Optimization Method for the Structure of a Single-Screw Mixing Structure with Direct Writing Forming Based on a Global Optimization Algorithm

Abstract

The present invention is an optimization method for the structure of a single-screw mixing for direct writing based on a global optimization algorithm. The parameters to be optimized include six parameters: the width of the screw groove, the depth of the screw groove, the major diameter of the screw, the length of the screw, the compression angle, and the length of the extrusion section. First, constraint conditions are established according to the law of conservation of mass. Then, a parameter model is established based on the flow rate and pressure balance relationship of the slurry in the barrel. Finally, with the goal of minimizing the numerical solution of the screw speed, considering the constraint conditions, the combinations formed by the six parameters to be optimized are used as individuals of the global optimization algorithm, and the screw speed corresponding to the parameter combination is used as the fitness value of the individual. The optimal parameter combination is obtained through iterative optimization. It not only shortens the optimization time, but also improves the printing ability and shortens the printing delay distance.

Description

Technical Field

[0001] The present invention belongs to the technical field of the preparation and additive manufacturing of ceramic matrix functionally gradient materials, and particularly relates to an optimization method for the direct writing forming single-screw mixing structure based on a global optimization algorithm. Background Art

[0002] Among numerous additive manufacturing technologies, direct writing forming has gradually become an important means for preparing ceramic matrix functionally gradient material parts with complex gradient changes due to its advantages such as simple structure and process, and wide material applicability. The real-time mixing of the slurry in the mixing chamber is an indispensable step in the direct writing forming process. The mixing structure uses a single screw to achieve slurry mixing and extrusion forming. On the premise of the same slurry feeding amount, the screw speed determines the printing ability. The greater the screw speed, the stronger the printing ability. The parameters of the mixing structure will directly affect the screw speed and indirectly affect the printing delay distance and printing resolution. Therefore, the optimization of the mixing structure is of great significance for improving the printing ability.

[0003] The optimization parameters of the single-screw mixing structure include six types: the width of the screw groove, the depth of the screw groove, the major diameter of the screw, the length of the screw, the compression angle, and the length of the extrusion section. The traditional method often uses the trial-and-error method to optimize the parameters of the mixing structure, that is, calculate the screw speed under different parameter combinations one by one, and the parameter combination corresponding to the minimum screw speed is the optimal parameter combination; due to the large number of parameter types and the values of each parameter, obtaining the optimal parameter combination requires a high time cost.

[0004] Therefore, the present invention proposes an optimization method for the direct writing forming single-screw mixing structure, which obtains the best parameter combination based on a global optimization algorithm, minimizes the numerical solution of the screw speed, and improves the printing ability while ensuring the printing quality. Summary of the Invention

[0005] Aiming at the deficiencies of the prior art, the technical problem to be solved by the present invention is to provide an optimization method for the direct writing forming single-screw mixing structure based on a global optimization algorithm.

[0006] The present invention solves the above technical problem by adopting the following technical solutions:

[0007] An optimization method for the direct writing forming single-screw mixing structure based on a global optimization algorithm, the mixing structure includes a barrel and a screw, and the barrel is divided into a mixing section and a compression extrusion forming section; characterized in that the parameters to be optimized in this method include six types: the width of the screw groove, the depth of the screw groove, the major diameter of the screw, the length of the screw, the compression angle, and the length of the extrusion section, and the method includes the following steps:

[0008] Step 1: According to the principle of mass conservation, establish the constraint conditions as:

[0009]

[0010] Wherein, Q in , Q out respectively represent the feeding flow rate and the extrusion flow rate of the mixing structure, d represents the diameter of the extrusion needle, and V s represents the moving speed of the printing platform;

[0011] Step 2: Establish a parameter model of Equation (2) according to the flow rate and pressure balance relationship of the slurry in the barrel;

[0012]

[0013]

[0014] In Equations (2) to (5), Q s is the extrusion and transportation flow rate of the screw, Q d is the dragging flow rate that plays a positive extrusion role, Q p is the pressure flow rate that plays a mixing role, n is the shear rheological behavior index of the slurry, W is the width of the screw groove, H is the depth of the screw groove, and v bz is the flow velocity of the slurry along the groove direction, ΔP b is the pressure difference of the compression extrusion forming section, μ is the shear viscosity of the slurry, L s is the length of the screw, D s is the major diameter of the screw, N s is the rotational speed of the screw, is the helix angle, and K is the shear rheological index of the slurry;

[0015] Step 3: Taking the minimum numerical solution of the screw rotational speed as the goal, considering the constraint conditions, use the global optimization algorithm to obtain the optimal parameter combination to complete the optimization of the direct forming single-screw mixing structure.

[0016] Further, the pressure difference of the compression extrusion forming section is expressed as:

[0017]

[0018] Wherein, θ is the compression angle, m is the tensile rheological behavior index of the slurry, l is the length of the extrusion section, and K σ is the tensile rheological index of the slurry.

[0019] Further, the shear and tensile rheological indices of the slurry are expressed as:

[0020]

[0021] Wherein, τ and σ are respectively the shear stress and the tensile stress of the slurry, are respectively the strain rates generated by the slurry under the action of the shear stress and the tensile stress.

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0023] Based on the relationship between the flow rate and pressure of the slurry in the barrel, the present invention establishes a parameter model. At the same time, based on the principle of mass conservation, constraint conditions are established. With the goal of minimizing the numerical solution of the screw rotation speed, a global optimization algorithm is used for optimization to optimize the mixing structure, thereby shortening the optimization time. It can be seen from the experimental results that the optimized screw rotation speed is significantly reduced. Under the same feed rate, the printing ability is significantly improved, the printing platform can match a higher moving speed, and at the same time, the printing delay distance is shortened, thereby improving the printing resolution. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is a schematic diagram of a single-screw mixing structure;

[0025] Figure 2 is a parameter schematic diagram of a single-screw mixing structure;

[0026] Figure 3 is an overall flow chart;

[0027] Figure 4 is a convergence curve diagram of the screw rotation speed;

[0028] Figure 5 is a structure comparison of the single-screw mixing structure before and after optimization and a change curve diagram of the volume fraction of slurry A at the outlet of the extrusion needle;

[0029] Figure 6 is a change curve diagram of the mixing uniformity of the two slurries at the outlet of the optimized extrusion needle. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0030] Specific embodiments are given below in conjunction with the accompanying drawings. The specific embodiments are only used to describe the technical solutions of the present invention in detail and do not limit the protection scope of this application.

[0031] Figure 1 is a schematic diagram of a single-screw mixing structure. The mixing structure includes a barrel and a screw inserted in the barrel. The barrel is divided into a mixing section and a compression and extrusion forming section; the upper end of the screw is connected to the motor through a coupling, and the rotation of the screw is realized through the motor to complete mixing and extrusion forming; two feed ports A and B are respectively arranged on both sides of the upper part of the barrel for introducing different printing raw materials; an extrusion needle is installed at the end of the barrel; on the premise of a certain feed flow rate of the mixing structure, the two feed ports on both sides of the barrel feed two slurries at a certain rate, and the two slurries are mixed in real time by the rotation of the screw, thereby realizing the printing of different material components. The optimization parameters of the mixing structure are divided into two parts: the screw and the barrel. The optimization parameters of the screw include the screw groove width W, the screw groove depth H, the major diameter D of the screw s and the screw length L s, the optimized parameters of the barrel include the compression angle θ and the extrusion section length l.

[0032] The present invention is an optimization method for the direct writing forming single-screw mixing structure based on the global optimization algorithm, including the following steps:

[0033] Step 1: According to the principle of mass conservation, the feeding flow rate of the mixing structure is equal to the extrusion flow rate, so there is the following constraint condition;

[0034]

[0035] In the formula, Q in , Q out respectively represent the feeding flow rate and the extrusion flow rate of the mixing structure, d represents the diameter of the extrusion needle, and V s represents the moving speed of the printing platform;

[0036] Step 2: Establish a parameter model of formula (2) according to the flow rate and pressure balance relationship of the slurry in the barrel;

[0037]

[0038] In formulas (2) to (5), Q s is the extrusion transportation flow rate of the screw, Q d is the dragging flow rate that plays a positive extrusion role, Q p is the pressure flow rate that plays a mixing role, n is the shear rheological behavior index (dimensionless) of the slurry, W is the width of the screw groove, H is the depth of the screw groove, v bz is the flow velocity of the slurry along the groove direction, ΔP b is the pressure difference of the compression extrusion forming section, μ is the shear viscosity of the slurry, L s is the length of the screw, D s is the major diameter of the screw, N s is the screw speed, is the helix angle, and K is the shear rheological index of the slurry;

[0039] The pressure difference of the compression extrusion forming section is mainly caused by the inconsistent stress generated by the shear and stretching of the slurry. According to the geometric shape of the compression extrusion forming section and the rheological properties of the slurry, the pressure difference of the compression extrusion forming section can be calculated, and the expression is:

[0040]

[0041] In the formula, θ is the compression angle, m is the tensile rheological behavior index (dimensionless) of the slurry, l is the extrusion section length, and K σ is the tensile rheological index of the slurry;

[0042] The slurry used in this embodiment is a ceramic slurry, which is a non-Newtonian fluid with shear-thinning properties. Its viscosity changes at different screw rotation speeds, thereby affecting the printing parameters. The rheological properties of the ceramic slurry under the rotation of the screw are characterized by the following power-law model, which respectively represent the relationships between the shear stress and tensile stress of the slurry and the strain rate;

[0043]

[0044] In the formula, τ is the shear stress of the slurry, is the strain rate generated by the slurry under the action of the shear stress;

[0045]

[0046] In the formula, σ is the tensile stress of the slurry, is the strain rate generated by the slurry under the action of the tensile stress.

[0047] Step 3: As can be seen from formula (2), the screw extrusion capacity (i.e., the extrusion flow rate) is directly proportional to the screw rotation speed. In order to enable the printing system to have higher printing capacity and ensure the printing quality, taking the equality of the feed flow rate and the extrusion flow rate in formula (1) as the constraint condition and the minimum numerical solution of the screw rotation speed as the objective;

[0048] Set the variable range of each optimization parameter. Taking a combination formed by six optimization parameters as an individual, use the global optimization algorithm to solve the six optimization parameters, take the screw rotation speed under the combination of the six optimization parameters as the fitness value of the individual, and iterate the population until the fitness values of all individuals converge or reach the maximum number of iterations; Calculate the screw rotation speed corresponding to each individual according to the parameter model in formula (2), and the parameter combination corresponding to the minimum screw rotation speed is the optimized parameter, completing the optimization of the single-screw mixing structure for direct writing forming. The global optimization algorithm includes genetic algorithm, simulated annealing algorithm, particle swarm algorithm, etc.

[0049] Example 1

[0050] The variable ranges of the optimization parameters of the single-screw mixing structure of the extrusion printer are shown in Table 1 below:

[0051] Table 1 Variable ranges of optimization parameters

[0052] Feed flow rate of the mixing structure <![CDATA[2.5mm 3 / s]]> Screw groove width 4 - 7 mm Outer diameter of the screw 7 - 8 mm Moving speed of the printing platform 12.7 mm / s Screw groove depth 2 - 3 mm Compression angle 10°-30° Diameter of the extrusion needle 0.5 mm Length of the screw 30 - 60 mm Length of the extrusion section 5 - 8 mm

[0053] The rheological parameters of two ceramic slurries with shear-thinning measured by a rotational and extensional rheometer are shown in Table 2:

[0054] Table 2 Rheological parameters of the slurry

[0055] Shear rheological index Shear rheological behavior index Tensile rheological index Tensile rheological behavior index Slurry A 59.59 0.31 143.68 0.42 Slurry B 67.68 0.32 155.6 0.45 Mixed slurry (1:1) 62.23 0.32 150.63 0.44

[0056] The parameter settings of the genetic algorithm are as follows: the coding length is 20 bits, the population size is 30, the maximum number of genetic generations is 100, the crossover probability is 0.7, and the mutation probability is 0.007. The optimization results of each parameter are shown in Table 3.

[0057] Table 3 Optimization Results

[0058] Screw groove width Screw groove depth Length of the screw Outer diameter of the screw Compression angle Length of the extrusion section 7 mm 2 mm 60 mm 8 mm 30° 5 mm

[0059] According to the optimization results in Table 3, the screw speed is calculated to be 6 rpm. Compared with the screw speed of 15 rpm before optimization, the optimized screw speed can match a higher feed speed, thereby increasing the printing speed and better improving the printing ability.

[0060] Based on the above optimized mixing structure, a simulation model based on computational fluid dynamics is established in the ANSYS FLUENT module. The simulation model uses transient analysis, simulates the rotation of the screw using the relative rotation method, sets the RNG k-ε fluid model, and monitors the volume fraction of slurry A at the outlet of the extrusion needle and the mixing uniformity of the two slurries. During the simulation process, the volume fraction of slurry B in the barrel is set to 100%, and starting from time 0, the two slurries are injected at a ratio of 1:1. The total feed flow rate of the mixing structure is maintained at 2.5 mm 3 / s. It can be Figure 5 seen that the optimized mixing structure can transition the slurry from 100% slurry B to the 1:1 mixed slurry faster. It can be Figure 6 seen that the mixing uniformity of the two slurries at the outlet of the extrusion needle is greater than 95%, meeting the actual printing requirements.

[0061] Matters not described in the present invention are applicable to the prior art.

Claims

1. An optimization method for the structure of a single-screw mixing structure formed by direct writing based on a global optimization algorithm. The mixing structure includes a barrel and a screw. The barrel is divided into a mixing section and a compression and extrusion forming section; the method is characterized in that, The parameters to be optimized in this method include the screw channel width, screw channel depth, major diameter of the screw, screw length, compression angle, and extrusion section length, and the method includes the following steps: Step 1: According to the principle of mass conservation, establish the constraint condition as: Where Q in and Q out represent the feeding flow rate and the extrusion flow rate of the mixing structure respectively, d represents the diameter of the extrusion needle, and V s represents the moving speed of the printing platform; Step 2: Establish the parameter model of Equation (2) based on the flow rate and pressure balance relationship of the slurry in the barrel; In formulas (2) to (5), Q s is the extrusion and transportation flow rate of the screw, Q d is the drag flow rate that plays a positive extrusion role, Q p is the pressure flow rate that plays a mixing role, n is the shear rheological behavior index of the slurry, W is the screw groove width, H is the screw groove depth, v bz is the flow velocity of the slurry along the groove direction, ΔP b is the pressure difference in the compression extrusion forming section, μ is the shear viscosity of the slurry, L s is the screw length, D s is the major diameter of the screw, N s is the screw rotation speed, is the helix angle, and K is the shear rheological index of the slurry; Step 3: Taking the minimum numerical solution of the screw speed as the goal, considering the constraint conditions, use the global optimization algorithm to obtain the optimal parameter combination to complete the optimization of the direct writing single-screw mixing structure.

2. The optimization method for the direct writing forming single-screw mixing structure based on the global optimization algorithm according to claim 1, characterized in that The pressure difference in the compression and extrusion forming section is expressed as: where θ is the compression angle, m is the tensile rheological behavior index of the slurry, l is the extrusion section length, and K σ is the tensile rheological index of the slurry.

3. The optimization method for the direct writing forming single-screw mixing structure based on the global optimization algorithm according to claim 2, characterized in that, The shear and tensile rheological indices of the slurry are expressed as: Where τ, σ are the shear stress and tensile stress of the slurry respectively, are the strain rates generated by the slurry under the action of shear stress and tensile stress respectively.

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