Оцінювання стандартної непевності типу “В” на основі складових адитивної та мультиплікативної похибок

Abstract

Запропоновано спосіб перерахунку адитивної та мультиплікативної складових похибок, аналітичні вирази яких отримуються розкладанням відповідного рівняння перетворення у ряд Тейлора, в стандартну непевність типу В. Цей спосіб апробовано під час оцінювання статичних характеристик засобу вимірювання кутової швидкості. Він дає змогу представляти характеристики точності засобів вимірювань відповідно до вимог міжнародних стандартів з оцінювання якості вимірювань. Предложен способ пересчета аддитивной и мультипликативной составляющих погрешностей, аналитические выражения которых получают путем разложения соответствующего уравнения преобразования в ряд Тейлора, в стандартную неопределенность типа В. Этот способ апробирован при оценке статических характеристик средства измерения угловой скорости. Он позволяет представлять характеристики точности средств измерений в соответствии с требованиями международных стандартов по оценке качества измерений. A method for conversion additive and multiplicative constituents of errors, analytical expressions are obtained by decomposition of the corresponding transformation equations in Taylor series in a standard uncertainty of type B. Decomposition of transformation equations used means of measuring in the Taylor series allows to obtain analytical expressions of basic static characteristics of the means of measuring on the basis of which it is possible to explore the characteristics of changes in the sensitivity of means of measuring, the nominal conversion function, influencing coefficients, additive and multiplicative errors in a deviation of influencing parameters on their nominal values. This method has been tested in the evaluation of static characteristics of measuring angular velocity. It allows you to represent the characteristics of precision of means of measurements in accordance with the requirements of international standards to assess the quality of measurements. These mathematical expressions allow investigation of basic metrological characteristics of a measuring angular velocity, and the causes and conditions that lead to increased measurement errors in the angular velocity of electric motors to be identified. To represent standard uncertainty of type B, which is caused by the presence of additive and multiplicative errors in the measurement means, mathematical expressions are proposed that allow recalculation of these errors to standard uncertainty. The mathematical expressions were tested using the example of the recalculation of additive and multiplicative errors of the measurement means of the torque in the standard uncertainty of type B. The resulting mathematical tools and characteristics of change of the basic static metrological measuring means for angular velocity give us the opportunity to identify the causes of increase in error in the measurement of angular velocity in electric motors. This enables us to explore how to diminish or eliminate them, and also to synthesise measuring means angular velocity with standardised metrological characteristics. To convert received instrumental error components measuring angular velocity in a standard uncertainty of type B and presentation characteristics of precision measuring instruments in accordance with the requirements of international standards to assess the quality of measurements suggested model equations given in the article. On the basis of the proposed model equations executed counts additive and multiplicative error components measuring the angular speed of the combined standard uncertainty of type B, which is caused by the presence of the instrumental components of errors in deviation vlyayuschih magnitude of its nominal value. The studies found that the type B standard uncertainty is 3.38 rad/s in the range of conversion from 0 to 100 rad/s rejecting influence quantity β from its nominal value of 0.01 radians.