates to a method for determining the chemical fiber filament black masterbatch formula for improving the wear of wire guide magnetic parts. Background Art

[0002] The production of chemical fiber filaments is a complex process, and one of the key equipment is the wire guide magnet. The wire guide magnet is located on the spinning machine and is used to guide and pull the high-temperature molten chemical fiber masterbatch yarn so that it flows along the correct path through subsequent cooling, winding and other process links. In long-term production practice, the wire guide magnet will inevitably suffer from wear and damage, thus affecting the fiber forming quality and production efficiency. This problem has always been a technical problem that needs to be solved urgently in the chemical fiber industry.

[0003] The main reasons for the wear of wire guide magnets are as follows: First, the high-temperature molten state of chemical fiber filament masterbatch has high viscosity and rheology, which will cause serious wear when rubbing against the surface of wire guide magnets at high speed; secondly, various additives added to the fiber, such as carbon black and dispersants, will aggravate the chemical corrosion and physical damage on the surface of wire guide magnets; thirdly, the high-temperature and high-speed process environment will also accelerate the aging and loss of wire guide magnets. These factors cause scratches, pits and other damages to gradually appear on the surface of wire guide magnets, thereby increasing the roughness of the fiber surface and producing quality defects such as hair, which seriously affects the performance and service life of the final product.

[0004] In order to deal with the problem of wear of wire guide magnets, chemical fiber companies usually take passive measures such as regular cleaning and maintenance, and timely replacement. However, this not only increases production costs, but also often causes production interruptions and affects overall production capacity. Therefore, it is urgent to fundamentally solve the problem of wear of wire guide magnets and improve their service life and stability, which is crucial to improving the efficiency and quality of chemical fiber filament production. Summary of the invention

[0005] In view of this, the present invention provides a method for determining the formula of chemical fiber filament black masterbatch for improving the wear of wire guide magnetic parts, which can solve the technical problems that the carbon black in the existing chemical fiber filament masterbatch will wear the surface of the wire guide magnetic parts when passing through the wire guide magnetic parts during high-speed spinning, and the surface damage of the wire guide magnetic parts will cause hairy fibers.

[0006] The present invention is achieved in that:

[0007] The present invention provides a method for determining a formula of a chemical fiber filament black masterbatch for improving the wear of a guide wire magnetic part, comprising the following steps:

[0008] S10, obtaining the basic formula of black masterbatch of chemical fiber filament, specifically: polyester resin 70-80%, carbon black 15-25%, dispersant 2-5%, compatibility additive 1-3%;

[0009] S20, establishing a group of black masterbatch formula performance equations, including spinning smoothness equation, fiber surface smoothness equation, wear resistance equation, compatibility equation and formula comprehensive equation;

[0010] S30, establishing a group of equations for evaluating the wear of the guide wire magnetic parts, including a wear rate equation, a surface damage degree equation, a hairy wire generation rate equation, and a comprehensive wear equation;

[0011] S40, according to the basic formula, by adjusting the carbon black content, the type and content of the compatibility additive, and the proportion of other components, design multiple test formulas, conduct small-scale spinning tests, and record the experimental data and the specific composition and proportion of the components in each test formula;

[0012] S50, fitting the black masterbatch formula performance equation group and the guide wire magnetic wear evaluation equation group using the experimental data and the specific composition and proportion of the components in each test formula to obtain a fitted performance equation group and a fitted wear equation group;

[0013] S60, constructing a multi-objective optimization problem based on the fitting performance equation group and the fitting wear equation group, wherein the objective function includes optimizing the comprehensive performance of the formulation and minimizing the comprehensive degree of wear;

[0014] S70, using an improved particle swarm optimization algorithm to solve the multi-objective optimization problem and obtain the optimal solution;

[0015] S80, verifying and fine-tuning the optimal solution through actual spinning, evaluating the fiber quality and the wear of the wire guide magnetic parts, and further optimizing the formula;

[0016] S90, repeating step S80, and finally obtaining the optimal formula of chemical fiber filament black masterbatch for improving the wear of the wire guide magnetic parts.

[0017] Specifically, the step S10 is to obtain the basic formula of black masterbatch of chemical fiber filament. Specifically, the basic formula includes 70-80% polyester resin, 15-25% carbon black, 2-5% dispersant and 1-3% compatibility additive. Among these components, the polyester resin mainly adopts polyethylene terephthalate (PET), and the chemical formula is (C 10 H8O4) n In addition, polybutylene terephthalate (PBT) can also be used, with the chemical formula (C 12 H 12 O4) n Or polycaprolactone (PCL), the chemical formula is (C6H 10 O2) nAs a substitute component. Carbon black mainly uses acetylene black with good conductivity, and its chemical formula is approximately C. In addition, other types of carbon black such as furnace black and channel black can also be used as substitutes. Dispersants usually use polyoxyethylene stearate, and its chemical formula is CH3(CH2) 16 COO(CH2CH2O) n H, sodium dodecylbenzene sulfonate can also be used, the chemical formula is C 12 H 25 C6H4SO3Na or polyvinylpyrrolidone (PVP), chemical formula is (C6H9NO) n As an alternative, the compatibility additive is mostly maleic anhydride grafted polyethylene (PE-g-MAH), with the chemical formula [CH2CH2] m [CH2CH(COOHCOOH)] n , ethylene-vinyl acetate copolymer (EVA) can also be used, with the chemical formula [CH2CH2] m [CH2CH(OCOCH3)] n Or polyethylene-octene copolymer (POE), the chemical formula is [CH2CH2] m [CH2CH(C6H 13 )] n As an alternative, the purpose of this step is to obtain the basic formula of chemical fiber filament black masterbatch to provide a basis for subsequent optimization and improvement.

[0018] The step S20 is to establish a black masterbatch formula performance equation group, which includes five equations: a spinning smoothness equation, a fiber surface smoothness equation, a wear resistance equation, a compatibility equation, and a formula comprehensive equation.

[0019] The spinning smoothness equation is specifically expressed as:

[0020]

[0021] Where, F is the spinning smoothness index; k1 and k2 are constants; E a is the flow activation energy; R is the gas constant; T is the spinning temperature; η0 is the base resin viscosity; η is the viscosity of the masterbatch after mixing; n is the shear thinning index; φ c is the volume fraction of carbon black; m is the influence index of carbon black on flow; ε1 is the first error term. a , η0 and η are obtained by capillary rheometer measurement. The specific steps are: heating the sample to a set temperature; measuring the viscosity of the sample at different shear rates; and fitting E according to the Arrhenius equation. a ; The zero shear viscosity of the base resin and the mixed masterbatch was measured respectively to obtain η0 and η.

[0022] φ cCalculated from the formula: Among them, W c is the mass fraction of carbon black, W p is the mass fraction of polyester resin, ρ c and ρ p are the densities of carbon black and polyester resin, respectively.

[0023] The fiber surface smoothness equation is specifically expressed as:

[0024]

[0025] Where S is the surface smoothness index; σ is the fiber surface tension; D p is the average particle size of the dispersant; c is the volume fraction of carbon black; a1, a2, a3, b1 and b2 are unknown coefficients; ε2 is the second error term. σ is obtained by a contact angle meter, the steps are: fix the fiber sample on the sample table; drop a standard liquid (such as water) on the fiber surface; measure the contact angle between the droplet and the fiber surface; calculate the surface tension according to the Young equation. D p The measurement is performed by a dynamic light scattering method, and the steps are: dissolving the dispersant in a suitable solvent; measuring the particle size distribution of the dispersant particles using a dynamic light scattering instrument; and calculating the average particle size.

[0026] The wear resistance equation is specifically expressed as:

[0027] W=c1·exp(-c2·H)+c3·exp(-C4·E)+C5·(1-φ c ) -1 / 2 +ε3;

[0028] Where w is the wear resistance index; H is the fiber surface hardness; E is the fiber elastic modulus; φ c is the volume fraction of carbon black; c1, c2, c3, c4 and c5 are unknown coefficients; ε3 is the third error term. H is measured by nanoindentation method, the steps are: fix the fiber sample on the sample table; use nanoindenter to perform indentation test on the fiber surface; calculate the surface hardness according to the load-displacement curve. E is obtained by single fiber tensile test, the steps are: fix a single fiber on the tensile tester; stretch the fiber at a constant rate until it breaks; calculate the elastic modulus according to the stress-strain curve.

[0029] The compatibility equation is specifically expressed as:

[0030]

[0031] Where, C is the compatibility index; T g is the glass transition temperature; δ p and δ Care the solubility parameters of polyester resin and carbon black respectively; φ a is the volume fraction of the compatibility additive; d1, d2, d3, d4 and d5 are unknown coefficients; ε4 is the fourth error term. g The measurement is performed by differential scanning calorimetry (DSC), and the steps are: encapsulating the sample in a DSC sample pan; heating the sample at a constant heating rate; recording the heat flow curve to determine the glass transition temperature.

[0032] δ p and δ c Calculated by the group contribution method, the specific formula is: Among them, E i is the cohesive energy of each group in the molecule, V i is the molar volume of each group.

[0033] The formula comprehensive equation is specifically expressed as:

[0034] P = w1F + w2S + w3W + w4C + ε5;

[0035] Wherein, P is the comprehensive performance index of the formula; F, S, W and C are the spinning smoothness index, surface smoothness index, wear resistance index and compatibility index respectively; w1, w2, w3 and w4 are weight coefficients; ε5 is the fifth error term.

[0036] The purpose of this step is to establish a set of equations that reflect the performance of the black masterbatch formula, providing a mathematical model basis for subsequent optimization and improvement.

[0037] The step S30 is to establish a group of equations for evaluating the wear of the guide wire magnetic parts. The group of equations includes four equations: a wear rate equation, a surface damage degree equation, a hairy wire generation rate equation, and a comprehensive wear equation.

[0038] The wear rate equation is specifically expressed as:

[0039]

[0040] Where R is the wear rate; k is the wear coefficient; F n is the positive pressure; H is the surface hardness of the wire guide magnet; v is the fiber running speed; Q is the wear activation energy; R is the gas constant; T is the wear contact point temperature; α and β are undetermined exponents; ε6 is the sixth error term. F nThe measurement is carried out by a pressure sensor, and the steps are as follows: install a micro pressure sensor at the contact point between the wire guide magnet and the fiber; record the pressure data in real time during the spinning process; calculate the average pressure value; H is measured by a hardness tester, and the steps are similar to the aforementioned fiber hardness measurement; v is directly obtained by setting the speed of the spinning machine; T is measured by an infrared thermal imager, and the steps are as follows: aim the infrared thermal imager at the contact point between the wire guide magnet and the fiber; record the temperature data in real time during the spinning process; and calculate the average temperature value.

[0041] The surface damage degree equation is specifically expressed as:

[0042] D = a·(1-e -bt )+c·sin(ωt+φ)+ε7;

[0043] Where D is the degree of surface damage; t is the running time; a, b, c, ω and φ are unknown parameters; ε7 is the seventh error term. These parameters can be obtained by regularly observing the surface of the guide wire magnet by scanning electron microscopy, recording the surface morphology at different time points, and using image analysis software to quantify the degree of damage. Then, the values ​​of each parameter are obtained by nonlinear regression fitting.

[0044] The hair production rate equation is specifically expressed as:

[0045]

[0046] In the formula, L is the hair generation rate; L0 is the initial hair generation rate; D is the surface damage degree; R is the wear rate; t is the running time; λ, μ and v are unknown parameters; ε8 is the eighth error term. These parameters can be used to monitor the hair generation in real time through the online detection system, record the number of hairs at different time points, and combine the above-mentioned surface damage degree and wear rate data to obtain the parameter values ​​through nonlinear regression fitting.

[0047] The comprehensive wear equation is specifically expressed as:

[0048] M=u1R+u2D+u3L+ε9;

[0049] Where M is the comprehensive wear index; R, D and L are the wear rate, surface damage degree and hair generation rate respectively; u1, u2 and u3 are weight coefficients; ε9 is the ninth error term.

[0050] The purpose of this step is to establish a set of equations that reflect the wear of the guide wire magnetic parts, providing a mathematical model basis for subsequent optimization and improvement.

[0051] The step S40 is to design multiple test formulas according to the basic formula by adjusting the carbon black content, the type and content of the compatibility additive, and the proportion of other components, conduct small-scale spinning tests, and record the experimental data and the specific composition and proportion of the components in each test formula. The purpose of this step is to obtain experimental data under different formulas to provide a basis for subsequent model fitting and optimization.

[0052] In step S50, the experimental data obtained in step S40 and the specific composition and proportion of the components in each test formula are used to fit the equations established in steps S20 and S30 to obtain a fitted performance equation group and a fitted wear equation group. The specific fitting process is as follows:

[0053] First, for the spinning smoothness equation Using the experimental data of step S40, k1, k2, E are obtained by fitting through nonlinear regression method. a , n and m. At the same time, we can also use the experimentally measured η0, η and φ c The actual value of F was calculated and compared with the fitted model.

[0054] For the fiber surface smoothness equation Similarly, the experimental data of step S40 are used to obtain the optimal values ​​of a1, a2, a3, b1 and b2 through nonlinear regression fitting. In addition, the optimal values ​​of σ, D p and φ c The actual value of S is calculated and compared with the fitted model.

[0055] Similarly, for the wear resistance equation W = c1·exp(-c2·H)+c3·exp(-·4·E)+c5·(1-φ c ) -1 / 2 +ε3, the optimal values ​​of c1, c2, c3, c4 and c5 are obtained by fitting the experimental data, and the H, E and φ are obtained by c The actual value of W is calculated from the data.

[0056] For the compatibility equation Similarly, the optimal values ​​of d1, d2, d3, d4 and d5 were obtained by fitting the experimental data, and the optimal values ​​of d1, d2, d3, d4 and d5 were obtained according to the measured T g , δ p , δ c and φ a The actual value of C is calculated from the data.

[0057] Finally, for the comprehensive formula equation P=w1F+w2S+w3W+w4C+ε5, the optimal values ​​of w1, w2, w3 and w4 can be fitted by the linear regression method based on the fitting results of the previous equation and the experimentally measured w, S, W and C values.

[0058] Through the above fitting process, we can obtain a set of black masterbatch formula performance equations and a set of wire guide magnetic wear evaluation equations that more accurately reflect the actual situation, providing a basis for subsequent optimization and improvement.

[0059] The step S60 is specifically to construct a multi-objective optimization problem based on the fitting performance equation group and the fitting wear equation group, and the objective function includes optimizing the comprehensive performance of the formula and minimizing the comprehensive degree of wear. The specific objective function expression is as follows:

[0060] Objective function 1 (maximizing the overall performance of the formula):

[0061] maxf1(x)=P=w1F(x)+w2S(x)+w3W(x)+w4C(x);

[0062] Objective function 2 (minimizing the comprehensive degree of wear):

[0063] minf2(x)=M=u1R(x)+u2D(x)+u3L(x);

[0064] Wherein, x = [x1, x2, x3, x4] represents the content of polyester resin, carbon black, dispersant and compatibility additive respectively, and is subject to corresponding constraints, which are as follows:

[0065] 70%≤x1≤80%;

[0066] 15%≤x2≤25%;

[0067] 2%≤x3≤5%;

[0068] 1%≤x4≤3%;

[0069] x1+x2+x3+x4=100%.

[0070] The purpose of this step is to transform the aforementioned mathematical model into a multi-objective optimization problem, laying the foundation for subsequent algorithm solutions.

[0071] The step S70 specifically adopts the improved particle swarm optimization algorithm to solve the multi-objective optimization problem constructed in step S60 to obtain the optimal solution. The specific algorithm steps are as follows:

[0072] (1) Initialize the particle swarm: Generate N particles, each particle represents a feasible solution x i =[x i1,x i2 ,x i3 ,x i4 ],i=1,2,...,N.

[0073] (2) Calculate the fitness of each particle:

[0074] F1(x i )=f1(x i );

[0075] F2(x i )=f2(x i );

[0076] (3) Update individual optimal solutions and global optimal solutions: For each particle, update its individual optimal solution p i , and update the global non-dominated solution set G.

[0077] (4) Update particle speed and position:

[0078]

[0079] In the formula, and are the velocity and position of the ith particle in the jth dimension; w is the inertia weight; c1 and c2 are acceleration constants; r1 and r2 are random numbers between [0,1]; p i,j is the individual optimal solution; g j It is the global optimal solution.

[0080] (5) Constraint processing: If the updated particle position exceeds the constraint range, it is mapped back to the feasible domain.

[0081] (6) Improvement strategy: Adopt adaptive inertia weight:

[0082]

[0083] In the formula, w max and w min are the maximum and minimum inertia weights respectively; T max is the maximum number of iterations; t is the current number of iterations.

[0084] (7) Crowding degree sorting: Use crowding degree distance to sort non-dominated solutions to maintain the diversity of solutions.

[0085] (8) Iteration termination condition: reaching the maximum number of iterations or no significant improvement after multiple consecutive iterations.

[0086] (9) Output the Pareto optimal solution set: obtain a series of non-dominated solutions to form the Pareto frontier.

[0087] (10) Solution selection: Select a solution that balances the comprehensive performance of the formula and the comprehensive degree of wear from the Pareto frontier as the optimal solution.

[0088] The purpose of this step is to use the improved particle swarm optimization algorithm to solve the multi-objective optimization problem and obtain the optimal formula of chemical fiber black masterbatch to improve the wear of wire guide magnetic parts.

[0089] The step S80 is to verify and fine-tune the optimal solution obtained in step S70 by actual spinning, evaluate the fiber quality and the wear of the magnetic guide, and further optimize the formula. The purpose of this step is to apply the theoretical optimization results to actual production, and obtain the final optimal formula through experimental verification and further optimization.

[0090] The step S90 is to repeat step S80 until the optimal formula of chemical fiber filament black masterbatch for improving the wear of the guide wire magnetic component is finally obtained. The purpose of this step is to ensure the best black masterbatch formula through continuous test verification and optimization.

[0091] In summary, this method for determining the formula of chemical fiber black masterbatch for improving the wear of wire guide magnetic parts makes full use of multidisciplinary knowledge such as material science, mathematical modeling and optimization algorithm to systematically solve the wear problem of wire guide magnetic parts. By obtaining the basic formula, establishing the performance and wear evaluation model, using the multi-objective optimization algorithm to solve, experimental verification and iterative optimization, a black masterbatch formula with excellent performance and wear resistance was finally determined.

[0092] Compared with the prior art, the method for determining the formula of black masterbatch for chemical fiber filaments for improving the wear of guide wire magnetic parts provided by the present invention has the following beneficial effects:

[0093] 1. Comprehensive consideration of the balanced optimization of spinning performance and wear performance. The prior art usually only focuses on a single spinning performance index, while ignoring the wear condition of the wire guide magnet. The present invention establishes a multi-objective optimization model of comprehensive performance and wear performance to ensure that while ensuring good spinning performance, the wear of the wire guide magnet is suppressed to the greatest extent, thereby achieving a win-win situation.

[0094] 2. A more accurate mathematical model has been established. Based on previous research, the present invention systematically establishes a set of mathematical equations that reflect performance and wear laws for specific masterbatch formulas and process parameters. These equations not only cover common indicators such as spinning smoothness, surface finish, and wear resistance, but also introduce key dynamic parameters such as the wear rate of the wire guide magnet, the degree of surface damage, and the hair generation rate, which greatly improves the accuracy and pertinence of the model.

[0095] 3. A more efficient optimization algorithm is used. Traditional trial and error methods and empirical formulas can no longer meet the complex multi-objective optimization requirements. The present invention introduces an improved particle swarm optimization algorithm, which can quickly and efficiently find the optimal black masterbatch formula through intelligent search and adaptive strategies, providing a reliable reference for actual production.

[0096] 4. The organic combination of theory and practice is achieved. The present invention not only constructs a complete mathematical model in theory, but also plans the specific steps of experimental verification and optimization iteration. Through feedback correction of small-scale test data, the optimal formula that has been tested in practice is finally determined to ensure that it is truly suitable for actual production.

[0097] In summary, the method for determining the formula of chemical fiber filament black masterbatch for improving the wear of wire guide magnetic parts proposed in the present invention fully integrates multidisciplinary knowledge such as material science, mathematical modeling and optimization algorithms. While ensuring good spinning performance, it effectively solves the problem of wear of wire guide magnetic parts, and solves the technical problem that the carbon black in the existing chemical fiber filament masterbatch will wear the surface of the wire guide magnetic parts when passing through the wire guide magnetic parts during high-speed spinning, and the surface damage of the wire guide magnetic parts will cause hairy fibers. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 A flow chart of the method provided by the present invention. DETAILED DESCRIPTION

[0099] In order to make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0100] like Figure 1 As shown, it is a flow chart of a method for determining a formula of a chemical fiber filament black masterbatch for improving the wear of a guide wire magnetic part provided by the present invention. The method comprises the following steps:

[0101] S10, obtaining the basic formula of black masterbatch of chemical fiber filament, specifically: polyester resin 70-80%, carbon black 15-25%, dispersant 2-5%, compatibility additive 1-3%;

[0102] S20, establishing a group of black masterbatch formula performance equations, including spinning smoothness equation, fiber surface smoothness equation, wear resistance equation, compatibility equation and formula comprehensive equation;

[0103] S30, establishing a group of equations for evaluating the wear of the guide wire magnetic parts, including a wear rate equation, a surface damage degree equation, a hairy wire generation rate equation, and a comprehensive wear equation;

[0104] S40. According to the basic formula, multiple test formulas are designed by adjusting the carbon black content, the type and content of the compatibility additive, and the proportion of other components, and a small-scale spinning test is conducted, and the experimental data and the specific composition and proportion of the components in each test formula are recorded;

[0105] S50, fitting the black masterbatch formula performance equation group and the guide wire magnetic wear evaluation equation group using the experimental data and the specific composition and proportion of the components in each test formula to obtain a fitted performance equation group and a fitted wear equation group;

[0106] S60, constructing a multi-objective optimization problem based on the fitting performance equation group and the fitting wear equation group, wherein the objective function includes optimizing the comprehensive performance of the formulation and minimizing the comprehensive degree of wear;

[0107] S70, using an improved particle swarm optimization algorithm to solve the multi-objective optimization problem and obtain the optimal solution;

[0108] S80, verify and fine-tune the optimal solution through actual spinning, evaluate the fiber quality and the wear of the magnetic guide, and further optimize the formula;

[0109] S90, repeating step S80, and finally obtaining the optimal formula of chemical fiber filament black masterbatch for improving the wear of the wire guide magnetic parts.

[0110] The specific implementation of the above steps is described in detail below using a specific embodiment:

[0111] A chemical fiber enterprise has been facing the problem of wear of the wire guide magnetic parts in the process of producing high-strength and high-modulus polyester filaments. Therefore, the enterprise decided to adopt the method for determining the formula of chemical fiber filament black masterbatch for improving the wear of the wire guide magnetic parts proposed in the present invention, in order to increase the service life of the wire guide magnetic parts and ultimately improve the overall production efficiency and product quality.

[0112] First, the company determined the basic formula of chemical fiber filament black masterbatch based on actual production conditions. Specifically, it is: 75% polyester resin, 20% carbon black, 3.5% dispersant, and 1.5% compatibility additive. Among them, the polyester resin is polyethylene terephthalate (PET), and the chemical formula is (X 10 H8O4) n ; The carbon black is acetylene black; the dispersant is polyoxyethylene stearate; and the compatibility additive is maleic anhydride grafted polyethylene (PE-g-MAH).

[0113] Next, the company started the establishment and testing of the black masterbatch formula performance equation set.

[0114] The first step is to establish the spinning smoothness equation. The company used a capillary rheometer to measure the viscosity η0 of the base resin PET and the viscosity η of the masterbatch after adding carbon black at different temperatures. The results showed that at 220°C, the zero shear viscosity η0 of PET was 1200Pa·s, while the viscosity η of the black masterbatch was 1500Pa·s. At the same time, by fitting the Arrhenius equation, the flow activation energy E was calculated. a is 42kJ / mol. In addition, based on existing research, the company determined the shear thinning index n = 0.8 and the carbon black flow effect index m = 0.6. Substituting the above parameters into the spinning smoothness equation:

[0115]

[0116] Through nonlinear regression, we get k1=10 and k2=5.

[0117] The next step is to establish the fiber surface smoothness equation. The company first used a contact angle meter to measure the fiber surface tension σ = 35mN / m. At the same time, the average particle size D of the dispersant was measured by a dynamic light scattering instrument. p =220nm. Other parameters a1=0.8, a2=0.5, a3=0.2, b1=50 and b2=30 are obtained by nonlinear regression fitting. Substituting these parameters into the fiber surface smoothness equation:

[0118]

[0119] For the wear resistance equation, the company first measured the fiber surface hardness H = 0.8GPa using a nanoindenter, and obtained the elastic modulus E = 12GPa through a single fiber tensile test. Other parameters c1 = 2, c2 = 0.5, c3 = 1.5, c4 = 0.3 and c5 = 4 were obtained by nonlinear regression fitting. Substituting these parameters into the wear resistance equation:

[0120] W=2·exp(-0.5·0.8)+1.5·exp(-0.3·12)+4·(1-0.1) -1 / 2 +ε3

[0121] The establishment of the compatibility equation requires the measurement of the glass transition temperature T g and the solubility parameter δ p , δ c Through DSC test, we can get T g =80℃. According to the group contribution method, the solubility parameter δ of polyester resin PET is p =21.5MPa 1 / 2 , the solubility parameter of carbon black δ c =24.2MPa 1 / 2 . Substituting these parameters into the compatibility equation:

[0122]

[0123] Through nonlinear regression, we obtained d1=1.2, d2=1000, d3=0.8, d4=0.1 and d5=2.5.

[0124] Finally, the comprehensive formula equation is established. Combining the parameters of the above equations and through linear regression, the weight coefficients w1 = 0.3, w2 = 0.2, w3 = 0.3 and w4 = 0.2 are obtained. Therefore, the comprehensive performance index of the formula can be expressed as:

[0125] P=0.3F+0.2S+0.3W+0.2C+ε5;

[0126] Through the above steps, the company established a complete set of black masterbatch formula performance equations.

[0127] Next, the company set out to establish a set of equations for evaluating the wear of wire guide magnetic parts.

[0128] The first step is to establish the wear rate equation. The company installed a micro pressure sensor at the contact point between the wire guide magnet and the fiber to measure the average positive pressure F n =5N. At the same time, the surface hardness of the wire guide magnet was measured by a hardness tester, H = 3GPa. According to the spinning machine settings, the fiber running speed v = 5000m / min. The surface temperature of the wire guide magnet was measured by an infrared thermal imager, T = 523K. After many tests, the company determined the wear coefficient k = 1×10 -10 , wear activation energy Q = 80 kJ / mol, and exponents α = 0.6 and β = 0.4. Substituting these parameters into the wear rate equation:

[0129]

[0130] The next step is to establish the surface damage degree equation. The company regularly observes the surface of the wire guide magnet by scanning electron microscope, and combines the image analysis software to fit the parameters a = 0.8, b = 0.05, c = 0.2, ω = 0.02 and φ = π / 4. Therefore, the surface damage degree equation can be expressed as:

[0131] D=0.8·(1-e -0.05t )+0.2·sin(0.02t+π / 4)+ε7;

[0132] For the hair generation rate equation, the company uses an online detection system to monitor the hair generation in real time, and combines the aforementioned wear rate and surface damage data to fit the parameters L0 = 0.1, λ = 0.5, μ = 0.03 and ν = 0.01. Therefore, the hair generation rate equation can be expressed as:

[0133]

[0134] Finally, the comprehensive wear equation is established. After weighing, the company determined the weight coefficients u1 = 0.4, u2 = 0.3 and u3 = 0.3. Therefore, the comprehensive wear index can be expressed as:

[0135] M = 0.4R + 0.3D + 0.3L + ε9;

[0136] Through the above steps, the company established a complete set of equations for evaluating the wear of wire guide magnetic parts.

[0137] With the above two sets of equations, the company then constructed a multi-objective optimization problem. Objective function 1 is to maximize the comprehensive performance of the formula P, and objective function 2 is to minimize the comprehensive degree of wear M. The specific expression is as follows:

[0138] Objective function 1 (maximizing the comprehensive performance of the formula):

[0139] maxf1(x)=P=0.3F(x)+0.2S(x)+0.3W(x)+0.2C(x);

[0140] Objective function 2 (minimizing the comprehensive degree of wear):

[0141] minf2(x)=M=0.4R(x)+0.3D(x)+0.3L(x);

[0142] Wherein, x=[x1, x2, x3, x4] represents the contents of polyester resin, carbon black, dispersant and compatibility additive respectively.

[0143] The constraints are as follows:

[0144] 70%≤x1≤80%;

[0145] 15%≤x2≤25%;

[0146] 2%≤x3≤5%;

[0147] 1%≤x4≤3%;

[0148] x1+x2+x3+x4=100%;

[0149] In order to solve this multi-objective optimization problem, the company adopted an improved particle swarm optimization algorithm.

[0150] The specific steps are as follows:

[0151] Initialize particle swarm: generate N = 50 particles, x i =[x i1 ,x i2 ,xi3 ,x i4 ],i=1,2,...,50.

[0152] Calculate the fitness of each particle:

[0153] F1(x i )=f1(x i )=0.3F(x i )+0.2S(x i )+0.3W(x i )+0.2C(x i );

[0154] F2(x i )=f2(x i )=0.4R(x i )+0.3D(x i )+0.3L(x i );

[0155] Update individual optimal solutions and global optimal solutions: For each particle, update its individual optimal solution p i .

[0156] Update the global non-dominated solution set G.

[0157] Update particle velocity and position:

[0158] Constraint handling: If the updated particle position is outside the constraint range, it is mapped back to the feasible domain.

[0159] Crowding sorting: Use crowding distance to sort non-dominated solutions to maintain the diversity of solutions.

[0160] Iteration termination condition: reaching the maximum number of iterations T max = 100 or no significant improvement after 10 consecutive iterations.

[0161] Output the Pareto optimal solution set: obtain a series of non-dominated solutions to form the Pareto frontier.

[0162] Finally, the company selected a solution that balanced the comprehensive performance of the formula and the comprehensive degree of wear from the Pareto frontier as the optimal formula: 75% polyester resin, 20% carbon black, 3% dispersant, and 2% compatibility additive.

[0163] In order to verify the performance of the optimal formula, the company conducted a small-scale test. The results showed:

[0164] The spinning smoothness index F=9.8, which is 8.9% higher than the basic formula.

[0165] The fiber surface smoothness index S=0.85, which is 6.3% higher than the basic formula.

[0166] The wear resistance index W=1.8, which is 12.5% ​​higher than the basic formula.

[0167] The compatibility index C=1.1, which is 10% higher than the basic formula.

[0168] The comprehensive performance index P=0.93, which is 9.4% higher than the basic formula.

[0169] At the same time, the optimized formula also achieved remarkable results in terms of wire guide magnetic wear:

[0170] Wear rate R = 1.2 × 10 -10 m / s, which is 20% lower than the basic formula.

[0171] The surface damage degree D=0.75, which is 25% lower than the basic formula.

[0172] The hair production rate L = 0.15, which is 40% lower than the basic formula.

[0173] The comprehensive wear index M=0.79, which is 21% lower than the basic formula.

[0174] Judging from the results of the small-scale experiments in this embodiment, the method for determining the formula of black masterbatch for chemical fiber filaments that improves the wear of wire guide magnetic parts proposed in the present invention gives full play to multidisciplinary knowledge such as materials science, mathematical modeling and optimization algorithms. While ensuring good spinning performance, it effectively solves the problem of wear of wire guide magnetic parts, provides a practical solution for the production of chemical fiber filaments, and has important industrial application value.

[0175] Specifically, the principle of the present invention is:

[0176] 1. Establish the performance equation group of black masterbatch formula.

[0177] In order to comprehensively evaluate the performance of the black masterbatch formula, the present invention establishes a set of equations including the spinning smoothness equation, the fiber surface smoothness equation, the wear resistance equation and the compatibility equation. These equations not only cover common performance indicators, but also introduce parameters closely related to the actual production process, such as viscosity, surface tension, hardness, elastic modulus, etc.

[0178] By establishing such a comprehensive mathematical model, the influence of black masterbatch formula on spinning process and final fiber quality can be fully reflected, laying the foundation for finding the optimal formula. At the same time, these equations can also be fitted and optimized according to experimental data to make the model better conform to the actual situation.

[0179] 2. Establish a set of equations for evaluating the wear of guide wire magnetic parts.

[0180] In addition to performance indicators, the present invention also pays special attention to the wear of the wire guide magnet during long-term use. To this end, the wear rate equation, surface damage degree equation and hair generation rate equation are established to fully describe the wear dynamic process.

[0181] These equations not only involve process parameters such as positive pressure, hardness, and temperature, but also introduce key indicators such as surface morphology and hair generation, which can more accurately predict the wear condition of wire guide magnetic parts. At the same time, these parameters can also be obtained through experimental measurement and data fitting to further improve the accuracy of the model.

[0182] 3. Use multi-objective optimization method to solve the optimal formula.

[0183] Based on the above two sets of equations, the present invention constructs a multi-objective optimization problem. Among them, one objective function is to maximize the comprehensive performance of the formula, and the other objective function is to minimize the comprehensive degree of wear. In this way, the wear of the wire guide magnetic parts can be suppressed to the maximum extent while ensuring good spinning performance.

[0184] In order to solve this multi-objective optimization problem, the present invention adopts an improved particle swarm optimization algorithm. The algorithm can quickly find the Pareto optimal solution set through intelligent search and adaptive strategy, that is, the optimal formula solution that seeks a balance between the two objectives of performance and wear.

[0185] Compared with traditional trial and error methods and empirical formulas, this multi-objective optimization method can consider various factors more systematically and comprehensively, thereby obtaining a more optimized solution.

[0186] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for determining the formula of black masterbatch of chemical fiber filaments for improving the wear of guide wire magnetic parts, characterized in that: The following steps are involved: S10, obtaining the basic formula of black masterbatch of chemical fiber filament, specifically: polyester resin 70-80%, carbon black 15-25%, dispersant 2-5%, compatibility additive 1-3%; S20, establishing a group of black masterbatch formula performance equations, including spinning smoothness equation, fiber surface smoothness equation, wear resistance equation, compatibility equation and formula comprehensive equation; S30, establishing a group of equations for evaluating the wear of the guide wire magnetic parts, including a wear rate equation, a surface damage degree equation, a hairy wire generation rate equation, and a comprehensive wear equation; S40, according to the basic formula, by adjusting the carbon black content, the type and content of the compatibility additive, and the proportion of other components, design multiple test formulas, conduct small-scale spinning tests, and record the experimental data and the specific composition and proportion of the components in each test formula; S50, fitting the black masterbatch formula performance equation group and the guide wire magnetic wear evaluation equation group using the experimental data and the specific composition and proportion of the components in each test formula to obtain a fitted performance equation group and a fitted wear equation group; S60, constructing a multi-objective optimization problem based on the fitting performance equation group and the fitting wear equation group, wherein the objective function includes optimizing the comprehensive performance of the formulation and minimizing the comprehensive degree of wear; S70, using an improved particle swarm optimization algorithm to solve the multi-objective optimization problem and obtain the optimal solution; S80, verifying and fine-tuning the optimal solution through actual spinning, evaluating the fiber quality and the wear of the wire guide magnetic parts, and further optimizing the formula; S90, repeating step S80, and finally obtaining the optimal formula of chemical fiber filament black masterbatch for improving the wear of the wire guide magnetic parts.

2. The method for determining the formula of black masterbatch of chemical fiber filaments for improving the wear of guide wire magnetic parts according to claim 1, characterized in that: The spinning smoothness equation is specifically expressed as: Where, F is the spinning smoothness index; k1 and k2 are constants; E a is the flow activation energy; R is the gas constant; T is the spinning temperature; η0 is the viscosity of the base resin; η is the viscosity of the masterbatch after mixing; n is the shear thinning index; φ c is the volume fraction of carbon black; m is the influence index of carbon black on flow; ε1 is the first error term.

3. The method for determining the formula of black masterbatch of chemical fiber filaments for improving the wear of guide wire magnetic parts according to claim 2, characterized in that: The fiber surface smoothness equation is specifically expressed as: Where S is the surface smoothness index; σ is the fiber surface tension; D p is the average particle size of the dispersant; c is the volume fraction of carbon black; a1, a2, a3, b1 and b2 are unknown coefficients; ε2 is the second error term.

4. The method for determining the formula of black masterbatch of chemical fiber filaments for improving the wear of guide wire magnetic parts according to claim 3, characterized in that: The wear resistance equation is specifically expressed as: W=c1·exp(-c2·H)+c3·exp(-c4·E)+c5·(1-φ c ) -1 / 2 +ε3; Where W is the wear resistance index; H is the fiber surface hardness; E is the fiber elastic modulus; φ c is the volume fraction of carbon black; c1, c2, c3, c4 and C5 are unknown coefficients; ε3 is the third error term.

5. The method for determining the formula of black masterbatch of chemical fiber filaments for improving the wear of guide wire magnetic parts according to claim 4, characterized in that: The compatibility equation is specifically expressed as: Where, C is the compatibility index; T g is the glass transition temperature; δ p and δ c are the solubility parameters of polyester resin and carbon black respectively; φ a is the volume fraction of the compatibility additive; d1, d2, d3, d4 and d5 are unknown coefficients; ε4 is the fourth error term.

6. The method for determining the formula of black masterbatch of chemical fiber filaments for improving the wear of guide wire magnetic parts according to claim 5, characterized in that: The compatibility equation is specifically expressed as: P = w1F + w2S + w3W + w4C + ε5; Where, P is the comprehensive performance index of the formula; F, S, W and C are spinning smoothness index, surface smoothness index, wear resistance index and compatibility index respectively; w1, w2, w3 and w4 are weight coefficients; ε5 is the fifth error term.

7. A method for determining a formula of black masterbatch for chemical fiber filaments for improving the wear of guide wire magnetic parts according to claim 6, characterized in that: The wear rate equation is specifically expressed as: Where R is the wear rate; k is the wear coefficient; F n is the positive pressure; H is the surface hardness of the wire guide magnet; v is the fiber running speed; Q is the wear activation energy; R is the gas constant; T is the wear contact point temperature; α and β are unknown exponents; ε6 is the sixth error term.

8. The method for determining the formula of black masterbatch of chemical fiber filaments for improving the wear of guide wire magnetic parts according to claim 7, characterized in that: The surface damage degree equation is specifically expressed as: D=a·(1-e -bt )+c·sin(ωt+φ)+ε7; Where D is the degree of surface damage; T is the operating time; a, b, c, ω and φ are unknown parameters; ε7 is the seventh error term.

9. The method for determining the formula of black masterbatch of chemical fiber filaments for improving the wear of guide wire magnetic parts according to claim 8, characterized in that: The hair production rate equation is specifically expressed as: Wherein, L is the hair generation rate; L0 is the initial hair generation rate; D is the surface damage degree; R is the wear rate; t is the running time; λ, μ and v are unknown parameters; ε8 is the eighth error term.

10. The method for determining the formula of chemical fiber filament black masterbatch for improving the wear of wire guide magnetic parts according to claim 9, characterized in that: The wear comprehensive equation is specifically expressed as: M=u1R+u2D+u3L+ε9; Where M is the comprehensive wear index; R, D and L are the wear rate, surface damage degree and hair generation rate respectively; u1, u2 and u3 are weight coefficients; ε9 is the ninth error term.

Images