In this paper, the grinding of powder inside a ball mill is studied using the Bonded Cell Method (BCM) implemented in the framework of Contact Dynamics. In BCM the parent particles are divided into cells that are glued to one another until, under the action of external loading, both a cohesion threshold and a certain distance threshold are reached. Numerical simulations of a rotating hollow cylinder filled with a mixture of heavy balls and powder crushable particles were carried out. Systems with balls of different sizes and/or numbers are compared in terms of the evolution of the powder particle size and specific surface. We find that, in general, the milling process is increasingly faster as the ball size increases. But energy dissipation due to increased collisions between balls slows down the grinding process and makes it energetically less efficient. On the other hand, when the total volume of balls is kept constant, the ball size is not relevant for the evolution of particle breakage except in the limit cases of very small and very large ball sizes.