Duct fabricated with additive manufacturing and having one or more curves
Curvilinear ducts manufactured by depositing one or more runs of material in a conjoined helix, a conjoined plurality of conjoined planar spirals, and a plurality of conjoined conical spirals.
1. A duct with a duct axis {right arrow over (d)}(t) described by the vector function:
{right arrow over (d)} ( t )=< a ( t ), b ( t ), c ( t )>,
the duct comprising:
a run of material having (i) a solid cross-section and (ii) a longitudinal axis {right arrow over (r)}(s) running through the solid cross-section and described by the vector function:
{right arrow over (r)} ( s )=< f ( s ), g ( s ), h ( s )>
that forms a helix around the duct axis {right arrow over (d)}(t);
wherein the duct axis {right arrow over (d)}(t) is characterized by a curvature κ(t) and a center of curvature {right arrow over (p)}(t) described by the vector function:
{right arrow over (p)} ( t )=<α( t ), β( t ), γ( t )>;
wherein the curvature κ(t)>0;
wherein the run of material is characterized by a conjoining axis j(t) at {right arrow over (r)}(s) such that j(t)∝∥{right arrow over (r)}(s)−{right arrow over (p)}(t)∥; and
wherein t is a real number in the domain t: [t 1 , t 2 ] and s is a real number in the domain s: [s 1 , s 2 ].
2. The duct of claim 1 wherein the run of material has an isolating axis i(t) at {right arrow over (r)}(s) such that i(t)∝∥{right arrow over (r)}(s)−{right arrow over (p)}(t)∥.
3. The duct of claim 1 wherein the run of material has an isolating axis i(t) at {right arrow over (r)}(s) that is constant.
4. The duct of claim 1 wherein the evolute of {right arrow over (d)}(t) is a non-planar space curve over the interval [t 1 , t 2 ].
5. The duct of claim 1 wherein the helix is a circular helix.
6. The duct of claim 1 wherein the range of j(t) is between 0.1 millimeters and 0.5 millimeters.
7. The duct of claim 1 wherein the run of material is chopped-fiber reinforced thermoplastic.
8. A duct with a duct axis {right arrow over (d)}(t) described by the vector function:
{right arrow over (d)} ( t )=< a ( t ), b ( t ), c ( t )>,
the duct comprising:
a run of material having a longitudinal axis {right arrow over (r)}(s,k) described by the vector function:
{right arrow over (r)} ( s,k )=< f ( s,k ), g ( s,k ), h ( s,k )>
that forms a first stack of planar spirals, comprising a first planar spiral around the duct axis {right arrow over (d)}(t);
wherein the first planar spiral is a rectangular-with-rounded-corners planar spiral;
wherein the duct axis {right arrow over (d)}(t) is characterized by a curvature κ(t) and a center of curvature {right arrow over (p)}(t) described by the vector function:
{right arrow over (p)} ( t )=<α( t ), β( t ), γ( t )>
wherein the curvature κ(t)>0;
wherein the run of material is characterized by a conjoining axis j(t) at {right arrow over (r)}(s,k) such that j(t)∝∥{right arrow over (r)}(s,k)−{right arrow over (p)}(t)∥; and
wherein t is a real number in the domain t: [t 1 , t 2 ], s is a real number in the domain s: [s 1 , s 2 ], and k is an integer.
9. The duct of claim 8 wherein the run of material has an isolating axis i(t) at {right arrow over (r)}(s,k) such that i(t)∝∥{right arrow over (r)}(s,k)−{right arrow over (p)}(t)∥.
10. The duct of claim 8 wherein the run of material has an isolating axis i(t) at {right arrow over (r)}(s,k) that is constant.
11. The duct of claim 8 wherein the first planar spiral is a conjoined planar spiral.
12. The duct of claim 8 wherein the first stack of planar spirals further comprises a second planar spiral around the duct axis {right arrow over (d)}(t), wherein the first planar spiral and the second planar spiral are conjoined with each other.
13. The duct of claim 8 wherein a second stack of planar spirals is further formed, wherein the first stack of planar spirals and the second stack of planar spirals are conjoined with each other.
14. The duct of claim 8 wherein the range of j(t) is between 0.1 millimeters and 0.5 millimeters.