Cool Down

The cool down stage can be modified, depending on desire of operator, to use a vacuum cool, helium injection cool, or controlled cool. The vacuum cool is the standard Arcam procedure for producing parts, where the build is allowed to cool (via conduction and radiation) until a minimum temperature is reached for helium injection (100-200°C). This is referred to as “slow cool”. Once a build is cooled below 100°C (as measured by the start plate thermocouple), it is considered safe to open to atmosphere. Helium can also be injected upon build completion to provide the addition of convective cooling to the top surface of the part. This has the effect of speeding up the cool down process (by at least 1 hour, depending on part size), which is why the helium injection method is also referred to as “fast cool”. Alternatively, the cool down process can be deliberately controlled by using the e-beam to heat a completed build. This is done by manually adjusting the current, using the “Start Plate Heating” function that is typically used for reheating a part after starting and stopping a build. The amount of heating provided by the e-beam can thus be adjusted in stages, which effectively allows for the in situ heat treatment (annealing, solution

treatment, aging, etc.) of the material. The impact of the cool down procedure on

microstructure (§VI.3.1) and mechanical properties (§VIII.4.1) is explored in a later chapters.

136 IV.3.5 Melt Pool Overlap

The minimum theoretical overlap to achieve fully dense material for overlapping spot melt pools must first be considered from the XY plane (lines must at least meet at edges). This can be done by calculating the intersection of circles (assuming spot melts are circular in nature), as described in Figure 61.

Figure 61. Four overlapping circles of radius, R, and spacing, d.

To begin, consider the areas of four overlapping circles, with the same radius, R:

𝒙^𝟐+ 𝒚^𝟐= 𝑹^𝟐

(𝒙 − 𝒅_𝒙)^𝟐+ 𝒚^𝟐= 𝑹^𝟐

137 𝒙^𝟐+ (𝒚 − 𝒅_𝒚)^𝟐= 𝑹^𝟐

(𝒙 − 𝒅_𝒙)^𝟐+ (𝒚 − 𝒅_𝒚)^𝟐= 𝑹^𝟐 (Eq. 8)

These equations can be combined to solve for position variables x and y, in terms of the spacing between circles in the x-direction (dx) and y-direction (dy):

𝑥 =^𝑑₂^𝑥 , 𝑦 =^𝑑₂^𝑦

By substituting into Equation 8, and requiring uniform overlap of 𝑑 = 𝑑_𝑥 = 𝑑_𝑦:

𝑅² = ^𝑑₄^𝑥2+^𝑑₄^𝑦2 = ^𝑑₂²

Which yields a theoretical minimum spot melt pool overlap, based on X-Y requirements of:

𝑑 = √2 ∗ 𝑅

The area of the overlap can be calculated by applying the equation for the area bound by the chord of a circle:

𝑨_{𝒄𝒉𝒐𝒓𝒅} = 𝑹^𝟐𝐜𝐨𝐬^−𝟏(_𝟐𝑹^𝒅) −^𝟏_𝟒𝒅√(𝟐𝑹 − 𝒅)(𝟐𝑹 + 𝒅)

(Eq. 9)

Which for the area bound by two circles, and applying the theoretical minimum, is:

𝑨_{𝒐𝒗𝒆𝒓𝒍𝒂𝒑}= 𝟐𝑨_{𝒄𝒉𝒐𝒓𝒅} = (^𝝅_𝟐− 𝟏) 𝑹^𝟐 (Eq. 10)

And if calculated for all four overlaps is:

𝑨 = 𝟒𝑨_{𝒐𝒗𝒆𝒓𝒍𝒂𝒑} = 𝟐(𝝅 − 𝟐)𝑹^𝟐 (Eq. 11)

138

Which matches previous derivations. [284] This, however, does not address the fact that the limiting overlap value may be caused by the X-Z requirements. To calculate a

theoretical minimum overlap for both spot and line melts in the X-Z direction, we can assume a Gaussian melt pool shape. The overlap is defined in Figure 62, where dx is the distance between melt pool centers, “a” is the depth of the melt pool, and h is the depth as which the melt pools overlap.

Figure 62. Two overlapping Gaussian distributions for modeling melt pool overlap in the X-Z direction.

Now the Gaussian function must be defined:

𝒛 = 𝒇(𝒙) = 𝒂 ∗

𝐞𝐱𝐩

Where “b” is the position of the center and “c” controls the width of the profile. Using this equation, profiles can be formulated for overlapping melt pools:

𝑧₁(𝑥) = 𝑎 ∗ exp (−_2𝑐^𝑥2₂) 𝑧₂(𝑥) = 𝑎 ∗ exp (−^{(𝑥−𝑑)}_2𝑐2²)

139

So, the minimum theoretical overlap of two adjacent line or spots must meet this value of spacing, d. Depending on processing conditions, the melt pool size and shape will change.

The minimum overlap to avoid porosity will then be limited by the smaller of either the X-Y limit or the X-Z limit. It is worth clarifying that as the value of d increases, overlap

decreases. So, decreasing d will increase overlap until the paths are coincident. While overlap should meet the minimum value to avoid porosity, it should also be minimized to avoid unnecessary remelting. It is also important to note that theoretical overlap

requirements do not account for a number of complicating factors, especially local process variability. Small fluctuations in a real system would likely lead to localized porosity

formation, if minimum parameters were used. Still, the minimum theoretical overlap may be used as a check on processing conditions and processing windows.

The process steps for melting metal are designated by the terms “contours” and “bulk” (or

“hatch”) melting. Contours are spot melts that melt the edge of the of a part layer (Figure 63a). The order of the spots is determined by an EBM control algorithm. After contours are made, the bulk of the part must be melted. This can be done by either rectilinear line melting (Figure 63b) or using spot melts (Figure 63c). The end result is full melting of the enclosed part slice (Figure 63d). If the speed of the beam is known (details on calculating speed are addressed in §V.1.3), the time for the bulk melt can be estimated for rectilinear infill. The number of spots and spot pulse time must be known to calculate the bulk melt time for spot melting.

140

Figure 63. The steps of melting; (a) contour melting using spot melts, (b) standard linear bulk melting, (c) alternative spot bulk melting, and (d) completed melt of a part slice for example geometry.

The amount of time required to melt example geometries is shown in Figure 64 for both spot and line melting. The line melting time is dependent on the angle of melting relative to the part because of the dependence of speed on line scan length; the number and length of lines changes for various rotations. Squares and triangles show a periodic structure,

whereas a more complex geometry has an optimal angle to minimize melt time. Spot melting time does not vary with angle and is constant. The equivalent time for bulk spot melting (if the layer is melted using only spot pulses) of each geometry is shown as a constant value in each graph for a point offset of 0.5mm and a pulse time of 0.5ms. While the spot time appears to always be fastest, the spot melt parameters used may have to be adjusted such that an increase in melt time is incurred; the constant value may be vertically translated, depending on parameter optimization, and may not always be fastest. Note that each pattern repeats certain symmetry; the rotation from 0-180 degrees is effectively the same as the rotation from 180-360 degrees. Melt time for line melts were calculated from average line speed for each rotation.

141

Figure 64. Melt time optimization for slices of a (a) square, (c) triangle, and (e) complex build. The standard linear melt is rotated through angles of 360 degrees to show variation for the (b) square, (d) triangle, and (f) complex build.

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CHAPTER V

IMPACT OF PROCESS PARAMETERS ON DEFECTS, PROCESS TIME, & THERMAL