Design of machine elements

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About the Author V B Bhandari retired as Professor and Head, Department of Mechanical Engineering at Vishwakarma Institute of Technology, Pune He holds First-Class BE and ME degrees in Mechanical Engineering from Pune University, and his teaching experience spans over 38 years in Government Colleges of Engineering at Pune, Karad and Aurangabad He was also a postgraduate teacher of Pune University, Shivaji University and Marathwada University Besides being a National Scholar, he has received five prizes from Pune University during his academic career Professor Bhandari was a member of ‘Board of Studies in Mechanical Engineering’ and a member of ‘Faculty of Engineering’ of Pune University He is a Fellow of Institution of Engineers (India), a Fellow of Institution of Mechanical Engineers (India) and a Senior Member of Computer Society of India He was a Fellow of Institution of Production Engineers (India) and a Member of American Society of Mechanical Engineers (USA) He has presented and published twenty technical papers in national and international conferences and journals, and is also the author of Introduction to Machine Design published by Tata McGraw Hill Education Private Limited Contents Preface Visual Walkthrough Introduction 1.1 Machine Design 1.2 Basic Procedure of Machine Design 1.3 Basic Requirements of Machine Elements 1.4 Design of Machine Elements 1.5 Traditional Design Methods 1.6 Design Synthesis 1.7 Use of Standards in Design 1.8 Selection of Preferred Sizes 11 1.9 Aesthetic Considerations in Design 14 1.10 Ergonomic Considerations in Design 15 1.11 Concurrent Engineering 17 Short Answer Questions 19 Problems for Practice 19 Engineering Materials 2.1 Stress–Strain Diagrams 20 2.2 Mechanical Properties of Engineering Materials 23 2.3 Cast Iron 26 2.4 BIS System of Designation of Steels 29 2.5 Plain-carbon Steels 30 2.6 Free-cutting Steels 32 2.7 Alloy Steels 32 2.8 Overseas Standards 34 2.9 Heat Treatment of Steels 36 2.10 Case Hardening of Steels 37 2.11 Cast Steel 38 xvii xxi 20 vi Contents 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 Aluminium Alloys 39 Copper Alloys 41 Die-casting Alloys 43 Ceramics 44 Plastics 45 Fibre-reinforced Plastics 48 Natural and Synthetic Rubbers 49 Creep 50 Selection of Material 51 Weighted Point Method 51 Short Answer Questions 53 Manufacturing Considerations in Design 3.1 Selection of Manufacturing Method 55 3.2 Design Considerations of Castings 57 3.3 Design Considerations of Forgings 59 3.4 Design Considerations of Machined Parts 61 3.5 Hot and Cold Working of Metals 62 3.6 Design Considerations of Welded Assemblies 62 3.7 Design for Manufacture and Assembly (DFMA) 64 3.8 Tolerances 65 3.9 Types of Fits 66 3.10 BIS System of Fits and Tolerances 67 3.11 Selection of Fits 69 3.12 Tolerances and Manufacturing Methods 69 3.13 Selective Assembly 70 3.14 Tolerances For Bolt Spacing 72 3.15 Surface Roughness 73 Short Answer Questions 73 Problems for Practice 74 55 Design Against Static Load 4.1 Modes of Failure 76 4.2 Factor of Safety 77 4.3 Stress–strain Relationship 79 4.4 Shear Stress and Shear Strain 80 4.5 Stresses Due To Bending Moment 81 4.6 Stresses Due To Torsional Moment 82 4.7 Eccentric Axial Loading 83 4.8 Design of Simple Machine Parts 84 4.9 Cotter Joint 85 4.10 Design Procedure for Cotter Joint 90 4.11 Knuckle Joint 94 4.12 Design Procedure for Knuckle Joint 99 4.13 Principal Stresses 104 4.14 Theories of Elastic Failure 106 76 Contents 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4.24 vii Maximum Principal Stress Theory 107 Maximum Shear Stress Theory 108 Distortion-Energy Theory 110 Selection and Use of Failure Theories 112 Levers 117 Design of Levers 118 Fracture Mechanics 128 Curved Beams 130 Thermal Stresses 135 Residual Stresses 136 Short Answer Questions 137 Problems for Practice 138 Design Against Fluctuating Load 5.1 Stress Concentration 141 5.2 Stress Concentration Factors 142 5.3 Reduction of Stress Concentration 145 5.4 Fluctuating Stresses 149 5.5 Fatigue Failure 151 5.6 Endurance Limit 152 5.7 Low-cycle and High-cycle Fatigue 153 5.8 Notch Sensitivity 154 5.9 Endurance Limit—Approximate Estimation 155 5.10 Reversed Stresses—Design for Finite and Infinite Life 159 5.11 Cumulative Damage in Fatigue 166 5.12 Soderberg and Goodman Lines 167 5.13 Modified Goodman Diagrams 168 5.14 Gerber Equation 174 5.15 Fatigue Design under Combined Stresses 177 5.16 Impact Stresses 180 Short Answer Questions 182 Problems for Practice 182 141 Power Screws 6.1 Power Screws 184 6.2 Forms of Threads 185 6.3 Multiple Threaded Screws 187 6.4 Terminology of Power Screw 187 6.5 Torque Requirement—Lifting Load 189 6.6 Torque Requirement—Lowering Load 189 6.7 Self-locking Screw 190 6.8 Efficiency of Square Threaded Screw 190 6.9 Efficiency of Self-locking Screw 192 6.10 Trapezoidal and Acme Threads 192 6.11 Collar Friction Torque 193 6.12 Overall Efficiency 194 184 viii Contents 6.13 6.14 6.15 6.16 6.17 Coefficient of Friction 194 Design of Screw and Nut 194 Design of Screw Jack 206 Differential and Compound Screws Recirculating Ball Screw 215 Short-Answer Questions 216 Problems for Practice 217 214 Threaded Joints 7.1 Threaded Joints 219 7.2 Basic Types of Screw Fastening 220 7.3 Cap Screws 222 7.4 Setscrews 223 7.5 Bolt of Uniform Strength 224 7.6 Locking Devices 225 7.7 Terminology of Screw Threads 227 7.8 ISO Metric Screw Threads 228 7.9 Materials and Manufacture 230 7.10 Bolted Joint—Simple Analysis 231 7.11 Eccentrically Loaded Bolted Joints in Shear 233 7.12 Eccentric Load Perpendicular to Axis of Bolt 235 7.13 Eccentric Load on Circular Base 242 7.14 Torque Requirement for Bolt Tightening 248 7.15 Dimensions of Fasteners 249 7.16 Design of Turnbuckle 251 7.17 Elastic Analysis of Bolted Joints 254 7.18 Bolted Joint under Fluctuating Load 257 Short-Answer Questions 269 Problems for Practice 269 219 Welded and Riveted Joints 8.1 Welded Joints 272 8.2 Welding Processes 273 8.3 Stress Relieving of Welded Joints 274 8.4 Butt Joints 274 8.5 Fillet Joints 275 8.6 Strength of Butt Welds 276 8.7 Strength of Parallel Fillet Welds 277 8.8 Strength of Transverse Fillet Welds 278 8.9 Maximum Shear Stress in Parallel Fillet Weld 281 8.10 Maximum Shear Stress in Transverse Fillet Weld 282 8.11 Axially Loaded Unsymmetrical Welded Joints 284 8.12 Eccentric Load in the Plane of Welds 285 8.13 Welded Joint Subjected to Bending Moment 290 8.14 Welded Joint Subjected to Torsional Moment 294 8.15 Strength of Welded Joints 295 272 Contents 8.16 8.17 8.18 8.19 8.20 8.21 8.22 8.23 8.24 8.25 8.26 8.27 8.28 8.29 ix Welded Joints Subjected to Fluctuating Forces 296 Welding Symbols 297 Weld Inspection 298 Riveted Joints 298 Types of Rivet Heads 301 Types of Riveted Joints 303 Rivet Materials 305 Types of Failure 306 Strength Equations 306 Efficiency of Joint 307 Caulking and Fullering 307 Longitudinal Butt Joint for Boiler Shell 311 Circumferential Lap Joint for Boiler Shells 318 Eccentrically Loaded Riveted Joint 321 Short-Answer Questions 325 Problems for Practice 325 Shafts, Keys and Couplings 9.1 Transmission Shafts 330 9.2 Shaft Design on Strength Basis 331 9.3 Shaft Design on Torsional Rigidity Basis 333 9.4 ASME Code for Shaft Design 334 9.5 Design of Hollow Shaft on Strength Basis 342 9.6 Design of Hollow Shaft on Torsional Rigidity Basis 344 9.7 Flexible Shafts 346 9.8 Keys 346 9.9 Saddle Keys 347 9.10 Sunk Keys 348 9.11 Feather Key 349 9.12 Woodruff Key 350 9.13 Design of Square and Flat Keys 350 9.14 Design of Kennedy Key 352 9.15 Splines 354 9.16 Couplings 356 9.17 Muff Coupling 357 9.18 Design Procedure for Muff Coupling 357 9.19 Clamp Coupling 359 9.20 Design Procedure for Clamp Coupling 360 9.21 Rigid Flange Couplings 362 9.22 Design Procedure for Rigid Flange Coupling 364 9.23 Bushed-pin Flexible Coupling 368 9.24 Design Procedure for Flexible Coupling 371 9.25 Design for Lateral Rigidity 376 9.26 Castigliano’s Theorem 380 330 x Contents 9.27 Area Moment Method 382 9.28 Graphical Integration Method 383 9.29 Critical Speed of Shafts 385 Short-Answer Questions 388 Problems for Practice 389 10 Springs 10.1 Springs 393 10.2 Types of Springs 393 10.3 Terminology of Helical Springs 395 10.4 Styles of End 396 10.5 Stress and Deflection Equations 397 10.6 Series and Parallel Connections 399 10.7 Spring Materials 401 10.8 Design of Helical Springs 403 10.9 Spring Design—Trial-and-Error Method 405 10.10 Design against Fluctuating Load 405 10.11 Concentric Springs 425 10.12 Optimum Design of Helical Spring 430 10.13 Surge in Spring 432 10.14 Helical Torsion Springs 433 10.15 Spiral Springs 435 10.16 Multi-Leaf Spring 437 10.17 Nipping of Leaf Springs 439 10.18 Belleville Spring 441 10.19 Shot Peening 443 Short-Answer Questions 443 Problems for Practice 444 393 11 Friction Clutches 11.1 Clutches 448 11.2 Torque Transmitting Capacity 450 11.3 Multi-disk Clutches 456 11.4 Friction Materials 459 11.5 Cone Clutches 461 11.6 Centrifugal Clutches 465 11.7 Energy Equation 467 11.8 Thermal Considerations 469 Short-Answer Questions 470 Problems for Practice 471 448 12 Brakes 12.1 Brakes 472 12.2 Energy Equations 472 12.3 Block Brake with Short Shoe 475 12.4 Block Brake with Long Shoe 480 472 Contents 12.5 12.6 12.7 12.8 12.9 xi Pivoted Block Brake with Long Shoe 482 Internal Expanding Brake 485 Band Brakes 490 Disk Brakes 493 Thermal Considerations 496 Short-Answer Questions 496 Problems for Practice 497 13 Belt Drives 13.1 Belt Drives 499 13.2 Belt Constructions 501 13.3 Geometrical Relationships 503 13.4 Analysis of Belt Tensions 504 13.5 Condition for Maximum Power 507 13.6 Condition for Maximum Power (Alternative Approach) 507 13.7 Characteristics of Belt Drives 509 13.8 Selection of Flat-belts from Manufacturer’s Catalogue 514 13.9 Pulleys for Flat Belts 517 13.10 Arms of Cast-iron Pulley 520 13.11 V-belts 522 13.12 Selection of V-belts 534 13.13 V-grooved Pulley 535 13.14 Belt-Tensioning Methods 540 13.15 Ribbed V-belts 540 Short-Answer Questions 542 Problems for Practice 542 499 14 Chain Drives 14.1 Chain Drives 544 14.2 Roller Chains 546 14.3 Geometric Relationships 548 14.4 Polygonal Effect 549 14.5 Power Rating of Roller Chains 549 14.6 Sprocket Wheels 551 14.7 Design of Chain Drive 553 14.8 Chain Lubrication 555 14.9 Silent Chain 562 Short-Answer Questions 562 Problems for Practice 563 544 15 Rolling Contact Bearings 15.1 Bearings 564 15.2 Types of Rolling-contact Bearings 565 15.3 Principle of Self-aligning Bearing 568 15.4 Selection of Bearing-type 569 15.5 Static Load Carrying Capacity 569 564 xii Contents 15.6 15.7 15.8 15.9 15.10 15.11 15.12 15.13 15.14 15.15 15.16 15.17 15.18 15.19 Stribeck’s Equation 569 Dynamic Load Carrying Capacity 571 Equivalent Bearing Load 571 Load-Life Relationship 572 Selection of Bearing Life 572 Load Factor 573 Selection of Bearing from Manufacturer’s Catalogue 573 Selection of Taper Roller Bearings 580 Design for Cyclic Loads and Speeds 588 Bearing with Probability of Survival other than 90 Per Cent 592 Needle Bearings 595 Bearing Failure—Causes and Remedies 596 Lubrication of Rolling Contact Bearings 596 Mounting of Bearing 597 Short-Answer Questions 598 Problems for Practice 599 16 Sliding Contact Bearings 16.1 Basic Modes of Lubrication 601 16.2 Viscosity 604 16.3 Measurement of Viscosity 605 16.4 Viscosity Index 605 16.5 Petroff’s Equation 606 16.6 McKee’s Investigation 607 16.7 Viscous Flow through Rectangular Slot 608 16.8 Hydrostatic Step Bearing 609 16.9 Energy Losses in Hydrostatic Bearing 611 16.10 Reynold’s Equation 619 16.11 Raimondi and Boyd Method 622 16.12 Temperature Rise 624 16.13 Bearing Design—Selection of Parameters 625 16.14 Bearing Constructions 634 16.15 Bearing Materials 635 16.16 Sintered Metal Bearings 637 16.17 Lubricating Oils 637 16.18 Additives for Mineral Oils 639 16.19 Selection of Lubricants 640 16.20 Greases 641 16.21 Bearing Failure—Causes and Remedies 641 16.22 Comparison of Rolling and Sliding Contact Bearings Short-Answer Questions 643 Problems for Practice 644 17 Spur Gears 17.1 Mechanical Drives 17.2 Gear Drives 647 601 642 646 646 920 Design of Machine Elements Width of flange = 2.5t = 2.5 (7) = 17.5 mm Depth of section = 6t = (7) = 42 mm Part 6: Design of tappet A tappet is a stud, which is subjected to compressive force (Pe) Suppose, dc = core diameter of stud (mm) sc = Pe Ê p d c2 ˆ ÁË ˜¯ or 50 = 2362 Ê p d c2 ˆ ÁË ˜¯ Ê Pmax.C ˆ 8(380.84)(8) ˆ or 300 = 1.184 ÊÁ t = KÁ ˜¯ Ë pd2 Ë p d ˜¯ d = 30.62 d = 5.53 or mm Step III D = Cd = (6) = 48 mm Step IV N= dc2 = 60.15 dc = 7.76 mm The nominal diameter (d) of the stud is given by, dc 7.76 = 9.7 or 10 mm = 0.8 0.8 The diameter of the circular end of the rocker arm (D3) and its depth (t3) are calculated by the following relationships: d= D3 = 2d = 2(10) = 20 mm t3 = 2d = 2(10) = 20 mm Part 7: Design of valve spring Assumptions (i) The spring index is (ii) The stiffness of spring is 10 N/mm (iii) Permissible torsional shear stress for the spring wire is 300 N/mm2 (iv) Modulus of rigidity for the spring wire is 84 ¥ 103 N/mm2 (v) Total gap between consecutive coils, when the spring is compressed by maximum force, is 15% of maximum compression Step I Maximum force on spring The initial spring force Pi is calculated as, Pi = 110.84 N The maximum force on spring (Pmax.) is given by, Pmax = Pi + kd = 110.84 + 10 (27) = 380.84 N (d = h = 27 mm) Step II Wire diameter The Wahl factor is given by, 4C - 0.615 4(8) - 0.615 K= + = + = 1.184 4C - C 4(8) - Mean coil diameter Step V Number of active turns (84 ¥ 103 )(6) Gd = = 12.3 or 13 8D k 8(48)3 (10) Total number of turns For square and ground ends Nt = N + = 13 + = 15 Step VI Maximum compression of spring d max = Pmax D3 N Gd = 8(380.84)(48)3 (13) (84 ¥ 103 )(6) = 40.24 mm Step VII Solid length of spring Solid length = Nt d = 15 (6) = 90 mm Step VIII Free length of spring Free length = solid length + dmax + 0.15 dmax = 90 + 40.24 + 0.15 (40.24) = 136.28 mm Step IX Pitch of coils free length 136.28 = ( N t - 1) (15 - 1) = 9.73 mm Pitch of coils = Part 8: Design of cam The diameter of camshaft (D¢) is obtained by the following empirical relationship: D¢ = 0.16D + 12.5 where, D = cylinder bore (mm) D¢ = 0.16D + 12.5 = 0.16 (250) + 12.5 = 52.5 or 55 mm The base circle diameter of the cam is at least mm more than the camshaft diameter Base circle diameter of cam = 55 + = 60 mm The diameter of the roller is calculated in the design of the forked arm Design of IC Engine Components Displacement diagram The displacement diagram is shown in Fig 25.44 The step by step approach to construct this diagram is as follows: Roller diameter = 50 mm Roller width = l2 = 25 mm Cam width = roller width = 25 mm Lift of valve = 27 mm Fig 25.44 921 Displacement Diagram (i) Draw a horizontal line OY It represents the angular rotation of the cam when the valve opens, i.e., 53.5° It is divided into two equal parts—OX and XY The line OX indicates the constant acceleration phase (26.75°) and line XY represents the constant deceleration phase (26.75°) (ii) Divide lines OX and XY each into four equal parts The total of eight parts are shown by numbers 1, 2, 3, …, Each part represents (53.5º/8) or 6.6875º of cam rotation (iii) Draw a vertical line YH equal to the valve lift, i.e., 27 mm (iv) Draw ordinates through points 1, 2, 3, ……, (v) Draw a vertical line XZ equal to the valve lift (i.e., 27 mm) Divide the line XZ into eight equal parts They are shown by points a, b, c, …, h Therefore, each part represents (27/8) or 3.375 mm of the valve lift (vi) Join lines Oa, Ob, Oc, Od that intersects the ordinates through 1, 2, and at points A, B, C, and D respectively (vii) Also, join lines Hd, He, Hf, and Hg that intersect the ordinates through 4, 5, and at points D, E, F, and G respectively (viii) Draw a smooth curve passing through points O, A, B, C and D It represents the parabolic curve for the constant acceleration phase (ix) Similarly, draw a smooth curve passing through points D, E, F, G, and H It represents the parabolic curve for the constant deceleration phase Cam profile The profile of the cam is shown in Fig 25.45 The step by step approach to construct this profile is as follows: (i) Draw a base circle with O1 as centre and radius equal to 30 mm (ii) Draw a prime circle with O1 as centre and radius equal to (radius of base circle + radius of roller), i.e., (30 + 25) or 55 mm (iii) Draw angle –OO1H equal to 53.5º It represents the angular rotation of cam when the valve opens (iv) Divide the angle –OO1H (53.5º) into eight equal parts Therefore, each part represents (53.5º/8) or 6.6875º of cam rotation The eight parts are shown by angles –O O11, –1O1 2, –2 O13, etc 922 Design of Machine Elements Fig 25.45 Cam Profile (v) Join points 1, 2, 3, etc., with the centre O1 and extend the radial lines beyond the prime circle as shown in Fig 25.45 (vi) Mark the distances 1A, 2B, 3C,… etc., from the displacement diagram shown in Fig 25.44, on the extension of radial lines beyond the prime circle (vii) Draw a smooth curve passing through points O, A, B, C, D, E, F, G, and H This curve is called the ‘pitch curve’ (viii) Draw circles with radii equal to the radius of the roller (25 mm) and centres at points O, A, B, C, D, E, F, G, and H (ix) The profile of the cam is a curve drawn tangential to these circles at the bottom as shown in Fig 25.45 This curve indicates the cam profile when the valve is open Only half the profile is drawn, but it is symmetrical about the line O1H Short-Answer Questions 25.1 What are the functions of engine cylinder? 25.2 What are the cooling systems for engine cylinders? Where you use them? 25.3 What are the advantages of cylinder liner? 25.4 What are dry and wet cylinder liners? 25.5 What are the desirable properties of cylinder materials? 25.6 Name the materials used for engine cylinder 25.7 What you understand by ‘bore’ of cylinder? 25.8 What are the functions of piston? 25.9 What are the design requirements of piston? 25.10 Name the materials used for engine piston 25.11 What are the advantages and disadvantages of aluminium piston over cast iron piston? 25.12 Why is piston made lightweight? 25.13 Name two criteria for calculating the thickness of piston head Design of IC Engine Components 25.14 Why is piston clearance necessary? What is its usual value? 25.15 What are the functions of piston ribs? 25.16 What is the function of the cup on piston head? 25.17 What are the functions of compression piston rings? 25.18 What are the functions of oil scraper rings? 25.19 Name the materials used for piston rings 25.20 Why are more number of thin piston rings preferred over small number of thick rings? 25.21 Name two design criteria for piston pin 25.22 How is piston pin secured to piston? 25.23 Why is piston pin located at or above the middle of the skirt length? 25.24 What is the function of connecting rod? 25.25 What is the manufacturing method for connecting rod? 25.26 Name the materials used for connecting rod 25.27 What are the lubricating methods for bearings at small and big ends of the connecting rod? 25.28 What are the forces acting on the connecting rod? 25.29 Why are connecting rods made of I sections? 25.30 What is the force on bolts of big end of connecting rod? 25.31 What is the difference between centre and overhung crankshafts? 25.32 Where you use overhung crankshafts? 25.33 Where you use centre crankshafts? 25.34 What is the main advantage of overhung crankshafts? 25.35 Name the materials for crankshafts 25.36 What is the manufacturing method for crankshaft? 25.37 When you use push rod? 25.38 Why is the design of exhaust valve more critical than that of an inlet valve? 25.39 Why is the area of inlet valve port more than that of an exhaust valve? 25.40 Why inlet and exhaust valves have conical heads and seats? 25.41 What is the function of rocker arm? 25.42 Why is rocker arm made of I section? 25.43 Name the materials for rocker arm 25.44 What is tappet? What is the stress in tappet? 923 25.45 What is the purpose of valve spring? 25.46 What is the criterion for design of push rod? Problems for Practice 25.1 The cylinder of a four-stroke diesel engine has the following specifications: Brake power = kW Speed = 800 rpm Indicated mean effective pressure = 0.3 MPa Mechanical efficiency = 80% Determine the bore and length of the cylinder liner [D = 118 mm (116.75); L = 204 mm (203.55)] 25.2 The cylinder of a four-stroke diesel engine has the following specifications: Cylinder bore = 150 mm Maximum gas pressure = MPa Allowable tensile stress = 50 N/mm2 Determine the thickness of cylinder wall Also, calculate the apparent and net circumferential and longitudinal stresses in cylinder wall [t = 10 mm (8.5); sc = 22.5 N/mm2; s1 = 10.55 N/mm2; (sc)net = 19.86 N/mm2; (s1)net = 4.93 N/mm2] 25.3 The bore of a cylinder of the four-stroke diesel engine is 120 mm The maximum gas pressure inside the cylinder is limited to MPa The cylinder head is made of cast iron and allowable tensile stress is 40 N/mm2 Determine the thickness of cylinder head The studs, which are made of steel, have allowable stress as 50 N/mm2 Calculate (i) number of studs, (ii) nominal diameter of studs, and (iii) pitch of studs [th = 16 mm (15.27); z = 6; d = 18 mm (17.33); pitch = 91.11 mm] 25.4 The following data is given for a four-stroke diesel engine: Cylinder bore = 100 mm Length of stroke = 125 mm Speed = 2000 rpm Brake mean effective pressure = 0.65 MPa Maximum gas pressure = MPa 924 Design of Machine Elements Fuel consumption = 0.25 kg per BP per h Higher calorific value of fuel = 42 000 kJ/kg Assume that 5% of the total heat developed in the cylinder is transmitted by the piston The piston is made of grey cast iron and the permissible tensile stress is 37.5 N/mm2 (k = 46.6 W/m/°C) The temperature difference between the centre and edge of the piston head is 220°C (i) Calculate the thickness of the piston head by strength consideration (ii) Calculate the thickness of the piston head by thermal consideration (iii) Which criterion decides the thickness of the piston head? (iv) State whether the ribs are required (v) If so, calculate the number and thickness of piston ribs (vi) State whether a cup is required in the top of piston head (vii) If so, calculate the radius of the cup [(i) 15.81 mm (ii) 12.05 mm (iii) strength (th= 16 mm) (iv) yes (v) ribs of mm thickness (vi) yes (vii) 70 mm] 25.5 The following data is given for the piston of a four-stroke diesel engine: Cylinder bore = 100 mm Material of piston rings = Grey cast iron Allowable tensile stress = 90 N/mm2 Allowable radial pressure on cylinder wall = 0.035 MPa Thickness of piston head = 16 mm Number of piston rings = Calculate: (i) radial width of piston rings; (ii) axial thickness of piston rings; (iii) gap between the free ends of the piston ring before assembly; (iv) gap between the free ends of the piston ring after assembly; (v) width of top land; (vi) width of ring grooves; (vii) thickness of piston barrel; and (viii) thickness of barrel at open end [(i) 4(3.42) mm (ii) mm (iii) 15 mm (iv) 0.3 mm (v) 18 mm (vi) 2.5 mm (vii) 12 (11.9) mm (viii) mm] 25.6 The following data is given for the piston of a four-stroke diesel engine: Cylinder bore = 100 mm Maximum gas pressure = MPa Allowable bearing pressure for skirt = 0.45 MPa Ratio of side thrust on liner to maximum gas load on piston = 0.1 Width of top land = 18 mm Width of ring grooves = 2.5 mm Total number of piston rings = Axial thickness of piston rings = mm Calculate: (i) length of skirt; and (ii) length of piston [(i) 87.27 mm (ii) 125 (124.77) mm] 25.7 The following data is given for the piston of a four-stroke diesel engine: Cylinder bore = 100 mm Maximum gas pressure = MPa Bearing pressure at small end of connecting rod = 25 MPa Length of piston pin in bush of small end = 0.45 D Mean diameter of piston boss = 1.4 ¥ outer diameter of piston pin Allowable bending stress for piston pin = 140 N/mm2 Calculate: (i) outer diameter of piston pin; (ii) inner diameter of piston pin; (iii) mean diameter of piston boss; and (iv) check the design for bending stresses [(i) 35 (34.91) mm (ii) 20 (21) mm (iii) 50 (49) mm (iv) 130.53 N/mm2] 25.8 Determine the dimensions of cross-section of the connecting rod, illustrated in Fig 25.14, for a diesel engine with the following data: Cylinder bore = 100 mm Length of connecting rod = 320 mm Maximum gas pressure = 2.45 MPa Factor of safety against buckling failure = [t = (5.5) mm] 25.9 Determine the dimensions of small and big end bearings of the connecting rod for a diesel engine with the following data: Cylinder bore = 100 mm Maximum gas pressure = 2.45 MPa (l/d) ratio for piston pin bearing = 1.5 (l/d) ratio for crank pin bearing = 1.4 Design of IC Engine Components Allowable bearing pressure for piston pin bearing = 15 MPa Allowable bearing pressure for crank pin bearing = 10 MPa [dp = 30 (29.24) mm lp = 45 mm dc = 38 (37.07) mm lc = 54 (53.2) mm] 25.10 The following data is given for the cap and bolts of the big end of the connecting rod: Engine speed = 1500 rpm Length of connecting rod = 320 mm Length of stroke = 140 mm Mass of reciprocating parts = 1.75 kg Length of crank pin = 54 mm Diameter of crank pin = 38 mm Permissible tensile stress for bolts = 120 N/mm2 Permissible bending stress for cap = 120 N/mm2 Calculate the nominal diameter of bolts and thickness of cap for the big end [d = mm (dc = 4.42 mm), tc = (5.49) mm] 25.11 The following data is given for a connecting rod: Engine speed = 1500 rpm Length of connecting rod = 320 mm Length of stroke = 140 mm Density of material = 7830 kg/m3 Thickness of web or flanges = mm Assume the cross-section illustrated in Fig 25.14 For this cross-section, Ê 5t ˆ Ê 419 ˆ t and y = ÁË ˜¯ A = 11t2 I xx = Á ˜ Ë 12 ¯ Calculate whipping stress in connecting rod [11.66 N/mm2] 25.12 The following data is given for the centre crankshaft of a single-cylinder vertical engine: Cylinder bore = 150 mm (L/r) ratio = 4.75 Maximum gas pressure = MPa Length of stroke = 200 mm Weight of flywheel cum belt pulley = 3.5 kN Total belt pull = 1.8 kN Allowable bending stress = 75 N/mm2 Allowable compressive stress = 75 N/mm2 925 Allowable shear stress = 40 N/mm2 Allowable bearing pressure = 10 MPa The main bearings are 350 mm apart and the third bearing is 400 mm apart from the main bearing on its side The belts are in the horizontal direction Consider the case of the crank at the top dead centre position and subjected to maximum bending moment Assume [(l/d) ratio = 1] for crank pin and calculate: (i) vertical and horizontal components of reactions at three bearings; (ii) Diameter and length of crank pin; (iii) width and thickness of crank web; (iv) total compressive stress in crank web; and (v) diameter of the shaft under flywheelcum belt pulley [(i) (R1 )v = (R2 )v = 35342.92 N;(R¢2 )v = (R¢3 )v = 1750 N; (R¢2 )h = (R¢3 )h = 900 N (ii) dc = 95(94.35) mm and lc = 95 mm (iii) t = 70(66.5) mm and w = 110(108.3) mm (iv) 40.98 N/mm2 (v) ds = 40 (37.67) mm] 25.13 Assume the data of Example 25.12 for the centre crankshaft of a single cylinder vertical engine The torque on the crankshaft is maximum when the crank turns through 25º from top dead centre and at this position the gas pressure inside the cylinder is 3.75 MPa Consider this position of the crank and the calculate: (i) components of force on crank pin; (ii) vertical and horizontal components of reactions at three bearings; (iii) diameter and length of the crank pin; (iv) diameter of shaft under flywheel; (v) diameter of shaft at the juncture of the right-hand crank web; (vi) maximum compressive stress in righthand crank web; and (vii) maximum reaction at main bearing and bearing pressure [(i) Pt = 33 366.19 N and Pr = 57 559.7 N (ii) (R1 )v = (R2 )v = 28779.85 N; (R1 )h = (R2 )h = 16 683.10 N; (R¢2 )v = (R¢3 )v = 1750 N; (R¢2 )h = (R¢3 )h = 900 N (iii) dc = lc = 95 (87.74) mm (iv) ds = 80 (75.35) mm (v) ds1 = 85 (83.3) mm (vi) (sc )max = 52.92 N/mm2 (vii) R2 = 32 231.2 N and pb = 4.46 N/mm2] 926 Design of Machine Elements 25.14 Design an exhaust valve for a horizontal diesel engine using the following data: Cylinder bore = 250 mm Length of stroke = 300 mm Engine speed = 600 rpm Maximum gas pressure = MPa Seat angle = 45° Mean velocity of gas through port = 50 m/s Allowable bending stress for valve = 50 N/mm2 Calculate: (i) diameter of the valve port; (ii) diameter of the valve head; (iii) thickness of the valve head; (iv) diameter of the valve stem; and (v) maximum lift of the valve [(i) 90 (86.6) mm (ii) 101 mm (iii) 11(10.69) mm (iv) 20 mm (17.6 to 22.25) (v) 31.82 mm] 25.15 Design a rocker arm for the exhaust valve of a four-stroke engine using the following data: Effective length of each arm = 150 mm Angle between two arms = 150° Diameter of valve head = 56 mm Lift of valve = 20 mm Mass of valve = 0.3 kg Engine speed = 500 rpm Back pressure when the exhaust valve opens = 0.35 MPa Maximum suction pressure = 0.025 MPa (below atmosphere) (l/d) ratio for fulcrum and roller pins = 1.25 Thickness of phosphor bronze bushings = mm Permissible bending stress = 70 N/mm2 Permissible shear stress = 42 N/mm2 Permissible compressive stress = 50 N/mm2 Permissible bearing pressure = MPa The valve opens 39° before the outer dead centre and closes 8° after the inner dead centre The motion of the valve is SHM without dwell in the fully opened condition The proportions of cross-section of the rocker arm are shown in Fig 25.39(b) Calculate: (i) acceleration of the valve; (ii) total force on the rocker arm; (iii) diameter and length of the fulcrum pin; (iv) bending stress in cross-section of the rocker arm at the fulcrum pin; (v) diameter and length of the roller pin; (vi) bending stress in the roller pin; (vii) dimensions of cross-section of the rocker arm; and (viii) nominal diameter of the tappet [(i) 68.35 m/s2 (ii) 944.14 N (iii) 20(17.08) and 25 mm (iv) 29.28 N/mm2 (v) 15(12.29) and 20(18.75) mm (vi) 11.87 N/mm2 (vii) t = 6(5.22) mm (viii) 6(5.83) mm] 25.16 Design a valve spring for the exhaust valve of a four-stroke engine using the following data: Diameter of valve head = 56 mm Lift of valve = 20 mm Maximum suction pressure = 0.025 MPa (below atmosphere) Stiffness of spring = 10 N/mm Spring index = Permissible torsional shear stress for spring wire = 300 N/mm2 Modulus of rigidity = 84 ¥ 103 N/mm2 Total gap between consecutive coils, when the spring is subjected to maximum force, can be taken as 15% of maximum compression Calculate: (i) maximum force on the spring; (ii) wire diameter; (iii) mean coil diameter; (iv) number of active turns; (v) total number of turns; (vi) free length of the spring; and (vii) pitch of coils [(i) 261.58 N (ii) (4.59) mm (iii) 40 mm (iv) 11(10.25) (v) 13 (vi) 97.27 mm (vii) 8.11 mm] References Alexandrov, M.P., Materials Handling Equipment, MIR Publishers, 1981 Alger J.R.M and C.V Hays, Creative Synthesis in Design, Prentice-Hall, 1964 American Chain Association, ‘Chains for Power Transmission and Materials Handling’ (Marcel Dekker) Bedford J.E., Form in Engineering Design, Oxford, 1954 Birmingham R., G Cleland, R Driver, D Maffin, Understanding Engineering Design, Prentice-Hall, 1998 Black P.H and O.E Adams, Jr, ‘Machine Design’ (McGraw-Hill, 1985) Blake A., Design of Curved Members for Machines, Industrial Press, 1966 Blodgett O.W., Design of Weldments, The James Lincoln Arc Welding Association, USA, 1972 Brownwell L.E and E.H Young, Process Equipment Design-Vessel Design, John Wiley, 1959 10 Buckingham E., Analytical Mechanics of Gears, McGraw-Hill, 1949 11 Buckingham E., Manual on Gear Design, A.G.M.A and Industrial Press, 1959 12 Burghardt M.D., Introduction to Engineering Design and Problem Solving, McGraw-Hill, 1999 13 Burr A.H and J.B Cheatham, Mechanical Analysis and Design, Prentice-Hall, 1997 14 Cameron A., Principles of Lubrication, Longman, 1966 15 Chironis N.P, Spring Design and Applications, McGraw-Hill, 1961 16 Chuse R., Unfired Pressure Vessels, McGraw-Hill, 1960 17 Chuse R., Pressure Vessels—The A.S.M.E Code Simplified, McGraw-Hill, 1977 18 Clauser H.R., Industrial and Engineering Materials, McGraw-Hill, 1975 19 Connor J.J.O and J Boyd, Standard Handbook of Lubricating Engineers, McGraw-Hill 20 Dieter G.E., Engineering Design—A Materials and Processing Approach, McGraw-Hill, 1987 21 Dixon J.R., Design Engineering-Inventiveness, Analysis and Decision Making, McGraw-Hill 1966 22 Dudley D.W., Practical Gear Design, McGraw-Hill, 1954 23 Dudley D.W., Gear Handbook, McGraw-Hill, 1962 24 Dobrovolsky V., K Zablonsky, S Mak, A Radchik, L Erlikh, Machine Elements—A Textbook, MIR Publishers, 1977 25 Eide A.R., R.D Jenison, L.H Mashaw, and L.L Northup, Introduction to Engineering Design, McGraw-Hill 1998 928 Design of Machine Elements 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 Ellinger J.H., Design Synthesis, John Wiley, 1968 Faires V.M., Design of Machine Elements, Macmillan, 1965 Flinn R.A and Trojan P.K., Engineering Materials and their Applications, Houghton Mifflin 1993 Frost N.E K.J Marsh, and L.P Pook, Metal Fatigue, Oxford, 1974 Fuller D.D., Theory and Practice of Lubrication, John Wiley, 1984 Gasson P.C and Mied D.C.M., Theory of Design, B.T Batsford, 1974 Granet I., Modem Materials Science, Prentice-Hall, 1980 Gray T.G.F and J Spence, Rational Welding Design Butterworths, 1982 Green R.E and C.J McCauley, Machinery’s Handbook, Industrial Press 1996 Griffiths A., Fasteners Handbook, Morgan-Grampian Gunther R.C., Lubrication, Bailey Brothers, 1971 Hahn G.J and S.S Shapiro, Statistical Models in Engineering, John Wiley, 1967 Hailing J., Principles of Tribology, Macmillan, 1975 Hamrock B.J., S.R Schmid, and B Jacobson, Fundamentals of Machine Elements, McGraw-Hill, 2005 Harris T.A., Rolling Bearing Analysis, John Wiley, 1966 Harvey F.F., Pressure Vessel Design, Von Nostrand, 1963 Hindhede U., J.R Zimmerman, R.B Hopkins, R.J Erisman, C.H Wendell, and J.D Long, Machine Design Fundamentals—A Practical Approach, Prentice-Hall, 1983 Horger O.J., A.S.M.E Handbook—Metal Engineering Design, McGraw-Hill Immer J.R., Materials Handling, McGraw-Hill, 1953 Jenson J.E., Forging Industry Handbook, Forging Industries Association, USA, 1970 Johnson R.C., Mechanical Design Synthesis with Optimization Applications, Von Nostrand-Reynold, 1971 Jones J.C., Design Methods—Seeds of Human Future, John Wiley, 1971 Juvinall R.C., Engineering Considerations of Stress, Strain and Strength, McGraw-Hill, 1967 Juvinall R.C and K.M Marshek, Fundamentals of Machine Components Design, John Wiley, 1991 Kenney J.F and E.S Keeping, Mathematics of Statistics, Von Nostrand, 1965 Mayer E., Mechanical Seals, Iliffe Books, 1969 Merrit H.E., Gear Engineering, Pitman, 1971 Michalec G.W., Precision Gearing—Theory and Practice John, Wiley, 1966 Morrison D., Engineering Design—The Choice of Favorable Systems, McGraw-Hill, 1968 Mott L.M., Machine Elements in Mechanical Design, Prentice Hall, 1999 Movnin M and D Goltziker, Machine Design, MIR Publishers, 1975 Neale N.J., Tribology Handbook, Butterworth, 1973 Niemann G., Machine Elements—Design Calculations in Mechanical Engineering, Springer Verlag, 1963 Norton R.L., Design of Machinery, Tata-McGraw-Hill, 2005 Nortan R.L., Machine Design—An Integrated Approach, Pearson Eduacation, 2000 Orlov P., Fundamentals of Machine Design, (Five volumes), MIR Publishers, 1976 Orthwein W.C., Clutches and Brakes—Design and Selection, Marcel Dekker, 1986 Orthewein W.C., Machine Components Design, West Publishing, 1996 Osgood C.C., Fatigue Design, Wiley Interscience, 1970 Palmgren A., Ball and Roller Bearing Engineering, SKF Industries, 1959 Peck H., Ball and Parallel Roller Bearings—Design Applications, Pitman, 1971 References 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 929 Phelan R.M., Fundamentals of Mechanical Design, Tata McGraw-Hill, 1975 Peterson R.E., Stress Concentration Design Factors, John Wiley, 1959 Petroski H., Invention by Design, Harvard University, 1996 Plaines D., Cast Metals Handbook, American Foundrymen’s Association Redford G.D., Mechanical Engineering Design—An Introduction, Macmillan, 1973 Redford G.D and D.B Richardson, The Management of Production, Macmillan, 1972 Reshetov D.N., Machine Design, MIR Publishers, 1978 Roark R.I., Formulas for Stress and Strain, McGraw-Hill, 1965 Rudenko N., Materials Handling Equipment, MIR Publishers, 1969 Rudolf L., Brake Design and Safety, Society of Automotive Engineers, 1992 Ruiz C and F Koenigsberger, Design for Strength and Production, Macmillan, 1970 Sabroff A.M., F.W Boulger, and H.J Henning, Forging Materials and Practices, Reinhold, 1968 Schlenker B.R., Introduction to Materials Science, John Wiley, 1969 Boresi A.P and O.M Sidebottom, (Seely FB and Smith J.O.), Advanced Mechanics of Materials, John Wiley, 1984 Shaw M.C and E.F Macks, Analysis and Lubrication of Bearings, McGraw-Hill, 1949 Shigley J.E and C.R Mischke, Standard Handbook of Machine Design, McGraw-Hill, 1986 Shigley J.E and C.R., Mechanical Engineering Design, McGraw-Hill, 2001 Sines G and J.L Waisman, Metal Fatigue, McGraw-Hill, 1959 Spotts M.F, Mechanical Design Analysis, Prentice-Hall, 1964 Spotts M.F and T.E Shoup, Design of Machine Elements, Prentice-Hall, 1998 Timoshenko S.P., Strength of Materials: Part II—Advanced Theory and Problems, Von Nostrand, 1966 Ullman D.G., The Mechanical Design Process, McGraw-Hill, 1997 Verman L.C., Standardization—A New Discipline, Affiliated East-West, 1973 Wahl A.M., Mechanical Springs, McGraw-Hill, 1963 Wieser P.F., Steel Castings Handbook, Steel Founder’s Society of America, 1980 Wilcock D.F and E.R Booser, Bearing Design and Applications, McGraw-Hill, 1957 Woolman J and R.A Mottram, The Mechanical and Physical Properties of British Standard EN Steels, (Three volumes), The British Iron and Steel Research Association, Pergamon Press, 1968 Index A additives 639 Aesthetic considerations 14 Aluminium alloys 39 angular contact 566 area compensation method 792 Area moment method 382 ASME code 334 autofrettage 775 B back stop 492 backlash 658 Barlow’s equation 773 Belleville 441 Belt pulleys 517, 535 Belt tensioning 540 Belts drives 503, 504, 510 Belts 501, 502, 509 Belts 540 bending stresses 290 Bevel gears 712, 714, 721, 722, 723, 727 Birnie’s equation 772 Boiler shell joint 311 Boiler shell joints 318 Bolted joint 233, 242, 254, 255, 257 Brakes 475, 476, 480, 482, 484, 490, 491, 492, 493 Buckingham equation-dynamic lcad 676 Buckingham equation-wear 678 Buckingham’s equation-dynamic load 702 Buckingham’s equation-dynamic load 723 Buckingham’s equation-wear 703 Buckingham’s equation-wear 722 Buckling of columns 807 butt joint 274 C Case hardening 37 Cast iron 26 Cast steel 38 Castigliano’s theorem 380 Casting design 57 caulking and fullering 307 centre cranksshaft 881 centrifugal 465 Ceramics 44 Chain drives 544 Chain sprockets 551 Chains 545, 546, 549, 550, 555, 562 Charles Renard 11 circular base 242 circumferential 318 clamp 359 Clavarinds equation 772 closely coiled 394 Clutches 449, 450, 456, 461, 465 code 10 coefficient of fluctuations of energy 752 coefficient of speed fluctuations 752 Cold working 62 compound 214 compound 775 concentric 425 Index Concurrent engineering 17 Cone 461 conne 858 connecting rod 867 construction 634 construction 783 constructions 798 Copper alloys 41 Cotter joint 85 Couplings 357, 359, 362, 368 creep 509 Creep 50 crossed 504 crossed 708 Cumulative damage in fatigue 166 Curved beans 130 Cyclic stresses fluctuating stresses 149 repeated stresses 150 reversed stresses 150 Cylinders 768, 770, 771, 772, 773, 775, 779, 844 cylinder liners 844 cylindrical roller 566 D deep groove 565 Design synthesis DFMA 64 Dic casting alloys 43 differential band 491 differential 214 disk 493 domed heads 786 double enveloping 732 double 706 drums 806 dynamic load capacity 571 E Eccentric axial load 83 eccentric load 233 eccentric load 321 eccentric loading 285 efficiency 307 elastic analysis 254 end styles 396 Endurance limit 152 energy equation 467 931 Engine components 844, 853, 856, 858, 867, 881, 892, 903, 904, 906, 910, 911 equivalent dynamic load 571 Ergonomic considerations 15 Euler’s equation 807 F Factor of safety 77 failures 306 failures 596 failures 641 falure 550 fatigue diagram 406 Fatigue failure 151 feather 349 Fibre-reinforced plastics 48 fillet joint 275 Fits 66 flat 501 flat 517 flexible shaft 346 flexible 368 fluctuating load 257 fluctuating stresses 296 Flywheel 750, 752, 753, 755, 756 Forging design 59 formative teeth 696 formative 714 Fracture mechanics 128 frequency distribution 814 frequency polygon 816 Friction materials 459 friction 738 G gaskets 779 gear blank 667 Gear drives 647 Gerber equation 174 Goodman diagrams 168 Goodman line 167 Graphical integration method 382 Greases 641 H Hard/soft gasket 255 head 301 Heat treatments 36 932 Index Helical gears 696, 702, 703, 706, 708 Henry Dreyfuss Herringbone gears 706 High cycle fatigue 154 histogram 816 hollow shaft 342 Hooke’s law 21 Hot working 62 hydrodynamic 601 hydrostatic 603 hypoid 712 I Impact stresses 180 interference 657 internal expanding 484 Internal gears 688 ISO dimension series 576 J Johnson’s equation 807 K Kennedy 352 Keys 347, 348, 349, 350, 352 Knuckle joint 94 Kuguel’s equality 157 L Lame’s equation 771 lateral rigidity basis 375 Law of gearing 649 lays 799 Leaves 117 Lewis equation 672 Lewis equation 702 Lewis equation 721 Lewis from factor 673 link 545 load factor 573 longitudinal 311 long-shoe block 480 Low cycle fatigue 153 lubricating oils 637 lubrication 555 lubrication 596 Lubrication 601, 603 lubrication 690 M Machine design definition basic procedure Machine elements basic requirements design procedure Machined components—design 61 Man-machine relationship 16 Manufacturing processes 55 Material selection 51 materials 305 materials 401 materials 635 materials 741 materials 750 Mckee’s investigation 607 mean 817 Mechanical drives 646 Mechanical properties 23 Miner’s equation 166 Modes of failure 76 More R.R 152 mountings 597 muff 357 multi-disk 456 multi-leaf 437 multiple threaded 187 N Natural tolerances 825 needle 595 Newton’s law 605 nipping 439 normal curve 821 Notch sensitivity 154 O Oil seals 796 open 503 openings 791 Overseas standards P Peterson R.E 142 34 Index Petroff’s equation 606 piston 853 piston pin 858 piston rings 856 Plastics 45 plvoted block 482 polygonal effect 549 population combinations 823 Power screws 187, 190, 214, 216 Preferred numbers basic series 11 derived series 12 Principal stresses 104 probabilistic approach 830 probability 819 push rod 911 Q quarter-turn 510 R Raimondi-Boyd method 622 Rayleigh-Ritz equation 386 Recirculating ball 216 Reliability 829 Residual stresses 136 Reynold’s equation 619 ribbed-v belts 540 rigid 362 rimmed 755 Rivet 301 Rivet 305 Riveted joints 303, 306, 307, 321 rocker arm 906 roller 546 Rolling contact bearings 565, 566, 567, 569, 571, 573, 576, 595, 596, 597 round 501 Rubber 49 S saddle 347 SAE oils 640 Selective assembly 70 self aligning 567 self locking 190 self-energizing 476 Sequential design process 18 933 series and parallel 399 Shaft design 331, 333, 334, 342, 346, 375 sheaves 804 short-shoe block 475 Shot peening 443 side crankshaft 892 silent 562 simple band 490 Simultaneous design process 18 Single-plate 450 Sliding contact bearings 634 Sliding contact bearings 635, 637, 639, 640, 641 S-N curve 153 Soderberg line 167 solid disk 753 Sommer feld number 622 spiral 435 spiral 727 Splines 354 Spring index 395 Springs 393, 394, 396, 399, 401, 406, 425, 433, 435, 437, 439, 441 Spur gears 653, 656, 657, 658, 665, 667, 672, 673, 676, 678, 690 Square-jaw 449 standard deviation 817 Standard systems 653 standard variable 818 Standardization Standards 10 static load capacity 569 Statistical considerations 814, 816, 817, 818, 819, 821, 823, 825, 830 Steels alloy 32 designation 29 free cutting 32 plain carbon 30 strength basis 331 strength rating 742 Stress concentration 141 stresses 756 Stresses bending 81 compressive 80 direct shear 80 tensile 79 torsional shear 82 Stress-strain diagram 20 Stribeck’s equation 569 sunk 348 934 Index Surface roughness 73 Surge 432 symbols 297 T taper roller 567 testing 298 Theories of failure distortion energy 110 principal stress 107 shear stress 108 thermal considerations 745 Thermal stresses 135 thick 770 thick-film 601 thin 768 thin-film 603 thrust 567 Tolerances 65 tooth failures 665 torsion 433 torsional rigidity basis 333 torsional stresses 294 Traditional design methods craft evolution design by drawing trains 656 Tredgold’s approximation 714 types types 303 393 U Unfired pressure vessels 783, 786, 791, 792 V valve gear mechanism 903 Valves 904 valve spring 910 v-belts 502 velocity factor 676 v-grooved 535 Viscosity 604, 605 W Wahl factor 398 wear rating 744 Weighted point method 51 Welded assemblies—design 62 Welded joints 274, 275, 285, 290, 294, 296, 297, 298 Wiebull distribution 592 Wire ropes 798, 799, 804, 806 Whipping stresses 875 woodruff 350 Worm gears 732, 738, 741, 742, 744, 745