      Effects of Twist Drill Point Geometry on Torque and Thrust
Satoshi EMA*
In this study, the effects of the point geometry on cutting performance of twist drills with straight lips areinvestigated systematically. Many drills with different web thicknesses, point angles, lip relief angles, helix angles
and margin lengths were used, and torque and thrust in drillings were measured. The experimental results areassessed using variance analysis. Torque significantly increases with the web thickness and the margin length, andconversely decreases with the helix angle. There is an optimum point angle to minimize torque. Thrust significantly
increases with the web thickness and the relief angle, and conversely decreases with the point angle and the helix
angle. Twist drills with a web thickness of 1.0 to 1.5 mm, a point angle of about 118 deg., a relief angle of 8 to 13
deg., a helix angle of 29 to 39 deg. and a margin length of about 1 mm, are effective to reduce torque and thrust.

1. INTRODUCTION
In drilling operations, torque, thrust and drill life is significant criteria to evaluate the drill performance. Therefore, many
investigations on torque and thrust have been performed for various drill diameters, drill point shapes, workpiece materials andcutting conditions, and important findings to reduce torque and thrust or predict them have been obtained [1 - 14]. Particularly
regarding the relationships between drill point geometry and torque and thrust, Galloway [2] reported the effects of point angle,relief angle and helix angle. Kinman [3] showed the effect of chisel edge angle, while Lorenz [10] clarified the effect of helix
angle. Watson [12] showed the effects of point angle and relief angle. However, no twist drill has been reported which
simultaneously shows the effects of all the point parameters on torque and thrust. Although drill flute shapes vary with point
parameters, no study to date on the cutting performance of all drills with straight lips for conical grinding has been reported.
In this study, torque and thrust were measured using five types of drills, which have different web thicknesses, point angles, liprelief angles, helix angles and margin lengths, respectively. The experimental results obtained were assessed using varianceanalysis, and the effects of the point geometry on the cutting performance of twist drills with straight lips were systematicallyinvestigated.

NOMENCLATURE
DDrc
Fc
Hrl
MaNr
To
Th
WtD
J0
N
[*drill diameter (mm)
relative depth between thinned chisel edge parts (mm)
nominal cutting force (kN)
relative lip height (mm)
margin length (mm)
spindle speed of drilling machine (rpm)
drill radius (mm)
torque in drilling (kN㨯mm)
thrust in drilling (kN)
web thickness (mm)
relief angle at drill outer corner (deg.)
helix angle of drill flute (deg.)
point angle (deg.)
chisel edge angle (deg.)

Faculty of Education, Gifu University, 1 - 1 Yanagido, Gifu-shi 501-1193, JAPAN
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2. DRILL POINT GEOMETRY
According to British Standard [15] and American National Standard [16] describing twist drill features, a twist drill point
geometry with straight lips is identified by a web thickness Wt, a point angle 2N, a lip relief angle D0, a helix angle J0, a margin
length Ma and a chisel edge angle [as shown in Fig. 1. Therefore, in order to clarify the effects of all the point parameters except
for a chisel edge angle on torque and thrust, the five types of drills listed in Table 1 were used in the experiment. For example,W-type drills (W1-,W2- and W3-drills) are ones having different web thicknesses (Wt = 1.0, 1.5 and 2.0 mm, respectively), but theother point parameters, i.e., 2N, D0, J0 and Ma, are kept constant as indicated in Table 1. P-, R-, H- and M-type drills are ones
having different point angles, lip relief angles, helix angles and margin lengths, respectively, and coded in the same manner as
W-type drills. P2-, R2-, H2- and M2-drills are the same as a W2-drill. As shown in Table 1, W-, R-, H- and M-type drills
were varied at three levels but four levels for P-type drills. All the twist drills used in this experiment were straight shank twist drills
with 9 mm in diameter, 124 mm in overall length and 89 mm in flute length, and made of high speed tool steel. Two drills wereprepared for each drill shown in Table 1.

Fig. 1 Drill point geometry
Table 1 Dimensions and angles of drill point
DrillWeb Thickness
Wt (mm)Point Angle
2N (deg.)

Relief Angle
D0 (deg)

Helix Angle
J0 (deg.)

Margin Length
Ma (mm)Chisel Edge angle[ (deg.)

W1
W2
W3
P1
P2(W2)P3
P4
R1
R2(W2)R3
H1
H2(W2)H3
M2(W2)
M3
M41.0
1.5
2.0
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5

118
118
118
110
118
130
140
118
118
118
118
118
118
118
118
118

13
13
13
13
13
13
13
8
13
18
13
13
13
13
13
13

29
29
29
29
29
29
29
29
29
29
22
29
39
29
29
29

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.5
2.0

130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130






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



    In this experiment, all the drill points were shaped by a conical grinding method. In order that a drill lip becomes straight inthis method, a flute shape in a plane normal to the drill axis (particularly A - B in Fig. 8 which generates a lip) must be variedcorresponding to the web thickness Wt, the point angle 2N and the helix angle J0, as described by the following parametricequations [2];Wtcosec I2 (1)Wttan  0 cot I cot  I D
where r and Q are the polar coordinates of the flute shape and Iis the web angle. Therefore, the flute shapes of R- and M-type
drills were the same as the flute shape of W2-drill, while the flute shapes of W-, P- and H-type drills differed from that of W2-drill.
Conical grinding operations were carried out carefully so that each drill had the point angle and the relief angle prescribed in Table
1. Table 2 shows the mean relative lip height Hrl, which indicates the symmetry of two lips.
Since the increase of the web thickness enlarges a chisel edge, thrust in drilling operations may increase due to the enlarged
chisel edge. Therefore, a thinning operation for the chisel edge was carried out for all but the W1-drill, which had the shortest
chisel edge. The thinning operation was carried out carefully so that the depth of the thinned chisel edge parts (hatched portions inFig. 1) was kept at round 0.3 mm. The mean relative depth between these two thinned parts (Drc = Dc1 - Dc2) is listed in Table 2.
r

Table 2 Relative lip height and relative depth between thinned chisel edge parts
DrillHrl (mm)Drc (mm)

W1
W2
W3
P1
P2(W2)P3
P4R1R2(W2)R3
H1H2(W2)
H3
M2(W2)
M3
M4

0.007
0.052
0.022
0.000
0.052
0.037
0.060
0.000
0.052
0.027
0.010
0.052
0.017
0.052
0.047
0.065

0.088
0.110
0.031
0.088
0.070
0.045
0.113
0.088
0.025
0.052
0.088
0.046
0.088
0.042
0.057

3. EXPERIMENTAL METHOD
Drilling tests were performed on a drilling machine in order to measure torque and thrust. The experimental apparatus usedis shown in Fig. 2. A drill was equipped in the spindle, and a workpiece was fixed on a dynamometer as shown in the figure.
While the drill was boring a hole with a depth of 15 mm, the torque and the thrust generated on the workpiece were detected by thedynamometer and stored in a microcomputer through amplifiers and an A/D converter.
Two spindle speeds of 530 and 690 rpm were used, and the feed rate was constant at 0.1 mm/rev. The dimensions ofworkpieces used were 25 mm in diameter and 25 mm in length, and the material was rolled steel for general structure with a tensile
strength of 450 MPa and a hardness of 143 HB. All drilling tests were carried out without coolant. The experiment wasrepeated four times for each drill.
As described above, the drill point geometry and the spindle speed were varied as two main factors. Therefore, two factorial
experiments for each type of drills were performed, consisting of six different combinations of factors (eight combinations for Ptype drills). The effects of the drill point geometry and the spindle speed on torque and thrust were then assessed using varianceanalysis.


Fig. 2 Experimental set-up for measuring torque and thrust

4. EXPERIMENTAL RESULTS
4.1. Procedure for variance analysis
Figures 3 to 7 show the experimental results of torque and thrust obtained from the use of W-, P-, R-, H- and M-type drills,respectively. In the figures, the average values of torques or thrusts measured in eight drilling operations are plotted.
The procedure for variance analysis is shown in Table 3, in which the torque obtained from the use of W-type drills wasanalyzed. The main effects on the torque of the web thickness Wt and the spindle speed N, and the effect of their interaction on
the torque, are shown in the same table. The effect of the web thickness Wt on the torque is significant at the 1 % critical rate
indicated by the asterisk, because the F-ratio = 6.56 of the  web thickness is larger than F(2,42)0.01 = 5.16 obtained from theF-distribution table [19]. The effects of the spindle speed N and the interaction Wt×N on the torque are insignificant. The
F-ratios of the web thickness Wt, the spindle speed N and the interaction between them Wt×N obtained from Table 3 aresummarized in Table 4 together with the F-ratios of the other drill point parameters.
Furthermore, in order to investigate the effects between two different levels (drills) in the same type of drills on torque andthrust, the following variance analysis was performed. The mean difference in torque and the mean difference in thrust between
two different drills were obtained, and the results are summarized in Table 5. The values with an asterisk in the table aresignificant at the 1 % critical rate, because, for example, the mean difference in torque between W1- and W2-drills (307 N㨯mm) islarger than the value obtained from the following equation [19].
ª 2S' E ºt 0.01 >hk q  1 @ «»¬ kq ¼

0.5

 295

Where h = 3, k = 2 and q = 8 are the level of W-type drills, the level of the spindle speeds and the repetition of the experiments foreach drill, respectively. S’E is the mean square of the residual error (95395) indicated in Table 3, and t0.01[hk(q-1)] is the valueof the t-distribution with the 1 % critical rate. Based upon these variance analyses shown in Tables 4 and 5, the experimental
values of torque and thrust plotted in Figs. 3 to 7 were linked using curved lines.
Table 3 Variance analysis for torque of W-type drills
SourceSum of squares

Web thickness Wt
1252470
Spindle speed N
369440Interaction Wt×N
252660Residual error
4006570
Total
5881140(a) F(2, 42)0.01 = 5.16; (b) F(1, 42)0.01 = 7.29.
d.f.

Mean squares

F-ratio

Significance

21
24247

62635
369440126330
95395

6.56
3.87
1.32*(a)(b)(a)

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Table 4 F-ratios of torque and thrust
F-ratio
TorqueThrust
Web thickness Wt
6.56
*(a)
77.35
Spindle speed N
3.87
(b)
2.68
Interaction Wt×N
1.32
(a)
0.22
Point Angle 2N
8.91
*(c)
19.21
Spindle speed N
21.18
*(d)
3.25
Interaction 2N×N
0.66
(c)
0.20
2.37(a)12.10
Relief Angle DSpindle speed N
7.29
*(b)
12.32
Interaction D×N
1.35(a)
0.97
14.38
*(a)
40.38
Helix Angle J0
Spindle speed N20.79
*(b)
12.99
Interaction J0×N
2.00
(a)
3.59
28.06
*(a)
32.99
Margin Length Ma
Spindle speed N
20.00
*(b)
4.41
Interaction Ma×N
1.32
(a)
0.78
* significance(a) F(2, 42)0.01 = 5.16 (b) F(1, 42) 0.01 = 7.29(c) F(3, 56) 0.01 = 4.17 (d) F(1, 56) 0.01 = 7.13

*(a)
(b)
(a)
*(c)
(d)
(c)
*(a)
*(b)
(a)
*(a)
*(b)
(a)
*(a)
(b)
(a)

Table 5 Differences in torque and thrust between two different drills
Drill
W1
W2
W3
P1P2P3P4R1R2R3H1H2H3M2M3M4Torque (N㨯mm)
W1307*
369*
P1-292*-121-67
R1-191-32
H1-440*-387*

W2W363P2P3171*
226*
R255R3159
H2H353M2301*
517*

Thrust (N)P4-M3

M4217*-

W1144*
380*
P1-56*-77*-119*
R12772*
H1-132*-157*

W2W3235*
P2P3-21-63*
R2-42R345*
H2H3-25
M238*-54*

P4-M3

M4-92*-

4.2. Effect of spindle speed
Table 4 shows that the effects of the spindle speed N on torque are significant except for W-type drills, whereas the effects ofthe spindle speed on thrust are insignificant except for R- and H-type drills. Figures 4 to 7 show that the increase in spindle speed,(i.e., the increase in cutting speed) diminishes the torque.
As a drilling action is mainly carried out at the lips and the chisel edge of a drill, torque and thrust are influenced by cuttingforce generated at the lips and the chisel edge. Most of the torque is due to the cutting action at the lips, because the drill radiusalong the lips is longer than the radius along the chisel edge. On the other hand, a considerable amount of thrust is due to thecutting action at the chisel edge [4, 7]. This is in turn due to a large negative rake angle along with a very small cutting velocity inthe chisel edge zone. Therefore, it is clarified that the effect of the spindle speed on torque is generally greater than the effect of
the spindle speed on the thrust within the cutting conditions and the workpiece material used in the experiment.

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4.3. Effect of web thickness
Table 4 shows that the effects of the web thickness Wt on the torque and the thrust are significant at the 1 % critical rate. Asshown in Fig. 3 and Table 5, the thrust shows an extreme increase with web thickness, since the chisel edge length increases withthe web thickness. In addition, the rake angle at the thinned chisel edge parts of W2- and W3-drills is still negative. On the otherhand, the torque slightly increases between the web thickness Wt = 1.0 and 1.5 mm, but hardly between Wt = 1.5 and 2.0 mm,
since the torque depends mainly on the cutting action at the lips. Therefore, it is clarified that the effect of the web thickness on
the thrust is greater than the effect of the web thickness on the torque.

Fig. 3 Torque and thrust of W-type drills

4.4. Effect of point angle
Table 4 shows that the effects of the point angle 2N on the torque and the thrust are significant. Figure 4 and Table 5 showthat the thrust slightly decreases with the point angle. Since torque is lowest at 118 deg., this point angle is desirable to minimize
torque.

Fig. 4 Torque and thrust of P-type drills

4.5. Effect of relief angle
The effect of the relief angle D0 on the thrust is significant, whereas the effect on the torque is insignificant as shown in Table 4.
It is clear from Fig. 5 and Table 5 that the thrust does not vary between the relief angle D0 = 8 and 13 deg., but slightly increases
between D0 = 13 and 18 deg.. On the other hand, the torque maintains a constant value corresponding to the spindle speed.
    Therefore, the effect of the relief angle on the thrust is greater than on the torque. In addition, the increase in relief angle oftencauses whirling vibration in drilling operations [17, 18]. Therefore, a relief angle of 8 to 13 deg. is suitable to diminish thrust andsuppress the whirling vibration in drilling.

Fig. 5 Torque and thrust of R-type drills

4.6. Effect of helix angle
Table 4 shows the significant effects of the helix angle J0 on the torque and the thrust. It is clear from Fig. 6 and Table 5 thatthe torque and the thrust rapidly decreases between the helix angle J0 = 22 and 29 deg., since a rake angle on the lips increases withthe helix angle. However, the torque and the thrust remain constant in spite of the further increase in helix angle. This may be
explained by the fact that an excessive helix angle makes a chip flow difficult in the flutes, because the increase in helix angle
decreases the area of the flute zone as shown in Fig. 8. Furthermore, an excessive increase in helix angle weakens the drill lips.
Therefore, a helix angle of 29 to 39 deg. is suitable to diminish torque and thrust.

Fig. 6 Torque and thrust of H-type drills

4.7. Effect of Margin length
It is found from Table 4 that the effects of the margin length Ma on the torque and the thrust are significant. Figure 7 andTable 5 show that the torque considerably increases with the margin length due to the friction between the drill margin and theinner surface of a hole bored. Therefore, it is important to avoid the use of drills with unnecessarily large margin in order toreduce the torque; a margin length of about 1 mm is suitable.



Fig. 7 Torque and thrust of M-type drills

4.8. Comparison of all drills
The effects of each drill point parameter on torque and thrust have been clarified in the previous sections, but a comparison of
all the drills used in the experiment was not made. Therefore, a mean torque for each drill was obtained including the two spindle
speeds. Figure 9 shows the mean torques for all the drills arranged in order of magnitude.  Figure 10 shows the mean thrusts
obtained by the same manner as for torque. In terms of torque, W1-drill is the most effective, followed by W2- and H3-drills, inthat order. As for thrust, W1-drill is the most effective, followed by P4- and M4-drills. Thus, the cutting performance of drills
should be assessed using both torque and thrust.

Fig. 8 Flute shape in a plane normal to drill axis (D = 9 mm, Wt = 1.5 mm, 2k = 118 deg.)

Fig. 9 Torque of all drills    

Fig. 10 Thrust of all drills

In an assumption that the torque measured during a drilling operation acts at the middle of a lip (a half of drill radius r = 9/4mm), a nominal cutting force Fc was calculated from the following equation.

Fcª§ T0 · 2º2«¨ ¸  Th »«¬© r ¹»¼

0.5(3)

Figure 11 shows the nominal cutting forces estimated in this manner. It is found from the figure that W1-, W2- and H3-drills areeffective. W3-, M-4 and H1-drills are  less effective because of the largest thrust in W3-drill, the largest torque in M4-drill
and the considerably large torque and thrust in H1-drill, as shown in Figs. 9 and 10. In addition, the nominal cutting forces
estimated for other lip positions within r = 9/4 ± 0.5 mm are similar to the results shown in Fig. 11.
W1-, W2- and H3-drills are
similar to the drills recommended in handbooks for producing holes in steel materials [20, 21]. The results obtained in this study
provide evidence to explain why these drills are widely used in practical operations.
Fig. 11 Nominal cutting force of all drills

5. CONCLUSIONSTorque and thrust in drillings were measured using twist drills with various point shapes. The effects of the point geometry on
the cutting performance of twist drills were assessed by variance analysis, and the following conclusions can be made within thecutting conditions and the workpiece material used in the experiment.
(1) The effect of the spindle speed on torque is generally significant, and the increase in spindle speed reduces torque. However,
the effect of spindle speed on thrust is generally insignificant.
(2) Torque significantly increases with the web thickness and the margin length, and conversely decreases with the helix angle.
Torque is not affected by the relief angle. There is an optimum point angle to minimize torque. Thrust significantly
increases with the web thickness and the relief angle, and conversely decreases with the point angle and the helix angle.
The margin length generally does not affect thrust.
(3) Twist drills with a web thickness of 1.0 to 1.5 mm, a point angle of about 118 deg., a relief angle of 8 to 13 deg., a helix angleof 29 to 39 deg., and a margin length of about 1 mm, are effective to reduce torque and thrust.

REFERENCES[1] M. C. Shaw and C. J. Oxford, Jr., Trans. ASME 79, 139 (1957).
[2] D. F. Galloway, Trans. ASME 79, 191 (1957).
[3] M. D. Kinman, Machinery 1, 1014 (1963).
[4] S. Bera and A. Bhattacharyya, Proc. 8th Int. MTDR Conf. 879 (1967).
[5] G. F. Micheletti and R. Levi, Proc. 8th Int. MTDR Conf. 863 (1967).
[6] R. A. Williams, Int. J. Prod. Res. 8-4, 325 (1970).
[7] Bhattacharyya, Ajet Bhattacharyya, A. B. Chatterjee and I. Han, Trans. ASME, Series B 93-4, 1073 (1971).
[8] R. A. Williams, Trans. ASME, Series B 96-4, 1207 (1974).
[9] S. Wiriyacosol and E. J. A. Armarego, Ann. CIRP 28-1, 87 (1979).
[10] G. Lorenz, Ann. CIRP 28-1, 83 (1979).
[11] T. J. Roadinger and M. A. Townsend, Trans. ASME J. Engng Ind. 102-1, 37 (1980).
[12] R. Watson, Int. J. Mach. Tools Des. Res. 25-4, 347-404 (1985).
[13] Rubenstein, W. S. Lau and M. Wang, Int. J. Mach. Tools Manufact. 29-3, 441 (1989).
[14] Rubenstein, W.S. Lau, Z. J. Pei and M. Wang, Int. J. Mach. Tools Manufact. 29-3, 453 (1989).
[15] British Standard, B.S. 328, Part 1 (1959).
[16] American National Standard, A.N.S.I. B94.11M (1979).
[17] H. Fujii, E. Marui and S. Ema, Trans. ASME J. Engng Ind. 108-3, 157-168 (1986).
[18] S. Ema, H. Fujii and E. Marui, Trans. ASME J. Engng Ind. 110-4, 315 (1988).
[19] C. Chatfield, Statistics for Technology, Chapman and Hall, London (1983).
[20] S. T. M. E., Tool Engineers Handbook, McGraw-Hill, New York (1958).
[21] Metal Cutting Tool Handbook, Metal Cutting Tool Institute (1965).

