Depositing arced portions of fiber-reinforced thermoplastic filament
A technique for depositing fiber-reinforced thermoplastic filament in an arc is disclosed that mitigates the centripetal forces that arise in the prior art. In accordance with the illustrative embodiment, the centripetal forces are ameliorated by twisting the filament while depositing it in an arc.
1. A method of depositing a thermoplastic filament that comprises (i) a longitudinal axis L and (ii) a reinforcing fiber that is substantially parallel to the longitudinal axis L, the method comprising:
depositing a first portion of a segment of the thermoplastic filament in a straight line without twisting the thermoplastic filament around the longitudinal axis L and without twisting the reinforcing fiber around the longitudinal axis L, wherein the first straight portion of the segment has a length of S 1 as measured along the longitudinal axis L; and
depositing a second portion of the segment of the thermoplastic filament in a first arc of θ 1 radians and radius R 1 while twisting the second portion and the reinforcing fiber φ 1 radians around the longitudinal axis L, wherein the second portion of the segment has a length of S 2 as measured along the longitudinal axis L; and
depositing a third portion of the segment of the thermoplastic filament in a straight line without twisting the thermoplastic filament around the longitudinal axis L and without twisting the reinforcing fiber around the longitudinal axis L, wherein the third portion of the segment has a length of S 3 as measured along the longitudinal axis L;
wherein the first portion of the segment and the second portion of the segment are contiguous; and
wherein the second portion of the segment and the third portion of the segment are contiguous;
wherein S 1 , S 2 , S 3 , and R 1 are positive real numbers, and wherein θ 1 and φ 1 are real non-zero numbers.
2. The method of claim 1 wherein φ 1 =2πN 1 , where N 1 is a non-zero integer.
3. The method of claim 1 wherein φ 1 =2π.
4. The method of claim 1 wherein the reinforcing fiber in the thermoplastic filament in the second portion of the segment has the form of a helix with a rate of twist of
d
φ
1
d
S
2
≠
0
such that
d
2
φ
1
d
S
2
2
=
0.
5. A method of depositing a thermoplastic filament that comprises (i) a longitudinal axis L and (ii) a reinforcing fiber that is substantially parallel to the longitudinal axis L, the method comprising:
depositing a first portion of the segment of the thermoplastic filament in a first arc of θ 1 radians and radius R 1 while twisting the first portion and the reinforcing fiber φ 1 radians around the longitudinal axis L, wherein the first portion of the segment has a length of S 1 as measured along the longitudinal axis L;
depositing a second portion of the segment of the thermoplastic filament in a straight line without twisting the thermoplastic filament around the longitudinal axis L and without twisting the reinforcing fiber around the longitudinal axis L, wherein the second portion of the segment has a length of 52 as measured along the longitudinal axis L; and
depositing a third portion of the segment of the thermoplastic filament in a second arc of θ 2 radians and radius R 2 while twisting the third portion and the reinforcing fiber φ 2 radians around the longitudinal axis L, wherein the third portion of the segment has a length of S 3 as measured along the longitudinal axis L;
wherein the first portion of the segment and the second portion of the segment are contiguous;
wherein the second portion of the segment and the third portion of the segment are contiguous; and
wherein S 1 , S 2 , S 3 , R 1 , and R 2 are positive real numbers, and wherein θ 1 , θ 2 , φ 1 , and φ 2 are real non-zero numbers.
6. The method of claim 5 wherein φ 1 =2πN 1 and φ 2 =2πN 2 , and wherein N 1 and N 2 are non-zero integers.
7. The method of claim 6 wherein N 1 =−N 2 .
8. The method of claim 6 wherein N 1 =1 and N 2 =−1.
9. The method of claim 5 wherein θ 1 ≠θ 2 and φ 1 =φ 2 .
10. The method of claim 5 wherein R 1 ≠R 2 and φ 1 =φ 2 .
11. The method of claim 5 wherein R 1 θ 1 ≠R 2 θ 2 and φ 1 =φ 2 .
12. The method of claim 5 wherein the reinforcing fiber in the thermoplastic filament in the second portion of the segment has the form of a helix with a rate of
d
φ
1
d
S
1
≠
0
such that
d
2
φ
1
d
S
1
2
=
0
;
and
wherein the reinforcing fiber in the thermoplastic filament in the third portion of the segment has the form of a helix with a rate of twist of
d
φ
2
d
S
3
≠
0
such that
d
2
φ
2
d
S
3
2
=
0.
13. A method of depositing a thermoplastic filament that comprises (i) a longitudinal axis L and (ii) a reinforcing fiber that is substantially parallel to the longitudinal axis L, the method comprising:
depositing a first portion of a segment of the thermoplastic filament in a first arc of θ 1 radians and radius R 1 while twisting the first portion and the reinforcing fiber pi radians around the longitudinal axis L, wherein the first portion of the segment has a length of S 1 as measured along the longitudinal axis L; and
depositing a second portion of the segment of the thermoplastic filament in a second arc of θ 2 radians and radius R 2 while twisting the second portion and the reinforcing fiber φ 2 radians around the longitudinal axis L, wherein the second portion of the segment has a length of S 2 as measured along the longitudinal axis L;
wherein the first portion of the segment and the second portion of the segment are contiguous; and
wherein S 1 , S 2 , R 1 , and R 2 are positive real numbers, and wherein θ 1 , θ 2 , φ 1 , and φ 2 are real non-zero numbers.
14. The method of claim 13 wherein φ 1 =2πN 1 and φ 2 =2πN 2 , and wherein N 1 and N 2 are non-zero integers.
15. The method of claim 14 wherein N 1 =−N 2 .
16. The method of claim 14 wherein N 1 =1 and N 2 =−1.
17. The method of claim 13 wherein θ 1 ≠θ 2 and φ 1 =φ 2 .
18. The method of claim 13 wherein R 1 ≠R 2 and φ 1 =φ 2 .
19. The method of claim 13 wherein R 1 θ 1 ≠R 2 θ 2 and φ 1 =φ 2 .
20. The method of claim 13 wherein the reinforcing fiber in the thermoplastic filament in the first portion of the segment has the form of a helix around a curved portion of the longitudinal axis L with a rate of twist of
d
φ
1
d
S
1
≠
0
such that
d
2
φ
1
d
S
1
2
=
0
;
and
wherein the reinforcing fiber in the thermoplastic filament in the second portion of the segment has the form of a helix around a curved portion of the longitudinal axis L with a rate of
d
φ
2
d
S
2
≠
0
such that
d
2
φ
2
d
S
2
2
=
0.