A method of determining direct write 3D printing ink extrusion flow rate

Abstract

The application discloses a kind of methods for determining direct writing 3D printing ink extrusion flow, steps are as follows: S1, the expression of the relationship between ink pressure in needle tube and ink extrusion flow in nozzle is determined, S2, the flow expression of ink in nozzle under unit pressure is determined, S3, the shear force expression of nozzle wall surface is determined, S4, based on the formula determined in step S1, step S2 and step S3, the contact between formula is established using Simulink tool in Matlab software, to calculate the time domain result of ink extrusion flow Q;The method overcomes the problem that existing method cannot accurately and completely characterize direct writing 3D printing ink extrusion flow, obtains the direct writing 3D printing ink extrusion flow in time domain, and the conformity with actual extrusion condition is high, can accurately and completely reflect the ink extrusion flow in direct writing 3D printing, simple operation, high precision, good practicability.

Description

Technical Field

[0001] The present invention relates to the technical field of additive manufacturing, and in particular to a method for determining the extrusion flow rate of direct-write 3D printing ink. Background Art

[0002] Direct-write 3D printing has been one of the most popular additive manufacturing technologies in recent years. Based on its operating principle, it falls under the category of material extrusion additive manufacturing: the material is prepared into an ink with excellent printing properties, which is then squeezed out of a syringe by a piston and stacked layer by layer on a substrate to form a three-dimensional part. Compared to other additive manufacturing technologies, this technology offers significant advantages in material compatibility and equipment flexibility. Currently, materials suitable for this technology include polymers, biomaterials, conductive metals, ceramics, cellulose materials, and functional materials with physical effects such as acoustics, light, electromagnetics, and heat. Applications include rubber engineering, tissue engineering and regenerative medicine, batteries, electronic circuits, ceramics engineering, clothing, sensors, and 4D printing.

[0003] The extrusion flow rate of direct-write 3D printing ink is a key process parameter that determines the quality of ink extrusion and deposition. Currently, a common method uses the law of conservation of mass to calculate the extrusion flow rate as a constant. However, the actual extrusion flow rate of direct-write 3D printing ink is not a constant, and therefore, existing methods cannot accurately and completely characterize the extrusion flow rate of direct-write 3D printing ink. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for determining the extrusion flow rate of direct writing 3D printing ink, which overcomes the problem that the extrusion flow rate of direct writing 3D printing ink is calculated by treating the extrusion flow rate as a constant through the law of conservation of mass, but the extrusion flow rate of the actual direct writing 3D printing ink extrusion process is not a constant, resulting in the inability to accurately and completely characterize the extrusion flow rate of direct writing 3D printing ink.

[0005] To this end, the technical solution of the present invention is as follows:

[0006] A method for determining the extrusion flow rate of direct-write 3D printing ink, comprising the following steps:

[0007] S1. The expression for determining the relationship between the ink pressure in the needle tube and the ink extrusion flow rate in the nozzle is:

[0008]

[0009] Where A p is the inner cross-sectional area of ​​the needle tube, v pis the downward movement speed of the piston, Q is the ink extrusion flow rate, V0 is the initial volume of the ink in the needle tube, t is the extrusion time, B is the bulk modulus of the ink, dp is the pressure change of the ink in the needle tube, and dt is the time change;

[0010] S2. Determine the flow rate of ink in the nozzle under unit pressure as follows:

[0011]

[0012] Where Q u is the steady-state flow rate of ink in the nozzle under unit pressure, π is the radian value of pi, D n is the inner diameter of the nozzle, p is the pressure of the ink in the needle tube, K is the viscosity coefficient of the ink, n is the flow coefficient of the ink, τ w is the shear force on the nozzle wall, τ0 is the yield stress of the ink;

[0013] S3. Determine the shear force expression on the nozzle wall as follows:

[0014]

[0015] Where, τ w is the shear force on the nozzle wall, D n is the inner diameter of the nozzle, L n is the length of the nozzle, p is the pressure of the ink in the needle tube, ρ is the density of the ink, g is the acceleration of gravity, and u is the average flow velocity of the ink in the nozzle;

[0016] S4. Based on the formulas determined in step S1, step S2, and step S3, the Simulink tool in Matlab software is used to establish connections between the formulas to calculate the time domain result of the ink extrusion flow rate Q.

[0017] Furthermore, the specific implementation steps of step S4 are as follows:

[0018] S401, constructing a simulation model of ink extrusion flow in the Simulink tool of Matlab software, including: a first calculation module, an integrator, a second calculation module and a multiplier; wherein,

[0019] The first calculation module is constructed based on the expression of the relationship between the ink pressure in the needle tube and the ink extrusion flow rate in the nozzle. It has two input terminals and one output terminal. The first input terminal of the first calculation module is used to input known parameters, including the bulk modulus B of the ink, the downward movement speed v of the piston, and the ink pressure. p , the inner cross-sectional area A of the needle tube p and the initial volume V0 of the ink in the needle tube; the second input end of the first calculation module is used to input the variable Q; the output end of the first calculation module outputs

[0020] The input terminal of the integrator is connected to the output terminal of the first calculation module to The pressure p of the ink in the needle tube is obtained by time integration and output through the output end of the integrator;

[0021] The second calculation module is constructed based on the expression of the relationship between the ink pressure in the needle tube and the ink extrusion flow rate in the nozzle, as well as the shear force expression of the nozzle wall. It is provided with three input ends and one output end. The first input end of the second calculation module is used to input known parameters, including the density ρ of the ink, the viscosity coefficient K of the ink, the flow coefficient n of the ink, the yield stress τ0 of the ink, the inner diameter D of the nozzle, and the ink viscosity coefficient K. n and the nozzle length L n The second input of the second calculation module is connected to the output of the integrator for inputting the pressure p of the ink in the needle tube. The third input of the second calculation module is used to input the variable Q. The output of the second calculation module outputs the flow rate Q of the ink in the nozzle under unit pressure. u ;

[0022] The input end of the multiplier is connected to the output end of the integrator and the output end of the second calculation module respectively, so as to input the pressure p of the ink in the needle tube and the flow rate Q of the ink in the nozzle under unit pressure into the multiplier. u The output terminal of the multiplier outputs the variable Q, and the output terminal of the multiplier is also connected to the second input terminal of the first calculation module and the third input terminal of the second calculation module respectively;

[0023] S402, the bulk modulus B of the ink and the downward movement speed v of the piston p , the inner cross-sectional area A of the needle tube p The initial volume V0 of the ink in the needle tube is input into the first calculation module, and the density ρ of the ink, the viscosity coefficient K of the ink, the flow coefficient n of the ink, the yield stress τ0 of the ink, the inner diameter D of the nozzle are calculated. n and the nozzle length L n Enter the second calculation module, set the output time interval of the variable Q to 0.1s, run the simulation model of the ink extrusion flow rate, and obtain the time domain result of the ink extrusion flow rate Q.

[0024] Compared with the existing technology, the method for determining the extrusion flow rate of direct writing 3D printing ink overcomes the problem that the existing method for determining the extrusion flow rate of direct writing 3D printing ink calculates the flow rate by treating the extrusion flow rate as a constant through the law of conservation of mass, but the extrusion flow rate of the actual direct writing 3D printing ink extrusion process is not a constant, resulting in the inability to accurately and completely characterize the extrusion flow rate of direct writing 3D printing ink. This method can obtain the extrusion flow rate of direct writing 3D printing ink in the time domain, which is highly consistent with the actual extrusion situation, and can accurately and completely reflect the extrusion flow rate of ink in direct writing 3D printing. It is simple to operate, has high precision and good practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is a flow chart of the method for determining the extrusion flow rate of direct-write 3D printing ink of the present invention;

[0026] Figure 2 This is a flowchart of the specific calculation process of step S4 of the method for determining the extrusion flow rate of direct writing 3D printing ink of the present invention;

[0027] FIG3( a ) is a schematic diagram of the time domain result of the ink extrusion flow rate obtained in step S4 in an embodiment of the present invention;

[0028] FIG3( b ) is a schematic diagram of a partially enlarged view of the time domain result of the ink extrusion flow rate obtained in step S4 at the extrusion start time (0-1.2 s) in an embodiment of the present invention;

[0029] FIG3( c ) is a schematic diagram of a partially enlarged view of the time domain result of the ink extrusion flow rate obtained in step S4 at the end of extrusion (359.9-360.2 s) in an embodiment of the present invention; DETAILED DESCRIPTION

[0030] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the following embodiments are by no means intended to limit the present invention in any way.

[0031] See also Figure 1 The specific implementation steps of the method for determining the extrusion flow rate of direct writing 3D printing ink are as follows:

[0032] S1. The expression for determining the relationship between the ink pressure in the needle tube and the ink extrusion flow rate in the nozzle is:

[0033]

[0034] Where A p is the inner cross-sectional area of ​​the needle tube, v pis the downward movement speed of the piston, Q is the ink extrusion flow rate, V0 is the initial volume of the ink in the syringe, t is the extrusion time, B is the bulk modulus of the ink, dp is the pressure change of the ink in the syringe, and dt is the time change; in the above formula, except for dp, dt and Q which are unknown quantities, other parameters can be obtained through experimental tests.

[0035] S2. Determine the flow rate of ink in the nozzle under unit pressure as follows:

[0036]

[0037] Where Q u is the steady-state flow rate of ink in the nozzle under unit pressure, π is the radian value of pi, D n is the inner diameter of the nozzle, p is the pressure of the ink in the needle tube, K is the viscosity coefficient of the ink, n is the flow coefficient of the ink, τ w is the shear force on the nozzle wall, τ0 is the yield stress of the ink;

[0038] S3. Determine the shear force expression on the nozzle wall as follows:

[0039]

[0040] Where, τ w is the shear force on the nozzle wall, D n is the inner diameter of the nozzle, L n is the length of the nozzle, p is the pressure of the ink in the needle tube, ρ is the density of the ink, and g is the acceleration of gravity 9.8m / s 2 , u is the average flow velocity of ink in the nozzle;

[0041] S4. Using the Simulink tool in Matlab software, a simulation model of the ink extrusion flow rate is constructed to obtain a time domain result of the ink extrusion flow rate Q;

[0042] S401, see attached Figure 2 , a simulation model of ink extrusion flow is constructed in the Simulink tool of Matlab software, including: a first calculation module, an integrator, a second calculation module and a multiplier; wherein,

[0043] The first calculation module is constructed based on the expression of the relationship between the ink pressure in the needle tube and the ink extrusion flow rate in the nozzle. It has two input terminals and one output terminal. The first input terminal of the first calculation module is used to input known parameters, including the bulk modulus B of the ink, the downward movement speed v of the piston, and the ink pressure. p , the inner cross-sectional area A of the needle tube p and the initial volume V0 of the ink in the needle tube; the second input end of the first calculation module is used to input the variable Q; the output end of the first calculation module outputs

[0044] The input terminal of the integrator is connected to the output terminal of the first calculation module to The pressure p of the ink in the needle tube is obtained by time integration and output through the output end of the integrator;

[0045] The second calculation module is constructed based on the expression of the relationship between the ink pressure in the needle tube and the ink extrusion flow rate in the nozzle, as well as the shear force expression of the nozzle wall. It is provided with three input ends and one output end. The first input end of the second calculation module is used to input known parameters, including the density ρ of the ink, the viscosity coefficient K of the ink, the flow coefficient n of the ink, the yield stress τ0 of the ink, the inner diameter D of the nozzle, and the ink viscosity coefficient K. n and the nozzle length L n The second input of the second calculation module is connected to the output of the integrator for inputting the pressure p of the ink in the needle tube. The third input of the second calculation module is used to input the variable Q. The output of the second calculation module outputs the flow rate Q of the ink in the nozzle under unit pressure. u ;

[0046] The input end of the multiplier is connected to the output end of the integrator and the output end of the second calculation module respectively, so as to input the pressure p of the ink in the needle tube and the flow rate Q of the ink in the nozzle under unit pressure into the multiplier. u The output terminal of the multiplier outputs the variable Q, and the output terminal of the multiplier is also connected to the second input terminal of the first calculation module and the third input terminal of the second calculation module respectively;

[0047] S402, the bulk modulus B of the ink and the downward movement speed v of the piston p , the inner cross-sectional area A of the needle tube p The initial volume V0 of the ink in the needle tube is input into the first calculation module, and the density ρ of the ink, the viscosity coefficient K of the ink, the flow coefficient n of the ink, the yield stress τ0 of the ink, the inner diameter D of the nozzle are calculated. n and the nozzle length L n Enter the second calculation module, set the output time interval of the variable Q to 0.1s, run the simulation model of the ink extrusion flow rate, and obtain the time domain result of the ink extrusion flow rate Q.

[0048] In this embodiment, based on the material parameters of the selected ink and the geometric parameters set by the direct writing 3D printer, the known parameters input in step S4 are determined as follows: the bulk modulus B of the ink is 1.13×10 9 Pa, the inner cross-sectional area of ​​the needle tube A p 366mm 2 , the initial volume V0 of the ink in the needle is 10000mm 2 , the density of ink is ρ1020kg / m3 , the ink's consistency coefficient K is 132.72 Pa·s n , the ink flow coefficient n is 0.268, the ink yield stress τ0 is 90Pa, and the nozzle inner diameter D n 0.55mm 2 , the length of the nozzle L n is 18 mm, the downward movement speed of the piston v p 0.0136mm / s; set the ink extrusion time to 1~360s, and the time interval of the simulation data to 0.1s;

[0049] As shown in Figure 3(a), it is a schematic diagram of the time domain results of the ink extrusion flow obtained through step S4 in this embodiment; wherein, as shown in Figure 3(b), it is a local enlarged diagram of the initial stage in the time domain result schematic diagram of Figure 3(a), that is, the time period from the start of extrusion 0s to the extrusion 1.2s; as shown in Figure 3(c), it is a local enlarged diagram of the end of extrusion in the time domain result schematic diagram of Figure 3(a), that is, the time period from extrusion 359.9s to extrusion 360.2s; it can be seen from Figures 3(b) and 3(c) that the extrusion flow is unstable at the start and end of extrusion, which is consistent with the actual extrusion situation, and also illustrates that the existing method of treating the extrusion flow as a constant cannot characterize the time domain results of the extrusion flow, solves the problems mentioned in the background technology, and further proves that this method does indeed further improve the effectiveness and accuracy of the ink extrusion flow determination results compared with the existing methods.

Claims

1. A method for determining the extrusion flow rate of direct writing 3D printing ink, characterized in that: Here are the steps: S1. The expression for determining the relationship between the ink pressure in the needle tube and the ink extrusion flow rate in the nozzle is: Where A p is the inner cross-sectional area of ​​the needle tube, v p is the downward movement speed of the piston, Q is the ink extrusion flow rate, V0 is the initial volume of the ink in the needle tube, t is the extrusion time, B is the bulk modulus of the ink, dp is the pressure change of the ink in the needle tube, and dt is the time change; S2. Determine the flow rate of ink in the nozzle under unit pressure as follows: Where Q u is the steady-state flow rate of ink in the nozzle under unit pressure, π is the radian value of pi, D n is the inner diameter of the nozzle, p is the pressure of the ink in the needle tube, K is the viscosity coefficient of the ink, n is the flow coefficient of the ink, τ w is the shear force on the nozzle wall, τ0 is the yield stress of the ink; S3. Determine the shear force expression on the nozzle wall as follows: Where, τ w is the shear force on the nozzle wall, D n is the inner diameter of the nozzle, L n is the length of the nozzle, p is the pressure of the ink in the needle tube, ρ is the density of the ink, g is the acceleration of gravity, and u is the average flow velocity of the ink in the nozzle; S4. Based on the formulas determined in step S1, step S2, and step S3, the Simulink tool in Matlab software is used to establish connections between the formulas to calculate the time domain result of the ink extrusion flow rate Q.

2. The method for determining the extrusion flow rate of direct writing 3D printing ink according to claim 1, characterized in that: The specific implementation steps of step S4 are as follows: S401, constructing a simulation model of ink extrusion flow in the Simulink tool of Matlab software, including: a first calculation module, an integrator, a second calculation module and a multiplier; wherein, The first calculation module is constructed based on the expression of the relationship between the ink pressure in the needle tube and the ink extrusion flow rate in the nozzle. It has two input terminals and one output terminal. The first input terminal of the first calculation module is used to input known parameters, including the bulk modulus B of the ink, the downward movement speed v of the piston, and the ink pressure. p , the inner cross-sectional area A of the needle tube p and the initial volume V0 of the ink in the needle tube; the second input end of the first calculation module is used to input the variable Q; the output end of the first calculation module outputs The input terminal of the integrator is connected to the output terminal of the first calculation module to The pressure p of the ink in the needle tube is obtained by time integration and output through the output end of the integrator; The second calculation module is constructed based on the expression of the relationship between the ink pressure in the needle tube and the ink extrusion flow rate in the nozzle, as well as the shear force expression of the nozzle wall. It is provided with three input ends and one output end. The first input end of the second calculation module is used to input known parameters, including the density ρ of the ink, the viscosity coefficient K of the ink, the flow coefficient n of the ink, the yield stress τ0 of the ink, the inner diameter D of the nozzle, and the ink viscosity coefficient K. n and the nozzle length L n The second input of the second calculation module is connected to the output of the integrator for inputting the pressure p of the ink in the needle tube. The third input of the second calculation module is used to input the variable Q. The output of the second calculation module outputs the flow rate Q of the ink in the nozzle under unit pressure. u ; The input end of the multiplier is connected to the output end of the integrator and the output end of the second calculation module respectively, so as to input the pressure p of the ink in the needle tube and the flow rate Q of the ink in the nozzle under unit pressure into the multiplier. u The output terminal of the multiplier outputs the variable Q, and the output terminal of the multiplier is also connected to the second input terminal of the first calculation module and the third input terminal of the second calculation module respectively; S402, the bulk modulus B of the ink and the downward movement speed v of the piston p , the inner cross-sectional area A of the needle tube p The initial volume V0 of the ink in the needle tube is input into the first calculation module, and the density ρ of the ink, the viscosity coefficient K of the ink, the flow coefficient n of the ink, the yield stress τ0 of the ink, the inner diameter D of the nozzle are calculated. n and the nozzle length L n Enter the second calculation module, set the output time interval of the variable Q to 0.1s, run the simulation model of the ink extrusion flow rate, and obtain the time domain result of the ink extrusion flow rate Q.

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