Powder bed melt scan parameters and process monitoring based on calibrated molten pool model

Abstract

A method of generating scan parameters for a powder bed melt additive manufacturing process, the method comprising: receiving at least one desired characteristic (105) of a material modification zone formed by exposing a powder bed to an energy beam to melt the material and / or alter the microstructure of the material; and determining a scanning parameter (106) of the energy beam estimated by the powder bed melting model to produce a material modified zone having a characteristic corresponding to the at least one desired characteristic (105). The powder bed fusion model may include a lookup table or function that associates the at least one characteristic with one or more scan parameters. The generation of the lookup table or function may include receiving a measured or numerically calculated characteristic of a material modification zone for each of a plurality of material modification zones formed by exposing the material to an energy beam to melt the material and / or alter the microstructure of the material, each material modification area is generated by using different groups of scanning parameters; calibrating parameters of the powder bed melt model using the measured or numerically calculated characteristics to provide a calibrated powder bed melt model; and generating a lookup table or function based on the calibrated powder bed fusion model. The calibrated powder bed melting model may be used to inspect a powder bed melting process or equipment. The powder bed melt model may include a heat conduction model that models a material modification zone using an equivalent volume heat source.

Description

Technical Field

[0001] The present invention relates to improvements in or relating to powder bed fusion, and in particular to modeling of powder bed fusion processes. Modeling can be applied in the process of generating scanning parameters for a powder bed fusion process or characterizing or validating a powder bed fusion process. The powder bed fusion process can be characterized by the temperature in a material modification zone formed by exposing the powder bed to an energy beam to melt the material and / or change the microstructure of the material. The powder bed fusion process can be characterized by the shape of the material modification zone, such as its depth, width and / or length. The model can be used to predict the characteristics of a material modification zone (such as a molten pool) generated by energy beam exposure based on input parameters (such as scanning parameters). Background Art

[0002] Powder bed fusion is an additive manufacturing (AM) process that builds metal parts layer by layer by selectively melting regions of a powder bed with an energy beam, such as a laser or electron beam. Much research is currently being devoted to the numerical simulation of this process.

[0003] Acta Materialia 108 36-45 (2016), SA Khairallah, AT Anderson, A. Rubenchik, WE King, “Laser powder bed fusion additive manufacturing: Physics of complex melt flow and formation mechanism ofpores, spatter and denudation zones” discloses mesoscale multiphysics numerical models describing the interaction of the heat source with the substrate and powder layer, which incorporate temperature-dependent properties (e.g., viscosity, surface tension) and effects (e.g., vapor pressure and buoyancy) in the molten metal. Such models are computationally intensive and are currently limited to single laser scan tracks of a few millimeters in length. However, they provide useful insights into the relevant physics and mechanisms of pore and spatter generation. X. Li, C. Zhao, T. Sun, and W. Tan, “Revealing transient powder-gas interaction in laser powderbed fusion process through multi-physics modeling and high-speed synchrotron x-ray imaging,” Additive Manufacturing 35 101362 (2020), and Y. A. Mayi, M. Dal, P. Peyre, M. Bellet, C. Metton, C. Moriconi, and R. Fabbro, “Laser-induced plume investigated by finite element modelling and scaling of particle entrainment in laser powder bed fusion,” Journal of Physics D - Applied Physics 53(7) 075306 (2020). In their paper “Mesoscale fusion”, they extended the mesoscale model to combine incompressible condensed phases (solid and liquid metal) with compressible gas phases (vapor metal and shielding gas) to study ablation due to the motion of individual powder particles, but so far only for laser spot illumination.

[0004] Introducing simplifying assumptions into the underlying physics in the numerical model means that detailed effects such as splash generation are excluded, but solving the model is less computationally intensive.

[0005] C. Bruna-Rosso, AG Demir, and B. Previtali, “Selective laser melting finite element modeling: Validation with high-speed imaging and lack of fusion defects prediction,” Materials & Design, 156, 143-153 (2018), discloses modeling powder bed melting using a volume source. The volume source was experimentally calibrated based on micrographs of a cross section of the melt pool and images of the top surface along the length of the melt pool. The range of laser power and scan speed restricts the melt pool to a conduction mode for which a volume source is not optimal.

[0006] EJ Schwalbach, SPDonegan, MG Chapman, KJ Chaput, MA Groeber, "A discrete source model of powder bed fusion additive manufacturing thermal history", Additive Manufacturing, 25, 485-498 (2019), calibrated a volumetric source for modeling powder bed fusion that includes a depth component proportional to the depth-to-width aspect ratio of the melt pool. The fit was performed only in the center of a relatively narrow range of laser power and scan speed process settings, without taking into account the length of the source. Summary of the invention

[0007] According to a first aspect of the present invention, a method for generating scanning parameters for a powder bed fusion additive manufacturing process is provided, the method comprising: receiving at least one desired characteristic of a material modification zone, which is formed by exposing a powder bed to an energy beam to melt the material and / or change the microstructure of the material; and determining scanning parameters of the energy beam estimated by a powder bed fusion model to produce a material modification zone having characteristics corresponding to the at least one desired characteristic.

[0008] In this way, instead of selecting a set of scanning parameters, the user sets the desired results (properties) for the material modification zone method and derives the scanning parameters from them. The desired property can be a non-transient property of the material modification zone that remains after the material modification zone solidifies. For example, a mechanical property, such as microstructure, grain orientation or residual stress; or a geometric property, such as the size of the material modification zone. Alternatively, the desired property can be a transient property of the material modification zone that exists only during the molten pool formation process, preferably a spatial transient property. For example, a thermal property, such as the temperature distribution on the material modification zone, a temperature isosurface, a spatial or temporal temperature gradient of the material modification zone, or a cooling rate. The property can exist in the melting mode (conduction, transition or keyhole mode) in which the material modification zone is to be formed. Since the conduction of heat through the object depends on the geometry of the part, the energy required to achieve the desired property may be different in different areas of the part being built. Therefore, even if the desired property of different exposures is the same, different scanning parameters can be determined for these different exposures. The property is the temperature reached during the melting process or is related to the temperature.

[0009] The property corresponding to the at least one desired property may be a property that is related to or matches the desired property.Thus, the property of the material modification zone is selected or determined based on the desired property.

[0010] The method may include determining a spatial distribution of temperature based on desired characteristics of the material modification zone, and solving a model of the spatial distribution of temperature to determine scanning parameters.

[0011] The material modified zone may be a molten zone (a zone of molten material, such as a melt pool) and / or a heat affected zone (HAZ). A heat affected zone is a region of solidified material, such as a solid material formed by melting a powder using a previous exposure, which is not melted by the exposure, but the exposure causes heating of the solidified material, thereby causing a change in its microstructure. The material modified zone may be a zone defined by a phase change boundary in the heat affected zone or the molten zone. The material modified zone may be a zone defined by a solidus and / or liquidus boundary.

[0012] The desired characteristic may be a size (e.g., depth, width, and / or length) of the material modified zone, and the method generates scan parameters predicted to produce a material modified zone of such size. In one embodiment, the at least one desired dimension is the melt pool depth and the melt pool length. The melt pool width may be derived from another parameter, such as from the melt pool depth (e.g., based on a desired melt pool aspect ratio) or from the energy beam spot diameter, such as 1 / e 2 Spot diameter.

[0013] The method may include determining scanning parameters estimated by a powder bed fusion model to produce a molten pool in a transition mode. It will be understood that "conduction mode" as used herein means that the energy of the energy beam is coupled into the powder bed primarily by thermal conduction, thereby producing a molten pool having a width greater than depth. This is in contrast to a keyhole mode, in which a hole is formed in the molten pool in which the material is vaporized by exposure to the energy beam. The molten pool formed in the keyhole mode has a deep and narrow profile with a depth-to-width ratio greater than 1.5. There is a transition mode between the conduction mode and the keyhole mode, in which energy is not dissipated quickly enough and the processing temperature is raised above the vaporization temperature. The depth of the molten pool increases, and penetration of the molten pool can begin. A molten pool in a transition mode typically has a depth-to-width ratio greater than 0.5 but less than 1.5.

[0014] The powder bed fusion model may include a lookup table or function that associates the at least one desired characteristic with one or more scanning parameters. The lookup table or function may include or define intermediate values ​​extrapolated from measured melt pool characteristics under known scanning parameters (e.g., the model has been calibrated based on experimental data or numerical data generated by a mesoscale multiphysics numerical model and intermediate values ​​extrapolated therefrom). The lookup table or function may define a relationship between the at least one desired characteristic and the scanning parameters. The lookup table or function may associate the desired characteristic with energy density, power density, energy beam power and / or scanning speed. The lookup table or function may associate the desired characteristic with different scanning parameters based on the initial temperature of the material.

[0015] The energy density E can be related to the power density of the energy beam by the following equation: Related to the scanning speed or equivalent scanning speed v:

[0016]

[0017] An equivalent scan speed can be determined for a scan defined as a number of point exposures, typically defined by point distance and exposure time (and optionally a jump delay) rather than by scan speed. The powder density can be converted to Related to the laser power q and the energy beam spot diameter d:

[0018]

[0019] Thus, the scanning parameters of scanning speed, spot distance, spot exposure time, energy beam power and / or energy beam spot diameter / size can be determined by the energy beam density, which is determined by solving the model for the desired size. The scanning parameters can include the laser fill spacing. The scanning parameters can include the cyclic frequency at which the cyclic scanning path cycles back to intersect itself (such as a prolate cycloid scanning path).

[0020] The powder bed fusion model can be a heat conduction model. The powder bed fusion model can be a heat conduction only model, in which heat transfer due to radiation, evaporation and convection in the molten pool is neglected. This simplification assumes that conduction dominates when removing heat from the material modification zone, and it can be assumed that for the powder bed fusion model, the calculated temperature in the solid material up to the boundary of the material modification zone is sufficiently accurate. The powder bed fusion model can be a finite difference, finite volume finite element model. The powder bed fusion model can model the latent heat of fusion and / or temperature dependence properties of the material undergoing melting / microstructural changes.

[0021] The powder bed fusion model can take into account the initial temperature of the powder when it is exposed to the energy beam. The powder bed fusion model can determine the initial temperature of each exposure point based on the position and time when the powder was previously exposed to the energy beam. The estimated energy density required to achieve the desired characteristics of the material modification zone will vary with different initial temperatures at the exposure point. The powder bed fusion model can determine the initial temperature based on the geometry of the part being built. For example, the cooling rate of the exposure point can vary depending on whether the exposure point is adjacent to the solidified material or powder and / or is located above the solidified material or powder. The initial temperature can be calculated based on the position of the exposure in the scan path (such as a laser fill line) (at the beginning, middle or end of the scan path) and / or whether the exposure is adjacent to another scan path (such as a laser fill line) and / or whether the molten powder is higher than the solidified material or powder. The initial temperature can be determined based on the width of the solidified material adjacent to the exposure and / or the thickness of the solidified material below the exposure. The initial temperature can be determined using a sensor that measures the temperature of the powder bed and / or the solidified material. For example, the sensor can be an infrared sensor, such as an IR camera. Thus, the method may include receiving a geometric definition of a part and generating scanning parameters based on the received geometric definition.

[0022] Solving the powder bed fusion model can include using an equivalent volumetric heat source having a size corresponding to the at least one desired size of the material modification zone to estimate the heat input to be supplied to such a volumetric heat source. Based on the estimated heat input, scanning parameters can be determined. For example, solving the powder bed fusion model can include estimating the required energy density using an equivalent volumetric heat source having a size corresponding to the at least one desired size.

[0023] The method may include receiving thermal properties of a material of a part to be built using a powder bed fusion additive manufacturing process and using the thermal properties to solve a powder bed fusion model. The method may include receiving an identification of a material and retrieving the thermal properties of the material from a memory.

[0024] The method can generate scanning parameters that vary between exposure points along the scanning path. In this way, these scanning parameters differ from traditional scanning parameters that are usually fixed for the scanning path.

[0025] The steps of the first aspect described above may be implemented by a computer.

[0026] According to a second aspect of the invention, there is provided a method of manufacturing a part, the method comprising building the part by employing powder bed fusion using scanning parameters determined using the method according to the first aspect of the invention.

[0027] According to a third aspect of the present invention, there is provided a data carrier having instructions thereon, wherein when the instructions are executed by a processor of a powder bed fusion additive manufacturing apparatus, the processor controls the powder bed fusion additive manufacturing apparatus to perform the method of the second aspect of the present invention.

[0028] According to a fourth aspect of the present invention, a method for generating a lookup table or function for the first aspect of the present invention is provided, the method comprising: for each of a plurality of material modification zones formed by exposing the material to an energy beam to melt the material and / or change the microstructure of the material, receiving measured or numerically calculated properties of the material modification zone, each material modification zone being generated using a different set of scanning parameters; using the measured or numerically calculated properties to calibrate parameters of a powder bed fusion model to provide a calibrated powder bed fusion model; and generating a lookup table or function based on the calibrated powder bed fusion model.

[0029] The characteristic of the material modified zone may be a geometric characteristic of the material modified zone, such as a size. The material modified zone may be a zone defined by a phase change boundary in a heat affected zone or a molten zone. Thus, the material modified zone may represent a measurement of a zone where the temperature is increased above a phase change temperature, such as above a melting point temperature (solidus temperature or liquidus temperature) due to exposure or above a temperature that causes grain refinement. Thus, the method may include extracting the spatial distribution of the temperature measurements from the size of the material modified zone.

[0030] The characteristic may be measured using a sensor during the melting process. For example, the characteristic may include a temperature (or a value derived from the temperature, such as an average value) measured in the material modification zone using a sensor (such as an infrared imaging sensor). For example, the infrared imaging sensor may be able to measure the temperature of the top surface of the molten pool. Alternatively, the characteristic may include the size of the material modification zone measured using an imaging sensor (such as a camera), or a size inferred from a measurement of another characteristic of the melting process (or a value derived from the size, such as an average value). For example, the melting pattern and therefore the shape of the molten pool can be determined by measuring the turbulence of the generated plasma plume, as disclosed in PCT / GB 2022 / 050677, the entire contents of which are incorporated herein by reference.

[0031] The method can use the Inverse Heat Conduction Problem (IHCP) approach to calibrate the powder bed fusion model. The advantage of the IHCP approach is that it enables a systematic calibration of the powder bed fusion model. Physical effects that are computationally expensive to model, such as heat absorption from real sources and Marangoni convection in the melt pool, can be implicitly incorporated into the powder bed fusion model. The parameters of the powder bed fusion model can describe the equivalent heat source used in the powder bed fusion model to represent regions with temperatures above the phase change temperature as determined by measured or calculated values ​​of the material modification zone. With the set functional form of the equivalent heat source, the IHCP method is simplified to estimating a limited number of parameters describing the equivalent heat source.

[0032] The equivalent heat source may include a volumetric heat source. The volumetric heat source may be defined by two segments of curved three-dimensional shapes. The two curved three-dimensional shapes may not contain vertices or edges. The equivalent volumetric heat source may include a front segment that models the front of the molten pool in the scanning direction and a rear segment that models the rear of the molten pool in the scanning direction. The front segment includes a planar top surface, a planar rear surface, and a continuous curved front surface extending from the edge of the planar top surface to the edge of the planar rear surface. The rear segment may include a planar top surface, a planar front surface, and a continuous curved rear surface extending from the edge of the planar top surface to the edge of the planar front surface. The rear surface of the front segment and the front surface of the rear segment may be coincident. The curved surfaces of the two segments may be discontinuous at the boundary between the two segments (wherein the rear surface of the front segment coincides with the front surface of the rear segment). By allowing a discontinuity at the boundary between the two sections, the length of the rear section can be increased without distributing an increased proportion of the energy beam power to the rear section, which would reduce penetration of the front section. It is believed that this more accurately reproduces the penetration observed in powder bed fusion experiments. The two sections will typically be different, for example having different lengths, widths and / or depths.

[0033] The equivalent volume heat source may comprise a dual ellipsoidal volume heat source.The term "dual ellipsoidal volume heat source" as used herein refers to a volume defined by segments of two ellipsoids.

[0034] The equivalent heat source may include a combination of volumetric heat sources and point and / or line heat sources.

[0035] Generating a lookup table or function may include using a calibrated powder bed fusion model to differentially calculate scanning parameters that produce a material modification zone with intermediate characteristics based on measured or numerically calculated characteristics. The characteristic may be the depth of the equivalent heat source. Additionally or alternatively, the characteristic may be the absorptivity of the equivalent heat source. Further additionally or alternatively, the characteristic may be the length of the equivalent heat source. The length of the equivalent heat source may be the length from the rear section of the equivalent heat source to the front section of the equivalent heat source. The lookup table or function may relate the characteristics of the material modification zone to the energy density or power density of the energy beam used in the powder bed fusion additive manufacturing process.

[0036] The steps of the fourth aspect above may be implemented by a computer.

[0037] The method may include melting the material at different points in the powder bed or on the substrate using different sets of scanning parameters. The method may include measuring properties of the subsequently solidified material at the different points.

[0038] According to a fifth aspect of the present invention, a method for inspecting a powder bed fusion process or a powder bed fusion device that performs the powder bed fusion process comprises: receiving measured properties of a material modification zone formed by exposing the material to an energy beam to melt the material and / or change the microstructure of the material; and determining whether the powder bed fusion process or the powder bed fusion device has changed by comparing the measured properties with properties predicted by a powder bed fusion model calibrated using measurement values ​​obtained from a previous powder bed fusion process.

[0039] For example, the powder bed fusion model may be calibrated using melt pool measurements obtained from material previously solidified by the powder bed fusion apparatus. If the difference between the size of the melt pool produced during a later powder bed fusion process and the size predicted by the calibrated powder bed fusion model is outside an acceptable range, this may indicate that the conditions produced by the powder bed fusion apparatus have drifted by an unacceptable amount. The method may include generating an alarm if the difference is outside an acceptable range.

[0040] The powder bed fusion model may be calibrated for a powder bed fusion machine. For example, the coupling of the laser beam to the powder may be different for different powder bed fusion machines, and therefore, the powder bed fusion model may need to be calibrated individually for different machines. A change in the melt pool size measured at a later date from the melt pool size predicted by the powder bed fusion model may indicate a change or drift in the powder bed fusion machine or process.

[0041] The powder bed fusion model may be in accordance with the powder bed fusion model described with respect to other aspects of the present invention.

[0042] According to a sixth aspect of the present invention, there is provided a data carrier having instructions thereon, wherein when the instructions are executed by a processor, the processor is caused to execute the methods of the first, fourth and fifth aspects of the present invention.

[0043] According to a seventh aspect of the present invention, there is provided a device comprising a processor, the processor being arranged to perform the method of the first, fourth or fifth aspect of the present invention.

[0044] The data carrier of any of the aspects of the present invention may be a suitable medium for providing instructions to a machine, such as a non-transitory data carrier, for example a floppy disk, CD ROM, DVD ROM / RAM (including -R / -RW and +R / +RW), HD DVD, BluRay (TM) optical disk, memory (such as Memory Stick (TM), SD card, Compact Flash card, etc.), disk drive (such as hard disk drive), magnetic tape, any magnetic / optical storage; or a transient data carrier, such as a signal on a wire or optical fiber or a wireless signal, such as a signal sent on a wired or wireless network (such as Internet download, FTP transfer, etc.). BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a schematic diagram of an apparatus according to an embodiment of the present invention;

[0046] Figure 2 shows the double ellipsoidal volume heat source given by equation (1), where σ x1 = σ y , σ x2 = 4σ x1 , and σ z = 3σ x1 . (a) r1 = 0.6, such that r1 / σ x1 > r2 / σ x2 (b) Source continuity on the plane x = 0 requires r1 / σ x1 = r2 / σ x2 ;

[0047] Figure 3 shows the temperature distribution around the heat source (in K), where: (a) Figure 2 (a) Volume heat source, laser spot diameter d = 4σ y = 50 μm; (b) the source is a point heat source at d = 0 μm; (c) the Figure 3 (b) The difference between the temperature and the analytical solution of equation (7) (in K);

[0048] Figure 4 Shown are the melt pool solidification boundaries obtained from a micrograph of a single track experiment. This is a composite image: the tracks are spaced 1 mm apart on the substrate;

[0049] Figure 5 is the objective function F(η, 2σ z , 2σ x2 ) example, based on Figure 4 Calculated from a single trajectory experiment at v = 0.8 m / s. (a) Objective function plotted over the range of three parameters describing the double ellipsoidal heat source, where η is the absorptivity, 2σ z is the depth, and σ x2 / σ x1 is the length of the posterior ellipsoid relative to the anterior ellipsoid. The minimum value confirmed is at η = 0.73, 2σ z = 93 μm, and σ x2 / σ x2 = 8.85. (b)-(d) Objective functions on the plane passing through the minimum value shown in (a), where “X” indicates the fitted minimum value on each plane;

[0050] Figure 6 Shown are the fitted parameters describing the volumetric heat source for a single-track experiment: (a) absorptivity, η; (b) depth, 2σ z ; and (c) the length of the posterior ellipsoid relative to the anterior ellipsoid, σ x2 / σ x1 ;

[0051] Figure 7 Shown are the temperature distributions (in K) around a volume heat source fitted to the melt pool boundary for a single-track experiment at: (a) 0.7 m / s; (b) 1.0 m / s; (c) 1.4 m / s; and (d) 1.8 m / s. Figure 4 The experimental melt pool boundary points used for fitting are shown as white dots in the front view. The target melt pool length used in the fitting is indicated by a white circle in the side view;

[0052] Figure 8Examples of island scanning micrographs: (a) substrate only, 200 W, 1.0 m / s; (d) with powder, 200 W, 0.8 m / s. Temperature distributions calculated from the fitted volumetric heat source: (b) and (d) correspond to (a) and (c), respectively, using the same Figure 7 The same temperature scale, and at T = T m The solidification boundary of the molten pool at is the white line;

[0053] Fig. 9 The results of island scans of the substrate only at the indicated laser powers and scan speeds are shown. The left half of each image shows a micrograph of the first track of each island. The right half of each image shows the melt pool boundary points obtained from the micrographs, which are reflected in the line y = 0, shown as white points. It also shows the temperature distribution calculated from the fitted volumetric heat source in each case, using the same Figure 7 Same temperature scale, T = T m The solidification boundary of the molten pool at is shown as a white line;

[0054] Fig.10 The results of island scans with powder layers at the indicated laser powers and scan speeds are shown. The left half of each image shows a micrograph of the first trajectory for each island. The right half of each image shows the melt pool boundary points obtained from the micrographs, which are reflected in the line y = 0, shown as white points. It also shows the temperature distribution calculated from the fitted volumetric heat source in each case, using the same Figure 7 Same temperature scale, T = T m The solidification boundary of the molten pool at is shown as a white line;

[0055] Fig.11 Shown are the fitted parameters describing the volumetric heat source for the island scanning experiment: (a) absorptivity, η; (b) depth, 2σ z ; (c) and (d) the length of the posterior ellipsoid relative to the anterior ellipsoid, σ x2 / σ x1 The fitted heat source parameters for the single-track experiments are also included. Material properties for Ti-6Al-4V: α = 9.44 × 10 -6 m 2 / s, k = 32.67 W / (m K), and T m = 1970 K. The legend shown in (b) is the same for all figures;

[0056] Fig.12Energy density plotted against experimental melt pool depth for all results is shown. Ti-6Al-4V results calculated based on melt pool depth from: JJS Dilip, S Zhang, C. Teng, K. Zeng, C. Robinson, D. Pal, and B. Stucker, “Influence of processing parameters on the evolution of melt pool, porosity, and microstructures in Ti-6Al-4V alloy parts fabricated by selective laser melting,” Progress in Additive Manufacturing, 2 157-167 (2017);

[0057] Fig.13 a is a plot of the experimentally measured melt pool depths of adjacent tracks (laser filling lines) in island scanning under different scanning parameters versus the distance from the island edge when the first track is formed; Fig.13 b is the initial temperature of the powder bed at the exposure point of the island scan predicted by the heat accumulation model under different scanning parameters; and Fig.13 c is the relationship between the predicted initial temperature of the powder bed and the resulting melt pool depth for different scanning parameters used in the lookup table or function; and

[0058] Fig.14 is a schematic diagram showing the island and laser fill line at distance y. DETAILED DESCRIPTION

[0059] refer to Figure 1, the apparatus comprises a computer 101, the computer comprising a memory 102. The computer is arranged to receive a geometrical definition 104 of a part to be built using a powder bed fusion apparatus (e.g. in the form of an STL or CAD file), and at least one desired characteristic 105 of a material modification zone formed by exposing a powder bed to an energy beam to melt the material and / or change the microstructure of the material. In this embodiment, the characteristic is a melt pool size 105. A computer program is stored in the memory of the computer 101, which causes a processor 101a of the computer 101 to generate scanning parameters of a powder bed fusion process for building a part based on the received geometrical definition of the part and at least one desired melt pool size 105 (such as width, depth, length and / or aspect ratio). The melt pool size can be specified directly by a user, or can be specified by reference to the desired microstructure of the part or melt pool mode (conduction, transition or keyhole mode). For example, certain melt pool shapes and geometric arrangements of the melt pool can produce specific microstructures, such as those described in WO 2020 / 249932 and WO 2021 / 234368, the entire contents of which are incorporated herein by reference. The melt pool size can specify an acceptable range of melt pool sizes. The input can also include a confirmation of the material of the part to be built, the computer program is configured to cause the processor to retrieve the thermal properties of the material stored therein from the memory 102, and / or the user can confirm the properties of the material. In this embodiment, the thermal properties of the material are the thermal conductivity, thermal diffusivity, and melting temperature of the material.

[0060] The computer program is configured to generate scan parameters for building a part predicted by the powder bed fusion model to obtain a melt pool size that matches the at least one desired melt pool size 105. The powder bed fusion model used in this embodiment is a conduction-only model using a volumetric heat source calibrated based on experimental results as described below.

[0061] The computer 101 generates a build file 106 including scanning parameters, and the build file 106 is sent to the powder bed fusion additive manufacturing device 103. The powder bed fusion additive manufacturing device 103 can then be made to build a part according to the instructions of the build file 106. The computer 101, the memory 102, and the powder bed fusion additive manufacturing device 103 can be located locally or remotely from each other.

[0062] Powder Bed Fusion Model

[0063] The direct heat conduction problem uses known heat input parameters (such as laser power, scanning speed and spot diameter) and material thermal properties to calculate the temperature distribution. The powder bed fusion model of this embodiment considers the opposite direction: it uses the temperature distribution (herein referred to as the equivalent heat source) (such as the measured or expected melt pool size) to estimate the heat input of known thermal properties, or to estimate the thermal properties of a known heat input; called the inverse heat conduction problem (IHCP).

[0064] The advantage of the IHCP method is that physical effects that are computationally expensive to model, such as heat absorption from real sources and Marangoni convection in the melt pool, are implicitly incorporated into the equivalent heat source. If the functional form of the heat source (representing the equivalent heat source of the melt pool) is assumed, the IHCP method can be reduced to estimating a finite number of parameters that describe it. Minimizing the objective function that defines the functional form of the heat source becomes a least squares fit to an overdetermined system of equations.

[0065] In this embodiment, a dual ellipsoidal volume heat source proposed in J. Goldak, A. Chakravarti, and M. Bibby, "A new finite-element model for welding heat-sources," Metallurgical Transactions B - Process Metallurgy, 15(2) 299-305 (1984) is used as the functional form of the equivalent heat source. It is believed that the dual ellipsoidal volume heat source represents the increased penetration of the weld pool front due to vapor depression during powder bed melting.

[0066] The power density Q (in W / m3) of the double ellipsoidal volume heat source is given by equation (1), as Figure 2 shown.

[0067] (1)

[0068] where the subscripts i = 1,2 denote two ellipsoids, one in front of the plane x = 0 and the other behind it. Each ellipsoid represents a two-dimensional Gaussian distribution on the top surface z = 0 combined with a Gaussian distribution in the z direction. The laser is assumed to scan in the positive x direction. The width of the Gaussian in each direction is described by its standard deviation σ. For fiber laser processing, 1 / e 2 The beam diameter d = 4σ is generally accepted. The front and rear heat source ellipsoids described by equation (1) extend to infinite volume in all directions, including negative z values ​​above the substrate surface in the plane z = 0. Therefore, the total power absorbed in the infinite volume is given by:

[0069] ηq = r1ηq + r2ηq, that is, r1 + r2 = 1(2)

[0070] where q is the laser power (in W), η is the absorptivity, and r i (a number between 0 and 1) is the fraction of the laser power in the front and back ellipsoids. This relationship is consistent with analytical calculations of the temperature distribution from the applied heat source: the total power is applied to an infinite volume, and the subsequent integration restricts the region of interest to the substrate in a semi-infinite volume below the plane z = 0.

[0071] Figure 2 The heat source of equation (1) is shown, where z ≥ 0, i.e. within the semi-infinite volume of the workpiece. The black outlines indicate the ± 2σ range of the two ellipsoids in all directions. The width of both ellipsoids is the same and is assumed to be equal to the laser spot diameter 4σ y = d. The length of the front ellipsoid is assumed to be equal to the laser spot radius, i.e. 2σ x1 = d / 2 or 2σ x1 = 2σ y The remaining properties of the source must be determined by calibration: the depths of the two ellipsoids are given by 2σ z Given, the independent length of the posterior ellipsoid is given by 2σ x2 and the absorption rate η is defined. Figure 2 (a) shows σ x2 = 4σ x1 and r1 = 0.6. The red shading indicates the constant power density surface, where the power density on the ± 2σ boundaries of the front ellipsoid is taken. Figure 2 The value chosen in (a), r1 / σ x1 > r2 / σ x2 , and hence the power density on the ± 2σ boundaries of the front ellipsoid is greater than that of the rear ellipsoid: Therefore, Figure 2 The constant power density surface of the posterior ellipsoid in (a) is closer to the origin.

[0072] To avoid specifying r1, we can assume that the source is continuous on the plane x = 0, as Figure 2 (b), which requires r1 / σ in equation (2) x1 = r2 / σ x2 However, it has been found that in many cases this continuous heat source cannot reproduce the penetration observed in powder bed fusion experiments. This is because as the back ellipsoid length 2σ x2 As , the heat source continuity constraint requires that R2 also increase, thereby distributing a proportion of the increased laser power to the rear ellipsoid, reducing penetration in the front. Figure 2(a) and the choice of r1 is discussed later. The discontinuity in the power density on the plane x = 0 emphasizes that the equivalent heat source is not an exact model of the physical source, but rather a representation of the heat input that will produce the desired temperature distribution at the experimentally measured locations of the IHCP fit. Figure 2 The temperature field generated by the heat source in (a) is continuous, as shown below.

[0073] The IHCP method requires the calculation of the response function T at each location n using a direct conduction model of an equivalent heat source n :

[0074]

[0075] (3)

[0076] where φ x1 = 4α (t - τ) + 2σ x1 2 etc., α is the thermal diffusivity (in m 2 / s), k is the thermal conductivity (W / (mK)). T0 is the initial temperature of the semi-infinite domain at t = 0, and (x', y') is the position of the heat source on the surface z = 0 at time t.

[0077] By setting r1 = r2 = 0.5, σ x1 = σ x2 = σ y = σ and σ z = 0, we can get the known solution of the surface Gaussian heat source, thus:

[0078]

[0079]

[0080] (4)

[0081] In addition, the temperature distribution of the point source is obtained by setting σ = 0 in equation (5), thus obtaining:

[0082] (5)

[0083] Equation (5) has the advantage of being integrable to produce a steady-state analytical solution for a point source.

[0084] (6)

[0085] where ξ = x - vt represents a quasi-stationary reference frame, and r = .

[0086] Figure 3 (a) shows the temperature distribution calculated using equation (3) over an integration time sufficient for the temperature to reach a steady state in the plotted volume. The source parameters are Figure 2 (a) where d = 4σ y = 50 μm, and its ±2σ range is indicated by black lines in the side and front views. As mentioned above, the conduction model alone cannot give useful information about the interior of the molten pool, so above the melting temperature T m The upper limit of the temperature in the curve is T m The calculated melt pool boundary T = T m Indicated by the white line. The side view of the melt pool is taken in the plane y = 0. The front view is obtained by taking the highest temperature among all x values ​​at each yz position: it is equivalent to the melt pool cross section that will be recorded in the micrograph. All temperature distributions for the side and front views presented in this paper are calculated in this way. The material properties used in the calculations are those of stainless steel: α = 7.11 × 10 -6 m 2 / s, k = 35.14 W / (m K), and T m = 1648 K. These values ​​are used for all temperature calculations in this article: the choice of values ​​is discussed later.

[0087] Figure 3 (b) shows the temperature distribution calculated again using the semi-analytical solution of equation (3), but converting the volume heat source parameters to point heat sources: that is, r1 = r2 = 0.5, and σ x1 = σ x2 = σ y = σ z = 0. The integration time is sufficient for the temperature to reach a steady state in the plotted volume. Figure 3 (c) shows Figure 3 (b) and the analytical steady-state temperature of the point source given by equation (6). This difference is essentially zero everywhere at the level of numerical accuracy calculated. The largest difference occurs just below the point source due to singularities in the analytical solution: its magnitude is irrelevant and it occurs anyway at locations in the melt pool where the temperature is not of interest. The exact agreement between the semi-analytical and analytical solutions shows that equations (3) to (6) are consistent and that the numerical integration is performed exactly. The integration is performed in Matlab using the integrate() function, which uses adaptive quadrature to define the subintervals to automatically accommodate large changes in the gradient of the integral.

[0088] for Figure 3 a and Figure 3b Both, laser power q = 50 W, scanning speed v = 0.5 m / s.

[0089] Figure 3 It is shown that the double ellipsoid source can reproduce the increased penetration of the melt pool front compared to the point source, which reflects the effect of vapor depression. For the same laser power and scanning speed, the double ellipsoid source reduces the melt pool width and length on the top surface compared to the point source because the heat input increases through the source depth 2σ. z Distribute deeper into the material.

[0090] Example

[0091] Single-track experiments were performed in an open-architecture laser PBF system. Island scanning experiments were performed in a system with a flow straightener that provided a laminar flow of Ar gas through the powder bed at a speed of approximately 2.1 m / s. In all experiments, a single-mode fiber laser (SPI 400W CW, 1070 nm) was used with a focused 4Dσ diameter of 50 μm.

[0092] Single track experiments were performed only on substrates made of stainless steel SS304L (i.e. without powder), whose surface was roughened by manual circular rubbing with P400 sandpaper. Single tracks of 20 mm in length were recorded at different scanning speeds at a laser power of 200 W to obtain melt pool cross-sections from the conduction mode (1.8 m / s) up to the keyhole mode (0.5 m / s). A delay of about three minutes was set between scanning each track to allow the substrate to return to ambient temperature, which was monitored with a K-type thermocouple fixed to its rear surface. To produce micrographs, the samples were diamond cut perpendicular to the scanning direction and machine polished using silicon carbide abrasive papers (240 to 2000 grit) and cashmere cloth. The samples were then electrolytically etched at 10 V, 5 A in a solution of deanodized water and oxalic acid in a ratio of 10:1. The melt pool solidification boundary was imaged with a 20x objective on an Alicona Infinite Focus.

[0093] Island scanning experiments were performed on the substrate alone and on the substrate covered with a powder layer. The substrate was again stainless steel SS304L and the powder consisted of a 50 μm thick layer of gas atomized stainless steel SS316L with particle sizes ranging from 15 μm to 45 μm and an average diameter of 30 μm. 5 × 5 mm images were recorded at two laser powers (100 W and 200 W) and scan speeds ranging from 0.4 m / s to 1.0 m / s. 2The laser fill spacing between adjacent tracks in an island was 80 μm, and the laser off time was 1 ms. The sample was sectioned perpendicular to the scan direction at the center of the island, followed by the same polishing and etching process described previously. The specimen was again allowed to cool to ambient temperature between island scans in order to eliminate accumulated thermal effects.

[0094] result

[0095] Single track experiment

[0096] Figure 4 Shown are the melt pool solidification boundaries obtained from micrographs of a single track experiment. The laser power was q = 200 W and d = 50 μm at the indicated scanning speeds. Each boundary was manually sampled at 33 positions. The section at v = 0.5 m / s was excluded because it is clearly in an unstable keyhole mode: the small black areas are voids in the melt pool. The temperatures at these yz points on the melt pool boundaries correspond to the melting point T of the stainless steel. m These experimental temperature measurements used in equation (1) to adjust the three parameters describing the heat source, namely the absorptivity η and its depth 2σ z and the rear length 2σ x2 , to adjust the volume heat source T from equation (3) n The calculated temperature minimizes the objective function. At the two edges and the center of each molten pool, the weighted functions of these experimental points are added together. Set equal to 1: The weighting at the midpoint in each half of the melt pool follows a cosine curve. This approach emphasizes the influence of the melt pool width and depth on the fitting parameters and reduces the influence of the midpoint. The melt pool boundary is constantly subject to small perturbations, so we aim to capture the main features rather than trying to achieve an exact fit to the contour.

[0097] Figure 3 It shows that increasing the source depth by 2σ z While keeping other parameters constant, the length of the melt pool can be reduced. In practice, it can be expected that Marangoni convection and the momentum imparted by the recoil pressure lengthen the melt pool. Therefore, additional points are included in the fit of the rear of the melt pool on the top surface: this prevents the fitting of the melt pool cross section due to the source depth 2σ z As the absorption increases, the melt pool length will be unrealistically shortened while penetration increases. The melt pool length was not measured during these experiments. Instead, the temperature at a point corresponding to the calculated melt pool length for a Gaussian source with the same absorbed laser power, scanning speed, and spot diameter was included as an additional point in the objective function. The absorbed laser power included the current value of the absorptivity η during each iterative fit. The weighting function for this additional point is is set equal to the sum of all weighting factors for the melt pool boundary points so that length and boundary residuals have similar importance in the final fit. Experimental points incorporating the top surface of the melt pool are discussed later, but this does not affect the IHCP method proposed here.

[0098] For each melt pool, equation (1) was minimized at 34 points (33 cross sections, 1 length) to determine the heat source parameters η, 2σ z and 2σ x2 , i.e., the absorptivity, depth, and back length of the heat source. Due to the inherent constraint of the volume heat source in Eq. (3), no additional regularization term is required. The diameter of the heat source is fixed to match the laser spot diameter, d = 4σ y = 50 μm, the length of the front ellipsoid is set equal to the laser spot radius, d / 2 = 2σ x1 = 25 μm. The ratio of the laser power between the front and rear ellipsoids is set to r1 = 0.6, which will be discussed later. Minimization is performed in Matlab using the fminsearch() function. The initial condition for minimization represents a perfectly absorbing circular surface Gaussian source that matches the laser spot diameter, i.e., η = 1, 2σ z = 0, and 2σ x2 = 25 μm. The rear length parameter 2σ is expressed as the ratio σx2 / σx1 x2 This is convenient, since the front length 2σx1 = 25 μm remains constant during the fit: hence σ x2 / σ x1 = 1 is the initial condition for minimization. Figure 5 (a) shows an example of the objective function F(η, 2σz, 2σx2) computed for a three-dimensional volume for three fitting parameters. Computing the objective function for this volume is not necessary to perform the minimization: it is used here to demonstrate that the objective function is well behaved and a unique solution can be confirmed. Figure 5 (b) to Figure 5 (d) shows Figure 5 (a) Objective function on three orthogonal planes intersecting at their minimum. A unique solution was found for all reported experiments.

[0099] Figure 6 Three fitted heat source parameters determined at each laser scanning speed are shown. Figure 6 (a) shows that the fitted absorptivity η increases from ~0.4 at high speeds in the conduction melt pool mode to ~0.8 at lower speeds in the transition mode, which is consistent with experimental measurements. The absorptivity increases due to the increase in the depth of the stable vapor depression, which increases the depth-to-width aspect ratio of the melt pool. Therefore, the heat source depth 2σ at high speeds in the conduction mode is zis approximately zero, corresponding to a surface Gaussian distribution, Figure 6 (b). Source depth increases as velocity decreases, which corresponds to increased penetration at the front of the melt pool. Similarly, Figure 6 (c) shows the length 2σ of the rear ellipsoid at high scanning speed in conduction mode x2 This also corresponds to a ratio of σ x2 / σ x1 = 1. The length of the back ellipsoid increases at lower speeds so that with increasing source depth 2σ z Increase and maintain the melt pool length.

[0100] Figure 7 The melt pool profile calculated from the heat source using the fitting parameters is shown for a sample of laser scanning speeds. As mentioned above, the upper temperature limit is the melting point T m , the white line indicates the molten pool boundary T = T m , the black line shows the ± 2σ range of the volume heat source. Figure 4 The 33 experimental melt pool boundary points used to fit the heat source in the respective cases are shown as white dots in the front view. The melt pool boundary predicted by the fitted heat source agrees well with the experimental points. Additional points used in the fit of the target melt pool length on the top surface are shown as white circles in the side view. The IHCP fitting method is the same for all laser scan speeds and manages the continuity between the conduction melt pool mode profile and the transition melt pool mode distribution. The increased penetration at the front of the melt pool in the side view is consistent with the recent x-ray images.

[0101] Island scanning experiment

[0102] Figure 8 (a) shows an example micrograph recorded for the substrate only, and Figure 8 (c) shows an example micrograph with a powder layer. The first track is on the left of both images, with the laser scanning in alternating directions on each subsequent track. The entire 5 × 5 mm 2 First 20 tracks of an island. The buildup of heat during the island scanning process can be observed from the increase in cross-sectional area of ​​later tracks. The form of each track along the island is generally the same, however there are slight differences in the exact shape due to the constant fluctuation of the melt boundary, as observed by x-ray imaging. For powders, the slight variations in melt pool depth and shape are even more significant than for the substrate alone, due to fluctuations in absorbed laser power caused by the movement of the powder bed and powder particles above it. The accumulated powder bead is larger for the first track than for subsequent tracks, as powder can be rolled in from both sides of the melt pool.

[0103] Fig. 9 All island scan experimental results for substrate only are shown, Fig.10The results of island scanning experiments with powder are shown. The left half of each image shows a micrograph of the first trajectory of each island. The melt pool boundary position was sampled at 17 points, which are represented as white points in the right half of each image, reflected on the line y = 0. The right half of each image also shows the front view temperature distribution calculated with the fitted heat source parameters. The weight of the fit (by choosing the weighting function ) is the width and depth of the melt pool boundary, rather than the intermediate “wine glass” feature at low laser power and scan speed (e.g. Fig.10 , 100W, 0.4 m / s) and excessive penetration at high powers (e.g. Fig.10 , 200 W, 0.6 m / s); for laser powder bed melting, neither of these two profiles is usually preferred. Transition pool profiles (e.g. Fig.10 , 200 W, 0.8 m / s; and 100 W, 0.5 m / s) are generally preferred because they are more efficient than shallower conduction weld pool modes (e.g. Fig.10 , 100 W, 0.6 m / s), the transition pool profile improves the remelting efficiency.

[0104] Fig.11 (a) to Fig.11 (c) shows the plotted relationship between the three fitted heat source parameters and the experimental melt pool depth D for all island scans. Figure 5 The fitting parameters of the single-track experiment are also included. At a given laser power, the absorption rate η increases as the laser scanning speed decreases (i.e., as the melt pool depth increases). Fig.11 Figure 2.2 shows the average heat source depth of the stainless steel sample. The average heat source depth of the stainless steel sample was 2σ. The average heat source depth of the stainless steel sample was 2σ. The average heat source depth of the stainless steel sample was 2σ. The average heat source depth of the stainless steel sample was 2σ. The average heat source depth of the stainless steel sample was 2σ. The average heat source depth of the stainless steel sample was 2σ. z As the experimentally measured melt pool depth changes linearly, e.g. Fig.11 (b). However, the length of the heat source rear 2σ x2 There is no direct relationship between the depth of the molten pool, such as Fig.11 (c) shows a linear trend line to indicate the general trend: for a shallow molten pool in a conductive state, the heat source tends to an ideal surface Gaussian distribution, where σ x2 / σ x1 = 1 and 2σ z =0; As the depth of the molten pool increases and the absorbed power increases, the length of the heat source rear 2σ x2 Must be increased to achieve the target weld pool length. Fig.11(d) shows the change of the molten pool length L' in the molten pool calculated using the fitting parameters, where the fitting parameters include Fig.11 σ in (c) x2 / σ x1 The rear length of the heat source is given by 2σ x2 , set σ x2 / σ x1 = 1 and keep other fitting parameters unchanged. The increase of molten pool length is related to the rear length of heat source 2σ x2 There is a direct relationship between the target melt pool length and the powder layer. This increase can be applied regardless of how the target melt pool length is determined, such as calculation (as used here) or from experimental measurements. Overall, the powder layer was observed to have little effect on the melt pool profile below the surface, which corresponds to experimental observations of laser powder bed melting processes, where the laser directly interacts with the melt pool and the powder tumbles or is entrained into the melt trajectory.

[0105] Absorption rate η and depth 2σ z The heat source fitting parameters jointly influence the shape of the melt pool cross section, as indicated by their well-behaved relationship with the melt pool depth over a range of laser powers and scanning speeds, see Fig.11 (a) and Fig.11 (b) Increasing the absorptivity η, while keeping all other parameters constant, increases the cross-sectional area of ​​the melt pool, but its aspect ratio remains relatively unchanged. On the other hand, increasing the heat source depth 2σ z , while keeping all other parameters constant, will increase the melt pool aspect ratio. Fig.11 (d) shows the increase in the heat source rear length 2σ x2 Increases the length of the weld pool: it produces a small change in the cross-sectional profile of the weld pool. Fig.11 These observations provide insight into the characteristics of the volumetric heat source. For a given process setting, the melt pool depth needs to be measured experimentally before the source parameters can be determined. Therefore, more information is required if the heat source parameters are to be interpolated at intermediate process settings that were not used in the calibration experiments.

[0106] Energy density E = φ / v, where φ is the power density 4q / d 2 , can be used to predict the stability of vapor depressions under process settings typically used in laser powder bed fusion. In particular, a linear relationship is observed between the vapor depression depth and the energy density. This energy density depends only on the process settings (q, v, and d) and does not include the powder layer thickness or the laser filling spacing. Fig.12 The experimentally measured melt pool depths for all stainless steel experiments reported here are plotted versus energy density. Single-trace experiments were performed in a modified system of island scanning results, resulting in different linear fits in the two cases. The energy density therefore enables predictions of the melt pool depth, see Fig.12 , from which the melt pool depth can be determined the absorptivity η and the heat source depth 2σ at any intermediate process setting between those settings for which the experiment has been carried out z , see Fig.11 (a) and Fig.11 (b); then select the length 2σ behind the heat source x2 To increase the calculated melt pool length to the target value, see Fig.11 (d) Similarly, the model can be used to estimate the intermediate process settings required to produce a desired (user-specified) melt pool depth / size. Thus, the desired predictive capability for a range of laser powder bed melting settings can be achieved based on a relatively small set of calibration experiments.

[0107] The IHCP calibration described here provides a systematic approach to incorporating volumetric heat sources into semi-analytical and numerical conduction-only models. The heat sources indirectly incorporate more complex physical phenomena via calibration to experimental data, but at a significantly lower computational cost, enabling realistic effects such as absorptivity and remelting depth to be incorporated into process planning. Source calibration also incorporates machine-specific settings that affect the laser powder bed melting process. For example, Fig.12 It is shown that in the experimental system used to record the island scan, at a given line energy, the melt pool depth is greater than in the single track experiment: the differences between the systems include a stronger shielding gas cross-flow for the island scan, which improves the removal of process fumes. Fig.11 , at a given line energy, increasing depth produces different heat source parameters. The calibration method can therefore be used as a systematic approach to characterize individual laser powder bed fusion systems and quantify the inevitable drift in their settings over time.

[0108] Fig.12 The melt pool depths obtained from Ti-6Al-4V melt pool cross-sections recorded on a commercial EOS M270 PBF system over a range of laser powers and scan speeds are combined. It is believed that for other materials, only the melt pool depth and length need to be calibrated according to the energy density, and the fitting parameters η and 2σ obtained here for stainless steel and Ti-6Al-4V can be applied. z The relationship between.

[0109] It is beneficial to incorporate the melt pool length into the IHCP method: without incorporation, the heat source depth 2σ of the transition melt pool z The increase of will shorten the melt pool length, see Figure 3. For the results for stainless steel and Ti-6Al-4V, the melt pool length calculated using a Gaussian source (at the same absorbed laser power, scan speed, and spot diameter) is used. In practice, the experimental melt pool length can be longer: numerical modeling shows that including latent heat can increase the melt pool length by up to 34% compared to conduction alone. Alternatively, an experimentally measured melt pool length recorded under the same conditions as the melt pool cross section can be used. In practice, it is also feasible to combine experimental points from other locations around the melt pool boundary on the top surface. Fig.11 (d) shows the increase in target melt pool length and the length behind the heat source 2σ x2 Directly related, where the absorption rate η and the heat source 2σ z (which controls the melt pool size and aspect ratio) is very small. Finally, whatever method is used to determine the target melt pool length can be incorporated into the IHCP method presented in this paper.

[0110] Single track melt pool cross sections are often used to infer powder bed melting process settings, such as the Ti-6Al-4V results. However, the process evolves from the first track during the island scan due to the increase in temperature and adjacent beads from the previous track; the melt pool depth of adjacent tracks in the island scan may increase due to heat accumulation from the previous exposure. Similarly, the process evolves between layers, especially in layers 1 to 10, as the steady-state powder layer thickness is established. The calibration method can be extended to obtain heat source fit parameters that describe the evolution of different aspects of the process. For example, Figure 8 (b) and Figure 8 (d) shows the simulated melt pool profiles of subsequent tracks in the island scan without calibrating each track individually. Figure 8 and Fig. 9 The heat source is calibrated in the first trajectory, but for each trajectory, the source depth is 2σ z increases proportionally to the experimentally observed depth, which in turn correlates to a temperature increase in the workpiece.

[0111] The initial temperature of the powder bed can be calculated based on modeling the heat accumulation as it is scanned along a scan path (such as a laser fill line). Fig.13 a shows the experimentally measured melt pool depth versus the distance y from the island edge ( Fig.14 y) where a first laser fill line 201 is performed at an edge 200 of an island and a subsequent laser fill line 202 is performed adjacent to the last formed laser fill line. The distance y is in a direction perpendicular to the laser fill direction. As can be seen from this graph, the melt pool depth increases steadily from the initial depth on the first laser fill line until a steady state is reached.

[0112] Fig.13b shows the initial temperature of the powder bed at the exposure point, with distance y predicted by the heat accumulation model. It can be seen that the initial temperature increases steadily from the first laser fill line until a steady state is reached.

[0113] Fig.13 c combined Fig.13 a and Fig.13 The data provided in Figure 2a and b are provided to provide a relationship between the melt pool depth and the initial temperature for each set of scan parameters. Such a relationship can be used to modify the predicted melt pool depth for a set of scan parameters as the initial temperature changes due to heat accumulation from previous exposure. In order to obtain the desired melt pool depth, the scan parameters can be changed based on the prediction of the initial temperature from the heat accumulation model and the determined correlation with the melt pool depth to ensure that the melt pool depth remains within an acceptable range of the desired melt pool depth. Therefore, the heat accumulation model in the powder bed can be used to feed the initial temperature into the volumetric heat source model in order to determine the scan parameters based on the desired characteristics of the melt pool.

[0114] about Figure 1 , it can be pointed out that it is best to fix the ratio r1 of the laser power in the front ellipsoid in order to reproduce the increased penetration of the front part of the melt pool. For the melt pool sections reported here, the heat source parameter fitting was successfully performed for fixed values ​​of r1 in the range 0.6 ≤ r1 ≤ 0.9. Changing r1 only resulted in a small change in the fitted source parameters and the obtained melt pool shape was almost the same. Increasing r1: Decreases the fitted absorptivity η and the heat source depth 2σ z , because the front of the molten pool gets more power to achieve the required penetration; the length behind the heat source is increased by 2σ x2 To compensate for the reduced power in the rear ellipsoid in order to achieve the target melt pool length, r1 = 0.6 was chosen for all results presented here to minimize the heat source rear length 2σ x2 , as it is the smallest "physical" aspect of the equivalent heat source compared to the actual focused laser beam. It can be found that r1 ≤ 0.5 generally does not produce the desired increased penetration in the front of the melt pool and the fitting residuals are large.

[0115] The second "indirect" fitting parameter is the temperature T when calculating temperature-dependent material properties. propThe effect of changing material properties on the calculated melt pool can be understood by considering the steady-state temperature distribution of a scanning point source, see Equation (6). The first term q / (2 πkr) is the hemispherical steady-state temperature distribution of a stationary point source. Reducing the thermal conductivity k increases the melt pool radius by a factor of 1 / k. On the top surface, the rear position of the melt pool of the scanning laser beam is equal to this radius: it is unaffected by the laser scanning speed v, since y = z = 0 on the top surface centerline and the exponential term has no effect when ξ = -r. Elsewhere on the top surface, away from the melt pool centerline, reducing the thermal diffusivity α (or increasing v) reduces the width, producing a narrower melt pool.

[0116] The material properties of SS316L calculated at the melting temperature were used, i.e., for all stainless steel results presented here, T prop = Tm = 1648 K. The solidus temperature was chosen rather than the liquidus temperature (1673 K) because the two boundaries cannot be distinguished in the micrographs and therefore it represents the temperature of the material immediately surrounding the measured melt pool boundary. Small differences in the material properties between these two temperatures have no significant effect on the calculated temperature distribution or the fitted heat source parameters. Even significantly different T prop Nor does it significantly change the fitted heat source parameters: T has been successfully performed for all data sets. prop = 300 K heat source parameter fitting. At this lower T prop Under T, both the thermal conductivity k and thermal diffusivity α of SS316L decrease. As mentioned in the previous paragraph, a decrease in k increases the melt pool length. It also increases the melt pool width because the increase caused by k offsets the smaller decrease caused by α. prop :Reduce the fitting absorptivity η and heat source depth 2σ z , because the power required to calculate the same molten pool cross section is smaller; the rear length of the heat source is increased by 2σ x2 To accommodate the increased melt pool length. Choose a higher T prop To minimize the length 2σ behind the heat source x2 , also because it is the smallest "physical" aspect of the equivalent heat source compared to an actual focused laser beam.

[0117] A systematic IHCP method for calibrating a volumetric heat source for modeling laser powder bed melting has been introduced and shown to be applicable to both conduction and transitional melt pool modes. The heat source absorptivity η and depth 2σ have been found to be z A clear relationship has been found between η and the experimental melt pool depth. In addition, a linear relationship between energy density and melt pool depth has been reported, enabling the determination of η and 2σ at intermediate process settings between a smaller number of calibration experiments. z , or between η and 2σz The process setting is determined at the middle value of . The increase of the molten pool length is related to the rear length of the heat source 2σ x2 The linear relationship between can be used to achieve the target melt pool length.

[0118] The melt pool profile calculated from the fitted heat sources yields the shape observed in recent experiments, including increased front penetration due to vapor depression under the laser spot at higher energy densities, but at significantly reduced computational cost. Heat sources calibrated from the first track of the island scan are successfully applied to reproduce the evolution of the melt pool in the presence of heat accumulation in adjacent tracks. The presented calibration method enables experimentally representative heat sources to be incorporated into conduction-only semi-analytical and numerical models to improve build planning.

[0119] It will be appreciated that changes and modifications may be made to the above described embodiments without departing from the invention as defined herein. For example, other volumetric shapes may be used for the equivalent volumetric heat source. The equivalent volumetric heat source may be defined by a front volumetric element and a rear volumetric element, one or both of which are not segments of an ellipsoid.

Claims

1. A method for generating scanning parameters for a powder bed fusion additive manufacturing process, the method comprising: Receiving at least one desired characteristic of a material modified zone, wherein the material modified zone is formed by exposing a powder bed to an energy beam to melt the material and / or change the microstructure of the material; and determining scanning parameters of the energy beam estimated by a powder bed melting model to produce a material modified zone having characteristics corresponding to the at least one desired characteristic.

2. The method according to claim 1, wherein: The material modification zone is a molten pool.

3. The method according to claim 2, wherein: The at least one desired characteristic includes melt pool size.

4. A method according to any one of the preceding claims, comprising determining scanning parameters estimated from a powder bed fusion model to produce a melt pool in transition mode.

5. A method according to any one of the preceding claims, wherein: The powder bed fusion model includes a lookup table or function relating the at least one characteristic to one or more scanning parameters.

6. The method according to claim 5, wherein: The lookup table or function includes or defines intermediate values ​​extrapolated from measured properties of the material modification zone under known scanning parameters.

7. The method according to claim 5 or claim 6, wherein: The lookup table or function relates a single value of the property to a plurality of different scanning parameters based on an initial temperature of the material.

8. A method according to any one of the preceding claims, wherein: The scanning parameters are determined based on an energy beam density determined by solving the powder bed fusion model for the desired properties.

9. A method according to any one of the preceding claims, wherein: The powder bed fusion model is a heat conduction only model.

10. A method according to any one of the preceding claims, wherein: The powder bed fusion model takes into account the initial temperature of the powder when exposed to the energy beam.

11. The method according to claim 10, wherein: The powder bed fusion model determines the initial temperature at each exposure point based on the position and time when the powder was previously exposed to the energy beam.

12. A method according to any one of the preceding claims, wherein: Solving the powder bed fusion model includes using an equivalent volumetric heat source having dimensions corresponding to the at least one desired melt pool dimension to estimate a heat input to be supplied to such volumetric heat source.

13. A method of manufacturing a part, the method comprising building the part using powder bed fusion by scanning parameters determined using the method of any one of claims 1 to 12.

14. A data carrier having instructions thereon, wherein: When the instructions are executed by a processor of a powder bed fusion additive manufacturing device, the processor controls the powder bed fusion additive manufacturing device to execute the method as claimed in claim 13.

15. A method of generating a look-up table or function for use in the method of claims 1 to 12, the method comprising: receiving, for each of a plurality of material-modified regions formed by exposing the material to an energy beam to melt the material and / or change the microstructure of the material, a measured or numerically calculated property of the material-modified region, each material-modified region being generated using a different set of scanning parameters; calibrating parameters of a powder bed fusion model using the measured or numerically calculated characteristics to provide a calibrated powder bed fusion model; and generating the lookup table or function based on the calibrated powder bed fusion model.

16. The method according to claim 15, comprising: The powder bed fusion model was calibrated using an inverse heat conduction problem approach.

17. The method according to claim 15 or claim 16, wherein: The parameters of the powder bed fusion model describe the equivalent heat sources used in the powder bed fusion model to represent the melt pool.

18. The method according to any one of claims 15 to 17, wherein: The equivalent volume heat source is defined by two segments of a curved three-dimensional shape.

19. The method according to claim 18, wherein: The equivalent volume heat source includes a front section modeling a front portion of the material modification zone in a scanning direction and a rear section modeling a rear portion of the material modification zone in the scanning direction.

20. The method according to claim 19, wherein: The front section includes a planar top surface, a planar rear surface, and a continuously curved front surface extending from an edge of the planar top surface to an edge of the planar rear surface; the rear section includes a planar top surface, a planar front surface, and a continuously curved rear surface extending from an edge of the planar top surface to an edge of the planar front surface, further wherein, The rear face of the front section coincides with the front face of the rear section, and the curved faces of the two sections are discontinuous at a boundary between the two sections.

21. The method according to any one of claims 15 to 20, wherein: Generating the lookup table or function based on the calibrated powder bed fusion model includes interpolating values ​​for intermediate properties of the material modification regions from values ​​for measured or numerically calculated properties provided by the powder bed fusion model.

22. A method according to any one of claims 15 to 21, comprising: The material is solidified using material powder bed fusion, the material is solidified at different points using different sets of scanning parameters, and properties of the solidified material are measured.

23. A method of inspecting a powder bed fusion process or a powder bed fusion apparatus performing the powder bed fusion process, comprising: Receiving measured properties of a material modification zone formed by exposing the material to an energy beam to melt the material and / or change the microstructure of the material; and determining whether a powder bed fusion process or a powder bed fusion apparatus has changed by comparing the measured properties with properties predicted by a powder bed fusion model calibrated using measurements obtained from a previous powder bed fusion process.

24. A data carrier having instructions thereon, wherein: When the instructions are executed by a processor, the processor is caused to perform the method according to any one of claims 1 to 12 and 15 to 23.

25. An apparatus comprising a processor arranged to perform the method of any one of claims 1 to 12 and 15 to 23.

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