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Lecture Notes of Chinmay Das

1

DESIGN OF SINGLE POINT CUTTING TOOL

Objective: To remove greatest amount of material in the shortest length of time

consistent with finish requirements, work and tool rigidity, available power of the

machine, and relative cost of labour and cutting tools.[1]

In design of a single point cutting tool the following factors are to be considered.

i) Type of work piece material and tool material;

ii) Type of operation and surface finish required;

iii) Optimum tool angles;

iv) Permissible cutting speed, feed and depth of cut;

v) Cutting forces;

vi) Condition of work holding:

a) Work held as a cantilever;

b) Work held in between two centres, both of which can be live or one live and

the other dead.

c) Work held in chuck and tailstock centre.

vii) Overhung of the tool from the tool post;

viii) Accuracy of the work in terms of permissible deflection (maximum) of job with

respect to the tool.

Figure 4.1: Various turning operations


2

General recommendations for geometry of single point turning tools

High Speed Steel and Cast Alloy Tools Material BHN Back

Rake

Side

rake

End

Relief

Side

Relief

ECEA

Gray or flake graphite cast iron 140 5 10 6 6 6

Nodular or ductile cast iron 180 3 8 5 5 5

Malleable cast iron 220 0 5 5 5 5

Free machining plain carbon

steel, plain carbon steel

180 10 12 8 8 5

Free machining alloy steel 250 8 10 6 6 5

Alloy steels, cast steels 350 0 8 5 5 5

Hot work die steel, tool steel 500 0 5 5 5 5

Ferritic stainless steel 180 5 8 6 6 6

Austenitic stainless steel 200 5 6 6 6 6

180 5 8 6 6 6 Martensitic stainless steel

440 0 5 5 5 5

Precipitation hardening stainless

steel

220-320 0 5 5 5 5

Aluminium alloys 40*-110 20 15 12 10 5

Magnesium alloys 30*-80 20 15 12 10 5

Copper alloys 120-185 5 10 8 8 5

Titanium alloys 280-360 0 5 5 5 5

High temperature alloys 260-320 5 6 5 5 5

Table-I: Recommended tool geometry for single point cutting turning tools [2]

Carbide Tools

Brazed Throwaway Material BHN Back

Rake Side

rake Back

Rake Side

rake

End

Relief

Side

Relief ECEA

Gray or flake graphite cast iron 140 0 6 5 neg 5 neg 5 5 5

Nodular or ductile cast iron 180 0 6 5 neg 5 neg 5 5 5

Malleable cast iron 220 5 neg 5 neg 5 neg 5 neg 5 5 5

Free machining plain carbon

steel, plain carbon steel

180 0 6 5 neg 5 neg 5 5 5

Free machining alloy steel 250 0 6 5 neg 5 neg 5 5 5

Alloy steels, cast steels 350 0 6 5 neg 5 neg 5 5 5

Hot work die steel, tool steel 500 5 neg 5 neg 5 neg 5 neg 5 5 5

Ferritic stainless steel 180 0 6 0 5 5 5 5

Austenitic stainless steel 200 0 6 0 5 5 5 5

Martensitic stainless steel 180 0 6 0 5 5 5 5

440 0 6 5 neg 5 neg 5 5 5

Precipitation hardening

stainless steel

220-320 0 6 0 5 5 5 5

Aluminium alloys 40*-110 3 15 0 5 8 8 5

Magnesium alloys 30*-80 3 15 0 5 8 8 5

Copper alloys 120-185 5 8 0 5 5 5 5

Titanium alloys 280-360 0 6 0 5 5 5 5

High temperature alloys 260-320 0 6 0 5 5 5 5

Table-II: Recommended tool geometry for single point cutting turning tools [2]


3

Permissible Cutting Speed, Feed and Depth of Cut

Depth of cut has the greatest influence upon the cutting force, followed by feed,

with cutting speed having the least influence. Feed has the greatest effect on surface

finish when it is set according to nose radius. The cutting speed has maximum influence

on temperature generated at cutting zone during machining. Considering all above

factors, the tool designer has to make correct compromise so as to get best machining

operation under the given condition.

A general rule used by many production people to achieve the greatest machining

efficiency is to use the heaviest feed that will allow the required surface finish, use the

maximum depth of cut consistent with available power and rigidity of workpiece and

machine, and then establish the cutting speed to give the desired tool life. Too fast a

cutting speed will increase tool costs and down time for tool changing. Too slow a speed

simply cannot produce enough pieces to make a profit. Somewhere between too fast and

too slow is a cutting speed that will give the best tool life for overall efficiency.

Usually the best cutting speed is the one that will reduce the total cost of

machining to a minimum cost per piece. However, cost may be secondary, the objective

may be to set the maximum production rate. Many variables like the cost of labour on the

machines, over head costs, set up time, tool costs, tool changing time, time to machine

the workpiece, tool grinding time, grinding room labour costs etc. determine the

minimum cost and maximum production rate. The majority of these variables may be

changed to known quantities for a particular job. When these quantities are determined, it

is possible to plot costs and production rates vs. cutting speeds. The resulting graph

will show speeds for minimum cost and maximum production rate. The theoretical best

cutting speed will lie between the points of minimum cost and maximum production.

Figure 4.2: Cutting Speed vs. Production Rate


4

The recommended Cutting speeds and feeds for various work and tool materials.

HSS Cast Alloy Carbide Oxide Steel Condition BHN

Speed

m/min

Feed

mm/rev

Speed

m/min

Feed

mm/rev

Speed

m/min

Feed

mm/rev

Speed

m/min

Feed

mm/rev

Low

Carbon, free

machining

Cold drawn 170-

190 57 0.3 75 0.3 190 0.38 180-450 0.13-0.5

Medium

Carbon, free

machining

Cold drawn 200-

230 42 0.3 60 0.3 126 0.3 135-375 0.13-0.5

Medium

Carbon, free

machining

Quenched

and

tempered

250-

300 29 0.3 36 0.3 120 0.3 120-300

0.13-

0.38

Plain low

carbon Annealed

110-

165 42 0.3 54 0.3 158 0.38 165-450

0.13-

0.38

Plain

medium

carbon( 0.4

to 0.5 C)

Annealed 120-

185 30 0.3 45 0.3 143 0.38 135-300

0.13-

0.38

Plain high

carbon( 0.55

to 0.95 C)

Annealed 170-

200 27 0.3 42 0.3 128 0.3 128-270

0.13-

0.38

Plain

medium

carbon

Quenched

and

tempered

210-

250 24 0.25 38 0.25 120 0.3 120-240

0.13-

0.38

Quenched

and

tempered

260-

310 21 0.25 33 0.25 100 0.25 98-225

0.13-

0.38

Plain high

carbon

Quenched

and

tempered

320-

375 15 0.25 21 0.25 68 0.25 75-210

0.13-

0.38

Resulfurized

alloys Annealed

160-

210 38 0.3 53 0.3 128 0.38 135-300

0.13-

0.38

Leaded

alloy Annealed

140-

190 45 0.3 68 0.3 143 0.38 180-600 0.13-0.5

Normalised 250-

300 24 0.25 33 0.25 120 0.3 150-300 0.13-0.5

Alloy steels Annealed 150-

240 24-33 0.25 32 0.25 90-128 0.38 100-300 0.13-0.5

Normalised

or Quenched

and

tempered

240-

310 20 0.25 26 0.25 98 0.3 90-300

0.13-

0.38

Quenched

and

tempered

315-

370 14 0.25 20 0.25 83 0.25 90-270

0.13-

0.38

Quenched

and

tempered

380-

440 10 0.2 17 0.25 75 0.25 75-240 0.13-0.3

Quenched

and

tempered

450-

500 8 0.2 14 0.25 54 0.25 80-210

0.13-

0.25

Quenched

and

tempered

510-

560 5 0.2 8 0.25 36 0.25 60-180 0.07-0.2

Table-III: Cutting speeds and feeds for turning steels [3]


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HSS Cast Alloy Carbide Work material Condition BHN Speed

m/min

Feed

mm/rev

Speed

m/min

Feed

mm/r

ev

Speed

m/min

Fee

d

mm

/rev

Aluminium Alloys Non-heat-treatable cast alloys Cast 50-70 300 0.3 360 0.3 Max 0.38

Heat –treatable cast alloys Solution-

treated and

aged

70-105 210 0.3 300 0.3 Max 0.38

Non-heat-treatable wrought alloys Cold-Drawn 40-70 210 0.3 360 0.3 Max 0.38

Heat-treatable wrought alloys Solution-

treated and

aged

65-105 210 0.3 300 0.3 Max 0.38

Magnesium Alloys Cast alloys:

A10,A12,AZ63,AZ63X,AZ101,AZ

92,AZ92X,AS100,AZ90,AZ90X,

Cast 35-70 300 0.3 450 0.3 Max 0.3

Wrought alloys:

AT35,AZ31,AZ61,AZ80

Cold drawn 40-80 300 0.3 450 0.3 Max 0.3

Copper alloys Group-I Wrought or

cast 120-160 120 0.25 200 0.25 300 0.25

Group-II Wrought or

cast 165-180 80 0.25 150 0.25 250 0.25

Group-III Wrought or

cast 172-205 37 0.25 100 0.25 180 0.25

Titanium Alloys Commercially pure Wrought or

cast 150-200 45 0.25 48 0.25 112 0.25

Alloys:

MST 5 A1-2.5Sn,

RS110C,A110AT,Ti

6Ai-4Zr-1v,Ti, 8A11Mo-IV

Wrought or

cast 250-320 10 o.25 15 0.25 45 0.25

Ti6A1-4V,Ti

2A1-16V,Ti

4A1-4Mo-4V

Wrought or

cast Over 320 5 o.25 7 0.25 40 0.25

Table-IV: Cutting speeds and feeds for turning non-ferrous materials [3]

Cutting Forces during Turning The single point cutting tools being used for turning, shaping, planing, slotting, boring etc.

are characterised by having only one cutting force during machining. But that force is

resolved into two or three components for ease of analysis and exploitation.

Tangential or Cutting Force, Pz

This acts in the direction tangent to the revolving member and is sometimes

referred to as turning force. It is usually the highest of the three forces and constitutes

approximately 99 percent of the total power required by the tool.

Longitudinal or Feed Force, Px

This acts in a direction parallel to the axis of the work. It averages about 40

percent as high as the tangential force. Since the feeding velocity is very low, the power

required is usually 1 percent of the total.


6

Figure 4.3: Cutting Forces in Turning

Radial Force, Py

This acts in a radial direction from the centre of the work piece. It is the force that

holds the tool to the correct depth of cut. It is the smallest of the three tool forces-only 20

percent as large as the tangential force. It requires no power in that there is no velocity in

the radial direction. It should be kept to a minimum to reduce deflection, vibration and

chatter.

Calculation of Cutting Forces

From Merchant’s Circle Diagram for turning operation, we have

Tangential or Cutting Force [1]

Pz = {t so τs cos (η- γ0)} ⁄ { Sinβ0 cos(β0 + η- γ0)} [4.1]

Where, t = depth of cut

so = feed

τs = dynamic shear stress

η = coefficient of friction at chip-tool interface

γ0 = orthogonal rake

β0 = shear angle in orthogonal cutting

For brittle work materials, like grey cast iron, usually, 2 β0 + η - γ0

= 90

o

and τs remains

almost unchanged.

Then for turning brittle material, the cutting force

Pz = {t so τs cos (900 – 2 β0)} ⁄ { Sinβ0 cos(90

0 – 2 β0)} [4.2]

Or, Pz = 2 t so τs cot β0 [4.3]

Where, cot β0 = ζ – tan γ0 [4.4]


7

And ζ = chip reduction coefficient = a2 ⁄ a1 = a2 ⁄ so sin Φ [4.5]

Where, a2 = chip thickness and Φ = principal cutting edge angle

It is difficult to measure chip thickness and evaluate the values of ζ while machining

brittle materials and the value of τs is roughly estimated from

τs = 0.175 BHN [4.6]

Where, BHN= Brinnel Hardness Number

But most of the engineering materials are ductile in nature and even some semi-

brittle materials behave ductile under the cutting condition.

The angle relationship reasonably accurately applicable for ductile metals is

β0 + η - γ0

= 45

0 [4.7]

And the value of τs is obtained from,

τs = 0.186 BHN ( approximate) [4.8]

Or, τs = 0.74 σu ε0.6 ∆

( more suitable and accurate) [4.9]

Where, σu = ultimate tensile strength of the work material

ε = cutting strain ≈ ζ – tan γ0

∆ = % elongation

Substituting Equation 4.7 in Equation 4.1, we get

Pz = t so τs (cot β0 + 1) [4.10]

Again, cot β0 = ζ – tan γ0

So, Pz = t so τs(ζ – tan γ0 + 1) [4.11]

Longitudinal or Feed Force, Px and Radial Force, Py

From Merchant’s Circle Diagram for turning operation, we have

Pxy = Pz tan (η– γ0) [4.12]

Combining Equation 4.12 in Equation 4.1, we get

Pxy = {t so τs sin (900 –2 β0)} ⁄ { Sinβ0 cos(90

0 – 2 β0)} [4.13]

Again, using the angle relationship β0 + η - γ0

= 45

0, for ductile material

Pxy = t so τs (cot β0 – 1) [4.14]

Pxy = t so τs (ζ – tan γ0 – 1) [4.15]

Where, τs is 0.74 σu ε0.6 ∆

or 0.186 BHN It is already known,

Px = Pxy sinΦ and

Py = Pxy cosΦ Therefore,

Px= t so τs (ζ – tan γ0 – 1) sinΦ [4.16]

Py= t so τs (ζ – tan γ0 – 1) cosΦ [4.17]


8

Calculation of Tool Cross Section

Figure 4.4: Cutting Tool Cross Section

The shank of a cutting tool is generally analyzed for strength and rigidity. The tool is

assumed to be loaded as a cantilever by tool forces at the cutting edge as shown in

Figure 4.4. The deflection at the cutting edge is limited to a certain value depending on

the size of the machine, cutting conditions and tool overhung. The tool overhung (Le) is

related also to the shank size as well as to end fixity conditions. The recommended value

of (Le/ H) is between 1.2 and 2. The common value for Le is 25 to 40 mm.

Checking for strength:

We know that the bending moment due to cutting force Pz is Pz Le at the tool post. If the

height and width of cutting tool are H and B respectively, then

Pz Le = 1/6 BH2 σ1 [4.18]

Where, σ1= tensile stress induced in the cutting tool body

= 6 Pz Le / BH2 [4.19]

If the effect of Px is included, then it becomes a case for unsymmetrical bending.

σ = σ1 + σ2 = (6 Pz Le / BH2) + (6 Px Le / HB

2) [4.20]

Where, σ is permissible stress for cutting tool material = σut / factor of safety

σut = ultimate tensile strength of cutting tool materials

= 1000 N / mm2 for HSS

= 700 N / mm2 for HCS

factor of safety = 10 for rough machining

= 4 for finish machining

The Standard Cutting Tool Cross Section:

Figure 4.5: Types of Cutting Tool Cross section

The numerical values obtained for height and width of cutting tool from above equation

should be standardized as per BIS specification. The designation of a tool shank section

shall indicate the diameter, or the height and width in case of rectangular or square

shanks and IS number.


9

Example 1: A shank having a circular cross section of 8 mm diameter shall be designated

as: Shank Section 08 IS: 1983

Example 2: A shank having a square cross section h = 8 mm and b = 8 mm shall be

designated as: Shank Section 0808 IS: 1983

Rectangular

h x b

height to width ratio ( approx)

Round

d

Square

h x b

1.25 : 1 1.6 : 1 2 : 1

6 6 x 6 (6 x 5) 6 x 4 (6 x 3)

8 8 x 8 (8 x6) 8 x 5 (8 x 4)

10 10 x 10 (10 x 8) 10 x 6 (10 x 5)

12 12 x 12 (12 x 10) 12 x 8 (12 x 6)

16 16 x 16 (16 x 12) 16 x 10 (16 x 8)

20 20 x 20 (20 x 16) 20 x 12 (20 x 10)

25 25 x 25 (25 x 20) 25 x 16 (25x 12)

32 32 x 32 (32 x 25) 32 x 20 (32 x 16)

40 40 x40 (40 x 32) 40 x 25 (40 x 20)

50 50 x 50 (50 x 40) 50 x 32 (50 x 25)

63 63 x 63 (63 x 50) 63 x 40 (63x 32)

* Non preferred sizes are in brackets.

Checking for deflection:

The deflection of tool tip due to cutting force, Pz is given as

δ = (4 Pz Le3) / EBH

3 [4.21]

Where, E = Modulus of elasticity for tool materials

= 224000 N / mm2 for HSS

= 700000 N / mm2 for C2 Carbide

= 560000 N / mm2 for C6 Carbide

= 420000 N / mm2 for TiC and Ceramics

The permissible deflection of shank ranges from 0.04 mm in finishing cuts to 0.1 mm in

roughing cuts. [4]

Design of Chip Breakers

During the high speed machining of ductile materials, long chips are continuously

produced which must be broken into small pieces for easy disposal and to protect the

finished surface from coiling chips. Chip breakers may be added to a cutting tool for this

purpose.

Types of Chip Breaker:

Several types of chip breaking devices are in use. Sometimes a small step or shelf

is ground on the tool face for this purpose. Its depth is usually from 0.3 mm to 0.8 mm

(its width depends on feed and depth of cut). If the size of the shelf is properly chosen, it

will break a continuous chip into short pieces. This type of chip breaker considerably

increases the tool cost on carbide tools.

A cutting tool with a groove and ridge type chip breaker has a groove of 2.5 mm

to 13 mm width, 0.1 mm to 0.15 mm depth and a radius of 0.5 mm to 3 mm. A narrow


10

ridge or land is provided along the cutting edge for strength. With this form of tool face ,

the chip flows into the groove and is forced into curl. The closer the groove is to the

cutting edge, the smaller the radius will be and the tighter the chip will curl. In semi-

finish and finish turning of steel, the chip will break into short coiled pieces. This type of

chip breaker, requiring power consumption and depending less upon feed or depth of cut

than other types, is suitable for high feeds.

Separate type chip breakers, often adjustable are also in use in tipped tools,

particularly with throwaway type inserts.

Figure 4.6: Types of Chip Breakers-I

Figure 4.7: Types of Chip Breakers-II


11

Design of Tool Tips

The extensive application of cemented carbides in single point metal cutting practice has

led to the introduction of tipped tools when an insert is either brazed or clamped on to the

shank. The carbide tip must be so designed as to ensure that the resultant force P always

passes through the nest of tip in the shank and keeps the tip in compression. Various tip

designs are employed depending on the type of processing, feed and depth of cut. The

seat or recess for the tip in the shank may be either open, semi-open, closed or of the slot

type.

Figure 4.8: Typical Tip Styles

Figure 4.9: Seat for Tip in the Shank


12

The Tip Dimensions:

Figure 4.10: Dimensions of Tip in the Shank

The Seat Angle = θ = 250

to 300

G ≥ 3

2H

The thickness of standard tip = c= 2.5 mm to 12 mm

b/ c = 1.6 to 2.7 and E = G + b sin θ + c cos θ ≥ H

Where H = Tool shank height

F = Dimension for line of centres of lathe [ 5]

Problem 1: Design a HSS cutting tool to machine mild steel work piece in a lathe.

Assume suitable data.

Solution: Since not much data available to solve above problem, we have to make following

assumptions.

1. BHN of material = 200 Kg/ mm2

2. Back Rake Angle, Side Rake Angle and Side Cutting Edge Angle for HSS tool for

machining mild steel are 100, 12

0 , 45

0 respectively.

3. Dynamic Shear Stress of mild steel can be calculated using τs = 0.186 BHN Kg/ mm2

4. Ultimate Tensile Strength of HSS is 1000 N / mm2 .

5. Factor of Safety for rough machining is 10.

6. Shank of Tool Section is square.

7. Tool Over Hung is 30 mm.

8. Chip Reduction Co-efficient is 2.5 for rough machining.

Calculation:

Conversion of tool angles from ASA system to ORS

tan γ0 = tan γy cosΦ + tan γx sinΦ

= tan 10 cos 45 + tan 12 sin 45

= 0.273

or, γ0 = 15.260


13

Dynamic Shear Stress of mild steel is τs = 0.186 BHN Kg/ mm2

= 0.186 x 200 = 37.2 Kg/ mm

2 = 372 N / mm

2

Selecting depth of cut 2 mm and feed 0.3 mm/ rev, we have

Pz = t so τs(ζ – tan γ0 + 1) = 2 x 0.3 x 372 ( 2.5 – tan15.26 + 1) = 720.26 ≈ 720 N

Px = t so τs (ζ – tan γ0 – 1) sinΦ = 2 x 0.3 x 372 ( 2.5 – tan15.26– 1)sin 45 = 193.6 ≈ 194 N

σ = σ ut / FOS = 1000/ 10 = σ 1 + σ 2 = (6 Pz Le / BH2) + (6 Px Le / HB

2)

Here Le = 30 mm, and H=B

So, 100 = {( 6 x 720 x 30 ) / B3 } + {( 6 x 194 x 30 ) / B

3 }

or, B = 11.805 mm

The nearest standard cross section value is 12 mm. Therefore cross section of tool shank

selected is 12 mm x 12mm.

Checking for deflection:

δ = (4 Pz Le3) / EBH

3 = ( 4 x 720 x 30

3 ) / ( 224000 x 12

4 )

= 0.016 mm , which is within the permissible limit.

Power consumed = Pz x Vc = 720 x { 50 / 60}= 599 W ≈ 0.6 KW

Cutting Tool Specification 1212 IS: 1983

Cutting Tool Material can be M2 (T83 W6 Mo5 Cr4 V2) or T1 ( T72 W18 Cr4 V1)

Generally M type HSS materials are cheaper compared to T type material.

The various M type HSS materials are M1, M2, M3, M4, M7, M10, M33, M36, M41,

M42, M43, M44, M45, and M46.

The various T type HSS materials are T1, T2, T4 and T6.

The design of chip breaker is optional.

Reference:

1. Manufacturing Science-II by A.B. Chattopadhyay, NPTEL website at

www.nptel.iitm.ac.in

2. Tool Design by Cyril Donaldson, page 304

3. ASTME, “Manufacturing, Planning and Estimating Hand Book”, F.W.Wilson(ed),

McGraw-Hill, New York, 1963

4. Metal Cutting- Theory and Practice by A. Bhattacharyya, page 577

5. Metal Cutting- Theory and Practice by A. Bhattacharyya, page 580

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