Fixed Fastner Equation: Projected vs. Non-projected Tolerance Zone

[mh5096]

For years, I have always used the formula "H=F+T1+T2" for fixed fastener tolerance calculations but recently upon reviewing 14.5, I came across Appendix B section B.4 & B.5
These sections state that for a projected tolerance zone, the formula above applies but if the tolerance zone is not projected which is most cases the formula to use is "H = F + T1 + T2*(1+(2P/D))"
where:
H = MMC of hole
F = MMC of fastner
P = Maximum thickness of part width clearance hole or maximum projection of fastener, such as a stud
T1 = Diameter of tolerance zone (Clearance hole)
T2 = Diameter of tolerance zone (tapped/tight hole)
D = Minimum depth of thread or minimum thickness of part with restrained or fixed fastener.

So my question is, why do we traditionally use the projected tolerance zone equation even though a vast majority of positional tolerances are not projected? (the use of projection will vary from industry to industry but in my experience it is rarely used)

This has been bugging me for the past few days so any insight would be much appreciated!

-Matt

 

[drawoh]

mh5096,

You can work all of this out from first principals. A fixed fastener has a maximum diameter and a positional tolerance. If you add the positional tolerance to the maximum fastener diameter, you have defined your keep-out space. Your hole must not encroach on this. After that, it is all algebra and math. Try making a diagram.

The point of a projected tolerance is that a screw or pin in an accurate hole may extend some distance above the surface. This must be accounted for in your clearance analysis.

--
JHG