METHOD FOR PRODUCTION OF A THREE-DIMENSIONAL BODY.

专利摘要:
method for producing a three-dimensional body. The invention relates to a method for producing a three-dimensional body by successively providing dust layers and jointly fusing selected areas of said layers, the areas of which correspond to successive cross-sections of the three-dimensional body, wherein the method comprises the following: steps for at least one of said layers: applying to at least one dust layer in a work area and fusing together a selected area of the at least one dust layer by supplying power from a radiation gun to the selected area . The invention comprises the steps of: establishing a intended beam path to be used when fusing the selected area of at least one dust layer together, calculating a temperature in at least one dust layer along the intended beam path as a function of a specific energy deposition of an imaginary beam which is assumed to move along the intended beam path, to adjust the specific energy deposition of the imaginary beam along the intended beam path depending on the calculated temperature and the set of conditions for the joint fusion step of the selected area, and provide, based on calculations and adjustments, an operating scheme for the actual beam energy deposition to be used for the intended beam path when joint fusion of the selected area of at least one layer.
公开号:BR112013009155B1
申请号:R112013009155-0
申请日:2011-01-28
公开日:2018-02-06
发明作者:Snis Anders
申请人:Arcam Ab；
IPC主号:

专利说明:

(54) Title: METHOD FOR PRODUCTION OF A THREE-DIMENSIONAL BODY. (51) Int.CI .: B22F 3/105; B29C 67/00 (73) Holder (s): ARCAM AB (72) Inventor (s): ANDERS SNIS
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METHOD FOR PRODUCTION OF A THREE-DIMENSIONAL BODY
TECHNICAL FIELD [001] This invention refers to a method for producing a three-dimensional body by successively providing powder layers and jointly merging selected areas of said layers, whose areas correspond to successive cross sections of the three-dimensional body.
BACKGROUND OF THE INVENTION [002] Equipment for producing a three-dimensional object, layer by layer, using a powder material that can be melted together and solidified when irradiated with a high energy beam of electromagnetic radiation or electrons are known from US4863538 , US5647931 and SE524467, for example. Such equipment includes, for example, a powder supplier, means for successively applying layers of powder on a vertically adjustable platform or work area and means for directing the beam over the work area. The powder sinters or melts and solidifies as the beam, layer by layer, moves over the work area.
[003] When melting or sintering a powder using a high energy beam, it is important to have a complete control of the temperature of the irradiated material, in order to provide the object with appropriate material properties and to avoid geometric deformations. For example, a very high local temperature can destroy the object being produced, and a very uneven temperature distribution can lead to cracks. In addition, in order to provide a complete melt, the temperature of the upper layers of the powder bed must be kept above a minimum during the melting step. In addition to maintaining temperature control, it is usually important to try to reduce production time, that is, to try to direct the beam as efficiently as possible over the selected area.
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2/33 [004] Only a selected part or area of each layer of powder is melted together. The beam is directed in a certain path over each selected area in a pattern of fine line or sweep, which makes the area completely fused together. Often this tracker pattern takes the form of parallel lines distributed at equal distances over the selected area. Each of these selected areas, which can include several parts of areas, corresponds to a cross section of the object being formed in the dust bed.
[005] Directing the beam in a track pattern with parallel lines can be done by tracking the lines in order. Due to the heat transfer from the heated material along the previously traced lines, the temperature in the material along a certain line to be traced will be higher than the start temperature (that is, higher than the temperature in the material when the first line is traced). At least when using a high-energy beam, this temperature formation must be taken into account in order to maintain an appropriate local temperature within the material.
[006] One way to take this into account is to adjust the beam energy input in response to temperature formation. This could be done, for example, by varying the beam energy or by varying the speed at which the beam moves over the dust layer. An example is to increase the beam speed at beam turn positions, where the end of a first scan line is closed to the start of a second scan line. However, to do this properly, it is necessary to have information about the temperature in the material. This temperature, or, more precisely, the surface temperature of the dust bed, can be measured using a heat chamber. Real-time corrections or beam control based on input from such a chamber are, however, difficult to perform properly due to the system's long response time (even if actions are taken to
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3/33 decrease the temperature immediately when a high temperature has been detected, the temperature will likely continue to rise for some time). A heat chamber can thus be useful to check, after production, if something went wrong in the production process.
[007] US5904890 reports a method where the beam scan speed is varied as a function of the length of the scan lines in a scan pattern with parallel lines. The beam speed is lower for longer scan lines, and higher for shorter lines, in order to avoid variation in cooling when the beam is far from a certain area. The objective is to achieve a homogeneous density distribution in the product produced. This method can be useful with respect to the temperature formation mentioned above, if the beam speed is high compared to the length of the scan lines. However, if the scan lines are long, the beam speed should be adjusted only at the end parts of the scan lines, and, if the lines are distributed over several selected areas of the same dust layer or in a different pattern, the formation of temperature will not be similar in all parts of the area (s). In addition, if the beam energy is high, a more complex tracker pattern may be required. In such cases, the formation of temperature will not be taken into account adequately only when varying the beam speed with respect to the length of the scan lines.
[008] WO2008 / 013483 reports a method where parallel scan lines are scanned in a particular way, such that a minimum safety distance is established between consecutively scanned lines. Formation of temperature (and charged particles) between the scan lines is therefore taken into account when preventing the occurrence of heat transfer interference between consecutively scanned lines. The method is initially intended for preheating the dust layer with a high beam speed and high
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4/33 beam energy, but it can also be used to prevent heat transfer interference during the powder melting step. However, this would lead to a time-consuming production process.
[009] Thus, there is a need for more elaborate scanning strategies, which allow complete temperature control, as well as time-efficient production.
SUMMARY OF THE INVENTION [0010] An object of the invention is to provide a method of the type discussed above for the production of a three-dimensional body, the method of which exhibits improved possibilities for controlling the temperature and the increasing speed of production. This object is achieved by means of the method defined by the technical characteristics contained in independent claim 1. The dependent claims contain advantageous modalities, further developments and variants of the invention.
[0011] The invention relates to a method for producing a three-dimensional body by means of successive provision of layers of powder and joint fusion of selected areas of said layers, whose areas correspond to successive cross sections of the three-dimensional body, in which the method comprises the following steps for at least one of said layers: applying at least one layer of powder to a work area and fusing together a selected area of at least one layer of powder by supplying energy from a radiation gun to the selected area.
[0012] The invention is characterized by the fact that the method comprises the steps of: establishing a desired beam path to be used when the selected area of at least one layer of powder is fused together; calculating a temperature in at least one layer of dust along the intended beam path as a function of a specific energy deposition of an imaginary beam, which is assumed to move along the desired beam path; adjust deposition
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5/33 specific energy of the imaginary beam along the intended beam path depending on the calculated temperature and the set of conditions for the joint melting step of the selected area and provide, based on calculations and adjustments, an operation scheme for the specific energy deposition of the actual beam to be used for the intended beam path when fusing the selected area of at least one layer together.
[0013] The term “intended beam path” refers to the line or track pattern that is arranged across the selected area and refers to at least part of the path of the precise beam location intended to follow when the beam is scanned over the selected area for the purpose of melting / melting the powder within that area. In principle, the desired beam path can take any shape, as long as it provides a complete melting of the powder within the selected area, that is, it can, for example, be segmented or continuous and include both straight and curved portions. In addition, the beam path can vary, even if the line pattern is the same, for example, if lines are scanned in a different order or if an individual line is scanned in the opposite direction.
[0014] The step of "calculating the temperature in at least one layer of dust along the intended beam path as a function of a specific energy deposition of an imaginary beam, which is assumed to move along the intended beam path ”Means that a local temperature or local temperature distribution at or near the intended beam path along its length is calculated, for example, by calculating the local temperature (distribution) at a number of points distributed along the path of target beam, taking into account the energy deposited for the material through an imaginary beam, which is assumed to generate a specific deposition of energy, while moving along the intended beam path.
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6/33 [0015] The local temperature of the dust layer at a certain point along the desired beam path (that is, over a certain period of time) depends, for example, on the initial temperature distribution in the material layer, on the properties thermal effects of the material (such as thermal conductivity), the history of the specific energy deposition of the imaginary beam (including the current position of the beam and how much energy or force that was deposited on the material layer during its journey to the current position) and the geometric pattern of the beam path.
[0016] The term "specific beam energy deposition" refers to the energy deposited by the beam (imaginary or real) per unit time and layer area unit (precise location size and beam force), that is, the force deposited per unit area, divided by beam speed. Thus, varying the specific energy deposition can be done by varying the speed at which the beam moves over the layer surface, by varying the beam strength and / or by varying the size of the precise beam location ( that is, the surface area of a layer directly exposed to the beam at a certain point in time). In the calculations, the history of the specific energy deposition of the imaginary beam also includes, therefore, variations in the speed, force or size of the precise location. Also the shape of the beam and the energy / force distribution in the beam can be varied and included in the calculations.
[0017] Calculations can be complicated and time consuming, and several simplifications can be made, which allow a sufficiently accurate temperature to be calculated, while still taking into account the history of specific energy deposition (which can strongly affect the temperature at a point in the intended beam path, where the beam has not yet reached, but where the heat has been conducted from previous “fused” parts of the intended beam path).
[0018] The step of “adjusting the specific energy deposition of the imaginary beam along the desired beam path depending on the
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7/33 calculated temperature and the set of conditions for the joint melting step of the selected area ”means that at least one of the beam parameters, that is, the beam speed, force and / or size of the precise location, is adjusted on a certain point in the intended beam path, for example, calculations indicate that the temperature becomes higher at a certain point than a condition setting for the maximum temperature (what would be called, for example, an increase in beam speed or reduction in beam strength close to that particular point or to a change in the history of specific energy deposition to indirectly reduce thermally driven heating from that point from previous parts of the beam path).
[0019] Adjustments of the specific energy deposition of the imaginary beam along the desired beam path can be treated in such a way that temperature recalculations along (parts of) the path are made using other beam parameters. Alternatively or as a complement, it is possible to make use of a set of predetermined data related to the material to be melted, wherein said data set comprises appropriate values of the specific energy deposition as a function of the calculated temperature and the set of conditions . Such predetermined data is useful for avoiding time-consuming recalculations and can, for example, be used when the temperature is calculated at a number of points distributed along the desired beam path. Depending on the temperature calculated at a "near" point positioned relatively close to and in front of a point corresponding to the current position of the imaginary beam, an appropriate value for the specific energy deposition to be used when moving the beam from the current position until it reach the “next” point can be directly obtained from predetermined data. This procedure is repeated for the remaining points distributed along the desired beam path.
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In this way, therefore, the specific energy deposition is adjusted step by step along the desired beam path.
[0020] The term "operating scheme" (for specific energy deposition) refers to how specific energy deposition, that is, how each of the speed, strength and precise location size of the actual beam is supposed to vary with time (or with position along the beam path, since that position refers to time) during the powder melting stage. Thus, the operating scheme contains information on how the speed, strength and precise spot size of the beam should vary when the selected area is merged. The step of providing or determining / establishing this operation scheme is a way of extracting and summarizing the results from previous steps. In the example above, with step-by-step adjustments to the specific energy deposition, the operation scheme includes step-by-step variations of beam parameters. The operation may also include information on beam parameter adjustments for parts of the desired beam path, where temperature calculations and specific energy deposition adjustments may not be necessary, such as for an initial part of the desired beam path.
[0021] The temperature in the materials refers to their energy content. Therefore, it is possible, instead of calculating the actual temperature, to calculate and make use of another parameter related to temperature and energy. The term calculated temperature also covers such related parameters.
[0022] The steps of establishing the desired beam path, calculating the temperature along the desired beam path, adjusting the specific deposition of imaginary energy and determining the operation scheme do not necessarily have to be performed at a given moment or strictly in the order indicated. For example, calculations and adjustments can be performed alternatively, and the
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9/33 operation can be determined step by step by fractions of the entire beam path. In addition, although the step of establishing the intended beam path may be simpler - a pre-configured line pattern, with parallel and straight lines equally spaced and with a given scanning direction, this step can comprise calculations and adjustments to find a favorable line pattern and a desired desired beam path, finally selected.
[0023] Therefore, the invention briefly refers to a method in which the specific energy deposition of the beam to be used when the powder is melted together can be preset to vary in response to the temperature formation for the particular scanning pattern to be used by calculating the resulting temperature along the beam path for different specific depositions of energy and conditions. In other words, the inventive method makes it possible to predetermine, through calculation and adaptation, how the specific energy deposition of the beam should vary with time (or position on the selected area), when it passes along the path pattern and merges the dust.
[0024] Various conditions can be used in the calculations to improve the operation scheme of the specific energy deposition, such as minimizing the production time, avoiding exceeding a certain maximum temperature, avoiding exceeding a certain temperature during a certain interval period, minimizing the highest temperature reached, obtaining the same width of the molten material along the beam path and various combinations of these conditions, such as a compromise between minimizing the production time and the highest temperature reached. Several possible beam paths can be evaluated before selecting the desired one.
[0025] To simplify and speed up calculations, conditions may include pre-configured (pre-calculated) values for one or two of the
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10/33 beam parameters (speed, force and precise location size) and / or pre-configured beam path, such as a set of parallel lines positioned at a similar distance from each other.
[0026] The inventive method is generic and can be applied to any geometry of the selected area. It should be noted that a layer of dust may comprise several selected areas, which may have similar or different geometries.
[0027] When an operation scheme of adequate specific energy deposition is determined, this scheme is used for the current joint melting / melting of (part of) the selected area of the layer in question. The inventive method is preferably used over all or at least over most layers in the formed object.
[0028] An effect of the invention is that it provides complete control of the temperature and temperature distribution of the selected area and makes it possible to plan the stage in a sophisticated way. This in turn can be used to avoid reaching very high temperatures (which can destroy the product being formed), to obtain a homogeneous temperature distribution (which improves the product's properties by reducing stress and formation cracking) and to speed up production (which makes production more profitable).
[0029] In an advantageous form of invention, the method comprises the step of using the operating scheme for the specific deposition of energy when the selected area of at least one layer of powder is melted together.
[0030] In an additional advantageous embodiment of the invention, the specific energy deposition is the energy deposited by the beam per unit time and area unit, divided by the beam speed, and that specific energy deposition can be varied by varying one
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11/33 beam speed, a beam force and / or a precise beam spot size.
[0031] In a further advantageous embodiment of the invention, the method comprises the use of a predetermined data set related to the material to be melted, wherein said data set comprises specific energy deposition values to be selected as a function of temperature calculated and the set of conditions.
[0032] In a further advantageous embodiment of the invention the set of conditions for the melting step includes one or more of the following conditions for at least one layer of powder: maximum temperature; working temperature: melting depth and melting width.
[0033] In a further advantageous embodiment of the invention the step of calculating the temperature includes the step of solving the time-dependent heat equation.
[0034] In a further advantageous embodiment of the invention, the step of calculating the temperature includes calculating the local temperature distribution along the intended beam path.
[0035] In an additional advantageous embodiment of the invention, the step of calculating the temperature includes several calculations carried out within or close to a number of points distributed along the desired beam path.
[0036] In a variant of this modality, the maximum distance between adjacent points of the calculation is adjusted by adjusting a limit value for the allowed change in the specific energy deposition between the adjacent points. For example, if only the beam speed is varied, a maximum allowable change to the beam speed is adjusted.
[0037] In an additional advantageous embodiment of the invention, the step of establishing the desired beam path includes the step of: making temperature calculations along a plurality of beam paths
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12/33 possible and select the desired beam path out of said plurality of beam paths.
BRIEF DESCRIPTION OF THE FIGURES [0038] In the description of the invention given below reference is made to the following figures, which show:
Figure 1 shows, in a schematic view, an example of a known device for producing a three-dimensional product to which the inventive method can be applied,
Figure 2 shows a schematic view of the surface temperature profile and the corresponding melting depth and width in a box where the beam travels in the direction of the positive x-axis,
Figures 3-5 show some temperature distribution profiles, calculated by FEM, together with approximate distributions according to the Gaussian series in equation 3.
Figure 6 shows distances with dotted lines and point to point, and respectively, where wf) θ is _the position in the global coordinate system for exponential terms, and where ey É, t
Ά ^ are the coordinates in the global coordinate system for line segment k of line j.
Figure 7 shows an example of a desired beam path for a selected area that is shaped like a trapezoid isosceles, where the desired beam path is such that the beam begins to sweep the lines from the bottom to the top, while changes the direction from left to right and from right to left, and
Figure 8 shows an operation scheme determined for the specific beam energy deposition to be used for the intended beam path shown in figure 7, in which the specific energy deposition in this example is varied by varying the beam speed.
DESCRIPTION OF EXEMPLARY MODALITIES OF THE INVENTION
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13/33 [0039] Figure 1 shows an example of a known device 1 for producing a three-dimensional product. The device 1 comprises a vertically adjustable work table 2, on which a three-dimensional product 3 must be formed, one or more powder distributors 4, means 28 arranged to successively distribute a thin layer of powder on the work table 2 to form a powder bed 5, a radiation gun 6 in the form of an electron gun to supply energy to the powder bed 5 as well as to fuse together parts of the powder bed 5, deflection and beam molding coils 7 to guide and shape the electron beam emitted by the radiation gun 6 on said work table 2, and a control unit 8 arranged to control the various parts of the device
1.
[0040] In a typical duty cycle, worktable 2 is reduced, a new layer of powder is applied to a work area on top of the dust bed 5, and the electron beam is swept over selected parts of the layer upper 5 'of the powder bed 5. At first, this cycle is repeated until the product is ready. An expert in the field is familiar with the general function and composition of devices for producing a three-dimensional product, both with respect to the type shown in Figure 1, and with devices equipped with a laser cannon instead of an electron cannon.
[0041] Conventionally, devices fitted with an electron gun work with a vacuum normally below at least 10-2 mbar, in order to prevent the electron beam from interacting with atoms or molecules located between the electron gun and the work area. .
[0042] An example of a selected powder layer that is in the form of a trapezoidal isosceles is shown in figure 7. The desired beam path is also shown.
[0043] An embodiment of the inventive method will now be described. In an example of this modality, the desired beam path
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14/33 follows a plurality of straight and parallel lines (fine line or scan lines) distributed at an equal distance from each other. The adjusted beam parameter is, in this example, the beam speed. In the calculations, the beam speed is adjusted in such a way that the width of the molten material, at a specific depth (see melting width and melting depth in figure 2), becomes equal over the entire beam path. This allows the use of a fixed distance between the parallel parts of the beam path. Remaining parameters are predetermined (or calculated from other predetermined parameters).
[0044] According to an overview, the method modality can be described as follows:
1. Data consisting of temperature profiles and related beam parameters (precise spot size and beam speed) for different settings of material properties, material temperatures and beam forces are created and stored in a database. These data are obtained through FEM calculations in a simple geometry similar to the test box shown in figure 2.
2. The machine used to produce the three-dimensional body calculates, in real time, the local temperature distribution for each of the number of points distributed along the beam path (path) when solving a time-dependent heat equation. The solution to the equation is obtained by expanding the temperature profiles of fine line lines previously fused (that is, imaginary fused) with Gaussian envelopes. The temperature profiles corresponding to the beam used and the material parameters are obtained from the database.
3. The beam parameters at a specific point are selected depending on the calculated local temperature distribution, and they are obtained from pre-calculated data in the database (when comparing the calculated temperature distribution with the prePetition temperature profiles 870170088814 , of 11/17/2017, page 20/51
15/33 calculated for the material used and when selecting parameters corresponding to the profile that best fits the calculated distribution).
4. Once a fine line is ready, the temperature profile at the end of the line is also approximated by the Gaussian functions, and steps 2 and 3 (ie, the previous two steps) are repeated for the next line thin line.
[0045] The expression in which the calculations are performed in real time means that the powder is melted at the same time as the calculations. Normally, calculations of the beam parameter operating scheme for a subsequent layer are performed while a previous layer is fused. In principle, it is possible to do all calculations and determinations of the operation scheme for all layers before starting the first layer fusion process, but this would normally lead to a waiting time before starting production. At the other extreme, calculations and determinations of the operation scheme are made for points along the beam path, very close to where the actual beam is positioned, but this would lead to a very small margin to make corrections or recalculations, if anything went wrong in calculations or merger.
Introduction to method modality [0046] To obtain appropriate data necessary to control the melting process according to the described method, consider the time-dependent heat equation without heat source and on the homogeneous material domain - .LTj <y <Lrr · and
Equation 1a.
^ Πτ, ν, ζ, ί) - —7 Γ (.ϊ, ^ ζ, /) = 0 cif í.; P [0047] Here, T (x, y, z, t) is the time-dependent temperature distribution, λ is the thermal conductivity, c _P is the heat capacity and p is the density of the material.
[0048] The boundary conditions are summarized as follows:
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Γ = ν -> ± tt _f z —ϊ —dd [0049] A Gaussian source term at z = 0, moving in the x direction, is used to describe the imaginary energy beam. Radiation through the same top surface is assumed to follow Stefan's law - Boltzmann
Equation 1c.
dz
- ™ / íO «nx, y, 0, f) ⁴ -lf) [0050] Here, Pin is the absorbed beam force, v _x is the beam speed, σ is the variation (precise beam location size) , radcoeff is the radiation coefficient from the surface and T _sur is the surrounding temperature above the surface.
[0051] To is the working temperature, that is, the desired temperature of the material before melting / melting.
[0052] To reduce the time it will take to generate the data, it may be appropriate to remove the time dependency by assuming that the temperature distribution around the precise moving location has reached the uniform state (x = x-tv _x , dt = -dx / v _x )
Equation 2a.
- VA 7U _Λ z) - - V ^J = 0 rhr <γρ
Equation 2b.
ZU Ι ', Ο)
-raiicwfr (nx, yJ) Y-rl}
Equation 2c.
[0053] The heat equations above can be solved with FEM techniques, for example, for several different adjustments of material properties, To and beam adjustments.
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17/33 [0054] Figure 2 shows how this procedure can work.
[0055] Figure 2 depicts a “test box” where the beam is oriented in the direction of the positive x axis. The surface temperature profile is shown together with a piece in which the melting volume is represented by the isothermal curve corresponding to the melting temperature of the material. Here, the beam parameters, vx and σ have been refined to obtain a specific melting volume profile in terms of melting depth and melting width. In addition, the maximum temperature inside the material was limited by Tmax. Obviously there may be other conditions used to improve the beam parameters. For example, minimizing the temperature gradients in the melt volumes could be such a condition.
[0056] The temperature profiles needed to describe the energy input at the end of a fine line will be obtained by approaching T (x, y, z) in equation 2a with a series of Gaussian functions. By doing this, it will be possible, later, to obtain an analytical solution for temperature distribution in the half-infinity domain, even for an arbitrary number of fine line lines. The T 'series (x, y, z) will be:
Equation 3.
r = j'b '
T (av, z) »/ '(a. V, z) = + ^ 4expf- (AA / wj, F / o * Ixxpí-z / σ_,) cxpf-r ^: / σ,) [0057] The parameters A, σ _{; and} a can be obtained from a nonlinear square smart point adjustment T (x, y, z) and T '(x, y, z). Here, xpost is the position x of the exponential term i along the beam path. In the beam coordinate system it will be a negative value, since the beam is assumed to travel in the positive x direction and is located at x = 0.
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18/33 [0058] In figures 3-5, some temperature distributions, calculated by FEM, are shown together with the approximate distribution according to equation 3.
[0059] The goodness of the setting is mainly determined by the number of Gaussian functions used. In the example below, N is equal to the value 10 to 12, meaning that there are 30 to 60 Gaussian functions used for each temperature profile.
Time-dependent temperature distribution within the material [0060] The time-dependent temperature distribution, T (x, y, z, t), within the material after the beam has swept a line is obtained by the Green and joint convolution functions with the initial conditions (x, z), obtained from equation 3:
Equation 4.
ruy, z, r) = cxp
£ 4> cxp (ζ-ζΎ
ADt exp-Ϊ, where d = ± [0061] Here we assume that the material temperature is equal to Tsurt and different from To-. The heat loss through the surface is now brought to zero:
-lAr (xj, 0, í) = 0 dz [0062] When the beam swept the lines Μ, the right hand side of equation 4 is replaced by a sum:
Equation 5.
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19/33 “| 4nD (í-q)) f, _ll3 {
Ο '->' J exp
4 /) (/ -ί Λ β κ μ
Expί exp
CXp
4Ώ (/ - ς I
W-q) + exp ΐ
40 (1-Μ dy'dx'-T _ai where tj is equal to the time when line j was completed, To] is the temperature around the precise location when line j was completed, T'j (x ', y ', z) is the temperature distribution according to equation 3 for line je H (t-tj) is the heavy side step function defined as:
«„ = U ^<0 μ, /> ο [0063] When inserting the expression for T '(x, y, z) (equation 4) to equation 5, it must be kept in mind that the x, xpos and y coordinates in equation 3 they refer to a local coordinate system centered around the end point of line j, with the x axis pointing in the direction of the beam movement for this line, whereas the x and y coordinates in equation 5 refer to the global coordinate system determined by the surface of the part. Furthermore, if the beam path of line j has to be described by the various line segments, each with a different direction, y in equation 3 should be replaced by what is the distance between line segment k to line j, and the point (x ', y'), and x'-xposi must be replaced by, which is the distance between the position of the exponential term / in the line segment and the projection point of (x ', y') in line segment (see figure 6).
[0064] In this way, any type of beam path can be considered. However, it must be remembered that the distribution in equation 3 is obtained from a straight line simulation. So, if the curvature of the beam path is very significant just by placing the terms in equation 3 along that path with the same distances,
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20/33 as determined by the xposi values, can be a much poorer approximation. In such a case, an FEM solution in the curved geometry may be necessary.
[0065] Figure 6 shows distances in dotted line and point to point, ^{f /} * 'and respectively. ^tJcpüS) '> yp ° ^s /> is the position in the global coordinate system for exponential terms. <Aú /> are the coordinates in the global coordinate system for line segment k of line j.
[0066] For each line segment kj, which contains at least one exponential term, positioned in 'W ™ /'', the squared distances' ^ must be expressed as a linear combination of the terms < ^{ax + by} ' ^{+ G} f , otherwise, it will not be possible to solve the integrals analytically in equation 5. This is done in the equation below.
(/.y ₌ ς / · Vl ^1.1 UV / [7 (jÍ ·· -.ν '·> - -t-ov ¹ - /'> ⁼
L * / = f- 52 Γ + ÍJ ^J l
= vs' - Z ^J sin 9
Uj;) '= (j / mv * · - ϊ ¹ ) -' -yy [0067] Here we assume that the beam is moved from point 1 to point 2 and that line segment 1 is the last segment of line of line j. Thus, line segments are added backwards.
[0068] H is the absolute value of the x position of the exponential term / for line j from equation 4, that is, the x position in the beam path coordinate system of line j.
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21/33 [0069] Putting them all together will give the following expression for the time-dependent temperature distribution when the beam swept the M lines:
Equation 6.
+ _{ΣΤ ϋ;} · + J = l cxp
U’-yT
4D (t-tA
ÍIJ cxp cxp (Jf + cxp £ Σ 4 'expÇ - U /. F ι σ; jexp (- (</ *'. Í σ /), “* 'Ί' = iL 'cxp -z ¹ - / O! .U ¹ Α ^ ώ'-Γ _Η , - + £ --— £ £ At
l. * l 1 * 4
Where:
[0070] K2 is the number of straight line segments for the j-stroke.
[0071] ** is the number of exponential terms on each line segment kj.
[0072] In subsequent sections analytical expressions for the terms within the sums will be derived. However, it should be mentioned that using the expression above for nw, (í _{S it} will be possible to calculate the temperature for more or less any type of beam path and that the calculations can be done efficiently in a multi CPU configuration, 0 which means that the calculation can be done in real time.
Property and integration of Gaussian functions [0073] In order to solve the expression in equation 6, some properties of Gaussian functions must be known.
1. Multiplying two Gaussian functions is another Gaussian function:
Petition 870170088814, of 11/17/2017, p. 27/51
22/33
A = exp cxp /
ff-,
2. Integrals of a Gaussian:
Jexp
H
Jcxp
L Vito σ {u — bzY ^r (0 + bzy
Integrals for calculating T ’(x, y, z, t)
First consider the integrals in the z direction:
exp “Ά fcxp U-Á)
W-i ,.)
f u + 2'r V + cxp ίϊ { -ί ^{, 3} / σ ) (// + J exp —Π
exp (-z ^{, J} ís + fy
4Οΐί-Γ;>
411 (/ - /,) f y. e * p (- - A / C; k ¹⁺ } exp (- fe ⁺ A '^ ϊ V- ^r = cxp (-; ^rl / tst tz _Jir fA Λ: ^v Htfc
i j>> / +11 + L σ ‘/ ί
wfe
Ίί c
V '/ 7 yito /, 2 = 0 J. J / rcflUz Φ 0 [0074] where
Petition 870170088814, of 11/17/2017, p. 28/51
23/33
According to considering the integrals x and y:
In the case where all line segments are parallel, there is no need to differentiate between x and y, since the coordinate system can be easily transformed to align with the dashed lines. Thus, in the example below, it is assumed that all lines are parallel to the x axis.
Where:
Petition 870170088814, of 11/17/2017, p. 29/51
24/33 = <(4 £> i -ί. ^ '. Ν + σ ^ (σ;', Γ ^, / 'λ »· ₌ 4-fe-4'O_k-wf
4Diff- / ,.) σ '<= (((4ΰίί-ί _Γ ^' + (<) Τ ν >>
-d ¹ /;
<= cxp
(4ΰ (ί- /,)) ' ^Ι / ^{+ σ} :. (0 //., (. k .-,) ·) 4DÍ / - / JV J cxp <J
If the line segments are not parallel and have an arbitrary direction, algebra becomes a little more involved. In such a case, consider, first, the integration x:
_t <- it -. <} ^! + there! - <) ^r j γ!
- η Χ.η '- -> · *'),:
X
I___1_ ϋσ. ''
U ^χ · * cx [i (((a * - .'CT ^ _ f ~ ^J i X 5Í ~ .Γ ¹ > ~ Λ 4 ~ Λί '1 _ ((JÍ - />
“F__í-L- ± n) - £ = * p (- Ur - A 'O / U ^r =. </ . ^ ιποξ ΐτ' · where:
Petition 870170088814, of 11/17/2017, p. 30/51
25/33 (Τζ + (σ ')' f
4; = ^σ I (W -LJ '* + α *, (σ') '^ <· σ = kr + krr
4DÍ / - / J
cxp / k /
, ι. * /! (j; -jy)
0 / --Or + (. O-y, o .υ
O -; * ⁷ 1 ¹ ϊΐ / 4 -x'j ² +0 -y '/ σ 'ί · ^τ ' //
V = aUaU - '^ ₊ σΊσ ») -' X ^ · ' ₌
-W ₃ “', ϊν Μι Ά ν' ₍ *, * ,.
Οι '-Λ,') íi - V c
«. <V. r 4 mr ₌
Οι -4Ϋ) <H) '4, ⁺ <ín) fr) λΜ ^' - / ')
0 -j >
-G .; ' l l) O - *':' GRANDFATHER - J ! - <(<) 'd
- a > -υ -j ) ο-μολ-, ο _LKp .
(Λ-ίι -.! · ¹ ^ + Λ}) '= / i-csp- (Í- /) ·' σ, i, -fcí I-¾ + 3 ^) '(«-Akf + fl)
A «= e J - L jf_ [(c + 4> í -, j + J. f
I - u
Like this:
rrcV Λ cxp í (r-yr (Tu
Petition 870170088814, of 11/17/2017, p. 31/51
26/33
Now, consider y integration:
40 (1- /,} (ízWr f, <cxpf i R rs * ο4-- ^ν >
íAp (- (jyw.s * '- í- ¹ )' ίσ) exp (- {t - v ¹ ) '/ σ, Jf / v xp (-U- vy / aj / i ^ where:
= ((40 (/ - /,) ^ + (^ ¹ } ^-1 4, = σζ (4Ο (/ - ί _/ ) Γ _Λ · + σ; (σ · Γλ ^; · = ex _P - 'exp - '} 40 (/ - /.) J <ϊ;
^σ £ = (^ .0 '}'
Λ »= exp α-, α ^ / <Α-, ·> η tfj - · gfl '
IT * exp) ί
Summary of total expression rv, v, z,!} = Τ, + £ -! - Y YaíriW fr (4ltO (7 £ r ^L '
Í-K,
Exponential term positions:
I. 'Ml, -; --_- 1-: V. = | -W | - £ Xi ~ Á f - Jj · ') ^S
Í-L
There in '
THE, *,
A ~ Ί v> - V>
- ^l 2 ^J 1 xpusç = Λ / - V eesft yposF -γ - / * 'muQ
Α> =
Λϋ , 2 = 0
A ^ JiiãVstti
Petition 870170088814, of 11/17/2017, p. 32/51
27/33 where:

J = E, cxp t ^ -41 f csp
40 (/ - /,)
Parallel lines:
('-A') = o, 3 * X '= X where:
σζ = ((4 /) 0 -ί,)) · ¹ + (σ <ΓΓ = ^σ £ ( ^4β ('- ο>) ^{1 χ + σ} ΐ (°. · ;. Γ ^χ ρ ™>> ^:
Λ »cxp < / cxp .Vpih ,.
4O (/ - f,) <= ((4 ^ -9) - ¹ + krt '
A (w - /.> N (<) X
Jj ^ exp
4D (/ - / J /
CSip tr.
Arbitrary direction of the fine lines:
(X - X) φ o, (X '“X'> í <.» Where:
Petition 870170088814, of 11/17/2017, p. 33/51
28/33 ® σ {+ η <; -1,) 1 ¹ γ + α 'ξσ;)' .τ / nfr
TL ·> , ) Κ / - · Τ · Ρ’Α · |
Λ ^μ -ύΧΠ
4 /) (/ - /,)
Lip (Ο '+ τπτ _Ι_ _] _ π ^Γ <τ' _íh = h £ _ü ___ í_Yf [í-Α-ΑΤ + <Α '· -Α ··> Α ^σ 'v;. JJ
-kr-bjí '(A - .r,' l · ____ ..
(> -FAvíõ
AM ¹ * ύ, -'- υΐ, 1 A.. i. í. , 1. A., (V -ϊ, ·} ϊ / --t. -Gv ->,>
/THE. έ. .
ΟΙ '”. ^r :) σ = ας (σ} '(/' -ιί ·) / '(> * -yí') = σ fcs) '</ d = (j - ar *' MA -j <) jr = c :
xpj: xp. 1, A. _w -b. r *. *. □ *. .
ί, (.v, -.η'Μ> '| - -n-Vlr / -J-,) (A>
ÇJfl { ^a - ^T tf - A ') H (rr - fr-r' (r + J}) ⁸ = / Twip - {<: - /}; -0,) / (++ Jr
-σ, (α;) {'' - '^ Λ-ι-σΛ :.)' (ír-frkcW) (ττA = espr (cy- - <t + - _ J (f _and + ό} - o +, fr) ^{: ίΧ} Ρ Tü σξ = (((4/3 (/ - 9) - ¹ + ^) ^-1 ) ^-1 = ^σ . “, í ⁴ w -çX ^{v + c} faíY y ^ '
CXp
-yp ^ JY
4D (/ - ^) _; ^σ >: = (^. ^^ + (0,.) - ¹ ) ^-
J'i Ykbi + sAh <4-, -4>
σί = <* P exp
J ί í-4 - * r
Calculation of beam parameters along the fine line
Petition 870170088814, of 11/17/2017, p. 34/51
29/33 [0075] Since the (imaginary) beam sweeps along the fine trace paths, the temperature around the precise location can now be calculated from the expression in equation 6 and by inserting pre Gaussian functions -calculated for the temperature profiles for the previous lines of fine line.
[0076] By knowing the temperature and having access to improved data for the beam parameters for different conditions, it will be possible to adjust the beam energy input (that is, the specific energy deposition) in an appropriate way.
Example [0077] In the following fine trace example (see figure 7), a trapezoid will be cast with a constant beam force and the beam speed will be varied, in order to have constant melting depth and width. The desired beam path is such that the beam begins to sweep the lines in figure 7 from the bottom to the top by changing the direction from left to right and from right to left.
[0078] The precise location size has been optimized for Tsurf, the temperature at the front to melt, such that the maximum temperature in the fusion pool is limited to Tmax. This means that the first fine line is scanned with a constant speed and a precise fixed location size. All other lines are scanned with the same precise location size and strength, but with different speeds and variations. The speed at each point of the calculation distributed along the desired beam path is obtained by first calculating the temperature distribution around the point and then from the speed versus the temperature data in the database. The speed in the database has been optimized for specific beam adjustments (strength and precise location size) and temperature, such that the melting depth and melting width are the same for all lines. At the end of each fine line the temperature profile created by the imaginary beam
Petition 870170088814, of 11/17/2017, p. 35/51
30/33 is modeled by Gaussian functions taken from the database. The temperature range of the database was from Tsurf to Tmelt, and the temperature step for the pre-calculated data was set to 20 K. A research table procedure was used to record the nearest speed and speed functions. Gaussian for the calculated temperature.
[0079] The resulting speed profiles along each fine line are depicted in figure 8. These profiles are based on calculations of the local temperature distributions along the intended beam path and correspond to the operation scheme determined for the deposition specific beam energy to be used for the intended beam path, when the selected area of at least one layer is fused together, in which the specific energy deposition in this example is varied by varying the beam speed.
[0080] In the example above, the smart procedure step was used to obtain the temperature and speed along the lines. This means that, first, the temperature at a specific point along the line was calculated using equation 6 for parallel lines. Second, the speed was obtained from the temperature when using the database as a research table. The next point along the thin line can be calculated with a fixed distance, Ar, where the time step would be equal to Air / Speed. However, since the temperature gradients vary very dramatically with respect to time and the space coordinates of a fixed distance procedure was not enough. In some places a small step would be necessary, whereas in other places a much longer step could be sufficiently precise. Instead, a maximum allowed change in speed was used. From this, the maximum difference allowed in temperature could be obtained and, when numerically calculating the derivatives of the temperature with respect to both time
Petition 870170088814, of 11/17/2017, p. 36/51
31/33 as well as space, the spatial step allowed to the maximum could be obtained.
[0081] The derived algorithm was quite efficient and there were no problems to include up to thousands of fine line lines in a real-time calculation. The term real-time calculation refers to a calculation in which the time to calculate the speed along the fine line will be less than the current fusion time.
[0082] The invention is not limited by the modalities described above, but can be modified in several ways, within the scope of the claims. For example, it is possible to use a more detailed and complex description of the fusion process when improving the beam parameters and creating the database; the powder can be modeled as a non-homogeneous material together with melting enthalpies and a detailed model of freezing melting process.
[0083] Calculations according to equation 6 can be used to improve the fine line strategy with respect, for example, to the minimum melting / melting time. For such an improvement there is no need to make all calculations in real time, as long as they are made possible from a practical point of view. However, it should be beneficial if the calculation for each possible hairline strategy can be done in real time. Thus, there will be no need to save all the data obtained from the improvement stage. Instead, the information to be saved during the refinement step can be limited, for example, to fine-line angles, distances between fine-line lines, position of the fine-line with respect to the part, etc.
[0084] The described method can be combined, for example, with a method used to calculate the beam force necessary to maintain the parts to be formed at a specific temperature, as described in WO 2004/056511. Thus, the total energy input can be
Petition 870170088814, of 11/17/2017, p. 37/51
32/33 calculated from the energy balance calculation including the part geometry, considering that the method described here is used to control the local energy or force deposition provided by the beam during fusion.
[0085] The described method uses a homogeneous material model to obtain the local temperature (distributions) along the fine line. However, local differences in material properties can be modeled by using different D values at different locations. For example, sections that are very thin can be modeled by having a lower thermal conductivity. There is no limitation in the method for expanding the database with improved data, even for such sections. Similarly, it is possible to take into account that the lower layers in the powder bed are located closer to the adjustable work table, which probably has thermal properties that differ from that of the powder bed.
[0086] It is possible to establish the desired beam path for only a part of the selected area before calculating and determining the operation scheme for that part of the selected area. In addition, it is possible to calculate and determine the operating scheme for only part of a fully established intended beam path. The step of merging the selected area of at least one layer together can be started while the steps of establishing a desired beam path, calculating the temperature etc. with respect to an unfused portion of the selected area are in progress. In addition, the at least one layer of dust may comprise more than one selected area; these selected areas (part) can have different shapes and can be manipulated separately.
[0087] As explained above, in the temperature calculations along the intended beam path, the energy deposited by the (imaginary) beam along the path to a certain point in time is taken into account when calculating the temperature for the same point in
Petition 870170088814, of 11/17/2017, p. 38/51
33/33 time is realized. This form of temperature formation is adequately taken into account.
[0088] In the example described above, temperature calculations are performed on a number of positions distributed along the desired beam path, and in each of these positions a local temperature distribution is calculated. In addition, the local temperature distribution is calculated at a position one step ahead of the position of the imaginary beam. The specific energy deposition to be used when moving the beam, that individual step to the next position a little ahead, is obtained from a database containing a number of specific pre-calculated energy depositions (that is, beam speeds in the example described) for different local temperature distributions (for the powder material used and for certain melting conditions), where the local temperature distribution calculated in the next position is used to select the appropriate value or values from of the database.
Petition 870170088814, of 11/17/2017, p. 39/51
1/3

权利要求:
Claims (10)
[1]
1. Method for the production of a three-dimensional body (3) by means of the successive provision of powder layers and joint fusion of selected areas of the said layers, whose areas correspond to successive cross sections of the three-dimensional body (3), in which the method comprises the following steps for at least one of those layers:
- apply at least one layer of powder to a work area,
- fusing together a selected area of at least one layer of dust by supplying energy from a radiation gun (6) to the selected area, characterized by the fact that it comprises the steps of:
- establish a desired beam path to be used when fusing the selected area of at least one layer of dust together,
- calculating a temperature in at least one layer of dust along the intended beam path as a function of a specific deposition of energy from an imaginary beam, which is assumed to move along the desired beam path,
- adjust the specific energy deposition of the imaginary beam along the desired beam path depending on the calculated temperature and the set of conditions for the joint melting step of the selected area, and
- provide, based on calculations and adjustments, an operation scheme for the specific energy deposition of the real beam to be used for the intended beam path when the selected area of at least one layer is fused together.
[2]
2. Method, according to claim 1, characterized by the fact that it comprises the step of using the operation scheme for the specific deposition of energy when the selected area of at least one layer of powder is melted together.
Petition 870170088814, of 11/17/2017, p. 40/51
2/3
[3]
Method according to either of claims 1 or 2, characterized in that the specific energy deposition is the energy deposited by the beam per unit time and area unit divided by the beam speed, and that the specific deposition of energy can be varied by varying a beam speed, a beam energy and / or a precise beam location size.
[4]
4. Method according to any one of the preceding claims, characterized by the fact that the method comprises the use of a set of predetermined data related to the material to be melted, in which said data set comprises values of specific energy deposition to be selected as a function of the calculated temperature and set of conditions.
[5]
5. Method according to any one of the preceding claims, characterized by the fact that the set of conditions for the melting step includes one or more of the following conditions for at least one layer of powder: maximum temperature; working temperature: melting depth and melting width.
[6]
6. Method according to any one of the preceding claims, characterized by the fact that the step of calculating the temperature includes the step of solving a time-dependent heat equation.
[7]
Method according to any of the preceding claims, characterized in that the step of calculating the temperature includes calculating a local temperature distribution along the intended beam path.
[8]
8. Method, according to any one of the preceding claims, characterized by the fact that the step of calculating the temperature includes several calculations performed within or close to a number of points distributed along the intended beam path.
Petition 870170088814, of 11/17/2017, p. 41/51
3/3
[9]
9. Method, according to claim 8, characterized by the fact that the maximum distance between adjacent calculation points is set by setting a limit value for the permitted change in the specific energy deposition between the adjacent points.
[10]
10. Method according to any of the preceding claims, characterized by the fact that the step of establishing the intended beam path includes the steps of:
- make temperature calculations over a plurality of possible beam paths and
- selecting the desired beam path out of said plurality of beam paths.
Petition 870170088814, of 11/17/2017, p. 42/51
1/8

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法律状态:
2017-08-22| B06A| Patent application procedure suspended [chapter 6.1 patent gazette]|

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2017-12-19| B09A| Decision: intention to grant [chapter 9.1 patent gazette]|

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2018-02-06| B16A| Patent or certificate of addition of invention granted [chapter 16.1 patent gazette]|

优先权:

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申请号 | 申请日 | 专利标题

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PCT/SE2011/050093|WO2012102655A1|2011-01-28|2011-01-28|Method for production of a three-dimensional body|

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