Machine Elements Life and Design

Machine Elements Life and Design
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Boris M. Klebanov , David M. Barlam , Frederic E. Nystrom
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1 سبتمبر 2020
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Machine Elements Life and Design
Boris M. Klebanov
David M. Barlam
Frederic E. Nystrom
Table of Contents
PART I Deformations and Displacements . 1
Chapter 1 Deformations in Mechanisms and Load Distribution over the Mated
Surfaces of Parts .3
Reference 9
Chapter 2 Movements in Rigid Connections and Damage to the Joint Surfaces 11
2.1 Interference-Fit Connections (IFCs) 11
2.1.1 IFCs Loaded with a Torque .11
2.1.2 IFCs Loaded with Bending Moment .12
2.2 Bolted Connections (BCs) 14
2.2.1 Forces in Tightened BC under Centrically Applied Load .16
2.2.2 Forces in Tightened BC under an Eccentrically Applied Load 18
2.3 Damage to the Mating Surfaces in the Slip Area 19
References 20
Chapter 3 Deformations and Stress Patterns in Machine Components .21
3.1 Structure and Strength of Metals .21
3.2 Deformations in the Elastic Range 24
3.3 Elastoplastic Deformation (EPD) of Parts .32
3.4 Surface Plastic Deformation (SPD) .36
References 39
PART II Elements and Units of Machines 41
Chapter 4 Shafts 43
4.1 Selecting the Basic Shaft Size .43
4.2 Elements of Shaft Design .46
4.3 Hollow Shafts .53
4.4 Selection of a Loading Layout for Strength Analysis .54
4.5 Analysis of Shaft Deformations .58
References 65
Chapter 5 Shaft-to-Hub Connections 67
5.1 General Considerations and Comparison .67
5.1.1 Interference-Fit Connections (IFCs) 67
5.1.2 Key Joints .69
5.1.3 Splined Joints (SJs) 705.2 Strength Calculation and Design of IFCs 71
5.2.1 Calculation for Total Slippage .71
5.2.1.1 Surface Pressure 72
5.2.1.2 Coefficient of Friction .74
5.2.2 Design of IFCs .77
5.3 Design and Strength Calculation of Key Joints .79
5.3.1 Role of IFC in the Key Joint .79
5.3.2 Strength of Keys .85
5.3.3 Strength of the Shaft Near the Keyway .86
5.3.4 Strength of Hub Near the Keyway 88
5.3.5 Round Keys 92
5.4 Splined Joints .93
5.4.1 SJs Loaded with Torque Only 94
5.4.2 SJs Loaded with Torque and Radial Force 97
5.4.3 Allowable Bearing Stresses in SJs .100
5.4.4 Lubrication of SJs 101
References 102
Chapter 6 Supports and Bearings 103
6.1 Types and Location of Supports 103
6.2 Rolling Bearings (RBs) 108
6.2.1 Design of RBs 108
6.2.2 Stresses and Failures in RBs 111
6.2.3 Design of Supports with Rolling Bearings 115
6.2.4 Choice and Arrangement of Supports 121
6.2.5 Fits for Bearing Seats .123
6.2.6 Requirements for Surfaces Adjoined to RBs .131
6.2.7 Elastic Deformation of RBs under Load .133
6.2.8 RBs with Raceways on the Parts of the Mechanism .135
6.2.9 Lubrication of RBs .137
6.3 Sliding Bearings (SBs) .138
6.3.1 Friction of Lubricated Surfaces 138
6.3.2 Types of SBs .140
6.3.3 Materials Used in SBs 141
6.3.4 Design of Radial SBs .144
6.3.5 Design of Thrust SBs .149
6.3.6 Surfaces Connected with SBs: Features Required 151
6.3.7 Oil Supply to SBs .153
References 158
Chapter 7 Gears .159
7.1 Geometry and Kinematics of Gearing .160
7.2 Forces in Spur Gearing and Stresses in Teeth .167
7.3 Kinds of Tooth Failure .170
7.4 Contact Strength (Pitting Resistance) of Teeth 174
7.5 Bending Strength (Breakage Resistance) of Gear Teeth .181
7.6 Unevenness of Load Distribution across the Face Width (Factor KW) .187
7.7 Dynamic Load in the Gear Mesh and Factor Kd .195
7.8 Load Distribution in Double-Helical Gears (Factor KWh) .197
7.9 Backlash in the Gear Mesh 1987.10 Lubrication of Gears .200
7.11 Cooling of Gears 208
References 213
Chapter 8 Gear Design 215
8.1 Gear and Shaft: Integrate or Separate? 215
8.2 Spur and Helical Gears 217
8.3 Built-up Gear Wheels .224
8.4 Manufacturing Requirements and Gear Design 235
8.5 Bevel Gears .238
8.6 Design of Teeth 239
References 240
Chapter 9 Housings .241
9.1 The Function of Housings 241
9.2 Materials for Housings .243
9.3 Design of Housings 248
9.3.1 Housings Split through the Axes of Shafts 248
9.3.1.1 Design of Mounting Feet 250
9.3.1.2 Design of Lifting Elements .251
9.3.2 Housings Split at Right Angle to the Axes of the Shafts 251
9.3.3 Nonsplit Housings 253
9.4 Deformations and Stiffness Problems 254
9.5 Housing Seals .255
9.5.1 Sealing of Rigid Connections (Static Seals) 255
9.5.2 Sealing Movable Joints 262
9.5.2.1 Noncontact Seals .262
9.5.2.2 Contact Seals .264
9.5.2.3 Combined Seals .274
References 275
Chapter 10 Bolted Connections (BCs) 277
10.1 Load Distribution between the Bolts .278
10.1.1 Load Distribution in Bolted Joints Loaded in Shear .282
10.1.2 Load Distribution in Bolted Joints Loaded in Tension .287
10.2 Tightening of Bolts .292
10.2.1 Tightening Accuracy .292
10.2.2 Stability of Tightening 295
10.2.2.1 Self-Loosening of Bolts 295
10.2.2.2 Plastic Deformation of Fasteners and Connected Parts .295
10.2.3 Locking of Fasteners .300
10.3 Correlation between Working Load and Tightening Force of the Bolt 302
10.3.1 Load Normal to Joint Surface 302
10.3.2 Shear Load 305
10.3.3 Bending Load 311
10.4 Strength of Fasteners 313
10.4.1 Static Strength .313
10.4.2 Fatigue Strength 317
References 319Chapter 11 Connection of Units .321
11.1 Housing Connections 321
11.2 Shaft Connections .329
11.2.1 Alignment of Shafts 329
11.2.2 Rigid Couplings 334
11.2.3 Resilient Couplings .336
11.2.4 Gear Couplings .342
References 352
PART III Life Prediction of Machine Parts 355
Chapter 12 Strength of Metal Parts 357
12.1 Strength of Metals 359
12.1.1 Strength at a Static Load 359
12.1.2 Fatigue Strength (Stress Method) .363
12.1.3 Limited Fatigue Life under Irregular Loading (Stress Method) 374
12.1.4 Fatigue Life (Strain Method) 376
12.2 Strength of Machine Elements .386
12.2.1 Surface Finish .387
12.2.2 Dimensions of the Part .387
12.2.3 Stress Concentration .388
12.2.4 Use of Factors K
S, Kd, and Ke .389
12.3 Comparative Calculations for Strength 390
12.4 Real Strength of Materials .395
References 396
Chapter 13 Calculations for Strength 397
13.1 Characteristics of Stresses in the Part 397
13.1.1 Estimation of External Loads .397
13.1.2 Determination of Forces Applied to the Part .398
13.1.3 Estimation of Stresses in the Part .403
13.2 Safety Factors .404
13.3 Errors Due to Inappropriate Use of FEM 405
13.3.1 Design Principles and Precision of FEM .405
13.3.2 Design of Model for FEM Computation 407
13.3.3 Interpretation of Boundary Conditions .409
13.3.4 Is the Computer Program Correct? 412
13.3.5 More about Simplified Analytical Models .412
13.3.6 Consideration of Deformations .416
13.4 Human Error .416
13.4.1 Arithmetic .416
13.4.2 Units (Dimensions) .417
13.4.3 Is This Formula Correct? 418
References 419
Chapter 14 Finale 421
Index
423
Index
A
Abrasive wear, 115, 171, 192
Action, line of, 161, 163–164, 195
Addendum. See Tooth
Admissible stress, 86, 356–359, 364, 387, 389, 391–392,
394–395, 404
Alignment, 8, 56, 58, 104–105, 197, 236, 249, 253–255,
265, 274
angular, 85, 96, 106, 109–110, 121, 331, 344–345
radial, 330
of shaft, 119, 329–334
techniques, unit connections, 333
of teeth, 197
Aluminum alloy, 19, 46, 110, 143, 151, 245, 297, 316, 323,
325, 380
Angle
helix, 76, 103–104, 165–166, 193, 197–198, 219, 224,
236
pressure, 96, 103, 117, 160, 168, 173, 186, 196, 220
slope, 60, 63, 65, 357, 384, 412
Angular misalignment, 345
effect on shaft, bearing loads, 331
Arrangement, of bearings, 121–123, 130
Assembled gears, 238
Attachment point, 278, 280, 282, 291, 416
Axial fixation, shafts, 104
Axial force (load), 5, 8, 13–14, 63, 67, 71, 74–75, 80–84,
103, 115–123, 129, 132–133, 136–137, 141, 152,
197–198, 219–220, 227, 236, 246, 249, 255, 274,
301, 311, 339, 342, 408–409
Axles, 3, 44, 71, 106, 137, 200, 241, 273, 284, 357
B
Babbit alloys, 143–144, 149, 151
Backlash, 102–103, 198–199, 242
gear mesh, 198–200
Ball bearing, 108–109, 117–118, 129, 132, 134–135, 255,
374, 418
Bandage gears, local slippage, 229
Base circle, 160–161, 163, 195
Base pitch, 160–161, 163, 169, 181–182, 195–196
Basquin’s formula, 382
Beam supports, strength calculations, 408
Bearing stress, 86, 92–93, 95–96, 100–101, 296
Bearing surface, 84, 141, 146, 149, 151, 293, 295–298,
300–301, 311, 318
Bearings
adsorbed oil film, 138
alignment, 119, 151–152, 249
arrangement, 122–123
axial movement under load, shaft misalignment from,
119
ball, 51, 108–109, 117–118, 123, 129, 132, 134–136,
255, 374, 418
clearance in, 117
comparison of, 111
cylindrical roller, axial load, 116
diesel engine crank mechanism, oil ducts, 157
double-row, 56
elastic deformation, 133–135
failure, 108, 111–115
fits, 44, 123–131
flat working surface, sliding thrust, 150
four-point ball, 123, 136
Hersey-Stribeck diagram, 140
high-speed roller, compared, 111
hollow shaft, 152, 154
housing oil ducts, 154
hydrodynamic oil film, sliding, 141
load distribution, 57, 128
lubricated surfaces, contact of, 139
lubrication of, 137–140
needle, 110
oil distribution grooves, 146–147
oil supply, plain, spline connections, 157
planet wheel, sliding, 148
radial, 117
radial ball, assembling, 109
ring fastening, 129
roller without inner rings, 135
rollers, ring, shaft, interaction, 124
rolling, 108–138
rotating oil pressure, 155
self-aligning, 151–152
self-made roller, 136
shaft shoulder height, 133
sliding, 138–158, 197
straight roller, 106, 110, 113, 116–118, 120–121,
134–136, 418
tapered roller, 118–119, 122, 129–130, 132, 134, 255,
270
two-cylinder contact, stresses in, 112
two-row, 110
types of, 108, 140–141
Bending deformation, 4, 7, 25, 56, 58, 67, 152, 181,
217–219, 227, 247, 250, 273, 282, 310, 318, 329,
365
gears, failure, toothed rim, 218
straight beam, 25
Bending moment
between bearings, angular deformation, 59
bolts, 291424 Machine Elements: Life and Design
Bending strength, 4, 44, 161, 169–170, 173, 176, 179, 181,
183–187, 192, 199, 232, 240, 348
Bending strength of teeth, 232
Bending stress, 14, 37–39, 56, 75–77, 84, 91, 166,
168–169, 181–183, 185–187, 193–194, 197, 218,
249–250, 267–268, 310–311, 331, 357, 359, 364,
390, 399
Bevel gears, 107, 136, 179–180, 186, 200, 208, 238–239,
252–253, 256
Block brake, 5
Bolted connections, 11, 14–19, 226, 256, 277–319, 368,
403–404
aluminum parts, 296
bending, threads, 318
bending moment, 291
bolt design comparison, 298
bolt joint loaded in tension, bending, analytical model,
288
bolt shank, maximal, average tension stresses, 304
bolt tension force, eccentric, coaxially applied loads, 303
bolted joints loaded in shear, load distribution in,
282–287
center of gravity, 285
center of rotation, 285
comparative calculations of, 292
cone-fitted bolts, flange connection with, 293
contours, complex, 290
fastener strength, 313–319
fatigue strength, 317–319
static strength, 313–317
fitted bolts, connection with, 307
flange connection
slip in, 310
types, 306
helical insert for thread reinforcement, 316
high fatigue strength bolt design, 318
load distribution, loaded in tension, 287–292
load distribution between bolts, 278–292
loaded in shear, 283
loaded with shear forces, 305
locking fasteners, 300
long stud bolt vibrations, 312
parallelogram of forces, false use, 281
rib, 279
statically determinate, indeterminate beams, 280
thin-walled tubes, flange connection of, 278
tightened bolt connection, stress distribution, 297
tightening of bolts, 292–302
accuracy, 292–295
stability of tightening, 295–299
working load, tightening force of bolt, correlation,
302–313
bending load, 311–313
load normal to joint surface, 302–305
shear load, 305–311
Bolted joint
concentric, eccentric loading, 16
concentrically loaded, 16
eccentrically loaded, 16
two part, 14
Bolts
centrically loaded, 16–18, 282
eccentrically loaded, 16, 18–19, 303
elongation, 294
fitted, 226, 282, 287, 307–309, 316, 319
locking of, 300–302
stability of tightening, 295–302
strength
fatigue, 317–319
static, 313–317
tapered, 309–310
tightening, 292–302
accuracy, 292–295
tightening accuracy, 292–295
tightening force, 257, 278, 302–313
tightening torque, 80–81, 83–84, 292–295, 301, 306, 313
working load, tightening force of bolt, correlation,
302–313
bending load, 311–313
load normal to joint surface, 302–305
shear load, 305–311
Boundary condition, 85, 241, 292, 409–411, 416
Brake, 4–5, 130, 292
Broaching, 71
Broken sections, 26
Bronze, 95, 107, 143–144, 146, 148, 316
Buckling, 46
Built-up gear wheels, 224–235
Burnishing, 20, 37–38, 53
C
Cage, 107–111, 115, 123, 136–137
Cantilever beam, strength calculations, 407
finite element method, 410
Carburizing, 20, 44, 101, 132, 239, 265, 270
Case hardening, 115, 184, 225
Cast housing, 153, 173, 245–246
Casting materials
cast steel, 244–245
gray cast iron, 31, 200, 221, 232–233, 244–245, 260,
293, 316
Centrifugal force, 8, 74, 102, 110, 115, 137, 155–156, 201,
275
Change of clearance, unit connections, driving/driven teeth,
349
Chrome plating, 270
Clearance, 3–5, 8, 18, 56–57, 70–71, 78, 85, 95, 98,
103–105, 107, 115, 117–120, 122–123, 126–129,
131, 133–135, 141, 145, 149, 151–152, 198,
235–236, 263–265, 267–269, 272–273, 294, 305,
309, 318, 329, 332–333, 343, 348–349
Coating, 20, 137, 141, 143, 173, 243–244, 271, 295
Coefficient, 18–19, 27–28, 31, 64, 67–69, 72, 74–77,
79–81, 83, 89, 95, 117, 120–121, 125, 127,
134–135, 139–140, 143–144, 171, 183, 228–230,
232–234, 264, 272, 278, 293–295, 301, 305–308,
315, 317, 357, 379–380, 382–384, 386, 393, 404
of friction, 69, 72, 74–77, 79–80, 83, 95, 120, 139–140,
228–229, 232–233, 293, 295, 306–307, 315, 350Index 425
Cold rolling, residual stress distribution after, 37
Cold working, 44, 53
Combined load, 117, 119
Comparative calculations, 175, 187, 226, 231, 282, 284,
292, 390
Compliance, 7, 15, 17–18, 44, 57, 72, 97, 125, 131,
151–152, 187, 217–218, 279, 282–283, 291,
298–299, 302–303, 313, 330, 336, 404,
411–412
Compressive force, 18, 226
Compressive stress, 15, 20, 35–39, 50, 53, 112, 172,
184–185, 227
Computer program, 58, 149, 241, 355, 397, 403, 407,
412
Conical gears, rigidity with, 222
Connections
alignment techniques, 333
bolted, 11, 14–15, 19, 226, 256, 277, 279, 281, 283,
285, 287, 289, 291–295, 297, 299, 301, 303,
305, 307–309, 311, 313, 315, 317, 319, 368,
403–404
change of clearance, 349
crowded tooth, contact patch, 352
crowned teeth shape, 345
deformations, 322, 324
design, 322
enlarged tooth length, 348
flange, 103–104, 275, 277–278, 292, 303, 305–306,
308–310, 319, 342
frame twisting, 323
gear coupling, 343
hobbing, 346
housing connections, 321–329
interference fit, 102
shaft connections, 329–352
splined, 93
stress calculation, 324
tapered, 67–68, 73, 80
Contact length, 113
Contact line, 113, 165–169, 174, 177, 188, 194
Contact patch, unit connections, crowded tooth,
352
Contact pattern, 107, 253–254
Contact pressure, 13, 20, 51–53, 69, 96, 230, 303
Contact ratio, 161, 163, 165–166, 194–196
Contact seals, 264–274
lip-type seals, 269–271
mechanical seals, 272–274
O-rings, 268–269
piston ring packing, 265–268
Contact strength, of teeth, 174–181
Contact stress, 100, 110, 112, 117, 129, 168–169,
173–174, 176, 179, 183, 193
loaded tooth, 168
Cooling, 74, 103, 131, 149, 173, 200, 206, 208–212,
247, 270–271, 273–274, 338, 343
gears, 208–212
Copper alloys, 146, 209, 266, 293
Copper plating
Cotter pin, 206, 300
Couplings, 20, 43–44, 68–69, 95, 104, 156, 174, 197, 208,
292–293, 321–323, 331, 334, 336–343, 347–352,
398
gear type
resilient, 292, 336, 342
rigid, 68, 334
Crack propagation, 387
Critical frequency, 45, 312–313, 336, 399, 403
Critical load, 18
Crowned teeth, 343, 345–346, 352
Crystal cell, 22
Crystal lattice, 21–24, 172, 357, 376, 380
imperfections, 22
Crystal structure, 21
Crystals, in metal structure, 23
Cyclic load, 24, 31, 36, 91, 111, 148, 277, 311, 398
Cyclic properties, 391
Cylindrical roller bearing, axial load, 116
D
D’Alembert principle, 166
Damage accumulation, 404
Damage to joint surfaces, rigid connections, movements in,
11–20
bolted connections, 14–19
bolted joint
concentric, eccentric loading, 16
two part, 14
eccentrically loaded bolted connection, deformations, 19
fretting, strength-damaging effect, 20
interference-fit connection, self-dismantling under
bending load, 14
interference-fit connections, 11–14
load distribution nonuniformity, 13
loaded with bending moment, 12–14
loaded with torque, 11–12
torsional deformation, 12
mating surfaces, slip area, damage to, 19–20
tightened bolt connection, forces in, 16
Dead center, 3
Dedendum. See Tooth
Deflection, 17, 54, 58, 84, 151, 196, 325, 332
Deformation
bending, 4, 7, 25, 37, 39, 56, 58–60, 67, 152, 181,
217–219, 227, 247, 250, 273, 282, 310, 318, 329,
365
elastic, 4, 8–9, 19, 24–35, 65, 68, 93, 104, 110, 112–114,
117–118, 122, 131, 133–135, 142, 151, 168, 187,
196, 215, 219, 229, 241–242, 263, 273, 297, 299,
307, 315, 333, 349, 418
elasto-plastic, 32–36
housings, 254–255
mated part surfaces, 3–9
shafts, analysis, 58–65
stress patterns, machine components, 21–39
bending deformation, straight beam, 25
bending stresses, T-beam, 37
broken sections, 26
burnishing shafts, roller shapes, 38426 Machine Elements: Life and Design
cold rolling, residual stress distribution after, 37
crystal cell, 22
crystal lattice, 22
crystals, in metal structure, 23
dislocation, movement under load, 22
elasto-plastic deformation, parts, 32–36
elasto-plastic deformation effectiveness, 34
filleted bar, strain distribution, 28
grains in metal structure, 23
metal strength, 21–24
metal structure, 21–24
notched strip in tension, stress concentration, 30
plane sections, 26
reversed bending, loss of residual stress from, 39
shot peening, residual stress distribution after, 37
straight bar, strain distribution, 26
stress-strain diagrams, 32
surface plastic deformation, 36–39
thin-walled beams, deformation of, 25
surface, plastic, 36–39, 53, 190, 295
unit connections, 322, 324
Deformation pattern, 29, 278, 281, 287, 416
Design
elements, shafts, 46–53
of housings, 248–254
unit connections, 322
Diagram, stress-strain, 32, 360
Diameter, pitch, 63, 100, 160, 167, 179, 183, 186, 220,
232–233, 350
Diametral pitch, 96, 136, 160, 181, 183
Dimension factor, 90
Disk thickness, gears, 221
Disk-type gears, deformation, 219
Dislocation, 21–24, 31, 380
movement under load, 22
Displacement, 1, 4, 8, 23, 56, 85, 93, 98, 101–102,
104–105, 115, 122, 132, 145–146, 152, 154, 158,
173, 183, 194, 198–199, 229–230, 236, 238–239,
251, 255–256, 263, 307–308, 319, 332, 401–402,
405, 407–411, 416
Distortion, 110–112, 115, 132, 143, 172, 238
Distribution, load, 1, 3–9, 11–13, 56–58, 65, 76, 85–195,
197–198, 200, 213, 217–220, 223, 226, 241, 250,
255, 257, 277–292, 301, 317–318, 336, 338–340,
349–350, 352, 403
Double-helical gears, 103, 197–199, 235–236
bearings or, 197
load distribution, 197–198
overload factor, 198
Double-reduction gear, shaft-to-hub connections,
intermediate shaft, 76
Double-row bearings, 56
Durability, 20, 31, 51, 69, 108, 176, 270, 355–356, 359,
374, 384–385
Dynamic analysis, 195, 397
Dynamic factor, 76, 182
Dynamic load, 76, 131, 175, 182, 185, 195–196, 398
E
Eccentric loading, 19, 303
Eccentricity, 104, 107, 263
Efficiency, 159, 204, 208, 210–212
Elastic deformation, 4, 8–9, 19, 24, 32, 34–35, 65, 68, 93,
104, 110, 112–114, 117–118, 122, 131, 133, 142,
151, 168, 187, 196, 215, 219, 229, 241–242, 263,
273, 297, 299, 307, 315, 333, 349, 418
shafts, gear rim displacements, 8
Elastic elongation, 32, 299
Elastic range
deformation beam, 33
deformations in, 24–31
Elasto-plastic deformation, 32–36
effectiveness, 34
parts, 32–36
Elasto-plastic range
deformation beam, 33
torsional deformation, 35
Elastomeric spider, flexible coupling, 337
Elements of machines, 41–353
Elliptic fillet, 318
Elongation, 6, 17, 26, 28, 30, 32, 268, 294, 296, 299, 315,
361, 378, 386, 396, 406
elastic, 32, 299
plastic, 32, 315
Endurance limit, 365
Energy loss, 24, 210, 264, 270
Engineering stress, 377–378
Enlarged tooth length, unit connections, 348
Equivalent number of cycles, 178, 375–376
Equivalent radius, 113, 168–169, 174
Equivalent stress, 83, 91, 306, 314–315, 327, 362, 371–373,
385
Escalator drive unit, foundation for proof test, 328
Escalator main drive, 62–63
External loads, strength calculations, 397
F F
ace, gear, load distribution across, 218
Face width, 8, 54, 63, 65, 106, 165–166, 168, 171, 174–175,
179–182, 185, 187, 190, 192–195, 198–200, 205,
213, 217, 219–220, 224, 228, 347
Factor
of load distribution, 175
of safety, 127, 287, 368
Failures
of bearings, 108, 111–115
of gears, 170–173, 176, 218
Fan cooling, 208
Fasteners, 102, 282, 292, 295–296, 300–301, 311, 313–319,
411
fatigue strength, 317–319
static strength, 313–317
Fatigue
high cycle (HCF), 364, 376, 395
low cycle (LCF), 363–364, 376, 378, 384–385, 391
Fatigue crack, 6, 11, 19, 37, 71, 86, 114, 170, 172, 215,
218, 292–293, 317, 363–364, 377, 387
Fatigue failure, 51, 177, 218, 358
Fatigue life (strain method), 376–386
Fatigue limit, 18, 51, 53, 90–91, 112, 143, 177–178, 317,
357, 364–365, 367, 374, 376, 387–390, 396Index 427
Fatigue strength, 13, 19, 37, 44, 51–53, 68, 79, 88–89, 313,
317–318, 357, 359, 361, 363–374, 382, 384, 387,
390, 395–396
Fillet radius, 29, 38, 47–50, 53, 86, 89, 184, 219, 318
Filleted bar, strain distribution, 28
Finish. See Surface finish
Finite element method (FEM), 7–9, 15, 30, 54, 73, 85–86,
88, 90, 97, 169, 181, 183, 185, 194, 231, 241,
278, 282, 286–287, 290–291, 299, 303, 305, 321,
403–416
boundary condition interpretation, 409–413
computer program, 412
deformations, 416
design principles, precision, 405–407
model design for, 407–409
simplified analytical models, 412–416
Fits for rolling bearings, 123–131
Flange attachment, gear, 223
Flange connection, 103–104, 275, 277–278, 292, 303,
305–306, 308–310, 319, 342
Flat working surface, sliding thrust bearing, 150
Flexible coupling
with pins, rubber sleeves, 336
with rubber pads, 337
Flexible couplings, with elastomeric elements, 341
Forced-feed lubrication, 203–206
Forces
in tightened bolt connection, 16
Four-point ball bearing, 123, 136
Fragility, 170
Frame strength, 322
Frame twisting, unit connections, 323
Frequency, natural (critical), 45, 312–313, 336, 399, 403
Fretting, 19–20, 51, 53, 65, 68, 71, 88, 95, 127, 144, 215,
217, 278, 292–293, 364
strength-damaging effect, 20
Friction coefficient, 19, 67–68, 72, 74–75, 89, 117, 121,
125, 127, 140, 171, 228, 230, 234, 264, 272, 278,
294, 301, 305–306, 308, 315, 339, 351–352
static, 74
Friction force, 11, 14, 72, 75, 79, 89, 91, 93, 110, 117, 120,
124–125, 138, 164–167, 171, 173–174, 197–198,
223, 226, 228–229, 268, 270, 272, 277, 282, 285,
287, 292, 294, 301, 305–310, 338, 350, 411
Friction modes, 139–140, 270
Function of housings, 241–243
G
Gears
assembled, 238
backlash, 198–200
gear mesh, 198–200
bandage, local slippage, 229
bending deformation, failure, toothed rim, 218
bending stress, 187
loaded tooth, 168
in tooth root, load distribution influence, 194
bevel, 207, 238–239
bevel gears, 238–239
built-up gear wheels, 224–235
clearance, 237
conical, rigidity with, 222
contact stress, loaded tooth, 168
cooling, 208–212
cooling process, 209
coupling
bending moment, 350
unit connections, 343
misalignment, 343
couplings, 342–352
design, 215–240
disk thickness, gears, 221
disk-type, deformation, 219
double-helical, 197–198
double-helical ear, 235
double-helical gear, overload factor, 198
double-helical gears
bearings or, 197
load distribution, 197–198
face, load distribution across, 218
flange attachment, 223
gear, shaft, connection, 216
gear mesh, factor, dynamic load, 195–197
gear tooth failures, 170
geometry, 160, 162, 197
geometry of, 160–167
grinding wheels types, 237
heating process, 209
helical, 164–168, 176, 178–180, 186, 198–199, 206,
217–224, 227, 238, 240, 255
helical gear, 217–224
hobbing machine, double-helical gear, 235
involute teeth geometry, 160
kinematics of, 160–167
leading, lagging surfaces in contact, 165
load distribution unevenness across face, 87–195
local separation, rim from center, 232
lubrication, 200–207
lubrication grooves, scraper, 203
manufacturing requirements, 235–238
mesh, backlash, 198–200
non-surface-hardened teeth, fatigue life line, 178
number of teeth, tooth shape dependence on, 161
oil bath lubrication, gears, 200
oil collector, lubrication holes, 203
oil level indicators, 204
oil spray, direction on gears, 206
oil sprayers, 205
output shaft, 46
pinion shaft design, 216
pitch change, from deflection under load, 196
pitch deviations, tooth impact by, 195
pump, gears, 55
ratio, 76, 163, 179–180, 202, 417
ribbed wall, stresses in, 228
rim, 170, 238
center of gear, connections, 225
shaft with, 215–217
shapes, 217
shrink-fit connection between rim, center, surface
pressure, 230428 Machine Elements: Life and Design
sketch, 7
spur, 99, 107, 116, 160–164, 166–169, 171, 174, 176,
181, 186, 195–196, 199, 206, 213, 217–226, 238,
240, 417
spur gear, 217–224
spur gear geometry, 162
spur gear teeth, helical teeth, contact lines, 167
spur gearing forces, 167–169
stress amplitude, number of cycles to failure,
dependence, 176
teeth, 8, 36, 44, 63, 76, 96, 99, 103, 132, 136, 160–161,
167–169, 172, 174–187, 196, 205, 215, 228, 237,
239–240, 242, 253, 255
bending strength, 181–187
contact strength, 174–181
stresses in, 167–169
teeth design, 239–240
teeth machining tools, clearing space, 237
tooth design, 239
tooth engagement, 162
tooth failure, 170–173
tooth failures, 170
tooth load, 167
tooth misalignment, load distribution, contact line, 188
tooth root shape, grinding influence, 184
tooth spaces, oil drain, 199
types, 216
uneven load distribution, gear sensitivity, 190
vertical output shaft, two-stage bevel-planetary gear,
207
wear-prone gear, run-in process, 191
welded, 225
welded to shaft/hub, 217
Geometry of gears, 160–167
Gerber failure line, 369
Goodman diagram, 367–368
Grains in metal structure, 23
Gravitation, 241, 409
Gravity, center of, 251, 282–283, 285, 324, 414
Grease lubrication, 101, 137
Grinding wheels types, 237
Grooves in bearings, 146–147
H
Hardened layer, 20, 50, 53, 114–115, 135–136, 170,
172–173
Hardness, 44, 68, 101, 111, 116, 127, 135, 137, 142–144,
151, 172–173, 176–178, 180, 182, 186–187, 190,
221, 244, 260, 265–266, 301, 309, 337, 339, 359,
361–362, 364, 384, 395–396
steel mechanical properties, 362
Harmonic drive, 208
Heat transfer factor, 208
Heat treatment, 43, 112, 172, 184, 222, 225, 227, 237–238,
240, 242, 246–247, 270, 361, 384, 387, 391,
395–396
Heating, 8, 38, 74, 78–79, 111, 131, 138, 172, 200,
209–211, 262, 271, 338, 413
of gears, 209
of rubber elements, 338
Helical gear, 164–166, 168, 176, 178–180, 186, 198–199,
206, 217–224, 227, 238, 240, 255
Herringbone gear, 197–198
Hertzian stress, 114, 135, 168, 171, 174–175, 177
loaded tooth, 168
Hertz’s formula, 168, 174
High-speed roller bearings, compared, 111
Hob radial motion, tooth thickness, relationship, 347
Hobbing, 235–236, 346
Hollow shafts, 46, 51–54, 131–132, 152, 154, 334–335
deformation, 152
design, 52
oil supply through, 154
Hooke’s law, 377–378, 389, 405–406
Housing
connections, 321–329
deformations, 254–255
design, 8, 248–255
function, 241–243
material, 243, 245–246
materials for, 243–247
nonsplit, 253–254
seals, 255–275
split at right angle to axes of shafts, 251–253
split through axes of shafts, 248–251
lifting elements, 251
mounting feet, 250–251
stiffness, 254–255
Hub strength, 90–91
Human error, strength calculations, 416–419
arithmetic, 416–417
units, 417–419
Hydrodynamic, 9, 139–141, 149–152, 155–156, 174, 206,
275
oil film, 9, 141
Hypotheses, of plane cross section, 24–25, 33
Hysteresis loop, 380, 382
I
Idling gears, 161, 336–337
Impact load, 108, 170, 181, 243–244, 336
Impact toughness, 359, 396
Imperfections of crystal lattice, 22
Induction hardening, 20, 53, 101, 228
Interference fit connections, 102
Interference-fit connections, 11–14
friction coefficient, 74–77
load distribution, 13
load distribution nonuniformity, 13
loaded with bending moment, 12–14
loaded with torque, 11–12
self-dismantling under bending load, 14
shaft-to-hub connections, 67–69, 71–79
design, 77–79
easily disassembled, 69
slippage, 13
torsional deformation, 12
Internal stress, 24, 31, 37, 246–247, 332
Involute profile of teeth, 161, 184, 196
Involute teeth geometry, 160Index 429
J
Jam nuts, 300
Joints
bolted, 11, 14, 16, 20, 226, 240–241, 287, 319, 403
keyed, 67
loaded in shear, 277, 282–283, 287, 310, 341
loaded in tension, 14, 254, 282, 287–288, 359, 405
separation of, 245, 254–255, 277
splined, 67, 70, 93
Journal, shaft
K
Key displacement, shaft-to-hub connections, 85
Key joints
design, strength calculation, shaft-to-hub connections,
79–93
hub near keyway, strength, 88–92
keys, strength, 85–86
role of interference-fit connections, 79–85
round keys, 92–93
shaft near keyway, strength, 86–88
hub strength, 79–93
keys strength, 85–86
shaft strength, 86–88
shaft-to-hub connections, 69–70
Key-joints, 67
Keyed hub, stress in, shaft-to-hub connections, 88–89
Keyway deformation under load, shaft-to-hub connections,
88
Keyway end, stress concentration, shaft-to-hub
connections, 87
Kinematics, 5, 160, 183, 256, 399
L
Labyrinth seal, 206, 269, 274
Lame formula, 126
Layout of shaft loading scheme, 54–58
Leading, lagging surfaces in contact, 165
Leading surfaces, 165, 171
Leak-proofness, 275
Length of action, 161, 173, 183
Length of contact, 113
Life factor, 176–177
Life prediction, 355, 364, 395, 404
machine parts, 421
metal part strength, 357–396
strength calculations, 397–419
Lifting device, 4
Lifting drum, with driving shaft, strength calculations, 398
Lifting element, 251
Limited fatigue life, irregular loading (stress method),
374–376
Linear expansion factor, 78, 245
Lip-type seals, 269–271
Load
cyclic, 24, 31, 36, 91, 111, 148, 277, 311, 398
impact, 108, 170, 181, 243–244, 336
Load capacity
Load distribution
across face, 87–195
along the teeth, 7–8, 65, 96–97, 99, 106, 170, 190
between the bolt, 223, 226, 277–278, 403
bolted joints loaded in shear, 282–287
between bolts, 278–292
double-helical gear, 197–198
mated part surfaces, 3–9
between the teeth, 96–97, 99–100, 350
unevenness across face, gears, 87–195
Load distribution factor, 189, 194
Loading layout, shafts, strength analysis, 54–58
Loading types, strength calculations, 401
Locking fastener, 300–301
Long addendum design, 161, 183, 186
Loose spline joint lubrication, shaft-to-hub connections,
101
Low-cycle fatigue, 363, 376, 378, 384–385, 391
Lubrication
bearings, 137–140
forced-feed, 203–206
gears, 200–207
grease, 101, 137
grooves, scraper, 203
pressure-fed, 107
splash, 107, 201
spline joint, 101
M
Machine element strength, 386–390
dimensions of part, 387–388
stress concentration, 388–389
surface finish, 387
Machine parts, life prediction, 355–421
Magnesium alloy, 221, 245, 296, 301
Manufacturing requirements, 235–238
Margin of safety, 170, 173
Mated part surfaces, deformations, load distribution, 3–9
Materials for housings, 243–247
Mating surfaces, slip area, damage to, 19–20
Maximal principal stress, 88
Maximal stress, 24, 27–31, 48, 77, 83, 85, 89–90, 171, 268,
303, 305, 317, 319, 357, 364, 367, 370–371, 374,
376, 389, 398, 404, 413
Mean stress, 31, 90–91, 317, 364, 366–367, 369–371, 373,
385
Mechanical properties, 34, 53, 245, 267, 317, 359,
361–362, 387, 395
Mechanical seals, 272–274
Mesh, gear, factor, dynamic load, 195–197
Metal strength, 21–24, 357–396
bending loads, bars subjected to, stress distribution, 387
comparative calculations, 390–395
cyclic stress-strain curve construction, 381
fatigue life (strain method), 376–386
fatigue limit vs. mean stress, Goodman diagram, 367430 Machine Elements: Life and Design
fatigue strength (stress method), 363–374
hardness, steel mechanical properties, 362
hysteresis loops, cyclic deformation transition period,
380
limited fatigue life, irregular loading (stress method),
374–376
machine element strength, 386–390
dimensions of part, 387–388
stress concentration, 388–389
surface finish, 387
maximal stress, vs. mean stress, Serensen diagram, 370
monotonic, cyclic stress-strain curves, differences, 382
real material strength, 395–396
rotating-bending endurance test machine, 366
shaft with fillet, 393
static load, strength at, 259–363
strain-life curves, 383
stress-strain diagram, 360
stress variation with time, 365
stresses, frequencies, spectrum, 375
tensile test specimen, 360
Metal structure, 21–24
Micro-slip, 229
Miner’s rule, 374
Minimal stress, 366
Misaligned hubs, 344
Misalignment
angular, 85, 96, 106, 109–110, 121, 331, 344–345
of shafts, 329
Modification of profile, 170, 173, 196, 239
Modulus
of elasticity
of section, 46, 411, 413, 415
Moment of inertia, 12, 45, 60, 64, 258, 260–261, 267, 281,
314, 323, 325–326, 330, 408, 413–415
Monotonic loading, 379–381
Movable joints, sealing, 262–275
combined seals, 274–275
contact seals, 264–274
lip-type seals, 269–271
mechanical seals, 272–274
O-rings, 268–269
piston ring packing, 265–268
noncontact seals, 262–264
Movements, rigid connections, joint surface damage, 11–20
bolted connections, 14–19
bolted joint
concentric, eccentric loading, 16
two part, 14
eccentrically loaded bolted connection, deformations, 19
fretting, strength-damaging effect, 20
interference-fit connection, self-dismantling under
bending load, 14
interference-fit connection slippage, 13
interference-fit connections, 11–14
load distribution nonuniformity, 13
loaded with bending moment, 12–14
loaded with torque, 11–12
torsional deformation, 12
mating surfaces, slip area, damage to, 19–20
tightened bolt connection, forces in, 16
N
Necking, 359, 361, 378
Needle bearing, 110
Neuber’s formula, 388
Neutral axis, 26, 34, 36, 289
Nitriding, 20, 44, 53, 101, 132, 172, 193, 225, 227, 266, 270
Non-surface-hardened teeth, fatigue life line, 178
Noncontact seals, 262–264
Notched strip in tension, stress concentration, 30
Number of cycles
Number of reversals, 383
Number of teeth, 93, 96–97, 160–161, 165, 183, 186,
194–195, 239
tooth shape dependence on, 161
Nuts
O
O-rings, 256, 262, 264, 268–269, 272–274
Offset, 8
Oil bath lubrication, gears, 200
Oil collector, lubrication holes, 203
Oil-distributing grooves, 146, 154, 156–157
Oil distribution, 146–147
Oil level indicators, 204
Oil spray, direction on gears, 206
Oil sprayers, 205
Oil supply, 101, 201, 206, 313
plain bearings, spline connections, 157
Oil wedge, 116, 139–140, 146–147, 149–153
One-pair engagement, 161
Outside diameter, 161, 163, 296
Overhung bending moment, angular deformation, 60
Overhung force, 59
Overhung radial force, angular deformation, 59
Overload factor, 198
P P
almgren-Miner rule, 374
Parallel link mechanism, 3, 242
Parametric excitation, 165, 195, 222
Parametric resonance, 195
Pattern
deformation, 21–39, 278, 281, 287, 416
strain, 26, 28, 32
stress, 21–39, 174, 194, 409, 411
Pin
Index 431
Pinion
Pinion shaft design, gear, 216
Piston pin loading, 9
Piston ring packing, 265–268
Pitch, diametral, 96, 136, 160, 181, 183
Pitch change, from deflection under load, 196
Pitch circle, 160
Pitch deviations, tooth impact by, 195
Pitch diameter, 63, 100, 160, 167, 179, 183, 186, 220,
232–233, 350
Pitch point, 163–164, 166, 169, 173–174, 183
Plane cross sections hypothesis, 34
Plane sections, 26
Planet carrier, 106, 137
Planet wheel, 44, 105–106, 110, 136–137, 148, 215
sliding bearing, 148
Planet wheel bearings, 106
Planetary gear, 106, 178, 186, 208, 213, 215, 240
Plastic deformation
Point of attachment, 277, 283
Point of contact, 161, 164–166
Poisson’s ratio, 415
Porosity, 251
Power loss, 103, 109, 208, 210, 227
Pressure angle
Pressure lubrication system, 107
Profile
involute, 161, 184, 196
working, 160–161
Profile modification, 170, 173, 196, 239
Pure shear, 386
Q
Quantity of oil, 199, 205
R
Radial ball bearing, assembling, 109
Radial bearings
axial play, 117
radial clearance, 117
Radial force
Radial misalignment, effect on shaft, bearing loads, 330
Radial sliding bearing, 197
Radius of curvature, 113, 161, 168–169, 174
Ramberg-Osgood equation, 379
Ratio
contact, 161, 163, 165–166, 194–196
gear, 76, 163, 179–180, 202, 417
Real material strength, 395–396
Reliability
Removable shaft shoulders, 49
Residual stresses, 34–39, 50, 111, 361, 364, 388
Resilience, 44, 63–64, 133–134
Resilient coupling, 292, 336–342
Resonance vibration, 45
Reversed bending, loss of residual stress from, 39
Ribbed plate, strength calculations, 413–414
Rigid connections
damage to joint surfaces, movements in, 11–20
bolted connections, 14–19
eccentrically loaded bolted connection, deformations,
19
fretting, strength-damaging effect, 20
interference-fit connection, self-dismantling under
bending load, 14
interference-fit connection slippage, 13
interference-fit connections, 11–14
mating surfaces, slip area, damage to, 19–20
tightened bolt connection, forces in, 16
seals, 255–262
movable joints, sealing, 262–275
Rigid couplings, 334–336
Rigidity
Rim
center of gear, connections, 225
gear, 170, 218, 225, 230, 232, 238
Roller bearings, 46, 55–56, 104, 106–107, 109–114,
116–123, 125, 129–130, 132, 134–137, 158,
197–198, 255, 270, 339, 418
Rolling bearings, 43–44, 47, 56, 95, 107–138, 158, 201,
245, 271, 275, 333
bearing seats, fits for, 123–131
choice, arrangement of supports, 121–123
design, 108–111, 115–121
elastic deformation, under load, 133–135
failures, 111–115
lubrication, 137–138
with raceways on parts of mechanism, 135–137
stress, 111–115
surfaces adjoined to, requirements, 131–133
types, 108
Root fillet, 169, 240
Round keys, 92, 238
Round pins, shaft-to-hub connections, 92
S
Safety factor
Seals, 101, 115, 173, 203, 206, 255–275
combined, 262, 274
contact, 262, 264, 275
labyrinth, 206, 269, 274432 Machine Elements: Life and Design
lip-type, 269–271
mechanical, 264, 272–275
noncontact, 262–264
O-ring, 268
piston ring, 264–268, 275
rigid connections, 255–262
movable joints, sealing, 262–275
Section modulus, 46, 411, 413, 415
Seizure, 19, 68, 137, 143, 154, 294, 302
Self-aligning bearings, 151
Self-aligning thrust bearings, 152
Self-alignment, 142, 152, 197, 219, 272–273, 311
Self-dismantling, 14, 75
Self-locking nuts, 300, 302
Self-made roller bearings, 136
Sensitivity, 18, 31, 109, 117, 190, 303, 393, 404
Serensen’s fatigue line, 384
Serrated lock washer, 300–301
Service life, 2, 101, 107, 109, 112, 123, 127, 129–131,
173–180, 217, 219, 239, 265, 270, 321, 339,
349, 356, 358, 364, 375–376, 398
Shaft, gear, connection, 216
Shaft alignment, 329–334
Shaft connections, 329–352
gear couplings, 342–352
resilient couplings, 336–342
rigid couplings, 334–336
shaft alignment, 329–334
Shaft couplings, 334–352
Shaft deflection, 58, 151
Shaft design, 46
Shaft dimensions, 53
Shaft journal, 56, 69, 104, 107, 141, 143–147, 149,
153, 236
Shaft keyway, tension stress, shaft-to-hub connections,
87
Shaft loading layout, 55
Shaft misalignment
coupling serviceability, 338
from displacement in bearings, 105
Shaft-mounted gear motor, 335
Shaft seals, 257, 275
Shaft shoulders, 47, 49, 51, 131–133, 146, 152
Shaft-to-hub connections, 67–102
comparisons, 67–71
double-reduction gear, intermediate shaft, 76
interference-fit connections, 67–69, 71–79
design, 77–79
easily disassembled, 69
total slippage calculation, 71–77
interference-fit main dimensions, 73
key displacement, 85
key joints, 69–70
design, strength calculation, 79–93
keyed hub, stress in, 88–89
keyway deformation under load, 88
keyway end, stress concentration, 87
load distribution, 85
loose spline joint lubrication, 101
parameters, calculated KJs, 89
round pins, 92
shaft keyway, tension stress, 87
spline connection centering, additional surfaces, 94
spline joints, load distribution, 97
spline shapes, 94
splined joints, 70–71, 93–102
bearing stresses in, 100–101
loaded with torque, radial force, 97–100
loaded with torque only, 94–97
thin-walled parts, key joints, 92
toothed rim dissymmetry, spline connection influence,
100
tractor gear box, intermediate shaft, 95
Shaft with gear, 215–217
Shafts, 43–65
bearings, load distribution between, 57
bending moment applied between bearings, angular
deformation, 59
deformation analysis, 58–65
design elements, 46–53
escalator main drive, 62
escalator main drive shaft with pinion, 63
gear output shaft, 46
gear pump, gears, 55
hollow shaft, ball bearing, locknut, spline, 51
hollow shaft design, 52
hollow shafts, 53–54
loading layout, for strength analysis, 54–58
overhung bending moment, angular deformation, 60
overhung radial force, angular deformation, 59
press fit on shaft fatigue strength, decreasing detrimental
effect, 52
radial force applied between bearings, angular
deformation, 58
removable shaft shoulders, 49
shaft loading layout, 55
shouldered shafts, lines of forces, 48
size selection, 43–46
splined shafts, 54
tilt in bearings, 56
Shapes, gears, 217
Shear modulus, 12, 323, 325
Shear stress, 9, 46, 79, 81, 83, 86, 90–91, 114, 135–136,
172, 309, 316, 361–364, 368, 370, 372, 376,
385–386, 399
Shot peening, 20, 37–38, 53
residual stress distribution after, 37
Shouldered shafts, lines of forces, 48
Shrink-fitted rim, 228–229, 235
Simplified analytical models, 412–413, 418
Sines’ criterion, 373
Size factor, 185, 357, 388, 390
Size selection, shafts, 43–46
Sleeve coupling, 334
Sliding (plane, sleeve) bearings, 138–158, 197
design, 144–151
lubricated surface friction, 138–140
materials, 141–144
oil supply to, 153–158
radial, 144–149
against rotation, axial displacement fixation, 145
surfaces connected with, 151–153Index 433
thrust, 149–151
types, 140–141
Sliding thrust bearing, with tapered working surface, 150
Sliding velocity (speed), 109, 138, 140, 153, 164, 172–173,
183, 194, 270, 352
Slip plane, 22–24, 376
Slippage calculation, interference-fit connections,
shaft-to-hub connections, 71–77
friction coefficient, 74–77
surface pressure, 72–74
Slope angle, 60, 63, 65, 357, 384, 412
Spacing of bolts, 259
Spalling, 172
Spherical bearing, 106
Splash lubrication, 107, 201
Spline connection centering, additional surfaces,
shaft-to-hub connections, 94
Spline joints, load distribution, shaft-to-hub connections,
97
Spline shapes, shaft-to-hub connections, 94
Splined connection, 93
Splined joints, 67, 70–71, 93–102
Splined shafts, 54
Split (cotter) pins, 300, 302
Split through axes of shafts, 248–251
lifting elements, 251
mounting feet, 250–251
Spring lock washers, 300–302
Spur gears
forces, 167–169
geometry, 162
teeth, helical teeth, contact lines, 167
Static load
strength at, 259–363
Static strength
Steels
Straight bar, strain distribution, 26
Straight roller bearing, 106, 110, 113, 116–118, 120–121,
134–136, 418
Strain, elastic, 377
Strain analysis, 5, 241
Strain hardening, 361, 379–380
Strain method, 363, 376–377, 388–395
Strain pattern, 32
Strength
bending
calculation
calculations, 397–419
beam supports, 408
cantilever beam, 407
finite element method, 410
displacements within single element, distribution, 405
external loads, estimation, 397
finite element method, inappropriate use, errors,
405–416
boundary condition interpretation, 409–413
computer program, 412
deformations, 416
design principles, precision, 405–407
model design for, 407–409
simplified analytical models, 412–416
forces applied to part, determination, 398–403
human error, 416–419
arithmetic, 416–417
units, 417–418
lifting drum, with driving shaft, 398
loading types, 401
ribbed plate, 413–414
safety factors, 404–405
stresses, characteristics, 397–404
stresses in part, estimation, 403–404
tensioned bar, distribution of load, strain, 406
two-support beam, 411
fatigue
hub, 90–91
metal, 21–24, 357–396
bending loads, bars subjected to, stress distribution,
387
comparative calculations, 390–395
cyclic stress-strain curve construction, 381
fatigue life (strain method), 376–386
fatigue limit vs. mean stress, Goodman diagram, 367
fatigue strength (stress method), 363–374
hardness, steel mechanical properties, 362
hysteresis loops, cyclic deformation transition period,
380
limited fatigue life, irregular loading (stress method),
374–376
machine element strength, 386–390
maximal stress, vs. mean stress, Serensen diagram,
370
monotonic, cyclic stress-strain curves, differences,
382
real material strength, 395–396
rotating-bending endurance test machine, 366
shaft with fillet, 393
static load, strength at, 259–363
strain-life curves, 383
stress-strain diagram, 360
stress variation with time, 365
stresses, frequencies, spectrum, 375
tensile test specimen, 360434 Machine Elements: Life and Design
static
tensile
thread, 81
ultimate, 359, 377
yield, 143, 380–381
Stress
admissible, 86, 356–359, 364, 387, 389, 391–392,
394–395, 404
alternating, 366
amplitude, 176
bearing, 86, 92–93, 95–96, 100–101, 296
bending
calculation, 324
compressive, 15, 20, 35–39, 50, 53, 112, 172,
184–185, 227
contact, 100, 110, 112, 117, 129, 168–169, 173–174,
176, 179, 183, 193
engineering, 377–378
equivalent
Hertzian, 114, 135, 168, 171, 174–175, 177
internal, 24, 31, 37, 246–247, 332
maximal,
mean, 31, 90–91, 317, 364, 366–367, 369–371, 373, 385
minimal, 366
shear
tension
Von-Mises, 88–89
yield, 24, 31–32, 34, 39, 53, 82, 86, 144–145, 361, 364
Stress concentration
Stress concentration factor (SCF), 29–31, 49, 52, 54, 86,
90, 94, 184–186, 357, 389, 392–393
Stress method, 363–364, 374, 376, 388–395
Stress pattern, 21–39, 174, 194, 409, 411
bending deformation, straight beam, 25
bending stresses, T-beam, 37
broken sections, 26
burnishing shafts, roller shapes, 38
cold rolling, residual stress distribution after, 37
crystal cell, 22
crystal lattice, 22
imperfections, 22
crystals, in metal structure, 23
dislocation, movement under load, 22
elastic range
deformation beam, 33
deformations in, 24–31
elasto-plastic deformation, parts, 32–36
elasto-plastic deformation effectiveness, 34
elasto-plastic range
deformation beam, 33
torsional deformation, 35
filleted bar, strain distribution, 28
grains in metal structure, 23
metal strength, 21–24
metal structure, 21–24
notched strip in tension, stress concentration, 30
plane sections, 26
reversed bending, loss of residual stress from, 39
shot peening, residual stress distribution after, 37
straight bar, strain distribution, 26
stress-strain diagrams, 32
surface plastic deformation, 36–39
thin-walled beams, deformation of, 25
Stress raiser, 29–31, 51, 78, 169, 318, 357, 388–389,
392–393
Stress release, 31
Stress-strain diagram, 32, 360, 377
Stresses, 397–404
contact (Hertzian), 100, 110, 112, 114, 117, 129, 135,
168–169, 171, 173–177, 179, 183, 193
Structural change, 1, 24, 242
Stud-bolts, 312
Supports, 103–158
axial fixation, shafts, 104
planet wheel bearings, 106
shaft misalignment, from displacement in bearings, 105
types, 103–108
Surface finish, 256, 387–388, 390
strenght, 387
Surface hardening, 20, 44, 53, 132, 170, 228, 232, 239–240
Surface layer
Surface plastic deformation, 36–39, 53, 190, 295
Surface pressure
Surface quality factor, 90
T T
ab washers, 206, 296–297, 299–302
Tapered connection, 67–68, 73, 80
Tapered roller bearing, 118–119, 122, 129–130, 132, 134,
255, 270
Tapered roller bearings, 119, 130
Teeth, gears
bending strength, 181–187
contact strength, 174–181
stresses in, 167–169
Teeth machining tools, clearing space, 237
Temperature limits, 111
Tensile strength, 43–45, 65, 78, 80, 89, 215, 244, 267, 297,
317, 359–360, 363, 384, 387, 390, 396
Tension stress, 7, 13, 36–38, 81–83, 86, 88, 114, 185,
277–278, 301, 304, 412–413, 416
Tensioned bar, distribution of load, strain, strength
calculations, 406
Test specimen, 360
Thermal expansion, 103, 129, 242, 409Index 435
Thin-walled beams, deformation of, 25
Thread strength, 81
Tightened bolted connections
under centrically applied load, 16–18
under eccentrically applied load, 18–19
forces in, 16
Tightening bolts, 292–302
accuracy, 292–295
stability of tightening, 295–299
fasteners, plastic deformation, 295–299
locking of fasteners, 300–302
self-loosening, bolts, 295
Tightening force
Tightening torque, 80–81, 83–84, 292–295, 301, 306, 313
Tilt in bearings, 56
Timoshenko’s correction, 407
Tip relief, 182
Tooth
active profile, 184
addendum, 173
bending strength, 181
breakage, 170, 173, 218
design, 239
engagement, 162
failure, gears, 170–173
fillet, 71
generation process, 183
load, 167
misalignment, load distribution, contact line, 188
root, 161, 164, 183–185, 194, 238–239
root shape, grinding influence, 184
shape, 161, 173, 183
spaces, oil drain, 199
thickness, 104, 186, 346–348
Toothed rim dissymmetry, spline connection influence,
shaft-to-hub connections, 100
Tractor gear box, intermediate shaft, shaft-to-hub
connections, 95
Tresca criterion, 386
True strain, 378
True stress, 377–378, 382
Twisted rubber element, shear stress distribution, 341
Two-pair engagement, 181
Two-row spherical roller bearing, 110
Two-support beam, strength calculations, 411
Types of gears, 216
Types of supports, 103–108
U
Ultimate strength, ultimate stress, 31, 359, 377
Uncertainty, 31, 56, 300–301, 356
Uneven load distribution, gear sensitivity, 190
Unit connections, 321–353
housing connections, 321–329
shaft connections, 329–352
gear couplings, 342–352
resilient couplings, 336–342
rigid couplings, 334–336
shaft alignment, 329–334
Units
Units of machines, 41–353
V V
acancy, 21
Velocity, sliding, 109, 138, 140, 153, 164, 172–173, 183,
194, 270, 352
Vertical output shaft, two-stage bevel-planetary gear, 207
Vibration
Viscosity
Von-Mises stress, 88–89
W W
arpage, 172, 215, 222, 227, 237, 247
Waviness, 72, 107, 172, 174
Wear
Wear resistance, 70, 101, 132, 143, 243, 245, 271–272
Weight,
shaft alignment, working forces, 332
Welded gear, 225
Welding, 5, 127, 142–143, 153, 172, 224–225, 244, 247
Width, face
Working load, tightening force of bolt, correlation, 302–313
bending load, 311–313
load normal to joint surface, 302–305
shear load, 305–311
Working profile, 160–161
Working surface
Worm gear, 208, 213, 240–241, 253
Y Y
ield point, yield stress,
Yield strength, 143, 380–381
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