7/26/2019 machining with

1/15

Dr. N. VENKAIAH

Assistant Professor

Mechanical Engineering Department

NIT Warangal 50 00!

Disclaimer

The content presente" here is not entirel# m# o$n. %ome portions are ta&en from

"ifferent so'rces $ith great regar". This content is solel# for class room teaching

an" not for an# commercial 'se.

"The greatest test of courage on earth is to bear defeat without

losing heart."

- Robert G. Ingersoll

7/26/2019 machining with

2/15

2

Total production cost per component

(Total unit cost)

=

Cost of Machining

+

Non-productive cost

+

Cost of tool

+

Tool changing cost

Note: Fixed costs li!e material cost are not ta!en into account "ecause

the# $ill not affect optimi%ation&

7/26/2019 machining with

3/15

3

Machining cost = CmTm

Where,

Cm = labor cost per unit time + overhead charges (depreciation +

indirect labor + maintenance)

Machining time for a single pass

where,

= Actual length of cut

( = approach and over run)

= spindle speed, rpm = tool feed, mm/revSpeed, , is determined from cutting velocit

m

w

LT =

Nf

L

= L + A + O A, O

N fN

=

,

m/min where is dia! of the "ob before cut#$$$

#$$$m

V

DNV D

DL

T Vf

=

=

7/26/2019 machining with

4/15

4

%on&productive cost = CnTn

Where,

Cn = 'reparation cost + Set up cost + oading and unloading cost +

dle time cost + other non&machining time costs

Tn = %on&machining time

*suall epressed as a fied cost in upees per piece!

7/26/2019 machining with

5/15

5

e

-ost of .ool = -ost of cutting edge %umber of cutting edges used

=

where,

-ost of a cutting edge

m

e

TCT

C =

or 0SS tools1

nitial cost of tool + egrind cost %umber of regrinds

%umber of regrinds + #eC =

or -arbide and -eramic tools with throw awa tips1

-ost of insert

%umber of cutting edges per inserteC =

7/26/2019 machining with

6/15

6

c m

c

.ool changing cost

= %umber of tool changes .ime re2uired for each change -ost

=

where,

.ool chaning time (.ime re2uired to grind and change a tool)

mT T CT

T =

7/26/2019 machining with

7/15

7

Non-productive cost

Tool changing cost

7/26/2019 machining with

8/15

8

Minimizing the Manufacturing Cost

# #

# #

p m n e c m

#/ #/

m n e m c

# #

m n e m c

.otal production cost per piece, +

+#$$$ #$$$ #$$$

+#$$$ #$$$ #$$$

n n

n n

m mm n

n n

n

n

T TC = C T C T C T C

T T

DL DL V DL V= C C T C C T

Vf Vf C Vf C

DL DL V DL V

= C C T C C T Vf f f C C

+ +

+ +

+ +

( ) ( )# #

# #

3 3# #m e m c3

or minimi4ing the cost,

= $

i!e,

#+ $ # # $

#$$$ #$$$ #$$$n n

n n

p

n n

C

V

DL DL DLC C V C T V

f V fC fC

+ + =

7/26/2019 machining with

9/15

9

( ) ( )

( ) ( )

( ) ( )

( ) ( )

# #

# #

# #

# #

# #

# #

3 3# #

m e m c3

3 3# #m m c e3

3 3 3# #m c e

# #m c e

m m c

# # #

# #

# # ## #

# #

# # #

n n

n n

n n

n n

n n

n n

n n

n n

n n

n n

C C V C T V V C C

C C T V C V V C C

V VC V T V C V

C C

V VC T C

C C

VC C T C

= + = =

=

= ( ) ( )

( ) ( )

( )

# #

#

#

# #e

#m m c e

e# c

m

# #

#

#

n n

n

n

n n

n

n

VC C

VC C T C

C

CV

TC C

+

= +

= + ( )

e#c

m

5ptimum cutting speed for minimum co

#

st

opt n

n

CV

C

T C

=

+

Minimizing the Manufacturing Cost

7/26/2019 machining with

10/15

10

Maximizing the Prouction !ate

( )

#

#

#

p

m

m

p

3#3

#

ate of production,

Where,

.otal manufacturing time

=

#$$$ #$$$

.o maimi4e , minimi4e

$

! !,

#+ # $

#$$$ #$$$

n

n

n

p

p

n c

n c

p

p

nc

R T

T

T

T T T T

DL DL VT T

Vf Vf C

R T

T

V

i e

DL DLT V

f V fC

=

=

+ +

= + +

=

=

( )

( )

( )

( )

#

#

3#3

#

p

#

#

c

#= #

#

5ptimum cutting speed for Ma+!

#

#

n

n

opt n

no

nc

c

t c

n

p

n

VT VV

C

T

C

T

C

V

R

V

T

T

=

=

=

7/26/2019 machining with

11/15

11

Non-productive

cost

Tool changing

cost

7/26/2019 machining with

12/15

12

Pro"#em

A #$$ mm long 67 mm diameter bar is to be turned at a feed of $!38

mm/rev! the operating cost is s! #$ per minute and the tool cost is s! 97per edge! .he tool changing time is : min! a carbide tool is used with two

cutting fluids for which the tool life e2uations are as given below1

-utting fluid # & VT$!33=89

-utting fluid 3 & VT$!63

=89

ind out which cutting fluid is better on relative cost!

7/26/2019 machining with

13/15

13

$o#ution

D= 67 mm, L= #$$ mm, f= $!38 mm/rev!,

Cm= s! #$/min, Ce= s! 97, Tc= : min

( )

( )

## ##

e## c

m

33 33

e#3 c

m

3;!86m/min, :$!99 min

#

3:!#m/min, 3:!:: min

#

n

n

n

n

CV T =

CT

C

CV T =C

TC

= =

+

= =

+

m#

#

m3

3

+67+#$$#!:6 min#$$$ #$$$+3;!86+$!38

+67+#$$#!96 min

#$$$ #$$$+3:!#+$!38

DLT V f

DLT

V f

= = =

= = =

7/26/2019 machining with

14/15

14

$o#ution

# #

p# m # e c m# #

3 3p3 m 3 e c m

3 3

p# p3

#!:6 #!:6#$#!:6 97 :#$ s!#

:$!99 :$!99

#!96 #!96#$#!96 97 :#$ s!37!::/-omponent

3:!:: 3:!::

0ence cutting fluid # is be

m m

m

m mm

T T

C = C T C T C T T

=

T TC = C T C T C

T T

=

C C

+ +

+ + =

+ +

+ + =

< tter

7/26/2019 machining with

15/15

15

Pro"#em

A tool used in a turning operation is of bra4ed&carbide tip tpe! ts cost is

s! :7$ and on average it can be reground ten times! .he cost of regrindingis s! :7! .he lathe cost is s! 3 lah and is used < hours/da, 7 das/wee

and 7$ wees/ear! ts cost is to be amorti4ed over #$ ears and the

machine overheads are #$$>! .he operators wage is s! 3$/hour and the

operator overheads are #$$>! .he tool life e2uation is VT$!37 = 9 where Vis

in m/s and Tis in s! .he tool changing time is : min and handling time percomponent is 7 min! .he cutting distance per component is #$$ m!

-alculate1

a) the minimum production cost and

b) the minimum production time!

Sol!