6.2 Circularity and Cylindricity

6.2 Circularity and Cylindricity

Quick Answer: Circularity (roundness) controls individual cross-sections of a surface; cylindricity controls the whole cylinder at once. Circularity's zone is two concentric circles per cross-section and never references a datum. Cylindricity's zone is two concentric coaxial cylinders, simultaneously controlling circularity, straightness, and taper. Both are form controls with no datum reference. Senior questions focus on what cylindricity bundles versus what circularity leaves uncontrolled, and on the trade-off against profile or runout.

Circularity — per-section roundness

Circularity (still commonly called "roundness") uses a circularity symbol and a tolerance value t. For any single cross-section perpendicular to the feature's axis (or, for a sphere, any great-circle section), the surface must lie within a zone of two concentric circles separated radially by t. The zone is located and oriented to minimize departure—it floats per section, and circularity does not reference a datum.

Critical features:

• Each cross-section is evaluated independently. A part can be a stack of perfectly round sections of different diameters and still pass circularity while failing cylindricity (taper).
• The zone may translate to the actual center of each section; it is not pinned to the drawing axis.
• Circularity does not control taper, straightness of the axis, or the size of the feature (size is governed by the ± limits and Rule #1).
• Circularity is the natural control for bearing journals, seal surfaces, and ball/spherical interfaces where local roundness governs function but taper along the length is tolerated by the assembly.

Worked example — bearing journal

A bearing journal Ø25 h6 (Ø25 +0/−0.013) carries a circularity tolerance of 0.003. At three cross-sections the roundness deviation is measured:

• Section A: 0.002 mm — conforming
• Section B: 0.004 mm — nonconforming
• Section C: 0.0015 mm — conforming

The part fails because any single nonconforming section fails the feature. The diameter at each section could be within the size limits and the part can still fail circularity; size compliance is necessary but not sufficient.

Trap: circularity vs concentricity/runout

Circularity does not locate the section's center on the datum axis. A shaft section can be perfectly round yet displaced off-axis; circularity passes, but runout or position would catch the offset. This is a common Senior distractor that confuses circularity (form) with runout (composite form + location).

Cylindricity — the whole cylinder at once

Cylindricity uses a cylindricity symbol and a tolerance value t. The entire cylindrical surface must lie within a zone of two concentric coaxial cylinders separated radially by t. The zone is free to translate and orient to minimize the separation, but the two cylinders share a common axis.

What cylindricity simultaneously controls:

• Circularity of every cross-section (because the zone bounds each section to an annular band).
• Straightness of every longitudinal surface element (the generators lie between the coaxial cylinders).
• Taper along the length (the two coaxial cylinders constrain diameter variation end-to-end).

What cylindricity does not control:

• Size — the diameter must still satisfy the ± limits and Rule #1.
• Location or orientation of the axis — the cylinder zone floats; it does not pin the axis to a datum. Runout or position controls location.
• A datum reference is not allowed on cylindricity (it is a form control); a drawing that adds datums to a cylindricity callout is incorrect.

Circularity vs cylindricity vs profile vs runout — selection table

Worked example — hydraulic ram

A hydraulic ram Ø40 f7 (Ø40 −0.025/−0.050) carries a cylindricity tolerance of 0.005. The ram is measured on a roundness/straightness/taper machine:

• Roundness (worst section): 0.003 mm
• Generator straightness (worst line): 0.006 mm
• Taper (diameter difference end-to-end): 0.002 mm

The cylindricity deviation is the smallest radial separation between two coaxial cylinders containing the whole surface. The dominant term here is generator straightness (0.006), so cylindricity is approximately 0.006 mm, exceeding 0.005. The ram is nonconforming even though circularity alone would pass. This is the Senior insight: cylindricity is not "circularity over the length"; it is the maximum of circularity, generator straightness, and taper, all bundled.

Trade-off traps

• Cylindricity is expensive to verify. Unlike circularity (which needs a turntable per section), cylindricity needs a 3-D trace or a precision V-block/center method. Senior exam questions ask about inspection cost trade-offs: if function tolerates taper, use circularity; if taper matters, cylindricity; if location matters, runout.
• Cylindricity does not control size or location. A cylindricity 0.01 ram can still be Ø40.000 when the low limit is Ø39.950; size is governed by the ± dimension and Rule #1, not by the cylindricity symbol.
• Adding a datum to cylindricity is a drawing error. If the designer wants the cylinder controlled relative to a datum axis, the correct control is total runout or profile, not cylindricity-with-datum.

Senior application takeaways

• Use circularity when local roundness governs function and taper/axis straightness are acceptable.
• Use cylindricity when the full cylinder must be round, straight, and untapered, and datum reference is not needed.
• Switch to total runout when the cylinder must also rotate true to a datum axis; switch to profile when size, form, and location all belong in one callout.
• Never let a circularity-pass result imply cylindricity-pass; cylindricity is the strict superset.