My gear cutters are 24DP. Many people want to build my engines, but have 32 dp or 48 dp gear cutters. If my engine plans call for a 2:1 ratio and 1.563" center distance, this works out fine using a 25 tooth gear and a 50 tooth 24 dp gear. Are there combinations of other gear sets that will still give 2:1 ratio and 1.563" center distance?Brian
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A little gear help please
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A little gear help please
Last edited by brian Rupnow; 02102021, 06:21 PM.Brian Rupnow
Design engineer
Barrie, Ontario, CanadaTags: None

DP is teeth per inch of diameter.
So going from 24DP to 48 DP, the tooth count doubles, and the size stays the same. At least the pitch circle does.... the OD will be smaller due to the tooth size lowering the "addendum" outside of the pitch circle.
The OD will be a bit less, but that will not affect the spacing, which is based on the pitch circle.2801 3147 6749 8779 4900 4900 4900
Keep eye on ball.
Hashim Khan
It's just a box of rain, I don't know who put it there.

Unfortunately the pitch diameter is fixed by the tooth form.
Pitch diameter = # of teeth/Pitch
25 teeth/24 dp = 1.041 PD
50 teeth/24 dp = 2.083 PD
You need to calculate different combinations that result in the same PD's
This is an excellent gear resource, enter the # of teeth and the DP and it will give you the relevant dimensions plus CAD drawings.
https://www.rushgears.com/techtools...lacement_parts
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Center distance for mating spur gears is equal to 1/2 the pitch diameter of each gear, added together. My first post had an incorrect center to center distance in it. I have edited that to correct it.BrianLast edited by brian Rupnow; 02102021, 06:22 PM.Brian Rupnow
Design engineer
Barrie, Ontario, Canada
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Brian, have you ever heard of gearotic motion software? Its intended for cutting gears on a cnc machine BUT it gives all the dimensions, center distances and much more as well as a drawing of the gears, even animates them. You can print the gears out at 1:1 also which is very handy. Its very easy to use and there is a free trial. Its perfect for this sort of whatif sort of engineering. First gears I made were helical 90 degree drive and worked out perfect first time. Along with gears, it does ratchets, sprockets, timing pulleys and much more all of which could come in handy for your engine building.
Its basically a simple to use cad especially for gears.
https://www.gear2motion.com/Last edited by Sparky_NY; 02102021, 07:31 PM.
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Is it possible? Yes. And No.
You have two 24 DP gears with 25 and 50 teeth. And as you and others have said, their PDs are 1.0417" and 2.0833". This comes from the equation:
PD = N / DP
N = Tooth Count
When you work this backwards, you want to keep those two PDs the same so the gear spacing and the gear ratio both remain the same. So you need to use those two PDs for your calculations. Notice that these two PDs have the desired gear ratio of 2::1.
2.0833" / 1.0417" = 2
So keeping those two PDs, and trying to switch to a different DP we rearrange the equation above into:
N = PD x DP
That is the same equation, but it is rearranged.
So for 48 DP we get
N = 1.0417 x 48
and
N = 50 for the smaller gear
and
N = 2.0833 x 48
and
N = 100 for the larger gear
There is a small rounding error in both of these, but that is all it is, a rounding error. Two 48 DP gears with tooth counts of 50 and 100 will fulfill the stated conditions: a 2::1 gear ratio and a 1.563" center distance. That center distance is exactly the same as your original 24 DP gears. So there is your "YES".
But if I carry out the same calculation for 32 DP gears I get:
N = 1.0417 x 32
and
N = 33.333 teeth for the smaller gear
and
N = 2.0833 x 32
and
N = 66.666 for the larger gear
And since you can not have 1/3 or 2/3s of a tooth, you can not use a 32 DP for your substitution.
32 DP is a definite NO.
So, what DPs will work?
You will need to scale your DP (24) by a factor that will also scale your tooth counts (25 and 50). Notice that 48 DP is exactly twice your 24 DP and the tooth counts for a 48 DP gears are twice the original tooth counts or 50 and 100. That works. In fact, we can multiply the original 24 DP by any whole number (2, 3, 4, 5, etc.) and the tooth counts by that same factor and it will work.
But are those multiplies all the additional DPs that will work. We can pick any two whole numbers that give the same 2::1 gear ratio and then calculate the DP. As an example, 13 and 26 teeth.
We turn that same equation around in a different way to solve for the DP:
PD = N / DP
becomes
DP = N / PD
And solving for DP we get:
DP = 13 / 1.0417
DP = 12.4796...
and
DP = 26 / 2.0833
DP = 12.4796...
That is not a DP that you are going to easily find any cutters for, but it is a valid DP. And cutters could be made. Some gears have been made in exactly this manner: start with a shaft spacing and a desired gear ratio and calculate the needed DP. Then they make the cutters and make the gears with them. It can solve some design problems.
This is probably the way that any ratios that are not whole number multiples of 24 is going to turn out. The three numbers we are working with are 24, 25, and 50. These three numbers do not share any common factors. So it is probably impossible to find any additional factors other than the integers I listed above that will result in a whole number for the DP.Paul A.
SE Texas
And if you look REAL close at an analog signal,
You will find that it has discrete steps.
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Originally posted by Bented View PostUnfortunately the pitch diameter is fixed by the tooth form.
Pitch diameter = # of teeth/Pitch
25 teeth/24 dp = 1.041 PD
50 teeth/24 dp = 2.083 PD
You need to calculate different combinations that result in the same PD's
The OD is affected by tooth form etc. The PD is not. Where do you see any reference to tooth form in the PD equation?
The 50 tooth 48 DP gear has the same pitch diameter as the 25 tooth 24 DP gear, for instance. The actual OD will be different, because the tooth is smaller with a 48 DP gear, and the fixed addition of 2 teeth is not "proportional".
But, the center to center distance should be OK, depending on the allowance that was given for clearance. The smaller tooth will give a different clearance (backlash) for the same CC allowance.
The basic starting point for determining CC distance is the pitch diameters, which theoretically touch with perfectly mated gears of perfect form.
So doubling the DP and the tooth count will in fact be fine, depending on the extra allowance given for backlash (clearance). Going that direction the OD should be OK as well (halving the DP and tooth count might not be).Last edited by J Tiers; 02102021, 09:34 PM.2801 3147 6749 8779 4900 4900 4900
Keep eye on ball.
Hashim Khan
It's just a box of rain, I don't know who put it there.
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If you like spreadsheets you can run through the combinations using the formula DP=(3xteeth)/(2xspacing) where teeth is the smaller gear. This formula is specific to the 2:1 ratio needed for camshafts of course. You don't get many whole number DP results but a few like 33 teeth gives 31.7DP. Is that close enough to 32 to use the same cutter? Probably for this aplication as the cutters are approximations anyway.
You could rearrange the formula to give teeth for a given DP but you just end up with fractional teeth which are rather weak.
For your next engine please start with a design criterion of gear spacing exactly 1.5in which works everything out perfectly with small gear teeth = DP.
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The center distance between two gears is
C = (D_G + D_P)/2
where D_G and D_P are the pitch diameters of the gear and pinion.
Knowing that D = N/DP you can write this as
C = (N_G + N_P)/(2*DP)
where N_G and N_P are the tooth numbers of the gear and pinion.
For your specific gear set, N_G = 2*N_P, so this reduces to
C = (3/2)*N_P/DP
Your center distance C = 19/16" = 25/16", so the number of teeth on the pinion is
N_P = (25/16)*(2/3)*DP = (25/24)*DP
or N_P = 25 for a DP of 24.
For any other diametral pitch with a center distance of 19/16", the number of teeth on the pinion is N_P = (25/24)*DP, which must be a whole number. This will only work for other wholenumber (not fractional) DPs that are multiples of 24. For a DP of 32, this gives the N_P = 331/3, clearly not a whole number.
As Baz pointed out above, if you would have used a center spacing of C = 1.5" (3/2"), then the number of teeth on the pinion for your 2:! ratio is N_P = DP, which works for any wholenumber diametral pitch.Last edited by DrMike; 02112021, 09:00 AM.
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