Applied Mechanical Design
Ammar Grous
Contents
Preface xiii
Introduction . xv
Chapter 1. Case Study-based Design Methodology . 1
1.1. Methodology for designing a project product 1
1.2. Main players involved in the design process 2
1.3. Conceptualization and creativity . 4
1.4. Functional analysis in design: the FAST method 4
1.4.1. Decision-support tools in design . 5
1.5. Functional specifications (FS) . 7
1.5.1. Operational functions, using the APTE method
or octopus diagram . 8
1.5.2. Linguistic (or syntactical) writing of the
functional specifications 10
1.6. Failure Mode Effects and Criticality Analysis . 10
1.7. PERT method 13
1.7.1. Logic of construction of the graph per level of operations 14
1.7.2. Statistical approach to the PERT diagram using the
Gamma distribution 16
1.8. The Gantt method (Henry Gantt’s graph, devised 1910) . 17
1.9. Principal functions of a product 20
1.10. Functional analysis in mechanical design . 21
1.10.1. Product cost in mechanical design . 22
1.10.2. Creation- and monitoring sheets in mechanical design . 22
1.11. Scientific writing on a project 28
1.11.1. Project process . 28
1.11.2. Development of the conceptual model . 29vi Applied Mechanical Design
1.11.3. Development (recap) on a spiral model 30
1.12. Esthetics of materials in mechanical design 30
1.13. Conclusion . 31
Chapter 2. Materials and Geometry in Applied Mechanical Design,
Followed by Case Studies . 33
2.1. Introduction to materials in design 33
2.2. Optimization of mass in mechanical design . 38
2.3. Case study of modeling based on the material–geometry couple 39
2.4. Geometry by standard sections in strength of materials 42
2.4.1. Choice of materials in design (airplanes and bikes) 46
2.4.2. Form factors ψ of some usual cross-sections . 49
2.4.3. Form factors in mechanical design . 50
2.5. Case study of design of multi-purpose items 51
2.6. Case study of superposed bimetallic materials . 55
2.7. Curving and incurvate elements by sweeping of sheet metals 58
2.7.1. Sensible choice of optimizing materials in Palmer micrometers 59
2.8. Conclusion 60
Chapter 3. Geometrical Specification of GPS and
ISO Products: Case Studies of Hertzian Contacts 63
3.1. Introduction 63
3.2. Dimensional and geometrical tolerances in design . 65
3.2.1. Case study of a bicycle wheel hub 67
3.3. Envelopes and cylinders under pressure (for R/e < 20) 72
3.4. Case study 76
3.5. Rotating cylinders with a full round cross-section: flywheel . 76
3.5.1. Materials used for flywheels with centrifugal effects . 78
3.6. Press fit and thermal effects through bracing 80
3.7. Case study applied to bolted tanks 83
3.8. Case studies applied to contact stresses (Hertz) in design 89
3.8.1. First case: sphere-to-sphere contact . 90
3.8.2. Second case: contact between two parallel cylinders . 93
3.9. Conclusion 96
Chapter 4. Design of Incurvate Geometries by Sweeping . 97
4.1. Introduction 97
4.2. Case studies 99
4.2.1. Case study 1: frame sweeping 99
4.2.2. Case study 2: frame sweeping 101
4.2.3. Case study 3: frame sweeping 104Contents vii
4.2.4. Case study 4: frame sweeping 106
4.2.5. Case study 5: example of a connecting rod of SAE 8650 109
4.2.6. Case study 6: swept double elbow 111
4.2.7. Case study 7: frame sweeping 113
4.3. Conclusion 115
Chapter 5. Principles for Calculations in Mechanical
Design: Theory and Problems. Strength of Materials
in Constructions 117
5.1. Essential criteria of constructions in design . 117
5.1.1. Stress intensification in shafts and beams 118
5.1.2. Homogeneous, solid, round sections 119
5.1.3. Homogeneous, solid, square sections with recessed section . 119
5.1.4. Homogeneous, hollow, square sections, with no
external variation 120
5.1.5. Homogeneous, solid, round sections with a shoulder
(shouldered shaft) . 121
5.1.6. Homogeneous, solid, rectangular or square sections,
with a groove 121
5.1.7. Homogeneous, hollow, round and flat sections
(pierced flat piece with an axle) . 122
5.1.8. Homogeneous, hollow, round sections (shaft with groove) . 122
5.2. Principles of calculations for constructions in design . 123
5.2.1. Example on stress intensifications 124
5.2.2. Case study on torsion angles . 126
5.2.3. Case study: Tresca and von Mises yield criteria 130
5.3. Pressurized recipients and/or containers . 133
5.4. Calculation principles and solution method for
compound loading 135
5.4.1. Case study: mechanical fit . 138
5.4.2. Case study of a profiled piece stressed under
conditions of elasticity . 143
5.5. Buckling of elements of machines, beams, bars, shafts
and stems 144
5.5.1. Case study: buckling of an I-beam according to
AISI specifications . 147
5.5.2. Case study: I-beams and U-beams, homogeneous
and isotropic . 149
5.6. Design of stationary and rotating shafts . 152
5.6.1. Design (dimensioning) of shafts subjected to rigidity 154
5.6.2. Case study 1, solution 1 156viii Applied Mechanical Design
5.6.3. Case study 2 with solution: shear, moments,
slope, elasticity deflection. Applied SOM in mechanics
and civil engineering 156
5.7. Power transmission elements: gear systems and pulleys . 159
5.7.1. Case study 159
5.7.2. Case study: statement of problem 2 . 161
5.7.3. Case study: statement of problem 3 . 163
5.8. Sizing and design of couplings 165
5.8.1. Design of a universal coupling, known as a Hooke
coupling . 167
5.9. Design of beams and columns . 170
5.9.1. Solved case study: bending and torsion of a shaft . 172
5.9.2. Case study 3: equivalent bending moment and ideal
moment on a shaft . 176
5.9.3. Case studies: maximum performance of pre-stressed
bi-materials . 177
5.9.4. Case study: deflection and buckling of elements
of machines . 178
5.10. Case studies using the Castigliano method . 180
5.11. Conclusion . 183
Chapter 6. Noise and Vibration in Machine Parts . 185
6.1. Noise and vibration in mechanical systems . 185
6.1.1. Aerodynamism of moving mechanical bodies . 188
6.2. Case study 1 . 189
6.2.1. Lightweight vehicles and trucks . 189
6.2.2. Case study 1 . 191
6.2.3. Case study of the rotor blade of a fire brigade helicopter 194
6.3. Vibration of machines in mechanical design 195
6.4. Case studies with a numerical solution 201
6.4.1. Case study: input parameters: M = 1; k = 1; φ0 = 1
and c = 2.25 . 201
6.4.2. Case study: system with free vibrations . 202
6.4.3. Case study: problem with solution and discussion 204
6.4.4. Case study: problem 3 with solution . 206
6.4.5. Case study: problem 2. Engine represented on two springs . 207
6.4.6. Case study based on a concrete problem with solution 212
6.5. Critical speeds of shafts in mechanical systems 215
6.5.1. Case study with solution and discussion 218
6.5.2. Method of approximation using the Dunkerley equations 222
6.5.3. Method of approximation using the Rayleigh–Ritz equation 223Contents ix
6.5.4. Method of approximation using the equations of the
rotation frequencies 224
6.5.5. Method for solving the function F(ωc): roots → (r0 and r1) . 224
6.6. Conclusion 225
Chapter 7. Principles of Calculations for Fatigue and Failure 227
7.1. Mechanical elements of failure through fatigue 227
7.2. Analysis of materials and sizing in applied design . 229
7.3. Sizing of pivot joints with bearings 232
7.3.1. Basic formulae for calculating lifetime . 233
7.3.2. Determination of the minimum viscosity necessary . 238
7.4. Faults of form and position of ranges on the operating
clearance fit 239
7.5. Friction and speed of bearings . 240
7.6. Sizing of bearing pivot joints and lifetime 241
7.7. Case study: statement of the problem 243
7.7.1. Internal clearance fit of bearings . 244
7.8. Biaxial stresses combined with shear for ductile materials
in concrete application 246
7.9. Fundaments of sizing in mechanical design. Soderberg equations
in fatigue of ductile materials 248
7.9.1. Application of Soderberg equations . 248
7.9.2. Stress intensification factors (SIFs) . 249
7.9.3. Case study 250
7.10. Welding and fatigue 253
7.10.1. Case study: calculation of resistance of weld joints in design . 254
7.10.2. Real-world case study: welded cross-shaped structure . 256
7.10.3. Case study: fracture mechanics and stresses . 261
7.10.4. Case study in fatigue fracture mechanics . 262
7.11. Limits of performance and of strength in the elastic domain 267
7.12. Proposed project: outboard motor for a small boat 269
7.13. Conclusion . 270
Chapter 8. Friction, Brakes and Gear Systems . 271
8.1. Friction, materials and design of assembled systems . 271
8.2. Buttressing of mechanical connections . 274
8.3. Case study: principles of calculations for brakes 279
8.3.1. Design of a double brake block by calculation . 281
8.3.2. Design of inner double-shoe block brake 282
8.3.3. Design of a band brake block . 284
8.3.4. Examples of principles of calculations for brake design,
with solutions 287x Applied Mechanical Design
8.3.5. Case study: hypothesis of the design of a
double-shoe brake . 289
8.3.6. Case study: hypothesis of the band brake whose drum
has a radius R (mm and in) 291
8.3.7. Case study: differential brake using a roller pressed
against a drum 292
8.3.8. Symmetrical shoe brake pressed against a drum with radius R . 294
8.4. Principles of calculations of a gear system or gear disc 298
8.4.1. Case study: principles of calculations for gear systems . 299
8.4.2. Analysis and choice of the dimensions of the cam gear system . 300
8.4.3. Sizing of a cam gear system and case study 301
8.4.4. Case study: principles of calculations for gear systems
in design . 304
8.4.5. Conical gear system 307
8.5. Flywheels and rims (discs and rims) . 309
8.5.1. Flywheel for a solid disc 311
8.5.2. Flywheel system with rim and discs (internal and external)
made of cast iron 312
8.5.3. Flywheel: numerical applications. Hypothesis II . 314
8.6. Conclusion 315
Chapter 9. Sizing of Creations 317
9.1. Elastic machine elements and bolted assemblies 317
9.2. Dimensions (sizing) of bolted assemblies 321
9.3. Fatigue, shocks and endurance of bolted assemblies 324
9.4. Springs in mechanical design . 325
9.4.1. Materials and geometry of compression springs 326
9.4.2. Case study of helical springs in mechanical design 338
9.4.3. Case study of a spring in a rocker switch 340
9.4.4. Verification of buckling of compression spring 344
9.5. Simple blade and spiral blade springs 345
9.6. Main expressions of design calculations for Belleville washers . 346
9.7. Power transmission. Case study: hoist 347
9.7.1. Power transmission and simple drum brake 348
9.8. Case study on couplings 350
9.8.1. Case study: analysis in design of brake elements . 351
9.9. Case study on power transmission: external spring clutch 352
9.9.1. Case studies: power transmission. Bolted assembly . 353
9.9.2. Computer-assisted design of a hub (bolted assembly) 355
9.10. Couplings and machine elements subjected to stress at high speeds 356
9.10.1. Determination of the error in position of the shaft 357
9.10.2. Determination of the output velocity of the shaft 358Contents xi
9.11. Design of spring rings . 359
9.12. Principle of calculations for a Belleville washer: case study 361
9.13. Determination of the pressing moment for a bolted assembly . 362
9.14. Power transmission by epicyclic gear system . 363
9.15. Conclusion . 365
Chapter 10. Design of Plastic Products 367
10.1. Calculations for the design of plastic parts . 367
10.1.1. Mechanical parameters used during traction tests 368
10.2. Jointing of a ball bearing in a metal casing 370
10.3. Cylindrical clip of PP (e.g. blinds): force exerted . 371
10.3.1. Spherical clip of a PP: force exerted 374
10.4. Types of clip fitting: counter-cylindrical cantilever . 376
10.4.1. Conical cantilever . 378
10.4.2. Short cantilever 378
10.5. Configuration of strips: two-dimensional spline interpolation . 381
10.5.1. Graphs of the model of the original surface 383
10.6. Press assembly . 383
10.7. Reduction of stress relaxation: bolts and self-tapping screws 385
10.8. Case study: piping link 386
10.9. Assembly by forced jointing . 388
10.10. Stress and thermal swelling in assembled materials 391
10.10.1. Stress intensifications 393
10.11. Capacity and reliability of roller bearings (plastic and otherwise) 395
10.12. Safe stress of the appropriate material for a plastic clutch system 396
10.13. Case study: plastic ball bearings 398
10.13.1. Calculation of the lifetime of roller bearings 401
10.14. Limits of performances of polymer design 401
10.15. Case study: fan with plastic blades 402
10.16. Conclusion . 404
Chapter 11. Mechanical Design Projects . 405
11.1. Proposed projects in mechanical design 405
11.2. Case studies of hoisting and handling devices . 405
11.3. Projects design proposal for a lifting winch 406
11.3.1. Case study: parameters in sketching a lifting hook . 408
11.3.2. Principles of calculations of the resistance of a lifting hook 409
11.3.3. Calculation and design (choice) of the round-wire coil spring . 412
11.4. Calculation and design of a bolted assembly . 414
11.5. Yield of power transmission of a screw mechanism . 417
11.5.1. Calculations of stresses on the threads of a screw mechanism . 419xii Applied Mechanical Design
11.5.2. Calculations of stresses at the root of the thread in a
screw mechanism 420
11.5.3. Case study: numerical applications . 420
11.6. Project 2: case studies: scooter 424
11.6.1. Presentation of the main parts 426
11.7. Project 3: dental hygiene dummy 428
11.7.1. Support clamped to the lab bench in the dental
hygiene department 435
11.7.2. Case studies of a complete block and crank link . 438
11.7.3. Explanatory photographic definition of the final product 439
Conclusion 443
Appendix . 445
Bibliography . 467
Index .
Index
A
airplane, 39, 191, 192
amplitude, 197–199, 206, 212–215,
221, 324
approximation, 221–225, 254, 313,
314
APTE, 7–9, 432
assemblies,
B
Bayes, 6
beam(s),
bearing,
bending,
blade, 194, 195, 326, 327, 345, 403
bolts,
bracing, 65, 72, 80–83
brakes,
buckling,
buttressing, 274, 275, 277
C
cam, 299–304, 368
cantilever, 157, 376–378, 399
capacity, 233, 234, 300, 302, 395
clamp, 113, 115, 436, 437
clearance fit,
clip, 111–113, 371–378, 387
clipping,
coefficient,
Applied Mechanical Design, First Edition. Ammar Grous.
ISTE Ltd 2018. Published by ISTE Ltd and John Wiley & Sons, Inc.472 Applied Mechanical Design
column,
compression,
connection,
connecting rod, 109, 117
contact,
coupling, 55, 165–168, 350, 353–
358, 380
cracks, 327
creep, 383–387
criteria,
speed, 215
criticality, 10, 11, 12
cylinder, 75, 76, 84, 85, 89, 312, 313,
315, 438
D
damping, 186, 196–198, 200–214,
222, 225
deflection,
displacement,
dummy, 113, 429, 430–442
E
elbow, 58, 111
elongation, 85, 322, 324, 339, 342,
369, 380, 387
equilibrium,
expansion, 55, 56, 59, 60, 67, 70, 83,
387, 391, 392
F
failure,
fan, 126, 250, 251, 402–404
FAST, 4, 5, 76, 145, 356, 434
fatigue,
fiber,
finesse, 37, 42
fishing reel, 385, 386
FMECA, 10–13, 25, 26, 100, 102–
104, 109–115
forces,
form factors, 44, 45, 49, 50, 128, 150,
270Index 473
frequency,
friction,
G, H
Gantt, 13, 17–20, 27
gears, 218, 301
geometrical product
specifications, 63, 434
handling, 4, 352, 405
heat-hardening, 367
Hertz, 65, 67, 76, 89, 91, 92, 94, 232,
234, 262, 440
hoist, 11, 12, 347, 352
hoisting, 405
Hooke,
hub,
I, J
indices, 44, 60, 80, 268
inertia,
interference, 65, 67, 69–72, 81–83,
126, 352, 383–385
interpolation, 381–383
jack, 131, 277
jaws, 21, 429-433
joint, 87, 88, 135, 239, 240, 244, 254,
259, 260, 318, 322, 355–358, 363,
374, 389, 390, 414
jointing, 370, 388, 390
L
load,
loading,
loft, 381
M, N
materials,
metrology, 4, 23, 24, 28–30, 51, 60,
61, 185, 241, 321, 381, 382, 433,
437, 438
micrometer, 59, 60
Mohr, 92, 94, 130, 136
moment,
noise, 60, 185, 219, 225, 235, 242,
275
notch, 106, 107, 249–252474 Applied Mechanical Design
O, P
optimization, 32, 38, 39, 44, 45, 49,
78, 135, 172, 253
oscillation, 186, 197
outboard, 269, 270
performance,
pipe, 131, 388
pivot,
plastic,
polymer,
pressure,
project,
pulley, 155, 159–161, 163, 166, 167,
172–174, 284, 303
R
random, 185–188, 237
recipient, 135
relaxation,
reliability,
resonance, 200, 206, 208, 212, 214
rim, 309–315
rings,
S
safety,
scooter, 34, 424–428
shaft,
shear,
shell,
sizing,
skull, 428–433, 437
slide, 95, 274–276
Soderberg, 248
sphere, 89, 90, 93, 433, 438
spiral, 30, 326, 345
spires, 325–345, 352, 353, 356, 412,
413, 416, 417, 435
spline, 115, 381Index 475
spring,
standards,
static,
steering, 424, 426
stick-slip, 274–277
stiffness,
stresses,
strip, 55, 57, 378–381
structures,
supports, 88, 104, 189, 211, 217, 308,
317, 318
sweep, 97, 115
T
table, 6, 31, 39–42, 113, 229, 233,
352
tank,
torque,
transmissibility, 204, 210, 215
transmission,
Tresca,
V, W
vat, 84, 85, 131
vibration, 60, 185, 196–200, 205–
208, 212–219, 275
wiscosity, 238, 398
Von Mises, 83, 132, 137, 404
Wahl, 328, 330, 340–343
wall,
welding, 61, 253, 270, 368
wings, 189, 192, 194
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