Optimal wave with respect to efficiency in percussive drilling with integral drill steel

The problem considered is that of finding the optimum wave of given finite duration that maximizes the efficiency of conversion of wave energy into work in percussive drilling with integral drill steel (drill rod with integrated bit). A 1D model is used for the drill rod, and the bit-rock interaction is represented by a piecewise linear force versus penetration relation with different penetration resistances for primary loading and for unloading/reloading. A functional expressing the dependence of the efficiency on the incident wave is derived and maximized. The optimal incident wave has exponential shape with time constant for the growth rate equal to the characteristic response time of the percussive drill system, including the rock. The maximal efficiency increases monotonously with the duration of the optimal wave. It approaches zero for very short waves and unity for very long waves. Optimal waves of short duration are close to rectangular while those of long duration approach the semi-infinite exponential wave derived by Long in the 1960s. Optimal waves of medium or longer duration give significantly higher efficiencies than commonly used rectangular waves of the same duration.