DescriptionThis reference work provides a comprehensive insight into past developments in the application of non-linear dynamics, such as production systems in the manufacturing and process engineering, mechanical engineering and plant construction and automation technology. As such, it is the first publication to document the successful implementation of non-linear dynamics into current tasks or problems of engineering thus far unsolved. The interdisciplinary team of contributors from research and industry establishes ties between mechanical methods of manufacturing and new methods reaching the dynamics of production lines and complete production systems.
1 Dynamical Systems and Production Systems.
1.2 The Bucket Brigade Production System.
1.2.2 Non-constant Speeds.
1.2.3 Bucket Brigades and Learning.
1.3 Fluid Models of Production Networks.
1.4 Dynamics of Supply Chains.
1.4.1 Simulation and Control.
2 Method of Stabilization of a Target Regime in Manufacturing and Logistics.
2.1.1 Stabilization of a Target Regime (STR Method).
2.1.2 Constraints-based Hierarchy of Models.
2.1.3 The Algorithm of the Optimal Management of the Systems in Work-sharing Manufacturing.
2.2 The Hierarchy of Models.
2.3 Dynamics of the Models in the Hierarchy.
2.4 Algorithm of Stabilization of the Target Regime for OWS Models.
2.5 Concluding Remarks.
3 Manufacturing Systems with Restricted Buffer Sizes.
3.2 Hybrid Models.
3.2.1 Switched Arrival and Server Systems.
3.2.2 Limiting Cases.
3.2.3 Dynamics and Bifurcations.
3.2.4 Modified Switching Rules.
3.2.5 Manufacturing Systems with Setup Times.
3.3 Performance of Manufacturing Systems.
3.3.1 Evaluation of Cost Functions.
3.3.2 Optimization and Chaos Control.
3.4 Switched Discrete Deterministic Systems.
3.4.2 Small Stochastic Disturbances.
4 Modeling and Analysis of a Re-entrant Manufacturing System.
4.1.1 Re-entrant Manufacturing Systems and Models.
4.1.2 Control Policies and Their Analysis.
4.2 “Two Products – Two Stages” Re-entrant Manufacturing System.
4.3 Dynamical Model.
4.4 Analysis of Dynamics.
4.4.1 Sensitivity to Initial Conditions.
4.4.2 Ergodicity and Stationarity.
4.5 Dynamical Concept for Manufacturing Control.
4.6 Simulation Model.
4.7 Analysis of Scheduling Policies.
4.8 Conclusion and Outlook.
5 Nonlinear Models for Control of Manufacturing Systems.
5.2 Extensions to the Standard Fluid Model.
5.2.1 A Common Fluid Model.
5.2.2 An Extension.
5.2.3 An Approximation to the Extended Fluid Model.
5.2.4 A Hybrid Model.
5.3 A New Flow Model.
5.3.1 Introduction to Traffic Flow Theory: the LWR Model.
5.3.2 A Traffic Flow Model for Manufacturing Flow.
5.4 The Manufacturing Flow Model Revisited.
5.5 Concluding Remarks.
6 Modeling and Optimization of Production Processes: Lessons from Traffic Dynamics.
6.1 Modeling the Dynamics of Supply Networks.
6.1.1 Modeling One-dimensional Supply Chains.
6.1.2 “Bull-whip Effect” and Stop-and-Go Traffic.
6.1.3 Dynamical Solution and Resonance Effects.
6.1.4 Discussion of Some Control Strategies.
6.1.5 Production Units in Terms of Queueing Theoretical Quantities.
6.1.6 Calculation of the Cycle Times.
6.1.7 Feeding Rates, Production Speeds and Inventories.
6.1.8 Impact of the Supply Network’s Topology.
6.1.9 Advantages and Extensions.
6.2 Many-particle Models of Production Processes.
6.2.1 Learning from Pedestrians.
6.2.2 Optimal Self-organization and Noise-induced Ordering.
6.2.3 “Slower-is-Faster Effect” in Merging Flows.
6.2.4 Optimization of Multi-object Flows.
6.3 Summary and Outlook.
II Machine Tools and Manufacturing Processes.
7 Nonlinear Dynamics of High-speed Milling Subjected to Regenerative Effect.
7.2 Nonlinear Dynamics of Turning.
7.2.1 Modeling of Turning.
7.2.2 Bifurcation Analysis of Turning.
7.2.3 Global Dynamics of Self-interrupted Cutting.
7.3 Nonlinear Vibrations of High-speed Milling.
7.3.1 Modeling of High-speed Milling.
7.3.2 Bifurcation Analysis of High-speed Milling.
7.3.3 Global Dynamics of Parametrically Interrupted Cutting.
8 Mode-coupled Regenerative Machine Tool Vibrations.
8.2 Metal Cutting.
8.2.1 Oblique Cutting.
8.3 Three-degree-of-freedom Model of Metal Cutting.
8.3.1 Cutting Forces.
8.3.2 The Equations of Motion.
8.4 Estimation of Model Parameters.
8.4.1 Structural Parameters.
8.4.2 Cutting Force Parameters.
8.4.3 Model Parameters.
8.5 Analysis of the Model.
8.5.1 Classical Limit.
8.5.2 Stability Analysis of the Undamped System Without Delay.
8.5.3 Stability Analysis of the Two-degree-of-freedom Model with Delay.
9 Influence of the Workpiece Profile on the Self-excited Vibrations in a Metal Turning Process.
9.2 Modeling of Turning Process.
9.3 Analytical Investigations of Primary Cutting.
9.4 Numerical Analysis of Primary Cutting.
9.5 Numerical Investigation of Finishing Cutting Dynamics.
10 Modeling of High-speed Milling for Prediction of Regenerative Chatter.
10.2.1 Material Model.
10.2.2 Machine Model.
10.2.3 The Total Milling Model.
10.3 Stability Analysis of the Milling System.
10.3.1 Method of D-partition.
11 Nonlinear Dynamics of an External Cylindrical Grinding System and a Strategy for Chatter Compensation.
11.2 Wheel–Workpiece Dynamics.
11.2.1 Chatter Vibrations.
11.2.3 Hilbert Transform.
11.2.4 Chatter Detection .
11.3 Modeling of Mechanical Structure Dynamics.
11.3.1 Model of Guideway Connection.
11.3.2 Resonances in Guideway System.
11.4 Feed Drive.
11.4.1 Requirements for the Infeed Drive.
11.4.2 Nonlinear Effects and Control Scheme.
11.4.3 Compensation of Cogging.
11.5 Waviness Compensation.
12 Problems Arising in Finite-Element Simulations of the Chip Formation Process Under High Speed Cutting Conditions.
12.2 Orthogonal Cutting Process.
12.2.2 Material Laws.
12.2.3 Remeshing and Chip Separation.
12.3 Simulation Results and the Comparison with Experimental Results.
12.3.1 Process Parameters.
12.3.2 Cutting Forces and Chip Geometry.
12.3.3 Residual Stresses.
12.3.4 Additional Analysis of the Forming Model.
12.4 Analysis of the Thermal Effects on the Tool.
12.5 3D Model for an Outer Turning Process.
12.6 Conclusions and Outlook.
13 Finite-element Simulation of Nonlinear Dynamical Effects in Coating–Substrate Systems.
13.2 Mechanics of Chip Formation in Cutting Processes.
13.2.1 Basic Assumptions of Modeling.
13.2.2 Investigations of the Nonlinear Dynamical Cutting Process.
13.2.3 Results of Nonlinear Dynamical Loading of the Coating-Substrate System.
13.3 Modeling and Simulation of Coating–Substrate Systems.
13.3.1 3D Coating–Substrate Simulations Based on Parallel Computing.
13.3.2 Indenter Test Simulation.
13.4 Time Series Analysis.
14 Investigation of Nonlinear Dynamic Effects in Loaded Layer–Substrate Systems Through Molecular Dynamics Simulation.
14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
14.2 Layer–Substrate System Configuration and Material Representation . . . . . 252
14.3 Properties of the Relaxed System . . . . . . . . . . . . . . . . . . . . . . . . 254
14.3.1 Stress Distributions in the Relaxed System.
14.3.2 Interface Properties.
14.4 Response of the Loaded Layer–Substrate System.
14.4.1 Deformation and Forces.
14.4.2 Stress Distribution in the Loaded Layer–Substrate System.
15 Simulation, Experimental Investigation and Control of Thermal Behavior in Modular Tool Systems.
15.2 Investigated Tool Mountings.
15.3 Project Realization.
15.3.1 Determination of Replacement Heat-transmission Coefficient for Component Joints in a FE Model.
15.3.2 Building of the Test Stand for Tool Investigations with Fixed Shaft.
15.3.3 Thermographic Investigations.
15.4 Maximal Correlation and Optimal Transformations.
15.4.1 Reconstruction of Thermally Induced Displacements in Finite-element Models.
15.4.2 Reconstruction of Thermally Induced Displacements in Real Data.
15.5 The Thermal Behavior of a Modular Tool System in a Working Milling Machine.
16 Wrinkling in Sheet Metal Spinning 287
16.2 Wrinkling in Sheet Metal Spinning.
16.3 Influence of Nonlinear Dynamic Effects on Wrinkling .
16.4 The Spinning Process as a Frictional Contact Problem.
16.5 Time-series Analysis.
16.6 Finite-element Model.
17 Nonlinear Vibrations During the Pass in a Steckel Mill Strip Coiling Process.
17.2 Mechanical Model of the Coiling Process.
17.3 Results of the Simulation.
III Dynamics of Robots and Machines.
18 New Type of Forming Machine.
18.2 Theoretical Analysis of Motion with Rigid Impacts.
18.2.1 Symmetric Case.
18.2.2 Asymmetric Cases.
18.5 Comparison of Simulation and Experimental Results.
18.6 Analysis of Motion with Soft Impacts.
19 Nonlinear Vibration in Gear Systems.
19.2 One-stage Gear Model.
19.3 Vibrations of a Gear System in Presence of a Weak Resonance Term.
19.4 Vibrations of a Gear System with a Flexible Shaft.
20 Measurement and Identification of Pre-sliding Friction Dynamics.
20.2 Friction Characterization.
20.2.1 Friction Model Structures.
20.2.2 Acquisition of Friction Data.
20.2.3 Simulation of Friction Data.
20.3 Identification Methods and Results.
20.4 Regression and Time-Series Modeling.
20.4.1 NARMAX Models.
20.4.2 Support Vector Models.
20.4.3 Local Models.
20.4.4 Neural Network Methods.
20.4.5 Numerical Results of Black-box Methods.
20.5 Identification of Physics-based Models.
20.5.1 The Linear Regression (LR) Approach.
20.5.2 The Dynamic Linear Regression (DLR) Approach.
20.5.3 The Nonlinear Regression (NLR) Approach.
20.5.4 Model Order Selection and Assessment.
20.5.5 Identification Results.
20.6 Discussion and Conclusions.
21 Coordination of Mechanical Systems.
21.2 Dynamic Model of the Robot Manipulators.
21.3 Coordination Controller.
21.3.1 Feedback-Control Law.
21.3.2 An Observer for the Coordination Errors (e, e).
21.3.3 An Observer for the Slave Joint State (q<sub>s</sub>, q<sub>s</sub>).
21.3.4 Estimated Values for (q<sub>m</sub>, q<sub>m</sub>).
21.3.5 Ultimate Boundedness of the Closed-loop System.
21.4 Experimental Case Study.
21.4.1 Joint Space Dynamics.
21.4.2 Experimental Results.
21.5 Conclusions and Further Extensions.
IV Non-conventional Manufacturing Processes.
22 Nonlinear Dynamics and Control of Ripple Formation in Abrasive Water-jet Cutting.
22.2 Phenomenology of Ripple Formation.
22.2.1 Ripple Amplitude and Lag.
22.2.2 Ripple Wavelength.
22.3 Cutting Processes and Pattern Formation.
22.3.1 Pattern Formation by Front Instabilities.
22.3.2 Phenomenological Theory of the Evolution of Cutting Fronts.
22.3.3 Solution of Model Equation.
22.3.4 Spontaneous Ripple Formation.
22.3.5 Suppression of Spontaneous Ripple Formation by Periodic Modulation.
22.4 Experimental Results for Ripple Suppression.
23 Modeling and Simulation of Process Monitoring and Control in Laser Cutting.
23.2 Diagnosis and Analysis of Dynamic Features.
23.3 Coupled Equations of Motion.
23.3.1 Axial Dynamics of the Melting Front.
23.3.2 Lateral Dynamics of the Melting Front.
23.3.3 Melt Flow.
23.4 Heat Convection Influences Ripple Formation .
23.5 Observation of the Cutting Front.
23.6 Quality Classes: Observation and Modeling.
23.8 Analysis Using Spectral Methods.
23.9 Conclusion and Outlook.
24 Approximate Model for Laser Welding.
24.1.1 Technical Motivation and Physical Task.
24.1.2 Asymptotic Methodology.
24.1.3 Former Works.
24.2 Motion of the Melting Front.
24.2.1 Similarities of Thermal Material Processes.
24.2.2 The One-phase problem.
24.2.3 Approximate Equations of Motion.
24.3 Motion of the Capillary.
24.3.1 Experimental Observation and Physical Analysis.
24.3.2 Mathematical Problem Formulation.
24.3.3 Boundary-layer Character of the Melt Flow.
24.3.4 Flow at the Stagnation Point.
24.3.5 Flow Around the Capillary.
24.5 Conclusion and Outlook.
25 Short-time Dynamics in Laser Material Processing.
25.2 The Free Boundary Problem.
25.3 Finite-dimensional Approximations.
26 An Approach to a Process Model of Laser Beam Melt Ablation Using Methods of Linear and Nonlinear Data Analysis.
26.2 Experimental Setup.
26.3 Linear and Nonlinear Data Analysis.
26.4 A Stochastic Process Model.
27 Dynamics-based Monitoring of Manufacturing Processes: Detection of Transitions Between Process States.
27.2 Information Rate.
27.3 Examples of Transitions.
27.3.3 Laser-beam Welding.
27.4 Discussion and Conclusions.
V Chemical and Electro-chemical Processes.
28 Real-time Monitoring of Dynamical State Changes in Staged Coal Combustion.
28.2.1 Practical Approach.
28.2.2 Example Application.
28.2.3 Future Developments.
28.2.4 Broader Implications.
29 Towards Constructive Nonlinear Dynamics – Case Studies in Chemical Process Design.
29.1 Nonlinear Dynamics Analysis in Chemical Engineering.
29.2 Analysis-based Process Design.
29.2.1 Illustrative Example.
29.2.2 Continuation Analysis.
29.3 Analysis-based Control System Design.
29.3.1 Illustrative Example.
29.3.2 Controller Tuning Procedure.
29.4 Limitations of Analysis-based Design.
29.5 Constructive Methods.
29.5.1 Normal Vector-based Constraints for Parametric Robustness.
29.5.2 Optimization with Robust Stability and Feasibility Constraints.
29.5.3 Optimization with Parametric Robustness with Respect to Hysteresis.
29.6 Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524
30 Nonlinear Dynamics in Chemical Engineering and Electro-chemical Manufactory Technologies.
30.3 Surface Structuring by Micro-electropolishing.
30.4 Etching Processes: Structure Formation on the Rotating Disk Electrode.
30.5 Oscillating BZ Reactors Coupled via Liquid Membranes.
30.6 Reaction in Mono-porous Foams.
31 Galvanostatic Studies of an Oxygen-evolving Electrode.
31.1.1 N-NDR and N-HNDR Behavior.
31.3.1 Cyclic Voltammogram.
31.3.2 Methanol and Ethanol.
31.3.4 Phosphoric Acid.
32 Wavelet Analysis of Electropolished Surfaces.
32.2 The Experimental Setup.
32.3 Continuous Wavelet Transform.
32.4 Characteristic Length Scales and Scaling Regions.
32.5 Multi-fractal Analysis.
32.6 Stochastic Analysis.
33 Spatial Inhomogeneity in Lead–Acid Batteries.
33.2.1 Local Potential Measurements with Ag/AgCl Electrodes.
33.2.2 Local Potential Measurements with Auxiliary Lead Electrodes.
33.3 Results and Discussion.
33.3.1 Local Potential Measurements with Ag/AgCl Electrodes.
33.3.2 Local Potential Measurements with Lead Electrodes.
33.4 Conclusions and Future Work.