An analytical study of percussive energy transfer in hydraulic rock drills

Mining Science and Technology, 13 (1991) 57-68

57

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

An analytical study of percussive energy transfer in hydraulic rock drills Wu Changming Division of Mining Equipment Engineering. Lule& University of Technology, Luled, Sweden (Received July 6, 1990; accepted November 1, 1990)

ABSTRACT Wu, C., 1991. An analytical study of percussive energy transfer in hydraulic rock drills. Min. Sci. Technol., 13: 57-68. An analytical model analyzing stress wave generation and propagation, and percussive energy transfer of hydraulic rock drills is introduced. The model takes into account the local deformation of impact ends of piston and shank adapter. A good agreement between theoretical and experimental results is obtained. The percussive energy transfer of hydraulic rock drills is analyzed with the model. The analysis indicates that the local deformation, when it is within the practical range, does not have a large influence on the efficiency of energy transfer in hydraulic rock drills.

Introduction

The energy transfer in percussive rock drills has been studied analytically, numerically and experimentally over a long period of time [1-6,16-18]. In recent years more advanced numerical simulation programs, which can be used to analyze practical rock drills, have been developed [7-9]. However the influence of local deformation at impact ends has not been sufficiently investigated. In the study of the percussive system of rock drills, the classical theory assumes perfect contact between the impact ends of piston and shank adapter so that the generated stress wave rises abruptly from zero to a high level. In reality, however, the impact ends are always locally deformed during impact and the stress wave generated rises gradually. Therefore, the stress wave patterns obtained from classical theory deviate from the wave patterns observed in practice. Using this theory, one can not analyze the effect of local deformation on the efficiency of percussive energy transfer. 0167-9031/91/$03.50

In a recent study [10], it was shown that local deformation has a significant effect on the percussive energy transfer in pneumatic rock drills. When the impact ends are locally deformed to some extent during impact, high energy transfer efficiency for the first incident stress wave would be obtained in pneumatic top hammer rock drills. In this paper, an analytical model for hydraulic rock drills is introduced which takes into account the local deformation of the impact ends. Two dimensionless parameters (oe and/3) related to the dimensions of piston, the local deformation of impact ends, and bit force and penetration characteristics at b i t rock interface are introduced. This model has been validated by laboratory experiments. A comparison of theoretical and experimental results shows good agreement. Furthermore this model is used to analyze the efficiency of energy transfer in such rock drills. The possibility of energy transfer to rock for the second incident stress wave is also analyzed. High efficiency can be obtained by achieving proper values of the two dimensionless

© 1991 - Elsevier Science Publishers B.V.

58

parameters. The theoretical analysis indicates that the local deformation reduces the efficiency of energy transfer in hydraulic rock drills by a small amount. The analysis is based on the following assumptions: (1) A cylindrical piston impacts directly on a long rod of uniform cross section, and both the piston and rod have the same cross sectional area and material. (2) No flexural stress waves are generated. (3) All the impact energy is transmitted from the piston-rod impact interface to the bit-rock interface in the form of longitudinal stress wave. (4) The effects of joints and bit on the transmission of stress wave are negligible. (5) The sign for compressive stress and the corresponding particle speed is positive.

Stress wave generation and forces at bit-rock interface

Stress wave generation When a piston impacts a rod, a compressive stress wave is generated in the rod and transmitted towards the bit. Because of the curvature of the impact ends, inaccurate alignment of piston and rod, and the effect of the air film trapped between the impact ends, local deformation of the contact surface will always occur and affect the stress wave pattern. In earlier studies such local deformation has not been taken into account leading to erroneous results. The influence of such local deformations on the generation of stress waves is taken into account in this analytical model. To simplify the problem, the local deformation is treated as a linear spring-type deformation. Here, we assume a weightless spring with a constant k s between the impact ends. Fig. 1 shows a simplified hydraulic percussive system in which the spring symbolizes deformation of the impact ends.

WU

Piston

Rod

CHANGMING

Rock

"N, H

Ik Vr Fig. 1. A simplified hydraulic percussive system.

Before impact, the piston moves with speed Vp0 towards the stationary rod. We may imagine that there is a compressive and a tensile stress wave in the piston (see Fig. 2, where L = piston length). The compressive stress wave transmits towards the right with a magnitude of ZVpo/2A while the tensile stress wave transmits in the opposite direction with a magnitude of -ZVpo/2A. The resultant stress and particle speed of the piston due to these two stress waves are zero and Vp0 respectively. Immediately after impact, the compressive wave propagates towards the rod Vpo

Before Impact

u__ g Vpo/2A

--N

ZVpo/2A

. . . .

J

After Impact E, 0 < t < L/c

I t = L/e

1 i i

L/e < t < 2L/c

J ,i

I

t = 2L/c

i i i

I t > 2 /o

I

: I

J

Fig. 2. Stress wave generation and propagation process.

PERCUSSIVEENERGYTRANSFERIN HYDRAULICROCKDRILLS

59

and is partly transmitted and partly reflected at p i s t o n - r o d interface. The reflected part will be reflected at the free end of the piston and transmitted again towards the rod. Let: Opi = compressive stress wave in the piston moving towards the c o m m o n plane of impact; Vpi= particle speed of the piston at impact end due to Opi, where Opi = ZVpi/A; opt = tensile stress wave in the piston reflected from the c o m m o n plane of impact; Vpr= particle speed of the piston at impact end due to ~pr' ~pr = -- ZVpr/A ; Op = resultant stress at the impact end of the piston, Op = Op~+ Opt; Vp = absolute particle speed of the piston at impact end, Vp = Vpi + Vpr; Oi = stress wave transmitted into the rod from the c o m m o n plane of impact; Vi = particle speed of the rod at impact end due to oi, O"i = ZVi/A; Where: Z = AE/c--characteristic impedance of the piston and rod; A - - c r o s s sectional area of the piston and rod; E Young's modulus of elasticity; C -~- speed of longitudinal stress waves in the piston and rod. For the spring:

Let Oil and ai2 denote a i for period 0 _< t __ tdl (tall = 2L/c) respectively. For the period 0 _< t _< tdl , the stress wave %i is:

dF dt

=<(vo- vi)

(1)

Since the force ( F ) sustained by the spring is the same force acting on the piston and rod:

F = aiA = apA

(2)

Using eqns. (1) and (2) together with a i = ZVi/A , Opi = Z V p i / A , O p r = - Z V p r / A , Op = %i + %r and Vp = Vpi + Vpr, a differential equation (3) describing the stress wave a i can be obtained: 2k s 2k s d----/-+ - - Z---Oi = " Z -Opi

do i

(3)

ZVP° =--F°

%i=

2A

A

0 < t < t_u l _

(4)

Where F o = ZVpo/2. Substituting eqn. (4) into (3) and integrating with initial condition %(0) = 0 yields: ail=-~(1--e

-(2ks/z)t)

0_
(5)

The reflected stress wave %r for this period is: Yo 2k A- e - ( # z )

OPr =- Oil -- OPi

t

(6)

After time tal, this stress wave (%r) gets reflected at the left free end of the piston and reaches the c o m m o n plane of impact. So for the period t >_ taa, the stress wave op~ is: Opi =

~-e -(2kjZ)(t-(2L/e))

t~

tda

(7)

Substituting eqn. (7) into (3) and integrating with initial condition oi2 (tda) = % (to0 yields: 0ri2=

FO[~-ke(4LkJZc) "t

7

+(1

4Lkszc]_] e ( 4 L k J Z c ) _

1] e -(2ks/z)'

t ~ /dl

(8)

The reflected stress wave apt = a i r - Opi from the c o m m o n plane of impact in this period is negligible. The stress wave generation and propagation process is shown in Fig. 2. The incident stress wave to b i t - r o c k interface--eqns. (5) and ( 8 ) - - m a y be written as: ( ~--(l--e ro -4'at)

0<__I"
(9a)

~i=/ ~-[4,8 Fo e4B-'r + (1 --4/3) e4 # - 1] e -4#" ~->1

(9b)

Where 13 and "r are dimensionless variables, a n d / 3 = LKs/AE and r = ct/2L.

60

w u CHANGMING 1.4-

observed that the loading and unloading slopes are almost linear for some b i t - r o c k combinations. It is therefore reasonable to assume linear slopes. These linear bit force and penetration relationships are represented b y a simple model showla in Fig. 4(a, b). In Fig. 4 the loading slope is k while the unloading slope is k/3,. W h e n the first incident stress wave arrives at the b i t - r o c k interface, a bit force F b and a reflected stress wave or are generated. During the loading period, F b increases from zero to a m a x i m u m F b m a x at which the bit attains a m a x i m u m penetration. After that the bit force decreases from F b m a x t o 0 , and the bit attains the final penetration Uf. Work W a is performed on the rock by the first incident stress wave and:

1,2 ¸ 1.0 _

208

)

-

0.8_

p=

0.0

~

p

=

3

, l l l l l t j l l l l l l l [ l l l l ~ l l l ' [ l l l l l

0.0

0.2

0.4

0.5

1.0

03

1.2

1.4

' l l l l l l l

1,6

1.8

2.0

T

Fig. 3. T h e o r e t i c a l i n c i d e n t stress w a v e p a t t e r n s for

different values of B. The corresponding force F i is therefore: f F0(l - e -4Br)

0<• < 1

Fi = ~ F0(4 fl e4fl'r q- (1 - 4fl) e 4B -- 1) e -4/~*

"r > 1

(10)

F i / F o is shown for different fl in Fig. 3. 1 1 Z Y ~2 W l = - 2 G m a x U f - 2 k Xbmax

F o r the classical theory the generated incident stress wave is: ori =

Fo/A 0

O_<'r_< 1 ~->1

Since the rod length is assumed to be much longer than the piston length, the piston has separated from the rod when the reflected stress wave or arrives at the impact end of the rod. At this free end or is reflected again to form a second incident stress wave, o2i. W h e n o2i arrives at the b i t - r o c k interface o i = a r = 0 and the bit is at rest on the rock surface. Therefore, another bit force F2b, is generated, which increases and decreases as shown in Fig. 4 b y the dashed lines. If the m a x i m u m bit force, Fzbmax, generated this time is less than the m a x i m u m bit force, Fbmax generated b y the first incident stress wave (Fig. 4a) no

(11)

This is a special case in our model for k s = oc.

Forces at bit-rock interface A lot of experimental work has been done on bit force and penetration relationships [4,11-18] and there are several different theoretical models for bit force and penetration relationships. In order to simplify the problem we will chose the simplest model for this study. F r o m the experimental results it is

Fb

Fb

~ (a)

Uf

(12)

Fbmax

F'2brnax Fbmox/~// I

iI !

k/~//'/ ' I

F2bmax

I

j

(b)

Uf U'2r

I

I

U~

Fig. 4. Idealized bit force and penetration characteristics. (a) Maximum bit force generated by second incident stress wave, F2bmax, is less than the maximum bit force of the original incident stress wave, Fbm~x.(b) F2bmaxis greater than Fbmax

•

61

PERCUSSIVE ENERGY TRANSFER IN HYDRAULIC ROCK DRILLS

further work will be done. However, if F2bma x is greater than F b m a x , further work, W2, is performed on the rock (Fig. 4(b)) and:

Fb 2 = 4a e -(2'~/v)~

2/

f

Ao i e (2~/v)~dr

r_> r 1

(17)

1 W 2 = ~- ( f 2 b m a x q- F b r n a x ) ( g 2 f _

gf)

2

1 - - Y (F2bmax -- f 2 m a x )

(13)

2k

At ~- = 0 the bit force is zero and at "r = r 1 the bit force should be continuous, so that the initial conditions for eqns. (16) and (17) are, respectively:

Bit forces generated by the first incident stress wave

Fbl(0 ) = 0

(18)

Let Fba and Fb2 denote bit force F b for the loading and unloading periods, respectively. The bit force can then be expressed as:

Fb2 ('rl) = Fbl(I"1)

(19)

Fbl = k U

0 < t < t1

k Fb2=-~(U-

Uf)

Fbl(~ _<1)

t >---t1

Where: U = penetration; k = loading slope; 2/= unloading parameter, 0 < 2/< 1. 2/= 0 corresponds to a completely inelastic behavior of the rock, while 2/= 1 corresponds to a completely elastic behavior of the rock and is equivalent to no work done b y a rock drill. W e assume 74=0 and 2/=gl in this study. Once the incident stress wave, oi, and rock characteristics k and 2/ are known, the bit forces, Fba and Fb2 for loading and unloading periods can be obtained as [10]:

2k e_(k/z)t f Aoi e(k/Z) t dt r b l = --2-

O<_t<_t 1

(14) /, 2k F b 2 - 2/Z e - ( k / v z ) t J A o i e (k/v~), dt

t

> t1

(15) Where t I is the time at which the bit force F b arrives at its maximum. In terms of dimensionless variables r and a, where a = L k / A E , and let ,r1 = C t l / 2 L , eqns. (14) and (15) can be written as:

Fba=4~e-2~'fAoie2~'dr

For our model, substituting equation (9a) into (16), and integrating with the initial condition (18), Fbl(~
O
(16)

=

e 2F0(1

+ _a - - Z ~ (e

- e-aB')]

(1 + 2or,r) e -2°~')

(a ~ 2/3) (a = 2fl)

(20) For time period 1 < ~-< r l , F b l ( r _ > l ) is obtained by substituting equation (9b) into (16) and integrating: Fbl(r >_1)

={

(a v~ 2fl)

/4F0

e2°.,2 + C, + D2)

(21) Where: B = 2a - 4/3; C = (1 - 4fl) e 4/~ - 1; D 1 and D 2 = constants obtained b y using initial condition Fbl(, >_1) ( r = 1) = Fbl(~_<1) ( r = 1). 1 - e - 2 a q01 =

0 2 ~---

o~

(e_2a

a - 2-------fl

- e-4e)

2a e -2a 4/3 (B - 1) e 4B+B

Ce~

B 2

B

1 - (1 + 2 a ) e -2a 2a e -2~

--

o~ e 2 ~

--

C

62

WU CHANGMING

F b has the m a x i m u m Fbmax at r l, and Fbmax is easy to obtain using a computer. The expression for Fb2 is obtained by substituting equation (9b) into (17):

F r o m eqns. (10), (20) and (23) we obtain: F2i(,r <1) [Fo(B

j :

a "2~' - . f 4 P 4 F 0 ; e - t /v, [ F ( B r _ l )

C s, e4#+"-+~ e

Fb2=14Fo~e_(2a/v)r(2fle4B.,r2+C,r+D2)

+D1]l

e -2at + C e -4B'-

1)

= ~Fo [(4o/r + 1) e-2~" - 1] ~F0(2

(a 4' 2fl7)

( o / = 2fl)

1)

e -2a'-

(o/4: 2fl)

(a

m) (26)

(22) Where: B = ( 2 o / - 4/33,)/3,; C = (1 - 4fl) e 4B - - 1; D 1 and D 2 = constants obtained by using the initial condition (19). For the classical theory the bit force is:

~ 2Fo(1 - e -(k/z)') Fb = ~ 2F0(1 e -(k,/z)tl)

0 < t < t1 e -(k/zv)(t-'0

= /2Fo(1 - e - 2 ' ' )

~ 2Fo(1 e -2a) e -(2a/v)(r-1)

t > t~

0<~-<1

(23)

r>_ 1

Where q = 2L/c. The bit force has Fbmax at r = I so that:

Fbma = 2Fo(1- e -2~)

Where: B=2(1-

C-

Bit forces generated by the second incident stress wave The purpose of deriving bit force F2b in this study is to obtain the m a x i m u m bit force F2bmax and check under what conditions further work will be done by the second incident stress wave. Since the first tensile part of the reflected stress wave, F r, is reflected as the compressive part of the second incident stress wave, F2i, and m a y do further work, only this part is analyzed. The first part of F2i is: F2i(r <1) = -- Fr(~._
2o/

'

1.

o / - 2fi

(24)

(25)

)"

When the second stress wave arrives at b i t - r o c k interface, the bit force generated increases first along the dashed line shown in Fig. 4 with loading slope k / y . Hence eqn. (17) can be used to calculate the bit force F2b when it is less than Fbmax. Substituting eqn. (26) into (17) and integrating with initial condition F=b ( 0 ) = 0 yields: 4Fo~e-(Z~/v)~(BeDT+CeEr_

The reflected impulsive force from b i t - r o c k interface is: F r = r b -- F i

o/ o/--2]3

f

g e(2a/v)~+Cl)

(a 4= 2fl)

eO-+ el F2b =

o,

Y e(2~/v)r C2]

-Td (a = 2fl)

+

o,

.,..,-

"[ e(2a/y),r (~ = ~ )

(27) Where: B and C are as defined in eqn. (26): D = 2a(1 - V)/Y E = 2(ay C1 - 2 a

2fiy)/y B D

C E

PERCUSSIVEENERGYTRANSFERIN HYDRAULICROCKDRILLS 4a

,/

1

c2 = D + c,-

D

Y

Y

- y)

For the case where F2b exceeds Fbmax, F2b will increase with loading slope k once it has exceeded Fbmax. If T2 denote the time at which F2b = Fbmax , and F2b 2 denotes the bit force after time r2, f2b 2 c a n be obtained by substituting eqn. (26) into (16) and integrating. The solution is:

[

4Foae-Z,~.(B~.+~ e 2 ( . - ~ e 2 ° ' - c4) (~ =~2B)

(28)

(a = 2fl) ~(~ = ~) Where C4, C5 and C6 are constants, and can be obtained by integrating with initial condition F2b2 ( r 2) = Fbm,~.

Laboratory testing

In order to validate the model developed above, some laboratory tests were performed

/

• 1 ~

,

-

using a drop tester. A schematic diagram of the experiment is shown in Fig. 5. Cylindrical pistons with a diameter of 20 mm and lengths of 300, 400 and 500 mm, an integral steel with a chisel bit (Sandvik H22, 2550 mm long) and a large piece of Swedish granite rock (550 × 550 × 500 mm 3) were used. The drop height was about 4.5 m and the effect of friction between the piston and the guide rods was observed to be negligible. Therefore the piston impact speed is: Vp0 = 2 ~ h = 9.4 ( m / s )

2B).

Fzb2=14Foote_2~,((2~r+l)r_ ~_~e2~,+Cs)

63

Piston -

Bridge [___~ Digital ] A__mPlifier ] I°seill°sc°p e[

Rock

Fig. 5. Diagram to show the experimental set-up.

Where g is the gravitational acceleration. To measure the signals, a pair of strain gauges (HBM 6/120 LY 11) were placed in diametrically opposite positions on the rod 1360 mm from the impact end. This was so that the incident and reflected stress waves would not overlap, and the reflected stress wave would not be overlapped by the second incident stress wave at the measuring position. The strain gauges were connected to a Wheatstone bridge and an amplifier (Peekel CA 400) in such a way that the contributions from unintentional bending were canceled. The signals were recorded by a digital oscilloscope (Nicolet 1090) using a sampling interval of I Ixs. The recorded signals were transferred to a personal computer for further evaluation. From the stress wave signals recorded, the wave speed was estimated to be about 5170 m / s in the drill rod. Young's modulus for the piston and rod was taken to be 2.1 × 1011 ( N / m 2) in the data analysis. Bit forces and the penetration were calculated from the recorded incident and reflected stress waves by a computer program in which the change of characteristic impedance along the rod and bit is taken into account. The parameters ks, k and y determined from the experimental results were used in the theoretical analysis (eqns. 20-28). One example of experimental and theoretical results is shown in Fig. 6 where the length,

64

wo CHANGMING

801 60

v

4o 20

2

....

-60| -( a - )

......... o

~ ......... 2

Experimental

i

4 Time

(10 -4

6 see)

8

10

120:

~oo i 8oi ~"

6o;

v

40;

,,~

2°i

'~ -20

ExooLo,o,

-60~ -80-".

(b)

-100:

,

,, .......

L .........

100

80-

60-

k~ 0 40. -o b~ 20"

i ......... 6

4

Time

120-

~

i .........

2

(10-*

i ......... 8

i 10

sec)

///

Efficiency of energy transfer and discussion

Efficiency of energy transfer Efficiency of energy transfer for a rock drilling percussive system is defined as the conversion efficiency of the kinetic energy of a piston into work done by a bit on the rock. The kinetic energy (W1) of the piston is:

0"

(c)

-20 0.0

....

o.'1 .... o.~ .... o.b .... Penetration (mm)

diameter and impact speed of the piston, and the values of parameters k, k s and 7 used in the theoretical analysis are given. F r o m these figures it can be seen that the patterns of theoretical stress waves based on our model are m u c h closer to the experimental results than those based on the classical theory. Thus, our model has the potential to be more useful in analyzing the energy transfer of hydraulic rock drills. In the experiments, the pistons always reb o u n d before the reflected stress wave reaches the c o m m o n plane of impact so that some kinetic energy is trapped in the piston without transmitting to the rod as stress wave energy. This means that the magnitude of theoretical stress waves is always higher than that of the experimental stress waves. The second incident and reflected stress wave signals were also recorded in the experiments. Analysis showed, however, that the second incident stress wave did not do any further work at all in our experiments. The first tensile part of the first reflected stress wave is very small (see Fig. 6a), which also indicates that their second incident stress waves will not be able to do any further work.

o.~ ....

o.b

Fig. 6. A comparison of a set of experimental and theoretical results. (a) Experimental and theoretical (our model) stress waves. (b) Experimental and theoretical (classical) stress waves. (c) Dynamic bit force and penetration curve. L = 40 (mm); d = 20 (ram); Vpo = 9.4 ( m / s ) ; k s = 6 x 1 0 8 ( N / m ) ; k = 3.4x108 ( N / m ) , -f = 0.51.

1

2

wl = gMV 0 Where M = piston weight. The work, W1 done by the first incident stress wave is given in eqn. (12). In some cases further work, W2, m a y be done by the second incident stress wave. W2 is given i n

PERCUSSIVE ENERGY TRANSFER IN HYDRAULIC ROCK DRILLS

65

eqn. (13). Therefore, the efficiency of energy transfer for a rock drilling percussive system m a y be expressed as:

sponding contour plot showing clearly how the efficiency '01 changes with c~ and /3. The efficiency '01 has a m a x i m u m value of 0.815(1 -3') at o~= 0.63 a n d / 3 = m. The possibility of further work being carried out by the second incident stress wave varies with dimensionless variables a and /3, and the unloading parameter y. Figure 8 shows 77 versus o~ and 1/13 for 3' = 0.1. 7/ and '02 versus o~ and 3' for 1//3 = 0.1 are shown in Figs. 9 and 10, respectively.

'01 = W 1 / W i -

'02 = W 2 / W / -

__(max)2 1-3" 4~

-1- -( 3 ' 4~x

(29)

F2bmax2-- Fbmax F 0 ) (30)

(F2bma x > Fbmax )

/ l-,(bmaxt

'0 "~" '01 "q- '02

=

To

/

Discussion

(F2bmax > Gmax)

1 -- "g ( Fbmax t 2

~

Fo ]

( F 2 b m a x -~ G m a x )

(31) Where: '01 = energy transfer efficiency for first penetration; '02 = energy transfer efficiency for second penetration; '0 = total energy transfer efficiency. For our model, the efficiency of energy transfer '01 for the first penetration is shown graphically in Fig. 7. Fig. 7a is a surface plot of the efficiency '01 and Fig. 7(b) is the corre-

It can be seen from Figs. 7 - 1 0 that the dimensionless parameter o~ has a significant influence on the efficiency of energy transfer. For optimal energy transfer during the first penetration, o~ should be 0.63. Higher or lower values of o~ will decrease the energy transfer efficiency '01. Since o~=Lk/AE, a higher value of a m a y occur due to any one of, or a combination of: long piston length, very hard rock and small diameter of piston and rod. For higher values of a, the first tensile part of the reflected stress wave is small and will never do any more work after being reflected as the second incident stress wave. The main

,°

0:,///iilttl/III:

20 30 4.0 a Fig. 7. Theoretical energy transfer efficiency, ~h (1 - 2¢), versus a and 1/18. (a) Surface plot. (b) Contour plot.

(a)

(b)

/

0

10

66

wu CHANGMING

y=0.1 o

¢0~ o

o~ o

0 0 0

0.50

u~

o

0

o~

0

0

0

"~'m~b~b~ :~ ~

0

"

b~

O !i iOi (a)

(b) °'°°o.ls' ' ~.00

~'.~s ' 'i.;o'

'~.~5 ' '4.00

C(

Fig. 8. Theoretical energy transfer efficiency 4(1 - y) versus a and 1//3, for 7 = 0.1. (a) Surface plot. (b) Contour plot.

0.99

,

I o

,

,

9~

~

o

o d

,

,

,

d

d

,

,

,

o '

d

d

o

o~

d

d

(5

(5

6

d

1//3 = 9 . 1 0.74

o

0.50

dO~dd

0.25 o (5odd

(a)

(b)

0.08.~5

d

I

i iii 4.oJ I 1'.751'I , l, 2.50 , I, , ,I i 3.25

i

i

i

4.00

Fig. 9. Theoretical energy transfer efficiency 4(1 - 7) versus a and y, for 1//3 = 0.1. (a) Surface plot. (b) Contour plot.

,z

0.99

1//3 = 9 . 1

0.74

x..

" %

0.50

..~

(b) o.o

0"

,,

1.75

,,,

,,,

2.50

,,1111

3.25

' 4.00

Fig. 10. Theoretical energy transfer efficiency 7/2(]_- 7) versus a and 7, for 1//3 = 0.1 (a) Surface plot. (b) Contour plot.

PERCUSSIVE

ENERGY

TRANSFER

IN HYDRAULIC

67

ROCK DRILLS

part of the reflected stress wave is compressive and large, so that the rod will be compressed first and then rebound from the rock. Therefore, the total energy transfer // is equal to //1 in this case. Lower values of a m a y occur due to any one of, or a combination of: short piston length, very soft rock and large diameter of piston and rod. For lower a values, the first tensile part of the reflected stress wave is large. After being reflected it is able to do some further work when Y is less than about 0.4. In this case the total energy transfer efficiency // may increase and be larger than /11"

The energy transfer efficiency decreases with decreasing /3 or increasing local deformation of the impact ends for a hydraulic drilling system. The local deformation does not reduce the efficiency very much and does not have m u c h influence on the further work done by the second incident stress wave. The unloading parameter, T, affects the energy transfer directly. The smaller T is, the greater the energy transfer efficiency, //, will be. Even if a is less than 0.63, no further work could be done by the second incident stress wave if T is larger than about 0.4.

Conclusions A n analytical model, which accounts for the local deformation at impact ends, is introduced for hydraulic rock drills. The agreement between the theoretical and experimental results, obtained from a drop tester, is satisfactory. The stress wave patterns of our mode] are closer to the practical stress wave patterns than the results from classical theory. This model has been used to study the efficiency of percussive energy transfer in hydraulic rock drills. The local deformation of impact ends always decreases the energy

transfer efficiency, but its influence is very small. The dimensionless variable a is important for the design of hydraulic rock drills. The energy transfer efficiency, //1, for the first incident stress wave has its m a x i m u m values, when a = 0.63. Even though the second incident stress wave may do further work, it is better to have high efficiency//1 when drilling long holes, since stress wave propagation in rods always causes fatigue and results in some energy conversion to heat. D u e to the fact that a is a function of piston length ( L ) and diameter (D), and loading slope ( k ) of bit force and penetration curve, it is possible to achieve the optimum value of a by adjusting the piston length and diameter, and obtain appropriate k and T values with good bit design. If these parameters were adjusted an improved energy transfer efficiency would be obtained.

Acknowledgements The author would like to thank Professor Sven G r a n h o l m for his careful guidance, encouragement and valuable comments on this study. The author would also like to thank Mr. U d a y K u m a r for his help in text presentation.

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