Graph Theory Heat Flux Simulation for Additive Manufacturing

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Solution Overview

Problem

In metal additive manufacturing, inadequate heat dissipation leads to high failure rates of manufactured parts due to issues like warping and thermal stress-induced cracking, primarily caused by constrained heat flux, which current computational models are unable to efficiently address.

Innovation Solution

The implementation of graph theoretic modeling to simulate heat diffusion and estimate heat flux in metal additive manufacturing parts, allowing for rapid and accurate computation of heat distribution, reducing computation time from hours to minutes, and guiding part design and process parameter optimization.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If moving heat source finite element analysis techniques are used to simulate heat flux in metal additive manufacturing, then measurement precision and reliability are improved, but loss of time and productivity deteriorate due to computation taking several hours on a supercomputer

Engineering Contradiction:

Improveheat flux estimation accuracyVSAvoidcomputation time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The patent replaces the traditional finite element analysis computational mechanics system with a graph theory-based mathematical model. This substitution transforms the complex partial differential equation solving process into a simplified heat diffusion simulation on graphs, achieving comparable accuracy with dramatically reduced computational requirements that enable execution on desktop computers rather than supercomputers

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent changes the fundamental parameters and approach of heat flux simulation by transitioning from continuous finite element meshes to discrete graph representations. This parameter transformation allows the system to maintain measurement precision while reducing computational complexity and execution time from hours to minutes

Inventive Principle:

Principle #35Parameter changes

2Reliability

If moving heat source finite element analysis techniques are used to simulate heat flux in metal additive manufacturing, then reliability of heat flux prediction is improved, but device complexity and cost deteriorate due to requiring supercomputer resources

Engineering Contradiction:

Improveheat flux prediction reliabilityVSAvoidcomputational system complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent substitutes the complex supercomputer-based finite element analysis system with a simplified graph theory computational model. This replacement maintains prediction reliability by preserving the essential heat diffusion physics while eliminating the need for complex computational infrastructure, enabling execution on standard desktop computers

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent employs a computationally inexpensive graph-based model that can be rapidly executed on ordinary hardware rather than expensive supercomputing resources. This approach treats the simulation as a lightweight computational tool that can be run frequently during design iterations without incurring high computational costs

Inventive Principle:

Principle #27Cheap short-living objects (Disposable)

3Manufacturing precision

If conventional computational thermal models are used to estimate heat flux in metal additive manufacturing, then manufacturing precision can be improved, but productivity deteriorates due to time-consuming simulations

Engineering Contradiction:

Improvepart qualityVSAvoiddesign iteration speed

Core Design Contradiction:

Manufacturing precisionVSProductivity

Solution Approach 1:

The patent replaces conventional time-consuming thermal computational models with a graph theory-based simulation system that delivers comparable manufacturing precision for heat flux estimation. This substitution enables rapid what-if analysis and design iteration, transforming productivity by reducing simulation time from hours to minutes while maintaining the accuracy needed for quality part manufacturing

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

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 part failure rates, scrap, and rework by providing computationally efficient and accurate simulations of heat flux, enabling optimal part design and process parameter selection, and can be implemented on desktop computers, making it more accessible and cost-effective.

Implementation Method 1

the techniques disclosed herein simulate heat diffusion over graphs to approximate the heat flux in metal AM parts as a function of their geometry

Methodology Applied

Scientific EffectHeat diffusion: Conduction (thermal)

Data Source

PatentUS12093614B2Simulating heat flux in additive manufacturing

Publication Date: 2024.09.17 NUTECH VENTURES LTD

AI summary

Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for simulating heat transfer in additive manufacturing. Implementations disclosed herein convert a model of an object into a node representation of the object, and generate an adjacency matrix of the object based on the node representation. For each layer of nodes in the node representation, implementations apply a simulated heat to the layer of nodes, and estimating a diffusion of heat to other nodes based on the adjacency matrix. Implementations generate a representation of an estimated heat distribution within the object.