Method for optimizing electrofluid printing parameters

Abstract

The invention belongs to the technical field of advanced manufacturing, and discloses a method for optimizing electrofluid printing parameters, which comprises the following steps: 1) carrying out an electrofluid printing experiment, and determining key influence factors of electrofluid printing resolution; 2) determining a parameter level value of an influence factor of the electrofluid printing resolution; 3) obtaining an experimental sample of the electrofluid printing resolution; 4) carrying out range analysis; 5) acquiring a simulation experiment sample; (6) a function relation between the influence factors and the electrofluid printing resolution is obtained; 7) determining the correctness of the function relational expression; 8) generating an initial population through a genetic algorithm; 9) obtaining a current evolution algebra gen and an optimal fitness value; 10) performing interlace operation on the population; 11) performing mutation operation on the population; 12) performing evolution reversal on the population; 13) selecting an optimal individual; and 14) re-judging after the population is updated. According to the method, the regression analysis method and the genetic algorithm are combined to optimize the electrofluid printing parameters, the problems that in the actual experiment process, multiple parameter level combinations exist, and the optimal parameters are difficult to determine are solved, the robust performance is excellent, the calculation process is simple, and scientific guidance is provided for electrofluid printing parameter optimization design.

Description

Technical Field

[0001] The present invention belongs to the field of advanced manufacturing technology, and particularly relates to a method for optimizing electrohydrodynamic printing parameters. Background Art

[0002] Electrohydrodynamic Jet Printing (EHD) is a high-precision printing technology that uses an electric field to control jet generation and deposition. Since its discovery in the mid-20th century, it has shown great application potential in the fields of electronic device manufacturing, biomedicine, optoelectronic devices, etc.

[0003] However, the processes of jet generation and deposition in electrohydrodynamic printing are affected by multiple factors such as voltage, solution concentration, printing height, nozzle size, and printing speed. The effects of these parameters on the resolution are different, and there are complex interactions among them. The adjustment and setting of parameters have a direct and significant impact on the printing resolution. To achieve the best printing resolution, a large number of experimental studies are usually required on these parameters to find the optimal combination among them. However, this experimental method not only consumes a large amount of human and material resources but also makes the experimental process complex and costly. Each experiment requires delicate settings and long-term observations, which not only increases the workload but is also easily interfered by changes in the external environment, resulting in poor repeatability of the results. Therefore, an optimization algorithm can be used to systematically design and analyze experimental data, thereby reducing the number of experiments and optimizing the printing parameter configuration. The optimization algorithm can efficiently find the key factors affecting the resolution and their optimal combination conditions, thereby improving the experimental efficiency and achieving more precise resolution optimization. Among them, regression analysis and genetic algorithm are two effective optimization tools that can help solve this complex multi-variable optimization problem. Regression analysis is a statistical method that can effectively find the key factors affecting jet formation and deposition and their optimal combination conditions by designing experiments, constructing models, and optimizing responses. Through regression analysis, a relationship model can be established between parameters such as voltage, solution concentration, and printing height and the electrohydrodynamic printing resolution, so as to find the optimal parameter combination in the experiment, reduce the number of experiments and time, and improve the experimental efficiency. The genetic algorithm is an optimization algorithm based on natural selection and genetic variation, which can find the optimal solution among a large number of parameter combinations by simulating the biological evolution process. The genetic algorithm can handle complex multi-variable optimization problems and achieve optimal control of the printing process and improve the printing quality and efficiency by continuously iterating and selecting excellent features. Summary of the Invention

[0004] The object of the present invention is to provide a method for optimizing electrohydrodynamic printing parameters in view of the deficiencies of the prior art. This method first selects four key factors affecting the resolution of electrohydrodynamic printing, namely the working voltage, printing speed, working distance, and liquid supply flow rate, designs an orthogonal experiment to study the influence of each factor on the resolution of electrohydrodynamic printing, reveals the mapping relationship between the resolution of electrohydrodynamic printing and the key factors through regression analysis of the orthogonal experiment results, and then uses the genetic algorithm toolbox in MATLAB software to iteratively select the level values of the influencing factors with the highest resolution as the goal, and evolves the optimal parameter combination to achieve high-resolution production and manufacturing of electrohydrodynamic printing. This method has excellent robustness, a simple calculation process, can facilitate the later parameter optimization design, and the optimized calculation results are relatively ideal, providing scientific guidance for high-resolution printing and manufacturing of electrohydrodynamic printing.

[0005] To achieve the above object, the specific technical solution adopted by the present invention is as follows:

[0006] An electrohydrodynamic jet printing device includes a micro-injection pump, a high-voltage power supply, and a motion module. The micro-injection pump is connected to an electrohydrodynamic printing nozzle through a liquid supply conduit. The substrate is installed on the upper surface of the motion module. One end of the high-voltage power supply is connected to the electrohydrodynamic printing nozzle, and the other end is connected to the substrate. A voltage of 400 - 5000V is applied between the electrohydrodynamic printing nozzle and the substrate, thereby forming an electric field between the electrohydrodynamic printing nozzle and the substrate. The industrial control computer is electrically connected to the motion module. The micro-injection pump contains functional material ink, and the outer wall of the electrohydrodynamic printing nozzle is hydrophobized.

[0007] A method for optimizing electrohydrodynamic printing parameters includes the following steps:

[0008] S1. Obtain experimental samples of the resolution of electrohydrodynamic printing;

[0009] S2. Conduct range analysis;

[0010] S3. Construct a functional relationship between the influencing factors and the resolution of electrohydrodynamic printing, and perform quadratic multiple regression fitting on the function to obtain a quadratic polynomial regression equation;

[0011] S4. Optimize the above regression equation using the genetic algorithm;

[0012] S5. According to the value range of the influencing factors set in the factor parameter table, obtain that the optimal values of the design variables with the optimal combination of x1, x2, x3, and x4 are 3kv, 10mm / s, 0.2mm, and 2μL / min respectively;

[0013] S6. Verify the obtained optimal parameter combination to verify the correctness of the predicted value of the optimal parameter combination.

[0014] Further, step S1 is specifically as follows:

[0015] Select the working voltage, printing speed, working distance, and liquid supply flow rate as the influencing factor values, that is, independent variables; the dependent variable is the electrohydrodynamic printing resolution (i.e., the minimum line width). An orthogonal experimental design model is adopted to generate 16 groups of experimental samples for printing tests, obtain the resolution under each influencing factor value, and thus obtain the experimental samples.

[0016] Further, step S2 is specifically as follows:

[0017] Use range analysis to calculate and analyze the experimental results obtained in S1 to obtain the range values of the working voltage, printing speed, working distance, and liquid supply flow rate.

[0018] Further, step S3 is specifically as follows:

[0019] Combined with the experimental samples, select the second-order polynomial model based on the Taylor expansion as the functional relationship between the variables and the target:

[0020]

[0021] After the above formula is expanded, it is as follows:

[0022]

[0023] Among them, is the linear term, is the quadratic term, is the cross term, α0 is the constant term, α i is the linear term coefficient, α ii is the quadratic term coefficient, α ij is the cross term coefficient, ε is the error term, z is the target value, x1 represents the working voltage, x2 represents the printing speed, x3 represents the working distance, x4 represents the liquid supply flow rate, z represents the minimum line width, a - o are all constants, and n is the number of variables.

[0024] Perform quadratic multiple regression fitting on the experimental factor combinations and their results, calculate the coefficients of the regression equation, and obtain the quadratic polynomial regression equation of the resolution (z) with respect to the working voltage (x1), printing speed (x2), working distance (x3), and liquid supply flow rate (x4) as:

[0025]

[0026] To ensure the credibility of the regression equation, the data is subjected to correlation verification to obtain the correlation evaluation index of the regression equation. Use R 2 to represent the correlation coefficient of the regression equation. The closer R 2 is to 1, the greater the correlation between the independent variable and the dependent variable, and the more reliable the regression equation. The correlation coefficient R of the embodiment2 is 0.924, indicating that the functional relationship is credible.

[0027] Further, step S4 is specifically as follows:

[0028] Step a: Generate an initial population in a random manner;

[0029] Step b: Obtain the current generation number gen and the optimal fitness value;

[0030] Use the built-in algorithm of MATLAB to obtain the current generation number gen and the optimal fitness value;

[0031] Step c: Perform crossover operations on the populations respectively;

[0032] Perform crossover operations on the two populations of electrohydrodynamic printing parameters and electrohydrodynamic printing resolution respectively;

[0033] Step d: Perform mutation operations on the populations respectively;

[0034] Perform mutation operations on the two populations of electrohydrodynamic printing parameters and electrohydrodynamic printing resolution respectively;

[0035] Step e: Perform evolutionary reversal on the populations respectively;

[0036] Perform evolutionary reversal on the two populations of electrohydrodynamic printing parameters and electrohydrodynamic printing resolution respectively;

[0037] Step f: Calculate the fitness function value of the populations as a whole, and select the best individual using the elitist strategy;

[0038] Calculate the fitness function value of the electrohydrodynamic printing resolution population as a whole, and select the best individual using the elitist strategy;

[0039] Step g: Rejudge after the population is updated,

[0040] Rejudge after the echo loss population is updated. If the gen value is less than 50 and the num value is greater than 0, perform local catastrophe on the population, and then return to step b. Otherwise, directly return to step b; The maximum number of generations of the algorithm is set to 50 generations, and the evolution terminates when the gen value exceeds 50.

[0041] Further, step S6 is specifically as follows:

[0042] According to the optimal parameter combination obtained above, that is, the working voltage is ±3 kV, the printing speed is 10 mm / s, the working distance is 0.2 mm, and the liquid supply flow rate is 2 μL / min, an electrohydrodynamic printing experiment verification is carried out to verify the correctness of the predicted value of the optimal parameter combination. Uniformly select 5 lines from the printing results and label them as array line 1, array line 2, array line 3, array line 4, and array line 5 respectively; measure the width values of the 5 lines respectively, and calculate the average value of the 5 measurement results. Through the analysis of the optimized parameter level combination, it is found that the printed line width obtained by the optimized optimal parameter combination is 70 μm, which is 15 μm lower than the minimum size of 85 μm before optimization, and the degree of decrease is 17.6%, which proves the effectiveness of the regression analysis-genetic algorithm in optimizing the electrohydrodynamic printing resolution.

[0043] Advantages of the present invention:

[0044] (1) The present invention proposes to use the regression analysis-genetic algorithm to optimize the electrohydrodynamic printing parameters, which solves the problem of numerous parameter level combinations in the actual experimental process and is difficult to determine the optimal parameters. An orthogonal design is used to establish parameter level combinations for experiments, the relationship between the experimental results and factors is analyzed by regression analysis to obtain an analysis model, the reliability of the model is determined, and the model is substituted into the genetic algorithm to find the optimal solution, and the optimized parameters are found to achieve stable printing of high-resolution micro-nano structures.

[0045] (2) The present invention combines the regression analysis-genetic algorithm to optimize the electrohydrodynamic printing resolution, has excellent robustness, and the calculation process is simple, which can provide scientific guidance for the parameter optimization design in the high-resolution printing process of electrohydrodynamic printing. Description of the drawings

[0046] Figure 1 Schematic diagram of the electrohydrodynamic printing device for the embodiment;

[0047] Figure 2 Schematic diagram of the method flow for the embodiment.

[0048] Figure 3 Schematic diagram of the mean value change during the optimization process for the embodiment;

[0049] Figure 4 Schematic diagram of the change of the optimal solution during the optimization process for the embodiment. Detailed implementation manners

[0050] The present invention will be further described below with reference to the drawings.

[0051] Embodiment 1

[0052] As Figure 1As shown in the figure, the electrohydrodynamic printing device of the present invention includes a micro-injection pump 1, a high-voltage power supply 3, and a motion module 5. The micro-injection pump 1 is connected to an electrohydrodynamic printing nozzle 2 through a liquid supply conduit 7. A substrate 4 is installed on the upper surface of the motion module 5. One end of the high-voltage power supply 3 is connected to the electrohydrodynamic printing nozzle 2, and the other end is connected to the substrate 4. A voltage of 400 - 5000V is applied between the electrohydrodynamic printing nozzle 2 and the substrate 4, so as to form an electric field between the electrohydrodynamic printing nozzle 2 and the substrate 4. An industrial control computer 6 is electrically connected to the motion module 5. The micro-injection pump 1 is filled with functional material ink. The outer wall of the electrohydrodynamic printing nozzle 2 is hydrophobized, which can effectively prevent the material from climbing along the outer wall.

[0053] The functional material ink is transported through the liquid supply conduit 7 to the nozzle of the electrohydrodynamic printing nozzle 2 at a flow rate of 0.01 - 1 μL / min under the thrust of the micro-injection pump 1. The industrial control computer 6 sends motion commands to the motion module 5 by using the programmed motion control software. The high-voltage power supply 3 provides a voltage of 400 - 5000V to the electrohydrodynamic printing nozzle 2, forming an electric field between the electrohydrodynamic printing nozzle 2 and the substrate 4. Under the action of the electric field force, the functional material ink is dragged into a stable jet with a size of 100 nm - 50 μm, and micro-nano structures can be printed on the substrate 4.

[0054] Example 2

[0055] As Figure 2 shown, a method for optimizing electrohydrodynamic printing parameters includes the following steps:

[0056] S1. Obtain experimental samples of electrohydrodynamic printing resolution:

[0057] Select the working voltage, printing speed, working distance, and liquid supply flow rate as the influencing factor values, that is, independent variables. The dependent variable is the electrohydrodynamic printing resolution (i.e., the minimum line width). Using the orthogonal experimental design model, 16 groups of experimental samples are generated for printing experiments, and the resolutions under each influencing factor value are obtained, thereby obtaining the experimental samples.

[0058] S2. Conduct range analysis:

[0059] Use range analysis to calculate and analyze the experimental results obtained in S1, and obtain the range values of the working voltage, printing speed, working distance, and liquid supply flow rate, as shown in Table 1;

[0060] Table 1 Range analysis result table

[0061]

[0062] S3. Construct the functional relationship between the influencing factors and the electrohydrodynamic printing resolution, and perform quadratic multiple regression fitting on the function to obtain the quadratic polynomial regression equation

[0063] According to calculus knowledge, any function can be approximately represented by several polynomials in segments. Therefore, in practical problems, regardless of the complexity of the relationship between variables and results, polynomial regression can always be used for analysis and calculation. Since there are 4 design variables in the present invention and the functional relationship between the variables and the target is non-linear, combined with the experimental samples in Table 2, a second-order polynomial model based on the Taylor expansion is selected as the functional relationship between the variables and the target:

[0064]

[0065] After expanding the above formula, it is as follows:

[0066]

[0067] Among them, is the linear term, is the quadratic term, is the cross term, α0 is the constant term, α i is the coefficient of the linear term, α ii is the coefficient of the quadratic term, α ij is the coefficient of the cross term, ε is the error term, z is the target value, x1 represents the working voltage, x2 represents the printing speed, x3 represents the working distance, x4 represents the liquid supply flow rate, z represents the minimum line width, a - o are all constants, and n is the number of variables.

[0068] Table 2 Orthogonal test table and test results of L4 4

[0069]

[0070]

[0071] Perform quadratic multiple regression fitting on the experimental factor combinations and their results in Table 1, calculate the coefficients of the regression equation, as shown in Table 3, and obtain the quadratic polynomial regression equation of the resolution (z) with respect to the working voltage (x1), printing speed (x2), working distance (x3), and liquid supply flow rate (x4) as:

[0072]

[0073] Table 3 Regression coefficients

[0074]

[0075]

[0076] To ensure the credibility of the regression equation, the data in Table 1 was subjected to correlation verification, and the correlation evaluation index of the regression equation was obtained. The results are shown in Table 4; use R 2 to represent the correlation coefficient of the regression equation, R​2 The closer it is to 1, the greater the correlation between the independent variable and the dependent variable, and the more reliable the regression equation. The correlation coefficient R of the embodiment 2 is 0.924, indicating that the functional relationship is credible.

[0077] Table 4 Analysis of Variance

[0078]

[0079] S4. Optimize the above regression equation using the genetic algorithm

[0080] This algorithm first randomly determines a set of initial solutions from the domain, and then searches for the optimal or sub-optimal solutions of the objective function within the domain range. The parameter settings are shown in Table 5;

[0081] Table 5 Genetic Algorithm Parameter Settings Table

[0082]

[0083]

[0084] Specifically, the steps are as follows:

[0085] Step a: Generate an initial population randomly;

[0086] Step b: Obtain the current generation number gen and the optimal fitness value;

[0087] Use the built-in algorithm of MATLAB to obtain the current generation number gen and the optimal fitness value;

[0088] Step c: Perform crossover operations on the population respectively;

[0089] Perform crossover operations on the two populations of electrohydrodynamic printing parameters and electrohydrodynamic printing resolution respectively;

[0090] Step d: Perform mutation operations on the population respectively;

[0091] Perform mutation operations on the two populations of electrohydrodynamic printing parameters and electrohydrodynamic printing resolution respectively;

[0092] Step e: Perform evolutionary reversal on the population respectively;

[0093] Perform evolutionary reversal on the two populations of electrohydrodynamic printing parameters and electrohydrodynamic printing resolution respectively;

[0094] Step f: Calculate the fitness function value of the population as a whole and select the best individual using the elitist strategy;

[0095] Calculate the fitness function value of the electrohydrodynamic printing resolution population as a whole and select the best individual using the elitist strategy;

[0096] Step g: Rejudge after the population update,

[0097] After the population update of the return loss, rejudge. If the gen value is less than 50 and the num value is greater than 0, implement local catastrophe on the population, and then return to step b. Otherwise, directly return to step b. The maximum number of genetic generations of the algorithm is set to 50 generations. If the gen value exceeds 50, terminate the evolution.

[0098] S5. According to the value range of the influencing factors set in the factor parameter table, the optimal combination is obtained. The best values of the design variables of x1, x2, x3, and x4 are 3 kv, 10 mm / s, 0.2 mm, and 2 μL / min respectively, where the factor parameter table is shown in Table 5.

[0099] S6. Verify the obtained optimal parameter combination to verify the correctness of the predicted value of the best parameter combination

[0100] According to the optimal parameter combination obtained above, that is, the working voltage is ±3 kv, the printing speed is 10 mm / s, the working distance is 0.2 mm, and the liquid supply flow rate is 2 μL / min, conduct an electrohydrodynamic printing experiment verification to verify the correctness of the predicted value of the best parameter combination. Evenly select 5 lines from the printing results and label them as array line 1, array line 2, array line 3, array line 4, and array line 5 respectively. Measure the width values of the 5 lines respectively, and calculate the average value of the 5 measurement results. The measurement results are shown in Table 6. By analyzing the optimized parameter level combination, it is found that the printed line width obtained by the optimized optimal parameter combination is 70 μm, which is 15 μm lower than the minimum size of 85 μm before optimization, and the decrease degree is 17.6%, which proves the effectiveness of the regression analysis - genetic algorithm in optimizing the electrohydrodynamic printing resolution.

[0101] Table 6 Comparison of results before and after optimization

[0102]

[0103] The above describes the basic principle and main features of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements. The protection scope claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. An electrohydrodynamic printing device, characterized in that, It includes a micro-injection pump (1), a high-voltage power supply (3) and a motion module (5). The micro-injection pump (1) is connected to an electrohydrodynamic printing nozzle (2) through a liquid supply conduit (7). A substrate (4) is mounted on the upper surface of the motion module (5). One end of the high-voltage power supply (3) is connected to the electrohydrodynamic printing nozzle (2), and the other end is connected to the substrate (4). A voltage of 400 - 5000V is applied between the electrohydrodynamic printing nozzle (2) and the substrate (4), so as to form an electric field between the electrohydrodynamic printing nozzle (2) and the substrate (4). An industrial control computer (6) is electrically connected to the motion module (5). The micro-injection pump (1) is filled with functional material ink, and the outer wall of the electrohydrodynamic printing nozzle (2) is hydrophobized.

2. A method for optimizing electrohydrodynamic printing parameters, the method being based on the printing device according to claim 1, characterized in that It includes the following steps: S1. Obtain experimental samples of electrohydrodynamic printing resolution; S2. Conduct range analysis; S3. Construct a functional relationship between influencing factors and electrohydrodynamic printing resolution, and perform quadratic multiple regression fitting on the function to obtain a quadratic polynomial regression equation; S4. Optimize the above regression equation using a genetic algorithm; S5. According to the value range of influencing factors set in the factor parameter table, obtain that the optimal values of the design variables with the optimal combination of x1, x2, x3, x4 are 3kv, 10mm / s, 0.2mm, and 2μL / min respectively; S6. Verify the obtained optimal parameter combination to verify the correctness of the predicted value of the optimal parameter combination.

Images