Physical and mathematical model of the process of measuring torque force

The state of the reference base, designed to reproduce the unit of torque of force in the range of large values, is analyzed. An analysis of publications on reference installations has confirmed the relevance of developing and implementing high-precision reference installations that reproduce a unit of torque in the range of more than 20 kN·m. To achieve high accuracy of reproducing the unit of torque of the force, special design solutions are used in installations that exclude the infl uence of the parasitic components of the force vector and the radius vector of the shoulder on the measured (reproducible) value – the modulus of the torque vector of the force. In addition, they use expensive materials and place high demands on the precision of manufacturing parts. To successfully solve the problems of creating reference installations reproducing a unit of force torque in the range of more than 20 kN·m, a generalized physical and mathematical model of the force torque measurement process based on the classical defi nition of force torque as the vector product of the force vector and the radius vector of the shoulder has been developed in conditions of limited fi nancial possibilities. The developed generalized physical and mathematical model makes it possible to take into account the infl uence on the measurement results of the design features of measuring installations and methodological and instrumental factors related to the measurement methods of force vectors and the radius vector of the shoulder, as well as the technical means used in reproducing and transmitting the unit of torque of force in accordance with the measurement methods. A preliminary mathematical modeling of the process of reproducing the unit of torque of force has been carried out, and the infl uence of the measurement error of the radius of the shoulder vector and the accuracy of the axis of rotation on the uncertainty of the force torque measurements has been estimated. As a result, the applicability of the developed generalized physical and mathematical model of the process of measuring the torque of a force for estimating the uncertainty of measurements by the Monte Carlo method and determining the requirements for the components of the projected installation is shown. The results obtained make it possible to design installations for reproducing the unit of torque of a force in the range of large values using digital modeling.

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