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7.2
7.3		  Screw Gear Calculations
 Axial Thrust Of Helical Gears 		354
355
SECTION 8 BEVEL GEARING 356
8.1
8.2
8.3
8.4
8.5		 Development And Geometry Of Bevel Gears
Bevel Gear Tooth Proportions
Velocity Ratio
Forms Of Bevel Teeth
Bevel Gear Calculations 		356
356
357
357
357
8.5.1
8.5.2
8.5.3
8.5.4		 Gleason Straight Bevel Gears
Standard Straight Bevel Gears
Gleason Spiral Bevel Gears
Gleason Zerol Spiral Bevel Gears 		358
358
358
361
SECTION 9  WORM MESH 361
9.1  Worm Mesh Geometry 362
9.1.1
9.1.2
9.1.3
9.1.4		 Worm Tooth Proportions
Number of Threads
Pitch Diameters, Lead and Lead Angle
Center Distance 		362
362
362
362
9.2  Cylindrical Worm Gear Calculations  362
9.2.1
9.2.2		 Axial Module Worm Gears 
Normal Module System Worm Gears 		 363
363
9.3
9.4		  Crowning Of The Worm Gear Tooth 
 Self-Locking Of Worm Mesh 		 363
365
SECTION 10 TOOTH THICKNESS 366
10.1  Chordal Thickness Measurement  366
10.1.1
10.1.2
10.1.3
10.1.4
10.1.5		 Spur Gears 
Spur Racks and Helical Racks 
Helical Gears 
Bevel Gears 
Worms and Worm Gears 		 366
366
366
366
366
10.2 Span Measurement Of Teeth  366
10.2.1
10.2.2		 Spur and Internal Gears 
Helical Gears 		 366
366
10.3 Over Pin (Ball) Measurement  370
10.3.1
10.3.2
10.3.3
10.3.4
10.3.5		 Spur Gears 
Spur Racks and Helical Racks 
Internal Gears 
Helical Gears 
Three Wire Method of Worm Measurement 		 370
371
371
371
371
10.4 Over Pins Measurements For Fine Pitch Gears With Specific Numbers Of Teeth  371
SECTION 11 CONTACT RATIO  382
11.1
11.2
11.3
11.4		 Radial Contact Ratio Of Spur And Helical Gears, ea 
Contact Ratio Of Bevel Gears, ea 
Contact Ratio For Nonparallel And Nonintersecting Axes Pairs, e  
Axial (Overlap) Contact Ratio, eb 		 382
382
382
383
SECTION 12  GEAR TOOTH MODIFICATIONS  383
12.1
12.2
12.3		 Tooth Tip Relief 
Crowning And Side Relieving 
Topping And Semitopping 		 383
384
384
SECTION 13  GEAR TRAINS  384
13.1 Single-Stage Gear Train 384
13.1.1  Types of Single-Stage Gear Trains  384
13.2 
13.3 		 Two-Stage Gear Train 
Planetary Gear System 		 385
385
13.3.1
13.3.2		 Relationship Among the Gears in a Planetary Gear System 
Speed Ratio of Planetary Gear System 		 385
386
13.4 Constrained Gear System  386
SECTION 14 BACKLASH  387
14.1
14.2		 Definition Of Backlash 
Backlash Relationships 		 387
388
14.2.1
14.2.2 
14.2.3 
14.2.4 
14.2.5 		 Backlash of a Spur Gear Mesh 
Backlash of Helical Gear Mesh 
Backlash of Straight Bevel Gear Mesh 
Backlash of a Spiral Bevel Gear Mesh 
Backlash of Worm Gear Mesh 		 389
389
389
389
390
14.3
14.4 		 Tooth Thickness And Backlash 
Gear Train And Backlash 		 390
390

326