Applied Mechanical Design

Ammar Grous, CEGEP de l'Outaouais, Gatineau, Quebec, Canada.

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 29

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 104

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 1 156

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 223

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 287

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 358

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 419

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 471