Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
10th Edition
ISBN: 9780073398204
Author: Richard G Budynas, Keith J Nisbett
Publisher: McGraw-Hill Education
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Chapter 15, Problem 11P
Apply the relations of Prob. 15-7 to Ex. 15-1 and find the Brinell case hardness of the gears for equal allowable load Wt in bending and wear. Check your work by reworking Ex. 15-1 to see if you are correct. How would you go about the heat treatment of the gears?
EXAMPLE 15-1 A pair of identical straight-tooth miter gears listed in a catalog has a diametral pitch of 5 at the large end, 25 teeth, a 1.10-in face width, and a 20° normal pressure angle; the gears are grade 1 steel through-hardened with a core and case hardness of 180 Brinell. The gears are uncrowned and intended for general industrial use. They have a quality number of Qv = 7. It is likely that the application intended will require outboard mounting of the gears. Use a safety factor of 1, a 107 cycle life, and a 0.99 reliability.
- (a) For a speed of 600 rev/min find the power rating of this gearset based on AGMA bending strength.
- (b) For the same conditions as in part (a) find the power rating of this gearset based on AGMA wear strength.
- (c) For a reliability of 0.995, a gear life of 109 revolutions, and a safety factor of SF = SH = 1.5, find the power rating for this gearset using AGMA strengths.
15-7 In straight-bevel gearing, there are some analogs to Eqs. (14-44) and (14-45) pp. 766 and 767, respectively. If we have a pinion core with a hardness of (HB)11 and we try equal power ratings, the transmitted load Wt can be made equal in all four cases. It is possible to find these relations:
| Core | Case | |
| Pinion | (HB)11 | (HB)12 |
| Gear | (HB)21 | (HB)22 |
- (a) For carburized case-hardened gear steel with core AGMA bending strength (sat)G and pinion core strength (sat)P, show that the relationship is
(sat)G=(sat)PJpJGm−0.0323G
This allows (HB)21 to be related to (HB)11.
- (b) Show that the AGMA contact strength of the gear case (sac)G can be related to the AGMA core bending strength of the pinion core (sat)P by
(sac)G=Cp(CL)GCH√S2H(sat)P(KL)PKxJPKTCsCxcNPIKs
If factors of safety are applied to the transmitted load Wt, then SH = √SF and S2H/SF is unity. The result allows (HB)22 to be related to (HB)11.
- (c) Show that the AGMA contact strength of the gear (sac)G is related to the contact strength of the pinion (sac)P by
(sac)P=(sac)Gm0.0602GCH
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Chapter 15 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
Ch. 15 - An uncrowned straight-bevel pinion has 20 teeth, a...Ch. 15 - For the gearset and conditions of Prob. 15-1, find...Ch. 15 - An uncrowned straight-bevel pinion has 30 teeth, a...Ch. 15 - For the gearset and conditions of Prob. 15-3, find...Ch. 15 - An uncrowned straight-bevel pinion has 22 teeth, a...Ch. 15 - Prob. 6PCh. 15 - In straight-bevel gearing, there are some analogs...Ch. 15 - Refer to your solution to Probs. 15-1 and 15-2. If...Ch. 15 - Prob. 9PCh. 15 - Prob. 10P
Ch. 15 - Apply the relations of Prob. 15-7 to Ex. 15-1 and...Ch. 15 - Prob. 14PCh. 15 - 15-15 to 15-22 As in Ex. 15-4, design a...Ch. 15 - 15-15 to 1 5-22 As in Ex. 154, design a...Ch. 15 - 15-15 to 15-22 As in Ex. 15-4, design a...Ch. 15 - 15-15 to 15-22 As in Ex. 15-4, design a...Ch. 15 - 15-15 to 15-22 As in Ex. 15-4, design a...Ch. 15 - 15-15 to 15-22 As in Ex. 15-4, design a...Ch. 15 - 15-15 to 15-22 As in Ex. 15-4, design a...Ch. 15 - Prob. 22P
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