I have been told that a diamond knurl does NOT need the "right" size.
Yep, you're right--size doesn't matter but the TPI does. It WOULD be the same for straight knurls too. It's like matching gears.
If the TPI doesn't fall close to a factor of the stock circumference, the knurl will start to over or under track. The teeth will start to slide into the previous track and cause chips. Makes for an ugly knurl too. Adding oil will just make it slide easier.
Divide the circumference by the reciprical of the TPI (Pitch). This gives you the Pitch applied to the stock. If there's more than about .2 (off zero) in the decimal, you'll get a messy knurl. If the division results in no remainder (.0), you'll get a perfect match.
Cir
------ = Stock Pitch
Pitch
Knurl---TPI----Pitch
Fine----33----0.03030
Medium--21----0.04762
Course--14----0.07143
USING 1 1/2" STOCK--
Fine Example:
1.5 x Pi
-------- = 155.5 (Not a good match- ".5")
0.03030
Medium Example:
1.5 x Pi
-------- = 99.0 (Perfect match ".0")
0.04762
Course Example:
1.5 x Pi
-------- = 66.0 (Perfect match ".0")
0.07143
So for 1.5" stock, a Medium (21tpi) or Course (14tpi) knurl would give the best results. A Fine (33tpi) would cause the pitch to HALF-TRACK (.5) on the stock. (Really ugly knurl)
The same applies to straight knurls.
Forgot to add:
If you want to use a specific TPI knurl (Fine, Medium, Course), then you need to adjust the diameter of your stock for the best fit. Therefor; to use a FINE TPI knurl on 1 1/2" stock, you'd have to turn the stock down to 1.496 or 1.494. This would give you a stock pitch of 155.1 and 154.9 respectively. This falls within the .2 off zero.