The Selection of Manufacturing Engineering Process

The Selection of Manufacturing Engineering Process; By Dr. Saied. M. Darwish

1

CHAPER ONE: Fits and Tolerances

CHAPTER ONE: FITS AND TOLERANCES

1.1 Dimensional Tolerances Some of the dimensional tolerances terms are defined as

following:

1.1.1 Dimension:

A geometrical characteristic such as length, diameter, angle, center distance, etc.

1.1.2 Size:

Size is the designation of magnitude (when a value is assigned to a dimension, it is referred to

as the size of the dimension.)

1.1.3 Actual size (of a part):

The value of the size as practically obtained by measurements.

1.1.4 Basic size:

The size by reference to which the limits of size are fixed.

Figure: 1 Basic terms of dimensions and limits


2


1.1.5 Design size:

The combination of the basic size and the limits of size chosen by the designer.

11..6 Limits of size:

The two extreme permissible sizes of a part between which the actual size should lie.

1.1.7 Maximum limit of size:

The greater of the two limits of size.

1.1.8 Minimum limit of size:

The smaller of the two limits of size.

1.1.9 Maximum material limit:

The maximum limit of size of an external dimension or the minimum limit of size of an

internal dimension.

1.1.10 Minimum material limit:

The minimum limit of size of an external dimension or the maximum limit of size of an

internal dimension.

1.1.11 Tolerance:

Difference between the maximum limit of size and the minimum limit of size (difference

between upper deviation and the lower deviation).


3

Tolerance

Tolerance zone

Zone line


1.1.12 Zero line:

The zero line is the line of zero deviation and represents the basic size.

1.1.13 Upper deviation:

Algebraical difference between the maximum limit of size and the corresponding basic size.

1.1.14 Lower deviation:

Algebraical difference between the minimum limit of size and the corresponding basic size.

1.1.15 Tolerance zone:

Zone comprised between the two lines representing the limits of tolerance, and defined by its

magnitude (tolerance) and by its position to the zero line.

1.1.16 Unilateral tolerance:

Is the tolerance in which the variation in size is permitted only in one direction from the basic

size.

1.1.17 Bilateral tolerance:

Is the tolerance in which the variation in size is permitted in both directions from the basic

size.


4

Basic shaft

Basic hole


1.1.18 Shaft:

Term used by convention to designate all external features of a part, including parts which are

not cylindrical.

1.1.19 Hole:

Term used by convention to designate all internal features of parts, including parts which are

not cylindrical.

1.1.20 Basic shaft:

It is the shaft, the upper deviation of which is zero. It is the shaft chosen, as a basis for a shaft

basis system of fit.

1.1.21 Basic hole:

It is the hole, the lower deviation of which is zero. It is the hole chosen, as a basis for a hole

basis system of fit.

1.1.22 Fit: Relationship resulting from the difference, before assembly, between the sizes of

the two parts which are to be assembled.


5

Clearance fit

shaft

hole

Interference fit

hole

shaft


Figure 2: Clearance and interference fits

1.1.23 Basic size of a fit:

Common value of the basic size of the two parts of a fit.

1.1.24 Clearance fit:

The fit which always provides a clearance (the tolerance zone of the hole is entirely above

that of the shaft)

1.1.25 Interference fit:

The fit which always provides an interference (the tolerance zone of the hole is entirely

below that of the shaft)


6

Min. clearance

shaft

hole

Max. clearanceshaft

holeMax. clearance

shaft

hole


1.1.26 Transition fit:

The fit which may provide either a clearance or an interference (the tolerance zones of the

hole and the shaft overlap)

1.1.27 Minimum clearance:

In a clearance fit, difference between the minimum size of the hole and the maximum size of

the shaft.

1.1.28 Maximum clearance:

In a clearance or a transition fit, difference between the maximum size of the hole and the

minimum size of the shaft.


7

Max. interference

shaft

hole

shaft

hole

Max. interference

Min. interference

hole

shaft


1.1.29 Minimum interference:

In an interference fit, magnitude of the (negative) difference between the maximum size of

the hole and the minimum size of the shaft, before assembly.

1.1.30 Maximum interference:

Magnitude of the (negative) difference between the minimum size of the hole and the

maximum size of the shaft, before assembly.

1.1.31 Shaft-basis system of fits:

System of fits in which different clearances and interferences are obtained by associating

various holes with a single basic shaft.

1.1.32 Hole-basis system of fits:

System of fits in which different clearances and interferences are obtained by associating

various shafts with a single basic hole.


8


Figure 3: Basic hole and shaft system


9

Figure 4: Hole and shaft system


10


1.2 Symbols for Tolerances and Deviation and Symbols for Fits

1.2.1 Tolerance values:

The tolerance value is a function of the basic size and is indicated by a number

called the grade.

1.2.2 Tolerance position:

The position of the tolerance zone with respect to the zero line, is indicated by a

letter symbol, a capital letter for holes and a small letter for shafts.

The tolerance size thus defined by its basic value followed by a symbol composed

of a letter and a number.

Example: 45 g7

1.2.3 A fit:

A fit is indicated by the basic size common to both components, followed by

symbol corresponding to each component, the hole being quoted first

Example: 45 H8 g7

Possibly 45 H8 g7

Or 45 H8/g7

1.3: Grades of tolerances

Eighteen grades of tolerances are provided IT01, ITO and IT1 to IT16

The Table 1.1 gives the possible degrees of precision or grade of tolerance, achieved with

different machine tools.


11


Table 1.1: Possible degree of precision or grade of tolerance

Tolerance grade Intended for Applicable to components or machines

I T 01

Gauges

Slip blocks, Reference gauges I T 0

I T 1

I T 2

High quality gauges I T 3

I T 4

I T 5

Fits

Ball bearing

I T 6 Grinding, Honing

I T 7 Broaching

I T 8 Center lathe turning

I T 9 Worn automatic lathe

I T 10 Milling

I T 11 Drilling, Rough turning

I T 12

Not for fits

Light press work

I T 13 Press work

I T 14 Die casting

I T 15 Stamping

I T 16 Sand casting


12

Figute 5: Position of the various tolerance zones for a given diameter in the ISO system


13

Figure 6: Respective positions of various tolerance zones for hole


14


1.4 Fundamental tolerance unit

1.4.1Values of standard tolerances:

T = 10 0.2 (G 1)

(0.45 3D + 0.001D)

G = Tolerance grade IT6 IT 16

K = multiplier factor, depending on the tolerance grade G

1.4.2 Fundamental deviations:

1.4.2.1 Shaft deviation:

1) For each letter symbol defining the position of the tolerance zone, the magnitude

and sign of one of the two deviations which is known as the fundamental deviations (upper

deviation) es or lower deviation ei are determined by a formulae given in Table 6.

2) The other deviation is derived from the first one using the magnitude of the

standard tolerance IT, by means of the following algebraic relationship:

or

3) The fundamental deviation given by the formulae in Table 6 is, in principle, that

corresponding to that limit closet to the zero line, in other words, the upper deviation es for

shafts (a) to (h), and the lower deviation ei for shafts (j) to (Zc).

ei = es IT

es = ei + IT


15


1.4.2.2 Hole deviation:

For each letter symbol, defining the position of the tolerance zone, the magnitude and

sign of the fundamental deviation (lower deviation EI for holes (A) to (H) and upper

deviation ES for holes (J) to (Zc), are derived from the fundamental deviation es or ei

of the shaft with the same letter.

1) EI = - es for A to H

ES = -ei for J to Zc

2) The other deviation is derived from the first one, using the magnitude of the tolerance IT

by means of the following relationships.

or

1.4.3 Numerical values:

Fundamental shaft deviations:

Table 1.2 gives, for each dimension step, the values of the fundamental shaft

deviation:

Upper deviation es for shafts with symbols (a) to (h).

Lower deviation ei for shafts with symbols (J) to (Zc).

The other deviation can be derived from the fundamental deviation, as indicated before, by

adding or subtracting, as the case may be, the value of the standard tolerance IT are given

in Table 1.2 for the grade in question.

ES = EI + IT

EI = ES - IT


16


Figure 7:

Two comparable fits, with basic hole and basic shaft, in which a hole of a given grade is

associated with a shaft with next finer grade (H7/P6 and P7/h6), have exactly the same

clearance or interference.


17

Table 1.2: Values of fundamental tolerances

Grade 01 0 1 2 3 4 5 6 7 8 10 11 12 13 14* 15* 16*

Sta

ndar

d t

ole

rance

s in

mic

rons(

0.0

01m

m)

for

dia

met

er

step

s in

mil

lim

eter

s

< 3 0.3 0.5 0.8 1.2 2 3 4 6 10 14 40 60 100 140 250 400 600

> 3 to 6 0.4 0.6 1 1.5 2.5 4 5 8 12 18 48 75 120 180 300 480 750

> 6 to 10 0.4 0.6 1 1.5 2.5 4 6 9 15 22 58 90 150 220 360 580 900

> 10 to 18 0.5 0.8 1.2 2 3 5 8 11 18 27 70 110 180 270 430 700 1100

> 18 to 30 0.6 1 1.5 2.5 4 6 9 13 21 33 84 130 210 330 520 810 1300

> 30 to 50 0.6 1 1.5 2.5 4 7 11 16 25 39 100 160 250 390 620 1000 1600

> 50 to 80 0.8 1.2 2 3 5 8 13 19 30 46 120 190 300 460 740 1200 1900

> 80 to 120 1 1.5 2.5 4 6 10 15 22 35 54 140 220 350 540 870 1400 2200

> 120 to 180 1.2 2 3.5 5 8 12 18 25 40 63 160 250 400 630 1000 1600 2500

> 180 to 250 2 3 4.5 7 10 14 20 29 46 72 185 290 460 720 1150 1850 2900

> 250 to 315 2.5 4 6 8 12 16 23 32 52 81 210 320 520 810 1300 2100 3200

> 315 to 400 3 5 7 9 13 18 25 36 57 89 230 360 570 890 1400 2300 3600

> 400 to 500 4 6 8 10 15 20 27 40 63 97 250 400 630 970 1550 2500 4000

up to 1 mm, grades 14 to 16 are not provided

The Selection of Manufacturing Engineering Process; By Dr. Saied. M. Darwi h 19


PROBLEMS

Problem 1

Define each of the following terms (use sketches whenever possible)

Basic size - Dimension - Size - Maximum material limit - Upper deviation - Lower

deviation - Basic hole - Basic shaft - Transition fit - Clearance fit - Maximum

interference Straightness error - Cylindricity error - Roundness error - Run out (axial

and radial).

Problem 2

A shaft with a nominal size of 42 mm is fitted with an inner ring. The fitting condition is

K 5/h6.

- Determine the type of fit between the shaft and the hole.

- Mention, whether it is a hole-based or a shaft-based.

- Find the shaft and hole dimensions with upper and lower deviations.

Problem 3

(a) Describe by sketch the available classes of fits. What is the

difference between the unilateral and bilateral tolerance systems.

Then sketch a unilateral hole-based clearance fit.

(b) A shaft with a nominal size of 35 mm is fitted with an inner region of a ball

bearing bearing (hole). The fitting condition is H7/P6

- Determine which type of the fit class is between the shaft and the hole. Find the

hole and shaft dimensions with upper and lower deviations.

Problem 4

Figure (1-a), shows a stepped shaft with four concentric diameters and a flange which must

run true with the datum axis. The shaft is to be located within journals at X and Y and these

are identified as datums. Fig. (1-b) shows a group of dial gauges used to test the geometrical

tolerances given in Fig. (1-a). Define each of these geometrical tolerances, ten give the

reading that each dial gauge should indicate.


CHAPTER ONE: Fits and Tolerances


CHAPTER TWO: FUNDAMENTALS OF METAL CUTTING

2.1 Geometry of single point tool

The chip removal process may be performed by cutting tools of definite geometry. These

cutting tools can be classified as single point cutting tool, used in lathe, planer and, slotter

and multi point cutting tool used in milling, drilling and broaching.

A typical single point cutting tool for lathe and its geometry is shown in figure 2.1.

Figure 2.1: Nomenclature of a single point cutting tool

2.1.1 Right cut tool

A right cut tool is the tool in which the main cutting edge faces the headstock of the lathe,

when the tool is clamped and in this case the tool cuts from right to left.

2.1.2 Left cut tool

In this case the main cutting edge faces the tailstock of the lathe and consequently the tool

cuts from left to right as shown in figure 2.2.


CHAPTER TWO: Fundamentals of Metal Cutting

Left cut Right cut

Figure 2.2: Two basic types of single point cutting tools

2.1.3 Tool planes

To define the tool angles, some reference planes are suggested.

a-The basic plane: Is the plane containing the tool base.

b-Auxiliary plane of main cutting edge: Is the plane containing the main cutting edge and

perpendicular to the basic plane.

c- Auxiliary plane perpendicular to the projection of main cutting edge: It is the plane

perpendicular to the projection of the main cutting edge and both planes mentioned above. As

shown in figure 2.3

Figure 2.3: Tool planes



2.2 Tool angles

The main tools angles are shown Figure 2.4.

Figure 2.4: Single point cutting tool angles

2.2.1 Clearance angle : It is the angle between the main flank and the auxiliary plane z,

measured in the auxiliary plane c.

2.2.2 Wedge angle : It is the angle between the tool face and the main flank, measured in

the auxiliary plane c.

2.2.3 Rake angle : It is the angle between the tool face and a plane passing through the

point of the intersection of the main cutting edge with auxiliary plane c and parallel to the

basic plane a, it also measured in the auxiliary plane c.

2.2.4 Cutting angle : It is the sum of the clearance angle and wedge angle.



According to the figure.

90

The rake angle may be positive when the face slopes downwards, and negative when the face

slope is upward, with respect to the basic plane. It is equal to zero when the face is parallel to

the basic plane.

2.2.5 Auxiliary angles

In addition to the above mentioned main angles, the single point tool has auxiliary angles,

90'''

2.2.6 Nose angle

It is the angle included between the projections of the main and auxiliary cutting edges on the

basic plane.

2.2.7 Setting angles

It is the angle between the projection of the main cutting edge on the basic plane and the

direction of the feed.

Generally the tool angles are chosen with respect to:

1- The material to be machined, negative rake for hard and brittle materials and positive

for ductile materials.

2- The tool material.

3- The machining method.



2.3 Requirements of tool materials:

2.3.1 High hardness and high hot hardness: The tool material must posses higher hardness

then that of the machined workpiece. It should have high hot hardness, (the ability to retain

hardness at high temperatures).

2.3.2 High wear resistance: The tool material must resist mechanical abrasion caused by the

sliding contact with the chips and machined surfaces.

2.3.3 High strength and toughness (impact resistance): The tool material should have

sufficient strength and toughness to withstand static and impact loads.

2.3.4 High thermal conductivity: Cutting tool materials possing higher thermal

conductivity is desirable, since it enables part of the heat generated at the cutting edge

to be transferred readily to the tool post and machine parts.

2.3.5 Low cost: For economical production, the tool cost must be as low as possible.

2.4 Common tool materials

2.4.1 Tool carbon steels: It contain 0.6 1.4 percent carbon and low percentages of Mn, Si,

S, P, and heat treated, it withstand temperatures < 250C.

2.4.2 Alloy tool steels: The cutting performance of steel can be improved by adding alloying

elements such as chromium (Cr), vanadium (V), molybdenum (Mo) and tungsten (Tn). When

these steels properly heat treated, they can work at temperatures up to 300C.

2.4.3 High speed steels: It contain 8 19% tungsten and 3.8 4.6% chromium. They can

withstand temperatures up to 600C.

2.4.4 Cemented carbides: Also known as sintered carbide, they have high wear resistance at

high temperatures. These carbides are used to produces cutting tools by powder metallurgy

technology.



Carbide cutting tools can be used at considerably higher cutting speeds, and they can be used

in case of those materials which are hard and difficult to cut by other tools. The applications

of common sintered carbides are summarized in Table 2.1.

Common types of carbides used in the manufacturing of cutting tool are as following.

2.4.4.1 Straight tungsten cemented carbide: It consists of grains of tungsten carbide held in

a matrix of cobalt. It also known as tungsten carbide, used for machining of cast iron and

other ductile materials.

CoWC Tungsten Carbide

2.4.4.2 Titanium -Tungsten cemented carbides: Contain grains of solid solution of

tungsten carbide in carbide of titanium bonded by cobalt. It can be used for machining of

unhardened carbon and alloy steel.

WC + TiC + Co Titanium-tungsten Carbide

Tungsten Titanium Cobalt

Carbide Carbide (binding agent)

2.4.4.3 Titanium Tantalum Tungsten cemented carbides: Contain grains of solid

solution of titanium carbide in tantalum and tungsten carbide, cobalt is used as binding agent.

TiC + WC + TaC + Co

Titanium Tungsten Tantalum Cobalt

Carbide Carbide Carbide (binding agent)

According to ISO, sintered carbides are grouped into three main groups, identified by the

letters P(blue), M(yellow), and K(red).



1- GroupP: Mainly intended for machining of steels and they contain a relatively

higher percentage of titanium carbide and tantalum carbide. Titanium carbide and

tantalum carbide are characterized by their hardness and lower toughness. Therefore,

they can withstand high speeds but they are sensitive to shocks and vibration.

2- Group K: Mainly composed of tungsten carbide and Cobalt. Tungsten carbide is

characterized by its toughness, used for machining materials producing short broken

chips and they withstand shocks and vibrations.

3- Group M: It is an intermediate group that contains higher percentage of tungsten

carbide. They are tougher than those in group P. used for machining of cast iron and

steels.

2.4.5 Ceramic tool materials

Ceramic materials are made by compacting followed by sintering of aluminum oxides at high

temperature (1700C). They are enable to machine all materials at very high cutting speeds

with higher surface finish and no coolant is required. The ceramic tools are inexpensive as

compared with cemented carbide tools. Al2O3 is the common material used in producing

ceramic. Brittleness and low impact strength are the disadvantages of ceramic. When ceramic

tools replaced sintered carbides, the machining time is reduced by 30 50 %, due to the

increase in cutting speeds.

2.4.6 Diamonds

Diamonds are the hardest materials; they can work up to 1500C. It is found in nature or

synthetically produced from ordinary graphite by subjecting it to extremely high pressures

and temperatures. They are used for finishing ferrous metals and alloys, dressing and truing

grinding wheels. Metal cutting tools, wire drawing dies, penetrators of hardness testers, and

lapping powder are common applications of diamonds.



2.4.7 Cubic Boron Nitride (CBN)

Cubic Boron Nitride is the hardest known material next to diamond. It is ment to transform

the crystal structure of carbon from hexagonal to cubic. CBN does not react with iron and

nickel, therefore the applications of CBN is the machining of steel and nickel based alloys.

CBN is expensive, and the application must justify the additional tooling cost.

Figure 2.5: Improvement in cutting tool materials have reduced machining time

Figure 2.6: Typical hot hardness relationship for selected tool materials. Plain carbon steel

shows a rapid loss of hardness as temperature increases, while cemented carbide and

ceramics are significantly harder at elevated temperatures.



2.5 Methods of fixation of sintered carbides, ceramics and diamond tools

The cutting tools made from sintered carbides, ceramic and diamonds are available in the

form of tips (inserts). These inserts can be used with the common tool shank. There are two

methods of fixation commonly used. One is brazing and the other is mechanical clamping,

both methods have their advantages and disadvantages.

2.5.1 Mechanical clamping

Mechanical clamping is used for cemented carbides, ceramics, and other hard materials. In

this method the cemented carbide, ceramic, and diamond inserts clamped mechanically with

the tool shank.

2.5.2 Brazing

In this method of fixation, the tool bits are bonded with the shank by applying soldering

materials.

2.6 Disadvantages of mechanical clamping

Mechanical clamping of cutting inserts does not always ensure a contact stiffness that

is sufficiently high to prevent vibrations which develop in machining.

These vibrations shorten the life of the insert and often produce machined surfaces

with poor finish.

The clamping arrangement is often of comparatively large size, which in many cases

limits the cutting parameters of the tool such as depth of cut, width of cut.

2.7 Disadvantages of brazing

Micro fissures are often produced due to the high temperature of the brazing

operation.

The proportion of rejects due to cracks in tips is 10 40%.

High skills is required for brazing.

Difficulty in changing the worn insert.



Figure 2.7: Method of fixation brazing and mechanical clamping



Table (2.1): Application of different types of sintered carbides

Group Type Material machined Application

P

(blue)

P01 Steel and cast steel

Fine turning and boring, high speeds,

small chip cross-sections, high accuracy

and good surface quality, vibrations not

allowed.

P10 Steel and cast steel

Turning, copying, threading, milling,

high speeds, small and medium chip

cross-section

P20 Steel, carbon steel, tempered

cast iron

Turning, copying, milling, medium chip

cross-section, medium speeds, fine

planning

P30 Steel, carbon steel, tempered

cast iron

Turning, milling, planning, small and

medium speeds, medium and great chip

cross-sections

P40

&P50

Steel, carbon steel with

enclosures

Turning, planning, low speeds, great

chip cross-sections may be applied on

automatics

M

(yellow)

M10

Steel, carbon steel,

manganese carbon steel, cast

iron, alloy cast iron

Turning, planning, low speeds, great

chip cross-sections may be applied on

automatics

M20 Steel, cast steel, austen steel,

manganese steels, cast iron,

Turning, milling, medium cutting

speeds, medium chip cross-sections

M30 Steel, cast steel, austen steel,

cast iron, heat resistant steels

Turning, milling, planning, medium

cutting speeds, medium chip cross-

sections

M40 Automatic steels, light

metals

Turning, form turning, cutting off;

applied on automatics

K

(red)

K01

Hard cast iron, aluminum

alloys with high Si contents,

hard steels, plastics,

porcelane

Turning, fine turning and boring, fine

milling, scraping

K10 Cast iron BH>220, copper,

brass, aluminum, wood

Turning, milling, boring, reaming,

scraping, broaching

K20 Cast iron BH


Table (2.2): Composition, mechanical and physical properties of different types of

sintered carbide.

Group Material

machined Type

Har

dnes

s 1

Toughnes

s

2

Composition Spec.

wt.

g/cm3 V

icker

s

Kg/m

m2

Ben

d s

tr.

Kg/m

m2

Com

pr.

Str

.

Kg/m

m2

Mod. of elast.

Kg/.mm2

Ceoff.

of lin.

exp.

10-6

/C Hea

t co

nd.

Cal

/cm

.C.s

TiC

TaC

%

Co

%

WC

%

P (blue)

Steel, Cast

Steels,

tempered C.I.

P 01.2

P 01.3

P 01.4

P 05

P 10

P 20

P 25

P 30

P 40

P 50

1 2

64

43

33

18

28

14

20

8

12

15

6

6

5

5

9

10

9

10

13

17

Rest

7.2

8.5

10.1

12.2

10.7

11.9

12.5

13.1

12.7

12.5

1800

1750

1750

1700

1600

1500

1450

1450

1400

1300

75

90

100

110

130

150

175

175

190

210

490

500

500

500

470

400

45,000

53,000

54,000

55,000

56,000

56,000

52,000

7.5

6

6.5

6

6

5.5

5.5

0.04

0.07

0.08

0.14

0.14

M

(yellow)

C.I, alloy C.I.

tempered

C.I., non-

ferrous

metals,

Steels,

Manganese

steel, steel,

cast steel

M 01

M 20

M 30

M 40

1 2

10

10

10

6

6

8

9

15

Rest

13.1

13.4

14.4

13.6

1700

1550

1450

1300

135

160

180

210

500

480

440

53000

57000

5400

5.5

5.5

0.12

0.15

K (red)

C.I. hard C.I;

nitrided steel,

non-ferrous

metals, wood,

plastics, non

metallic

materials

K 01

K 05

K 10

K 20

K 30

K 40

1 2

4

3

2

2

1

-

4

6

6

6

9

12

Rest

15.0

14.5

14.8

14.8

14.5

14.3

1800

1750

1650

1550

1400

1300

120

135

150

170

190

210

590

570

550

480

450

63000

63000

62000

58000

57000

5

5

5

5.5

0.19

0.19

0.17

0.16



Table (2.3) : Ks Values according to Prof. Kienzle (1957)

Material Strength or

hardness

Kg/mm2

z 1 - z

ks = ks1.1 h-z

Ks 1.1

h = 1mm h = 0.1mm h = 2.5mm

St 50 52 0.26 0.74 199 361 158

St 60 62 0.17 0.83 211 308 182

St 70 72 0.30 0.70 226 450 174

Ck 45 67 0.14 0.86 222 304 196

Ck 60 77 0.18 0.82 231 315 181

16Mn Cr5 77 0.26 0.74 210 383 167

18Cr Ni5 63 0.30 0.70 226 451 175

34Cr Mo4 73 0.26 0.74 250 450 200

Hard CI RC 46 0.19 0.81 206 319 174

Grey CI HB 200 0.26 0.74 116 211 93


CHAPTER THREE: Mechanics of Metal Cutting

CHAPTER THREE: MECHANICS OF METAL CUTTING

3.1 Mechanics of metal cutting

Till now, there is conflicting evidence about the nature of the deformation zone in metal

cutting. This has led to two basic schools of thought in analyzing the metal cutting

operation.

Many workers such as Merchant have favored the thin plane model, where as some

others such as Palmer & Oxley have based their analysis on a thick plastic zone.

The observations indicate that the thick model may describe the cutting process at very

low cutting speed, and at higher cutting speeds, the thin model is likely to be the most

useful for practical cutting conditions.

Here we shall deal only with Merchant analysis which is based on the thin-zone model.

Figure 3.1: The two basic models for chip formation

3.2 Basic methods of metal cutting

There are two basic methods of metal cutting using a single point tool, namely orthogonal

or two dimensional and oblique or three dimensional cutting.

3.2.1 Oblique cutting

In this case the resulting cutting force R is resolved into three mutually perpendicular

components acting on the tool, as shown in figure 3.2, these components are



A: The main cutting force Ps, which is tangential to the surface of the cut and

coincidence with the direction of the cutting speed V.

B: The axial or feed force Pf which acts parallel to the work axis, in the opposite

direction of the feed motion.

C: Radial force Pr which is acting in a direction perpendicular to the axis of the

work.

The resultant cutting force R is

222

rfs PPPR

The relationship between the three components, depends on the cutting variables, tool

geometry, work material, and tool wear.

Figure 3.2: Force components in Oblique cutting



3.2.2 Orthogonal cutting

The essential features of orthogonal cutting are:

1: The cutting edge of the tool is perpendicular to the direction of tool travel.

2: The cutting edge clears the width of the workpiece on either ends.

3: Only two perpendicular components of the cutting force are acting on the tool, that is

the entire force system lies in a single plane as shown in figure 3.3

Figure 3.3: Orthogonal cutting

3.3 Measuring the cutting force components

When using the three components force dynamometer, the values of the three

components can be measured.

1: The main cutting force Ps is the power component and is responsible for

producing internal shear.

2: The feed force Pf forms the energy required to feed the tool into the work.



3: The radial force Pr is a result of the elastic deflection of the work surface being

cut.

Both Ps and Pf are responsible for lateral deflection and hence the accuracy of the

product.

The examples of orthogonal cutting are mentioned in figure 3.4

Figure 3.4: Examples of orthogonal cutting



PROBLEMS

Problem 1

A shaper tool, making an orthogonal cut, has a -10 rake angle. The depth of cut t1 = 0.6

mm, the width of cut b = 3 mm. The cutting speed Vc = 40 m/min. Two components

dynamometer is used to determine the main cutting force (Ps = 3600 N), and normal

component (Pf = 2400 N). A high speed photograph shows a shear plane angle 20.

Calculate:

1. The expected chip thickness t2.

2. The shearing stress on the shear plane s 3. The machining power Pm.

4. The specific cutting energy ks.

Draw to scale the Merchant force diagram and determine

1. Friction force Pfr

2. Shearing forced Psh

Problem 2

Derive an expression for the spec. cutting energy ks in terms of shear angle and the

shear strength of the work material s in orthogonal cutting.

Problem 3

An orthogonal cut 3.0 mm wide is made at a speed of 45 m/min and a feed rate of 25

mm/rev, with a high-speed steel tool having a 15 rake angle. The chip thickness ratio r

is found to be 0.58, the cutting force, Ps is 1000 N and the normal force Pf is 280 N.

Calculate:

- chip thickness t2.

- shear plane angle - resultant cutting force R.

- machining power Pm and spec. cutting energy ks

Draw to scale the Merchant force diagram and determine

- coeff. of friction on the tool face

- the force component normal to the shear plane Pns



Problem 4

A workpiece is being cut at Vc = 100 m/min. The machining power is found to be 3 kW.

The feed f = 0.2 mm/rev., and depth of cut t=0.5mm.

a) What is the main cutting force Ps in N.

b) What is the spec. cutting energy ks in N/mm2.

c) Estimate the necessary machining time if the diameter of the machined bar is

D = 50 mm and its length = 250 mm.

Problem 5

Calculate the main cutting force component Ps for the following turning

operation:

Material: mild steel

spec. cutting energy ks = 3500 N/mm2

initial diam. of work = 80 mm final diam. of work = 74 mm )

feed rate f = 0.4 mm/rev,

Calculate then the machining power if the spindle speed n = 710 r.p.m.

Problem 6

In a test to determine the main cutting force through power measurement during turning

operation, the following data are obtained.

Input power at full load W1 = 2100 Watt

Input power at no load W2 = 500 Watt

Calculate:

1- The spec. cutting energy ks of the machined material if Vc = 30 m/min,

chip cross-section = 0.25x1.5 mm2.

2- The lathe efficiency under the given machining conditions.


CHAPTER FOUR: Tool Wear and Tool Life

CHAPTER FOUR: TOOL WEAR AND TOOL LIFE

4.1 Tool wear

During the cutting operation, the cutting edge is stressed mechanically and thermally

until it becomes completely blunt and unable to cut, 100 % wear occurs both on face and

flank, but depending on the machining conditions, one of the types of wear predominate.

Figure 4.1: Sketch of worn cutting tool, showing the principal locations and types of wear

that occur during oblique cutting



In case of crater wear:

M

T

K

Kq

q should not exceed a certain value ( 0.4 0.6), otherwise weakening of the tool and

catastrophic fracture of cutting edge occur.

The measurement of the amount of crater wear is not as simple as that of the flank wear.

The dependence of the flank wear on the time of the tool operation is shown below.

Figure 4.2: Tool wear as a function of cutting time, flank wear is used here as the

measure of tool wear.

within interval I:

The flank wear increases rapidly till point a. Rapid increase of the wear is due to the

unevenness of the newly sharpened edge is being quickly smoothed.

within interval II:

It increases at normal rate and termed as normal wear, and the slope of the wearing curve

is dependent upon the cutting conditions such as speed, geometry, work piece material

and coolant type.

I II III



within interval III:

The flank wear increases rapidly till the cutting edge is completely damaged and any

control is hardly possible. The reason is the appearance of the flank wear associated with

the formation of thermal cracks and plastic deformation.

Once the tool enters in the destructive wear interval III, it is uneconomical to sharpen the

tool, the machining accuracy is lost.

The moment when the tool becomes completely blunt is recognized by appearance of

bright strip on the machined surface (H.S.S. tools), and by intensive sparking in the place

of cut, in case of widia tool.

4.2 Tool life (cutting edge durability)

The tool life or cutting edge durability is the total time at which the tool is able to take off

the chip. It is the sum of actual cutting times in which the tool is operating from

sharpening to economical blunting. In other words, the tool life is the cutting time elapsed

between two consecutive sharpening. The tool life can be expressed in different ways:

1- Actual cutting time to failure.

2- Length of work cut to failure.

3- Volume of material removed to failure.

4- Number of components produced to failure.

5- Cutting speed for a given time of failure.

Factors affecting tool life:

1- Material of machined workpiece.

2- Required surface quality of the workpiece.

3- Tool material.

4- Tool geometry and sharpening condition.

5- Fixation of tool and workpiece.



6- Machining variables such as, speed, feed, and depth of cut.

7- Type of coolant used.

8- Condition of cutting tool with respect to vibrations.

The most important factor affecting the tool life is the cutting speed. Therefore, its effect

will be discussed in detail.

Figure 4.3: Effect of cutting speed on tool flank wear for three cutting speeds.

Hypothetical values of speed and tool life are shown for a tool life criterion of 0.020 inch

flank wear.

4.3 Taylor tool life equation:

If the tool life values for the three wear curves are plotted on a natural log log graph,

cutting speed versus tool life. The resulting relationship is a straight line as shown in

figure 4.4.



Figure 4.4: Natural log log plot of cutting speed versus tool life.

The discovery of this relation around 1900 is credited to F.W. Taylor. It can be expressed

in equation form and it is called Taylor tool life equation.

CVT n

where:

V = cutting speed (m/min)

T = Tool life (min)

C = a constant representing the cutting speed that results in 1 min tool life

n can be found as following:

nnTVTV 2211

n

T

T

V

V

2

1

1

2

21

12

loglog

loglog

TT

VVn



4.4 Tool life criterion in production:

The criterion of Taylor equation is not practical in a factory environment, the following

are some alternates that are more convenient to use in production:

a- Changes in the sound emitting from operation.

b- Degradation of the surface finish on work.

c- Complete failure of cutting edge.

d- Workpiece count.

e- Chips become ribbon form or string

4.5 Machining economic:

Besides technical considerations, the economic of metal removal process is very

important. In machining a certain part, we want to determine the parameters that will give

us either the minimum cost per part or the maximum production rate.

Figure 4.5: Cost per unit for a machining process versus cutting speed.



Figure 4.6: Production time versus cutting speed

The time needed to produce a part is:

p

cmlp

N

TTTT

Where:

Tl = time involved in loading and unloading the part, changing speed and

feed rates.

Tm = machining time per part.

Tc = time required to grind the tool.

Np = number of parts machined per tool ground.



fV

LD

fN

LTm

From tool life equation, we have:

CVT n

n

V

CT

1

Where T, is time, in minutes, required to reach a flank wear of certain dimension, after

which the tool has to be reground or changed. The number of pieces per tool grind is thus

can be obtained as following:

m

pT

TN

or

1)/1(

/1

n

n

pLDV

fCN

In order to find the optimum cutting speed and also the optimum tool life for maximum

production, we have to differentiate Tp with respect to V and set it to zero.

V

Tp

we find that the optimum cutting speed Vopt now becomes,



ncopt

Tn

CV

1/1

and the optimum tool life is,

copt TnT 1/1

4.6 Cutting fluids

Cutting fluids also known as lubricants or coolants, are used extensively in machining

operations to:

1- Reduce friction and wear, thus improving tool life and surface finish.

2- Reduce forces and energy consumption.

3- Cool the cutting zone, thus reducing workpiece temperature and distortion.

4- Wash away the chips.

5- Protect the newly machined surfaces from environmental corrosion.



Table 4.1 Relative severity of machining operations

Cutting operations Operation

severity Cutting speed

Cutting fluid

activity

Broaching (internal) High

High

High

Tapping

Broaching (external)

Form and threading

Grinding

Gear shaping

Thread rolling

Reaming

Deep drilling

Hobbing

Milling

Turning

Band and hack

sawing

Severity:

It is defined as the magnitude of temperatures and forces encountered, the tendency for

built up edge formation, the ease with which chips are disposed of from the cutting zone.

4.7 Effect of cutting fluids on machining:

A machining operation is being carried out with an effective cutting fluid, explain the

changes in the mechanics of the cutting operation and total energy consumption if the

fluid is shut off.



When the fluid is shut off, the following chain of events take place:

1- Friction at the tool chip interface increases.

2- The shear angle decreases.

3- The chip is thicker.

4- A built-up edge is likely to form.

As a consequence:

a- The shear energy in the primary zone increases.

b- The friction energy in the secondary zone increases.

c- The total energy increases.

d- Surface finish is likely to deteriorate.

e- The temperature in the cutting zone increases, hence the tool wear increases.

f- Tolerances may be difficult to maintain because of the increased temperature

and expansion of the workpiece during machining.

4.8 Selection of cutting fluid:

The selection of a cutting fluid should include the following consideration.

a- Effect on workpiece material. (Washing machined parts to remove any cutting

fluid residual).

b- Effect on machine tool (Compatibility with the machine member materials).

c- Biological effects (human and environment).

4.9 Continuous chips with built-up-edge:

On closely observing the cutting edge of the tool, a small lump of material known as

built-up-edge (BUE) is found to be welded on it.

Increased temperature of metal being machined in conjunction with high pressure exerted

by the tool, will change the metal into plastic state.

The hardness of the BUE may be two or three times that of the metal being machined,

that is the reason why the cutting edge remains active even when it is covered with BUE.

The BUE, changes the tool geometry, for instance, the cutting angle is less then the actual

cutting angle



The BUE effects:

1- Tool wear

2- Cutting forces

3- Surface roughness

BUE is formed periodically on the tools, when it reaches a comparatively large size, it

breaks off and carried away by both, the chip and workpiece. It affects dimensional

accuracy and surface finish.

The tool rake angle and the cutting speed V, have a combined influence on the formation

of the BUE, as shown in the figure below.

As it is clear from the figure, the machining condition should be selected to avoid the

formation of BUE.

Carbide and ceramic tipped tools are less inclined to have BUE then metal tool.



Problems

Problem 1

The durability of a turning tool at V = 50 m/min was found to be 30 min. If Taylor

exponent n = 0.25, calculate:

(a) Cutting edge durability at v=30 m/min

(b) Cutting speed corresponding to T = 120 min.

Problem 2

The durability of a cutting tool is 40 min at a cutting speed of 120 m/min, and 100 min at

a cutting speed of 60 m/min, calculate:

(a) Taylor exp. n, and Taylor const. C, if VT n = C

(b) T V = 70, and V T=120

Problem 3

For a given metal cutting operation, it has been found that the economical durability is 64

min. Determine the economical cutting speed Vopt, if, VT 1/3

= 100

Calculate then Topt and Vopt if tool exchange time TC = 13.5 min.

Problem 4

A tool used for metal cutting operation shows a tool life-speed relationship of

V T 0.125

= 44.5

Originally, 15 minutes were required to replace a dull tool, but a new tool holder has

made it possible to reduce the time to 5 minutes. What increase in cutting speed does this

permit to obtain the max. rate of production from the operation?

Problem 5

The outside diameter of a cylinder made of titanium alloy is to be turned. The starting

diameter = 500 mm and the length = 1000 mm. Cutting conditions are f = 0.4 mm/rev

and d = 3.0mm. The cut will be made with a cemented carbide cutting tool whose Taylor

tool life parameters are n=0.23 and C=400 (m/min). Compute the cutting speed that will

make the tool life equal to the machining time.


CHAPTER FIVE: Drilling Operation

CHAPTER FIVE: DRILLING OPERATION

5.1 Drilling operation

Drilling is an extensively used process, by which through or blind holes are originated or

enlarged in the workpiece.

The process involves feeding a rotating cutting tool into a stationery workpiece.

Drilling should be considered as a roughing operation and therefore the accuracy and

surface roughness in drilling are not of much concern.

Figure 5.1 : Drill operation

If high accuracy and high quality finish are required, drilling must be followed by some

other operations such as reaming, boring or internal grinding.

(a)

(b)

(c)

(d)

Figure 5.2: Sequence of operations required to obtained an accurate size hole: (a)

centering and countersinking, (b) drilling, (c) boring, and (d) reaming

Mt

V



5.2 Twist drill nomenclature

The most widely employed drilling tool is the twist drill which is available in diameters

ranging 0.25 to 80 mm. The twist drill consists of a shank, neck, body and point as shown

in figure.

Figure 5.3: Nomenclature and geometry of conventional twist drills

5.2.1 The body

It is a portion of the drill extending from the neck to the outer corners of the cutting lip. It

is provided with two helical flutes for the admission of coolant and ejection of the chips.

5.2.2 The shank

It is a part of the drill through which it is held and driven. It may be straight and held by

three jaws drilling chuck, or taper and held through friction by a special sleeve.



Figure 5.4: Taper shank

5.2.3 The neck

It is the section of reduced diameter between the body and the shank.

5.3 Drilling angles

5.3.1 Point angle: The point angle on a conventional drill is 118o for drilling medium

carbon steel and cast iron, where it should be 125o for drilling hardened steel, and 130

o to

140o for drilling brass and bronzes.

Figure 5.5: Point angle

5.3.2 The lip clearance angle

The lip clearance angle vary according to the drilled material, for hard material the range

is 6 9o and for soft materials up to 15o.

Figure5.6: Lip angle



5.3.3 The chisel edge angle

The chisel edge angle is also vary according to the drilled materials, for hard material it

should be 120o and for soft materials 135

o.

Figure 5.7: Chisel angle

5.4 Drill materials

Twist drills are manufactured by High speed steel, and also carbide tipped design.

5.5 Torque, power and cutting force components in drilling

The cutting force component in drilling operation is shown in figure. These components

are assumed to be acting at the mid point of both main cutting edges (lips, at a distance of

D/4).

On each lip three components mutually perpendicular to each other are acting namely Ps,

Pf and Pr. as shown in figure 5.8.



The magnitude of these components depends on the following:

1. Properties of the material to be drilled.

2. Tool geometry of the twist drill.

3. Chip cross-section area.

4. Cutting conditions, such as feed, cutting speed, coolant

Figure5.8: Cutting force components in drilling.

5.5.1 The main cutting force Ps

It is a horizontal force, acting on each lip in the direction of the cutting speed V, and can

be calculated by the formula:

AKP ss

Where

Ks = specific cutting resistance of the material to be drilled.

A = chip cross-section area = S/2 * D/2 or (D*S)/4 or b*h



The detail is shown in figure 5.9.

Figure 5.9: Chip cross section in drilling

5.5.2 The feed force Pf

The feed force Pf acts on each lip vertically upwards in the direction of the feed. It

produces the penetration of the drill into the work.

5.5.3 The radial force Pr

The radial force acting on both lips towards the center are considered in the majority of

cases to counterbalance each other. In case if the drill is not properly sharpened, radial

forces on both lips are not equal. It causes holes not to be accurate and stressing of the

machine spindle bearings.

5.5.4 Drilling torque

The required torque for drilling operation M, can be calculated if the main cutting force

Ps and the drill diameter are known.



2/DPM s

2/4

DSD

Ks

8

2 SDKsM

5.5.5 The total drilling power

The total drilling power N is equal to the main drilling power Ns plus the feed power Nf

which is negligible if compared with Ns.

fs NNN

nSPVP fs 22/2

VPs

mech

smotor

VPN

the machining time is:

Nf

DLtm

)4/(

And material removal rate is

41000

SDDNQ

10004

2

NSDQ



5.6 Reaming

Reaming removes a small amount of material from the surface of holes. It is done for two

purposes.

1. To bring holes to a more exact size.

2. To improve the finish of an existing hole.

No special machines are built for reaming operation. The same machine tool that was

employed for drilling the hole can be utilized for reaming operation by changing the

cutting tool.

To obtain proper results, only a minimum amount of material (as little as 0.125mm)

should be left for removal by reaming. A properly reamed hole will be within 0.025mm

of the correct size and have a fine finish.

Figure 5.10: Typical reamer

5.6.1 Type of reamers

Following types of reamers are commonly used:

1. Hand reamers

2. Machine or chucking reamers

3. Expansion reamers (to compensate for wear)

4. Taper reamers are used for finishing holes to an exact taper

5.6.2 To meet quality requirements

Including both finish and accuracy (tolerances on diameter, roundness, straightness)

reamers must have adequate support for the cutting edges, and reamer deflection must be

minimal.



Reaming speed is usually two third the speed for drilling the same materials. However,

for close tolerances and fine finish, speed should be slower.

Reamers tend to chatter when not held securely, when the work or work holder is loose or

when the reamers are not properly ground.

5.7 Boring and boring machines

Boring is similar to turning. It uses a straight point tool against a rotating workpiece. The

difference is that boring is performed on the inside of an existing hole rather than the

outside diameter of an existing cylinder.

Machine tools used to perform boring operations are called boring machines. Boring

machines can be horizontal or vertical. The designation refers to the orientation of the

axis of rotation of the machine spindle or workpiece.

In a horizontal boring operation, the setup can be arranged in either of two ways.

First setup

In this setup the work is fixed to a rotating spindle, and the tool is attached to a boring bar

that feeds the tool into the work, as shown in figure 5.11. The boring bar in this setup

must be very stiff to avoid deflection and vibration during operation. (the boring bar is

made of cemented carbide).

Figure 5.11: First setup of boring; boring bar is fed into a rotating workpiece.



Second setup

In this setup the tool is mounted to a boring bar and the boring bar is supported and

rotated between centers as shown in figure 5.12. The work is fastened to a feeding

mechanism that feeds it past the tool. This setup can be used to perform boring operation

on conventional engine lathe.

Figure 5.12: Second setup of boring; work is fed past a rotating boring bar.

5.8 Vertical boring machine

A vertical boring machine is shown in figure 5.13. This machine is used for heavy

workparts.

Workparts up to 40 feet diameter can be machined on vertical boring machines.

Figure 5.13: A vertical boring mill.



PROBLEMS

Problem 1

In a drilling operation:

Hole diameter =30 mm

Hole depth = 100mm

Cutting speed = 300 r.p.m

Feed =0.25 mm/rev

Specific cutting resistance = 2000

N/mm2

Calculate:

a- The chip area. b- The main cutting force.

c- Machining time.

d- Material removal rate.

Problem 2 In a drilling operation using a twist drill, the lip angle is 120 degree (standard), the spindle speed is 300 rpm, the feed is 0.2 mm/rev and the drill diameter is 10 mm. Calculate:

a - the machining time to drill a through hole 30 mm long. b - the drill torque in [N-m] assuming that specific cutting resistance for the work. material is 200 Kg/mm

2.

c - the amount of material removed at the first 10 sec after full engagement of drill.

d - the cutting power if cutting force is 2000 N.

Problem 3

A gun drilling operation is used to drill a 7/16 in.- diameter hole to a certain depth. It

takes 4.5 min to perform the drilling operation using high-pressure fluid delivery of

coolant to the drill point. The cutting conditions are N = 300 rev/min at a feed = 0.001

in./rev. To improve the surface finish in the hole, it has been decided to increase the

speed by 20% and decrease the feed by 25%. How long will it take to perform the

operation at the new cutting conditions?


CHAPTER SIX: Milling Operation

CHAPTER SIX: MILLING OPERTAION

6.1 Milling operation

Milling is a machining operation in which a workpiece is feed past a rotating cylindrical

tool with multiple cutting edges. This cutting tool in milling is known as milling cutter

and the machine tool that traditionally performs the operation is called milling machine.

Milling is an interrupted cutting operation, the teeth of milling cutter enter and exit the

work during each revolution. This interrupted cutting operation subjects the teeth to a

cycle of impact force and thermal shock on every rotation as shown in figure 6.1. A chip

of variable thickness is produced.

Figure 6.1: Conventional face milling with cutting force diagram for Fc, showing the

interrupted nature of process.

6.2 Types of milling operations

There are two basic types of milling operations.

6.2.1 Peripheral or slab milling: In this milling operation the axis of tool is parallel to

the surface being machined. In this operation there are two opposite directions of rotation

that the cutter can have with respect to the work. These cutter directions distinguished

two forms of milling operations, up milling and down milling.



Figure 6.2: Peripheral milling operation.

Figure 6.3: Peripheral milling operations: (a) slab milling, (b) slotting, (c) side milling,

and (d) straddle milling.

6.2.1.1 Up milling: In up milling the direction of motion of the cutter teeth is opposite to

the feed direction. In this type of milling operation, the chip formed by each cutter tooth

starts out very thin and increases in thickness during the sweep of the cutter. The chip

length is longer than in down milling.

The cutter tends to push the work along and lift it upward from the table, therefore

greater clamping force must be employed. In up milling, chips can be carried into the

newly machined surface, causing the surface finish to be poorer.



6.2.1.2Down milling: In down milling, the direction of motion of the cutter teeth is same

as the feed direction. In this operation each chip starts out thick and reduces in thickness

throughout the cut. The length of the chip in down milling is less than in up milling. This

tends to increase tool life. The cutter force direction is downwards, tending to hold the

work against the work table.

Figure 6.4: Two forms of milling with a 20-tooth cutter: (a) up milling and (b) down

milling.

6.3 Face milling

In face milling the axis of the cutter is perpendicular to the surface being milled, as

shown in the figure 6.5.

Figure 6.5: Face milling.



Figure 6.6: Face milling operations: (a) conventional face milling, (b) partial face milling,

(c) end milling, (d) profile milling, (e) pocket milling, and (f) surface contouring.

6.4 Cutting conditions in milling

The cutting speed is determined at the outside diameter of a milling cutter. This can be

converted to spindle rotation speed.

D

VN

Where

N = spindle speed in rpm

V = cutting speed

D = diameter of milling cutter



6.5 Chip thickness in milling

Figure 6.7: Chip thickness detail in milling operation.

The milling operation is characterized by the changing of chip thickness as the cutting

proceeds. Therefore the maximum and mean values of chip thickness are to be calculated

Since the chip thickness is an important factor for calculating the cutter forces and power,

therefore the maximum and mean values of chip thickness will be calculated. From figure

6.7

eezezn

USh sin*sin

em hh 2/1

Where

Sz = feed of workpiece/tooth = U/(n-z)

e = angle of rotation of milling cutter during which each tooth remains

engaged in workpiece material



U = feed of workpiece/min.

n = rotational speed of cutter in rpm

z = number of teeth on cutter

since e is small such that sin e = e

2

22

/2/

)2/()2/(sin De

D

eDDe

where

e = depth of cut

D = outside diameter of milling cutter

Substituting the values of sine, we get

since hm = he therefore

6.6 Cutting forces and power in milling

In figure 6.9, the resultant force R acting on a single tooth in peripheral milling operation

can be resolved into tangential and radial components (Ps, Pr) or horizontal and vertical

components (Ph, Pv).

Therefore

22

rs PPR

dezn

Uhe /

2

dezn

Uhe /



22

Vh PPR

In case of helical milling cutter, there will be an axial component Pa acts along the cutter

axis and its magnitude depends on the helix angle of the cutter. In this case the resultant

cutting forces on each tooth is given by:

Figure 6.8: Cutting force components in milling operation.

222

ars PPPR

6.7 The main cutting force Ps in peripheral milling

hbKP ss

h = momentary chip thickness changing from zero to he in up milling

or from he to zero in down milling



ess hbKP max

Dezn

zubKzPs /

*max

Dezn

ubKsP

means/

*

The total mean tangential force is:

Dezn

ubKZP setotalmeans /

*)(

Where

Ze = numbet of cutting teeth in the same moment

2

ee ZZ

In peripheral milling:

2 /sin Deee

Therefore

DeZ

Ze /

Dezn

UbKDe

ZP stotals /

*/)(



smeantotals KDn

beUP

)(

6.8 The cutting power in peripheral milling

The main chipping power Ns can be calculated as follows:

VPN meantotalss )(

10260

1

1000

nDK

Dn

beUN ss

(kW)

ss KbeU

N

100010260 (kW)

The feed power Nf is given by:

100010260

UPN

f

f (kW)

The total power is:

sfse NNNN (approximately)

mech

smot

KbeUN

1

100010260

(kW)



6.9 Machining time in peripheral milling

From figure, it can be noted,

lCeDeL 2)(2

U

Lt

Where

U = feed of the workpiece per minuite

6.10 Material removal rate

Material removal rate can be calculated as following:

t

eWLMRR

Where

L = length of the cut

W= width of the cut

e = depth of the cut

t = machining time



PROBLEMS

Problem 1

A slab milling operation is performed to finish the top surface of a steel rectangular

workpiece 250 mm long by 75 mm wide. The helical milling cutter, which is 65 mm in

diameter and has eight teeth, is set up to overhang the width of the part on both sides.

Cutting conditions are v=35 m/min, f = 0.225 mm/tooth, and d = 0.250 in.

Determine:

(a) the time to make one pass across the surface

(b) the metal removal rate during the cut.

Problem 2

A peripheral milling operation is performed on the top surface of a rectangular workpart

that is 300 mm long by 100 mm wide. The milling cutter, which is 75 mm in diameter

and has four teeth, overhanges the width of the part on both sides. Cutting conditions are

V = 80 m/min, f = 0.2 mm/tooth, and d = 7.0 mm.

Determine:

(a) the time to make one pass across the surface

(b) the material removal rate during the cut.

Problem 3

In horizontal milling, the following conditions exist:

Work (mild steel with specific cutting energy 3200 N/mm2); Cutter (No. of teeth 12, tool

diameter 120 mm, tool width 30 mm); Machining parameters (cutting velocity 45 m/min,

feed velocity 360 mm/min, depth of cut 2.5 mm).

Calculate:

(a) Maximum chip thickness.

(b) Maximum tangential force/tooth.

(c) Machining time for one travel, if work length is 450 mm.

(d) Machining power


CHAPTER SEVEN: Grinding Operation

CHAPTER SEVEN: GRINDING OPERATION

7.1 Grinding operation

Grinding is a material removal process in which abrasive particles bonded as grinding

wheel that operates at very high surface speeds. The grinding wheel is precisely balanced

for high rotational speeds.

Grinding may be linked to the milling process. Cutting occurs on either the periphery or

the face of the grinding wheel, similar to peripheral milling and face milling. Figure 7.1

7.2 Significant differences between grinding and milling

1. The abrasive grains in the wheel are much smaller than the teeth on the milling

cutter.

2. Cutting speeds in grinding are much higher than in milling.

3. A grinding wheel is self sharpening (as the wheel wears, the abrasive particles

become dull and either fracture to create fresh cutting edges or are pulled out of

the surface of the wheel to expose new grains).

Figure 7.1: (a) The geometry of surface grinding, showing cutting conditions; (b)

assumed longitudinal shape and (c) cross-section of a single chip.



7.3 The grinding wheel

The grinding wheel consists of abrasive particles and bonding materials. The bonding

material holds particles in place and establishes the structure and shape of the wheel.

7.4 Abrasive material

General properties of an abrasive material used in grinding wheels include high hardness,

wear resistance, and toughness.

The abrasive materials of greatest commercial importance are:

1. Aluminum oxide (Al2O3)

2. Silicon carbide (SiCa)

3. Cubic boron nitride (CBN)

4. Diamond (natural and synthetic)

7.5 Grain size

There are two main grain sizes available, small grain size, suitable for hard materials

grinding with better surface finish. Large grain size is suitable for soft materials with high

material removal rate.

7.6 Bonding materials

The bonding material must be able to withstand the centrifugal forces and high

temperatures. Following are some common bonding materials:

1. Vitrified bond (clay and ceramic materials)

2. Silicate bond (sodium silicate)

3. Rubber bond

4. Metallic bond (usual bond)

Marking system for conventional grinding wheels

The grinding wheels come with the following marking system.

A 46 H 6 V xx

(Abrasive type) (Grain size) (Grade) (structure) (Bond type) (Manufacturers

record)



Abrasive type: A = Aluminum oxide

C = Silicon

Grain size: Coarse = 8, 10, 12, 14, 16, 20, 24

Medium = 30, 36, 46, 54, 60

Fine = 70, 80, - - - - - - 180

Very fine = 220, 240, - - - - -600

Grade (A H) A = Soft, M = Medium, Z = Hard

Structure 1 Very dense

15 Very open

Bond type B = Resinoid

E = Shellac

R = Rubber

S = Silicate

V = Vitrified

7.7 Standard grinding wheel shapes

Grinding wheels are available in different shapes, in figure some standard grinding wheel

shapes are shown.

Figure 7.2: Some standard grinding wheel shapes: (a) straight, (b) recessed two sides, (c)

metal wheel frame with abrasive bonded to outside circumference, (d) abrasive cutoff

wheel, (e) cylinder wheel, (f) straight cup wheel, and (g) flaring cup wheel



7.8 Dressing of grinding wheel

As the wheel is used, there is a tendency for the wheel to become loaded with metallic

chips and the grains become dull or glaze. To improve the condition of wheel a process

termed as wheel dressing is used as shown in figure 7.3.

Figure7.3: Schematic arrangement of stick dressing.

7.9Truing of grinding wheel

Grinding wheels loose their geometry during use. Truing operation restores the original

shape. A single point diamond tool is used to true the wheel as shown in figure 7.4.

Figure 7.4: Diamond nibs may be used for truing wheels in batch operations

Dressing stick

Pushed into the wheel at

constant force or constant

infeed rate

Grinding wheel



7.10 Grinding operations and grinding machines

7.10.1 Cylindrical grinding:

Cylindrical grinding as its name suggests, is used for rotational parts. These grinding

operations are divided into two basic types.

(a) External cylindrical grinding which is similar to external turning. The grinding

machine used for these operations closely resemble a lathe in which the tool post has

been replaced by a high speed motor to rotate the grinding wheel. The cylindrical

workpiec is rotated between centers. Two types of feed motion are possible, traverse

feed and plunge cut, as shown in figure 7.5 (a). In traverse feed, the grinding wheel is

fed in a direction parallel to the axis of rotation of the workpiece. In plunge cut, the

grinding wheel is fed radially into the work.

(b) Internal cylindrical grinding operates somewhat like a boring operation. The

workpiece is usually held in a chuck and rotated to provide surface speed. The wheel

is fed in either of two ways: (1) traverse feed or (2) plunge feed as shown in figure

7.6. The wheel diameter in internal cylindrical grinding must be smaller than the

original bore hole. Internal grinding is used to finish the hardened inside surfaces of

bearing races and bushing surfaces as shown in figure 7.5 (b).



Figure 7.5: Two types of cylindrical grinding: (a) external and (b) internal

Figure 7.6: Two types of feed motion in external cylindrical: (a) traverse feed and (b)

plunge-cut.

7.10.2 Surface grinding

Surface grinding is normally used to grind plain flat surfaces. It is performed using either

the periphery of the grinding wheel or the flat face of the wheel. Since the work is held

in a horizontal orientation, peripheral grinding is performed by rotating the wheel about

a horizontal axis, and face grinding is performed by rotating the wheel about a vertical

axis.



Four types of surface grinding machines are used in surface grinding operation. (a)

horizontal spindle with reciprocating worktable, (b) horizontal spindle with rotating

worktable, (c) vertical spindle with reciprocating worktable, and (d) verticall spindle with

rotating worktable.

Figure 7.7: Four types of surface grinding: (a) horizontal spindle with reciprocating

worktable, (b) horizontal spindle with rotating worktable, (c) vertical spindle with

reciprocating worktable, and (d) vertical spindle with rotating worktable.

7.10.3 Centerless grinding

Centerless grinding has a number of advantages over cylindrical grinding. It is a self

centering, the stock removal rate is higher, and the work is firmly held by the support

plate and control or regulating wheel, which results in better dimensional accuracy, as

mentioned in figure 7.8 and 7.9.



Figure 7.8: External centerless grinding.

Figure 7.9: Internal centerless grinding.

7.11 Forces and power in grinding

There are three force components involved in the grinding operation, as shown in figure

7.10.

Pr = Radial force, Pa = Axial force, Ps = Mai

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