Unequally Disposed Profile (Ⓤ)

The Ⓤ modifier that shifts a profile zone off-center — more of the tolerance on one side of the true profile than the other.

Definition

By default, a profile tolerance zone is bisected by the true profile: half the tolerance outside the material, half inside — an equal bilateral zone. The Ⓤ modifier (unequally disposed profile) shifts that split. It is written directly after the profile tolerance value as t Ⓤ u, where u is the amount of the total tolerance t that lies OUTSIDE the material; the remainder, t − u, lies inside. The zone width never changes — only its position relative to the true profile does. 0.2 Ⓤ 0.05 is a 0.2-wide zone with 0.05 outside and 0.15 inside.

The two limiting cases: unilateral zones

Set u equal to t and the entire zone lies outside the material — unilateral outside. Set u to zero and the entire zone lies inside — unilateral inside. Both appear constantly on castings and forgings: a casting's profile callout placed fully outside guarantees machining stock on every surface, because the as-cast surface may only err in the direction that leaves material for the finish pass. Without Ⓤ the same callout would let the casting run thin, scrapping the part at machining.

Why shift the zone?

• Machining stock on castings and forgings — the whole zone goes outside so every part carries material to clean up
• Coating and plating allowance — keep most of the zone on the side the coating will occupy, so the post-plate surface lands in tolerance
• Edge and wall protection — concentrate the tolerance away from the thin wall or sharp edge that actually matters
• Functional offset — the mating condition genuinely sits closer to one side of the nominal surface than the other

Reading a feature control frame

⌓ 0.4 Ⓤ 0.3 A B reads as: profile of a surface, total zone 0.4 wide, unequally disposed with 0.3 outside the material (0.1 inside), referenced to datums A and B. The Ⓤ and its value live in the tolerance compartment, immediately after the total value — exactly the slot Ⓜ, Ⓛ and Ⓟ occupy on other controls. The value after Ⓤ is always the OUTSIDE portion; writing the inside portion there is the classic misread, and it produces a mirrored zone.

ISO difference

ISO 1101 writes the same intent differently: the UZ modifier followed by a signed offset of the zone CENTER — 0.4 UZ +0.1 puts the zone's midplane 0.1 outside the true profile, which equals 0.4 Ⓤ 0.3 under ASME. The offset direction and the reference point both differ (ASME counts from the outside surface inward; ISO locates the center), so converting between the systems is arithmetic worth double-checking, not a symbol swap.

Measurement

CMM / scanning — best-fit or datum-aligned against the true profile, then report each point's deviation with its sign; the outside-direction deviations must stay within u, the inside-direction deviations within t − u. The only change from an ordinary profile evaluation is that the acceptance band is no longer symmetric.

Optical comparator — overlay the shifted tolerance band, not the symmetric one: the band's centerline sits u − t/2 from the true profile on the drawing's overlay, so off-the-shelf equal-band templates misjudge parts near the limits.