Pär Johannesson received his PhD in Mathematical Statistics in 1999 at Lund Institute of Technology, Sweden, with a thesis on statistical load analysis for fatigue. During 2000 and 2001 he had a position as PostDoc at Mathematical Statistics, Chalmers within a joint project with PSA Peugeot Citroën, where he stayed one year at the Division of Automotive Research and Innovations in Paris. From 2002 to 2010 he was an applied researcher at the Fraunhofer-Chalmers Research Centre for Industrial Mathematics in Göteborg, and in 2010 he was a guest researcher at Chalmers. He is currently working as a research engineer at SP Technical Research Institute of Sweden, mainly within industrial and research projects on statistical methods for load analysis, reliability and fatigue.

Michael Speckert received his PhD in Mathematics at the University of Kaiserslautern in 1990. From 1991 to 1993 he worked at TECMATH in the human modelling department on optimization algorithms. From 1993 to 2004 he worked at TECMATH and LMS in the departments for load data analysis and fatigue life estimation in the area of method as well as software development. Since 2004 he works at the department for Dynamics and Durability at Fraunhofer ITWM as an applied researcher. His main working areas are statistical and fatigue oriented load data analysis and multi body simulation techniques.

About the Editors xiii

Contributors xv

Series Editor's Preface xvii

Preface xix

Acknowledgements xxi

Part I OVERVIEW

1 Introduction 3

1.1 Durability in Vehicle Engineering 4

1.2 Reliability, Variation and Robustness 6

1.3 Load Description for Trucks 7

1.4 Why Is Load Analysis Important? 9

1.5 The Structure of the Book 10

2 Loads for Durability 15

2.1 Fatigue and Load Analysis 15

2.2 Loads in View of Fatigue Design 23

2.3 Loads in View of System Response 25

2.4 Loads in View of Variability 27

2.5 Summary 29

Part II METHODS FOR LOAD ANALYSIS

3 Basics of Load Analysis 33

3.1 Amplitude-based Methods 35

3.2 Frequency-based Methods 72

3.3 Multi-input Loads 91

3.4 Summary 105

4 Load Editing and Generation of Time Signals 107

4.1 Introduction 107

4.2 Data Inspections and Corrections 110

4.3 Load Editing in the Time Domain 115

4.4 Load Editing in the Rainflow Domain 139

4.5 Generation of Time Signals 156

4.6 Summary 167

5 Response of Mechanical Systems 169

5.1 General Description of Mechanical Systems 169

5.2 Multibody Simulation (MBS) for Durability Applications or: from System Loads to Component Loads 173

5.3 Finite Element Models (FEM) for Durability Applications or: from Component Loads to Local Stress-strain Histories 186

5.4 Invariant System Loads 193

5.5 Summary 200

6 Models for Random Loads 203

6.1 Introduction 203

6.2 Basics on Random Processes 206

6.3 Statistical Approach to Estimate Load Severity 209

6.4 The Monte Carlo Method 215

6.5 Expected Damage for Gaussian Loads 218

6.6 Non-Gaussian Loads: the Role of Upcrossing Intensity 224

6.7 The Coefficient of Variation for Damage 230

6.8 Markov Loads 235

6.9 Summary 249

7 Load Variation and Reliability 253

7.1 Modelling of Variability in Loads 253

7.2 Reliability Assessment 256

7.3 The Full Probabilistic Model 258

7.4 The First-Moment Method 263

7.5 The Second-Moment Method 264

7.6 The Fatigue Load-Strength Model 265

7.7 Summary 284

Part III LOAD ANALYSIS IN VIEW OF THE VEHICLE DESIGN PROCESS

8 Evaluation of Customer Loads 287

8.1 Introduction 287

8.2 Survey Sampling 288

8.3 Load Measurement Uncertainty 295

8.4 Random Sampling of Customers 303

8.5 Customer Usage and Load Environment 308

8.6 Vehicle-Independent Load Descriptions 314

8.7 Discussion and Summary 318

9 Derivation of Design Loads 321

9.1 Introduction 321

9.2 From Customer Usage Profiles to Design Targets 324

9.3 Synthetic Load Models 333

9.4 Random Load Descriptions 335

9.5 Applying Reconstruction Methods 336

9.6 Standardized Load Spectra 341

9.7 Proving Ground Loads 342

9.8 Optimized Combination of Test Track Events 342

9.9 Discussion and Summary 354

10 Verification of Systems and Components 357

10.1 Introduction 357

10.2 Generating Loads for Testing 363

10.3 Planning and Evaluation of Tests 365

10.4 Discussion and Summary 379

A Fatigue Models and Life Prediction 383

A.1 Short, Long or Infinite Life 383

A.2 Cumulative Fatigue 384

B Statistics and Probability 387

B.1 Further Reading 387

B.2 Some Common Distributions 387

B.3 Extreme Value Distributions 389

C Fourier Analysis 391

C.1 Fourier Transformation 391

C.2 Fourier Series 392

C.3 Sampling and the Nyquist-Shannon Theorem 393

C.4 DFT/FFT (Discrete Fourier Transformation) 394

D Finite Element Analysis 395

D.1 Kinematics of Flexible Bodies 395

D.2 Equations of Equilibrium 396

D.3 Linear Elastic Material Behaviour 397

D.4 Some Basics on Discretization Methods 397

D.5 Dynamic Equations 399

E Multibody System Simulation 401

E.1 Linear Models 401

E.2 Mathematical Description of Multibody Systems 402

F Software for Load Analysis 407

F.1 Some Dedicated Software Packages 407

F.2 Some Software Packages for Fatigue Analysis 408

F.3 WAFO - a Toolbox for Matlab 408

Bibliography 411

Index 423