Flatness, Parallelism, and a Rocking Plate
A 300 × 200 × 12 mm ground steel plate has its top face controlled by flatness 0.02 plus parallelism 0.05 to datum A, the bottom face. The grinder produces parts that pass at the CMM: flatness 0.018, parallelism 0.041. At incoming inspection a technician sets each plate on three adjustable jacks, zeroes a dial indicator on the highest point, sweeps the surface, and reads 0.06 mm total indicator movement on several parts. He records 'flatness 0.06' and rejects the lot. The same plate also carries a 40 ±0.10 mm slot whose width is controlled by flatness 0.03 applied to the width feature.
1. Is the flatness 0.02 redundant given the parallelism 0.05? Answer by describing the shape of the two tolerance zones.
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Not redundant - it is a refinement.
- Parallelism 0.05 to A: the top surface must lie between two parallel planes 0.05 apart that are oriented parallel to datum A. Inside that zone the surface may still be dished, bowed or twisted by as much as 0.05, because parallelism constrains orientation and only secondarily limits form by the width of the zone.
- Flatness 0.02: the top surface must lie between two parallel planes 0.02 apart, with no datum and no orientation constraint. The planes may be tilted to any attitude; only the separation matters.
So a plate bowed 0.045 but sitting flat relative to A passes parallelism and fails flatness. The flatness callout tightens the form requirement from 0.05 to 0.02 - it is doing real work.
Consistency check: a refinement must be tighter than the control it refines, i.e. 0.02 < 0.05. If the drawing had flatness 0.08 with parallelism 0.05, the flatness would be unachievable as a refinement and should be flagged: no surface can have 0.08 of form error and still fit inside a 0.05 wide oriented zone.
2. Explain the technician's 0.06 reading and state the correct evaluation procedure. Does his result prove the parts are nonconforming?
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What he measured: setting the plate on three jacks establishes a plane through three support points. Sweeping the surface and taking total indicator movement gives the separation of two planes parallel to that arbitrary jack plane that enclose all points. That quantity includes both the form error and the tilt of the surface relative to the jack plane, so it is always ≥ the true minimum-zone flatness, and the gap grows as the part is more dished or warped relative to the chosen three points.
Correct definition: flatness is the separation of the two closest parallel planes that enclose the entire surface - the minimum zone, evaluated with no datum, no fixturing and no preset orientation. It is a property of the surface alone.
Does 0.06 prove nonconformance? No. It proves only that the surface does not fit in 0.02 of a particular orientation. If the CMM's minimum-zone evaluation gives 0.018, the part conforms, and the CMM value is the one the drawing describes.
How to confirm without a CMM: repeat the sweep from several random three-point attitudes and take the minimum reading, or use a lapping plate / optical flat and count fringes. If the minimum over many attitudes still exceeds the tolerance, the part is genuinely out. Any inspection method that fixes an arbitrary plane first is measuring the wrong thing.
3. The slot width is 40 ±0.10 and carries flatness 0.03. What does that control, and how does it interact with Rule #1?
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What it controls: applied to a feature of size, flatness does not act on the two surfaces independently - it controls the derived median plane of the width. The median plane must lie within two parallel planes 0.03 apart. Practically, it limits bowing or warping of the slot: the two walls may each be out of flat, but their mid-surface must stay within 0.03.
Interaction with Rule #1: the envelope requirement applies independently and separately. For this internal feature, no point of either wall may intrude inside a perfect 39.90 wide boundary (MMC). That is a surface requirement enforced by the actual mating envelope.
Why both are needed:
- Rule #1 only guarantees perfect form at MMC. As the slot opens toward LMC (40.10), the walls may become progressively more bowed with no violation - the envelope has grown to 40.10 and the surfaces still fit inside it.
- The median-plane flatness is what keeps the slot straight in a functional sense at every size, e.g. so a mating tongue does not bind.
The two are checked differently: Rule #1 by the actual mating envelope (a gauge or an envelope calculation), median-plane flatness by deriving the mid-surface from opposed-point measurements. A part can satisfy one and violate the other, which is why the drawing needs both numbers.