Synergetics and Fractals in Tribology (eBook)

Preface 6
Contents 8
Introduction 12
1 Key Features and Operating Conditions of Tribocoupling 14
1.1 Friction, Wear, and Lubrication. Concepts Development 14
1.2 Performance Analysis of Oil Field Equipment in Terms of Mechanical--Chemical Defectiveness 21
1.2.1 Assessment of the Level of Corrosive Mechanical Fracture in Equipment 22
1.2.2 Mathematical Modeling of Mechanical--Chemical Defectiveness and Calculations on Durability 25
1.3 Performance Analysis of Oil Field Equipment in Terms of Non-stationary Loading 26
Literatures 34
2 Scientific Foundations of Stochastic Tribomodeling 36
2.1 Probability Analysis of Generalized Variables Based on Stochastic Nature of Parameters 37
2.2 Varying Generalized Variable When Planning Experiments 60
2.3 Application of Group Method of Data Handling with Respect to Tribotechnical Problems 62
2.3.1 Development of Mathematical Model with Initial Variables 64
2.3.2 Development of Mathematical Model with Generalized Variables 67
Literatures 70
3 Synergetic Model of Fracture and Mechanics of Fatigue Cracks During Friction 72
3.1 Synergetic Analysis of Plastic Deformation and Fracture Using Bifurcation Doubling Model 73
3.2 Application of Generalized Golden Ratios to Control Self-similarity and Stability Properties of Fractal Structure Distribution in Fatigue Cracks of Solids 91
3.3 Bifurcation Doubling Model (Feigenbaum Scheme) for Fatigue Crack Growth 102
3.3.1 Universality of the Feigenbaum Theory to Describe the Behavior of Nonlinear Systems 103
3.3.2 Bifurcation Doubling Process Forecasting 119
3.3.3 Analysis of the Noise Impact on the Feigenbaum Behavior 130
3.4 Synergetics of the Restructuring of Crystal Structures with Condensed State Under the Influence of External Forces 134
Literatures 149
4 Fractal Kinetics of Fracture 154
4.1 The Concept of Fractal---Fractal Dimension 154
4.2 Fractals in Condensed Matter Physics 156
4.3 Fractal Properties of Hierarchical Structures of Potential Relief 160
4.4 Kinetics of Fracture from Positions of the Theory of Fractals 166
4.5 Relationship Analysis of the Fractal Dimension of Pre-fracture Dissipative Structures with Mechanical Properties and Critical States of Deformation of Metals and Alloys 177
Literatures 188
5 Multifractal Analysis of Fatigue Failure 191
5.1 Key Concepts of Multifractal Analysis---Generalized Fractal Dimensions 191
5.2 Multifractal Nature of Micro-Cracks Merger 198
5.3 Multifractal Singularity Spectrum of Time Series 211
5.3.1 Standard Multifractal Formalism and Singularity Spectrum 213
5.3.2 Wavelet Transform Modulus Maxima Method 217
5.3.3 Multifractal Fluctuation Analysis 222
5.3.4 Simple Multifractal Time Series Models 228
Literatures 231
6 Fractal Analysis of Fatigue Failure of Kinematic Pair (Oil--Gas Xmas Tree Valve) 234
6.1 Design Features and Operating Conditions of Flow Control Devices 235
6.2 Contact Interaction Between the Bolt and Nut. N.E. Zhukovsky Problem 240
6.3 Load Distribution on Screw of Kinematic Pair 242
6.4 Study of Wear of the Valve Kinematic Pair in the Elastic--Plastic Deformation Zone 249
6.5 Assessment of Tribological Characteristics of Kinematic Pair 258
6.6 Mechanics of Frictional Conical Surfaces of Xmas Tree Valves 270
6.7 Fractal Dimension and Analysis of Fatigue Non-spreading Cracks of the Kinematic Pair of Valve 275
6.8 Improving Durability of the Kinematic Pair of Valve 284
6.9 Test Stand of the Kinematic Pair of Valve 285
6.10 Choosing a Lubricant for the Direct Flow Valve of Xmas Tree 291
Literatures 297
7 Fractal Fatigue Analysis of Valve Units of Sucker Rod Pumps 300
7.1 Design and Analysis of Operating Conditions of Valve Units 300
7.2 Analytical Dependencies for Assessing the Tightness of Valve Units 301
7.3 Wear and Its Determination in Valve Units 307
7.4 Fluid Leakage and Its Determination in Valve Units 312
7.5 Recommendation for Improving the Wear Resistance of Valve Units 315
7.6 Fractal Dimension Analysis of Cumulative Crack Area of Valve Fracture 317
7.6.1 Measurement and Fractal Structure Analysis of the Rough Surfaces 318
7.6.2 Durability Modeling of Submersible Pumps Depending on Fractal Dimension of Surface Breakage and Cumulative Crack Area of Valve Fracture 321
7.7 Kinetics of Damage at Contact Fatigue of Parts of Submersible Pump 324
7.8 Contact Interaction Diagnosis of Solids at Friction Using Fractal Analysis 327
7.8.1 Emergence of Fractal Structures Through the Evolution of Complex Systems 329
7.8.2 Dependence of Contour Pressure on Roughness at Elastic and Plastic Contacts 331
7.8.3 Calculation of Fractal Dimension on Supporting Surface Curve at Threshold Values of Injection 335
7.8.4 Calculation of Power Spectrum of Roughness Profile and Contact Regime Diagnosis of Metal Bodies 337
Literatures 341
8 Flicker Noise Spectroscopy (FNS) of Dynamics Signals and Its Application in Wear of Oil-Field Compressor Units (OFCU) 343
8.1 Analysis of Technical Manufacturing Characteristics of Operating Oil-Field Compressor Units 343
8.2 Flicker Noise Spectroscopy---A New Approach to Solving the Problem of Extracting Information from Complex Dynamic Signals 345
8.3 Essence of Flicker Noise Spectroscopy 350
8.4 Flicker Noise and Self-similar Criticality 352
8.5 Conceptual Foundations of Flicker Noise Spectroscopy 356
8.6 Assessment of Irregularities-Bursts and Catastrophic Changes in the State of Oil-Field Compressor Units 360
8.6.1 Formulation of the Problem and Solution Method 360
8.6.2 Parameterization of Singular Component of Signal Power Spectrum 361
8.6.3 Precursor Calculation of System Catastrophic States 369
8.7 Parameterization of Signal Regular Component 371
8.8 Joining Asymptotic Representations of the Structure Function /widetilde{/Phi }_{{/varvec R}}^{{{/varvec (2)}}} /left({/varvec /tau}/right) 381
Literatures 389