Rate-of-Loading Effects in Chisel Impact
Authors: Appl F.C. , Gatley W.S. 
Published: December 2007

Abstract
This paper presents a combined analytical and experimental study of chisel penetration vs time during chisel impact on rock, a problem of fundamental importance in improving the performance of roller-cone bits or percussion drilling tools. For a given force-time relationship between chisel and rock, the problem of determining the penetration (displacement) vs time of the chisel is formidable. This is so because the rock is a non-linear system with distributed mass and distributed damping (friction, dissipation of energy due to rupture, etc.). Since the literature does not contain adaptable solutions, the rock behavior to impact was simulated approximately by an "equivalent" lumped system, that is, an "equivalent" mass, spring, dash pot system. With this assumption, an analytical solution was found for chisel penetration vs time due to a sinusoidal load between chisel and rock. From this solution were found curves, in terms of dimensionless variables, for the maximum depth of penetration vs the frequency of the sinusoidal loading and for the energy transfer vs frequency. The results of this analysis were used to predict the penetration rate of rotary rock bits vs rotary speed. The curve indicated that an optimum speed exists. To verify this analysis, an experimental apparatus was constructed and used to apply a sinusoidal pulse to a chisel penetrating a rock specimen under atmospheric conditions. Strain gauges were mounted on the chisel shank and a velocity transducer was mounted between the chisel and the rock surface. The velocity was integrated electrically and picked up simultaneously with the strain gauge signal on an oscilloscope. Permanent records were made photo graphically to provide simultaneous records of force vs time and penetration vs time. In comparing the experimental results for limestone and dolomite with the theoretical results, good agreement was found in the frequency range of the experiments. Unfortunately, the inertia effect (peak penetration) indicated by the theory occurs at a frequency much higher than could be obtained experimentally with the apparatus constructed. A "rate-of-loading" effect is indicated theoretically, but has not yet been verified experimentally.

Introduction
The process of drilling with percussion tools or rotary rock bits is basically related to the transient response of rock to surface impact. Each time a bit tooth contacts the rock, high stresses are developed which result in penetration and rock removal. As the tooth moves on, stresses are relieved and a new cycle begins as the next tooth contacts the rock. Thus the drilling process, which consists of an endless succession of these cycles, can be studied in terms of a single cycle. It is apparent, therefore, that the study of single-chisel impact on rock is fundamentally important in improving the performance of roller-cone and percussive-type drills. Previous studies in this area have been conducted by Simon and Hartman by means of drop tests. In these tests a chisel was attached to a weight and allowed to fall, due to the force of gravity, so that the chisel was driven into a rock specimen upon impact. Strain gauges were attached to the chisel shank and the resulting force-vs-time curves were recorded photographically from an oscilloscope screen. The depth of penetration and crater dimensions were also measured. These tests have provided much valuable information but, as mentioned by the investigators, have not provided complete information on the effect of "rate of loading". This is partly due to the fact that the chisel motion during drop tests is not a controlled motion which can be varied in form and frequency. Therefore, it seemed that additional information could be obtained by studying chisel impact under conditions where both the motion and the frequency of loading could be controlled.
SPEJ
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