Pressure Advance and Input Shaper

Physics and Mathematical Principles

Pressure Advance (Linear Advance)

In FDM printing, the extruder pushes solid plastic filament into a heated zone where it melts and is forced through a narrow nozzle orifice. Melted plastic behaves as a non-Newtonian, viscoelastic fluid under high pressure. Additionally, the solid filament acting as a piston experiences elastic compression, and Bowden tubes allow the filament to bend and store potential energy like a spring.

When the print head accelerates, there is a delay between the extruder movement and the actual flow of plastic from the nozzle. When the print head decelerates (e.g., approaching a corner), the residual pressure inside the nozzle melt chamber forces extra plastic out, leading to:

• Bulging corners (over-extrusion due to excess pressure during deceleration).
• Thin start lines (under-extrusion due to lag in pressure build-up during acceleration).

The mathematical model for Linear/Pressure Advance adjusts the extruder position ($E$) based on the instantaneous velocity of the extrusion axis: