Position and Profile Analysis for Hole Patterns and Contours

Single-hole bonus math is the start. Real parts have patterns of holes, datum shift, composite frames and curved profiles, and a CMM report that may or may not reflect them. At the advanced level, you can look at that report and say what the drawing truly asks. You can also work out what tolerance a pair of mating parts needs, and catch a pattern that was rejected when it should have passed. Everything here is a plain-language reading of ideas in ASME Y14.5. Always check the edition the drawing names. Reminder: the frame number is a total zone width, and a position value is twice the distance from true position.

What You Will Be Able to Do

• Work a pattern position report with bonus and datum shift.
• Calculate position tolerances with the floating and fixed fastener formulas.
• Explain zero tolerance at MMC.
• Read a composite position frame, and inspect both segments.
• Apply the simultaneous requirement.
• Report profile correctly, with and without datums.

Working a Pattern Report

Worked example. A plate has four holes sized 0.250 to 0.260, with a frame of Position | Ø 0.008 (M) | A | B (M) | C. Datum B has 0.004 inch of total looseness on its boundary, so the part may shift 0.002 in any direction.

The CMM reports the following, with no shift applied.

Now find each hole's zone. Bonus is actual size minus 0.250.

It looks like two rejects. But look at the pattern: all four holes sit high in X. The drawing allows the whole pattern to shift up to 0.002, as one piece, relative to datum B. So move every hole by -0.002 in X.

The part is good. The first report rejected it because the program treated B as if it had no modifier. Note what was done. The shift moved all the holes together. It did not add 0.004 to each hole's zone, and it did not change the spacing between the holes.

A hole's own bonus applies only to that hole. Datum shift applies to the pattern. Keep them apart.

Sizing Tolerances: The Fastener Formulas

These formulas turn fit into a position tolerance. They assume both parts are at MMC, which is the worst case, and that the fastener is perfectly straight.

Here H is the hole's MMC size, F is the fastener's MMC size, and T is the position tolerance.

Floating Fastener

Both parts have clearance holes, and a bolt and nut pull them together. The fastener floats in both.

T = H - F

Worked example. Clearance holes at an MMC of 0.281 and bolts at an MMC of 0.250. T = 0.281 - 0.250 = 0.031. Each part gets a position tolerance of Ø 0.031 at MMC.

Fixed Fastener

One part has a clearance hole, and the other has a tapped hole or a press-fit pin. The fastener is held in place on one side, so only one hole's clearance is available to share.

T1 + T2 = H - F

With an equal split, T = (H - F) / 2.

Worked example. The same 0.281 hole and 0.250 bolt, with the bolt threaded into the second part. The total is 0.031, so an equal split gives Ø 0.0155 each. You can split it unevenly. Tapped holes are often harder to place, so you might give 0.018 to the tapped part and 0.013 to the clearance part. Together they must not exceed 0.031.

So going from a floating to a fixed fastener cuts the tolerance on each part in half. That is one reason to use through bolts when you can.

Why Fixed Fasteners Need a Projected Zone

The fixed fastener formula assumes the hole's axis is square to the surface. A tapped hole that leans makes the bolt lean, and the worst point is up where the bolt passes through the mating part. A zone inside the hole does not see that. So a projected tolerance zone (P) is used, with a height at least equal to the thickness of the mating part.

If a drawing shows a fixed fastener with no projected zone and tight clearance, ask about it. Parts can pass and not assemble.

Zero Tolerance at MMC

A frame can read Position | Ø 0.000 (M) | A | B | C. That is not a demand for perfect holes. It moves all the tolerance into one pool, so the shop can spend it on size or on location as the job needs.

Worked example. Compare two callouts for the same hole.

Both have the same worst-case boundary of 0.242, so both give the same assembly. But a hole at 0.246, right on location, would be rejected under the regular callout for being undersize, even though a Ø 0.242 pin fits it. The zero callout accepts it. You get more usable parts and no change in function. A shop can choose to drill larger or smaller depending on how its location runs.

It looks scary on a quote, so explain it. A hole at the low limit of 0.242 has no location tolerance, and one at 0.260 has Ø 0.018.

Composite Position

Sometimes the location of a pattern can be loose, but the holes must be tight to each other. A composite frame says this with two lines that share one position symbol.

Upper line: Position | Ø 0.030 (M) | A | B | C

Lower line: Position | Ø 0.008 (M) | A

The upper segment is the pattern-locating tolerance zone framework (PLTZF). It locates the whole pattern relative to A, B and C.

The lower segment is the feature-relating tolerance zone framework (FRTZF). It controls the holes to each other, and it controls orientation to any datums it repeats. Here it repeats A, so the holes must be square to A. It does not locate the pattern from B or C.

Worked example. All four holes sit 0.012 high in X, relative to B and C, and their spacing is perfect. Assume all are at MMC.

1. Upper check: each hole is Ø 0.024 from true position. That is under Ø 0.030, so it passes.
2. Lower check: the Ø 0.008 zones can float as a group to fit the holes, since no location datum applies. Spacing is perfect, so it passes.

The same part under a single-line Ø 0.008 frame to A, B and C would fail. The composite frame is telling you that the pattern can drift, and only the spacing needs to be tight.

Two checks, two alignments. A CMM has to do this in two steps. The lower check lets the pattern move and rotate, keeping only orientation to A. A report with one position number per hole has not checked a composite frame.

Composite Versus Two Single Frames

Two separate position symbols, stacked, read differently from a composite frame with one symbol. In two single-segment frames, the lower frame's datums control both location and orientation. So a lower frame referencing A and B ties the holes to B in location as well as orientation. In a composite frame, a lower reference to B only controls orientation. Look at how many position symbols appear. That is the key.

The Simultaneous Requirement

Two patterns measured to the same datums, in the same order, with the same modifiers, count as one pattern. That is the default rule, called the simultaneous requirement. If datum shift is involved, one single shift has to work for all those features at the same time.

Worked example. A plate has four bolt holes and two dowel holes, both to A and B (M). The bolt holes need a shift of -0.002 in X to pass, and the dowel holes need +0.001. Under the simultaneous requirement, they cannot have different shifts, so the part fails, even though each group passes alone.

If the groups do not need to relate in assembly, the drawing can release them with a note, usually SEP REQT (separate requirement). The lower segment of a composite frame is treated as separate by default, unless the drawing says otherwise. Read the frame and the notes. Do not assume.

Profile of a Surface

Profile controls a shape with a zone that follows the true shape. It can take the place of plus-or-minus dimensions on a surface, and it can control size, form, orientation and location at once, depending on the datums.

Equal Zones and How to Report Them

With no modifier, the zone is split equally. A profile of 0.010 means 0.005 each way from the true surface.

Worked example. A surface has a profile of 0.010 to A, B and C. A CMM scan gives deviations from +0.0032 to -0.0021.

The zone is fixed by the datums, and it is centered on the true shape. So the worst deviation decides it: 2 x 0.0032 = 0.0064. That is under 0.010, so the part passes. Reporting the spread of 0.0053 would understate the result.

Now say there are no datums in the frame. The zone is free to float. It only has to fit the shape, so the spread of 0.0053 is what counts. The same scan gives a different number because the drawing asks a different question. Check how your software reports this.

A related trap: a part with deviations of +0.006 and +0.002 has a spread of only 0.004, but it fails a 0.010 zone located by datums, because +0.006 sits outside the 0.005 half-zone.

Unequal Zones

The (U) modifier shifts the zone. The first number is the total width. The second is how much of it lies on the side that adds material.

Worked example. A frame reads profile 0.020 (U) 0.015. The zone is 0.020 wide. It allows 0.015 of added material, and 0.005 of removed material. A casting that must not cut below its true surface might use (U) with the second number equal to the total, which puts the whole zone on the outside.

Composite Profile

Like position, profile can have two segments under one symbol.

• The upper segment locates the surface to its datums, with a wider zone.
• The lower segment refines orientation or form with a tighter zone. It can float inside the upper zone.

So a frame of 0.040 to A, B and C, over 0.010 to A, says: the surface may sit anywhere within the wider zone, but its shape, and its tilt to A, must be held much tighter. That suits a part where location is loose and shape is critical.

Common Mistakes

Check Your Understanding

1. Two parts have clearance holes with an MMC of 0.344, and bolts have an MMC of 0.312. What is the position tolerance for each part?

Floating fastener: T = 0.344 - 0.312 = 0.032, so Ø 0.032 for each part.

2. One part is changed so that the bolt threads into it. Same numbers. What is the total, and what is an equal split?

Fixed fastener. The total is 0.032, and an equal split gives Ø 0.016 each. A projected zone is also worth asking about.

3. A designer needs bolt holes tight to each other, but the group can sit loosely on the plate. How can the drawing say that?

With a composite frame: a wide upper segment to the datums and a tight lower segment for spacing. One tight frame to all the datums would reject plates that work.

4. A located profile of 0.008 shows deviations from +0.0035 to +0.0045. What do you report?

2 x 0.0045 = 0.009, over 0.008, so it fails. The spread of 0.001 looks small, but the surface sits off center in a fixed zone.

5. A cast surface must never end up below its true shape. How can a profile callout say that?

With the (U) modifier and the second number equal to the total. That puts the whole zone on the side that adds material.

Key Takeaways

• Bonus belongs to each hole. Datum shift moves the whole pattern, and neither one changes hole spacing.
• Floating fastener: T = H - F. Fixed fastener: T1 + T2 = H - F, and think about a projected zone.
• Zero at MMC moves tolerance into size and keeps the same virtual condition.
• A composite frame needs two checks: pattern location, then feature relationship.
• Patterns to the same datums and modifiers share one shift unless the drawing separates them.
• On a located profile, double the worst deviation. On a floating profile, use the spread.