CN119407203B - A rapid prediction method for multi-layer deposition profile using coaxial laser powder feeding - Google Patents
A rapid prediction method for multi-layer deposition profile using coaxial laser powder feedingInfo
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- B33Y10/00—Processes of additive manufacturing
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Abstract
本发明涉及金属增材制造技术领域，具体涉及一种激光同轴送粉多层沉积轮廓快速预测方法。所述方法包括如下步骤：获取粉末浓度的空间分布；利用所述空间分布，获得粉末遮蔽后的激光强度分布；根据所述激光强度分布，获得基板温度场；通过所述基板温度场，获得沉积层的接触角和截面面积；基于所述接触角和所述截面面积，构建单道单层沉积轮廓的预测模型；依据所述预测模型，获得单道多层沉积轮廓；根据所述单道多层沉积轮廓，实现对激光同轴送粉多层沉积层轮廓的快速预测。本发明极大提升了不同工艺参数组合下的构件表面形貌预测效率，有效解决了实验过程复杂和成本高的问题，也解决了数值模拟空间分辨率高、计算规模大和时间成本高的问题。
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
The invention relates to the technical field of metal additive manufacturing, in particular to a laser coaxial powder feeding multilayer deposition profile rapid prediction method.
Background
The laser coaxial powder feeding is an important technology in metal additive manufacturing, and the technology utilizes a carrier gas type powder feeder to convey metal powder, and the powder flow is conveyed into light spots, so that line-by-line and layer-by-layer deposition forming is realized. Has wide application prospect in the additive manufacturing of large-scale components and the composite and gradient component manufacturing of various materials on the same material. However, the laser coaxial powder feeding technology still faces many challenges in engineering application, especially in terms of surface forming quality control, surface defects such as uneven top surface, dimensional deviation, rough side wall, adhesion of unmelted powder, stacking corrugation of side wall and the like of a component still commonly exist, so that the subsequent finishing cutting allowance is large, and the real near-net forming is difficult to realize.
In the prior art, an experimental method or a numerical simulation method is generally adopted to study the surface forming quality. On the one hand, the acquisition of the forming quality characterization data through experiments is the most direct mode, but is limited by detection means and experimental cost, so that the research requirements under a large number of process parameter combinations are difficult to meet. On the other hand, the surface forming quality is researched through numerical simulation, a high-fidelity model is required to be established to describe the fine defects, but due to high spatial resolution and large calculation scale, the calculation time of a single calculation example is usually more than tens of hours, the requirement of efficient prediction is difficult to meet, and in addition, a theory or analysis model can directly embody physical meaning, but is limited by the complexity of physical problems, and the complex physical phenomenon is difficult to accurately describe. Therefore, it is highly desirable to establish an efficient, accurate and physically significant prediction method to achieve rapid mapping of process parameters to component surface profiles.
At present, the research work for the laser coaxial powder feeding multilayer deposition profile is not much, and a specific laser coaxial powder feeding multilayer deposition profile prediction method with low cost, high precision and high efficiency is not available.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a laser coaxial powder feeding multilayer deposition profile rapid prediction method.
The invention provides a laser coaxial powder feeding multilayer deposition profile rapid prediction method, which comprises the following steps:
The method comprises the steps of obtaining spatial distribution of powder concentration, obtaining laser intensity distribution after powder shielding by utilizing the spatial distribution, obtaining a substrate temperature field according to the laser intensity distribution, obtaining a contact angle and a cross-sectional area of a deposition layer through the substrate temperature field, constructing a single-channel single-layer deposition profile prediction model based on the contact angle and the cross-sectional area, obtaining a single-channel multi-layer deposition profile according to the prediction model, and realizing rapid prediction of the laser coaxial powder feeding multi-layer deposition profile according to the single-channel multi-layer deposition profile. The invention greatly improves the predicting efficiency of the surface morphology of the component under the combination of different technological parameters, reduces the trial-and-error cost of a large number of experiments, generates excellent economic benefit, shortens the calculating time of the high-fidelity numerical simulation 'day' level to the 'second' level, enables the real-time predicting of the surface forming quality to be possible, effectively solves the problems of complex process and high cost existing in the acquisition of the profile of the deposition layer through experiments, and also solves the problems of high spatial resolution, large calculating scale and low efficiency existing in the solution of the profile of the deposition layer through numerical simulation.
Optionally, the acquiring the spatial distribution of the powder concentration includes acquiring the spatial distribution of the powder concentration in the front waist region, the waist region and the rear waist region, the spatial distribution including an annular gaussian distribution of the front waist region, a circular gaussian distribution of the waist region and a divergent distribution of the rear waist region, the spatial distribution satisfying the following expression:
Wherein, the For the concentration of the powder in the space,In order to obtain a concentration of powder in the plane,、For the radius of distribution of the powder at the level of the different areas,For the horizontal distance of the powder flow center to the center line,For the area demarcation distance of the powder flow,Is the distance of the focal plane and,In the form of a spatial radial coordinate,As the attitude of the vehicle,In the form of a space-height,Is the distribution of the powder concentration in the transverse plane. The invention clearly depicts the distribution characteristics of the powder concentration in the front and back and the central part of the space waist region through the space distribution expression of the powder concentration, not only effectively reflects the distribution characteristics of the powder concentration in different regions, but also provides important clues for understanding the space distribution rule of the powder.
Optionally, the obtaining the laser intensity distribution after powder shielding by using the spatial distribution comprises obtaining the laser intensity distribution after powder shielding by using the spatial distribution and the surface heat source Gaussian intensity distribution, wherein the laser intensity distribution satisfies the following expression:
Wherein, the For the intensity distribution after the laser light has been attenuated,For a gaussian intensity distribution of the surface heat source,For the concentration of the powder in the space,In order to achieve a powder radius,For the vertical axis coordinates of the initial point of contact of the laser with the powder stream,In the form of a spatial radial coordinate,As the attitude of the vehicle,Is a space height. According to the invention, through the spatial distribution of the powder concentration and the Gaussian intensity distribution of the surface heat source, the laser intensity distribution expression after powder shielding is constructed, the non-uniformity of the powder concentration in the space is considered, and the intensity distribution characteristic of the laser source is considered, so that the laser intensity distribution after powder shielding can be more accurately obtained, and the method has important significance in scientific research and industrial application.
Optionally, the step of obtaining the substrate temperature field according to the laser intensity distribution comprises the steps of establishing an analysis model of the substrate temperature field under a mobile Gaussian heat source according to the laser intensity distribution, obtaining the upper surface temperature of the substrate through the analysis model, obtaining the heat loss power of the upper surface of the substrate according to the upper surface temperature of the substrate, and obtaining the substrate temperature field based on the heat loss power of the upper surface of the substrate and the analysis solution of the analysis model. The present invention describes the complete process of deriving the substrate temperature field from the laser intensity distribution. The method has the advantages that the analysis model of the substrate temperature field under the mobile Gaussian heat source is established by utilizing laser intensity distribution, a basis is provided for subsequent calculation, the temperature of the upper surface of the substrate is calculated through the analysis model, an important index for evaluating the laser heat effect is obtained, the heat loss power of the upper surface of the substrate is deduced according to the temperature of the upper surface of the substrate, the heat loss condition of the heat on the upper surface of the substrate is reflected, and the substrate temperature field is obtained through the analysis solution of the upper surface heat loss power and the analysis model, so that accurate mapping from the laser intensity to the substrate temperature field is realized.
Optionally, the temperature increment of the substrate temperature field satisfies the following expression:
Wherein, the In order to increase the temperature of the product,For the laser power to be high,Power is lost to the upper surface of the substrate,Is the standard deviation of the intensity of the laser,In order for the absorption rate to be high,In order to achieve a material density of the material,Is the value of the state of gravity,For the specific heat of the material,Is made of a material with a heat conductivity coefficient,In order to achieve the speed of movement of the laser,In order to move the time step over,For the reference time step(s),、、Is a spatial coordinate point. The invention constructs the temperature increment expression of the substrate temperature field by considering the heat loss power of the upper surface of the substrate, and is used for describing the dynamic change of the substrate temperature field. The expression has the following effects that the heat loss power of the upper surface of the substrate is taken into consideration, the temperature of the substrate is regulated along with the change of the heat loss in the laser processing process, the thermal effect of the laser and the substrate during interaction can be more accurately analyzed, the key links such as heat absorption, heat conduction and heat dissipation are included, the theoretical basis is provided for accurately controlling the temperature distribution in the laser processing process, the process parameters are helped to be optimized, the thermal deformation and the thermal stress are reduced, the processing quality and the processing efficiency are improved, and the expression has important significance in the high-precision processing fields such as laser cutting, welding and cladding.
Optionally, the step of obtaining the contact angle and the cross-sectional area of the deposition layer through the substrate temperature field comprises the steps of obtaining a molten pool size through the substrate temperature field, obtaining the powder utilization rate and the contact angle of the deposition layer based on the molten pool size, and obtaining the cross-sectional area of the deposition layer according to the powder utilization rate. The invention precisely deduces the key characteristics of the deposition layer through the temperature field of the substrate. The method has the advantages that firstly, the size of a molten pool is accurately measured by using the distribution information of a substrate temperature field, the size of the molten pool not only reflects the efficiency of a melting process, but also directly influences the formation of a subsequent deposition layer, secondly, the powder utilization rate for measuring the use efficiency of materials and the contact angle of the deposition layer for revealing the bonding state between the deposition layer and the substrate are calculated based on the size of the molten pool, which is important for ensuring the stability and strength of the deposition layer, thirdly, the cross-sectional area of the deposition layer is deduced by using the powder utilization rate, and the cross-sectional area reflects the shape and the size of the deposition layer, so that the method has important reference value for evaluating the deposition effect and the subsequent processing.
Optionally, constructing the prediction model of the single-channel monolayer deposition profile based on the contact angle and the cross-sectional area comprises constructing the prediction model of the single-channel monolayer 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:
Wherein, the As a function of the surface tension coefficient,For the curvature of the profile,Is the pressure difference of the gas-liquid surface. The single-channel single-layer deposition contour prediction model constructed by the invention fully utilizes three key elements of a contact angle, a cross-sectional area and a Young-Laplace equation. The method has the specific effects that firstly, the contact angle is used as an important index of interface characteristics between the deposition layer and the substrate, key information about the expansion trend of the deposition layer is provided for a model, secondly, the cross-sectional area directly reflects the form and the size of the deposition layer and becomes data necessary for predicting the deposition profile, thirdly, the introduced Young-Laplace equation describes the relationship between the liquid interface curvature and the interface tension, and the expansion and the form change of the deposition layer on the substrate can be more accurately represented by combining the contact angle and the cross-sectional area.
Optionally, the predictive model of the single-pass single-layer deposition profile satisfies the following expression:
Wherein, the As a function of the surface tension coefficient,As the first derivative of the distance of the profile curve from the central axis,As the second derivative of the profile curve from the center axis distance,As the coefficient of the light-emitting diode,The value of the state of gravity is calculated,In order to achieve a material density of the material,Is a single pass single layer deposition profile,Is the liquid metal volume fraction. The prediction model constructed by the invention is an advanced expression integrating scientificity, practicability and accuracy, skillfully integrates the physical principle of a Young-Laplace equation, thereby ensuring the accuracy and reliability of a prediction result, providing powerful support for the optimization of a deposition process, and injecting new vitality for the research and development of related fields.
Optionally, obtaining the single-channel multi-layer deposition profile according to the prediction model comprises obtaining a single-channel single-layer deposition profile according to the prediction model, and performing profile processing on the single-channel single-layer deposition profile by using a profile construction mode to obtain the single-channel multi-layer deposition profile. The method obtains the single-channel multi-layer deposition profile through the single-channel single-layer deposition profile prediction model, the whole process shows technical advancement and practicability, the profile processing mode 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.
The outline building method comprises a direct stacking building method and an indirect stacking building method of outlines, wherein the direct stacking building method comprises a building method that a plurality of single-layer deposition layer sections are directly stacked after melting areas are considered, and the indirect stacking building method comprises a building method that the cross-sectional areas of the single-layer deposition layer sections are stacked first and then stacked. The invention discloses a direct stacking construction mode and an indirect stacking construction mode in a contour construction mode, wherein the direct stacking construction mode emphasizes the direct superposition of the cross-sectional area of each single-layer deposition layer after the fusion area is considered, and can be closer to the fusion combination between layers in the actual deposition process, so that the construction precision is improved.
Drawings
FIG. 1 is a flow chart of a method for rapidly predicting a laser coaxial powder feeding multilayer deposition profile according to an embodiment of the invention;
FIG. 2 is a flow chart of performing calculations according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a laser coaxial powder feeding process according to an embodiment of the present invention;
FIG. 4 is a schematic illustration of the geometric profile of a nozzle and powder flow thereunder according to an embodiment of the present invention;
FIG. 5 is a schematic illustration of powder-to-laser shielding in a micro-element according to an embodiment of the present invention;
FIG. 6 is a flow chart of heat loss power calculation according to an embodiment of the present invention;
FIG. 7 is a top view of a laser coaxial powder feeding process according to an embodiment of the present invention;
FIG. 8 is a schematic diagram of a laser coaxial powder feeding model according to an embodiment of the present invention;
FIG. 9 is a schematic cross-sectional view of a cladding layer according to an embodiment of the present invention;
FIG. 10 is a flow chart of a single pass single layer deposition profile calculation in accordance with an embodiment of the present invention;
FIG. 11 is a schematic cross-sectional view of a single pass multilayer deposition in accordance with an embodiment of the present invention;
FIG. 12 is a schematic illustration of single pass multi-layer deposition in accordance with an embodiment of the present invention.
Detailed Description
Specific embodiments of the invention will be described in detail below, it being noted that the embodiments described herein are for illustration only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. It will be apparent, however, to one skilled in the art that these specific details need not be employed to practice the present invention. In other instances, well-known circuits, software, or methods have not been described in detail in order not to obscure the invention.
Reference throughout this specification to "one embodiment," "an embodiment," "one example," or "an example" means 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. Thus, the appearances of the phrases "in one embodiment," "in an embodiment," "one 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 combination and/or sub-combination in one or more embodiments or examples. Moreover, those of ordinary skill in the art will appreciate that the illustrations provided herein are for illustrative purposes and that the illustrations are not necessarily drawn to scale.
Referring to fig. 1, an embodiment of the present invention provides a method for rapidly predicting a laser coaxial powder feeding multi-layer deposition profile, which includes the following steps:
S1, obtaining the spatial distribution of the powder concentration.
In one embodiment, the nozzle parameters and powder spatial distribution parameters are measured based on a laser coaxial powder delivery process. The laser coaxial powder feeding process is shown in figure 2, and the laser beam is processed at a processing speedAlong the positive directionAnd scanning in the direction, wherein the origin of coordinates of the scanning is fixed at the center of a laser beam spot on the substrate. The distance between the coaxial powder feeding nozzle and the plane of the substrate is. The laser beam passes through the central cavity of the nozzle and the powder particles are conveyed in a conical annular channel coaxial with the laser beam. The geometric profile of the nozzle and the powder flow thereunder on any vertical symmetry plane is shown in fig. 3.
Further, on the nozzle outlet plane, at the originFor the center of the nozzle, a coordinate system is established. The included angle of the annular channel relative to the central line (Z axis) is. The powder flow will typically diverge to some extent at the nozzle outlet with an angle of up-down divergence ofAnd. The powder particles ejected from the annular outlet flow downwards, and the laser beam and the powder flow are arranged in the annular outletThe points then interact and the powder flow undergoes a converging-then-diverging process.
Further, according to the distribution characteristics of the powder on horizontal sections at different positions, the powder flow is roughly divided into three areas, namely a front waist area of annular Gaussian distribution, a waist area of circular Gaussian distribution and a rear waist area of divergent distribution, wherein the analytical expression of the powder concentration spatial distribution is as follows:
Wherein, the For the concentration of the powder in the space,In order to obtain a concentration of powder in the plane,、For the radius of distribution of the powder at the level of the different areas,For the horizontal distance of the powder flow center to the center line,For the area demarcation distance of the powder flow,Is the distance of the focal plane and,In the form of a spatial radial coordinate,As the attitude of the vehicle,In the form of a space-height,Is the distribution of the powder concentration in the transverse plane. Wherein, the The following expression is satisfied:
It should be noted that the distribution of the 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 stream is proportional to the powder concentration. Therefore, the brightness distribution in the photographed powder flow front image reflects the distribution of the powder flow density, i.e., the greater the brightness, the greater the density, and the smaller the brightness, the smaller the density.
Further, the image is converted into a gray image by image processing software, and the brightness of the powder flow is converted into gray intensity.
Further, pairs of gray images at different locationsAndFitting to obtain a concentration distribution analysis solution.
S2, obtaining laser intensity distribution after powder shielding by utilizing the spatial distribution.
In one embodiment, the laser intensity distribution after powder masking is studied based on the spatial distribution of the powder flow and the attenuation effect of the powder on the laser intensity.
Specifically, in the present embodiment, a gaussian distribution of surface heat sources is employed, the intensity distribution of whichThe following expression is satisfied:
Wherein, the For the laser power to be high,Is the radius of the laser spot,For the distance from the laser center to be found. The attenuation of the laser power intensity by the powder flow can be calculated according to the intensity distribution expression of the Gaussian distribution surface heat source, as shown in FIG. 4, the area is selected asThe height isIs a very small element of (a). Attenuation coefficientAnd laser intensity in a infinitesimalThe following relationship is satisfied:
Wherein, the The shadow area, which is a powder, can be expressed as:
Wherein, the Is the radius of the powder.
Further, the attenuation coefficientThe following expression is satisfied:
further, the above is in the interval Integrating, thus, the total attenuation of the laser intensityCan be expressed as:
Wherein, the For initial contact of the laser with the powder flowThe vertical axis coordinates of the points are shown in fig. 4. Intensity distribution after laser attenuationThe solution can be found by:
Wherein, the For the intensity distribution after the laser light has been attenuated,For a gaussian intensity distribution of the surface heat source,For the concentration of the powder in the space,In order to achieve a powder radius,In the form of a spatial radial coordinate,As the attitude of the vehicle,Is a space height.
S3, obtaining a substrate temperature field according to the laser intensity distribution.
Wherein, step S3 further comprises the following steps:
s31, establishing an analysis model of the substrate temperature field under the mobile Gaussian heat source according to the laser intensity distribution.
In one embodiment, the process of creating an analytical model of the substrate temperature field under a moving gaussian heat source is as follows:
first, in the solid domain, regardless of convection within the puddle, the heat transfer equation can be written as:
Wherein, the Is the temperature of the liquid at which the liquid is to be cooled,Is the density of the material, which is the density of the material,Is the specific heat of the material,Is the heat conductivity coefficient of the material,Is a laser heat source.Is a source term for the phase change introduction of materials, and can be expressed as:
Wherein, the In order to achieve the density of the metal material,Is the latent heat of fusion of the metallic material,As a liquid metal volume fraction, it can be expressed as:
Wherein, the For solidus, liquidus temperatures of materials, an arctangent function can be introduced to approximateThe expression is as follows:
Wherein, the Obtained by fitting and then pairingThe derivative is expressed as:
further, will The definition is as follows:
further, the heat transfer equation is organized as:
It should be noted that the laser intensity distribution represents Is a distribution of (a). The laser beam interacts with the powder and the temperature of the powder is raised while the laser intensity is attenuated by the powder flow. The total attenuation can be divided into the sum of powder absorption and scattering. In the laser coaxial powder feeding process, the scattering phenomenon can be ignored because the size of the powder is far larger than the wavelength of the laser, and most of the attenuated laser energy is absorbed by the powder.
Further, the analytical solution of the instantaneous point heat source is solved by integrating the whole interval by using the green function method.
Specifically, by superposing the instantaneous gaussian surface heat sources in a continuous sequence and at a certain distance and rest intervals, a temperature response expression of the moving gaussian surface heat source when moving on the semi-infinite medium surface is obtained. When the laser power isAt a speed ofEdge of the flangeAxis movement, absorptivity isThe temperature increment analysis solution is as follows:
Wherein, the For the standard deviation of laser intensity, the time is extremely short, assuming thatIs constant, and can be obtained by the following steps:
Wherein, the In order to increase the temperature of the product,For the laser power to be high,In order for the absorption rate to be high,In order to achieve a material density of the material,Is the value of the state of gravity,For the specific heat of the material,Is made of a material with a heat conductivity coefficient,In order to move the time step over,For the reference time step(s),、、Is a spatial coordinate point.
S32, obtaining the upper surface temperature of the substrate through the analysis model.
In one embodiment, the change in material properties with temperature is consideredThe influence of (2) to the timeDivided into a plurality of time steps with time intervals ofCalculating the temperature field after each time step, thereby updating the material properties and the next calculated material propertiesTherefore, the upper surface temperature of the substrate satisfies the following relation:
Wherein, the The upper surface temperature of the substrate can be represented and solved by a temperature increment analysis solution expressionTaking material parametersMaterial properties at temperatureTemperature increment of point。
S33, obtaining the heat loss power of the upper surface of the substrate according to the temperature of the upper surface of the substrate.
In one embodiment, the heat loss is equivalent to the power loss of the upper surface of the substrate, i.e. the heat loss powerWhich satisfies the following relation:
Wherein, the In order to be at the temperature of the environment,For the convective heat transfer coefficient,For the stefin-boltzmann constant,In order for the emissivity to be high,Is the latent heat of vaporization of the material,In order to be a molar mass of the molecule,The pressure of the air is set to be the atmospheric pressure,Is a gas constant which is a general purpose gas constant,Is the upper surface area of the substrate.
S34, obtaining a substrate temperature field based on the heat loss power of the upper surface of the substrate and the analytic solution of the analytic model.
In one embodiment, considering the heat loss power, in combination with the expression of the temperature increment resolution, the final temperature increment may be obtained as follows:
further, to determine each time step Finding the appropriate one in an iterative mannerThe flow is as in fig. 5. And updating the power considering the heat loss in each time step, and solving the temperature field through a temperature field analysis model.
S4, obtaining the contact angle and the cross-sectional area of the deposited layer through the substrate temperature field.
Wherein, step S4 further comprises the following steps:
s41, obtaining the size of a molten pool through the substrate temperature field.
In one embodiment, the projection of the puddle onto the substrate surface is approximated by a solid-liquid line, as shown in FIG. 6. The points A, B, C and D are positioned on the boundary of the molten pool, and the expression of the solution can be obtained according to the temperature increment analysis:
further, the bath boundary may be approximated as two semi-ellipses, and the solidus may thus be expressed as:
S42, based on the size of the molten pool, obtaining the powder utilization rate and the contact angle of the deposited layer.
In one embodiment, it is determined that only powder entering the molten pool is utilized according to an expression of a shadow area of the powder, the molten pool is divided into two semi-ellipses with a heat source center as a boundary point, powder concentrations at respective positions are found according to a spatial distribution expression of the powder concentrations, the spatial distribution expression of the powder concentrations is integrated on the two semi-ellipses, and a utilization ratio of the powder is obtained, the utilization ratio of the powder satisfying the following expression:
Wherein, the Is the molten pool area.
Further, a contact angle of the deposit layer is calculated from a bath boundary line expression, the expression of the contact angle being as follows:
s43, obtaining the cross-sectional area of the deposited layer according to the powder utilization rate.
In one embodiment, the area of the cross section of the deposited layer is calculated according to the scanning speed, the powder feeding speed and the powder utilization rate, and the area of the cross section of the deposited layer meets the following expression:
Wherein, the Is the powder feeding rate.
S5, constructing a single-channel monolayer deposition profile prediction model based on the contact angle and the cross-sectional area.
In one embodiment, the surface tension of the deposited layer is first described using the Young-Laplace equation, which is as follows:
Wherein, the As a function of the surface tension coefficient,For the curvature of the profile,Is the pressure difference of the gas-liquid surface. According to the assumption that the curvature radius of the surface of the deposition layer along the Y axis is infinite curvature, the curvature is as follows:
Wherein R is the radius of the contour curve from the central axis, where Respectively isIs used for the first and second derivatives of (a),Is a single pass single layer deposition profile.
Further, to simplify the modeling process, the fluid momentum equation is written in the form of:
Where ρ is the density and g is the gravity state value. Let the pressure at the top of the radius be The fluid momentum equation can be written as:
Wherein, the Substituting the contour curvature and the fluid momentum equation into a Young-Laplace equation to obtain a sedimentary layer contour equation for coefficients related to the contour top curvature and the sedimentary layer height, wherein the sedimentary layer contour equation is as follows:
Further, to avoid singularities in the equation, it is assumed that the profile of the deposited layer at a small distance from the top is parabolic, expressed as:
Wherein, the Is a coefficient.
Further, according to the parabolic expression and the sedimentary layer profile equation, and takingAt the same time, the following steps are obtained:
further, the deposition layer profile equation is arranged to obtain a single-channel single-layer deposition profile prediction model, and the prediction model meets the following expression:
Wherein, the As a function of the surface tension coefficient,As the first derivative of the distance of the profile curve from the central axis,As the second derivative of the profile curve from the center axis distance,As the coefficient of the light-emitting diode,The value of the state of gravity is calculated,In order to achieve a material density of the material,Is a single pass single layer deposition profile,Is the liquid metal volume fraction.
It should be noted that the process of laser coaxial powder feeding processing is shown in fig. 7, and the shape of the liquid metal is mainly affected by surface tension, gravity and pressure. In order to describe the shape of the deposited layer in the process, the following assumption is made that the metal is in a liquid state before the stress reaches equilibrium, the deposited layer is symmetrically distributed, and the surface of the deposited layer is alongThe radius of curvature of the axis is infinite and the Marangoni effect acts primarily in the tangential direction, so its effect on the surface of the deposited layer is exerted indirectly by influencing the flow rate, which is neglected here.
S6, obtaining a single-channel single-layer deposition profile according to the prediction model.
Wherein, step S6 further comprises the following steps:
s61, obtaining a single-channel multilayer deposition profile according to the prediction model.
In one embodiment, a particle swarm optimization algorithm is used to solve for the single-pass monolayer deposition profile based on its predictive modelAnd (3) withIs a solution to the optimization of (3). First, a high-fidelity numerical model is adopted for the contact angleAnd (3) calibrating, namely associating the calibration value with the technological parameter, and taking the calibrated value as a model input parameter, wherein the surface tension coefficient is regarded as a constant.
Further, for the theoretical model after calibration, the unknown sediment layer height is obtained through a fourth-order Runge-Kutta algorithmCoefficient ofThe calculated contour area and contact angleCompared with the known values, the optimal solution is obtained through a particle swarm optimization algorithm, and a single-channel single-layer deposition profile curve under a specific working condition can be rapidly calculated usually only by 0.1s, and the flow is shown in fig. 9.
S62, performing contour processing on the single-channel single-layer deposition contour by utilizing a contour construction mode to obtain a single-channel multi-layer deposition contour.
For multi-layer deposition, the laser printing head is lifted to a certain height before each deposition along the same path and in the same direction, so that a thin-wall workpiece is obtained. The processing is simplified as shown in fig. 10, where points M and N are two end points of the deposited layer, and assuming that the deposited width and the cross-sectional area of each layer are unchanged, two situations occur in the processing, namely, the maximum width of the surface profile of the deposited layer of the first layer exceeds the bottom width of the deposited layer, and the maximum width of the surface profile of the deposited layer of the first layer is the bottom width.
When the first case is encountered, in one embodiment, the single-pass multi-layer profile is built by a direct stack build-up comprising a build-up in which a plurality of single-layer deposited layer sections are directly stacked after consideration of the melt area.
Specifically, the deposited layer profile of the first layer is determined according to the geometric prediction result of the single-channel single-layer deposited profileAndAnd (5) point coordinates.
Further, the endpoint coordinates of the next layer are determinedAndCoordinates of pointsThe coordinates are not changed and the coordinate values are not changed,The coordinates take the maximum value of the layer profile and the cross-sectional area of the next layer。Powder utilization efficiency solving is performed on a new plane after the profile of the upper deposition layer and the laser head are lifted by a certain height, as shown in fig. 11, namely:
Wherein, the Is the firstThe secondary deposition lifts the melting areas with different heights, the melting shape is assumed to be the same as the shape of the initial molten pool, and the geometric outline of the next layer is determined according to the endpoint coordinates, the cross-sectional area and the same geometric prediction method of the single-channel single-layer deposition outline, so that the multi-layer outline is solved.
When the second situation is encountered, in another embodiment, a single-channel multi-layer profile is constructed by an indirect stacking construction mode of stacking first and then stacking, wherein the indirect stacking construction mode comprises a construction mode of stacking a plurality of single-layer deposition layer sections first in cross-sectional area and then stacking.
Specifically, according to a prediction model of a single-channel single-layer deposition profile, determining a first layer deposition layer profile and a second layer deposition layer profileA point(s),A point coordinate;
further, the end point of the second layer is maintained AndIs not changed, and the cross-sectional area of the second layer is solved based on the powder utilization efficiency taking the melting area into consideration, Determining the profile of the second layer by a single pass single layer deposition profile geometry prediction method, and so on, in the firstIn the construction of the layer profile of the layer deposition,If at this time the firstThe maximum width of the layer appearance outline is no longer the width of the outline endpoint, and then the first case solving method is adopted to obtain the multi-layer outline.
S7, according to the single-channel single-layer deposition profile, the laser coaxial powder feeding multi-layer deposition profile is rapidly predicted.
In one embodiment, the profile curve optimization is performed according to the single-channel single-layer deposition profile. The optimizing process comprises the following steps:
Firstly, carrying out model training on a prediction model of a single-channel single-layer deposition contour in single-channel multi-layer deposition by utilizing historical data of equipment parameters and process parameters to obtain an optimized prediction model of the single-channel single-layer deposition contour;
Further, according to the optimized prediction model, an optimized single-channel single-layer deposition profile is obtained;
Further, according to the optimized single-channel single-layer deposition profile, the optimized single-channel multi-layer deposition profile is obtained by using a direct stacking construction mode or an indirect stacking construction mode, as shown in fig. 12;
Further, the optimized single-channel multilayer deposition profile is used for realizing rapid prediction of the laser coaxial powder feeding multilayer deposition profile.
In summary, the efficient surface profile prediction model established by the invention greatly improves the prediction efficiency of the surface profile of the component under different process parameter combinations, reduces the trial-and-error cost of a large number of experiments, generates excellent economic benefits, shortens the calculation time of the high-fidelity numerical simulation 'day' level to the 'second' level, and enables the real-time prediction of the surface forming quality to be possible. According to the invention, firstly, physical quantities such as the spatial distribution position of powder and the like in the coaxial powder feeding process are deduced according to the geometric relationship. Meanwhile, according to parameters such as the volume fraction of the powder, a theoretical model considering the laser shielding effect is established, and the heat source power model is corrected. Then, according to the heat source model, the influence of heat loss and phase change is considered on the basis of Eagar-Tsai model, so that the prediction of the spatial distribution of the temperature field is realized. Furthermore, on the basis of the spatial distribution of the temperature field, the melting size and morphology are obtained. And preliminarily determining the area of the cross section of the cladding layer according to the relation between the conservation of fluid mass and the conservation of momentum. As the morphology is influenced by the surface tension of the liquid metal, the equilibrium relationship between the surface tension and the pressure difference is obtained by describing the morphology by using a Young-Laplace equation. On the basis, according to the mass conservation and momentum conservation relations, a semi-analytical solution of the stacked geometric configuration in the multilayer scanning process is further established, and finally, a high-efficiency prediction model of the surface forming quality is established, so that the rapid and accurate prediction of the contour of the laser coaxial powder feeding technical component is realized, a map of the mapping relation between the richer technological parameters and the contour of the sedimentary layer is formed, and the optimization research of the technological parameters of the shape control of the laser coaxial powder feeding is powerfully supported.
It should be noted that the above embodiments are only used to illustrate the technical solution of the present invention, but not to limit the technical solution of the present invention, and although the detailed description of the present invention is given with reference to the above embodiments, it should be understood by those skilled in the art that the technical solution described in the above embodiments may be modified or some or all technical features may be equivalently replaced, and these modifications or substitutions do not make the essence of the corresponding technical solution deviate from the scope of the technical solution of the embodiments of the present invention, and all the modifications or substitutions are included in the scope of the claims and the specification of the present invention.
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