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Measurement uncertainty

Many factors influence the measurement result

Every measurement of sizes on workpieces such as length, angle, radius, form and position is subject to measurement uncertainty. All factors influencing the measuring process, such as machine technology, workpiece properties, geometry of the features, environment and operator, add up to the size of this uncertainty. Depending on the type of feature, the uncertainty of the measurement points has a different effect on the measurement result. For example, with the same machine technology, the radius of a sector of a circle can be measured much less accurately than that of a full circle. When measuring angles or axis directions, the length of the legs is directly included in the measurement uncertainty (Fig. 67). Other workpiece properties such as form, roughness and contamination also influence the result. In the case of multisensor coordinate measuring machines, the parameters of the sensors are particularly important for the achievable measurement uncertainty, in addition to other machine properties. Table 1 summarises, according to six important sensor types, which parameters influence the measurement error of the machine or the measurement uncertainty of the overall process.

<p>Fig. 67: Dependence of the measurement uncertainty on the geometry of the features: a) Comparison of radius and diameter measurement with circular sector and full circle, b) Angle measurement with different leg lengths, c) Position tolerance with different reference lengths</p>

Estimating measurement uncertainty theoretically

According to DIN EN ISO 15530[11], there are various methods for determining the measurement uncertainty: If only lengths are measured, it is possible to use the specified length measurement error directly for estimation. Improvements to the results, e.g. by measurement of many points and mathematical best fit, and the negative influence of the properties of the measuring object must also be taken into account. According to the "Guide to the specification of uncertainty in measurement" (GUM,[12]), the measurement uncertainty is to be determined by a mathematical superposition of the individually estimated error components as a measurement uncertainty balance (not quite aptly referred to as a measurement uncertainty budget). This has been prepared for the Department of coordinate metrology in VDI 2617 Sheet 11.

Estimating measurement uncertainty theoretically
<p>Table 1: Factors influencing measurement uncertainty: sensor properties (green), workpiece and measuring process properties (orange)</p>

Determine measurement uncertainty by simulated measurement

For tactile coordinate measuring machines, the measurement uncertainty can be estimated by mathematical simulation (virtual coordinate measuring machine). This procedure is described in DIN EN ISO 15530 Part 4 and in VDI/VDE 2617 Sheet 7. This method is not available for optical coordinate measuring machines and machines with multi-sensor systems or X-ray tomography, as error simulation is not yet mastered for these sensors.

Determining measurement uncertainty experimentally

DIN EN ISO 15530 Part 3 describes a method for determining the measurement uncertainty by measuring calibrated workpieces. This method can also be used to determine correction values (substitution method), which can be used to significantly reduce the systematic component of the measurement uncertainty. This is common, for example, when measuring gauges and shafts. This method does not take into account the influence of changing surface properties of the workpieces, such as the position of the machining marks, the colour and the degree of reflection. A test on real workpieces is the most reliable method for this. This method has often been used to estimate the overall measurement uncertainty. It is described in numerous factory standards and introduced under the term "measuring machine capability analysis". Representative measurements are used to test both the reproducibility and the traceability of the measurement on Individual calibrated parts. The reproducibility of the measurement is determined by measuring different parts of the same type (typical representatives) several times and summarising the results. In this way, environmental influences as well as influences of the measuring object itself (surface, colour) and influences by the operator (clamping and unclamping) can be examined together with the random errors of the measuring machine. However, in order to obtain a total amount for the measurement uncertainty, influencing parameters not taken into account during the test phase, such as long-term temperature fluctuations, must also be estimated. With multi-sensor coordinate measuring machines, it is also possible to replace the calibration of the parts by measuring with highly accurate sensors (e.g. with the Werth Fiber Probe®) on the same coordinate measuring machine. In this way, the sensor-specific measurement errors of e.g. optical measurements can be checked.