Design and analysis of composite structures for auotmotive applications : Chassis and driventrain

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Design and Analysis of Composite Structures for Automotive Applications

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Automotive Series

Advanced Battery Management Technologies for Electric Vehicles

Rui Xiong, Weixiang Shen

Noise and Vibration Control in Automotive Bodies

Jian Pang

Automotive Power Transmission Systems

Yi Zhang, Chris Mi

High Speed Off-Road Vehicles: Suspensions, Tracks, Wheels and Dynamics

Bruce Maclaurin

Hybrid Electric Vehicles: Principles and Applications with Practical Perspectives,

2nd Edition

Chris Mi, M. Abul Masrur

Hybrid Electric Vehicle System Modeling and Control, 2nd Edition

Wei Liu

Thermal Management of Electric Vehicle Battery Systems

Ibrahim Dincer, Halil S. Hamut, Nader Javani

Automotive Aerodynamics

Joseph Katz

The Global Automotive Industry

Paul Nieuwenhuis, Peter Wells

Vehicle Dynamics

Martin Meywerk

Modelling, Simulation and Control of Two-Wheeled Vehicles

Mara Tanelli, Matteo Corno, Sergio Saveresi

Vehicle Gearbox Noise and Vibration: Measurement, Signal Analysis, Signal Pro￾cessing and Noise Reduction Measures

Jiri Tuma

Modeling and Control of Engines and Drivelines

Lars Eriksson, Lars Nielsen

Advanced Composite Materials for Automotive Applications: Structural Integrity

and Crashworthiness

Ahmed Elmarakbi

Guide to Load Analysis for Durability in Vehicle Engineering

P. Johannesson, M. Speckert

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Design and Analysis of Composite Structures for

Automotive Applications

Chassis and Drivetrain

Vladimir Kobelev

Department of Natural Sciences, University of Siegen, Germany

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This edition first published 2019

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Library of Congress Cataloging-in-Publication Data

Names: Kobelev, Vladimir, 1959- author.

Title: Design and analysis of composite structures for automotive

applications : chassis and drivetrain / Vladimir Kobelev, Department of

Natural Sciences, University of Siegen, Germany.

Description: First edition. | Hoboken, NJ : Wiley, 2019. | Series: Automotive

series | Includes bibliographical references and index. |

Identifiers: LCCN 2019005286 (print) | LCCN 2019011866 (ebook) | ISBN

9781119513841 (Adobe PDF) | ISBN 9781119513865 (ePub) | ISBN 9781119513858

(hardback)

Subjects: LCSH: Automobiles–Chassis. | Automobiles–Power trains. |

Automobiles–Design and construction.

Classification: LCC TL255 (ebook) | LCC TL255 .K635 2019 (print) | DDC

629.2/4–dc23

LC record available at https://lccn.loc.gov/2019005286

Cover Design: Wiley

Cover Images: © Vladimir Kobelev, Background: © solarseven/ShuWerstock

Set in 10/12pt WarnockPro by SPi Global, Chennai, India

Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY

10 9 8 7 6 5 4 3 2 1

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v

Contents

Foreword xiii

Series Preface xv

List of Symbols and Abbreviations xvii

Introduction xxiii

About the Companion Website xxxv

1 Elastic Anisotropic Behavior of Composite Materials 1

1.1 Anisotropic Elasticity of Composite Materials 1

1.1.1 Fourth Rank Tensor Notation of Hooke’s Law 1

1.1.2 Voigt’s Matrix Notation of Hooke’s Law 2

1.1.3 Kelvin’s Matrix Notation of Hooke’s Law 5

1.2 Unidirectional Fiber Bundle 7

1.2.1 Components of a Unidirectional Fiber Bundle 7

1.2.2 Elastic Properties of a Unidirectional Fiber Bundle 7

1.2.3 Effective Elastic Constants of Unidirectional Composites 8

1.3 Rotational Transformations of Material Laws, Stress and Strain 10

1.3.1 Rotation of Fourth Rank Elasticity Tensors 11

1.3.2 Rotation of Elasticity Matrices in Voigt’s Notation 11

1.3.3 Rotation of Elasticity Matrices in Kelvin’s Notation 13

1.4 Elasticity Matrices for Laminated Plates 14

1.4.1 Voigt’s Matrix Notation for Anisotropic Plates 14

1.4.2 Rotation of Matrices in Voigt’s Notation 15

1.4.3 Kelvin’s Matrix Notation for Anisotropic Plates 15

1.4.4 Rotation of Matrices in Kelvin’s Notation 16

1.5 Coupling Effects of Anisotropic Laminates 17

1.5.1 Orthotropic Laminate Without Coupling 17

1.5.2 Anisotropic Laminate Without Coupling 17

1.5.3 Anisotropic Laminate With Coupling 17

1.5.4 Coupling Effects in Laminated Thin-Walled Sections 18

1.6 Conclusions 18

References 19

2 Phenomenological Failure Criteria of Composites 21

2.1 Phenomenological Failure Criteria 21

2.1.1 Criteria for Static Failure Behavior 21

2.1.2 Stress Failure Criteria for Isotropic Homogenous Materials 21

2.1.3 Phenomenological Failure Criteria for Composites 22

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vi Contents

2.1.4 Phenomenological Criteria Without Stress Coupling 23

2.1.4.1 Criterion of Maximum Averaged Stresses 23

2.1.4.2 Criterion of Maximum Averaged Strains 24

2.1.5 Phenomenological Criteria with Stress Coupling 24

2.1.5.1 Mises–Hill Anisotropic Failure Criterion 24

2.1.5.2 Pressure-Sensitive Mises–Hill Anisotropic Failure Criterion 26

2.1.5.3 Tensor-Polynomial Failure Criterion 27

2.1.5.4 Tsai–Wu Criterion 30

2.1.5.5 Assessment of Coefficients in Tensor-Polynomial Criteria 30

2.2 Differentiating Criteria 33

2.2.1 Fiber and Intermediate Break Criteria 33

2.2.2 Hashin Strength Criterion 33

2.2.3 Delamination Criteria 35

2.3 Physically Based Failure Criteria 35

2.3.1 Puck Criterion 35

2.3.2 Cuntze Criterion 36

2.4 Rotational Transformation of Anisotropic Failure Criteria 37

2.5 Conclusions 40

References 40

3 Micromechanical Failure Criteria of Composites 45

3.1 Pullout of Fibers from the Elastic-Plastic Matrix 45

3.1.1 Axial Tension of Fiber and Matrix 45

3.1.2 Shear Stresses in Matrix Cylinders 51

3.1.3 Coupled Elongation of Fibers and Matrix 53

3.1.4 Failures in Matrix and Fibers 54

3.1.4.1 Equations for Mean Axial Displacements of Fibers and Matrix 54

3.1.4.2 Solutions of Equations for Mean Axial Displacements of Fibers and

Matrix 56

3.1.5 Rupture of Matrix and Pullout of Fibers from Crack Edges in a Matrix 57

3.1.5.1 Elastic Elongation (Case I) 57

3.1.5.2 Plastic Sliding on the Fiber Surface (Case II) 58

3.1.5.3 Fiber Breakage (Case III) 58

3.1.6 Rupture of Fibers, Matrix Joints and Crack Edges 59

3.2 Crack Bridging in Elastic-Plastic Unidirectional Composites 60

3.2.1 Crack Bridging in Unidirectional Fiber-Reinforced Composites 60

3.2.2 Matrix Crack Growth 61

3.2.3 Fiber Crack Growth 62

3.2.4 Penny-Shaped Crack 65

3.2.4.1 Crack in a Transversal-Isotropic Medium 65

3.2.4.2 Mechanisms of the Fracture Process 66

3.2.4.3 Crack Bridging in an Orthotropic Body With Disk Crack 66

3.2.4.4 Solution to an Axially Symmetric Crack Problem 68

3.2.5 Plane Crack Problem 72

3.2.5.1 Equations of the Plane Crack Problem 72

3.2.5.2 Solution to the Plane Crack Problem 74

3.3 Debonding of Fibers in Unidirectional Composites 75

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Contents vii

3.3.1 Axial Deformation of Unidirectional Fiber Composites 75

3.3.2 Stresses in Unidirectional Composite in Cases of Ideal Debonding or

Adhesion 79

3.3.2.1 Equations of an Axially Loaded Unidirectional Compound Medium (A) 79

3.3.2.2 Total Debonding (B) 82

3.3.2.3 Ideal Adhesion (C) 83

3.3.3 Stresses in a Unidirectional Composite in a Case of Partial Debonding 84

3.3.3.1 Partial Radial Load on the Fiber Surface 84

3.3.3.2 Partial Radial Load on the Matrix Cavity Surface 84

3.3.3.3 Partial Debonding With Central Adhesion Region (D) 85

3.3.3.4 Partial Debonding With Central Debonding Region (E) 88

3.3.3.5 Semi-Infinite Debonding With Central Debonding Region (F) 89

3.3.4 Contact Problem for a Finite Adhesion Region 89

3.3.5 Debonding of a Semi-Infinite Adhesion Region 93

3.3.6 Debonding of Fibers from a Matrix Under Cyclic Deformation 95

3.4 Conclusions 98

References 98

4 Optimization Principles for Structural Elements Made of

Composites 105

4.1 Stiffness Optimization of Anisotropic Structural Elements 105

4.1.1 Optimization Problem 105

4.1.2 Optimality Conditions 106

4.1.3 Optimal Solutions in Anti-Plane Elasticity 109

4.1.4 Optimal Solutions in Plane Elasticity 109

4.2 Optimization of Strength and Loading Capacity of Anisotropic

Elements 110

4.2.1 Optimization Problem 110

4.2.2 Optimality Conditions 113

4.2.3 Optimal Solutions in Anti-Plane Elasticity 114

4.2.4 Optimal Solutions in Plane Elasticity 114

4.3 Optimization of Accumulated Elastic Energy in Flexible Anisotropic

Elements 116

4.3.1 Optimization Problem 116

4.3.2 Optimality Conditions 117

4.3.3 Optimal Solutions in Anti-Plane Elasticity 118

4.3.4 Optimal Solutions in Plane Elasticity 119

4.4 Optimal Anisotropy in a Twisted Rod 119

4.5 Optimal Anisotropy of Bending Console 122

4.6 Optimization of Plates in Bending 123

4.7 Conclusions 125

References 125

5 Optimization of Composite Driveshaft 129

5.1 Torsion of Anisotropic Shafts With Solid Cross-Sections 129

5.2 Thin-Walled Anisotropic Driveshaft with Closed Profile 132

5.2.1 Geometry of Cross-Section 132

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viii Contents

5.2.2 Main Kinematic Hypothesis 133

5.3 Deformation of a Composite Thin-Walled Rod 135

5.3.1 Equations of Deformation of a Anisotropic Thin-Walled Rod 135

5.3.2 Boundary Conditions 138

5.3.2.1 Ideal Fixing 138

5.3.2.2 Ideally Free End 138

5.3.2.3 Boundary Conditions of the Intermediate Type 140

5.3.3 Governing Equations in Special Cases of Symmetry 140

5.3.3.1 Orthotropic Material 140

5.3.3.2 Constant Elastic Properties Along the Arc of a Cross-Section 140

5.3.4 Symmetry of Section 140

5.4 Buckling of Composite Driveshafts Under a Twist Moment 141

5.4.1 Greenhill’s Buckling of Driveshafts 141

5.4.2 Optimal Shape of the Solid Cross-Section for Driveshaft 143

5.4.3 Hollow Circular and Triangular Cross-Sections 144

5.5 Patents for Composite Driveshafts 146

5.6 Conclusions 150

References 150

6 Dynamics of a Vehicle with Rigid Structural Elements of Chassis 155

6.1 Classification of Wheel Suspensions 155

6.1.1 Common Designs of Suspensions 155

6.1.2 Types of Twist-Beam Axles 156

6.1.3 Kinematics of Wheel Suspensions 157

6.2 Fundamental Models in Vehicle Dynamics 159

6.2.1 Basic Variables of Vehicle Dynamics 159

6.2.2 Coordinate Systems of Vehicle and Local Coordinate Systems 161

6.2.2.1 Earth-Fixed Coordinate System 161

6.2.2.2 Vehicle-Fixed Coordinate System 162

6.2.2.3 Horizontal Coordinate System 162

6.2.2.4 Wheel Coordinate System 162

6.2.3 Angle Definitions 162

6.2.4 Components of Force and Moments in Car Dynamics 163

6.2.5 Degrees of Freedom of a Vehicle 163

6.3 Forces Between Tires and Road 167

6.3.1 Tire Slip 167

6.3.2 Side Slip Curve and Lateral Force Properties 168

6.4 Dynamic Equations of a Single-Track Model 170

6.4.1 Hypotheses of a Single-Track Model 170

6.4.2 Moments and Forces in a Single-Track Model 171

6.4.3 Balance of Forces and Moments in a Single-Track Model 173

6.4.4 Steady Cornering 174

6.4.4.1 Necessary Steer Angle for Steady Cornering 174

6.4.4.2 Yaw Gain Factor and Steer Angle Gradient 175

6.4.4.3 Classification of Self-Steering Behavior 176

6.4.5 Non-Steady Cornering 179

6.4.5.1 Equations of Non-Stationary Cornering 179

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Contents ix

6.4.5.2 Oscillatory Behavior of Vehicle During Non-Steady Cornering 180

6.4.6 Anti-Roll Bars Made of Composite Materials 181

6.5 Conclusions 182

References 182

7 Dynamics of a Vehicle With Flexible, Anisotropic Structural Elements

of Chassis 183

7.1 Effects of Body and Chassis Elasticity on Vehicle Dynamics 183

7.1.1 Influence of Body Stiffness on Vehicle Dynamics 183

7.1.2 Lateral Dynamics of Vehicles With Stiff Rear Axles 184

7.1.3 Induced Effects on Wheel Orientation and Positioning of Vehicles with

Flexible Rear Axle 185

7.2 Self-Steering Behavior of a Vehicle With Coupling of Bending and

Torsion 188

7.2.1 Countersteering for Vehicles with Twist-Beam Axles 188

7.2.1.1 Countersteering Mechanisms 188

7.2.1.2 Countersteering by Anisotropic Coupling of Bending and Torsion 190

7.2.2 Bending-Twist Coupling of a Countersteering Twist-Beam Axle 192

7.2.3 Roll Angle of Vehicle 193

7.2.3.1 Relationship Between Roll Angle and Centrifugal Force 193

7.2.3.2 Lateral Reaction Forces on Wheels 193

7.2.3.3 Steer Angles on Front Wheels 194

7.2.3.4 Steer Angles on Rear Wheels 194

7.3 Steady Cornering of a Flexible Vehicle 196

7.3.1 Stationary Cornering of a Car With a Flexible Chassis 196

7.3.2 Necessary Steer Angles for Coupling and Flexibility of Chassis 196

7.3.2.1 Limit Case: Lateral Acceleration Vanishes 196

7.3.2.2 Absolutely Rigid Front and Rear Wheel Suspensions 197

7.3.2.3 Bending and Torsion of a Twist Member Completely Decoupled 197

7.3.2.4 General Case of Coupling Between Bending and Torsion of a Twist

Member 198

7.3.2.5 Neutral Steering Caused by Coupling Between Bending and Torsion of a

Twist Member 198

7.4 Estimation of Coupling Constant for a Twist Member 199

7.4.1 Coupling Between Vehicle Roll Angle and Twist of Cross-Member 199

7.4.2 Stiffness Parameters of a Twist-Beam Axle 200

7.4.2.1 Roll Spring Rate 200

7.4.2.2 Lateral Stiffness 201

7.4.2.3 Camber Stiffness 203

7.5 Design of the Countersteering Twist-Beam Axle 203

7.5.1 Requirements for a Countersteering Twist-Beam Axle 203

7.5.2 Selection and Calculation of the Cross-Section for the Cross-Member 205

7.5.3 Elements of a Countersteering Twist-Beam Axle 208

7.6 Patents on Twist-Beam Axles 211

7.7 Conclusions 214

References 214

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x Contents

8 Design and Optimization of Composite Springs 217

8.1 Design and Optimization of Anisotropic Helical Springs 217

8.1.1 Forces and Moments in Helical Composite Springs 217

8.1.2 Symmetrically Designed Solid Bar With Circular Cross-Section 220

8.1.3 Stiffness and Stored Energy of Helical Composite Springs 223

8.1.4 Spring Rates of Helical Composite Springs 225

8.1.5 Helical Composite Springs of Minimal Mass 228

8.1.5.1 Optimization Problem 228

8.1.5.2 Optimal Composite Spring for the Anisotropic Mises–Hill Strength

Criterion 228

8.1.6 Axial and Twist Vibrations of Helical Springs 231

8.2 Conical Springs Made of Composite Material 233

8.2.1 Geometry of an Anisotropic Conical Spring in an Undeformed State 233

8.2.2 Curvature and Strain Deviations 235

8.2.3 Thin-Walled Conical Shells Made of Anisotropic Materials 236

8.2.4 Variation Principle 237

8.2.5 Structural Optimization of a Conical Spring Due to Ply Orientation 239

8.2.6 Conical Spring Made of Orthotropic Material 241

8.2.7 Bounds for Stiffness of a Spring Made of Orthotropic Material 243

8.3 Alternative Concepts for Chassis Springs Made of Composites 244

8.4 Conclusions 248

References 249

9 Equivalent Beams of Helical Anisotropic Springs 255

9.1 Helical Compression Springs Made of Composite Materials 255

9.1.1 Statics of the Equivalent Beam for an Anisotropic Spring 255

9.1.2 Dynamics of an Equivalent Beam for an Anisotropic Spring 258

9.2 Transverse Vibrations of a Composite Spring 260

9.2.1 Separation of Variables 260

9.2.2 Fundamental Frequencies of Transversal Vibrations 262

9.2.3 Transverse Vibrations of a Symmetrically Stacked Helical Spring 264

9.3 Side Buckling of a Helical Composite Spring 265

9.3.1 Buckling Under Axial Force 265

9.3.2 Simplified Formulas for Buckling of a Symmetrically Stacked Helical

Spring 266

9.4 Conclusions 267

References 267

10 Composite Leaf Springs 269

10.1 Longitudinally Mounted Leaf Springs for Solid Axles 269

10.1.1 Predominantly Bending-Loaded Leaf Springs 269

10.1.2 Moments and Forces of Leaf Springs in a Pure Bending State 270

10.1.3 Optimization of Leaf Springs for an Anisotropic Mises–Hill Criterion 272

10.2 Leaf-Tension Springs 275

10.2.1 Combined Bending and Tension of a Spring 275

10.2.2 Forces and Rates of Leaf-Tension Springs 277

10.3 Transversally Mounted Leaf Springs 278

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Contents xi

10.3.1 Axle Concepts of Transverse Leaf Springs 278

10.3.2 Analysis of a Transverse Leaf Spring 280

10.3.3 Examples and Patents for Transversely Mounted Leaf Springs 283

10.4 Conclusions 286

References 287

11 Meander-Shaped Springs 289

11.1 Meander-Shaped Compression Springs for Automotive Suspensions 289

11.1.1 Bending Stress State of Corrugated Springs 289

11.1.2 “Equivalent Beam” of a Meander Spring 292

11.1.3 Axial and Lateral Stiffness of Corrugated Springs 292

11.1.4 Effective Spring Constants of Meander and Coil Springs for Bending and

Compression 293

11.2 Multiarc-Profiled Spring Under Axial Compressive Load 294

11.2.1 Multiarc Meander Spring With Constant Cross-Section 294

11.2.2 Multiarc Meander Spring With Optimal Cross-Section 297

11.2.3 Comparison of Masses for Fixed Spring Rate and Stress 298

11.3 Sinusoidal Spring Under Compressive Axial Load 299

11.3.1 Sinusoidal Meander Spring With Constant Cross-Section 299

11.3.2 Sinusoidal Meander Spring With Optimal Cross-Section 301

11.3.3 Comparison of Masses for Fixed Spring Rate and Stress 302

11.4 Bending Stiffness of Meander Spring With a Constant Cross-Section 303

11.4.1 Bending Stiffness of a Multiarc Meander Spring With a Constant

Cross-Section 303

11.4.2 Bending Stiffness of a Sinusoidal Meander Spring with a Constant

Cross-Section 303

11.5 Stability of Corrugated Springs 304

11.5.1 Euler’s Buckling of an Axially Compressed Rod 304

11.5.2 Side Buckling of Meander Springs 306

11.6 Patents for Chassis Springs Made of Composites in Meandering Form 307

11.7 Conclusions 314

References 315

12 Hereditary Mechanics of Composite Springs and Driveshafts 317

12.1 Elements of Hereditary Mechanics of Composite Materials 317

12.1.1 Mechanisms of Time-Dependent Deformation of Composites 317

12.1.2 Linear Viscoelasticity of Composites 318

12.1.3 Nonlinear Creep Mechanics of Anisotropic Materials 319

12.1.4 Anisotropic Norton–Bailey Law 321

12.2 Creep and Relaxation of Twisted Composite Shafts 322

12.2.1 Constitutive Equations for Relaxation in Torsion of Anisotropic Shafts 322

12.2.2 Torque Relaxation for an Anisotropic Norton–Bailey Law 322

12.3 Creep and Relaxation of Composite Helical Coiled Springs 323

12.3.1 Compression and Tension Composite Springs 323

12.3.2 Relaxation of Helical Composite Springs 324

12.3.3 Creep of Helical Composite Compression Springs 324

12.4 Creep and Relaxation of Composite Springs in a State of Pure Bending 325

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xii Contents

12.4.1 Constitutive Equations for Bending Relaxation 325

12.4.2 Relaxation of the Bending Moment for the Anisotropic Norton–Bailey

Law 326

12.4.3 Creep in a State of Bending 326

12.5 Conclusions 327

References 327

Appendix A Mechanical Properties of Composites 331

A.1 Fibers 331

A.1.1 Glass Fibers 331

A.1.2 Carbon Fibers 331

A.1.3 Aramid Fibers 331

A.2 Physical Properties of Resin 332

A.3 Laminates 334

A.3.1 Unidirectional Fiber-Reinforced Composite Material 334

A.3.2 Fabric 334

A.3.3 Non-Woven Fabric 334

References 335

Appendix B Anisotropic Elasticity 337

B.1 Elastic Orthotropic Body 337

B.2 Distortion Energy and Supplementary Energy 338

B.3 Plane Elasticity Problems 339

B.3.1 Plane Strain State 339

B.3.2 Plane Stress State 339

B.4 Generalized Airy Stress Function 340

B.4.1 Plane Stress State 340

B.4.2 Plane Strain State 340

B.4.3 Rotationally Symmetric Elasticity Problems 340

Appendix C Integral Transforms in Elasticity 343

C.1 One-Dimensional Integral Transform 343

C.2 Two-Dimensional Fourier Transform 344

C.3 Potential Functions for Plane Elasticity Problems 344

C.4 Rotationally Symmetric, Spatial Elasticity Problems 346

C.5 Application of the Fourier Transformation to Plane Elasticity Problems 348

C.6 Application of the Hankel Transformation to Spatial, Rotation-Symmetric

Elasticity Problems 349

Index 351

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xiii

Foreword

From a materials science point of view, composite materials of glass and carbon fibers

have a specific potential and already some practical importance in several applications

under high dynamic loads. Comparing the fibers, glass fibers are the better material for

spring applications because their lower modulus of elasticity compared to carbon fibers.

This is favorable in terms of high strokes and deformation requirements. Due to their

high specific strength and the stiffness of composite materials, it is in principle possi￾ble to achieve weight savings of 30 – 70% of the weight of a steel spring depending on

application. In addition to reduce the unsprung masses for suspension, it is also possible

to improve driving dynamics as well as noise, vibration and hardness behavior (NVH),

since the material properties are better in some significant areas. Furthermore, due to

the high corrosion resistance and resistance against other environmental influences, sur￾face protection is not necessary in most of the applications.

However, the usage of composite materials for springs have not reached high quan￾tities due to some limitations. Load transmission requires special designs. Consider￾ing suspension coil springs, high loads transverse to the main load direction occur.

Therefore, the load transmission does not follow ideally to the fiber direction and only

medium loads can act on the matrix. In addition, in the case of large-scale production

and the available manufacturing processes, value adjustments must be made in com￾parison with units made of steel. These are currently the focus of research and develop￾ment efforts throughout the world. Endless, unidirectional fiber materials, such as those

used for structural elements in automotive engineering, exhibit strong anisotropic, i.e.

direction-dependent, properties. The fibers used are oriented with respect to the loads

that occur. Therefore, the leaf spring, where loading results almost in tension stresses

of the fibers is the perfect match with composite materials. Huge weight reduction up

to 75% is possible to achieve by using the material properties and the design flexibil￾ity of glass fiber reinforced composite in the best way. A single composite tension leaf

spring can substitute a steel multi-leaf spring with a progressive spring load characteris￾tic.The special design leads to a very homogenous, progressive spring characteristic and

therefore, a better driving performance. Furthermore, we know already some designs for

suspension steel coil springs substitution such as one-by-one substitution by compos￾ite coil spring and a meander spring design. In both case these springs do need special

tools for the design and did not reach the market breakthrough due to huge different

load-rate requirements within the platforms.

There are some processes existing for the production of glass fiber composite springs.

Nevertheless, the prepreg process (pre-impregnated fibers) has proven itself as the best

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xiv Foreword

due to the realizable good properties under dynamic loads. Prepreg processes result in

an optimal adhesive strength due to low porosity and allows flexibility in design, such as

geometry, width and height of the spring. It is also possible to produce the elements of

chassis in general and suspension particular using the resin injection process. For this

resin injection process, a fiber structure is first produced from the dry reinforcement

fibers, which follows the desired component geometry. If required, structural cohesion

can be achieved using textile methods, such as sewing or bonding, which bond the fibers

together. Such fiber structures are called preforms. The injection of the resin influences

the orientation of the fibers and therefore, those springs do not reach the performance

of prepreg composites due to potential ondulation.

Automotive manufacturers’ requirements for carbon dioxide reduction, lower vehicle

weight, the reduction of unsprung masses and the robustness of the springs, especially in

the event of corrosion, will further increase in the future. The optimal application of the

materials used plays a decisive role, supported by material properties, best technology

and processes as well as an efficient design.Therefore, alternative materials, such as com￾posites, may become higher importance for dynamic loaded suspension applications.

Prof. Dr. Vladimir Kobelev was born in Rostow-na Donu, Russian Federation. He stud￾ied Physical Engineering at the Moscow Institute of Physics and Technology. After his

PhD at the Department of Aerophysics and Space Research (FAKI), he habilitated at the

University of Siegen, Scientific-Technical Faculty. Today, Prof. Kobelev is lecturer and

APL professor at the University of Siegen in the subject area of Mechanical Engineering.

In his industrial career, Prof. Kobelev is an employee at Mubea, a successful

automotive supplier located near Cologne/Germany. In the Corporate Engineering

Department, Prof. Kobelev is responsible for the development of calculation methods

and physical modeling of Mubea components.

Joerg Neubrand

CTO, Managing Director and

Member of the Executice Board of the Mubea Group

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Series Preface

Fuel efficiency continues to “drive” significant research and development in the

automotive sector. In many instances, this is propelled by regulations that target

reduced emissions as well as reduced fuel consumption. Even with more efficient vehi￾cles and electric hybrid or purely electric driven systems, the need for reduced energy

consumption is demanded by the market. This is due to the fact that the customer

base is demanding increased efficiency as this brings better performance, lower costs

and extended range of the vehicle. One clear means by which fuel efficiency can be

enhanced is by reducing the weight of the vehicle. Lightweighting can be accomplished

by a number of means, one of which is lighter weight material substitution. That is to

say, one may substitute a lighter material for a heavier one on a vehicle component.

Composites have been used to replace metal components in efforts to lightweight

aircraft for decades. More recently, advances in materials, manufacture, and design

have made composites cost effective and viable in the automotive sector. Two major

stumbling blocks that have hindered composite use in the automotive sector are the

cost of the composite components, and the ability to rapidly and economically produce

such components in quantities that are needed by the automotive sector. Recently, these

stumbling blocks have been overcome. However, for most commercial automotive

applications, composites remain relegated to less critical elements of the vehicle system

such as body panels. The use of composite for more critical vehicle applications such as

suspension and drive train elements have been left to extremely demanding automotive

scenarios such as Formula One. However, this scenario is about to change.

Design and Analysis of Composite Structures for Automotive Applications, provides an

in-depth technical analysis of critical suspension and drive train elements with a focus

on composite materials.This includes basic principles for the design and optimization of

critical vehicle elements using composite materials, as well as classical concepts related

to mass reduction in automotive systems. The author, Professor Kobelev, skillfully

integrates concepts related to vehicle parameters such as stiffness into overall vehicle

dynamics using closed form solutions that are described in exquisite detail. The discus￾sions focus on key elements of the vehicle including suspension and powertrain. These

discussions are both comprehensive as well as the first of their kind in a text book, mak￾ing this text an important reference for any automotive engineer on the leading edge.

Design and Analysis of Composite Structures for Automotive Applications is part of

the Automotive Series that addresses new and emerging technologies in automotive

engineering, supporting the development of next generation vehicles using next gener￾ation technologies, as well as new design and manufacturing methodologies. The series