How many teeth are on a ring gear and pinion for a 4.11 gear ratio?

Answer 1

One key to this design problem is to remember that gears must have a whole number of teeth. It is impossible to roll a gear against another gear that has, say, half, a tooth somewhere among the whole teeth. So gears always have a whole number of teeth.

Another key is that the gear ratio is the ratio of the numbers of teeth on two gears, N1 divided by N2. The result of this division often produces a fraction AND the fraction is often ROUNDED OFF in printed materials. Because of this round-off, you cannot be certain what the actual fraction is. This means that, even when you find whole-number values for N1 and N2, you cannot be certain that they represent the exact numbers.

So, here is how to find the pair of gears from a given gear ratio such as 4.11. First, examine the fraction, 0.11, from the ratio. Find a whole number m such that m times the fractional part of the gear ratio gives another whole number almost exactly? Try m = 2, 3, 4 ... up to 16 or even more until you find a good fit.

For the given problem, 9 x 0.11 = 0.99, which is almost 1.

That whole number m is the SMALLEST possible number of teeth for one gear.

Multiply the gear ratio by m and round to a whole number to get the least number of teeth on the second gear. So, 9 teeth is the smallest number of teeth for one gear and 9 x 4.11 = 36.99 (that is, 37) is the smallest number of teeth for the other gear.

You can multiply the number of teeth on both gears by any whole number without changing the gear ratio. So, 2 x 9 = 18 teeth and 2 x 37 = 74 teeth also have the ratio 37 / 9 = 4.11111...

Here is how to tweak the result if the fraction you chose didn't give a satisfactory result:

Multiply the number of teeth from the trial answer by any whole number, say 2 or 20.

20 x 9 = 180 and 20 x 37 = 740

Now subtract 1 from the number of teeth on the larger gear and calculate the gear ratio.

740 - 1 = 739 and 739 / 180 = 4.105555...

Alternatively, add a tooth to the larger gear and check that ratio: 741 / 180 = 4.116666...

One key to this design problem is to remember that gears must have a whole number of teeth. It is impossible to roll a gear against another gear that has, say, half, a tooth somewhere among the whole teeth. So gears always have a whole number of teeth.

Another key is that the gear ratio is the ratio of the numbers of teeth on two gears, N1 divided by N2. The result of this division often produces a fraction AND the fraction is often ROUNDED OFF in printed materials. Because of this round-off, you cannot be certain what the actual fraction is. This means that, even when you find whole-number values for N1 and N2, you cannot be certain that they represent the exact numbers.

So, here is how to find the pair of gears from a given gear ratio such as 4.11. First, examine the fraction, 0.11, from the ratio. Find a whole number m such that m times the fractional part of the gear ratio gives another whole number almost exactly? Try m = 2, 3, 4 ... up to 16 or even more until you find a good fit.

For the given problem, 9 x 0.11 = 0.99, which is almost 1.

That whole number m is the SMALLEST possible number of teeth for one gear.

Multiply the gear ratio by m and round to a whole number to get the least number of teeth on the second gear. So, 9 teeth is the smallest number of teeth for one gear and 9 x 4.11 = 36.99 (that is, 37) is the smallest number of teeth for the other gear.

You can multiply the number of teeth on both gears by any whole number without changing the gear ratio. So, 2 x 9 = 18 teeth and 2 x 37 = 74 teeth also have the ratio 37 / 9 = 4.11111...

Here is how to tweak the result if the fraction you chose didn't give a satisfactory result:

Multiply the number of teeth from the trial answer by any whole number, say 2 or 20.

20 x 9 = 180 and 20 x 37 = 740

Now subtract 1 from the number of teeth on the larger gear and calculate the gear ratio.

740 - 1 = 739 and 739 / 180 = 4.105555...

Alternatively, add a tooth to the larger gear and check that ratio: 741 / 180 = 4.116666...