Section 25.
8 Machlnmg Econom|cs
Vibrations from internal machine sources-as well as from external sources,
such as nearby machines on the same floor-must be avoided as much as possible.
Laser metrology is used for feed and position control, and the machines are equipped
with highly advanced computer-control systems and with thermal and geometric
error-compensating features.
General Considerations for Precision Machining. There are several important fac-
tors in precision and ultraprecision machining and machine tools, somewhat similar
to those in high-speed machining:
I.Machine-tool design, construction, and assembly-providing stiffness, damp-
ing, and geometric accuracy.
2. Motion control of various components-both linear and rotational.
3. Spindle technology.
4. Thermal growth of the machine tool, compensation for thermal growth, and
control of the machine-tool environment.
5. Cutting-tool selection and application.
6. Machining parameters.
7. Real-time performance and control of the machine tool and implementation of
a tool-condition monitoring system.
25.8 Machining Economics
In the Introduction to Part I\L it was stated that the important limitations of machin-
ing operations include (a) the relatively longer time required to machine a part com-
pared with forming and shaping it, (b) the need to reduce noncutting time, and (c) the
fact that material is inevitably wasted. Despite these drawbacks, machining is indis-
pensable, particularly for producing complex workpiece shapes with external and in-
ternal features and for obtaining high dimensional accuracy and surface finish.
We have outlined the material and process parameters that are relevant to effi-
cient machining operations. In analyzing the economics of machining, however, several
other factors have to be considered. As will be described in greater detail in Chapter 40,
these factors include the costs involved in (a) machine tools, work-holding devices and
fixtures, and cutting tools; (b) labor and overhead; (c) the time consumed in setting up
the machine for a particular operation; (d) material handling and movement, such as
loading the blank and unloading the machined part; (e) gaging for dimensional accu-
racy and surface finish; and (f) cutting times and noncutting times.
Actual machining time is an important consideration. Recall also the discus-
sion in Section 25.5 on the importance of noncutting time in assessing the economic
relevance of high-speed machining. Unless noncutting time is a significant portion of
the floor-to-floor time, high-speed machining should not be considered-except if
its other benefits are relevant.
Minimizing Machining Cost per Piece. As in all manufacturing processes and op-
erations, the relevant parameters in machining can be selected and specified in such
a manner that the machining cost per piece (as well as machining time per piece) is
minimized. Various methods and approaches have been developed to accomplish
this goal. With the increasing use of software and user-friendly computers, this task
now has become easier. However, in order for the results to be reliable, it is essential
that input data be accurate and up to date. Described next is one of the simpler and
more common methods of analyzing machining costs in a turning operation.
Chapter 25 Machining Centers, Machine-Tool Structures, and Machining Economics
In machining a part by turning, the total machining cost per piece, Cp, is given
by
Cp = Cm + CS + C) + C,, (25.1)
Where
Cm = Machining cost
C, = Cost of setting up for machining-including mounting the cutter, setting
up fixtures, and preparing the machine tool for the operation
C) = Cost of loading, unloading, and machine handling
C, = Tooling cost, often only about 5% of the total cutting operation. Conse-
quently, using the least expensive tool is not always an effective Way of
reducing machining costs
The machining cost is given by
Cm = T,,,(Lm + Bm), (25.2)
Where Tm is the machining time per piece, L," is the labor cost of production person-
nel per hour, and Bm is the burden rate, or overhead charge, of the machine-includ-
ing depreciation, maintenance, indirect labor, and the like. The setup cost is a fixed
figure in dollars per piece. The loading, unloading, and machine-handling cost is
C1 = T,(Lm + Bm), (25.3)
where T) is the time involved in loading and unloading the part, in changing speeds
and feed rates, and so on. The tooling cost is
1 1
Ct :T
Ni
+ + +
Nf +
where N, is the number of parts machined per insert, Nf is the number of parts that
can be produced per insert face, TC is the time required to change the insert, T, is the
time required to index the insert, and Di is the depreciation of the insert in dollars.
The time required to produce one part is
_ Tc Ti
Tp-T]`l' Tm+K“|-my
Tm = 1
fN
L
= i
where Tm has to be calculated for each particular operation. For example, let’s con-
sider a turning operation; the machining time (see Section 23.2) is
7TLD
fV
Where L is the length of cut, f is the feed, N is the angular speed (rpm) of the Work-
piece, D is the workpiece diameter, and V is the cutting speed. Note that appropri-
(25.6)
ate units must be used in all these equations. From the Taylor tool-life equation
[Eq. (21.20b)], We have
C 1/n
T = (V) - ,
<
25.7 >
Where T is the time, in minutes, required to reach a flank Wear of certain dimension,
after which the tool has to be reground or changed. The number of pieces per insert
face is thus simply
T
N) = T, (25.8)
Section 25.8 Machining Economics
and the number of pieces per insert is given by
T
N, = mNf = (25.9)
Sometimes not all of the faces are used before the insert is discarded, so it should
L
be recognized that rn corresponds to the number of faces that are actually used,
not the number of faces provided per insert. The combination of Eqs. (25.6)-
(25.8) gives
m C1/n
Ni - (25.10)
71'LDV(1/"VI
The cost per piece, Cp, in Eq. (25.1) can now be defined in terms of several variables.
To find the optimum cutting speed and the optimum tool life for minimum cost, We
differentiate Cp with respect to V and set it to zero. Thus,
5
6C
= 0. (25.11)
Thus, the optimum cutting speed, VU, is
vo = 1 n 1 QL” + BM H, (25.12)
(Z - 1> {;(TC(Lm + Bm) + Di] + T,(L,,, + Bm)
and the optimum tool life, TO, is
1
1 ;[TC(Lm + Bm) + D,] + T,(Lm + Bm)
To = - 1> Lm + Bm _ (25.13)
To find the optimum cutting speed and the optimum tool life for maximum pro-
duction, We differentiate Tp with respect to V and set the result to zero. Thus, We
have
TGTI,
GV
= 0.
<
2 .14
5 )
The optimum cutting speed now becomes
c
1 + T,
71 WZ
and the optimum tool life is
To = -n -1 ~m
1 TC
+ T, _ (25.16)
A qualitative plot of minimum cost per piece and minimum time per piece (i.e.,
the maximum production rate) is given in Fig. 25.17. The cost of a machined surface
also depends on the finish required: The machining cost increases rapidly with finer
surface finish.
Chapter 25 Machining Centers, Machine-Tool Structures, and Machining Economics
T Total cost
3 "_ “_”
~§ Machining cost
5
ff Tool-change cost
(IJ
8 Nonproductive cost
Tool cost
,-11:1
Cutting speed ->
ia)
-*E l<- High-efficiency machining range
1
O Total time
_Q
Q.
L
8E ""' '“"""' __
Machining time
l:
L Tooi-changing time
Nonproductive time
Cutting speed ->
(b)
FIGURE 25.|1 Graphs showing (a) cost per piece and (b) time per piece in machining. Note
the optimum speeds for both cost and time. The range between the two is known as the high-
efficiency machining range.
The preceding analysis indicates the importance of identifying all relevant pa-
rameters in a machining operation, determining various cost factors, obtaining rele-
vant tool-life curves for the particular operation, and properly measuring the
various time intervals involved in the overall operation. The importance of obtain-
ing accurate data is shown clearly in Fig. 25.17, as small changes in cutting speed
can have a significant effect on the minimum cost or time per piece.
Such an analysis is typically done for all manufacturing processes, and it can
be a valuable tool for guiding process selection. For example, the cost per part in a
sand-casting process to produce blanks and in a machining operation to achieve
final tolerances can be calculated from an equation similar to Eq. (25 .1), but includ-
ing costs associated with sand casting (the cost of mold production, pattern depreci-
ation, etc.). A similar calculation can be performed on a processing approach that
uses powder metallurgy (thus increasing die and machinery costs), but requires less
machining because of its ability to achieve tighter tolerances, thereby reducing ma-
chining costs. A comparison of cost estimates can then help determine a processing
strategy, as discussed in greater detail in Section 40.9.
