Geometrical tolerances: form, orientation, location and datums
Tolerance zones, the ISO 1101 characteristics, feature control frame and datums, why position beats toleranced dimensions, the independency principle and maximum material.
Dimensional tolerances control sizes, but not shape. A shaft can have every diameter within tolerance and still be slightly bent, or oval; a hole can have the right diameter but a tilted axis. These defects call for geometrical tolerances, governed by ISO 1101 and also known by the American acronym GD&T (Geometric Dimensioning and Tolerancing).
The idea: the tolerance zone
Every geometrical tolerance defines a zone in which the real feature must lie entirely:
- for flatness, the space between two parallel planes a distance
apart; - for straightness of an axis, a cylinder of diameter ;
- for roundness, the ring between two concentric circles whose radii differ by ;
- for position of a hole, a cylinder of diameter centred on the theoretical position.
The characteristics
| Type | Characteristics | Datum |
|---|---|---|
| form | straightness, flatness, roundness, cylindricity | no |
| orientation | parallelism, perpendicularity, angularity | yes |
| location | position, coaxiality and concentricity, symmetry | yes |
| run-out | circular run-out, total run-out | yes |
| profile | profile of a line, profile of a surface | sometimes |
Form tolerances concern a feature on its own: a surface is flat or not regardless of the rest of the part. All the others concern a feature relative to another, the datum: a face is parallel *to something*, a hole is located *relative to something*.
How they are written
The tolerance is written in a feature control frame divided into boxes, linked to the feature by a leader line:
- the symbol of the characteristic (for example two parallel lines for parallelism, a circle with a cross for position);
- the tolerance value in millimetres, preceded by ⌀ if the zone is cylindrical;
- the datum letters, in order of importance.
Datums are marked on the drawing with a capital letter in a box, linked to the surface by a filled triangle. A part resting on three datums A, B, C is held as if in a vice: A is the face it sits on (three contact points), B the one it is pushed against sideways (two points), C the one that stops the last sliding (one point). This “3-2-1” scheme reproduces how the part will be held for machining and inspection.
Why position beats toleranced dimensions
Suppose a hole must be placed 30 mm from two edges, with dimensions ±0.1 mm. The zone where its centre may fall is a square of 0.2 × 0.2 mm. But what matters for fitting a screw is the distance from the correct position, in any direction: along the diagonal of the square the centre may move by 
mm, along the sides only 0.1.
With a position tolerance of ⌀0.28 relative to the datums, the 30 mm dimensions become theoretically exact dimensions (written in a box, with no tolerance) and the zone becomes a circle of diameter 0.28 mm. The circle contains the earlier square and has an area about 57% larger (
mm² against 0.04 mm²): more parts are accepted, all equally good for assembly. It is one of the reasons the automotive and aerospace industries use GD&T systematically.
The independency principle
Under ISO 8015 each dimensional or geometrical requirement applies on its own, independently of the others: the diameter of a shaft controls only local sizes, not its form. If you want the shaft to fit in any case into a hole of its maximum size, you add the symbol Ⓔ (envelope requirement): the part must not cross the perfect cylinder of maximum diameter. The American standard ASME Y14.5 instead makes the envelope the default rule. It is a detail that matters when working with suppliers from different countries.
The maximum material requirement
The symbol Ⓜ after the tolerance value indicates the maximum material requirement: the tolerance applies to the part in the worst condition for assembly (smallest hole, largest shaft) and grows as the real part moves away from that condition. A hole with position ⌀0.2 Ⓜ, if machined 0.1 mm larger than its minimum, may be displaced more, up to ⌀0.3, because the screw will still go in. It is checked with a functional gauge: a plate with fixed pins that mimics the mating part.
An example from electronics
Geometrical tolerances matter in electronic projects too. The front panel of a unit with four connectors must have its holes positioned relative to the board’s fixing holes, otherwise the connectors will not come through. A heat sink must have a base that is flat within a few hundredths of a millimetre, otherwise air pockets remain between the heat sink and the component and the thermal resistance rises. Heat sink and processor datasheets state exactly the flatness required.
