Meniscus Damping Model for Arbitrary Nozzle Geometries

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Solution Overview

Problem

In additive manufacturing, the inconsistency in droplet jetting due to unpredictable meniscus oscillations in the nozzle affects the quality of 3D printed parts, as traditional Computational Fluid Dynamics (CFD) methods are computationally expensive and time-consuming for calculating damping rates for arbitrary nozzle geometries.

Innovation Solution

A model is developed to predict the angular oscillation frequency and damping rate of the meniscus by transforming the problem into a discrete quadratic eigenvalue problem using the Finite Element Method (FEM), allowing for rapid prototyping of 3D printhead nozzles and diagnostic tools for nozzle issues.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If traditional Computational Fluid Dynamics (CFD) methods are used to calculate damping rates for arbitrary nozzle geometries, then calculation accuracy is improved, but computation time increases significantly

Engineering Contradiction:

Improvecalculation accuracyVSAvoidcomputation time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The patent segments the continuous CFD simulation process into discrete modal analysis components. By decomposing the fluid-structure interaction into separate structural modes and fluid pressure fields, the method enables independent calculation of each mode's contribution to damping, significantly reducing computational complexity while maintaining accuracy for arbitrary nozzle geometries

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent replaces the traditional mechanical CFD simulation approach with an analytical modal analysis method. Instead of solving full Navier-Stokes equations numerically, the method uses structural vibration modes combined with fluid pressure work integrals to calculate damping rates, substituting a computationally intensive mechanical simulation with a more efficient analytical framework

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Productivity

If rapid prototyping of nozzles is implemented to improve productivity, then design iteration speed increases, but droplet ejection consistency may deteriorate due to insufficient damping rate optimization

Engineering Contradiction:

Improvedesign iteration speedVSAvoiddroplet ejection consistency

Core Design Contradiction:

ProductivityVSReliability

Solution Approach 1:

The patent applies preliminary action by calculating and optimizing damping rates during the nozzle design phase using the efficient modal analysis method. By determining the optimal nozzle geometry that maximizes damping before manufacturing, the method ensures droplet ejection consistency is built into the design, allowing rapid iteration without sacrificing reliability

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent implements feedback by using the calculated damping rates to guide nozzle geometry modifications. The modal analysis provides quantitative feedback on how design changes affect meniscus oscillation damping, enabling iterative optimization that maintains droplet ejection consistency while improving productivity

Inventive Principle:

Principle #23Feedback

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

This approach significantly reduces computation time, enabling the rapid design of nozzles with improved damping rates for consistent droplet ejection and higher quality prints, while also providing a diagnostic tool for real-time monitoring and correction of nozzle issues.

Implementation Method 1

predict the angular oscillation frequency and damping rate of the meniscus

Methodology Applied

Scientific EffectMeniscus oscillation: Harmonic Oscillator

Implementation Method 2

damping rate of the meniscus

Methodology Applied

Scientific EffectDamping: Damping

Data Source

PatentUS20240211655A1Modeling of liquid-gas meniscus dynamics for arbitrary nozzle geometries

Publication Date: 2024.06.27 GENESEE VALLEY INNOVATIONS LLC

AI summary

Techniques for determining a damping rate of unforced oscillations of a meniscus are disclosed. An example method includes receiving input describing a shape of a container, physical parameters of a liquid inside the container, and an equilibrium shape of the meniscus. The method also includes generating a mesh conforming to the shape of the container and generating a discrete version of a continuous eigenvalue problem based on this mesh. The method also includes computing, at appropriate mesh nodes, values for pressure, velocity components, and meniscus surface deformation corresponding to a suitable number of least-damped late-time oscillation modes of the liquid and computing an angular frequency and damping rate of these least-damped late-time oscillation modes from the discrete version of the continuous eigenvalue problem. The method also includes identifying the mode that has the lowest damping rate and computing a liquid relaxation time by inverting the damping rate of the identified mode.