Models for Weld Temperatures in Additive Manufacturing

• Daniel Bowers, Applied Mathematics, University of Delaware

• David Edwards, Mathematics, University of Delaware

Additive Manufacturing is an increasingly popular technique in the world of manufacturing. It’s very efficient and precise, and we are looking to improve upon the build quality. We are investigating the strength of the build between layers. The goal of this project is to develop a model to evaluate the weld strength in the 3D printing process. The strength of a weld layer is given by the area of contact and the temperature of the dispensed filament. The larger the area of contact and the higher the weld temperature, the stronger the weld becomes. Stronger welds means stronger and more reliable builds

We can start to evaluate this by using the standard heat equation and tinkering with it to fit within our problem. Once we have a model for our problem, we can start finding ways to solve for our temperature equation. We can use numerical methods to get increasingly close approximations to the actual answer. The method we used is the Crank-Nicolson scheme, a method to approximate solutions to partial differential equations. We have code to evaluate the Crank Nicolson scheme. Using test cases with exact solutions, we have been able to demonstrate the accuracy of our code and determine how reliable it is. The test cases become more and more similar to the real case. Oncewe have reliable code, we can then fit our solution to the experimental data and use those temperature calculations to determine the weld strength.

After this project, one may want to investigate to see how this model holds for different filament materials and build shapes. This will hopefully lead to developments in the world of additive manufacturing and increase its utility. This work builds off of previous works of Dr. David A. Edwards using experimental data from Johnathan E. Seppala.