This paper explores a possible theoretical basis for the failure of attempts to develop rotary-vibratory drilling units. With the critical needs in geothermal blast hole excavation and oil exploration, this nation cannot overlook the possibility of accelerating the drilling process by factors of 2 to 20 over the conventional rotary drilling rates. This paper develops the theory for the dynamic response of a vibrating drill string in a viscous drilling fluid with the energy lost to shear work. It develops the relations for power delivery to the rock as well as the total vibratory power to drive the system. Thus vibratory power losses can be computed by a difference. Part II of this paper applied this theory to a typical effort at developing a rotary-vibratory drilling unit. In the case studied, the power delivery was ineffective and at certain frequencies large losses resulted.

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