Calculating Gears

This should be easy, I've done it before several times but now the brain has gone to sleep!

I need to cut 2 gears to give a ratio of 2 to 1 with a centre distance of 0.731.

The exact tooth form is not important and the smallest cutter I have is for 20DP at 14.5 pressure angle.

Ideally, the tooth counts should be 40T and 80T and I'm not averse to buying or making a cutter, but what do I buy or make?

Any help most gratefully received to help the headache go away.

Brian

Is that 0.731 mm, inches, feet, etc? 

If it's inches then you are at about 82DP so with 80dp being the nearest common size play with the tooth count. 39T/78T would be about right with a PCD of 0.73125" or make a custom 82DP cutter and keep your tooth count to 40/80

Edited By JasonB on 07/01/2021 17:24:32

I have never cut gears, but I would think there is an online calculator available out there.

Should have said the other alternative is to alter the ctr distance to 0.750" then you can use an 80DP cutter and keep to your tooth counts or buy off the shelf 40/80 gears in 80DP.

Edited By JasonB on 07/01/2021 17:40:17

Many thanks for your help Jason. The centres SHOULD have been at 0.750 Inches but in order to achieve other dimensions I had to make it 0.731 inches.

Just to complicate matters I have come across another drawing that gives 28T and 56T but with the same centres. Does that make the 80DP more in line with the 0.731 centres that I have? especially if I adjust the depth of cut.

Brian

Consider two gears at a centre distance D. The two gears touch on their pitch circles, so for 1:1 ratio, each pitch circle has has a radius of D/2 or 1/2 * D. That means each gear has a pitch circle diameter of D.

The total (sum) of the pitch circle diameters is 2D and the gears share this 2D in proportion to their ratio (i.e. 1 * D each for 1:1 ratio).

Now, for 1:2 ratio, one pitch circle will have radius D/3 (or 1/3 * D) and the other 2D/3 (or 2/3 * D). The corresponding pitch circle diameters will be 2D/3 and 4D/3.

Again, the sum of the pitch circle diameters is 2D and the gears share this in proportion to their ratio (i.e. 1/3 * 2D for one and 2/3 * 2D for the other).

Let us try a 13:27 ratio. One gear will have a PCD of 13/40 * 2D and the other a PCD of 27/40 * 2D, the sum of the PCD's again being 2D.

So the general rule is to take twice the centre distance and pro-rata it according to the gear ratio.

This gives you the PCD of each gear that will fit in the space and achieve the ratio you want. These two numbers are inviolate.

You then choose a tooth count and calculate a DP/MOD for this count or you choose a DP/MOD and calculate the number of teeth.

For any given space and given ratio, you can use big gears with few teeth or small gears with lots of teeth.

That would work out at about 57.5 DP which is quite a way from either of the common DPs of 48 and 64. for the 0.731" but if the 0.75" ctrs were used that would be an even 56DP.

Out of interest what scale are you building the ford to as that can often be worked back to see if the original size was a standard one. For example if you were building to 1/8th scale then the 80DP size would equate to 10DP on the original, 1/16th scale 5DP.

How I calculate these. 0.731ctrs x 2 = 1.462 x 80 dp = 116.96 total no of teeth in gear pair, 117/ 3 gives 39 and 78 as true gear pair for 2:1 ratio. Reduce 78 tooth gear to give centres required.

If your centre distance is 0.731 inches, a 20 DP cutter will be of little use. You need to think in terms of a much higher DP

The least that you would be aiming for would be a 12/24 train,

0.731 inch is 18.5674 mm so you could think about using Module gears, BUT you will not get an exact number of teeth for either DP or Module gears..

Are you certain of the centre distance?

0.750 might be more likely if the rest of the device is Imperial., or 19 mm if Metric, and using standard gear proportions.

Just a thought! that might point you in the right direction.

Howard

Many thanks all for trying to help.

Jason, the scale is 1/4 and there are 2 conflicting drawings for the same parts, with different tooth counts and, although not relevant for my problem, parts of the valve gear including the ignition advance are different between 2 drawings.

The essential point is that I need to end up with a 2:1 ratio with centres of 0.731 inches. If it comes to, I can grind a fly cutter if I know what the dimensions should be. The gears are in brass and only 0.078 inches thick.

Brian

Sorry, Brian ... This only does Module and the centre distance is a tad too big : but it gets you in the right ballpark.

Module 0.6 Gears 21 tooth and 42 tooth

MichaelG.

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This should do you for the two custom 82DP cutters so you can keep the 40/80T ratio and 0.731" ctrs. Dimensions in thou. Based on Ivan Laws button method will work with a single point or multi tooth cutter. Click for larger image

Ignor the mm it was easier to work in a larger size but this is the two gears 40/80T 82DP

Edited By JasonB on 07/01/2021 19:57:39

Edited By JasonB on 07/01/2021 20:08:06

Many thanks for that Michael but I think that Jason has cracked it. Many thanks Jason, you're an absolute star!!!

I can easily make those two form cutters with the equipment I have.

Brian

For Brian, or anyone else with a similar query ...

I have just downloaded a very simple [and free] iOS App which does these calculations

... highly recommended if you have a suitable device

**LINK**

https://apps.apple.com/gb/app/spur-gear-calculator/id827110560

No fancy graphics ... but it seems to get the sums right

MichaelG.

.

Edited By Michael Gilligan on 07/01/2021 23:39:28

The HPC gearing book suggests another alternative with 0.25 Mod gears of 25 and 50 teeth. They will give a centre to centre gear spacing of 18.75 mm which is 0.738 inches in old money

Regards

Brian