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 |  موضوع: كتاب Machine Tool Structures Volume 1 الأربعاء 03 سبتمبر 2014, 9:45 pm | |
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أحضرت لكم كتاب
Machine Tool Structures Volume 1
F. Koenigsberger D. Sc., Dr.-Ing. E.h.
Professor of Machine Tool Engineering
U.M.I.S.T., Manchester
J. TLUSTY Dr. Sc.
Head of Machine Tool Research
VÜOSO, Prague
و المحتوى كما يلي :
Table of contents
Section 1
Select Chapter 1 - General Specification of the Problems
Chapter 1 - General Specification of the Problems
Pages 3-25
Select Chapter 2 - Static and Dynamic Stiffness
Book Chapterno Access
Chapter 2 - Static and Dynamic Stiffness
Pages 27-111
Section 2: Stability Against Chatter
Select Chapter 1 - General Features of Chatter
Chapter 1 - General Features of Chatter
Pages 115-132
Select Chapter 2 - the Theory of Chatter and Stability Analysis
Chapter 2 - the Theory of Chatter and Stability Analysis
Pages 133-177
Select Chapter 3 - Procedure in the Investigation of the Stability of Machine Tools
Book Chapterno Access
Chapter 3 - Procedure in the Investigation of the Stability of Machine Tools
Pages 179-212
Select Chapter 4 - Examples of the Analysis of the Stability of Machine Tools
Book Chapterno Access
Chapter 4 - Examples of the Analysis of the Stability of Machine Tools
Pages 213-282
Select Chapter 5 - Damping and Dampers
Book Chapterno Access
Chapter 5 - Damping and Dampers
Pages 283-310
Select Chapter 6 - Chatter in Grinding
Book Chapterno Access
Chapter 6 - Chatter in Grinding
Pages 311-341
Section 3
Select Chapter 1 - Static Deformations of Machine Tool Structures
Book Chapterno Access
Chapter 1 - Static Deformations of Machine Tool Structures
Pages 345-450
Select Chapter 2 - Structural Analysis
Book Chapterno Access
Chapter 2 - Structural Analysis
Pages 451-508
Select INDEX
Book chapterFull text access
INDEX
Pages 509-519
Absolute displacements 31
Acceptance tests 42
Accessibility 7, 23
Accuracy 27,28,34,42,66,73,451
Angle of twist see Twist angle
Apertures
effect on stiffness of thin-walled beams 389
see also Openings
Archer's consistent mass matrix 475-6
Automatic control 7
Axial deformation of beam 476-7
Backlash 33
Beam
axial deformation of 476-7
in planar bending 475, 478
spring systems depicted as 144
thin-walled, weakened by apertures 389
Bed
deformations of 393,415-16
twisting moment acting on 396
see also Lathe bed and under Boring machine; Jig
boring machine; Foundations
Bending 7
of box section 350-6
planar, beam in 475, 478
Bending moments 434, 444
box structures without partitions 374
constant-thickness partitions 370
deformation of wall loaded by 384-9
frame-type partitions 371
lathe bed 424, 425
Bi-moment 362, 363, 445
Boring
forced vibrations 94
form error in, copying of 94-95
operational conditions 4
Boring bar, dampers 304-5, 309, 310
Boring machine
horizontal
axes of stiffness of boring spindle 273
compliances and directions of modes 268-9
coordinates 45
deformations of bed 431-41, 446
location of boring tool 274
modal shapes 269, 272
stability analysis 265-74
stiffness of column 441-5
stiffness criterion and bed 49
table-type 47, 182
jig see Jig boring machine
operational conditions 4
table deflection 12
with travelling headstock, weight deformation 45
Boring mill, single column 182
Box structure 7, 16, 18-19
closed 349
stresses and deformations 350-6
correction coefficients for apertures 389
displacements of arbitrary point in 367-9
general form of section of 348
introducing forces between cross-partitions 378
loaded in front wall 385
open 349
relation between coefficient of damping and geometric dimensions 377
stiffened by cross-partitions 366
stiffness of 388
thin-walled 345,347,443
basic equations 348-9
influence of shearing forces 369
local deformations and stresses in 379-89
membrane theory 348
non-uniform torsion 360-3
simple torsion 356-9
with varying section 393
with flexurally rigid walls 375-9
without partitions 374-5
Buckling of walls 8
Buckling stresses 8
C-shaped frame 7, 20, 23
Castigliano's first theorem 459-60
Castigliano's theorem of least work 375
Casting, core sand removal after 17
Cemented carbide tools 187
Centre, reactions at 56-57
Centroidal principal axis 426, 427
Characteristic number 362
Chatter
basic diagram of 118
basic patterns of 115-20
critical limit case of 166, 167
effect of cutting speed 127, 187
effect of feed 125
effect of machine tool properties 128
effect of material 125
effect of stiffness 128-30
effect of tool geometry 128
frequency of 187, 217, 224, 228, 247, 271, 277
509510 INDEX
Chatter (cont.j
general features of 115-32
grinding wheel trueing 325
in grinding 311-35
centreless grinding 321-2
critical frequency corresponding to maximum
rate of increase in 331
cylindrical plunge grinding 313-17
experimental research results 311-26
internal grinding 322-5
interpretation of results of theory 334-5
peripheral surface grinding 311-13
phase relationship with grinding wheel undulation 331-2
phase relationship with undulation on workpiece 334
relationoffrequency to stiffness of contact 331
theoretical solution 326-34
in milling 179-80
influence of cutting conditions on 124-32
parameters influencing occurrence of 118
regenerative 121-3
stability against, optimizing of damper for 298-
302
surface patterns 187
theory of 133-77
see also Stability analysis
Chip
cross-section of 29
cross-section parameters 119
free fall of 15-16
Chip thickness 29
and force 119
radial, variation of 89
variation in milling 11, 127
Chip width 29, 118
in cutting tests 188, 191
limit 118, 125,244,246,247
Clamping 19,241-2
influence on stability 128-31
Compatibility conditions 389, 463, 465
Compliance
between tool point and work piece 485
concept of 31
cross 485
definition 32
direct 67, 485
dynamic 40-42, 87, 94, 96
expression for 33
maximum 56, 68, 85
minimum 56, 69, 85
negative 57, 58
of cylindrical workpiece 63
of workpiece 61
reduced 37
relative 64-71
resulting 54-64, 85
static 31-40
torsional 37
Computer analysis 504
Computer installations 451
Computer programme 464, 467
Computing techniques 452, 504
Concrete, deformation of 435
Consistent mass model 483
Constants of orthotropy 434
Coordinate systems 28-31
cutting process 29-31
machine tool 29
milling cutters 30
"Copying" error 67, 69
Copying rates 65
Core holes 17
Core sand removal after casting 17
Correcting coefficients 345, 389, 398, 445
Coupling coefficient 164-9, 326, 331
Cross-partitions
box structure stiffened by 366
introducing forces into box structures between
378
see also Partitions
Cross-rail, deformation of 43
Cutting force 31
and vibration, intensity of coupling 119, 122
deformations caused by 28, 52-87
formula for 120
in cutting operations, deformations caused by
64-71
in grinding, deformations caused by 72-87
vibrations excited by 89-96
Cutting process
coordinate systems 29-31
coupling coefficient in transfer function of
164
deformations caused by cutting forces in 64-71
directional orientation of 130-2, 182, 189, 191,
223
on centre lathe 254, 257, 258
stability 115, 130-2
transfer function 119, 145
Cutting speed, effect on chatter 127, 187
Cutting tests 184, 187-91, 233-4, 244, 251, 253
conditions for 217, 233
evaluation of 203-6
results of 217, 234, 246, 261, 265, 267, 271, 274
Cutting tool, plunge 183
Dampers 288-9
absolute 289
optimizing of 293-302
examples of use of 303-10
impact 309
with dry friction 309
in form of additional vibratory system 304, 310
locations of 288-9
relative 288
relative viscous 303INDEX 511
Dampers (cont.)
shock 308
theory of 310
turning tools 310
types 310
see also Energy absorbers
Damping 16, 242-3, 283-310
distribution over structure 284
heavy 485
idealization of 283-4
in
guideways 286
in
joints 285-7
influence of material 285
lubrication and pressure 286
influence of welds 290-1
internal 284,290,292
linear 283 x
measurements of 284
relation between specific pressure and surface
quality 286-7
viscous 283, 284, 290, 303, 485
incorporation of 485-6
see also Energy absorbers
Damping capacity 453
Damping coefficient 283, 289, 300, 302, 304, 377
Damping elements, plastics materials 307-8
Damping factors 142
Damping force 283, 453
Damping ratio 283, 284, 287, 288, 297, 301, 302,
486
Deflections
between tool and workpiece 64
in
grinding machine 74
of column in directions of principal centroidal
axes 443-5
of surface of elastic half-space loaded on area of
rectangle 446-9
of surface of elastic rectangular plates loaded on
part of area 401-11
Deformation condition 361
Deformations 27
axial, of beam 476-7
caused by cutting forces 28, 52-87
in
cutting operations 64-71
in
grinding 72-87
caused by twisting moment 356-66
caused by weight forces 27, 42-52
during turning, workpiece shape error due to 13
in internal grinding 96
of bed 415-16
of horizontal boring machine 431-41, 446
of closed box structures subjected to bending and
shear 350-6
of concrete 435
of constant thickness partitions without openings
369-71
of cross-rail 43
of elastic semi-space loaded on part of surface by
pressure 411-15
of frame-type partitions 371
of isotropic and orthotropic rectangular plates 401
of machine tool structures 345-8
of piano-milling machine components 10
of structures with compliant partitions 369-74
of system tool-machine-workpiece 54
of thin-walled box structures 378-89
of thin-walled structures with open sections 366-7
of wall loaded by bending moments 384-9
of wall loaded tangentially along upper side
382^
relation with force 31
Depth of cut 29, 64
concept of 30
limit 244
variation during profile turning 11
Diagonal mass model 482
Direction cosine factors 461
Directional factors 143, 144, 148, 151, 156, 179,
182, 238-9, 271, 300
Directional orientation
of centre lathe 254, 257, 258
of cutting process 130-2, 182, 189, 191, 223
of face milling 265-7
Displacement compatibility equations 457
Displacement function 477, 479, 481
Displacements
absolute 31
Maxwell's formula for 370
of arbitrary point in box structures 367-9
relative 31, 54
unit 346
vibratory 30
see also Force-displacement
Drilling, operational conditions 4
Drilling machine
forces acting on frame 20
operational conditions 4
twist drill displacements 23
Driving pin, reactions at 56-57
Dynamic analysis 470-86
piano-milling machine 494-8
Dynamic behaviour 452, 453, 470
Dynamic characteristics 487
lathe beds 16, 17
tool-workpiece 483
Dynamic data, measurement by excitation tests
191-203
Dynamic forces 452
Dynamic matrix 482, 483, 486
Dynamic measurement, arrangement for 202
Dynamic parameters, measurement of 234
Dynamic resistance 298
Dynamometers, strain-gauge 198
Efficiency
production 5
technical and economic 4512 INDEX
Eigenvalue problem 470, 482-3, 486, 507-8
Eigenvalues 470, 482-3, 486, 507-8
Eigenvectors 386, 470, 482, 507-8
Elastic foundations
coefficient of compliance of pads 401
compliance of supports made as screw bolts 398
flexure in horizontal plane 395
flexure in vertical plane 395
relationship between compliance of bed and dimensions of workpiece 399
relationship of coefficient c3 and specific pressure
in area of wedge pad 400
thin-walled structures on 393-401
torsion in 395-6
wedge supporting pad 398
Elastic half-space loaded on area of rectangle, deflections of surface of 446-9
Elastic semi-space loaded on part of surface by
pressure, deformations of 411-15
Electromagnetic unbalance of electro-motors 288
Electro-motors, electromagnetic unbalance of 288
Element labelling 464, 469
End deflections 459
End flexibility 459
Energy absorbers 289-93
dry friction 289-91
materials with high internal damping 292-3
plastic materials 292-3
viscous friction 291
Equilibrium condition 360, 416, 457, 462, 463,
465
Equilibrium matrix 463
Euler's relation 381
Excitation tests 253, 266, 279
Exciters 193-8
absolute 194, 196,203
electro-dynamic 193-4,202
electro-hydraulic 198,202
electro-magnetic 194-7, 202, 220, 279
mechanical 193
relative 193
Feed, effect on chatter 125-7
Feed rate per revolution 64-66
Flexiblity see Compliance
Flexibility cofficient 431, 439
Flexibility matrix 458, 461, 462, 464, 465, 467,
470, 474, 482, 486
Flexibility method of static analysis 456
Flexibility terms 460
Flexural stiffness 409
Flexure moments 367
Floor area requirements and size capacity 24
Flow of forces, within machine structure 9
Force/deflection relationship 459
Force-displacement characteristics, non-linear 33
Force-displacement relationship 33
Force-displacement transfer function 119
Force method of static analysis 456
Force transducers 198
Forced vibrations see Vibration
Forces
acting on drilling machine frame 20
acting on machine tool structure 9
acting on milling machine frame 20-22
acting on planing machine frame 22
acting on shaping machine frame 22
flow of, within machine structure 9
occurring during machining operation 27
relation with deformation 31
weight, deformations caused by 27, 42-52
Form error 64-71, 81, 82, 85-87, 94-95
Foundations
elastic
coefficient of compliance of pads 401
compliance of supports made as crew bolts
398
flexure in horizontal plane 395
flexure in vertical plane 395
relationship between compliance of bed and
dimensions of workpiece 399
relationship of coefficient c3 and specific pressure in area of wedge pad 400
thin-walled structures on 393-401
torsion in 395-6
wedge supporting pad 398
flow of forces in 9
Frame
C-shaped 7, 20, 23
closed 7
Frequency response
derivation of 483-5
of single degree-of-freedom system 293-5
of vibrations absorber 293
Friction
dry
as energy absorber 289-91
impact damper 309
viscous, as energy absorber 291
(/-diagrams 158
resolving of 210
tool structures 210-12
G-function of a particular system 174
Gear hobbing
cutting tests 187
surface patterns of chatter 115
Geometric condition for phase shift of subsequent
undulations 169-70
Geometric instability, centreless grinding 321
Geometrical constants 461,464
Grinding
centreless
chatter 321-2
geometric instability 321
profilogram 322INDEX 513
Grinding (cont.)
chatter 311-35
critical frequency corresponding to maximum
rate of increase in 331
experimental research results 311-26
interpretation of results of theory 334-5
phase relationship with grinding wheel undulation 331-2
phase relationship with undulation on workpiece 334
relation of frequency to stiffness of contact 331
theoretical solution 326-34
cutting force 79
deformations caused by 72-87
cylindrical
operational conditions 4
ratio μ 74
cylindrical plunge, chatter 313-17
cylindrical traverse 78
directions of natural vibrations, cutting force and
normal to cut surface 328
external plunge 81
"gain" in transfer function of 327
internal 73
chatter 322-5
deformations in 96
forced vibrations 94
ratio μ 74
peripheral surface, chatter 311-13
plunge
penetration of wheel into workpiece 75-76, 78
step at end of infeed 83-84
relation of critical frequency to coefficient of coupling with various contact stiffness between
wheel and workpiece 331
self-excited vibrations 325
sparking-out phase 79-80
spring force balance 79
stock removal during 76-87
surface 78
variation of run-out during infeed phase and sparking-out 81-82
vibratory system in 328
Grinding cycle 82
Grinding force depth coefficient 72, 73
Grinding machines
cylindrical 73, 97
modal shapes and receptances 100
operational conditions 4
relative vibration between grinding wheel and
workpiece 97-98
resulting compliance variation 63
variation of waviness and of surface roughness
105-9
vibration record after modification 101-9
deflections 74
dynamic properties 328
internal 73
stiffness, ratio μ 73-87
surface
modes of vibration 97
weight deformation 45
vibration 7, 311
Grinding wheel 72
elastic properties of 328
generation of waviness on 333
peripheral speed 72
phase relationship between chatter and undulation 331-2
profilograms 317
relation of chatter frequency to hardness of 315
relationship between waviness and ground surface
317
selection 78
stiffness of 331
trueing, chatter in 325
undulations on 333
variation of chatter frequency with width of 315
Grinding wheel-spindle system, natural frequency
of 312-13
Ground surfaces, profilograms of 101
Guideways
curvature 45
damping in 286
hydrostatic 45
non-rectilinear 43
Harmonic components of vibrations 100
Harmonic forces 452
Harmonic vibration 470, 482
Hooke's law 349
Hydraulic cylinder and piston 291
Hydrostatic bearing 278-9
I-section 7
Inertia forces 477
Instability
geometric, centreless grinding 321
zone of, graphical solution of 329
Installation 5
Integration constants 403, 405, 408, 410, 411, 434
Isotropie plate 401,433
Jig boring machine
location of levels in measurement of deformations
46
location of pads supporting bed and resulting
twist of bed 46
torque diagrams and twist angle 47
twist angle and relative spindle-workpiece displacement for two types of beds in relation
to dislocation of pads 48
Joints, damping in 285-7
Kinetic energy 477-9514 INDEX
Lagrange's inertial force expressio n 477, 479
Laplace operator 486
Lathe
centre
actual orientation and optimal orientation
257-8
correlation of design of spindle and its mounting, static stiffness and />lim 251
cutting tests 189
directional orientation of cutting process of
254, 257, 258
floor area requirements 24
horizontal vibration 248
modal shapes 253, 257, 259-60
operational conditions 4
polar diagrams 254-7
price as function of centre height 24
relative viscous damper 303
resulting compliance variation 63
stability analysis 243-65
stability with different types of centres 251
tai Istock design 260-5
to ol position variation 131
v ibratory system 244, 257
copying
layout of 14
weight deformation 44
forces acting on carriage and slide 420
forces acting on centre of tailstock 418
forces acting on structure 418
front-operated automatic, floor area requirements 24
"short bed", floor area requirements 24
temperature changes effect on alignment of headstock 13
universal, various arrangements 180
vertical
giant, exciter tests 279
giant, modal shapes 280
modal shape 277, 278
stability analysis 274-80
weight deformation 45
Lathe bed
bending moments 434, 444
box section and ribbing 16
direct static compliance with workpiece clamped
in chuck 259
dynamic characteristics of 16-17
free length of 426
load acting on 420-6
stiffeners 16
stiffness of 416-31
Layout requirements 6
Lead angles in turning 243
Limit chip width 118, 125, 244, 246, 247
Load-carrying capacity 6
Load/deflection characteristics 487
Loading conditions, variations in 11
Loss factor 286
Lumped constants model 454-6, 485
piano-milling machine 468, 486-504
portal frame 453
Lumped mass system 477
Lumped viscous damping elements 485
Machine tool
coordinate systems 29
general requirements 3
structural layout 3
structure division into small units 5
Maintenance 5, 24
Mass coefficients 477, 481
Mass matrix 471-5, 479, 486
alternative 475-6
complete 480,481,482
six coordinate node 476
Material constants 461,464
Mathematical models 451
alternative formulations 453-4
basic requirements 452
Matrix algebra 504-8
Matrix notation 504-8
Matrix techniques 454
Maxwell-Mohr method 367
Maxwell's formulae 370, 373, 374
Membrane stress 349
Membrane theory 350. 369, 375, 376, 441
Metal removal parameter 73
Milling
analysis of configurations 490
average directions of axes 30
chatter in 179-80
chip thickness variation during 11
face
chip thickness variation 127
chip width 118
depth of cut 30
diagrammatic illustration of 89
directional orientation of 265-7
harmonic components of total circumferential
force 92
limit depth of cut for various orientations 131-2
operational conditions 4
orientations 35
relation b\[m, a 125
surface patterns of chatter 115
total circumferential force variation 91
variation of circumferential force on one cutter
tooth 90
geometric condition for phase-shift of undulations 170-6
slab
chip thickness variation 127
depth of cut 30
forced vibrations 93
operational conditions 4
vibration in 93INDEX 515
Milling cutters, coordinate system 30
Milling machine
coordinate axes 31
forces acting on frame 20-22
horizontal
cutting tests 189-91
stiffness of column 441-5
horizontal knee-type
damper on overarm 305-8
natural vibrations 160
stability analysis 213-31
various arrangements 180-1
operational conditions 4
piano see Piano-milling machine
resulting compliance variation 64
torsional vibrations in gear drive of spindle 93
vertical knee-type
stability analysis 232-43
static analysis 42
various arrangements 182
Minimum deformation energy 426
Modal shapes
centre lathe 253, 257, 259-60
estimation of 454
giant vertical lathe 280
horizontal boring machine 269-72
measurement of 185, 192, 203, 211, 221, 236-8
of double column vertical lathe 278
of single column vertical lathe 277
piano-milling machine 494
Mode compliances and directions, horizontal boring machine 269
Mode coupling principle 123
Mode natural frequencies 486
Model analysis 451
piano-milling machine 498-504
Model techniques 451
Mountings 89
elastic vibration isolating 111
natural frequency of 110
special cases 111
transmissibility ratio of 109-10
Natural frequencies 7, 9, 16
mode 486
of grinding wheel-spindle system 312-13
of individual modes 210-11
of mounting 110
of system crossrail-column-bed 277
of system workpiece-table-spindle-bed 277
optimum 301
Node deflections 458, 470
Node labelling 464, 469
Node mass matrix 474
"Normal to cut surface" 120
One-dimensional closed structure 465
One-dimensional open structure 456
Openings
non-stiffened 445
stiffened 445
see also Apertures
Operational conditions 3
factors affecting 19
Orthogonality of modes 484
Orthonormalized modes 484
Orthotropic plate 401, 431
Orthotropy, constants of 434
Partitions
choice of thickness of 369
compliant, deformations of structures with
369-74
constant thickness, without openings, stresses and
deformations of 369
frame-type 443
stresses and deformations of 371-4
rigid 367
stiffness of 446
see also Cross-partitions
Performance, factors affecting 5
Performance requirements 4
Phase shift
between change of chip thickness and of cutting
force 120, 124, 164
between force and displacement 134-7
of coupling coefficient 165, 168, 169
of subsequent undulations, geometric condition
for 169-70
of undulations between subsequent cutter teeth
175
Planar bending, beam in 475, 478
Planing
operational conditions 4
surface patterns of chatter 115
Planing machine
effect of weight of bed 7
forces acting on frame 22
operational conditions 4
Piano-milling machine
basic structure incorporating three heads 487
topological model 488
clamping devices 19
column/base joint flexibility 498
column design 493, 496-8
cross-beam effectiveness 493-4, 498
cross-sectional configurations selected for calculation 488
cross-slide/column fixation 500
cross-slide/column joint flexibility 498-9
cross-slide tool point deflections 493
cross-slide variations 493, 498
cutting force components 490
deformation of components 10
deformation of cross-rail 43
deformations analysis 489516 INDEX
Piano-milling machine (cont.)
displacement of spindle axis 10
dynamic analysis 494-8
lumped constants model 468, 486-504
modal shapes 494
model analysis 498-504
natural frequencies
and deformation shapes 494
and mode shapes of perspex model 504
static analysis 488-90, 4 9 3 ^
static flexibility of cross-slide tool points and natural frequencies 490
tool point deflections
for all milling configurations with table movement 491
for cross-slide milling head 493
Plastic materials
damping elements 307-8
for springs 307
Plastics, energy absorbers 292-3
Plate
isotropic 401,433
orthotropic 401, 431
partial loading of rectangular 401-11
Plunge cutting tool 183
Poisson's ratio 349, 397, 411
Polar diagram 59, 155, 158, 254-7, 260-1
Portal frame, lumped constants model of 453
Power capacity 5
Principal second moments of area 426
Principal sector area of section 358, 360
Principal sector moment 361
Principal sector point 358, 360
Qualitative performance 5
Rayleigh-Ritz method 454
Receptance 40, 87, 135, 139, 163: 174, 485
absolute 88, 234, 242
horizontal boring machine 267
cross 40, 144, 146, 148, 165, 168, 191, 206, 284,
328
modified 167, 173
direct 40, 144, 148, 191, 207, 234
measurement of 218
imaginary 135, 139, 141
measurement of 185,191, 192, 202,203, 206-12,
284
partial 299
real 135, 137, 139, 141, 148, 160, 219, 234, 267-8,
299-302
resolving 219
resulting 144
Receptance curves 137
Redundant forces 469
Regenerative chatter principle 121-3
Relative displacements 31
Repair work 5
Replacement of parts 5
Resonance vibrations 7, 9
Ribs, ribbing 15-16, 18, 347, 366
Rigid mass connected to structural node 475
Rigidity see Stiffness
Rotary inertia 481
Rubber, energy absorbers 292-3
Run-out error 81
St. Venant's principle 375
Section variation in thin-walled box shells 393
Sector second moment of area 362, 443
Self-induced forces 452-3
Setting operations 7
Shape coefficients 138
Shaping, operational conditions 4
Shaping machine
forces acting on frame 22
operational conditions 4
Shear of box sections 350-6
Shear/bending deflection 460
Shear centre 351, 354, 356, 364, 430
Shear deformation 481
Shear flow 349, 350-6, 361, 369, 370, 386, 387,
389, 429
Shear flow coefficients 368
Shear forces 367, 369, 424, 426, 427, 444
Shear stresses 411
Shearing strain 349
Size capacity 3
and floor area requirements 24
and price for centre lathes 24
Slotting machine, forces acting on frame 22
Space structures
non-conservative 485
statically determinate 459-64
statically indeterminate 465-70
Spindle axis displacement of piano-milling machine 10-11
Spring systems 33, 34
depicted as beams 144
elementary 35
preloaded springs 38-40
rule for stiffness improvement 37
springs connected in parallel 37-38
springs connected in series 36
see also Stiffness
Springs, plastic materials for 307
Stability
against chatter, optimizing of damper for
298-302
and orientation of cutting process 130-32
and real receptance 300-2
critical limit of 147, 149, 329
effect of geometric condition for phase shift of
subsequent undulations 169-70
infinite 156-7INDEX 517
Stability (cont.)
influence of clamping 128-31
investigation procedure 179-212
check of results of design changes 186
limit of 145, 147, 149-51, 155, 160, 163, 165,
167, 230, 329
curves for 217
graphical solution of 223, 238
solutions of 240-3, 280
measurement of 118
of cutting processes 115
recommendations for improvement of 225
solution of 253
see also Cutting tests
Stability analysis 145-63, 169, 185-6
centre lathes 243-65
examples of 213-80
giant vertical lathe 280
horizontal knee-type milling machine 213-31
horizontal milling and boring machine 265-74
vertical knee-type milling machine 232-43
vertical lathes 274-82
Stability charts 170
Standard parts 5
Static analysis 456-70
flexibility (or "force") method 456-9
piano-milling machine 488-90,493-4
Statically determinate space structures 459-64
Statically indeterminate reactions, determination of
426-8
Statically indeterminate space structures 465-70
Stiffeners 19
for lathe bed 15
Stiffness 24,27-111
basic concepts and notations 28-42
bending 346
calculation of 345, 346
compressive or tensile 346
concept of 31
criteria 27-28
deformations caused by cutting forces 52-87
deformations caused by weight forces 42-52
forced vibrations 87-111
cross 31
dimension of 33
direct 31
dynamic 40-42, 451
effect on chatter 128-30
expression for 33
expressions for basic law of 37
grinding machines, ratio μ 73-87
influence of material on 347
of bed 428-31
of box structure 388
of grinding wheel 331
of lathe bed 14-16,416-31
of partitions 446
of system bed-foundation-ground 400
of thin-walled beams weakened by apertures 389
radial 73
reduced 35
relation between static and dynamic analysis
41-42
resulting 34, 38, 41, 128
static 31-40,451,487
torsional 346-7, 365, 389, 396, 409, 434
see also Torsional stiffness factor
"weak links" 42
see also Spring systems
Stiffness characteristics
of different cross-section 7
of structural elements 18-19
Stiffness coefficients 395, 397
Stiffness performance of machine tool structure 10
Stiffness requirements 5, 6
Stiffness-to-weight ratio 7
"Stiffnesses" of vibration system modes 141
Strain energy 379, 460
Strain-gauge dynamometers 198
Strain-gauge transducers 200
Stresses
buckling 8
of closed box structures subjected to bending and
shear 350-6
of constant thickness partitions without openings
369-71
of frame-type partitions 371
of thin-walled box structures 378-89
with open sections. 366-7
produced by twisting moment 356-66
tangential 349
working 6
Structural analysis 451-508
basic requirements 452
see also Dynamic analysis; Static analysis
Structural layout, factors determining 3
Structural nodes 475
Surface topography 451
Swarf removal 14
Tangential second moment of area 360, 364, 443
Tangential stress 349
Temperature changes, effect upon alignment of lathe
headstock 13
Thin-walled box structure see Box structure
Thin-walled structures
on elastic foundations 393-401
with open sections, deformations and stresses in
366-7
Tlusty-Polacek theory 164
Tool displacements, effect upon diametral error of
turned workpiece 13-14
Tool geometry, effect on chatter 128
Tool point flexibilities 487
Tool position
arrangement on centre lathe 14
variation on centre lathe 131518 INDEX
Tool-workpiece dynamic characteristics 483
Tools, cemented carbide 187
Torque diagram 47
Torsion 7
in elastic foundations 395-6
non-uniform
of thin-walled sections 360-3
solution of basic equation 363-5
structures with deformable sections 366-7
simple, of thin-walled box structures 356-9
Torsional stiffness 346-7, 365, 389, 396, 409, 434
Torsional stiffness factor 357, 365
Total strain energy expression 460
Transducers
force 198
strain-gauge 200
vibration 198-200
Transfer function
cutting process 145
coupling coefficient in 164
force-displacement 119
relating vibration to force 119
vibratory system 166
Transmissibility ratio of mounting 109-10
Tuned vibration absorbers see Vibration absorbers
Turning
chip width 118
depth of cut 30
geometric condition for phase-shift of undulations 170, 174
lead angles in 243
of cylindrical workpiece between centres 54-55
operational conditions 4
overhung 251
profile, depth of cut variation during 11
relation b\\m, a 125
surface patterns of chatter 115
workpiece shape error due to deformations during 13
Turning tools, use of shock-damper 310
Twist angle 47, 444
Twisting moments 367, 423, 425, 434
acting on bed 396
single, structure loaded by 363
stresses and deformations produced by 356-66
uniform, structure loaded on part of length by
364
Unit displacement 346
Unit error 65-67
Vectors 506-7
Velocity component principle 124
Vibration 7
amplitudes of 207
and cutting force, intensity of coupling 119,122
damped free 486
directions of, between tool and workpiece 211
excited by cutting force 89-96
forced 28,284,483
as stiffness criterion 87-111
effect on ground surface 101
grinding machine 97, 311
harmonic 141
harmonic components of 100
horizontal, centre lathe 248
in milling 93
miscellaneous sources of 96-109
of floor in various factories 110
of structure 482
of various systems 133-44
relative tool-workpiece 111
resonance 7, 9
resulting 141, 142
self-excited 28, 31, 93-94, 115, 325
basic diagram 146
basic theory 145-63
basic theory, further aspects 163-77
closed-loop system 115, 145, 147
mode coupling principle 123
principles of 121-4
regenerative chatter principle 121-3
velocity component principle 124
source outside machine 109-11
transverse 16
Vibration absorbers 88
frequency response of 293
tuned 287,291-2
see also Dampers
Vibration transducers 198-200
Vibrators see Exciters
Vibratory displacements 30
Vibratory systems, centre lathe 244, 257
conditions required of 191-2
degrees-of-freedom 151, 168
directional orientation 182
machine-tool-workpiece 191
many degrees-of-freedom with different directions 142-4
more than two degrees-of-freedom 160
n degrees-of-freedom 208, 284, 483
parameters of 179, 185
single degree-of-freedom 133-7, 148, 157, 288,
293-5, 299, 330
directional orientation 150
graphical solution 329
transfer function of 166
two degrees-of-freedom 157
electric model 300
with different directions 141-2
unidirectional, with two degrees-of-freedom 137-41
Walls, structural requirements 9
Warping of single-box structure with rectangular
section 358INDEX 519
Warping coefficient 361
Warping function 361
Weight of structure 7
Weight forces, deformations caused by 27,
Workpiece
compliance of 61
cylindrical, compliance of 63
1-52 deformations produced by 431-9
shape error due to deformations during turning
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