## Measuring Uncertainty

Every measurement of dimensions such as size, angle, radius, form and position on workpieces is subject to a certain measuring uncertainty. The entire measuring process including the machine technology, the attributes of the part, the geometry of the features measured, the environment and the operator all influence the magnitude of this measuring uncertainty.The geometry of the features has an especially strong influence on the results of real measurements. Thus, using identical machine technology, the radius of a sector, for example, can be measured much less accurately than that of a full circle. When measuring angles or axis directions, the length of the sides are calculated directly into the measuring uncertainty (Fig. 54).

Other part attributes such as form, roughness and contamination exert additional influence. For multisensor coordinate measuring machines, the parameters of the sensors are especially important for the attainable measuring uncertainty and must be added to the other machine attributes. Classified according to five important sensor types, Table 1 summarizes which parameters influence the measuring uncertainty of the machine and of the entire process.

Various methods can be used to determine the measuring uncertainty [6]. If only measures of length are used, the *maximum permissible error* MPE_{E} can be used for assessment purposes. However, this value does not actually constitute the uncertainty and is only used to evaluate a particular case. Improvements of results (for example, such as those achieved by measuring a large number of points or through mathematical best fit) and the negative influence of attributes of the workpiece are not taken into consideration. According to the “Guide to the Expression of Uncertainty in Measurement” (also known as the “GUM”), the measuring uncertainty should be determined by mathematically superimposing the individually evaluated error components (error budget). The procedure described below is based on this principle.

The measuring uncertainty can be assessed for a subdomain of tactile coordinate metrology by means of *mathematical simulation* (a virtual coordinate measuring machine). This process is described in the standard ISO 15530-4. This standard is not yet available for optical or multisensor coordinate measuring machines, since reliable error simulation has not yet been mastered for optical sensor systems.

The standard ISO 15530-3 contains a process for determining the measuring uncertainty by *measuring calibrated workpieces*. This technique can also be used to determine correction values (substitution method) which can be used to substantially reduce the systematic portion of the measuring uncertainty. It is commonly used in the measurement of gages and shafts, for example.

This method does not take into account the influence of changing workpiece surface attributes such as the position of ghost lines, color, and radiant reflectivity. *Testing of real parts* is still the most reliable method. This method has

often been used to assess the overall measuring uncertainty. It is described in numerous company standards and has been introduced under the term “Measurement System Capability”. Through representative measurements,

both the repeatability and the traceability of the measurement to individual externally cali- brated components are checked. The repeatability of the measurement is checked by continuously measuring different parts of the same type (representatives of a typical manufacturing process) and jointly evaluating them. Ambient influences, influences of the workpiece itself (surface, color) and influences caused by the operator (clamping and unclamping) can all be examined in conjunction with random errors caused by the measuring machine. However, in order to obtain the total measuring uncertainty, influencing parameters not taken into account during the test phase (i.e., long-term temperature fluctuations) must also be assessed.

With multisensor coordinate measuring machines, it is also possible to alternatively perform measurements with precision sensors (such as the Werth Fiber Probe) or calibrate parts on the same coordinate measuring machine. Systematic errors of dimension in optical measurements can thus be checked.