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An uncrowned straight-bevel pinion has 20 teeth, a diametral pitch of 6 teeth/in, and a transmission accuracy number of 6. Both the pinion and gear are made of through-hardened steel with a Brinell hardness of 300. The driven gear has 60 teeth. The gearset has a life goal of 109 revolutions of the pinion with a reliability of 0.999. The shaft angle is 90°, and the pinion speed is 900 rev/min. The face width is 1.25 in, and the normal pressure angle is 20°. The pinion is mounted outboard of its bearings, and the gear is straddle-mounted. Based on the AGMA bending strength, what is the power rating of the gearset? Use K0 = 1 and SF = SH = 1.
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The power rating of gear-set for bending.
Answer to Problem 1P
The power rating for gear-set for bending is
Explanation of Solution
Write the expression for pitch diameter of gear.
Here, the pitch diameter of gear is
Write the expression for pitch diameter of pinion.
Here, the pitch diameter of pinion is
Write the expression for speed ratio of gear set.
Here, the speed ratio is
Write the expression for pitch line velocity.
Here, the pitch line velocity is
Write the expression for dynamic factor.
Here, dynamic factor is
Write the expression for constant
Here, the transmission accuracy number is
Write the expression for constant
Write the expression for maximum pitch line velocity.
Here, maximum pitch line velocity is
Write the expression for size factor for
Here, size factor is
Write the expression for load distribution factor.
Here, load distribution factor is
Write the critical expression for stress cycle factor for pinion.
Here, the stress cycle factor for pinion is
Write the critical expression for stress cycle factor for gear.
Here, the stress cycle factor for gear is
Write the expression for reliability factor for bending strength.
Here, the reliability factor is
Write the expression for allowable bending stress number.
Here, the allowable bending stress number 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
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
Write the expression for transmitted load by pinion.
Here, the transmitted load by pinion is
Write the expression for transmitted load on gear.
Here, the transmitted load on gear is
Conclusion:
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Refer to Figure 15-7 “Bending factor
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Refer to Figure 15-7 “Bending factor
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The power rating for a gear-set for bending is defined as minimum of power rating in bending for pinion and gear, so that the bending of teeth on both gear and pinion can be saved.
Thus, the power rating for gear-set for bending is
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Chapter 15 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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