Mechanical design of machine element

294 Chapter / Geometry Determination failure because of high stresses or strains, low strength, or a critical combination of these Typically, a designer first identifies the potential critical sections, then identifies the possible critical points within each critical section Finally, appropriate calculations are made to determine the governing critical points so that the calculated dimensions will assure safe operation of the part over its prescribed design lifetime The number of potential critical points requiring investigation in any given machine part is directly dependent upon the experience and insight of the designer A very inexperienced designer may have to analyze many, many potential critical points A very experienced and insightful designer, analyzing the same part, may only need to investigate one or a few critical points because of ingrained knowledge about failure modes, how forces and moments reflect upon the part, and how stresses and strains are distributed across the part In the end, the careful inexperienced designer and the experienced expert should both reach the same conclusions about where the governing critical points are located, but the expert designer typically does so with a smaller investment of time and effort Example 6.2 Critical Point Selection It is desired to examine member A shown in Figure E6.1B of Example 6.1, with the objective of establishing critical sections and critical points in preparation for calculating dimensions and finalizing the shape of the part With this objective, select appropriate critical sections and critical points, give the rationale for the points you pick, and make sketches showing the locations of the selected critical points Solution In the solution of Example 6.1, it was established that member A is subjected to cantilever bending, torsion, and transverse shear, giving rise to the proposed geometry shown in Figure E6.1B Member A is again sketched in Figure E6.2 to show the cross-sectional geometry more cleady Since cantilever bending produced by an end-load results in a maximum bending moment at the fixed end, as well as uniform transverse shear along the whole beam length, and since there is a constant torsional moment all along the beam length, critical section at the fixed end is clearly a well-justified selection Also, it may be noted that the annular wall is thinnest where the tapered section blends into the raised cylindrical mounting pad near the free end At this location the bending moment is less than at the fixed end, transverse shear is the same, and torsional moment is the same as at critical section 1, but the wall is thinner and stress concentration must be accounted for; hence critical section should also be investigated At critical section 1, four critical points may initially be chosen, as shown in Figure E6.2(b) At critical points A and B, bending and torsion combine, and at critical points C and D, torsion and transverse shear combine In both cases potentially critical multiaxial stress states are produced Since the state of stress at A is the same as at B (except that Transforming Combined Stress Failure Theories into Combined Stress Design Equations bending produces tension at A and compression at B), investigation of critical point A is alone sufficient Also, since torsional shear stress adds to transverse shear stress at D and subtracts at C, investigation of critical point D is alone sufficient Therefore, it is concluded that critical points A and D should be investigated, with the knowledge that Band C are less serious A similar consideration of critical section leads to the similar conclusion that critical points E and H should be investigated, knowing that A and C are less serious Summarizing, critical points A, D, E, and H should be investigated If a designer has doubts about any other potential critical point within the member, it too should be investigated 6.4 Transforming Combined Stress Failure Theories into Combined Stress Desi~n Equations The state of stress at a critical point is typically multiaxial; therefore, as discussed in 4.6, the use of a combined stress theory of failure is usually necessary in critical point analysis Further, as discussed in 5.2, dimensions are usually determined by making sure that the maximum operating stress levels not exceed the design-allowable stress at any critical point A useful formulation may be obtained by transforming the combined stress failure theories given in (4-83), (4-84), (4-87), and (4-95) into combined stress design equations, from which required dimensions may be calculated at any critical point Such transformations may be accomplished by using only the equal signs of the failure theory equations, and inserting the design-allowable stress in place of the failure strength in each equation The resulting combined stress design equations then contain known loads, known material strength properties corresponding to the governing failure mode, known safety factor, and unknown dimensions The unknown dimensions may be calculated by inverting the applicable combined stres~ design equation Details of a solution may be complicated, often requiring iterative techniques The rules for selecting the applicable design equation, based on material ductility, are the same as the rules for failure theory selection given in 4.6 In more detail, if a material exhibits brittle behavior (elongation less than percent in inches), the maximum normal stress failure theory, given by (4-83) and (4-84), would be transformed into the maximum normal stress design equations 295 296 Chapter / Geometry Determination Also for ductile behavior, the distortion energy failure theory given by (4-95), and supplemented by (4-96), would be transformed into the distortion energy design equation where (71) (72' and (73 are the three principal normal stresses produced by the loading at the critical point In all of the above equations known loads, known material strength properties, and known safety factor would be inserted and design dimensions (the only unknowns) would be found by solving the equation 6.5 Simplifying Assumptions: The Need and the Risk After the initial proposal for the shape of each of the parts and their arrangement in the assembled machine, and after all critical points have been identified, the critical dimensions may be calculated for each part In principle, this task merely involves utilizing the stress and deflection analysis equations of Chapter and the multiaxial stress design equations of 6.4 In practice, the complexities of complicated geometry, redundant structure, and implicit or higher-order mathematical models often require one or more simplifying assumptions in order to obtain a manageable solution to the problem of determining the dimensions Simplifying assumptions may be made with respect to loading, load distribution, support configuration, geometric shape, force flow, predominating stresses, stress distribution, applicable mathematical models, or any other aspect of the design task, to make possible a solution The purpose of making simplifying assumptions is to reduce a complicated real problem to a pertinent but solvable mathematical model The coarsest simplifying assumption would be to assume the "answer" with no analysis For an experienced designer, a routine application, light loads, and minimal failure consequences, directly assuming the dimensions might be acceptable The most refined analysis might involve very few simplifying assumptions, modeling the loading and geometry in great detail, possibly creating in the process very detailed and complicated mathematical models that require massive computational codes and large investments of time and effort to find the dimensions For very critical applications, where loading is complicated, failure consequences are potentially catastrophic, and the nature of the application will reasonably support large investments, such detailed modeling might be acceptable (but usually would be used only after initially exercising simpler models) Typically, a few well-chosen simplifying assumptions are needed to reduce the real design problem to one that can be tentatively solved with a reasonable effort More accurate analyses may be made in subsequent iterations, if necessary The risk of making simplifying assumptions must always be considered; if the assumptions are not true, the resulting model will not reflect the performance of the real machine The resulting poor predictions might be responsible for premature failure or unsafe operation unless the analysis is further refined 6.6 Iteration Revisited Many details of the mechanical design process have been examined since design was first characterized in 1.4 as an iterative decision-making process Now that the basic principles and guidelines for determining shape and size have been presented, and details of material selection, failure mode assessment, stress and deflection analysis, and safety factor determination have been discussed, it seems appropriate to briefly revisit the important role of iteration in design Iteration Revisited During the first iteration a designer typically concentrates on meeting functional performance specifications by selecting candidate materials and potential geometric arrangements that will provide strength and life adequate for the loads, environment, and potential failure modes governing the application An appropriate safety factor is chosen to account for uncertainties, and carefully chosen simplifying assumptions are made to implement a manageable solution to the task of determining critical dimensions A consideration of manufacturing processes is also appropriate in the first iteration Integrating the selection of the manufacturing process with the design of the product is necessary if the advantages and economies of modem manufacturing methods are to be realized A second iteration usually establishes nominal dimensions and detailed material specifications that will safely satisfy performance, strength, and life requirements Many loops may be embedded in this iteration Typically, a third iteration carefully audits the second iteration design from the perspectives of fabrication, assembly, inspection, maintenance, and cost This is often accomplished by utilizing modem methods for global optimization of the manufacturing system, a process usually called design for manufacture (DFM).5 A final iteration, undertaken before the design is released, typically includes the establishment of fits and tolerances for each part, and final modifications based on the thirditeration audit A final safety factor check is then usually made to assure that strength and life of the proposed design meet specifications without wasting materials or resources As important as understanding the iterative nature of the design process is understanding the serial nature of the iteration process Inefficiencies generated by deeply embedded early design decisions may make cost reduction or improved manufacturability difficult and expensive at later stages Such inefficiencies are being addressed in many modem facilities by implementing the simultaneous engineering approach Simultaneous engineering involves on-line computer linkages among all activities, including design, manufacturing, testing, production, marketing, sales, and distribution, with early and continuous input and auditing throughout the design, development, and field service phases of the product Using this approach, the vari~us iterations and modifications are incorporated so rapidly, and communicated so widely, that inputs and changes from all departments are virtually simultaneous Continuing the examination of member A, already described in Examples 6.1 and 6.2, it is desired to find dimensions of the annular cross section shown in Figure E6.2 of Example 6.2, at critical section The load P to be supported is 10,000 lb The distance from the fixed wall to load P is is = 10 inches, and the distance from the centerline of member A to load P is iT = inches (see Figure E6.1A of Example 6.1) The tentative material selection for this first cut analysis is 1020 cold-drawn steel, and it has been determined that yielding is the probable failure mode A preliminary analysis has indicated that a design safety factor of nd = is appropriate Determine the dimensions of member A at critical section Solution From Figure E6.2, the dimensions to be determined at critical section include outside diameter do, inside diameter di, wall thickness t, and fillet radius r, all unknown The length of the raised pad, ie' is also unknown, but is required for calculation of bending moment M2 at critical section The material properties of interest for 1020 CD steel are 5See 7.4 297 Syp = 51,000 psi e(2 inches) = 15% ( Table 3.3) (1) (Table 3.10) From the solution to Example 6.2, the critical points to be analyzed for section are c.p E (bending and torsion) and c.p H (torsion and transverse shear), as shown in Figure E6.2 To start the solution, the following simplifying assumptions may be made: The annular wall is thin, so assume = di = d (2) t = O.ld (3) and A common proportion for bearing surfaces is to make diameter equal to length, so assume ~=d ~ At critical section 2, the bending moment M2 may be written as M2 Pic = -2 = Pd 1O,000d = 2- = 5000d m-lb (5) and torsional moment T2 may be written as T2 = PiT = 10,000(8) = 80,000 in-lb (6) Examining c.p E first, the elemental volume depicting the state of stress may be constructed as shown in Figure E6.3A The nominal axial stress ax-nom' caused by bending moment M2, may be written as M2c ax-nom and the nominal shearing stress Txy-nom' (7) = I caused by torsional moment T2a Txy-nom = - J T2' may be written as (8) For thin annular sections,6 the area moment of inertia, I, about the neutral axis of bending, and the polar moment of inertia, J, may be approximated as I= 7Td t and (9) Iteration Revisited 299 TABLE E6.3A Iteration d, in d6 3.55 3.60 3.65 3.63 2001.57 2176.78 2364.60 2287.91 Sequence to Find Diameter 22.92d2 288.85 297.43 305.35 302.01 d Result 1712.72 < 2000 1879.35 < 2000 2059.25 > 2000 1985.90 (close) Iteration Revisited 301 TABLE E6.3B Iteration d I 2.50 2.25 2.00 1.75 Sequence to Find Inside Diameter d; J, in4 Txz-tor A, in2 Txz-ts TXl (Jeq 13.21 14.53 15.48 16.13 13,959 12,691 11,912 11,432 5.44 6.37 7.21 7.94 4671 3989 3524 3200 18,630 16,680 15,436 14,632 32,268 > 25,500 28,891 > 25,500 26,736 > 25,500 25,343 (close enough) Fits, Tolerances, and Finishes 303 Figure E6.3C Sketch showing recommended initial dimensions at critical section of member A of the bracket shown in Example 6.1 at critical section I before the initial design proposal for member A is completed It should also be clear by now that writing or utilizing appropriate software to expedite the solution to an iterative design problem, such as the one just completed, is often justified 6.7 Fits, Tolerances, and Finishes All of the discussions so far in this chapter have dealt with determination of the "macrogeometry" of machine parts In many cases the "microgeometry" of a machine part, or an assembly of parts, also has great importance in terms of proper function, prevention of premature failure, ease of manufacture and assembly, and cost The important microgeometric design issues include: (1) the specification of the fits between mating parts to assure proper function, (2) the specification of allowable variation in manufactured part dimensions (tolerances) that will simultaneously guarantee the specified fit, expedite assembly, and optimize overall cost, and (3) the specification of surface texture and condition that will ensure proper function, minimize failure potential, and optimize overall cost Some examples of machine parts and assemblies in which one or more of the micro geometric design issues may be important are: The press fit connection between a flywheel hub and the shaft upon which it is mounted (see Chapters and 18) The fit must be tight enough to assure proper retention, yet the stresses generated must be within the design-allowable range, and assembly of the flywheel to the shaft must be feasible Both fits and tolerances are at issue The light interference fit between the inner race of a ball bearing and the shaft mounting pad upon which it is installed (see Chapter 11) The fit must be tight enough to prevent relative motion during operation, yet not so tight that internal interference between the balls and their races, generated by elastic expansion of the inner race when pressed on the shaft, shortens the bearing life Premature failure due to fretting fatigue, initiated between the inside of the inner race and the shaft, might also be a consideration, as might be operational constraints on radial stiffness or the need to accommodate thermal expansion Fits, tolerances, and surface textures are all important issues ,1 The radial clearance between a hydrodynamically lubricated plain bearing sleeve and the mating journal of a rotating shaft, as well as the surface roughnesses of the mating bearing surfaces (see Chapter 10) The clearance must be large enough to allow development of a "thick" film of lubricant between the bearing sleeve and the shaft journal, yet small enough to limit the rate of oil flow through the bearing clearance space so that hydrodynamic pressure can develop to support the load The surface roughness of each member must be small enough so that roughness protuberances not penetrate the lubricant film to cause "metal-to-metal" contact, yet large enough to allow ease of manufacture and a reasonable cost Tolerances and surface texture are issues of importance 822 References Shigley, J E., and Mischke, C R eds., Standard Handbook of Machine Design, McGraw-Hill, New York, 1986 10 Shigley, J E., and Mischke, C R., Mechanical Engineering Design, 5th ed., McGraw-Hill, New York, 1989 Burr, A H., and Cheatham, J B., Mechanical Analysis and Design, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1995 11 Currie, G., Fundamental Mechanics of Fluids, 2nd ed., McGraw-Hill, New York, 1989 Deutschman, A D., Michels, W J., and Wilson, C E., Machine Design-Theory and Practice, Macmillan, New York, 1975 12 Sommerfeld, A., "Zur Hydrodynamischen Theorie der Schmiermittel-Reibung" ("On the Hydrodynamic Theory of Lubrication"), Z Math Physik, v 50, p 97 ff., 1904 10 Peterson, R E., Stress Concentration York, 1974 Factors, Wiley, New 11 Lingaiah, K., Machine Design Data Handbook, McGrawHill, New York, 1994 12 Walsh, R A., McGraw-Hill Machining and Metalworking Handbook, McGraw-Hill, New York, 1994 13 Pestel, E c., and Leckie, E A., Matrix Methods in Elastomechanics, McGraw-Hill, New York, 1963 14 Rieder, W G., and Busby, H R., Introductory Engineering Modeling Emphasizing Differential Models and Computer Simulations, Wiley, New York, 1986 Chapter The ASME Boiler and Pressure Vessel Code, Sections I-XI, American Society of Mechanical Engineers, New York, 1995 Timoshenko, S., and Goodier, J N., Theory of Elasticity, McGraw-Hill, New York, 1951 Pilkey, W D., Peterson 2nd ed., Wiley, 1997 s Stress Concentration Factors, 13 Fuller, D D., Theory and Practice of Lubrication for Engineers, Wiley, New York, 1956 Chapter 11 "Power and Motion Control," Publishing, Cleveland, June 1989 Machine Design, Penton Load Ratings and Fatigue Life for Ball Bearings, ANSU AFBMA Standard 9-1990, American National Standards Institute, New York, 1990 Load Ratings and Fatigue Life for Roller Bearings, ANSUAFBMA Standard 11-1990, American National Standards Institute, New York, 1990 Shaft and Housing Fits for Metric Radial Ball and Roller Bearings (Except Tapered Roller Bearings) Conforming to Basic Boundary Plans, ANSUABMA Standard 7-1995, American National Standards Institute, New York, 1995 SKF,® "General Prussia, PA, 1991 Catalog 4000 US," SKFUSA, King of Chapter 10 Timken,® "The Tapered Roller Bearing Guide," Timken Company, Canton, OH, 1994 Machine Design: Mechanical Drives Reference Issue, Penton Publishing, Cleveland, Oct 13, 1988 Tallian, T E., "On Competing Failure Modes in Rolling Contact," Trans ASLE, v 10, pp 418-439, 1967 Hersey, M D., Theory and Research in Lubrication, Wiley, New York, 1966 Skurka, J C., "Elastohydrodynamic Lubrication of Roller Bearings," J Lubr Technology, v 92, pp 281-291, 1970 Burr, A H., and Cheatham, J B., Mechanical Analysis and Design, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1995 Hamrock, B J., Fundamentals McGraw-Hill, New York, 1993 Hamrock, B J., Fundamentals McGraw-Hill, New York, 1993 of Fluid Film Lubrication, of Fluid Film Lubrication, Juvinall, R C., and Marshek, K M., Fundamentals of Machine Component Design, 2nd ed., Wiley, New York, 1991 Raymondi, A A., and Boyd, J., "A Solution for the Finite Journal Bearing and Its Application to Analysis and Design," Parts I, II, III, Trans American Society of Lubrication Engineers, v I, no I, pp 159-209, 1958 Tower, B., "Reports on Friction Experiments," Proc Inst Mech Engr., First Report Nov 1883, Second Report 1885, Third Report 1888, Fourth Report, 1891 Reynolds, 0., "On the Theory of Lubrication and Its Application to Mr Beauchamp Tower's Experiments," Phil Trans Roy Soc (London), v 177, p 157 ff., 1886 Spotts, M E, Design of Machine Elements, 2nd ed., Prentice-Hall, New York, 1953 Chapter 12 Acme Screw Threads, ASME B1.5-1988, American Society of Mechanical Engineers, New York, 1988 Stub Acme Screw Threads, ASME B1.8-1988, American Society of Mechanical Engineers, New York, 1988 Buttress Inch Screw Threads, 7deg/45deg Form with 0.6 Pitch Basic Height of Thread Engagement, ASME B 1.9-1973 (RI992), American Society of Mechanical Engineers, New York, 1992 Lingaiah, K., Machine Design Data Handbook, McGrawHill, New York, 1994 Parker, L., and Levin, A., " '97 Check Found Stabilizer Piece Worn," USA Today, v 18, no 107, p 73A, Arlington, VA, Feb 14,2000 References 823 Chapter 13 Chapter 15 Parmley, R 0., ed., Standard Handbook of Fastening and Joining, 2nd ed., McGraw-Hill, New York, 1989 Dudley, D W, Handbook McGraw-Hill, New York, 1984 DeGarmo, E P., Materials and Processes in Manufacturing, Macmillan, New York, 1979 Phelan, R M., Fundamentals of Mechanical ed., McGraw-Hill, New York, 1970 Unified Inch Screw Threads (UN and UNR Thread Form), ASME B1.1-1989, American Society of Mechanical Engineers, New York, 1989 Wilson, C E., Sadler, J P., and Michels, W J., Kinematics and Dynamics of Machinery, Harper & Row Publishers, New York, 1983 Metric Screw Threads-M Profile, ASME B1.13M-1995, American Society of Mechanical Engineers, New York, 1995 Mabie, H H., and Ocvirk, E W., Mechanisms and Dynamics of Machinery, Wiley, New York, 1975 Metric Screw Threads-MS Profile, ASME B1.21M-1978, American Society of Mechanical Engineers, New York, 1978 Juvinall, R L., and Marshek, K., Fundamentals of Machine Component Design, 2nd ed., Wiley, New York, 1991 Ito, Y, Toyoda, J., and Nagata, S., "Interface Pressure Distribution in a Bolt-Flange Assembly," ASME Paper No 77WAiDE-ll,1977 Norton, R L., Machine Design, Prentice-Hall, dle River, NJ, 1996 Little, R E., "Bolted Joints; How Much Give?," Machine Design, Nov 9, 1967 Houser, D R, "Gear Noise Sources and Their Prediction Using Mathematical Models," Gear Design, AE 15, SAE International, Warrendale, PA, 1990 Bruhn, E E, Analysis and Design of Flight Vehicle Structures, Tristate Offset Company, 817 Main Street, Cincinnati, OH 45202, 1965 Connor, L P, ed., Welding Handbook, 8th ed., v I, American Welding Society, Miami, FL, 1987 10 Norris, C H., "Photoelastic Investigation of Stress Distribution in Transverse Fillet Welds," Welding Journal, v 24, p 557, 1945 of Practical Gear Design, Design, 3rd Upper Sad- ANSI/AGMA 1010-E95 (Revision of AGMA 10.04), American National Standard, Appearance of Gear Teeth-Terminology of Wear and Failure, American Gear Manufacturers Association, Alexandria, VA, Dec 13, 1995 Breen, D H., "Fundamentals of Gear/Strength Relationships; Materials," Gear Design, AEI5, SAE International, Warrendale, PA, 1990 New York, 10 ANSI/AGMA 2001-C95, American National Standard, Fundamental Rating Factors and Calculation Methods for Involute and Helical Gear Teeth, American Gear Manufacturers Association, Alexandria, VA, Jan 12, 1995 12 Wileman, J., Choudhury, M., and Green, 1., "Computation of Member Stiffness in Bolted Connections," Journal of Mechanical Design, Transactions of the American Society of Mechanical Engineers, v 113, Dec., 1991, New York 11 US AS B6.1-1968, USA Standard System-Tooth Proportions for Coarse Pitch Involute Spur Gears, American Gear Manufacturers Association, Alexandria, VA, Jan 27, 1968 13 Jenny, C L., and O'Brien, A, eds., Welding Handbook, 9th ed., v 1, American Welding Society, Miami, FL, 2001 12 AGMA 370.D1, AGMA Design Manual for Fine-Pitch Gearing, American Gear Manufacturers Association, Alexandria, VA, Apri11973 Chapter 14 13 Szczepanski, G S., Savoy, J P., Jr., and Youngdale, R A, "Chapter 14, The Application of Graphics Engineering to Gear Design," Gear Design, AE 15, SAE International, Warrendale, PA,1990 11 Deutschman, A D., Michels, W J., and Wilson, C E., Machine Design, 1975 Theory and Practice, Macmillan, Spring Design Manual, AE-21, 2nd ed., Society of Automotive Engineers, Warrendale, PA, 1996 Design Handbook: Engineering Guide to Spring Design, Associated Spring, Barnes Group, Bristol, CT, 1987 Wahl, A M., Mechanical York, 1963 Springs, McGraw-Hill, New Timoshenko, S., and Goodier, N., Theory of Elasticity, McGraw-Hill, New York, 1951 14 ANSI/AGMA 2000-A88, American National Standard, Gear Classification and Inspection Handbook, American Gear Manufacturers Association, Alexandria, VA 15 DIN, Toleranzen fUr Stirnradverzahnungen, DIN 3963, Aug 1978 (German) DIN 3962 and Collins, A, Failure of Materials in Mechanical Design, 2nd ed., John Wiley & Sons, New York, 1993 16 Lewis, Wilfred, "Investigation of the Strength of Gear Teeth," Proceedings of Engineers Club, Philadelphia, 1893 Juvinall, R c., and Marshek, K M., Fundamentals of Machine Component Design, 2nd ed., Wiley, New York, 1991 17 Buckingham, Earle, Analytical McGraw-Hill, New York, 1949 Maier, K W, "Springs That Store Energy Best," Product Engineering, v 29, no 45, Nov 10, 1958 18 Lipson, C., and Juvinall, R L., Handbook Strength, Macmillan, New York, 1963 Mechanics of Gears, of Stress and 824 References 19 Juvinall, R L., Engineering Considerations of Stress, Strain and Strength, McGraw-Hill, New York, 1967 Wire Rope Users Manual, 3rd ed., Wire Rope Technical Board, (888)289-9782 20 AGMA 908-B89, Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur; Helical, and Gear Teeth, American Gear Manufacturers Association, Alexandria, VA,April 1989 Ready-Flex Standard Flexible Shafts and Ratio Drives, S S White Technologies, Inc., Piscataway, NJ, 08854, 1994 Flexible Shaft Engineering Handbook, Stow Mfg Co., Binghamton, NY, 13702, 1965 21 Drago, R J., "How to Design Quieter Transmissions," Machine Design, Penton Media, Inc., Cleveland, Dec 11, 1980 Shigley, J E., and Mischke, C R, Mechanical Engineering Design, 5th ed., McGraw-Hill, New York, 1989 22 ANSI/AGMA 6021-G89, For Shaft-Mounted and Screw Conveyor Drives Using Spur; Helical and Herringbone Gears, American Gear Manufacturers Association, Alexandria, VA, November 1989 Marco, S M., Starkey, W L., and Hornung, K G., "Factors Which Influence the Fatigue Life of a V-belt," Engineering for Industry, Transactions of ASME, Series, 3, vol 82, no 1, Feb 1960, pp 47-59 23 ANSI/AGMA 2005-C96, Design Manual for Bevel Gears, American Gear Manufacturers Association, Alexandria, VA, 1996 Worley, W S., "Design of V-Belt Drives for Mass Produced Machines," Product Engineering, vol 24, 1953, pp 154-160 24 Coleman, w., "Guide to Bevel Gears," Product Engineering, McGraw-Hill, New York, June 10, 1963 10 Oliver, L R, Johnson, C 0., and Breig, W E, "V-Belt Life Prediction and Power Rating," Paper No 75-WA/DE 26, 25 Coleman, w., "Design of Bevel Gears," Product Engineer- ASME, 1975 11 Gerbert, Goran, Traction Belt Mechanics, Machine and Vehide Design, Chalmers University of Technology, 412 96 Goteborg, Sweden, 1999 Herringbone ing, McGraw-Hill, New York, July 8, 1963 26 Straight Bevel Gear Design, Gleason Works, Machine Di- vision, Rochester, NY, 1980 27 ANSI/AGMA2003-B97, Rating the Pitting Resistance and Bending Strength of Generated Straight Bevel, Zerol Bevel, and Spiral Bevel Gear Teeth, American Gear Manufacturers Association, Alexandria, VA, 1997 28 ANSI/AGMA 6022-C93, Design Manual for Cylindrical American Gear Manufacturers Association, Alexandria, VA, Dec 16, 1993 Worm Gearing, 29 ANSI/AGMA 6034-B92, Practice for Enclosed Cylindrical Worm Gear Speed Reducers and Gearmotors, American Gear Manufacturers Association, Alexandria, VA, 1992 12 Dayco Synchro-Cog® Drive Design, Publication 105180, Dayco Products, Inc., Dayton, OH, 45401, 1998 13 Eagle Pd® Synchronous Belts and Sprockets, Engineering Manual, Goodyear Tire and Rubber Company, Akron, OH, 1999 14 Engineering Class Chain Publication 2M-3/86, Jeffrey Chain Corp., Morristown, TN, 37813, 1986 15 ANSI B29.1M-1993, "Precision Power Transmission Roller Chains, Attachments, and Sprockets," ASME, New York, 1993 30 Buckingham, E., and Ryffel, Design of Worm and Spiral Buckingham Associates, Springfield, VT, 1973 Reprinted 1984 by Hurd's Offset Printing Corp., Springfield, VT 16 ANSI B29.3M-1994, "Double-Pitch Power Transmission Roller Chains and Sprockets," ASME, New York, 1994 17 Starkey, W L., and Cress, H A., "An Analysis of Critical Stresses and Mode of Failure of a Wire Rope," Engineering for Industry, Trans ASME, v 81, 1959, p 307 ff Chapter 16 Shigley, E., and Mischke, C R., Standard Handbook of Machine Design, 2nd ed., McGraw-Hill Book Co., New York, 1996 Hibbeler, R c., Engineering Mechanics: Dynamics, 2nd ed., Macmillan, New York, 1978 18 Timoshenko, S., Strength of Materials, Part I, D Van Nostrand, New York, 1955 19 Drucker, D L., and Tachau, H., "A New Design Criterion for Wire Rope," Trans ASME, v 67, 1945 p A-33 20 Spotts, M E, Design of Machine Elements, 6th ed., Prentice-Hall, Englewood Cliffs, NJ, 1985 Chapter 17 Chapter 18 Industrial V-Belt Drives-Design Guide, Publication 102161, Dayco Products Inc., Dayton, OH, 45401, 1998 Hibbeler, R C., Engineering Mechanics: Dynamics, 2nd ed., Macmillan, New York, 1978 Shigley, J E., and Mischke, C R, Standard Handbook of Machine Design, 2nd ed., McGraw-Hill, New York, 1996 Lingaiah, K., Machine Design Data Handbook, McGrawHill, New York, 1994 Jeffrey Chain Shigley, J H., and Mishke, C R., Standard Handbook of Machine Design, 2nd ed., McGraw-Hill, New York, 1996 Gears, Whitney Chain Catalog WC97/CAT.Rl, Corp., Morristown, TN, 37813, 1997 References Faupel, J R., and Fisher, F E., Engineering ed., Wiley, New York, 1981 Design, 2nd Chapter 19 ANSI Z535.4, "American National Standard for Product Safety Signs and Labels," American National Standards Institute, 1991 ANSI Z535.1 "American National Standard Safety Color Waldron, K J., and Kinzel, G L., Kinematics, Dynamics and Design of Machinery, Wiley, New York, 1999 Chapter 20 Dieter, G E., Volume Chair, Volume 20-Material Selection and Design, ASM Handbook, ASM International, Material Park, OR, 1997 Engineers' Handbook, Code," American National Standards Institute, 1991 ANSI Z535.2, "American National Standard for Environ- Mabie, R R., and Ocvirk, F W., Mechanisms and Dynamics of Machinery, Wiley, New York, 1975 Kutz, M., ed., Mechanical New York, 1986 825 Wiley, mental and Facility Safety Signs," American National Standards Institute, 1991 ANSI 2535.3, "Criteria for Safety Symbols," American National Standards Institute, 1991 ANSI Z535.5, "Specifications for Accident Prevention Tags," American National Standards Institute, 1991 All Chapter Openers Chapter 15 © CORBIS Page 559: Courtesy Quality Transmission Components Chapter 11 Chapter 16 Page 411: Courtesy RBC Bearings Page 660: Photo by George Achorn Courtesy Swedespeed Chapter 12 Chapter 17 Page 441: Courtesy RBC Bearings Page 698: Courtesy Rexnord Corporation Chapter 14 Page 515: Courtesy Associated Spring 826 Abrasive wear, 23, 25, 106, 109 Acme thread, 441, 442, 447, 448 Adhesivebonding, 506-510 Adhesive wear, 23, 25, 106, 109 American Bearing ManufacturersAssociation (ABMA),410 AmericanGear ManufacturersAssociation (AGMA),568 Angle shapes (equal leg), section properties, 817 Angular velocity ratio, 558, 563-567 Anthropometrics,5 Archard adhesive wear constant, 107, 108 Area moment of inertia (table), 171 Ashby charts, 142-148, 151-158 ASME Boiler and PressureVesselCode, 362 Asperities,surface, 106, 389 Assembly,design for, 317, 318 Assemblyprocess, selection, 317, 318 Backlash (gears), 579 Ball screws (see power screws) Baseplates,788, 789 Bases, 788 Beam springs,535-544 (also see springs) Bearings: antifriction (see rolling element bearings) basic load rating, 109 journal (see plain bearings) plain (see plain bearings) rolling element (see rolling element bearings) sleeve (see plain bearings) sliding (see plain bearings) Belleville springs (coned disk) 547, 548 Belts: failure modes, 701, 702 flat, 703, 707 flat belt selection,705-707 materials,703 synchronous,718, 719 timing, 718, 719 uses,697 V-belts,707-718 V-beltdatum system, 710 V-beltpitch system,710 V-belt selection, 713-718 Bending: curved beams, 227-232 gear teeth (see gears) load, shear, and moment diagrams (table), 165-169 neutral axis, 170, 173,227 neutral surface, 170, 173 pure bending, 169 spring rate, 239 straightbeams, 165-172 transverseloads, 172-176 transverse shear, 172-176 Bevel gears, 621-633 (also see gears) Biaxial brittle fracture strength data, 204 Biaxial state of stress, 164, 194-201 Biaxial yield strengthdata, 205 Body forces, 160 Boundaryconditions,365, 368 Brinnelling,23, 24 Bolts, (see fasteners) Brakes: band, 680, 684 caliper,687, 688 cone, 690, 691 design procedure,663, 664 disk, 685, 690 external shoe, 660, 665, 679 failure modes, 661 friction coefficients(table), 662, 663 friction lining materials,662, 663 internal shoe, 660, 665, 679, 680 long-shoedrum type, 675-680 multiple disk, 685-690 materials, 661-663 self-energizing,665 self-locking,665 short-shoedrum type, 665-674 temperaturerise, 668 types, 659-661 uniform pressure assumption(disk), 687 uniform wear assumption(disk) 686, 687 uses, 658, 659 Brinnelling,23, 24 Brittle fracture, 23, 24, 34-43, 204 Buckling, 23, 27, 81-92 Buckling: column, 82, 83 critical buckling load, 82-90 critical unit load, 86 effective column length, 85 effective slendernessratio, 86 end support influence,83, 85 Euler's critical load, 85 Euler-Engesser equation, 86 externallypressurizedthin-walledtube, 91 helical coil springs, 527, 528 initially crooked columns, 86, 87 local buckling, 88 long columns, 87, 88 long thin rod, 90 onset of, 81 pin-jointed mechanism,82, 83 primary buckling, 88 secant formula, 86, 87 short columns, 87, 88 thin deep beam, 91 Buckling avoidanceguideline,287, 288 Butt welds, 499, 500 Buttress thread, 441, 442 Castigliano's theorem, 191-194 Cathodic protection, 112 Chains: chordal action, 722, 723 failure modes, 719-723 inverted tooth, 728 materials, 720, 721 multiple strand factors (table), 722 precision roller chain, 721-728 precision roller chain, selection,723-728 polygonal action, 722, 723 silent, 728 uses, 697 Channel shape, sectionproperties, 816 Clutches: band,680-684 827 828 Index Clutches (continued): cone,690-691 design procedure, 663, 664 disk, 685-690 failure modes, 661 friction coefficients (table), 662, 663 friction lining materials, 662, 663 materials, 661-663 multiple disk, 685-690 temperature rise, 668 types, 659-661 uniform pressure assumption (disk), 687 uniform wear assumption (disk), 686, 687 uses, 658, 659 Code of ethics (NSPE), 14, 15,804-808 Codes, 13 Codes and standards, 13 Coefficient of speed fluctuation (flywheels), 748,749 Cold-rolling, 247 Columns (see buckling) Combined creep and fatigue, 23-28 Combined stress design equations, 295, 296 Combined stress theory of failure, 33, 203-208, 295, 296 Conceptual design, Concurrent design, 313, 316 Concurrent engineering, 313, 316 Conforming surface guideline, 288, 289 Configurational guidelines, 284-293 Configurational guidelines: buckling avoidance, 287, 288 conforming surface, 288, 289 direct load path, 284, 285 hollow cylinder and I-beam, 288 lazy material removal, 289, 290 load spreading, 291, 292 merging shape, 290, 291 strain matching, 291 triangle-tetrahedron, 286, 287 Corrosion fatigue, 23, 28, III Corrosion-fatigue strength properties (table), 139 Critical point accessibility, design for, 319, 320 Critical sections, 293-295 Corrosion wear, 23, 28 Couplings: bellows, 343, 344 elastomeric disk, 343, 344 Critical speed, rotating shafts, 338-340 Critical stress intensity factor, 35, 36, 40 Cumulative creep prediction, 104, 105 Cumulative damage, 43, 66-72 failure modes, 343-345 flexible, 341, 343-345 flexible disk, 343, 344 gear, 343, 344 rigid, 341-343, 349-352 roller chain, 343, 344 Cumulative distribution function, 54 Curved beams, 227-232 Curved surfaces in contact, 232-237 Customer attributes, 3, Customer perceptions, CV joint, 345 rubber cap, 344 sliding disk, 343, 344 Cycle counting, rain flow method, 66-72 Cyclic equivalent stress, 208-211 spring, 343, 344 universal joint (D-joint), 345 Crack: Cyclic multiaxial state of stress, 208-211 Cyclic stresses, 43-81 initiation, 43, 73-76 length,36 opening mode (Mode 1),35 propagation, 34, 43, 76-81 size, unstable (critical), 43, 76-80 surface, 35 surface flaw shape parameter, through-the-thickness, 35-38 Crankshafts: center cranks, 771 design procedure, 772-786 disk cranks, 771 failure modes, 772 materials, 772 side cranks, 771 types, 771 uses, 770, 771 Creep, 23, 26, 98-105 Creep: 35, 38 Deflection: axial loading, 188 bending, 166-169, 188, 189 Castigliano's theorem, 191-194 cylinders in contact, 235 shafts,331-338 spheres in contact, 235 Hertz contact, 235, 432 436 torsional loading, 188 Deflection analysis, 163 Design: concurrent, 313, 316 detail design, embodiment design, fail safe design, intermediate design, mechanical design, I preliminary design, 7, safe life design, constant creep rate, 102 cumulative creep, 104, 105 Larson-Miller theory, 101 Logarithmic creep, 103 Design Design Design Design equations, combined stress, 295, 296 for assembly (DFA), 317, 318 for manufacturing (DFM), 317 for "X" (DFX), 313, 314 tailored shape, 285, 286 Constant thickness disk flywheel, 757-761 (also see flywheels) Contact stresses (Hertz), cylinders, 234- Log-log stress-time creep law, 103 Long-term creep 100-105 parabolic creep, 103 Robinson hypothesis, 104, 105 Design safety factor, 7, 33, 267-270, 279 Design reviews, 10,800 Design steps, 9-11 Detail design, 237 Contact stresses (Hertz), spheres, 232, 233 Corrosion: biological corrosion, 23, 25, III cathodic protection, 112 cavitation corrosion, 23, 25, III direct chemical attack, 23, 25, III erosion corrosion, 23, 25, III Stage I transient creep, 103 Stage II steady-state creep, 103 true creep strain, 102 under uniaxial stress, 101-105 Creep buckling, 23, 28 Creep deformation, 100 Creep-limited maximum stress (table), 135 Development and field service, Dilatation energy per unit volume, 206 Direct load path guideline, 284, 285 Direct shear, spring rate, 239 Disassembly, design for, 319, 320 Distortion energy design equation, 296 Distortion energy failure theory, 33, 203, 205-208 galvanic corrosion, 23, 25, Ill, 112 hydrogen damage, 23, 25, Ill, 113 intergranular corrosion, 23, 25, Ill, 113 Creep strain, 99 Creep rupture, 98-100 Creep testing: Distortion energy per unit volume, 206 Distortion energy theory of failure, 33, 203, 205-208 pitting corrosion, 23, 25, Ill, 112 protection, 112 sacrificial anode, 112 selective leaching, 23, 25, III stress corrosion, 23, 28,111-113 abridged method, 100 mechanical acceleration method, 100 thermal acceleration method, 100 Critical points, 293-295, 451 459, 471 473,547 Distribution function (see probability density function) Ductile rupture, 23, 24, 33, 34 Ductility properties (table), 136, 137 Durability of gear teeth (see gears) Index Effective stress, 207 Efficiency: power screws,444-450 worm gears, 638-640 Elastic instability(see buckling) Elastic strain, 31, 32 Elastic stress-strainrelationships,202, 203 Elasticity theory (see theory of elasticity) Elevated temperaturestrength (table), 133, 134 Embodimentdesign, Energy methods: Castigliano's theorem, 191-194 impact, 93-98 Engineeringstrain, 30 Engineeringstress-straindiagram, 29 Environmentaleffects, 254, 255 Epicylic gears, 563-567 Equilibrium, 160, 161,365,373,392 Equivalent alternatingstress amplitude, 208-211 Equivalent cyclic stress, 208-211 Equivalent mean stress, 208-211 Equivalent stress, 72, 207, 208-211 Ergonomics,5 Ethics, 13, 14 Ethics: Code of, 14, 15,804-808 Ethical dilemma, 14 Euler's critical load, 85 External energy,94 Fail safe design, 9, 278 Failure analysis, 118 Failure criteria, 22 Failure modes, 23-28 (also see mechanical failure) Failure preventionperspective,22-118 Failure theories: distortion energy theory (also known as octahedralshear stress theory, Huber-von-Mises-Henky theory, or von Mises theory), 33, 203 fatigue, 202-211 maximumnormal stress theory (also known as Rankine theory), 203, 204 maximum shearing stress theory (also known as Tresca-Guesttheory), 33, 203 selectionof, 207 Fasteners: bolts, 464, 473 critical points 471-473, 492-494 failure modes, 472-473 head styles, 465 lead (thread),466 materials,469-471 metric threads, 468 multiple threads, 466 reduced-body bolts, 464, 465 rivets, 491-494 screw thread standards,465, 466 thread angle, 466 thread series, 469 thread major diameter,466 thread minor diameter (root), 466 thread specifications,469 thread stresses,471-473 threaded, 463, 464-473 tightening,482, 483 torque coefficient,483 unified inch, threads, 467, 468 Fastener loosening,482, 483 Fasteningmethods,462-510 Fatigue: completelyreversed stress, 44, 59 corrosion fatigue, 23 crack growthrate, 77 crack initiation,43, 73-76 crack propagation,34, 43, 76-81 critical (unstable)crack size, 43, 76-80 cumulativedamage, 43, 66-72 cycle ratio, 66-69 cyclic strain-hardeningexponent, 74, 75 cyclic strengthcoefficient,74, 75 damage fraction, 66-69 definitionsfor constant-amplitudestress time pattern, 44, 45 estimatingpropertiesof a part, 58 elastic strain amplitude,74, 75 estimating S-N curves, 48-50 factors that may affect S-N curves, 49-59 failure theories, 208-211 fatigue life, 43 fatigue limit, 46, 47 fatigue strength46, 47 final fracture, 76-81 fluctuatingloads, 43 fracture mechanicsapproach (F-M approach), 44, 73-81 fretting fatigue 23, 26, 113, 114, 116 high-cyclefatigue, 23, 24, 43-81 histogram,46 impact fatigue, 23 infinitelife design, 57 life improvementfrom residual stress, 251-254 life improvementfrom shot-peening, 251-254 linear damage rule, 66-69 loading spectra,44 local stress-strainapproachto crack initiation, 73-76 low-cyclefatigue, 23, 24, 44 master diagram, 60-61 modifiedGoodmanrelationships,60, 62-66 multiaxialcyclic stresses,72 Neuber rule, 74 nonzero mean stress, 45, 59-66 Palmgren-Miner hypothesis, 66-69 829 Paris Law, 77 plastic strain amplitude,74, 75 probability of failure, 47 rain flow cycle counting, 55, 66-72 range of stress, 45, 77 released tension, 45 reliability,47 reversals to failure, 74, 75 sample standarddeviation,46 sample mean, 46 scatter of life data, 46 S-N curves, 46 SNP curves, 46, 47 standard deviation of fatigue strength, 54 strain-controlledfatigue (see low-cycle fatigue) stress life approach (S-N approach),43, 44, 50 strength-influencingfactors for S-N curves, 49-59 strengthreliabilityfactors, 49 stress intensity factor range, 77 stress spectra,44, 66 surface fatigue, 23, 24 test method influenceon S-N data, 50 thermal fatigue, 23, 24 total strain amplitude,74, 75 zero-meanstress, 44, 59 Fatigue limit, 46, 47 Fatigue strength,46, 47 Fatigue strengthreduction factor, 222 Fatigue stress concentrationfactor, 213, 214 Fillet welds, 500-506 Finishes, 308, 310 Fits, 303-309 Flexible shafts: maximumoperating torque (tables),740, 741 selectionprocedure,741-743 uses, 699-701 Fluctuatingloads, 43 Flywheels: bending in flywheelrim, 755, 756 coefficientof speed fluctuation,748, 749 connectionto shaft, 766, 767 constant thickness disk, 757-761 design for speed control, 749-751 energy management,747-751 failure modes, 753 fluctuatingduty cycles, 747-751 materials, 753 rotating free ring, 754, 755 spoke-and-rim,753-757 tension in flywheelspokes, 756, 757 types, 752 uniform strengthdisk, 761, 762 uniform strength disk with rim, 763-766 uses, 746 Force analysis, 161, 162 Force flow lines, 161, 162, 212 830 Index Force-induced elastic deformation, 23, 24, 28-3 I Fracture mechanics, 34 43 Fracture mechanics approach to fatigue, 73-81 Fracture toughness, plane strain, 36, 39 Frames: C-frame, 789 design procedure, 790-795 failure modes, 789 materials, 789 O-frame, 789 open truss, 788, 789 stressed-skin structure, 788, 789 thin-walled shell, 788, 789 Free body diagram, 160, 161, 162,249,366, 445 Fretting, 23, 26, 113-117 Fretting: fretting action, 26, 113 fretting corrosion, 23, 26, 113, 114 fretting fatigue, 23, 26, 113, 114, 116 fretting wear, 23, 26, 113, 116 maps, 116 minimizing or preventing fretting damage, 116, 117 Friction coefficients (table), 809-811 Friction wheel drives, 557, 558 Galling, 23, 27, 107 Gasketed joints, 473-482 Gasket materials, (table), 478 Gears: angular velocity ratio, 558, 563-567, 571 backlash, 579 bevel: applications, 560, 561 bending (tooth)-AGMA refined approach, 626, 627 design procedure, 627 -{i33 force analysis, 624, 625 nomenclature, 621 -{i24 standard AGMA tooth proportions (table), 624 stress analysis, 625-627 surface durability using AGMA refined approach, 626, 627 compound, 563-567 epicyclic (planetary), 563-567 external, 557, 558 face gears, 561 failure modes, 567, 568 fundamental law, 558 helical: applications, 560 bending (tooth)-AGMA refined approach, 614, 615 contact-pattern, 609 design procedure, 615 -{i21 force analysis, 613, 614 nomenclature, 608, 610 standard AGMA tooth proportions (table), 611 stress analysis, 614, 615 surface durability using AGMA refined approach, 614, 615 herringbone, 560 hypoid,561 internal, 557, 558 involute, 570-579 Lewis equation (bending), 588, 599 Lewis form factor, 589 line of action (pressure line), 570 manufacturing cost trends, 585 manufacturing methods: accuracy requirements (table), 584, 585 gear cutting, 579-581 gear finishing, 581 profile modification, 582-584 materials, 568-570 rack and pinion, 560 reduction ratios, 563-567 selection of type, 558-563 simple, 563-567 spiroid,561 straight tooth spur: angular velocity ratio, 558, 563-567, 571 applications, 558, 560 approximate actual sizes, 575 bending (tooth)-AGMA refined approach,592-599 bending (tooth)-simplified approach, 588-592 conjug~te action, 570 design procedure, 607, 608 force analysis, 586, 587 involute profile, 570-579 lubrication, 605-607 nomenclature, 557, 572 standard AGMA tooth proportions (table), 575 stress analysis, 592-604 surface durability using AGMA refined approach, 601-605 surface durability using Hertz contact stresses, 599-601 tooth profile, 570-579 surface durability, 109,599-605,614, 615,626,627 tooth bending, 588-599, 614, 615, 626, 627 tooth durability, 599-605, 614, 615, 626, 627,641 trains, 563-567 types, 558-563 uses, 557, 558 worm: allowable tangential gear force, 641, 642 applications, 562 bending (tooth), 641 common thread profiles, 635 design procedure, 642-649 efficiency, 638-640 force analysis, 638-640 nomenclature, 634 stress analysis, 640-642 surface durability, 641 typical tooth proportions, (table), 636 Zerol, 560,561 Geometric compatability, 365, 367, 372 Geometry determination, 283-310 Graphical integration, 332-338 Hardness properties (table), 138 Heat affected zone (HAZ), 499 Helical coil springs, 515, 521-535 (also see springs) Helical gears, 608-621 (also see gears) Hertz contact deflection, 235, 432-436 Hertz contact spring rate, 239, 432 Hertz contact stress, 24, 109, 188, 232-237 High-speed-rotors (see flywheels) Hollow cylinder guideline, 288 Hooke's Law, 32, 94, 189,202,203,206, 365,367,373 Horsepower relationship, 180 Housings, 789 Huber-von-Mises-Hencky Theory (see distortion energy theory) Human factors engineering, House of quality, I-beam guideline, 288 I-beams, section properties, 815 Impact, 23, 26, 92-98 Impact: deflection, 93-98 deformation, 23, 26 energy method, 93-98 fatigue, 23 fracture, 23, 26 fretting, 23 stress, 93-98 stress wave propagation, 93 suddenly applied load, 93, 95 wear, 23, 26 Industrial designers, Inspectability, Inspectability, design for, 319, 320 Interference fits: design procedure, 376 381 failure modes, 363 uses, 362, 363 Intermediate design, Involute gear teeth, 570-579 Involute splines, 353 Iteration, 7, 296 Jack screws (see power screws) Joints: adhesively bonded, 506 510 advantages of adhesive bonding, 506 Index bolted, 463, 464-491 butt welds, 499, 500 centroid of bolt pattern 484 485 centroid of weld pattern SOl eccentric loading, 483 491, 500-506 failure modes, 464 465 fillet welds, 500-506 gasketed, 473 482 moment of inertia, 485, 486, 504 multiply bolted, 483 multiply riveted, 494 multiply welded, 501-506 preloaded, 474-482 rivet material, 491 riveted, 491-494 stiffness, 473-482 torsion-like shear, 484-491 types, 462, 463 weld edge preparation, 496, 497 weld electrode specifications, 498 weld types, 496, 497 weldability, 498 welded, 494-506 weld heat affected zone (HAZ), 499 weld stress concentration factors, 497 weld symbol, 495-497 Sommerfeld data, 393-397 thick film (full film), 385, 389 405 thin film (partial film), 385-389 Tower experiments, 392 viscosity, 390, 391, 394 zero film, 385 Maintenance, design for, 313, 319, 320 Manufacturing, 313-320 Manufacturing, design for, 317 Manufacturing process, selection, 314-317 Mass moments of inertia (table), 812 Maximum shearing stress design equation, 295 Maximum shearing stress failure theory, 203, 205 Maximum normal stress design equation, 295 831 galling, 23, 27, 107 impact, 23, 26, 92-98 modes of, 23-28 radiation damage, 23, 27, 139, 140 seizure, 23, 27, 107 spalling, 23, 27 stress corrosion, 23, 28, 113 stress rupture, 23, 27, 98-105 temperature-induced elastic deformation, 23,24,31,32 thermal relaxation, 23, 27 thermal shock, 23, 27 wear, 23, 25, 105-1l1 yielding, 23, 24, 32, 33 Modified square thread, 441, 442 Mohr's circle (strain), 202 Mohr's circle (stress), 198-201 Moment diagrams, bending (table) 165- Maximum normal stress failure theory, 203, 204 Membrane analogy, 181-183 Machinability index (table), 141 Manufacturing process suitability (table), 140 Marketing specialists, I, Mass moment of inertia, (table), 812 Materials: application requirements, 131 Ashby charts, 142-148, 151-158 mechanical properties (tables), 39, 132-142, 143-148 performance evaluation indices, 131 selection by Ashby method, 142-148, 151-158 selection by rank-ordered data table, 142-151 169 Moment of inertia, area (table), 171 Moment of inertia, mass (table), 812 Multiaxial cyclic stress, 208-21l Multiaxial fatigue failure theories, 208-21l Multiaxial state of stress, 164, 194-21l Multiple threads, 442, 443 Larson-Miller parameter, 101 Lazy-material removal guideline, 289, 290 Lead screws (see power screws) Leaf springs, 535-544 (also see springs) Lessons learned strategy, 12 Lewis equation (see gears) selection steps, 130 Materials cost index (table), 141 Mean, 272 Mechanical design: concepts, definition, Normal (Gaussian) distribution, Normal stress, 163, 164 Notch sensitivity, 220 223 Line of action (see gears), 570 Linear actuators (see power screws) Linear elastic fracture mechanics (LEFM), 34-43 Load sharing, 237-243 Load spreading guideline, 291, 292 Loading severity parameter, 203 Lubrication: boundary, 386-389 elastohydrodynamic (squeeze film) 386, 431,605-607 hydrodynamic, 386, 389-405 hydrostatic, 386 Petroff's equation, 392 pV product, 386-389 Raimondi and Boyd data, 393-397 failure prevention perspective, 22-1l8 Merging shape guideline, 290, 291 Mode I crack displacement, 35 Mode II crack displacement, 35 Mode ill crack displacement, 35 Mechanical failure: brinnelling, 23, 24 brittle fracture, 23, 24, 34-43 buckling, 23, 27, 81-92 combined creep and fatigue, 23, 28 corrosion, 23, 24, IIl-1l3 corrosion fatigue, 23, 28, III corrosion wear, 23, 28, III creep, 23, 26, 98-105 creep buckling, 23, 28 ductile rupture, 23, 24, 33, 34 Keys, 341-352 Keys: failure modes, 346 square, 345-352 stress concentration factors (keyway), 217,347,349 Woodruff, 345, 347 Kinematic viscosity, 390, 391, 394 Reynolds equation, 392, 393 plain bearings, 383, 385-405 rolling element bearings, 431 solid film, 386 fatigue 23, 24, 43-81 force-induced elastic deformation, 30 fretting, 23, 26, 1l3-1l7 National Society of Professional Engineers (NSPE), Code of Ethics, 14, 15, 804-808 Neuber rule, 74 Newtonian fluid, 390 Newton's law of cooling: bearings, 398 brakes, 668 gears, fiJ7 Nondestructive evaluation (NDE), 319 272-275 Octahedral shear stress theory of failure (see distortion energy failure theory) 23, 24, Paris Law (fatigue), 77 Petroff's equation, 392 Pins, 356, 357 Plain bearings: advantages, 383, 384 design criteria, 399 design procedure, 400 405 eccentricity ratio, 394, 401 failure modes, 384 lubrication, 383, 385 405 materials, 385 oil film temperature rise, 396, 398 recommended clearances (table) 400, 401 uses, 383 Plane cross section properties (table) 171 Plane strain: critical stress intensity factor, 40 definition, 39 minimum thickness for, 39, 40 832 Index Plane strain fracture toughness, 36, 39, 40, Recycling, design for, 319, 320 Rotors, high-speed (see flywheels) 77 Plane stress, critical stress intensity factor, Redundant assemblies, 237-243 Redundant supports, 191-194, 237-243 Rotating free ring, 754, 755 40 Planetary gears, 563-567 Plastic strain, 32 Policy of least commitment, Power, as related to torque and speed, 180 Redundancy, component level, 278 Redundancy, sub-system level, 278 Reliability, 47, 271-279 Reliability: allocation, 276 Safe life design, Safety factor: design, 7, 33, existing, 270, rating factors, Power screws: Acme thread, 441, 442, 447, 448 back driving, 446 ball screws, 443 buttress thread, 441, 442 design procedure, 450-459 efficiency, 444-450 failure modes, 443, 444 helix angle, 442 lead (thread), 442 lead angle, 442, 447 materials, 444 modified square thread, 441, 442 multiple threads, 442, 443 overhauling, 447 pitch, 442 self-locking, 447 square thread, 441, 442, 446 thread angle, 441 threads, 441-447 torque, 444-450 uses, 440 Preliminary design, 7, Preloading, 243-247,432-436 Presetting, 247 Pressure vessels: ASME Boiler and Pressure Vessel Code, 362 failure modes, 363 longitudinal stress, 366 materials, 363, 364 tangential (hoop) stress, 366 thick wall, 362, 366-372 thin wall, 362, 365, 366 uses, 362 Prestressing, 248, 249 Principal normal stresses, 195-201 Principal planes, 195-201 Principal stresses, 195-201,369 Principal shearing stresses, 195-201 Projected area, 366 Probability density function, 271-274 Probability of failure, 47, 271-273 Probabilistic design, 271 Product design team, 1,2,3 Product marketing concept, block diagrams, 277 definition, 271 equal apportionment, 278 functional block diagrams, 277, 278 goals, 276 log-normal distribution, 272 normal cumulative distribution, 272-274 normal distribution, 272-275 parallel components, 277, 278 population mean, 272 population standard deviation, 272 population variance, 272 redundancy at component level, 278 redundancy at subsystem level, 278 series components, 277, 278 Six Sigma, 276 specification, 279 standard normal variable (table), 273, 274 system, 276-278 Weibull distribution, 272 Residual stresses, 247-254, 497 Residual stresses: cold-rolling, 247 estimating, 248-254 267-270, 279 271 268 rating numbers, 268, 269, 279 Safety issues: devices, 795, 797-800 guards, 795, 796 hazards, 795 risk, 795 Sample mean, 46 Sample standard deviation, 46 Screw threads: Acme, 441, 442, 447, 448 buttress, 441, 442 failure modes, 443, 444 helix angle, 442 lead, 442 lead angle, 442, 447 modified square, 441, 442 multiple threads, 442, 443 pitch, 442 square, 441, 442, 446 thread angle, 441 Screws, power (see power screws) Seizure, 23, 27, 107 Setscrews, 345, 354, 355 Setscrews: fatigue life improvement, 251-254 presetting, 247 prestressing, 248, 249 holding power, 355 types of points, 355 Shaft deflection, 331-338 shot-peening, 247 weldments, 497 Shaft strength, 325-331 Shafts: Resilience properties (table), 137 Resonance, 324, 339 Retrospective design, 117, 118 Reynolds equation, 392, 393 Rivets (see fasteners) Rolling element bearings: ball, 410, 411 basic dynamic load rating, 415 basic static load rating, 415 enclosure, 436, 437 failure modes, 413 force-deflection curves, 432-436 lubrication, 431 materials, 413, 414 mounting practice, 436, 437 preloading,243-247 reliability, 415, 416 connection to flywheel, 766, 767 critical speed, 338-340 design equations, deflection based, 331-338 design equations, strength based, 325-331 design layout, 323 design procedure, 340, 341 failure modes, 323, 324 flexible (see flexible shafts) materials, 324, 325 standard for design of, 325 uses, 321-323 vibration, 338-340 Shear center, 185-188 Shearing stress, 163, 164, 172-176 Shock (see impact) Radiation damage, 23, 27, 139, 140 Radiation exposure influence on properties roller, 410, 412 selection for spectrum loading, 414, 427430 Shot-peening, 247 Shot-peening, fatigue life improvement, 251-254 (table), 139, 140 Rain flow cycle counting (fatigue), 55, 66-72 Rankine's theory (see maximum normal selection for steady loads, 414, 416-427 stiffness, 432-436 types, 410-412 Simplifying assumptions, 296 Six Sigma, 276 Slider-crank mechanism, 770 uses, 409 Solid bodies, properties of (table), 812 stress theory) Index Spalling, 23, 27 Specification, reliability, 279 Specifications, engineering, 2, 8, II, 130 Stages of design, 7-9 Standard deviation, 272 Standard normal variable, 54, (table) 273- Specifications, threads, 469 S-N curves, estimating, 48-50 S-N curves, strength-influencing 49-59 274 Standards, 13 State of stress: biaxial, 164, 194-201,366 weldment, 497 Stress corrosion, 23, 28, III Stress cubic equation, 195-198 Stress intensity: Splines, 341, 352-354 Splines: failure modes, 352 fitted, 355 involute, 353 straight, 352, 353 stress concentration factors, 217, 353 Spoke-and-rim flywheel, 753-757 (also see flywheels) multiaxial, 164, 194-201,203 multiaxial cyclic, 72, 208-211 triaxial, 164, 195 uniaxial, 35, 164, 203 Stiffness, joints, 473 482 Stiffness properties of materials (table), 136 Straight tooth spur gears, 570-608 (also see gears) Strain amplitude, elastic, 74,75 critical, 35 stress intensity factor, 35 Stress intensity factor, 35-38 Stress patterns: bending, 165-172 direct stress, 165 surface contact stress, 165, 188 torsional shear, 165, 179-188 transverse shear, 165, 172-179 Spring index, 523 Springs: Belleville (coned disk), 547, 548 buckling of helical coil, 527, 528 curvature factor in helical coil, 523 end loop stress concentration, 523, 524 Strain Strain Strain Strain Strain Strain Stress relaxation, 27 Stress rupture, 23,27,98-105 Stress rupture strength (table), 134 Stress wave propagation, 93 Structural adhesives (table), 509 Structural shapes, section properties, factors, amplitude, plastic, 74, 75 amplitude, total, 74 75 cubic equation, 201, 202 energy, 94 163 189-194.206 energy per unit volume 206 gage 202 shaft spline, 217, 353 theoretical elastic, 213 torsion of helical coil spring, 545 energy storage, 548-55 I fatigue shearing strength (table) 530 helical coil, 515, 521-535, 545 helical coil design procedure, 529-535 helical coil nomenclature, 521 helical coil spring index, 523 helical coil spring rate, 525, 526 leaf springs, 535-544 leaf spring design procedure, 540-544 Strain-matching guideline 291 Strain rosette 202 Strength at elevated temperature (table), 133 134 Strength properties (table) 132 133 Strength reduction factor, 222 Strength/weight ratio (table), 133 Stress (see "stress patterns" and "state of stress") 813-817 Suddenly applied load, 95 Superposition principle of, 32 Surface contact stress, 188 Surface forces, 160 Surging, helical coil springs, 527-529 System reliability, 276-278 leaf-spring spring-rate, linear, 238 Stress, equivalent, 72 Stress concentration, 212-226 Tapered fits 354 Temperature-induced Stress concentration: actual local stress, 212 23.24,31,32 Theoretical stress concentration 538 machine elements as, 238-243 nonlinear softening, 238 nonlinear stiffening (hardening), parallel, 237-243 series 237-243 238 shackles, 538, 540 spiral torsion, 546, 547 surging torsion torsion torsion of helical coil, 527-529 bar, 544-547 in helical coil, 522 springs, 544-547 torsion tubes, 544 torsional shear yield strength (table), 530 transverse shear in helical coil, 522 highly local, 212-227 multiple notches, 214, 220 nominal stress, 212 notch root, 212 notch sensitivity index, 220-223 strength reduction factor, 222 widely distributed, 212, 228, 229 Stress concentration factors: crankshaft fillet, 219 833 Tailored-shape guideline, 285-286 elastic deformation, factor, 213 Theories of failure: distortion energy theory, 203, 205-208 maximum shearing stress theory, 203, 205 maximum normal stress theory, 203, 204 selection of, 207 Theory of elasticity principles, 364-366 Thermal conductivity (table), 141, 142 Thermal expansion coefficient (table), 135 curved beams, 228, 229 cyclic multiaxial states of stress, 222 end-of hub pressed on shaft, 220, 374 Thermal shock, 23, 27 Thermal relaxation, 23, 27 Thermal stress (temperature fatigue, 213, 214 fatigue of brittle materials, 222 fatigue of ductile materials, 222 flat bar with shoulder fillet, 217, 218 gear tooth fillet, 219 helical coil spring in torsion, 545 32 Threads: fasteners, 465 473 power screws, 441 447 Tolerances, 303-309 Tooth bending, 588-599, 614, 615, 626, 627 direct shear, 239 helical coil, 525, 526 intermediate and low-cycle range, 222 keyways (profiled, sled runner), 347, 349 (also see gears) Topological interference, Hertz contact, 239 leaf springs, 538 keyways (Woodruff), 347 screw threads, 214 Torsion: circular cross section, 179, 180, 183, 184 linearized, 239, 432 torsional, 239 shaft diametral hole, 216 shaft fillet, 214, 215 deflection, 188 non circular cross section, 181-184 shaft groove 215, 216 shaft keyway, 217, 347, 349 shear center in bending, 185-188 spring rate, 239 Wahl factor, 523, 524 Spring rate (spring constant), 29, 237-243, 525, 526 Spring rate: axial, 30, 238 bending, 239 Spur gears, 570-608 (also see gears) Square thread, 441, 442, 446 induced stress), 770 834 Index Torsionbar springs,544-547 (also see springs) Total strainenergyper unit volume,206 Toughnessproperties(tables),39, 137 Transverseshear, 172-176 Tresca-Guesttheory (see maximumshearing stress theory) Triangle-tetrahedronguideline,286, 287 Uniaxialstate of stress, 35, 164,203 Units, 14-20 Units: absolutesystem, 15, 16 base units, 15 conversiontable, 18 derived units, 15 foot-pound-secondsystem(fps), 14 gravitationalsystem, 15 inch-pound-secondsystem(ips), 14 Internationalsystem(SI), 14 standardprefixes,17 Universaljoint, 345 Variance,272 Virtuesof simplicity,10 Viscosity,390, 391, 394 von Mises stress, 207 von Mises theory (see distortionenergytheory) Wahlfactor,523, 524 Wear,23, 25,105-111 Wear: abrasivewear,23, 25, 106, 109 abrasivewear constant, 108 adhesivewear,23, 25, 106, 109 Archardadhesivewear constant, 107, 108 corrosionwear,23, 25,106 deformationwear,23, 26, 106 frettingwear, 23, 26, 113, 116 impact wear,23, 26 mean nominalcontactpressure, 107, 108 principleof conversion,107 principleof diversion,107 principleof protectivelayers, 107 surfacefatiguewear, 23, 25, 106, 109 three-bodywear, 108 two-bodywear, 108 Weibulldistribution,272 Weldability,498 Weldedjoints (seejoints, welded) Weld symbol,495-497 Wide flangebeam, sectionproperties,813, 814 Wire rope: failure modes,728-730 fatigue data, 734 materials, 731,732 selectionprocedure,734-739 stresses,731, 733, 734 uses, 699, 700 Wormgears, 634-649 (also see gears) Yielding,23, 24, 32, 33, 39, 205 Yieldstrength,biaxial, 205 Seleded Conversion Relations"ips Quantity Conversion Force Length Area Volume Mass 1b = 4.448 N in = 25.4 mm in2 = 645.16 mm2 in3 = 16387.2 mm3 slug = 32.17 1b kg = 2.21 1b kg = 9.81 N psi = 6895 Pa Pa = N / m2 psi = 6.895 X 10-3 MPa ksi = 6.895 MPa 106 psi = 6.895 GPa 11b/in= 175.126N/m in / sec = 0.0254 m / sec in / sec2 = 0.0254 m / sec2 in-1b = 0.1138 N-m hp = 745.7 W (watts) in-1b = 0.1138 N-m ksi Jill = 1.10 MpaJffi in4 = 4.162 X 10-7 m4 in-1b-sec2 = 0.1138 N-m-sec2 Pressure Stress Modulus of Elasticity Spring rate Velocity Acceleration Work, energy Power Moment, torque Stress intensity Area moment of inertia Mass moment of inertia A Truncated List of Standard 51 Prefixes Name giga mega kilo centi mili micro nano Symbol G M k c m J1 n Factor 109 106 103 10-2 10-3 10-6 10-9 ... determination of the "macrogeometry" of machine parts In many cases the "microgeometry" of a machine part, or an assembly of parts, also has great importance in terms of proper function, prevention of premature... heavy dependence of both fail-safe design and safe life design upon regular inspection of critical points was emphasized Nevertheless, designers have rarely considered inspectability of critical points... definition of mechanical design given in 1.4, design for resource conservation and minimization of adverse environmental impact are increasingly important responsibilities to be addressed at the design