Gear Train horsepower calculation

[srkirkpatrick]

I am designing a gear train for my basic mechanisms class that consists of three shafts. The input horsepower is 10 and rpm is 1750. I calculated the torque of the first shaft to be 360 but I am not sure if the horsepower stays the same throughout the whole train or not. The first shaft has a 14t gear meshing witha 40t gear on shaft two. Shaft two then has a 22t gear meshing with a 48t gear on shaft three for an output rpm of 281. In order to calculate the torque and force per tooth of each gear do I just use the input horsepower? Thanks in advance for any help.

 

[SteamKing]

The torque will be multiplied (or reduced) depending on the ratio of gears between the input and output. Except for minor frictional losses in the geartrain, power in should be approx. the same as power out. (Well-designed gear boxes usually have 2-3% loss).

For example, the first gear ratio is 40:14 or a ratio of 2.857 : 1. The input speed of 1750 rpm is slowed to 1750/2.857 = 612.5 RPM, and the input torque is multiplied to become 360*2.857 = 1028.6 in-lb.

 

[srkirkpatrick]

So is the 1028.6 in-lb the torque for the entire second shaft (the 40t and 22t gears) or the torque for the 40t gear alone? Thank you!

 

[SteamKing]

Assuming that the shaft connecting the 40t gear and the 22t gear is a regular shaft, the torque will be the same along the length. Look at it this way, if the 40t gear makes one revolution, the 22t gear will also make one revolution. There is nothing between the two gears which will cause the torque to decrease, except for minor frictional losses in the shaft bearings.

 

[alphy]

I would like to first clarify that horsepower is a unit of power, not torque. Torque is measured in units of force multiplied by distance, such as pound-feet or Newton-meters. Therefore, it is important to use the correct units when calculating and discussing power and torque.

To answer your question, the input horsepower will not stay the same throughout the gear train. As the gears mesh and transfer power from one shaft to another, there will be some power loss due to friction and other factors. This means that the output horsepower will be less than the input horsepower.

To calculate the torque and force per tooth of each gear, you will need to consider the gear ratio and the rotational speed of each shaft. The gear ratio is the ratio of the number of teeth on the first gear to the number of teeth on the second gear. In this case, the gear ratio for the first gear pair is 40/14 = 2.86, and the gear ratio for the second gear pair is 48/22 = 2.18.

To calculate the torque on the second shaft, you can use the formula T2 = T1 x (N2/N1), where T1 is the torque on the first shaft, N1 is the rotational speed of the first shaft, and N2 is the rotational speed of the second shaft. For the first gear pair, this would be T2 = 360 x (1750/1750) = 360 pound-feet. For the second gear pair, it would be T3 = 360 x (1750/281) = 2238 pound-feet.

To calculate the force per tooth, you will also need to know the pitch diameter of each gear. The force per tooth is equal to the torque divided by the pitch diameter. For example, for the 40-tooth gear on the second shaft, the force per tooth would be 360/8 inches = 45 pounds. You can use this same calculation for the other gears in the gear train.

I hope this helps in your gear train design. It is important to keep in mind that there may be other factors to consider, such as gear efficiency, lubrication, and load distribution, that could affect the final horsepower and torque calculations. It may also be helpful to consult with a mechanical engineer for more precise calculations and recommendations.