A numerical simulation method based on electron beam powder bed melting

Abstract

The present invention discloses a numerical simulation method based on electron beam powder bed melting. According to the particle size distribution, powder layer thickness, and scraper movement speed of metal powder particles during powder spreading, a powder spreading simulation model of an electron beam additive manufacturing equipment is established. Through the powder spreading simulation model, a certain number of powder particles are generated. Under the action of the scraper, a powder bed model is obtained in the laying area. The powder bed model is extracted and a substrate is established below the model to obtain a discrete powder bed particle model. The heat transfer, mass transfer control equation of the powder bed particles under the action of the electron beam and the vapor recoil force are solved in the calculation domain of the discrete powder bed particle model to obtain the temperature field, morphology change, and forming quality of the molten pool. The present invention simulates the process of electron beam and powder particle coupling at the mesoscopic scale, numerically simulates the electron beam powder bed under multi-physical field coupling, and can provide guidance for the actual processing process by observing the temperature field and molten pool morphology under different process parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of computer numerical simulation in additive manufacturing, and particularly to a numerical simulation method based on electron beam powder bed melting. Background Art

[0002] Electron beam powder bed melting technology is a rapid prototyping technology that has received extensive attention in recent years. Compared with laser additive manufacturing technology, it has a higher energy density, and due to the higher preheating temperature, no subsequent heat treatment is required after forming. Electron beam powder bed melting technology uses an electron beam as a heat source. The electron beam accelerated by voltage bombards the powder bed at high speed, converting kinetic energy into heat energy to melt the powder. Therefore, the final quality of the formed part is related to the interaction and coupling effect between the electron beam and the powder. Most previous simulations of the molten pool have focused on the field of laser additive manufacturing, and a continuum grid is used to simulate the powder bed, without fully considering the influence brought by discrete powder particles, and it is impossible to accurately obtain the detailed information of the actual powder heating, melting, flowing, evaporating, and solidifying.

[0003] In addition, there are few studies on the action mechanism between the electron beam and the powder layer and the process control of heat and mass transfer in the molten pool. In the actual manufacturing process, there are voids between powder particles and the powder particle sizes are also different, which results in different absorption of electron beam energy by the powder bed compared with the continuum. Summary of the Invention

[0004] The present invention mainly aims at the problems in the prior art, and the purpose is to provide a numerical simulation method based on electron beam powder bed melting. Discrete powder particles are used at the mesoscopic scale to simulate the heat and mass transfer process of the molten pool, record the entire process of powder heating, melting, flowing, evaporating, and solidifying, observe the changes in the temperature field and the morphology of the molten pool during the process, and consider the influence of process parameters on the morphology of the molten pool, solving the problem in the prior art that only a macroscopic continuum model is established without considering the influence of discrete powder on the simulation process of electron beam powder bed melting.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A numerical simulation method based on electron beam powder bed melting, comprising the following steps:

[0007] Step 1, collect the particle size distribution, powder layer thickness, and scraper movement speed of metal powder particles during powder spreading by an electron beam additive manufacturing equipment; establish a powder spreading simulation model of the electron beam additive manufacturing equipment according to the particle size distribution, powder layer thickness, and scraper movement speed of the metal powder particles;

[0008] Step 2: Based on the contact force of the metal powder particle material, generate particles with a normal distribution of particle sizes through a powder spreading simulation model. Under the action of the scraper, a powder bed model is obtained in the spreading area. Extract the powder bed model and establish a substrate with the same area as the powder bed model under the powder bed model to obtain a discrete powder bed particle model.

[0009] Step 3: After meshing the discrete powder bed particle model, use it as the computational domain.

[0010] Step 4: When the metal powder particles are heated to form a molten pool, apply the vapor recoil force to the surface of the molten pool, and solve the heat transfer and mass transfer control equations of the powder bed particles under the action of the electron beam in the computational domain to obtain the temperature field, morphology change and forming quality of the molten pool.

[0011] Furthermore, the contact force of the metal powder particle material includes the contact force and van der Waals force between powder particles; the contact force is simulated through the Hertz contact model; the van der Waals force is simulated through the JKR cohesion model.

[0012] Furthermore, the Hertz contact model is as follows:

[0013]

[0014]

[0015] F s =-S s δ s

[0016]

[0017] where F n and are the normal contact force and damping force of the particle respectively, F s and are the tangential contact force and damping force of the particle respectively; E * 、R * and m * are Young's modulus, equivalent radius and mass respectively; δ n 、S n and v n are the overlap amount, normal stiffness and velocity component respectively; δ s 、S s and v s are the overlap amount, tangential stiffness and velocity component respectively; β is a constant related to the coefficient of restitution.

[0018] Furthermore, the JKR cohesion model is as follows:

[0019]

[0020] Among them, γ is the surface energy of the particle, and E * is the Young's modulus, α is the equivalent radius of the contact area, and R * is the equivalent radius of the particle.

[0021] Furthermore, the control equations for heat and mass transfer of particles in the powder bed under the action of an electron beam are as follows:

[0022] Continuity equation:

[0023]

[0024] Momentum conservation equation:

[0025]

[0026] Energy conservation equation:

[0027]

[0028] In the formula, ρ, p, and T are density, pressure, and temperature respectively, u is the fluid motion velocity in the x direction, K0 is the thermal conductivity, μ is the liquid viscosity, t is time, f l is the liquid volume fraction, T ref is the reference temperature, ΔH is the enthalpy of evaporation, and q is the heat source.

[0029] Furthermore, the heat source is calculated by the following formula:

[0030]

[0031] In the formula, Q is the heat flux density, R is the electron beam spot radius, x is the coordinate along the x-axis, y is the coordinate along the y-axis, x s is the initial coordinate of the x-axis, and y s is the initial coordinate of the y-axis.

[0032] Furthermore, the vapor recoil force p rec is calculated by the following formula:

[0033]

[0034] In the formula, p ag is the ambient pressure, ΔH v is the enthalpy of evaporation, T is the temperature, T b is the boiling point of the material, and R g is the gas constant.

[0035] Furthermore, the discrete element method is used to generate particles with a normal distribution of particle sizes above the substrate.

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0037] The present invention considers various physical phenomena such as powder heating, melting, flowing, evaporation, and solidification, establishes a powder bed particle model, avoids the defect of the continuum model ignoring fluid flow, is closer to the physical reality, and provides a basis for effectively simulating the electron beam powder bed melting technology; adds boundary conditions such as heat sources as source terms into the control equations, and considers the influence of vapor recoil force on the molten pool, establishes the control equations for the multi-physics coupling of electron beam powder bed melting, solves the heat and mass transfer process of the powder bed under the action of the electron beam, can obtain the temperature field of the heat and mass transfer process of the powder particles and the molten pool morphology information, observes the entire process of particle heating, melting, flowing, evaporation, and solidification at different times, and obtains the temperature field information and molten pool cross-section information changing with time, and can preliminarily predict whether manufacturing defects such as balling and porosity will occur under the current process parameters according to the results. The present invention can obtain the temperature field and the change of the molten pool morphology under different process parameters, which has guiding significance for practical engineering Brief Description of the Drawings

[0038] Figure 1 is the flow chart of the numerical simulation method based on electron powder bed melting of the present invention;

[0039] Figure 2 is the powder spreading simulation model established;

[0040] Figure 3 is the particle size distribution curve graph;

[0041] Figure 4 is the mesoscopic scale powder bed model established by the present invention;

[0042] Figure 5 is the molten pool morphology and temperature field of the powder bed particles heated and melted under the action of the electron beam;

[0043] Figure 6 is the melt flow behavior of the cross-section and longitudinal section of the molten pool; wherein, (a) is the melt flow behavior of the cross-section of the molten pool, and (b) is the melt flow behavior of the longitudinal section of the molten pool;

[0044] Figure 7 are the defects generated under different process parameters; wherein, (a) is the balling defect generated under a lower heat input (power 100W, scanning speed 1m / s), and (b) is the porosity defect generated under a higher heat input (power 1800W, scanning speed 1m / s).

[0045] Figure 8 is the schematic diagram of the actual printing and forming effect of the weld bead under the optimal process parameters obtained according to the present method. Detailed Embodiments

[0046] The present invention will be described in detail below in conjunction with the drawings and specific embodiments.

[0047] Since most powder particles are spherical and have a larger surface area compared to continuous bodies, their heat transfer conditions are very different. Therefore, it is of great significance to simulate the heat and mass transfer process of the electron beam powder bed using a discrete powder particle model at the mesoscopic scale.

[0048] The present invention provides a numerical simulation method based on electron beam powder bed melting, as Figure 1 shown, and is specifically implemented according to the following steps:

[0049] Step 1, according to the actual situation, first measure the scraper movement speed, the particle size distribution of the metal powder particles used, and the powder layer thickness during powder spreading of the electron beam additive manufacturing equipment; establish a powder spreading simulation model of the electron beam additive manufacturing equipment according to the actual powder spreading process. The powder spreading simulation model includes a scraper, a substrate, and a spreading area, as Figure 2 shown. Since the number of powder particles is in the hundreds of millions during actual powder spreading and it is difficult for current computer performance to simulate them simultaneously, a small selected area is simulated. Among them, the scraper size is 5mm×0.2mm×3mm, located on one side above the substrate, and the bottom contacts the upper surface of the substrate; the substrate size is 5mm×5mmm×1mm, located in the bottom area; a spreading area with a size of 1mm×0.6mm×0.1mm is set on the other side of the upper surface of the substrate to obtain the powder spreading simulation model.

[0050] Step 2, define the contact force, van der Waals force, and parameters (including rolling friction, static friction, and restitution coefficient between particles) of the metal powder particle material. Among them, the contact force between powder particles is simulated using the Hertz contact model, and the van der Waals force between powder particles is simulated using the JKR cohesion model; the specific process is as follows:

[0051] Hertz contact model:

[0052]

[0053]

[0054] F s =-S s δ s

[0055]

[0056] Among them, F n and are the normal contact force and damping force of the particle respectively, and F s and are the tangential contact force and damping force of the particle respectively; E * 、R * and m *are the Young's modulus, equivalent radius, and mass; δ n , S n and v n are the overlap, normal stiffness, and velocity component respectively; δ s , S s and v s are the overlap, tangential stiffness, and velocity component respectively; β is a constant related to the coefficient of restitution.

[0057] The JKR cohesion model is:

[0058]

[0059] where γ is the particle surface energy, E * is the Young's modulus, α is the equivalent radius of the contact area, R * is the particle equivalent radius.

[0060] Step 3: Define that the particle size of the particle material in the powder spreading simulation model follows a normal distribution according to the actual powder particle size distribution measured in Step 1, as Figure 3 shown;

[0061] Step 4: Set the scraper speed and direction. Among them, the scraper speed is set to 0.02 m / s according to the actual measured scraper movement speed value in Step 1, and the direction is along the positive x-axis; Based on the Hertz contact model and JKR cohesion model established in Step 2, through the powder spreading simulation model established in Step 1, a certain number of particles with a normal distribution of particle size are generated above the substrate using the discrete element method. Under the action of the scraper, a laying area model with a layer thickness of 0.1 mm consistent with the actual layer thickness is obtained in the laying area. Then, the laying area model is extracted, and a substrate with the same area and a height of 0.3 mm is established below to obtain the final discrete powder bed particle model as Figure 4 shown, and the size of the entire simulation area is 1 mm × 0.6 mm × 0.6 mm;

[0062] Step 5: In the actual electron beam additive manufacturing process, there are multiple processes including heating, melting, flowing, evaporation, and solidification of powder particles, forming a molten pool with very complex flow, and the physical process is very complex. For simplicity in simulation, the hydrodynamic control equations based on the Eulerian description are used for solution. The main basic assumptions of these control equations are: (1) The liquid in the molten pool is a Newtonian, incompressible fluid; (2) The densities of the metal liquid phase and solid phase are constant; (3) The mushy zone around the molten pool is an isotropic porous medium. Based on this, the thermal boundary conditions in the actual manufacturing process are written into the source term of the control equations to construct the heat transfer and mass transfer control equations of the powder bed particles under the action of the electron beam. The specific process is as follows:

[0063] Continuity equation:

[0064]

[0065] Momentum conservation equation:

[0066]

[0067] Energy conservation equation:

[0068]

[0069] Where ρ, p, and T are density, pressure, and temperature respectively, u is the fluid motion velocity in the x - direction, K0 is the thermal conductivity, μ is the liquid viscosity, t is time, f l is the liquid volume fraction, T ref is the reference temperature, ΔH is the enthalpy of evaporation, and q is the heat source.

[0070] Among them, the heat source is selected as the Gaussian surface heat source q:

[0071]

[0072] Where Q is the heat flux density, R is the electron beam spot radius, x is the coordinate along the x - axis, y is the coordinate along the y - axis, x s is the initial coordinate of the x - axis, y s is the initial coordinate of the y - axis;

[0073] Step 6, during the electron beam additive manufacturing process, the heat input is extremely high, quickly reaching the evaporation temperature of the powder material and generating a vapor recoil force p rec , which affects the flow and morphology of the molten pool. The vapor recoil force p rec is applied to the surface of the molten pool as a force boundary condition and solved during the simulation. Define the vapor recoil force p rec as:

[0074]

[0075] Where p ag is the ambient pressure, ΔH v is the enthalpy of evaporation, T is the temperature, T b is the boiling point of the material, R g is the gas constant;

[0076] Step 7, define the thermophysical parameters of the discrete powder bed particle model and the substrate obtained in Step 4 and divide the mesh. Among them, the thermophysical parameters mainly include parameters such as density, thermal conductivity, viscosity, and surface tension that vary with temperature; during the solution calculation, substitute the thermophysical parameters into the control equations in Step 5; divide the mesh of the discrete powder bed model obtained in Step 4, with a mesh size of 5 μm, as the final solution calculation domain;

[0077] Step 8: Set the time step. Using the discrete powder bed model obtained in Step 7 as the computational domain, solve the control equations for heat transfer and mass transfer of the powder bed particles under the action of the electron beam in the computational domain to obtain the temperature field, topography change, and forming quality of the molten pool.

[0078] Among them, the time step is set according to the total time of the simulation.

[0079] In the present invention, the solution adopts the volume of fluid method, which requires dividing the computational domain into small grids and separately solving the distribution of the solid-liquid interface for each grid. During the simulation, the vapor recoil force is used as the force boundary condition and is solved synchronously with the three control equations with heat boundary conditions added in Step 5. That is, the present invention adopts the discrete element method and the volume of fluid method to realize the numerical simulation of the powder bed.

[0080] The present invention first uses the discrete element method to establish a discrete powder bed particle model. Since there are many powder particles in the actual manufacturing process, full simulation requires too high computer performance. Therefore, to reduce the calculation cost and time, a smaller model is used for simulation. The substrate size is 5mm×5mm×1mm, the scraper size is 5mm×0.2mm×3mm, and the powder bed model size is 1mm×0.6mm×0.1mm. The final obtained entire computational domain is 1mm×0.6mm×0.6mm. Secondly, the control equations for heat transfer and mass transfer of the powder bed particles under the action of the electron beam are constructed.

[0081] By solving the above continuity, momentum, and energy conservation equations and the vapor recoil force, the final temperature field and molten pool topography are obtained. By simulating the heat transfer and mass transfer process of the powder bed under the action of the electron beam, the molten pool topography and temperature field of the powder bed heated and melted as shown in (a) and (b) in Figure 5 and Figure 6 are obtained, as well as the flow behavior of the cross-section and longitudinal section of the molten pool melt. Finally, by setting different process parameters (low heat input (100W, 1m / s) and high heat input (1800W, 1m / s)), the possible spheroidization and pore defects shown in (a) and (b) in Figure 7 are obtained. Among them, Figure 5 is the top view of the molten pool, and the powder particles are melted into a linear melting channel along the scanning direction. Figure 6 In (a) and (b) in Figure 7 are the flow behaviors of the cross-section and longitudinal section of the molten pool. Under the action of the Marangoni force, the cross-section of the molten pool flows from the middle to both sides, while in the longitudinal section, it flows towards the tail of the molten pool. Finally, by setting the process parameters of low heat input (100W, 1m / s) and high heat input (1800W, 1m / s), the possible spheroidization and pore defects shown in

[0082] Under medium (600W, 1m / s) process parameters, the actual solidified melt channel morphology obtained is shown in Figure 8 .

Claims

1. A numerical simulation method based on electron beam powder bed melting, characterized in that Including the following steps: Step 1: Collect the particle size distribution, powder layer thickness, and scraper movement speed of metal powder particles during powder spreading of the electron beam additive manufacturing equipment; establish a powder spreading simulation model of the electron beam additive manufacturing equipment according to the particle size distribution, powder layer thickness, and scraper movement speed of the metal powder particles; Step 2: Based on the contact force of the metal powder particle material, generate particles with a normal distribution of particle sizes through the powder spreading simulation model. Under the action of the scraper, a powder bed model is obtained in the laying area. The powder bed model is extracted, and a substrate with the same area as the powder bed model is established below the powder bed model to obtain a discrete powder bed particle model; Step 3: After meshing the discrete powder bed particle model, it is used as the computational domain; Step 4: After the metal powder particles are heated to form a molten pool, the vapor recoil force is applied to the surface of the molten pool, and the heat transfer and mass transfer control equation of the powder bed particles under the action of the electron beam is solved in the computational domain to obtain the temperature field, morphology change, and forming quality of the molten pool; The heat transfer and mass transfer control equation of the powder bed particles under the action of the electron beam is as follows: Continuity equation: Momentum conservation equation: Energy conservation equation: wherein, are density, pressure and temperature respectively, is the fluid motion velocity in the thermal conductivity, is the liquid viscosity, is time, is the liquid volume fraction, is the reference temperature, is the enthalpy of evaporation, is the heat source.

2. The numerical simulation method based on electron beam powder bed melting according to claim 1, wherein The contact force of the metal powder particle material includes the contact force and van der Waals force between powder particles; the contact force is simulated through the Hertz contact model; the van der Waals force is simulated through the JKR cohesion model.

3. A numerical simulation method based on electron beam powder bed melting according to claim 1, characterized in that The Hertz contact model is as follows: Wherein, and are the normal contact force and damping force of the particle respectively, and are the tangential contact force and damping force of the particle respectively; 、 and are Young's modulus, equivalent radius and mass respectively; 、 and are the overlap amount, normal stiffness and velocity component respectively; 、 and are the overlap amount, tangential stiffness and velocity component respectively; is a constant related to the restitution coefficient.

4. A numerical simulation method based on electron beam powder bed melting according to claim 1, characterized in that The JKR cohesion model is as follows: Among them, is the surface energy of the particle, is the Young's modulus, is the equivalent radius of the contact area, is the equivalent radius of the particle.

5. A numerical simulation method based on electron beam powder bed melting according to claim 1, characterized in that The heat source is calculated by the following formula: In the formula, Q is the heat flux density, R is the electron beam spot radius, x is along x axis coordinate, y is along y axis coordinate, is x axis initial coordinate, is y axis initial coordinate.

6. A numerical simulation method based on electron beam powder bed melting according to claim 1, characterized in that, Steam reaction force Calculated by the following formula: Wherein, is the ambient pressure, is the enthalpy of evaporation, T is the temperature, is the boiling point of the material, is the gas constant.

7. A numerical simulation method based on electron beam powder bed melting according to claim 1, characterized in that The discrete element method is used to generate particles with a normal distribution of particle sizes above the substrate.

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