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<p>We analyze the state of the reference base aimed at reproducing the unit of torque force within the range of its high values. The analysis of available publications dealing with reference installations confirms the urgency of development and implementation of high-precision reference installations reproducing the unit of torque within the range greater than 20 kN&#xa0;⋅ m. To guarantee high accuracy of reproducing the unit of torque, special design solutions are used for the installations in order to exclude the influence of parasitic components of the force vector and the radius vector of the arm on the measured (reproduced) value, i.e., the modulus of the torque vector. Note that these solutions are connected with the use of costly materials and impose high demands on the precision of manufacturing the required parts. To successfully solve the problems of creating reference installations capable of reproducing the unit of torque force for the torques higher than 20 kN&#xa0;⋅ m under the conditions of restricted financial possibilities, we developed a&#xa0;generalized physical and mathematical model of the process of measuring torque forces based on the classical definition of torque as the vector product of the force vector by the radius vector of the arm. The developed generalized physical and mathematical model makes it possible to take into account the influence of the specific features of measuring installations and various methodological and instrumental factors related to the procedures of measuring force vectors and the radius vector of the arm, as well as the technical means used to reproduce and transfer the unit of torque force (according to the applied measurement methods), on the measurement data. A&#xa0;preliminary mathematical modeling of the process of reproducing the unit of torque force has been carried out and the influence of the measurement error of the arm radius vector and the accuracy of location of the axis of rotation on the uncertainty of measuring the torque force has been estimated. As a&#xa0;result, the applicability of the developed generalized physical and mathematical model of the process of measuring of torque forces aimed at estimating the uncertainty of measurements by the Monte Carlo method and specifying the requirements to the components of the designed installation is demonstrated. The accumulated results make it possible to create installations intended for reproducing the unit of torque force within the range of its large values with the help of numerical modeling.</p>

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Physical and mathematical model of the process of measuring torque force

  • 期刊论文

  • 发表日期：

    2026年5月6日

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  • V. A. Ivanchura,
  • S. V. Medvedevskikh,
  • V. Sh. Sulaberidze

摘要

We analyze the state of the reference base aimed at reproducing the unit of torque force within the range of its high values. The analysis of available publications dealing with reference installations confirms the urgency of development and implementation of high-precision reference installations reproducing the unit of torque within the range greater than 20 kN ⋅ m. To guarantee high accuracy of reproducing the unit of torque, special design solutions are used for the installations in order to exclude the influence of parasitic components of the force vector and the radius vector of the arm on the measured (reproduced) value, i.e., the modulus of the torque vector. Note that these solutions are connected with the use of costly materials and impose high demands on the precision of manufacturing the required parts. To successfully solve the problems of creating reference installations capable of reproducing the unit of torque force for the torques higher than 20 kN ⋅ m under the conditions of restricted financial possibilities, we developed a generalized physical and mathematical model of the process of measuring torque forces based on the classical definition of torque as the vector product of the force vector by the radius vector of the arm. The developed generalized physical and mathematical model makes it possible to take into account the influence of the specific features of measuring installations and various methodological and instrumental factors related to the procedures of measuring force vectors and the radius vector of the arm, as well as the technical means used to reproduce and transfer the unit of torque force (according to the applied measurement methods), on the measurement data. A preliminary mathematical modeling of the process of reproducing the unit of torque force has been carried out and the influence of the measurement error of the arm radius vector and the accuracy of location of the axis of rotation on the uncertainty of measuring the torque force has been estimated. As a result, the applicability of the developed generalized physical and mathematical model of the process of measuring of torque forces aimed at estimating the uncertainty of measurements by the Monte Carlo method and specifying the requirements to the components of the designed installation is demonstrated. The accumulated results make it possible to create installations intended for reproducing the unit of torque force within the range of its large values with the help of numerical modeling.