Research Article Open Access

Evaluation of Binary and Ternary Models in Powder Packing Density for Additive Manufacturing Applications

Taher M. Abu-Lebdeh1 and Oluwatobiloba Adetokunbo Kalejaiye1
  • 1 North Carolina A&T State University, United States


Powder packing is a very important aspect of additive manufacturing (3-D printing), as it directly impacts the final physical and mechanical properties of the printed objects. Improving the packing density of powder directly impacts the microstructure of the finished 3D-printed product, which also contributes to the surface finish. In order to achieve the densest packing for a powder, different sizes of that powder must be mixed together in such a way that we minimize the voids, thereby increasing the density of the powder. To achieve this, a model that predicts the volume fraction of each powder grade becomes necessary to predict the maximum possible powder density. A wide variety of models have been developed for packing density which can be classified as: Binary Mixture Models, Ternary Mixture Models and Multi-Component Mixture Models. In this project, the Furnas ternary model and the modified Toufar binary model were used to evaluate the packing density of Boron powder. Two sets of Boron powders were used for the analysis: First set: d10 = 75 µm, d50 = 90 µm, d90 = 106 µm and the second set: d10 = 3.11 µm, d50 = 14.0 µm, d90 = 30.2 µm. The three different sizes of each powder were randomly mixed to obtain the maximum packing density and compared with the theoretical packing density obtained by Furnas ternary model. The three sizes were then reduced to two sizes to obtain the packing density and compare the result with the modified Toufar binary model. Different mix rations were performed to evaluate the results obtained from both Furnas model and modified Toufar model. Results indicated that the models accurately predicted the maximum density of metal powder. Packing density obtained experimentally was 1.73 g/cm3 at a mix ratio (coarse: Fine) of 89:11, while the values obtained by Furnas model and modified Toufar were 1.72 at 87:13 mix and 1.73 g/cm3 at 89:11 mix respectively.

American Journal of Engineering and Applied Sciences
Volume 14 No. 2, 2021, 314-322


Submitted On: 19 April 2021 Published On: 15 June 2021

How to Cite: Abu-Lebdeh, T. M. & Kalejaiye, O. A. (2021). Evaluation of Binary and Ternary Models in Powder Packing Density for Additive Manufacturing Applications. American Journal of Engineering and Applied Sciences, 14(2), 314-322.

  • 2 Citations



  • Furnas Model
  • Ternary Mixture
  • Binary Mixture
  • Modified Toufar Model
  • Packing Density
  • Metal Powder
  • Additive Manufacturing