Source: International Journal of Rock Mechanics and Mining Sciences 37 (2000) 599 – 613
In this work a study of impact in Down-the-Hole (DTH) rock drilling is carried out. We present an alternative to a method previously introduced by Lundberg and his co-workers. Our model is formulated in terms of the impulse-momentum principle while Lundberg's method is based in solving the one-dimensional wave equation. In the case of DTH drilling, the study of the subject becomes easier because the handling of many bodies interacting dynamically is simplified, and different boundary conditions, such as constant body forces, distributed forces and initial strains, can be directly included. The rock-bit interaction is modeled using both a non-linear spring and a variable gap using experimental parameter data obtained by other researchers and by a normalized quasi-static penetration test described in this work. The simulation results are in good agreement with results in previous publications as well as with experimental validation measurements carried out by the authors. © 2000 Elsevier Science Ltd. All rights reserved.
Keywords: Rock drilling; Stress wave propagation; DTH hammers
Pneumatic Down-the-Hole drilling (DTH) is a rotary percussive drilling technique generally used in medium to hard rock formations. A pneumatic hammer is used in which energy from air at high pressure is converted into kinetic energy of a piston. The piston later impacts a drill bit, which is in contact with the rock usually through tungsten-carbide inserts. Before impact, a thrust force is being applied over the bit head and the entire hammer is continuously rotated. At the body interfaces and also at every geometric singularity within each body (i.e. section change) the stress wave originated by the impact is partially reflected and transmitted. Hence at any instant the stress wave pattern can be complex. The stress wave actually transmitted to the rock is only a fraction of the initial stress wave. The rock itself while absorbing most of the energy from the incoming stress wave, will also reflect a certain amount back to the hammer and its supporting structure.
The objective of our research was to develop a model to study by simulation the effect of geometry, mass distribution, boundary conditions and type of rock on the stress wave transmission efficiency of the Down-the-Hole hammer. The numerical method that we have developed can be used as a tool for the design of pneumatic Down-the-Hole hammers since it allows prediction of the efficiency of the energy transmission to the rock, which is a central aspect of the performance of the hammer.
The penetration rate of drilling is the single most important performance parameter when two hammers are compared. Other measurements of interest are the air consumption, the impact frequency rate, the working air pressure, the thrust force and the rotation torque. The last two parameters are estimated by reading the input pressure to the hydraulic motor or hydraulic cylinder, respectively.
In a laboratory environment other important parameters can be measured such as piston impact and reflected velocity, piston stroke, air output temperature, chamber instantaneous pressures and piston instantaneous position. In addition, for a single impact using a drop-hammer, the maximum penetration depth can be measured as well as the specific fracture energy. All this information can be used to study the hammer from a thermodynamic point of view, as well as from an impact point of view — both aspects having the largest influences in the performance of the hammer.
Due to the complicated nature of the problem, for many years the effect of the design parameters has been studied empirically. The works of Clark [1] and Hustrulid and Fairhurst [2] are good examples of this approach, where experimental expressions are derived to model the impact in rock drilling and these expressions are then used to predict hammer performance. Purely analytical models are not generally used because in practice pneumatic hammer components have complex shapes and even the most advanced analytical methods described in the scientific literature are restricted to simple geometric shapes [3]. On the other hand, numerical methods based on finite elements are at present widely used for solving contact problems. However, the latest developments generally account for impact among elastic solid bodies only, which is short of what is needed if rock behaviour is to be considered. Examples of recent developments in this area are the works of Zavarise et al. [4], Christensen et al. [5], Hu [6] and Wasfy and Noor [7].
Eventually it is expected that with the finite element method it will be possible to model accurately the impact, including rock behaviour. Until now, the methodology proposed by Lundberg et al. [8 – 10] has been the most convenient approach because of its relative simplicity and accuracy. In his method, the stress wave equation is solved algorithmically in a manner somewhat similar to the method of characteristics used to solve differential equations in fluid mechanics [11]. Thus, at uniform time intervals the behaviour of the stress wave can be observed. The rock-bit interaction is modeled according to an experimental model particular to the drill bit being used and the rock being drilled, which is obtained by laboratory tests.
It must be noted that Lundberg and his co-workers have analyzed the problem of Top-of-the-Hole drilling (TOH). That case is simpler than Down-the-Hole (DTH) impact because the piston is no longer in contact with the drilling rod when the stress wave reaches the rock; hence, there is hardly any chance of additional impacts between the rod and piston. Furthermore, in TOH, the rod and bit are always in contact with each other; while in a DTH rig, the hammer cylinder can separate from the drill bit as they can slide with respect to each other.
In a Down-the-Hole simulation, it is desirable to account for the possibility of a transient gap between the hammer cylinder and the drill-bit head, or for more than one impact between drill-bit and piston (or drill bit and rock). In addition, it is convenient to facilitate the handling of various load cases (i.e. initial strain, distributed thrust force) and initial conditions. For this reason, we have preferred to formulate our model based in the impulse-momentum principle. Hence the solid bodies are discretized into nodes and elements, and the corresponding impulse-momentum equations are applied iteratively assuming that a wave travels at the speed of sound in the medium. The modeling of the rock-bit interaction is conducted according to the same scheme used by Lundberg, in which it is assumed that the rock behaves as a non-linear spring whose parameters depend on the nature of the rock being drilled, as well as the drill-bit geometry. The parameters are obtained empirically and in addition to the dynamic experimental methods described by Carlsson et al. [12] or Xiaohe et al. [13], a quasi-static method based on the measurement of the penetration force on the rock can be used as a good approximation.