ME 322- Professor Molian's Lecture Notes on












US industries spend annually $60 billion to perform metal removal operations that range from simple clean-up of castings or welds to high precision work.

What is Machining?

 Machining is a process designed to change the size, shape, and surface of a material through removal of materials that could be achieved by straining the material to fracture or by thermal evaporation.

 Why Machining?

 Offers important benefits such as

 Excellent dimensional tolerances

-Example is forged crankshaft where holes and bearing surfaces require tight tolerances.

- Sharp corners, grooves, fillets, various geometry

-Example is a copper mirror by diamond turning

- Parts such as crank and camshafts undergo distortion during heat treatment. Machining is a process for "straightening" the parts.

There are limitations that include

 o Material waste

o Time consuming

o Energy, capital and labor intensive

  What constitutes a machining system?

A machining system consists of three components: machine tool, cutting

tool, and workpiece (part to be machined).

How do we classify machining processes?

  See Figure 1 and also Figure 8.1 of Text.


Chip Forming Processes Chipless Forming Processes

(Cutting) (Finishing) (Non-traditional)

Turning Grinding Electrical Discharge

Boring Lapping Laser

Drilling Honing Plasma

Milling Polishing Water-jet

Planing Buffing Chemical

Shaping Electrochemical




What are the three fundamental machining parameters?


Cutting speed (V) is the largest of the relative velocities of cutting tool or workpiece. In turning (Figure 2), it is the speed of the workpiece while in drilling and milling, it is the speed of the cutting tool. In turning, it is given by the surface speed of the workpiece, V = p D1N where D1 is the diameter of the workpiece.

Depth of cut (d) is the distance the cutting tool penetrates into the workpiece. In turning, for example, it is given by: d = (D1-D2)/2

Feed (f) is movement of the tool per revolution. In turning, it is the distance the tool travels in one revolution of the workpiece and is given the units of mm/rev or in./rev.


What is Material Removal Rate (MRR)?

The volume of material removed per minute. In turning, MRR= Vfd.


 In general, machining is 3D-process. For providing an understanding of mechanics of machining, we simplify the process into a 2D-process called as Orthogonal Cutting as shown in Figure 3. In orthogonal cutting, the workpiece is a flat plate (it can be a thin tube too) and is machined using a wedge-shaped tool with a rake angle of a and a relief angle of q . The workpiece is moving at a cutting speed of V with a depth of cut to. The width remains unaffected.

 The chip formation is a localized shear process in a narrow region where the metal is compressed and then made to flow on the face of the tool. See the diagram (Figure 4) and video of an aluminum plate machined.

The shear angle, f , is of fundamental importance. A smaller angle implies a large shear plane leading to requirement of high cutting forces. Let us develop some equations that help us understand the process better.

 1. Cutting ratio, r

  See Figure 8.2. If the chip thickness is tc, then we can show that

  r = to/tc = Sin f /Cos(f -a )


r is always less than unity. Rearranging the equation gives,

  tan f = r Cos a /(1-r Sin a )

 2. Shear Strain


Consider a square element subjected to a shear stress. If the distance sheared is "a" and the edge length of square is "b", then the shear strain is given by: g = a/b.

In metal cutting, the shearing process is similar to a deck of playing cards sliding against each other as shown in figure. See Figure 8.3. We can write:

  g = AB/OC = (AO + OB)/OC = Cot f + tan (f -a )

 Low shear and rake angles result in high g . A value of g >5 indicates much greater deformation in machining than in metal forming where it is under 1.



3. Velocity Ratio

  If the velocities are considered (see Figure 8.3),

  Q = w toV = w tc Vc

  V/Cos (f -a ) = Vs / Cos a = Vc/Sin f


4. Shear Strain-rate

  dg /dt = Vs/d where d = OC ~ 10-3 to 10-4 inch

  Shear strain rate is on the order of 103- 106/sec

 Thus, it is this combination of large strains and high strain rates make it difficult to predict chip formation.


  1. Chip Formation (Figures 8.4 through 8.9)


Chip formation affects the surface finish, cutting forces, temperature, tool life and dimensional tolerance. A chip consists of two sides 1) the side in contact with the tool is called shiny side (flat, uniform) due to frictional effects, 2) the other side is the free workpiece surface that has a jagged appearance due to shear.

  1. Continuous


- Narrow shear zone, there is also a secondary shear zone

- Excellent finish

- Usually for ductile metals

- Occurs at high cutting speed and rake angle but may form at low speed, low rake angle in castoff soft metals, and characterized by

Wider shear zone that causes distortion, poor finish, residual stresses

-Entanglement of chips with the tool holder. Use chip-breakers.


B. BUE (continuous)


Built-up-edge (BUE) forms when there is a chemical affinity between workpiece and the tool. It becomes unstable, breaks up and then forms again. The process is repeated continuously.


- Favorable growth conditions such as high strain-hardening, low speed, large depth of cut, low rake angle, and high temperature

- Degrades the surface finish changes tool geometry

- Thin BUE helps to improve the tool life

- Cutting fluids will prevent the formation of BUE


  1. Discontinuous

-Occurs in brittle materials

-Inclusions/impurities promote this

- Very low or hi V

-Large depth of cut

-Lack of cutting fluid

Because of the discontinuous nature of the chips, forces vary continually leading to vibrations and chatter in the machine tool with the end results of poor surface finish and loose tolerances.


D. Serrated chips


- Semicontinuous with zones of high and low shear strains


6. Force Analysis


The objectives are:


  1. to properly design machine tools for vibration and chatter-free operations.
  2. to understand how material strength affects the cutting forces.

3. to determine the HP of motor to be installed on the machine tool.


The forces acting on the cutting tool are shown in Figure 8.12. Except Fc and Ft, all other forces can not be experimentally measured. A dynamometer (force transducer) mounted on the workpiece or tool holder is used to measure Fc and Ft. Draw the free body diagrams of chip, tool and workpiece to understand how the forces act on. We can write the forces as:


R = (Fc2 + Ft2)1/2 = (Fs2 + Fn2)1/2 = (F2 + N2)1/2

Fc = R cos (b -a )

Ft = R sin(b -a )

Fs = R cos(f +b -a )

Ft = R Sin(f +b -a )


These forces are small on the order of few hundred newtons, but the local stresses are very high due to smaller contact areas leading to wear, chipping, fracture. The tool-chip contact length is also small (about 1 mm).


Coefficient of Friction


At the tool-chip interface, there is friction. The coefficient of friction, m , can be written as:

  m = F/N = tan b

 F and N are expressed in terms of other forces using a circular force diagram shown in Figure 5.

  F = Fc sin a + Ft cos a and N = Fc cos a - Ft sin a

m = F/N = (Ft + Fc tan a )/ (Fc-Ft tan a )

m is on the order of 0.5 to 2 indicating the chip faces considerable frictional resistance when climbing over the tool face.


Cutting and Thrust Forces

We rewrite the cutting force, Fc = R cos (b -a )

  where R = K fadbV-c where K, a, b, c = constants

 From Tables 8.2 and 8.3, you note that Fc increases with increasing d, decreasing V, and decreasing rake angle.

 We rewrite the thrust force, Ft = R sin(b -a )=K fadbV-c sin(b -a )

 Thrust force causes deflection of the tool and reduces the depth of cut and affect tolerances. The machine tool and tool holder must be stiff enough to withstand Ft.

  Ft = Fc tan (b -a )

 and since Fc is always positive, Ft can be positive or negative depending on (b -a ). Negative Ft implies upward force. See Figure 8.13. High rake angle and low friction generally result in upward forces. High rake angles are not common in machining.


Shear Angle

 This is a challenging parameter to determine. Several theories are advanced to find the shear angle. One of the earliest analyses (Merchant's) says, "the shear angle leads to maximum shear stress".

 Hence we write, t = Fs/As = R cos(f +b -a )/(w to/sin f )

 Differentiate the shear stress the shear angle and set it equal to zero (assume that b is independent of f ), then we find


f = 45 + (a -b )/2

 see Figure 8.17 to see how this equation poorly predicts the experimental data. Note another equation (8.21) has been developed but does equally poor in predicting the experimental data.

As the rake angle increases, the shear angle increases. An increase in shear angle will reduce the chip thickness (how) and reduce the temperature rise.

 Let us substitute the above equation in Fc, which becomes


Fc = R cos (b -a ) = R sin 2f

Stresses in shear plane

There are two stresses in the shear plane caused by Fs and Fn. The average shear stress is:

  t = Fs/As and s = Fn/As


WORK OUT PROBLEMS 8.91, 92 and 93.


7. Power Analysis

The cutting force system in 3D-turning consists of three forces: Fc is the largest force that accounts for 99% the power required, Ft requires very small power because feed rates are very small, and Fr the radial force contributes very small also because velocity in the radial direction is negligible.

 Ignoring the thrust and radial forces, the total input power to cutting is given by:

Pc = FcV

Pc = Ps + Pf = FsVs + F Vc

  where Ps = power required for shearing

Pf = power to overcome tool-chip interface friction

Additional power for creating new surfaces and for momentum changes as the metal crosses the shear plane is considered small.

In terms of specific energy or UNIT POWER (specific energy, energy per unit volume of material removal), UNIT POWER IS A MATERIALS PROPERTY.

UNIT POWER = ut = FcV/w toV = Fc/w to

 See Table 8.4 for unit power of different materials. This UNIT POWER has been corrected for motor efficiency, which is assumed to be 80%. That is, Pmotor = Pc/0.8 . For dull tools, you have to multiply the table data by 1.25.

 We can also find out the portion of frictional specific energy,

  uf = [sin b sin f / cos (b -a ) cos (f -a )] ut

Note that us = ut - uf

 Usually 30-40% of the total energy goes to overcome the friction. Go through example problems 8.1 and 8.2.




  1. Heat and Temperature in Metal Cutting

 The energy dissipated in cutting operations is largely converted into heat, raising the temperature of chip, tool, and workpiece. The cutting fluid, if used, is an excellent heat sink. There are three sources for heat development:


    1. the shear process itself.
    2. the tool-chip interface friction.
    3. the flank of the tool rubbing the workpiece (especially if the tool is dull).

 Most of the heat produced is carried by the chip (see Figure 8.22) implying that the shear process (plastic deformation) is most effective in producing heat. Experimental data showed that

 o typical values of the temperature rise are 600 to 1500oF

see Figure 8.19 and Figure 8.21

o Temperature can adversely affect the following:

  On the cutting tool - Reduce strength and wear resistance

On the workpiece- Dimensional accuracy and surface integrity

  Temperature rise is obtained using thermocouples and infrared pyrometers (experimental) and by heat flow models. Temperature rise in orthogonal cutting is predicted by:

T = 1.2 (Yf/r c) (Vto/K)1/3

T= Mean value at tool-chip interface, oF

Yf= Flow stress of workpiece, psi

r c= Volumetric specific heat of workpiece, oF

K =Thermal diffusivity of workpiece, in2/sec

Thermal properties of tool are relatively unimportant.






1. Cutting ratio = chip-thickness ratio = to/tc = Sin f /Cos (f -a )

  1. Shear strain, g = Cot f + tan (f -a )
  2. Velocity ratio, V/Cos (f -a ) = Vs / Cos a = Vc/Sin f
  3. Shear strain rate = Vs/d where d = 0.01 to 0.001 mm
  4. Shear angle, f = 45 + a /2-b /2

Typical a = -10o to +20o for which f <20o

6. R = (Fc2 + Ft2)1/2 = (Fs2 + Fn2)1/2 = (F2 + N2)1/2

Fc = R cos (b -a )

Ft = R sin(b -a )

Fs = R cos(f +b -a )

Ft = R Sin(f +b -a )

7. Coefficient of friction, m = F/N = (Ft + Fc tan a )/ (Fc-Ft tan a )

8. Stresses in shear plane, t = Fs/As and s = Fn/As

9. Power analysis

UNIT POWER = ut = Fc/w to

Friction UNIT POWER = uf = [sin b sin f / cos (b -a ) cos (f -a )] ut

10. Temperature rise at the tool-chip

T = 1.2 (Yf/(c) (Vto/K)1/3



Tool Wear

See Figures 8.23, 8.24 and 8.25

  o Degrades the surface finish

o Increases the tolerance and

o Increases the cost of machining


_PRIVATE __Types of wear



Temperature, Adhesion, Abrasion, Plastic flow


Temperature, Diffusion, Oxidation

Chipping, Fracture

Mechanical shock and Thermal fatigue (interrupted cutting)


Adhesion: High pressure/temperature cause adhesion of of asperities between the tool and the chip.

Abrasion: Hard particles in the workpiece cause abrasion of the tool-- Dominant mechanism for flank

Plastic Flow: High temperature softens the tool and high stresses cause the plastic deformation of the cutting edges

Diffusion: Exchange of atoms across the contact boundary between the chip and the tool. Tool may lose "hard atoms"

 Tool Life is determined by different types of wear. Flank wear is said to be the governing factor.

 Flank wear increases with time as shown in Figure 6. In the break-in period, the cutting edges lose their sharpness rapidly. In the steady-state, there is an uniform wear, and in the accelerated region, there is rapid wear due to high-temperature.

If we plot flank wear as a function of time, we find Figure 7. Flank wear (also called as wear land) is the distance VB which is the criterion for tool life (tool has to be resharpened or changed). VB is measured using a toolmaker's microscope.

 See Table 8.6 for the maximum value of VB allowed for different machining operations.

  VB is established based on Taylor's tool life equation given by

V Tn = C (for given values of d, f)

V = cutting speed, most critical parameter

T = tool life, minutes, to develop flank wearland VB

C = constant = Tool life for 1 min

 See Figure 8.27. The plot is log-log. In general, T = 60-120 min for HSS tool to develop VB and 30-60 min for carbide tool to develop VB.


  Factors affecting n, C

  C is influenced by the type of workpiece and cutting conditions.

n is a function of the cutting tool material

 Since flank wear is cumbersome to evaluate in production environment, several simple, subjective criteria may be used.

 -- Complete failure of the cutting edge

-- Visible observation of the flank wear

-- Fingernail test across the cutting edge

-- Changes in the sound

--Changes in chip formation

-- Degradation of surface finish

-- Increased consumption of power

(watt meter connected to the machine tool)

-- Number of workpieces machined

-- Cutting time

 Surface Finish and Integrity

 Finish represents geometric properties while integrity pertains to properties such as fatigue life, corrosion etc. Read Section 4.2.1 for more information on surface integrity.

_PRIVATE __Finish (geometric features)







Residual stresses

Phase transformation

Plastic deformation




Figure 4.2 shows the surface terminology and symbols.


Roughness -- closely spaced , irregular deviations

Waviness -- greater spacing deviations caused by the deflections of tools, dies, thermal warping, uneven lubrication, vibrations etc

Flaws -- scratches, holes, cracks, depressions, inclusions

Lay - direction of the predominant surface pattern

 Measures of Surface Roughness

 1. Arithmetic average (AA) - Widely adopted

2. Root mean square (RMS) - Used mostly prior to 1950

3. Roughness height (Peak-to-valley distance)


Surface profilometer (Figure 4.4) is used to measure surface roughness. Read section 4.3.

 Figure 8.33 shows the roughness data for various machining processes. Variables that influence the roughness are:


BUE - more damaging effect on roughness

Tool radius- sharper the tool, higher would be roughness

Feed - larger the feed, higher is roughness

Vibration/chatter - increase the roughness



Machinability is a term that includes several parameters: finish, integrity, tool life, cutting speed, force, chip formation, composition and properties of material etc. In general, tool life and surface finish are measures of machinability. The ratings are given for materials. AISI 1112 steel is given rating of 100. What it means is that, the steel can be machined at 100 fpm for 60 minutes of tool life. Some other materials ratings are:

  Material Machinability Rating

AISI 3140 55

Brass 300

2011 Al 200

Gray iron 70

Inconel 30



Tool Materials

  A cutting tool is subjected to:

o High temperatures (300 to 1500oF)

o High contact stresses (103 to 106 psi)

o High speed chips (10 to 1000 fpm)

  Required Properties

o Hot hardness

o Wear resistance

o Chemical inertness

o Toughness (for interrupted machining)


Tool Materials




Cast Alloys



WC, TiC, some Co


Si3N4, CBN, Diamond



Cutting Fluids

 Cutting fluids reduce the heat, wash away the chips, and protect the machined surface from oxidation. It is a coolant as well as a lubricant. See Figure 8.49 for the high activity of cutting fluids.

 The cutting fluid accelerates the thermal cycling in interrupted cutting operations such as in milling. This condition leads to thermal stresses and causes cracking. The mechanism of cutting fluid action involves capillary action in which case the fluid should have small molecules and proper wetting of the surface (see Figure 8.50). The cutting fluids are applied in flood or in mist conditions. Flood cooling is applied in lathe, milling, gun drilling, and end milling. Mist cooling is applied in grinding.

 Selection of the cutting fluid depends on the workpiece (minimize chemical reactions, staining, stress corrosion etc), on the machine tool (slideways and bearings are to be compatible with the fluids), and on the operator safety.



Lathes - Oldest machine tools

 Engine Lathe - Simple and versatile but require a skilled machinist because all controls are manipulated by hand. It is inefficient for large production runs (Figure 8.55).

Tracer Lathe - Machine tool with an attachment that is capable of turning parts with various contours.

Turret Lathe - Several cutting tools are mounted on the turret in the cross-slide. They are capable of performing multiple operations such as turning, boring, drilling, facing, thread cutting.

Automatic Lathes - Also called as chucking machines, they are usually vertical and do not have tailstock and are used for machining regular and irregular shapes.

CNC Lathe- turret lathe controlled by CNC. Automated, suitable for low to medium volumes of production (Figure 8.56).


Operations on a Lathe

SEE Figure 8.51. Straight turning, taper turning, grooving, threading, facing, profiling, drilling, boring, cutting off, and knurling.


 The turning parameters include tool geometry, feed, depth of cut, and cutting speed.

 Tool Geometry

 Turning operations use single-point geometry cutting tools. The tool geometry affects cutting speed, chip control, surface finish, tolerances (vibration and chatter) and cutting force. The geometry of a right-hand cutting tool (i.e. tool travels from right to left) is shown in Figure 8.52.

The effects of tool geomtery on various aspects are given in the table below.

 Feed, Depth of Cut, and Cutting speed

 See Table 8.14 for a summary

See Table 8.12 for typical values of cutting parameters.

 Forces in Turning

 See Figure 8.53. These forces are important in the design of machine tools as well as in the deflection of tools for precision machining.

 WORKOUT PROBLEMS 8.96, 8.100, 8.101, 8.102, and 8.103

 Turning Process Capabilities

 1. Production Rates - See Table 8.15, relative ratings

  1. High-speed machining, > 2000 fpm

-Important in aerospace and automotive to improve productivity only when cutting time is the largest.

  1. Ultraprecision machining - surface finish in nanometers, and accuracies in sub-micron range. Examples are optical mirrors, computer memory disks, drums for copying machines. Diamond turning is common. The workpiece materials include Cu, Al, Ag, Au, Ni, and plastics. The depth of cut is in the nanometer range. High-stiffness machine tools, vibration-isolation tables, and dust-free environment are needed.
  2. Hard turning - use CBN tools for finish-machining hardened steels.





Rake Angles

-5 to 20

Control chip flow

Reduce Fc

Reduce Temp

Improve surface finish

Weakens edges

Difficult to grind

Decrease cutting angles

Relief (about 6)

Reduce friction

Less flank wear

High stresses on the edge

Side cutting (about 15)

Reduce the heat

Change f and d

Improve surface finish1

Separate the tool and workpiece,

Tool chatter

End cutting (about 15)

Reduce heat

Reduce surface finish1, Chatter

 Nose radius (about 1/8")

Improve cutting speed

Improve surface finish2

Separate tool and work

Tool chatter

1. hmax = f/(cot Cb + tan Cs)

2. hmax = f2/8R


Equations 1 and 2 do not include the effects of workpiece material, vibration and type of machine tool.


 Boring consists of producing circular, internal profiles in hollow workpieces or on holes. The boring bar is long and must be stiff. Boring can be accomplished in the lathe or in boring mills if large pieces are used. SEE Figure 8.58.


 Drilling machine, called as drill presses, are vertical machine tools. Significant problems include the chip disposal, accurate locations, carefulness in preventing the drill from breaking and supplying cutting fluid.

Operations: Drilling, Reaming, Tapping


 See Figure 8.60

Drilling - uses standard chisel-point twist drills with diameters ranging from 0.006 in. to 3 in. Trepanning technique can be used to drill larger diameter holes about 6 in.

Core Drilling - Drill a larger hole on a smaller hole.

Step drilling - Double sized drill

Counterboring - stepper hole. Useful to seat bolt heads in the holes.

Countersinking -Hole is cone shaped for flat head screws.

Reaming - Enlarge the hole, provide better tolerance/finish.

Center Drilling - To begin the center for a hole.

Gun Drilling- deep holes with aspect ratios > 300


 Is an operation to make an existing hole dimensionally more accurate than can be obtained by drilling alone and to improve surface finish. A reamer is a multiple-edge cutting tool that removes very little material. The most accurate holes are produced by a sequence of operations that involve centering, drilling, boring, and reaming.


 Internal threads in the holes of workpieces are produced by taps. After tapping, the tool is mechanically collapsed and removed without having to rotate it. Sizes up to 4 in.

 Mechanics of Drilling Table 8.17 for parameters

 Axial speed of the drill = f N = feed rate and

MRR = (Hole area) (fN)

Horse power for drilling is to overcome thrust and torque forces.

UNIT POWER = (power for torque + power for thrust)/MRR


Thrust force, if excessive, will break the tool. Usually it is small, on the order of few hundred lbs. It is a function of cutting parameters in addition to the strength of workpiece material. It can be small when compared with torque. WORK OUT PROBLEMS 8.104 and 8.105


 Includes a number of processes that are capable of producing a variety of configurations. See Figure 8.63.

 Types of milling machines and their components

  1. Horizontal spindle (see Figure 8.70)
  2. Vertical spindle (see Figure 8.71)

 Three forms of milling:

o Slab Milling (Horizontal)

o Face Milling (Vertical)

o End Milling (Vertical)

 See Table 8.18 for milling parameters and formulas.


Slab milling , (see Figure 8.64) also called as peripheral milling, the axis of cutter rotation is parallel to the workpiece surface. The depth of cut is in the range 0.04" to 0.3". Go through Example 8.8

Face milling, (see Figure 8.65) the cutter is mounted on a spindle having axis of rotation perpendicular to the workpiece surface. See next apages for calculations. Go through Example 8.9.

End milling, where the cutter is smaller than the face miller, can be used to produce various profiles including dies.


Conventional (Up) and Climb (Down) milling

 Up Milling

- Beginning chip thickness is small


1. Oxide scale or hard surface of work does not matter

2. Rigidity is not critical because the cutter is opposed by the feed of the work (machine is even).


1. Tool chatter

2. Feed marks

3. Clamp workpiece

(work moves up)

Down Milling

- Beginning chip thickness is large


1. Low temperature (long tool life)

2. Smaller feed marks

3. Downward part of cutting force holds the workpiece (slender parts)



1. Rigid setup is needed due to the cutter pulling the workpiece along.

2. Not suitable for oxide scale surfaces.


WORK OUT PROBLEMS 8.106, 107, 108, 109, 110 and 111.