Journal of Earth Science, Vol. 20, No. 5, p. 868–878, October 2009 Printed in China DOI: 10.1007/s12583-009-0073-5
ISSN 1674-487X
Numerical Simulation of Impact on Pneumatic DTH Hammer Percussive Drilling Bu Changgen* (卜长根), Qu Yegao (瞿叶高), Cheng Zhiqiang (程志强), Liu Baolin (刘宝林) School of Engineering and Technology, China University of Geosciences, Beijing 100083, China ABSTRACT: The process of DTH (down-the-hole) hammer drilling has been characterized as a very complex phenomenon due to its high nonlinearity, large deformation and damage behaviors. Taking brittle materials (concrete, granite and sandstone) as impact specimens, the explicit time integration nonlinear finite element code LS-DYNA was employed to analyze the impact process and the penetration boundary conditions of DTH hammer percussive drilling system. Compared with previous studies, the present model contains several new features. One is that the 3D effects of DTH hammer drilling system were considered. Another important feature is that it took the coupling effects of brittle materials into account to the bit-specimen boundary of the drilling system. This distinguishes it from the traditional approaches to the bit-rock intersection, in which nonlinear spring models are usually imposed. The impact forces, bit insert penetrations and force-penetration curves of concrete, granite and sandstone under DTH hammer impact have been recorded; the formation of craters and fractures has been also investigated. The impact loads of piston-bit interaction appear to be relatively sensitive to piston impact velocity. The impact between piston-bit interaction occurs at two times larger forces, whereas the duration of the first impact doesn’t change with respect to the piston velocity. The material properties of impact specimen do not affect the first impact process between the piston and bit. However, the period between the two impacts and the magnitudes of the second impact forces greatly depend on the specimen material properties. It is found that the penetration depth of specimen is dependent on the impact force magnitude and the macro-mechanical properties of the brittle materials. KEY WORDS: pneumatic DTH hammer, percussive drilling, LS-DYNA, brittle material, impact force-penetration curve.
INTRODUCTION Pneumatic down-the-hole (DTH) hammer drilling is a rotary percussive drilling technique widely used in mining, exploration, water-well drilling, road construction, and other drilling operations around the world (Bu et al., 2006; Karanam and Misra, 1998). This study was supported by the National Natural Science Foundation of China (No. 50475056). *Corresponding author:
[email protected] Manuscript received February 2, 2009. Manuscript accepted June 22, 2009.
When the DTH hammer works, it generates percussive force to the bit to impact and shatter the ground and the rotational torque rotates it to tear and cut the fragments whilst the thrust force keeps it in contact with the ground during bit advancement. In the meantime, the drill cuttings and detritus in the form of fine particles and dust are brought from the hole to the ground surface via an air flushing medium as shown in Fig. 1. This drilling technique has a major advantage in that it can rapidly and economically produce holes in hard rocks for various construction and mining purposes. In the pneumatic DTH hammer, a piston moving with speed v0 collides with a drill bit. A stress wave
Numerical Simulation of Impact in Pneumatic DTH Hammer Percussive Drilling
Figure 1. Typical structure of pneumatic DTH drilling system. then begins to propagate through the drill bit towards the rock and backwards through the piston from the impact plane. The front end of the stress wave eventually reaches the rock interface, where the tungsten carbide inserts mounted on the drill bit surface generate high point stresses. Depending on the drilling ability of the rock, a certain amount of energy will be dissipated by the rock fragmentation. The remaining energy will be distributed among the piston, drill bit and other DTH hammer components according to their mass, stiffness and geometric properties. How the wave propagates in the piston, bit, rock and other components is of paramount importance in the impact process of the DTH hammer percussive drilling. The mechanics of percussive drilling has been analyzed numerically and experimentally since the early 1960s. The pioneering works on theoretical and experimental studies on the percussive drilling of rock were done by Hustrulid and Fairhurst (Hustrulid and
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Fairhurst, 1972a, b, 1971a, b; Fairhurst, 1961). They investigated in detail the energy transfer in percussive drilling, and thrust force requirements and some comments were done for the design of percussive drilling systems. Lundberg (1985, 1982, 1973a, b) set up the stress wave equations for the case of top-of-the-hole rock drilling in which a short piston strikes a long bar containing different cutter shapes, and carried out detailed investigations on stress wave mechanics of percussive drilling and developed a microcomputer simulation program. Microcomputer simulation studies (Lundberg, 1985, 1982) of percussive drilling systems have shown that the predicted values of impact stress, coefficient of hammer restitution and forces acting on the rock agree well with theoretical results. A similar approach was adopted by Stock and Schad (1992) to estimate the stresses at the interface between the tungsten-carbide inserts and the drill-bit body. Nordlund (1989) also studied the effects of the thrust force on percussive drilling using experimental data and Lundberg’s method. Chiang and Elías (2000) developed a different method to solve the impact of percussive drilling in terms of the impulsemomentum principle, in which the solid bodies in percussive drilling system were discretized into nodes and elements, and the corresponding impulse momentum equations were applied iteratively assuming that a wave travels at the speed of sound in the medium. Generally, the previous published works on percussive drilling system impact were based upon the solutions of the stress wave equation or the linear impulse momentum principle. In these works, the rock-bit interaction is usually modeled by a nonlinear spring, while the piston and the bit are often simplified as straight or cone-shaped bars. In fact, these simulation methods make use of a force-penetration curve to model the rock-bit interaction, therefore, the validity of the simulation results greatly depends on the availability and accuracy of this curve (Chiang, 2004). For this reason, many researchers have been active in developing better and simpler methods to obtain accurate force-penetration curves in rocks and other materials (Chiang, 2004; Carlsson et al., 1990; Pang et al., 1989). Actually, the piston and the bit in DTH hammer are usually thick and short, and have complex geo-
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metric shapes. These simplifications mentioned above in 1D elastic stress wave models or impulse momentum equations may bring great error to the results as they ignore the wave propagation attenuation and dispersion in piston and bit due to the radial inertia effects. Based on 3D axisymmetric finite element method, Lundberg and Okrouhlik (2006, 2001) investigated the 3D effects on the efficiency of DTH hammer drilling process. Chiang and Elías (2008) developed a more sophisticated finite element model to simulate the energy transmission, the bit-rock interaction, and the process of rock fragmentation in percussive drilling. However, the effects on wave reflection of local structures like spline and air slot are neglected in these models. Furthermore, it should be pointed out that bit-rock interaction conducted as a nonlinear spring is a quasi-static method based on the measurement of the penetration force on the rock, and can be used as just an approximation for those bits with one or two inserts. For bits with multi-inserts in DTH hammers, the nonlinear spring parameters are difficult to be obtained. Hence, the 1D wave model is restricted to the DTH hammer and has some limitations. Therefore, it is of great importance and interest to study the percussive drilling process of DTH hammer in order to achieve a better understanding of the percussive drilling mechanism. Taking brittle materials (concrete, granite and sandstone) as impact specimens, this work employs the explicit time integration nonlinear finite element code LS-DYNA to analyze the impact and penetration boundary conditions in pneumatic DTH hammer percussive drilling system. The force-penetration curves of concrete, granite and sandstone under DTH hammer impact have been recorded and the formation of the craters and fractures has been investigated. The simulated force-penetration curve is in fact the indication of the propagation of cracks and the formation of chips. According to the simulated results, it is believed that this numerical simulation method will contribute to an improved knowledge of the rock fragmentation process in DTH hammer drilling, which will in turn help enhance mining and drilling efficiency through the improved design of percussive drilling tools and equipment.
Bu Changgen, Qu Yegao, Cheng Zhiqiang and Liu Baolin
THEORETICAL BACKGROUND AND METHOD FORMULATION LS-DYNA is used in the simulation of DTH hammer percussive drilling system in the present study. This computer code performs nonlinear transient dynamic analysis of three-dimensional structures. LS-DYNA has a wide variety of analysis capabilities including a large number of material models, a variety of contact modeling options, a library of beam, plate, shell, and solid elements and robust algorithms for adaptively controlling the solution process (Hallquist, 2003). In the solution process, stress wave propagation and inertia effect are considered. Its principle algorithm adopts Lagrangian formulation. When a piston impacts a bit on a DTH hammer, their contact is assumed to have no friction. The governing equations for both bodies are the following. Equation of mass conservation (1) ρV=ρ0 where V represents the relative volume; ρ denotes the current density; and ρ0 denotes the reference density. Equation of momentum conservation σ ij , j + ρ fi = ρ ui (2) where σij,j represents the Cauchy stress; fi represents the body force density; and üi denotes the acceleration. Equation of energy conservation E = Vsij εij − ( p + q )V (3) where εij and p denote the deviatoric stresses and hydrostatic pressure, respectively, as given in sij = σ ij + ( p + q ) δ ij (4) where q represents the bulk viscosity; δij denotes the Kronecker delta (δij=1, if i=j; otherwise δij=0); and εij denotes the strain rate tensor 1 1 p = − σ ij δ ij − q = − σ kk − q (5) 3 3 Based on the virtual work principle, equation (2) can be expressed as a weak form of equilibrium equation ∫ ρ ui − σ ij , j − ρ f δ ui dv + ∫ σ ij n j − ti δ ui ds + v
(
)
(
∫ (σ ij − σ ij )n jδ ui ds = 0 +
−
)
(6)
where δui fulfills all boundary conditions, and the integrations are over the current geometry. Application of the divergence theorem gives ∫v σ ijδ ui , j dv = ∫ σ ij n jδ ui ds + (7) + − σ − σ n δ u d s ∫ ij ij j i
(
)
(
)
Numerical Simulation of Impact in Pneumatic DTH Hammer Percussive Drilling
and noting that
inserts are listed in Table 1.
(σ ijδ ui ) , j −σ ij , jδ ui = σ ijδ ui, j
(8)
leads to the weak form of the equilibrium equation δπ = ∫ ρ uiδ ui dv + ∫ σ ijδ ui , j dv − ∫ ρ fiδ ui dv − v
∫v
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v
v
(9)
tiδ ui ds = 0
If the finite element technique is interconnected using a matrix form, Equation (9) becomes m
t ⎧ ρ N t Nadv + ∫vm B σdv ⎫⎪ ⎪ ∫vm (10) ⎬ =0 ∑⎨ t N t td s ⎪ m =1 ⎪ − ∫ ρ N bdv − ∫ ∂b1 ⎩ vm ⎭ where N is an interpolation matrix; σ is the stress vector; B is the strain-displacement matrix; a is the nodal acceleration vector; b is the body force load vector; and t is applied traction load. The equation is integrated in time and is applied to evaluate the equation of state and for a global energy balance. n
FINITE ELEMENT MODEL OF DTH HAMMER PERCUSSIVE DRILLING SYSTEM For numerical simulation and evaluation of the impact process of DTH hammer, a pneumatic hammer JW150 manufactured in Jiaxing City, China, was selected as an example as shown in Fig. 2.
Equivalent Strength Model of Brittle Specimen To fully describe the dynamic effect of brittle specimens within the impact procedure, several models have been implemented in LS-DYNA, designed for special purposes such as damage, effect of strain rate and cracks. This investigation employs results from the perforation simulations with the LS-DYNA and the “Johnson-Holmsquist concrete” material model (Holmquist et al., 1993) to forecast brittle Table 1
Material parameters of piston, bit and tungsten carbide inserts
Part in DTH hammer
Density 3
ρ (kg/m )
Modulus of
Poisson
elasticity E (GPa)
ratio
Piston
7 850
206.0
0.3
Bit
7 850
206.0
0.3
Tungsten
14 500
588.0
0.22
carbide inserts
Percussive Drilling System of DTH Hammer As shown in Fig. 3, the analysis model of JW150 DTH hammer percussive drilling system is composed of piston, bit, and rock. The piston mass is given an initial velocity v0 and forced down to strike the anvil of bit which is in contact with the fixed specimen. Material Models and Finite Element Discretization In this analysis, the piston, bit and tungsten carbide inserts were assumed as isotropic elastic materials, defined as *MAT_ELASTIC in LS-DYNA. The material parameters of piston, bit and tungsten carbide
Figure 2. Diagram showing the structure model of JW150 DTH hammer.
Figure 3. Diagram showing the analysis model of JW150 DTH hammer.
Bu Changgen, Qu Yegao, Cheng Zhiqiang and Liu Baolin
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specimen behavior under DTH hammer impact. Figure 4 illustrates a general overview of the “Johnson-Holmsquist Concrete” mode. The equivalent strength component of the model is given by σ * = ⎡⎣ A (1 − D ) + BP* N ⎤⎦ ⋅ 1 + C ln ε* (11) The normalized equivalent stress is given by * σ =σ/f’C, where σ represents the actual equivalent stress; and f’C denotes the quasi-static uniaxial compressive strength; P* denotes the normalized pressure, shown as P*=P/f’C; ε* denotes the dimensionless strain rate, given by ε* = ε ε0 ; ε represents the actual strain rate; ε0 = 1.0 s −1 represents the reference strain rate; D (0≤D≤1) denotes the damage parameter, and the normalized largest tensile strength is given by T*=T/f’C, where T represents the maximum tensile stress. Additionally A, B, N, C, and Smax denote the material parameters, respectively as normalized cohesive strength, normalized pressure hardening coefficient, pressure hardening exponent, strain rate coefficient and normalized maximum strength.
(
)
Figure 5. Diagram showing damage failure model of brittle specimen. EFmin. minimum plastic strain of material fracture.
strain increment and plastic volumetric strain increment, respectively, during one cycle of integral computation. The equation
f p = ε pf + μpf = D1 ( P* + T * )
D2
(13)
represents the plastic strain to fracture under a constant pressure, where D1 and D2 represent damage constants.
Figure 4. Diagram showing the equivalent strength model. Accumulated Damage Failure Model The accumulated damage failure model for brittle specimen is illustrated in Fig. 5. The “JohnsonHolmquist concrete” model considered, owing to plastic volumetric strain. The damage model is written as Δε p + Δμp D=∑ f (12) ε p + μpf
where Δεp and Δμp represent the equivalent plastic
Equation of State (EOS) EOS describes the relationship between hydrostatic pressure and volume. The loading and unloading process of brittle specimen can be divided into three response regions, as depicted in Fig. 6. The first zone is the linear elastic zone, arising at P≤Pcrush, where the material is in elastic state. The elastic bulk modulus is given by k=Pcrush/μcrush, where Pcrush and μcrush represent the pressure and volumetric strain arising in a uniaxial compression test. Within the elastic zone, the loading and unloading equation of state is given by P=kμ (14) where μ=ρ/ρ0–1; ρ denotes the current density; and ρ0 denotes the reference density. The second zone arises at Pcrush
