A method for calculating the minimum distance between the electrodes in electrostatic flocking process based on dynamic research

Abstract

The present application relates to the technical field of electrostatic flocking, and discloses a calculation method of minimum electrode plate spacing in electrostatic flocking process based on kinetic research, comprising the following steps: step one, approximating the state of the flocking in the electric field as an elongated ellipsoid; step two, calculating the time t1 when the flocking completes rotation; step three, calculating the free-fall speed v1 and the generated displacement S1 when the flocking completes rotation; step four, calculating the generated translation displacement S2 when the flocking reaches the speed v3; v3 refers to 99% of the maximum translation speed v2; step five, ensuring the minimum electrode plate spacing S z =S1+S2 in which the flocking is vertically implanted in the adhesive at the maximum speed. The present application establishes the rotation equation and translation equation describing the movement of the flocking in the electric field, and solves the equations by using MATLAB. Through image and data analysis, it is shown that the minimum electrode plate spacing is linearly positively correlated with the flocking linear density.

Description

Technical Field

[0001] This invention belongs to the technical field of electrostatic flocking, and more specifically relates to a method for calculating the minimum electrode spacing in an electrostatic flocking process based on kinetic research. Background Technology

[0002] Electrostatic flocking utilizes Coulomb's driving force to eject short fibers from a charging source onto the surface of an adhesive-coated substrate, forming a dense arrangement of fibers perpendicular to the substrate, thereby endowing the substrate with new properties and characteristics. As an advanced preparation method, electrostatic flocking technology has shown broad application prospects in numerous fields such as textiles, materials, packaging, biology, environmental protection, and medicine.

[0003] Depending on the direction of the flock's flight, flocking processes can be categorized into descending, ascending, and lateral flocking methods. Electrostatic flocked fabrics consist of a base fabric, flock fibers, and an adhesive, with descending flocking being the most common method. The performance of the flocking adhesive is a key factor in the performance of the flocked fabric, and flocking adhesives have been improved and innovated to meet different application requirements.

[0004] In electrostatic flocking, the electrode spacing, electric field strength, and flock length have a crucial impact on the flocking effect. With electrode spacings of 3, 6, and 9 cm, the percentages of carbon fibers with an angle to the base fabric ranging from 75° to 90° were 0.64, 0.75, and 0.74, respectively (ZFYu, S.Wei, JDGuo, Fabrication of aligned carbon-fiber / polymer TIMs using electrostatic flocking method. J. Mater. Sci.: Mater. in Electron. 30, 10233-10243 (2019).). This indicates that a 6 cm electrode spacing already satisfies the requirement of rotating the carbon fibers from the horizontal direction to the direction of the electric field lines.

[0005] Liu, Lifang, et al. (Optimal design of superfine polyamide fabric by electrostatic flocking technology. Textile Research journal. 81, 3-9 (2011).) used superfine nylon fibers to produce flocked fabrics. They found that flocking density increased with decreasing electrode spacing, increasing electric field strength, and extending flocking time. However, these conclusions were based on experimental results and did not include theoretical calculations or analyses of the effects of various parameters on the flocking effect.

[0006] Popkov et al. (Fiber charging dynamics and motion in an electrostatic field. pp. 40-43, 95, 1983.) created an experimental apparatus for studying fiber charging and motion. They used cotton fibers to study the fiber charging dynamics and motion in an electrostatic field, and measured and calculated the charge and force on a single fiber in the electrostatic field. However, these research results still have some gaps in guiding the flocking process. Summary of the Invention

[0007] In view of this, the present invention proposes a method for calculating the minimum electrode spacing in the electrostatic flocking process based on dynamic research. By studying the dynamic phenomena in the electrostatic flocking process, the minimum electrode spacing that ensures the flock is vertically implanted into the adhesive at the maximum speed is calculated by solving the motion equations using MATLAB. This aims to reduce the electrode voltage and lower production costs and safety hazards.

[0008] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0009] A method for calculating the minimum electrode spacing in an electrostatic flocking process based on kinetic studies includes the following steps:

[0010] Step 1: Approximate the state of the fluff in the electric field as a slender ellipsoid, with the length of the fluff being l and the diameter being d. Then the three axes of the ellipsoid are a, b, and c, where a = l / 2.

[0011] In an electrostatic field, the fibers first rotate in the direction of the electric force, and when they rotate to be parallel to the electric force, the fibers are fully charged. Then they begin to translate along the direction of the electric force.

[0012] Step 2: Calculate the time t1 for the fibers to complete their rotation;

[0013] The fibers in the electrostatic field rotate under the action of the moment of inertia M, the air resistance torque M1, and the rotational torque M2. The second-order ordinary differential equation (10) is obtained from this rotation process:

[0014]

[0015] in:

[0016] By solving the rotation equation (10) using MATLAB, the relationship curve between the angle between the fiber axis and the direction of the electric force and time can be obtained. The fiber undergoes damped oscillation at a certain frequency in the direction of the electric force in the electrostatic field until it becomes parallel to the direction of the electric force. During the damped oscillation process, the relationship curve between the angle and time is closest to 0.5°.

[0017] The time corresponding to the peak of (0.00872 rad) is the time t1 for the fluff to complete its rotation;

[0018] Step 3: Calculate the free fall velocity v1 and displacement S1 of the fluff when it completes its rotation;

[0019] During the downward flocking process, the flocking fibers undergo free fall motion while rotating, resulting in displacement. The flocking fibers are subject to air resistance and gravity during free fall, and their velocity equation is shown in equation (17), and their displacement equation is shown in equation (18).

[0020]

[0021]

[0022] Solve equations (17) and (18) using MATLAB to obtain the free fall velocity v1 and the resulting displacement S1;

[0023] Step 4: Calculate the translational displacement S2 when the fibers reach velocity v3 during the translation process; v3 refers to 99% of the maximum translational velocity v2.

[0024] During translational motion, the fibers in an electrostatic field are mainly subjected to the electric force F. q Gravity G and air resistance F R Under the influence of the electric field, translational motion occurs. Since gravity is much smaller than electric force, the effect of gravity is ignored, resulting in the translational velocity equation (14) and the translational displacement equation (15):

[0025]

[0026]

[0027] Using MATLAB to solve equations (14) and (15), we can obtain the velocity and time curves, displacement and time curves during the translation process of the fluff, and obtain the translational displacement S2 at v3.

[0028] Step 5: Ensure the fibers are vertically implanted into the adhesive at the minimum electrode spacing S at maximum speed. z =S1+S2.

[0029] Further optimized, the eccentricity of the ellipsoid polarization coefficient

[0030]

[0031] Furthermore, under the same electric field strength, the electrotreated fluff can acquire saturated charge regardless of whether it is charged by electrodes or by two electrodes, and the charge q it carries is calculated as shown in equation (1):

[0032]

[0033] In the formula: l is the length of the fluff, m; d is the diameter of the fluff, m; E0 is the electric field strength, V / m; ε0 is the vacuum permittivity, 8.85 × 10⁻⁶. -12 F / m.

[0034] In a further preferred embodiment, in step two, the fibers in the electrostatic field rotate under the action of the moment of inertia M, the air resistance torque M1 and the rotational torque M2. The rotation process is described by equation (2), where θ is the angle between the fiber axis and the direction of the electric field force.

[0035]

[0036] If the fluff is considered as a hard cylindrical object that rotates around the center, the formula for calculating the moment of inertia is (3), where m is the mass of the fluff in kg.

[0037]

[0038] The rotation of the fluff is a damped vibration with a low speed. The air resistance is proportional to the speed, and the calculation of air resistance is shown in equation (4); where: C x ρ is the air drag coefficient, 1.8; ρ is the air density, 1.295 kg / m³. 3 x is the distance from the analysis element on the pile to the pile center, in meters; S is the maximum cross-sectional area between the analysis element on the pile and the pile center, in meters. 2 ;

[0039]

[0040] The element drag torque of the analyzed element on the pile is ΔM1, as shown in equation (5):

[0041]

[0042] Solving equation (5) yields equation (6):

[0043]

[0044] The calculation of the rotational torque M2 is shown in equation (7):

[0045]

[0046] Substituting equation (1) into equation (7), we obtain equation (8):

[0047]

[0048] Substituting equations (3), (6), and (8) into equation (2) yields equation (9):

[0049]

[0050] Equation (9) is transformed into a second-order ordinary differential equation (10):

[0051]

[0052] in:

[0053] Further preferred, in equations (17) and (18) of step three, Where C x ρ is the air drag coefficient, 1.8; ρ is the air density, 1.295 kg / m³. 3 .

[0054] In a further preferred embodiment, the calculation method for the maximum translational velocity v2 in step three is as follows:

[0055] Neglecting the interaction forces between the fibers, the fibers are mainly subjected to the electric force F when translating in the electric field. q Gravity G and air resistance F R The equation for the translational velocity of a single hair is given by equation (11), where v is the instantaneous velocity of the hair during the translation process, in m / s:

[0056]

[0057] After the fibers are oriented, the electric field force F q The calculation is as shown in equation (12):

[0058]

[0059] The air resistance F experienced by the fibers R The calculation formula is as follows (13):

[0060]

[0061] Because gravity G is much smaller than electric force F q Simplifying equation (11) yields the translational velocity equation (14) and the translational displacement equation (15):

[0062]

[0063]

[0064] in,

[0065] Solving the ordinary differential equation (14) yields the translational velocity formula as shown in equation (16):

[0066]

[0067] Using MATLAB to solve the translational velocity equation (14), the relationship curve between translational velocity and time is obtained; from the relationship curve, it can be seen that the acceleration of the wool's translational motion decreases with increasing time until it becomes 0, in equation (16) That is the maximum translational velocity v2.

[0068] Compared with the prior art, the present invention has the following advantages:

[0069] (1) The rotational and translational equations describing the motion of the fibers in the electric field were established and solved using MATLAB. The motion process of the fibers was visually demonstrated through image and data analysis. The calculation results show that the rotation of the fibers exhibits damped oscillations; as time increases, the angle between the fiber axis and the electric field gradually decreases until it becomes parallel to the electric field. The translational motion of the fibers first undergoes variable acceleration linear motion, with the acceleration decreasing with time until it reaches zero, and then it undergoes uniform linear motion.

[0070] (2) The rotation time of the fibers is independent of the fiber length and electric field strength, but is linearly positively correlated with the linear density. A two-variable linear equation t1 = 0.0085N can be used. dtex It is represented by +0.0416.

[0071] (3) The maximum translational velocity of the fibers is proportional to the electric field strength. When the electric field strength is constant, the maximum translational velocity of the fibers is linearly positively correlated with its aspect ratio, which can be expressed by the two-variable linear equation v2=0.041r+5.4203.

[0072] (4) The minimum electrode spacing is linearly positively correlated with the cord density, which can be expressed by a two-variable linear equation S. z =0.9431N dtex The value is expressed as +2.5582. The electric field strength and fluff length have no effect on the minimum electrode spacing.

[0073] (5) In the flocking test, the minimum electrode spacing is first calculated from the flock linear density, and then different electrode voltages are tested. The optimal electrode voltage is determined based on the flocking effect and flocking fastness. Attached Figure Description

[0074] Figure 1 A theoretical model for the downy fibers;

[0075] Figure 2 The force analysis of the fibers in an electric field shows the rotation process (left figure) and the translation process (right figure).

[0076] Figure 3 The graph shows the relationship between the included angle and time for five types of fluff during rotation.

[0077] Figure 4The graphs show the relationship between the translational velocity of five types of down and time.

[0078] Figure 5 The graph shows the relationship between the maximum translational velocity of the fibers and the aspect ratio.

[0079] Figure 6 This is a graph showing the relationship between the included angle and time during the rotation of the fibers in Example 3.

[0080] Figure 7 The graph shows the free fall velocity (left) and displacement (right) of the fluff during rotation in Example 3.

[0081] Figure 8 This is a graph showing the relationship between the translational velocity of the fibers and time in Example 3;

[0082] Figure 9 This is a graph showing the relationship between displacement and time during the translational motion of the fibers in Example 3.

[0083] Figure 10 A graph showing the relationship between the rotation time of the pile and the linear density of the pile;

[0084] Figure 11 A graph showing the relationship between minimum electrode spacing and fluff linear density;

[0085] Figure 12 The graph shows the relationship between the included angle and time during the rotation of the fluff under different electric field intensities.

[0086] Figure 13 The graph shows the relationship between translational velocity and time under different electric field intensities. Detailed Implementation

[0087] The present invention will be further described in detail below with reference to the embodiments, and the technical content and effects thereof are not limited thereto.

[0088] Step 1, such as Figure 1 As shown, the state of the fluff in the electric field can be approximated as a slender ellipsoid with length l and diameter d. Then the three axes of the ellipsoid are a, b, and c, where a = l / 2. Eccentricity of the ellipsoid polarization coefficient

[0089] like Figure 2 As shown, in an electrostatic field, the fibers first rotate in the direction of the electric force, and then rotate until they are parallel to the electric force, at which point the fibers are fully charged. Subsequently, they undergo translational motion along the direction of the electric force. Under the same electric field strength, the fibers treated with electrocoating can carry a saturated charge whether charged by an electrode or by two electrodes. The charge q carried by the fibers is calculated as shown in equation (1):

[0090]

[0091] In the formula: l is the length of the fluff, m; d is the diameter of the fluff, m; E0 is the electric field strength, V / m; ε0 is the vacuum permittivity, 8.85 × 10⁻⁶. -12 F / m.

[0092] Step 2: Calculate the time t1 for the fibers to complete their rotation;

[0093] The fibers in the electrostatic field rotate under the action of the moment of inertia M, the air resistance torque M1 and the rotational torque M2. The rotation process is described by equation (2), where θ is the angle between the fiber axis and the direction of the electric field force.

[0094]

[0095] If the fluff is considered as a hard cylindrical object that rotates around the center, the formula for calculating the moment of inertia is (3), where m is the mass of the fluff in kg.

[0096]

[0097] The rotation of the fluff is a damped vibration with a low speed. The air resistance is proportional to the speed, and the calculation of air resistance is shown in equation (4); where: C x ρ is the air drag coefficient, 1.8; ρ is the air density, 1.295 kg / m³. 3 x is the distance from the analysis element on the pile to the pile center, in meters; S is the maximum cross-sectional area between the analysis element on the pile and the pile center, in meters. 2 ;

[0098]

[0099] The element drag torque of the analyzed element on the pile is ΔM1, as shown in equation (5):

[0100]

[0101] Solving equation (5) yields equation (6):

[0102]

[0103] The calculation of the rotational torque M2 is shown in equation (7):

[0104]

[0105] Substituting equation (1) into equation (7), we obtain equation (8):

[0106]

[0107] Substituting equations (3), (6), and (8) into equation (2) yields equation (9):

[0108]

[0109] Equation (9) is transformed into a second-order ordinary differential equation (10):

[0110]

[0111] in:

[0112] Step 3: Calculate the free fall velocity v1 and displacement S1 of the fluff when it completes its rotation;

[0113] To achieve the best flocking effect, the flock must be vertically implanted into the adhesive at maximum translational velocity during the flocking process. This means that the flock must complete its rotation and reach maximum translational velocity before reaching the electrode plate. During the descending flocking process, the flock undergoes free fall motion and displacement while rotating. The flock is subject to air resistance and gravity during free fall, and its velocity equation is shown in equation (17), and its displacement equation is shown in equation (18).

[0114]

[0115]

[0116] In equations (17) and (18),

[0117] Solve equations (17) and (18) using MATLAB to obtain the free fall velocity v1 and the resulting displacement S1.

[0118] Step 4: Calculate the translational displacement S2 when the fibers reach velocity v3; v3 refers to 99% of the maximum translational velocity v2.

[0119] The method for calculating the maximum translational velocity is as follows:

[0120] Neglecting the interaction forces between the fibers, the fibers are mainly subjected to the electric force F when translating in the electric field. q Gravity G and air resistance F R The equation for the translational velocity of a single hair is given by equation (11), where v is the instantaneous velocity of the hair during the translation process, in m / s:

[0121]

[0122] After the fibers are oriented, the electric field force F q The calculation is as shown in equation (12):

[0123]

[0124] The air resistance F experienced by the fibers R The calculation formula is as follows (13):

[0125]

[0126] Because gravity G is much smaller than electric force F q Simplifying equation (11) yields the translational velocity equation (14) and the translational displacement equation (15):

[0127]

[0128]

[0129] in,

[0130] Solving the ordinary differential equation (14) yields the translational velocity formula as shown in equation (16):

[0131]

[0132] The translational velocity equation (14) was solved using MATLAB, and the relationship curve between the translational velocity and time was obtained. The curve shows that the acceleration of the wool's translational motion decreases with increasing time until it reaches zero. In equation (16)... That is the maximum translational velocity v2.

[0133] Using MATLAB to solve equations (14) and (15), we can obtain the velocity and time curves, displacement and time curves of the wool translation process, and obtain the translational displacement S2 at v3.

[0134] Step 5: Ensure the fibers are vertically implanted into the adhesive at the minimum electrode spacing S at maximum speed. z =S1+S2.

[0135] Example 1

[0136] With a plate voltage of 50kV and a plate spacing of 10cm, as shown in Table 1, five different specifications of fluff were selected to analyze the effects of fluff linear density and length on its rotation and translation processes.

[0137] Table 1

[0138]

[0139] By solving the rotation equation (10) using Matlab, the relationship curve between the angle between the fiber axis and the electric field direction and time is obtained, as shown in the figure. Figure 3As shown in Table 2, the fibers in the electrostatic field undergo damped oscillations at a certain frequency in the direction of the electric field force until they become parallel to the direction of the electric field force. During the damped oscillation process, the fibers are considered to have completed rotation when the maximum oscillation angle is 0.5° (0.00872 rad). The time for the fibers to complete rotation is called the rotation time t1. The rotation times of the five types of fibers are shown in Table 2.

[0140] Table 2

[0141]

[0142] Table 2 shows that when the length of the fibers is equal, the greater the linear density, the longer the rotation time; however, when the linear density is equal, the length of the fibers has no effect on the rotation time. Therefore, the rotation time of the fibers in the electric field is related to the linear density; the greater the linear density, the longer the rotation time.

[0143] Example 2

[0144] The translational velocities of the five types of fibers were calculated according to equation (16), as shown in Table 3. The relationship between translational velocity and time was obtained by solving equation (14) using MATLAB, as shown in Table 3. Figure 4 As shown. By Figure 4 It can be seen that the translational process is a linear motion with variable acceleration, and the acceleration decreases as time increases until it becomes 0, as shown in equation (16). That is the maximum translational velocity. (From Table 3 and...) Figure 6 It can be seen that when the length of the fibers is equal, the greater the linear density, the smaller the maximum translational velocity, and the longer it takes for the fibers to reach the maximum translational velocity; when the linear density is equal, the maximum translational velocity increases with the increase of the fiber length, and the time to reach the maximum translational velocity is shorter.

[0145] Table 3

[0146]

[0147]

[0148] According to Table 3, the relationship between the maximum translational velocity of the fibers and the aspect ratio is shown below. Figure 5 .Depend on Figure 5 It can be seen that the maximum translational velocity of the fibers is basically linearly positively correlated with their aspect ratio. That is, the larger the aspect ratio of the fibers, the greater the maximum translational velocity. The relationship between the two can be represented by the two-variable linear equation v2 = 0.041r + 5.4203.

[0149] Example 3

[0150] Taking 1.5dtex×0.8mm pile as an example:

[0151] Using MATLAB to solve equation (10), the rotation process curve of the fluff is obtained, as shown below. Figure 6 As shown, the rotation time t1 of the fluff is 0.04894s.

[0152] Using MATLAB to solve equations (17) and (18), the free-fall velocity and displacement generated during the rotation of the fluff are obtained, such as... Figure 7 As shown in the figure, the free fall velocity v1 when the fluff completes its rotation is 0.3091 m / s, and the resulting displacement S1 is 0.009288 m.

[0153] Solving the translational velocity equation (14) using MATLAB yields the curve showing the relationship between translational velocity and time, as shown below. Figure 8 As shown. From Figure 8 It can be seen that the time required to reach the maximum translational velocity of 8.07 m / s is 0.0082 s; while the time to reach 99% of the maximum velocity, i.e., the velocity of 7.988 m / s, is 0.0041 s. When calculating the translational displacement of the pile, it is also necessary to consider the free fall velocity v1 when the pile completes its rotation, which is the initial velocity of the pile's translation. Solving equation (15) yields the curve of displacement and time generated during the pile's translation process, as shown in the figure. Figure 9 As shown. From Figure 9 It can be seen that during the process from 0.0041s to 0.0082s, the velocity of the flocking fibers remained essentially unchanged, but a displacement of 3.4cm was generated. In the electrostatic flocking process, in order to maintain equal electric field strength, the electrode voltage must be increased accordingly as the electrode spacing increases. However, increasing the electrode voltage not only consumes electricity and increases production costs, but may also increase safety hazards. Therefore, considering both translational velocity and electrode voltage, the displacement generated when the flocking fibers reach 99% of their maximum translational velocity is defined as the translational displacement S2. Figure 9 It can be seen that the translational displacement generated when the fibers reach a translational velocity v3 is 0.02597m, and the translational velocity v3 refers to 99% of the maximum translational velocity v2. The minimum electrode spacing S is required to ensure that the fibers are vertically implanted into the adhesive at maximum speed. z The sum of S1 and S2, i.e., S z ≈1.0+2.6=3.6cm.

[0154] Example 4

[0155] Eight other types of nylon fibers were selected, and the minimum electrode spacing for these fibers at an electric field strength of 50 kV / 10 cm was calculated according to the method in Example 3. The results are shown in Table 4. Table 4 shows that the displacement generated when the fibers complete rotation is only related to the linear density; the higher the linear density, the longer the rotation time, and the greater the displacement. During the translational motion of the fibers, when the linear density is equal, the longer the fibers, the greater the maximum translational velocity, but the shorter the time to reach the maximum translational velocity, and the displacement remains unchanged when the maximum translational velocity is finally reached.

[0156] Table 4

[0157]

[0158] Based on the data in Table 4, plot the relationship between linear density and rotation time, as follows: Figure 10 As shown. From Figure 10 It can be seen that the rotation time of the fibers is linearly positively correlated with the linear density, which can be expressed by the bivariate linear equation t1 = 0.0085N. dtex +0.0416 is used to describe the relationship between the two.

[0159] Similarly, based on the data in Table 4, a graph showing the relationship between linear density and minimum plate spacing is plotted, as follows. Figure 11 As shown. From Figure 11 It can be seen that the minimum plate spacing is also linearly positively correlated with the linear density, which can be expressed by the bivariate linear equation S. z =0.9431N dtex +2.5582 is used to describe the relationship between the two.

[0160] Example 5

[0161] Investigating the effect of electric field strength on the movement of fluff:

[0162] The electric field strength is determined by both the plate voltage and the plate spacing, both of which greatly affect the motion of the fibers in the electric field. When the voltage is too low, the fibers cannot be charged through ionization discharge, preventing them from rising; when the plate voltage is too high, it can ionize the air to generate electric sparks, which can then break down the plates or even ignite the fibers. From the rotational equation (10) and the translational velocity equation (14), it can be seen that for fibers of the same linear density, the values ​​of p1 and p2 remain constant, while the values ​​of q1 and q2 are related to the length of the fibers (m and k are both determined by the length l) and the electric field strength E0. With a plate spacing of 10 cm and plate voltages set to 30 kV, 50 kV, 70 kV, and 90 kV respectively, the influence of the electric field strength on the fiber motion process is analyzed using a 1.5 dtex × 0.8 mm fiber as an example.

[0163] (1) Rotation process

[0164] By solving the rotation equation (10) using MATLAB, the relationship curves between the included angle and time during the rotation of the fluff under four electric field intensities were obtained, as follows: Figure 12 As shown. From Figure 12 It can be seen that when the distance between the plates is constant, as the voltage between the plates increases, the electric field strength increases, and the frequency of damped oscillation of the fluff in the direction of the electric field force increases, but the rate of change of the included angle θ is the same, that is, the electric field strength has no effect on the rotation time t1.

[0165] (2) Translation process

[0166] Using MATLAB to solve the translational velocity equation (14), the relationship curves between translational velocity and time under four electric field intensities are obtained, as follows: Figure 13 As shown. From Figure 13 It can be seen that as the electric field strength increases, the maximum translational velocity of the flock increases, while the time to reach the maximum translational velocity decreases. Furthermore, the maximum translational velocity of the flock is directly proportional to the electric field strength. An increase in maximum translational velocity increases the flock momentum (mv), leading to a greater depth of the flocking adhesive. In the flocking process, the flock momentum cannot be too large; excessive momentum can cause the flock to bend and deform after adhesive implantation. When the flock linear density is selected, the appropriate electric field strength can be determined by experimentally observing the flocking effect.

[0167] (3) Plate spacing

[0168] From formulas (17) and (18), it can be seen that the displacement generated by the fluff during rotation is related to p2, and the value of p2 is independent of the electric field strength. That is, no matter how the electric field strength changes, the displacement S1 generated when the fluff completes rotation will not change. According to the calculation method of Example 3, the displacement generated by the translation process under four electric field strengths was obtained, and the results are shown in Table 5. It can be seen from Table 5 that the electric field strength has no effect on the minimum electrode spacing.

[0169] Table 5

[0170]

[0171] The above embodiments of the present invention are merely illustrative examples and are not intended to limit the implementation of the invention. Those skilled in the art can make other variations and modifications based on the above description. It is impossible to exhaustively list all possible implementations here. All obvious variations or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A method for calculating the minimum electrode spacing in an electrostatic flocking process based on kinetic research, characterized in that, Includes the following steps: Step 1: Approximate the state of the fluff in the electric field as a long, thin ellipsoid, and the length of the fluff... l , diameter is d The lengths of the three axes of the ellipsoid are respectively a , b and c , , ; Eccentricity of the ellipsoid ; In an electrostatic field, the fibers first rotate in the direction of the electric force, and when they rotate to be parallel to the electric force, the fibers are fully charged. Then they begin to translate along the direction of the electric force. Step 2: Calculate the time it takes for the fibers to complete their rotation. t 1; The fibers in an electrostatic field are in a moment of inertia M air drag torque M 1 and torque M Under the action of 2, rotation occurs, and from this rotation process, the second-order ordinary differential equation (10) is obtained: （10） in: , C x ρ is the air drag coefficient, 1.8; ρ is the air density, 1.295 kg / m³. 3 ; d is the diameter of the down, m; l is the length of the down, m; m is the mass of the down, kg; The vacuum permittivity is 8.85 × 10⁻⁶. -12 F / m; Electric field strength, V / m; The polarization coefficient is... ; By solving the rotation equation (10) using MATLAB, the relationship curve between the angle between the axial direction of the fibers and the direction of the electric force and time is obtained. The fibers oscillate with damping at a certain frequency in the direction of the electric force in the electrostatic field until they are parallel to the direction of the electric force. During the damping oscillation, the time corresponding to the peak of the angle-time relationship curve that is closest to 0.5° is the time for the fibers to complete the rotation. t 1; Step 3: Calculate the free fall velocity of the fibers when they complete their rotation. v 1 and the resulting displacement S 1; During the downward flocking process, the flocking fibers undergo free fall motion and displacement while rotating. The flocking fibers are subject to air resistance and gravity during free fall motion. The velocity equation is shown in equation (17), and the displacement equation is shown in equation (18). （17） （18） Solving equations (17) and (18) using MATLAB yields the following results. t The free fall velocity of the fluff at time 1 v 1 and the resulting displacement S 1; Step 4: Calculate the velocity reached by the fibers during the translation process. v At time 3, the resulting displacement S 2; v 3 refers to 99% of the maximum translational velocity. v 2; The fibers in an electrostatic field experience an electric force during translation. F q ,gravity G and air resistance F R Since gravity is much smaller than electric force, we can ignore the influence of gravity and obtain the translational velocity equation as shown in equation (14) and the translational displacement equation as shown in equation (15): （14） （15） in, , ; Solving equations (14) and (15) using MATLAB yields the velocity-time curves and displacement-time curves of the fluff translation process. v Translational displacement at time 3 S 2; Step 5: Ensure the fibers are vertically implanted into the adhesive at the minimum electrode spacing at maximum speed. S z = S 1+ S 2.

2. The method for calculating the minimum electrode spacing in the electrostatic flocking process based on kinetic research as described in claim 1, characterized in that, Under the same electric field strength, the electrotreated fluff can acquire a saturated charge regardless of whether it is charged through electrodes or two electrodes. q The calculation is as shown in equation (1): （1） In the formula: l The length of the downy fibers is in meters (m). d The diameter of the downy hair, in meters (m); E 0 represents the electric field strength, in V / m; ε 0 is the vacuum permittivity, 8.85 × 10⁻⁶. -12 F / m.

3. The method for calculating the minimum electrode spacing in the electrostatic flocking process based on kinetic research as described in claim 1, characterized in that, In step two, the fibers in the electrostatic field are in a state of inertia. M air drag torque M 1 and torque M The rotation occurs under the action of 2, and the rotation process is described by equation (2), where θ The angle between the axial direction of the fibers and the direction of the electric field force; （2） Treating the fluff as a rigid cylindrical object rotating around its center, the formula for calculating the moment of inertia is equation (3), where... m The mass of the down is expressed in kg. （3） The rotation of the fluff is a damped vibration with a low speed. The air resistance is proportional to the speed, and the calculation of air resistance is shown in equation (4); where: C x ρ is the air drag coefficient, 1.8; ρ is the air density, 1.295 kg / m³. 3 ; x denoted as the distance in meters from the center of the pile to the analysis unit on the pile. S The maximum cross-sectional area between the analysis element on the pile and the center of the pile is m. 2 ; （4） The element drag torque of the analyzed element on the pile is See equation (5): （5） Solving equation (5) yields equation (6): （6） Rotational torque M 2. The calculation is shown in equation (7): （7） Substituting equation (1) into equation (7), we obtain equation (8): （8） Substituting equations (3), (6), and (8) into equation (2) yields equation (9): （9） Equation (9) is transformed into a second-order ordinary differential equation (10): （10） in: , .

4. The method for calculating the minimum electrode spacing in the electrostatic flocking process based on kinetic research as described in claim 1, characterized in that, In step four, the maximum translational velocity v The calculation method for 2 is as follows: Neglecting the interaction forces between the fibers, the fibers experience an electric force when translating within the electric field. F q ,gravity G and air resistance F R The equation for the translational velocity of a single hair is given by equation (11), where... v The instantaneous velocity of the fibers during translation is given in m / s. （11） After the fibers are oriented, the electric field force F q The calculation is as shown in equation (12): （12） Air resistance experienced by the fibers F R The calculation formula is as follows (13): （13） Due to gravity G Much smaller than electric field force F q Simplifying equation (11) yields the translational velocity equation (14) and the translational displacement equation (15): （14） （15） in, , ; Solving the ordinary differential equation (14) yields the translational velocity formula as shown in equation (16): （16） Using MATLAB to solve the translational velocity equation (14), the relationship curve between translational velocity and time is obtained; from the relationship curve, it can be seen that the acceleration of the wool's translational motion decreases with increasing time until it becomes 0, in equation (16) That is, the maximum translational speed v 2.

5. The method for calculating the minimum electrode spacing in the electrostatic flocking process based on kinetic research as described in claim 1, characterized in that, There is a linear correlation between the minimum plate spacing and the fiber density, which can be expressed using a bivariate linear equation. S z =0.9431 N dtex It is represented by +2.5582.

6. The method for calculating the minimum electrode spacing in the electrostatic flocking process based on kinetic research as described in claim 1, characterized in that, The rotation time of the fibers is linearly correlated with their linear density, which can be expressed using a bivariate linear equation. t 1 = 0.0085 N dtex It is represented by +0.0416.

7. The method for calculating the minimum electrode spacing in the electrostatic flocking process based on kinetic research as described in claim 1, characterized in that, When the electric field strength is constant, the maximum translational velocity of the fibers is related to their aspect ratio. r Related, a binary linear equation can be used. v 2 = 0.041 r It is represented by +5.4203.

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