How to calculate gear sizes

[Westozy]

Hi all,
I have often been asked how I calculate gear sizes, I made a tutorial for a friend and thought our machinists here might benefit aswel! Cheers, Gwyn

How to calculate gear sizes and ratios


Calculating a gear train ratio is quite simple and the same theory applies to pulleys. A 15mm pulley driving a 45mm pulley has a 1:3 ratio a gear with 15 teeth driving a gear with 45 teeth will be the same 1:3. (As long as the “Module” or tooth shape is the same size). Every gear has a “Pitch Circle Diameter”, a “Tip Diameter” and a “Root Diameter”. The Pitch Circle Diameter or P.C.D. is about halfway up the tooth form and it is the point of contact where it will touch the other meshing gear. The tip diameter is obviously the outside diameter of the gear blank and the root diameter is diameter of the gear blank at the base of the teeth. To cut a gear successfully the tool must be able to fit into the gaps between the teeth where it meets the root diameter. In the example shown here, the gap between the Module 1 teeth at the root diameter is 1.33mm. We can cut these teeth with a 1.5mm cutter, it is 0.17mm too big but it will do the job quite well. A 1.2mm cutter would be ideal but 1.5mm is fine for low speed plastic gears used in flight simulator parts.


Gear-theory.jpg


In figure 1, I have drawn and labeled a pair of gears. Gear one has 45Teeth and Gear two has 15Teeth. This is a typical gear train that I would use on a throttle quad, the 45T would be blended with the base of a throttle lever and the 15T would be attached to a potentiometer. A swing of 90 degrees on the throttle lever would produce 270 degrees of rotation on the pot. A normal pot has about 300 degrees of available rotation so using 270 degrees will give good resolution and long life.
The 45T gear has a PCD of 67.5mm and the 15T has a PCD of 22.5mm, if we add the PCDs together and divide them by two, the centre to centre distance is determined (C/C). It really is that simple and there’s not much more to it.
When you have drawn a gear in Involute, save the file as a DXF somewhere and then open it in VCarve. Once it is there, select all (CTRL A) and copy (CTRL C), it can then be blended with the base of a throttle lever in another session of VCarve. The pasted gear can be dragged over to the centre point of the throttle lever and it will ‘snap to’ the centre. Then use the scissors to remove the unwanted parts of the gear and lever body. When the lever appears to have a partial gear around the bottom, select both parts and use the ‘Join vectors’ tool to connect them together.
Multiple gear trains are also called ‘Compound’ gear trains – If we use the 1:3 gear train example, that is a 15T (gear 1) driving 45T (gear 2). If the 45T gear has a 15T gear (gear 3) glued to the side of it and this one is driving another 45T gear (gear 4), the final drive ratio is multiplied. 1:3 x 1:3 = 1:9. The ratio from gear 1 to gear 4 = 1:9. It will take 9 turns of gear one to produce one turn of gear 4. A compound gear train is required to drive trim wheel indicators, I have made a good 1:15 gear train for my A320TQs. I haven’t done a Boeing one yet but I will when I start on the B737TQ body, the lever drawing is just about done.

Gwyn Perrett
www.aerosimsolutions.com.au

[Tom_G_2010]

Gwyn,

Thanks, this is good info. I have a somewhat related question: Given a sprocket or timing belt pulley of size A and another of size B with a distance center to center between them of C is there a simple formula to calculate chain or belt length?

I will be setting up a few of gear reduction arrangements to interface pots and at a later date Force Feedback Motors. Some of it uses basic spur gears while other parts use timing belts and pulleys, or roller chain and sprockets. I can do out the long math piece by piece to figure it out, but am curious if you know of a more structured formula for this.

Thanks!
Tom G.

[Westozy]

Gwyn,

Thanks, this is good info. I have a somewhat related question: Given a sprocket or timing belt pulley of size A and another of size B with a distance center to center between them of C is there a simple formula to calculate chain or belt length?

I will be setting up a few of gear reduction arrangements to interface pots and at a later date Force Feedback Motors. Some of it uses basic spur gears while other parts use timing belts and pulleys, or roller chain and sprockets. I can do out the long math piece by piece to figure it out, but am curious if you know of a more structured formula for this.

Thanks!
Tom G.

Good question Tom,
I don't think I have ever done this in my engineering trade as a calculation, I have fitted chains but it has been wrap the chain around the sprockets and then cut the appropriate link. Then fit a spring loaded roller tensioner to take out the slack. I did have a look online for you and found this neat little calculator which should answer your question!! http://iprr.topcities.com/chain.htm

Cheers Gwyn

[Tom_G_2010]

That's perfect. I've often done as you have with other projects when I had roller chain in bulk at my disposal. At this point in my pit build though I'm really counting pennies and have found some online sources that will sell chain in short lengths. I'm doing what I can to calculate the needed lengths and round up to allow for cutting a link or two and using tensioners.

[IanH1960]

Hi Tom,

There are a few timing belt calculators out there - for a US based one have a look at:

http://www.sdp-si.com/cd/default.htm

..might be of interest. You can quickly run the calculator several times to home in on an answer if it doesn't give it directly.

Ian