# Accuracy of measurement of mechanical quantities using the theory of fuzzy sets

## Authors

• D.A. Kataiev National Aviation University
• D.M. Kvashuk National Aviation University
• S.M. Dumbrava National Aviation University

## Keywords:

electric motor, theory of fuzzy sets, torque, coordinate measuring arm, measurement error, coordinate measurements, calculation method

## Abstract

Proposals regarding the use of the theory of fuzzy variables for measuring mechanical quantities have a perspective in the field of formalized information, when there is uncertainty, and it is quite difficult to obtain precise parameters of a measurement quantity by traditional methods due to a number of objective reasons. The article presents the results of a theoretical study of the possibilities of measuring mechanical quantities using the tools of the theory of fuzzy variables. The coordinate measuring arm (CMM) is considered as a tool for controlling the accuracy of the dimensions of parts, as well as a converter of the rotational parameters of the electric motor. Each of the methods of measuring the specified physical quantities has its own characteristics of controlling the accuracy and reliability of the obtained data. Therefore, in order to study the properties of the theory of fuzzy sets, during its application in various measuring instruments, a number of experiments were conducted on models for measuring the rotational moment and geometric characteristics of physical objects. For this purpose, the working principle of the KVR and its components is highlighted, the methods and tools used for the calibration of the KVR are described, in order to ensure its high accuracy and reliability. Methods and means of measuring torques of electric motors are presented. Modeling of the accuracy of the obtained data was carried out, using the specified measurement methods, for this a number of mathematical models were used, which take into account the error of measuring devices. A comparison of the research results characterizing the tools of the theory of fuzzy logic as a universal tool for determining the reliability of the obtained data during the measurement of mechanical quantities is given.

## References

Саункін В.Т. Дослідження похибки обробки при використанні засобів активного контролю / В.Т. Саункін, С.Г. Онищук // Вісник Тернопільського державного технічного університету. – Тернопіль: ТДТУ, 2010. – № 4 (15). – С. 85-89.

Gåsvik, K.J. Optical metrology. – John Wiley & Sons, 2023. – 392 р.

Gonella L. Proposal for a revision of the measure theory and terminology // Alta Frequenza, 1975. – Vol. XLIV. – No. 10.

Michał K. Urbański, Janusz Wa¸sowski. Fuzzy measurement theory. Measurement. – Vol. 41. – Iss. 4. – 2008. – P. 391-402.

Solopchenko G.N., Reznik L.K., Johnson W.C. Fuzzy intervals as a basis for measurement theory. NAFIPS/IFIS/NASA '94. Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference. The Industrial Fuzzy Control and Intellige, San Antonio, TX, USA, 1994. – Р. 405-406.

Murtha J. Applications of fuzzy logic in operational meteorology. Scientific Services and Professional Development Newsletter, Canadian Forces Weather Service, 1995. – Р. 42-54.

Czichos H., Saito T., Smith L.E. (Eds.). Springer handbook of metrology and testing. – Springer Science & Business Media, 2011. – 100 р.

Hansen H.N., Carneiro K., Haitjema H., De Chiffre L. Dimensional micro and nano metrology. CIRP annals. – Vol. 55. – Iss. 2. – 2006. – P. 721-743.

Bland J.M., Altman D.G. Measurement error. BMJ: British medical journal. – Vol. 312(7047). – 1996. – 1654 p.

Diaa F. ElKott. Automatic Sampling for CMM Inspection Planning of Free Form Surfaces / Diaa F. ElKott. Windsor. – Canada: Ontario, 2011. – 162 p.

EN ISO 15530-3:2011 Geometrical product specifications (GPS) – Coordinate measuring machines (CMM): Technique for determining the uncertainty of measurement – Part 3: Use of calibrated workpieces or measurement standards.

Caulfield H.J., Ludman J., Shamir J. (1999). Fuzzy Metrology. In Fuzzy Theory Systems. – 1999. – P. 747-758.

Fuller W.A. Measurement error models. – John Wiley & Sons, 2009.