Pressed Pin, Bonus, and Whether a Gauge Is Even Legal
A Ø12.00/11.96 steel dowel is pressed into a plate whose mounting face is datum A. The drawing requires perpendicularity Ø0.08 Ⓜ to A on the pin. Two parts are measured: Part A, pin size 11.97 all around and straight, with its axis tilted so that it would need a Ø0.105 cylinder perpendicular to A to contain it end to end; Part B, pin size 11.96, axis running straight and square to A at its ends but bowed, with a maximum departure of 0.060 mm from the straight line joining its ends. The shop wants to accept both because 'everything is under 0.08'. A colleague proposes a Ø12.08 gauge hole in a flat plate as the acceptance tool.
1. Compute the virtual condition and the tolerance available on each part, and evaluate Part A.
Read the worked answer
Virtual condition (external feature) = MMC + geometric tolerance = 12.00 + 0.08 = Ø12.08.
Part A
- Size 11.97, so bonus = 12.00 − 11.97 = 0.03
- Total perpendicularity zone = 0.08 + 0.03 = Ø0.11
- Required zone to contain the tilted axis = Ø0.105
The zone for an orientation control is a cylinder oriented perpendicular to A; its location is not fixed by the datum reference frame, because perpendicularity controls orientation only. So the absolute position of the axis in space is irrelevant here - only how far the axis deviates from perpendicular matters, and that is exactly the 0.105 figure.
0.105 ≤ 0.11 → Part A conforms, with 0.005 mm to spare.
Note how thin the margin is: at MMC (11.98 or larger holes... i.e. a full-size 12.00 pin) the zone would be only Ø0.08 and Part A would fail. The Ⓜ modifier is the only reason this part is good, which makes it a genuine process risk, not just a paperwork pass.
2. Evaluate Part B, taking Rule #1 into account. Do perpendicularity and the envelope requirement give the same answer?
Read the worked answer
Perpendicularity check: size 11.96 gives bonus 0.04, so the zone is Ø0.12. The bow departs 0.060 from the end-to-end line, and the zone may translate and rotate about A's normal only insofar as orientation permits - a curved axis with 0.060 of bow fits inside a Ø0.12 cylinder perpendicular to A. Passes perpendicularity (and only just - a bow of exactly 0.06 against a radius of 0.06).
Envelope check (Rule #1): independent of the feature control frame, the pin's surface must not violate a perfect cylinder at MMC, Ø12.00. For a straight pin the smallest circumscribed cylinder equals the measured size; for a bowed pin it does not. The bow pushes the outer material away from the chord, so the circumscribed cylinder is approximately 11.96 + 0.060 = Ø12.02, which exceeds Ø12.00.
The two checks disagree, and that is the point of the question: Rule #1 is a size/form requirement, perpendicularity at Ⓜ is an orientation requirement. A bowed pin can be perfectly square to A at both ends and still be unusable, because it will not pass through a Ø12.00 hole. Part B is nonconforming - to Rule #1, not to the perpendicularity callout.
Part B illustrates why 'everything is under 0.08' is not a valid acceptance criterion on a drawing that also invokes the envelope requirement.
3. Would the proposed Ø12.08 gauge be a valid acceptance tool for this drawing? Justify your answer and state what you would change.
Read the worked answer
No - not for this drawing.
The gauge combines a size boundary with a fixed location (the hole sits at a definite spot in the plate, square to A). But the drawing controls orientation only. A legal part may conform to perpendicularity while sitting wherever the press operation put it: the floating zone allows the axis to be far from the gauge's centreline, so a conforming part can be rejected. Conversely the gauge does not check Rule #1 at all - Part B's Ø12.02 envelope would clear a Ø12.08 hole and be accepted, even though it violates the Ø12.00 MMC boundary.
So the proposed gauge fails in both directions: false rejects on location, false accepts on envelope.
What to do:
- If the function is 'the pin must enter a mating hole at a definite location', the drawing is wrong - it should specify position Ø0.08 Ⓜ to A|B|C, which does fix the location and makes a Ø12.08 gauge exactly correct.
- If the function is only 'the pin must be square enough', keep perpendicularity and inspect it as orientation (a CMM best-fit line, or a squareness fixture that lets the part slide), plus a separate envelope check for Rule #1 - a ring gauge at Ø12.00 or a full-form scan.
Never build a hard gauge for a control that does not locate.