The relevant components of the measurement uncertainty are

- centring of the workpiece on the spindle of the roundness measuring machine,

- radial movement and tilt movement of the spindle of the roundness measuring machine,

- deviations of the length measuring device of the roundness measuring machine.

It is assumed that the roundness measuring machine is operated in a measurement room with air conditioning (e.g. 20°C ± 0.5 °C) and without vibration influences from the environment, all according to the specifications of the measurement equipment manufacturer/supplier, that the measurement time is 15 minutes at the maximum, that the workpiece is mounted on the roundness measuring machine without any elastic deformation, and that workpiece and roundness measuring machine are handled and operated according to the specifications of the measurement equipment manufacturer/supplier. If these assumptions are not fulfilled additional components of the measurement uncertainty have to be taken into consideration.

The angle, which defines the direction of measuring the radial deviation of the workpiece, is given by the eccentricity of the workpiece and the smallest radius of the workpiece. The direct influence of this wrong direction is only a 2^nd order effect – maximum measurement value of length measuring device times
(1 – COS(angle)) -, which can be neglected except in cases with very small workpiece radii and small tolerances.

The indirect influence of the eccentricity is the influence on the measurement value of the length measuring device, which is enlarged by twice the eccentricity. The uncertainties due to the length measuring device see below.

Generally the radial and tilt movement of the spindle of the roundness measuring machine are given as a measurement uncertainty with a coverage factor k=2. The standard uncertainty is then half the value of the measurement uncertainty.

In general the radial movement is given at the height of the table of the roundness measuring machine and the influence of the tilt movement is given by an additional value for the radial movement per 100 mm above the table.

The deviations of the length measuring device are given in general as a percentage of the measurement value. This corresponds to a range of the deviations. The distribution of the deviations within this range can be assumed to be rectangular, and with these assumptions the standard uncertainty can be calculated.

If the standard uncertainty due to the length measuring device is the largest of the standard uncertainties the measurement uncertainty can be improved by improving the centring of the workpiece on the spindle of the roundness measuring machine, i.e. by an organisational change.

Combined standard uncertainty u_c

The square root of the squared sum of the three standard uncertainty, from the centring, from the radial movement of the spindle and from the length measuring device, corresponds to the combined standard uncertainty.

Measurement uncertainty U (k=2)

The measurement uncertainty is equal to the combined standard uncertainty multiplied by the coverage factor k, which should be stated with the measurement uncertainty.

In general the coverage factor is chosen as 2, in critical cases it is 3.

Zone of conformance

If the tolerance zone for roundness is reduced by the measurement uncertainty the remaining zone is the zone of conformance. Any measurement value for roundness has to be within the zone of conformance, if conformance with the specification – with the tolerance – has to be proven.

If the measurement uncertainty is larger than the tolerance, i.e. the zone of conformance is negative, conformance with specification cannot be proven. In such cases the first step is to reduce the measurement uncertainty, e.g. by improved centring of the workpiece, by an improved length measuring device, by measuring as near as possible to the table of the roundness measuring machine, by an improved spindle of the roundness measuring machine.