Method of dimensionality reduction in contact mechanics and friction:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2015
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XVII, 265 S. graph. Darst. |
| ISBN: | 3642538754 9783642538759 |
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MARC
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| 245 | 1 | 0 | |a Method of dimensionality reduction in contact mechanics and friction |c Valentin L. Popov ; Markus Heß |
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Record in the Search Index
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CONTENTS
1 INTRODUCTION 1
1.1 GOAL OF THIS BOOK 1
1.2 METHOD OF DIMENSIONALITY REDUCTION AS THE LINK BETWEEN
THE MICRO- AND MACRO-SCALES 3
1.3 STRUCTURE OF THE BOOK 4
REFERENCES 5
2 SEPARATION OF THE ELASTIC
AND INERTIA! PROPERTIES
IN THREE-DIMENSIONAL SYSTEMS 7
2.1 INTRODUCTION 7
2.2 THE QUASI-STATIC STATE 8
2.3 ELASTIC ENERGY AS A LOCAL PROPERTY 8
2.4 KINETIC ENERGY AS A GLOBAL
PROPERTY 9
2.5 PROBLEMS 14
REFERENCES 18
3 NORMAL CONTACT PROBLEMS WITH
AXIALLY-SYMMETRIC BODIES
WITHOUT ADHESION 19
3.1 MAPPING OF THREE-DIMENSIONAL CONTACT PROBLEMS ONTO
ONE DIMENSION: THE BASIC IDEA 19
3.2 THE RULES OF GEIKE AND POPOV AND THE RULES OF HEB
FOR NORMAL CONTACT PROBLEMS 20
3.3 GENERAL MAPPING OF AXIALLY-SYMMETRIC PROFILES 25
3.4 THE MAPPING OF STRESS 27
3.5 THE MAPPING OF NON-AXIALLY-SYMMETRIC BODIES 28
3.6 PROBLEMS 29
REFERENCES 36
XI
HTTP://D-NB.INFO/1045098213
XII CONTENTS
4 NORMAL CONTACT WITH ADHESION 39
4.1 INTRODUCTION 39
4.2 RULE OF HELI FOR THE ADHESIVE CONTACT BETWEEN
AXIALLY-SYMMETRIC BODIES 40
4.3 THE ADHESIVE
CONTACT AND GRIFFITH CRACK 41
4.4 FULL REDUCTION OF THE ADHESIVE, ELASTIC CONTACT 46
4.5 EXAMPLE: ADHESION OF A SPHERE WITH A SUPERIMPOSED
RADIAL WAVEFORM 51
4.6 PROBLEMS 56
REFERENCES 62
5 TANGENTIAL CONTACT 65
5.1 INTRODUCTION 65
5.2 TANGENTIAL CONTACT WITH FRICTION FOR PARABOLIC BODIES 66
5.3 TANGENTIAL CONTACT WITH FRICTION FOR ARBITRARY
AXIALLY-SYMMETRIC BODIES 68
5.4 MAPPING OF STRESSES IN THE TANGENTIAL CONTACT 72
5.5 MAPPING OF LOCAL SLIP 73
5.6 PROBLEMS 75
REFERENCES 86
6 ROLLING CONTACT 87
6.1 THE MAPPING OF STEADY-STATE ROLLING CONTACTS 87
6.2 RULES FOR THE EXACT MAPPING OF ROLLING CONTACTS 90
6.3 SHAKEDOWN AND CREEP IN OSCILLATING ROLLING CONTACTS 90
6.4 PROBLEMS 96
REFERENCES 97
7 CONTACTS WITH ELASTOMERS 99
7.1 INTRODUCTION 99
7.2 STRESS RELAXATION IN ELASTOMERS 100
7.3 APPLICATION OF THE METHOD OF DIMENSIONALITY REDUCTION
IN VISCOELASTIC MEDIA: THE
BASIC IDEA 102
7.4 RADOK'S METHOD OF THE FUNCTIONAL EQUATIONS 103
7.5 FORMULATION OF THE REDUCTION METHOD FOR LINEARLY
VISCOUS ELASTOMERS 106
7.6 THE GENERAL VISCOELASTIC MATERIAL LAW 107
7.7 PROBLEMS 108
REFERENCES 112
8 HEAT TRANSFER
AND HEAT GENERATION 115
8.1 THERMAL CONDUCTIVITY AND RESISTANCE 115
8.2 TEMPERATURE DISTRIBUTION FOR A POINT HEAT SOURCE
ON A CONDUCTIVE HALF-SPACE 116
CONTENTS XM
8.3 THE UNIVERSAL DEPENDENCE OF THERMAL CONDUCTIVITY
AND CONTACT STIFFNESS 118
8.4 THE IMPLEMENTATION OF THE STEADY-STATE CURRENT FLOW
WITHIN THE FRAMEWORK OF THE
REDUCTION METHOD 119
8.5 HEAT GENERATION AND TEMPERATURE IN THE CONTACT
OF ELASTIC BODIES 122
8.6 HEAT GENERATION AND TEMPERATURE IN THE CONTACT
OF VISCOELASTIC BODIES 124
8.7 PROBLEMS 125
REFERENCES 129
9 ADHESION WITH ELASTOMERS 131
9.1 INTRODUCTION 131
9.2 STRESS CONCENTRATION NEAR THE BOUNDARY
OF AN ADHESIVE CONTACT 131
9.3 DEFORMATION CRITERION 133
9.4 STRESS CRITERION 134
9.5 ADHESIVE CONTACTS WITHOUT INITIAL STRESS 134
9.6 PROBLEMS 135
REFERENCES 141
10 NORMAL CONTACT OF ROUGH
SURFACES 143
10.1 INTRODUCTION 143
10.2 RANDOMLY ROUGH, STATISTICALLY ISOTROPIC SURFACES 144
10.3 FRACTAL, SELF-AFFINE
SURFACES 145
10.4 GENERATING THE EQUIVALENT ONE-DIMENSIONAL SYSTEM 146
10.5 NUMERICAL RESULTS OF THE BOUNDARY ELEMENT METHOD
AND THE METHOD OF DIMENSIONALITY REDUCTION 149
10.6 SELF-AFFINITY AND THE METHOD OF DIMENSIONALITY REDUCTION 153
10.7 CONTACT MECHANICS FOR SELF-AFFINE SURFACES FOR * 1 H 3. 154
10.8 EQUIVALENCE BETWEEN ROUGH SELF-AFFINE
AND AXIALLY-SYMMETRIC CONTACTS WITH THE SAME
HURST EXPONENT 157
10.9 PROBLEMS 159
REFERENCES 163
11 FRICTIONAL FORCE 165
11.1 INTRODUCTION 165
11.2 ENERGY DISSIPATION IN AN ELASTOMER WITH LINEAR RHEOLOGY 166
11.3 FRICTIONAL FORCE BETWEEN A RIGID AXIALLY-SYMMETRIC
INDENTER AND AN ELASTOMER 167
11.3.1 PARABOLIC INDENTER 167
11.3.2 AXIALLY-SYMMETRIC INDENTER WITH AN ARBITRARY FORM . 168
11.4 THE HALF-SPACE APPROXIMATION 169
XIV CONTENTS
11.5 CALCULATION OF THE FRICTIONAL FORCE WITH A CONICAL
INDENTER WITHIN THE FRAMEWORK OF THE METHOD
OF
DIMENSIONALITY REDUCTION 170
11.6 CORRECTION COEFFICIENT FOR THE CONVERSION FROM
THREE-DIMENSIONAL TO ONE-DIMENSIONAL PROFILES 173
11.7 CONTACTS BETWEEN ROUGH SURFACES 176
11.8 CONTACT OF A FLAT, SMOOTH ELASTOMER WITH A NOMINALLY
FLAT, ROUGH BODY 176
11.9 CONTACT BETWEEN A ROUGH ELASTOMER AND A RIGID,
ROUGH SURFACE 177
11.10 PROBLEMS 178
REFERENCES 188
12 FRICTIONAL DAMPING 189
12.1 INTRODUCTION 189
12.2 DAMPING BY DRY FRICTION 189
12.3 DAMPING OF ELASTOMERS FOR NORMAL OSCILLATIONS 192
12.4 PROBLEMS 193
REFERENCE 195
13 THE COUPLING TO MACROSCOPIC
DYNAMICS 197
13.1 INTRODUCTION 197
13.2 HYBRID MODELS: FOREGOING THE FORMULATION OF AN
EXPLICIT
LAW OF FRICTION 197
13.3 SIMULATION OF A MICRO-DRIVE 200
13.3.1 CREATING A MACROSCOPIC MODEL 201
13.3.2 CREATING A MICROSCOPIC MODEL 201
13.4 PROBLEMS 203
REFERENCES 206
14 ACOUSTIC EMISSION IN ROLLING CONTACTS 207
14.1 INTRODUCTION 207
14.2 ACOUSTIC EMISSION RESULTING FROM THE ROLLING
OF A WHEEL*AN ANALYTICAL SOLUTION 208
14.3 ACOUSTIC EMISSION RESULTING FROM ROLLING
OF A WHEEL*A DYNAMIC SIMULATION 211
REFERENCES 214
15 COUPLING TO THE MICROSCALE 215
15.1 INTRODUCTION 215
15.2 NON-LINEAR STIFFNESS ON THE "MICROSCALE" 215
15.3 COUPLING WITH THE MICROSCALE USING THE EXAMPLE
OF THE HERTZIAN CONTACT 216
CONTENTS
XV
15.4 COUPLING WITH THE MICROSCALE FOR THE CASE
OF A RANDOMLY ROUGH, FRACTAL SURFACE 217
REFERENCES 219
16 AND NOW WHAT? 221
16.1 INTRODUCTION 221
16.2 LINEAR SCANS FOR DIRECT
APPLICATION IN THE
ONE-DIMENSIONAL MODEL 221
16.3 ANISOTROPY: LINEAR SCANS IN THE
DIRECTION OF MOTION? 222
16.4 CAN THE METHOD OF DIMENSIONALITY REDUCTION
ALSO BE APPLIED TO NON-RANDOMLY ROUGH SURFACES? 223
16.5 HETEROGENEOUS SYSTEMS 224
16.6 FRACTURE AND PLASTIC DEFORMATION IN THE METHOD
OF DIMENSIONALITY REDUCTION 224
REFERENCES 225
17 APPENDIX 1: EXACT SOLUTIONS IN THREE DIMENSIONS
FOR THE NORMAL CONTACT OF AXIALLY-SYMMETRIC
BODIES 227
17.1 INTRODUCTION 227
17.2 NORMAL CONTACTS WITHOUT ADHESION 230
17.2.1 SINGLE-TERM PROFILES*POWER FUNCTION 231
17.2.2 THE SPECIAL CASE OF THE FLAT, CYLINDRICAL INDENTER . 232
17.2.3 SUPERPOSITION PRINCIPLE FOR MULTI-TERMED PROFILES . 232
17.3 NORMAL CONTACTS WITH ADHESION ACCORDING
TO THE GENERALIZED JKR
THEORY 233
17.4 THE MAPPING OF STRESSES 237
REFERENCES 238
18 APPENDIX 2: EXACT
SOLUTIONS IN THREE DIMENSIONS
FOR THE
TANGENTIAL CONTACT OF AXIALLY-SYMMETRIC
BODIES 239
REFERENCES 243
19 APPENDIX 3: REPLACING THE MATERIAL PROPERTIES WITH RADOK'S
METHOD OF FUNCTIONAL EQUATIONS 245
19.1 INTRODUCTION 245
19.2 THE FUNDAMENTAL SOLUTION FOR THE LINEARLY VISCOUS
MATERIAL MODEL 245
19.3 THE FUNDAMENTAL SOLUTION FOR THE LINEARLY VISCOUS,
INCOMPRESSIBLE MATERIAL MODEL 248
19.4 APPLYING THE REDUCTION METHOD TO THE GENERAL LINEARLY
VISCOELASTIC MATERIAL MODEL 249
19.5 SIMPLIFICATION: THE
INCOMPRESSIBLE, VISCOELASTIC
MATERIAL MODEL 251
XVI CONTENTS
19.6 SIMPLIFICATION: APPROXIMATION OF THE RELAXATION
FUNCTION BY DISCRETE MODELS 252
REFERENCES 252
20 APPENDIX 4: DETERMINING TWO-DIMENSIONAL
POWER SPECTRUMS
FROM ONE-DIMENSIONAL SCANS 255
20.1 INTRODUCTION 255
20.2 DEFINITIONS 255
20.3 RELATIONSHIP BETWEEN THE ONE-DIMENSIONAL AND THE
TWO-DIMENSIONAL POWER SPECTRA 256
20.4 ONE-DIMENSIONAL AND TWO-DIMENSIONAL POWER SPECTRA
FOR RANDOMLY ROUGH, SELF-AFFINE
SURFACES 258
REFERENCES 259
INDEX
261 |
| any_adam_object | 1 |
| author | Popov, Valentin Leonidovič 1959- Heß, Markus |
| author_GND | (DE-588)137675437 (DE-588)17336912X |
| author_facet | Popov, Valentin Leonidovič 1959- Heß, Markus |
| author_role | aut aut |
| author_sort | Popov, Valentin Leonidovič 1959- |
| author_variant | v l p vl vlp m h mh |
| building | Verbundindex |
| bvnumber | BV042046054 |
| classification_rvk | UF 1500 |
| ctrlnum | (OCoLC)865736531 (DE-599)DNB1045098213 |
| dewey-full | 621.89 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 621 - Applied physics |
| dewey-raw | 621.89 |
| dewey-search | 621.89 |
| dewey-sort | 3621.89 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Maschinenbau / Maschinenwesen Physik Mathematik |
| format | Book |
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| isbn | 3642538754 9783642538759 |
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| physical | XVII, 265 S. graph. Darst. |
| publishDate | 2015 |
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| publisher | Springer |
| record_format | marc |
| spelling | Popov, Valentin Leonidovič 1959- Verfasser (DE-588)137675437 aut Method of dimensionality reduction in contact mechanics and friction Valentin L. Popov ; Markus Heß Berlin [u.a.] Springer 2015 XVII, 265 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Rauigkeit (DE-588)4128988-2 gnd rswk-swf Dimensionsreduktion (DE-588)4224279-4 gnd rswk-swf Kontaktmechanik (DE-588)4798356-5 gnd rswk-swf Oberfläche (DE-588)4042907-6 gnd rswk-swf Tribologie (DE-588)4060847-5 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Kontaktmechanik (DE-588)4798356-5 s Tribologie (DE-588)4060847-5 s Oberfläche (DE-588)4042907-6 s Rauigkeit (DE-588)4128988-2 s Dimensionsreduktion (DE-588)4224279-4 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Heß, Markus Verfasser (DE-588)17336912X aut Erscheint auch als Online-Ausgabe 978-3-642-53876-6 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4537652&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027487230&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Popov, Valentin Leonidovič 1959- Heß, Markus Method of dimensionality reduction in contact mechanics and friction Rauigkeit (DE-588)4128988-2 gnd Dimensionsreduktion (DE-588)4224279-4 gnd Kontaktmechanik (DE-588)4798356-5 gnd Oberfläche (DE-588)4042907-6 gnd Tribologie (DE-588)4060847-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4128988-2 (DE-588)4224279-4 (DE-588)4798356-5 (DE-588)4042907-6 (DE-588)4060847-5 (DE-588)4114528-8 |
| title | Method of dimensionality reduction in contact mechanics and friction |
| title_auth | Method of dimensionality reduction in contact mechanics and friction |
| title_exact_search | Method of dimensionality reduction in contact mechanics and friction |
| title_full | Method of dimensionality reduction in contact mechanics and friction Valentin L. Popov ; Markus Heß |
| title_fullStr | Method of dimensionality reduction in contact mechanics and friction Valentin L. Popov ; Markus Heß |
| title_full_unstemmed | Method of dimensionality reduction in contact mechanics and friction Valentin L. Popov ; Markus Heß |
| title_short | Method of dimensionality reduction in contact mechanics and friction |
| title_sort | method of dimensionality reduction in contact mechanics and friction |
| topic | Rauigkeit (DE-588)4128988-2 gnd Dimensionsreduktion (DE-588)4224279-4 gnd Kontaktmechanik (DE-588)4798356-5 gnd Oberfläche (DE-588)4042907-6 gnd Tribologie (DE-588)4060847-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Rauigkeit Dimensionsreduktion Kontaktmechanik Oberfläche Tribologie Mathematisches Modell |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4537652&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027487230&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT popovvalentinleonidovic methodofdimensionalityreductionincontactmechanicsandfriction AT heßmarkus methodofdimensionalityreductionincontactmechanicsandfriction |