Correct Geometry Of 4 Jaw Chuck Jaw

With my Phase II 4 jaw, no two jaws were the same. Some had more taper than the others. The idea of starting off with a slight taper makes sense but it bothered me that no two jaws were ground the same. So I ground them more uniform on the lathe and removed the taper.
The radius of the curvature on the jaw pads was determined by how far apart the jaws were when grinding but had to be smaller than the through hole as you mentioned.
 
With my Phase II 4 jaw, no two jaws were the same. Some had more taper than the others. The idea of starting off with a slight taper makes sense but it bothered me that no two jaws were ground the same. So I ground them more uniform on the lathe and removed the taper.
The radius of the curvature on the jaw pads was determined by how far apart the jaws were when grinding but had to be smaller than the through hole as you mentioned.
With the Grizzly 4 jaw chuck, replacement jaws are available. They are also not numbered or uniquely identified in any way. The gripping surface is ground curved with a radius of about 1.1" while the through hole in my chuck has a diameter of about 1.5" or a .75" radius. This indicates to me that the jaws are ground remotely from the chuck.

My intention is to regrind them as you have done. I have designed a plate to properly load the jaws to stabilize them and to provide a bias in them same direction as the jaws see in use. I also designed a mounting adapter for my 1/4" die grinder so I can mount the grinder in my QCTP. I can then grind a cylindrical surface or, if I wish, use the compound to grind a very slight taper.
 
RJ Interesting topic.
While I don't know the correct taper I might have an idea on how to find it.
About 20 years ago I was building a heated press for veneering cigar humidors, I had a 30 ton hydraulic press and made a 12" x 10" platen made out of a sheet heating element sandwiched between two pieces of 1" aluminum plate. Between the press ram and the platen was a 12" x 10" x .75" steel plate with a 6" x 2" d. steel bar welded to the center and 8 @ .25" steel plate gussets welded to the bar, running to the corners and centers of the bottom plate. I was having a lot of trouble getting even pressure over the entire surface, the special polyester sheet adhesive required a minimum 120 psi over the entire surface to bond correctly (I was shooting for 150). Then McMaster Carr to the rescue, they have a pressure sensitive film that shows the distribution of pressure. It worked very well, the first test clearly revealed the pattern of the gussets and bar in the center, it was almost unbelievable how much deflection telegraphed through all that metal. With the aid of the film I was able to redesign the whole contraption to give fairly even pressure over the entire surface.
I think you could use thin strips of this film between the chuck jaws and test bar to read the pressure distribution and grind the taper of the jaws till its even...
 
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I think you could use thin strips of this film between the chuck jaws and test bar to read the pressure distribution and grind the taper of the jaws till its even...
I think I'd grind for light pressure in the back to allow for future wear.

You might be able to approximate this with bluing.
 
RJ Interesting topic.
......
........Then McMaster Carr to the rescue, they have a pressure sensitive film that shows the distribution of pressure. It worked very well, the first test clearly revealed the pattern of the gussets and bar in the center, it was almost unlovable how much deflection telegraphed through all that metal. With the aid of the film I was able to redesign the whole contraption to give fairly even pressure over the entire surface.
I think you could use thin strips of this film between the chuck jaws and test bar to read the pressure distribution and grind the taper of the jaws till its even...
There is a product called Plastigage which will measure clearances . It is used extensively by engine rebuilders. It is a small diameter plastic rod which, when placed in a bearing journal, will deform to a flattened shape. The width of the flat is compared to a calibration chart to determine the bearing clearance. It comes in three different sizes to cover the range from .001" - .009".
 
An update:

I mounted my 4 jaw on the lathe and checked the face for runout and it was about a thousandth over 6". I then mounted a 1" dia. bar in the chuck and adjusted for less than a half thousandth runout at the jaws and tightened. Going out 9" from the chuck, I could move the bar to any number of "stable" positions within a 10 thousandths diameter circle.

This convinced me that I need to grind those jaws if I want to use the chuck for any serious work. One of the comments that was made to the post on HM was that a cylindrical grind would eventually go bell mouthed on you, requiring a regrind to correct. From what I have seen, this would likely be decades of use for me though so I'll most likely go with the straight cylindrical grind.
 
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