Dynamics of mechanical systems with Coulomb friction:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Berlin [u.a.]
Springer
2003
|
| Series: | Foundations of engineering mechanics
Engineering online library |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 255 - 267 |
| Physical Description: | 269 S. graph. Darst. : 24 cm |
| ISBN: | 3540006540 |
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| 245 | 1 | 0 | |a Dynamics of mechanical systems with Coulomb friction |c Le xuan Anh |
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Record in the Search Index
| _version_ | 1804130068408041472 |
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| adam_text | LE XUAN ANH DYNAMICS OF MECHANICAL SYSTEMS WITH COULOMB FRICTION
TRANSLATED BY ALEXANDER K. BELYAEV WITH 59 FIGURES SPRINGER CONTENTS
INTRODUCTION 3 1 DEVELOPMENT OF THE THEORY OF MOTION FOR SYSTEMS WITH
COULOMB FRICTION 11 1.1 COULOMB S LAW OF FRICTION 11 1.2 MAIN
PECULIARITIES OF SYSTEMS WITH COULOMB FRICTION AND THE SPECIFIC PROBLEMS
OF THE THEORY OF MOTION 12 1.2.1 THE PRINCIPLE PECULIARITY 13 1.2.2
NON-CLOSED SYSTEM OF EQUATIONS FOR THE DYNAMICS OF SYSTEMS WITH FRICTION
AND THE PROBLEM OF DERIVING THESE EQUATIONS 14 1.2.3 NON-CORRECTNESS OF
THE EQUATIONS FOR SYSTEMS WITH FRICTION AND THE PROBLEM OF SOLVING
PAINLEVE S PARADOXES 15 1.2.4 THE PROBLEM OF DETERMINING THE FORCES OF
FRICTION ACT- ING ON PARTICLES 17 1.2.5 RETAINING THE STATE OF REST AND
TRANSITION TO MOTION 18 1.2.6 THE PROBLEM OF DETERMINING THE PROPERTY OF
SELF-BRAKING 19 1.2.7 APPEARANCE OF SELF-EXCITED OSCILLATIONS 19 1.3
VARIOUS INTERPRETATIONS OF PAINLEVE S PARADOXES 20 1.4 PRINCIPLES OF THE
GENERAL THEORY OF SYSTEMS WITH COULOMB FRICTION 25 1.5 LAWS OF COULOMB
FRICTION AND THE THEORY OF FRICTIONAL SELF- EXCITED OSCILLATIONS 32 6
CONTENTS 2 SYSTEMS WITH A SINGLE DEGREE OF FREEDOM AND A SINGLE FRIC-
TIONAL PAIR 37 2.1 LAGRANGE S EQUATIONS WITH A REMOVED CONTACT
CONSTRAINT . . 37 2.2 KINEMATIC EXPRESSION FOR SLIP WITH ROLLING 44
2.2.1 VELOCITY OF SLIP AND THE VELOCITIES OF CHANGE OF THE CONTACT PLACE
DUE TO THE TRACE OF THE CONTACT . . . . 44 2.2.2 ANGULAR VELOCITY 45 2.3
EQUATION FOR THE CONSTRAINT FORCE AND PAINLEVE S PARADOXES . 49 2.3.1
SOLUTION FOR THE ACCELERATION AND THE CONSTRAINT FORCE 50 2.3.2
CRITERION FOR THE PARADOXES 51 2.4 IMMOVABLE CONTACT AND TRANSITION TO
SLIPPING 53 2.5 SELF-BRAKING AND THE ANGLE OF STAGNATION 57 2.5.1 THE
CASE OF NO PARADOXES 58 2.5.2 THE CASE OF PARADOXES (N L 1) 64 3
ACCOUNTING FOR DRY FRICTION IN MECHANISMS. EXAMPLES OF
SINGLE-DEGREE-OF-FREEDOM SYSTEMS WITH A SINGLE FRICTIONAL PAIR 67 3.1
TWO SIMPLE EXAMPLES 67 3.1.1 FIRST EXAMPLE 67 3.1.2 SECOND EXAMPLE 69
3.2 THE PAINLEVE-KLEIN EXTENDED SCHEME 70 3.2.1 DIFFERENTIAL EQUATIONS
OF MOTION, EXPRESSION FOR THE REACTION FORCE, CONDITION FOR THE
PARADOXES AND THE LAW OF MOTION 72 3.2.2 IMMOVABLE CONTACT AND
TRANSITION TO SLIP 74 3.2.3 THE STAGNATION ANGLE AND THE PROPERTY OF
SELF-BRAKING IN THE CASE OF NO PARADOXES 75 3.2.4 SELF-BRAKING UNDER THE
CONDITION OF PARADOXES . . . . 77 3.3 STACKER 79 3.3.1 PURE ROLLING OF
THE RIGID BODY MODEL 79 3.3.2 SLIP OF THE DRIVING WHEEL FOR THE RIGID
BODY MODEL . 82 3.3.3 SPEED-UP OF STACKER 84 3.3.4 PURE ROLLING IN THE
CASE OF TANGENTIAL COMPLIANCE . . 85 3.3.5 ROLLING WITH ACCOUNT OF
COMPLIANCE 87 3.3.6 SPEED-UP WITH ACCOUNT OF COMPLIANCE 88 3.3.7
NUMERICAL EXAMPLE . 91 3.4 EPICYCLIC MECHANISM WITH CYLINDRIC TEETH OF
THE INVOLUTE GEARING 94 3.4.1 DIFFERENTIAL EQUATION OF MOTION, EQUATIONS
FOR THE RE- ACTION FORCE AND THE CONDITIONS FOR PARADOXES 95 3.4.2
RELATIONSHIPS BETWEEN THE TORQUES AT REST AND IN THE TRANSITION TO
MOTION 100 3.4.3 REGIME OF UNIFORM MOTION 103 3.5 GEAR TRANSMISSION WITH
IMMOVABLE ROTATION AXES 103 CONTENTS 7 3.5.1 DIFFERENTIAL EQUATIONS OF
MOTION AND THE CONDITION FOR ABSENCE OF PARADOXES 104 3.5.2 REGIME OF
UNIFORM MOTION 106 3.5.3 TRANSITION FROM THE STATE OF REST TO MOTION 109
3.6 CRANK MECHANISM 110 3.6.1 EQUATION OF MOTION AND REACTION FORCE 110
3.6.2 CONDITION FOR COMPLETE ABSENCE OF PARADOXES .... 112 3.6.3 THE
PROPERTY OF SELF-BRAKING IN THE CASE OF NO PARADOXES 114 3.7 LINK
MECHANISM OF A PLANING MACHINE 115 3.7.1 DIFFERENTIAL EQUATIONS OF
MOTION AND THE EXPRESSION FOR THE REACTION FORCE 115 3.7.2 FEASIBILITY
OF PAINLEVE S PARADOXES 119 3.7.3 THE PROPERTY OF SELF-BRAKING 121 3.7.4
NUMERICAL EXAMPLE 123 SYSTEMS WITH MANY DEGREES OF FREEDOM AND A SINGLE
FRIC- TIONAL PAIR. SOLVING PAINLEVE S PARADOXES 125 4.1 LAGRANGE S
EQUATIONS WITH A REMOVED CONSTRAINT 125 4.2 EQUATION FOR THE CONSTRAINT
FORCE, DIFFERENTIAL EQUATION OF MO- TION AND THE CRITERION OF PARADOXES
128 4.2.1 DETERMINATION OF THE CONSTRAINT FORCE AND ACCELERATION 128
4.2.2 CRITERION OF PAINLEVE S PARADOXES 131 4.3 DETERMINATION OF THE
TRUE MOTION 132 4.3.1 LIMITING PROCESS 133 4.3.2 TRUE MOTIONS UNDER THE
PARADOXES 137 4.4 TRUE MOTIONS IN THE PAINLEVE-KLEIN PROBLEM IN
PARADOXICAL SITUATIONS 141 4.4.1 EQUATIONS FOR THE REACTION FORCE 142
4.4.2 TRUE MOTIONS FOR THE PARADOXES 143 4.5 ELLIPTIC PENDULUM 145 4.6
THE ZHUKOVSKY-FROUDE PENDULUM 148 4.6.1 EQUATION FOR THE REACTION FORCE
AND CONDITION FOR THE NON-EXISTENCE OF THE SOLUTION 150 4.6.2 THE
EQUILIBRIUM POSITION AND FREE OSCILLATIONS .... 152 4.6.3 REGIME OF
JOINT ROTATION OF THE JOURNAL AND THE PIN . 153 4.7 A CONDITION OF
INSTABILITY FOR THE STATIONARY REGIME OF METAL CUTTING 155 4.7.1
DERIVATION OF THE EQUATIONS OF MOTION 155 4.7.2 SOLVING THE EQUATIONS
157 4.7.3 RELATIONSHIP BETWEEN INSTABILITY OF CUTTING AND PAINLEVE S
PARADOX 159 4.7.4 BORING WITH AN AXIAL FEED 161 CONTENTS SYSTEMS WITH
SEVERAL FRICTIONAL PAIRS. PAINLEVE S LAW OF FRIC- TION. EQUATIONS FOR
THE PERTURBED MOTION TAKING ACCOUNT OF CONTACT COMPLIANCE 163 5.1
EQUATIONS FOR SYSTEMS WITH COULOMB FRICTION 163 5.1.1 SYSTEM WITH
REMOVED CONSTRAINTS 163 5.1.2 SOLVING THE MAIN SYSTEM 166 5.1.3 THE CASE
OF N = 1,771 = 1 169 5.2 MATHEMATICAL DESCRIPTION OF THE PAINLEVE LAW OF
FRICTION . . 170 5.2.1 ACCELERATIONS DUE TO TWO SYSTEMS OF EXTERNAL
FORCES . 170 5.2.2 IMPROVED PAINLEVE S EQUATIONS 172 5.2.3 IMPROVED
PAINLEVE S THEOREM 174 5.3 FORCES OF FRICTION IN THE PAINLEVE-KLEIN
PROBLEM 176 5.4 THE CONTACT COMPLIANCE AND EQUATIONS OF PERTURBED
TRAJEC- TORIES 177 5.4.1 LAGRANGE S EQUATIONS FOR SYSTEMS WITH ELASTIC
CONTACT JOINTS 177 5.4.2 EQUATIONS FOR PERTURBED REACTION FORCES 179 5.5
PAINLEVE S SCHEME WITH TWO FRICTIONAL PAIRS 181 5.5.1 LAGRANGE S
EQUATIONS, REACTION FORCES AND THE EQUA- TIONS OF MOTION WITH ELIMINATED
REACTION FORCES . . . 182 5.5.2 FEASIBILITY OF PAINLEVE S PARADOXES 184
5.5.3 EXPRESSIONS FOR THE FRICTIONAL FORCE IN TERMS OF THE FRICTION
COEFFICIENTS 185 5.5.4 PAINLEVE S SCHEME FOR COMPLIANT CONTACTS 186 5.6
SLIDERS OF METAL-CUTTING MACHINE TOOLS 187 5.6.1 DERIVATION OF EQUATIONS
OF MOTION AND EXPRESSIONS FOR THE REACTION FORCES 187 5.6.2 SIGNS OF THE
REACTION FORCES AND FEASIBILITY OF PARADOXES 189 5.6.3 FORCES OF
FRICTION 191 5.7 CONCLUDING REMARKS ABOUT PAINLEVE S PARADOXES 192 5.7.1
ON EQUATIONS OF SYSTEMS WITH COULOMB FRICTION . . . 192 5.7.2 ON
CONDITIONS OF THE PARADOXES 193 5.7.3 ON THE REASONS FOR THE PARADOXES
193 5.7.4 ON THE LAWS OF MOTION IN THE PARADOXICAL SITUATIONS 193 5.7.5
ON THE INITIAL MOTION OF AN IMMOVABLE CONTACT . . . 194 5.7.6 ON
SELF-BRAKING 194 5.7.7 ON THE MATHEMATICAL DESCRIPTION OF PAINLEVE S LAW
. 195 5.7.8 ON EXAMPLES . 195 EXPERIMENTAL INVESTIGATIONS INTO THE FORCE
OF FRICTION UNDER SELF-EXCITED OSCILLATIONS 197 6.1 EXPERIMENTAL SETUPS
198 6.1.1 THE FIRST SETUP 198 6.1.2 THE SECOND SETUP 200 6.1.3 THE THIRD
SETUP 201 CONTENTS 6.2 DETERMINING THE FORCES BY MEANS OF AN OSCILLOGRAM
202 6.3 CHANGE IN THE FORCE OF FRICTION UNDER BREAK-DOWN OF THE MAX-
IMUM FRICTION IN THE CASE OF A CHANGE IN THE VELOCITY OF MOTION206 6.4
DEPENDENCE OF THE FRICTION FORCE ON THE RATE OF TANGENTIAL LOADING 209
6.5 PLAUSIBILITY OF THE DEPENDENCE F + (F) 213 6.5.1 CONTROL TESTS 213
6.5.2 ESTIMATING THE NUMERICAL CHARACTERISTICS 213 6.5.3 STATISTICAL
PROPERTIES OF THE DEPENDENCES 214 6.5.4 TEST DATA OF OTHER AUTHORS 215
6.6 CHARACTERISTIC OF THE FORCE OF SLIDING FRICTION 215 FORCE AND SMALL
DISPLACEMENT IN THE CONTACT 217 7.1 COMPONENTS OF THE SMALL DISPLACEMENT
217 7.1.1 DEFINITION OF BREAK-DOWN AND INITIAL BREAK-DOWN . . 217 7.1.2
REVERSIBLE AND IRREVERSIBLE COMPONENTS 218 7.1.3 INFLUENCE OF THE
INTERMEDIATE STOP AND REVERSE ON THE IRREVERSIBLE DISPLACEMENT 220 7.1.4
DEPENDENCE OF THE TOTAL SMALL DISPLACEMENT ON THE RATE OF TANGENTIAL
LOADING 222 7.1.5 SMALL DISPLACEMENT OF PARTS OF THE CONTACT 223 7.1.6
COMPARING THE VALUES OF SMALL DISPLACEMENT WITH EX- ISTING DATA 225 7.2
REMARKS ON FRICTION BETWEEN STEEL AND POLYAMIDE 226 7.2.1 ON CRITICAL
VALUES OF THE FORCE OF FRICTION 226 7.2.2 TIME LAG OF SMALL DISPLACEMENT
226 7.2.3 IMMOVABLE AND VISCOUS COMPONENTS OF THE FORCE OF FRICTION 229
7.3 CONCLUSIONS 230 FRICTIONAL SELF-EXCITED OSCILLATIONS 231 8.1
SELF-EXCITED OSCILLATIONS DUE TO HARD EXCITATION 231 8.1.1 THE CASE OF
NO STRUCTURAL DAMPING 231 8.1.2 INCLUDING DAMPING 237 8.2 SELF-EXCITED
OSCILLATIONS UNDER BOTH HARD AND SOFT EXCITATIONS 240 8.2.1 EQUATIONS OF
MOTION 240 8.2.2 CRITICAL VELOCITIES 242 8.2.3 AMPLITUDE OF
AUTO-OSCILLATION 244 8.2.4 PERIOD OF AUTO-OSCILLATION 246 8.2.5
SELF-EXCITATION OF SYSTEMS 247 8.3 ACCURACY OF THE DISPLACEMENT 249
REFERENCES 255 INDEX 268
|
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| id | DE-604.BV017219087 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:15:09Z |
| institution | BVB |
| isbn | 3540006540 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010376601 |
| oclc_num | 249383823 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-29T DE-634 DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-29T DE-634 DE-83 |
| physical | 269 S. graph. Darst. : 24 cm |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| series2 | Foundations of engineering mechanics Engineering online library |
| spelling | Le, Xuan-Anh Verfasser aut Dynamics of mechanical systems with Coulomb friction Le xuan Anh Berlin [u.a.] Springer 2003 269 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Foundations of engineering mechanics Engineering online library Literaturverz. S. 255 - 267 Mechanisches System - Coulombsches Reibungsgesetz Friction Mechanics, Analytic Mechanisches System (DE-588)4132811-5 gnd rswk-swf Coulombsches Reibungsgesetz (DE-588)4371918-1 gnd rswk-swf Mechanisches System (DE-588)4132811-5 s Coulombsches Reibungsgesetz (DE-588)4371918-1 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010376601&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Le, Xuan-Anh Dynamics of mechanical systems with Coulomb friction Mechanisches System - Coulombsches Reibungsgesetz Friction Mechanics, Analytic Mechanisches System (DE-588)4132811-5 gnd Coulombsches Reibungsgesetz (DE-588)4371918-1 gnd |
| subject_GND | (DE-588)4132811-5 (DE-588)4371918-1 |
| title | Dynamics of mechanical systems with Coulomb friction |
| title_auth | Dynamics of mechanical systems with Coulomb friction |
| title_exact_search | Dynamics of mechanical systems with Coulomb friction |
| title_full | Dynamics of mechanical systems with Coulomb friction Le xuan Anh |
| title_fullStr | Dynamics of mechanical systems with Coulomb friction Le xuan Anh |
| title_full_unstemmed | Dynamics of mechanical systems with Coulomb friction Le xuan Anh |
| title_short | Dynamics of mechanical systems with Coulomb friction |
| title_sort | dynamics of mechanical systems with coulomb friction |
| topic | Mechanisches System - Coulombsches Reibungsgesetz Friction Mechanics, Analytic Mechanisches System (DE-588)4132811-5 gnd Coulombsches Reibungsgesetz (DE-588)4371918-1 gnd |
| topic_facet | Mechanisches System - Coulombsches Reibungsgesetz Friction Mechanics, Analytic Mechanisches System Coulombsches Reibungsgesetz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010376601&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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