Gear Reducer Design: How to Calculate Input & Output

[JJLIM90]

Im having trouble with designing gear. I was given only the output speed and input. May i know what are the required steps to follow to design a gear reducer?

 

[JasonD]

The gear ratio is equal to the inverse of the speed ratio:

$\frac{Tooth Count 1}{Tooth Count 2} =\frac{Speed 2}{Speed 1}$

This can be rewritten in any number of fashions. For example:

$ToothCount1*Speed1 = ToothCount2*Speed2$

Or, rearrange to solve for your unknown. In your case, though, you are given only the two speeds which leaves you with a fraction. You can pick any combination of gears to generate the required fraction.

Let's say you were given an input speed of 500 rpm and an output speed of 250 rpm, then your velocity ratio would be:

$\frac{Speed 2}{Speed 1} = \frac{250 rpm}{500 rpm} = \frac{1}{2}$

and any combination of gears that resulted in a ratio of 1/2 would give you the required velocity ratio:

$\frac{Tooth Count 1}{Tooth Count 2} =\frac{1}{2} = \frac{20}{40} = \frac{30}{60} = \frac{17}{34} ...$

For most chain drive systems, there are some general rules that are considered "good practice":

• Use at least a 17-tooth sprocket
• The larger the sprockets, the quieter the drive
• Pair even and odd tooth sprockets to prevent chain-cog matching (which results in excessive wear)

 

[JJLIM90]

Based on the toothCount calculated, how can i get the suitable pitch and diameter for the gear systems?

 

[SteamKing]

That will depend on several other factors, including, but not limited to, the maximum practical gear size, the amount of power or torque to be transmitted, and whether the stresses in the gear teeth are high enough to expect failure.

 

[JasonD]

As SteamKing implied, there is no quick and easy answer to your newest question. You'll need to read some tutorials or get your hands on some books. I learned from "Shigley's Mechanical Engineering".

To give you a direction, you'll first need to know the power requirements, torque loads, and physical constraints of the system. Designing a chain drive system requires keeping all of these issues in balance.

 

[JJLIM90]

Im having Shirley's Textbook too!

I have glanced through the chapter about gears but found no direct relationship between the torque/power and the diameter/pitch...

May i know what should i do when i have known the power input?

 

[JasonD]

Look through the section titled Roller Chain (17-5 in my U.S. 9th edition).

You already know the input speed and you should be able to figure out the system's horsepower. At this point you can find a suitable ANSI chain number from the Tabulated Horsepower Table (Table 17-20 in my edition). For example, if the slower of the two sprockets/gears (usually the driving gear) is running at 600 rpm and the system must transmit 10 horsepower, then the smallest suitable chain size is the number 60 chain in a bath lubrication.

There are other ways to transmit 10 horsepower at 600 rpm with smaller chain sizes by using multi-strand systems. Use the allowable horsepower formula (Eq 17-37 in my edition) which corrects for the extra strands and adjusts for tooth counts other than 17. The multi-strand approach is useful it you have limits on the amount of radial space that the gears can use and are not squeezed in their axial direction.

 

[JJLIM90]

However for roller chain design, is it applicable to use for gear design?

 

[JasonD]

I am sorry; I had just assumed you were designing a chain drive. Unfortunately, I don't have experience in the area in which you are working. A quick look through Shigley's suggests that the section titled "Force Analysis - Spur Gearing" may be useful to you.