A rapid prediction method for multi-layer deposition profile using coaxial laser powder feeding

Abstract

The present invention relates to the technical field of metal additive manufacturing, and specifically to a method for rapid prediction of multi-layer deposition profiles using coaxial laser powder feeding. The method comprises the following steps: obtaining the spatial distribution of powder concentration; using the spatial distribution to obtain the laser intensity distribution after powder shielding; obtaining the substrate temperature field according to the laser intensity distribution; obtaining the contact angle and cross-sectional area of ​​the deposition layer through the substrate temperature field; constructing a prediction model for a single-channel single-layer deposition profile based on the contact angle and the cross-sectional area; obtaining a single-channel multi-layer deposition profile based on the prediction model; and realizing rapid prediction of the profile of a multi-layer deposition layer using coaxial laser powder feeding based on the single-channel multi-layer deposition profile. The present invention greatly improves the efficiency of component surface morphology prediction under different process parameter combinations, effectively solves the problems of complex experimental process and high cost, and also solves the problems of high spatial resolution, large calculation scale and high time cost of numerical simulation.

Description

Technical Field

[0001] The present invention relates to the technical field of metal additive manufacturing, and in particular to a method for quickly predicting the profile of multi-layer deposition using laser coaxial powder feeding. Background Art

[0002] Laser coaxial powder feeding is an important technology in metal additive manufacturing. This technology uses a gas-carrying powder feeder to transport metal powder, and delivers the powder flow into the light spot to achieve line-by-line and layer-by-layer deposition forming. It has broad application prospects in the additive manufacturing of large components and the composite and gradient component manufacturing of multiple materials on the same material. However, laser coaxial powder feeding technology still faces many challenges in engineering applications, especially in surface forming quality control. Surface defects such as uneven top surface of components, dimensional deviation, rough side walls, unmelted powder adhesion, and side wall stacking corrugations are still common. These defects lead to large cutting allowances in subsequent finishing, making it difficult to achieve true "near-net" forming.

[0003] In the existing technology, experimental methods or numerical simulation methods are usually used to study the surface forming quality. On the one hand, obtaining forming quality characterization data through experiments is the most direct way, but it is limited by detection methods and experimental costs, and it is difficult to meet the research needs under a large number of process parameter combinations. On the other hand, to study the surface forming quality through numerical simulation, it is necessary to establish a high-fidelity model to describe subtle defects, but due to its high spatial resolution and large calculation scale, the calculation time of a single case is usually more than tens of hours, which is difficult to meet the needs of efficient prediction; in addition, theoretical or analytical models can directly reflect the physical meaning, but are limited by the complexity of physical problems and it is difficult to accurately describe complex physical phenomena. Therefore, there is an urgent need to establish an efficient, accurate and physically meaningful prediction method to achieve rapid mapping of process parameters and component surface profiles.

[0004] At present, there is not much research on the profile of multi-layer deposition using laser coaxial powder feeding, and there is no specific low-cost, high-precision and high-efficiency method for predicting the profile of multi-layer deposition using laser coaxial powder feeding. Summary of the Invention

[0005] In view of the defects in the prior art, the present invention provides a method for quickly predicting the profile of multi-layer deposition using laser coaxial powder feeding.

[0006] The present invention provides a method for rapidly predicting the profile of a multi-layer deposition using laser coaxial powder feeding, comprising the following steps:

[0007] Obtain the spatial distribution of powder concentration; obtain the laser intensity distribution after powder shielding using the spatial distribution; obtain the substrate temperature field based on the laser intensity distribution; obtain the contact angle and cross-sectional area of ​​the deposited layer through the substrate temperature field; construct a prediction model for a single-channel single-layer deposition profile based on the contact angle and the cross-sectional area; obtain a single-channel multi-layer deposition profile based on the prediction model; and achieve rapid prediction of the profile of a multi-layer deposition layer with coaxial laser powder feeding based on the single-channel multi-layer deposition profile. The present invention greatly improves the efficiency of component surface morphology prediction under different process parameter combinations, reduces the trial and error costs of a large number of experiments, generates excellent economic benefits, and shortens the calculation time of high-fidelity numerical simulation from "days" to "seconds", making it possible to predict surface forming quality in real time, effectively solving the problems of complex process and high cost of obtaining the deposited layer profile through experiments, and also solving the problems of high spatial resolution, large calculation scale and low efficiency of solving the deposited layer profile through numerical simulation.

[0008] Optionally, obtaining the spatial distribution of the powder concentration includes obtaining the spatial distribution of the powder concentration in the front waist region, the waist region, and the back waist region, wherein the spatial distribution includes an annular Gaussian distribution in the front waist region, a circular Gaussian distribution in the waist region, and a divergent distribution in the back waist region, and the spatial distribution satisfies the following expression:

[0009]

[0010] in, is the powder concentration in the space, is the powder concentration in the plane, 、 is the distribution radius of the powder on the horizontal plane in different areas, is the horizontal distance from the center of the powder flow to the center line, is the regional boundary distance of the powder flow, is the distance to the focal plane, is the radial coordinate in space, is the spatial azimuth, is the space height, The present invention uses the spatial distribution expression of powder concentration to clearly depict the distribution characteristics of powder concentration in the front, back, and center parts of the waist region. This not only effectively reflects the distribution characteristics of powder concentration in different regions, but also provides important clues for understanding the spatial distribution law of powder.

[0011] Optionally, the obtaining of the laser intensity distribution after powder shielding by using the spatial distribution includes: obtaining the laser intensity distribution after powder shielding by using the spatial distribution and a Gaussian intensity distribution of a surface heat source, wherein the laser intensity distribution satisfies the following expression:

[0012]

[0013] in, is the intensity distribution after laser attenuation, is the Gaussian intensity distribution of the surface heat source, is the powder concentration in the space, is the powder radius, is the vertical coordinate of the initial contact point between the laser and the powder flow, is the radial coordinate in space, is the spatial azimuth, The present invention constructs an expression for the laser intensity distribution after powder shielding by combining the spatial distribution of powder concentration and the Gaussian intensity distribution of the surface heat source. This expression not only takes into account the spatial non-uniformity of powder concentration but also the intensity distribution characteristics of the laser source itself. This allows for a more accurate determination of the laser intensity distribution after powder shielding, which is of great significance in scientific research and industrial applications.

[0014] Optionally, obtaining the substrate temperature field according to the laser intensity distribution includes: establishing an analytical model of the substrate temperature field under a moving Gaussian heat source according to the laser intensity distribution; obtaining the substrate upper surface temperature through the analytical model; obtaining the substrate upper surface heat loss power according to the substrate upper surface temperature; and obtaining the substrate temperature field based on the substrate upper surface heat loss power and the analytical solution of the analytical model. The present invention describes the complete process of deriving the substrate temperature field from the laser intensity distribution. The specific effects are as follows: First, an analytical model of the substrate temperature field under a moving Gaussian heat source is established using the laser intensity distribution, which provides a basis for subsequent calculations; second, the temperature of the substrate upper surface is calculated through the analytical model, and an important indicator for evaluating the laser thermal effect is obtained; third, the heat loss power of the substrate upper surface is derived based on the temperature of the substrate upper surface, which reflects the heat dissipation on the substrate upper surface; fourth, the substrate temperature field is obtained through the upper surface heat loss power and the analytical solution of the analytical model, realizing the accurate mapping from laser intensity to substrate temperature field.

[0015] Optionally, the temperature increment of the substrate temperature field satisfies the following expression:

[0016]

[0017] in, is the temperature increment, is the laser power, is the heat loss power on the substrate surface, is the standard deviation of laser intensity, is the absorption rate, is the material density, is the gravity state value, is the material specific heat, is the thermal conductivity of the material, is the laser moving speed, is the moving time step, is the reference time step, 、 、 is a spatial coordinate point. The present invention constructs a temperature increment expression for the substrate temperature field by considering the heat loss power on the upper surface of the substrate, which is used to describe the dynamic changes of the substrate temperature field. This expression has the following effects: First, it not only takes the heat loss power on the upper surface of the substrate into consideration as a key parameter, but also reflects how the substrate temperature adjusts with the change of heat loss during the laser processing process, and can more accurately analyze the thermal effects of the interaction between the laser and the substrate, including key links such as heat absorption, conduction and dissipation; second, it provides a theoretical basis for accurately controlling the temperature distribution during laser processing, helps to optimize process parameters, reduce thermal deformation and thermal stress, and thus improve processing quality and efficiency, which is of great significance in high-precision processing fields such as laser cutting, welding, and cladding.

[0018] Optionally, obtaining the contact angle and cross-sectional area of ​​the deposited layer through the substrate temperature field includes: obtaining the molten pool size through the substrate temperature field; obtaining the powder utilization rate and the contact angle of the deposited layer based on the molten pool size; and obtaining the cross-sectional area of ​​the deposited layer based on the powder utilization rate. The present invention accurately derives the key characteristics of the deposited layer through the substrate temperature field. The specific effects are as follows: First, the molten pool size is accurately measured using the distribution information of the substrate temperature field. The molten pool size not only reflects the efficiency of the melting process, but also directly affects the formation of the subsequent deposited layer; second, based on the molten pool size, the powder utilization rate that measures the efficiency of material use and the contact angle of the deposited layer that reveals the bonding state between the deposited layer and the substrate are calculated, which are crucial for ensuring the stability and strength of the deposited layer; third, the cross-sectional area of ​​the deposited layer is derived using the powder utilization rate. The cross-sectional area reflects the morphology and size of the deposited layer, and has important reference value for evaluating the deposition effect and subsequent processing.

[0019] Optionally, constructing a prediction model for a single-pass single-layer deposition profile based on the contact angle and the cross-sectional area includes: constructing a prediction model for a single-pass single-layer deposition profile based on the contact angle, the cross-sectional area, and a Young-Laplace equation, wherein the Young-Laplace equation satisfies the following expression:

[0020]

[0021] in, is the surface tension coefficient, is the contour curvature, is the pressure difference between the gas and liquid surfaces. The single-channel single-layer deposition profile prediction model constructed by the present invention makes full use of the three key elements of contact angle, cross-sectional area and Young-Laplace equation. The specific effects are as follows: First, the contact angle, as an important indicator of the interface characteristics between the deposited layer and the substrate, provides the model with key information about the expansion trend of the deposited layer; second, the cross-sectional area directly reflects the morphology and size of the deposited layer, becoming an indispensable data for predicting the deposition profile; third, the Young-Laplace equation introduced describes the relationship between the curvature of the liquid interface and the interfacial tension. Combined with the contact angle and cross-sectional area, it can more accurately describe the expansion and morphological changes of the deposited layer on the substrate.

[0022] Optionally, the prediction model of the single-pass single-layer deposition profile satisfies the following expression:

[0023]

[0024] in, is the surface tension coefficient, is the first-order derivative of the distance between the contour curve and the central axis, is the second-order derivative of the distance between the contour curve and the central axis, is the coefficient, is the gravity state value, is the material density, is the single-channel single-layer deposition profile, is the liquid metal volume fraction. The prediction model constructed in this invention is an advanced expression that combines scientificity, practicality, and accuracy. It cleverly incorporates the physical principles of the Young-Laplace equation to ensure the accuracy and reliability of the prediction results. This not only provides strong support for the optimization of deposition processes, but also injects new vitality into research and development in related fields.

[0025] Optionally, obtaining a single-pass multi-layer deposition profile based on the prediction model includes: obtaining a single-pass single-layer deposition profile based on the prediction model; and performing profile processing on the single-pass single-layer deposition profile using a profile construction method to obtain a single-pass multi-layer deposition profile. The present invention obtains a single-pass multi-layer deposition profile using a prediction model for the single-pass single-layer deposition profile. This entire process demonstrates the technological sophistication and practicality of the technology. The profile processing method not only improves the accuracy and reliability of the deposition profile but also provides richer and more accurate technical support for subsequent analysis and research.

[0026] Optionally, the contour construction method includes a direct stacking construction method and an indirect stacking construction method of the contour; the direct stacking construction method includes a construction method in which the cross-sections of multiple single-layer deposited layers are directly stacked after considering the melting area; the indirect stacking construction method includes a construction method in which the cross-sections of multiple single-layer deposited layers are first superimposed and then stacked. The present invention describes the direct stacking construction method and the indirect stacking construction method in the contour construction method; the direct stacking construction method emphasizes the direct superposition of the cross-sectional area of ​​each single-layer deposited layer after considering the melting area, which can be closer to the fusion bonding between layers in the actual deposition process, thereby improving the construction accuracy; the indirect stacking construction method first superimposes the cross-sectional areas of multiple single-layer deposited layers and then stacks them, which takes more consideration of the interaction between the deposited layers and the overall structural stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 This is a flow chart of a method for rapid prediction of a multi-layer deposition profile using coaxial laser powder feeding according to an embodiment of the present invention;

[0028] Figure 2 A flowchart of performing calculations according to an embodiment of the present invention;

[0029] Figure 3 This is a schematic diagram of the laser coaxial powder feeding process according to an embodiment of the present invention;

[0030] Figure 4 Schematic diagram of the geometric outline of the nozzle and the powder flow below it according to an embodiment of the present invention;

[0031] Figure 5 Schematic diagram of laser shielding by powder in a microelement according to an embodiment of the present invention;

[0032] Figure 6 This is a flow chart of heat loss power calculation according to an embodiment of the present invention;

[0033] Figure 7 A top view of the laser coaxial powder feeding process according to an embodiment of the present invention;

[0034] Figure 8 This is a schematic diagram of a laser coaxial powder feeding model according to an embodiment of the present invention;

[0035] Figure 9 is a schematic cross-sectional view of a cladding layer according to an embodiment of the present invention;

[0036] Figure 10 A flow chart showing calculation of a single-pass single-layer deposition profile according to an embodiment of the present invention;

[0037] Figure 11 A schematic cross-sectional view of a single-pass multi-layer deposition process according to an embodiment of the present invention;

[0038] Figure 12Schematic diagram of single-pass multi-layer deposition according to an embodiment of the present invention. DETAILED DESCRIPTION

[0039] Specific embodiments of the present invention will be described in detail below. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the present invention. In the following description, numerous specific details are set forth to provide a thorough understanding of the present invention. However, it will be apparent to one of ordinary skill in the art that these specific details are not necessarily required to practice the present invention. In other instances, well-known circuits, software, or methods are not specifically described to avoid obscuring the present invention.

[0040] Throughout this specification, references to "one embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with the embodiment or example is included in at least one embodiment of the present invention. Therefore, appearances of the phrases "in one embodiment," "in an embodiment," "an example," or "an example" in various places throughout this specification are not necessarily all referring to the same embodiment or example. Furthermore, the particular features, structures, or characteristics may be combined in any suitable combinations and / or subcombinations in one or more embodiments or examples. Furthermore, those of ordinary skill in the art will appreciate that the figures provided herein are for illustrative purposes only and are not necessarily drawn to scale.

[0041] See Figure 1 An embodiment of the present invention provides a method for quickly predicting the profile of a multi-layer deposition using coaxial laser powder feeding, the method comprising the following steps:

[0042] S1. Obtain the spatial distribution of powder concentration.

[0043] In one embodiment, the nozzle parameters and powder spatial distribution parameters are measured based on the laser coaxial powder feeding process. Figure 2 As shown, the laser beam is processed at a speed of Yanzheng The coordinate origin is fixed at the center of the laser beam spot on the substrate. The distance between the coaxial powder feeding nozzle and the substrate plane is The laser beam passes through the central cavity of the nozzle, and the powder particles are transported in a conical annular channel coaxial with the laser beam. On any vertical symmetric plane, the geometric profile of the nozzle and the powder flow below it is as follows: Figure 3 shown.

[0044] Furthermore, on the nozzle outlet plane, with the origin A coordinate system is established for the nozzle center The angle of the annular channel relative to the center line (Z axis) is The powder flow will usually diverge to a certain extent at the nozzle outlet, with the upper and lower divergence angles being and The powder particles ejected from the annular outlet flow downward, and the laser beam and powder flow After the points interact with each other, the powder flow undergoes a process of first convergence and then divergence.

[0045] Furthermore, according to the distribution characteristics of the powder on the horizontal cross-section at different positions, the powder flow is roughly divided into three regions: the front waist region of the annular Gaussian distribution, the waist region of the circular Gaussian distribution, and the back waist region of the divergent distribution. The analytical expression of the spatial distribution of the powder concentration is:

[0046]

[0047] in, is the powder concentration in the space, is the powder concentration in the plane, 、 is the distribution radius of the powder on the horizontal plane in different areas, is the horizontal distance from the center of the powder flow to the center line, is the regional boundary distance of the powder flow, is the distance to the focal plane, is the radial coordinate in space, is the spatial azimuth, is the space height, is the distribution of powder concentration on the transverse plane. Satisfies the following expression:

[0048]

[0049] It's important to note that the distribution of powder concentration in the transverse plane is represented by the brightness distribution of the powder flow. According to Mie theory, the brightness of a powder flow is proportional to its concentration. Therefore, the brightness distribution in the captured frontal view of the powder flow reflects the distribution of the powder flow concentration: greater brightness indicates greater concentration, and lower brightness indicates lower concentration.

[0050] Furthermore, the image is converted into a grayscale image by image processing software, and the brightness of the powder flow is converted into grayscale intensity.

[0051] Furthermore, according to the grayscale images at different positions and Fitting is performed to obtain the analytical solution of the concentration distribution.

[0052] S2. Using the spatial distribution, obtain the laser intensity distribution after powder shielding.

[0053] In one embodiment, the laser intensity distribution after powder shielding is studied based on the spatial distribution of the powder flow and the attenuation effect of the powder on the laser intensity.

[0054] Specifically, in this embodiment, a Gaussian distributed surface heat source is used, and its intensity distribution is Satisfies the following expression:

[0055]

[0056] in, is the laser power, is the laser spot radius, is the distance from the laser center to the point being sought. The attenuation of the laser power intensity by the powder flow can be calculated based on the intensity distribution expression of the Gaussian distribution surface heat source above, as follows: Figure 4 As shown, the selected area is , height is The attenuation coefficient The laser intensity in the microelement The following relations are satisfied:

[0057]

[0058] in, is the shaded area of ​​the powder, which can be expressed as:

[0059]

[0060] in, is the powder radius.

[0061] Furthermore, the attenuation coefficient Satisfies the following expression:

[0062]

[0063] Furthermore, the above formula is applied to the interval Therefore, the total attenuation of laser intensity is It can be expressed as:

[0064]

[0065] in, Initial contact between laser and powder flow The vertical coordinate of the point, such as Figure 4 As shown. Intensity distribution after laser attenuation It can be solved by the following formula:

[0066]

[0067] in, is the intensity distribution after laser attenuation, is the Gaussian intensity distribution of the surface heat source, is the powder concentration in the space, is the powder radius, is the radial coordinate in space, is the spatial azimuth, The height of the space.

[0068] S3. Obtaining the substrate temperature field according to the laser intensity distribution.

[0069] Wherein, step S3 further includes the following steps:

[0070] S31. Based on the laser intensity distribution, an analytical model of the substrate temperature field under a moving Gaussian heat source is established.

[0071] In one embodiment, the process of establishing an analytical model of the substrate temperature field under a moving Gaussian heat source is as follows:

[0072] First, in the solid domain, without considering convection in the molten pool, the heat transfer equation can be written as:

[0073]

[0074] in, is the temperature, is the material density, is the material specific heat, is the thermal conductivity of the material, Laser heat source. is the source term introduced by the material phase change and can be expressed as:

[0075]

[0076] in, is the density of the metal material, is the latent heat of melting of the metal material, is the volume fraction of liquid metal, which can be expressed as:

[0077]

[0078] in, is the solidus and liquidus temperature of the material, and the inverse tangent function can be introduced to approximate , which is expressed as follows:

[0079]

[0080] in, It is obtained by fitting and then The derivative is expressed as:

[0081]

[0082] Further, Defined as:

[0083]

[0084] Furthermore, the heat transfer equation is organized as:

[0085]

[0086] It should be noted that the laser intensity distribution represents The laser beam interacts with the powder, raising the powder temperature. Simultaneously, the laser intensity is affected by the powder flow and attenuates. The total attenuation can be divided into the sum of powder absorption and scattering. In the coaxial laser powder feeding process, since the powder size is much larger than the laser wavelength, scattering can be ignored, and the attenuated laser energy is mostly absorbed by the powder.

[0087] Furthermore, the Green's function method is used to integrate the entire interval to obtain the analytical solution of the instantaneous point heat source.

[0088] Specifically, by superimposing instantaneous Gaussian surface heat sources in a continuous order and at a certain distance, the temperature response expression of the moving Gaussian surface heat source when it moves on the semi-infinite medium surface is obtained. , the speed is ,along Axis movement, absorption rate , and the analytical solution of the temperature increment is:

[0089]

[0090] in, is the standard deviation of laser intensity. When the time is very short, it is assumed that is a constant, so we can get:

[0091]

[0092] in, is the temperature increment, is the laser power, is the absorption rate, is the material density, is the gravity state value, is the material specific heat, is the thermal conductivity of the material, is the moving time step, is the reference time step, 、 、 is the spatial coordinate point.

[0093] S32. Obtain the surface temperature of the substrate through the analytical model.

[0094] In one embodiment, the material properties are considered to vary with temperature and The impact of time Divide into multiple time steps with a time interval of , calculate the temperature field after each time step to update the material properties and , therefore, the relationship satisfied by the surface temperature of the substrate is as follows:

[0095]

[0096]

[0097] in, Represents the surface temperature of the substrate, which can be solved by analytically solving the expression of temperature increment , material parameters are taken Material properties at temperature and Temperature increment at a point .

[0098] S33. Obtain the heat loss power of the upper surface of the substrate based on the upper surface temperature of the substrate.

[0099] In one embodiment, the heat loss is equivalent to the power loss on the upper surface of the substrate, that is, the heat loss power , which satisfies the following relationship:

[0100]

[0101] in, is the ambient temperature, is the convective heat transfer coefficient, is the Stefan-Boltzmann constant, is the emissivity, is the latent heat of vaporization of the material, is the molar mass of the molecule, is atmospheric pressure, is the universal gas constant, The upper surface area of ​​the substrate.

[0102] S34. Obtain the substrate temperature field based on the heat loss power on the upper surface of the substrate and the analytical solution of the analytical model.

[0103] In one embodiment, considering the heat loss power and combining the expression of the analytical solution of the temperature increment, the final temperature increment can be obtained, which is expressed as follows:

[0104]

[0105] Furthermore, to determine the , take an iterative approach to find the appropriate , the process is as follows Figure 5 The power considering heat loss is updated at each time step, and the temperature field is solved through the temperature field analytical model.

[0106] S4. Obtain the contact angle and cross-sectional area of ​​the deposited layer through the substrate temperature field.

[0107] Wherein, step S4 further includes the following steps:

[0108] S41. Obtain the molten pool size through the substrate temperature field.

[0109] In one embodiment, the projection of the molten pool on the substrate surface is approximated by the solid-liquid line, such as Figure 6 As shown. Among them, points A, B, C, and D are located on the boundary of the molten pool. According to the expression of the analytical solution of the temperature increment, we can get:

[0110]

[0111] Furthermore, the molten pool boundary can be approximated as two semi-ellipses, and the solidus can be expressed as:

[0112]

[0113] S42. Based on the molten pool size, obtain the powder utilization rate and the contact angle of the deposited layer.

[0114] In one embodiment, based on the expression for the powder shadow area, it is determined that only the powder entering the molten pool is utilized. The molten pool is divided into two semi-ellipses with the center of the heat source as the boundary point. The powder concentration at each position is calculated based on the spatial distribution expression of the powder concentration. The spatial distribution expression of the powder concentration is integrated over the two semi-ellipses to obtain the powder utilization rate. The powder utilization rate satisfies the following expression:

[0115]

[0116] in, The molten pool area.

[0117] Furthermore, the contact angle of the deposited layer is calculated based on the molten pool boundary line expression. The expression of the contact angle is as follows:

[0118]

[0119] S43. Obtain the cross-sectional area of ​​the deposited layer according to the powder utilization rate.

[0120] In one embodiment, the cross-sectional area of ​​the deposited layer is calculated based on the scanning speed, the powder feeding rate, and the powder utilization rate. The cross-sectional area of ​​the deposited layer satisfies the following expression:

[0121]

[0122] in, is the powder feeding rate.

[0123] S5. Based on the contact angle and the cross-sectional area, a prediction model for a single-pass single-layer deposition profile is constructed.

[0124] In one embodiment, the surface tension of the deposited layer is first described using the Young-Laplace equation, which is as follows:

[0125]

[0126] in, is the surface tension coefficient, is the contour curvature, is the pressure difference between the gas and liquid surfaces. Based on the assumption that the curvature radius of the sedimentary layer surface along the Y axis is infinite, its curvature is:

[0127]

[0128] Where 𝑅 is the radius of the contour curve from the central axis, where They are The first and second order derivatives of It is the single-channel single-layer deposition profile.

[0129] Furthermore, in order to simplify the modeling process, the fluid momentum equation is written as follows, considering the steady flow of the sediment layer:

[0130]

[0131] Where 𝜌 is the density and 𝑔 is the gravity state value. Assume that the pressure at the top of the radius is , the fluid momentum equation can be written as:

[0132]

[0133] in, is a coefficient related to the top curvature of the profile and the height of the sediment layer. According to the profile curvature and the fluid momentum equation, the sediment layer profile equation is substituted into the Young-Laplace equation. The sediment layer profile equation is as follows:

[0134]

[0135] Furthermore, to avoid the singularity of the equation, it is assumed that the sedimentary layer profile at a short distance from the top is a parabola, and its expression is:

[0136]

[0137] in, is the coefficient.

[0138] Furthermore, according to the above parabolic expression and sediment profile equation, and taking When , we get:

[0139]

[0140] Furthermore, the sedimentary layer profile equation is sorted out to obtain a prediction model for a single-channel single-layer sedimentary profile, which satisfies the following expression:

[0141]

[0142] in, is the surface tension coefficient, is the first-order derivative of the distance between the contour curve and the central axis, is the second-order derivative of the distance between the contour curve and the central axis, is the coefficient, is the gravity state value, is the material density, is the single-channel single-layer deposition profile, is the volume fraction of liquid metal.

[0143] It should be noted that the process of laser coaxial powder feeding processing is as follows Figure 7 As shown in Figure 2, the shape of liquid metal is mainly affected by surface tension, gravity and pressure. In order to describe the shape of the deposited layer during processing, the following assumptions are made: the metal is in liquid state before the force reaches equilibrium; the deposited layer is symmetrically distributed, and the surface of the deposited layer is along the The radius of curvature of the axis is infinite; the Marangoni effect mainly acts in the tangential direction, so its effect on the sediment surface is indirectly exerted by affecting the flow velocity and is ignored here.

[0144] S6. Obtain a single-channel single-layer deposition profile based on the prediction model.

[0145] Wherein, step S6 further includes the following steps:

[0146] S61. Obtain a single-pass multi-layer deposition profile based on the prediction model.

[0147] In one embodiment, based on the prediction model of single-pass single-layer deposition profile, the particle swarm optimization algorithm is used to obtain and First, a high-fidelity numerical model is used to calculate the contact angle The surface tension coefficient is considered as a constant.

[0148] Furthermore, for the calibrated theoretical model, the unknown sediment layer height is obtained by the fourth-order Runge-Kutta algorithm. and coefficients , the calculated contour area and contact angle Compared with the known values, the optimal solution is obtained through the particle swarm optimization algorithm. It usually takes only 0.1s to quickly calculate the single-pass single-layer deposition profile curve under specific working conditions. The process is as follows: Figure 9 shown.

[0149] S62. Perform contour processing on the single-pass single-layer deposition contour using a contour construction method to obtain a single-pass multi-layer deposition contour.

[0150] For multi-layer deposition, that is, along the same path and in the same direction, the laser print head is raised to a certain height before each deposition, so as to obtain a thin-walled workpiece. The processing process is simplified, such as Figure 10 As shown in the figure, points M and N are the two endpoints of the deposition layer respectively. Assuming that the width and cross-sectional area of ​​each deposition layer remain unchanged, the following two situations will occur during the processing: one is that the maximum width of the surface profile of the first deposition layer exceeds the bottom width of the deposition layer; the other is that the maximum width of the surface profile of the first deposition layer is the bottom width.

[0151] When the first case is encountered, in one embodiment, a single-channel multi-layer profile is constructed by a direct stacking construction method; the direct stacking construction method includes a construction method in which multiple single-layer deposited layer sections are directly stacked after considering the melting area.

[0152] Specifically, the first layer's deposition profile and the and Point coordinates.

[0153] Further, determine the endpoint coordinates of the next layer, the endpoint and Point coordinates The coordinates remain unchanged. The coordinates take the maximum value of the contour of this layer, and the cross-sectional area of ​​the next layer . The powder utilization efficiency is calculated based on the profile of the previous deposition layer and the laser head being raised to a certain height on the new plane, such as Figure 11 As shown, that is:

[0154]

[0155] in, For the The secondary deposition raises the molten area to different heights. The molten shape is assumed to be the same as the initial molten pool shape. The geometric contour of the next layer is determined based on the endpoint coordinates, cross-sectional area and the same single-pass single-layer deposition contour geometric prediction method to solve the multi-layer contour.

[0156] When encountering the second situation, in another embodiment, an indirect stacking construction method of first superimposing and then stacking is adopted to construct a single-channel multi-layer profile; the indirect stacking construction method includes a construction method of first superimposing the cross-sectional area of ​​multiple single-layer deposition layer sections and then stacking them.

[0157] Specifically, the first layer of sedimentation profile and the point, Point coordinates;

[0158] Furthermore, maintain the endpoints of the second layer and The coordinates remain unchanged, and the cross-sectional area of ​​the second layer is solved based on the powder utilization efficiency considering the melting area. , , the second layer profile is determined by the single-pass single-layer deposition profile geometry prediction method, and so on. When constructing the profile of the sedimentary layer, , if at this time The maximum width of the contour of the layer is no longer the width of the contour endpoint. Then the solution method of the first case is used to obtain the contour of multiple layers.

[0159] S7. Based on the single-pass single-layer deposition profile, a rapid prediction of the laser coaxial powder feeding multi-layer deposition profile is achieved.

[0160] In one embodiment, the profile curve is optimized based on the single-pass single-layer deposition profile. The steps of the optimization process are as follows:

[0161] First, the historical data of equipment parameters and process parameters are used to train the prediction model of the single-pass single-layer deposition profile in single-pass multi-layer deposition to obtain the optimized prediction model of the single-pass single-layer deposition profile.

[0162] Further, according to the optimization prediction model, an optimized single-pass single-layer deposition profile is obtained;

[0163] Furthermore, according to the optimized single-pass single-layer deposition profile, a direct stacking construction method or an indirect stacking construction method is used to obtain an optimized single-pass multilayer deposition profile, such as Figure 12 As shown;

[0164] Furthermore, the optimized single-pass multi-layer deposition profile is used to quickly predict the laser coaxial powder feeding multi-layer deposition profile.

[0165] In summary, the surface profile efficient prediction model established by the present invention greatly improves the efficiency of component surface morphology prediction under different process parameter combinations, reduces the trial and error costs of a large number of experiments, produces excellent economic benefits, and shortens the calculation time of high-fidelity numerical simulation from "days" to "seconds", making it possible to predict the surface forming quality in real time. The present invention first derives physical quantities such as the spatial distribution position of powder during coaxial powder feeding based on geometric relationships. At the same time, based on parameters such as powder volume fraction, a theoretical model considering the laser shielding effect is established to correct the heat source power model. Subsequently, based on the above-mentioned heat source model, the influence of heat loss and phase change is considered on the basis of the Eagar-Tsai model to realize the prediction of the spatial distribution of the temperature field. Furthermore, based on the spatial distribution of the temperature field, the melting size and morphology are obtained. According to the relationship between the conservation of mass and the conservation of momentum of the fluid, the area of ​​the cross section of the cladding layer is preliminarily determined. Since the morphology is affected by the surface tension of the liquid metal, the Young-Laplace equation is used to describe it to obtain the equilibrium relationship between the surface tension and the pressure difference. On this basis, according to the relationship between conservation of mass and conservation of momentum, a semi-analytical solution of the geometric configuration of stacking in the multi-layer scanning process was further established, and finally an efficient prediction model of surface forming quality was established to achieve rapid and accurate prediction of the contours of components of laser coaxial powder feeding technology, forming a relatively rich mapping relationship map between process parameters and deposited layer contours, which strongly supports the research on the optimization of the "shape control" process parameters of laser coaxial powder feeding.

[0166] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or make equivalent replacements for some or all of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and description of the present invention.

Claims

1. A method for rapid prediction of multi-layer deposition profile using coaxial laser powder feeding, characterized in that: The method comprises the following steps: Obtain the spatial distribution of powder concentration; Using the spatial distribution, obtaining the laser intensity distribution after powder shielding; obtaining a substrate temperature field according to the laser intensity distribution; The contact angle and cross-sectional area of ​​the deposited layer are obtained through the substrate temperature field, including: Obtaining the size of the molten pool through the substrate temperature field; Based on the molten pool size, obtaining powder utilization and contact angle of the deposited layer; Obtaining a cross-sectional area of ​​a deposited layer according to the powder utilization rate; Based on the contact angle and the cross-sectional area, a prediction model for a single-pass single-layer deposition profile is constructed, comprising: Based on the contact angle, the cross-sectional area and the Young-Laplace equation, a prediction model for a single-pass single-layer deposition profile is constructed. The Young-Laplace equation satisfies the following expression: in, is the surface tension coefficient, is the contour curvature, is the pressure difference between the gas and liquid surfaces; The prediction model of the single-pass single-layer deposition profile satisfies the following expression: in, is the surface tension coefficient, is the first-order derivative of the distance between the contour curve and the central axis, is the second-order derivative of the distance between the contour curve and the central axis, is the coefficient, is the gravity state value, is the material density, is the single-channel single-layer deposition profile, is the liquid metal volume fraction; Obtaining a single-pass multi-layer deposition profile based on the prediction model; According to the single-pass multi-layer deposition profile, a rapid prediction of the laser coaxial powder feeding multi-layer deposition profile is achieved.

2. The method for rapid prediction of multi-layer deposition profile by laser coaxial powder feeding according to claim 1, characterized in that: The obtaining of the spatial distribution of powder concentration comprises: The spatial distribution of powder concentration in the front waist region, waist region, and back waist region is obtained. The spatial distribution includes an annular Gaussian distribution in the front waist region, a circular Gaussian distribution in the waist region, and a divergent distribution in the back waist region. The spatial distribution satisfies the following expression: in, is the powder concentration in the space, is the powder concentration in the plane, 、 is the distribution radius of the powder on the horizontal plane in different areas, is the horizontal distance from the center of the powder flow to the center line, is the regional boundary distance of the powder flow, is the distance to the focal plane, is the radial coordinate in space, is the spatial azimuth, is the space height, is the distribution of powder concentration in the transverse plane.

3. The method for rapid prediction of multi-layer deposition profile by laser coaxial powder feeding according to claim 1, characterized in that: The method of obtaining the laser intensity distribution after powder shielding by utilizing the spatial distribution includes: The laser intensity distribution after powder shielding is obtained by using the spatial distribution and the Gaussian intensity distribution of the surface heat source. The laser intensity distribution satisfies the following expression: in, is the intensity distribution after laser attenuation, is the Gaussian intensity distribution of the surface heat source, is the powder concentration in the space, is the powder radius, is the vertical coordinate of the initial contact point between the laser and the powder flow, is the radial coordinate in space, is the spatial azimuth, The height of the space.

4. The method for rapid prediction of multi-layer deposition profile by laser coaxial powder feeding according to claim 1, characterized in that: The obtaining of the substrate temperature field according to the laser intensity distribution comprises: According to the laser intensity distribution, an analytical model of the substrate temperature field under a moving Gaussian heat source is established; Obtaining the upper surface temperature of the substrate through the analytical model; Obtaining heat loss power on the upper surface of the substrate according to the upper surface temperature of the substrate; The substrate temperature field is obtained based on the heat loss power on the upper surface of the substrate and the analytical solution of the analytical model.

5. The method for rapid prediction of multi-layer deposition profile using coaxial laser powder feeding according to claim 4, characterized in that: The temperature increment of the substrate temperature field satisfies the following expression: in, is the temperature increment, is the laser power, is the heat loss power on the substrate surface, is the standard deviation of laser intensity, is the absorption rate, is the material density, is the gravity state value, is the material specific heat, is the thermal conductivity of the material, is the laser moving speed, is the moving time step, is the reference time step, 、 、 is the spatial coordinate point.

6. The method for rapid prediction of multi-layer deposition profile by laser coaxial powder feeding according to claim 1, characterized in that: Obtaining a single-pass multi-layer deposition profile based on the prediction model includes: Obtaining a single-pass single-layer deposition profile based on the prediction model; The single-pass single-layer deposition profile is processed using a profile construction method to obtain a single-pass multi-layer deposition profile.

7. The method for rapid prediction of multi-layer deposition profile using coaxial laser powder feeding according to claim 6, characterized in that: The outline construction method includes a direct stacking construction method and an indirect stacking construction method of the outline; The direct stacking construction method includes a construction method in which multiple single-layer deposited layer sections are directly stacked after considering the melting area; The indirect stacking construction method includes a construction method in which the cross-sectional areas of multiple single-layer deposited layers are first superimposed and then stacked.

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