JP6768459B2 - Three-dimensional laminated molding method and three-dimensional laminated molding equipment - Google Patents

Description

The present invention relates to a three-dimensional laminated modeling method for forming a three-dimensional modeled object by an electron beam, and a three-dimensional laminated modeling apparatus.

In the conventional three-dimensional laminated modeling device, a layer of powder is laid and a light beam is irradiated on the layer to integrate it with the solidified layer of the lower layer, and in the middle of the work of manufacturing the modeled object, A modeled object is formed by performing a step of separating or removing the powder that is not integrated with the modeled object and a process of re-irradiating the light beam to melt and solidify the powder adhering to the surface of the modeled object (for example). Patent Document 1).

In addition, a device for forming by melting a metal powder with an electron beam (for example, Patent Document 2) and a modeling device for processing an end portion with a laser beam after melting with an electron beam (for example, Patent Document 3) have also been proposed. There is.

JP-A-2002-382201 Japanese Unexamined Patent Publication No. 2010-255557 JP 2015-168877

In Patent Document 1, during the production of a powder sintered part, an already sintered model and an unsintered powder are separated or removed. Since it is necessary to perform laminated modeling again after removal, the entire modeled object is not taken out from the powder, and it is on the surface of the complex shape of the modeled object or on the surface behind the irradiation direction of the light beam during laminated modeling. The powder could not be removed, it was difficult to re-irradiate the light beam, and it was difficult to smooth the surface. Further, the light beam for re-irradiation is controlled by the movement of the XY drive mechanism of the optical fiber that supplies the light beam, or by a deflection device such as a galvano scanner. For this reason, it is difficult to quickly control the position and focus of the light beam with respect to the curved or uneven surface of the surface of the modeled object, the energy density applied to the surface is not uniform, and the degree of surface treatment and curing is not uniform. It was difficult to smooth the surface due to variations in the surface.

Further, in the laminated modeling method described in Patent Document 1, it is difficult for the raw material powder to absorb the energy of the light beam. In particular, when the raw material is a metal material, it is reflected on the surface of the metal powder of the light beam, and the heat required for melting is not given, and a modeled object is formed by insufficient melting, resulting in melt solidification. The modeled object sometimes collapsed in a post-process such as removing the unworn powder. Furthermore, in order to perform surface treatment in the middle of the laminated molding, a means is taken to expose the end face of the unfinished model and irradiate the light beam, and the surface is locally heated during the laminated molding. , There was a problem that the modeled object was thermally deformed.

In Patent Document 3, the surface is smoothed by re-irradiating the electron beam from the same direction after melting with the electron beam, but the end portion cannot be smoothed. Further, Patent Document 3 proposes that the unmelted metal powder remaining at the end after being melted by the electron beam is performed by a laser beam having a higher energy than the energy of the electron beam. However, in this modeling method, it is proposed. It requires two heat sources, an electron beam and a high-energy laser beam.

The present invention has been made to solve the above problems, and uses only an electron beam as a heat source to form a surface of a metal model, particularly a surface that becomes a side surface during laminated modeling, that is, an end face. This is to obtain a three-dimensional laminated molding method and a three-dimensional laminated molding apparatus capable of smoothing and smoothing the unevenness of the above.

In the three-dimensional laminated molding method of the present invention, the metal powder spread in layers is irradiated with a first electron beam to melt the metal powder, and then the metal powder is solidified and then solidified on the metal powder in layers. And irradiating the first electron beam to melt the newly spread metal powder and then forming a solidified metal solidified layer is repeated to form a primary model in which the metal is solidified. In the laminated molding step, the metal powder that adheres to the primary model without solidification is removed to form the secondary model, and the secondary model is irradiated with a second electron beam. have a surface treatment step by re-melting the surface of the next shaped object to form a shaped object, the surface treatment step, by moving at least one of the second electron beam and the secondary shaped object, the second The electron beam of the above moves and irradiates so as to intersect the boundary line of the metal solidified layer on the surface of the secondary model, and the melting formed on the surface of the secondary model by the irradiation of the second electron beam. The width in the direction in which the second electron beam moves on the surface of the secondary model in the pond is at least twice the thickness of one layer of the metal solidified layer formed in the laminated molding process. The parameters of the electron beam are set .

Further, the three-dimensional laminated modeling apparatus of the present invention includes a first electron beam irradiation chamber and a first electron gun, and in the first electron beam irradiation chamber, a first electron beam is formed on a metal powder spread in layers. The metal powder is spread in layers on the metal solidified layer formed by solidifying after irradiating the metal powder with a first electron beam to melt the newly spread metal powder. The first electron beam irradiator, which is controlled so that the metal forms a solidified primary model by repeating the process of solidifying and forming a metal solidified layer, adheres to the primary model without solidifying. A metal powder remover equipped with a metal powder removing chamber for removing the metal powder and making the primary model a secondary model, a second electron beam irradiation chamber and a second electron gun, and a second electron A second electron beam irradiator configured to irradiate the secondary model with a second electron beam and remelt the surface of the secondary model to form the model in the beam irradiation chamber . The second electron beam moves on the surface of the secondary model, and the second electron beam vibrates in a direction parallel to the direction of movement on the surface of the secondary model .

According to the present invention, since the metal powder adhering to the primary model is removed and then the surface is melted, it is possible to form a model in which the unevenness of the end surface, which is the side surface during modeling, is smoothed.

It is sectional drawing for demonstrating the 3D laminated modeling method and 3D laminated modeling apparatus according to Embodiment 1 of this invention. It is a 1st cross-sectional schematic diagram for demonstrating the 3D laminated modeling method by Embodiment 1 of this invention and the laminated modeling process in 3D laminated modeling apparatus. It is a 2nd cross-sectional schematic diagram for demonstrating the 3D laminated modeling method by Embodiment 1 of this invention and the laminated modeling process in 3D laminated modeling apparatus. It is a 3rd cross-sectional schematic diagram for demonstrating the 3D laminated modeling method by Embodiment 1 of this invention, and the laminated modeling process in 3D laminated modeling apparatus. It is sectional drawing for demonstrating the three-dimensional laminated molding method according to Embodiment 1 of this invention, and the metal powder removal process in a three-dimensional laminated molding apparatus. It is sectional drawing for demonstrating the 3D laminated modeling method and the surface treatment process in the 3D laminated modeling apparatus according to Embodiment 1 of this invention. It is a perspective schematic diagram for demonstrating the electron beam irradiation direction of the 3D laminated modeling method and the surface treatment process in the 3D laminated modeling apparatus according to Embodiment 1 of this invention. FIG. 5 is an enlarged cross-sectional view showing an end portion of a modeled object after a metal powder removing step in the three-dimensional laminated modeling method and the three-dimensional laminated modeling apparatus according to the first embodiment of the present invention. It is sectional drawing which shows the state of the side surface of the modeled object after the metal powder removal process in the 3D laminated modeling method and the 3D laminated modeling apparatus according to Embodiment 1 of this invention. It is sectional drawing which shows the state of the upper surface surface of the modeled object after the metal powder removal step in the 3D laminated modeling method and the 3D laminated modeling apparatus according to Embodiment 1 of this invention. It is sectional drawing which shows the state of the back surface surface of the modeled object after the metal powder removal process in the 3D laminated modeling method and the 3D laminated modeling apparatus according to Embodiment 1 of this invention. It is a conceptual perspective view for demonstrating the three-dimensional laminated modeling method and the laminated modeling process in a three-dimensional laminated modeling apparatus according to the first embodiment of the present invention. It is a conceptual perspective view for demonstrating the three-dimensional laminated modeling method and the surface treatment process in a three-dimensional laminated modeling apparatus according to Embodiment 1 of the present invention. It is a conceptual diagram for demonstrating the three-dimensional laminated modeling method and the surface treatment process in the three-dimensional laminated modeling apparatus according to Embodiment 1 of this invention. FIG. 5 is an enlarged cross-sectional view showing a state of the surface of a modeled object in a surface treatment step in the three-dimensional laminated modeling method and the three-dimensional laminated modeling apparatus according to the first embodiment of the present invention. It is an enlarged cross-sectional view which shows the state of the surface of the modeled object of the surface treatment process in the 3D laminated modeling method and the 3D laminated modeling apparatus by the comparative example. It is a diagram explaining the beam diameter of an electron beam. It is sectional drawing which shows the state of the side surface of the modeled object after the surface treatment process in the 3D laminated modeling method and the 3D laminated modeling apparatus according to Embodiment 1 of this invention. It is sectional drawing which shows the state of the upper surface surface of the modeled object after the surface treatment process in the 3D laminated modeling method and the 3D laminated modeling apparatus according to Embodiment 1 of this invention. It is sectional drawing which shows the state of the back surface surface of the modeled object after the surface treatment process in the 3D laminated modeling method and the 3D laminated modeling apparatus according to Embodiment 1 of this invention. It is sectional drawing for demonstrating the 3D laminated modeling method and the surface treatment process in the 3D laminated modeling apparatus according to Embodiment 2 of this invention. It is sectional drawing for demonstrating the 3D laminated modeling method and the surface treatment process in 3D laminated modeling apparatus according to Embodiment 3 of this invention. It is sectional drawing for demonstrating the structure of the electron beam irradiator of the 3D laminated modeling method and the surface treatment process in the 3D laminated modeling apparatus according to Embodiment 3 of this invention. It is a conceptual perspective view for demonstrating the three-dimensional laminated modeling method and the surface treatment process in the three-dimensional laminated modeling apparatus according to Embodiment 4 of this invention. It is a conceptual diagram for demonstrating the irradiation direction of the electron beam of the 3D laminated modeling method and the laminated modeling process and the surface treatment process in the 3D laminated modeling apparatus according to Embodiment 4 of the present invention. It is sectional drawing which shows the schematic structure of the 3D laminated modeling apparatus according to Embodiment 5 of this invention. It is sectional drawing which shows the schematic structure of the 3D laminated modeling apparatus according to Embodiment 6 of this invention.

Embodiment 1.
FIG. 1 is a schematic view showing each step of the three-dimensional laminated molding method according to the first embodiment of the present invention, and is shown by a cross-sectional view of a three-dimensional laminated molding apparatus in each step. The three-dimensional laminated molding method according to the present invention includes a laminated molding step, a metal powder removing step, and a surface treatment step. 1A and 1B are diagrams showing a laminated molding process, FIGS. 1C and 1D are diagrams showing a metal powder removing process, and FIG. 1E is a diagram showing a surface treatment process.

Metal powder is used as a raw material in order to perform three-dimensional laminated modeling of metal materials. As shown in FIGS. 1A and 1B, the primary model 81 is formed from the metal powder in the laminated modeling process. The metal powder 6 is supplied to the modeling box 4 installed in the electron beam irradiation chamber 3 which is a processing chamber by the dust feeder 7, and the metal powder 6 is laid in layers. A part of the layered metal powder is irradiated with an electron beam 2 generated from the electron gun 1 to melt and solidify a predetermined portion of the metal powder. After the layered metal powder of a predetermined portion is solidified, the elevating stage 5 is lowered by a predetermined distance, the metal powder is supplied from the dusting machine 7, and the metal powder is spread in layers on the solidified metal. Then, a part of the layered metal powder is irradiated with an electron beam 2 generated from the electron gun 1 to melt and solidify a predetermined portion of the metal powder. At this time, a solidified portion is formed together with the already solidified portion of the lower layer. By repeating these thin layers of powder laying and beam irradiation, as shown in FIG. 1B, an integrated metal primary model 81 is formed. The unmelted metal powder 6 remains around the primary model 81.

In the next metal powder removing step, as shown in FIGS. 1C and 1D, the unmelted metal powder 6 around the primary model 81 is removed. The primary model 81 with the unmelted metal powder 6 attached around it is installed in the metal powder removing chamber 11 provided with the jet nozzle 12, and a high-pressure gas is injected from the jet nozzle 12 to inject the unmelted metal. Remove the powder 6. The metal powder in the portion not irradiated with the electron beam has not been melted, but has been heated to a high temperature, so that it adheres around the primary model 81. The metal powder in the unmelted portion is removed by blowing a gas, and the metal powder is taken out as a secondary model 82 from which the metal powder has been removed.

In the surface treatment step, the secondary model 82 is installed in the electron beam irradiation chamber 23, which is a processing chamber, and the surface of the secondary model 82 is irradiated with the electron beam 22 generated from the electron gun 21. The irradiation position of the electron beam is moved at high speed on the surface of the secondary model 82 by deflection. Only the thin layer on the surface of the secondary model 82 melts and solidifies. The unevenness of the surface is averaged and smoothed by melting and solidification by the electron beam, and the final model 8 can be obtained.

Each process will be described in detail. 2 to 4 are views showing a metal powder laminating molding step by a cross-sectional view of an electron beam irradiator 100 used in the laminating molding step. The electron beam irradiator 100 includes an electron gun 1 and an electron beam irradiation chamber 3 as main components. The electron gun 1 has an electron source 31 that generates an electron beam 2, a focusing lens 32 that focuses the generated electron beam 2 on the metal powder 6, and an irradiation position of the electron beam 2 is moved to a predetermined position on the metal powder 6. It is composed of a deflector 33 for scanning. The electron beam irradiator and its components used in the laminating molding step are described as the first electron beam irradiator 100, the first electron gun 1, the first electron beam irradiation chamber 3, and the electron beam 2. It may be referred to as a first electron beam with a "first".

The electron gun control device 34 is configured to control the electron source 31 via the electron beam current controller 35, the focusing lens 32 via the focusing lens power supply 36, and the deflector 33 via the deflection power supply 37. There is. The electron gun control device 34 stores in advance beam current data 341, beam focus control data 342, and deflection data 343 created according to a predetermined shape for each layer of each layer according to the shape of the modeled object. Based on these data, it is configured to control the beam irradiation position by beam current, beam focus, and deflection.

The central beam axis 25, which is the central path of the electron beam in the laminated molding process, is shown in the figure. The central beam axis 25 corresponds to the trajectory of the electron beam when no deflection is applied. In the electron beam irradiation chamber 3, a stacking tank 150 composed of a modeling box 4, an elevating stage 5 for moving the metal powder and the modeled object each time the lamination is repeated, and a dusting machine 7 for laying a new layer of metal powder. Is placed. In addition, a vacuum pump for vacuum exhaust, a vacuum exhaust system such as a vacuum gauge, a control device for a mechanism, and the like are provided, but they are omitted because they are not directly related to the present invention.

As the metal powder, metal powder such as Ti, various steels, and Cu is used according to the application. As the metal powder, a metal powder having an average particle size of 20 to 200 μm is selected. The modeling box 4 is filled with metal powder. FIG. 2 is a diagram showing a state in which an electron beam is irradiated after a plurality of stacking is repeated. The electron beam 2 is deflected according to the data of the electron gun control device 34, and the metal powder of the portion irradiated with the electron beam is melted and solidified.

The energy absorption rate of the metal material for the electron beam is as high as 80 to 90%, and there is no influence of reflection on the surface of the metal powder. The metal powder is heated efficiently and stably melts and solidifies. Since the metal powder in the portion not irradiated with the electron beam is not melted, the metal powders are not firmly fixed to each other.

FIG. 3 shows a state in which a predetermined region of the surface layer of the metal powder 6 is scanned with an electron beam to melt and solidify the metal powder 6 in the state of FIG. 2, and then the metal powder is newly supplied by the dust feeder 7. Shown. After the elevating stage 5 descends downward by one layer of the laminate from the state shown in FIG. 2, a new metal powder has a constant layer thickness while moving on the metal powder already laid by the dusting machine 7. Lay out. The layer thickness is often selected in the range of 20 to 200 μm.

FIG. 4 shows how the electron beam 2 is irradiated to the new layer. The electron gun control device 34 controls the deflector 33 according to the deflection data according to the beam irradiation position of the new layer, and the electron beam is irradiated. It melts together with the already solidified portion of the lower layer and solidifies together to form the solidified portion 80. In addition to the above-mentioned melting and solidification of the metal powder, the electron beam may be irradiated to keep the temperature of the entire metal powder at a preset temperature.

The metal powder is spread and irradiated with an electron beam to solidify the metal powder into a predetermined shape. The powder laying and electron beam irradiation are repeated until the height of the laminated structure reaches a predetermined value, the primary modeled object 81 is formed, and the layered modeling process is completed. During this period, the metal powder is only irradiated with an electron beam for melting and solidifying for laminated molding and an electron beam for keeping the temperature of the entire metal powder at a high temperature. No extra heating or local heating is performed, and thermal deformation of the modeled object is suppressed.

The metal powder removing step will be described. FIG. 5 is an explanatory diagram of a metal powder removing step by the metal powder removing machine 200. The metal powder removing machine 200 includes a metal powder removing chamber 11 and a jet nozzle 12 as main components. Unmelted metal powder 6 is attached around the primary model 81. Since the temperature of the entire metal powder is maintained at a predetermined high temperature, the metal powder in the parts other than the melt-solidified pattern is not melted, but the shaped objects and the metal powders adhere to each other. The modeled object to which the unmelted metal powder is attached is placed in the metal powder removing chamber 11. The unmelted metal powder is removed from the primary model 81 by injecting a high-pressure gas from the jet nozzle 12. Unevenness remains on the surface of the secondary model 82 from which the unmelted metal powder has been removed. On the electron beam irradiation side, the surface perpendicular to the beam axis in the lamination molding process has small surface irregularities. On the other hand, the surface parallel to the beam axis in the laminated modeling process and the surface opposite to the beam irradiation side have large irregularities. When the metal powder is a material that is easily oxidized or the particle size is small, an inert gas may be used as the gas to be sprayed in order to prevent oxidation and ignition of the powder. Further, other methods such as a method of applying mechanical vibration or impact may be used.

Next, the surface treatment step will be described. FIG. 6 is a diagram showing the surface treatment step by a cross-sectional view of the electron beam irradiator 300 used in the surface treatment step. The electron beam irradiator 300 used in the surface treatment step includes an electron gun 1 and an electron beam irradiation chamber 3 as main components. The electron gun 21 is composed of an electron source 41, a focusing lens 42, and a deflector 43. The electron gun control device 44 is configured to control the electron source 41 via the electron beam current controller 45, the focusing lens 42 via the focusing lens power supply 46, and the deflector 43 via the deflection power supply 47. There is. The electron gun control device 44 stores beam current data 441, beam focus control data 442, and deflection data 443 created according to the shape of the modeled object and the position arranged in the processing chamber, and based on these data. It is configured to control the beam current, the focus of the beam, and the beam irradiation position by deflection. The central beam axis 26, which is the central path of the electron beam in the surface treatment step, is shown in the figure. The central beam axis 26 corresponds to the trajectory of the electron beam when no deflection is applied. The secondary model 82 was arranged so that the central beam axis 26 in the surface treatment process was perpendicular to the center beam axis 25 in the laminated modeling process. The electron beam irradiator and its components used in the surface treatment step can be used as in the second electron gun 21, the second electron beam irradiation chamber 23, the second electron beam irradiator 300, and the electron beam 22. May be referred to as a second electron beam 22 with a "second".

Here, with reference to FIG. 7, the angle formed by the central beam shaft 25 in the laminating molding process and the central beam axis 26 in the surface treatment process will be described. The angle α formed by the central beam shaft 25 in the lamination molding process is set with respect to the boundary surface 60 between the layers in the lamination, and the angle β formed by the central beam shaft 26 in the surface treatment step with respect to the boundary surface 60 between the layers in the lamination. The polarity of the angle is positive on the central beam axis side in the lamination molding process. The angle θ between α-β and the central beam axis 25 and the central beam axis 26
And. α is usually 90 degrees. In the case of the examples shown in FIGS. 2 to 4 and 6, α is 90 degrees, β is 0 degrees, and θ is 90 degrees.

Based on the data stored in the electron gun control device 44, the electron beam 22 is deflected and the irradiation position of the electron beam 22 moves according to the surface shape of the secondary model 82 to move the surface of the secondary model 82. To scan. In the region irradiated with the electron beam 22, 10 to 300 μm in the surface depth direction melts, and when the electron beam passes by, it solidifies.

Here, the unevenness of the surface of the modeled object will be described. FIG. 8 shows a schematic view of a cross section of the secondary model 82. The figure shows a pattern in which three solidified metal layers 51 are laminated. For the sake of explanation, the metal powder 52 before melting is drawn. The left side of the figure is the end face 53 of the secondary model 82. Although reducing the thickness of one layer of lamination is advantageous for improving accuracy, the number of laminations required per the same height increases, so that the molding time increases significantly. A suitable stack thickness is 50 to 200 μm. As described above, a metal powder having an average particle size of 20 to 200 μm is used, and the thickness of one layer of the metal solidified layer 51 and the average particle size are close to each other. In particular, the average particle size is 50 to 100 μm, and the thickness of the laminate is often around 100 μm. In many cases, the thickness of the laminate and the average particle size are close to each other. On the surface of the end face 53 of the secondary model 82, incompletely bonded portions and excess shaped portions are formed and unevenness is generated. As shown in the figure, the shape of the end face of the one-layer fused portion when the electron beam is irradiated. Since the particle size is larger than the layer thickness, the unevenness increases due to the influence of the grain shape. The surface irregularities on the surface perpendicular to the central beam axis 25 during the laminated molding are small, and the surface irregularities increase as they approach parallel to the central beam axis 25. The surface on the back side with respect to the electron beam irradiation direction also has large irregularities on the surface as well as the end surface.

Examples of irregularities on the surface of the modeled object after modeling are shown in FIGS. 9, 10 and 11. The figure is a cross-sectional pattern on the surface of the modeled object. The horizontal direction is parallel to the surface, and the vertical direction is the appearance of unevenness there. FIG. 9 is a surface parallel to the central beam axis 25 during laminated molding, FIG. 10 is a surface orthogonal to the central beam axis 25, and FIG. 11 is a surface on the back side with respect to the electron beam irradiation side. As for each surface roughness, Ra is a surface 29 μm parallel to the central beam axis 25 in the laminating molding process.
A surface orthogonal to the central beam axis 25 in the laminating molding process 9 μm
27 μm on the back side with respect to the electron beam irradiation side of the lamination molding process
It was about. As described above, in the plane parallel to the central beam axis 25 at the time of laminating modeling, continuous convexes or continuous concaves are often generated along the laminating direction.

The irradiation direction of the electron beam in the surface treatment step on the secondary model 82 will be described. FIG. 12 shows the positional relationship between the primary model 81 and the electron beam 2 in the laminated modeling process. The shape of the modeled object is shown by the example of a sphere. The dotted line on the surface of the sphere indicates the boundary line 61 of each layer of the stack. The central beam axis 25 is oriented perpendicular to the interface of each layer in the stack. FIG. 13 shows the irradiation direction of the electron beam 22 on the secondary model 82 in the surface treatment step. The central beam axis 26 of the electron beam 22 in the surface treatment step is irradiated in a direction substantially perpendicular to the central beam axis 25 of the electron beam 2 in the laminated molding step. Therefore, in the surface treatment step, the electron beam can be efficiently irradiated to the surface parallel to the central beam axis 25 at the time of laminated molding. Reference numeral 71 denotes a locus of the irradiation position of the electron beam on the modeled object.

FIG. 14 shows the irradiation locus 71 of the electron beam 22 on the secondary model 82 in the surface treatment step. The irradiation position of the electron beam moves in the vertical direction in the figure. After the electron beam irradiation position moves to the upper end, it moves to the right in the figure and moves downward with an interval of the locus shown by 72. Hereinafter, this reciprocating movement is repeated. Therefore, the locus of the irradiation position of the electron beam is orthogonal to the boundary line 61 of each layer of the lamination in the lamination molding step. The electron beam irradiation position is preferably controlled by the deflector 43 of the electron beam 22.

By irradiating the surface of the secondary model 82 with an electron beam, a molten pool in which the metal is melted is formed. The molten pool moves as the irradiation position of the electron beam moves. Since the molten pool generated when the electron beam is irradiated becomes an ellipse with the moving direction of the electron beam as the major axis, if the electron beam is moved in the direction orthogonal to the boundary line of each layer of the stack as described above, It is possible to form a long molten pool that spans a plurality of laminated layers and melt the unevenness formed in each laminated layer to enhance the smoothing effect.

In the above, the example in which the electron beam is controlled by the deflector 43 to move on the surface of the modeled object (move to the right in the figure) to irradiate the object has been described. However, the traveling direction of the electron beam is fixed. It is also possible to move the irradiation position of the electron beam on the surface of the modeled object while rotating the secondary modeled object 82 on a rotating stage or the like. In this case, the surface of the secondary model 82 can be efficiently irradiated with the electron beam, and the surface treatment can be performed in a short time. Needless to say, both the electron beam and the modeled object may be moved.

Here, the smoothing of the surface of the modeled object by irradiating the electron beam will be described with reference to FIGS. 15 and 16. The figure shows the state 75 of the unevenness on the surface of the secondary model. The spacing between irregularities (interval between convex and convex or between concave and concave) depends on the layer thickness of one layer of the laminate and the particle size of the metal powder. In the experiment as an example, when the thickness of one layer of the laminate was 100 μm and the average particle size of the metal powder was 60 μm, the interval between the irregularities was often 100 to 200 μm.

When the uneven portion is irradiated with the electron beam 22, the molten pool 76 is formed. The electron beam 22 is moving in the direction of arrow 78 in the figure. W in the figure indicates the width of the molten pool. The uneven portion melts and solidifies in order from the terminal portion of the electron beam 22. As shown in FIG. 15, when the width w of the molten pool 76 is a wide range equal to or larger than the interval of the unevenness, the unevenness is melted and averaged, so that the unevenness becomes small and smoothed. As shown in FIG. 16, when the width w of the molten pool 76 is narrower than the distance between the irregularities, the smoothing effect of the irregularities becomes small. Therefore, it is preferable that the width w of the molten pool is equal to or larger than the preset size corresponding to the interval between the irregularities. As described above, the spacing between the irregularities is generated corresponding to the thickness of the solidified metal layer formed in the laminating molding step. Therefore, it is preferable that the width w of the molten pool in the thickness direction of the metal solidified layer formed in the laminated molding step is twice or more the thickness of the metal solidified layer.

The parameters of the electron beam 22 such as the beam diameter, the beam power, and the beam intensity distribution shape are adjusted in order to adjust the width w of the molten pool. That is, the parameters of the electron beam 22 are set so that the width w of the molten pool in the thickness direction of the metal solidified layer formed in the laminated molding step is equal to or larger than a preset dimension. Here, the beam diameter will be described. FIG. 17 shows the beam profile of the focused electron beam. The horizontal axis is the radial dimension, and the vertical axis is the current density. The beam diameter is represented by the width (full width at half maximum) d of the beam having half the current density with respect to the peak value Jp of the current density. Further, the beam may have a shape with a flat intensity distribution. In this case, the beam diameter can be defined as the diameter of the flat portion.

When an appropriate beam power is applied, the width w of the molten pool is equivalent to the beam diameter, so it is preferable to control the beam diameter to be at least twice the layer thickness of the laminated layer. When the layer thickness is 100 μm, the beam diameter is 200.
μm or more is good. The beam diameter can be easily adjusted by adjusting the focused state of the electron beam at the beam irradiation position. The focused state of the electron beam can be adjusted by the focusing lens current. The beam power is often adjusted by keeping the accelerating voltage for accelerating the electron beam at the electron source 41 constant and changing the current value of the electron beam.

If the width of the molten pool is too wide, the originally required shape, such as small protrusions and edges, may become smooth. In order to accurately form irregularities larger than 200 μm, it is desirable that the upper limit of the molten pool and beam diameter is smaller than about 5 times the laminated thickness. From these facts, it is desirable to form a molten pool that is 2 to 5 times the laminated thickness. For this purpose, it is desirable to control the beam diameter to be 2 to 5 times the laminated thickness. The protrusions, edges, and other parts that require precision may be controlled so as not to irradiate the surface-treated beam. This can be controlled by deflection data based on the shape data.

Here, the result by one example is shown. Experiments were conducted using a powder with an average Ti particle size of 60 μm and a layer thickness of 100 μmm. The electron beam was deflected so that the moving direction of the irradiation position of the electron beam was perpendicular to the boundary line of each layer of the stack. The beam moving speed is 1 m / s and the beam power is 600 W. At this time, the interval between the trajectory of the electron beam (the interval indicated by reference numeral 72 in FIG. 14) was set to 100 μm. Examples of surface irregularities of the final modeled product after the surface treatment step are FIG. 18 (plane parallel to the beam axis during laminated molding), FIG. 19 (plane orthogonal to the beam axis), and FIG. 20 (with respect to the beam irradiation side). Shown on the back side). By the surface treatment, the surface roughness Ra of the surface parallel to the beam axis, the surface orthogonal to the beam axis, and the surface on the back side with respect to the beam irradiation side at the time of laminated molding was improved as follows.

In this way, the three-dimensional laminated modeling method and device are separated into a laminated modeling step, a metal powder removing step, and a surface treatment step, and the laminated modeling is completed, and the secondary model from which the metal powder has been removed is subjected to the laminated modeling step. Since the electron beam can be irradiated from a direction different from the central beam axis, the electron beam can be irradiated to the surface of the secondary model having large irregularities and large surface roughness, and the effect of smoothing the surface can be obtained. It was.

Since the electron beam is applied to the heat source, it is efficiently heated without being affected by reflection on the surface of the metal powder, melted and solidified, and there is an effect that stable production can be performed without collapse of the modeled object. In addition, after the process of laminated modeling is completed and the formation of the modeled object is completed, it is configured to irradiate an electron beam as a heat source for surface treatment, so that thermal deformation of the modeled object can be suppressed and highly accurate laminated modeling is possible. Has the effect of becoming.

Furthermore, by moving the beam irradiation position so that the trajectory of the electron beam irradiation position in the surface treatment process is orthogonal to the boundary line of each layer of the lamination in the lamination molding process, the effect of reducing surface irregularities can be achieved. There was an effect that could be increased.

The moving direction of the electron beam irradiation position in the surface treatment step is not limited to the direction orthogonal to the boundary line between the layers of the stack, but the irradiation position of the electron beam intersects the boundary line between the layers of the stack. The same effect can be obtained as long as the molten pool that moves and is formed at that time has a layer thickness of one layer or more in the lamination and extends over the interval of the unevenness of the modeled object.

As shown by showing that the surface treatment can be performed in a short time by rotating the secondary model in the surface treatment step, the electron beam in the surface treatment step is relative to the axis of the electron beam in the laminated molding step. By changing the direction of the beam axis, it was possible to obtain the effect of surface treatment in a short time.

Although FIG. 13 shows an example in which the electron gun is arranged horizontally, the electron gun is fixed upward and the direction of the secondary model 82 is changed to a direction different from the direction of the primary model 81. The same effect can be obtained by irradiating the beam 22. Further, the case where the angle θ (= α-β, see FIG. 8) formed by the central beam axis 25 in the laminating molding process and the central beam axis 26 in the surface treatment process is 90 degrees is shown, but the angle θ is limited to 90 degrees. The same effect can be obtained as long as the surface of the modeled object can be efficiently irradiated with the electron beam.

In addition, the three-dimensional laminated modeling method and apparatus have the effect of being able to stably supply a highly accurate modeled object having a complicated shape without finishing.

Embodiment 2.
FIG. 21 shows a pattern of electron beam irradiation in the surface treatment step in the three-dimensional laminated molding method according to the second embodiment of the present invention by a cross-sectional view of the electron beam irradiator 300. An electron beam with an output of kw order usually has a depth of focus of several mm or more. In the range where there is no beam aberration due to deflection, when the electron beam is irradiated to the flat surface of the modeled object, the effect does not change even if the influence of the focus fluctuation is ignored. The depth of focus is finite, and when the shape of the modeled object is complicated, such as a combination of curved surfaces and multiple surfaces, and a combination of holes and dents, the effect of surface treatment can be enhanced by correcting the focus.

The focus of the electron beam is adjusted to keep the molten state of the beam irradiation part constant, and stable surface treatment is performed. In the present embodiment, the focal length of the focusing lens is adjusted so that the surface of the modeled object is in focus. FIG. 21 shows an example in which a spherical secondary model 82 is irradiated with an electron beam. When the irradiation direction of the electron beam is deflected to 91, the electron beam is focused at the position of the surface 92 of the secondary model 82. When the irradiation direction of the electron beam is moved to 93 by the control of the deflector 43, the focus is at the position of 94 when the focus is not adjusted. By adjusting the focusing lens 42 and moving the focal point away from the position indicated by 95, the electron beam can always be focused on the surface of the secondary model 82.

Electron guns usually use a magnetically focused lens, which can be adjusted by controlling the lens current value. There is no need to control the beam irradiation head with a mechanical drive device like an optical beam or a galvanometer scanner. By electrically controlling the current of the focusing lens in synchronization with the control signal of the deflector 43 that controls the beam irradiation direction, the electron beam can always be focused on the surface of the secondary model 82. As a result, the surface could be treated stably, and a model 8 having a smooth surface could be obtained. For the focused lens current, the current value corresponding to the focal length according to the beam irradiation position is calculated in advance based on the shape data of the modeled object.

In the case of an electron beam, the moving speed of the electron beam on the modeled object in surface treatment is as high as 1 to 10 m / s, but since the focused lens current is electrically controlled, no mechanical movement is required. Yes, it is possible to correct the focus so that it follows the beam movement sufficiently. The same effect can be obtained by using the focusing lens 42 in combination with two focusing lenses, a DC focusing lens and a high-speed operation focusing lens (called a dynamic focus lens) for correction.

In the three-dimensional laminated modeling method and apparatus according to the second embodiment of the present invention, as shown in the first embodiment, the surface of the secondary model 82 having large irregularities and a large surface roughness can be irradiated with an electron beam. In addition to the effect of smoothing the surface, the electron beam irradiation position and beam diameter are controlled according to the surface shape of the modeled object, so the surface can be smoothed even on a modeled object with a complicated surface shape. There is an effect that can be done. In FIG. 21, the spherical shaped object has been described, but the surface treatment can be similarly applied to other complicated shaped objects.

Embodiment 3.
FIG. 22 shows a pattern of electron beam irradiation in the surface treatment step in the three-dimensional laminated molding method according to the third embodiment of the present invention by a cross-sectional view of the electron beam irradiator 300. When the electron beam is irradiated in a certain direction, the electron beam is vibrated in the direction perpendicular to the beam axis with the width of the arrow 96, that is, so-called beam oscillation is applied to irradiate the electron beam. FIG. 23 is a diagram illustrating a configuration of an electron gun 21 for applying beam oscillation. The deflector 43 controls the beam irradiation position (irradiation direction) of the electron beam 22. The deflector 43 is driven via the deflection power supply 47 by the signal obtained by adding the deflection data 402 indicating the movement of the beam position and the beam oscillation signal 403 by the adder 401. The oscillation signal is a high-frequency triangular wave of about several kHz to 100 kHz, and the amplitude is selected to be about 0.1 to 2 mm depending on the amplitude of the beam irradiation position. The deflection data is data that moves the normal beam irradiation position. Due to the oscillation signal, the electron beam oscillates at a high frequency with a small amplitude indicated by the thin line arrow 96 on the work 193, and the beam irradiation position moves as shown by the thick line arrow 192. Since the electron beam has a high beam oscillation frequency, it acts on the work as if the beam diameter was apparently increased.

In FIG. 22, when the surface of the secondary model 82 is irradiated with an electron beam by beam deflection, a high-frequency oscillation signal is superimposed on the deflector 43, and beam oscillation is added to vibrate the beam irradiation position. Vibrate by the width indicated by 96. Oscillation amplitude 0.5 mm,
Beam oscillation was applied with a frequency of 10 kHz and an oscillation waveform triangular wave, and the width of the molten pool for surface treatment could be controlled stably.

As described in the first embodiment, in order to smooth the surface of the modeled object, it is possible to enhance the effect by controlling the width of the molten pool according to the thickness of the laminated layer and the particle size of the metal powder. it can. The width of the molten pool can be controlled by beam power, but the melting depth also changes at the same time. By using beam oscillation, it is possible to increase the width of the molten pool without increasing the penetration width in the depth direction and keeping the heat effect small.

In the three-dimensional laminated modeling method and apparatus according to the third embodiment, as shown in the first and second embodiments, the surface of the modeled object has large irregularities and a large surface roughness can be smoothed, and the surface shape is complicated. In addition to having the effect of smoothing the surface of an object, it also has the effect of smoothing the surface while keeping the heat effect on the modeled object small.

Further, when the thickness of one layer in the laminated modeling step is changed or when the particle size of the metal powder is changed, the interval between the irregularities on the surface of the modeled object changes. In order to adjust the width of the molten pool that is optimal for smoothing the unevenness of the surface, the amplitude of the beam oscillation is suitable, and a model with a smooth surface can be easily manufactured.

Embodiment 4.
The pattern of electron beam irradiation in the surface treatment step in the three-dimensional laminated molding method according to the fourth embodiment of the present invention is shown as a conceptual diagram in FIG. The electron gun 21 was arranged at a position where the angle θ formed by the central beam shaft 26 in the surface treatment step was 135 degrees with respect to the central beam shaft 25 in the laminating molding step. When the central beam axis 25 in the laminated molding process and the central beam axis in the surface treatment process intersect, the angle θ is simply represented. If they do not intersect, they are defined by the angle with respect to the interface between the layers in the stack, as described in FIG.

According to the fourth embodiment, in the surface treatment step, the electron beam can be efficiently irradiated to the surface which is the back side of the modeled object when viewed from the electron beam irradiation side during the laminated modeling. The surface roughness of the back surface of the secondary model 82 has the same unevenness as the side surface. In the surface treatment step, the back surface can be efficiently irradiated with an electron beam, the unevenness of the surface can be reduced, and the front surface can be smoothed. FIG. 25 shows an example of the device configuration. FIG. 25A on the left side is a diagram showing a laminated molding process, and FIG. 25B on the right side is a diagram showing a surface treatment process. In the figure, the arrangement directions of the primary model 81 in the laminated modeling process and the secondary model 82 in the surface treatment process are set to the same direction, and the arrangement directions of the respective electron guns are changed. However, the arrangement direction of the modeled object may be changed by using electron guns having the same beam axis direction. Further, the same electron gun as the electron gun 1 and the electron gun 21, and the same electron beam irradiation chamber as the electron beam irradiation chamber 3 and the electron beam irradiation chamber 23 may be used. In the above, an example is shown in which the angle formed by the central beam shaft 25 during laminated molding and the central beam shaft 26 during surface treatment is 135 degrees, but the angle between 90 degrees and 180 degrees as θ depends on the shape of the modeled object. You just have to choose.

In the conventional laminated molding method described in Patent Document 1, a layer of powder is laid and the layer is irradiated with a light beam to repeatedly integrate with the solidified layer of the lower layer, and during the laminated molding work. , The modeled object in the middle of the laminated modeling was taken out from the powder layer, and the end face was irradiated with a light beam from the horizontal direction. Since the end face is irradiated with the light beam in the middle of the laminated modeling, the light beam is horizontally lifted from the layer of powder laid immediately before so that the laminated modeling can be performed again. A complicated method of irradiating from the direction is used. However, even with this method, when the light beam is re-irradiated, most of the modeled object is buried in metal powder, and the light beam cannot be irradiated in any direction, especially from the bottom to the top. There was a challenge.

In the three-dimensional laminated molding method and apparatus according to the fourth embodiment of the present invention, as described above, the secondary molding step, the metal powder removing step, and the surface treatment step are separated, and the laminated molding is completed and the metal powder is removed. Since the modeled object is configured to be able to irradiate the electron beam from any direction, the surface of the secondary modeled object, which is on the opposite side of the beam irradiation direction in the laminated modeling process, is also irradiated with the electron beam in the surface treatment process. It is possible to obtain the effect of smoothing the surface.

Embodiment 5.
FIG. 26 is a cross-sectional view showing a schematic configuration of a three-dimensional laminated modeling apparatus according to the fifth embodiment of the present invention. In the three-dimensional laminated molding apparatus according to the fifth embodiment, as the three-dimensional laminated molding apparatus, a first electron beam irradiator 100 that executes a laminated molding step, a metal powder removing machine 200 that executes a metal powder removing step, and a surface treatment step. It has a second electron beam irradiator 300 for executing the above, and is configured to be capable of continuous processing. The electron beam irradiation chamber 3 of the first electron beam irradiator 100 and the metal powder removal chamber 11 of the metal powder remover 200 are partitioned by a first gate 102. The first gate 102 is closed during the laminating molding process, and after the laminating molding process is completed, the first gate 102 is opened and the primary model 81 to which the unmelted metal powder is attached is passed through the first gate 102 to metal. It is sent to the powder removing device 200. The metal powder removing chamber 11 of the metal powder removing machine 200 and the second electron beam irradiating chamber 23 of the second electron beam irradiator 300 are separated by a second gate 203. While the metal powder removing step is being performed in the metal powder removing machine 200, the first gate 102 and the second gate 203 are closed. After the metal powder removing step is completed, the second gate 203 is opened, and the secondary model 82 from which the adhering metal powder has been removed is sent to the second electron beam irradiation chamber 23. After that, the surface treatment step is executed in the second electron beam irradiation chamber 23. It also has a transport mechanism such as a stage for moving each model to be processed between the metal powder removal chamber and each electron beam irradiation chamber.

The first electron beam irradiator 100, the metal powder remover 200, the second electron beam irradiator 300, and each gate are controlled by the central control device 50, and the laminating molding step, the metal powder removing step, and the surface treatment step are executed. Will be done. The central control device 50 includes a CPU and a memory, and the CPU performs necessary arithmetic processing based on the control parameters of each device stored in the memory and sends a command to each device. A local control device such as an electron gun control device may be provided between the central control device 50 and each device. Further, the central control device 50 may be composed of a plurality of computers.

According to the fifth embodiment, continuous processing of laminated molding, removal of metal powder, and surface treatment becomes possible, and the effect of improving productivity can be obtained.

Embodiment 6.
FIG. 27 is a cross-sectional view showing a schematic configuration of a three-dimensional laminated modeling apparatus according to the sixth embodiment of the present invention. The three-dimensional laminated molding apparatus according to the sixth embodiment includes an electron beam irradiator 110 that executes a laminated molding step and a surface treatment step, and a metal powder remover 200 that executes a metal powder removing step as the three-dimensional laminated modeling apparatus. , It is configured so that each process can be processed continuously. The electron beam irradiation chamber 3 of the electron beam irradiator 110 and the metal powder removal chamber 11 of the metal powder remover 200 are partitioned by a gate 103. The gate 103 is closed during the laminating molding step, and after the laminating molding step is completed, the gate 103 is opened and the modeled object 81 to which the unmelted metal powder is attached is sent to the metal powder removing chamber 11 through the gate 103. The gate 103 is closed while the metal powder removing step is being performed in the metal powder removing chamber 11. After the metal powder removing step is completed, the gate 103 is opened, and the secondary model 82 from which the adhered metal powder has been removed is sent to the electron beam irradiation chamber 3 again. After that, the surface treatment step is executed in the electron beam irradiator 110. When executing the surface treatment step, the stacking tank 150 is retracted so that the secondary model 82 can be irradiated with the second electron beam. It also has a transport mechanism such as a stage for moving each model to be processed between the electron beam irradiation chamber and the metal powder removal chamber.

The electron beam irradiator 110, the metal powder remover 200, and the gate 103 are controlled by the central control device 501, and a laminating molding step, a metal powder removing step, and a surface treatment step are executed.

In the three-dimensional laminated modeling apparatus according to the sixth embodiment, the electron beam irradiator 110 used in the laminated modeling step is also used in the surface treatment step. In the fifth embodiment, the first electron gun 1 and the second electron gun 21 are the same electron gun, and the first electron beam irradiation chamber 3 and the second electron beam irradiation chamber 23 are the same electrons. This corresponds to the case where the beam irradiation chamber is used, that is, the case where the first electron beam irradiator 100 and the second electron beam irradiator 300 are the same electron beam irradiator 110. The final model 8 is completed by moving the model 8 between the electron beam irradiation stage 105 and the metal powder removal stage 106 for processing. According to the sixth embodiment, in addition to the effect of the fifth embodiment, the electron gun 1, the accompanying power source, the exhaust system, and the like can be shared, and the equipment cost can be suppressed.

In the present invention, each embodiment can be combined, and each embodiment can be appropriately modified or omitted within the scope of the invention.

1 electron gun (first electron gun), 2 electron-beam (first electron beam), three electron beam irradiation chamber (first electron beam irradiation chamber), 4 modeling box, 5 temperature descending stage, 6 Metal powder , 7 Powder dispenser, 8 Modeled object, 81 Primary modeled object, 82 Secondary modeled object, 11 Metal powder removal chamber, 12 Jet nozzle, 21 Electron gun (second electron gun), 22 Electron beam (second electron) Beam), 23 electron beam irradiation chamber (second electron beam irradiation chamber), 25 central beam axis of laminated molding process, 26 central beam axis of surface treatment process, 76 molten pool, 100 electron beam irradiator (first electron) Beam irradiator), 110 electron beam irradiator, 300 electron beam irradiator (second electron beam irradiator, 150 stacking tank, 200 metal powder remover, 102 first gate, 103 gate, 203 second gate,

Claims (14)

A first electron beam is irradiated on the metal powder spread in layers to melt the metal powder, and then the metal powder is spread in layers on a solidified metal layer formed by solidification, and the first electron beam is spread. A laminated molding step of forming a primary model in which the metal is solidified by repeating the process of forming a solidified metal solidified layer after melting the newly spread metal powder by irradiating with the metal powder.
In the laminated molding step, a metal powder removing step of removing the metal powder adhering to the primary shaped object without solidifying to form a secondary shaped object, and
Have a surface treatment step of forming a shaped product by irradiating a second electron beam to remelt the surface of the secondary molded article to the secondary molded product,
In the surface treatment step, by moving at least one of the second electron beam and the secondary model, the second electron beam is the boundary between the layers of the metal solidified layer on the surface of the secondary model. While moving to cross the line and irradiating,
The width of the direction in which the second electron beam moves on the surface of the secondary model in the molten pool formed on the surface of the secondary model by the irradiation of the second electron beam is the width of the laminated modeling step. A three-dimensional laminated modeling method, characterized in that the parameters of the second electron beam are set so as to be at least twice the thickness of one layer of the metal solidified layer formed in 1 . The three-dimensional laminated molding method according to claim 1, wherein in the metal powder removing step, gas is injected onto the surface of the primary modeled object to remove the metal powder adhering to the primary modeled object. The three-dimensional laminated modeling method according to claim 1 or 2 , wherein the first electron beam is deflected to scan on the metal powders spread in layers to melt the metal powders. Claims 1 to 3 are characterized in that the direction of the central beam axis of the second electron beam with respect to the secondary model is different from the direction of the central beam axis of the first electron beam with respect to the primary model. The three-dimensional laminated modeling method according to any one of the above. The angle formed by the central beam axis of the first electron beam with respect to the surface of the metal solidified layer and the angle formed by the central beam axis of the second electron beam with respect to the surface of the metal solidified layer. The three-dimensional laminated molding method according to claim 4 , wherein the difference from the angle is an angle in the range of 90 degrees to 180 degrees. The second electron beam according to any one of claims 1 to 5 , wherein the second electron beam scans on the secondary model by deflecting and remelts the surface of the secondary model. Three-dimensional laminated modeling method. The three-dimensional laminated modeling method according to any one of claims 1 to 6, wherein the parameter of the second electron beam is beam power. The three-dimensional laminated modeling method according to any one of claims 1 to 6, wherein the parameter of the second electron beam is a beam diameter. The second electron beam is an electron beam vibrated in a direction parallel to the direction in which the second electron beam moves , and is characterized in that the width of the vibration is adjusted to control the width of the molten pool. The three-dimensional laminated molding method according to any one of claims 1 to 6 . A first electron beam irradiation chamber and a first electron gun are provided, and in the first electron beam irradiation chamber, the metal powder spread in layers is irradiated with the first electron beam to melt the metal powder. A metal powder is spread in a layer on the metal solidified layer formed by post-solidification, and the first electron beam is irradiated to melt the newly spread metal powder and then solidified to form a solidified metal layer. The first electron beam irradiator, which is controlled to form a primary model in which the metal is solidified by repeating the formation of
A metal powder remover equipped with a metal powder removing chamber for removing metal powder adhering to the primary model without solidifying and using the primary model as a secondary model.
A second electron beam irradiation chamber and a second electron gun are provided, and in the second electron beam irradiation chamber, the secondary model is irradiated with a second electron beam to re-surface the surface of the secondary model. It is equipped with a second electron beam irradiator configured to melt to form a model .
The second electron beam moves on the surface of the secondary model, and the second electron beam vibrates in a direction parallel to the direction of movement on the surface of the secondary model. A three-dimensional laminated molding device characterized by this. The first electron beam irradiation chamber and the metal powder removal chamber are connected via a first gate, and the metal powder removal chamber and the second electron beam irradiation chamber are connected to a second gate. The three-dimensional laminated molding apparatus according to claim 10 , wherein the three-dimensional laminated molding apparatus is connected via a beam. The first electron beam irradiation chamber and the second electron beam irradiation chamber are the same electron beam irradiation chamber, and the first electron gun and the second electron gun are the same electron gun. The three-dimensional laminated molding apparatus according to claim 10 . The three-dimensional laminated modeling apparatus according to claim 12 , wherein the electron beam irradiation chamber and the metal powder removing chamber are connected via a gate. The feature is that the direction of the central beam axis of the second electron beam with respect to the secondary model is different from the direction of the central beam axis of the first electron beam with respect to the primary model. The three-dimensional laminated modeling apparatus according to any one of claims 10 to 13 .

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