- Positional Tolerances Using the Bolt and Screw Models
- Positional Tolerances from First Principles

- Calculations from ASME Y14.5M-1994 Appendix B

The GD&T positional tolerance defines a tolerance zone within which the centre of the hole must be located. The hole is located with respect to one or more datums.

In most cases, this is exactly what you want to specify, so positional tolerances ought to be the prefered method.

There are several ways to apply tolerances to holes and to their positions.

See
Figure 7
. is the positional tolerance to be called up on
the drawing for a bolted assembly. is the diametral clearance.

For a bolted assembly, the geometric tolerance is ...

(11) |

For a screwed assembly...

For a screwed assembly, the geometric tolerance is...

(12) |

Let's ignore the bolt and screw models preceding.

We want to install a fastener, and we want the clearance holes to clear it. In the following analyses, we assume that the parts are located by datums A, B and C which are external to the hole pattern.

We locate our bolt at the exact nominal position.

Located exactly at nominal position, an infinitesimally larger clearance hole will clear the bolt. As the hole gets larger, it can shift some distance off nominal and still clear the bolt, as shown in Figure 8 . Note that the geometric tolerance applies to the hole, only.

Figure 9 shows the dimension specification we want to use on each part that requires a clearance hole. The zero positional tolerance applies only at MMC, the minimum clearance diameter. In the LMC case, you have the maximum sized hole, shifted the maximum clearance off to one side. The maximum diameter allows for the off-centre error as well as the error in the hole diameter.

(13) |

The hole *must* be larger than the bolt.

For our maximum diameter, we must allow for a reasonable positional tolerance plus a reasonable tolerance on the hole diameter which would be .

(14) |

See Figure 10 . For simplicity, we assume that the positional tolerance is the same for the tapped hole and the clearance hole.

Our two parts require the dimension specifications shown in Figure 11 . The tapped hole shown is metric, with a major diameter of and a pitch which is not used on these calculations.

The screw is potentially able to occupy a space of , as shown on Figure 10 . The clearance hole must clear this.

(15) |

The positional tolerance of the tapped hole controls from the
part's surface to the bottom of the tapped hole. Your clearance
hole must clear whatever sticks *out* of the tapped hole. If your
clearance hole goes through a thick plate, you should add a projected
tolerance zone to your feature control frame, or at least, increase
a bit.

Specifying MMC on a tapped hole makes no sense to me. Tapped holes are self-centreing, so there is no bonus tolerance!

For the clearance hole, again, we add a reasonable positional tolerance , and the clearance hole tolerance to get...

(16) |

It is not necessary for the positional tolerance to be identical for the tapped hole and the clearance hole. If the tapped hole is in a machined part and the clearance is in a sheet metal part or a weldment, an accurate will allow for a sloppier . Or, vice versa!

If you are checking a drawing dimensioned like Figure 9 , you can verify that the tolerance is fabricatable.

Obviously, maximally tight values for and should not exceed the difference between and .

ASME Y14.5M-1994 proposes the fixed fastener case, equivalent to my bolts, and the floating fastener case, equivalent to my screws.

= | minimum depth of thread or minimum thickness of part with restrained or fixed fastener | |

= | maximum diameter of fastener (MMC limit) | |

= | minimum diameter of clearance hole (MMC limit) | |

= | maximum thickness of part with clearance hole, or maximum projection of fastener, such as a stud. | |

= | positional tolerance diameter |

The floating fastener case...

or...

The fixed fastener case...

or...

An interesting problem came up on Eng-Tips forums,
`http://www.eng-tips.com`. We are assembling two parts, one of
which was designed and manufactured outside. We control the dimensions
and tolerances only of the other part. The device is assembled using
screws and nuts, so the floating fastener case applies. We can modify
the equation for two sets of tolerances as follows...

The manufactured part has a clearance hole and they have specified an orthogonal tolerance of . This is equivalent to a geometric tolerance of .

Let's set , and solve for .

The calculated clearance hole is smaller than the screw!

Let's try again, setting , and solving for .

Now the result makes sense. If you provide a zero clearance hole, you may allow a 0.004" positional tolerance. This violates our standard model in which the bolt is located at the exact nominal position, but it is a perfectly functional assembly.

When you solve this problem, solve for the tolerance, not the hole diameter.