Numerically investigating the crushing of sandstone by a tooth hob

To investigate the mechanical process that occurs between rocks and tooth hobs, the crushing of sandstone with a tooth hob was simulated using reconstructed multi-mineral mesoscopic numerical models of various grain-sized sandstone samples. When a piece of sandstone is crushed by the tooth of a hob rolling at a constant speed, the resultant reaction forces of the sandstone on the tooth first hinder and then contribute to the rolling of the hob. The absolute value of the longitudinal reaction force is significantly higher than that of the lateral reaction force. Because the tooth was subjected to reaction forces from the sandstone, forces and moments were applied to the hob in order to keep the hob rolling. The applied forces were equal in value and opposite in direction to the reaction forces of the sandstone on the tooth. Three typical curves of the work done by the applied forces and moment were obtained, and the contribution of the applied lateral force and moment to the total work done for crushing sandstones was variable; however, no work was done by the applied longitudinal force. Moreover, the applied longitudinal force and total work were positively correlated with the strength of sandstone samples. The total work, applied forces, and moment increased with the maximum penetration depth of the tooth in the sandstone.