8-98 GEARING Angular straight bevel gears ° ° ͚ ° ␥ ϭ ͚ N n ϩ ͚ ͚ ° ␥ ϭ Ϫ ͚ N n Ϫ ° Ϫ ͚ ␥ ⌫ϭn N ⌫ϭ͚ Ϫ ␥ ° m m ϭ N ␥ n ⌫ m N n x o ϭ A ␥ Ϫ a op ␥ X o ϭ A ⌫Ϫa oG ⌫ K Spiral Bevel Gears for 90° Shaft Angle ° Angular Spiral Bevel Gears K ° m ° n ϭ n ⌫ ␥ ⌫ ϭ m Fig. 8.3.14 Table 8.3.10 Spiral Bevel Gear Dimensions n h k ϭ P d N h i ϭ P d P d ␾ F ͚ d ϭ n P d D ϭ N P d ␥ ϭ Ϫ n N ϭ ° Ϫ ␥ A O ϭ D ⌫ p ϭ P d A OP ϭ h k Ϫ a OG a OG ϭ P d ϩ P d N n b OP ϭ h t Ϫ a OP b OG ϭ h t Ϫ a OG c ϭ h t Ϫ h k ␦ p ϭ Ϫ b OP A O ␦ G ϭ Ϫ b OG A O ␥ O ϭ ␥ ϩ ␦ G ⌫ O ϭ⌫ϩ ␦ P ␥ R ϭ ␥ Ϫ ␦ P ⌫ R ϭ⌫Ϫ ␦ G d O ϭ d ϩ a OP ␥ D O ϭ D ϩ a OG ⌫ x O ϭ D Ϫ a OP ␥ X O ϭ d Ϫ a OG ⌫ t ϭ p Ϫ TTϭ p a OP Ϫ a OG ␾ ␾ Ϫ K P d ° Copyright (C) 1999 by The McGraw-Hill Companies, Inc. All rights reserved. Use of this product is subject to the terms of its License Agreement. Click here to view. STRENGTH AND DURABILITY 8-103 Geometry factor I 012345678910 Gear ratio D 2 /D 1 N p у 50 0.16 0.14 0.12 0.10 0.08 0.06 Number of teeth in pinion N p ϭ 30 N p ϭ 24 N p ϭ 16 All curves are for the lowest point of single tooth contact on the pinion Fig. 8.3.23 I ° Source: ANSI/AGMA 2018-01, with permission. Geometry factor I 012345678910 Gear ratio D 2 /D 1 N p у 50 0.18 0.16 0.14 0.12 0.10 0.08 Number of teeth in pinion N p ϭ 30 N p ϭ 24 N p ϭ 16 All curves are for the lowest point of single tooth contact on the pinion Fig. 8.3.24 I ° Source: ANSI/AGMA 2018-01, with permission. Copyright (C) 1999 by The McGraw-Hill Companies, Inc. All rights reserved. Use of this product is subject to the terms of its License Agreement. Click here to view. 8-104 GEARING Geometry factor J 12 Number of teeth for which geometry factor is desired 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 Addendum 1.000 2.400 Whole depth Pinion addendum 1.000 Gear addendum 1.000 20° 0.35 r T Generating rack 1 pitch 15 17 20 24 30 35 40 45 50 60 80 125 275 ϱ Load applied at tip of tooth 1000 Number of teeth in mating gear Load applied at highest point of single tooth contact 170 85 50 35 25 17 Fig. 8.3.25 J ° Source: ANSI/AGMA 2018-01, with permission. Geometry factor J 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 12 Number of teeth for which geometry factor is desired Addendum 1.000 2.350 Whole depth Pinion addendum 1.000 Gear addendum 1.000 25° 0.27 r T Generating rack One Pitch 15 17 20 24 30 35 40 45 50 60 80 125 275 ϱ Load applied at tip of tooth 1000 Number of teeth in mating gear Load applied at highest point of single tooth contact 170 85 50 35 25 17 Fig. 8.3.26 J ° Source: ANSI/AGMA 2018-01, with permission. Copyright (C) 1999 by The McGraw-Hill Companies, Inc. All rights reserved. Use of this product is subject to the terms of its License Agreement. Click here to view. STRENGTH AND DURABILITY 8-105 Geometry factor J 0.70 0.60 0.50 0.40 0.30 0° Tooth height Generating rack 20° 0.157 P nd r T ϭ 2.157 P nd 1.0 P nd Add. 5° 10° 15° 20° 25° 30° 35° 500 150 60 Number of teeth 30 20 Helix angle ⌿ Standard addendum, finishing hob Fig. 8.3.27 J ° Source: ANSI/AGMA 2018-01, with permission. Geometry factor J 0.70 0.60 0.50 0.40 0.30 0° Tooth height Generating rack 20° 0.4276 P nd r T ϭ 2.355 P nd 1.0 P nd Add. 5° 10° 15° 20° 25° 30° 35° 500 150 60 Number of teeth 30 20 Helix angle ⌿ Standard addendum, full fillet hob Fig. 8.3.28 J ° Source: ANSI/AGMA 2018-01, with permission. Copyright (C) 1999 by The McGraw-Hill Companies, Inc. All rights reserved. Use of this product is subject to the terms of its License Agreement. Click here to view. 8-106 GEARING Geometry factor J 0.80 0.70 0.60 0.50 0.40 0° Tooth height Generating rack 25° 0.27 P nd r T ϭ 2.35 P nd 1.0 P nd Add. 5° 10° 15° 20° 25° 30° 35° 500 150 60 Number of teeth 30 20 Helix angle ␺ Standard addendum, full fillet hob Fig. 8.3.29 J ° Source: ANSI/AGMA 2018-01, with permission. Modifying factor 0° 5° 10° 15° 20° Helix angle, ␺ 25° 30° 500 1.05 1.00 0.95 0.90 0.85 30 20 35° Number of teeth in mating element 150 75 50 Fig. 8.3.30 J ° J Source: ANSI/AGMA 2018-01, with permission. Copyright (C) 1999 by The McGraw-Hill Companies, Inc. All rights reserved. Use of this product is subject to the terms of its License Agreement. Click here to view. Modifying factor 0° 5° 10° 15° 20° Helix angle ␺ 25° 30° 500 150 75 50 1.05 1.00 0.95 0.90 0.85 30 20 35° Number of teeth in mating element Fig. 8.3.31 J ° J Source: ANSI/AGMA 6010-E88, with permission. Table 8.3.15 Allowable Contact Stress Number s ac for Steel Gears s ac Table 8.3.16 Allowable Contact Stress Number s ac for Iron and Bronze Gears s ac 8-107 Copyright (C) 1999 by The McGraw-Hill Companies, Inc. All rights reserved. Use of this product is subject to the terms of its License Agreement. Click here to view. 8-110 GEARING Stress cycle factor Z N 10 2 Number of load cycles N 4.0 3.0 2.0 1.1 1.0 0.9 0.8 0.7 0.6 5.0 0.5 Nitrided Z N ϭ 1.249 N Ϫ0.0138 Z N ϭ 2.466 N Ϫ0.056 NOTE: The choice of Z N in the shaded zone is influenced by: Lubrication regime Failure criteria Smoothness of operation required Pitchline velocity Gear material cleanliness Material ductility and fracture toughness Residual stress Z N ϭ 1.4488 N Ϫ0.023 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 Fig. 8.3.35 Z N Source: ANSI/AGMA 2001-C95, with permission. Hardness ratio factor C H Caculated hardness ratio, H BP H BG 1.14 1.12 1.10 1.08 1.06 1.04 1.02 1.00 0 2 4 6 8 10 12 14 16 18 20 Single reduction gear ratio H BG ϭ gear Brinell hardness number H BP ϭ pinion Brinell hardness number 1.7 1.6 1.5 1.4 1.3 1.2 When Use C H ϭ 1 Ͻ 1.2, H BP H BG Fig. 8.3.36 C H Source: ANSI/AGMA 2001-C95, with permission. Copyright (C) 1999 by The McGraw-Hill Companies, Inc. All rights reserved. Use of this product is subject to the terms of its License Agreement. Click here to view. Allowable bending stress number S at ,1000lb/in 2 50 40 30 20 10 150 200 250 300 Brinell hardness H B 350 400 450 Metallurgical and quality control procedures required Grade 2 S at ϭ 102 H B ϩ 16 400 Grade 1 S at ϭ 77.3 H B ϩ 12,800 Fig. 8.3.39 s at Source: ANSI/AGMA 2001-C95, with permission. Allowable bending stress number S at , 1000lb/in 2 80 70 60 50 40 30 20 250 275 300 325 Core hardness H B 350 Metallurgical and quality control procedures required Grade 2 S at ϭ 108.6 H B ϩ 15 890 Grade 1 S at ϭ 82.3 H B ϩ 12 150 Fig. 8.3.40 s at Source: ANSI/AGMA 2001-C95, with permission. Allowable bending stress number S at , 1000lb/in 2 70 60 50 40 30 250 275 300 325 Core hardness H B 350 Metallurgical and quality control procedures required Grade 3 – 2.5% chrome S at ϭ 105.2 H B ϩ 29 280 Grade 2 – 2.5% chrome S at ϭ 105.2 H B ϩ 22 280 Grade 1 – 2.5% chrome S at ϭ 105.2 H B ϩ 9280 Grade 2 – nitralloy S at ϭ 1113.8 H B ϩ 16 650 Grade 1 – nitralloy S at ϭ 86.2 H B ϩ 12 730 Fig. 8.3.41 s at Source: ANSI/AGMA 2001-C95, with permission. 8-112 Copyright (C) 1999 by The McGraw-Hill Companies, Inc. All rights reserved. Use of this product is subject to the terms of its License Agreement. Click here to view. Table 8.3.20 Viscosity Ranges for AGMA Lubricants a b c ° a d d d ° ° e f e ° ° a b c d Comp e ° ° ° ° f Table 8.3.21 AGMA Lubricant Number Guidelines for Open Gearing (Continuous Method of Application) a,b c ° ° Ϫ d d e f a b c d e ° ° ° ° f ° ° ° ° Table 8.3.22 AGMA Lubricant Number Guidelines for Open Gearing Intermittent Applications a,b,c ge d ° ° f Ϫ a b c d e f g 8-114 Copyright (C) 1999 by The McGraw-Hill Companies, Inc. All rights reserved. Use of this product is subject to the terms of its License Agreement. Click here to view. . conditions. Fig. 8. 4.17 General practice for the thickness of babbitt lining and shells is as fol- lows: Fig. 8. 4. 18, b ϭ 1 ⁄ 32 d ϩ 1 ⁄ 8 in, S ϭ 0.18d for bronze or steel ϭ 0.2d for cast iron; Fig. 8. 4.18a,. 0.7 0.75 0 .8 0 .85 0.9 A 24.0 28. 1 33 .8 41.6 53.3 72.0 105 173 237 360 613 1,320 B 18. 9 23.2 29.0 38. 2 52.7 77.9 1 28 246 344 634 1,260 3,360 ␧ 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0. 98 0.99 A 1,620. 2,070 2,620 3,530 5,040 7 ,80 0 13,700 30,600 121,000 B 4,340 5 ,81 0 8, 040 11 ,80 0 18, 400 32,100 65,300 179,000 3 48, 000 Fig. 8. 4.13 Oil delivery with bottom wick (Fig. 8. 4.11). Current practice is