Preface to the English Edition 6
Contents 8
Purpose and Structure of theDynamics of Machinery 14
Chapter 1 Model Generation and Parameter Identification 18
1.1 Classification of Calculation Models 18
1.1.1 General Principles 18
1.1.2 Examples 23
1.2 Determination of Mass Parameters 27
1.2.1 Overview 27
1.2.2 Mass and Position of the Center of Gravity 28
1.2.3 Moment of Inertia about an Axis 30
1.2.4 Moment of Inertia Tensor 34
1.3 Spring Characteristics 38
1.3.1 General Context 38
1.3.2 Machine Elements, Sub-Assemblies 42
1.3.3 Rubber Springs 49
1.3.4 Problems P1.1 to P1.3 51
1.3.5 Solutions S1.1 to S1.3 53
1.4 Damping Characteristics 55
1.4.1 General Context 55
1.4.2 Methods for Determining Characteristic DampingParameters 60
1.4.3 Empirical Damping Values 64
1.5 Characteristic Excitation Parameters 68
1.5.1 Periodic Excitation 68
1.5.2 Transient Excitation 69
1.5.3 Problems P1.4 to P1.6 75
1.5.4 Solutions S1.4 to S1.6 76
Chapter 2 Dynamics of Rigid Machines 80
2.1 Introduction 80
2.2 Kinematics of a Rigid Body 81
2.2.1 Coordinate Transformations 81
2.2.2 Kinematic Parameters 86
2.2.3 Kinematics of the Gimbal-Mounted Gyroscope 88
2.2.4 Problems P2.1 and P2.2 89
2.2.5 Solutions S2.1 and S2.2 91
2.3 Kinetics of the Rigid Body 95
2.3.1 Kinetic Energy and Moment of Inertia Tensor 95
2.3.2 Principles of Linear Momentum and of Angular Momentum 100
2.3.3 Kinetics of Edge Mills 103
2.3.4 Problems P2.3 and P2.4 106
2.3.5 Solutions S2.3 and S2.4 108
2.4 Kinetics of Multibody Systems 113
2.4.1 Mechanisms with Multiple Drives 113
2.4.2 Planar Mechanisms 125
2.4.3 States of Motion of a Rigid Machine 135
2.4.4 Solution of the Equations of Motion 137
2.4.5 Example: Press Drive 142
2.4.6 Problems P2.5 to P2.8 146
2.4.7 Solutions S2.5 to S2.8 149
2.5 Joint Forces and Foundation Loading 154
2.5.1 General Perspective 154
2.5.2 Calculating Joint Forces 155
2.5.3 Calculation of the Forces Acting onto the Frame 158
2.5.4 Joint Forces in the Linkage of a Processing Machine 161
2.5.5 Problems P2.9 and P2.10 163
2.5.6 Solutions S2.9 and S2.10 164
2.6 Methods of Mass Balancing 166
2.6.1 Objective 166
2.6.2 Counterbalancing of Rigid Rotors 166
2.6.3 Mass Balancing of Planar Mechanisms 173
2.6.4 Problems P2.11 to P2.14 180
2.6.5 Solutions S2.11 to S2.14 183
Chapter 3 Foundation and Vibration Isolation 189
3.1 Introductory Remarks 189
3.2 Foundation Loading for Periodic Excitation 193
3.2.1 Minimal Models with One Degree of Freedom 193
3.2.2 Block Foundations 203
3.2.3 Foundations with Two Degrees of Freedom – VibrationAbsorption 212
3.2.4 Example: Vibrations of an Engine-Generator System 216
3.2.5 Problems P3.1 to P3.3 218
3.2.6 Solutions to Problems S3.1 to S3.3 220
3.3 Foundations under Impact Loading 223
3.3.1 Modeling Forging Hammers 223
3.3.2 Calculation Model with Two Degrees of Freedom 225
3.3.3 Problems P3.4 to P3.6 228
3.3.4 Solutions S3.4 to S3.6 230
Chapter 4 Torsional Oscillators and LongitudinalOscillators 235
4.1 Introduction 235
4.2 Free Vibrations of Torsional Oscillators 241
4.2.1 Models with Two Degrees of Freedom 241
4.2.2 Oscillator Chains with Multiple Degrees of Freedom 246
4.2.3 Evaluation of Natural Frequencies and Mode Shapes 250
4.2.4 Examples 254
4.2.5 Problems P4.1 to P4.3 263
4.2.6 Solutions S4.1 to S4.3 265
4.3 Forced Vibrations of Discrete Torsional Oscillators 271
4.3.1 Periodic Excitation 271
4.3.2 Examples 275
4.3.3 Transient Excitation 284
4.3.4 Problems P4.4 to P4.6 290
4.3.5 Solutions S4.4 to S4.6 292
4.4 Absorbers and Dampers in Drive Systems 295
4.4.1 Introduction 295
4.4.2 Design of an Undamped Absorber 296
4.4.3 Design of a Spring-Constrained Damper 298
4.4.4 Design of a Springless Damper 301
4.4.5 Examples 303
4.5 Parameter-Excited Vibrationsby Gear Mechanisms with Varying Transmission Ratio 307
4.5.1 Problem Formulation/Equation of Motion 307
4.5.2 Solution of the Equation of Motion, Stability Behavior 309
4.5.3 Examples 311
4.5.4 Problems P4.7 and P4.8 318
4.5.5 Solutions S4.7 and S4.8 320
Chapter 5 Bending Oscillators 322
5.1 Problem Development 322
5.2 Fundamentals 323
5.2.1 Self-Centering in a Symmetrical Rotor 323
5.2.2 Passing through the Resonance Point 326
5.2.3 Rotating Shaft with Disk (Gyroscopic Effect) 327
5.2.4 Bending Oscillators with a Finite Number of Degrees ofFreedom 337
5.2.5 Examples 339
5.2.6 Problems P5.1 to P5.3 346
5.2.7 Solutions S5.1 to S5.3 347
5.3 Beam with Distributed Mass 349
5.3.1 General Perspective 349
5.3.2 Straight Beam on Two Supports 354
5.3.3 Estimates by Dunkerley and Neuber 357
5.4 Model Generation for Rotors 358
5.4.1 General Considerations 358
5.4.2 Example: Grinding Spindle 361
5.5 Problems P5.4 to P5.6 362
5.6 Solutions S5.4 to S5.6 363
Chapter 6 Linear Oscillators with Multiple Degrees ofFreedom 366
6.1 Introduction 366
6.2 Equations of Motion 369
6.2.1 Mass, Spring, and Compliance matrix 369
6.2.2 Examples 374
6.2.3 Problems P6.1 to P6.3 383
6.2.4 Solutions S6.1 to S6.3 384
6.3 Free Undamped Vibrations 386
6.3.1 Natural Frequencies, Mode Shapes, Eigenforces 386
6.3.2 Orthogonality and Modal Coordinates 389
6.3.3 Initial Conditions, Initial Energy, Estimates 392
6.3.4 Examples 394
6.3.5 Problems P6.4 to P6.6 406
6.3.6 Solutions S6.4 to S6.6 407
6.4 Structure and Parameter Changes 410
6.4.1 Rayleigh Quotient 410
6.4.2 Sensitivity of Natural Frequencies and Mode Shapes 411
6.4.3 Reduction of Degrees of Freedom 416
6.4.4 Influence of Constraints on Natural Frequencies and ModeShapes 418
6.4.5 Examples of the Reduction of Degrees of Freedom 422
6.4.6 Problems P6.7 to P6.9 430
6.4.7 Solutions S6.7 to S6.9 431
6.5 Forced Undamped Vibrations 437
6.5.1 General Solution 437
6.5.2 Harmonic Excitation (resonance, absorption) 438
6.5.3 Transient Excitation (Rectangular Impulse) 444
6.5.4 Examples 448
6.5.5 Problems P6.10 to P6.12 451
6.5.6 Solutions S6.10 to S6.12 452
6.6 Damped Vibrations 455
6.6.1 Determination of Damping 455
6.6.2 Free Damped Vibrations 456
6.6.3 Harmonic Excitation 458
6.6.4 Periodic Excitation 463
6.6.5 Examples 466
6.6.6 Problems P6.13 to P6.16 471
6.6.7 Solutions S6.13 to S6.16 471
Chapter 7 Simple Nonlinear and Self-Excited Oscillators 476
7.1 Introduction 476
7.2 Nonlinear Oscillators 479
7.2.1 Undamped Free Nonlinear Oscillators 479
7.2.2 Forced Vibrations with Harmonic Excitation 482
7.2.3 Examples 487
7.2.4 Problems P7.1 to P7.2 499
7.2.5 Solutions S7.1 and S7.2 500
7.3 Self-Excited Oscillators 501
7.3.1 General Perspective 501
7.3.2 Examples 502
7.3.3 Problems P7.3 and P7.4 511
7.3.4 Solutions S7.3 and S7.4 513
Chapter 8 Rules for Dynamically Favorable Designs 516
Chapter 9 Relations to System Dynamics and Mechatronics 522
9.1 Introduction 522
9.2 Closed-Loop Controlled Systems 525
9.2.1 General Perspective 525
9.2.2 Example: Influencing Frame Vibrations by a Controller 527
Symbols 535
References 540
Index 542