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Passive Vibration Control of a 3-D Printer Gantry

Maharshi A. Sharma, Albert E. Patterson

TL;DR

The paper addresses vibration-induced position errors in fused filament fabrication gantries by developing a three-stage spring–mass–damper model and integrating a passive vibration countermeasure attached to the extruder carriage. It extends a conservative Newton–Euler framework to include damping and belt preload, then converts the dynamics to a state-space form for analysis. Through a case study using orthogonal design of experiments, it demonstrates that carefully tuned passive parameters $(m_7, k_7, \beta_7)$ can substantially mitigate vibration, with specific combinations yielding near-ideal motion, while mis-tuning can worsen performance. The work lays the groundwork for hybrid active–passive control approaches and highlights potential benefits for FFF machines and other open-loop robotic systems in terms of speed, accuracy, and robustness.

Abstract

Improved additive manufacturing capabilities are vital for the future development and improvement of ubiquitous robotic systems. These machines can be integrated into existing robotic systems to allow manufacturing and repair of components, as well as fabrication of custom parts for the robots themselves. The fused filament fabrication (FFF) process is one of the most common and well-developed AM processes but suffers from the effects of vibration-induced position error, particularly as the printing speed is raised. This project adapted and expanded a dynamic model of an FFF gantry system to include a passive spring-mass-damper system controller attached to the extruder carriage and tuned using optimal parameters. A case study was conducted to demonstrate the effects and generate recommendations for implementation. This work is also valuable for other mechatronic systems which operate using an open-loop control system and which suffer from vibration, including numerous robotic systems, pick-and-place machines, positioners, and similar.

Passive Vibration Control of a 3-D Printer Gantry

TL;DR

The paper addresses vibration-induced position errors in fused filament fabrication gantries by developing a three-stage spring–mass–damper model and integrating a passive vibration countermeasure attached to the extruder carriage. It extends a conservative Newton–Euler framework to include damping and belt preload, then converts the dynamics to a state-space form for analysis. Through a case study using orthogonal design of experiments, it demonstrates that carefully tuned passive parameters can substantially mitigate vibration, with specific combinations yielding near-ideal motion, while mis-tuning can worsen performance. The work lays the groundwork for hybrid active–passive control approaches and highlights potential benefits for FFF machines and other open-loop robotic systems in terms of speed, accuracy, and robustness.

Abstract

Improved additive manufacturing capabilities are vital for the future development and improvement of ubiquitous robotic systems. These machines can be integrated into existing robotic systems to allow manufacturing and repair of components, as well as fabrication of custom parts for the robots themselves. The fused filament fabrication (FFF) process is one of the most common and well-developed AM processes but suffers from the effects of vibration-induced position error, particularly as the printing speed is raised. This project adapted and expanded a dynamic model of an FFF gantry system to include a passive spring-mass-damper system controller attached to the extruder carriage and tuned using optimal parameters. A case study was conducted to demonstrate the effects and generate recommendations for implementation. This work is also valuable for other mechatronic systems which operate using an open-loop control system and which suffer from vibration, including numerous robotic systems, pick-and-place machines, positioners, and similar.

Paper Structure

This paper contains 10 sections, 27 equations, 4 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. DYNAMIC MODEL
  3. System Model
  4. Newton-Euler Decomposition
  5. Nonconservative Model
  6. State Space Model
  7. PASSIVE CONTROL ON EXTRUDER
  8. CASE STUDY
  9. HYBRID ACTIVE-PASSIVE CONTROL
  10. CONCLUSIONS

Figures (4)

  • Figure 1: FFF gantry system model, considering only the motion of the extrusion head and system along the X-axis. In this model, the Y-axis build plate is fixed, and the Z-axis is assummed to be a fixed distance. This is realistic for standard FFF printer configurations as shown.
  • Figure 2: Passive controller as a spring-mass-damper system which can be tuned to counteract the natural vibration of the system
  • Figure 3: Position and velocity plots with the passive spring-mass-damper system attached for the none text cases.
  • Figure 4: Hybrid active-passive control concept for the extruder carriage.