ISO 1101 coaxiality tolerance: calculation and inspection
On the design drawing of a shielded alternator rotor, the intermediate guide seat carries the geometric requirement ◎ ⌀0.04 A-B. The precision grinding setter has to make sure the axis of the ground cylinder doesn’t stray from the ideal line joining datum bearings A and B. A misalignment of a few hundredths causes destructive magnetic vibration as soon as the rotor speeds up.
The ISO 1101 coaxiality tolerance zone
An ISO 1101 coaxiality tolerance defines a cylindrical tolerance zone of diameter t whose centre line coincides exactly with the specified datum axis. The axis extracted from the inspected surface must lie entirely inside this theoretical enveloping cylinder for the part to be declared conforming.
| Characteristic | Coaxiality specification (◎) | Radial runout specification (↗) |
|---|---|---|
| Tolerance zone | Cylinder of diameter t centred on the datum axis | 2D circular zone per cross-section |
| Effect of roundness | Excluded (only the median axis is assessed) | Included (eccentricity + ovality combined) |
| Preferred measuring means | CMM, by reconstructing the axes | Dial indicator on a bench between centres |
| Geometric severity | Pure check of the relative position of the axis | Combined check of form and position |
The coaxiality symbol (two concentric circles, ◎) must not be confused with radial runout, which takes in the local form errors of the outer surface.
Establishing the datum axis and extracting the median axis
The coaxiality calculation starts by establishing, physically or digitally, the datum axis A-B. When the datum is a common datum (A-B), the mean axis is the straight line through the geometric centres of the two seats A and B.
On a coordinate measuring machine, the probe takes several series of points on cylinder A and on cylinder B, to calculate their respective mean axes by least squares.
Then the probe measures a series of circular sections along the toleranced cylinder, to extract the position of the actual centres.
The eccentricity e is the largest distance measured between the datum line A-B and the calculated centres of the toleranced cylinder.
The analysis of ISO 1101 geometric symbols gives more detail on setting up complex datums.
Converting between eccentricity and coaxiality diameter
The coaxiality value is always expressed as the diameter of a cylindrical zone, written ⌀t.
If the CMM gives the largest vector eccentricity e between the actual axis and the datum axis, the equivalent coaxiality diameter is twice that eccentricity:
t = 2 × e
If the drawing reads ◎ ⌀0.04 A-B, the largest eccentricity allowed between the axis of the seat and the datum axis A-B must not exceed:
e max = 0.04 / 2 = 0.020 mm, i.e. 20 µm
Any radial deviation above 20 microns pushes the actual axis outside the 0.04 mm cylindrical tolerance zone.
Example: assessing an alternator rotor shaft
A metrologist inspects the seat of a 35 mm diameter rotor shaft dimensioned ◎ ⌀0.04 A-B. Datum seats A and B are each 40 mm long and 250 mm apart.
The check is done on a CMM in a laboratory held at 20 °C.
- Probe datum cylinders A and B to build the centre line A-B.
- Probe three sections of the toleranced seat (left, centre, right).
- Worst eccentricity found, at the centre: e = 0.024 mm.
- Effective coaxiality diameter: t = 2 × 0.024 = 0.048 mm.
- Compare with the drawing: 0.048 mm against 0.040 mm allowed.
Verdict: the measured coaxiality (0.048 mm) exceeds the allowed limit by 0.008 mm (8 microns). The rotor is declared non-conforming and must be straightened between centres or reground.
Practical pitfalls when inspecting coaxiality
The first pitfall is measuring coaxiality with a dial indicator on V-blocks without correcting for roundness error. If the part is 0.03 mm out of round, the indicator will show a 0.03 mm variation even when the geometric axis is perfectly coaxial. Taking this direct reading for coaxiality leads to scrapping a part whose axis is in fact correct.
The second comes from datum seats A and B that are too short. If seat A is only 5 mm long, the uncertainty on the orientation of its median axis is magnified over the whole length of the part.
The third is confusing the coaxiality symbol ◎ with the position symbol ⌖. A position tolerance relative to a datum doesn’t call for the same datum frame construction, and allows the maximum material condition (MMC) modifier, which ISO 1101 rules out for pure coaxiality.
To record these axis values in your inspection grids without errors, CoteCote’s tooling extracts the geometric specifications and fills your dimensional inspection tables directly.