Optimal wave shape with respect to efficiency in percussive drilling with detachable drill bit

• The optimal incident wave shape maximizing the efficiency of wave energy conversion to work at a drill bit is determined.
• For long incident waves the bit mass strongly influences the optimal wave shape.
• Significantly higher efficiencies can often be achieved with optimal waves than with commonly-used rectangular waves.
• Sometimes, nearly optimal waves can be realized through impact but generally other means are needed.

The problem of finding the optimal incident wave of given duration that maximizes the efficiency of conversion of wave energy into work in percussive drilling with detachable drill bit is considered. The drill rod is modelled as 1D linearly elastic and the drill bit as a rigid mass. The bit/rock interaction is described by a history-dependent force versus penetration relation with different constant slopes for primary loading and unloading/reloading. A functional expressing the dependence of the efficiency on the shape of an arbitrary incident wave of given duration is derived and maximized. For short incident waves, there is a weak influence of the bit mass on the optimal wave shape which is nearly rectangular. For longer incident waves, there is a strong influence of the bit mass on the optimal wave shape which significantly differs from rectangular. The efficiencies for optimal waves approach those for rectangular waves for short waves. For long waves they approach or assume values which are independent of wave duration but decrease with increasing bit mass. Relative to commonly-used rectangular waves significant increase in efficiency can be achieved through optimization of the wave shape if the wave is not too short. Optimal incident waves can be realized accurately, e.g., by piezoelectric means.