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Derive a general analytical model ( equation ) for the volume build rate of a direct, vector - scan, single - laser SL process in

Derive a general analytical model (equation) for the volume build rate of a direct, vector-scan, single-laser SL process in terms of the following parameters: Effective laser spot size or cured line width on the surface (Lw); Cured layer thickness (Zr); Laser scan speed (Vs); and time per layer to configure the next layer of liquid resin, the recoating or wiper time (tw). Assume neighboring (cured) tracks in a layer are just touching (not overlapping) at the surface, but overlap about 10% maximum with the layer (tracks) below. Assume the uncured volume of resin between tracks is part of the build volume. Note that linear shrinkage (SL) is already included in the track cross-section dimensions, but not in the length direction.
For Zr = Lw =0.1 mm, Vs =2000 mm/s, and a volume curing shrinkage of 15%, calculate the following:
(a) The volume build rate (cm3/h), neglecting the wiper time.
(b) The time to build a single 10 x 10 cm layer and a 10-cm cube (=1 L).
(c) For what wiper cycle time, does the wiper time add 10% to the total time in (b).
(d) For what (smaller) layer area does the wiper time in (c) double the total time.
(e) For a 10.0 x 10.0 cm cured layer, if the first track defines the outer edges of the layer, what must be the length of the edges scanned by the laser.
(f) Repeat part (b) for the laser set at the fill or hatch mode, where Lw =0.5 mm and Zr =0.1 mm.

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