# Modeling and Compensation Methods for Trajectory Errors in Continuous Fiber-Reinforced Thermoplastic Composites Using 3D Printing

## TL;DR

This paper introduces a method to reduce defects in 3D printed fiber-reinforced composites by modeling and compensating for printing trajectory errors.

## Contribution

The novel contribution is a trajectory error model and compensation method based on maximum printable curvature for 3D printing of fiber-reinforced composites.

## Key findings

- The error model accurately predicts printed trajectory errors, especially for obtuse angles.
- Error compensation reduces fiber bundle folding and twisting defects effectively.
- The method shows potential for application in other continuous fiber printing types.

## Abstract

Defects arising from the 3D printing process of continuous fiber-reinforced thermoplastic composites primarily hinder their overall performance. These defects particularly include twisting, folding, and breakage of the fiber bundle, which are induced by printing trajectory errors. This study presents a follow-up theory assumption to address such issues, elucidates the formation mechanism of printing trajectory errors, and examines the impact of key geometric parameters—trace curvature, nozzle diameter, and fiber bundle diameter—on these errors. An error model for printing trajectory is established, accompanied by the proposal of a trajectory error compensation method premised on maximum printable curvature. The presented case study uses CCFRF/PA as an exemplar; here, the printing layer height is 0.1~0.3 mm, the fiber bundle radius is 0.2 mm, and the printing speed is 600 mm/min. The maximum printing curvature, gauged by the printing trajectory of a clothoid, is found to be 0.416 mm−1. Experimental results demonstrate that the error model provides accurate predictions of the printed trajectory error, particularly when the printed trajectory forms an obtuse angle. The average prediction deviations for line profile, deviation kurtosis, and deviation area ratio are 36.029%, 47.238%, and 2.045%, respectively. The error compensation effectively mitigates the defects of fiber bundle folding and twisting, while maintaining the printing trajectory error within minimal range. These results indicate that the proposed method substantially enhances the internal defects of 3D printed components and may potentially be applied to other continuous fiber printing types.