Compound gear train problem (WHY IS IT SO HARD )

In summary, the problem at hand involves calculating the angular acceleration of a fan at 2600 RPM, but there are no given moments of inertia for the gears in the system. The torque load on the output shaft caused by the fan is assumed to be a form of torque lost due to air resistance. The basic formulation being used is to sum the torques with respect to the input, which is equal to the torque applied by the motor minus the torque load from the output shaft with respect to the gear ratios. However, the moment of inertia of the gears is not necessary to calculate in this situation. If needed, the gears' sizes and center distance can be used to calculate the moment of inertia, but it is not required.
  • #1
Compound gear train problem (WHY IS IT SO HARD!)

Homework Statement



http://img5.imageshack.us/img5/1663/problemw.jpg [Broken]

I need to calculate the angular acceleration of the fan at 2600 RPM (motor speed) depicted by figure 4.

Homework Equations



Sum(torques with respect to input) = (torque applied by motor)-(torque load from output shaft with respect to gear ratios)

THEN

Sum(torques with respect to input) =( sum of intertia's with respect to input and gear ratio's) x (angular acceleration of input shaft)

The Attempt at a Solution



Now my problem is that there are no moments of inertia given for the gears in the system. I'm assuming the torque load on the output shaft caused by the fan is a form of torque lost due to air resistance of the fan. Thus the faster the fan the higher the torque lost.

Basic formulation I'm using is:

Sum(torques with respect to input) = (torque applied by motor)-(torque load from output shaft with respect to gear ratios)

THEN

Sum(torques with respect to input) =( sum of intertia's with respect to input and gear ratio's) x (angular acceleration of input shaft)

Then I can use the (angular acceleration of input shaft) to find the angular acceleration of the output shaft using gear ratios.

My main problem is that I don't have all the intertia's of the gear system! So do I simply ignore the other moment of inertia's or is there a correct way of calculating them!

A little advice / help please!
 
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  • #2


No need to calculate the moment of intertia of gears.

It is small compare to the work loss from the other side.

If you really need to calculate that.

We know the gears sizes d=N/P (N:number of teeth ,P:diametial pitch, d:diateter)
The same P is required to compose the gears.

We known the center distance c = (d59+d21)/2 =(d55+d21)/2

P59=P21, P55=P21 => d59:d21 = 59:21

Then we can calculate the diameter of gears by finding the hand book.

There is a fixed specification by product.

Then see what material you use.

Having say so ,you DO NOT need to calculate the intertial .lol
 
  • #3


Compound gear train problems can be challenging because they involve multiple gears with different sizes and ratios, making it difficult to determine the overall moment of inertia and torque load on the output shaft. In order to accurately solve this problem, it is important to consider the individual gear ratios and their effects on the overall system. This can be done by breaking down the system into smaller, more manageable parts and analyzing each gear ratio individually. Additionally, it may be helpful to make assumptions about the moment of inertia and torque load in order to simplify the problem and get a rough estimate of the solution. It may also be necessary to consult with a mechanical engineer or use computer software to accurately calculate the moment of inertia and torque load for each gear in the system. Overall, the complexity of compound gear train problems is what makes them challenging, but with careful analysis and consideration of all factors, a solution can be determined.
 

What is a compound gear train?

A compound gear train is a mechanism that consists of multiple gears connected together to transfer motion and power from one source to another. It is commonly used in machines and mechanical systems to increase or decrease speed and torque.

Why is solving compound gear train problems difficult?

Solving compound gear train problems can be challenging because it involves complex calculations and understanding of gear ratios, angular velocities, and torque. Additionally, the number of gears in a compound gear train can vary, making the problem more complicated.

What are the different types of compound gear trains?

The two main types of compound gear trains are the compound train and the epicyclic train. In a compound train, all gears are connected to a single output shaft, while in an epicyclic train, one or more gears rotate around a central gear.

How do you calculate gear ratios in a compound gear train?

To calculate the gear ratio in a compound gear train, you need to multiply the individual gear ratios of each gear. For example, if gear A has a ratio of 2:1 and gear B has a ratio of 3:1, the overall gear ratio would be 6:1 (2x3=6).

What are some practical applications of compound gear trains?

Compound gear trains are commonly used in automobiles, bicycles, and other machinery to transmit power and control speed. They are also used in clock mechanisms and other precision instruments. In industrial settings, compound gear trains are utilized in conveyor systems, machine tools, and other equipment that requires precise control of speed and torque.

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