Which Datum Should Be Primary, and How Much Shift Is Legal?
A cast aluminum cover is bolted to a gearbox with four M8 screws through a machined flange. The drawing locates the four clearance holes with position Ø0.4 Ⓜ to A|B|C, where A is the 180 × 120 mm machined flange face, B is a Ø10.00/10.05 dowel hole, and C is a second Ø10.00/10.05 dowel hole 120 mm from B. Both B and C carry the Ⓜ modifier. The vendor's CMM aligns the part with a Gaussian best-fit plane through the flange face, then aligns rotation and translation to the two measured dowel-hole axes. Parts pass at the vendor but jam on the customer's assembly fixture, which seats the cover on a flat plate, locates on two Ø10.05 pins at basic spacing, and then drives the screws.
1. For the stated datum reference frame, state how many degrees of freedom each datum removes and how the datum A simulator should be established. Is the vendor's Gaussian best-fit plane a valid datum A?
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Degrees of freedom removed
| Datum | Feature | DOF removed | Remaining |
|---|---|---|---|
| A (primary) | flange face, plane | 3 - T_z, R_x, R_y | T_x, T_y, R_z |
| B (secondary) | dowel hole, axis normal to A | 2 - T_x, T_y | R_z |
| C (tertiary) | dowel hole, axis normal to A | 1 - R_z (clocking) | none |
The two holes work as a pair: B positions, C clocks. Because both are normal to A, they cannot remove any rotation about themselves until A has already fixed the tilt.
Datum A simulator: A must be the constrained plane contacting the high points of the flange face - the plane of the datum feature simulator that stops the part from rocking (minimum-rock condition), not an average through the surface. A face that is bowed 0.1 mm is simulated by the plane touching its three high points, and the whole part is then referenced to that plane.
The Gaussian best-fit plane is not a valid simulator. A least-squares plane splits the bow, tipping the datum reference frame by roughly half the bow relative to the true constrained contact. Every measured position then shifts, and by an amount that depends on where the bow runs - which is exactly the kind of error that produces pass/fail disagreements between a CMM and a hard fixture.
2. Explain, using datum feature shift, why the same parts pass on the vendor's CMM and jam on the customer's fixture. Quantify the shift available.
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Shift available: with B and C at Ⓜ, the datum features are simulated at their maximum material boundary - MMB for an internal feature is its MMC, Ø10.00. A dowel hole produced at Ø10.05 therefore permits 10.05 − 10.00 = 0.05 mm of diametral shift at B, and the same at C. Shift at B translates the whole pattern; shift at C rotates it about B. Both are legitimate extra tolerance granted by the drawing, because in assembly the dowels can rattle in oversize holes.
Why the vendor passes more parts:
- The Gaussian best-fit plane tilts the DRF, as discussed in the previous task.
- Aligning to the two measured hole axes at full best-fit is equivalent to giving away the entire available shift plus an unconstrained optimised rotation - a best-fit alignment always flatters the result, because it chooses the frame that minimises the reported error.
The CMM is therefore answering a different question: 'is there some legal datum reference frame in which this part conforms?' The fixture asks 'does the part assemble when the pins are at their worst-case positions?' The second question is the one the drawing is trying to control.
Implication: the fixture result is the authoritative one. The drawing calls out MMB, and a MMB gathering gauge is precisely the correct embodiment of that requirement - the CMM should be programmed to emulate it (fixed pins at Ø10.05, datum A on high points, shift consumed physically rather than by best fit) before it is used for acceptance.
3. The customer proposes removing the Ⓜ from B and C and calling them at RFS. Predict the consequences and state when that change would be correct.
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What changes: at RFS, the datum features are simulated at their actual mating envelope - no shift. The effective tolerance for the four clearance holes drops by up to 0.05 mm at B and up to 0.05 at C, so the positional requirement becomes materially tighter with no change to the printed value of 0.4.
Consequences:
- Some parts that currently assemble will be rejected. Expect the rejection rate to rise immediately after the changeover, because the process was tuned against the shift-permitted condition.
- The CMM and the fixture should now agree, since a best-fit alignment is no longer defensible as 'using the available shift'.
- If the dowels are a light clearance fit, the change is over-conservative: it assumes the part must locate perfectly on the dowels with zero clearance, which never happens at assembly.
When RFS would be correct: when the datum features genuinely engage with no clearance - an expanding mandrel, a press-fit dowel, or a taper - so that the mating simulator really is at the actual mating envelope. In that case a best-fit alignment genuinely overstates the shift and RFS is the honest call. With Ø10.00/10.05 holes on Ø10.00 dowels, MMB is the correct choice and the fix belongs in the CMM program, not on the drawing.