## IMEKO Event Proceedings

Page 811 of 851 Results 8101 - 8110 of 8504

**UNCERTAINTY CALCULATIONS USING FREE CAS SOFTWARE MAXIMA**

There are many computer software packages available for the calculation of measurement uncertainties. Some are free and open source, but many are not free to use or are restricted to non-commercial use. Not in all cases, however, is it necessary or advisable to purchase and learn to use a more or less fully featured software package. Some simple calculations can be done using free spreadsheet software contained in LibreOffice or OpenOffice. Also, MS Excel is often already available on the PC.

In some other cases the calculations are not simple, especially when the partial derivatives of the model functions have to be calculated. It would then be agood idea to use a free computer algebra system (CAS). This software facilitates symbolic mathematics.

This paper shows how to use the free CAS Maxima for calculating uncertainties of the torque values realized in a torque standard machine. The tool can also be used for the independent verification of uncertainty calculation results. Some additional tools can make the use of Maxima even simpler.

**UNCERTAINTY CONTRIBUTION IN THE CASE OF COSINE FUNCTION WITH ZERO ESTIMATE – A PROPOSAL**

The model function of the torque generated in a static torque standard machine contains a cosine function for the inclination of the lever against the horizontal plane. An inclined lever has a shorter effective lever arm length, and a smaller torque is generated in this case. The uncertainty analysis of this model function gives a zero sensitivity coefficient for the inclination angle when the estimate of the angle is zero – a mathematical correct, but from the uncertainty point of view, obviously improper result. A method for dealing with this problem is proposed in this paper.

**UNCERTAINTY CONTRIBUTIONS IN SINUSOIDAL FORCE MEASUREMENT**

This paper describes one of the uncertainty contributions which can be derived from sinusoidal force measurements. These measurements are based on the application of a scanning vibrometer and the use of triaxial accelerometers. The measuring of many acceleration points on the top mass of the transducer makes it possible to obtain acceleration distributions from which a standard deviation can be derived; the triaxial accelerometer allow the observance of certain effects, like rocking modes, or other problems related to specific excitation frequencies of the force transducer. Both measurements can be related to each other.

**UNCERTAINTY CONTRIBUTIONS OF THE IMPACT FORCE MACHINE AT PTB**

This paper gives a comprehensive overview about the contributions to the measurement uncertainty of the 20 kN Impact Force Machine at PTB. Various influences resulting from interferometric velocity measurements, data analyses, mass determinations and parasitic forces are described and estimated by theoretical or experimental data if possible.

**UNCERTAINTY ESTIMATE OF COMBINATION OF VERIFIED WEIGHTS**

Weights are frequently used in combinations. In most cases it is assumed that weights of the same set have large covariances. The safest approach is to assume that the correlation coefficient is equal to one. However, this may lead to an overestimation of the combined uncertainty. A model can be constructed, based on the calibration/verification method suggested by the OIML (Organisation Internationale de Métrologie Légale), to avoid the unnecessary overestimation of the combined uncertainty. The model suggests that the uncertainty of combinations of weights with the same nominal value can be easily calculated to reduce the combined uncertainty. It also explains that magnitude of the correlation among weights with different nominal values depends on the accuracy class of the weights.

**UNCERTAINTY ESTIMATION BASED ON INVERSE MODELS: AN OPEN QUESTION**

In measurement science and its technological application most of the measurement methods are indirect. In order to measure the unknown physical quantity y we have to develop a forward model which relates this quantity to another quantity x directly measurable: x → y. Often the measurement model available is of opposite nature, i.e. y → x. It is thus necessary to invert the available model; this operation in some cases can lead to unacceptable level of uncertainty on the results. This paper shows the properties of some algorithms for processing measured data using ill posed inverse models employed for determining the distribution of indirectly measured quantities. The inversion procedure requires regularisation techniques in order to limit the uncertainty affecting the indirect measurements.

**UNCERTAINTY ESTIMATION FOR LASER TRIANGULATION HEIGHT MEASUREMENT**

According to the Guide to the Expression of Uncertainty in Measurement, measurement uncertainty in quality control is especially important, as the measured value determines either the acceptance or rejection of a product. As the coordinate measuring machines are not capable of 100% dimensional quality control, the use of optical methods is growing. The problem here is still the lack of methods for metrological verification. The available regulations and norms are not directly applicable for all optical measurement principles. One example is the laser triangulation method. It has been used in the in-process production control in height measurement (1D), profile reconstruction (2D) or complete 3D scanning for over 30 years.

This paperwork presents proposals of the procedure of measurements uncertainty evaluation for laser triangulation method. This method is designed for a semi-automatic determination of measure of the accuracy of shape reconstruction on the technical level and for a specific sensor. The process of the measurement in case of the laser triangulation method was divided into four sub-processes. The uncertainty for each of them can be estimated separately.

Thanks to the presented method, the process of the triangulation system accuracy evaluation is remarkably quicker, in comparison with the typical multiple measurement with the use of reference objects.

The correctness of the procedure was verified by the comparative research, which was based on the method of multiple height measurement of the set of block gauges.

**UNCERTAINTY ESTIMATION OF A LIQUID FLOW STANDARD SYSTEM WITH SMALL FLOW RATES**

A liquid flow standard system has been used to calibrate liquid volume of a fuel-oil flow meter at small flow rates between 50 L/h and 700 L/h. However, the system has not been used to calibrate volume flow rate because the system runs at the standing-start-and-finish mode. To calibrate the volume flow rate of the fuel-oil flow meter, a flow diverter was installed and its performance was estimated in terms of measurement uncertainty. Diversion timing errors were corrected by linear curve fitting between measured and corrected elapsed time. Uncertainty contributions of the diversion timing errors amounted more than 60 % of the total uncertainty levels. The expanded uncertainty of volume flow rate was estimated to be more than 0.55 % in (50 ~ 700) L/h (*k* = 2.26) when the collected weight of liquid was about 10 kg. The expanded uncertainty became larger as the collected liquid weight was reduced.

**UNCERTAINTY ESTIMATION OF A LIQUID FLOW STANDARD SYSTEM WITH SMALL FLOW RATES IN KRISS**

A liquid flow standard system has been used to calibrate liquid volume at a specific flow rate. However, liquid flow rate has not been considered as a calibration item due to lack of flow diversion mechanism. To enable the liquid flow rate calibration service, uncertainty due to flow diversion was estimated. Diversion timing error as well as temperature dependence on the flow rate was considered. Uncertainty contributions by the two factors were largest more than 40 % of the total uncertainty. On the while, the uncertainty contributions due to other factors were less than 5 %.

**UNCERTAINTY ESTIMATION OF LATTICE PARAMETERS MEASURED BY X-RAY DIFFRACTION**

Abstract: The uncertainties in lattice parameters determination, for X-Ray Diffractometers with Bragg- Brentano geometry, were estimated according GUM recommendations using the Monte Carlo simulation approach. The analyzed specimen was a Corundum NIST 1976 SRM Standard. Misalignment of instrument (zero 2theta offset and peak position) is an important error source, and should be kept (2θ) < 0.015° to be able to perform lattice parameters measurements with an accuracy = 0.0001 Angstrons. Sample displacement is in general the main source of error, and the above mentioned misalignment of instrument (0.015°) only becomes dominant as error source if the sample displacement is very small (<10 µm). The analysis showed that sample absorption (Corundum) is negligible as error source, if compared with sample displacement and equipment misalignment. Other possible sources of systematic error are discussed.

Page 811 of 851 Results 8101 - 8110 of 8504