CHAPTER THREE

FUNDAMENTALS OF CUTTING PROCESS: The common feature is the use of a cutting tool to form
a chip that is removed from the work-part. To perform the operation, relative motion is required between
the tool and work. This relative motion is achieved in most machining operations by means of a primary
motion, called the cutting speed, and a secondary motion, called the feed. The shape of the tool and its
penetration into the work surface, combined with these motions, produces the desired geometry of the
resulting work surface. A cutting tool has one or more sharp cutting edges and is made of a material that is
harder than the work material. The cutting edge serves to separate a chip from the parent work material. A
simplified model of machining is available that neglects many of the geometric complexities, yet describes
the mechanics of the process quite well. It is called the orthogonal cutting. Although an actual machining
process is three-dimensional, the orthogonal model has only two dimensions that play active roles in the
analysis.
3.1. FUNDAMENTALS OF CUTTING KINEMATICS:
Orthogonal cutting uses a wedge-shaped tool in which the cutting edge is perpendicular to the direction of
cutting speed. As the tool is forced in to the material the chip is formed by shear deformation along a plane
called the shear plane. Along the shear plane, where the bulk of the mechanical energy is consumed in
machining, the material is plastically deformed. The tool in orthogonal cutting has only two elements of
geometry: rake angle and clearance angle. As indicated previously, the rake angle determines the direction
that the chip flows as itis formed from the work-part; and the clearance angle provides a small clearance
between the tool flank and the newly generated work surface. During cutting, the cutting edge of the tool
is positioned a certain distance below the original work surface. This corresponds to the thickness of the
chip prior to chip formation to. As the chip is formed along the shear plane, its thickness increases to tc. The
ratio of to to tc is called the chip thickness ratio (or simply the chip ratio) r:

Since the chip thickness after cutting is always greater than the corresponding
thickness before cutting, the chip ratio will always be less than 1.0.

The geometry of the orthogonal cutting model allows us to

establish an important relationship between the chip
thickness ratio, the rake angle, and the shear plane angle.
Let ls be the length of the shear plane. We can make the
substitutions: to = ls sinϕ, and tc = ls cos( - ).

Example: In a machining operation that approximates orthogonal cutting, the cutting tool has a rake angle
=100. The chip thickness before the cut to = 0.50 mm and the chip thickness after the cut tc = 1.125 mm.
Calculate the shear plane angle and the shear strain in the operation.
Solution: The chip thickness ratio The shear plane angle can be

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3.2. TYPES OF CHIPS PRODUCED IN METAL-CUTTING:

Dis-continuous chip: When relatively brittle materials (e.g., cast irons) are machined at low cutting speeds,
the chips often form into separate. This tends to impart an irregular texture to the machined surface. High
tool-chip friction and large feed and depth of cut promote the formation of this chip type.
Continuous chip: When ductile work materials are cut at high speeds and relatively small feeds and
depths, long continuous chips are formed. A good surface finish typically results when this chip type is
formed. A sharp cutting edge on the tool and low tool–chip friction encourage the formation of continuous
chips. Long, continuous chips (as in turning) can cause problems with regard to chip disposal and/or
tangling about the tool. To solve these problems, turning tools are often equipped with chip breakers.
Continuous chip with built-up edge: When machining ductile materials at low-to medium cutting
speeds, friction between tool and chip tends to cause portions of the work material to adhere to the rake
face of the tool near the cutting edge. This formation is called a built-up edge (BUE). The formation of a
BUE is cyclical; it forms and grows, then becomes unstable and breaks off. Much of the detached BUE is
carried away with the chip, sometimes taking portions of the tool rake face with it, which reduces the life
of the cutting tool. Portions of the detached BUE that are not carried off with the chip become imbedded
in the newly created work surface, causing the surface to become rough.
Serrated chips: These chips are semi-continuous in the sense that they possess a saw-tooth appearance
that is produced by a cyclical chip formation of alternating high shear strain followed by low shear strain.
This fourth type of chip is most closely associated with certain difficult-to-machine metals such as
titanium alloys, nickel-base super alloys, and austenitic stainless steels when they are machined at higher
cutting speeds. However, the phenomenon is also found with more common work metals (e.g., steels)
when they are cut at high speeds

Fig: (a) discontinuous, (b) continuous, (c) Built-up edge, (d) serrated.

3.3. CUTTING FORCES AND POWER:

CUTTING FORCES: Several forces can be defined relative to the orthogonal cutting model. Based on
these forces, shear stress, coefficient of friction, and certain other relationships can be defined.
The forces applied against the chip by the tool can be separated into two mutually perpendicular
components: friction force and normal force to friction. The friction force F is the frictional force resisting

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the flow of the chip along the rake face of the tool. The normal force to friction N is perpendicular to the
friction force.
These two components can be used to define the coefficient of friction between the tool
and the chip:

The friction angle is related to the coefficient of friction

The shear force Fs is the force that causes shear deformation to occur in the shear plane and
the normal force to shear Fn is perpendicular to the shear force
Where As = area of the shear plane. This shear plane area can be calculated

The two force components Fs and Fn yields the resultant force R’. In order for the forces acting on the chip
to be in balance, this resultant R’ must be equal in magnitude, opposite in direction, and collinear with the
resultant R.

Fig: (a) forces acting on the chip in orthogonal cutting, (b) forces acting on the tool that can be measured.

Fig: Force diagram showing geometric relationships between F, N, Fs, Fn, Fc, and Ft.
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The cutting force Fc is in the direction of cutting, the same direction as the cutting speed v, and the thrust
force Ft is perpendicular to the cutting force and is associated with the chip thickness before the cut to. The
cutting force and thrust force are together with their resultant force R’’.
Equations can be derived to relate the four force components that cannot be measured to the two forces that
can be measured. Using the force diagram, the following trigonometric relationships can be derived:

If cutting force and thrust force are known, these four equations can be used
to calculate estimates of shear force, friction force, and normal force to
friction. Based on these force estimates, shear stress and coefficient of
friction can be determined.

Example: the cutting force and thrust force are measured during an orthogonal cutting operation: Fc
=1559 N and F =1271 N. The width of the orthogonal cutting operation w = 3.0 mm. Based on these
data, determine the shear strength of the work material. Rake angle = 100, and shear plane angle 
= 25.40.
Solution: Shear force can be computed
Fs =1559cos25.40 - 1271sin25.4 = 863N
Shear plane area

Shear stress, which equals the shear strength

CUTTING POWER: A machining operation requires power. The product of cutting force and speed gives
the power (energy per unit time) required to perform a machining operation:

Where Pc = cutting power, N-m/s; Fc = cutting force, N; and v = cutting speed, m/s
Example: Determine cutting power and specific energy in the machining operation if the cutting
speed = 100 m/min. Fc = 1557 N.
Solution: Pc = (1,557N)(100m/min) =155,700N-m/min
= 155,700J/min
= 155,700J/min/60sec = 2595J/s = 2595W

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3.4.MACHINABILITY: Properties of the work material have a significant influence on the success
of the machining operation. These properties and other characteristics of the work are often
summarized in the term ‘‘machinability.’’ Machinability denotes the relative ease with which a
material (usually a metal) can be machined using appropriate tooling and cutting conditions.
There are various criteria used to evaluate machinability, the most important of which are: Tool life, forces
and power, surface finish, and ease of chip disposal.
Although machinability generally refers to the work material, it should be recognized that machining
performance depends on more than just material. The type of machining operation, tooling, and cutting
conditions are also important factors. In addition, the machinability criterion is a source of variation. One
material may yield a longer tool life, whereas another material provides a better surface finish. All of these
factors make evaluation of machinability difficult.
Machinability testing usually involves a comparison of work materials. The machining performance of a
test material is measured relative to that of a base (standard) material. Possible measures of performance
in machinability testing include: Tool life, tool wear, cutting force, power in the operation, cutting
temperature, and material removal rate under standard test conditions. The relative performance is
expressed as an index number, called the machinability rating (MR). The base material used as the
standard is given a machinability rating of 1.00. B1112 steel is often used as the base material in
machinability comparisons. Materials that are easier to machine than the base have ratings greater than
1.00, and materials that are more difficult to machine have ratings less than 1.00. Machinability ratings
are often expressed as percentages rather than index numbers. Let us illustrate how a machinability rating
might be determined using a tool life test as the basis of comparison.
Example: A series of tool life tests are conducted on two work materials under identical cutting conditions,
varying only speed in the test procedure. The first material, defined as the base material, yields a Taylor
tool life equation VT 0.28 = 350, and the other material (test material) yields a Taylor equation VT 0.27 =
440, where speed is in m/min and tool life is in min. Determine the machinability rating of the test material
using the cutting speed that provides a 60-min tool life as the basis of comparison.
Solution: The base material has a machinability rating = 1.0.
Its V60 value can be determined from the Taylor tool life equation as follows:
V60 = (350/600.28) = 111m/min
The cutting speed at a 60-min tool life for the test material is determined similarly:
V60= (440/600:27) = 146m/min
Accordingly, the machinability rating can be calculated as
MR (for the test material) = 146/111 = 1.31 (131%)
Therefore, since MR for the test material is greater than 1.00 the materials are easier to machine.

3.5.TOOL LIFE, TOOL WEAR AND TOOL FAILURE:

Machining operations are accomplished using cutting tools. The high forces and temperatures during
machining create a very harsh environment for the tool. If cutting force becomes too high, the tool
fractures. If cutting temperature becomes too high, the tool material softens and fails. If neither of these
conditions causes the tool to fail, continual wear of the cutting edge ultimately leads to failure.

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TOOL LIFE: generally indicates the amount of satisfactory performance or service rendered by a fresh
tool or a cutting point till it is declared failed.
 Definition 1: It means the span of actual machining time by which a fresh tool can work before
attaining the specified limit of tool wear. Mostly tool life is decided by the machining time.
 Definition 2: The length of time of satisfactory service or amount of acceptable output provided by a
fresh tool prior to it is required to replace or recondition.
 Definition 3: It generally indicates the amount of satisfactory performance or service rendered by a
fresh tool or a cutting point till it is declared failed.
Tool life: is defined as the length of cutting time that the tool can be used. Operating the tool until final
catastrophic failure is one way of defining tool life. However, in production, it is often a disadvantage to
use the tool until this failure occurs because of difficulties in re-sharpening the tool and problems with
work surface quality.
F. W. Taylor can be expressed in equation form and is called the Taylor tool life equation:
where v = cutting speed, m/min; T = tool life, min; and n and C are parameters whose values
depend on feed, depth of cut, work material, tooling, and the tool life criterion used. The
value of n is relative constant for a given tool material, whereas the value of C depends on
tool material, work material, and cutting conditions.

Basically, F.W.Taylor states that higher cutting

speeds result in shorter tool lives. Relating the
parameters n and C to figure, n is the slope of the
plot (expressed in linear terms rather than in the
scale of the axes), and C is the intercept on the speed
axis. C represents the cutting speed that results in a
1-min tool life.

Fig: Natural log–log plot of cutting speed vs. tool life.

Example: Taylor Tool Life Equation: Determine the values of C and n in the plot of Figure,
using two of the three points on the curve and solving simultaneous equations.
Solution: Choosing the two extreme
points:
V=160m/min, T=5min; and
V =100m/min, T=41 min; we have

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TOOL WEAR: Gradual wear occurs at two principal locations on a cutting tool: the top rake face and the
flank. Accordingly, two main types of tool wear can be distinguished: crater wear and flank wear. We will
use a single-point tool to explain tool wear and the mechanisms that cause it. Crater wear consists of a
cavity in the rake face of the tool that forms and grows from the action of the chip sliding against the
surface. High stresses and temperatures characterize the tool–chip contact interface, contributing to the
wearing action. The crater can be measured either by its depth or its area. Flank wear occurs on the flank,
or relief face, of the tool. It results from rubbing between the newly generated work surface and the flank
face adjacent to the cutting edge. Flank wear is measured by the width of the wear band, FW. This wear
band is sometimes called the flank wear land. Certain features of flank wear can be identified.
First, an extreme condition of flank wear often appears on the cutting edge at the location corresponding to
the original surface of the work-part. This is called notch wear. It occurs because the original work surface
is harder and/or more abrasive than the internal material, which could be caused by work hardening from
cold drawing or previous machining, sand particles in the surface from casting, or other reasons. As a
consequence of the harder surface, wear is accelerated at this location.
A second region of flank wear that can be identified is nose radius wear; this occurs on the nose radius
leading into the end cutting edge.

Fig: (a) Worn cutting tool (b) Crater wear and (c) flank wear on a cemented carbide tool

The mechanisms that cause wear at the tool–chip and tool–work interfaces in machining can be
summarized as follows:
 Abrasion: This is a mechanical wearing action caused by hard particles in the work material gouging
and removing small portions of the tool. This abrasive action occurs in both flank wear and crater
wear; it is a significant cause of flank wear.
 Adhesion: When two metals are forced into contact under high pressure and temperature, adhesion
or welding occur between them. These conditions are present between the chip and the rake face of
the tool. As the chip flows across the tool, small particles of the tool are broken away from the
surface, resulting in attrition of the surface.
 Diffusion: This is a process in which an exchange of atoms takes place across a close contact
boundary between two materials. In the case of tool wear, diffusion occurs at the tool–chip boundary,
causing the tool surface to become depleted of the atoms responsible for its hardness. As this process
continues, the tool surface becomes more susceptible to abrasion and adhesion. Diffusion is believed
to be a principal mechanism of crater wear.

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  Chemical reactions: The high temperatures and clean surfaces at the tool–chip interface in
machining at high speeds can result in chemical reactions, in particular, oxidation, on the rake face
of the tool. The oxidized layer, being softer than the parent tool material, is sheared away, exposing
new material to sustain the reaction process.
 Plastic deformation: Another mechanism that contributes to tool wear is plastic deformation of the
cutting edge. The cutting forces acting on the cutting edge at high temperature cause the edge to
deform plastically, making it more vulnerable to abrasion of the tool surface. Plastic deformation
contributes mainly to flank wear.
 Most of these tool-wear mechanisms are accelerated at higher cutting speeds and temperatures.
Diffusion and chemical reaction are especially sensitive to elevated temperature.

TOOL FAILURE: As cutting proceeds, the various wear mechanisms result in increasing levels of wear
on the cutting tool. The general relationship of tool wear versus cutting time. Although the relationship
shown is for flank wear, a similar relationship occurs for crater wear. Three regions can usually be
identified in the typical wear growth curve. The first is the break-in period, in which the sharp cutting
edge wears rapidly at the beginning of its use. This first region occurs within the first few minutes of
cutting. The break-in period is followed by wear that occurs at a fairly uniform rate. This is called the
steady-state wear region. In our figure, this region is pictured as a linear function of time, although there
are deviations from the straight line in actual machining. Finally, wear reaches a level at which the wear
rate begins to accelerate. This marks the beginning of the failure region, in which cutting temperatures are
higher, and the general efficiency of the machining process is reduced. If allowed to continue, the tool
finally fails by temperature failure.

Fig: (a) Tool wear as a function of cutting time. (b) Effect of cutting speed on tool flank wear
(FW) for three cutting speeds.

The slope of the tool wear curve in the steady-state region is affected by work material and cutting
conditions. Harder work materials cause the wear rate (slope of the tool wear curve) to increase. Increased
speed, feed, and depthof cut have a similar effect, with speed being the most important of the three. As
cutting speed is increased, wear rate increases so the same level of wear is reached in less time.
There are three possible modes by which a cutting tool can fail in machining:
 Fracture failure. This mode of failure occurs when the cutting force at the tool point becomes
excessive, causing it to fail suddenly by brittle fracture.

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  Temperature failure. This failure occurs when the cutting temperature is too high for the tool
material, causing the material at the tool point to soften, which leads to plastic deformation and loss
of the sharp edge.
 Gradual wear. Gradual wearing of the cutting edge causes loss of tool shape, reduction in cutting
efficiency, an acceleration of wearing as the tool becomes heavily worn, and finally tool failure in a
manner similar to a temperature failure.

CORNER WEAR: occurs on the tool corner. Can be considered as a part of the wear land and
respectively flank wear since there is no distinguished boundary between the corner wear and flank wear
land. We consider corner wear as a separate wear type because of its importance for the precision of
machining. Corner wear actually shortens the cutting tool thus increasing gradually the dimension of
machined surface and introducing a significant dimensional error in machining.

3.6. TOOL GEOMETRY:

A cutting tool must possess a shape that is suited to the machining operation. One important way to classify
cutting tools is according to the machining process. Cutting tools can be divided into single-point tools and
multiple-cutting-edge tools.
Single-point tools are used in turning, boring, shaping, and planing.

Fig: angle of single point cutting tools

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Many of the principles that apply to single-point tools also apply to the other cutting-tool types, simply
because the mechanism of chip formation is basically the same for all machining operations.
 In a single-point tool, the orientation of the rake face is defined by two angles, back rake angle and
side rake angle. Together, these angles are influential in determining the direction of chip flow across
the rake face.
 The flank surface of the tool is defined by the end relief angle (ERA) and side relief angle (SRA).
These angles determine the amount of clearance between the tool and the freshly cut work surface.
 The cutting edge of a single point tool is divided into two sections, side cutting edge and end cutting
edge. These two sections are separated by the tool point called the nose radius.
 The side cutting edge angle (SCEA) determines the entry of the tool in to the work and can be used
to reduce the sudden force the tool experiences as it enters a work-part.
 Nose radius (NR) determines to a large degree the texture of the surface generated in the operation.
A very pointed tool (small nose radius) results in very pronounced feed marks on the surface.
 End cutting edge angle (ECEA) provides a clearance between the trailing edge of the tool and the
newly generated work surface, thus reducing rubbing and friction against the surface.
 Tool geometry for a single-point tool. When specified in the following order, they are collectively
called the tool geometry signature: back rake angle, side rake angle, end relief angle, side relief
angle, end cutting edge angle, side cutting edge angle, and nose radius.
 For example, a single-point tool used in turning might have the following signature: 5, 5, 7, 7, 20, 15,
0.8mm.

Multiple-cutting-edge tools are used in drilling, reaming, tapping, milling, broaching, and sawing.

Fig: Tool geometry of twist drill

Fig: Tool geometry elements of a four tooth face milling cutter: (a) side view (b) bottom view
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3.7. SURFACE FINISH: Because machining is often the manufacturing process that determines the final
geometry and dimensions of the part, it is also the process that determines the part’s surface texture.
The roughness of a machined surface depends on many factors that can be grouped as follows: Geometric
factors, work material factors, and vibration and machine tool factors.
Geometric Factors: These are the machining parameters that determine the surface geometry of a
machined part. They include: Type of machining operation; cutting tool geometry, most importantly nose
radius; and feed. The surface geometry that would result from these factors is referred to as the ‘‘ideal’’ or
‘‘theoretical’’ surface roughness, which is the finish that would be obtained in the absence of work material,
vibration, and machine tool factors.
Work Material Factors: Achieving the ideal surface finish is not possible in most machining operations
because of factors related to the work material and its interaction with the tool. Work material factors that
affect finish include:
 Built-up edge effects as the BUE cyclically forms and breaks away, particles are deposited on the
newly created work surface, causing it to have a rough ‘‘sandpaper’’ texture;
 Damage to the surface caused by the chip curling back into the work;
 Tearing of the work surface during chip formation when machining ductile materials;
 Cracks in the surface caused by discontinuous chip formation when machining brittle materials; and
 Friction between the tool flank and the newly generated work surface. These work material factors
are influenced by cutting speed and rake angle, such that an increase in cutting speed or rake angle
generally improves surface finish.
Vibration and Machine Tool Factors: These factors are related to the machine tool, tooling, and setup
in the operation. They include chatter or vibration in the machine tool or cutting tool; deflections in the
fixturing, often resulting in vibration; and backlash in the feed mechanism, particularly on older machine
tools. If these machine tool factors can be minimized or eliminated, the surface roughness in machining
will be determined primarily by geometric and work material factors described in the preceding. Possible
steps to reduce or eliminate vibration include:
 Adding stiffness and/or damping to the setup,
 Operating at speeds that do not cause cyclical forces whose frequency approaches the natural
frequency of the machine tool system,
 Reducing feeds and depths to reduce forces in cutting, and
 Changing the cutter design to reduce forces. Work-piece geometry can sometimes play a role in
chatter. Thin cross sections tend to increase the likelihood of chatter, requiring additional supports
to alleviate the condition

.
Fig: Deviations from nominal surface used in the two definitions of surface roughness.
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3.8.PRODUCTIVITY: Manufacturing engineering provides staff support to the operating departments
to solve technical production problems. It should also be engaged in continuous efforts to reduce
production costs, increase productivity, and improve product quality. Continuous improvement in an
organization is generally implemented using worker teams that have been organized to solve specific
problems that are identified in production. The problems are not limited to quality issues. They may
include productivity, cost, safety, or any other area of interest to the organization. The choice of any
machining method should take into consideration a rate of production that is inversely proportional to
machining time. Methods of raising productivity include the use of the following:
 High machining speeds
 High feed rates
 Multiple cutting tools
 Stacking multiple parts
 Minimization of the secondary (noncutting) time
 Automatic feeding and tool changing mechanisms
 High power densities

3.9.OPTIMIZATION: Product design is usually an iterative process that includes recognition of a need
for a product, problem definition, creative synthesis of a solution, analysis and optimization,
evaluation, and documentation. The overall quality of the resulting design is likely to be the most
important factor up on which the commercial success of a product depends. In addition, a very
significant portion of the final cost of the product is determined by decisions made during product
design. Manufacturing engineering is a technical staff function that is concerned with planning the
manufacturing processes for the economic production of high-quality products. Its principal role is to
engineer the transition of the product from design specification to physical product. Its overall goal is
to optimize production in a particular organization. The scope of manufacturing engineering includes
many activities and responsibilities that depend on the type of production operations accomplished by
the organization. The usual activities include the following:
 Process planning. As our definition suggests, this is the principal activity of manufacturing
engineering. Process planning includes (a) deciding what processes and methods should be used
and in what sequence, (b) determining tooling requirements, (c) selecting production equipment
and systems, and (d) estimating costs of production for the selected processes, tooling, and
equipment.
 Problem solving and continuous improvement. Manufacturing engineering provides staff support
to the operating departments (parts fabrication and product assembly) to solve technical production
problems. It should also be engaged in continuous efforts to reduce production costs, increase
productivity, and improve product quality.
 Design for manufacturability. In this function, which chronologically precedes the other two,
manufacturing engineers serve as manufacturability advisors to product designers. The objective
is to develop product designs that not only meet functional and performance requirements, but that
also can be produced at reasonable cost with minimum technical problems at highest possible
quality in the shortest possible time.
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