Pulley calculations.... help!

[AdeV]

So, I just took delivery of a 3phase 6kva alternator head - a brushed unit unfortunately, but at less than £400, I'm not arguing. The biggest issue is it's a 3000rpm unit, and I don't have a suitable pulley. I'm trying to work out what size pulley I need to buy, to attach it to a 6-horse Lister CS.... and yes, I know that's not enough horses to run the alt flat out, but I can't see me ever needing 6kva of 3-phasedness, except maybe starting the lathe, and the flywheel momentum should take care of that.

Anyhoo... I have the heavy S-o-M flywheels on my Lister which, I believe, are 23-5/8" diameter (not sure why they didn't make 'em 24"). But that's the OD, and not the belt diameter... I've checked my Machinery's Handbook, and it seems to suggest you just multiply out the pulley ODs; but the actual working diameter is the "datum diameter" - and there's no "fixed" datum diameter for a B-section belt. Which seems a bit mad.

So... given I want to run a 23-5/8" OD flywheel at 650rpm to turn an X" OD pulley at 3000rpm.... what is X? I guess it doesn't matter if it's a tiny bit out, as I can just tweak the governer to suit, and I'm sure that running at something like 653rpm or 646rpm won't hurt the Lister...

BTW, I currently have a 10" pulley on the 1500rpm ST head, and that's too big for it - the engine is running at around 600rpm & is consequently under power...

All thoughts & solutions appreciated, ta! 

[squarebob]

Here is a pulley Calc spreadsheet that I got from another forum. Don't change the red numbers, those are the ones the spreadsheet is calculating. If you go to the Surplus Center website and look up pulleys, they list the datum diameter for both a and b belts on most of the pulleys. I would assume the datum diameter on the CS would be real close to 24" or 24.25". The spreadsheet then tells me I need a driven pulley diameter of 5.2" According to the data from surplus center, a 5.45 OD pulley has a Datum dia. of 5.1. This would mean an Engine RPM of 637.5 to reach 3000 RPM on the driven pulley. This might help get you in the range you need to be.

https://www.surpluscenter.com/item.asp?item=1-BK57-D&catname=powerTrans

[LowGear]

Interesting calculator.  A little confusing with all the inter-referencing cells but they balance out as you modify each one that is black.

Thanks.

Casey

[AdeV]

Thanks Bob, that's a mighty handy spreadsheet    I suspect shipping from Surplus Centre to the UK would be prohibitive, but we've got some pulley suppliers over here which I'll go look for.

Thanks again!

[Lloyd]

Hey guys, I posted a spread sheet in a topic here some months ago.

follow this link http://www.microcogen.info/index.php?topic=2102.msg24862#msg24862

I built the spread sheet attached, and it is a not confusing to use.

Lloyd

[AdeV]

Thanks Lloyd - I missed that one.... (maybe I should have searched first....  )

[Ronmar]

3000RPM at generator divided by 650RPM at engine is a 4.6154:1 RPM ratio.  You need to maintain this same relationship between pullies, so a 23.625" drive pully divided by 4.6154 equates to a 5.119" pully on the generator head... 5 and 1/8" rounded into practical dimensions?

I don't think your ST pully is too big, it is a little too small.  At a given engine RPM, if you decreased the generator pully size, this increases the ratio to the engine pully which increases the generator RPM.  This would require you to LOWER the engine RPM further to get the generator head back down to 1500 RPM/50HZ...  Same math applied to the 1500 RPM ST head, 1500/650 is a 2.3077:1 RPM ratio  23.625"/2.3077 = 10.2375" generator pully.  You will note that this is exactly twice the size of the one calculated above, or around 10 and 1/4"...

How did you measure 600 engine RPM with the ST attached?  IF you are running 1500RPM/50HZ at the generator head, with a 10" generator pully and a 23.625" OD flywheel, I calculate you are running at 634 engine RPM...  Jumping 1/4" in generator pully size would only get you 16 engine RPM:)

[mbryner]

Totally agree w/ Ronmar:   you don't need a spreadsheet (and what exactly is datum diameter?)   Anyway, it's just a ratio of pulleys and rpms.   Actually, it's a ratio of rpms and circumferences, but since circumference = pi * diameter, the 'pi' drops out of both sides of the equation.

If "x" is the variable, then:

x                 650
--------  =    -------
23.625         3000   

x = ( 650 / 3000 ) * 23.625

x =  5.12"

[LowGear]

Spreadsheets are the source of truth and The American Way!

Casey

[Lloyd]

Totally agree w/ Ronmar:   you don't need a spreadsheet (and what exactly is datum diameter?)   Anyway, it's just a ratio of pulleys and rpms.   Actually, it's a ratio of rpms and circumferences, but since circumference = pi * diameter, the 'pi' drops out of both sides of the equation.

If "x" is the variable, then:

x                 650
--------  =    -------
23.625         3000    

x = ( 650 / 3000 ) * 23.625

x =  5.12"

The datum center is the measure of the true diameter of the pulley in relation to the belt used. An "A belt" rides lower  in the pulley then a "B belt", which effects the real answer.

Think of my little spreadsheet as a laser focused calculator. It uses the same math eq, but you can do 10 what if scenarios, to every long hand calc. your way. The beauty of algebra, with any three known you can find the missing.

Lloyd