Measurement of forces, temperatures and wear of PDC cutters in rock cutting

Wear, 169 (1993)

Measurement rock cutting F.C. Appl, Department

(Received

9

9-24

of forces, temperatures

C. Carl Wilson

of Mechanical

Engineering,

and wear of PDC cutters in

and Induvadan

Lakshman

D&and

State

Hall, Kansas

August 24, 1992; revised and accepted

University,

Manhattan,

KS 66506-5106

(USA)

April 22, 1993)

Abstract The introduction of PDC bits in the oil well industry by General Electric in 1973 was a significant advancement in drilling technology. To understand the potential of these bits, cutting mechanics and heat transfer models were previously developed. In the current work a series of cutting experiments was made on granite rock in order to understand better the effects of cutter temperatures and forces on PDC bit life, especially the existence of a critical temperature. The experiments consisted of cutting granite cylinders on a lathe with a single PDC cutter. During the tests, cutter forces were measured with a lathe dynamometer and cutter temperatures were measured with thermocouples mounted on the cutter. The cutting fluid used was either an air jet, air mist jet or a water jet. The force and temperature data were recorded by a computer data acquisition system, and wear profiles of the cutters were determined by measurements with dial indicators. A new cutter wear model has been developed from the cutting experiments, and the theory agrees well with experimental data. It has been learned that cutting of hard formations is possible by controlling the temperature of PDC cutters, within the critical limit, with an adequate amount of cooling. Another significant result is that the contact stress on the carbide is not negligible, which is contrary to what was previously believed. This is a practical disadvantage for drilling because it leads to higher forces on the cutters. This often results in lower penetration rates because of bit weight limitations.

1. Introduction

PDC bits have proved successful in drilling soft to medium rock formations because they achieve high rates of penetration (ROP) while also maintaining long bit life [l]. Because of this success it is desired to obtain these same benefits in drilling harder formations, or soft formations with hard stringers. In drilling harder formations, however, both ROP and bit life may be substantially reduced, owing to the combined effects of increased stresses on the cutters, increased abrasive wear rate and larger scale fracture or chipping of the cutters. Furthermore, it has recently been shown [2] that bit whirling causes severe cutter impact which results in severe chipping, especially when the cutters are new and unworn. This leads to rapid formation of large wear flats, which means that bit weight must be increased to maintain ROP. High cutter temperatures may then result if hydraulic cleaning and cooling of the cutters is marginal or inadequate. Recently developed low-friction gauge bits [2] promise to greatly reduce or eliminate bit whirling, in which case bit life will depend primarily on the abrasive wear rate of the cutters.

0043-1648/93/$6.00

The abrasive wear rate of PDC cutters depends not only on the rock properties but also on the temperature developed at the diamond-rock interface of the cutter wear flats. An indirect correlation of cutter wear rate with temperature was found by Lee and Hibbs [3] who conducted lathe cutting tests with single PDC cutters at various cutting velocities. Wear rate gradually increased with velocity up to 125 m min-‘, above which there was an abrupt increase of roughly an order of magnitude. It was suspected that this was due to increased cutter temperature, resulting from the increased cutting velocity. Further evidence of this was found by conducting a series of microhardness OS. temperature tests on the same type of cutters. There was a gradual decrease in the hardness up to a critical temperature of about 700 “C, above which the hardness decreased abruptly. Ortega and Glowka [3] report further work by Hibbs who measured cutter temperature by thermocouples in cutting tests on Tennessee marble using cutters with pre-ground wear flats. The maximum temperatures in these tests were of the order of 200 “C and hence well below the critical diamond temperature. Glowka and Stone [4] found a correlation of theoretically predicted wear flat temperatures with cutter

0 1993 - Elsevier

Sequoia.

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wear rates from previously obtained experimental cutting tests. They concluded that the critical temperature was 350 “C. From this they derived an equation for the critical normal force on a cutter which corresponded to the critical temperature [5]. Glowka [6] continued this work by establishing empirical relations for cutter forces for new and worn cutters based on cutting tests. However, the wear flats were not test-worn, but either machine-ground, laboratory-worn or field-worn on drill bits. All indications are that the wear rate of PDC cutters is significantly affected by cutter temperature, but there have not been any direct cutting tests in which both the cutter temperature and the cutter wear rate were determined experimentally. Therefore, to help clarify the effect of temperature on wear rate, a series of cutting tests was made by cutting granite cylinders on a conventional lathe with single PDC cutters. The temperatures at three locations on the cutters were measured by means of thermocouples, and cutting forces were measured by a strain gauge force dynamometer. Data was recorded simultaneously during the cutting process by a computerized data acquisition system. The specific objectives of this work may be summarized as follows: 1. Develop experimental techniques to measure cutter forces and cutter temperature simultaneously during controlled rock cutting tests of granite rock with PDC cutters. 2. Develop experimental techniques to apply and con-, trol different types of cutting fluids. 3. Develop experimental and analytical methods to determine the volume of diamond wear, volume of carbide wear, volume of rock removed, diamond wear “flat” area and carbide wear “flat” area for each series of cutting tests conducted with one cutting edge of a PDC cutter. 4. Determine the correlation of cutter forces with the depth of cut, diamond wear flat area and carbide wear flat area. This includes the transition from new to worn cutters. It is especially desired to separate the cutting components of the forces (due to the cutting action on the rake face) and the components which arise due to rubbing between the diamond and carbide wear flats and the rock. This will allow determination of the normal and tangential stresses which occur on the diamond and carbide portions of the wear flat, and hence the respective coefficients of friction. Previously developed cutting theory will be used to find the portions of the cutter forces which occur on the rake face. 5. Determine the correlation of cutter temperature with cutter forces and wear flat area. 6. Determine the correlation of diamond wear rate with depth of cut, wear flat area and cutter tem-

7. Experimentally observe cuttrr htlrnout and determine the c.ritical tcmpcraturc* ot rhc, ;llamond whcrc thr Wt’;lt r;Itc‘ iirarnati‘.ali~. IIICl'c'ilSCS

2. Experimental techniques The rock cutting experiments were carried out on granite cylinders, which represents one of the hardest formations in oil well drilling. The experiments involved cutting the granite cylinders on a lathe using a single PDC cutter. Two types of granite cylinder were used in the tests: Georgia granite and Barre granite. The Georgia granite cylinders were 203 mm diameter by 254 mm long and the Barre granite was 229 mm diameter by 216 mm long. The experimental setup consisted of a conventional lathe with electronic speed control,
11

Fig. 2. Bracket to hold the PDC cutter.

the cutting tip. The portion within 5.72 mm of the tip was open and exposed to chips and the cutting fluid. The purpose of the ceramic was to isolate the diamond face thermally (i.e. a metal clamp would act as a heat sink). 2.2. ~~a~~rement of cutting forces The tool holder containing the cutter was supported by a 3 axis strain gauge type force dynamometer mounted on the lathe cross slide, The dynamometer was custom built for this purpose by Lebow. The x-direction is the normal or radial direction of the rock cylinder, the ydirection is the circumferential or cutting direction and the r-direction is the side or feed direction towards the tail stock. The dynamometer was designed for force ranges O-Z.7 kN for X, O-1.8 kN for y and O-l.8 kN for z with an allowance of 50% overload. Cutting forces were sampled at 1 s intervals, and since there was a considerable amount of fluctuation, the forces were plotted using a moving 10 s average. Moving averages of the force data were calculated by a Lotus l-2-3 macro. 2.3. ~~asur~rnent of cutter t~m~eraiur~~ Three type K thermocouples were located on the cutter at positions as shown in Fig. 3. The most important temperature measurement was T, because it was closest to the cutting tip. It was desired to measure the temperature at the diamond carbide interface close to the tip. To do this a 1.78 mm hole was drilled into the carbide backup by EDM to within about 0.254 mm of the diamond layer. The centre of the hoIe was 2.54 mm from the cutting tip. ThermocoupIe wires (0.254 mm diameter} were spark welded to the thin layer of carbide at the bottom of the hole. After verifying that the wires were separated above the welded junction and that they did not touch the sides of the hole, the hole was filled with high-temperature ceramic epoxy. As a check on the temperature T, a the~ocouple junction was located on the top surface of the diamond between the square ceramic insert and the diamond surface. It was located approximately 6.38 mm from the cutting tip. Since it was not possible to weld it to the diamond, a junction was formed by clamping two

---r6.635

T

3.5 3

1

Fig. 3. Thermocouple

locations

on the PDC cutter.

crossed thermocouple wires between the ceramic and the diamond. Since the diameter of the wires was only 0.127 mm, the wires had su~cient ductility to be readily flattened out, and in the process form a good junction which was in intimate contact with the surface of the diamond. The measured values of temperature at this junction, T,, followed the values of T,. This was reassuring because T, was located only about 3.8 mm further from the tip than T,. The third temperature junction T3 was located on the centre of the bottom surface of the cutter on the carbide layer. The junction was formed by spark welding directly to the carbide. As expected, the values of temperature 7; were lower than values of T2 because of the greater distance from the cutting tip. The values did, however, track T, and 7’:! rather well. 2.4. Cutting jluids: eflects on forces, temperature and wear rate

Experimental cutting tests were made using dry air, air mist or tap water as the cutting fluid. The fluid was applied during the test by a single jet mounted vertically 33 mm above the tip of the cutter. It was found early in the test program that the dry air and air mist removed the chips satisfactorily but did not

12

F.C. Appl ef al. I Forces, rempertrtures and wear of I’DC‘ cuttm

provide sufficient cooling. Forces and temperatures were low when beginning a series of cuts with a new cutter because the cutter has a sharp cutting edge. Soon after cutting begins, however, the cutting edge begins to chip and the diamond begins to wear, forming a wear flat. As the flat grows larger it progresses into the carbide. During the cutting process the diamond and carbide wear flats rub against the rock surface and consequently there are normal and tangential stresses on these areas. The tangential stresses are caused by rubbing friction and hence there is a substantial amount of heat generated at the interface of the wear flat and the rock surface. Therefore the cutting forces and temperatures increase as cutting continues. In turn, the increased normal force and temperature at the sliding interface cause the wear rate of the cutter to increase and hence the cutter wear flat area increases at an increasing rate. The wear rate of the cutter is primarily controlled by the diamond wear rate because the abrasive wear resistance of diamond is of the order of 100 times greater than that of carbide. Furthermore, the wear rate of diamond increases as temperature increases. As the area of the wear flat continues to increase more rapidly, the temperature of the diamond soon reaches the critical level where the diamond loses its mechanical strength and the wear rate becomes catastrophic, resulting in cutter failure. When using dry air or air mist the cutters usually failed during the second or third cut of the series. At failure, the rapid rise in forces and temperatures was quite dramatic (Fig. 4).

Fig. 4. Typical experimental

data. Force

and temperature

in rock cuthg

‘I‘he tests with air and air mist titc not reprcscntativr: of diamond bit drilling, whcrc the cutters are imtnerscd in drilling mud which is continualiy circulated between the bit face and the rock surface. Water-based muds arc commonly used, so tap water was used as the cutting fluid

for

most of the laboratov

zutting

cxperinlcnts

The water was applied by means ot ;I 0.79 mm diamctcl jet located 33 mm above the till CI~the cutter. Thiz provided both chip removal and cooling of lhc cutter In fact, the effect of water cooling was dramatic compared with that of air or mist. With an ample supply of water the cutter temperatures could be maintained at much lower levels during the course of a considerable number of cuts. The water removed a substantial part of the heat generated at the cutting tip. The difference between using water or ,iir waq even greater than expected.

2.5. Wear measurements

Wear measurement is one of the important considerations in the present study. The wear profile of the diamond cutting edge was measured using a dial indicator with a wedge-shaped stylus. This dial indicator was mounted on a fixture attached to the tail stock of the lathe. Before the first cut, when the cutter was new, the profile of the cutter was taken by moving the cutting edge (held by the tool holder and mounted on the tool post) using the lathe carriage. The variation of the profile of the cutting edge of the cutter was recorded at 0.254 mm intervals of carriage travel. These intervals

vs. time for test series 2, cut No. 25.

F.C. Appl et al. I Forces,

temperatures

were determined by another dial indicator mounted on the lathe bed, which measured carriage movement. At the end of each run the cutting edge was observed under good lighting and often, even if only slight wear was detected, the profile was taken. The profiles taken after different runs were plotted on large sheets of graph paper for better understanding. As the tests were progressing, the importance of cutter wear profiles was recognized and profiles were then taken more frequently. To calculate the volume of diamond wear and the volume of carbide wear the geometry of the cutter was carefully studied and numerical integration was used to calculate these wear volumes. A computer program was written to do this. The projected length and projected area of the wear flats were also calculated.

3. Description

of experiments

The objective of the experiments was to determine how wear rate depended on cutter temperature, cutting velocity and cooling rate; also how temperature depends on cutting velocity, cooling rate and wear flat area. A total of 24 series of experiments were made, each series consisting of several cuts with one cutting edge of the cutter. Table 1 is a summary of these tests. By rotating TABLE

Series

1. Summary

Runs

of rock

Cutter

cutting

experimental

Rock

13

and wear of PDC cutters in rock cutting

the cutters in the tool holder, up to three different cutting edges per cutter could be obtained; these are labelled A, B, C. The controlled or independent variables were: cutting speed V (m min-‘); feed f (mm rev-‘); depth of cut d (mm); and coolant (type and flow rate). Since coolant controls and the effects of coolant were least known, it was felt that this should be investigated first. As the tests progressed, it was realized (after test series 5) that the cutting temperature (T,: the thermocouple about 0.254 mm from the cutting edge) could be controlled by the coolant. Thus after series 5, in most cases, the cutting temperature T, was a controlled variable. Test series were stopped when the tool burned up, or when cutter forces got too high for the dynamometer (F, over 2.7 kN), or when wear had progressed enough that the depth of cut could not be obtained. The cutting tool fed from right to left across the granite cylinder, and it was noted that forces and temperature dropped off during the last 12 mm of the cut, perhaps due to the rock not being confined at the left end. At the beginning of each series of cuts, if there was sufficient taper on the rock, a clean-up cut was made with cutter No. 1. The three types of coolant used were air jet (to blow away the grit), spray mist and water jet (0.79 mm

parameters

Velocity, V (m min-‘)

Feed, f (mm rev-‘)

Depth

of cut,

d

Coolant

(mm)

1 2 3 4 5 6

34 25 2 3 7 10

1A 2A 2B 3A 4A 5A

Georgia granite (254 mm long)

152 152 152 152 152 152

0.508 0.508 0.184 0.184 0.184 0.508

0.508 0.508 1.397 1.397 1.397 0.508

Dry and spray Dry (air jet) Dry (air jet) Spary mist Water jet Mostly dry

7 8 9 10 11 12 13

10 3 7 15 2 10 4

5A 5A 2c 4B 4B 4c 6C

New log of Georgia granite (254 mm long)

152 152 152 152 152 152 91.4

0.184 1.016 0.254 0.254 0.184 0.184 0.184

0.508 0.254 1.016 1.016 1.397 1.397 1.397

Water jet T, = 140 “C T, =400 “C r, = 200 “C T, =500 “C r, =500 “C Dry (air jet)

14

4

7c

Barre granite (216 mm long)

152

0.184

1.397

15

4

5C

91.4

2.540 (thread)

16 17

6 5

6A 7B

91.4 91.4

0.184 0.184

18 19 20

7 6 5

8A 9A 8B

91.4 152 30.5

0.184 0.064 0.184

0.127 (half thread) 1.397 1.397 1.397 1.397 1.397

T, = 140 “C (water jet) r, = 140 “C

21 22 23 24

3 1 3 10

10B c2 9B 6B

152 152 152 152

0.184

1.397

T> =400

0.184 1.016 0.254,

1.397 1.397 0.508,

Dry Dry Water

Barre granite (216 mm long)

0.508

1.016

T, T, T, T, T,

= 140 =500 = 200 =200 =200

“C “C “C “C “C “C

jet

mist

diameter nozzle). Air and spray mist were not very effective coolants, but the water jet was so effective that, as previously noted, it was decided to use it to controf the temperature T1. When spray mist or the water jet was used, the granite was wet down just prior to cutting. During each controlled temperature test run, the coolant flow rate was manually adjusted during the run to hold T3 near the desired value, as displayed on the computer screen. Two types of granite rock (Georgia Elberton granite and Barre granite) were used during the series of tests. In comparing test results between granites, we believe that the type of granite did not have a significant effect on the test results. Figure 4 is a typical record of the test data for dry cutting and Fig. 5 shows a typical controlled temperature test with water jet cooling. Figure 6 is a typical plot of cutter wear profiles.

on the cutter, even when the iulrur 1.4uew ano has cg sharp cutting edge.

The normal and tangential cutting forces tar new cutters FNc and FTCwere determined by first calculating the projected area of the cut&. Then, using the cutting model of Prakash, the values of normal and tangential force per unit area (projected) were determined. These are F&.4, and FUcJA,. The values of F,, and F.,., were then obtained by multiplying these by A,. ‘The rock parameters used to represent the granite are as follows: Unconfined compressive strength: u;, = 262 MPa Angle of internal friction: cy= 3P” Limiting value of shear strength: r.!:,--@Xl MPa Additional

input parameters

ai i‘

Friction adhesion coefhcient: HI = ii 7 Rake angie of cutter: LY,-- -- I(!” 4. Analysis of forces on PDC cutters

With these values the following results were obtained

As expected, the forces acting on PDC cutters are smallest when the cutter is new, and then increase significantly as the cutter wears and develops a wear flat. The forces can be decomposed into two categories: those on the rake face due to cutting and chip formation, and those on the flank or wear flat of the cutter. The cutting forces can be theoretically determined using the analytical cutting model of Prakash (71 and are found to be a relatively small part of the total forces

Fig. 5. Typical

experimental

data. Force

and temperature

F,,JA, = 229 MPa FTc/Ap= 508 MPa Shear angle @= 15.8” Table 3 shows experimental values of the normai and tangential cutter forces FN and FT at the beginning of the initial cuts when the cutting edge was new and unworn. Also shown are the theoretical values of the rake face cutting forces FNc and F:,. The fact that FN, is smail compared to FN indicates that there was sub-

us. time for test series 10, cut No. 6.

F.C. Appl et al. I Forces,

9

10

temperatures

and wear of PDC cutters in rock cutting

14

12

15

16

X (mm)

[,-

Cut No 0 +

I

CulNoG+-+CutNo'

-t3-

Cut No G *

1

Cut No 7

Fig. 6. Typical wear profiles of a cutter. stantial

normal force on the flank of the cutter even though there was a flank clearance angle of 10” (corresponding to -10” rake angle). The forces on the unworn flank of the cutter are designated as “nose” forces FNn and FTn which are

F,, = FN - FNc

(1)

F-,.,,= FT - F,,

(2)

Evidently these forces arise in much the same manner as the forces on an indenter, but there is no known theoretical model of them. It is instructive, therefore, to consider the nature of these nose forces for new cutters. Most likely they closely depend on the area of the cutter flank that is in contact with the rock. The contact area, in turn, should be closely related to the length of the cutting edge of the cutter which engages the rock. For practical purposes the projected (straight line) length of the cutting edge W, was used for analysis. This was determined from the depth of cut d and the feed rate J The effective depth of cut t was also determined. Values of W, and t are shown in Table 1. Figure 7 is a plot of the nose force FNn US. W, which appears to be a linear relation which does not pass through the origin. A least squares fit of the data indicates that F,,=O.l61W,-0.193

(3) Figure 8 is a plot of FTn2)s. W,, from which it appears that FTn is essentially 0. This result was unexpected but can be explained by further consideration of the flank forces on the cutter as shown in Fig. 9. With (Y,= -10” and pd=0.18:

FNn= F,,* cos(a,,) -F,, sin(aJ

= l.O16F,,

FTn= F,, sin(%) + F,, cos(a,,) = O.O04F,,

(4)

(5) This supports the experimental results that there is a substantial normal nose force but negligible tangential nose force on new cutters with -10” rake angle.

4.2. Worn cutters As cutters wear and develop a wear flat the normal and tangential forces on the cutter increase. Again these were separated into two parts: the cutting forces on the rake face FNC and FTC and the forces on the wear flat FNw and FTw. The cutting forces were determined using the cutting theory of Prakash in the same manner as for new cutters. The forces FNw and FTw are due to normal and friction stresses on the wear flat. At first the wear flat occurs only on the diamond, but it then increases in size and extends into the carbide backup. It is of particular interest to consider the wear flat forces as wear proceeds, to determine what proportions occur on the diamond and carbide respectively. Values were determined for the experimental forces FN and FT near the end of the cut, wear flat areas of the diamond and carbide&, and&, the projected area of the cut A,, the cutting forces FNC and FTC and the forces on the wear flat FNw and FTw. The wear flat areas were calculated using the experimental values of the projected width of the wear flat, W,. The projected area of the cut was assumed to be the product of the depth of cut and the feed rate. The values of A+, Acp, FNw and FTw are shown in Table 3. The nature of the stress distribution on the diamond wear flat area and the carbide wear flat area has not been clearly established and has been the subject of some disagreement. It has been proposed by Barr [8] that the normal stress on the carbide should be only about 1% of the stress on the diamond because the two materials wear away simultaneously but the wear resistance of the diamond is of the order of 100 times that of the carbide. It has also been proposed that the average normal stress on the diamond is equal to the compressive strength of the rock. Since the wear flat areas of diamond and carbide have been determined for the cutting tests, these ideas were investigated.

Stratapax 29 2B 3A 4A 5A 2c 5B 4c 6C 7c 5c 7B

1980 2 3 4 5 6 9 11 12 13 14 15 17

~~~

Cutter No.

1 I 1 1 1 1 1 1 1 1 1 1 1

Cut No.

2. Experimental

Test series

TABLE

98.5 152 152 152 152 152 152 152 152 152 152 91.4 91.4

v (m mm-‘)

and theoretical

0.152 0.635 1.397 1.473 1.295 0.673 1.207 1.384 1.422 1.422 0.914 0.086 1.486

(mm)

d

0.0635 0.508 0.184 0.184 0.184 0.508 0.254 0.184 0.184 0.184 0.184 2.54 0.184

(mm rev-‘)

f Water Air Air Mist Water Air Water Water Water Air Water Water Water

Coolant

data. Cutting granite cylinders

0.050 0.578 0.589 0.667 0.543 0.387 0.476 0.525 0.538 0.427 0.489 0.144 0.558

X (kN) 0.010 0.141 0.167 0.144 0.118 0.080 0.111 0.156 0.142 0.153 0.123 0.037 0.196

fkN)

with new PDC

0.005 0.124 0.222 0.179 0.148 0.031 0.072 0.182 0.214 0.105 0.141 0.018 0.182

&I)

0.592 0.630 0.691 0.562 0.388 0.481 0.556 0.578 0.440 0.509 0.146 0.587

0.050

;&)

cutters: force

0.010 0.141 0.167 0.144 0.118 0.080 0.111 0.156 0.142 0.153 0.123 0.037 0.196

;;N,

analysis

0.0022 0.0736 0.0588 0.0621 0.0546 0.0780 0.0701 0.0583 0.0599 0.0599 0.0385 0.0282 0.0626

& 0.005 0.163 0.131 0.138 0.121 0.173 0.155 0.129 0.133 0.133 0.085 0.063 0.139

0.048 0.518 0.571 0.629 0.508 0.310 0.411 0.498 0.518 0.380 0.471 0.117 0.524

0.0049 - 0.0223 0.0363 0.0064 - 0.0027 - 0.0931 - 0.0443 0.0263 0.0094 0.0206 0.0374 -- 0.0252 0.0568

1.455 3.155 4.399 4.514 4.239 3.241 4.128 4.379 4.437 4.437 3.576 2.136 4.534

(mm’) 0.0097 0.322 0.257 0.271 0.239 0.341 0.306 0.255 0.262 0.262 0.168 0.123 0.274

WP (mm)

4

0.0066 0.1021 0.0584 0.0602 0.0561 0.1052 0.0742 0.0582 0.0589 0.0589 0.0470 0.0577 0.0605

(mm)

t

F.C. Appl et al. I Forces,

L

[ -

Fig.

7. Normal

1 PROIECIED

EXPERIMENTAL

nose

force

WIOIH

temperatures

4 3 OF CUT (mm)

--D.i)3

US. projected

+ O.lSl*Wp

1

width.

Fig.

_

? - 8.178I 0

L

i 9

Fig.

8. Tangent

_

--..._-. _ ._

PRDIECT:D WlDlH OF 'CU7 (mm)

4

_.__._

force

vs. projected

I

of nose

forces

on a new

cutter.

(7)

where pd and pFL, are the coefficients of friction on the diamond and carbide respectively. Figure 11 is a plot of FTW IIS. A,,. A least squares curve fit of the data indicates that ,ucLd =0.18 and pL,= 0.092.

width.

When the value of FNwwas compared with the product of the compressive strength a, and the projected diamond wear flat area A,, it was found that there was good comparison for the lower values of wear, when the wear flat had not progressed into the carbide, but as the wear progressed into the carbide the values of FNWincreas,d more rapidly. It appears, therefore, that the normal stress on the carbide is not negligible in granite cutting. To determine the average normal stress on the carbide an empirical relation for the normal force FNW was assumed in the form FNw= a,,&, + Q$,

9. Schematic

f’nv= /-woA+ + WA,

EXPERIMENTAL-O

nose

17

and wear of PDC cutters in rock cutting

(6)

where a,=262 MPa. The value of-u, was found by a least squares curve fit of the data as shown in Fig. 10: a,= 122 MPa. Thus the average normal stress on the carbide is nearly half that on the diamond, which is much higher than expected. The tangential force on the wear flat is due to sliding friction on the diamond and carbide portions of the wear flat. It was therefore assumed that F-,-,., can be represented in the form

4.3. Correlation of normal force, diamond wear area and diamond temperature As has been shown, as the cutter wears and the wear flat area increases there are proportionally larger normal and tangential forces on the wear flat area due to the sliding interaction with the rock surface. The increased tangential or sliding force causes a similar increase in the amount of heat generated at the interface, which in turn leads to an increase in diamond temperature. This is shown particularly well by test series 2. Since wear measurements were not made for every cut, several of the values of A, were determined by interpolation as shown in Fig. 12. The close correlation between F, and A, is shown in Fig. 13.

5. Wear rate of PDC cutters

Typically when cutting rock with a PDC cutter the cutter is new, with a sharp cutting edge when cutting begins and the cutting forces are relatively small. Soon after cutting begins, however, a wear flat starts to develop and the forces begin to increase. The amount

F.C. Appl et al. J Forces, temperutures and wear of P/X.’ cutter.s in rock CUIIUII,

18

TABLE 3. Experimental and theoretical data cutting cylinders with worn PDC cutters: force analysis Test series 5

Cutter No. 4A

Cut No.

granite

Ad,> (mm*)

/I,, (mm’)

FNW

F,,

W)

W)

1 2 3 4 5

2.15 2.77 3.02 3.28 3.40

1.97 5.58 7.92 11.09 12.30

1.32 2.16 2.26 2.47 2.46

0.159 0.25 I 0.320 0.364 0.338

0.0455

8

5A

22 23

3.44 3.55

12.75 13.86

2.42 3.09

0.323 0.370

9

2c

1 4 5 6 7

1.74 2.73 2.99 3.46 3.66

0.71 5.20 7.59 12.92 15.06

0.54 1.21 1.22 2.08 2.59

0.005 0.102 0.133 0.246 0.355

7 9 11 13 14 15

2.43 2.73 2.87 3.13 3.07 3.13

3.18 5.24 6.40 9.3 I 8.52 9.23

1.61

0.1x5 0.223 0.201 0.20s 0.184 0.175

4 6 7 8 9

2.32 2.47 3.05 3.41 3.60

2.73 3.51 8.34 12.45 14.43

2.14 2.71

0.152 0.134 0.190 0.277 0.332

10

12

4B

4c

1.72 2.lh 2.00

1.92 1.92 1.39 1.42

1.79

14

7c

1 2 3 4

2.77 3.51 3.63 3.72

5.62 13.45 14.70 15.72

1.06 2.00 2.33 3.25

0.115 0.241 0.292 0.428

16

6A

3 4 5

2.93 3.18 3.77

7.13 10.06 16.34

1.84 2.57 2.31

0.270 0.386 0.348

17

7B

2

2.66

4.78

1.42

0.215

1980

Stratapax

0.092 0.137 0.122 0.175 0.185 0.176 0.210 0.178 0.235 0.191 0.213 0.242 0.270 0.300 0.287 0.269 0.215 0.153 0.321 0.285 0.334 0.391 0.388 0.389

0.0215 0.0211 0.0189 0.0278 0.0282 0.0255 0.0299 0.0224 0.0184 0.0259 0.0282 0.0326 0.0504 0.0398 0.0393 0.0353 0.0175 0.0206 0.0553 0.0375 0.0428 0.0509 0.0500 0.0558

2 3 4 5 6 7 8 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

0.269 0.297 0.321 0.350 0.376 0.397 0.427 0.486 0.512 0.517 0.531 0.555 0.576 0.649 0.656 0.665 0.695 0.714 0.746 0.770 0.806 0.928 0.955 0.992

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -

(continued)

0.04 1 I 0.0193

0.0482 0.0442 0.0437 0.049’; 11.0551 if.053 i 0.0437 X055.1; 0.0575 0.0562 0.1).553 1I.OSS.i

0

1 WEAR 1

Fig. 10. Normal

THEORETKAC

fRtA (sq +

nun;

EXPERiMENTAL

force on wear flat us. wear area of diamond.

of heat generated also starts to increase, owing to the increased rubbing friction of the wear flat on the rock surface. The diamond wear rate is often considered to be the ratio of the wear volume of the diamond to the rock volume removed. The effective life of diamond drill bits and diamond core bits is closely related to the wear rate of the cutters, and hence wear rate consideration is an important part of economical bit design and operation. As cutter wear progresses and the amount of heat generated increases, it is probable that the temperature of the cutter will also increase, especially if the amount of cooling provided by the cutting fluid is inadequate. This may result in increased rate of diamond wear. Thus, one of the principal reasons for conducting this

F.C. Appl et al. / Forces, temperatures and wear of PDC cutters in rock cutting

Fig. il. Tangent

I

z r’

force on wear flat vs. wear area of diamond.

i’

/-

0.0 _ 0

1200

600

ROCK VOLUMEVR(cu cm)

-

!merpoimed

Vklues -

Me2sured Wear

Fig. 12. Rock volume removed KY. wear area.

2.

1 1

0.44 !

0

WEAR / j-

Fig. 13. Correlation area.

L*x

I

ixceFr

AREi

Ad (sq .m; -

TemperEwe

T1

/

of normal force and temperature

2~s. wear

19

series of rock cutting tests with PDC cutters was to determine experimentally the effect of cutter temperature on the wear rate of the diamond. Since it has been shown [9] that the hardness of the PDC diamond decreases with increasing temperature and that when the temperature reaches about 700 “C the hardness falls essentially to zero, it was expected that the diamond wear rate would gradually increase with increased temperature up to a critical temperature where wear rate would increase catastrophically. The wear rate should correlate most closely with the temperature of the diamond wear flat; however, it was not possible to measure this directly, owing to the intimate contact with the rock. The best available experimental temperature is the temperature T,, which was measured at the same location in each cutter (2.54 mm from the unworn cutting tip). This should be closely related to the temperature on the wear flat and hence values of 7; will be used to analyse and model the effect of cutter temperature on diamond wear rate. It has been generally supposed that if the cutter temperature remained constant as the cutter wore, the diamond wear volume Vdwould be directly proportional to the volume of rock removed V,. Guided by this hypothesis it was found that the temperature T, could be controlled and maintained reasonably constant during each cut by varying the amount of cooling water applied to the cutter. Then for each series of cuts the wear volume of the diamond was dete~ined as a function of the volume of rock removed. The diamond wear volume was calculated from the measured values of the wear profiles by numerical integration and the volume of rock removed for each cut was found by calculating the decrease in volume of the rock cylinder using the values of the average rock diameter dvVeat the beginning and end of the cut. The average values of cutter temperature for each cut Tlave were found by averaging the values of T,. A typical plot of T,,,, and incremental diamond wear rate (A~~/A~~) vs. cut number is shown in Fig. 14. These graphs showed that in most of the test series the average temperature was nearly constant, but that the incremental wear rate was not constant. This same data can be portrayed in a different manner by plotting the volume of diamond wear Vd WS.the volume of rock removed V,, as shown in Figs. 15 and 16. Again, these graphs show that the wear rate is not constant during the test series and in most cases it increases as cutting proceeds. This was an unexpected result because it does not agree with the supposition that wear rate would be constant when temperature was constant. It was aIso surprising that there was so much variation in the curves from one test series to another. It was clear that a new model of diamond wear waz; needed to correlate the experimental data.

F.C. Appl et al. I Forces, temperatures and wear of PLK’ cutters in rock cuttm~

20 Series

12 Cutter

4C

Slider

$j====f

~

;

15P

/

F

3

looF

/

/

50-

*

i2 1'

0 0

1

3

2

+

4 5 cur No.

Tl

7

8

go

Fig. 17. Schematic

of slider wear

Wear Ratio

-

Fig. 14. Typical temperature

6

and wear ratio VS. cut number.

CUTTING SPEED

152 m/nun

__-f_

Fig. 18. Model of sliding wear of diamond

lil

wear flat

1606

ROCH VOLUYt VR (CY cm)

wear of the slider is of the form dVJdt=CF,, Fig. 15. Diamond 152 m min-‘.

wear volume ~1s.volume of rock removed

CUTTING SPEED

dLldt

(81

-

where V, is the volume of wear of the slider, F,, is the normal force on the slider, L is the distance of sliding, t is time and C is the wear constant. It is often found that the wear mechanism is influenced by temperature at the sliding junction, and hence a more general form for the wear rate is

91.4 wmin

dV,/df = C F,, (dL/ck)

f(T)

(9)

where T is the temperature at the sliding junction and f(T) is a function of temperature. To extend these concepts to the diamond wear rate of a PDC cutter, consider the diamond wear flat as the slider, as shown in Fig. 18. Then the time rate of diamond wear becomes dV,ldt = C, Fw

Fig. 16. Diamond 91.4 m min-‘.

5.1. Analytical

wear volume VS. volume of rock removed

model

of diamond

-

wear

In basic studies of sliding wear, as shown in Fig. 17 it is generally found that the time rate of volume of

(dUdQ

f(T,)

(10)

where FNwd is the normal force on the diamond wear flat, L is the cutting distance and Vd is the volume of diamond wear. Now it has been found that the normal force on the diamond wear flat is F Nwd= wt,p

(11)

21

F.C. Appl et al. / Forces, temperatures and wear of PDC cutters in rock cutting

where a, is the unconfined compressive strength of rock and A,, is the projected area of the diamond wear flat. Furthermore, the time rate of rock removed in cutting is dV,/dt =A, tildt

(12)

where V, is the volume of rock removed and A, is the projected area of cut. Substituting the relation for FNwd and dividing leads to the following relation for the diamond wear: dV,ldVR = (dV&)/(dV&)

dV,/dV,= G~o(A,,I’,Wd = &JQV’J

(14)

This is a new and interesting relation for diamond wear rate of PDC cutters, particularly because it contains the factor Adp/Ap. In fact, according to this, the rate of wear depends on the area of the wear flat A+, which in turn is closely related by geometry to the volume of diamond wear V,. Thus the greater the amount of prior wear, the greater the wear rate. This behaviour is reflected by V, vs. V, curves which generally curve upward as evidenced by many of the experimental curves. Formally, the initial wear rate is zero and would remain zero until some wear occurred. The initial wear “event” might be the formation of a small chip for which the time of occurrence and the size of the chip are probabilistic in nature. Since this initial wear event influences the entirety of the succeeding wear behaviour of the cutter it is to be expected that the wear curves will be varied in nature and not necessarily repeatable. This reasoning seems plausible as far as it goes, but the situation is actually more complex because the previous wear rate relation may not be valid for new cutters. It has been shown that before the diamond wear flat is formed there is a normal nose force on the flank of the cutter FNn. Perhaps then the wear rate relation for new cutters corresponds to substituting this for @,A+. Then dv,ldv,

= C,(F,,IA,)f(T,)

(15)

This might better explain how wear gets started, after which there is a gradual transition from this relation to eqn. (14) as the wear flat enlarges. According to this, wear would always be initiated, but the initial events are likely to be somewhat probabilistic in nature and hence the former conclusions remain valid.

were therefore analysed to determine how well the model would correlate with the data and to establish the dependence of wear rate on cutter temperature, i.e. F(T,). To obtain the temperature relation, the quantity (AV,,/AV,)I(A,JA,) was calculated and plotted vs. Tlave as shown in Fig. 19. As expected, it was found that in most of the test series the values for the first few cuts were erratic because the model does not represent these cases well. These values were therefore not included in Fig. 19. For the most part, the remaining values correlate reasonably well with TI. The results show that the diamond wear rate increases with respect to temperature TI up to approximately 500 “C. Basically, it is expected that the diamond wear rate depends on the diamond hardness in an inverse manner. As Lee and Hibbs found [9], the diamond hardness varies linearly with respect to temperature up to 700 “C. An empirical fit of their data for hardness indicates that H=C(1944-

(16)

where H is hardness, C is a constant and T is the diamond temperature. Therefore it was first supposed that F(T,) would have the form

w-1)=

“;l)c3

(C,

(17)

where C1, C, and C, are constants and (C,- T,) represents the hardness. The constants were determined by a least squares fit of the data, which resulted in 9.50 x 105

F(T1) = (1934 _

(18)

,)3.94

Although this is in agreement with the hardness data, in so far as C,= 1934, it is found that a linear relation fits the experimental data equally well. This is

9-

3 8?T 7v 45 % 4K 3b rl 2l-

5.2. Correlation of the wear rate model with

OJ 0

experimental data

Generally the proposed wear rate model agrees with the observed behaviour of the experiments. The data

7)

Fig.

100

19. Diamond

200 wear

300 400 T1 0 rate

VS. average

500

600

temperature.

7 IO

22

F.C. Appl et ul. I Forces, temperatuwr

which is shown in Fig. 19. The correct form for F(‘l‘!) cannot be determined at this time because there is too much scatter in the experimental data. However, the overall correlation of either is reasonably good considering the large number of varied cuts that are represented by the data. 5.3. Critical temperature and failure of PDC cutten Cutting experiments showed that whenever the measured diamond temperature T, exceeds 500 “C the wear rate abruptly increased by a factor of approximately 50. From a practical standpoint this amounts to catastrophic failure of the cutter. This result was at first puzzling because the abrupt decrease in diamond hardness occurred at about 700 “C, which is 200 “C beyond the critical value of T1. Yet, from all appearances, it seemed that the diamond at the cutting tip had reached the critical temperature of 700 “C. Therefore, to determine if this was true a cutter was instrumented with three thermocouples at distances of 1.27 mm, 3.38 mm and 9.88 mm from the cutting tip (test series 21). The plots of the temperatures measured by these thermocouples indicate that it is reasonable to believe that when T, reached 500 “C in the previous tests the temperature at the cutting tip had reached 700 “C. Thus, there again seems to be good correlation between the cutting tip temperature at failure and the temperature at which hardness abruptly decreases. Further evidence of this is found by examining the behaviour of the normal force and temperature Tl in series 2 (cut 25) (Fig. 4), series 3 (cut 2), series 4 (cut 3) and series 13 (cut 4). In all cases there was an abrupt change in slope of T, at values of T, equal to 500 “C, 470 “C, 500 “C and 525 “C: respectively. There were corresponding abrupt increases of the slopes of X, which means that the wear rate had abruptly increased and the wear flat area A, was rapidly increasing. It is also observed that in all cases T, subsequently peaked at values of 800 “C, 830 “C, 780 “C and 870 “C, respectively. The average value is 820 “C. Since this behaviour of cutter failure was so consistent it is believed that in essence what happened was that the diamond tip reached the critical temperature of 700 “C when T,- 500 “C and thereafter had lost all cutting ability. The carbide backing had not yet lost its strength and therefore the carbide continued cutting as if the diamond was not there. The temperature continued to increase up to approximately 820 “C (tip temperature in excess of 1000 “C) when apparently the hardness of the carbide had decreased to the point where it could no longer cut the granite. This is further supported by observing that after reaching the peak temperature the values of X began to decline, indicating that the cutter could no longer continue cutting. Approximate analysis of the wear rate of the cutters (based on the wear volume

b* r(

42l

0

._...___ 100

v_T_--

j-m--. -7

Tl Fig. 20. Diamond cutter

failure

--T--T------’

200 300 400 500 600 700 800 900 wear

rate

(Cl

7~. average

temperature

(including

rate).

of the diamond) was made for the four cases being considered and the wear rates were 30.1, 74.4, 63.1 and 49.8 times the rates at 7’, =500 “C. On average, the “effective” wear rate of the diamond abruptly increased by a factor of 54. This is shown graphically in Fig. 20. In summary, a reasonable theory of the wear rate of PDC cutters in cutting granite has been developed and correlated with the experimental cutting data. The results show that the wear rate continuously increases as the cutter tip temperature increases to a tip temperature of approximately 700 “C, whereupon the diamond has lost all cutting ability. The carbide continues to cut up to about 1000 “C, but the effective diamond wear rate is 54 times greater. The carbide then reaches the cutting limit when the temperature is about 1020 “(‘.

6. Discussion Since the introduction of PDC bits they have almost completely replaced three cone bits in soft, non-abrasive formations. The ultimate goal is to drill all kinds of formations using PDC bits. Hence it is necessary to achieve strong bits which can drill with high rates of penetration without losing their life. This research work was devoted to studying the wear behaviour of PDC bits in drilling hard rock formations. It has been observed that without ample amounts of cooling, it is not possible to cut the hardest formations such as granite. This was clearly observed in air- and mist-cooled tests. Of equal importance, however, it was found that the temperature of the cutter can be controlled within the desired limit with an adequate amount of cooling. This prevents burning even after wear flat formation, and allows continuous cutting. With inadequate cooling the cutter will easily burn up after the

F.C. Appf ef al. / Forces, ~er~pe~a~l~res and wear of PDC cutters in rock crrriing

formation. This was observed in several test series, and is an important result of the research. The significance of this is that during drilling with PDC bits, cuttings may accumulate in front of the cutters, thus preventing the drilling fluid from reaching the diamond face of the cutters. This will, in essence, prevent heat removal from the cutter and will result in high cutter temperature and consequent cutter failure. It would be a valuable improvement in drilling technology if thermo~uples were mounted on the cutters to monitor the temperatures. Then if overheating was detected, corrective action could be taken before excessive damage occurred. An important discovery from the experiments was that the wear rate of the diamond is not constant when the cutter temperature is constant. This was unexpected, but upon further consideration was explained by a new theory of diamond wear rate during cutting. Wear of new cutters begins by initial chipping of the cutting edge. This varies substantially from cutter to cutter and appears to be probabilistic in nature, Once the wear has begun, then the wear rate depends on the present wear state A, as well as cutter temperature. Another result of the cutting tests was that the contact stress between the carbide portion of the cutter wear flats and rock surface was much larger than expected. It was previously believed that the normal stress on the carbide would be only a few per cent as large as the normal stress on the diamond wear flat. Instead it was found to be nearly 47% as large. This result has important practical implications for bit design, because as the wear flats become larger, substantial increases in bit weight are required to maintain a reasonable rate of penetration. In many cases the bit weight will become larger than desired and then the bit must be replaced. This adversely affects the economics of drilling. Hence it is important to design bits with limited areas of the carbide backup. It is also important to learn more about “lip” formation in different rocks and how bit vibration affects the “lips”. Perhaps there are design changes and changes in operation procedures that will enhance “lip” formation and thereby lead to higher rates of penetration and longer bit life. This would de~nitely lead to lower drilling costs.

wear

flat

7. Conclusions The conclusions from this work in cutting granite rock with PDC cutters over the range of variables studied are as follows: 1. Initiation of cutter wear was variable in nature and was generally not repeatable. It appears to depend on initial edge chipping.

23

2. Cutter forces and temperature correlate closely with the wear flat area of the cutter. Cutter forces are relatively small for new cutters 3. and then increase rapidly as the wear flat area increases. 4. The normal stress on the carbide portion of the cutter wear flat was estimated to be 47% as large as that on the diamond wear flat area. 5. Cutters could be successfully cooled with water, but with air the temperature continued to increase rapidly until cutter burnout occurred. 6. Cutter temperature could be controlled by adjusting the flow rate of the water jet. This allowed cutting tests to be made at nearly constant temperature. 7. Cutter burnout occurs rapidly when cutter temperature reaches the critical temperature which was estimated to be 700 “C. 8. Cutter wear rate gradually increases with increased cutter temperature up to the critical temperature. 9. The proposed theoretical model of diamond wear rate correlates reasonably well with the experimental data.

Acknowledgment

This work was supported by the National Science Foundation Grant No. CBT-8819165.

References J.F. Brett, T.M. Warren and S.M. Behr, Bit whirl - a new theory of PDC bit failure, SPE Drillirg Erg., 5 (1990) 275-281. T.M. Warren, J.F. Brett and LA. Sinor, Development of a whirl-resistant bit, .SPE Ddhg Eng., 5 (1990) 267-274. A. Ortega and D.A. Glowka, Frictional heating and convective cooling of polycrystalline diamond drag tools during rock cutting, SPE J., 24 (1984) 121-128. D.A. Glowka and CM. Stone, Thermal response of potycrystalline compact cutters under simufated downhole conditions, SPE J., 25 (1985) 143-156. D.A. Glowka and CM. Stone, Effects of thermal and mechanical loading on PDC bit life, SPE ~~~Iiffg Eng., 1 (1986) 201-204. D.A. Glowka. Use of single-cutter data in the analysis of PDC bit designs: Part 1 - Development of a PDC cutting force model, SPE f. Petrol. Tech., 41 (1989) 797-849. V. Prakash, Rock cutting theory for PDC Cutters, MS The&, Kansas State University, 1982. J.D. Barr, optimization of radial distribution of Stratapax cutters in rock drilling bits, ASME Eng. Sources Tech. Conf., New Orleans, 3-7 February, 1980. M. Lee and LE. Hibbs, Jr., Role of deformation twin bands in the wear processes of polycrystalline diamond tools, in KC. Ludema, W.A. Glaeser and S.K. Rhee (eds.), Wear of hfaretials, ASME, New York, 1979, p_ 485.

24

Appendix:

AC, Ad A dp AP

F.C. Appl et al. / Forces,

temperatures

Nomenclature

projected area of carbide wear surface area of diamond wear surface projected area of diamond wear surface projected area of cut

c, Cl, G constants depth of cut feed rate wear rate functions of temperature normal force on cutter normal force due to cutting normal force on flank of new cutter normal force on new cutter normal force on slider tangential force on cutter tangential force due to cutting tangential force on new cutter tangential force on flank of new cutter

and wear of‘ p’uc‘ cutters in rock cuttmg

diamond hardness length of cutting or sliding friction adhesion coefficient for rock effective depth of cut; time temperatures at thermocouples cutting velocity volume of rock removed volume of diamond wear volume of wear of slider projected width of wear flat; projected width of cut components of cutting force measured with dynamometer angle of internal friction of rock normal rake angle of cutter coefficients of friction on diamond and carbide wear flats normal stress on carbide compressive strength of rock shear stress asymptote of rock shear angle