Arczewski / Blajer / Fraczek Multibody Dynamics

Computational Methods and Applications
1. Auflage 2010
ISBN: 978-90-481-9971-6
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 327 Seiten

The ECCOMAS Thematic Conference “Multibody Dynamics 2009” was held in Warsaw, representing the fourth edition of a series which began in Lisbon (2003), and was then continued in Madrid (2005) and Milan (2007), held under the auspices of the European Community on Computational Methods in Applied Sciences (ECCOMAS). The conference provided a forum for exchanging ideas and results of several topics related to computational methods and applications in multibody dynamics, through the participation of 219 scientists from 27 countries, mostly from Europe but also from America and Asia. This book contains the revised and extended versions of invited conference papers, reporting on the state-of-the-art in the advances of computational multibody models, from the theoretical developments to practical engineering applications. By providing a helpful overview of the most active areas and the recent efforts of many prominent research groups in the field of multibody dynamics, this book can be highly valuable for both experienced researches who want to keep updated with the latest developments in this field and researches approaching the field for the first time.

Autoren/Hrsg.

Arczewski, Krzysztof

Blajer, Wojciech

Fraczek, Janusz

Wojtyra, Marek

Inhaltsverzeichnis

1;Preface
;6
2;Contents
;8
3;A Flexible Multibody Pantograph Model for the Analysis of the Catenary–Pantograph Contact;10
3.1;1 Introduction;10
3.2;2 Flexible Multibody Systems;13
3.2.1;2.1 Flexible Body Equations of Motion;13
3.2.2;2.2 Kinematic Joints with Virtual Bodies;16
3.3;3 Co-simulation of Multibody and Finite Element Codes;18
3.3.1;3.1 Integration of the Finite Elements Equations of Motion;19
3.3.2;3.2 Integration of the Multibody Equations of Motion;20
3.3.3;3.3 Co-simulation Using Different Codes;20
3.4;4 Analysis of the Pantograph–Catenary Contact Problem;23
3.4.1;4.1 Pantograph Multibody Models;23
3.4.2;4.2 Catenary Finite Element Model;30
3.4.3;4.3 Simulation Scenario and Results;31
3.5;5 Conclusions;33
3.6;References;34
4;Maneuvering Multibody Dynamics: New Developments for Models with Fast Solution Scales and Pilot-in-the-Loop Effects;37
4.1;1 Introduction;37
4.2;2 Coupled Pilot-Vehicle Model;41
4.3;3 Formulation of Maneuvers as Optimal Control Problems;42
4.4;4 Direct Solution of Maneuver Optimal Control Problems;44
4.4.1;4.1 Direct Transcription;44
4.4.2;4.2 Direct Multiple and Hybrid Single–Multiple Shooting;45
4.5;5 Applications and Results;47
4.5.1;5.1 Lateral Reposition MTE;47
4.5.2;5.2 Category-A Fly-Away;50
4.6;6 Concluding Remarks;53
4.7;References;54
5;Optimization of Multibody Systems and Their Structural Components;57
5.1;1 Introduction;57
5.2;2 Optimization of Flexible Multibody Systems;60
5.2.1;2.1 Equations of Motion;60
5.2.2;2.2 Formulation of the Optimization Problem;61
5.2.3;2.3 Time Integration Method;61
5.2.4;2.4 Evaluation of the Objective Function and of the Design Constraints;62
5.2.5;2.5 Sensitivity Analysis;63
5.2.6;2.6 Optimization Algorithms;65
5.3;3 Topology Optimization Techniques;67
5.3.1;3.1 Application to the Design of Static Trusses;68
5.3.2;3.2 Topology Optimization of Multibody Systems;69
5.4;4 Example;71
5.4.1;4.1 Problem Description;71
5.4.2;4.2 Optimization;72
5.5;5 Conclusions;74
5.6;References;74
6;Real-Time Aeroservoelastic Analysis of Wind-Turbines by Free Multibody Software;77
6.1;1 Introduction;77
6.2;2 Approach;78
6.3;3 Wind-Turbine Description;80
6.4;4 Baseline Controller;81
6.5;5 Multibody Model;83
6.5.1;5.1 Unconstrained Dynamics;83
6.5.2;5.2 Constrained Dynamics;84
6.5.3;5.3 Structural Flexibility;85
6.5.4;5.4 Numerical Integration;85
6.5.5;5.5 CART Wind Turbine Multibody Model;86
6.6;6 Real-Time Simulation;88
6.7;7 Conclusions;91
6.8;8 Additional Material;92
6.9;References;92
7;Comparison of Planar Structural Elements for Multibody Systems with Large Deformations;95
7.1;1 Introduction;96
7.2;2 Floating Frame of Reference Formulation;97
7.3;3 Absolute Nodal Coordinate Formulation;103
7.4;4 Numerical Examples;106
7.4.1;4.1 Static Example Problem;106
7.4.2;4.2 Dynamic Example Problems;108
7.5;5 Conclusions;112
7.6;References;112
8;Modeling and Analysis of Rigid Multibody Systems with Translational Clearance Joints Based on the Nonsmooth Dynamics Approach;114
8.1;1 Introduction;114
8.2;2 Basic Set-Valued Elements;116
8.3;3 Set-Valued Force Laws for Frictional Unilateral Contacts;118
8.4;4 Dynamics of Nonsmooth Rigid Multibody Systems;120
8.5;5 Moreau's Time-Stepping Method;123
8.6;4 Demonstrative Application to a Slider-Crank Mechanism;128
8.7;5 Conclusions;135
8.8;References;136
9;Application of General Multibody Methods to Robotics;138
9.1;1 Introduction;138
9.2;2 Absolute Coordinates Approach to Robot Kinematic Analysis and Singular Configuration Detection;139
9.2.1;2.1 Theoretical Background;140
9.2.2;2.2 Robotic Example;143
9.3;3 Simulation Study of Stewart Platform with Model-Based Control;145
9.3.1;3.1 Methods;145
9.3.1.1;3.1.1 Manipulator Kinematics;146
9.3.1.2;3.1.2 Manipulator Dynamics;148
9.3.1.3;3.1.3 Friction in Actuators;149
9.3.1.4;3.1.4 DC Motor;149
9.3.1.5;3.1.5 Control System;150
9.3.2;3.2 Results;151
9.4;4 Dynamic Analysis of a Flexible Power Transmission Mechanism;152
9.4.1;4.1 An Outline of Dynamic Analysis of Flexible MBS;153
9.4.2;4.2 Power Transmission Mechanism of POLYCRANK Robot;154
9.4.3;4.3 Dynamic Analysis of Power Transmission Mechanism;156
9.5;5 Conclusions;158
9.6;References;159
10;Energy Considerations for the Stabilization of Constrained Mechanical Systems with Velocity Projection;160
10.1;1 Introduction;160
10.2;2 Constrained Dynamics Formulation;161
10.3;3 Coordinate Projection;162
10.4;4 Total Energy Balance;164
10.5;5 Projection Energy Balance;167
10.5.1;5.1 Some Preliminary Results;167
10.5.2;5.2 Conditions for Energy Dissipation;168
10.6;6 Numerical Experiments;169
10.6.1;6.1 Two Particle System;169
10.6.2;6.2 Five-Bar Pendulum;173
10.7;7 Conclusions;176
10.8;References;177
11;A General Purpose Algorithm for Optimal Trajectory Planning of Closed Loop Multibody Systems;179
11.1;1 Introduction;179
11.2;2 Optimal Trajectory Planning Problem of Multibody Systems;181
11.2.1;2.1 Problem Formulation 1: Minimal Form of Equation of Motion;181
11.2.2;2.2 Problem Formulation 2: Augmented Equations;182
11.2.3;2.3 Solution Procedure for Optimal Trajectory Planning Problems;183
11.3;3 Optimal Trajectory Planning Algorithm Using Coordinate Partitioning and Embedding Techniques;185
11.4;4 Optimal Trajectory Planning Algorithm Based on an Augmented Formulation;188
11.5;5 Numerical Examples;191
11.5.1;5.1 Non-redundant Actuation System;191
11.5.2;5.2 Redundant Actuation System;194
11.6;6 Conclusions;197
11.7;References;198
12;Real-Time Simulation of Extended Vehicle Drivetrain Dynamics;200
12.1;1 Introduction;200
12.1.1;1.1 Notations;204
12.2;2 Powertrain System and Vehicle Dynamics;204
12.2.1;2.1 Multibody System;205
12.2.2;2.2 Control Units;207
12.2.3;2.3 Electrical System;207
12.2.4;2.4 Coupled System;208
12.2.5;2.5 Analysis Tasks;208
12.3;3 Time Integration;210
12.3.1;3.1 Office Simulation;210
12.3.2;3.2 Realtime Office;210
12.3.3;3.3 Realtime;211
12.4;4 Application;212
12.4.1;4.1 Model;213
12.4.2;4.2 Simulation Results;213
12.4.2.1;4.2.1 Realtime Calculations;214
12.4.2.2;4.2.2 Comparison Implicit and Explicit Solution;215
12.4.2.3;4.2.3 Comparison Realtime and Office;215
12.4.2.4;4.2.4 Comparison with Respect to System Evaluation;216
12.5;5 Conclusion;217
12.6;References;217
13;Assessment of Antagonistic Muscle Forces During Forearm Flexion/Extension;220
13.1;1 Introduction;221
13.1.1;1.1 Redundancy Problem Formulation;221
13.1.2;1.2 Classification of Solving Methods;222
13.1.3;1.3 Objective of this Study;223
13.2;2 Material and Methods;224
13.2.1;2.1 Principle;224
13.2.1.1;2.1.1 Protocol Step 1: Force Calibration;224
13.2.1.2;2.1.2 Protocol Step 2: Force Quantification;224
13.2.2;2.2 Experimental Set-up;225
13.2.3;2.3 Model and Hypotheses;226
13.2.4;2.4 Process of Muscle Force Quantification;228
13.2.4.1;2.4.1 Muscle Force Calibration;228
13.2.4.2;2.4.2 Muscle Force Quantification;232
13.3;3 Results;235
13.3.1;3.1 Joint Kinematics and Dynamics;235
13.3.2;3.2 Muscle Forces;236
13.3.2.1;3.2.1 Muscle Force Assessment;236
13.3.2.2;3.2.2 Statistical Validation;237
13.4;4 Discussion;238
13.4.1;4.1 Joint Kinematics and Dynamics;238
13.4.2;4.2 Muscle Force Quantification;239
13.4.2.1;4.2.1 EMG Processing and Parameter Choice;239
13.4.2.2;4.2.2 Comparison to Existing Methods;239
13.4.3;4.3 Prospects;240
13.5;References;241
14;Computing Time Reduction Possibilities in Multibody Dynamics;244
14.1;1 Introduction;244
14.2;2 Determination of a Suitable Initial Value;246
14.2.1;2.1 Kinematics;246
14.2.2;2.2 Kinetics;247
14.2.2.1;2.2.1 Geometry of the Excitation;247
14.2.2.2;2.2.2 Relationship of Tangential and Radial Belt Velocity;248
14.2.2.3;2.2.3 Tangential Balance of Forces;249
14.2.2.4;2.2.4 Radial Balance of Forces;250
14.2.2.5;2.2.5 Axial Balance of Forces;250
14.2.2.6;2.2.6 Change of the Running Radius;251
14.2.2.7;2.2.7 Summary of the Stationary Belt Model and Environment Interaction;251
14.2.2.8;2.2.8 Reduction of the Final Equations;253
14.3;3 Computational Effort During Integration;254
14.3.1;3.1 Stabilising Equations of Motion;255
14.3.1.1;3.1.1 Coordinate Settings;255
14.3.1.2;3.1.2 Equations of Motion;258
14.3.1.3;3.1.3 Analysis of Instability;259
14.3.2;3.2 Parallel Computing Architectures;261
14.4;4 Conclusion;262
14.5;References;263
15;Optimization-Based Design of Minimum Phase Underactuated Multibody Systems ;265
15.1;1 Introduction;265
15.2;2 Trajectory Tracking Control;266
15.2.1;2.1 Input–Output Normal-Form;267
15.2.2;2.2 Analysis of the Internal Dynamics;268
15.2.3;2.3 Feedback Linearization;269
15.2.4;2.4 Feed-forward Control Design;270
15.3;3 Design of Stable Zero-Dynamics;272
15.3.1;3.1 Identification of Possible Design Parameters;272
15.3.2;3.2 Optimization Criteria;274
15.3.3;3.3 Particle Swarm Optimization;276
15.4;4 Application Examples;277
15.4.1;4.1 Manipulator with One Passive Joint;277
15.4.1.1;4.1.1 System Without Disturbances and Uncertainties;279
15.4.1.2;4.1.2 System Under Disturbances and Uncertainties;281
15.4.2;4.2 Manipulator with Two Passive Joints;281
15.5;5 Conclusions;285
15.6;References;286
16;GPU-Based Parallel Computing for the Simulation of Complex Multibody Systems with Unilateral and Bilateral Constraints: An Overview;287
16.1;1 Introduction;287
16.2;2 Review of Computing on the Graphics Processing Unit;289
16.3;3 Large Scale Multibody Dynamics on the GPU;296
16.3.1;3.1 The Formulation of the Equations of Motion;296
16.3.2;3.2 The Time Stepping Solver;299
16.3.3;3.3 The GPU Formulation of the CCP Solver;302
16.4;4 Numerical Experiments;306
16.5;5 Conclusions and Directions of Future Work;309
16.6;References;310
17;Investigation of Gears Using an Elastic Multibody Model with Contact;312
17.1;1 Introduction;313
17.2;2 Classical Models;313
17.2.1;2.1 Finite Element Model;314
17.2.2;2.2 Rigid Body Model;314
17.2.3;2.3 Comparison;315
17.3;3 Elastic Multibody Model;317
17.3.1;3.1 Contact Algorithm;318
17.3.1.1;3.1.1 Coarse Collision Detection;318
17.3.1.2;3.1.2 Fine Collision Detection;319
17.3.2;3.2 Integration;320
17.4;4 Simulation Results;322
17.4.1;4.1 Spur Gears;322
17.4.2;4.2 Numerical Efficiency;323
17.4.3;4.3 Helical Gears;324
17.5;5 Experimental Results;326
17.6;6 Conclusions;328
17.7;References;329