Concept explainers
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
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
If factors of safety are applied to the transmitted load Wt, then SH =
- (c) Show that the AGMA contact strength of the gear (sac)G is related to the contact strength of the pinion (sac)P by
(a)
The relation between AGMA bending strength of gear with AGMA bending strength of pinion.
Answer to Problem 7P
The relation between AGMA bending strength of gear with AGMA bending strength of pinion is
Explanation of Solution
Write the expression for gear ratio of gear set.
Here, the gear ratio is
Write the critical expression for stress cycle factor of pinion for
Here, the stress cycle factor for pinion is
Write the critical expression for stress cycle factor of gear for
Here, the stress cycle factor for gear is
Write the expression for permissible bending stress for pinion.
Here, the permissible bending stress for pinion is
Write the expression for permissible bending stress for gear.
Here, the permissible bending stress for gear is
Substitute
Write the expression for bending stress for pinion.
Here, the bending stress in pinion is
Write the expression for bending stress for gear.
Here, the bending stress in gear is
For limiting condition bending stress in pinion is equal to allowable bending stress in pinion.
Substitute
For limiting condition bending stress in gear is equal to allowable bending stress in gear.
Substitute
Substitute
Substitute
Substitute
Conclusion:
Thus, the relation between AGMA bending strength of gear with AGMA bending strength of pinion is
(b)
The AGMA contact strength of the gear case relation with the AGMA core bending strength of the pinion core.
Answer to Problem 7P
The AGMA contact strength of the gear case is related to the AGMA core bending strength of the pinion core by
Explanation of Solution
Write the expression for pitch diameter of pinion.
Here, the pitch diameter of pinion is
Write the expression for permissible bending stress for pinion.
Here, the permissible bending stress for pinion is
Write the expression for bending stress for pinion.
Here, the bending stress in pinion is
For limiting condition bending stress in pinion is equal to allowable bending stress in pinion.
Substitute
Substitute
Write the expression for reliability factor for pitting.
Here, the reliability factor for pitting is
Write the expression for permissible contact stress number for gear.
Here, the permissible contact stress for gear is
Write the expression for contact stress for gear.
Here, the contact stress in gear is
For limiting condition contact stress in gear is equal to permissible contact stress in gear.
Substitute
Substitute
Substitute
Substitute
For equal amount of transmitted load
Substitute
Conclusion:
Thus, the AGMA contact strength of the gear case is related to the AGMA core bending strength of the pinion core by
(c)
The AGMA contact strength of gear relation with contact strength of pinion.
Answer to Problem 7P
The AGMA contact strength of gear is related to contact strength of pinion by
Explanation of Solution
Write the expression for gear ratio of gear set.
Write the expression for stress cycle factor for pitting resistance for pinion.
Here, the stress cycle factor for pitting resistance for pinion is
Write the critical expression for stress cycle factor for pitting resistance for gear.
Here, the stress cycle factor for pitting resistance for gear is
Write the expression for permissible contact stress number for pinion.
Here, the permissible contact stress number for pinion is
Write the expression for permissible contact stress number for gear.
Substitute
Write the expression for contact stress for pinion.
Here, the contact stress in pinion is
Write the expression for contact stress for gear.
Here, the contact stress in gear is
For limiting condition contact stress on gear and pinion is equal to permissible contact stress on gear and pinion.
Substitute
Substitute
Substitute
Substitute
Conclusion:
Thus, AGMA contact strength of gear is related to contact strength of pinion by
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Chapter 15 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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