Dynamic modelling of hardness changes of aluminium nanostructure during mechanical ball milling process

Document Type : Research Article


1 Young Researchers and Elite Club, Quchan Branch, Islamic Azad University, Quchan, Iran

2 Department of Chemical Engineering, University of Sistan and Baluchestan, Zahedan, Iran

3 Department of Chemical Engineering, Quchan Branch, Islamic Azad University, Quchan, Iran


In this research, the feasibility of using mathematical modelling in the ball milling process has been evaluated to verify the hardness changes of an aluminium nanostructure. Considering the model of normal force displacement (NFD), the radius of elastic-plastic and normal displacement of two balls were computed by applying analytical modelling and coding in MATLAB. Properties of balls and aluminium powder were entered into the software as input data. The impact radius and then the hardness of powder were calculated accordingly. The changes of aluminium powder hardness resulting from the collision of two spherical balls during the synthesis of an aluminium nanostructure were analytically derived and compared with experimental data obtained from the literature. Calculation of results accuracy shows the model has a better agreement with the experimental data at the beginning than the results from Maurice et al. (R2= 0.68 in this model).This research innovation is to combine the NFD model with hardness formulation to calculate final hardness.


  • Elastic and plastic deformation effects during collision were investigated.
  • The combination of NFD and powder hardness model shows better results.
  • This model is compared to Maurice et.al. The results show a 35% increase in model accuracy.


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