Watt balance layout: mathematical modeling of vertical guides based on iris springs

Abstract

The new definition of the kilogram in the International System of Units is connected with fixing the value of Planck's constant. Practical implementation of the new definition of the kilogram is carried out by comparing mechanical and electrical powers in watt balance. One of the main components of the watt balance is a coil with a current, moving in a constant homogeneous magnetic field. The parameters of the coil movement affect the accuracy of the watt balance. The main requirements for the movement of the coil are verticality and the absence of additional movements, including rotations around the axis. In this paper, we propose the use of iris springs as a guide to ensure vertical movement of the watt balance coil. A characteristic feature of iris springs is their low longitudinal stiffness with considerable stiffness in the transverse directions. Since the iris spring has a complex geometric shape, a model approach is developed in which the real spring is replaced by a model that retains basic properties of the original iris spring. The model of the petal of the iris spring is considered in the form of a rectangular plate with the corresponding equations of thin plate theory. The forces acting on the petal of the iris spring are calculated for given deformations. In the weighing mode the spring is practically not deformed, and its action on the coil with a current is of the order of 10–6 N. The angles of rotation of the inner ring of the spring for a given set of heights are calculated. The design of the iris spring is proposed, which provides a vertical movement of the coil without rotation relative to the body of the watt balance.