How to Turn Simple Gear Ratio Into Compound
Gear ratios and chemical compound gear ratios
Working out simple gear ratios (two gears)
A feature frequently requested in my gear program is that it should calculate and display the gear ratio.The reason it does non accept this feature is that the gear ratio is also the molar count ratio (of the ii gears), and that is a value that the user has to enter.
At left, the 2 meshing gears with 7 teeth and 21 teeth will have a ratio of vii:21 (which is the same equally 1:iii). That is to say, the 7-molar gear volition turn 3 times for ever one turn of the 21-tooth gear. The logic is elementary, each gear needs to rotate by the same number of teeth for them to mesh, and then the 7-molar gear, having 1 3rd the teeth, needs to plough 3 times every bit much
Determining what gears you lot need
Suppose you lot have a motor that turns 1200 RPM (revolutions per minute), and you need to turn something at 500 RPM.
The ratio yous need is 500:1200, or 5:12. However, simple gears with simply five teeth tend to run a bit crude, so your best bet is to brand (or obtain) gears with 10 and 24 teeth.
Determining compound gear ratios (multiple stages)
When a gear train has multiple stages, the gear ratio for the overall gearing system is the production of the private stages.For example, for the gear at left the blue gears are 7 and 21 teeth, while the green gears are 9 and 30 teeth. Thus, the start gear ratio is vii:21 and the second is 9:30. Multiplying the two together gives (7x9):(21x30) = 63 : 630, which is 1:10. Then the big green gear will make 1 turn for every 10 turns of the minor blue gear.
Working out what gears you lot need for designing multiple stage gearing
Any gear ratio that can exist achieved past multiple stages of gearing can also be produced by single phase gearing, simply for big gear ratios, the large gear can get unwieldy.
There are many ways to achieve a given reduction with multiple stages, but how to decide what tooth counts to use for the gears?
Suppose we need a gear ratio that is i:11, and we want the smallest gear to have no fewer than x teeth. Nosotros could do this with a 10-tooth and a 110-tooth gear. Lets write the ratio every bit
10:110
At present, let's imagine we put another gear in betwixt those. Permit's imagine putting a 35 tooth gear betwixt the 10 and the 110 molar gears. The gear ratio betwixt the 10 and the 110 molar gears will nevertheless be the same, though the x and 110 tooth gears will now rotate in the same direction, whereas before they turned in reverse directions.
With the 35-tooth gear in between, we can now call up of now having a 10:35 tooth reduction, followed by a 35:110 tooth reduction.
Nosotros can reduce the 35:110 to 7:22, but if we don't desire any gears smaller than 10 teeth, nosotros need to double that to 14:44. And then we tin at present make our 1:11 gearing with the post-obit stages:
10:35 and 14:44
Total number of teeth between the ii stages is 103 teeth, vs 120 for the original version. just more importantly, this gear set is smaller.
Common denominators are very important, and information technology may be necessary to selection a different intermediate tooth count to make reduction possible.. If, all the same, we wanted an 11 : 127 gear ratio, the only fashion to become that exact ratio would be with an xi tooth and a 127 tooth gear (or multiples thereof), because both are prime number numbers that can't be factored.
On further consideration of the above 1:eleven gearing instance, we could have washed even better if nosotros instead started with 1:xi every bit 12:132. Nosotros could then write this equally 12:44 and 44:132, and the 44:132 is a 1:3 ratio, which we could also make a 10:30. That would leave u.s. with 12:44 and x:30, which adds up to simply 96 teeth full. We could too swap the two large gears if we wanted to. For example, ten:44 and 12:30 multiplied together besides produce a 1:11 ratio.
Design example 2: Gears for clock face hour and infinitesimal hands
Suppose nosotros desire to make a i:12 reduction for a clock. 12 factors into 4 and three, so we could exercise a 1:4 and a 1:3 reduction. but allow's see if nosotros can make the ii ratios closer to each other.
Let's multiply both sides past viii, so our 1:12 ratio becomes 8:96.
To get the reduction ratio for both gears, we want each gear ratio to be most the square root of 12, which is about 3.464. Now eight * 3.464 is 27.7. So lets try 28 teeth for the intermediate gear.
So we tin can write 8:28:96 or 8:28 and 28:96 We can divide the right side by iv, so we get 8:28 and seven:24
It doesn't always piece of work out then nicely. Sometimes one side or the other doesn't take whatsoever common divisors, so you may need to attempt different values for the intermediate.
For a clock, the hours and minute easily have to be concentric, so both of these gear pairs have to take the same shaft spacing. If we use the same tooth pitch for both gears, the shafts will not line up.
Using my gear generator plan, I tin can just enter the shaft spacing, and the program volition recalculate the tooth size accordingly. I used viii cm for both sets.
I cut the gears out of some 10 mm thick plywood on the bandsaw.
If I place them on superlative of each other, the two sets of gears look almost identical, only they have slightly dissimilar ratios, and the teeth on ane gear up are slightly larger.
A shaft through the larger gear on the right couples to the smaller 7-tooth gear backside it, and the shorter "hours" paw is screwed straight to the large gear.
Now, if I had a timer motor that turned one turn per hr, I could make a really big clock with these gears.
"Build a clock" is suggestion I often get. Maybe i of these days I will build one, peradventure not. No need to suggest it at whatsoever charge per unit, because the thought has certainly occurred to me :)
DOWNLOAD HERE
How to Turn Simple Gear Ratio Into Compound UPDATED
Posted by: barbarahervelp1962.blogspot.com