Chapter 20
Fundamentals of
Machining/Orthogonal
Machining
(Part 2)
EIN 3390
Manufacturing Processes
Summer A, 2012
20.4 Orthogonal Machining (Two
Forces)
In Orthogonal Machining (OM), tool geometry is
simplified from 3-dimensional (oblique) geometry
Three basic orthogonal machining setup
1. Orthogonal Plate Machining (OPM) a plate in a
milling machine (low-speed cutting)
2. Orthogonal Tube Turning (OTT) end-cutting a
tube wall in a turning setup – medium-speed
ranges.
3. Orthogonal Disk Machining (ODM) end-cutting
a plate feeding in a facing direction – highspeed cutting.
FIGURE 20-13 Three ways to perform
orthogonal machining. (a) Orthogonal plate
machining on a horizontal milling machine, good
for low-speed cutting. (b) Orthogonal tube turning
on a lathe; high-speed cutting (see Figure 20-16).
(c) Orthogonal disk machining on a lathe;
very high-speed machining with tool feeding (ipr)
in the facing direction
FIGURE 20-14 Schematics of
the orthogonal plate machining
setups. (a) End view of table,
quick-stop device (QSD), and
plate being machined for OPM.
(b) Front view of horizontal
milling machine. (c) Orthogonal
plate machining with fixed tool,
moving plate. The feed
mechanism of the mill is used to
produce low cutting speeds. The
feed of the tool is t and the DOC
is w, the width of the plate.
FIGURE 20-15 Orthogonal
tube turning (OTT) produces a
two-force cutting operation at
speeds equivalent to those used
in most oblique machining
operations. The slight difference
in cutting speed between the
inside and outside edge of the
chip can be neglected.
FIGURE 20-16
Videograph
made from the
orthogonal plate
machining process.
FIGURE 20-17 Schematic
representation of the material
flow, that is, the chip-forming
shear process. f defines the
onset of shear or lower boundary.
y defines the direction of slip
due to dislocation movement.
tc
FIGURE 20-18 Three characteristic types of chips.
(Left to right) Discontinuous, continuous, and
continuous with built-up edge. Chip samples produced
by quick-stop technique. (Courtesy of Eugene Merchant
(deceased) at Cincinnati Milacron, Inc., Ohio.)
20.5 Merchant’s Model
Assume that 1) the shear process takes place on
a single narrow plane as A-B in figure 20- 19. 2)
tools cutting edge is perfectly sharp and no
contact is being made between the flank of the
tool and the new surface.
Chip thickness ratio based on trigonometry:
rc = t / tc = (AB sin f)/[AB cos(f - a)], or
tan f = (rc cosa)/(1 - rcsina)
Where AB – length of the shear plane from the tool tip to
the free surface.
20.5 Merchant’s Model
For consistency of volume,
rc = t / tc = (sin f)/[cos(f - a)] = Vc./V, and
Vs / V = (cos a)/[cos(f - a)]
Where V – velocity for workpiece pasing tool, Vc – chip
moving velocity, Vs – shearing velocity, f – onset of
shear angle, a - rake angle
.
FIGURE 20-19 Velocity
diagram associated with
Merchant’s orthogonal
machining model.
20.6 Mechanics of Machining
(statics)
Assume that the result force R acting on the
back of the chip is equal and opposite to the
resultant force R’ acting on the shear plane.
R is composed of friction force F and normal
force N acting on tool-chip interface contact
area.
R’ is composed of a shear force Fs and normal
force Fn acting on the shear plane area As.
R is also composed of cutting force Fc and tangential
(normal) force Ft acting on tool-chip interface contact
area. Ft = R sin (b - a)
FIGURE 20-20
Free-body diagram
of orthogonal chip
formation process,
showing equilibrium
condition
between resultant
forces R and R.
a
a
FIGURE 20-21 Merchant’s circular force diagram used
to derive equations for Fs , Fr , Ft , and N as functions
of Fc, Fr , f, a, and b.
20.6 Mechanics of Machining
(statics)
Friction force F and normal force N are:
F = Fc sina + Ft cosa ,
N = Fc cosa - Ft sina, and
b = tan-1 m = tan-1 (F/N),
Where m - friction coefficient, and b – the angle between normal
force N and resultant R. If a = 0, then F = Ft , and N = Fc . in this
case, the friction force and its normal can be directly measured by
dynamometer.
R = SQRT (Fc2 + Ft2 ),
Fs = Fc cosf - Ft sinf , and
Fn = Fc sinf + Ft cosf,
Where Fs is used to compute the shear stress on the shear plane
20.6 Mechanics of Machining
(statics)
Shear stress:
ts = Fs/As,
Where As - area of the shear plane,
As = (t w)/sinf
Where t – uncut ship thickness and w – width of workpiece.
ts = (Fcsinf cosf - Ft sin2f )/(tw) psi
In metal cutting shear stress is a material constant. For a
given metal, shear stress is not sensitive to variations in
cutting parameters, tool material, or cutting environment.
Once this value is known for a metal, it can be used in basic
engineering calculations for machining statics (forces and
deflection) and dynamics (vibration and chatter).
Fig. 20-22 shows some typical values for flow stress for a variety
of metals, plotted against hardness.
FIGURE 20-22 Shear
stress ts variation with
the Brinell hardness
number for a group of
steels and aerospace
alloys. Data of some
selected fcc metals are
also included. (Adapted
with permission from S.
Ramalingham and K. J.
Trigger, Advances in
Machine Tool Design and
Research, 1971,
Pergamon Press.)
20.7 Shear Strain g & Shear Front
Angle f
Use Merchant’s chip formation model, a new “stack-ofcards” model as shown in fig. 20-23 is developed. From
the model, strain is:
g = cosa/[sin(f + y) cos(f + y -a)]
where f - the angle of the onset of the shear plane, and y the shear front angle.
The special shear energy (shear energy/volume) equals
shear stress x shear strain:
Us = t .g
20.7 Shear Strain g & Shear Front
Angle f
g = AB/CD = AD/CD + DB/CD
= cot(f + y) + tan(f + y -a)
= cosa/[sin(f + y) cos(f + y -a)]
20.7 Shear Strain g & Shear Front Angle f
Use minimum energy principle, where will y take on
value (shear direction) to reduce shear energy to a
minimum:
d(Us)/dy = 0,
Solving the equation above,
cos(2f + 2y -a) = 0
2f + 2y - a = 900
y = 450 - f + a/2 , and
g = 2cosa/(1 + sina),
It shows the shear strain is dependent only on the rake
angle a.
FIGURE 20-23 The Black–Huang “stack-of-cards”
model for calculating shear strain in metal
cutting is based on Merchant’s bubble model for chip
formation, shown on the left.
20.8 Mechanics of Machining
(Dynamics)
Machining is a dynamic process of large strain
and high strain rate.
The process is a closed loop interactive
processes as shown on fig. 20-24.
FIGURE 20-24 Machining
dynamics is a closed-loop
interactive process that creates
a force-displacement response.
20.8 Mechanics of Machining (Dynamics)
Free vibration is the response to any initial condition or
sudden
change.
decreases
The
amplitude
of
the
vibration
with time and occurs at the natural
frequency of the system.
Forced vibration is the response to a periodic
(repeating with time) input. The response and input occur
at the same frequency. The amplitude of the vibration
remains constant for set input condition.
20.8 Mechanics of Machining (Dynamics)
Self-excited vibration is the periodic response of the
system to a constant input. The vibration may grow in
amplitude and occurs near natural frequency of the
system regardless of the input.
Chatter due to the
regeneration of waviness in the machining surface is the
most common metal cutting example.
FIGURE 20-25
There are three
types of vibration
in machining.
FIGURE 20-26 Some
examples of chatter that are
visible on the surfaces of the
workpiece.
20.8 Mechanics of Machining (Dynamics)
Factors affecting on the stability of machining
•Cutting
stiffness
of
workpiece
material
(machinability), Ks
•Cutting –process parameters (speed, feed, DOC,
total width of chip)
•Cutter geometry (rake and clearance angles, insert
size and shape)
•Dynamic characteristics of the machining process
(tooling, machining tool, fixture, and workpiece)
20.8 Mechanics of Machining (Dynamics)
Chip formation and regenerative Chatter
In machining, chip is formed due to shearing of
workpiece material over chip area (A = t x w), which
results in a cutting force.
Magnitude of the resulting cutting force is predominantly
determined by the material cutting stiffness Ks and the
chip area such that Fc = Ks t w.
The direction of the cutting force Fc in influenced
mainly by the geometries of rack and clearance angles
and edge prep.
FIGURE 20-27 When the
overlapping cuts get out of
phase with each other, a variable
chip thickness is produced,
resulting in a change in Fc on the
tool or workpiece.
20.8 Mechanics of Machining (Dynamics)
Factors Influencing Chatter:
Cutting stiffness Ks (Machinability): The larger stiffness, the larger
cutting force, and the less machining stability.
Speed: At slow speed (relative to the vibration frequency), as speed
increases, chatter gets more significant.
Feed: does not greatly influence stability, but control amplitude of
vibration.
DOC: The primary cause and control of chatter.
Total width of chip: DOC times number of cutting edges in cutting.
Increase number of engaged cutting edges will result in chatter.
20.8 Mechanics of Machining (Dynamics)
Factors Influencing Chatter:
Back rake angle: increasing it will reduce magnitude of
cutting force, and increase process stability.
Clearance angle: reducing it will increase frictional
contact between tool and workpiece, and may produce
process damping.
Size (nose radius), shape (diamond, triangular,
square, round) and lead angle of insert.
Effects of Temperature

Energy dissipated in cutting is converted to heat,
elevating temperature of chip, workpiece, and tool.

As speed increases, a greater percentage of the
heat ends up in the chip.

Three sources of heat:
◦ Shear front.
◦ Tool-chip interface contact region.
◦ Flank of the tool.
FIGURE 20-31 Distribution of
heat generated in machining to
the chip, tool, and workpiece.
Heat going to the environment
is not shown. Figure based on
the work of A. O. Schmidt.
FIGURE 20-31 Distribution of
heat generated in machining to
the chip, tool, and workpiece.
Heat going to the environment
is not shown. Figure based on
the work of A. O. Schmidt.
FIGURE 20-32 There are three main sources of heat in metal cutting. (1) Primary shear zone. (2)
Secondary shear zone tool–chip (T–C) interface. (3) Tool flank. The peak temperature occurs at the
center of the interface, in the shaded region.
FIGURE 20-32 There are three main sources of heat in metal cutting. (1) Primary shear zone. (2)
Secondary shear zone tool–chip (T–C) interface. (3) Tool flank. The peak temperature occurs at the
center of the interface, in the shaded region.
Effects of Temperature

Excessive temperature affects
◦ strength, hardness and wear resistance of cutting
tool.
◦ dimensional stability of the part being machined.
◦ machined surface properties due to thermal
damage
◦ the machine tool, if too excessive.
FIGURE 20-33 The typical relationship of temperature at the tool–chip interface to cutting
speed shows a rapid increase. Correspondingly, the tool wears at the interface rapidly with
increased temperature, often created by increased speed.
Summary
High-strength materials produce larger cutting forces than
materials of lower strength, causing greater tool and work
deflection; increased friction, heat generation, operation
temperature.
Work hardness prior to machining controls the onset of
shear.
Highly ductile materials generate extensive plastic
deformation of the chip, which increases heat,
temperature, and longer, continuous chips.
A variation of the continuous chip, often encountered in
machining ductile materials, is associated a bill-up-edge (BLE)
formation on the cutting tool. BLEs are not stable and will
break off periodically. BUE formation can be minimized by
reducing depth of cut, altering cutting speed, using positive
rake tools, applying a coolant, or changing cutting-tool
materials.
HW for Chapter 20
Review Questions:
15, and 24 (pages 557 – 558)
Problem 7.
After your calculation, please compare your
HPs and ts with HPs values in table 20-3, and ts
values in Figure 20-22.