Handbook of Mechanical Engineering Calculations ar Episode 2 Part 6 ppt

26.1

SECTION 26

METALWORKING AND

NONMETALLIC 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
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: 6, 10, 6, 6,

15, 15, 1

⁄16 R; the tool-changing time
4 min for both tools; the cost of a sharp

tool
$0.50 for HSS and $2.00 for cemented carbide; and M
machine labor

plus overhead rate, $/min
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, Tc, 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 Tc is:

1 t Tc


1 TCT n M

where Tc
minimum-cost tool life, min; n
slope of tool-life curve; M
machine

labor plus overhead rate, $/min; TCT
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 Tc


1 4 125 0.15

51.3 min

For cemented carbide, we have

1 t Tc



1 TCT n M

1 2


1 4 0.25 0.15

52 min

Thus, the Tc, 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 Tp, min, is given by

1

Tp

1 TCT n

where symbols are as before.

Substituting for high-speed steel we have

1

Tp
1
28 min 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
0.125 and ([1/n] 1)
7; for carbide, n
0.25 to 0.30 and ([1/n] 1)

3 for the 0.25 value; for cemented oxide or ceramic tools, n
0.50 to 0.70 and

([1/n] 1)
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 Tc equation of step 1 of the previous procedure with the same symbols.

Then, for cemented carbide,

1 t Tc


1 TCT n M

1 0.25


1 1 0.3 0.15

6.22 min

Likewise, using the same equation for cemented oxide,

1 t Tc


1 TCT n M

1 0.375


1 1 0.7 0.15

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

Tp

1 TCT
2.33 min 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

Tp

1 TCT n

0.45
20,000 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
(machining

time per piece)(labor overhead rate); (2) Machining time
[(length of piece

cut)(cut)]/ (feed)(rpm of cutter); (3) Tool cost
(tool-changing cost tool-grinding

cost per edge tool depreciation per edge tool inventory cost)/ (production per

edge); (4) Cost to change the tool
(tool-changing time)(the machine operator’s

rate overhead); (5) Tool-grinding cost per edge
[(grinding time)(grinder’s rate

overhead)]/ (edges per grind); (6) Brazed-tool depreciation cost per edge
(cost

of tool)/ (number of regrinds 1); (7) For disposable-insert toolholder or milling￾cutter head, Tool depreciation cost per edge
[(cost of disposable insert/ number

of cutting edges per insert) (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
(cost

of insert)/ [(number of regrinds per insert)(number of edges per grind)] (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
(number of tools at

machine number of tools in grinding room)(cost per tool)(inventory cost rate);

(10) Nonproductive cost
load and unload time (other noncutting time)(operator

labor overhead rate); (11) Total machining time
machine time from Eq. (1)

tool changing time 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