The invention relates to a method and an apparatus for the powder bed fusion process and to a storage medium comprising instructions to execute the method.

There are a number of additive manufacturing techniques, as well referred to as 3D-printing processes. One of these techniques is the so-called powder bed fusion process. Very briefly summarizing, the powder bed fusion process consists of iteratively applying a powder layer onto a support structure and selectively adhering powder particles to another or previously adhered agglomerates by heating the respective particles using an electron beam, a laser beam or any other kind of radiation beam (hereinafter jointly "beam" for short). Adhering particles of a powder bed by scanning a surface of the powder bed with a beam is referred to as fusing, regardless of the physical or chemical process (melting, sintering, welding, radiation induced chemical reaction, ...) that provides the result of adhered particles. Vividly speaking, sectional views of the product to be manufactured are so to speak written on each newly applied top layer by moving a beam spot over the surface of the upmost powder layer. By adding a new powder layer after each writing step a so-called powder bed is formed. Embedded in the powder bed is the already manufactured portion of the workpiece. Depending on the final product, sometimes additional auxiliary structures have to be "written" into the powder layer, but herein we do not focus on this aspect and we consider these to be a part of the workpiece. Once all layers have been written, the workpiece, potentially with its adhering auxiliary structures, may be removed from the powder bed and may be subjected to further processing, if required. The terms product and workpiece are used interchangeably in this field and hence herein.

The powder bed fusion process is very capable, but it is desirable to reduce the manufacturing times for a given workpiece. To this end, it has been suggested to use multiple beams which independently write a portion of each layer (i.e. a portion of the "sectional view") of the workpiece onto each layer of the powder bed. Further, in particular in case the up-facing surface of the powder is increased to manufacture larger workpieces, multiple beams sourced can be distributed at different locations above the powder bed to reduce imperfections due to beam expansion and parallaxes. This approach, however, has limitations, for example fumes being produced by a first beam may interfere with another beam, which is detrimental to the quality of the product. Other problems are related to heat dissipation in the powder bed or to beam spot distortion. Beam spot distortion describes the effect of an increasing elliptic distortion of the beam spot formed on the powder bed as a function of increasing deviation of the angle of incidence from a near normal incidence.

WO 2016/075026 A suggests optimizing a multi beam laser powder bed fusion process by virtually separating the surface of a powder bed into a number of surfaces sections, wherein each beam illuminates and hence fuses powder particles in a single surface section being assigned to said beam. Once all beams finished writing on a layer, i.e. when the next powder layer can be applied to the powder bed, the run-times of each beam source, as well referred to as "beam-on times" of the different beam sources are compared and the boundaries between the surface sections are adjusted to compensate for differences in the run times. For example, if beam source No. 1 has a lower beam-on time than beam source No. 2, when writing the layer No. l, the boundary between the surface sections being associated to beam sources No. 1 and No. 2 are shifted to increase the surface area of the surface section associated to beam source No. 1 and to decrease the surface section associated to beam source No. 2. Thereby, idle times of the beam sources are reduced when fusing the next layer, i.e. layer No. l + 1. Alternatively, the areas of the actually illuminated surfaces may be compared and based on the comparison the boundaries between the surface sections may be adjusted to compensate for differences in the actually illuminated surfaces.

WO 2020/178216 A suggests controlling the positions of the beam spots of a multi beam laser powder bed fusion process such that at - no point in time - any line connecting two beam spots is parallel to a flow direction of an inert gas flow over the powder bed.

DE 10 2013 205 724 A1 suggests improving the powder bed process by coordinating the direction in which the beam of a beam source scans a portion of the powder bed and the inert gas flow direction. This coordination can be obtained by limiting the angle of the scanning direction and the inert gas flow direction to the interval [22.5°, 337.5°], preferably to the interval [90° and 270°].

DE 10 2018 203 233 A1 suggests scanning a sectional view of a workpiece in the powder bed process by at least two lasers. Each laser is assigned a region of the sectional view, i.e. the respectively assigned region is scanned by the corresponding laser. The boundary between of these two neighbored regions of the sectional view is saw tooth line, to thereby increase the strength of the manufactured workpiece.

WO 2016/110 440 A1 as well relates to a multiple beam powder bed process. Each beam has a field of view and at least two of these fields of view are overlapping. To improve scanning speed, it is suggested to locate the sectional view to be irradiated by the beams at least in part in a portion of the powder bed in which the fields of view of at least two beams are overlapping. The sectional view is scanned by the beams at the same time, wherein the distance between the spots being irradiated at the same time is reduced over time until the irradiated spots of the beams at least partially, preferably fully overlap. The beam intensities are reduced with an increase of the overlap to maintain the energy being provided to each spot of the sectional view being scanned constant.

US 2016/0114432 A1 discloses a laser selective solidification apparatus and method, where the utilisation of a plurality of laser beams is balanced.

The object of the invention is thus to further improve the multi beam powder bed fusion process with the object of reducing the cost for manufacturing a workpiece.

The invention is based on the observation that the prior art suggestions for defining the boundary between two adjacent surface sections of the surface of a top layer of a powder bed is based on the beam-on times measured when writing the previous layer. This process iteratively finds the optimum boundary position and hence leads to a significant cumulation of idle times. This approach is further increasingly inefficient, the more the surface areas to be illuminated in the different surface sections change from layer to layer.

Solutions of the problem are described in the independent claims. The dependent claims relate to further improvements of the invention.

The method for manufacturing a workpiece comprises fusing an area A ("the area A", for short) of a surface of a layer of a fusible material ("the layer", for short). In practice, the layer may be the present upmost layer of a powder bed on top of a powder bed support of an additive manufacturing machine configured to use and/or to implement the powder bed fusion process. Once the area A of the of the top layer intended to be fused have been fused, the next layer may be applied to the powder bed, e.g. using a recoater. Initially, the upmost layer may be the first layer of the powder bed being subsequently deposited during the process.

As already apparent the term "area" does not denote the entire surface of the layer, but only a portion thereof that shall be fused. The symbol A thus represents a set of locations (points) that can be represented as vectors p, all in the plane defined by the surface of the layer, which shall be and during the process are irradiated by at least one beam spot being emitted by a beam source. The symbol |A| hence symbolizes a value indicative for the size of the surface of the aera A, i.e. |A| is the surface area of the area A. Using the skilled person's language|A| is a norm, generally referred to as ||A||, only for simplicity we omit herein the second set of vertical bars.

The area A may be the entire area EA of the layer to be irradiated, but in another example, the area A may be only a portion thereof, i.e. A ⊆ EA. For example, those parts of the entire area EA to be irradiated that define, e.g., a portion of the contour of the workpiece may be subtracted from the entire area to thereby obtain "the area A". The contour portions being subtracted may, for example, be irradiated always by the same beam source to increase the quality of the workpiece surface defined by said contour. Alternatively, or in addition, the 'entire area' EA may be divided in subareas, e.g. to improve fume management. As already stated "the area A" may be a subarea of the 'entire area EA'. Generalizing, one may thus say that the area A may be at least a portion of a sectional view of the workpiece to be manufactured by application of the laser powder bed fusion process, wherein the section plane corresponds to the position of the layer of fusible material to be irradiated.

The area A may comprise multiple subareas, we call sectors to distinguish the sectors verbally from the previously discussed 'subareas of the entire area to be irradiated'. The sectors may by spaced from each other, i.e. there may be a gap between neighboured sectors of the area A. Further, as already apparent, it is irrelevant for the invention to which layer the area A is associated. All that is required is that the area A can be irradiated by beams being emitted by the beam sources. When referencing to an area A on a particular layer, the symbol A^l may be used. Thus A¹ would be an area on the first layer of a powder bed, A² an area of subsequent layer of the powder bed, A^l is an area on the l^th-layer. If the up script is omitted this means that the position of the Area A in the sequence of layers is not relevant and may take any number.

The area A is typically determined by a so called "slicer" based on a CAD-model of the workpiece to be manufactured. But the invention is not limited to this example.

As already apparent from the wording fusing a surface area A of a layer of a fusible material, the method comprises fusing the portion of the fusible material of the layer as defined by the surface area A. To this end at least two spots of at least two beams are projected by at least two beam sources onto the set of locations defining the surface area A. The method can be used in case there are only two beam sources, but practice the number is higher. Typical values are, depending on the size of the layer, between 8 to 12, but the invention is not limited to this range. Future powder bed fusing apparatuses are expected to have even higher numbers of beam sources. Herein we symbolize the total number of beam sources being available by "n". This number "n" of beam sources being available may be different from the number of beam sources of the powder bed fusion apparatus. For example, if one or more beam sources has or have been assigned the task of fusing a contour portion which is not a portion of the area A, then these assigned beam source(s) cannot contribute to fusing the area A, while fusing the respective contour portion(s). Once the assigned contour portions have been fused, these beam sources can be used to fuse sections of the area and the number "n", hence can be increased. Another ground for a number "n" being smaller than the number of installed beam sources may be to reduce the thermal power that needs to be removed from the workpiece or simply because a section of the area would be so small that location management would be difficult. For example, if a section is very small, it can become almost impossible to avoid fusing the section while not operating in a smoke plume being produced by fusing the powder bed in another section. Thus, is short, the number "n" represents the number of lasers being assigned to jointly fuse an area A. As will become apparent below, the number may even change during the process of assigning locations of the area A to the sets of locations L_i (1 ≤ i ≤ n) which may then be fused by the corresponding i^th-beam source. This may, e.g., happen if it turns out that the size of the area of a set of locations L_i would be below a predefined threshold T_i.

Each of the n, (n ≥ 2) beam sources has a predefined field of view F_i, wherein the index i indicates the corresponding i^th-beam source, e.g. F₁ is the field of view of the first beam source, F₂ is the field of view of the second beam source, or more generally F_i is the field of view of the i^th -beam source. The field of view F_i is the surface portion of the layer that can be irradiated by the corresponding i^th-beam being emitted by the i^th-beam source. In practice, each field of view F_i may be defined by a scanner optic of the i^th -beam source. Constraints in the field of view F_i may be imposed by pivot ranges of a scanner optic, limits of (optional) focussing optics and as well by a limit of the acceptable beam distortion. In general, the field of view F_i can be understood as the portion of the layer that can be reasonably fused using the corresponding i^th-beam source. The field of view F_i can thus be expressed as set of vectors f_i on the surface of the layer that can be irradiated and hence fused using the i^th-beam source. Thus, |F_i| is the size of the portion of the surface of the layer that can be irradiated by the corresponding i^th-beam source. Further, each beam source i has a predefined fuse rate R_i (a positive real number), wherein the fuse rate indicates the size of the surface field of view that can be fused by the i^th-beam source per unit of time. The fuse rate R_i is a surface area per time and hence can be measured, e.g. in $\frac{m^2}{s}\left[\frac{{\mathit{meter}}^2}{\mathit{second}}\right]$ or the like. For example, when fusing a surface, the beam spot often travels along a first vector, defining a first fuse trace until a stop condition is reached. Then the beam may be switched off and the beam source is repositioned to a new start point. Next, the beam is switched on again and the beam spot travel may travel, e.g. parallel to the previously fused fuse trace. Calculation of the fuse rate R_i may thus account for the time being required to reposition the beam source. In practice the fuse rate R_i can be considered as a mean fuse rate that may be determined iteratively with an increasing accuracy. The fuse rates R_i may differ between different beam sources and may as well depend on a given material to be fused. At least for a given material, the fuse rates R_i are preferably at least almost the same, meaning that (1 ± β_Ri)R_i = R_j, ∀i ≠ j, i, j < n, wherein β_Ri ∈ $\left\{\frac{25}{100},\frac{20}{100},\frac{15}{100},\frac{10}{100}\frac{5}{100},\frac{25}{1000},\frac{1}{100},\frac{5}{1000},\frac{25}{10000},\frac{125}{10000},\frac{1}{1000},0\right\}$. In another example, the fuse rate R_i is simply the length (times the width) of a trace the i^th-laser scans per unit of time without accounting for the time required to reposition laser beam optics when starting a new trace.

Fusing the area A comprises irradiating different sets L_i of locations l_i on the layer using the i^th-beam source for the corresponding set of locations L_i, wherein the intersection of different sets of locations is preferably empty, i.e. preferably the relation L_i ∩ L_j = { } = 0, ∀i ≠ j holds. This means essentially, that each location p of the area A is fused only by a single beam source. Generally, it is preferred to use all beam sources of the powder bed fusing apparatus for fusing the area, but this is not required and, in some cases, not even possible (as explained above). Of course, the different sets of locations L_i may be irradiated at the same time. In practice the trajectories of the projections of the beam spots of different beams sources may overlap, e.g. similar to the overlapping of sections of a single beam's trajectory to ensure a given strength and surface quality in those regions of the layer, where the final workpiece shall not have a gap. There have been suggestions to fuse using overlapping sets of locations, but herein this is -although not excluded- not intended. Intended is |L_i ∩ L_j| ≤ β_L · Max({|Li|,|L_j|}), wherein β_L ∈ $\left\{\frac{25}{100},\frac{20}{100},\frac{15}{100},\frac{10}{100}\frac{5}{100},\frac{25}{1000},\frac{1}{100},\frac{5}{1000},\frac{25}{10000},\frac{125}{10000},\frac{1}{1000},0\right\}$, preferably β_L = 0. Thus, generally, it is intended to separate the area A into a number n sets of locations L_i, wherein n indicates the number of beam sources that shall be used. Preferably, n indicates the number of beam sources having a field of view with a non-vanishing overlap with the area A, i.e. the number of different indices for which F_i ∩ A ≠ { } in another example n indicates the number of beam sources having a field of view with an overlap with the area A being greater than a threshold T, i.e. only those beam sources are considered for which |F_i ∩ A| ≥ T_i. Preferably, prior to fusing the area A, an optimum fusing time t_o(i) is determined (step 1.1). Note that while preferably for all sets of locations L_i the steps 1.1 to 1.3 are executed as described, according to claim 1 these steps 1.1 to 1.3 are executed at least for the first index i = 1.

There are a number of possibilities to estimate an optimum fusing time t_o(i), and in a preferred example the optimum fusing time can be determined by dividing the size of the area |A| by the sum of the fuse rates R_i of all involved beam sources, hence $t_o\left(i\right)=\frac{\left|A\right|}{{\displaystyle {\sum }_{j=1}^n{R}_j}}$, ∀1 ≤ i ≤ n . In this case all beam sources would require the same amount of time to fuse their respective sets of locations L_i, i.e. idle times are minimized. Other estimations may be used as well. For example, one may use $t_o\left(i\right)=\frac{\left(1+{\beta }_{t,i}\right)\left|A\right|}{{\displaystyle {\sum }_{j=1}^n{R}_j}}$ or $t_o\left(i\right)=\frac{\left(1-{\beta }_{t,i}\right)\left|A\right|}{{\displaystyle {\sum }_{j=1}^n{R}_j}}$, wherein ${\beta }_{t,i}\in \left\{\frac{25}{100},\frac{20}{100},\frac{15}{100},\frac{10}{100}\frac{5}{100},\frac{25}{1000},\frac{1}{100},\frac{5}{1000},\frac{25}{10000},\frac{125}{10000},\frac{1}{1000},0\right\}$, preferably β_t,i = 0. Generalizing, any suited measure for an optimum fusing time t_o(i) can be chosen, preferably t_o(i) is selected to obey $\frac{\left(1-{\beta }_{t,i}\right)\left|A\right|}{{\displaystyle {\sum }_{j=1}^n{R}_j}}\le t_o\left(i\right)\le \frac{\left(1+{\beta }_{t,i}\right)\left|A\right|}{{\displaystyle {\sum }_{j=1}^n{R}_j}}$.

Thus, the optimum fusing time depends on the size of the surface area |A| to be fused, following the convention that an upscript indicates the number of a layer the optimum fusing time may as well be indicated as $t_o^l\left(i\right)$. Unless required we will omit the upscript as well as the indication of the associated beam source "(i)" for simplicity.

Equivalent to determining the optimum fusing time t_o(i), one may as well or in addition determined the optimum size of a corresponding fusing area $\left|L_i^{\mathit{opt}}\right|$. In a preferred example $\left|L_i^{\mathit{opt}}\right|=t_o\left(i\right)\cdot R_i$.

In addition, at least a first intersecting set IS₁ of the surface area A and the first field of view (F₁) of a first beam source are determined, hence IS₁: = A ∩ F₁. (step 1.2). This is equivalent to determining those vectors of the area A on the surface of the layer that generally could be irradiated and hence subjected to fusing by the 1^st-beam source. Further intersecting sets IS_i may be determined as well, wherein IS_i is the intersecting set being associated to the i^th-beam source. In an example, IS_i may generally be defined as IS_i = A ∩ F_i∀1 ≤ i ≤ n. But as will be apparent below, other definitions may be used as well. Further, it should be noted, that an intersecting set IS_i, i ≥ 2 is preferably determined after the set of locations L_i-1 has been determined as explained below. (Only for formal simplicity one may define L₀: = { } or more generally L_j := { }∀j ≤ 0, ∀ j > n.

In a further step, the size of at least the first intersecting set |IS₁| is compared to the product of the optimum fusing time t_o(i) with the fuse rate R_i of the corresponding i^th-beam source (step 1.3) and if the relation t_o(i) · R_i < |IS_i| holds true, then a subtrahend surface S₁ with S₁ ⊂ IS₁ and at least one of (1 - α₁) · (|IS₁| - t_o(i) · R₁) ≤ |S₁| ≤ (1 + α₁) · (|IS₁| - t_o(i) · R₁) and its equivalent $\left(1-{\alpha }_i\right)\left(\left|{\mathit{IS}}_1\right|-\left|L_1^{\mathit{opt}}\right|\right)\le \left|S_1\right|\le \left(1+{\alpha }_1\right)(\left|{\mathit{IS}}_1\right|-$ $\left|L_1^{\mathit{opt}}\right|)$ is determined wherein the condition that for each p₁ ∈ S₁, ∃ F_k|p₁ ∈ F_k , k ∈ {2, ..., n} is observed (step 1.3.1). α₁ can be considered as an error margin (hence α₁ = 0 is preferred) and is defined below in detail.

Again, by replacing the index 1 by the index i, the step may be generalized to obtain the i^th-subtrahend surface S_i being associated to the i^th-beam source, i.e. generalizing in case the condition t_o(i) · R_i < |IS_i| holds true, the i^th- subtrahend surface S_i is determined using the conditions S_i ⊂ IS_i and (1 - α_i) · (|IS_i| - t_o(i) · R_i) ≤ |S_i| ≤ (1 + α_i)(|IS_i| - t_o(i) · R_i) (and/or (1 - α_i)(|IS_i| - $\left|L_i^{\mathit{opt}}\right|)\le \left|S_i\right|\le \left(1+{\alpha }_i\right)\left(\left|{\mathit{IS}}_i\right|-\left|L_i^{\mathit{opt}}\right|\right)$) that for each p_i ∈ S_i, ∃ F_k|p_i ∈ F_k , k > i} is obeyed, wherein α_i ∈ {0.25, 0.2, 0.15, 0.1, 0.05, 0.025, 0.01, 0.005, 0}. Smaller values of α_i are preferred, in a particular preferred example α_i = 0. If α_i = 0, then the constraint on |S_i| simplifies to |S_i| = |IS_i| - t_o(i) · R_i. These constraints on S_i enable to determine L_i = IS_i - S_i, and to thereby determine a set of locations L_i which can be expected to be fused by the i^th-beam source almost exactly within the preselected optimum fusing time t_o(i). Thus, if all sets of locations {L_i} are, e.g., iteratively determined as explained above these are selected such that the time for fusing the aera is minimized. This minimization is due to the fact the suggested determination of the sets of locations {L_i} ensures, that within the error margins given by the β_t,i and α_i it can be expected that all beam sources require the same amount of time to fuse their respective set of locations L_i. Idling of beam sources is minimized.

Herein, we assume that the steps are reiterated for every i ≤ n, starting with the lowest value of i = 1 and then within each iteration the value is increased by one, i.e. prior to each repetition of step 1.1 or 1.2, i := i + 1 is executed.The condition ∀p_i ∈ S_i, ∃ F_k|p_i ∈ F_k , k > i} is based on the assumption that the subtrahend surfaces S_i are determined in ascending order, i.e. that i increases by one after a subtrahend surface S_i has been determined for particular i. This sequence is not necessary, but if it is released the condition "k > i" would read "wherein i may take any value for which a subtrahend surface S_k has not yet been determined". Both wordings are equivalent, as by renumbering the beam sources the same sequence of determining the subtrahend surfaces S_i can be obtained, while taking care that the index i steadly increases by 1 after a particular subtrahend surface has been determined.

Of course, the method can be repeated for each layer and hence the time for manufacturing a workpiece is minimized. For a given powder bed fusing apparatus, the cost for manufacturing the workpiece is reduced.

To reiterate it vividly, the subtrahend surfaces S_i are thus subsets of vectors of the area A, being selected such that the expected time < t_i > for irradiating the surface given by the set of locations L_i := IS_i - S_I equals the optimum fusing time t_o(i) with an accuracy being given by the selection of α_i, β_t,i. Assuming that t_o(i) · R_i < |IS_i| is true for all i and α = 0 as well as β_t,i = 0 then < t_i >= t_o(i) ∀i, i.e. the total time t_tot being required to fuse the area A using the n beam sources simultaneously is t_tot = Max(t_o(i)) and identical to the lower limit being inherent to the apparatus and the material to be fused. At this point it should be recalled that in practical applications, a workpiece may have thousands of layers, and thus small savings in irradiating an area on each layer accumulate to non-negligible cost savings.

Once S_i has been determined for a given i , the i^th-set of locations L_i can be determined using L_i := IS_i - S_i (step 1.3.2) and the method may proceed with fusing the corresponding set of locations of L_i using the i^th-beam source (step 1.4). Before continuing to execute step 1.4, preferably at least the steps 1.2 to 1.3.2 are repeated for each other beam source, i.e. for all remaining beam sources (1< i ≤ n). Step 1.4 is preferably executed for at least two different L_i, L_j, (i ≠ j) at the same time. The higher the number of beams that are irradiating their correspondingly assigned surfaces L_i simultaneously the better. Preferably, all n beam sources irradiate at the same time.

In case the size of a section L_i is below a given threshold, e.g. below the threshold T_i explained above, the section L_i may be set to zero (L_i := { }), which is equivalent to reducing the number of beam sources to n - 1, i.e. an i^th -beam source may be removed from the pool of n beam sources, if |L_i| < T_i.

There may be cases in which the overlap between the area A and a field of view F_i is so small that the time required to irradiate the corresponding interesting set IS_i = A ∩ F_i is smaller than the optimum time t_o(i), in this case t_o · R_i > |IS_i| is true. In this case one could simply assign L_i := IS_i, but in practice it may be necessary to have a defined shape of L_i or that L_i does not extend in predefined sectors of the area A. Thus, more generally, a subtrahend surface S_i is defined with S_i ⊂ IS_i under the condition that for each p_i ∈ S_i, ∃ F_k|p_i ∈ F_k , k > i . Further, in the case of t_o · R_i > |IS_i| then |S_i| is preferably minimized. Once S_i hast been determined, the set of locations L_i to be irradiated by the i^th-beam source is determined using L_i: = IS_i - S_i, i.e. the method may continue to step 1.4.

The condition "for each p_i ∈ S_i, ∃ F_k|p_i ∈ F_k , k > i " reads in plain language that for each vector p_i which vector p_i is an element of the subtrahend surface S_i exists at least one field of view F_k such that the field of view F_k comprises the vector p_i, wherein the index k is larger than the index i. This condition ensures that any point/location of the area A being removed from the intersecting set IS_i can be irradiated by at least one other beam source for which the set of locations L_k has not yet been determined, the latter following from k > i. Any location of the area A which can be fused by only by a limited number of beam sources forming a set of indices X is thus assigned at latest to set of locations L_Max(X) with the highest index of said set X.

The corresponding expectation value of the time for irradiating the surface of the layer with the i^th-beam source reads identically to the other case < t_i > = L_i/R_i. Generalizing, one may say that in case t_o · R_i ≥ |IS_i| ,i.e. in the "ELSE" case of step 1.3 (i.e. if (t_o · R_i ≥ |IS_i| ), steps 1.3.1 and 1.3.2 may be executed while the condition (1 - α_i) · (|IS_i| - t_o · R_i) ≤ |S_i| ≤ (1 + α_i) · (|IS_i| - t_o · R_i) is released.

Preferably, particularly in case t_o · R_i ≥ |IS_i| (but generally in any case), a corrected minimum time t_o(i + 1), as well referred to as $t_o^{\prime }$ may be calculated in a subsequent iteration of step 1.1 (i.e. after setting i:=i+1) using e.g. t_o(i) := $t_o\left(\mathrm{i}-1\right)+\frac{\left(t_o-<t_{i-1}>\right)\cdot R_{i-1}}{{\displaystyle {\sum }_{j=i}^{j\le n}{R}_j}}$. The corrected minimum time may then be used in future executions of steps 1.3 to 1.3.2 and instead of an initially calculated or estimated optimum fusing time. This adjustment of the optimum time t_o(i) enhances an even load distribution between the beam sources for which the set of locations has not yet been determined, i.e. the variation of |L_j| (i < j ≤ n) is reduced. This provides a further increase in efficient use of the apparatus' capabilities and hence translates in lower manufacturing costs of a corresponding workpiece.

The step of calculating a corrected minimum time can be generalized by recalculating a (corrected) minimum optimal time with each iteration, i.e. in step 1.1 t_o(i) may be $t_o\left(1\right)=\left(1\pm {\beta }_t\left(i\right)\right)\frac{\left|A\right|}{{\displaystyle {\sum }_j^n{R}_j}}$ and $t_o\left(i\right)=\left(1\pm {\beta }_{t,i}\right)\cdot \left(t_o\left(i-1\right)+\frac{t_{o\left(i-1\right)}\cdot R_{i-1}-\left|L_{i-1}\right|}{{\displaystyle {\sum }_{j=i}^n{R}_j}}\right)\forall 2\le i\le n$, being equivalent to $t_o\left(i\right)=\left(1\pm {\beta }_{t,i}\right)\frac{\left|A\right|-{\displaystyle {\sum }_{j=1}^{i-1}\left|L_j\right|}}{{\displaystyle {\sum }_{j=i}^n{R}_j}}$ wherein if i = 0 the term ${\displaystyle {\sum }_{j=1}^{i-1}\left|L_j\right|:=0}$ and hence $t_o\left(1\right)=\left(1\pm {\beta }_{t,i}\right)\frac{\left|A\right|}{{\displaystyle {\sum }_{j=1}^n{R}_j}}$. Again, the preferred case is β_t(i) = 0 and i indicates the i^th- execution of the steps. As already apparent, β_t,i as defined above serves as an error margin and t_o(i) is selected to be within boundaries being given by selection either the "+" or the "-" of "±". Generally, β_t,1 = β_t(i) can be different for every iteration only for simplicity we will write β_t as well. The of step calculating a corrected minimum time is particularly useful if the effects of non-negligible α_i sum up. In short both possibilities account for a potential difference between the optimum mean fusing time t_o and the actually expected fusing times < t_i > = |L_i|/R_i for each iteration of the calculation of L_i. If not addressed, these differences may lead to the situation that ILnl is significantly bigger that all other L_j, (1 ≤ j < n) , and hence significant idle times of the beam sources 1 to n - 1 reduce the efficiency of the additive manufacturing process. Thus, again the step of recalculating an updated optimum mean fusing time further contributes to reducing the operating costs per workpiece.

In case the size of a section L_i is below a given threshold, e.g. below the threshold T_i explained above, the section L_i may be set to zero (L_i := { }), which is equivalent to reducing the number of beam sources to n - 1, i.e. an i^th -beam source may be removed from the pool of n beam sources, if |L_i| < T_i.Of course, in this case it is preferred to calculate a corrected minimum time and/or a corrected optimum size of a corresponding fusing area $\left|L_i^{\mathit{opt}}\right|$.

The threshold T_i may be defined for each i^th-beam source individually. It may as well be set manually for each beam source individually or for all or a number of beam sources, e.g. based on the experience of an operator. In a preferred example, the threshold T_i is a set portion of the optimum size of the fusing area $\left|L_i^{\mathit{opt}}\right|$, e.g. $T_i=c_{T_i}\cdot \left|L_i^{\mathit{opt}}\right|$, wherein $$c_{T_i}\in \left\{0.95,0.9,0.8,0.7,0.6,0.5,0.4,0.3,0.2,0.1,0.05\right\}.$$

Preferably, the method further comprises to define at least a first (preferably meandering) line B_i,j and preferably as well a second (preferably meandering) line B_i,k, wherein the first (preferably meandering) line B_i,j extends (preferably meanders) in a first direction b₁ and the second (preferably meandering) line B_i,k extends (preferably meanders) in a second direction b₂ (step 4.1). The first (preferably meandering) line may be used to limit the extension the subtrahend surface S_i in a direction being at least essentially orthogonal to the first direction b₁. Similarly, the second (preferably meandering) line may be used to limit the extension the subtrahend surface S_i in a direction being at least essentially orthogonal to the second direction b₂. At least one of the first and second (preferably meandering) lines hence determines a first boundary of the subtrahend surface S_i (step 4.2). At least one of these first and second (preferably meandering) lines may be shifted to reduce ΔS_i, wherein ΔS_i = |t_o(i) · R_i - |IS_i - S_i||. Further preferably, when determining an S_j after another S_i (i.e. i < j ) and if the i^th-beam source and the j^th-beam source are neighbours (or at least have overlapping fields of view), then B_j,i = B_i,j.

During this shifting, the first (preferably meandering) line B_i,j is preferably shifted at least essentially orthogonal to the first direction b₁ and/or the second (preferably meandering) line is preferably shifted at least essentially orthogonal to the second direction b₂ to reduce ΔS_i, preferably until the condition 1.3.1 is met. As already apparent the two vectors b₁, b₂ are preferably linearly independent (condition 5), and particularly preferred they are at least essentially orthogonal to each other, i.e. preferably b₁ ⊥ b₂. Exceptionally the indices of the vectors b₁, b₂, ... are not associated with a beam source, these serve only to distinguish these vectors. The indices of the lines B_i,j however are associated to two beam sources, namely to the i^th- and to the j^th-beam source, after determining all L_i, the (preferably meandering) line B_i,j separates the sets of locations L_i and L_j.

A line B_i,j meanders along or in the direction b₁ if the line B_i,j has a first end point b_i,j,e that obeys the condition |b₁ · (b_i,j,l - b_i,j,e)| ≠ |b₁ · (b_i,j,m - b_i,j,e)| ∀b_i,j,l,b_i,j,m ∈ B_i,j, b_i,j,l ≠ b_i,j,m and if |b₁ · (b_i,j,l - b_i,j,e)| ≠ |b_⊥ · (b_i,j,m - b_i,j,e)| ∀b_i,j,l, b_i,j,m ∈ B_i,j, b_i,j,l ≠ b_i,j,m with b_⊥ ⊥ b₁ does not hold true.

Fusing the fusible material at the set of locations L_i may comprise pivoting the i^th-beam source while the i^th-beam source projects an i^th-beam spot to thereby move the i^th-beam spot along lines being multiples of a vector v_i. In a preferred example, the meandering lines comprise or consist of concatenated sections being, in alternating sequence, perpendicular to v_i or parallel to v_i(step 6).

Particularly preferred, the method further comprises to execute the steps 1.2 and 1.3 (and optionally of course as well all other steps) first for the beam source that has a field of view which has the least overlap with the fields of view of other beam sources. Next, the steps are executed for the beam source which field of view has the second least overlap with other fields of view and so. This helps to reduce the computational effort when calculating the corresponding subtrahend surfaces S_i, as in this way first those portions of the area are assigned to a set of locations L_i that in the worst case can be irradiated only by a single beam source, which may -if not accounted for- yield to the situation that a single beam source operates much longer than the others. Executing the steps 1.2 and 1.3 (and optionally of course as any of the other steps) first for the beam source that has a field of view which has the least overlap with the fields of view of other beam sources and so on may be obtained by sorting the indices of the beam sources such that the first (i = 1) beam source has the field of view F₁ that has the least overlap and second (i = 2) beam source has the field of view F₂ with the second least overlap and so forth. In other words, this means that preferably initially, but at latest prior to step 1.2 the indices of the fields of view F_i are preferably sorted to obey the condition $\mathit{Min}\left({\displaystyle {\sum }_j^{i\ne j}{F}_i\cap F_j}\right)\le \mathit{Min}\left({\displaystyle {\sum }_j^{i+1\ne j}{F}_{i+1}\cap F_j}\right)\forall i<n$ and that at least the steps 1.2 and 1.3 are repeated while increasing the value of the index with each repetition by one until the index i = n. Of course, for those F_i for which F_i ∩ A = { } sorting can be omitted as it is clear that the corresponding set of locations L_i is empty, i.e. L_i = { }.

In addition or alternatively, the method may comprise (as well prior to step 1.2), sorting the indices of the fields of view F_i to obey the condition |F_i ∩ A| ≤ |F_j ∩ A| ∀i < j and that steps 1.2 and 1.3 and optionally at least one of the steps 2.1 to 2.3 are repeated while increasing the value of the index with each repetition by one. Again, the position of the beam sources having an index i for which F_i ∩ A = {} can be selected arbitrarily. As well, this sorting step eases determining the subtrahend surfaces S_i, while maintaining the error margin α_i small, i.e. to reduce avoidable idle times of beam sources that generally could contribute to fusing the area A.

The method may further comprise, prior to determining a subtrahend surface S_i to assigning a portion C_i of the area A to a dedicated i^th-beam source. In practice the beam sources are calibrated to operate all in the same coordinate system. This calibration, however, is not perfect and can deteriorate during the process of manufacturing. When assigning particular portions C_i of the area A a priori to a certain dedicated i^th-beam source, imperfections of the workpiece can be reduced in this portion C_i, thus C_i ⊂ F_i, i.e. the portion C_i is within the field of view F_i. Normally, such an assignment increases the total manufacturing time, because the load distribution between the different beam-sources is deteriorated. In a preferred embodiment of the invention, this deterioration can be avoided by considering the additional constraint S_i ∩ C_i = { } when determining the subtrahend surface S_i, e.g. in steps 1.3.1 and/or 2.1. Obeying the additional constraint S_i ∩ C_i = { } ensures, that the portion C_i is a subset of the subsequently determined set of locations L_i being later irradiated by the i^th-beam source, and that the additional size of the set of locations L_i being due to the portion C_i is considered in the load balancing constraint (1 - α_i) · (|IS_i| -· t_o · R_i) ≤ |S_i| ≤ (1 + α_i) · (|IS_i| -· t_o · R_i) of steps 1.3.1.

In a preferred embodiment, when repeating step 1.2, the intersecting sets IS_j (j ≥ 2) are determined as ${\mathit{IS}}_j:=\left(A-{\displaystyle {\sum }_{i=1}^{i<j}{L}_i}\right)\cap F_j$. This step provides a number of advantages: The memory requirements are reduced and further determining a suited subtrahend surface S_i is significantly simplified, leading to further cost optimizations. The idea underlying this improvement is that those portions of the field of view F_i that already have been assigned to sets of locations L_i, (i < j) in previous executions i of at least one of the steps 1.2 to 1.3.2 and/or 1.2 to 2.3 do not need to be included in further considerations. As ${\displaystyle {\sum }_{i=1}^{1<0}{L}_i=0}$, the condition j ≥ 2 can be released, i.e. IS_j may be defined as IS_j := $\left(A-{\displaystyle {\sum }_{i=1}^{i<j}{L}_i}\right)\cap F_j\forall j\in I\forall j\in I$

During the fusing process, i.e. during operation of the beam sources it is preferred to establish an inert gas flow over the top of the powder bed to thereby remove fumes and other residues out of the fields of view F_i. Preferably, a flow in a flow direction parallel to the top surface of the layer is established, e.g. by arranging at least one inlet nozzle at a first side of the top layer and at least one outlet nozzle at the opposite side of the top layer and by establishing an inert gas flow from the inlet nozzle to the outlet nozzle, thereby defining a main flow direction. In other words, the method may further comprise establishing an inert gas flow in a flow direction d over the top of the powder bed, wherein d_h denotes the (preferably normalized) component of the flow direction being parallel to the layer of fusible material, i.e. the projection of the flow direction d onto the area A. For example, if the z-axis is perpendicular to the surface of the layer of fusible material (and hence to the area A), then using cartesian coordinates d_h = ${\left(d_x^2+d_y^2\right)}^{-\frac{1}{2}}{\left(d_x,d_y,0\right)}^T$, wherein ${\left(d_x^2+d_y^2\right)}^{-1/2}$ is only a normalization factor setting |d_h| = 1, and can be omitted. As usual d_x, d_y and d_z are the x-, y - and z-components of the vector d, respectively.

This flow direction parallel to the layer d_h is preferably correlated with the extension of the meandering lines B_i,j limiting the subtrahend surfaces S_i and which define the boundary between adjacent sets of locations L_i and L_i such that the boundary B_i,j between two sets of locations L_i and L_j has a first end point b_i,j,e that obeys the condition |d_h · (b_i,j,l - b_i,j,e)| ≠ |d_h · (b_i,j,m - b_i,j,e)| ∀b_i,j,l, b_i,j,m ∈ B_i, b_i,j,l ≠ b_i,j,m (condition 13.1). This means that any distance between the first end point b_i,j,e and any other point b_i,j,l of the boundary B_i,j exists only once. Hence, any subsection of B_i,j has a non-vanishing extension in the direction defined by the horizontal component of the flow direction d_h. In this case the relation |d_o · (b_i,j,l - b_i,j,e)| ≠ |d_o · (b_i,j,m - q_e)| ∀b_i,j,l, b_i,j,m ∈ B_i, b_i,j,l ≠ b_i,j,m (condition 13.2) with d_o ⊥ d_h is preferably not realized, thus B_i,j is not a straight line but meanders essentially parallel to the horizontal component of the flow direction d_h.

Alternatively, the boundary B_i,j may meander orthogonal to the horizontal component of the flow direction d_h. In this case the relation |d_o · (b_i,j,l - b_i,j,e)| ≠ |d_o · (b_i,j,m - q_e)| ∀b_i,j,l, b_i,j,m ∈ B_i, b_i,j,l ≠ b_i,j,m , wherein d_o ⊥ d_h is obeyed, while condition |d_h · (b_i,j,l - b_i,j,e)| ≠ |d_h · (b_i,j,m - q_e)| ∀b_i,j,l, b_i,j,m ∈ B_i, b_i,j,l ≠ b_i,j,m (condition 13.1) is preferably not realized.

These measures being referenced to as conditions 13.1 and 13.2 each vastly simplify to coordinate the movement of the n beam spots over the layer such that at any moment in time no beam spot is below fume that has been generated by another beam spot, while operating the beam sources simultaneously.

As stated above, the beam sources may be pivoted while irradiating the surface to thereby project beam spots onto the layer. Thus, preferably each beam spot is moved over the surface of the layer and thereby fuses the fusible material at the locations l_i of the respective set of locationsL_i . In other words, fusing the fusable material at the set of locations L_i comprises pivoting the i^th-beam source while the i^th-beam source projects the i^th-beam onto the area A to thereby move the i^th-beam spot. Preferably the movement of the i^th-beam spot can be described by a multiple of a vector v_i having a component being opposite to the flow direction d_h of the inert gas flow. The beam spot so to speak moves towards the gas inlet and hence the fusing process is less affected by fumes previously produces by said beam spot. Subsequently, the beam source may be switched of and repositioned to continue irradiating another subset of L_i while moving again in the direction being defined by v_i. The quality of the workpiece to be manufactures is increased accordingly.

For example, there may be at least two different meandering lines B_i,j, B_q,r, which are the boundaries between adjacent sets of locations L_i, L_j and L_q, L_r, respectively. Preferably, an end point of the first section B_i,j is as well an end point of the first section B_q,r. This measure aligns the corresponding sets of locations L_i, L_j, L_q and L_r, preferably parallel and orthogonal to the flow direction d_h being parallel to the layer. The latter can be obtained when, including the constraint on S_i that condition 13.1 or 13.2 applies to both, B_i,j and B_q,r. Thereby the computational effort of the method can be further reduced and idle times to avoid beam spots at locations of fume being produced by other beam spots can be reduced. Thus, the quality of the workpiece can be enhanced while at the same time manufacturing cost for a workpiece are reduced.

For example, if condition 13.1 applies to both, B_i,j and B_q,r, the sets of locations L_i, L_j, L_q and L_r, may be separated into m portions L_s,1, L_s,2, ... , L_s,m, , ( m ≥ 2) by lines meandering parallel to d_h and wherein |L_s,l| = |L_s,n| ± 0.15 · |L_s,n| ∀s ∈ {i, j, q, r}, l, n ≤ m, l ≠ n, (the factor 0.15 can be replaced by any other value of {0.1, 0.05, 0.025, 0.1, 0.005} ) wherein portions with the same second index are aligned parallel to d_h and in that only portions with the same second index are irradiated simultaneously. This provides for a very effective and simple measure to avoid that fumes being produces by any beam spot affects fusing of the fusible material by another beam spot. An increase of the number of portions enables to increase the minimum distance between two beam spots measured perpendicular to the vector d_h. Meandering parallel or orthogonal to d_h means that the distance measured parallel, or orthogonal, respectively, to d_h between an end point of the respective line and any other point of said line is unique (condition 13.1 or 13.2, respectively, applies to said line).

Preferably, the area A is separated into at least 2n stripes (generally into c · n stripes, wherein c is an integer with c ≥ 2) extending at least essentially parallel to the horizontal component d_h of the inert gas flow. Preferably, during fusing only locations l_i in every second stripe are fused at the same time. Thus, in between of two beam spots is at least a distance corresponding to the width of the corresponding. By choosing the width of the stripes, one can avoid that any beam spot fuses at a location with a significant concentration of fumes which has been produced by another beam spot. Thus, between two stripes being irradiated simultaneously, there are c - 1 stripes which are not irradiated, and their width is the minimum distance by which two beam spots are separated. As already apparent, the boundaries of at least some of the stripes are preferably given by the meandering lines as explained above.

Only to avoid any misunderstanding, we recall that as usual the layer is the top layer of a powder bed. Further, herein, as usual "{ }" symbolizes an empty set. Herein we use as well the number "0" to express that a set is empty, i.e. if a set V is empty is can be expressed as V = { } as well as V = 0 .

Herein at "least essentially perpendicular" or "least essentially orthogonal" expressed, that an angle of 90° is preferred, but that deviations may be accepted, the angle may thus be within 90° ± 45°, 90° ± 30°, 90° ± 15°, 90° ± 10°, 90° ± 5°, 90° ± 2.5°, 90° ± 1° or 90° ± 0°. Similarly, "least essentially parallel" allows for deviations from perfect parallel alignment, i.e. angles be within 0° ± 45°, 0° ± 30°, 0° ± 15°, 0° ± 10°, 0° ± 5°, 0° ± 2.5°, ° ± 1° or 0° ± 0° may be selected as well, wherein exactly parallel (±0°) is preferred. Further, two meandering lines meandering in the directions being given by vectors b₁ and b₂ are considered to be perpendicular or parallel, if these vectors b₁ and b₂ are perpendicular or parallel, respectively.

In the following the invention will be described by way of example, without limitation of the general inventive concept, on examples of embodiment with reference to the drawings.

• Figure 1 shows an additive manufacturing apparatus,
• Figure 2 shows a top view of the up facing surface of a powder bed,
• Figure 3 shows detail D₁ of Fig. 2.
• Figure 4 shows detail D₁₁ of Fig. 2.
• Figure 5 shows a flow diagram of a method for determining sets of locations L_i.

In figure 1 a first embodiment is shown. The additive manufacturing apparatus 1, is shown in a sectional view and has a process chamber 5, being enclosed by sidewalls 7, a bottom 8 and a ceiling 9. In the bottom is an opening 81. Below the opening is movably supported support 82 as indicated by the double headed arrow 2. On the top of the support is a powder bed 12 having a top layer with a surface 14. As sketched, a portion of a workpiece 6 may be embedded in the powder bed 12.

The surface 14 of the powder bed in Fig.1 can be irradiated by beam spots 22_i being projected by n beam sources 20_i. Depicted is a number of n = 8 beam sources 20_i but this is only a preferred example, any other number n ≥ 2 could have been chosen as well. For example, in Fig. 2 The powder particles of the powder bed 12 at locations l_i that are irradiated are by the i^th-beam spot 22_i being emitted by the i^th-beam source 20_i are fused together. In Fig. 1 only a single beam spot 22_i and a single location l_i are indicated for simplicity, in practice however it is preferred if at least two beam spots 22, e.g., at least three, at least four or at least five beam spots 22_i are emitted at the same time. Preferably all n beam sources 20_i each emit a beam spot 22_i to a location l_i (i.e. 1 ≤ i ≤ n) at the same time. The beam-sources 20_i may be pivoted, hence the beam spots 22_i may be moved over the surface 14 and each beam source 20_i may irradiate a set of locations L_i = {l_i}, wherein the index i indicates the corresponding beam source 20_i of the n beam sources. Once all sets of locations L_i have been irradiated an area $A={\displaystyle {\sum }_{i=1}^n{L}_i}$ has been irradiated (see Fig. 2). The area A may thus be a top surface of the corresponding layer of the workpiece 6 or at least a portion thereof. Once the area A has been irradiated, the support may be lowered by the thickness of a powder layer and a new powder layer may be applied, e.g. using a so called recoater, travelling over the opening 81. Subsequently, the next surface 14 of the new upmost layer of the powder bed 12 may be irradiated using the beam sources 20_i.

During fusing of the powder bed's surface 14 fumes occur at the locations l_i of the surface. These fumes may be removed from the process chamber by establishing an inert gas flow 3 above and over the surface 14 of the powder bed 12 being symbolized by dashed arrows 3. The dashed arrows 3 each have common projection on the bottom 8, being symbolized the dotted arrow d_h. The vector d_h is thus the direction of the horizontal component of the inert gas flow 3 above and over the surface 14. In other words, the inert gas flow 3 has a component d_h being parallel to the support's up facing surface.

A programmable electronic circuitry 10, briefly referred to as controller 10, controls at least a number of the beam sources 20_i. Preferably as well at least one of the inert gas flow 3, a recoater and the movement of the support 82 may be controlled by the controller 10.

Fig. 2 shows a top view of a surface 14 of a layer of a powder bed 12. Each cross 20₁ to 20₁₄ represent the position of a beam source 20_i (i.e. n = 14 in this example) above the surface 14. Or in other words, the position of the crosses 20 can be obtained by a projection of the beam sources 20 onto the surface 14. Only to enable to reference to particular beam source 20, we added a subscript to each cross, i.e. 20₁, 20₄, indicate the cross representing the projection of the first beam source and of the fourth beam source, respectively. Generally, 20_i, (1 ≤ i ≤ n) denotes the cross representing the i^th-beam source. Further, as already stated with respect to Fig. 1, the present choice of n = 14 is only an example. The only condition on the number n of beam sources is that n ≥ 2.

Each beam source20_i can irradiate a certain portion F_i of the surface 14. These surfaces F₁, ..., F₁₄ are referred to as fields of view F_i. Fig. 2 further shows an example area A. The embodiments of the invention enable to assign portions of the area A to the different beam sources and subsequently to fuse the powder in area A while operating a maximum amount of beam sources at the same time. Idle times of beam sources 20 are reduced. The area A can be calculated based on a CAD-model of the workpiece 5, wherein "CAD" stands for "Computer Aided Design" and a CAD-Model is hence a description of the workpiece enabling to manufacture it.

As already explained above, the beam sources are labelled with indices or in any other appropriate manner, that enables to distinguish two of them. Herein we assume that the sets of locations L_i to be irradiated by the i^th-beam source 20_i are determined in an ascending order, starting with the first beam source 20₁.This ascending order is not required, but simplifies to explain and understand the invention.

Once the beam sources 20_i are labelled and the area A to be irradiated has been determined intersecting sets IS_i of the fields of view F_i with the area A may be determined, generally IS_i = F_i ∩ A, as depicted in Fig. 5. The method thus comprises at least determining IS₁: = F₁ ∩ A. Further an optimum fusing time to (1) is determined. This may take place prior or after the step of determining IS₁. This optimum fusing time t_o(i) can be considered as an estimate of the time being required to fuse a subsequently determined portion L_i of the area A. In other words, the size of the set of locations |L_i| is determined such that it may be expected that the set of locations L_i can be fused by the i^th-beam source 20_i within the optimum fusing time t_o (i).

Preferably, the actual fusing times t_a(i) are all the same and in this case the optimum fusing time of the first beam source can be estimated as t_o(1) = $\left|A\right|/{\displaystyle {\sum }_{i=1}^n{R}_i}$, wherein the values R_i are the fusing rate of the i^th-beam source (see Fig. 5). As usual, the fusing rate R_i of the i^th-beam source is the quotient of the size of a test surface T and the time t_t(i) required to fuse said test surface, i.e. $R_i=\frac{\left|T\right|}{t_t\left(i\right)}$. This example of determining t_o(1) is not the only valid choice for t_o(i). Generally any value of t_o(i) being withing $\frac{\left(1\pm {\beta }_{t,i}\right)\left|A\right|}{{\displaystyle {\sum }_{i=1}^n{R}_i}}$ (i.e. $t_o\left(i\right)=\frac{\left(1\pm {\beta }_{t,i}\right)\left|A\right|}{{\displaystyle {\sum }_{i=1}^n{R}_i}}$) may be considered reasonable, generally $\frac{\left(1-{\beta }_{t,i}\right)\left|A\right|}{{\displaystyle {\sum }_{i=1}^n{R}_i}}\le t_o\left(i\right)\le \frac{\left(1+{\beta }_{t,i}\right)\left|A\right|}{{\displaystyle {\sum }_{i=1}^n{R}_i}}$ can be considered as a reasonable range for the margin, e.g. β_t,i E B, with B = {0.25, 0.2, 0.15, 0.1, 0.05, 0.025, 0.0125, 0.01, 0.005, 0.001}. Smaller values of β_t,i are preferred, particularly preferred is β_t,i = 0.

If t_o(1) has been determined, the method proceeds to determining the first subtrahend surface S₁ (see Fig. 5). The first subtrahend surface S₁ is a subset of the first intersecting set IS₁, i.e. S₁ ⊂ IS₁ and as the name implies, subtracted from IS₁ to thereby determine the first set of locations L₁. When determining the first subtrahend surface S₁, only those points of the first intersecting set IS₁ can be considered which are as well comprised in other fields of view F_k, (k ≠ 1). In more concise manner this can be expressed as ∀p₁ ∈ S₁ , ∃ F_k|p₁ ∈ F_k , k > 1, reading that for all points p₁ of the subtrahend surface S₁ exists a field of view F_k such that these points p₁ are element of at least one field of view F_k, wherein k may take any integer value greater than 1. This condition ensures that points being removed (subtracted) from the intersection set IS₁ can be irradiated by another beam source. Further, the size of |S₁| is adjusted to comply as good as reasonable with the constraint (1 - α₁) · (|IS₁| - t_o(1) · R₁) ≤ |S₁| ≤ (1 + α₁) · (|IS₁| - t_o(1) · R₁). This implies that |IS₁| ≥ (1 - α₁) · t_o(1) · R₁. As already explained above α_i E {0.25, 0.2, 0.15, 0.1, 0.05, 0.025, 0.01, 0.005, 0}Vi. The smaller α₁ is selected the better, i.e. particularly preferred α₁ = 0. Once S₁ has been determined the first set of locations L₁ which is to be irradiated by the first beam source is determined as L₁ := IS₁ - S₁.

There may be cases in which the constraint (1 - α₁) · (|IS₁| - t_o(1) · R₁) ≤ |S₁| ≤ (1 + α₁) · (|IS₁| - t_o(1) · R₁) cannot be met, because the size of IS₁ is smaller than (1 - α₁) · t_o(1) · R₁ (see Fig. 5). In this case one may select S₁ := { } = 0, but there may be other conditions to observe which may require to find a non-vanishing subtrahend surface S₁. This can be generalized into the following: If the constraint (1 - α_i) · (|IS_i| - t_o(i) · R_i) ≤ |S_i| ≤ (1 + α_i) · (|IS_i| - t_o(1) · R_i) cannot be met, because the size of IS_i (i.e. |IS_i|) is smaller than (1 - α_i) · t_o(i) · R_i. In this case one may select S_i :_ { } = 0, but there may be other conditions to observe which may require or at least render it favourable to find a non-vanishing subtrahend surface S_i. An example for choosing a non-vanishing subtrahend surface S_i is the case when the boundary between neighboured surfaces L_i, L_j shall have a predefined shape.

As already explained above, it is preferred if the sets of locations L_i have a size above a threshold T_i i.e. if |L_i| > T_i. If this condition cannot be met, S_i may be set to IS_i, i.e. S_i := IS_i being equivalent to removing the i^th beam source from the pool of available beam sources.

Subsequently, these steps may be repeated for the next beam source, which in this example is the second beam source. Formally this can be described as repeating the steps after replacing the index 1 by 2 and by using t_o(2) instead of t_o(1) (see Fig. 5). Hence this repetition provides the second set of locations L₂. In a more general manner one my say that once an i^th-set of locations L_i has been determined or at least could be determined because IS_i and S_i are known, the method is reiterated for all remaining beam sources or to say it differently i: = i + 1 until i = n. In an explicit language this means that preferably a new optimum time t_o(i) is determined for every i ∈ I. Preferably the new optimum time takes into account any deviation of the time(s) that can be expected < t_j > (j < i) to be required by the beam sources having a lower index. For example $t_o\left(i+1\right):=t_o\left(\mathrm{i}\right)+\frac{\left(t_o-<t_i>\right)\cdot R_i}{{\displaystyle {\sum }_{j=i+1}^{j\le n}{R}_j}}$, more generally and to allow small deviations from the suggested optimum value one may determine the updated optimum time to obey the constraint $\left(1-{\beta }_{t,i}\right)\left(t_o\left(i-1\right)+\frac{t_{o\left(i-1\right)}\cdot R_{i-1}-\left|L_{i-1}\right|}{{\displaystyle {\sum }_{j=i}^n{R}_j}}\right)\le t_o\left(i\right)\le$ $\left(1+{\beta }_{t,i}\right)\left(t_o\left(i-1\right)+\frac{t_{o\left(i-1\right)}\cdot R_{i-1}-\left|L_{i-1}\right|}{{\displaystyle {\sum }_{j=i}^n{R}_j}}\right)\forall 2\le i\le n$, being equivalent to $\left(1-{\beta }_{t,i}\right)\frac{\left|A\right|-{\displaystyle {\sum }_{j=1}^{i-1}\left|L_j\right|}}{{\displaystyle {\sum }_{j=i}^n{R}_j}}\le t_o\left(i\right)\le \left(1+{\beta }_{t,i}\right)\frac{\left|A\right|-{\displaystyle {\sum }_{j=1}^{i-1}\left|L_j\right|}}{{\displaystyle {\sum }_{j=i}^n{R}_j}}$ or in short t_o(i) = (1 ± ${\beta }_{t,i})=\frac{\left|A\right|-{\displaystyle {\sum }_{j=1}^{i-1}\left|L_j\right|}}{{\displaystyle {\sum }_{j=i}^n{R}_j}}$ wherein if i = 0 the term ${\displaystyle {\sum }_{j=1}^{i-1}\left|L_j\right|:=0}$ and hence $t_o\left(1\right)=\left(1\pm {\beta }_{t,i}\right)\frac{\left|A\right|}{{\displaystyle {\sum }_{j=1}^n{R}_j}}$. Again, the preferred case is β_t,i = 0.

Next or as well prior to determining the updated optimum fusing time t_o(i) the next intersecting set is determined using IS_i := F_i ∩ A.

Once IS_i and t_o(i) are determined, the method may proceed to the step of determining the corresponding subtrahend surface S_i, wherein S_i obey the condition ∀p₁ ∈ S₁ , ∃ F_k|p₁ ∈ F_k , k > i and if |IS_i| ≥ t_o(i) · R_i S_i further obeys (1 - α_i) · (|IS_i| - t_o(i) · R_i) ≤ |S_i| ≤ (1 - α_i) · (|IS_i| - t_o(i) · R_i), and α_i E {0.25, 0.2, 0.15, 0.1, 0.05, 0.025, 0.01, 0.005, 0}.

Once the IS_i and S_i are determined, the method may proceed to define L_i := IS_i - S_i, and to increase i by one (i := i + 1, unless i = n) and reiterate the process until n sets of locations L_i, 1 ≤ i ≤ n have been determined. The controller may then control the beam sources 20_i to project their respective beam spots 22_i onto the corresponding sets of locations L_i.

An example for determining a subtrahend surface S_i is explained with respect to Fig. 3. Fig. 3 shows the detail D of Fig. 2 with some extra information: Determining a subtrahend surface S_i may comprise to determine at least a first meandering line B_i,j. In the example of Fig. 3, there are two meandering lines, the first meandering B_1,j line extends parallel to flow direction d_h and the second meandering line B_1,k extends perpendicular to d_h, i.e. parallel to d_o (thus d_o ⊥ d_h). As can be seen, the first meandering line has a first end point b_1,l,e. The line B_i,j meanders a long or in the direction b₁ because the line B_1,j as a first end point b_1,j,e and any point b_1,j,l on the meandering line B_1,j has a unique distance to the first end point b_1,j,e, thus the meandering line B_1,j obeys the condition |b₁ · (b_i,j,l - b_i,j,_e)| ≠ |b₁ · (b_i,j,m - b_i,j,e)| ∀b_i,j,l, b_i,j,m ∈ B_i,j, b_i,j,l ≠ b_i,j,m , while in this example b₁ = d_h, being a preferred choice. Further orthogonal to b₁ the distances of the points of the meandering line B_1,j are not unique, i.e. |b_┴ · (b_1,j,l - b_1,j,e) I = |b_┴ · (b_1,j,m - b_1,j,e)| ∀b_1,j,l, b_1,j,m ∈ B_1,j, b_1,j,l ≠ b_1,j,m with b_⊥ ⊥ b₁ does not hold true. In the depicted preferred example, the first meandering line B_1,j has straight sections which can be described as multiples of a fusing vector v_i, and further straight sections extending in an angle, preferably orthogonally, to the fusing vector v_i. The corresponding vector is hence indicated as v_a The fusing vector v_i is a vector along which the i^th-beam spot is moved over the surface while fusing the set of locations L_i.

In the example of Fig. 3 there is an optional second meandering line B_1,k that meanders orthogonal to the first meandering line B_1,j. Thus |b₂ · (b_1,k,l - b_1,k,e)| ≠ |b₁ · (b_i,k,m - b_i,k,e)| ∀b_i,k,l, b_i,k,m ∈ B_1,k, b_i,k,l ≠ b_i,k,m, while in this example b₂ = b_o = b_⊥. It is emphasised that this choice is only an example, other choices may be used as well. Preferably, b₁ and b₂ are linearly independent (i.e. b₁ ≠ c · b₂∀c).

When determining the subtrahend surface S₁ (more generally S_i) one may simply shift the meandering lines B_1,j and B_1,k (more generally B_i,j and B_i,k ). In a preferred example embodiment, the corresponding meandering lines B_i,j and B_i,k may be shifted at least essentially perpendicularly (i.e. within 90° ± 45°, ±30°, ±15°, ±10°, ±5°, ±2.5°, ±1° or ±0°) to their respective vectors b₁ and b₂ until the conditions for S₁ (more generally S_i) are obeyed. In other words, the lines B_i,j and B_i,k may define inner boundaries of the subtrahend surface S_i, while the outer boundary may be provided by the boundary of the corresponding field of view F_i, or preferably by the outer boundary of IS_i, wherein the terms "inner" and "outer" reference to the location being defined by the centre of the field of viewF_i of the respective i^th beam source, being herein denoted by an "x" representing the corresponding projection of the i^th-beam source.

In the example of Fig. 3, only two meandering lines are required to determine the subtrahend surface S_i. In this example this is due to the location of the area A relative to the center of the first field of view F₁ (generally, center of the the i^th-field of view F_i).

If the geometry and/or the location of the area A relative to an i^th-beam sources field of view F_i is different, then three or four of the meandering lines may be required to determine the inner boundary of the subtrahend surface.

A corresponding example is shown in Fig. 4. Fig. 4 shows another detail of Fig. 2, being centred at the centre of the projection of the eleventh field of view F₁₁ of the 11^th-beam source. Again, the number 11 is just an example and may be generalized. When determining the 11^th-subtrahend surface S₁₁ one may again use meandering lines which in this case may be labelled B_11,j, B_11,k and B_11,l. When determining S₁₁, the first set and second sets of locations L₁ and L₂ have already been determined and hence the 11^th-intersecting set IS₁₁ is limited by B_1,j' and B_2,j". As can be seen in Fig. 2, the left-hand portion of the surface being delimited by B_1,j' and B_2,j" is not in the field of view F_i or any other beam source than of the 11^th-beam source. Thus, the constraint on S₁₁ that ∀p₁₁ E S₁₁ , ∃ F_k |p₁₁ E F_k , k > i cannot be met for the points p₁₁ in between of B_1,j' B_2,j" and to the left of the circle defining the boundary of F_13. Thus, as matter of the conditions on S_i it turns out that j' = j" = 11 and one obtains B_11,1 := B_1,11 and B_11,2 := B_2,11. Thereby, only the position of a single meandering line, B_11,1 has to be determined by shifting it for example at least essentially perpendicular to b₂, which in this example obeys b₂ ⊥ b_h. In Fig. 4 this shifting process is indicated by a double headed arrow. In other words, the meandering line B_11,1 (generally B_i,l) is shifted until the remaining conditions on S₁₁ (as an example for S_i are met). In the depicted example it is thus sufficient to determine the size of the surface being enclosed the contour of IS₁₁ and the meandering lines B_11,5, B_11,6 and B_11,1 to determine |IS₁₁ - S₁₁| (generally |IS_i - S_i|). If the size |IS₁₁ - S₁₁| is bigger (or smaller) then (1 ± α_i) · t_o(i) · R_i, then the meandering line B₁₁, l is slightly shifted to the left (or right, respectively) until (1 - α_i) · (|IS_i| - t_o · R_i) ≤ |S_i| ≤ (1 + α_i) · (|IS_i| - t_o · R_i).

The method may next proceed with determining the next subtrahend surface S_i+1 (in the given example with S₁₁₊₁ = S₁₂).

The example method can be implemented particularly easy, if the sequence of determining the subtrahend surfaces S_i is selected based on the ability of the i^th-beam source to contribute to fusing the area A. A measure for this ability to contribute can be considered as the size of the overlap of their respective fields of view F_i with the area A. Thus, as can be seen immediately, in the example of Fig. 2, |F₁ ∩ A| ≤ |F₂ ∩ A| or generally |F_i ∩ A| ≤ |F_i+1 ∩ A|, ∀1 ≤ i < n. In case |F_i ∩ A| = 0 then L_i = { } and it does not matter in which step of the sequence this result is assigned or determined. Thus, in a preferred example, the sequence of determining the subtrahend surfaces S_i and hence the sets of locations L_i preferably starts with the index representing the beam source having the field of view F_i with the smallest overlap with the area A and the indices are preferably sorted such that the |F_i ∩ A| = |IS_i| increases with i . Only to avoid any misunderstandings, it is repeated that of course if |IS_i| = 0 then it does not matter at which point in the method L_i := { } is executed, it may be at the beginning, at the end or at any other point in time.

1

additive manufacturing apparatus

2

double headed arrow indicating movement of support 82

3

inert gas flow

5

process chamber

6

workpiece (partially manufactured)

7

side walls of process chamber 5

8

bottom of process chamber 5

81

opening in bottom 8

82

movable supported support

9

ceiling of process chamber 5

10

programmable electronic circuitry / controller

12

fusible material

14

top surface of fusible material

20_i

i^th-beam source / projection of i^th-beam source

22_i

i^th-beam spot of i^th-beam source 20_i

F_i

fields of view of the i^th-beam source

L_i

set of locations {l_i} to be fused by the i^th-beam source 20_i

d_h

horizontal component of inter gas flow in process chamber 5

d_o

vector at least essentially perpendicular d_h

b_1,j,e

vector

b_1,j,l

vector

b_1,j,k

vector

b_2,j,l

vector

b_2,j,l

vector

b_2,j,k

vector

B_i,j

meandering lines (i, j ≤ n, i ≠ j)