Quasi-static stationary-periodic model of percussive deep drilling

Abstract

In the percussively deep drilling, the rock is modeled by an infinite elastic medium with a semi-infinite cylindrical bore-hole having a curvilinear bottom. First, the stationary indentation is formulated as a non-classical non-linear free-boundary contact problem with unknown rupturing and non-rupturing parts of the bore-hole boundary. Then the stationary-periodic per- cussive drilling problem is reduced to the stationary one on the rupture progression stage of the cycle and to the classical contact problem on the reverse and progression-before-rupture stages of the cycle. This provides a nonlinear progression - force diagram for the bit dynamics prediction.