A method for predicting geometric characteristics of polymer deposition during fused-filament-fabrication

Abstract

In recent years 3D printing has gained popularity amongst industry professionals and hobbyists alike, with many new types of Fused Filament Fabrication (FFF) apparatus types becoming available on the market. A massively overlooked component of FFF is the requirement for a simple method to calculate the geometries of polymer depositions extruded during the FFF process. Manufacturers have so far achieved adequate methods to calculate tool-paths through so called slicer software packages which calculate the required velocities of extrusion from prior knowledge and data. Presented here is a method for obtaining a series of equations for predicting height, width and cross-sectional area values for given processing parameters within the FFF process for initial laydown on to a glass surface.

Introduction

Fused filament fabrication (FFF), a form of Additive Manufacture (AM), is in common use in many research and industrial areas, mainly for its prototyping functionalities. This method of prototyping is carried out by extruding filaments of polymer material onto a build plate in order to build up a 3D object layer-by-layer [1], [2], [3], [4].The material used is a thermoplastic polymer, which is fed as a solid filament into a heated nozzle where it melts and flows as a polymer melt onto the preceding layer (Fig. 1). Here it cools rapidly and solidifies to form the new solid layer. The deposition method is typically a continuous deposited filament which is generated by traversing the nozzle around the build stage as material is extruded.

The influence of the temperature, flow, material properties and build strategy on the quality of the final product is of significant interest. Many articles have been published that study build strategies and the resulting mechanical properties [5], [6], [7], [8], [9], [10]. There is much less research, however, dedicated to understanding how the balance of extrusion parameters (extrusion velocity U_N, transverse nozzle velocity U_P and nozzle gap heights G_N) influences the deposited filament geometry.

Since tool paths are often directly calculated from 3D CAD data, there is little freedom in parameter control. A poor balance of these extrusion parameters can cause flaws within layer adhesion and lead to voids in the printed structure [11], [12]; voids between lines of extruded polymer can have adverse effects on mechanical properties within FFF components [6], [11], [13], [14].

There have been a number of modelling approaches to capture the deposition process; a review can be found by Turner et al. [15]. In particular Agarwala et al. [16] and Bellini et al. [17] approximate feed rates U₀ required for a particular filament width W and height H. Yardimci et al. [18] and Venkataraman et al. [19] have also explored the filament buckling mechanism that limits the feed rate. Spreading of the deposited filament has also been investigated by Crockett et al. [20], and a 2D simulation of this spreading process is presented by Bellini et al. [21]. However, it is noted by Turner et al. that ‘there has been a limited degree of experimental validation of process models.’

More recently experimental comparisons have been presented by Gleadall et al. [22], who employ a new computationally-efficient method based on conservation of volume to predict the geometry of a 3D lattice, and Comminal et al. [23], who employ a full (isothermal) computational fluid dynamics (CFD) model of a single deposited filament. Extrusion of single polymer filaments has many applications including antenna manufacture with conductive filaments [24], custom polymer vascular inserts [25] as well as scaffolding structures [26] for the initial layers of the FFF process.

Of particular interest to the AM community is a simplified model, which removes the need for knowledge of complex flow dynamics required by CFD simulations, that allows FFF users to quickly and efficiently test the effect of extrusion parameters on part geometry. CFD simulations, whilst having advanced in recent years in terms of efficiency are still very time consuming and require significant knowledge and training in comparison to a simplified mathematical model [27].

In particular, Comminal et al. [23] compare their full CFD model to a simplified model based on conservation of mass. Although this model is able to capture spreading of the filament in the xy-plane, this work does not explore the phenomenon of the actual filament height, H, extending above the nozzle gap size, G_N in the z-direction. This is a common effect observed in FFF printing [21] and causes complications when subsequent filaments of molten polymer are extruded.

In this paper, we investigate the influence of extrusion parameters on track dimensions for an extended range of print speed ratios (U_N/U_P) and nozzle gap sizes G_N using CT scanning. We present an idealised model based on conservation of mass (similar to Ref. [23]), which is able to account for the filament height expanding above the nozzle gap size (H > G_N) unlike previous studies. We compare two printing materials; ABS, an amorphous polymer melt containing rubber nanoparticles, and PLA, a semi-crystalline polymer melt. Volume changes during crystallization can often cause contraction of a melt upon cooling [28], thus ABS and PLA geometry is expected to differ significantly. Finally, we discuss the effect that changing the bed temperature has on filament spreading.