كتاب Fundamentals of Rοlling
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 كتاب Fundamentals of Rοlling

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كتاب Fundamentals of Rοlling  Empty
مُساهمةموضوع: كتاب Fundamentals of Rοlling    كتاب Fundamentals of Rοlling  Emptyالإثنين 11 يناير 2021, 6:14 pm

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أحضرت لكم كتاب
Fundamentals of Rοlling
Zygmunt Wusatowski , D.Se.
Professor of the Polytechnical University, Gliwice, Poland  

كتاب Fundamentals of Rοlling  F_o_r_12
و المحتوى كما يلي :


Table of Contents
Foreword
Preface
1. Phenomena Occurring during Plastic Working of Metals
1.1. Plastic Working by Rolling
1.2. Fundamental Phenomena Occurring in Plastic Working
1.3. Deformation of Single Crystals and Polycrystalline Aggregates
1.4. Cold Work and Strain-hardening of Metal
1.5. Recrystallization
1.6. Hot Working
2. Fundamental Principles of Plastic Working of Metals
2.1. Symbols, Formula, and Definitions
2.2. Constancy of Volume and Laws of Plastic Deformation
2.3. Stress-Strain Relationships and Condition of Plasticity
2.4. Yield Stress
2.5. Resistance of Metal to Deformation
2.6. Work of Plastic Deformation
3. Fundamentals of Rolling Processes
3.1. Basic Concepts and Symbols in Rolling
3.2. Geometrical and Trigonometrical Relations in Rolling
3.3. Flow of Metal in Rolling
3.4. Interdependence of Draught, Elongation and Spread of Metal in Hot Rolling
3.5. Calculation of Draught, Elongation and Spread in Symmetrical Passes During Rolling of Bars
3.6. Mechanism of Bite and Friction in Rolling
3.7. Calculation of Rolling Temperature
3.8. Calculation of Rolling Speed
3.8.1. Neutral Angle and Forward Slip when Rolling with Spread
3.8.2. Neutral Angle in Hot and Cold Rolling without Spread
3.8.3. Calculation of Rolling Speed of Bars and Sections
4. Roll Pressure, Torque, Work, and Power in Rolling

4.1. Roll Pressure and Load

4.1.1. Measurements of Pressure Distribution along the Arc of Contact in Hot and Cold Rolling

4.1.2. Determination of Roll Forces in Hot Rolling

4.2. Calculation of Roll Force in Hot Rolling

4.2.1. Tselikov's Method of Calculation of Roll Force [70]

4.2.2. Golovin-Tiagunov's Method of Calculation of Roll Force [70]

4.2.3. Samarin's Method of Calculation of Roll Force [70]

4.2.4. Ekelund's Method of Calculation of Roll Force [10]

4.2.5. Orowan-Pascoe Method of Calculation of Roll Force [10, 60]

4.2.6. Geleji's Method of Calculation of Roll Force [20]

4.2.7. Cook and McCrum's Method of Calculation of Roll Force [67]

4.2.8. Siebel's Method of Calculation of Roll Force [61]

4.3. Work, Torque, and Power in Rolling

4.3.1. Influence of Additional Friction and Deformation when Rolling in Box Passes [109]

4.3.2. Influence of Additional Friction and Deformation when Rolling in Breaking Down Passes [157]

4.3.3. Basic Formula for Calculation of Roll Power

4.3.4. Calculation of Rolling Work and Drive Power from Energy and Power Consumption Diagrams

4.4. Calculation of Roll Force in Cold Rolling

4.4.1. Tselikov's Method of Calculation of Roll Force in Cold Rolling

4.4.2. Ekelund's Method of Calculation of Roll Force in Cold Rolling

4.4.3. Siebel's Method of Calculation of Roll Force in Cold Rolling

4.4.4. Calculation of Roll Force in Cold Rolling from the Mean Resistance to Deformation [15, 31]

4.4.5. Calculation of Roll Force in Cold Rolling of Strip with Applied Front and Back Tension

4.4.6. Bland, Ford and Ellis's Graphical Method for Calculation of Roll Force

4.4.7. Trinks's Graphical Method for Determination of Roll Force in Keller's Form

4.4.8. Korolev-Nikolayevski's Method of Calculation of Roll Force in Cold Rolling

4.5. Calculation of Roll Torque and Power in Cold Rolling

4.5.1. Ford's Method of Calculation of Roll Torque

4.5.2. Tselikov's Method of Calculation of Roll Torque

4.5.3. Bland, Ford and Ellis's Graphical Method of Calculation of Roll Torque

4.5.4. Ford's Method of Calculation of Roll Torque with Applied Tension

4.5.5. Bland, Ford and Ellis's Method of Calculation of Roll Torque with Applied Tension

4.5.6. Other Methods of Calculation of Roll Torque

4.5.7. Effect of Strip Tension

4.6. Power of the Main Driving Motors

5. Rolls and Their Permissible Loading

5.1. Rolls and Roll Strength Calculations

5.2. Roll Deflection and Other Factors Affecting Variation of Thickness during Rolling of Sheet and Strip

5.3. Permissible Loading of Rolling Mills

5.4. Measurements in Rolling

5.4.1. Measurement of Roll Force and Torque by Means of Strain Gauges [112]

5.4.2. Measurement of Roll Force and Torque by Induction Sensors

5.4.3. Devices for Continuous Measurement of Strip Thickness

5.4.4. Measurement of Strip Tension

5.5. Evaluation of Measurements in Rolling Mills

6. Hot Rolling with Heavy Draughts

6.1. Elongation and Spread During Hot Rolling of Mild Steel with Heavy Draughts

6.2. Forward Slip and No-slip Angle in Rolling Mild Steel with Heavy Draughts

6.3. Roll Force and Torque in Rolling of Mild Steel

6.4. Flow of Metal and Structural Phenomena in Rolling

7. Principles of Roll Pass Design

7.1. Basic Definitions

7.2. Roll Pass Design and Basic Formula

7.2.1. Breaking-down Sequences [145]

7.2.2. Finishing Roll Passes for Bar Rolling [145]

7.2.3. Blooming Mill Pass Design

7.3. Graphical Method of Roll Pass Design

7.4. Transformation of Formula for Roll Pass Design

7.5. Design of Regular Sections and Breaking-down Systems by the Mean Heights Method

7.6. Theoretical Principles of Section Pass Design

7.6.1. Pass Design Methods for Sections Composed of Two Elements

7.6.2. Pass Design of Sections Composed of Three Elements

7.6.3. Pass Design for Angles, T-beams, Channels and I-beams [174]

7.6.4. Roll Pass Design of Angles

7.6.5. Roll Pass Design of T-beams

7.6.6. Roll Pass Design of Channels and I-Beams

7.6.7. K. Rytel's Method of Pass Design, Particularly for I-Beams [131]

7.6.8. Knifing Passes

7.6.9. General Principles of Sections Pass Design [113,130, 150]

7.6.10. Roll Wear

7.7. Principles of Roll Pass Design for Continuous Mills

7.7.1. Effect of Initial Cross-section

7.7.2. Effect of Roll Diameter

7.7.3. Effect of Roll Speed

7.7.4. Principles of Continuous Train Design and Rolling Speed Calculation

7.7.5. Calculation of Roll Speed in Rolling of Bars in Symmetrical Passes

7.8. Effective Radii and Neutral Lines

7.8.1. Calculation of Roll Diameters in Section Mills by C. Murski's Method [132 and 145]

7.8.2. Effective Radii and Neutral Axes of Passes in the Rolling of Shapes

7.9. Analysis of the Rolling of Small Sections
Appendix 1
Appendix 2
References
Index
Index
Absolute draught 20, 23, 74-77, 80, 124, 217,
441-5, 478, 496
maximum 71, 74, 445
mean 71, 74, 524
Absolute elongation 20, 30, 74
Absolute error 21
Absolute reduction 20, 74
Absolute spread 20, 74
Absolute temperature 21
Accumulation of energy in crystal lattices 12
Active pass 494
Actual work of plastic deformation 68,266, 309
Affinity of metal for oxygen, chemical 19
Angle
apex 110
of bite 46, 75-79, 81-82,120-36,147,183, 275,
476, 525, 529
maximum 79, 81, 122, 127, 525
of contact 79-80,123, 125-7
maximum 126
of distortion 33
of friction 21, 120-36
neutral 145, 158-202, 483
rolling 75, 78, 150
Angle pass 499
Anisotropic structure 11
Annealing 11
subcritical 14
Apex angle 110
Arc of contact 77-78, 83, 153, 220
Area of contact 85, 219-20
Average cold work, degree of 51
Axis
neutral 498, 624-47
roll 70,497
Back tension 206, 459
measurement of 212
Backward slip 147, 152-3
Bakhtinov's formula  s e e Formula for the calculation of free spread
Bar pass 499
Bar rolling 512
Barrel 392-3,424,498
Bearing pressure 403-8
Behaviour of metals, plastic 21, 31
Bending modulus 396
Bending moment 395, 397-9
Bending stress 396, 399, 404
Bite 120-36
angle of 46, 75-79, 81-82, 120-36, 147, 183,
275, 476, 525, 529
Blooming mill 316, 392, 417, 441, 460, 502
Blooming mill pass design 523-30
Blooming (roughing) pass 499
Blowholes, subcutaneous 22
Boczwar relation  s e e Relation between recrystallization temperature and melting temperature
Body-centred cubic crystal lattice 6
Boundary conditions
for criterion of yielding 36
for plastic strain 40
Box pass 275-92
open 499, 502
Box pass sequence 500, 508
Breadth 20, 70
Breaking-down pass 292-309, 499
Breaking-down pass sequence 500, 507-12
diamond 509
gothic square-gothic square 500
open box 500, 508
oval-oval 500
square-diamond-square 510
square-oval-square 511
square-square 500
Breaking-down systems design 541-56
Brittleness 46
Burning of steel 19
Calculated roll force 414
Calculated roll torque 416
Calculated value 21
Calculation
of elliptical ovals 112
of flat ovals 112-14
of form factors 546
of forward slip 160
of hexagonal ovals 114-18
of mean yield stress 335
of number of passes 502-3, 519, 523-4, 549
of oval dimensions 511
of pass dimensions 511-12,514
of resultant roll force 273
669 670  INDEX
Calculation (cont.)
of roll camber 426-9
of roll force 229-66, 273-5, 278-82, 289,
294-9, 331-58, 415
Bland, Ford and Ellis method 349-53
Cook-McCrum's method 238, 258-66
Ekelund's method 234, 254-66, 341
Geleji's method 237, 258-66
Golovin-Tiagunov's method 231, 254-66
Korolev-Nikolayevski's method 356-8
Orovan-Pascoe's method 235, 254-66
Samarin's method 250, 254-66
Siebel's method 250, 254-66, 275, 342
Trink's method 353-6
Tselikov's method 229, 254-66, 341
of roll strength 387-411
of roll torque 267, 278, 285-6, 291, 294-9,
309-19, 358-64
Bland, Ford and Ellis method 360, 362
Ford's method 361
Tselikov's method 359
of rolling speed 144-202, 615-24
of rolling temperature 136-44
of simple ovals 110-12
Camber 426-9
Capacity for deformation see Plasticity
Change in shape 20
Channel bar pass 499
Channels, pass design for 556, 589-94
Chemical affinity of metal for oxygen 19
Chilled cast iron rolls 387
Closed pass 494-5
Close-packed hexagonal crystal lattice 6
Coarsening of grain 17-18
Coefficient
of deformation 24, 39-40, 71, 559
of draught 20, 24, 71-72, 84-120, 149, 162,
478, 484-90, 537
maximum 71, 74
mean 71, 74, 155, 556
of dry friction 59
of elongation 20,24,26,48-49,71-73, 84-120,
149, 151, 321-7, 479, 503-7, 520-4, 549,
606
mean 502, 524-5, 558, 562
total 321-7, 505, 524-5
of forward slip 146, 177-82, 195
as a function of draught 177-82
of friction 59,61-64, 120-36,311
mean 128
of kinematic friction 21, 59
of loss 199
of rolling efficiency 311, 342
of spread 20, 24, 72, 84-120, 151, 153, 276,
483-6
of static friction 21, 59
Coercive force 11
Cogging mill 316
Cohesive force 3
Cold deformation 8
Cold plastic working of metals 2, 8-11, 15, 42
critical 14
Cold rolling 203, 211, 275, 331-72, 440-1, 536
Cold working range 46
Collar 496
double 496
end 496
inner 496
outer 496
resistance 496
single 496
Collective recrystallization 13
Common cast iron rolls 387
Compression 39
Compression patterns 38
Compressive forces 3
Compressive strength 19
Compressive stresses 59
Concave groove 495
Condition
of constant volume 22-24, 70, 88, 159, 506
of plasticity 30-42
of yielding see Criterion of yielding
Constancy of volume 21-30, 37, 88
Constant volume condition 22-24, 70, 88, 159,
506
Constant volume relationship 24
Constrained yield stress 21,42, 51,211,220,222,
226, 231, 239
mean 220,229
Contact
angle of 79-80, 123, 125-7
arc of 77-78, 83, 153, 220
area of 85, 219-20
Continuous mills, roll pass design for 610-24
Continuous rolling process 610
Continuous train design 615-24
Contraction 20
Convex groove 495
Cooling box 423
Cooling of rolls 423
Correction factor 93-107
for condition of rolling surface 93-95
for grade of steel 93-107
for rolling speed 93-95
for temperature 93-95
Criterion of yielding 35-36, 42, 63
boundary conditions for 36
Critical cold work 14
Cross-sectional area 20, 70
Crown 427
Crystal lattices 6, 12
accumulation of energy in 12
body-centred cubic 6
close-packed hexagonal 6
face-centred cubic 6
Crystal recovery 12 INDEX  671
Crystallization processes 18
internal 14
Crystallographic orientation 5
Crystallographic planes 5
Cubic lattice structure 7
Curve of spread 217
Dead diameter 498
Dead pass 494
Deformation 1-2
coefficient of 24, 39-40, 71, 559
elastic 2
in rolling 70
intensity of 45
intercrystalline 4-5
of a cubic element 30
of grains 5
of polycrystalline aggregates 4-8
of single crystals 4-8
parallelepipedal 21
permanent 2-3
plastic 2, 38
relative 23,43
strain energy of 34
total 2-3
velocity of 43
Deformation-energy theory 34, 41
Deformation work 21
specific 21
Degree
of cold work 8-13,51
average 51
formula for 9-10
of deformation 9, 12-14
of plasticity 3
of strain-hardening 15
Dependence
of ductility on temperature 18-19
of grain-growth on temperature 16
Design
of breaking-down systems 541-56
of continuous train 615-24
of regular sections 541-56
of roll cambers 427
of roll pass 494-660
Determination
of areas of squares and diamonds 555
of average yield stress 47
of mean and effective roll diameters 625
of mean height of section 557
of roll camber 438
of roll deflection 411
of roll forces in cold rolling 331-58
of roll forces in hot rolling 216-29
of roll speed 478
of spread 87
of torque distribution 378
Diagonal groove 495
Diagram
of elongations in two successive passes 552 3
of recrystallization, space 13-14
of strain-hardening 9
Diameter 20
barrel 498
Diamond pass 219, 499, 502
Diamond pass sequence 509
Direct draught 496
Direction of rolling 70
Directions of slip in crystal lattices 6
Displacement 5, 33
absolute 23
relative 3
Distortion, angle of 33
Distribution of compressive stresses 59
Disturbance of equilibrium
on grain boundaries 4-5
within the grains 4
Double collar 496
Draught 20,23,84-120
absolute 20,23,74-77,80,124,441-5,478,496
maximum 71, 74, 445
mean 71, 74, 524
coefficient of 20, 24, 71-72, 84-120, 149, 162,
478, 484-90, 537
maximum 71, 74
mean 71, 556
direct 496
lateral 496
maximum 71
natural 20
oblique 496
percentage 71
maximum 71, 74
mean 71, 74
relative 20, 74
maximum 71
mean 71
total 524
velocity of 44
Drawing 1
Drive 1
Drive loading with flywheel 377
Driving motors, power of 372-86
Driving torque, total 310
Dry friction 60, 128
coefficient of 59
Ductility 11, 18-19,46
Dulling of grooves 495-6
Duplex rolls 387
Dynamic torque 310, 314
Economic rolling, theoretical limit of 90-92
Edging pass 499, 502, 519, 526
Effect
of initial cross-section 612 672  INDEX
Effect (cont.)
of roll diameter 613
of roll speed 614
of strip tension 367-72
Effective radius 624-47
Effective roll diameter, mean 107
Effective work of plastic deformation 68
Efficiency of process 21
Effort of material relative to yield point 21
Ekelund's formula
for the calculation of roll force 234
for the calculation of yield stress 57
Elastic deformation 2
Elastic disturbance zone 207-8
Elastic limit 2
Elastic strain 2, 21, 23
Elasticity
modulus of 3, 21, 30
theory of 30
Elliptical ovals, calculation of 112
Elongation 2, 20, 67, 84-120, 477-82
absolute 20, 30, 74
coefficient of 20,24, 26, 48-49, 71-73, 84-120,
149, 151, 321-7, 479, 503-7, 520-4, 549
606
mean 502, 524-5, 558, 562
total 321-7, 505, 524-5
during hot rolling 477-82
natural 20
relative 20
End collar 496
Energy consumption in rolling 321-9, 331
364-6
Entry speed of stock 72, 145
Error
absolute 21
per cent 21
relative 21
Error ratio 21
Evaluation of rolling measurements 460-76
Exit speed of stock 72, 145, 175
Experimental rolling mill 488-9
Exponential coefficient 480-1
Extension 2
Extrusion 1
Face-centred cubic crystal lattice 6
Fatigue cracks 401
Fatigue limit 401
Finishing pass 499, 512
Finishing square 513
Fink's formula see Formula for the calculation
of the coefficient of forward slip
Flat bars 518
Flat ovals, calculation of 112-14
Flat pass 502
Flat rolling processes 647-60
Flow lines 3^t, 214
Flow of metal 82-84, 147, 491-3, 557-9, 563-4,
573, 583
Flying micrometer 456
Flywheel 314,319-22
kinetic energy of 319
Force 21
coercive 11
cohesive 3
compressive 3
frictional 59-62, 122
Ford's formula see Formula for the calculation
of degree of cold work
Forging 1
Form factor 88, 99, 107, 264-5, 398, 546
mean 107
Formation
of recrystallization nuclei 12
of twin crystals see Twinning
Forming pass 499
Formula for the calculation
of angle of bite 76-78
of average stress 35
of coefficient of elongation 93
of coefficient of forward slip 147
of coefficient of spread 93
of correction factor 93
of degree of cold work 9-10, 51
of effective work of deformation 68
of form factor 88
of free spread 86
of heat gain 139
of heat loss due to convection 139
of internal friction of viscous liquids 33
of length of sticking zone 208
of lever arm 270
of mean resistance to deformation 275
of neutral angle 183, 192
of plastic slip 33
of pressure of metal on the tool 65
of projected length of contact of a roll 332
of resistance to deformation 203, 356
of roll deflection 412
of roll factor 88
of roll force 229, 231, 233-9, 347, 349
of roll power 309
of rolling angle 78
of spread of alloy steels 95
of temperature drop 141-4
of theoretical work of deformation 266
of work of deformation 266
of yield criterion 35
of yield stress 50, 57
Formulae
for roll pass design 537-41
for the length of sticking zone 208
Forward slip 146, 152-3, 158-82, 482-7
coefficient of 146, 177-82, 195 INDEX  673
Fragmentation of grains 4, 7
Free rolling 123
Free spread 86
Friction 59, 120-36
angle of 21, 120-36
coefficient of 59, 61-64, 120-36, 311
mean 128
Frictional forces 59-62, 122
Frictional resistance 63-64
Frictional torque 311-14
Front tension 206, 459
Golovin-Tiagunov's formula for roll force 231
Gothic square construction 544
Gothic square-gothic square pass sequence 500
Gothic square pass 499, 502
Grade of steel, correction factor for 93-107
Grain boundaries 4, 7
Grain fragmentation 4, 7
Grain growth 13, 16
Grain slip 4-5
Graphical roll pass design 530-7
Groove 85, 495
concave 495
convex 495
diagonal 495
Groove depth 85, 495
Groove taper 495-6
Groove width 85
Group displacements of metal particles 4
Haag's formula 376
Heavy draughts 477-93
Height
of pass 218
of stock 20, 70
Hexagonal ovals, calculation of 114-18
Higher temperature range 46
Hitchcock's formula see Formula for the calculation of projected length of contact of a roll
Holzweiler method 514
Hooke's law 30
Hot plastic working 2, 15-19, 42, 51
incomplete 16
Hot rolling 203, 211,216-66,275,441
of mild steel 477-91
with heavy draughts 477-93
Hot section 494
Hot working range 46
Huber criterion of yielding 35
Hypothesis of parallelepipedal deformation 21,66
Idling torque 310, 314, 443
Incomplete hot plastic working 16
Induction loadmeter 454-6
Induction sensor 454-6
Inertia energy of flywheel 319-22
Influence
of absolute draught and roll diameter on the
coefficient of friction 124
of coefficient of friction on the resistance to
deformation 206
of cold work and temperature on grain size, 14
of cold work on grain size 13
of cold work on steel density 10
of deformation and temperature on recrystallization 15
of deformation rate on ductility and yield
stress 46, 51
of front and back tension on the resistance to
deformation 206
of hot working on grain size 16-17
of roll diameter on the resistance to deformation 206
of temperature on ductility of steel 18-19
of temperature on strain rate 46
of work hardening on roll pressure distribution 205
Initial cross-section 612
Inner collar 496
Intensity of deformation 45
Intercrystalline deformation 4-5
Intercrystalline matter 4, 6,14,19
Intermediate mill 316
Internal crystallization process 14
Introductory pass 499
Kinematic friction, coefficient of 21, 59
Knifing pass 499, 606-9
Korolev formulae see Formulae for the length
of sticking zone
Lateral draught 496
Laws of plastic deformation 21-30
Leader pass 499, 648-9, 652
Length 20,70
Lever arm 270
Limit
of elastic deformation see Elastic limit
of permanent (plastic) deformation see Yield
point
Limited plasticity 83
Line
of deflection 414
neutral 145, 395, 498, 624-47
Load 21
Loading of rolls, permissible 387-486
Loadmeter 452-4
induction 454-6
Longitudinal rolling 1, 69, 145
Loss, coefficient of 199
Lowest temperature range 46
Liiders lines see Flow lines 674  INDEX
Magnetic permeability 11
Mass 21
Maximum absolute draught 71, 74, 445
Maximum angle of bite 79, 81,122,127, 525
Maximum angle of contact 126
Maximum coefficient of draught 71,74
Maximum diameter 498
Maximum draught 71
Maximum percentage draught 71, 74
Maximum permissible draught 526
Maximum relative draught 71
Maximum roll forces as a function of permissible
bending stresses 463
Maximum shear theory 33
Maximum stress theory 33
Mean absolute draught 71, 74, 524
Mean coefficient of draught 71, 74, 155, 556
Mean coefficient of elongation 502, 524-5, 558,
562
Mean constrained yield stress 220, 229
Mean effective roll diameter 107
Mean form factor 107
Mean height 71
Mean height of the pass 218
Mean heights method of pass design 541-56
Mean percentage draught 71,74
Mean peripheral speed of rolls 195
Mean relative draught 71
Mean relative reduction 503
Mean resistance to deformation 21, 68, 220,
250-3, 260-4, 283-4, 300-2, 305-6, 343-4,
654
Mean resistance to flow 220
Mean roll factor 107
Mean speed of metal flow 152
Mean strain rate 44, 221-2
Mean working diameter 195
Mean yield stress 51, 226-8, 335-6, 341, 352
Measurement
of back tension 212
of exit speed 175
of roll force 449-56
by induction sensors 454-6
by means of strain gauges 450-4
of roll pressure distribution 211-16
of roll torque 449-56
by induction sensors 454-6
by means of strain gauges 450-4
of strip tension 449, 459
of strip thickness 449, 456-60
Measurements
in rolling 449-76
in rolling mills 460-76
Mechanism of bite 120-36
Metal flow 82-84, 147, 491-3, 557-9, 563-4,
573, 583
velocity of 84, 147-8, 151, 153, 491-3,
557-9, 563-4
mean 152
Metal flow lines 2-3, 214
Methods of rolling 1
Mild steel, hot rolling of 477-91
Mill, blooming 316, 392, 417, 441, 460, 502
Minimum diameter 498
Modulus
of elasticity 3, 21, 30
of plasticity 21,32
of rigidity 21, 412
of strain hardening 21
Moment of inertia 418
Motor power 440
Natural draught 20
Natural elongation 20
Natural spread 20
Navier and Stokes formulae see Formula for
the calculation of internal friction of viscous liquids
Neck 392-3, 398
Neutral angle 145,158-202,483
Neutral axis 498, 624-47
Neutral line 145, 395, 498, 624-47
Neutral plane 124, 145
Neutral zone 203
Nominal roll diameter 498
Nomogram for determination
of bite angle 81
of breaking-down systems 544-5
of coefficient of deformation 25
of draught coefficient in pass design 538-9
of draughts and reductions 531
of mean strain rate 223-5
of neutral angle 161, 190-1
of number of passes 27
of peripheral speed of rolls 146
of permissible absolute draughts 446
of radiation loss 138
of roll forces 366-7, 446-7
of roll torque 366-7, 466-7
of the areas of various ovals 113-17
Non-uniform deformation of metal 83
No-slip angle 482-7
Number of passes 27, 502-3, 519, 523-4, 549
Oblique draught 496
Open box pass 499, 502
Open pass 494
Optimum rolling programme 440
Orowan-Pascoe formulae for the calculation of
roll force 235
Otto's slide rule 540, 582
Outer collar 496
Oval-oval pass sequence 500
Oval pass 499, 502
Ovals
types of 110
elliptical 112 INDEX  675
Ovals (cont.)
flat 112-14
hexagonal 114-18
simple 110-12
Overdraught 496-7
Overheating of steel 19
Overloading of motors, permissible 374
Parallelepipedal deformation, hypothesis of
66
Pass 494
active 494
angle 499
blooming (roughing) 499
box 275-92
breaking-down 292-309, 499
closed 494-5
dead 494
edging 499, 502, 519, 526
finishing 499, 512
flat 502
forming 499
introductory 499
knifing 499, 606-9
leader 499, 648-9
preparatory 499
section 499
Pass design 494-660
blooming mill 523-30
mean heights method of 541-56
sections 556-610
Pass dimensions 511-12, 514, 529
Pass neutral axis 635
Pass schedule for rolling 406,413
Pass sequences 500-2
breaking-down 500, 507-12
Pavlov-Ekelund formula for the calculation
of neutral angle 183, 193
Per cent error 21
Percentage draught 74,162
maximum 71, 74
Percentage reduction 20, 72, 74, 229
Peripheral speed of rolls 145
mean 195
Permanent plastic deformation 2-3
limit of see Yield point
Permeability, magnetic 11
Permissible draught, maximum 526
Permissible loading
of rolling mills 440-9
of rolls 387-486
Permissible overloading of motors 374
Permissible roll force 414, 467
Permissible roll torque 416
Permissible stresses for rolls 401-2
Phenomena in plastic working 2-4
Phenomenon
of cold work 18
of friction 59-60
Pinion stand 1
Plane, neutral 124, 145
Planes of slip in crystal lattices 6
Plastic behaviour of metals 21, 31
Plastic deformation 1-2, 16, 38
laws of 21-30
of polycrystalline aggregates 4-8
of single crystals 4-8
work of 65-68, 266, 309, 368
Plastic disturbance zone 207-8
Plastic state of solid matter 3
Plastic strain 2, 21,23, 26, 28, 30,32
boundary conditions for 40
Plastic working of metals 1-19
principles of 20-68
Plasticity 6, 9
condition of 30-42
modulus of 21, 32
Plate mill 316, 392
Poisson's constant 21, 31-32
Poisson's ratio 21, 31
Polycrystalline aggregates 4-8
interaction of stresses in 7
plastic deformation of 4-8
Power 21
of driving motors 372-86
Power consumption in rolling 322-31
Practical condition for rolling 124
Preparatory oval 517
Preparatory pass 499
Preparatory square pass 502
Pressing 1
Principal strain 21
Principal stresses 21
Principle of constant volume 159
Principles
of plastic working 20-68
of roll pass design 494-660
Profile 494
Profile section of channel 643
Properties of steel, influence of cold working
10-12
Radiation gauge 457-8
Radiation loss in rolling bars 138
Rail pass 499
Range
cold working 46
higher temperature 46
hot working 46
lowest temperature 46
Rate
of deformation 16,42-46
of strain 44-47, 52
of strain-hardening 9
Reconstruction of space lattice 14 676  INDEX
Recrystallization 8, 11-18
collective 13
incomplete 16
space diagrams of 13-14
Recrystallization nuclei 12, 16
Recrystallization range 15-16
Recrystallization temperature 9, 12
Reduction 520-2
absolute 20, 74
percentage 72
relative 20, 48-49, 72, 74
mean 503
total 20
Regions
of limited plasticity 83
of plastic deformation 63
Regular sections 541-56
design of 541-56
Reheating 11-12
Relation
between coefficient of elongation and percentage reduction 72
between constrained yield stress and strain 67
between forward slip and spread coefficient
to draught coefficient 483
between forward slip and temperature 485
between friction coefficient and surface condition 61
between recrystallization temperature and
melting temperature 12
between yield stress and deformation 49
between yield stress and the strain rate and
temperature 52
Relative deformation 23, 43
Relative displacement 3
Relative draught 20, 74
maximum 71
mean 71
Relative elongation 20
Relative error 21
Relative reduction 20, 48^9, 72, 74
mean 503
Relative spread 20
Relative strain, velocity of 44
Resistance collar 496
Resistance to deformation 6, 58-65, 68, 204,
220,233-4, 250, 275, 278, 281-4, 290, 294,
305, 341-6, 356, 441
mean 21, 68, 220, 250-3, 260-4, 283-4,
300-2, 305-6, 343-4, 654
specific 21
Resistance to flow 63, 203
Resistance to friction 63-64, 204
Resultant roll force 273-5
Rigidity, modulus of 21, 412
Rod mill 316
Roll axis 70, 497
Roll barrel 392-3, 424, 498
Roll camber 420-40
calculation of 426-9
design of 427
Roll clearance 108-10
Roll cooling 423
Roll deflection 394-5, 411-40, 507
Roll diameter 80, 613, 624-5
nominal 498
Roll factor 88, 107
effective, mean 107
Roll flattening 421, 507
Roll force 394, 398-9, 411-12, 415, 440-1,
444-6, 487-8
calculated 414
calculation of 229-66, 273-5, 278-82, 289,
294-9, 331-58, 415
determination of 216-29, 331-58
due to bending stresses 411-12, 416, 437
due to shear stresses 411-12, 416, 437
in cold rolling 331-58
in hot rolling 216-66
measurement of 449-56
permissible 414, 467
resultant 273-5
total 411-12,416,419,428,430,436
Roll gap 80, 82, 125, 204, 411, 423-5, 435, 497
Roll hardness 387, 391
Roll heating 423
Roll jump 497
Roll neck 392-3, 398
Roll pass design 494-660
basic definitions of 494-501
formulae for 501-30, 537-41
graphical method of 530-7
theoretical principles of 556-647
Roll power, calculation of 309-31, 367
Roll pressure 203-29
Roll pressure distribution 204-7, 213-16
measurement of 211-16
Roll setting 497
Roll speed 478, 615-24
Roll strength calculation 387-411
Roll torque 310, 399, 416, 440-2, 446, 487-91
calculated 416
calculation of 267, 278, 285-6, 291, 294-9,
309-19, 358-64
characteristics of 471
dynamic 310
measurement of 449-56
permissible 416
static 311, 318
Roll wear 394, 426, 498, 609
Roll wobblers 392-3,401
Rolling
basic concepts in 69-75
bite in 120-36
deformation in 70
efficiency coefficient of 311, 342 INDEX  677
Rolling (cont.)
flow of metal in 82 84
friction in 120-36
geometrical relations in 75-82
in box passes 275-92
in breaking-down passes 292-309
longitudinal 1, 69, 145
measurements in 449-76
methods of 1
of bars 107-20
of sheet 411-40
of small sections 647-60
of strip 411-40
skew 1-2, 69
symbols in 69-75
transverse 1-2, 69
trigonometrical relations in 75-82
with slip 185
with spread 158-82
Rolling analysis 460-76
Rolling angle 75, 78, 150
Rolling equipment 1
Rolling line 498
Rolling load 487-91
Rolling mills 1
experimental 488-9
laboratory 211
measurements in 460-76
permissible loading of 440-9
Rolling process
continuous 610
flat 647-60
Rolling programme, optimum 440
Rolling schedule for sheets 330
Rolling speed 93-94, 305
calculation of 144-202, 615-24
Rolling temperature 136-44
range of 99
Roiling work 322-31
Rolls 387-476
calculation of 387-411
chilled cast iron 387
common cast iron 387
duplex 387
steel 387
Roughing mill 316
Round bars 514
Round pass 502
Round profile 515
Rounding of grooves 495-6
Samarin's formula for the calculation of roll
force 233
Seamless tubes 2
Section mill 316, 392, 624
Section pass 499
Sections
equal leg angle 556, 561, 581-8
I- 556, 581-5, 589-606
pass design for 556-610
regular 556
T- 556, 581-5, 588-9
Sedlaczek's formula 86
Shape sections 567
Shaped pass 502
Shear components 20
Shear stress 6
components 21
Shearing force 418-19
Sheet mill 316,392
Sheets 536
Siebel's correction factor 275
Siebel's equation for the mean resistance to
deformation 275
Siebel's formula see Formula for the calculation
of free spread
Simple ovals, calculation of 110-12
Sim's formula for the calculation of roll force 239
Single collar 496
Single crystals, plastic deformation of 4-8
Sizing diamond 513
Sizing oval pass 514
Sizing ovals 516-17
Skew rolling 1-2, 69
Slide rule
Otto's 540, 582
Wojtylak's 538
Slip, backward 147, 152-3
Slip along definite crystallographic planes see
Displacement
Slip friction 63-64, 82
Slip of grains see Grain slip
Slip theories in rolling 210
Slip velocity 33
Slipping 220
Slipping zone 207-8
Small sections rolling 647-57
Solidus line 19
Space diagram of recrystallization 13-14
Specific deformation work 21
Specific roll work 294-9
Specific weight 21-22
Speed distribution during rolling 476-7
Speed of rolls, peripheral 145, 195
Speed of stock
entry 72, 145
exit 72, 145, 175
Splitting of grains 7
Spray-jet cooling of rolls 423
Spread 20, 84-120, 158-82, 477-82, 488
absolute 20, 74
coefficient of 20, 24,72, 84-120,151,153,276,
483-6
curve of 217 678  INDEX
Spread (cont.)
free 86
natural 20
relative 20
Square bars 512
Square-diamond-square pass sequence 510
Square-oval-square pass sequence 511
Square pass 502
Square-square pass sequence 500
Stamping 1
Stands of rolls 1
State
of strain 20
of stress 21,31
of stress-strain in triaxial deformation 32
of stress-strain without lateral spread 35
plastic 3
Static friction 63
coefficient of 21, 59
Static load diagram 318
Static torque 311, 318
Static yield stress 21
Steel rolls 387
Stefan-Boltzmann relation 136
Sticking 220
Sticking zone 207-8
Strain 2, 20
elastic 2, 21, 23
plastic 2, 21, 23, 26, 28, 30, 32
principal 21
total 2,21,31
Strain energy of deformation 34
Strain gauge 450-4
Strain rate 44, 46, 52, 220-5
mean 44, 221-2
Strain-hardening 8-11, 15
modulus of 21
Strain-hardening curves 48-50
Strain-hardening formulae 49
Strain-hardening rate 9
Strength
calculation of rolls 387-411
compressive 19
Stress 2,21
normal 21
shear 21
state of 21, 31
Stress components 21
Stress concentration factor 429
Stress function 36
Stressless zone 207-8
Stress-strain curve 30, 42, 67
Stress-strain diagram 52
Stress-strain relationships 30-42
Stress-strain state 32, 35
Strip tension
effect 367-72
measurement of 449, 459
Strip thickness, measurement of 449, 456-60
Strippers 496
Strips 536
Structure, anisotropic 11
Subcritical annealing 14
Subcutaneous blowholes 22
Summary temperature drop 142
Tafel and Sedlaczek's formulae see Formula for
the calculation of free spread
Taper 495-6
Temperature 21
absolute 21
of fusion 4
of recrystallization 51
Temperature distribution of a roll 422
Temperature drop, summary 142
Temperature range, rolling 99
Tensile force 2
Tensile strength 2, 8
Tensiometer 459
Tension 39
back 206,459
front 206,459
Theoretical limit of economic rolling 90-92
Theoretical work of plastic deformation 66-68,
266
Theory
of elasticity 30
of maximum shear 33
of maximum stress 33
Thickness of plates 20
Thickness ratio see Roll factor
Thickness variation during rolling 411-40
Tiagunov's formula see Formula for the calculation of temperature drop
Time 21
Torque
dynamic 310, 314
idling 310,314,443
on the motor shaft 310, 316
static 311, 318
Torquemeter 452-4
induction 454-6
Total coefficient of elongation 321-7, 505,
524-5
Total deformation 2-3
Total draught 524
Total reduction 20
Total roll force 411-12,416, 419, 428, 430, 436
Total strain 2, 21, 31
Transverse rolling 1, 69
Triaxial deformation of a cubic element 22
True diameter 498
Tselikov's formula
for the calculation of free spread 86
for the calculation of neutral angle 183, 192 INDEX  679
Tselikov's formula (cont.)
for the calculation of roll foree 229
Tubes 2
Twin crystals 55
Twinning 5
Underdraught 496-7
Value
calculated 21
measured 21
Variation
of angle of bite with rolling speed 130
of coefficient of friction with rolling speed
131, 135
of coefficient of friction with temperature
130,132
of coefficient of friction with type of lubricant
134, 135
of coefficient of friction with various testing
conditions 61
of correction factor c with rolling speed 94
of correction factor d with draught coefficient
97, 100, 102, 104, 106
of correction factor d with temperature 98,
101,103,105
of yield stress with temperature 58
Velocity
of deformation 43
of draught 44
of metal flow 84, 147-8,151-3,491-3, 557-9,
563^*
of relative strain 44
Volume 20
constancy of 21-30, 37, 70, 88
Wear of the roll surface 394, 426, 498, 609
Weight, specific 21-22
Wire rod 518
Wobbler 392-3,401
Wojtylak's slide rule 538
Work hardened zone 207-8
Work of plastic deformation 65-68, 266-70, 309,
368
actual 68, 266, 309
effective 68
theoretical 66-68, 266
Working diameter 498
mean 195
Working radius, mean 197, 201
Wusatowski's formula 89, 477, 479, 551
Yield criterion 35, 42, 63
Yield point 2, 33
effort of material relative to 21
Yield stress 18-21, 42-58, 337-40, 342
constrained 21, 42, 51, 211, 220, 222, 226,
231, 239
mean 51, 226-8, 335-6, 341, 352
static 21
Yield stress curves 47, 52-57, 226-7
Young's modulus see Modulus of elasticity
Zolotnikov's formula see Formula for the calculation of free spread
Zone
elastic disturbance 207-8
neutral 203
plastic disturbance 207-8
slipping 207-8
sticking 207-8
stressless 207-8
work hardened 207-8  


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