Relating drilling parameters at the bit-rock interface: theoretical and field studies

Mining Science and Technology, 12 (1991) 6 7 - 7 7

67

Elsevier Science Publishers B.V., A m s t e r d a m

Relating drilling parameters at the bit-rock interface" theoretical and field studies Thomson Sinkala Division of Mining Equipment Engineering, Luled University of Technology, 951 87 LuleEt, Sweden (Received March 28, 1980; accepted May 14, 1990)

ABSTRACT

Sinkala, T. 1991. Relating drilling parameters at the bit-rock interface: theoretical and field studies. Min. Sci. Technol., 12: 67-77.

An explicit expression relating drilling parameters at the bit-rock contact is derived. The expression estimates the minimum torque, related to bit-rock contact only, required to maintain constant bit rotation. Theoretical results from the developed bit-rock contact relation agree very satisfactorily with those obtained from field tests and other previous experience.

Introduction

Drilling parameters with major effect on penetration rate

To date, considerable effort has been devoted to the study of relationships between various drilling parameters. Such investigations range from the purely theoretical to field activities [1]. Limitations of previous investigations have been discussed earlier [2]. In particular, almost all drilling rate theories developed in the past have not included the interaction between thrust, torque, and rock inhomogeneity, despite the strong effects of these on drilling rates. In the following sections, an attempt will be made to account for these parameters by examining the minimum torque, related to bit-rock contact only, required to maintain constant bit rotation. The present discussion concerns percussion drilling with independent rotation. A simplified working principle for this technique can be found, for example, [2]. 0167-9031/91/$03.50

For given drilling conditions, the effect of a number of drilling parameters on penetration (v) and penetration rate (R) in full-scale, upward percussion drilling may be assumed to be constant a n d / o r negligible without loss of generality. For instance, we could assume that: (1) flushing during upward drilling is efficient because gravity helps to remove the cuttings from the hole; (2) frictional resistance between drill rods and hole walls in short holes, and changes in button diameter (e0) and bit diameter (D) due to wear are negligible for a considerable number of metres; (3) the inclination of an undeflected drill string in undeviated holes, the impact energy ( E i ) , the joint system of the drill string, the

© 1991 - Elsevier Science Publishers B.V.

68

T. SINKALA

average rotation speed (n) and the impact frequency ( f ) are practically constant. Under these assumptions, penetration (~,) in full-scale percussion drilling would then be affected mainly by torque (-r), thrust ( F ) and the rock properties, whereas the penetration rate (R) would be affected mainly by the penetration (u) and the impact frequency ( f ) ; so:

R=(f)

X(p)

Assuming further that: (1) The drilling parameters referred to are only those parameters which act on the bit simultaneously with the stress wave energy induced by piston impacts on the drill string. (2) The torque and thrust act continuously on the bit. (3) The rock is sufficiently hard so that the action of thrust and torque cannot break and displace the rock without the action of the effective impact energy (Er). The main function of the thrust is to maintain bit-rock contact and to keep the drill string joints closed before the pulses arrive so that energy losses are minimized [1-3]. The torque is applied mainly to move bit inserts to new surfaces [1,3-5], and simultaneously to tighten drill string joints before the arrival of stress waves [2,5]. Bit rotation, of course, is not essential for button penetration. It is, however, necessary for overall bit advance--measured by the rate of total rock face advance R (in m/min). For a given rock and bit geometry there is a certain bit rotation angle at which the penetration rate is optimal [6,7].

predicting penetration rates. In this discussion therefore only those parameters which may be measured directly or indirectly at the bit-rock interface will be explicitly considered. Other parameters, such as rock properties and effective impact energy (Er) , will remain implicit, in, for example, assessing the magnitude of "step-wise" response penetration (1,) and "continuous" response torque ('r), in the formulation of the equations. A crater formed by a hemispherical indentor

P.A. Lindqvist [8] and R.G. Lundqvist [9] have investigated the instantaneous formation of a crater from a hemispherical button-rock contact. An example of the resulting hemispherical crater penetration is illustrated in Fig. 1. These studies, like earlier ones [1], considered only the thrust or indentation force. In defining the new relation for bitrock contact torque has been introduced (see Fig. 2(b)). Due to the continuous action of torque ('r) it is supposed that the chips (marked by the asterisk in Fig. 2(b)) on the left side of the button would be trapped between the button and the intact rock. The chips on the right side of button are assumed either to fly out of the crater, or be flushed out of the crater. Using Fig. 2(b) as the model, it is thought that the following could occur:

Iol

k4

,dl

(b)~

(el

(c) I ~

If)

Theoretical study of bit-rock interaction

In practice, rock properties (for example rock structure and compressive strength) are unknown in advance of drilling. It would therefore be advantageous if rock properties did not appear explicitly in equations for

Fig. 1. Observed sequence of events during the penetration of rock by a hemispherical b u t t o n (from [8]).

69

RELATINGDRILLINGPARAMETERSAT THE BIT-ROCKINTERFACE

(a) Buttons ~

.

Direction

Torque necessary to maintain constant drill bit rotation Let N be the n u m b e r of button inserts on the bit. To simplify the discussion, it is assumed that the bit b o d y has a flat end. If thrust is uniformly distributed on all the buttons, force (Fab) per b u t t o n would be: F Fab = ~

(b) /

k

/

e I r/ I / "~,.I /

t

"~}'/k

~

~ Bit body

Profile of "]1 Profile of button et f / button et depth ~' t l l depth

\ jw"

T; / Fig. 2. Trapping of rock chips between intact rock and

button due to action of torque (r). (a) Plan view. (b) Cross-sectional view of a single button. F = axial force; p = force acting at a point on the button.

Case 1: The b u t t o n slides out of crater while the chips remain stationary. This case would possibly incur the largest torque value with some penetration (v) and button-on-rock friction. Case 2: Only rock-on-rock sliding occurs while the b u t t o n - r o c k pieces interface is stationary. Case 3: The relative speed of rock chip m a y vary and m a y also differ from the speed of the button. It is thought that, when other drilling parameters remain constant, the torque required to rotate a bit depends, in general, on the penetration (v), the friction between rock and b u t t o n (/*br) and between the rock chips and rock mass (/.trr). Nevertheless, the torque can not be related to the coefficients of friction (~br and /*rr)" In this discussion, therefore only case 1 will be considered, with the assumption that b u t t o n on rock friction is zero, i.e. /~b~= 0. In this case r therefore depends only on the v.

(1)

Consider a single b u t t o n on the bit. For simplicity, suppose the button protrusion is hemispherical. Fig. 2(b) illustrates the forces acting on a b u t t o n and the associated instantaneously formed crater. The force ( p ) acts continuously on the button. The analysis is simplified b y considering the forces acting just after the b u t t o n has slid off the b o t t o m of the crater. This can occur due to the combined effects of bit rebounds [2] and applied torque. Contact forces are assumed to act on a single point of contact k (Fig. 2(b)) of the r o c k - b u t t o n contact, where v' = v. Taking moments about the contact point k (Fig. 2(b)) gives:

Fb pa = 7

(2)

Substituting for a and b:

r ~ ( 2 r v - v 2) P =

r-

(3)

where: r -- b u t t o n radius. In general, buttons on bits are so arranged that each circumferential row of buttons cuts a separate annular area on b u t t o n / r o c k contact surfaces. With some overlapping the button arrangement could supposedly cover the entire bit diameter (Fig. 2(a)). If the entire bit diameter is n o w considered (Fig. 3), let: D = bit diameter; d x -- thickness of an annular element of drill bit area (shaded area in Fig. 3);

70

T. SINKALA

Limits

For the b u t t o n geometry discussed, b o u n d a r y conditions for the equations rived are as follows: Normalized torque normalized penetration are defined by equations:

the deand the

3"r

"r, - F D = normalized torque

1,

D

Fig. 3. Elemental area on surface of bit bottom. (See text for explanation.)

= I,, = normalized penetration Then: _ .2)

= button density per unit area of drill bit. Then: N 4N - bit are~ - ~vrD

(4)

The area of the annular element (Fig. 3) is given by: d A = 27rx d x

(5)

'T$ =

1 2

(10) P$

F o r the assumed protrusion of a hemispherical b u t t o n out of a bit body, v, cannot possibly be larger than 1 / 2 since p < 0 / 2 . Equation (10) then gives: (11)

Force (t) per unit bit area is:

4Up t=p~=

~:D2

(6)

Hence, the elemental torque which m u s t be applied to sustain the bit rotation, for the area d A is: d~'elem =

tx

dA

Substituting for d A and t above from eqns. (5) and (6), respectively, yields: d'Felem ~--- 27rp~x

2 dx

(7)

Hence, the total torque which m u s t be applied to sustain the drill bit rotation is:

q7 D~ 3 r = 2vrp~ foD/ Zx 2 d x = -~p~

(8)

Substituting for p from eqn. (3), ~ from eqn. (4), and b u t t o n radius r by q)/2 in eqn. (8) gives: ~. = 3 F D ~((kl: q~ - - 2p~'2)

(9)

That branch of the square root has been chosen for which zero normalized torque (~-,) corresponds to zero normalized penetration (u,). The other branch, 1 / 2 < 1,, < 1, is rejected. In the treatment for percussion drilling given above, the applied torque ('r) is related to the applied thrust ( F ) , the drill bit diameter (D), the penetration (1,) and the average b u t t o n radius (q~/2). The reader might have noticed that the theoretical treatment of this p r o b l e m has been drastically simplified. Thus, for example, ~- is related to the above mentioned parameters through a static equilibrium equation for a drill b u t t o n in point contact with a rigid rock. Hence, rock deform a t i o n and rock fracturing, which might at first sight appear to be essential to the analysis of torque, thrust and penetration are not explicit in the analysis. This m a y appear to be contrary to intuition. Nevertheless, it will be shown through data f r o m field tests that the

71

R E L A T I N G D R I L L I N G PARAMETERS A T T H E B I T - R O C K I N T E R F A C E

formulae derived do in fact agree very satisfactorily with data from field tests.

Experimental study of the bit-rock interaction A series of drilling experiments was carried out at LKAB-Kiruna mine, Sweden. The holes were upward-directed normal production holes in sublevel caving. A hydraulic, tophammer percussive drill with independent rotation (a twin-boom Atlas Copco Simba H222 with a COP 1238 H F rock drill) was used. Both the button bit and X-bit were used for drilling. A Transtronic drilling processor TYP 93B was used to register data on one of the two rock drills on the rig. Information was recorded every 10 m m of drill bit advance while drilling. Among the parameters recorded were: hole length (L), penetration rate (R a), thrust on bit (F~), torque pressure (Pi), rotation speed (n) and percussion pressure (P). Methods by which the information recorded is converted to familiar forms of these parameters can be found in [2]. The rock in which drilling took place was mainly iron ore [10]. The texture of the ore was generally dense and fine grained. Some pyrite-rich fracture zones (10-20 cm) ran along the drift. Rock hardness values were: average compressive strength (oo) ~ 50 MPa minimum and 170 MPa maximum; and average tensile strength a t ~. 4 MPa m i n i m u m and 11 MPa maximum. In general, the waste rock was softer than the ore, and was mainly characterized by a high penetration rate. Hardness values for the waste rock could not, however, be obtained.

Examining the bit-rock relation using data from field tests At present, there is no way of estimating how many piston impacts are actually involved in every "total" rock face advance

recorded. Therefore only average values of the actual penetration (G) are used here. This G (from field data) is an average for every 10 m m (data sampling interval used) related to average bit advance, and is generally less than the penetration (1,) per piston impact. For simplicity of data treatment, it is assumed that the penetration per piston impact is approximately equal to the average penetration related to total bit advance. In our tests, the penetration rate ( R , ) is recorded in m / m i n , and the piston impact rate ( f ) is expressed as the number of impacts per second. Following the assumption above, ~ u~ = R/(6Of), where f = 100 impacts per second for the machine used. Substituting for u -- G in eqn. (9):

FD "r = --y- ×

~(60f¢~ R - Rz) 30/~- R

(12)

In practice, it is nearly always true that q5 >> G. For example, from field data the button diameter q~ ~ 10 mm, and the average approximate penetration per piston impact G ~ 0.1 mm. Equations (9) and (12) may then be written in the following approximate form: 2

~"

15fq~

(13)

In eqns. (12) and (13) R (or G), F, and ~" are variables while q~, f, and D have been assumed to be constant. For the argument on the validity of this assumption, see [2]. To evaluate this b i t - r o c k contact relation given in eqs. (12) or (13), more than 400 holes were drilled. The average recorded number of data points for each variable was about 1500. Using these data the validity of this bit-rock contact relation may now be tested as follows: Theoretically, if, in eqn. (13), the thrust ( F ) and penetration rate (R) remain constant, the torque (-r) should also remain constant. To check this argument in practice, constant values of thrust (F~) which had corre-

72

x. SINKALA

s p o n d i n g c o n s t a n t p e n e t r a t i o n r a t e s ( R a) w e r e s e l e c t e d f r o m a c t u a l field d a t a . R e s u l t s a r e s h o w n in T a b l e 1, w h e r e it is c l e a r l y seen t h a t c o r r e s p o n d i n g m a g n i t u d e s o f t o r q u e (~'a) a r e practically constant. The difference (e) between the average torque values and meas u r e d t o r q u e f o r t h e d a t a in t h e t a b l e h a s a m a x i m u m o f a b o u t 8%; this r e s u l t is v e r y encouraging. Comparison of experimental and theoretical t o r q u e v a l u e s f o r t h e s e tests w e r e p e r f o r m e d as f o l l o w s : The actual, measured values of thrust (Fa) a n d p e n e t r a t i o n r a t e ( R a) w e r e s u b s t i t u t e d in

e q n . (12). T h e r e s u l t i n g t h e o r e t i c a l v a l u e s o f t o r q u e (~-) w e r e t h e n c o m p a r e d w i t h t h e m e a s u r e d v a l u e s o f t h e t o r q u e (~'a)" Figure 4 shows a plot of theoretical torque ( ' r ) o b t a i n e d f r o m eqn. (12) v e r s u s a c t u a l ( m e a s u r e d ) t o r q u e (~-a), u s i n g d a t a w i t h 30% r e l a t i v e e r r o r (A,r) (see k e y t o T a b l e 1 f o r A,r d e f i n i t i o n ) . T h e a g r e e m e n t is c o n s i d e r e d t o b e good between the actual and the theoretical v a l u e s if t h e a s s u m p t i o n s m e n t i o n e d earlier a n d t h e field d r i l l i n g c o n d i t i o n s , a r e t a k e n into consideration. The results of a comparison between theoretical values and raw data (without scrutiny

TABLE 1 Magnitude of torque (ra) for constant penetration rate (Ra) and thrust (Fa) L (m)

Ra (m/min)

4.33 4.44 6.21 7.42 8.27

0.438 0.438 0.438 0.438 0.438

1.59 2.15 3.57 4.57

Fa (N)

'ra (Nm)

T (Nm)

AT (%)

Tav (Nm)

e (%)

Hole number

9 300.0 9 300.0 9 300.0 9 300.0 9 300.0

42.3 44.4 39.3 40.3 39.3

41.8 41.8 41.8 41.8 41.8

+ 1.20 + 6.22 - 5.98 - 3.59 - 5.98

41.1

2.87 7.98 4.43 1.99 4.43

fl 1.002

0.571 0.571 0.571 0.571

10100.0 10100.0 10100.0 10100.0

49.4 49.4 50.4 47.4

52.0 52.0 52.0 52.0

-

5.00 5.00 3.08 8.85

49.2

0.51 0.51 2.54 3.56

fll.002

2.76 3.02 4.24 5.86

0.595 0.595 0.595 0.595

8 700.0 8 700.0 8 700.0 8 700.0

42.3 45.4 43.4 42.3

45.8 45.8 45.8 45.8

-

7.64 0.87 5.24 7.64

43.4

2.42 4.73 0.12 2.42

k4.001

0.80 1.53 1.75 1.97 1.99 2.40 3.25 3.26 5.14

1.125 1.125 1.125 1.125 1.125 1.125 1.125 1.125 1.125

9 300.0 9 300.0 9 300.0 9 300.0 9 300.0 9 300.0 9 300.0 9 300.0 9 300.0

70.6 70.6 70.6 69.6 63.5 64.5 71.6 63.5 69.6

68.2 68.2 68.2 68.2 68.2 68.2 68.2 68.2 68.2

+ 3.52 + 3.52 + 3.52 + 2.05 - 6.89 - 5.43 + 4.99 - 6.89 + 2.05

68.2

3.47 3.47 3.47 2.00 6.94 5.47 4.93 6.94 2.00

f17.002

Note the magnitudes of (AT) and (e) L = hole length (location along hole from which data is sampled); R a = actual (measured) penetration rate; Fa = actual (measured) thrust; Ta = actual (measured) torque; Tav = average actual (measured) torque; T = theoretically predicted torque; A~- = (T -- Ta)/Ta = relative error between measured and theoretically predicted torque (T); e = ]Tav -- ~'a[/Tav = absolute deviation from average torque (Tav).

73

RELATING DRILLING PARAMETERS AT THE BIT-ROCK INTERFACE

for recording and other errors) are presented in Table 2. The comparison is in terms of relative error between the measured and the predicted penetration rates as a percentage of the theoretical penetration rates. The results obtained (shown in columns 4-6 in Table 2), indicate (as a percentage of the total number of data points), accepted for each hole when screened at 10%, 20%, and 30% relative error. There is more than 50% agreement between theoretical and actual raw values at 30% relative error for holes drilled with a button bit. The penetration rate (Ra) ha been used as a "screen" because, if eqn. (13) is considered, and the relative error of r is taken to be: AT

T-- r a

%

so that r =

Ta(AT + 1)

Then: T = kFaR

R -

-

-

2

The absolute relative error of R is then: R - R a IARl=

ra2 - r 2 =

T2

2 A T -I- A r 2 =

(1+AT)

2

t2ATI where it has been assumed that AT<< 1. Therefore, the error in R is twice as large as the error in r. Hence, using the penetration rate (Ra) to check the soundness of the data is on the safe side.

TABLE 2 C o m p a r i s o n b e t w e e n m e a s u r e d a n d theoretical values ( d a t a is as o b t a i n e d from the field; i.e. operational a n d recording, errors, etc., are present) Hole n u m b e r

Hole length (m)

N u m b e r of recorded data points per variable

Relative error between theoretical a n d actual p e n e t r a t i o n rates *

Ra, ra, a n d F a

10%

20%

30%

Button bit: K4.001 K5.001 Fll.003 F12.001 F17.002 Fll.012 F17.001 VF26.001 VF27.001 K27.004

13.24 24.24 12.43 10.81 16.40 24.80 11.99 16.93 15.34 22.87

1324 2424 1243 1081 1640 2480 1199 1693 1534 2287

19 24 18 21 23 17 24 19 18 25

37 45 38 39 41 35 60 34 32 49

53 63 52 56 71 54 72 50 46 74

X-bit VF31.001 ** VF31.002 VF33.001 VF33.002 VF36.002 ** VF36.003

19.35 12.82 20.18 18.13 17.80 21.17

1935 1282 2018 1813 1780 2117

9 14 14 14 10 13

19 26 26 28 21 22

31 38 38 40 34 37

* % / o f data accepted from total d a t a points given in c o l u m n 3 at error value indicated. * * N e w bit.

74

T. SINKALA IO0-

Penetration rate (R.) = 0.571 m/rain, constant 80.00 • ,.* ,,

Z 8° i ..-z

70.00

...~ 60.00

60 O

S

50.00

@

$

40 4,a

~ 40.00 $

O

$

> Pf=33 bars

20

~30.00 0 20.00 . . . . . . . .

~ld

. . . . . . .

Actual

~ld . . . . . . . ;Id

torque

. . . . . . .

(Ta) ,

~1[~. . . . . . . 1'(30

(Nm)

Fig. 4. Theoretical (T) versus actual torques (%) for data with relative error (AT) of 30% (q, = 9.5 mm and D = 76 m m ) .

The average diameter used for the blunted inserts was approximately 7 mm. Whenever a new X-bit was used, the measured values of the torque (%) were high, and did not agree accurately with the predicted values of the torque (~-). However, with used X-bits where the insert ends were blunted and smoothed, the fit obtained was much better, as demonstrated in Table 2. This suggests that the behaviour of blunted and smoothed X-bits resembles that of button bits.

5.00

;]60 ......

716b ......

Thrust

8166 ......

(F,),

(kN)

9'.00 . . . . . .

1'0.00

Fig. 5. Relationship between torque (Ta) and thrust (Fa) for constant penetration rate (Ra). The data is raw; i.e., operational, system and recording errors are present.

similar to an illustration by Knissel [13] shown in Fig. 8. This inverse proportionality has also been observed by Montabert (in [12]). According to eqn. (13), the torque (~-) increases as the penetration rate (R) increases. This is confirmed by the present data (see Table 1) and by studies by Knissel [13] and Montabert (in [12]). (See, for instance, Fig. 6.)

TORQUE

Examining bit-rock relation using present and past studies From eqn. (13), we can note that: if all other variables in this equation remain constant, the applied torque (~-) should be proportional to the applied thrust ( F ) . This relation is confirmed by the data from the present study (Fig. 5), observations by Unger and Fumanti [11] and is similar to the sketches presented in Montabert's work as reported by Pearse [12] illustrated in Figs. 6 and 7. From eqn. (13) we also see that the penetration rate (R) is inversely proportional to the square of the bit diameter (D). This is

.....

f Z

i

£~

I

I I

I I

I

FEED

THRUST b

!

:/.7.

/,,

J

J

I

I

MINIMT~

FEED THRUST

~ X [~TJH

Fig. 6. Sketch showing the relationship between thrust, torque and penetration rate (after [12]).

RELATING

DRILLING

PARAMETERS

AT THE BIT-ROCK

INTERFACE

TORQUE WEAK GROUND

MEDI~

GROUND

I

TORQUE

#

-- . . . . .

--

l

l l --~ l -

~

/ ---H~D

GROUND

I

• PRESET THRUST

T ~ U S T FOR WEAK GROUND

P

FEED THRUST

Fig. 7. Sketch showingthe relations~p between selected preset ma~mum torque and thrust for weak, medium, or hard rock (after [121). In Table 1, rock hardness is characterized by a low penetration rate (holes 4 and 11) for hard rock, and high penetration rate (hole 17) for soft rock. The penetration rate (R) and torque (~-) increase with a decrease in rock hardness. This is shown in Table 1 where for constant thrust (Fa), the torque (%) increases with increasing penetration rate (R~). These reFEED THRUST = i0 kN

I\

0

36

ROCK, O N TE

i

45

~6

17000 N1oo ,

6%

A

BIT DIAMETER,

!

66 (MM)

Fig. 8. Effect of bit diameter on penetration rate (after [131).

75

sults have also been obtained by Montabert (in [12]) (Fig. 7), and by Schunnesson [14]. Schunnesson also observed low torque (low penetration rate) in hard rocks, and high torque (high penetration rate) in soft rocks, for 115 m m diameter holes drilled using In The Hole hammer equipment. The machine used by Schunnesson [14] is programmed to drill at constant thrust. The observed variation in torque with penetration rate is of course expected, since one would expect a greater penetration rate in softer rocks than in hard rocks.

Discussion and conclusions

For the validity of the bit-rock contact relation developed here, it is essential that drill bit rotation be maintained; that is, there is no " j a m m i n g " of the drill bit. If drill bit rotation does not occur, the bit buttons (or inserts) will not impact virgin rock to create new craters on successive impacts, and zero overall bit advance will then be obtained. In the derivation, it will be noticed that the effects of frictional forces between a button and the rock at the b u t t o n - r o c k contact have not been included in the " b i t - r o c k contact relation", since we are only interested in the minimum torque ('r) required to maintain bit rotation. It should also be noted that the effect of rock breakage has not been considered explicitly in the calculations here. However, it may be argued that this assumption is justified because rock breakage in percussive drilling is due to percussion forces applied to new rock surfaces (rather than, for instance, torque and thrust on a bit during rotary drilling). Furthermore, the drastically simplified treatment of torque and bit rotation has been justified by the data obtained from field tests. When other drilli.ng parameters remain constant, the torque required to rotate a drill string is directly proportional to thrust (Fig. 5). After the rock has been penetrated, the

76 magnitude of the torque related to the drill string-rock contact, which is required to rotate buttons on the bit to new positions, depends on penetration, frictional forces and the rebound of the bit from the rock. F o r short ( = 20-25 m long) holes such as the ones examined here, it has been shown (Table 1, for instance) that the magnitude of this torque is essentially only what is necessary to overcome resistance (approximately equal to that caused b y the penetration) in order to maintain a constant bit rotation speed. These features have made it possible to employ torque in the Ntanje system as the key parameter for the automatic control of the drilling process in different rock conditions, and thereby minimise hole deviations [15]. Limitations of the b i t - r o c k contact relation One major source of discrepancy between the measured and theoretical torque was the recording instrument whose readings also included "off-rock" penetration rates ( R a ) , especially at "under-thrust" values (less than about 5 kN). W h e n such values of R a are used in eqn. (12) the theoretical values of torque ('r) will differ substantially from actual values. The remaining discrepancies m a y be due to deviations from assumptions made. Hole deviations; over- and under-thrusting of bit; bit or button wear and shape; resolution and precision of the registered data; the flushing efficiency; and fluctuations in piston impact frequency will definitely affect the accuracy of data used for discussing the b i t - r o c k contact relation. Furthermore, it is thought that, for a very porous rock and a very course-grained rock in relation to the bit b u t t o n size, eqn. (12) might not give accurate results. Here, apart from penetration (v), the porosity or grain coarseness might contribute substantially to corresponding torque (~'a) values. For very soft rocks, thrust (Fa) and torque ( ~ ) alone (that

T. S I N K A L A

is, with no percussion) might cause rock breakage, in which case, the relation developed in eqns. (1)-(13) will not apply.

Acknowledgements The author would like to thank L K A B Kiruna mine and Atlas C o p c o M C T AB for their material support, and also the Swedish R o c k Engineering Research F o u n d a t i o n (BeFo) for financial support.

References 1 Clark, B.G., Principles of rock drilling and bit wear. Q. Col. Sch. Mines, 77 (1) (1982). 2 Sinkala, T., Hole deviations in percussion drilling and control measures - theoretical and field studies. Ph.D. Thesis Lule~ Univ. Technol., Sweden (1989). 3 Lundberg, B., Some basic problems in percussive rock destruction. Ph.D. Thesis. Chalmers Univ. Technol., Gothenburg, Sweden (1971). 4 Hustrulid, W.A. and Falrhurst, C., A theoretical and experimental study of the percussive drilling of rock. Int. J. Rock Mech. Min. Sci, 8 (1981): 311-356. 5 Wijk, G., Indexation effects on mechanical rock destruction efficiency. SveDeFo Rep. DS 1982: 2, Stockholm (1982). 6 Atlas Copco, Manual. Atlas Copco AB, Stockholm, Sweden (1982). 7 Tampere, Tamrock Hand Book on Surface Drilling and Blasting. Tampere, Finland (1984). 8 Lindqvist, P.-A., Rock fragmentation by indentation and disc cutting - some theoretical and experimental studies. Ph.D. Thesis, Lule~ Univ. Technol., Sweden (1982). 9 Lundqvist, R.G., Hemispherical indentation and the design of 'button bits' for percussive drilling. In: Proc. Symp Rock Mech. 22nd (Cambridge) Am. Inst. Mech. Eng. (1981), pp. 219-222. 10 Liedberg, S., LKAB - mine internal rep. (1988/1989). 11 Unger, H.F. and Fumanti, R.R., Percussive drilling with independent rotation. U.S. Bur. Mines Rep. invest. 7692 (1972). 12 Pearse, G., Hydraulic rock drills. Min. Mag., (1985): 220-231. 13 Knissel, W., Results from hydraulic rock drill HBM 100. SIG. Inst. Min. Miner. Economics, West Germany, (1978). (In German).

RELATING

DRILLING

PARAMETERS

AT THE BIT-ROCK

INTERFACE

14 Schunnesson, H., Towards automated drilling in Sweden. In: IFAC Workshop on Advances in Automation of Underground Hard Rock Mining, 1st, 12-14th Sept. (Montreal) (1988). 15 Sinkala, T., precision drilling - - theoretical and

77 field studies. Part III: Improving hole straightness by automatic control of drilling parameters. Report No. Tule~ 1989: 022, G2000 89: 29, Lule~, Univ., Technol., Sweden (1989).