An efficient formulation for the simulation of elastic wave propagation in 1-dimensional collinding bodies (original) (raw)
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Numerical Solution of a Free-Boundary Problem for Percussive Deep Drilling Modeling by BEM
A numerical technique related to a stationary-periodic quasi-static model of rock percussive deep drilling is presented. The rock is modeled by an infinite elastic space with a semi-infinite circular cylindrical bore-hole having a curvilinear bottom. An auxiliary problem of stationary indentation of a rigid drill bit is considered first, where it is assumed that the indentation is produced by a stationary motion of the rupture front on which an appropriate rock strength condition is violated. The bore-hole boundary is not known in advance and consists of four parts: a traction-free non-rupturing part, a contact non-rupturing part, a traction-free part of the rupture front, and a contact part of the rupture front. Thus the problem is formulated as a non-classical non-linear free-boundary contact problem of elasticity. A multi-stage hierarchical iterative algorithm is implemented reducing the problem to a sequence of mixed problems of linear elasticity with known non-smooth infinite boundaries. The Boundary Element Method is used on each iteration step for numerical solution of the direct boundary integral equations of the axially-symmetric linear elastic problems. Then the stationaryperiodic percussive drilling problem is reduced to the stationary problem on the rupture stage of the cycle and to the classical contact problem on the reverse and progression-before-rupture stages of the cycle. A numerical example of the stress and displacement distributions, and progression-force diagram are presented.
Application of damage mechanics in percussive drilling modelling
A stationary-periodic quasi-static model of rock percussive deep drilling is introduced. First, an auxiliary problem of stationary indentation of a rigid indentor is considered. The rock is modelled by an infinite elastic medium with damage-induced material softening. The stationarity of the problem allows to reduce the damage history in a material point to the damage distribution down in space. The bore-hole is a semi-infinite cylinder with a curvilinear bottom. It is assumed the indentation is produced by a stationary motion of the rupture front at which an appropriate rock strength condition is violated. The bore-hole boundary is not known in advance and consists of four parts: a free of traction non-rupturing part, a contact non-rupturing part, a free of traction part of the rupture front, and a contact part of the rupture front. Thus the problem is formulated as a non-local non-linear free-boundary contact problem and algorithms of its numerical solution are discussed. The problem solution provides axial force necessary for the drill bit progression through the rock. Then the stationary-periodic percussive drilling problem is reduced to the stationary problem on the rupture progression stage of the cycle and to the classical contact problem on the reverse and progression-before-rupture stages of the cycle. As a result, this provides a nonlinear progression-force diagram.
Modeling impact in down-the-hole rock drilling
International Journal of Rock Mechanics and Mining Sciences, 2000
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 simpli®ed, and dierent 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.
International Journal of Rock Mechanics and Mining Sciences, 2019
Considering the strong nonlinearity of the percussive process, this paper used the finite element method to establish a three-dimensional percussive system model to study the energy transfer efficiency of percussive drilling. The model consists of 12-button bit model, damage-plasticity model for the rock, bit-rock interaction model, etc. The explicit dynamics solver in ABAQUS was adopted to solve the above model. In order to study different impactors, the percussive system was loaded by the prescribed pulse load that can be generated by ultrasonic impactor or electromagnetic impactor, and by impact hammer with initial velocity that can be driven by high-pressure fluid or compressed gas, respectively. The simulation results are as follows. Increasing load duration and dynamic amplitude of the pulse load can improve the input energy, output energy and energy transfer efficiency. With the increase of the load duration or dynamic amplitude, the energy transfer efficiency first increases rapidly in the low input energy phase and then increases slowly in the high input energy phase. For the three pulse shapes-sine, triangle, square in this paper, the input energy, output energy and energy transfer efficiency under the condition of square pulse are the largest when the load duration and dynamic amplitude of the pulse force are fixed. While, the energy transfer efficiency under the condition of square pulse are the smallest and that of sinusoidal pulse are the largest when the input energy of the pulse force is fixed. Both the output energy and the energy transfer efficiency under dynamic loading increase first and then decrease with the static load. For the impact hammer, the energy transfer efficiency increases with the impact velocity of impact hammer.
A finite element method for contact/impact
Finite Elements in Analysis and Design, 1998
Ideas from the analysis of differential-algebraic equations are applied to the numerical solution of frictionless contact/impact problems in solid mechanics. Index-one and two formulations for dynamic contact-impact within the context of the finite element method are derived. The resulting equations are shown to stabilize the kinematic fields at the contact interface, at the expense of a small energy loss, which is shown to decrease consistently with mesh refinement. This energy dissipation is shown to be necessary for the establishment of persistent contact. A Newmark-type time integration scheme is derived from the proposed formulation, and shown to yield excellent results in modeling the transition to contact/impact.
2011
Optimal force profiles are essential for 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 technique 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. However, this model does not account for penetration due to rotary drilling bit shear or fluid flow. The simulated rock model is tested for three different strength rock formations. -- 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 averag...
Dynamics of ultrasonic percussive drilling of hard rocks
Journal of Sound and Vibration, 2005
Ultrasonic percussive drilling with diamond-coated tools has been extensively studied under laboratory conditions on rocks such as sandstone, limestone, granite and basalt, in order to investigate the applicability of this technique to downhole drilling. An experimental set-up, a programme of work and example results are presented. The studies showed that an introduction of high-frequency axial vibration significantly enhances drilling rates compared to the traditional rotary type method. It has been found out that the material removal rate (MRR) as a function of static load has at least one maximum. Looking at the time histories of the measured drilling force, strong nonlinear effects have been observed, which were explained using simple nonlinear models. Among them, pure impact and impact with dry friction oscillators were used to provide an insight into the complex dynamics of ultrasonic percussive drilling. It is postulated that the main mechanism of the MRR enhancement is associated with high amplitudes of forces generated by impacts. Novel procedures for calculating MRR are proposed, explaining an experimentally observed fall of MRR at higher static loads. r
Modeling of dynamic fracture mechanism in rock masses due to wave propagation
International Journal of Engineering & Technology
Finding a new oil well is a stimulating experience at all levels, however, it’s only an important milestone on the road towards exploiting oil and gas. When it comes to well drilling, the condition of the ground that surrounds the oil plays a major role. While there are many factors that dictate the success of exploring and drilling wells, porosity and permeability of the surrounding stone are some of the most important components.This paper focuses on the effective way to increase the porosity and the permeability of the rock using explosives without damaging the rock. In order to reach our aim, a numerical simulation was conducted. In fact, a 2D distinct element code was used, and 4 models were constructed; in each model the number of explosives increase while the blast load per explosive decreases.The dynamic stresses, and velocity vectors of the wave propagation were analyzed to evaluate the behavior of rock masses in each model. Moreover, a grid of history points was studied in...
Granite rock fragmentation at percussive drilling - experimental and numerical investigation
International Journal for Numerical and Analytical Methods in Geomechanics, 2013
The aim of this study is to numerically model the fracture system at percussive drilling. Due to the complex behavior of rock materials, a continuum approach is employed relying upon a plasticity model with yield surface locus as a quadratic function of the mean pressure in the principal stress space coupled with an anisotropic damage model. In particular, Bohus granite rock is investigated and the material parameters are defined based on previous experiments. This includes different tests such as direct tension and compression, three point bending and quasi-oedometric tests to investigate the material behavior at both tension and confined compression stress states. The equation of motion is discretized using a FE approach and the explicit time integration method is employed. EOI (Edge-On Impact) tests are performed and the results are used to validate the numerical model. The percussive drilling problem is then modeled in 3D and the bit-rock interaction is considered using contact mechanics. The fracture mechanism in the rock and the bit penetration-resisting force response are realistically captured by the numerical model.