Study optimizes FFF nozzle shape: Conical geometry as the key to higher throughput

High-speed printers for fused filament fabrication are increasingly equipped with more powerful motors and hot ends. However, the actual bottleneck remains the nozzle, where the flow characteristics of the polymer melt limit the maximum possible volume flow. A new numerical study therefore systematically investigates how the internal geometry of the nozzle influences pressure loss and thus determines the achievable printing speed without larger heating elements or more powerful extruders.

In their paper “Numerical Optimization of Nozzle Shapes for Fused Deposition Modeling,” Steffen Tillmann, Felipe A. González, and Stefanie Elgeti develop an optimization framework that minimizes pressure loss in the nozzle. Although the authors refer to FDM, they address the same process as FFF. The focus is exclusively on the inner channel of the nozzle, not the melt zone or heat break. This allows the effect of the geometry to be considered in isolation, a parameter that nozzle manufacturers can adjust relatively easily.

The calculations are based on two material models that are widely used in the literature. A temperature-dependent, shear-thinning viscosity model depicts how the melt becomes more fluid as the temperature and shear rate increase. An isothermal viscoelastic model keeps the temperature constant and depicts the elastic effects of the polymer melt. Geometrically, the researchers consider a simple conical inner shape, described by the half opening angle, on the one hand, and a more flexible spline-based contour on the other.

The results are practical. In the viscous model, the optimal half-opening angle depends heavily on the feed rate or volume flow. At high throughputs, the favorable range is around 30 degrees; at lower feed rates, the optimal angles shift to larger values. The viscoelastic model shows a significantly weaker dependence on feed rate, which indicates a wider tolerance range for the nozzle angle when elastic effects dominate. According to these calculations, spline-based shapes only result in minor additional savings in pressure loss compared to a well-chosen cone angle.

In practice, this means that manufacturers can reduce pressure losses with a specifically selected cone geometry and thus either achieve higher volume flows with the same extruder force or reduce the force required for a given throughput. This is particularly interesting for printing farms with high accelerations and aggressive flow specifications, as less under-extrusion and more consistent web widths can be expected.

However, the study is limited to numerical results. The abstract does not mention specific geometric limits, exact nozzle openings, or absolute pressure values. Real hot ends also bring into play inflow effects, melt pool dynamics in the heating block, surface roughness, possible sliding on the wall, and pronounced temperature gradients. In addition, the nozzle only contributes to part of the total pressure loss, which is also influenced by heat break and filament compression. Different materials with varying shear thinning and elasticity also argue against a universal ideal angle.