Need info on sprocket size for Conveyor Speed

[Thomas42]

Hi guys its my first time here so im not to sure how this works. But anyway, my goal is to keep the same speed i got for my conveyor belt.
Right now i got a 10 HP motor at 1750 rpm. with a gearbox ratio of 25/03.

The sproket on the gearbox has 29 teeth and approx 12.5 inch diameter. The sproket on the conveyor Drum has 21 teeth and approx 9 inch diameter. Because this 10 HP will not be strong enaugh for the way we are going to run the conveyor in the futur i got a 20HP at 1750rpm with a gearbox of 32.05. So here is my question what size sprocket will i need to run the same conveyor at the same speed but whit this new gearbox.

The Drum on the conveyor is approximately 11 inch. If my tachometer is good it seems to be traveling at 55 RPM.

 

[Ken Roach]

Edit: got the reduction ratios wrong.. back in a moment

 

[Ken Roach]

Welcome to the forum!

This should be a simple matter of effective In:Out ratios. Both gearboxes and sprockets have In:Out ratios. For gearboxes it's expressed in turns, for sprockets it's expressed in diameter.

Draw yourself diagrams and do it on paper in whole numbers to help keep it clear.

Your existing gearbox is an In:Out ratio of 25:3, and your existing sprocket is an In:Out ratio of 12.5:9.

Express those as fractions and multiply them together: 25/3 * 25/18 = 625/54

Your new gearbox is an In:Out ratio of 32:5, and I think you're talking about a new sprocket on the gearbox, so that's a ratio of x:9.

Express those as fractions and multiply them together: 32/5 * x/9 = 32x/45

You want the two ratios to be equal, so it's an equation now.

32x/45 = 625/54 resolves to x/45 = 625/1728. Multiply both sides by 45 to get x.

So x = 28125/1728 = 16.276 inches diameter sprocket on the output of the new gearbox.

Who wants to check my math ? My sixth grade math teacher was Mrs. Anderson, by the way, who believed in the power of memorizing matrices.

 

[Pete.S.]

Both gearboxes and sprockets have In:Out ratios. For gearboxes it's expressed in turns, for sprockets it's expressed in diameter.

Hey Ken, aren't you confusing sprockets and pulleys? Pulleys are defined by their outside diameter but sprockets by the number of teeth.

I assumed Thomas42 was talking about:
motor -> gear box -> sprocket -> chain or timing belt -> sprocket on conveyor drum

Case 1: 1750 rpm 10HP motor -> gearbox ratio of 25:3 -> 29T sprocket -> 21T sprocket
Case 2: 1750 rpm 20HP motor -> gearbox ratio of 32:5 -> ???T sprocket -> 21T sprocket

PS. I get 38T sprocket in case 2.
But I get an rpm on the conveyor drum of 152 rpm so something is wrong if it measured 55 rpm...

.

 

[Ken Roach]

Good point, as the integer number of teeth is going to be the selectable thing for a sprocket.. they don't come in fractions.

Number of teeth x pitch = diameter along the center of the chain pins.

Run the same equations with 29:21 as the original sprocket ratio, and you come out with a 37.76 tooth sprocket. Obviously OP can't make it exactly the same speed, so he should select the closest thing he can get.

 

[L D[AR2P#0.0]]

Why did the OP change the gearbox ratio if the intention was to keep the conveyor speed the same?

 

[osmanmom]

Torque?

 

[Pete.S.]

Why did the OP change the gearbox ratio if the intention was to keep the conveyor speed the same?

Larger motors have larger diameter shafts so you might need another gearbox anyway or it wont fit. The larger motor and gearbox is probably something from another project/application.

 

[Bit_Bucket_07]

Torque?

There is nothing to be gained by changing the gearbox reduction ratio if the final drive ratio is going to be the same anyway.

 

[Tom Jenkins]

Thomas42, you do need to check that gear reducer ratio. Reducer ratios should be expressed as XX:1. 25/03 doensn't look valid to me.

If you are doubling the horsepower and torque you will probably need to increase the chain size as well, since you will be increasing the chain pull. I strongly suggest you contact a power transmission supplier for help. Here is some sample info:

https://www.mcmaster.com/#gear-reducers/=17jv36f
https://www.mcmaster.com/#roller-chain/=17jv4gw
https://www.mcmaster.com/#roller-chain-sprockets/=17jv4lb

At any rate Ken's and Pete's methodology is correct. You can check your solution by multiplying the gear and sprocket ratios to get the total ratio and dividing motor rpm by the total ratio to verify you get the correct final rpm.