Nice catch on the 20 incher

… boy, those hinges look oogly … I am anxiously awaiting how you handle those ...
You don't really need a pulley calculator … to a first order, the speed reduction (or increase) is directly proportional to the ratio of the pulley diameters … to be more accurate (especially for small diameter pulleys) you would use the ratio of pulley pitch diameter for the belt series you are using (given in a pulley catalog) …
So in your case of a 4” dia drive pulley and a 7” dia wheel pulley, the ratio is 4”/7” which is approximately a 0.571 reduction of speed at the wheel pulley. So if your motor speed is 1725 RPM, your wheel will be running (4/7)*1725 RPM = about 985 RPM. For a more accurate value, the McMaster Catalog lists 6.75” as a pitch diameter for a 7” and 3.75” pitch diameter for a 4” diameter zinc pulley with an “A” section V-belt. In this case, you would clackalate a driven wheel speed of (3.75/6.75)*1725 = approx 958 RPM (about 30RPM or 3% error from using straight pulley diameter).
So your blade speed for the 20” Bandsaw should be 958RPM x 2*pi * radius of the 20” wheel in feet = 958*2*3.1416*10/12 = approximately 5012 fpm … whew, blade really whistling along there …
My “American Machinists Handbook” gives recommended band speeds of 1500-6000 fpm for various non-ferrous metals (like aluminum, brass, or copper) but 50 to 250 fpm for various steel alloys … the harder the steel the slower the saw speed …
So to slow down the saw to be reasonably close to the middle of the steel range, say 150fpm, the driven wheel must run at approximately 28.6 RPM or 30RPM in big round numbers. This requires a 1725/30 which is approx. 58:1 speed reduction. The highest pulley reduction in zinc “A” section drive belt pulley systems, using McM-Carr catalog, would be a 10” to a 1.5” dia system (9.75 to 1.25 inch pitch diameters respectively) which would give you a 9.75/1.25= app. 7.8 to one reduction ratio … doing this twice on a jackshaft might get you 7.8*7.8 = approximately a 60:1 reduction … which might get you in the ballpark.
This is, however, the theoretical discussion … the 1.5 inch dia pulley is awfull small, and center to center distance of the pulleys need to be considered to make sure belt life is acceptable. Also the 1.5” pulley is not offered in a keyway version, and at the 1-2 hp range, I think a keyway would be necessary. In my opinion, I wouldn't use less than a 2 or 2.5 inch dia small pulley, which would result in a 9.75/1.75 = 5.6:1 single reduction for the 2” diameter small pulley (or 31: 1 with double setup and jackshaft – this would give you about a 300 fpm band speed = a bit high, but might work anyway). The 2.5 inch diameter pulley would give a 9.75/2.25 = 4.3:1 (18.5:1 ratio with double setup and jackshaft – gives about 488 fpm band speed).
To get some realism into this, I ran out to the shop to look at my vertical woodcutting bandsaws (I've got three 14 inchers .. a 50's delta, 60's Buffalo, and a Taiwanese knock-off). All three use 1720 RPM motors with a 2.5” and 6” pulley's to reduce the speed and give a theoretical 1720*(2.25/5.75)*2*pi*(7/12) = 2467 fpm or approximately a 2500 fpm band speed …
I have three horizontal 4x6 bandsaws (50's Craftsman, two Taiwan/Chinese knock-offs) and a 7x14 Carolina (US made) … went out and looked at those … all of 'em gotta gearbox, can't tell on the Carolina, as it's buried in the back …
So I went to the DoAll Vertical Metal bandsaw site … they got a bunch of 20 Inchers … looking at a 20x12 inch vertical … it's got band speeds ranging from 30 to 5500 fpm … has a two speed gearbox with 30-320fpm low range and 550-5500fpm high range .. looks like the gearbox mechanically is shifted between ranges and has a continuous adjustment of about 10:1 within the range, probably through an electrically variable speed drive.
I ain't got a whole bunch of experience with variable speed drives yet, but I just bought one for my 3 phase 1hp J-Head Bridgeport, mainly to get into a cheap and easy to use single to three phase converter … a converter more than the variable speed capability … I don't know the useful speed range this will provide the machine … it already has a heap of pulley systems to provide speed variability in the head. I assume that it's a 3 phase induction motor. The other motors I have stashed for other projects are a pile of 1-2.25 hp servo motors with drives from treadmills, these are already single phase motors … I don't know the speed variability available through those drives as I haven't fired up any yet … just waiting their turn in the project cue …
From a practical standpoint, I've been successful in metal cutting non-ferrous stuff (as well as wood) in my verticals and soft (mild) steel in my horizontals without paying any attention to band speed in all these years … I don't know I would want to cut steel in any of my verticals … takes so long with steady pressure to cut through any significant amount of steel, I just rather have the material clamped in the horizontal with the head weight providing the constant pressure, while I do something else worthwhile in the shop …
If I was dead set on making the vertical cut steels, I would think about some combination of the treadmill motors and double pulleys with jackshafts … you might consider the cost also … 2 sets of the zinc pulleys will run about $40 a set for a total of $80 not including the belts, shaft and bearings for the jackshafts … steel pulleys will run whole heaps more … but I think that you can get away with zinc at about 1 hp … if you don't abuse it … I'd also pay attention to the guy down under who has had the experience of smoking a motor by running it at too low a frequency … personally, I don't smoke anything other than salmon or beef or elk jerky ...
The 2012VH DoAll with Hydraulic table (to give a constant feed pressure/feed rate) appeared to be at about $26K new by comparison … whew … don't have enough biz to support that cost ...
Good luck on the project ...
