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An oscillating waterjet deep-kerfing technique
Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol. 15, pp. 135-144. © Pergamon Press Ltd 1978. Printed in Great Britain
0020-7624/78/0801-0135502.00/0
An Oscillating Waterjet Deep-Kerfing Technique JAMES M. R E I C H M A N * J O H N B. C H E U N G * Cutting deep slots in rock with a waterjet requires a nozzle configuration that can cut a kerf wide enough for the nozzle assembly to enter. A tool for cuttin9 such slots, which utilizes an oscillating mechanism, has been developed. This device uses only static seals and is inherently more reliable than a rotating device. Deep kerfing with waterjet should have applications in the areas of tunneling, mining, quarrying and trenching. The deep-kerfin9 tests have been conducted on a variety of rock. Based on test data, a physical model that can predict cutting rates has been developed. 7his model permits the study of various applications of deep-kerfing nozzles without requiring expensive experimental test programs.
1. I N T R O D U C T I O N Waterjet cutting applications in mining and tunneling operations have been limited in the past because deep slots, or kerfs, could not be made. With the ability to make deep kerfs, the possible applications of waterjets increase substantially. Some areas where deep-kerfing devices could be beneficial include tunneling, mining, quarrying and trenching. In these applications deepkerf waterjets could increase production or advance rates by increasing cutting rates and by decreasing the wear, and as such, the operating life of mechanical cutting devices. A single small-diameter waterjet can penetrate a slot only a limited distance before it 'bottoms out'l-l,2]. The reason for this limitation is believed to be that, in a narrow slot or kerr, the force of the jet is dissipated by the wall interaction with the free jet. Even if multiple, closely-spaced slots are cut, the depth to which the jets can penetrate into the slot is finite because the centerline pressure of the jet decays with the distance from the nozzle exit and becomes too small to cut effectively. In this paper, the development of a waterjet deep-kerfing device that overcomes these limitations is presented. Cutting deep slots or kerfs requires a slot wide enough for the nozzle to enter. With a wide slot, an optimum stand-off distance can be maintained between the nozzle and the material face to achieve the most effective cutting. If a constant stand-off distance is maintained, the jet can theoretically cut to any desired depth. Of the several ways of making a cut wider than the cutting nozzle, the most expedient is to use some form of rotating nozzle with angled jets to achieve the * Flow Industries. Inc.. Kent. WA 98031, U.S.A.
desired slot width. The inside of the slot can be completely covered using a device of this sort. Harris and Brierley [3] suggested such a device as an extension of their work on a rotating waterjet device. During development work on a rotating waterjet device for cutting deep kerfs, it was found that the critical problem was not the nozzle development, but the development of a reliable high-pressure (170~08 MPa) swivel. Since there was no apparent near-term solution to this problem, a non-rotating device was developed. This device consists of an oscillating nozzle assembly, in which the torsional flexibility of the tubing allows the nozzle to oscillate. Like a rotating nozzle device, a nozzle oscillating over a limited angle completely covers the material in the slot, but has none of the seal problems inherent in a high-pressure swivel. This study involved the development of the deepkerfing device, as well as the development of the oscillating nozzle. A kerfing model was developed, some experimental data were taken, and cutting rates were established for various applications. Results of this study show that: (a) deep-kerfing is feasible, (b) a reliable deep-kerfing device (with no high-wearing swivels) can be developed, (c) the device must be optimized for each application, and (d) a model for deep-kerfing can be used to find optimum conditions based on linear cutting data. 2. E X P E R I M E N T A L A P P R O A C H
2.1. Tool selection As mentioned in the Introduction, cutting deep slots requires a kerf that is sufficiently wider than the nozzle so that the nozzle can enter the kerf freely. The width of the slot is minimized to reduce the amount of mater135
i36
James M. Reichman and John B. Cheung
j-J
J
J
Side View of the Nozzle
{a) JewelOrifice
© FeedDirection of Rock 1
- - Front-FacingJet . . . . Reer-FacingJet (~ (b)
MetalOrifice
Fig. 1. Deep-kerf nozzles.
ial removed, and therefore the energy required to cut the slot is minimized. A narrow slot can best be made with a small nozzle assembly that consists of one or more angled jets. By angling the jets at a sufficiently steep angle, a kerf wider than the nozzle assembly can be obtained. Therefore, all the nozzles investigated in this program had angled jets. Additionally, a two-jet nozzle was used to balance the lateral forces on the nozzle. This balance is necessary because any wobble in the nozzle is undesirable, particularly when cutting slots with a depth of 1.5 m or more. Two similar nozzle designs were considered for this program; both were two-jet nozzles with the jets angled at 0.436 rad. One nozzle used sapphire jewel orifices while the other used nozzles machined in the nozzle body. Schematics of both types of nozzles are shown in Fig. 1. The sizes chosen for the nozzle exits were determined by the hydraulic power that was available and necessary to cut the rock.
Fig. 2. Coverage pattern for an oscillating jet.
lating nozzle. Two jets oscillating over a limited angle can completely cover the slot and will make a cut wide enough to allow the nozzle to freely enter the kerf. Figure 2 shows a schematic of the pattern covered by such a two-jet nozzle. The oscillating nozzle device has static seals; thus, the new tool is reliable and requires little maintenance. There are none of the inherent weaknesses of using high-pressure rotary seals. The oscillating nozzle device is, therefore, superior to rotating devices, and it makes deep-kerfing a more practical concept. A schematic of the device is shown in Fig. 3.
TubeConnector __
E
~] RigidMount
2.2. Nozzle motion The nozzle for deep-kerfing must move so that the nozzle completely covers the material and leaves no ridges which could potentially catch the nozzle. The initial approach was to use a nozzle rotating 2re rad to achieve coverage of the slot. This method proved to be inadequate because of the high wear rate of rotary seals at high pressures. The high speed of rotation is necessary to obtain an optimum linear traverse velocity for the jet, which for most rock is in excess of 500 mm s - 1. The high speed of rotation required to cut some rocks efficiently complicated the problem. It was obvious that an alternative method of achieving the motion was necessary if deep kerfing was to be a viable tool prior to the development of more reliable rotating seals for swivels. The selected method of nozzle motion uses an oscil-
Twist Length
3/8Tube Motor, VariableSpeed
Bearing~ r _ 1 AttachL-rx--r-l~J Arm [ ~
~(~Z~
MotorAttach~ate
TieRod
Nozzle~ ~-Tubingof LengthLWhich "/~ ActuallyEnterstheSlot
Fig. 3. System schematic for an oscillating deep-kerf device.
An Oscillating Waterjet Deep-Kerfing Technique 2.3. Rock selection Various well-characterized rocks, ranging from sandstone to granite, were tested to verify the feasibility of the deep-kerf concept. Deep-kerfing proved to be a feasible process for all the rocks tested. A parametric study on Wilkeson sandstone was conducted by varying the feed rate, oscillation rate, pressure and nozzle diameter. Wilkeson sandstone, found in western Washington State, has been used extensively by several investigators [4-1, so linear waterjet cutting data is available. Consequently, most of the data presented in this paper is for Wilkeson sandstone. Data for kerfing a variety of granites and limestones are also presented.
3. EXPERIMENTAL APPARATUS The pressure for the tests, which ranged from 103 to 412 MPa, was supplied by one or other of two Flow Industries, Inc., high-pressure intensifiers. One intensifier supplied 9.5 × 10-s mS s ~ of water at pressures up to 412 M P a and is rated at 37.3 kW. This intensifier was used in the small jet tests. For tests with larger diameter jets, a mobile, diesel-powered, 190 kW intensifier was used. This unit is capable of delivering 4.7 x 1 0 - 4 m S s -1 at 384MPa. The intensifier pumps were used to power nozzles ranging in size from 0.2 to 0.7 ram. The nozzle assemblies for the tests are shown in Fig. 1. The pressure at the nozzles was measured by a high-pressure gauge. The specimens for both linear-cutting and deep-kerfing tests were rigidly mounted on a test table. The nozzles were mounted on a traversing mechanism, which gives x-y-z motion. In the y direction the nozzle speed could be varied from 25.4 to 254 mm s-1. In addition, a rotary table was used to obtain linear velocities up to 508 mm s - l . For tests in which a rock was cut to any great depth, the z traverse (perpendicular to the rock face) was used in a stepwise manner, after a specified number of traverses. Thus, an effective cutting distance was maintained between the nozzle and cutting surface. A variable-speed 1.5kW motor powered the oscillator for the deep-kerf experiments. The oscillation frequency of the device could be varied between 8.3 and 33.3 Hz. The oscillation frequency that was used for each rock was chosen from the linear cutting data since oscillation frequency and linear nozzle-cutting velocity are directly related. For a stand-off distance of 0.5 in., the oscillation range available from the device corresponds to a traverse velocity of 190-762 mm s-1
4. KERFING M O D E L There are two ways of determining the cutting rates of a deep-kerfing nozzle. The first is by experimenting with the nozzle; the second is by developing a mathematical model, based on the rock removal mechanism of kerfing, which can predict kerfing rates and optimum
137
conditions from linear cutting data. A model that predicts the performance of a kerfing nozzle, based on the physical layout of the kerfing nozzle, the linear cutting data, and the operational parameters has been developed. Consider an oscillating angled jet impacting a rock surface operating in the mode shown in Fig. 6a. The jet cuts a circular arc in the rock, to a depth equal to the cosine of the angle of incidence (0) times h, the depth of cut when the angle is zero. The path of the moving jet is similar to that shown in Fig. 2. As an approximation, if co is high (about 20 Hz), and if the translation velocity is small (about 127mms-1), the cuts can be considered straight and parallel. If a second angled jet ( - 0 ) is moved along the work piece, it cuts parallel slots which intersect the slots of the first jet. This cutting pattern is shown in Fig. 4. The result of the motion of the two nozzles is that material is removed, and ridges are left along the bottom of the cuts. The size of the ridges is a function of the cutting parameters of the nozzle. The width of the cut is defined by the angle of oscillation q~. Changing the angle of the jet, the feed rate of the jet, or the oscillation of the jet changes the amount of material that remains in the slot. The predictions, based on this model, are presented below. As was previously stated, the depth of the cut in the slot is D = /1 cos 0.
(1)
The average spacing between slots S (ram) is
S _ V: 2o) 60
S = 30V:,
(2)
o) where ~o = oscillation frequency (counts/min), and V: = nozzle feed velocity (ram s-1). The rate of material removal can be defined by d V: where d is defined as overall or effective depth, and
d=D-D' and D' is the height of the ridges.
S Nozzle Centerline, Front-FacingJetL07 ~ dS
Hw
I [I £k~\, ,
/
Z'Y" D
,~.~//%// ,,,/%\/
Ma,.ia,RomovJ
\v /
~" MaterialRemaining Fig. 4. Kerfing model.
\,
/-- Centerline, Rear-FacingJet
138
James M. R e i c h m a n and J o h n B. C h e u n g
(a) Deep-kerfing cut
(b)
Three
parallel cu-l-s (mult-iple pass)
(clear
slol-
depth
= 51 m m )
Fig. 5. Oscillating kerfing cuts and parallel linear cuts.
M a x i m i z a t i o n of the material removal rate with respect to the feed velocity Vs can be obtained by setting --(dV~)
evz
= 0
,~;~[D(1- ~)V~] = O.
and D'
S
w
D - 2h sin 0
2h sin/)'
where w is the projected width of the cut. With the relationships
t3,
F r o m Fig. 4 it can be s h o w n that
30 Vr S
~
- - -
and 15l/~
D'
2 tan 0
2 tan 0'
(5)
(41
(O
7D'(~ '
An Oscillating Waterjet Deep-Kerfing Technique
oioo
where r = projected radius of oscillation of the jet (mm), q~ = angle of oscillation (rad), and V~ = linear traverse velocity (mm s- t) equation (5) can be rewritten as
D' D
rcr@ Vf hsinO 1/,
W
/,i÷~ ~=0 (al
(6)
2h sin 0
139
Furthermore, since r = I tan 0, where I is the stand-off distance, equation (6) becomes
D' D
rclq~ h cos 0
Vf
w 2h sin 0"
(7)
tp=x
(b)
Substituting equation (7) into dV: gives d V / = hcos 0(1
,~ = Rotation angle
rcl~ v: + h c o s 0 V~ 2h~nO
vs.
~u = Measurementof the initial nozzle angle with respectto the table motion
(8)
Fig. 6. Nozzle oscillation.
Equation (3) becomes 1+
w 2h sin 0
2glq~ Fy h cos 0 Vt
0,
and 17/_ V t h c o s 0 ( w ) 2rtl~ 1 + 2hsin~ '
(9)
where V: = optimum feed rate. The optimum material removal rate d Vy is given by dV:-
h 2 c°s2 OFt( 1 + - W ) 2" 47rl~ 2h sin 0
(10)
With this relationship, the optimum cutting rate can be predicted. In addition, equation (8) can be used to predict the rate of material removal dV/ at various forward advance rates Vr. 5. E X P E R I M E N T A L RESULTS Experiments were conducted on sandstone, granite and limestone. A typical kerf created by the oscillating nozzle is shown in Fig. 5a. The kerf shown in this figure was cut in granite by two 0.3-mm jets at 275MPa. The kerf was 51mm deep and was cut in 14 passes at a feed rate of 25.4 mm s- 1. As a comparison to deepkerf cutting, Fig. 5b shows linear cuts in concrete made by a single nozzle, with two parallel cuts spaced 6.35 mm apart. In this test, the pressure was 412 MPa, the nozzle diameter was 0.79mm, and the feed rate was 25.4 mm s-1. Comparison of the two pictures in Fig. 5 shows that the deep-kerf tool gives a wide slot (25.4mm) with parallel walls, which would allow cutting to any depth. The cut made in concrete tapers and is not wide enough for the nozzle to enter. The actual depth of the clear slot is only about 51 ram, and the jet has "bottomed out'. Figure 5a clearly demonstrates the type of cut necessary for kerfs of any depth. The oscillating device can be operated in two modes : in the first, the two jets point in the direction of translation (0 = 0) and oscillate with some fixed amplitude th about this initial position; in the second, the jets point outward at a predetermined angle 0, and oscillate
inward. The angles for these cases are shown in Fig. 6. For each of these modes both the angle of rotation needed for uniform coverage and a slot width greater than the diameter of the nozzle must be determined. The optimization for each case is shown in Figs. 7 and 8. Figure 7 shows the various oscillation angles and the resulting slot widths. Figure 8 shows the variation of q~ with a non-zero 0. The resulting kerf widths in these tests were all between 12.7 and 17.8 mm. The kerfing efficiency experiments were conducted with a constant stand-off distance of 12.7 mm between the nozzle and the rock. For one series of tests the pressure was fixed and the feed rate varied for a given diameter nozzle at a fixed ~b and 0. The feed rate was changed from 25.4 to 254 mm s- 1 in 25.4 mm s- 1 intervals. After each pass of the nozzle at a given feed rate, the maximum, minimum and average depths of the kerf were recorded. The block was then moved over, and
Jet Pressure
275 MPa
Standoff Distance
12.7 mm
Jet Angle
25 °
Jet Position
~ = 0
Width
(m)
Depth
(m)
50
17
1O
45
15
12
40
15
iO
35
13
12
Kerr Shape
- ~
Fig. 7. Kerfingtests; variation of ~b, 0 = 0'.
140
James M. Reichman and J o h n B. Cheung NPa
Jet Pressure
275
Standoff Distance
12.7 mm
Jet Angle
25 °
Jet P o s i t i o n
~ = 45 °
Minimum Depth (mm)
25
0
30
0
35
0.254
40
9.1
4~
7,6
Kerr Shap~
Fig. 8. Kerfing tests; variation of q~, ~O = 45".
another pass was made. Typical specimens are shown in Fig. 9, and the data from several series of tests in Wilkeson sandstone are shown in Table 1. Nozzle orifices of two sizes were used in the first series of tests on Wilkeson sandstone. The small jets were 0.3 m m in diameter while the large jets had a diameter of 0.7 mm. The small jets were run at 206 and 2 7 5 M P a , while the large jets were run at 103 and 172 MPa. Figure 10 compares these results. Plotted in this figure are two cases where the hydraulic horsepower is constant and one case where the horsepower is doubled. These curves show the effect of varying the pressure and flow rates. Lower pressures and greater flow rates are found to be more effective for cutting, assuming the hydraulic horsepowers stay the same. This is particularly true when the cutting pressure is
Traverse speeds" 2 5 - - 1 7 5 mrn/s, right to Pressure: 171.5 MPa Nozzle d i a m e t e r 0 . 8 mm Fig. 9. Typical kerting specimen.
left
An Oscillating Waterjet Deep-Kerfing Technique zA
1. O Jetl¥ = 0*
3. []
1300 r
0 s C . + = S0 o P = 103MPa
Jetl~ = 0¢ 0,Sc.+ = S0 o p = 172MPa
1170
d O = 0.7 m m Pov~" = 28kw
d O = 0,7 m m P o w ~ = 55kw
J~u~ = 0° 0~-+ = 40 ° p = 275 MPa
do = 0,3 m m power = 26 kw
I040 910
g 78O eso
A
11
5O
75
d "6
3$0
130 I
25
1oo
12~
150
175
225
200
Vek~.Ry (mn~T,¢¢}
I
280
Wi~
Fig. 10. C u t t i n g rates.
between two and six times the critical cutting pressure of the material. The phenomenon observed here is in agreement with results of other investigations [5-1. In these tests, doubling the hydraulic horsepower more than doubled the cutting removal rate. This effect can be seen by comparing curve 2 with curves 1 and 3 of Fig. 10. There is, therefore, a physical advantage in increasing the power of the jets. The next parameter studied was the frequency of oscillation. In this series of tests, the feed rate was held constant at 100 mm s-1, and the frequency was varied. Figure 11 shows the results of these tests. As shown, there is an optimum frequency for the area removal rate, which is between 19 and 22 HE. This range corresponds to surface jet velocities between 508 and 584 mm s-1, optimal for linear cutting of these rocks [6]. Thus, for future testing, the frequency of oscillation of the kerfing nozzles can be determined directly from linear cutting data. The next parameter examined was the feed rate of the kerfing nozzle. Again, as with linear cutting, the
'141
depth of cut per pass decreases as the feed rate increases (see Fig. 12). However, the parameter that must be optimized to optimize deep-kerfing performance is the product of the depth per pass and the feed rate. The optimum value of the feed rate can be found by plotting the product of the depth of cut and the feed rate. Figure 13 shows the plots for biotite granite. From this plot it can be seen that the optimum feed rate is approximately 100mm s-1 for this rock type. Data obtained at the optimum feed rate then can be used to predict the performance of trenching and drilling devices once the method of cutting the trench or hole is established. Since most experimental data was taken from single passes, an experiment was conducted to demonstrate that deep slots could be cut. Figure 14 shows a picture of 178-mm deep-kerf cut in sandstone. This cut was made at a feed rate of 25.4 mm s-1 and a pressure of 172 MPa. The stand-off distance was adjusted after every other pass. This cut clearly demonstrated the feasibility of cutting deep slots. In Fig. 14 the wall spacing is relatively constant, and the tool could continue to any desired depth.
6. COMPARISON OF KERFING DATA AND THEORY The kerfing theory discussed in section 3 has been evaluated on several rocks, for which both linear cutting data and kerfing data is available, The tests showed that, in general, the theory can predict the optimum cutting rate. For example, the experimental optimum cutting rate for Wilkeson sandstone at 275 MPa and 26kW is 127mms-1; the theory predicts 124.5 m m s -1 (see Fig. 10). The capability to predict the optimum cutting rate simply by specifying the operating parameters makes it possible to estimate the effectiveness of kerfing for various applications. This capa-
TABLE 1. EXPERIMENTAL DATA
Jilts ~
O s c . ~b
0° 0" 0° 0° 0° 0° 0~ 0° ()~ 0 0° 0° 0° 0~ 0'
50 ° 50' 50" 50 ° 50 ° 50 ° 50" 50 ° 50 ° 50" 50 ° 50 ° 50 ° 50" 50 °
v (mm s 25 51 76 102 127 152 178 254 25 51 76 102 127 137 178
1)
Nozzle pressure 172 172 172 172 172 172 172 172 103 103 103 103 103 103 103
MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa
Volume removal r a t e (m 3 × 109)
Width (mm)
Avg. H (mm)
Max. H (mm)
Min. H (mm)
1.64 2.73 2.67 2.96 3.14 3.14 3.28 5.46 1.0 1.55 1.14 1.18 0 0 0
17 17 15 17-18 14 13 11 14 15 15 14 13 13 13 13
14 12 9 6 6 6 6 5 9 7 4 3 -
20 15 12 8 8 8 8 8 12 8 5 4
13 10 8 5 4 4 --8 5 3 3
.
.
.
-.
-.
42
James M. Reichman and John B. Cheung
PO = 275 MPa do = 0,25 mm I = 12.5mm V f = 4 ips
125
1
Sandstone
Sarn~e #4
Granite
Sample #6
Granite
Sample #5
~----~
/
\
/
100
\
/
E
N
p
N
75
m 50
/b
~E "6
==
/
25
I
I
I
I
I
I
5
10
15
20
25
3O
Frequency of Nozzle Omcillation re (Hz)
Fig. 1 I. The effect of nozzle oscillation frequency on deep kerfing. Biotite Granite PO = 275 MPa t = 12.5mm d O = .25 m m
® 1250 rprn 14Q0 rpm
1,5
A
®
z~
I
I
25
50
I
I
I
75
100
125
Vf (mm/sec)
Fig. 12. Kerfing data: depth of kerv vs feed rate. +
20.5 Hz
[ ] 23 Hz
60
Biotite Granite Po = 343 MPa
4O
! = 12.5mm
[]
% E
~, = 50 °
30
Jets angled at 0 °
20
!
I
I
I
I
25
50
75
100
125
_._
I
I
150
175
Vf mrn/sec
Fig. 13. Kerfing data: area removal rate vs feed rate.
An Oscillating Waterjet Deep-Kerfing Technique
143
Fig. 14. 178 mm deep kerf in sandstone. bility will be valuable in the economic analysis of various kerfing concepts. The results of applying this theory under offoptimum conditions can be seen by plotting dVf v s Vf where the expression for dVr is given by equation (8) and then plotting these results vs the actual cutting data. Figure 15 is a plot of the resultant curve for Wilkeson sandstone at the conditions indicated. Comparison of the experimental curve with the curve predicted by the model shows that at off-optimum conditions the model over-predicts the experimental cutting data by 20-50~o. The discrepancy between model and experiment is not so great that the model cannot be used to estimate the kerfing rates at off-optimum conditions. The model does, however, predict the sharp dropoff that occurs with feed rates above the optimum. One possible reason in this discrepency is that the model curve is based on data obtained with a linear cut made with a single jewel in the kerfing nozzle while the data is for a dual orifice nozzle which produces a poorer quality jet due to the increased flow through the nozzle. If the relationship in equation (9) is used to predict the optimum cutting rate for several granites and limestones tested during this program, it is found that using the average experimental values p = 343MPa, d = 0 . 2 5 4 m m , l = 17.8mm, w = 3d, h = 2.54mm, Vt = 5 1 0 m m s -1, 0 = 25 °, q~ = 50°/180 ° = 0.278, and substituting into equation (9) gives
between 0.76 to 1.27 mm per pass. The area removal rate predicted by the theory is 7 7 m m 2 s-J. This rate compares to experimental values, which ranged from 64.5 to 129 mm 2 s -1 for the granites and limestones tested. These comparisons show that the theory predicts results well within the spread of the experimental data and that it adequately predicts the optimum conditions. 7. C O N C L U S I O N S This study demonstrates that waterjets can cut narrow slots to any reasonable depth (up to 2m). The tool developed for this purpose is an oscillating device, which uses no high-pressure rotary seals. Because motion is imparted to the nozzle by oscillation, not Po = 275 MPa do = 0.3 mrn Wilk~on Sandstone
Vt = 500 mm/sec h = 0.18
5OO
% g aoo
~
Experirne~ Opdmum
200 Theory BO~KIon a Unear Cut With
I/y = 52.3 mm s This value compares to an experimental ~'/between 51 and 76 mm s - 1 for the granites and limestones. The predicted depth of cut from the theory is 1.35 mm per pass, which compares to the experimental depth
5
I 50
I
75
I
100
I 125
1 150
I I I 175 200 225
• 250
Advance Rate Vf (ram/see)
Fig. 15. Kerfing theory vs experimental data (Wilkeson sandstone).
144
J a m e s M. R e i c h m a n and J o h n B. C h e u n g
rotation, and static seals can be used, an oscillating deep-kerr device is inherently a m o r e reliable tool. A physical m o d e l for deep-kerfing developed in this study gives a reasonable correlation between predicted rates based on linear cutting d a t a and actual experim e n t a l results o b t a i n e d from deep-kerfing tests. Use of the model greatly reduces the a m o u n t of testing necessary to determine o p t i m u m kerfing rates and facilitates conducting e c o n o m i c analysis for various waterjet deep kerfing applications at a m i n i m u m const.
Received 19 September 1977; in revised form 4 January 1978
REFERENCES 1. Brook N. & Summers D. A. The penetration of rocks by highspeed water jets. Int. J. Rock Mech. Min. Sci. 6, 249-259 (1969). 2. Olsen J. H. Jet slotting of concrete. BHRA 2nd Int. Jet Cutting Technology, Cambridge, MA (1974). 3. Harris H. D. & Brierly W. H. A rotating device and data on its use for slotting Berea sandstone. Int. J. Rock Mech, Min. Sci. Geomech. Abstr. 11, 359-366 (1974). 4. Crow S. C. A theory of hydraulic rock cutting. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 10, 567-584 (1973). 5. Summers D. A. Paper presented at Workshop on The Application of High-Pressure Water Jet Cutting Technology, University of Missouri at Roila (1975). 6. Huszarik F. A., Reichman J. M. & Cheung J. B. The use of high-pressure water jets for utility construction applications. Presented at ASTM Erosion, Prevention and Useful Applications Conference. Vail. Colorado (19771.
0020-7624/78/0801-0135502.00/0
An Oscillating Waterjet Deep-Kerfing Technique JAMES M. R E I C H M A N * J O H N B. C H E U N G * Cutting deep slots in rock with a waterjet requires a nozzle configuration that can cut a kerf wide enough for the nozzle assembly to enter. A tool for cuttin9 such slots, which utilizes an oscillating mechanism, has been developed. This device uses only static seals and is inherently more reliable than a rotating device. Deep kerfing with waterjet should have applications in the areas of tunneling, mining, quarrying and trenching. The deep-kerfin9 tests have been conducted on a variety of rock. Based on test data, a physical model that can predict cutting rates has been developed. 7his model permits the study of various applications of deep-kerfing nozzles without requiring expensive experimental test programs.
1. I N T R O D U C T I O N Waterjet cutting applications in mining and tunneling operations have been limited in the past because deep slots, or kerfs, could not be made. With the ability to make deep kerfs, the possible applications of waterjets increase substantially. Some areas where deep-kerfing devices could be beneficial include tunneling, mining, quarrying and trenching. In these applications deepkerf waterjets could increase production or advance rates by increasing cutting rates and by decreasing the wear, and as such, the operating life of mechanical cutting devices. A single small-diameter waterjet can penetrate a slot only a limited distance before it 'bottoms out'l-l,2]. The reason for this limitation is believed to be that, in a narrow slot or kerr, the force of the jet is dissipated by the wall interaction with the free jet. Even if multiple, closely-spaced slots are cut, the depth to which the jets can penetrate into the slot is finite because the centerline pressure of the jet decays with the distance from the nozzle exit and becomes too small to cut effectively. In this paper, the development of a waterjet deep-kerfing device that overcomes these limitations is presented. Cutting deep slots or kerfs requires a slot wide enough for the nozzle to enter. With a wide slot, an optimum stand-off distance can be maintained between the nozzle and the material face to achieve the most effective cutting. If a constant stand-off distance is maintained, the jet can theoretically cut to any desired depth. Of the several ways of making a cut wider than the cutting nozzle, the most expedient is to use some form of rotating nozzle with angled jets to achieve the * Flow Industries. Inc.. Kent. WA 98031, U.S.A.
desired slot width. The inside of the slot can be completely covered using a device of this sort. Harris and Brierley [3] suggested such a device as an extension of their work on a rotating waterjet device. During development work on a rotating waterjet device for cutting deep kerfs, it was found that the critical problem was not the nozzle development, but the development of a reliable high-pressure (170~08 MPa) swivel. Since there was no apparent near-term solution to this problem, a non-rotating device was developed. This device consists of an oscillating nozzle assembly, in which the torsional flexibility of the tubing allows the nozzle to oscillate. Like a rotating nozzle device, a nozzle oscillating over a limited angle completely covers the material in the slot, but has none of the seal problems inherent in a high-pressure swivel. This study involved the development of the deepkerfing device, as well as the development of the oscillating nozzle. A kerfing model was developed, some experimental data were taken, and cutting rates were established for various applications. Results of this study show that: (a) deep-kerfing is feasible, (b) a reliable deep-kerfing device (with no high-wearing swivels) can be developed, (c) the device must be optimized for each application, and (d) a model for deep-kerfing can be used to find optimum conditions based on linear cutting data. 2. E X P E R I M E N T A L A P P R O A C H
2.1. Tool selection As mentioned in the Introduction, cutting deep slots requires a kerf that is sufficiently wider than the nozzle so that the nozzle can enter the kerf freely. The width of the slot is minimized to reduce the amount of mater135
i36
James M. Reichman and John B. Cheung
j-J
J
J
Side View of the Nozzle
{a) JewelOrifice
© FeedDirection of Rock 1
- - Front-FacingJet . . . . Reer-FacingJet (~ (b)
MetalOrifice
Fig. 1. Deep-kerf nozzles.
ial removed, and therefore the energy required to cut the slot is minimized. A narrow slot can best be made with a small nozzle assembly that consists of one or more angled jets. By angling the jets at a sufficiently steep angle, a kerf wider than the nozzle assembly can be obtained. Therefore, all the nozzles investigated in this program had angled jets. Additionally, a two-jet nozzle was used to balance the lateral forces on the nozzle. This balance is necessary because any wobble in the nozzle is undesirable, particularly when cutting slots with a depth of 1.5 m or more. Two similar nozzle designs were considered for this program; both were two-jet nozzles with the jets angled at 0.436 rad. One nozzle used sapphire jewel orifices while the other used nozzles machined in the nozzle body. Schematics of both types of nozzles are shown in Fig. 1. The sizes chosen for the nozzle exits were determined by the hydraulic power that was available and necessary to cut the rock.
Fig. 2. Coverage pattern for an oscillating jet.
lating nozzle. Two jets oscillating over a limited angle can completely cover the slot and will make a cut wide enough to allow the nozzle to freely enter the kerf. Figure 2 shows a schematic of the pattern covered by such a two-jet nozzle. The oscillating nozzle device has static seals; thus, the new tool is reliable and requires little maintenance. There are none of the inherent weaknesses of using high-pressure rotary seals. The oscillating nozzle device is, therefore, superior to rotating devices, and it makes deep-kerfing a more practical concept. A schematic of the device is shown in Fig. 3.
TubeConnector __
E
~] RigidMount
2.2. Nozzle motion The nozzle for deep-kerfing must move so that the nozzle completely covers the material and leaves no ridges which could potentially catch the nozzle. The initial approach was to use a nozzle rotating 2re rad to achieve coverage of the slot. This method proved to be inadequate because of the high wear rate of rotary seals at high pressures. The high speed of rotation is necessary to obtain an optimum linear traverse velocity for the jet, which for most rock is in excess of 500 mm s - 1. The high speed of rotation required to cut some rocks efficiently complicated the problem. It was obvious that an alternative method of achieving the motion was necessary if deep kerfing was to be a viable tool prior to the development of more reliable rotating seals for swivels. The selected method of nozzle motion uses an oscil-
Twist Length
3/8Tube Motor, VariableSpeed
Bearing~ r _ 1 AttachL-rx--r-l~J Arm [ ~
~(~Z~
MotorAttach~ate
TieRod
Nozzle~ ~-Tubingof LengthLWhich "/~ ActuallyEnterstheSlot
Fig. 3. System schematic for an oscillating deep-kerf device.
An Oscillating Waterjet Deep-Kerfing Technique 2.3. Rock selection Various well-characterized rocks, ranging from sandstone to granite, were tested to verify the feasibility of the deep-kerf concept. Deep-kerfing proved to be a feasible process for all the rocks tested. A parametric study on Wilkeson sandstone was conducted by varying the feed rate, oscillation rate, pressure and nozzle diameter. Wilkeson sandstone, found in western Washington State, has been used extensively by several investigators [4-1, so linear waterjet cutting data is available. Consequently, most of the data presented in this paper is for Wilkeson sandstone. Data for kerfing a variety of granites and limestones are also presented.
3. EXPERIMENTAL APPARATUS The pressure for the tests, which ranged from 103 to 412 MPa, was supplied by one or other of two Flow Industries, Inc., high-pressure intensifiers. One intensifier supplied 9.5 × 10-s mS s ~ of water at pressures up to 412 M P a and is rated at 37.3 kW. This intensifier was used in the small jet tests. For tests with larger diameter jets, a mobile, diesel-powered, 190 kW intensifier was used. This unit is capable of delivering 4.7 x 1 0 - 4 m S s -1 at 384MPa. The intensifier pumps were used to power nozzles ranging in size from 0.2 to 0.7 ram. The nozzle assemblies for the tests are shown in Fig. 1. The pressure at the nozzles was measured by a high-pressure gauge. The specimens for both linear-cutting and deep-kerfing tests were rigidly mounted on a test table. The nozzles were mounted on a traversing mechanism, which gives x-y-z motion. In the y direction the nozzle speed could be varied from 25.4 to 254 mm s-1. In addition, a rotary table was used to obtain linear velocities up to 508 mm s - l . For tests in which a rock was cut to any great depth, the z traverse (perpendicular to the rock face) was used in a stepwise manner, after a specified number of traverses. Thus, an effective cutting distance was maintained between the nozzle and cutting surface. A variable-speed 1.5kW motor powered the oscillator for the deep-kerf experiments. The oscillation frequency of the device could be varied between 8.3 and 33.3 Hz. The oscillation frequency that was used for each rock was chosen from the linear cutting data since oscillation frequency and linear nozzle-cutting velocity are directly related. For a stand-off distance of 0.5 in., the oscillation range available from the device corresponds to a traverse velocity of 190-762 mm s-1
4. KERFING M O D E L There are two ways of determining the cutting rates of a deep-kerfing nozzle. The first is by experimenting with the nozzle; the second is by developing a mathematical model, based on the rock removal mechanism of kerfing, which can predict kerfing rates and optimum
137
conditions from linear cutting data. A model that predicts the performance of a kerfing nozzle, based on the physical layout of the kerfing nozzle, the linear cutting data, and the operational parameters has been developed. Consider an oscillating angled jet impacting a rock surface operating in the mode shown in Fig. 6a. The jet cuts a circular arc in the rock, to a depth equal to the cosine of the angle of incidence (0) times h, the depth of cut when the angle is zero. The path of the moving jet is similar to that shown in Fig. 2. As an approximation, if co is high (about 20 Hz), and if the translation velocity is small (about 127mms-1), the cuts can be considered straight and parallel. If a second angled jet ( - 0 ) is moved along the work piece, it cuts parallel slots which intersect the slots of the first jet. This cutting pattern is shown in Fig. 4. The result of the motion of the two nozzles is that material is removed, and ridges are left along the bottom of the cuts. The size of the ridges is a function of the cutting parameters of the nozzle. The width of the cut is defined by the angle of oscillation q~. Changing the angle of the jet, the feed rate of the jet, or the oscillation of the jet changes the amount of material that remains in the slot. The predictions, based on this model, are presented below. As was previously stated, the depth of the cut in the slot is D = /1 cos 0.
(1)
The average spacing between slots S (ram) is
S _ V: 2o) 60
S = 30V:,
(2)
o) where ~o = oscillation frequency (counts/min), and V: = nozzle feed velocity (ram s-1). The rate of material removal can be defined by d V: where d is defined as overall or effective depth, and
d=D-D' and D' is the height of the ridges.
S Nozzle Centerline, Front-FacingJetL07 ~ dS
Hw
I [I £k~\, ,
/
Z'Y" D
,~.~//%// ,,,/%\/
Ma,.ia,RomovJ
\v /
~" MaterialRemaining Fig. 4. Kerfing model.
\,
/-- Centerline, Rear-FacingJet
138
James M. R e i c h m a n and J o h n B. C h e u n g
(a) Deep-kerfing cut
(b)
Three
parallel cu-l-s (mult-iple pass)
(clear
slol-
depth
= 51 m m )
Fig. 5. Oscillating kerfing cuts and parallel linear cuts.
M a x i m i z a t i o n of the material removal rate with respect to the feed velocity Vs can be obtained by setting --(dV~)
evz
= 0
,~;~[D(1- ~)V~] = O.
and D'
S
w
D - 2h sin 0
2h sin/)'
where w is the projected width of the cut. With the relationships
t3,
F r o m Fig. 4 it can be s h o w n that
30 Vr S
~
- - -
and 15l/~
D'
2 tan 0
2 tan 0'
(5)
(41
(O
7D'(~ '
An Oscillating Waterjet Deep-Kerfing Technique
oioo
where r = projected radius of oscillation of the jet (mm), q~ = angle of oscillation (rad), and V~ = linear traverse velocity (mm s- t) equation (5) can be rewritten as
D' D
rcr@ Vf hsinO 1/,
W
/,i÷~ ~=0 (al
(6)
2h sin 0
139
Furthermore, since r = I tan 0, where I is the stand-off distance, equation (6) becomes
D' D
rclq~ h cos 0
Vf
w 2h sin 0"
(7)
tp=x
(b)
Substituting equation (7) into dV: gives d V / = hcos 0(1
,~ = Rotation angle
rcl~ v: + h c o s 0 V~ 2h~nO
vs.
~u = Measurementof the initial nozzle angle with respectto the table motion
(8)
Fig. 6. Nozzle oscillation.
Equation (3) becomes 1+
w 2h sin 0
2glq~ Fy h cos 0 Vt
0,
and 17/_ V t h c o s 0 ( w ) 2rtl~ 1 + 2hsin~ '
(9)
where V: = optimum feed rate. The optimum material removal rate d Vy is given by dV:-
h 2 c°s2 OFt( 1 + - W ) 2" 47rl~ 2h sin 0
(10)
With this relationship, the optimum cutting rate can be predicted. In addition, equation (8) can be used to predict the rate of material removal dV/ at various forward advance rates Vr. 5. E X P E R I M E N T A L RESULTS Experiments were conducted on sandstone, granite and limestone. A typical kerf created by the oscillating nozzle is shown in Fig. 5a. The kerf shown in this figure was cut in granite by two 0.3-mm jets at 275MPa. The kerf was 51mm deep and was cut in 14 passes at a feed rate of 25.4 mm s- 1. As a comparison to deepkerf cutting, Fig. 5b shows linear cuts in concrete made by a single nozzle, with two parallel cuts spaced 6.35 mm apart. In this test, the pressure was 412 MPa, the nozzle diameter was 0.79mm, and the feed rate was 25.4 mm s-1. Comparison of the two pictures in Fig. 5 shows that the deep-kerf tool gives a wide slot (25.4mm) with parallel walls, which would allow cutting to any depth. The cut made in concrete tapers and is not wide enough for the nozzle to enter. The actual depth of the clear slot is only about 51 ram, and the jet has "bottomed out'. Figure 5a clearly demonstrates the type of cut necessary for kerfs of any depth. The oscillating device can be operated in two modes : in the first, the two jets point in the direction of translation (0 = 0) and oscillate with some fixed amplitude th about this initial position; in the second, the jets point outward at a predetermined angle 0, and oscillate
inward. The angles for these cases are shown in Fig. 6. For each of these modes both the angle of rotation needed for uniform coverage and a slot width greater than the diameter of the nozzle must be determined. The optimization for each case is shown in Figs. 7 and 8. Figure 7 shows the various oscillation angles and the resulting slot widths. Figure 8 shows the variation of q~ with a non-zero 0. The resulting kerf widths in these tests were all between 12.7 and 17.8 mm. The kerfing efficiency experiments were conducted with a constant stand-off distance of 12.7 mm between the nozzle and the rock. For one series of tests the pressure was fixed and the feed rate varied for a given diameter nozzle at a fixed ~b and 0. The feed rate was changed from 25.4 to 254 mm s- 1 in 25.4 mm s- 1 intervals. After each pass of the nozzle at a given feed rate, the maximum, minimum and average depths of the kerf were recorded. The block was then moved over, and
Jet Pressure
275 MPa
Standoff Distance
12.7 mm
Jet Angle
25 °
Jet Position
~ = 0
Width
(m)
Depth
(m)
50
17
1O
45
15
12
40
15
iO
35
13
12
Kerr Shape
- ~
Fig. 7. Kerfingtests; variation of ~b, 0 = 0'.
140
James M. Reichman and J o h n B. Cheung NPa
Jet Pressure
275
Standoff Distance
12.7 mm
Jet Angle
25 °
Jet P o s i t i o n
~ = 45 °
Minimum Depth (mm)
25
0
30
0
35
0.254
40
9.1
4~
7,6
Kerr Shap~
Fig. 8. Kerfing tests; variation of q~, ~O = 45".
another pass was made. Typical specimens are shown in Fig. 9, and the data from several series of tests in Wilkeson sandstone are shown in Table 1. Nozzle orifices of two sizes were used in the first series of tests on Wilkeson sandstone. The small jets were 0.3 m m in diameter while the large jets had a diameter of 0.7 mm. The small jets were run at 206 and 2 7 5 M P a , while the large jets were run at 103 and 172 MPa. Figure 10 compares these results. Plotted in this figure are two cases where the hydraulic horsepower is constant and one case where the horsepower is doubled. These curves show the effect of varying the pressure and flow rates. Lower pressures and greater flow rates are found to be more effective for cutting, assuming the hydraulic horsepowers stay the same. This is particularly true when the cutting pressure is
Traverse speeds" 2 5 - - 1 7 5 mrn/s, right to Pressure: 171.5 MPa Nozzle d i a m e t e r 0 . 8 mm Fig. 9. Typical kerting specimen.
left
An Oscillating Waterjet Deep-Kerfing Technique zA
1. O Jetl¥ = 0*
3. []
1300 r
0 s C . + = S0 o P = 103MPa
Jetl~ = 0¢ 0,Sc.+ = S0 o p = 172MPa
1170
d O = 0.7 m m Pov~" = 28kw
d O = 0,7 m m P o w ~ = 55kw
J~u~ = 0° 0~-+ = 40 ° p = 275 MPa
do = 0,3 m m power = 26 kw
I040 910
g 78O eso
A
11
5O
75
d "6
3$0
130 I
25
1oo
12~
150
175
225
200
Vek~.Ry (mn~T,¢¢}
I
280
Wi~
Fig. 10. C u t t i n g rates.
between two and six times the critical cutting pressure of the material. The phenomenon observed here is in agreement with results of other investigations [5-1. In these tests, doubling the hydraulic horsepower more than doubled the cutting removal rate. This effect can be seen by comparing curve 2 with curves 1 and 3 of Fig. 10. There is, therefore, a physical advantage in increasing the power of the jets. The next parameter studied was the frequency of oscillation. In this series of tests, the feed rate was held constant at 100 mm s-1, and the frequency was varied. Figure 11 shows the results of these tests. As shown, there is an optimum frequency for the area removal rate, which is between 19 and 22 HE. This range corresponds to surface jet velocities between 508 and 584 mm s-1, optimal for linear cutting of these rocks [6]. Thus, for future testing, the frequency of oscillation of the kerfing nozzles can be determined directly from linear cutting data. The next parameter examined was the feed rate of the kerfing nozzle. Again, as with linear cutting, the
'141
depth of cut per pass decreases as the feed rate increases (see Fig. 12). However, the parameter that must be optimized to optimize deep-kerfing performance is the product of the depth per pass and the feed rate. The optimum value of the feed rate can be found by plotting the product of the depth of cut and the feed rate. Figure 13 shows the plots for biotite granite. From this plot it can be seen that the optimum feed rate is approximately 100mm s-1 for this rock type. Data obtained at the optimum feed rate then can be used to predict the performance of trenching and drilling devices once the method of cutting the trench or hole is established. Since most experimental data was taken from single passes, an experiment was conducted to demonstrate that deep slots could be cut. Figure 14 shows a picture of 178-mm deep-kerf cut in sandstone. This cut was made at a feed rate of 25.4 mm s-1 and a pressure of 172 MPa. The stand-off distance was adjusted after every other pass. This cut clearly demonstrated the feasibility of cutting deep slots. In Fig. 14 the wall spacing is relatively constant, and the tool could continue to any desired depth.
6. COMPARISON OF KERFING DATA AND THEORY The kerfing theory discussed in section 3 has been evaluated on several rocks, for which both linear cutting data and kerfing data is available, The tests showed that, in general, the theory can predict the optimum cutting rate. For example, the experimental optimum cutting rate for Wilkeson sandstone at 275 MPa and 26kW is 127mms-1; the theory predicts 124.5 m m s -1 (see Fig. 10). The capability to predict the optimum cutting rate simply by specifying the operating parameters makes it possible to estimate the effectiveness of kerfing for various applications. This capa-
TABLE 1. EXPERIMENTAL DATA
Jilts ~
O s c . ~b
0° 0" 0° 0° 0° 0° 0~ 0° ()~ 0 0° 0° 0° 0~ 0'
50 ° 50' 50" 50 ° 50 ° 50 ° 50" 50 ° 50 ° 50" 50 ° 50 ° 50 ° 50" 50 °
v (mm s 25 51 76 102 127 152 178 254 25 51 76 102 127 137 178
1)
Nozzle pressure 172 172 172 172 172 172 172 172 103 103 103 103 103 103 103
MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa MPa
Volume removal r a t e (m 3 × 109)
Width (mm)
Avg. H (mm)
Max. H (mm)
Min. H (mm)
1.64 2.73 2.67 2.96 3.14 3.14 3.28 5.46 1.0 1.55 1.14 1.18 0 0 0
17 17 15 17-18 14 13 11 14 15 15 14 13 13 13 13
14 12 9 6 6 6 6 5 9 7 4 3 -
20 15 12 8 8 8 8 8 12 8 5 4
13 10 8 5 4 4 --8 5 3 3
.
.
.
-.
-.
42
James M. Reichman and John B. Cheung
PO = 275 MPa do = 0,25 mm I = 12.5mm V f = 4 ips
125
1
Sandstone
Sarn~e #4
Granite
Sample #6
Granite
Sample #5
~----~
/
\
/
100
\
/
E
N
p
N
75
m 50
/b
~E "6
==
/
25
I
I
I
I
I
I
5
10
15
20
25
3O
Frequency of Nozzle Omcillation re (Hz)
Fig. 1 I. The effect of nozzle oscillation frequency on deep kerfing. Biotite Granite PO = 275 MPa t = 12.5mm d O = .25 m m
® 1250 rprn 14Q0 rpm
1,5
A
®
z~
I
I
25
50
I
I
I
75
100
125
Vf (mm/sec)
Fig. 12. Kerfing data: depth of kerv vs feed rate. +
20.5 Hz
[ ] 23 Hz
60
Biotite Granite Po = 343 MPa
4O
! = 12.5mm
[]
% E
~, = 50 °
30
Jets angled at 0 °
20
!
I
I
I
I
25
50
75
100
125
_._
I
I
150
175
Vf mrn/sec
Fig. 13. Kerfing data: area removal rate vs feed rate.
An Oscillating Waterjet Deep-Kerfing Technique
143
Fig. 14. 178 mm deep kerf in sandstone. bility will be valuable in the economic analysis of various kerfing concepts. The results of applying this theory under offoptimum conditions can be seen by plotting dVf v s Vf where the expression for dVr is given by equation (8) and then plotting these results vs the actual cutting data. Figure 15 is a plot of the resultant curve for Wilkeson sandstone at the conditions indicated. Comparison of the experimental curve with the curve predicted by the model shows that at off-optimum conditions the model over-predicts the experimental cutting data by 20-50~o. The discrepancy between model and experiment is not so great that the model cannot be used to estimate the kerfing rates at off-optimum conditions. The model does, however, predict the sharp dropoff that occurs with feed rates above the optimum. One possible reason in this discrepency is that the model curve is based on data obtained with a linear cut made with a single jewel in the kerfing nozzle while the data is for a dual orifice nozzle which produces a poorer quality jet due to the increased flow through the nozzle. If the relationship in equation (9) is used to predict the optimum cutting rate for several granites and limestones tested during this program, it is found that using the average experimental values p = 343MPa, d = 0 . 2 5 4 m m , l = 17.8mm, w = 3d, h = 2.54mm, Vt = 5 1 0 m m s -1, 0 = 25 °, q~ = 50°/180 ° = 0.278, and substituting into equation (9) gives
between 0.76 to 1.27 mm per pass. The area removal rate predicted by the theory is 7 7 m m 2 s-J. This rate compares to experimental values, which ranged from 64.5 to 129 mm 2 s -1 for the granites and limestones tested. These comparisons show that the theory predicts results well within the spread of the experimental data and that it adequately predicts the optimum conditions. 7. C O N C L U S I O N S This study demonstrates that waterjets can cut narrow slots to any reasonable depth (up to 2m). The tool developed for this purpose is an oscillating device, which uses no high-pressure rotary seals. Because motion is imparted to the nozzle by oscillation, not Po = 275 MPa do = 0.3 mrn Wilk~on Sandstone
Vt = 500 mm/sec h = 0.18
5OO
% g aoo
~
Experirne~ Opdmum
200 Theory BO~KIon a Unear Cut With
I/y = 52.3 mm s This value compares to an experimental ~'/between 51 and 76 mm s - 1 for the granites and limestones. The predicted depth of cut from the theory is 1.35 mm per pass, which compares to the experimental depth
5
I 50
I
75
I
100
I 125
1 150
I I I 175 200 225
• 250
Advance Rate Vf (ram/see)
Fig. 15. Kerfing theory vs experimental data (Wilkeson sandstone).
144
J a m e s M. R e i c h m a n and J o h n B. C h e u n g
rotation, and static seals can be used, an oscillating deep-kerr device is inherently a m o r e reliable tool. A physical m o d e l for deep-kerfing developed in this study gives a reasonable correlation between predicted rates based on linear cutting d a t a and actual experim e n t a l results o b t a i n e d from deep-kerfing tests. Use of the model greatly reduces the a m o u n t of testing necessary to determine o p t i m u m kerfing rates and facilitates conducting e c o n o m i c analysis for various waterjet deep kerfing applications at a m i n i m u m const.
Received 19 September 1977; in revised form 4 January 1978
REFERENCES 1. Brook N. & Summers D. A. The penetration of rocks by highspeed water jets. Int. J. Rock Mech. Min. Sci. 6, 249-259 (1969). 2. Olsen J. H. Jet slotting of concrete. BHRA 2nd Int. Jet Cutting Technology, Cambridge, MA (1974). 3. Harris H. D. & Brierly W. H. A rotating device and data on its use for slotting Berea sandstone. Int. J. Rock Mech, Min. Sci. Geomech. Abstr. 11, 359-366 (1974). 4. Crow S. C. A theory of hydraulic rock cutting. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 10, 567-584 (1973). 5. Summers D. A. Paper presented at Workshop on The Application of High-Pressure Water Jet Cutting Technology, University of Missouri at Roila (1975). 6. Huszarik F. A., Reichman J. M. & Cheung J. B. The use of high-pressure water jets for utility construction applications. Presented at ASTM Erosion, Prevention and Useful Applications Conference. Vail. Colorado (19771.