Publication Date



Ames Laboratory

Campus Units

Ames Laboratory

Report Number

IS-J 10507



Journal Title

Additive Manufacturing

Volume Number


First Page



In this work, we report a mathematical framework which predicts the degree of alignment (DoA) in an in-situ aligned additively manufactured 3D printed bonded magnets. A multiphysics model is developed which couples the harmonious interactions of magnetic particles in a viscous flowing polymer under the presence of an external magnetic field. The hydrodynamic fluid-particle interaction is paired with the magnetophoretic force to predict the particle trajectory and distribution during extrusion through a 3D printer nozzle. Succeeding the force balance, a magnetohydrodynamic torque equilibrium analysis is performed to predict the net-orientation of the magnetic particles as a function of the applied field strength, viscous forces, and particle-to-particle interactions (P2P). Experimental validation of the DoA predictions is performed using 65 vol% Nd-Fe-B+Sm-Fe-N in Nylon12 (DoAexp = 0.620 and DoAtheory = 0.686) and 15 vol% Sm-Co in PLA (DoAexp = 0.830 and DoAtheory = 0.863). A parametric analysis is performed to analyze the effect of operating and design parameters like alignment field strength, magnetic loading fraction, extrusion load, and particle size. The model predicts a competing behavior between particle-fluid and particle-particle interactions under the presence of an applied field. The model provides a framework to efficiently predict the DoA in tandem with a functionalized-magnetic 3D printer and allows the user to adjust the operating parameters according to the desired DoA.

DOE Contract Number(s)

AC02-07CH11358; AC05-00OR22725




Iowa State University Digital Repository, Ames IA (United States)

Available for download on Thursday, June 09, 2022