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B. J. Griffiths
R. J. Grieve
Department of Manufacturing and
Engineering Systems,
Brunei University,
England
Modelling Complex Force
Systems, Part 2: A Decomposition
of the Pad Forces in Deep Drilling
1
Introduction
This paper is a continuation of the earlier Part 1 paper [1]
in which it was shown that the force system existing during a
deep hole drilling operation was complex (see Fig. 1) and indeterminate using a single dynamometer approach. However,
by using complementary dynamometers in conjunction with a
force relationship to model the radial and tangential pad forces
(Fig. 2) the system could be analyzed. As a result, the following
forces were determined:
(a) The cutting force system (PT PF PR)
(b) The total force system at each pad (Rt, R2, ixR\, iiR2,
HLRU
ULRI)
(c) The radial forces at each pad (Fm, FR2t Bm, BR2)
In this paper the force model is developed further to analyze
(1) the tangential pad forces and (2) the power and energy
responsible for various actions of a deep drill.
2
Friction Coefficient (/tF)
It has been shown in the earlier paper that the forces of the
pads are made up of two sets of forces, namely, the friction
and the burnishing forces as shown in Fig. 1. Also, these two
separate actions of burnishing and rubbing are responsible for
on average 37 percent of the torque force and hence energy
expended in a deep drilling operation as shown by the torque
and thrust diagram of Fig. 3. If the two sets of forces associated
with these two actions can be separated it would be possible
to determine the relative energies associated with the burnishing
and hence surface integrity and the pad friction and hence hole
accuracy and precision.
To measure and separate the burnishing friction forces it is
necessary to incorporate two sets of load cells into the pads.
This would be particularly difficult because of the very small
region of the pads over which burnishing occurs. An alternative
approach which Would allow the pad forces to be analyzed
further is to assume that conventional coulomb friction conditions exist at each pad over the portions not concerned with
burnishing. This will allow the radial and tangential friction
forces to be related by a coulomb type friction coefficient {nc)
so that:
ixc = FTI /FR i = FT2/FR2
(1)
The values of this friction coefficient can be determined using
the procedure prescribed in Appendix 1 where the torque and
thrust dynamometer is used in conjunction with a special pilot
bush which has a hardened surface and a bore surface finish
equivalent to that of a deep drill hole. This dynamometer is
shown in Fig. 4. Thus, during phase C of a deep drilling
operation, frictional forces will be present over the full pad
length, which are comparable to the friction forces present
over part of the pad during normal deep drilling in phase E.
Although the forces in these two cases will not be the same,
the coulomb friction coefficient should be of a similar magnitude and it can be calculated using the following equation
whose derivation is given in Appendix 1:
lxc=M(h/d),
(T*Ru/Tc), (PT/PR))
(2)
8
the ratio TR*,/TC is found from the torque and thrust
dynamometer results by comparing the phase C forces produced by the dynamometer in conjunction with the hardened
pilot bush and with the extended pilot bush as shown in Table
1 below:
where the ratio TRl/Tc is calculated by the following:
TRu/Tc=
P h a s e [Cffardened~ CExtended\/[CExtended]
(3)
Figure 6(a) shows the variation of the pad components using
the results described in the table. It is interesting that the
variation with increase in feed follows the same trend indicated
by the full dynamometer results given in Fig. 3.
• the ratios h/d and PJ/PR are determined using the cutting
forces dynamometer described in the first paper [1].
The resulting variation of the friction coefficient iic with
feed is shown in Fig. 6(b). This coefficient is approximately
half of the total friction coefficient (^) and it follows the same
Table 1 Values of phase C torque using the different pilot bush configurations
Phase C torque
Hardened Pilot Bush
Contributed by the Production Engineering Division for publication in the
JOURNAL OF ENGINEERING FOR INDUSTRY. Manuscript received Sept. 1989; revised
May 1992. Associate Technical Editor: S. O. Kapoor.
Extended Pilot Bush
MAY 1993, Vol. 1157 177
Journal of Engineering for Industry
Copyright © 1993 by ASME
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nv^. PR3 ^ BR3 ^ FR3
Fig. 1
Fig. 2
The total force system
The force system with friction coefficients
trend in that it decreases with increasing feed. T h e range is
0.07 < fic < 0.125 with the mean value at approximately 0.085.
These values compare favorably with published values for lu-
bricated steel on steel. Wright Baker [2] quote about 0.05-0.15
for boundary conditions. Bowden a n d T a b o r [3] give a range
of 0.08 to 0.13 for standard cutting oils. It is also significant
Nomenclature
As per Part 1 of this paper, plus:
C 5 , C6, C-i = constants given in E q . (12)
r = drill radius
TB = burnishing torque
1 7 8 / V o l . 115, MAY 1993
TRu
TRl
j3
/x
=
=
=
rubbing or friction torque
rubbing torque when n o burnishing occurs
burnishing coefficient
friction coefficient
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O
Fc + P B +P R U = P D
o
Workpiece.
Pilot Bush.
WTRU=TD
Nm
50
/*
i^
a0
005
01
0-15
0-2 mm/rev.
0
O05
Feed.lflr
X0-1
Tp
0-15
0-2mm/rev.
Feed.lfl-
%
%
100
100
Pc
80
80
60
60
40
40
20
20
•—- \
•
TF
Fig. 5
=5
0
005
0-1
0-15
0-2mm/rev.
0
0O5
Feed.lfl
0-1
0-15
Feed .If 1
BIAHeller.
d=22mm.
n = 1400revs/min.
Material EN8.
Fig. 3
Torque and thrust components
Hi
Thin
Wall
3 ^
Drilling .
Tube.
Bush.
f~TWkA
Drilling
Fig. 4
Pilot
Table.
The torque and thrust dynamometer
Journal of Engineering for Industry
0-2mm/re
Entry forces and phases
that they show that for a low carbon steel the coefficient of
friction falls with increasing load which agrees with the above
trend shown in Fig. 6(b) since increasing feed means increasing
pad force. The friction values also compare favorably with
values given by Baier [4] for deep drilling. He investigated the
coulomb friction coefficient using a simulated deep drilling
operation where pads were pressed against a rotating bore in
the presence of a flowing deep drilling oil but without burnishing. For practical values of force and speed he quotes a
range of 0.06-0.1 which compares favorably with the range
given above. From his results Baier concludes that mixed friction conditions exist which indicates there is a combination of
metal to metal contact and hydrodynamic lubrication.
3 Burnishing Coefficient (/S)
So far it has been shown that the frictional forces can be
related by a coulomb coefficient. To allow the analysis to
proceed it is necessary to model the burnishing forces and this
can be done by assuming that there is a relationship between
the tangential and radial burnishing forces at each pad which
for convenience can be termed "the burnishing coefficient and
represented by /3." This will not be a friction type relationship
since the quickstop investigation [5] described in the first part
of this paper [1] showed that the burnishing action is comparable to a high negative rake cutting process or an ironing
process. The burnishing coefficient thus represents the ratio
of two forces associated with plastic flow. Thus it can be
assumed that:
P = BT1 /BR i = BT1/BR2
(4)
The friction and burnishing force systems acting on the pads
will together equal the total or overall force system given by
the following equation:
R\,i = BR\t2 + FRIZ = Bnyp + FnVfc
(5)
Using these equations the drilling torque components can be
analyzed. No attempt is made to analyze the thrust force components since the pad thrust is small in comparison to the total
drilling thrust.
If quantitative conclusions are to be reached as a result of
this analysis, practical values of the coefficient 0 are needed.
No values are available for deep drilling; however, in the quickMAY 1993, Vol. 115/179
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o/o
r
d = 22mm.
n= 1400 revs/min.
Matl. EN8.
100
80
TRU,
60
d=22mm.
n=1400revs/min.
Matl.ENB.
40
20
005
0-1
0-15
0-2
0-15
0-2 mm/rev.
f-
0-15
\
\
0-1
0'05
0-05
0-1
Feed.[fl-
Fig. 6
Variation of the coulomb friction coefficient
stop study the similarity between burnishing and high negative
rake cutting was noted and cutting force ratios have been
published for such tools. Two publications are relevant, both
of which used high negative rake tools to simulate the cutting
action of a single abrasive grit.
Rubenstein et al [6] machined blocks of lead and aluminium
at a very slow cutting speed of 1 in/min with 75 deg negative
rake angle high speed steel tools. They present cutting force
ratios which range from B = 0.313 to 0.667 and the average
of all their tabulated results is 0.387. Unfortunately, they did
not use conditions which allowed direct comparison with deep
drilling but comparable values can be obtained by extrapolation. Extrapolation to a depth and width of cut indicated by
the quickstop yields values of B = 0.30 and 0.71, respectively.
These extrapolated values thus have the effect of widening the
range of B values and therefore a mean 0.387 is still reasonable.
This very low cutting speed used by Rubenstein et al suggests
that their results may not represent cutting force ratios of more
typical machining conditions. However, the cutting force results produced by Komanduri [7] for more typical grinding
speeds are comparable to those of Rubenstein et al and therefore suggest that the results obtained from various slow speed
machining are not unreasonable. Komanduri machined steel
workpieces with 75 deg negative rake angle carbide tools at
speeds from 600-1800 ft/min and found values of /3 from 0.250.4. Conditions are not directly comparable to those of deep
drilling but extrapolation to typical values of depth and width
of cut yield B values of 0.286 and 0.333, respectively. These
ranges suggest a mean of approximately 0.320 which compares
1 8 0 / V o l , 115, MAY 1993
Fig. 7
Variation of burnishing and friction torque
favorably with the mean of 0.387 obtained from the results of
Rubenstein et al.
The deep hole drilling analysis can now be continued and
the value chosen for B is 0.35 which is the average of the
Rubenstein et al and Komanduri results. It is most likely that
the value of 8 will change with speed, and indeed both Rubenstein et al and Komanduri agree that 8 reduces with increasing width of cut (equivalent to the feed in deep hole drilling).
However, for convenience of analysis and as a first order
approximation a value of B is equal to 0.35 is assumed.
4 Friction and Burnishing Components of Torque
Now that the friction and the burnishing coefficients have
been defined it is possible to continue the model to determine
the ratio of the torque forces.
If the two sets of radial forces [i?i & R2 from Eq. (5)] are
added, it can be shown using the method given in Appendix
2 that:
TB/TD=TP/TD[l+(l/p-l/li)/(l/ii-llicy\
(6)
TRu/TD=TP/TD-TB/TD
(7)
From these equations the curves in Fig. 7 were plotted using
TP/TD, ixc values from above.
The curves show that as:
0- '/* then TB-TP& TRu-0
Indeed B cannot be less than fi because it will result in negative
values of TRu. Thus, the lower limit for B will be given by jt.
At the other end of the B range the curves show that as:
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d =22 mm
n = K00 revs/min
f = 0-1 mm/rev.
d = 22mm.
Torque or Power
n=UOOrevs/min.
1
I--'
Matl.EN8.
01
Feed,! f I
Fig. 8
0-15
Mat I. EN8.
6 = 0-35.
0-2mm/rev.
-
Variation of torque components
180 PAD
/3—oo then TB & TRu — constants
The two constants are not necessarily the same and the values
are dependent upon feed. The effect of feed upon the friction
torque ratio TRu/TD is seen to be much less than the effect on
the burnishing torque ratios. This is not unreasonable since
an increase in feed will dramatically increase the burnishing
area but only slightly decrease the friction area.
The curves in Fig. 8 show how the friction and burnishing
torque ratios vary with speed over the range at /3 values suggested above. Results indicate the burnishing torque (TB) is
generally greater than the rubbing torque. Taking a typical
feed of 0.1 millimeters/rev, the pad torque is 37 percent of
the total drilling torque of which 24 percent is due to burnishing
and 13 percent due to friction. As the feed is increased the
friction torque ratio increases whereas the burnishing torque
ratio decreases. The ratios are given by:
90°PAD
Fig. 9
18
° pAD
Torque component contributions
then be entirely dependent upon the burnishing torque reduction.
The only other person to have investigated the various torque
components is Weber [8]. To separate the friction and burnishing components he first drilled a 50 millimeter diameter
hole in C60 steel in the normal manner and then plugged the
hole with a bar of the same material and redrilled. He concluded that no burnishing would be present during the second
0.35>TB/TD>0.16
drilling operation albeit the surface finish improved by 17
percent and that there was a negligible difference in the friction
and
area at the two pads between the two drillings. By simple
0.16>TRU/TD>0.09
subtraction of the two torque readings, the burnishing torque
The friction range is 87 percent whereas the burnishing range and hence friction torque could be calculated. He found the
is much larger at 19 percent. This is consistent with an increase burnishing torque to be 15 percent of the total torque and the
in feed having a marked effect upon the burnishing area but friction torque 20 percent but this was for only one test. These
only a small effect on the friction area. The ratio is changed values compare with 24 percent and 13 percent given here.
with feed and suggests that the rate of change of the cutting Bearing in mind that the materials and'diameters were different
and friction forces is greater than that of the burnishing forces. it is thought the differences can be accounted for by Weber's
To observe the sensitivity of the friction and burnishing very different approach.
ratios to changes in |3, the ratios have been calculated for the
The diagram in Fig. 8 gives the average results found in this
limiting values suggested above. The largest value was /3 = investigation. The proportions of the total drilling torque or
0.71 (extrapolating Rubenstein et al.'s results) and the smallest power (since the two are directly related) required for metal
value was /3 = 0.25 (recorded by Komanduri). The effect of removal friction and burnishing are shown. Deep hole drilling
these ranges is seen from the envelopes added to Fig. 8 except has three significant advantages which are: a high metal refor the lower feed rates the value of /3 does not seem to cause moval rate, the production of precision holes, and the unique
a dramatic change in either ratio. It is of interest that both surface integrity. These three advantages can be linked to the
Rubenstein and Komanduri report that j3 decreases as the width three "actions" of a deep drill namely metal removal at the
of cut increases. The width of cut is equivalent to the feed rate cutting edge, friction at the pads and burnishing at the pads.
in deep drilling which means that /3 decreases as the feed in- Thus, referring to Fig. 9, it can be said that on average 63
creases. This would have the effect of reducing the rate of percent of the power extended in deep drilling is responsible
change of both ratios with feed so that they vary less. If this for the metal removal rate, 13 percent is responsible for the
did occur then it is feasible that the friction ratio would not hole quality, and 24 percent is responsible for the unique survary with feed and the reduction in pad torque with feed would face integrity.
Journal of Engineering for Industry
MAY 1993, Vol. 115/181
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5 The Individual Friction and Burnishing Forces at
each Pad
The friction and burnishing torque or energy components
have been determined for the combined pads as 13 percent and
24 percent, respectively. These components can be subdivided
further to determine the individual friction and burnishing
forces at both pads.
5.1. Tangential Burnishing and Friction Forces ( B n 2 ) . If
it is assumed that the tangential burnishing are directly related
to area, the forces can be separated. At each revolution the
drill moves forward a distance corresponding to the feed rate
(/) and this will be shared by each pad in proportion to their
angles. The angles are 85 and 182 deg from the cutting edge,
so the included angle is 97 deg. The ratio of the burnishing
tangential forces is given by:
BT1:BT2::263:91
therefore
Bn/BT2
= 263/97 = 2.71
so
Bn = 0.73
(TB/r) = 0.175 (TD/r)
BT2 = 0.21 {TB/r) = 0.065 (TD/r)
Thus, the burnishing tangential forces divide into a ratio of
3:1 as shown in Fig. 9 which means that the lions share of the
surface integrity is due to the 90 deg pad. For a typical feed
of 0.1. mm/rev, TD = 23 Nm and r is equal to 11 mm thus:
BT1,2 are equal to 366.6N,
135.21N
5.2 Tangential Friction Forces (Fn<2). The friction forces
can be determined because the ratio of the total pad forces is
known from the first paper [1] and the burnishing forces have
been calculated in the previous section.
First, the total tangential forces will be related by the previously determined pad ratios [1]:
lxR{/nR2 = (BTl+FTX)/{BT2
+ FT2)
(10)
Second, the friction forces will sum to the previously determined torque:
TRu = 0.UTD = r(FTl+FT2)
(11)
Third, the tangential burnishing forces Bna have been determined above and are given in Eqs. (8) and (9).
From these three sets of equations the friction forces can be
found using the method described in Appendix 3:
Fn = 0.058 {TD/r)
FT2 = Q.Q12(TD/r)
These have been added to the Fig. 10 diagram. For a typical
feed of 0.1 mm/rev, TD = 23 Nm and r = 11 mm thus:
FTia are equal to 121.3N, 150.5N.
These friction results show that as a first order approximation
the tangential forces are equal. The fact that these values are
low supports the suggestion that the situation is hydrodynamic.
6
Concluding Remarks
The model suggested for the solution of the complex force
system of a deep drilling operation has allowed all the pad
forces to be determined. In Part 1 of this two part paper the
main conclusions were:
• the 90 deg pad forces are 1.7 times greater than the 180
deg pad forces.
• the pad tangential forces are 17 percent of the radial
forces.
• the pad axial forces are 17 percent of the tangential
forces.
182/Vol. 115, MAY 1993
8
the pad radial indentation forces are 20 percent of the
total pad force.
8
the pad radial friction forces are 80 percent of the total
pad force.
In this second part of the paper the basic model proposed in
Part 1 has been extended to include a friction coefficient (ftc)
relating the nonindentation forces at both pads and a burnishing coefficient (B) relating the indentation forces at both
pads. Using the results from the deep drilling tests the percentage of the energy and power required for drilling is as
follows:
» 63 percent is expended at the cutting edge contributing
to the high metal removal rates of a deep drilling operation.
8
24 percent is expended at the front of the pads during
indentation and thus could be considered as the energy
required to produce the unique surface integrity.
8
13 percent is expended over the nonindentation length
of the pads and can be considered as contributing to the
precision and stability of a deep drilling operation.
In the last part of this paper the tangential friction and burnishing forces of both pads have been separated and the various
components determined such that:
8
18 percent of the total drilling power is burnishing at the
90 deg pad (BTl)
8
6 percent of the total drilling power is friction at the 90
deg pad (FTl)
9
6 percent of the total drilling power is burnishing at the
180 deg pad (BT2)
• 7 percent of the total drilling power is friction at the 180
deg pad (FT2)
so that one can say approximately
Fj\ = Fj-2 = BTI = Bn/3
therefore one can conclude that the major burnishing force
occurs at the 90 deg pad and is three times larger than the
other burnishing or friction forces.
Thus the mathematical models proposed in these 2 papers have
allowed a solution to the complex force system existing in a
deep hole drilling operation.
References
1 Griffiths, B. J., "Modelling Complex Manufacturing Force Systems, Part
1. The Cutting and Pad Forces in Deep Drilling," ASME JOURNAL OF ENGINEERING FOR INDUSTRY.
2 WrightBaker.H., 1969,Modem Workshop Technology, Part2, MacMillan
Publishers.
3 Bowden, F. P., and Tabor, D., The Friction and Lubrication of Solids,
Parts 1 and 2, Oxford University Press.
4 Baier, J., 1978, Messung Der Reibungsverhaltnisse an Den Stutzleisten von
B.T.A. Tiefbohrwerkzeugen," Fachgesprache Zwischen Industrie und Hochschule, Universitat Dortmund, 23rd June.
5 Griffiths, B. J., 1986, "The Development of a Quickstop Device for use
in Metal Cutting Hole Manufacturing Processes,'' The International Journal of
Machine Tool Design and Research, Vol. 26, No. 2. pp. 191-203.
6 Rubenstein, C , Grossmann, F. K., and Koenigsberger, F., 1967, "Force
Measurements during Cutting Tests with Single Point Tools Simulating the
Action of a Single Abrasive Grit," Science and Technology of Industrial Diamonds, Proceedings of the International Diamond Conference, 1966, Vol. 1,
Industrial Diamond Information Bureau, London, pp. 161-172.
7 Komanduri, R., 1971, "Some Aspects of Machining with Negative Rake
Tools Simulating Grinding," International Journal of Machine Tool Design and
Research, Vol. 11, pp. 223-233.
8 Weber, U., 1978, "Beitrag zur Messtechnischen Erfassung des Tiefbohrprozesses," Dr. Eng. Thesis, Universitat Dortmund, June.
A P P E N D I X
1
Coulomb Friction Coefficient (/JLC). When drilling during
phase C without burnishing, the friction forces will exist over
the full length of both pads. In this situation, the equations
for the friction coefficient calculation given in Appendix 3 of
the previous paper can be used here where 7^* is substituted
for TP & ixc for ^. Thus:
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(12)
C5fi? + C 6 /*2-C 7 = 0
therefore
where:
TRu/TB=(l/p-
1 / M ) / ( 1 / | I - 1/^C)
(13)
But
C5 = sin(a2 - «i)(sin «! - sin a2 - (2h T*Ru/dTc)
7> = r«„ + rB = rB(i + w i y
sm(a2 - ai) + (cos a 2 - cos a{)/k)
therefore
C6 = (1 - cos(a 2 - aO)(sin <xx + sin a 2 ) + (cos(a 2 - ai) - 1)
r P /r z ,=(i + r«„/7,B)rfl/rZ5
(cos a\ + cos a2)/k
Substituting for TRu/TB from Eq. (13) above gives:
C7 = 2ArLsin 2 (a2-a,)/c?r c
TB/TD= TP/TD[l + ( ( 1 / 0 - l/ji)/(l//i +1//*))]
where ai = 85 deg & a 2 = 182 deg.
TRu/TD=TP/TD-TB/TD
A P P E N D I X
2
A P P E N D I X
Calculation of Burnishing and Friction Torque Ratio.
From Fig. 4 of the first paper:
Ri+R2-BRi+
Tangential Force (F n i 2 ) Equations.
therefore
(Bn
(15)
3
From Eq. (10):
BTI +FJ-\ = (Bf2 + Fj-2)R\/R2
FRi + BR2 + FR2
(fi + Fd/p = (F„ +FT2)/^+
(14)
and
+BT2)/p
but
(16)
Taking the force situation at a typical feedrate of/ = 0 . 1 m m /
rev the following four equations can be substituted into Eq.
(16) to find the values of FTi and FT2:
(a) from the previous paper:
Tp =
r(Fl+F2)
Ri/R2=l.l
and
{b) from section 5.1 above:
TRU
= r (FTl + FT2)
BTl = 0.175 TD/r
and
id) from section 5.1 above:
TB =
r(BTl+Br2)
BT2 = 0.065 TD/r
thus:
(d) from Eq. (11) we get:
TP/n=TRu/nc+TB/.p
FT2 =
0.n{TD/r)-Fn
substituting these four equations into Eq. (16) and rearranging
gives:
but
Tp = TRU + TB
therefore
F-n =0.058 TD/r
and
TRu/n + TB/n = TRu/nc + TB/(3
therefore
FT2 = 0.072 TD/r
at a feed rate of 0.1 mm/rev.
7j!B(l/M-l//0 = 7i(l/|8-l//i)
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