9 Grinding: Fast Machining and

Finishing by Bonded Abrasives

Learning Objectives
chapter would enable the readers to:
The contents of this
their
main purposes, basic Identify the significant parameter and
.Be conversant with the grinding
thickness, forces
methods of grinding roles on uncut chip
principle and different and specific energy requirement grinding.
in
.Visualize the relative positioning ofthe grind-
and their motions Estimate grinding forces and temperature
wheel and the blank,
ing under different working conditions.
in various methods of grinding. and learn how to
T o know what is grindability
B e aware of various applications of grinding techniques.
improve it using special
in the industries.
based Be conversantwith the advanced grinding
Classify and specify grinding wheels
and technologies and their unique
characteristics.

structure and strength, and employ the super-

on material, Be aware of selection
as per requirement.
select appropriate wheel finishing techniques.
modes
Categorize the chips and the
grinding under
of such chip formation
in grinding
various conditions.

well
9.1 Introduction torm and
dimensional accuracy as as very

need very high tools at desirably

A of engineering c o m p o n e n t s conventional machining by cutting
large section
are n o t possible by that, hard or essen-
are needed.
Besides
which normally operations
ood surface finish, rate (MRR). In such cases, grinding are easily done by grinding
but are grinding.
removal be finished by machining but and sharp abrasive grits
gn material steels,
cannot

microchips
by the hard
characterized by
hardened metals, especially removed in the form ofmaterial.
tially nding
Grind generally
is generally
is
work material bond owever, unlike mmachining.
grinding, the
suitable However,
wheels by velocity.
" circular
and very high cutting
being strong
strongly held
in the abrasives
higher cutting
z o n e temperature.

much and are used, with prop

innumerable

andomly distrib
distributed produces
d produces
and have been
developed
Pri specific energy machines
now the
classification of such
grinding requires more
wheels and grinding
c o n c e r n e d people
should know
igurations, cconstruction,
o n s t r u c t i o n , designa
Differe types ofgrinding applications. The The general
conhiguratio
ele
select o r various
grinding applications. eels aare also important aspects.
wheels
their various grinding
h machines and of
processes and and u s e
mounting
methods of
ar the
ton, selection and
Cction
 330 Machining and Machine Tools

It is necessary understand the mechanisms and

to formation under different
modes of chip
conditions. To employ grinding etticiently and economically through improvement in grindabilit. ad grinding
dability, adequa
knowledge of mechanics and temperature of grinding are essential.
Grinding is inherently associated with some acute problems such as wheel loading, high curs
temperature and its detrimental etfects and rapid wheel wear. Several remedial measures have also com
up. For generl awareness and benefit of the readers, researchers and practicing engineers, the chronologil
developments in grinding technology in several directions need to be studied and exploited. Some speial
cial
techniques have been developed to overcome the acute problems in grinding and improvement of overall
grindability of both conventional and exotic materials.
Some enginering components suchas engine blocks (bore), spindles, bearings, etc. need, for their better
performance and durability, super-finishing even after fine machining, boring. broaching and grinding,
Different methods of super-finishing are used in industries; the appropriate method and
proper level of the
process paramerers are carefully selected according to specific requirements.

9.2 Basic Principles, Methods and Applications of Grindingg

9.2.1 Basic Principle and Various Methods of Grinding
Grinding is a well-known process in manufacturing and is widely employed mainly for finishing jobs of
metals, alloys, carbides, ceramics, metal matrix composites, ceramic matrix etc. with
sional accuracy, surface finish and form accuracy. composites, dimen-
high
Grinding can as well be employed for form machining and
stock or bulk material removal.
Hard and sharp-edged abrasive grits are used for material removal
in abrasive jet machining and (b)
by two ways: (a) jet of loose abrasives
being strongly embedded in hard matrix in the form of wheel or disc. In
grinding. the work material is removed in the form of microchips by the sharp abrasive grits held in the wheel
by bond materiaB: The material removal process is a combination of shearing. ploughing, rubbing, etc.
In grinding, generally the abrasive
grits do not possess any definite shape as in the case of cutters tor
machining operation. The statistical average rake angle of abrasive
grits held in a grinding wheel tends to be
highly negative (-60°). minimize the effect of high negative rake, the cutting speed
To
(often termed as grind
ing velocity or wheel speed) is kept very high as compared to machining. For conventional grinding wheels
the grinding velocity can be as high as 50 m/s for steel components.
he
grinding wheel rotates at high speed to achieve the high grinding
velocity. The
reciprocates or rotates in contact with the wheel. The speed of reciprocation or rotation of workpiece
either
the workpiece s
much less as
compared to the grinding velocity and is generally around 10-20 m/min for
ing wheel and steel as work material. The amount of engagement between the conventional grinu
the wne
is known as infeed. Infeed in workpiece and
grinding is typically very small and is in the range of 2-50 um in the case o
surface grinding of steel with conventional wheels. The
main purposes of
grinding are
1. Dimensional accuracy.
2. Good form and
positioning accuracy.
Good surface finish.
4.
Shaping and finishing objects of harder materials.
Figure 9.1 shows a typical method of grinding and scheme of removal ind
ingincludel1.2 of chips. The general methods org
 Machine loólsS
332 Machining and
-

Wheel

- Workpiece

axis wheel and reciprocating table.

Figure.9.3 | Surface grinding with vertical

2 Workpiece

Figure 9.4 | Surface grinding in horizontal spindle rotary table surface grinder.

4.
Grinding
9.6. This is
with vertical
spindle and rotary table: The principle of such grinding is shown in
mostly suitable for small workpieces in large quantities.
 Abrasives38
Grinding: Fast Machining and Finishing by Bonded

table surface grinder.

of tapered surface in horizontal spindle rotary
Figure 9.5 | Grinding a

Workpiece

Wheel
Workpiece

table.
Surface grinding with
vertical spindle and rotary
Figure 9.6|

9.2.1.2 Cylindrical Grinding

surfaces: straight, tapered, steps or profiles. Broadly there are three
This is used to finish external cylindrical
methods:
diferent rypes of cylindrical grinding tailstock
method, the workpiece is held berween headstock and
In this
1. Plain cylindrical grinding: wheel performs the grinding
action with its peripheral
centres as in centre
lathes. disc-type
A grinding such grinding as shown in Fig. 9.7.
are carried out in
and plunge feed grinding
surface. Both traverse

(b)
(a)
Traverse feed grinding and (b) plunge feed grinding
Figure 9.7 | Cylindrical grinding: (a)
 334 Machining and Machine Tools

Figure 9.8 | Universal cylindrical grinding.

2. Universal cylindrical grinding: Universal cylindrical grinding is similar to plain oylindrical
grinding except that the former is more versatile. In addition to small worktable swivel, this
system provides large swivel of the headstock, wheel head slide and wheel head mount on the
wheel head slide, as has been indicated in Fig. 9.8. This allows grinding ofsmall to wide taperO
the long and short workpieces.
3. Form cylindrical grinding: Principle of cylindrical grinding is being used for thread grinding with
specially formed wheel that matches the desired thread profile. A single ribbed wheel or a multi-
ribbed wheel is used as shown in Fig. 9.9.

9.2.1.3 Internal Grinding

This method is used to
finish internal cylindrical surfaces. The surface may be straight, tapered, grooved or

profles. Broadly there are three different types of internal grinding methods as follows:
1. Chucking type internal grinding: Figure 9.10 schematically shows chucking Ype internagn
and various motions required for the grinding action. The workpiece is usually mountod in a chuck
A magnetic face plate is also used. A small
grinding wheel performs the necessary grinding witn
peripheral surtace. Both traverse and plunge grinding can be carried out as shown in Fig. 9.10.

Grinding wheel

Workpiece

(a) (b)
Flgure 9.9| Thread grinding
with (a) single rib, (b) multi-ribbed whee.
 Grinding: FastMachining and Finishing by Bonded Abrasives 335
Plunge feed

Traverse
feed
(a) (b)
Figure 9.10 | Internal (a) traverse grinding and (b) plunge grinding

and/or of odd shape and hence

Planetary internal grinding: It is used where the workpiece heavy the
is
2.
cannot be rotated conveniently as shown in Fig.
9.11. In this method, workpiece does not rotate.
in the workpiece.
Instead, the grinding wheel orbits the axis of the hole
3. Internal form grinding.

Workpiece
Grinding wheel

Finished surface

Internal grinding in planetary grinder.

Figure 9.11 |

9.2.1.4 Centreless Grinding

surfaces in a production machine in which out-
also used for finishing cylindrical or blade. The workpiece
is
This method of grinding is between centers but bya work-support
is not held
side diameter of the workpiece Centreless grinding may be external
the grinding wheel.
wheel and ground by
rotated by m e a n s of regulating
as well as internal type.

External Centreless Ginding

It may be of three types:

1. Infeed or plunge feed type

2. End feed ype.
3. Through feed type. The opera-
centreless infeed grinding as shown in Fig. 9.12(a).
be ground by is used for
feed grinding shown in Fig. 9.12(b)
can
Parts with variable diameter with cylindrical grinder. End
plunge grinding wheel or the regulating wheel
tion is similar to
or tapered
surtace.
Ihe profile
of
the grnding
slender workpiece with straight the required taper on the workpiece.
needs be to prepared to get
properly
or of both the wheels
336 Machining and Machine Tools

(a) (b)
Figure 9.12 External centreless grinding (a) infeed and (b) end teed types. Wg s grinding wheel
of
and W, is regulating or guide wheel.

Grinding wheel

Guide wheel
Causes job
rotation
Causes axial
job feed
Figure 9.13 Centreless through-feed grinding9.
In through-feed centreless grinding, the
regulating wheel revolving at a much lower surtace speed
grinding wheel controls the rotation and longitudinal motion of the workpiece. The regulating wheel is than
kept
slightly
inclined to the axis of the
grinding wheel and the workpiece is automatically fed longitudinally as
shown in Fig. 9.13.

Internal Centreless Grinding

This method used for grinding cylindrical ard
is
various bushings, etc.).
tapered holes in cylindrical parts (e.g., cylindrical liners
The workpiece is rotated
grinding wheel as illustrateduerween
and is ground by the supporting roll, pressure roll and regulating wne
in Fig. 9.14.

9.2.1.5 Tool and Cutter

Grinding
Tool grinding may be divided into two
1. Tool manufacturing.
subgroups
2. Tool re-sharpening.

There are many types of tool and

tools are occasionally
cutter grinding machines to meet these requirements. Simple single-p oint
sharpened by hand on bench or
pedestal grinder. However, tools and cutters
 Grinding: Fast Machining and Finishing by Bonded Abrasives 337
-

Supporting roll
Pressure roll

rotation
Figure 9.14 Internal centreless grinding. Here is grinding wheel rotation, i s workpiece
and is wheel axialtravel.

machine commonly
like milling cutter, drills, reamers and hobs require proper grinding
complex geometry with
known as universal tool and cutter grinder. Present
trend is to use tool and cutter grinder equipped

computer numerical control (CNC) to grind tool angles, with high precision.

9.2.2 Difference Between Machining and Grinding

used to high dimensional and form accuracy
Grinding is basically a machining process and is generally thereimpartcertain differences between machining
However, are
and desirably good surface finish to the products.
and grinding such as
dispersed in a
milling where thousands of abrasive particles
are
is considered abrasive
1. Grinding as
embedded surfaces
on the of metallic discs.
matrix such as vitrified, resin, rubber, metals, etc. or

material removal by their smal sharp tips and edges

while high speed moving
These particles cause
surface.
past the work unlike in
2. The size, shape, spacing and geometry
of the grinding abrasives randomly and widely vary
cutting tools.
to 60 times higher than that in machining for
3. The
is
kept 20
cutting velocity in grinding forces.
(a) Reducing the overall cutting to achieve good surface finish and longer life of
and force per tooth (grit)
(b) Reducing chip load
the working abrasives.
or dislodgement of
few abrasives or grits out of thousands does not

Unlike in cutting tools, damage wheel.

hamper the performance of the grinding
practically
Auto-sharpening of
matrix bonded type wheels.
5. to remove unit volume of
6. Grinding of a given requires more (10-20 times) specifc energy
material
unfavourable geometry (e.g., large negative
rake, in average -40° to -60°) of
work material due to
action.
the grit tips and additional rubbing
works eftectively and efficiently almost irrespective of
7. Unlike conventional machining, grinding
of the work material.
strength and toughness
 tate at a
high speed to attain
unbalance in the
the wheel may lead high
mach hine damage, etc.
to
machine peripheral surface speed (grinding
Iheretore, it is essential vibration,
poor product velociry), anany
ou
t-of-roundness, wrong mounting. etc. to
balance quality,
wheels and to avoid ity, catastrophic
catastrophic wheel failure,
wnee
cuDer-abrasive wheels are trued to removeAfter mounting the wheel on the
eccentricity,
both non-unirorm
for form grinding.
Dressing eccentricity and spindle conventiona
emoving
removing old, dull grits
is a
process of out-of-roundness and impart
and accumulated opening up the whel, that is, to
desired proile
chip materials require
electroplated super-abrasive wheels (generally exposing new sharp grits by
truingg and dressing with the
are pertormed by monolayer wheels of any construction). exception of
exception or

Truing
and dressing
1. Single-point diamond dresser.
2. Multi-point diamond dresser.
3. Stationary or rotary diamond rolls.
4. Brake controlled
dressing unit with vitrified green (friable and
for super-abrasive whels). purer) silicon carbide wheels (mainly
5. Metal crusher (tool post
6. grinding wheel).
Diamond block dressing (profile
7. Abrasive sticks and wheels (for grinding wheels).
super-abrasive resinoid wheel running-in period).
The major parameters
governing the dressing process are:
1. The lead of the dresser (i.e., the
2. The wheel speed.
velocity of the dresser across the wheel).
3. The depth of dressing.
4 Number of passes.
5 The environment.
6.
6. Surface speed of rotating dresser (brake controlled
dressing).

9.5 Mechanism and Mechanics of Grinding

9.5.1 Similarity of Grinding with Plain Milling
The basic principle of material removal in grinding is very similar to that inmachining Figure 9.17 shows
how material removal is caused by the tiny cutting edges in a typical grinding process (surface
grinding).

Wheel V
Abrasive Bond
grain

Grinding
Workpiece- Chip

Workpiece

Figure 9.17 Material removal by abrasives in grinding.

346 Machining and Machine Tools

V
Feed

E
Figure 9.18 Material removal in plain milling.

Figure 9.18 schematically shows the plain milling process where chip formation takes place mostly due to
shearing action by each tooth of the milling cutter. In such machining operations, the tangential or the main
cutting force component can be analytically evaluated by simple equations.
In plain turning, for example, of ductile metals, the tangential cutting force component (P = P) is ana-
lytically evaluated from
P15f
where r is the depth of cut (mm); s, is the feed per tooth (mm/rev); , is the dynamic yield shearing strength
of the work material (MPa):fis the form factor = - tan + 1 (is the chip reduction coefficient; 1 is the
effective rake angle at the cutting edge). This equation can be rewritten as

P=Aup
where A is the cross-sectional area of the uncut chip at any instance = Ba,v p is the specific force; B is the
width of cut and a = uncut chip thickness. The value of p is governed mainly by 7, of the material at the cut-
ting condition and also by the value of fwhich again depends upon the cutting edge geometry particular

and the nature and extent ofchip-tool

interaction (i.e., friction, formation, ete.). From
built-up-edge
Fig. 9.18 the average chip thickness in plain milling can be derived as

(9.4)
4ag =s, sinVav, sino D
where d is the depth of cut and D, cutter diameter. Again

m (9.5)

where
sZN
is the feed in mm/min; Z, is the number ofteeth of the curter and N= rpm = V/D Then,

Sm (9.6)
aavg Z VITD] VD

(9.7)
4avg
mVe VD
 Grinding: Fast Machining and Finishing by Bonded AbraslvesS4

Here, m is the number of cutting edges per unit length along the cutting periphery. We will later show that
the expression for average uncut chip thickness produced by single grit in surface grinding is very simat
this expression for milling. The expression for average uneut chip thickness ( p e r grit in surtace grinding
under ideal condition (shearing) comes up to

(9.8)
m,P
whereis the surtace (cutting) velocity ofthe wheel: is the surface (feed) velocity of the job; d is the depth
ofcut: D is the diameter of the grinding wheel: m the number grits per unit length on the wheel periphery
is
and grinding
Equations (9.7) and (9.8) reveal the closeness of material removal actions in plain milling

9.5.2 Mechanism of Material Removal in Grinding

for
are quite simple and systematic
The mode and mechanism of chip formation in conventional machining
the spacing and geometry of cuting cdges
well-defined and tavourable tool geometry. However, in grinding, in
which complicates the mode of chip formation. The rake angle
are much
unfavourable and vary randomly,
removal is accomplished in different
within 30° and-75°. In grinding, material
grinding generally varies
-

modes in different apportionment as follows:

to that found in other machining
9.19(a)]: The mode of chip formation is similar
1. Shearing [Fig. difference that the chips are microscopic
in size.
etc. with the only
processes like rurning, milling,
These chips consist of fine lamellar
structure.

produced by sidewise displacement ofwork The

mate

2.
2. Ploughing [Fig. 9.19(6)J: In ploughing, chips are
rakes of the abrasive grits.
mainly due to pyramidal shape and high negative
rial by abrasive grits
leafy in appearance.
chips produced by ploughing generally
are
and second-
been identified-primary
Rubbing [Fig. 9.19()]: Two
different modes
ofrubbing haverubs the
3.
the tip of the abrasive grain against the work material along
In primary rubbing rubbing is the
ary rubbing. thickness reaches a critical depth. Secondary
until the local grit depth or chip Rubbing
grit path the work material. It occurs along the
entire grit path of motion.
wear flats with
rubbing of
debris as well as blocky microsized irregular chip particles.
produces fine wear

Abrasive grains

Chip
Chips
Workpiece

W e a r flat

(End view) (Side view)

(Side view) (c)
(b)
(a)
in grindingi (a) Shearing. (6) ploughing and (c) rubbina
Figure 9.19 Major modes of chip formation
348 Machining and Machine Tools

Fracturing and crushing: This mode of chip formation occurs in grinding britle materials such 2
as
ceramic, carbides, etc. where the chips are produced as ine powders of fractured debris for britrle
fracture of the work material ahead the grit.
5 Spherical chip formation: Inspection of grinding debris (swarf) reveals presence of spherical chips.
These chips are produced because of oxidation and burning of smaller chips while leaving the grind-
ing zone. Chip particles at high temperature leaving the grinding zone and entering the amosphere
would tend to oxidize and melt. During such oxidation or melting they take near-spherical shape.
Generally, super-abrasive wheels provide less rubbing and ploughing due to sharper grits and reten-
tion of sharpness of the grits during grinding.
is ideal and that
Figure 9.19 shows different chip morphologies. Among the aforesaid modes, shearing
next to

shows the wheel-job moions

is ploughing. Rest of the modes are unfavourable. Figure 9.20 schematically
travels
and the way of material removal in cylindrical grinding. In this figure, while the wheel at its periphery
from point P to R, the job at its periphery advances from point R to S. Therefore,

PR RS
(9.9)
VE Vw
maximum
where V, is the grinding velocity (m/s) and v is the work feed (m/s). Again, from Fig. 9.20, the
total uncut chip thickness SU can be expressed as

SU RSsin(6+0)
total number of grits, in a row

Let m be the number of grits per unit length on the wheel periphery. Then the
engaged ( ) are
N = m-PR
 undcr VAl
Figure 9.21typically shows grinding chips produced
wheel under different environments.
steel specimens by alumina

9.5.3 Mechanics of Grinding

deals with analysis and evaluation of the forces associated with grinding, for example.
Mechanics of grinding
The magnitude of the grinding forces and specific energy requirement are also
cutting forces in machining.
indices of grindability. The grinding forces, if large, cause not only more power or energy
very important
also dimensional and surface integrity of the products. Compared to
consumption but impair accuracy
forces and (5-10 times) specific energy
machining. grinding requires much larger cutting
more
conventional
for same work material and same MRR. The main reason is the very large value of the chip reduction coef-
ficient which directly affects the cutting forces, as

P=5, (G-tan + 1)
as high as
The value of remains within 1.5 and 5 in conventional machining but becomes extremely large,
shown in
20-40 due to large negative rake angle"' at the cutting tips of the abrasive grains as schematically
Fig. 9.22. With the increase in depth, the rake condition improves. surface
Figure 9.23 shows the force components that are encountered in plain grinding, such as cylindrical to rwo
grinding and fat surface grinding. In plain, grinding, the workpiece at the grinding zone is subjected
force components:
F- tangential component, called the main cutting force.
2. N-normal or radial force component.
 Vo

Figure 9.22| Variation in rake angle with increase in thickness of chips.

NY N
Figure 9.23 | Development of grinding forces.
The grinding wheel is also subjected to the same forces as reactions but obviously in opposite direction.
The grinding forces, F and Nare analogous respectively to Pz and Pxy of rurning process. In conventional
machining P usually happens to be smaller (around half) thanP, But in grinding, Nis almost always much
to penetration (of grits) effect.
greater (1.25-2.0 times) than F. This is attributed
Machinability characteristics of any tool-work combination are judged mainly by chip form, cutting
forces and temperature, tool wear and life, and surface finish. Similarly, grindability of any work material is
judged by chip formation mode, grinding forces and temperature, grinding ratio and surface quality of the
ground surfaces. Grinding behaviour of any work material is most conveniently and reasonably evaluated and
where
expressed by its specific energy requirement, U
U =Amount of energy required to remove unit volume of work material by grinding

In surface grinding, U, can be evaluated from

U. Bxd
FXV(|/mm*)
xvw (9.19)

where F is the tangential component of the grinding force; V. grinding velocity (m/s); B workpiece width
mm; dinfeed (um); «, work feed (m/s). The value of U, is an important index of grindabilityof any work
4.4.1 GRINDING

Though there various types of grinding operations, to understand the

are the
basic mechanics we shall
consider the most common grinding operation,
namely, surface grinding. Figure 4.57a shows the basic arrangement of
surface grinding, which has some similarity with the up milling operation
except that the cutting points are irregularly shaped and randomly distri.
buted (Fig. 4.57b). The grains actually taking part in the material removal
process are called the active grains. Gradually,
the sharp edges of the active
grains wear out and become blunt. This results in larger forces on the active
machining. When the cutting edge is too blunt and the force
grains during
high, the grain either get fractured or break away from
is sufficiently may
the wheel. When a fracture takes place, new, sharp cutting edges are

the
generated, and when the whole grain is removed, new grains (below
the grind-
layer of the active grains) become exposed and active. This gives
characteristics. So, the bonding strength, which
ing wheel self-sharpening
 MANUFACTURING SCIENCE

254

Form grinding
Surface grinding

|1

Cylindrical Internal|
cylindrical
grinding
grinding

4.56 Some common grinding operations.

Fig.
Active grains Wheel
Grinding wheel

v 10-80 m/sec
Work
Work

f0.2-0.6 m/sec
(a) Basic scheme (b) Cutting action of grains
Fig. 4.57 Details of surface grinding.
p o r t a n t charac-

dictates the maximum force a grain can withstand, is an impOre o

offthe
tho
teristic. The strength of bonding is
normally termed as tnc
plac wheel. A wheel with a strong bond is called hard and roduced

the Due to the nature of the

vice v nrodu
process, very hot and small chips a"
th wheel

Itshould be remembered that the term hard or soft in the context oro
does not refer to the hardness of the
abrasives.
 MACHINING PROCESSES 255
readily get welded
which may readi toeither the grit
hich
tothe workpiece. niece. Moreover, because of random (abrasive grain) or
grit orientation, a
back on
to tn 3y have a very large negative number
rake angle (Fig.
o fgrits
of han
than cut. These two
cut. factors make the 4.57b) and may rub
grindingprocess of
fromquite
rather

cient in comparison with the other machining operations the

ine fview of specific energy. Apart from this, since the
inetti

o
point

form of exceedingly small

material is
oved inin the torm
r e m o v e d

chips, the size effect is very

prominent.

Mechanics of Grinding
ln Our analysis of the grinding process, all grains arc assumed to be iden-
tical. To explain the mechanices, we consider two different types of opera-
tions, namely, () plunge grinding and (1i) surface grinding. Figure 4.58a

Wheel Ground face

Work Work (X-X
View)

Nature of ground face (c) Cross-section of

(a) Scheme of plunge (b)
typical chip
grinding

Fig. 4.58 Details of plunge grinding.

where a job of rectangular cross-
shows a simple plunge grinding operation
The active grains are
section is being fed radially at a rate f (mm/min).
The uncut thickness per grit (t1)
can
assumed to be uniformly distributed.
be expressed as
(4.60)
ZN mm,
Nis the
revolution in one line and
wDere Z is the number of active grains per width
diameter of the wheel is D, the average grain
pm of the wheel. If the 4.58b, and the
surface density of active
of shown in Fig. can be tound
ut is b (mm) as number of grains/revolution/line (2)
is C (mm-2), the
aDs
from the expression
(4.61)
Z= mDCb'.
cross-sections as shown
triangular
approximately 20. Since
uncut sections have lies between 10 and
b/t generally
g . 4.58c. The ratio
r.=
and (4.61) yield
an be written as r . t , equations
(4.60)
(4.62)
f
DNCr
 MACHINING PROCESSES 257
zer value of Fc implies a
Since
a higher possibility of dislodging the
from the wheel, a wheel appears to be
the wh softer if D, C,
grain and vice versa.
or N decreases
fincreases,
of Figure
or 4.59
4.59 shows the basic scheme
of chip formation
also, the uncut during surface
rinding. He cross-section is triangular. But the uncut

D/2
1ma

Fig. 4.59 Scheme of chip formation

during surface grinding.

and 1mar and bmax are their maxi-

thickness and width vary (as in milling)
values. The average values may be taken as one-half of these. The
mum

average length of chip is given as

But

cos=-dy-1- two
cos 8 can be expanded (keeping only
where d is the depth of cut.
as
terms since B is generally small)

cos B 1 -
Substituting this in
equation, we get B2Vd/D.
cua, using the foregoing
The expression for l, we obtain
(4.66)
lVDd. fdB, where B is
unit time is
removed per be approxi-
The total volume of material volume per chip
can
unit time
average
the width of the cut in m m . The of chips produced per
number
The we h a v e
mately taken as bmar'1mad. =
bnas/'1aas
as before,

is
is
icarly (7NDBC). Now, taking rs

(TNDBC) x tbnas'1=fdB
258 MANUFACTURING SCIENCE

or

(mNDBC)x br,i.! = fdB

or

J 6f
(4.67)
One-half of this value is to be taken as the mean uncut
thickness. T
power consumption can be found out, using the same
procedure a
described before. If U, is the specific energy, the power required is

W= BfdU w.
60 (4.68a)
The total tangential cutting force, expressed in newtons, is

60,000W_60,000BfdU.1000Bfdu
Fe ND TND x 60 ND 4.68b)
where N is the wheel rpm. The number of grits actively
engaged at a time
is CBl= CBV Dd and the average force
per grit is given by
60,000 W
Fc N.
TNDCBVDd
Substituting W from
equation (4.68a) and U as Uolt1.)-0.4 in the foregoing
expression and using equation (4.67), we obtain

F 369Ufod0gN
NU.8Di.2C.8N. (4.69)
Here too, that if N, D, or C decreases,
we see
be
orfor d increases, the wheel
appears to softer. This is because Fc
increases, causing a more frequent
dislodging of the abrasive grains.
It should be noted that in
is much more than the
grinding the radial thrust force Fr (Fig. 4.60)
tangential cutting component Fc unlike the otner
machining operations.In surface grinding,
the ratio Fr/Fc 2.

N
W)
Fc

Fia 1 60