Rigid Impact_the Mechnism Of Percussive Rock Drilling

ARMA 08-75 Rigid Impact – the Mechanism of Percussive Rock Drilling Dongmin Niu1 Copyright 2008, ARMA, American Rock Mechanics Association This paper was prepared for presentation at San Francisco 2008, the 42nd US Rock Mechanics Symposium and 2nd U.S.-Canada Rock Mechanics Symposium, held in San Francisco, June 29July 2, 2008. This paper was selected for presentation by an ARMA Technical Program Committee following review of information contained in submitted earlier by the author(s). The material, as presented, does not necessarily reflect any position of ARMA, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of ARMA is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgement of where and by whom the paper was presented.

ABSTRACT: Stress wave and its transmission has been the focus of the study of percussive rock drilling (PRD). However, there are confusions from practical applications, such as the relationship of drilling efficiency with the stress wave transmission and reflection. The paper introduced “rigid impact” theory based on the Impact Mechanics. The relationship of PRD efficiency with drill system parameters was also discussed. The paper proposed that the rigid impact work plays the key role in PRD. Stress wave generated in drill string by impact is actually an intermediate process resulting in the mass body movement. The rock breaking process under indent impact was also discussed based on the theory. The full understanding of the PRD mechanism would be significantly helpful to develop more efficient drilling systems.

1. Introduction

2. Confusions from stress wave theory

Percussive drilling is one of the most original ways ever since people started to use the blasting method to obtain minerals. It is still standard in the blasting holes drilling of hard rock mining and construction in general. Percussive rotary drilling gained more and more interests in oil and gas industries also since 1980’s because of its flexibility and higher efficiency in many applications, especially in hard rock formations. Some special PRD methods such as water and mud actuated hammers have also been developed, while the traditional PRD technologies are getting more sophisticated and powerful.

The one dimension stress wave transmission theory has long been well accepted and widely used to explain the PRD so far [2, 3]. Take a typical top hammer drilling system for instance. It consists of a piston, a shank adapter and/or rods and a bit. Currently, the most common description would be as below: The piston accelerates to a desired velocity and strikes the shank. Upon the impact, the drill rod particles achieve velocities, and therefore displacements in a direction away from the piston. The particles transmit this motion to adjacent particles which then repeat the process, creating a stress wave pulse. The same thing happens in piston. If the impact velocity is v , the particles’ velocities associated with the compressive waves going into the drill string and the piston are v / 2 and − v / 2 respectively. Therefore, when the latter wave reaches the free end of the piston, the velocity of the piston has been reduced to v −v/ 2 = v/ 2. At the free end of the piston, the compressive wave is reflected as a tensile wave with particle velocity −v/ 2 . When this wave reaches the impact interface, the velocity of the piston has been further reduced to v / 2 −v / 2 = 0 . Thus, from this time on, the piston is at rest and in the drill string there is a compressive wave with particle velocity v/2 and length 2Lp . The energy of this wave equals to the impact

Top hammer drilling and down the hole (DTH) or in the hole (ITH) drilling are the most commonly used PRD methods. Both of them use the same drilling concept, with different drill string combination. Researchers have been making great contributions so that the drilling rate has been increased from 3-5m/hr in 1900’s to 450m/hr now for underground small blast holes drilling, for either the drills or tools. One of the most significant works was by Hustrulid. W. A. and Fairhurst C. in early 1970’s [1]. Their comprehensive experiments and the theoretical analysis were based on the prerequisite that stress wave transmitted the impact energy into rock. However, there are still many questions could not be answered. Therefore, lack of full understanding of PRD mechanism is still one of the key restrictions for the development of more efficient drilling technology. 1

energy of the piston, transmitted into rock through the bit, causing the rock breakage. Based on the theory, the stress wave transmission is the core of PRD. Therefore, the amount of stress wave transmission and the reflection in a drilling system is directly an indication of drilling efficiency or rate of

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penetration and also determines the service life of the drilling system accordingly.

3.1

Perfectly rigid solid

The drill string will move in the impact direction upon the impact of the piston. The energy transfer in the system is described by principles of energy conservation as: 1 1 1 MpVp12 = MpVp2 2 + MsVs12 (1) 2 2 2 Where Vp1 is the speed of piston before impact；Vp2 is the speed of piston after impact (without the action force of pressurized oil or air); Vs1 is the speed of drill string after piston’s impact; Mp is the mass of piston; Ms is the mass of drill string (including shank, couplings, rods and bit).

However, the following questions and confusions are difficult to be explained based on the stress wave transmission theory (assuming that the contact areas and the materials of piston and shank are the same): • The piston is not likely at rest after striking if no other external forces applied. Actually, it rebounds and creates many vibration problems; • The stress wave experiences reflection and/or refraction during propagation along the drill string. One dimension wave propagation theory is a mathematical model, from which the wave transmission is supposed to be along a slender bar with uniform section and mediums are in full contact on the interface [4]. We can derive from it that the full contact of bit front face with rock will result in the most efficient stress wave or impact energy transmission. Obviously, such a conclusion is completely contradictory with the fact that sharper bits drill faster or penetrate deeper. But they have less contact area with rock surface in fact. For a normal button bit, we can estimate that the practical contact area is only about 10-20% of the bit front face area, and the sharper bits the less contact area; • From stress wave propagation theory, the drilling efficiency would be no difference for drill strings with different length, correspondingly different body mass (assuming there are no couplings involved); • When a bar with chisel end directly impacts rock surface with a significant speed, it causes rock breaking because of its kinetic energy. There is no stress wave within the bar before it hit the rock surface. That is actually the most original way of impact drilling. How the stress wave theory explains the phenomenon?

From the principle of balance of linear momentum, MpVp1=MpVp2 + MsVs1 (2) Combine equation (1) and (2), Mp − M s (3) Vp2=Vp1 × Mp+Ms 2 × Mp (4) Vs1=Vp1 × Mp+Ms The drill string will start to move apart from the piston at speed Vs1. When the bit contacts rock surface as the movement of the drill string, it creates an impact force Fi to rock surface. The impact force can be described by equation (5) from the principle of balance of linear momentum (5) Fi = Ms×Vs1/ Tb Where Tb is bit impact time. If the bit is in contact with rock surface when the piston hits the drill string, the bit impact work to rock surface equals the kinetic energy of piston’s impact due to perfect rigid assumption. The impact force to rock surface is Fi = Mp×Vp1 / Tb (6)

Combining the aforementioned questions, less than 20% of the total energy from an impact is used for breaking rock in PRD even without considering other consumptions such as frictions. The answer is really questionable. It is definitely necessary to review our understanding on PRD mechanism and to investigate the impact drilling process from the energy generation of a piston to the final dispersion of the energy in rock mass.

3.2 Ordinary elastic materials situation Practically, there are elastic deformations in the collision bodies, i.e. piston and drill string. Impact Mechanics theory is introduced below to discuss the process. Impact process can be, in general, literally described by the Impact Mechanics as follows [5]. Upon the impact, there is a large contact force on contact surfaces. It gives a large contact stress and corresponding strains and deformation. It has a resultant force of action or reaction that acts in opposite directions on the two colliding bodies and thereby resists interpenetration which would otherwise develop after incidence if the bodies did not deform. Initially the force increases with increasing indentation and it reduces the speed at which the bodies

3. Review of percussive drilling process The piston gains acceleration from high pressure hydraulic oil or pressurized air and hit a shank at speed Vp1. The process can be theoretically described by Physics in different situations. In the following discussion, the drilling string is static before impacted. 2

are approaching each other. At some instant during impact the work done by the contact force is sufficient to bring the speed of approach of the two bodies to zero. It happens in a very small area because of the high impact rate. It is like a short stiff spring which is compressed between the two bodies during the period of contact. Subsequently, the energy stored during compression drives the two bodies apart until finally they separate with velocities.

to rock surface with the amount equal to the kinetic energy Ms×Vs12/2 from deformation restoring. Similar to the discussion of equation (7), on the contact surface of bit and rock, the energy transformation is 1 1 (9) MsVs12 = MsVs2 2 + E2 + Er 2 2 Where Vs2 is the velocity of drill string after impacted by piston. E2 is the deformation energy within bit contact region. It is a negligible small part of the kinetic energy due to very big hardness difference of bit and rock. The bigger the hardness difference is, the less E2. Er is the deformation energy of rock in the contact region. It is the final effective energy causing rock breakage.

As compression restoring, the stresses generated by local deformation cause the stress waves that radiate away from the contact region. It will results in loss of a portion of energy by lattice friction. This is the energy dissipated in the collision [5]. It is only a few percent of the initial kinetic energy [6]. Energy dissipation can also be due to plastic deformation etc. It is defined by an energetic coefficient of restitution (COR) e, 0 ≤ e≤ ≤ 1, where 0 implies a perfect plastic collision (i.e., no final separation), while 1 implies a perfect elastic collision (i.e., no loss of kinetic energy of impact). For a collision of dissimilar materials, the composite COR e* is used.

From equation (8a), when rock is in very big mass (i.e. Mrock→∞), then Vs2= − e2* × Vs1 (10a) Where e2* is the composite COR of bit (tungsten carbide) rock collision. Combining with equation (8b), Vs2=

For the convenience, we use E1 to represent the portion of energy loss on the contact region of piston and drill string. So the energy transformation at the impact surface will be 1 1 1 (7) MpVp12 = MpVp2 2 + MsVs12 + Ε1 2 2 2 The equation can be expressed literally as follows. Piston impacts the drill string with kinetic energy

−e2* × (1+e1)MpVp1 Mp+Ms

(10b)

Vs2 represents the rebounding of drill string after bit impacts rock. It means that if the drill string is free of the restriction, it will rebound at a velocity Vs2. In practical drill system, a feeding force is applied to hold the bit in contact with rock. So the rebounding creates a backward impact work Ms×Vs22/2 on the feeding mechanism which creates mechanical problems. The harder the rock is, the bigger the e2*, the more severe the rebounding.

1 MpVp12 . 2

The energy is transformed into deformation energy, then

The separation velocity after collision is given by Impact Mechanics as below [5, p28]:

From equation (9), the energy transmitted into rock and therefore used for rock breaking is 1 1 Er = MsVs12 − MsVs2 2 − E2 2 2 1 (1+e1)2 (1 − e2*2 )MsMp = MpVp12 × − E2 2 (Mp+Ms)2 1 (11a) = MpVp12 × Α − E2 2 (1+e1) 2 (1 − e2* 2 )MsMp (11b) A= (Mp+Ms)2

(1+e1) × MsVp1 Mp+Ms (1+e1) × MpVp1 Vs1= Mp+Ms

A is an index indicating the efficiency of energy transformation of the drill system which include the drill string and rock properties. It can be used to evaluate the design of drilling system.

1 1 be restored to kinetic energy MpVp2 2 + MsVs12 with 2 2 some loss energy E1 after the impact. Therefore the drill string impacts rock surface with kinetic energy (or impact work)

Vp2=Vp1 −

1 MsVs12 . 2

(8a) (8b)

Where e1 is the COR of piston/drill string collision. When e1 =1 we have equation (3) and (4), the perfect solid case.

3.3 The efficiency of percussive rock drilling Fig 1 shows the relationship of index A with the mass ratio Ms/Mp (assume E2=0). The maximum value is achieved when Ms/Mp =1.

The drill string gains kinetic and/or strain potential energy. The energy then is transformed into impact work 3

In summary, the impact or percussive drilling utilizes the much higher action force generated from the impact work (kinetic energy) to break rock. For a given impact system, the sharper the bit is, the smaller the contact area with rock surface, the higher stress in the rock contact region and easier to break the rock. The impact velocity, the mass of piston and drill string, the elastic properties of piston, drill string and bit determine the overall impact efficiency. The friction happened with the impact was not taken in consideration.

80% A

e1=1

Ms/Mp =1

e1=0.9

60%

e1=0.8 e1=0.7

40%

e1=0.5

20% 0% 0

5

10

15

20

25

4. Rock breaking process under impact

Fig. 1 The relationship of index A with the mass ratio Ms/Mp (Assume E2=0; e2*=0.5)

The rock deformation energy Er is defined by equation (11a). It causes the rock breakage. The principle of interaction between bit front face and rock surface is fundamentally the same as for piston and drill string. However, the mechanical properties of rock and bit are different from those of steels. The rock in the contact region is compressed and the stress increases with the increasing indentation to an instant when the work done by the contact force is sufficient to bring the speed of drill string to zero. The contact stresses in a very small area of rock surface may exceed rock strength limit during the process, causing breakage (the crushed zone, refer to Fig. 3) when the impact speed Vs1, or the impact force is high enough.

In practical top hammer drilling system, the ratio is above 5, the index is below 40%. It can even be less than 10% for long extension drilling. DTH hammer method is more efficient from view point of Ms/Mp. However, the current pneumatic DTH drilling efficiency is restricted by low energy efficiency of air compressor and air system. For the situation of Ms/Mp<1, more investigations may be needed because Vs1 and Vp1 will be in the same direction. However it seldom happens in a practical application. Fig. 2 shows the general relation of drilling efficiency with material properties of the drill string and rock. The efficiency index A increases with increasing drill string rigidness (bigger e1) and decreasing rock hardness (smaller e2*). 100% A

In the contact region of rock, the maximum stress happens at a distance (=0.45a, [5]) beneath the dent where the stress level would exceed the yield value of the rock. Therefore, local failure happens and cracks initiate in the area. The test investigation done by Schormair N. [9] indicated that most of the cracks beneath the bore hole bottom surface run nearly parallel to the rock surface. The restoring of the elastic deformation of compressed rock creates a tensile stress zone. The cracks propagate by the tensile stress mainly in type I (opening) causing the spalling of a mass of rock. The contact region also generates stress waves and radiate away. The pre-existing fissures in the stress wave field grow and branch, potentially leading to a volume of rock broken. It heavily relies on the size, the orientation and the amount of pre-existing fissures. Big penetration rate can be expected in highly fractured rocks.

e2=0.2 0.3

80%

0.4 0.5

60%

0.6 e1=1

40%

0.9 0.8

20%

0.7 0.5

0% 0

Fig. 2

0.2

0.4

0.6

0.8

e1 /e2

1

The relationship of index A with e1and e2* (Ms/Mp=1)

The above calculated relationship is supported by a field test result of DTH drilling in Lac Des Iles Mine. Two brand new bits had same front head and flushing design, diameter 117mm. The masses were 9.4kg and 15kg respectively. The piston mass was 7kg. The drilling was during the same shift, same drill rig on same bench, holes depth was around 27m. The average rate of penetration (ROP) was 0.222m/min and 0.196m/min from 3 holes respectively for each bit. The actual ROP difference is 12%. The calculated difference of index A from equation (11b) is 11.3%, assuming e2*=0.5; e1=0.9.

The restoring of the compression drives the drill string away at velocity Vs2, namely the rebounding of drill string. The magnitude of Vs2 depends on the hardness of rock and bit front head or e2* as well as other parameters of the drill system, see equation (10). For very soft rock like soil, e2*→0, therefore Vs2 →0, there will be almost no rebounding. The harder the rock is, the bigger e2*, the more severe the rebounding.

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6. Conclusions 6.1 It is the rigid impact effect of the drill string that transfers the kinetic energy of piston to rock and causes the breakage. The piston’s impact is partially transformed into the kinetic energy of drill string, further transformed into impact work to break rock.

Fig. 3

6.2 The impact drilling efficiency of a drilling process depends on the impact rate Vp1, the mass Ms, Mp and the material properties e1 of the piston and the drill string and also rock properties e2*. Their relationship is defined by equation (11).

Rock breaking process under indent impact

In summary, rock break process under indent impact is in three zones: 1) crushed zone due to high contact stress; 2) spalling of a mass of rock from cracks propagation with the compression restoring of the contact region; and 3) a potential volume rock breakage from the growth of pre-existing fissures due to the influence of stress wave.

6.3 The stress wave induced in drill string by elastic deformation causes the energy loss in the rock drilling. It is, however, only a few percent of the initial kinetic energy. High rigid piston and drill string will give high drilling efficiency.

5. The role of elastic waves in PRD

6.4 The rock breaking process under indent impact is in three zones: 1) crushed zone due to high contact stress; 2) spalling of a mass of rock from cracks propagation due to compression restoring of the contact region; and 3) a volume rock break from preexisting fissures propagation due to the influence of stress waves.

The role of the stress wave in impact process was discussed by Kaufman [7]. When a stress pulse (or an impact force) applied on the face of a slender bar end, a stress wave is formed and travels back and forth along the bar. The reflection and refraction of the wave finally causes the mass movement of the bar. The role of the stress wave is to propagate the impact signal to all the particles of the bar and results in the movement of the whole body at speed V=δt/T υ0. Where δt and υ0 is the period of time and the speed of applied stress pulse; T is the period of time the wave travels through the bar.

The paper proposed the “rigid impact theory” for percussive rock drilling, discussed the relationship of the parameters of drill system with drilling efficiency. It is consistent with previous field test results. More work, especially controlled laboratory experiments are necessary to thoroughly accomplish the theory.

The traveling of the stress wave causes lattice friction, therefore heating the bar. It causes some energy loss. However, it is only a few percent of the initial kinetic energy for either elastic-only or elastic-plastic impact [6]. For a truly elastic impact hard sphere with a steel target, the fraction of the initial kinetic energy of the sphere 3/5 which dissipates as elastic waves is λ≈1.04(V/C0) . Where V is the velocity of impact and C0 is the velocity of longitudinal elastic wave along a thin rod of the target material.

References [1] Hustrulid. W. A. and Fairhurst C. (1971/1972). A Theoretical and Experimental Study of the Percussive Drilling of Rock, Part I-IV, Int. J. Rock Mech. Min. Sci., Vol.8, p311333; p335-340; Vol.9, p417-429; p431-442 [2] Heinio, M., Rock Excavation Handbook, Sandvik Tamrock Corp. 1999 [3] Nordbradt, A., Percussive rock drilling/ Experience and knowledge, CD version, Atlas Copco, 2006 [4] Wasley, J. Richard (1973). Stress Wave Propagation in Solids. Marcel Dekker, Inc. New York 1973 [5] Stronge W. J. Impact Mechanics, Cambridge University Press. 2000 [6] Hutchings I. M. 1979. Energy Absorbed by Elastic Waves during Plastic Impact, J. Phys. D: Appl. Phys. 12 1819-1824 [7] Kaufman, A.A; Levshin, A. (2004), the Role of Wave Propagation in the Motion of an Elastic Body, Eur. J. Phys. 25, 257-268 [8] Han G., Bruno M. (2005). Lab Investigation of Percussion Drilling: From Single Impact to Full Scale Fluid Hammer. ARMA/USRMS 06-962. [9] Schormair N. et al, (2006). The influence of anisotropy on hard rock drilling and cutting, IAEG Paper number 491

The deformation in rock upon the bit impact also generates stress waves. Its magnitude and frequency are different from that in drill string due to different properties of steels and rocks. The test results from G. Han’s [8] illustrated the stresses waves caused by single impact in drill rod and rock. The wave in rock was explained conventionally as being transmitted from drill string. Some of the elastic waves in drill string indeed will be transmitted into rock via bit. However, the amount of the transmission will be very limited as previously discussed.

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