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A dynamic model of the drilling action of percussive tools


A phenomenological model is proposed to explain the existence of sweet spot in the relationship between the rate
of penetration (ROP) and the weight-on-bit (WOB), i.e., the existence of an optimal WOB for which the ROP is maximized. The
reasons that have been previously proposed to explain the existence of a sweet spot include increasing wear of the bit, reduced
indexing, and poor cleaning of debris. Instead, motivated by experimental evidence, we consider an increase of the pseudo-stiffness
of the bit/rock interface (BRI) with the WOB, and investigate its consequence to the impact energy transmitted to rock. The model
approximates the dynamics underlying the drilling process by assuming that the impact of the hammer generates a longitudinal wave
in the bit. It is shown that the BRI pseudo-stiffness influences the stress and associated energy transmitted from the bit to the rock.
As a consequence, the drilling efficiency is affected by the dependence of the BRI stiffness on the WOB. According to this model,
there exist optimal conditions for the energy transfer from the bit to the rock in terms of the impedance ratio and the BRI stiffness.
The model confirms that there is a sweet spot as seen in practice, thus suggesting that the root cause of the existence of a sweet spot
in the ROP-WOB relationship lies in the nature of the BRI laws, rather than with issues related to indexing of the bit and/or cleaning
of the debris.


Academic chapter/article/Conference paper


  • Research Council of Norway (RCN) / 90280502
  • Research Council of Norway (RCN) / 254984





  • Norwegian University of Science and Technology
  • SINTEF Industry / Materials and Nanotechnology
  • University of Minnesota




American Rock Mechanics Association (ARMA)


Proceeding of 53th US Rock Mechanics / Geomechanics Symposium



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