Basic Twist Drill Geometry

1
Basic Twist Drill Geometry
Refer figure 2-2
Helix and clearance angles
where ?sin-1(W/r) web angle at a point
on the lip
2
Drill Point Specification

• D - nominal drill diameter
• 2W - web thickness
• dO - helix angle at outer corner
• ClO - lip clearance angle at outer corner
• 2p - point angle (of the lips)
• ? - chisel edge angle

Typical features identified in handbooks and
standards
3
Circumferential Clearance
Refer figure 2-3
Require hcgt0 and Clcgt0 for rcltrltR
As Oc and Oco approach zero, Clc and Clco
approach Cl and Clo
4
Development of Flute Profile 1
Refer figure 2-4
Coordinates of a point C on the AB generator at
radius r
Axial translation of a generator A1B1 rotated by ß
Coordinates of a point C1 on the A1B1 generator
at radius r
5
Development of Flute Profile 2
Refer figure 2-4
Rotation for C2 to cross reference normal plane
(z 0)
Coordinates of point C2 on A2B2, i.e. equations
for the flute profile in a normal plane to the
drill axis
6
Point Sharpening
Refer figure 2-6
Conical (flank) grinding is commonly mentioned
It can be shown that 2W function (?, Cx,
Cy) 2p function(?, ?, ?) ? function(?, ?, ?,
Cx, Cy) Clo function(?, ?, ?, Cx, Cy, R)
Five independent sharpening parameters ? -
semi-cone angle ? - angle between cone axis and
drill axis Cx, Cy - drill location ? -
orientation angle so that cone and flank
parameters coincide
Four equations, five unknowns
7
Setting the Point Grinder
Refer figure 2-6
Numerical simulation shows that low ? causes high
Clco even whole flank ground and small ?w and
large ? causes negative Clco

• Specifying Clco provides an extra equation to
  uniquely specify the grinder parameters
• Clco function(?, ?, ?, Cx, Cy, R)

Given variety of grinders actually used, range of
values for features for General Purpose drills
production variability each drill behaves as an
individual tool
8
The Chinese Standard
Refer figure 2-7
Covers a wider range of diameters than most
western standards (0.1 100 mm)

• Besides the usual point features being
  quantified, this standard also gives recommended
  values for other features such as the fluted land
  width, the margin width, the body clearance and
  projected distance between the heel corners
• Extra information allows Clco to be calculated

Relates several features to diameter, rather than
just giving a range (see table 2-2)
9
From the Chinese Standard
Refer figure 2-8

• Clearer specification of point features together
  with Clco allows ?, ?, ?, Cx and Cy, to be found
  for conical grinding
• Up to 25 mm, large variability in setting values
  but beyond 25 mm angles are constant and linear
  distances proportional to diameter

.
Findings
10
Chinese Point Sharpening
Refer figure 2-9
Suggested method of conical grinding found in a
Chinese (and Russian) handbook

• For all diameters ? 45 and 13lt?lt15, Cx
  (.07 to .05)D and Cy, (1.8 to 1.9)D
• ? implied to be 0
• Satisfying 2W yields very small ?
• Using these values will not satisfy standards for
  point features (table 2-3)

Method is simplified
? 0 cannot give straight lips. Generated lips
slightly curved.
11
Cutting Geometry and Action
Refer figure 2-10
Apparent instantaneous area of cut D.f/2
At least for some regions we will have to
consider the dynamic geometry so we need to know
the cutting velocities.
Since Vf ltlt V in the lip region can let Vw V,
also for some of chisel edge
12
Basic Geometry
Refer figure 2-10
View A in Pfe, the working plane, contains V and
Vf

• In view A, for a point Q on a lip, can see
• d
• Cl

Pre is the working reference plane and is the
radial plane through the drill axis
13
Lip Region Geometry - 1
Refer figure 2-10

• In view B, at point Q on a lip, are shown
• normal rake and clearance angles
• reference rake and clearance angles
• View C shows the cutting velocity and cutting
  edge in true length, hence shows inclination angle

View B is in the normal plane Pn at Q
View C is in the working cutting edge plane, Pse
14
Lip Region Geometry - 2
Refer figures 2-10 2-11
From view A
From projecting point Q onto view B
From view B
Substituting for d and ?
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15
Lip Region Geometry 3
Refer figures 2-10 2-11
Clref found by projecting points Q and b from
view A to view B, and substituting for z1
From view B
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Lip Region Geometry 4
Refer figures 2-10 2-11
Inclination i for point Q on lips is shown in
view C
Cutting action at lips is a complex oblique
process with variable Vw, an and i
Ambiguity of flank specification does not affect
lip geometry
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17
Chisel Edge Geometry
Refer figures 2-12 2-13
Require detailed knowledge of flank geometry
grinding method
Assume straight line normal to drill axis
Cannot ignore Vf on dynamic angles
Below some limit radius Clne becomes negative and
edge acts as an indentor
Inclination very small
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18
Forces and Power - empirical
Typical forms of empirical equations. Given
variations in design production results can be
considered only approximate.
Cast Iron Th C1.f 0.6.D Tq C2.f
0.6.D2 Steel Th C1.f 0.6.D Tq C2.f
0.78.D1.8 Tq C2.f 0.803.D1.803
Boston Oxford (¼ to 1½)
Kronenberg
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19
Forces and Power - Empirical
Dimensional analysis by Shaw Oxford
Assuming a 0.2 for steel, and testing general
purpose drills with 2rc/D 0.18
Th 0.195.(BHN).f 0.8.D0.8 0.0022.(BHN).D2 or
Th C4.(BHN).f 0.63.D Tq 0.087.(BHN).f
0.8.D1.8
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20
Mechanics of Cutting Approach - Lip Region 1
Refer figure 2-14a
t, rl, ß, K1P K1Q found from orthogonal tests
and thin shear zone model
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21
Mechanics of Cutting Approach - Lip Region 2
Refer figure 2-14a
Required elemental geometry
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22
Mechanics of Cutting Approach - Lip Region 3
From classical oblique cutting thin shear zone
model
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23
Mechanics of Cutting Approach - Lip Region 4
Elemental edge force components
Putting it all together
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24
Mechanics of Cutting Approach - Chisel Edge 1
Refer figure 2-14b
Elemental forces
Total thrust and torque on chisel edge
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25
Mechanics of Cutting Approach - Chisel Edge 2
Refer figure 2-14b
Elemental cut geometry
Force coefficients C1P and C1Q for discontinuous
chips found from special orthogonal database
Overall, for the chisel edge
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26
Mechanics of Cutting Approach
Refer flowchart
Overall results
Analysis is complicated so computerisation is
useful
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27
Predicted Characteristics
Refer figure 2-15
From application of Mechanics of Cutting model
For Plane Flank model
Th C1.f 0.6.D Tq C2.f 0.78.D1.8 Tq C2.f
0.803.D1.803
Compared with empirical results
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28
Geometric Similarity
Refer figure 2-17
All specified angles must be equal
All specified lengths must be in proportion
All angles at corresponding points r1 r2 must
be equal
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Forces for Geometric Similarity - 1
Refer figure 2-18
Uth and Utq are forces per unit area.
For geometrically similar annuli, fundamental
angles are equal, so the specific forces are too.
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30
Forces for Geometric Similarity - 2
Refer figure 2-18
Applying equations from previous slide
Applying to whole of the drills
C1 and C2 depend on feed and work material
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