disclaimer: I will be using caps a lot here for emphasis. I am not shouting at you but there are essentials you had better not miss.
@Nesse1 I've been doing machining for a very long time, and have done some very tight tolerance work. I would approach doing this job with extreme caution... With patience, attentiveness, and good research, what you want to do might be accomplished as a first-timer, but BE VERY CAREFUL.
The downside is a new spindle from PM. Arm yourself in the worst possible case by finding out what Matt will sell you one for, considering all the circumstances. I am sure that it is in both your best interests to try to fix what you have.
Do you know of a *really good* tool and die maker that can teach you lapping? this will help a LOT.
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To answer your question: Stoning is only one early step of several.
1. As @ponitiac428 and others have mentioned, you have to 'blue in' your spindle on a known 'perfect' chuck - which is likely one you have. You may already know how, or you might get some experienced guy at work to show you. Bluing for the first time takes instruction, an no amount of text description can get you to a place where you know you are doing it well.
1a. I personally only use "Prussian Blue" for bluing in, as you can get a *really thin* coat. Some guys coat the spindle, as you can more easily apply and control the thickness of the blueing compound. What you need to know is how much contact you have on your current spindle and where that contact is.
1b. For the most accurate mitigation of you spindle, you would have to blue your chuck taper and print it onto the spindle. Then you have direct evidence of what you need to do. There is a slight possibility that your spindle taper angle is slightly wrong, and what you have to do is change the wider portion of it. WITHOUT THIS STEP, YOU ARE FLYING BLIND, AND YOU ARE DEPENDING ON GOOD LUCK FOR A GOOD RESULT.
2. From the bluing step you may find the large part of the taper is too big, the smaller part is too big, or the whole taper makes good contact, but is just plain too big. This will be used to direct the efforts in step 3. Some things to think about - you have to go super slow. Every thou you take off id diameter of the taper results in 8 thou of movement of the chuck toward the seat.
3. You have to cover your ways in from of your spindle as you can end up with abrasive and metal bits where you don;t want them. you HAVE to use a lubricant when you are stoning for best results and swarf removal. If your stone gets loaded, you have to redress your stone and/or move to a clean section.
4. I believe you stated you had some 6 thousandths gap, so you would then know you are taking less than 1 thousandths off, of average. To do this you need to get a pristine die stone in the 400 or 600 range to start. I use Geiswein stones for their consistent quality (no affiliation). You should use a wide enough stone for control and avoid 'gouging' on the edge. If you have a very light touch, you can use a 1/2" wide by 1/4" thick stone, but if you are a beginner, you should start with a 3/4 or 1" wide stone. Use a backer for the stone of a paint stick or 3/4" wood to support the stone if you are new to this. I usually use a backer and I've done this before.
4a. After stoning, you have to print the taper... again. To do this you have to clean your taper THOROUGHLY. You will be doing this a bunch of times so you will get used to it. The goal is to keep or develop good contact. - that is, a consistent blue mark over as much of the spindle as you can get. You have to aim for perfect fit, but 75% will do if it is all the way around, and touching all the way across as well.
4b. Notice we haven't addressed getting closer to the seating surface, but just dressing the taper. You have to keep altering the taper until you get that good printing surface.
4c. Now that you have good printing, you set your compound with a tenths or half tenths indicator to do extra checking. You keep stoning and checking with the indicator and the bluing until you get to...
5. Once you are getting within a couple of thousandths or less you begin to move to a finer grit - 600 to 1000, for instance. 1000 is still not a proper finish to use for mounting your chucks, so when you are getting to ALMOST contact you have to turn to lapping. Again more taper checking and bluing.
6. For a beginner I wouldn't try lapping with lapping paste. You will get better result by using a 1" wide parallel (or substitute) with 3M lapping film taped to it. You need a really good flat surface (provided by the parallel) and you can get down to insane levels with this film, and it is not too expensive. DO NOT USE EMERY cloth, even at the higher grit numbers. The grit range on standard cheap emery cloth or paper is wider than you want to get the right finish, and polishing out scratches is a thankless task that wastes hours for about 10 bucks of proper lapping film. Another thing. You always lap using a lapping surface, such as a parallel or ground flat surface. Do not 'loop' the lapping film around the taper and holdit with your fingers. You won't get an accurate flat taper, it will just look shiny. The goal here is that you want the cams to draw - with some force - the chuck to the seat. You can apply enough pressure on the cams to bring a chuck quite a ways -at least 10 or 20 thou in D1-6, so perhaps 7 or 8 thou on the d1-4?
That's it for my brain dump. For about 6 thousandths expect to do at least 8 hours of stoning and checking, and about that again in lapping. By going slow, you won't go 'to far' and make the fix even more complicated, complex and far more time consuming.