059168 Advanced Manufacturing Process B

A collection of MATLAB scripts for 1D and 3D thermal modeling of laser-material interaction, developed for advanced manufacturing process simulation.

Visualizations from the 1D and 3D thermal models simulating laser-material interactions. In the 1D simulation, the heat source is applied at the surface (x=0) and switched off at t=1µs.

Story

This repository is a small collection of projects I developed for the "Advanced Manufacturing Process B" course. The curriculum was heavily focused on the use of lasers in modern manufacturing, and I found myself particularly drawn to modeling the complex thermal phenomena that occur when a high-energy beam meets a material.

These simulations were my attempt to go beyond empirical formulas and build a more intuitive understanding of the process. They helped me determine the optimal parameters for a laser ablation task we had in the lab, balancing precision with processing speed.

Overview

The repository contains two distinct thermal simulation models, both implemented in MATLAB. The goal is to predict the temperature distribution within a material under laser irradiation.

1D Thermal Model

Can be found in Thermal_Modelling_1D.m and focuses on a simplified scenario where the laser is treated as a motionless, extended planar heat source:

• Simulates the temperature profile along a single axis (depth) based on a motionless, extended planar heat source assumption.
• It calculates the temperature field as a function of space and time, considering only heat conduction.
• Material properties are sourced from Thermal-Properties.xlsx.

3D Thermal Model

Can be found in Thermal_Modelling_Moving_Point_3D.m and simulates a moving point heat source in a 3D space:

• Simulates the temperature distribution from a moving point heat source in a 3D space.
• This model was developed to find optimal parameters for creating a PCB circuit via laser ablation.
• It helps in analyzing the volume of vaporized material to tune laser power and speed.

Quick Start Guide

To run these simulations, you will need a working installation of MATLAB. Make sure to place both the scripts and the Thermal-Properties.xlsx file in the same directory.

You can tune the laser and material parameters directly in the scripts before running them.

Results and Analysis

The models produce detailed temperature profiles and visualizations of the affected material zones.

1D Model: Temperature Profiles

The 1D model is governed by the following relationship, describing temperature $T$ at depth $x$ and time $t$:

$$T(x, t) = T_0 + \frac{q_0 \sqrt{4 \alpha t}}{k} \text{ierfc}\left(\frac{x}{\sqrt{4 \alpha t}}\right)$$

Where:

• $T_0$: Initial material temperature
• $q_0$: Laser heat flux
• $k$: Thermal conductivity
• $\alpha$: Thermal diffusivity
• $ierfc$: Inverse complementary error function

The plots below show the temperature evolution in different materials when the laser is active from $t=0$ to $t=1$.

Temperature distribution as a function of depth at different points in time.

Temperature distribution as a function of time at different depths.

3D Model: Melted Region Analysis

For the moving point source, the temperature $T$ at a given point is calculated using:

$$r(\epsilon, y, z) = \sqrt{\epsilon^2 + y^2 + z^2}$$ $$T(\epsilon, y, z) = T_0 + \frac{P \eta}{2 \pi k r(\epsilon, y, z)} \cdot \exp\left(-\frac{v}{2 \alpha} \cdot (\epsilon + r(\epsilon, y, z))\right)$$

Where:

• $P$: Laser power
• $\eta$: Absorption coefficient
• $v$: Laser scanning velocity
• $r$: Distance from the heat source

This model allows for the visualization of the melted and vaporized zones, which is critical for tuning the ablation process.

3D representation of the melted region (light blue contour). Colors indicate the material's temperature.

Have a nice coding day,

Tommaso 🐼