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Self excited vibrations in machine tools and metal cutting

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SLI;IJ:Il;XCITED VlBi,A -riois ii 1 CHLU TOOLS ND METAL CUTTING

A.

$arcrp ra&id Ray

zbuitted to the Indian Intitzto of Tcchnology, Delhi for the award of the Degree of

DOCTOR OF PH ILO SOPHY

Department of applied Mechanics Indian Institute of Technology, Delhi

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OBR ' ICE

This is to certify that the thesis etit1ed

t

XCiD VBEUTIOIN MIIN TOOLS AND )T.L )T. CUTTING'

bar

Sankax'prasad R r has been prepared under xriy supervision in cyanform.t to the ru1e and regulations of the Iridiert Institute of Teoiio1ogyDe1hi. I further certify that the thesis has attained a standard required for a P *D. degree of the Institute, The research report and results presented.

in the thesis

have not been subnitted. for any degree in any other univer t .

head, Applied., I4echanics Department.

Indian Institute of Tec oloays Del .

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AC

ACNOWLDGMENT

The author is extremely grateful to Professor 13, Karunes, lead of the Applied Mechanics Department, Indian Institute of Technology, Delhi, for his helpful uidariee arid., constructive criticism without which this work would not have been posy ble.

FT

(aAwxARAa&D RAY)

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TABLE OF CONTENTS

ACKNOWLEDGEMENTS iii

Chapter

1.

2.

3.

40

INTRODUCTION AND REVIEW 1

1.1 Introduction 2

1.2 Review of Work on Static and

Kinetic Coefficient of Friction S 13 Review of work on Critical Velocity 11 STICK-SLIP MOTION IN MACHINE TOOLS 13

FRICTION GENERATED TOOL VIB1VtTION IN

QUA$IDYNAMIC CUTTING 36

3.1 The Scope of Discussion in the

Present Chapter 38

32 The Modelling of the System L jQ 3,3 Basic and Governing Equations 45 3,4 Method. of Numerical Solution 49

3.5

A Numerical Example 52

3.6 Results and Discussions

5 1

+

TOOL VIRTXON AND CHATTER IN D"IAMIC

CUTTING 60

)+.1 The Scope of Discussions in the

Present Chapter 62

+.2 The Modelling of the System 65 .3 Basic and Governing Equations 66 4,4 The Method of Numerical Solution 71

4.5 A Numerical Example 73

1,6 Numerical Results and Discussions 74

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4

INFLIJE E OF M&CHIN FLEXIBILITY ON

CHATTER 78

5.1 The Problem 79

5.2 The equations of Motion 81 5.3 Method of Numerical Solution 86 5.)

4

. The Numerical Example 89 5.5 Numerical Results and Discussions 90 6. CONCLUDING REMARKS 92

APPENDIX I 96

APPENDIX II 99

LIST OF RE NCFS 100

References

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