There seems to be something off with the formulas, though. Try plugging in my measurements into the formula:
Stock pulley diameter ~ 9.65mm
GT subplatter diameter ~ 101.18mm
US motor speed = 300rpm
US gearing ratio = 9
Using the above formulas, the actual pulley diameter of 9.65mm should require a (calculated) subplatter diameter of 86.85, which is significantly smaller than the actual subplatter diameter.
Or conversely, if plugging in the subplatter diameter and gearing ratio, the pulley diameter should be 11.24mm. But I know that the Michael Lim double pulley diameter is about 0.3mm larger than the stock, and the table runs much faster with a larger pulley diameter. Unless we are talking about an 11.24mm effective diameter.
And in my sh*ts and giggles experiment, increasing the subplatter diameter by 2mm brought the table to within 0.3% of 33.33 rpm.
watercourse. After Paul's point and with reference to Frank's latest post about how he comes to a correct pulley size, I now know that although the basic formulae are correct, there is one thing that cannot be done easily – and that is to determine the effective diameter of the pulley by measurement.
The pitch diameter of a pulley is not the outside diameter. Or the inside diameter. In fact, the pitch diameter is very difficult to measure directly.
from The Gizmologist's Lair
Having read around the subject a little (wiki and elsewhere) it seems that the point of highest tension in a belt is where the effective diameter would be measured, at least in theory. It appears that you cannot work backwards from an actual pulley/belt system to the real measurements. It's been just as hard for me to find out what the effective diameter of the sub-platter is once a round section belt is looped around it -it may be larger than it's nominal measurement and we can guess that that might be by the diameter of the belt (in motion, under tension).
So, long story short, it appears that without a more complete understanding of the subject, we can only use these measurements and formulae to aid thought experiments and get a general understanding of the problems of designing and using belt drives and hence how difficult is must be to get a perfect speed with any
belt driven system. And that goes for a Linn or a Rega!
With regards your figures, I think this:
Your target pulley size is 11.24mm. (As you are using a 101mm subplatter.) And that is, ignoring stated problems about arriving at a true effective diamter of the subplatter, pretty much a fact.
Your stock pulley is ~ 9.65mm. I assume that this is the interior estimate diameter measured at the apex of the 'V'.
Now, looking at my drawing I could make a sensible guess that the effective diameter is in the order of pulley diameter measurement at interior of V groove + 2 x radius of the belt (or 1 x diameter)
In your case that would be 9.65 + 1.78 = 11.43mm which in a thought experiment is not too far off what you need. Of course, it ignores the true point of the belt's highest tension, the belt's true thickness under tension and also the true effective diameter of the sub-platter + belt.
Of course, it's not much use in the practical world. In practice the whole equation of platter speed is made more complicated by differences in manufacturer's pulleys and sub-platters and combinations of them. It's remarkable that any Rega or any belt driven turntable runs at 100% correct speed. I'm just happy that mine runs at a pretty good constant speed.