Calculating gear ration for V belt?

Neil H · Oct 13, 2020

Hi, I have two pulleys attached with a V belt but I’m unsure how to calculate the gearing ratio. As the belt is in contact along the depth of its V groove then it has an inside and outside circumference for both pulleys with the inside dimensions always giving a higher gearing ration than the outside ones. I think.
Is this right and if so which is the correct circumference to use and why?

Unaonto · Oct 13, 2020

I am interested too.

malcolm rypauf · Oct 13, 2020

Simple answer: divide the outside diameter of the large pulley by the outside diameter of the small pulley and the result will be the ratio. You either multiply the the rpm for the driving pulley by the ratio to get the rpm of the driven pulley if the driver is larger than the driven or you divide the rpm of the driver pulley to get the rpm of the driven if the driver is smaller than the driven.

Peter Neill · Oct 13, 2020

If you just want to calculate the ratio, it doesn't matter, as long as you use the same reference point to measure both of them.
The same for using it to calculate output speed, use the same reference point.
Gear & pulley speeds are both calculated using the formula of driver/driven x input speed = output speed, but with gears the number of teeth are the divisor and with pulleys it's the diameter.

thermite · Oct 13, 2020

Neil H said:
Hi, I have two pulleys attached with a V belt but I’m unsure how to calculate the gearing ratio. As the belt is in contact along the depth of its V groove then it has an inside and outside circumference for both pulleys with the inside dimensions always giving a higher gearing ration than the outside ones. I think.
Is this right and if so which is the correct circumference to use and why?

The "pitch diameter". Needs a touch of calculating, but that is the median for the position of power transmission as the other parts of the Vee above (very little) or below (most of the depth.) flex around each size of pulley, transferring the power by the friction grip of their bulged sides.

Belt makers publish all that stuff for their various types of belts. Essentially an online design course.

Top of the vee goove walls are easier to just measure directly, and the ratios very close to PD anyway, so most folks just do that for all store-bought pulleys. Slip varies, so ratios are never perfect.

Vee, Poly Vee, MicroVee (nor flat belting.) are not "synchronous". All have slip.

Use a toothed belt - Gilmer or more recent shapes, such as Pirelli's - if you need that sort of repeatable / predictable / consistent ratio or positioning.

donie · Oct 13, 2020

Hey there troll!, you need a new V belt to rotate your brain...
What happened with your Monarchist fake forum ID, you were banned!
Looks like the thermite handle, is pooping out on its own..

Neil H · Oct 13, 2020

But I can take the same OD pully and increase the depth/width of the V groove and the pully will increase or decrease in speed relative to the other pully, so changing the gearing. If it was a timing belt you would use the diameter of the contact point of the belt with the pully, the size of the flanges would not be relevant.

Different reference points on the belt will give different ratios. The top of both belts will give a significantly different ratio to the bottom of both belts, the difference being proportional to the difference in the sizes of the pullies. An 8mm deep belt on a 24mm OD pully will lose one-third of its diameter but an 8mm belt on an 80mm OD pully will lose only one-tenth.

Thermite, That makes the most sense to me, the other parts of the belt must be stretching and compressing to some medium. I'll look up the catalog info see if I can find the pitch diameter.

I appreciate all the answers guys.

gbent · Oct 13, 2020

You are putting to much into the problem. Slip makes precise calculations worthless. Calculate the the ODs and subtract 4% slip.

DDoug · Oct 13, 2020

Neil H said:
Hi, I have two pulleys attached with a V belt but I’m unsure how to calculate the gearing ratio. As the belt is in contact along the depth of its V groove then it has an inside and outside circumference for both pulleys with the inside dimensions always giving a higher gearing ration than the outside ones. I think.
Is this right and if so which is the correct circumference to use and why?

"Gear Ratio" ???
I don't see anywhere gears are being applied, only belts.

atex57 · Oct 13, 2020

Gears have a pitch diameter, belts have a pitch length. A "B" belt has an outside length 3" longer than its designation. A B45 belt will measure 48" around the outside just as a gear measures larger than its pitch diameter.

Ed.

Screwmachine · Oct 13, 2020

Measure to the top of the belt on both pulleys. If you have a V that lets the belt sit 1/2" below the rim or 1/8" above you'll still be ok.

9100 · Oct 13, 2020

Most people here are being too scientific. Use a timing belt and count teeth. If one pulley has 10 teeth and the other has 20, the ratio will be 2/1. You don't need to worry about pitch diameter with a timing belt because it becomes a dependent variable and there is no slip.

Bill

Strostkovy · Oct 13, 2020

9100 said:
Most people here are being too scientific. Use a timing belt and count teeth. If one pulley has 10 teeth and the other has 20, the ratio will be 2/1. You don't need to worry about pitch diameter with a timing belt because it becomes a dependent variable and there is no slip.

Bill

I disagree. Toothed belts and pulleys are more expensive, run louder, are less tolerant to overload, and need more precise alignment. It might be entirely suitable for the unknown application, but I would assume any machine someone with this little experience would make would benefit from the simplicity and tolerance of a V belt.

In any case, ratio calculation is worth knowing regardless.

To answer the OP, pulleys have a pitch diameter that sits somewhere in between where the inside and outside of the belt ride. But the difference in ratio from calculating at pitch diameter vs inside or outside diameter is negligible for most applications. As mentioned before, be aware of slip.

The only catch I've seen is when measuring the OD of the pulleys and not noticing that one of them sticks way past where the belt rides. I only see this in scenarios where a pulley meant for a larger belt (or two possible sizes of belt) is used and the other is sized only to the belt in use.

Scottl · Oct 13, 2020

If you split the difference between the major diameter and the minor diameter you will be close. As others have stated each pulley is meant for a specific width and angle belt. Manufacturers publish the actual pitch diameter along with the OD and bore so a quick online search for a similar pulley should give you something to compare.

One trick is to pinch a new belt tight into the groove and measure the OD of the belt. The outside of the belt will have the same surface speed at both pulleys so measuring the belt OD at both and comparing the ratio should give you the speed ratio. As belts wear there is a very small change in ratio but for machinery driving purposes we don't need precision to six decimal space.

PS: When you buy say a 3.5" pulley of a given pitch the OD of the pulley will be larger. If you find a listing for a same pitch pulley with the same OD the pitch diameter will also be the same.

thermite · Oct 13, 2020

9100 said:
Most people here are being too scientific. Use a timing belt and count teeth. If one pulley has 10 teeth and the other has 20, the ratio will be 2/1. You don't need to worry about pitch diameter with a timing belt because it becomes a dependent variable and there is no slip.

Bill

Easy to say, but synchronous belt "pulleys" are actually a high-precision cousin to a GEAR and made to similar tolerances.

So they cost the very Earth, relatively, and are harder to DIY compared to Vee, Poly-vee, Micro-Vee, or flat belts. Same basic calculations, dividing and cutting process as generating gears.

Neil H · Oct 13, 2020

I have timing belts fitted currently but I’m testing V belts, the reason I’m trying to move to V belts is that I’d like the assembly to be as quiet as possible.

This gearing attaches an axel to a small flywheel to smooth out the motion of a hand-operated carriage so I’m testing to see if various V belts will work without noticeable slippage when in use.

I don't need to be precise with the gear ratio it just struck me as a problem and I wanted to know the correct way to calculate the solution. Pitch Diameter seems to be the answer but the root to it depends on the exact belt and manufacturer by the sound of it.

By gear ratio I just meant the relative speeding up or slowing down of the parts due to the different sizes of the pulleys, I’m not sure what else to call it.

I'm making my own pulleys with the listed angles from the belt manufacturers catalog so can't lift a pitch diameter straight from there but now I know what I’m looking for I’ll be able to get close enough, maybe even see how they arrive at the number.

I’m using aluminum at present but am looking to test Tufnol and maybe even try PU for the smaller one to see if I can increase the grip. I believe the manufacturer uses cast iron. These are small belts by the way. Cogged, 6mm wide, 4mm deep, 450mm long.

thermite · Oct 13, 2020

Neil H said:
I’m using aluminum at present but am looking to test Tufnol and maybe even try PU for the smaller one to see if I can increase the grip. I believe the manufacturer uses cast iron. These are small belts by the way. Cogged, 6mm wide, 4mm deep, 450mm long.

"Back in the day" (office automation goods- paper movement, my Day Job at the time), one went to W.F. Berg or PIC design - briefly Grob spline, and the Kidder Press Division of Moore business forms - for those parts. Cast-Iron, Delrin, brass, stainless etc. pulleys were all on-offer.

Browning, Morse, T.B. Woods, Maska et al AFAIK all now b'long Gates, Emerson, or one of the other belting / power transmission "major makers"?

"Light metal" alloy Vee-belt pulleys and step-pulley cones came from Chicago Die Casting or Congress. Add China and India, now?

Mind. that was right about fifty years ago, and there wasn't much mystery left in it, even then.

The guidance for use of designers WAS published, and VERY useful.

Surely it must still be around if one digs for it?

Strostkovy · Oct 13, 2020

Another name for pitch diameter is datum diameter, if that helps find data. But just going by OD will get you close enough.

L Vanice · Oct 13, 2020

thermite said:
"Back in the day" (office automation goods- paper movement, my Day Job at the time), one went to W.F. Berg or PIC design - briefly Grob spline, and the Kidder Press Division of Moore business forms - for those parts. Cast-Iron, Delrin, brass, stainless etc. pulleys were all on-offer.

Browning, Morse, T.B. Woods, Maska et al AFAIK all now b'long Gates, Emerson, or one of the other belting / power transmission "major makers"?

"Light metal" alloy Vee-belt pulleys and step-pulley cones came from Chicago Die Casting or Congress. Add China and India, now?

Mind. that was right about fifty years ago, and there wasn't much mystery left in it, even then.

The guidance for use of designers WAS published, and VERY useful.

Surely it must still be around if one digs for it?

Back in the 60's, I had a local power transmission dealer who was a Browning distributor. If I needed a top quality belt or cast iron pulley, that was my source. I was given a Browning catalog, as big as my local city phone book, and learned to use the detailed engineering information it provided. There were a few pages that told how to calculate belt drive ratios and there were many pages of stock V-belt pulleys that listed the needed dimensions. Pretty simple stuff, ratios, but still not 100% accurate because of slip and wear. Other pages told how to calculate power capacity for a drive and shaft center distance, all the stuff an engineer would need to design a drive. I still have a Browning catalog and have not designed a tricky drive for a long time, so I do not know where online to look for what used to be in that catalog.

Larry

Bill D · Oct 13, 2020

outer diameter is plenty accurate enough and the easiest to measure. I bought a cloth measuring tape at the dollar store just to measure belt length of assembled pulley sets.. Also sold for clothes making at the fabric stores.
Bil lD

Calculating gear ration for V belt?

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