Mark Frazier did a nice write up of his arbor build.
Listed under moderator projects, grinding ballancer.
Thats an odd taper. Is it related to a certain manufacturers products or an industry standard for grinding arbors.
The most common spindle adapter arbors have a 3.000"/ft taper, 1" I.D. at the large (inner) end. If that does not seem correct, here is a good reference to chase the correct one down: http://www.wmsopko.com/
If one is talking 7" grinding wheels or smaller of USA manufacture, balancing is generally unnecessary. That said, Sopko does offer balancing type wheel collets for 1- 1/4" diameter bore grinding wheels, I assume for very fussy finish grinding. Some import wheels will not deliver good finishes due to out of balance issues; I have had wheels that would not give good finishes due to out of balance; the bet thing to do is simply throw them away, as much as it pained me to do so, I finally did so.
I believe I would copy the one on the grinder and add the balance weights if not there. When I made mine, I got the design from Sopko's website. They have sketches of all kinds of designs and sizes but they are very expensive to buy.They also list them by brands and show detail and some dimensions. They are not too difficult to make but take a lot of time and have tight tolerances. You also would need to make the balancing stand. The stand I made is in moderator projects forum and easy to make. There is a fairly extensive write up about making the arbor in another thread. It is aso easier to make two or three at the same time than one at a time because the setups can be time consuming. I made two arbors. It took about 30 hours, but cost me nothing as I had the steel bar stock. They were about $700 apiece to buy from Sopko's. The only thing I purchased was the washers from Sopko's for $2 apiece.
OK I've got to ask: When you mean 'arbor' do you mean (A) the wheel adapter that fits the taper on your spindle? -OR- (B) do you mean a spindle that you put the mounted wheel on, in order to balance the wheel?
If A, then it is a lot of finiky work to make a balancing adapter and weights, and the $250 is generally worth it. If you are mounting a diamond wheel then you don't need as balancing adapter, because the wheel is mostly aluminum, and rarely out of balance.
If B, I have to make one for my grinder, but it is very straightforward turning job on the lathe, with tight tolerances on the taper. Since you only ever need one, it is very worth it to make one. A couple of hours for a skilled machinist.
You can static balance on your lathe if you make the arbor long enough to rid on a pair of parallels placed on the flats of your ways.
The arbor is the piece the wheel mounts on and it goes onto the spindle. The ones I wanted were $500 to $700 apiece. They are not hard to make, but time consuming and tight tolerances. ( Took me 30 hours to make two but cost me nothing). When making them, it is best to make several so you can change wheels without needing to rebalance each time.
There is a special shaft to hold the arbor on the balancer. The balancer is very easy to make (I have a write up in two places on this forum). The shaft is the hardest part. It must be exactly the same on both sides in order to function correctly.