Martin Halaj

Application of Monte Carlo Method for Evaluation of Uncertainties of ITS-90 by Standard Platinum Resistance Thermometer

Abstract Evaluation of uncertainties of the temperature measurement by standard platinum resistance thermometer calibrated at the defining fixed points according to ITS-90 is a problem that can be solved in different ways. The paper presents a procedure based on the propagation of distributions using the Monte Carlo method. The procedure employs generation of pseudo-random numbers for the input variables of resistances at the defining fixed points, supposing the multivariate Gaussian distribution for input quantities. This allows taking into account the correlations among resistances at the defining fixed points. Assumption of Gaussian probability density function is acceptable, with respect to the several sources of uncertainties of resistances. In the case of uncorrelated resistances at the defining fixed points, the method is applicable to any probability density function. Validation of the law of propagation of uncertainty using the Monte Carlo method is presented on the example of specific data for 25 Ω standard platinum resistance thermometer in the temperature range from 0 to 660 °C. Using this example, we demonstrate suitability of the method by validation of its results.

Theoretical Positioning Accuracy for Serial and Parallel Kinematic Structure

Abstract Modern production machines employ complex kinematic structures that shall enhance their performance. As those machines are very sophisticated electro-mechanical structures, their design is time consuming and financially demanding. Therefore, designers search for new possibilities how to estimate future properties of the machine as early as in the design phase. The paper gives a brief introduction to the adoption of methodology of measurement uncertainties into the design of production machines. The adapted methodology enables to estimate the theoretical positioning accuracy of the machine end effector that is one of the important indicators of machine performance. Both serial and parallel kinematic structures are considered in the paper. Methodology and sample calculations of theoretical positioning accuracy are presented for serial kinematic structure (represented by advanced plasma cutting head) and parallel kinematic structure, represented by one specific design named Tricept.