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26.1
SECTION 26
MET ALWORKING AND
NONMET ALLIC MATERIALS
PROCESSING
ECONOMICS OF MACHINING 26.2
Estimating Cutting Time with
Different Tool Materials 26.2
Comparing Finish Machining Time and
Costs with Different Tool Materials
26.6
Finding Minimum Cost and Maximum
Production Tool Life for Disposable
Tools 26.10
Computing Minimum Cost and
Maximum Production Tool Life for
Regrindable Tools 26.11
MACHINING PROCESS CALCULATIONS
26.12
Total Element Time and Total
Operation Time 26.12
Cutting Speeds for Various Materials
26.13
Depth of Cut and Cutting Time for a
Keyway 26.14
Milling-Machine Table Feed and
Cutter Approach 26.15
Dimensions of Tapers and Dovetails
26.15
Angle and Length of Cut from Given
Dimensions 26.16
Tool Feed Rate and Cutting Time
26.17
True Unit Time, Minimum Lot Size,
and Tool-Change Time 26.18
Time Required for Turning Operations
26.18
Time and Power to Drill, Bore,
Countersink, and Ream 26.20
Time Required for Facing Operations
26.20
Threading and Tapping Time 26.22
Turret-Lathe Power Input 26.23
Time to Cut a Thread on an Engine
Lathe 26.24
Time to Tap with a Drilling Machine
26.25
Milling Cutting Speed, Time, Feed,
Teeth Number, and Horsepower
26.26
Gang-, Multiple-, and For-Milling
Cutting Time 26.28
Shaper and Planer Cutting Speed,
Strokes, Cycle Time, Power 26.29
Grinding Feed and Work Time 26.30
Broaching Time and Production Rate
26.31
Hobbing, Splining, and Serrating Time
26.31
Time to Saw Metal with Power and
Band Saws 26.32
Oxyacetylene Cutting Time and Gas
Consumption 26.33
Comparison of Oxyacetylene and
Electric-Arc Welding 26.35
Presswork Force for Shearing and
Bending 26.36
Mechanical-Press Midstroke Capacity
26.36
Stripping Springs for Pressworking
Metals 26.37
Blanking, Drawing, and Necking
Metals 26.37
Metal Plating Time and Weight 26.38
Shrink- and Expansion-Fit Analyses
26.39
Press-Fit Force, Stress, and Slippage
Torque 26.40
Learning-Curve Analysis and
Construction 26.43
Learning-Curve Evaluation of
Manufacturing Time 26.44
Determining Brinell Hardness 26.47
Economical Cutting Speeds and
Production Rates 26.47
Optimum Lot Size in Manufacturing
26.49
Precision Dimensions at Various
Temperatures 26.50
Horsepower Required for
Metalworking 26.51
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Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS
26.2 DESIGN ENGINEERING
Cutting Speed for Lowest-Cost
Machining
26.53
Reorder Quantity for Out-of-Stock
Parts
26.54
Savings with More Machinable
Materials 26.55
Time Required for Thread Milling
26.55
Drill Penetration Rate and Centerless
Grinder Feed Rate 26.56
Bending, Dimpling, and Drawing
Metal Parts 26.56
Blank Diameters for Round Shells
26.60
Breakeven Considerations in
Manufacturing Operations 26.60
Calculating Geometric Dimensions of
Drawn Parts 26.62
Analyzing Stainless-Steel Molding
Methods 26.67
Reducing Machining Costs by
Designing with Shims
26.69
Analyzing Taper Fits for
Manufacturing and Design
26.73
Designing Parts for Expected Life
26.77
Wear Life of Rolling Surfaces 26.79
Factor of Safety and Allowable Stress
in Design 26.81
Rupture Factor and Allowable Stress
in Design 26.84
Force and Shrink Fit Stress,
Interference, and Torque 26.85
Selecting Bolt Diameter for Bolted
Pressurized Joint 26.87
Determining Required Tightening
Torque for a Bolted Joint 26.91
Selecting Safe Stress and Materials
for Plastic Gears 26.92
Economics of Machining
ESTIMATING CUTTING TIME AND COST WITH
DIFFERENT TOOL MATERIALS
A 9-in (22.86-cm) diameter steel shaft is to be ‘‘heavy roughed’’ with either of two
cutting tools—high-speed steel (HSS), or cemented carbide. The work material is
AISI 1050 having a hardness of 200 BHN. Feed rate is 0.125 in/r (3.17 mm/r);
depth of cut
ϭ 1.0 in (25.4 mm); tool life is based on 0.030-in (0.726-mm) flank
wear. Choose the most effective tool to use if the tool signature is:
Ϫ6, 10, 6, 6,
15, 15,
1
⁄
16
R; the tool-changing time ϭ 4 min for both tools; the cost of a sharp
tool
ϭ $0.50 for HSS and $2.00 for cemented carbide; and M ϭ machine labor
plus overhead rate, $ / min
ϭ 15 cents for each type of tool.
Calculation Procedure:
1. Determine the minimum-cost tool life for each type of tool material
Analyses of the economics metal of cutting with different types of cutting-tool
materials are often plotted on two bases—Figs. 1 and 2. Figure 1 shows the ma-
chining cost, tool cost, and nonproductive cost added to show the total cost per
piece. In Fig. 2, the machine time, tool-changing time, and nonproductive time are
added and plotted as the total time per piece.
Studies show that the cutting speed and production rate resulting from minimum-
cost tool life of approximately the same value is much higher for carbide tools than
for high-speed steel tools—150 ft/min (45.7 m/min) cutting speed for carbide tools
vs. 30 ft / min (9.14 m/min) for high-speed steel tools. These two values of cutting
speed will be used in this procedure.
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METALWORKING AND NONMETALLIC MATERIALS PROCESSING
METALWORKING AND NONMETALLIC MATERIALS PROCESSING 26.3
SI Values
200 fpm 60.9m/min
400 121.9
600 182.9
800 243.8
1000 304.8
1200 365.8
1400 426.7
FIGURE 1 Total cost per piece is found by adding the plots of ma-
chining costs, tool costs, and nonproductive costs. (T. E. Hayes and
American Machinist.)
The minimum-cost tool life, T
c
, is a function of the slope, n, of the tool-life
curve, Fig. 3. It can be said that n is one of the controlling influences on Hi-E
cutting conditions.* Thus, for high-speed steel, the expression for T
c
is:
1 t
T ϭϪ1 ϩ TCT
ͩͪͩ ͪ
c
nM
where T
c
ϭ minimum-cost tool life, min; n ϭ slope of tool-life curve; M ϭ machine
labor plus overhead rate, $ / min; TCT
ϭ tool-changing time, min. Substituting,
*The Hi-E term was originally coined by Thomas E. Hayes, Service Engineer, Metallurgical Products
Department, General Electric Company, and first published in his article, ‘‘How to Cut Costs with Carbides
by ‘Hi-E’ Machining.’’
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METALWORKING AND NONMETALLIC MATERIALS PROCESSING
26.4 DESIGN ENGINEERING
SI Values
200 fpm 60.9m/min
400 121.9
600 182.9
800 243.8
1000 304.8
1200 365.8
1400 426.7
FIGURE 2 Total time per piece is found by adding the plots of ma-
chine times, tool-changing time, and nonproductive time. (T. E. Hayes
and American Machinist.)
1 0.50
T ϭϪ1 ϩ 4
ͩͪͩͪ
c
125 0.15
ϭ 51.3 min
For cemented carbide, we have
1 t
T ϭϭ Ϫ1 ϩ TCT
ͩͪͩ ͪ
c
nM
12
ϭϪ1 ϩ 4
ͩͪͩͪ
0.25 0.15
ϭ 52 min
Thus, the T
c
, values for both tools are approximately the same.
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METALWORKING AND NONMETALLIC MATERIALS PROCESSING
METALWORKING AND NONMETALLIC MATERIALS PROCESSING 26.5
FIGURE 3 A combination of the total cost per piece and total
time per piece plots on a single graph forms the Hi-E range
between their respective minimum points. (Brierley and Siek-
mann.)
2. Compute the tool life for maximum productive rate
The tool life for maximum productive rate T
p
, min, is given by
1
T ϭϪ1 TCT
ͩͪ
p
n
where symbols are as before.
Substituting for high-speed steel we have
1
T ϭϪ1 ϭ 28 min
p
0.125
Entering Fig. 3 at 28 min and projecting to the HSS plot, we find that the cutting
speed should be 33 ft/min (10.1 m / min).
Using the same relation for cemented carbide, we find, entering Fig. 3 at 12
minute and projecting up to the cemented-carbide plot, the cutting speed to be 220
ft/min (67.1 m/min).
3. Tabulate the results of the calculations
List the cutting conditions for each type of tool material, as in Table 1. Studying
the results in Table 1 shows that only about 20 percent as much time is required
per piece with cemented-carbide tools as with HSS tools, and the total cost per
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METALWORKING AND NONMETALLIC MATERIALS PROCESSING
26.6 DESIGN ENGINEERING
TABLE 1 Operation of the Job Illustrated in Figure 1 at
Minimum Cost-Cutting Conditions Results in the Following
Economic Comparison. Machining Costs are Halved and
Production is Tripled*
Cutting conditions HSS
Cemented
carbide
Machine time per piece 45 min 9.1 min
Nonproductive time per piece 10 min 10 min
Labor plus overhead rate $0.15 $0.15
Machine cost per piece $6.75 $1.36
Nonproductive cost per piece $1.50 $1.50
Tool cost per piece $0.50 $2.00
Total cost per piece $8.75 $4.86
Total time per piece 55 min 19.1 min
Pieces per hour 1.1 3.1
*Brierley and Siekmann.
piece is only about 55 percent of that of HSS. Thus, the higher tool cost results in
greater productivity (3.1 pieces per hour vs. 1.1 pieces per hour).
Related Calculations. This procedure is the work of Robert G. Brierley, Tool
Applications Specialist, Metallurgical Products Department, General Electric Com-
pany and H. J. Siekmann, Vice President, Marketing, Martin Metals Company,
Division of Martin Marietta Corporation. If reflects the Hi-E approach used at
General Electric Company, plus the basics of metalworking physics.
The Hi-E range is shown in Fig. 4, which depicts a combination of the tool cost
per piece and total time per piece plotted on a single graph. The Hi-E range is
between the respective minimum points.
Since tool-life plots are important in the Hi-E analyses of machining economics,
the value of n is of much interest. Although n varies slightly as machining condi-
tions are changed, Brierley and Siekmann cite the following values for practical
everyday use to satisfy the calculations for the Hi-E range: For high-speed steel,
n
ϭ 0.125 and ([1/n] Ϫ 1) ϭ 7; for carbide, n ϭ 0.25 to 0.30 and ([1/n] Ϫ 1) ϭ
3 for the 0.25 value; for cemented oxide or ceramic tools, n ϭ 0.50 to 0.70 and
([1/n]
Ϫ 1) ϭ 1 for the 0.50 value. More exact values can be obtained from
tabulations available from ASTME.
The procedure given here was presented by the above two authors in their book
Machining Principles and Cost Control, McGraw-Hill.
COMPARING FINISH MACHINING TIME AND
COSTS FOR DIFFERENT TOOL MATERIALS
Compare machining costs and times for cemented-carbide and cemented-oxide tools
for a high-speed finishing operation using the data given in Fig. 5 and the equations
in the previous procedure. Tabulate the results for comparison.
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METALWORKING AND NONMETALLIC MATERIALS PROCESSING
METALWORKING AND NONMETALLIC MATERIALS PROCESSING 26.7
0.125 ipr 3.175 mm
1.000 in. 25.4 mm
0.030 in. 0.762 mm
FIGURE 4 Heavy roughing of a steel shaft with carbide widens the Hi-E range compared with
using high-speed steel. (Brierley and Siekmann.)
Calculation Procedure:
1. Find the minimum-cost tool life for each tool material
Use the T
c
equation of step 1 of the previous procedure with the same symbols.
Then, for cemented carbide,
1 t
T ϭϪ1 ϩ TCT
ͩͪͩ ͪ
c
nM
1 0.25
ϭϪ1 ϩ 1
ͩͪͩ ͪ
0.3 0.15
ϭ 6.22 min
Likewise, using the same equation for cemented oxide,
1 t
T ϭϪ1 ϩ TCT
ͩͪͩ ͪ
c
nM
1 0.375
ϭϪ1 ϩ 1
ͩͪͩ ͪ
0.7 0.15
ϭ 1.57 min
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METALWORKING AND NONMETALLIC MATERIALS PROCESSING
26.8 DESIGN ENGINEERING
SI Values
0.010 ipr 0.254 mm
1.000 in. 25.4 mm
0.030 in. 0.762 mm
FIGURE 5 A high-speed finishing operation switched to cemented oxide. (Brierley and Siek-
mann.)
2. Determine the tool life for the maximum productive rate
As in step 1, above, use the equation and symbols from step 2 in the previous
procedure. Thus, for cemented-carbide tools,
1
T ϭϪ1 TCT ϭ 2.33 min
ͩͪ
p
n
Projecting from 2.33 min on the horizontal scale in Fig. 5, we find the cutting speed
to be 1150 ft /min (350.5 m / min).
For cemented-oxide tools,
1
T ϭϪ1 TCT
ͩͪ
p
n
ϭ 0.45 ϭϾ20,000 ft/min
Plotting from 0.45 min, we find that the cutting speed would exceed 20,000 ft/min
(6096 m / min)
3. Summarize the calculations in tabular form
Table 2 summarizes the calculations for these two tooling materials. As you can
see, there is a significant difference in the machine time per piece: 1 7.2 min vs.
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METALWORKING AND NONMETALLIC MATERIALS PROCESSING
METALWORKING AND NONMETALLIC MATERIALS PROCESSING 26.9
TABLE 2 Minimum Cost-Cutting Conditions Using Cemented
Oxide Rather Than Carbide Halve the Machining Costs of This
Finishing Operation While Production Is Doubled*
Cutting conditions
Cemented
carbide
Cemented
oxide
Machine time per piece 17.2 min 1.63 min
Nonproductive time per piece 10 min 10 min
Labor plus overhead rate $0.15 $0.15
Machine cost per piece $2.50 $0.245
Nonproductive cost per piece $1.50 $1.50
Tool cost per piece $0.25 $0.375
Total cost per piece $4.25 $2.120
Total time per piece 27.2 min 11.63 min
Pieces per hour 2.2 5.4
*Brierley and Siekmann.
1.63 min. Likewise, the cost is at a 10-times ratio: $0.245 vs. $2.50, and the piece
output is more than double: 5.4 pieces per hour vs. 2.2 pieces per hour. As in the
previous procedure, the more expensive tool significantly increases the output while
reducing production costs.
Related Calculations. This procedure, like the previous one, is the work of
Brierley and Siekmann. Full citation information is given in the previous procedure.
In building their approach to the economics of machining, Brierley and Siek-
mann give a number of key equations that lead up to the steps presented in this
and the previous procedure. These equations are: (1) Machining cost
ϭ (machining
time per piece)(labor
ϩ overhead rate); (2) Machining time ϭ [(length of piece
cut)(cut)]/(feed)(rpm of cutter); (3) Tool cost
ϭ (tool-changing cost ϩ tool-grinding
cost per edge
ϩ tool depreciation per edge ϩ tool inventory cost)/(production per
edge); (4) Cost to change the tool
ϭ (tool-changing time)(the machine operator’s
rate
ϩ overhead); (5) Tool-grinding cost per edge ϭ [(grinding time)(grinder’s rate
ϩ overhead)]/(edges per grind); (6) Brazed-tool depreciation cost per edge ϭ (cost
of tool) / (number of regrinds
ϩ 1); (7) For disposable-insert toolholder or milling-
cutter head, Tool depreciation cost per edge
ϭ [(cost of disposable insert/number
of cutting edges per insert)
ϩ (cost of holder or head)]/[(number of inserts in life
of holder) (number of edges per insert)]; (8) For on-end insert toolholder or re-
gindable inserted-blade milling-cutter head, Tool depreciation cost per edge
ϭ (cost
of insert) / [(number of regrinds per insert)(number of edges per grind)]
ϩ (cost of
holder or head)/[(number of in life of holder or head)(number of regrinds per
insert)(number of edges per grind)]; (9) Tool inventory cost
ϭ (number of tools at
machine
ϩ number of tools in grinding room)(cost per tool)(inventory cost rate);
(10) Nonproductive cost
ϭ load and unload time ϩ (other noncutting time)(operator
labor
ϩ overhead rate); (11) Total machining time ϭ machine time from Eq. (1) ϩ
tool changing time ϩ nonproductive time.
Using the above eleven equations and the relations given in Figs. 3, 4, and 5,
the economics of machining can be planned in a preliminary way for a given
machine. Then the Hi-E approach and advances in it should be considered for in-
depth analysis of the economics of a given machining application.
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METALWORKING AND NONMETALLIC MATERIALS PROCESSING
26.10 DESIGN ENGINEERING
FINDING MINIMUM COST AND MAXIMUM
PRODUCTION TOOL LIFE FOR
DISPOSABLE TOOLS
Find the minimum cost and maximum production tool life for a disposable tool
having the following characteristics: price of insert plus toolholder depreciation,
P
ϭ $1.80; total cutting edges in the life of the insert, E ϭ 6; machine operator’s
rate, MR
ϭ $4.00/h; machine overhead rate, MO ϭ $8.00/h; tool-changing time,
TCT
ϭ 1 min; the constant for the slope of the tool-life line for carbide tools, n ϭ
3.5.
Calculation Procedure:
1. Find the minimum-cost tool life
The expression for the minimum-cost tool life, T
c
,isgivenby
1 t
T ϭϪ1 ϩ TCT
ͩͪͩ ͪ
c
nM
where
price of insert
ϩ toolholder depreciation 1.80
t ϭϭϭ0.30
total cutting edges in life of insert 6
labor per hour
ϩ overhead per hour 4.00 ϩ 8.00
M ϭϭϭ0.20
60 60
TCT
ϭ tool-changing time (min) ϭ 1
1
Ϫ 1 ϭ a constant (3.5) based on the slope
ͩͪ
n
of the tool-life line
Substituting,
0.30
T (min) ϭ 3.5 ϩ 1
ͩͪ
c
0.20
T (min)
ϭ 3.5 ϫ 2.5
c
T (min) ϭ 8.75
c
2. Calculate the maximum production tool life for this tool
To solve for T
p
, we need only the constant, n, and the tool-changing time. Or,
1
T ϭϪ1 TCT
ͩͪ
p
n
T
ϭ 3.5 ϫ 1
p
T ϭ 3.5
p
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METALWORKING AND NONMETALLIC MATERIALS PROCESSING
[...]... time, min; N ϭ number of pieces in lot; Us ϭ unit standard time, min For this machine, Tu ϭ 75 / 75 ϩ 5.0 ϭ 6.0 m in 2 Determine the most economical machine Call one machine X, the other Y Then (unit standard time of X, min)(number of pieces) ϩ (setup time of X, min) ϭ (unit standard time of Y, min)(number of pieces) ϩ (setup time of Y, min) For these two machines, since the number of pieces Z is unknown,... as in step 1 Length of cut is the length of the relief, Fig 9 A small amount of time is also required to handfeed the tool to the minor diameter of the relief This time is best obtained by observation of the operations The time required to point a bar, called pointing, is computed by using the relation in step 1 The length of cut is the distance from the end of the bar to the end of the tapered point,... major diameter of 2 in (5.1 cm), four threads per inch (1.575 threads per centimeter), a depth of 0.1350 in (3.4 mm), a cutting speed of 70 ft / min (0.4 m / s), and a depth of cut of 0.005 in (0.1 mm) per pass if the material cut is medium steel? How many passes of the tool are required? TABLE 5 Turret-Lathe Power Constant Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)... (diameter of arbor, in) ϩ 2 (face of cut, in ϩ 0.25) The 0.25 in (6.4 mm) is the allowance for clearance of the arbor Related Calculations Use the equation of step 1 to compute the cutting time for metal slitting, screw slotting, angle milling, T-slot milling, Woodruff key-seat milling, and profiling and routing of parts In T-slot milling, two steps are required—milling of the vertical member and milling of. .. nonmetallic materials DIMENSIONS OF TAPER AND DOVETAILS What are the taper per foot (TPF) and taper per inch (TPI) of an 18-in (45.7-cm) long part having a large diameter dl of 3 in (7.6 cm) and a small diameter of ds of 1.5 in (3.8 cm)? What is the length of a part with the same large and small diameters as the above part if the TPF is 3 in / ft (25 cm / m)? Determine the dimensions of the dovetail in Fig 7... 0.5 From a table of trigonometric functions, a ϭ cutting angle ϭ 26Њ34Ј, closely 2 Compute the length of the cut Use trigonometry to compute the length of cut Thus, sin a ϭ opposite side / hypotenuse, or 0.4472 ϭ (8 Ϫ 5) / hypotenuse; length of cut ϭ length of hypotenuse ϭ 3 / 0.4472 ϭ 6.7 in (17.0 cm) Related Calculations Use this general procedure to compute the angle and length of cut for any metallic... plates, consult The Welding Handbook, American Welding Society 2 Compute the gas consumption Gas consumption for oxyacetylene welding is given in cubic feet per foot of weld Using values from The Welding Handbook, or a similar reference, we see that oxygen consumption ϭ (ft3 O2 per ft of weld)(length of weld, ft); acetylene consumption ϭ (ft3 acetylene per ft of weld)(length of weld, ft) For this weld,... (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website METALWORKING AND NONMETALLIC MATERIALS PROCESSING METALWORKING AND NONMETALLIC MATERIALS PROCESSING 26.17 FIGURE 8 Length of cut of a part Calculation Procedure: 1 Compute the angle of the cut Use trigonometry to compute the angle of the cut... the axis of the bar, Fig 9 Use the relation in step 1 to compute the time to cut an internal or external chamfer The length of cut of a chamfer is the horizontal distance L, Fig 9 A hollow mill reduces the external diameter of a part The cutting time is computed by using the relation in step 1 The length of cut is shown in Fig 9 Compute the time to knurl, using the relation in step 1 The length of cut... through a 6-in (15.2-cm) thick piece of steel if the cone height of the drill is 0.5 in (1.3 cm), the feed is 0.002 in / r (0.05 mm / r), and the drill speed is 100 r / min? Calculation Procedure: 1 Compute the time required for drilling The time required to drill Td min ϭ L / ƒR, where L ϭ depth of hole ϭ length of cut, in In most drilling calculations, the height of the drill cone (point) is ignored . use is subject to the Terms of Use as given at the website.
Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS
26.2 DESIGN ENGINEERING
Cutting Speed. (cost
of insert) / [(number of regrinds per insert)(number of edges per grind)]
ϩ (cost of
holder or head)/[(number of in life of holder or head)(number of
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