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 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. 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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. Downloaded from Digital Engineering Library @ McGraw-Hill (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 26.3 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.’’ Downloaded from Digital Engineering Library @ McGraw-Hill (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 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. Downloaded from Digital Engineering Library @ McGraw-Hill (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 26.5 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 Downloaded from Digital Engineering Library @ McGraw-Hill (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 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. Downloaded from Digital Engineering Library @ McGraw-Hill (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 26.7 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 Downloaded from Digital Engineering Library @ McGraw-Hill (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 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. Downloaded from Digital Engineering Library @ McGraw-Hill (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 26.9 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. Downloaded from Digital Engineering Library @ McGraw-Hill (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 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 Downloaded from Digital Engineering Library @ McGraw-Hill (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