Optimal force profiles are essential to extracting maximum performance from a percussion drilling system. In this investigation, a visco-elasto-plastic model of rock is simulated using the bond graph modeling formalism to study the effect of different percussive force profiles on rock failure and to generate optimal force profiles. Physical parameters of the model are estimated from rock material properties like compressive strength, density, elastic modulus and Poisson's ratio using Hsieh's equations. The model predicts penetration due to crushing when applied force is greater than a threshold force of the rock medium. This model does not account for penetration due to rotary drilling bit shear or fluid flow. A Specific Energy Index (SEI) and a Performance Index (PI) are employed to evaluate percussive force profiles. SEI reflects the effects of rate of penetration (ROP) and average hammer power whereas PI considers rate of penetration, bit force, and input power. SEI is a limited metric because it recommends low frequencies and low rate of penetration. The Performance Index (PI) seems to strike a better compromise between ROP and power, and has the additional potential benefit of accounting for bit wear. The present model can be studied under both percussive and vibrational loading but here only percussive force profiles are analyzed. The model will be verified experimentally in future investigations.
Percussive drilling has been studied analytically, numerically and experimentally over many years [1-20]. In percussive drilling, an impact tool continuously rises and drops to generate short duration compressive loads to crush the rock material. In general, a piston driven by compressed air or hydraulic drilling mud converts its kinetic energy to impact energy by colliding with a steel rod or drill bit. This impact energy is transferred to the steel in the form of a stress wave that travels to the bit rock interface. Part of the energy in the wave goes to the rock, causing failure, and part of the energy is reflected back. The effective stress in breaking rock acts in an axial direction and in a pulsating manner [28]. A thrust force may be applied to keep the bit in contact with the rock. It is very important to study the response of rock formations under different types of impact loading in the analysis and design of percussion hammers. Rock behavior and breaking criteria have been studied and described by many authors [1, 2, 4-6, 8-10, 13, 19, 25]. Chang [12] considered the rock medium as a non- linear spring attached to the drill bit end which follows a forcedisplacement law for a particular rock-bit type. Lundberg et al. [16] presented two different rock models under impact loading. Pavaloski et al. [17] modeled the rock as a visco-elastic material whereas Fernando et al. [19] introduced a nonlinear spring -dashpot system. In an attempt to analyze percussive and other vibro-impact force profiles, the research described in this paper simulates a visco-elastoplastic rock model similar to Batako et al. [20] with 20sim bond graph based software [30].
