Designing tolerance for the misalignment of inner and outer yoke centers in the permanent magnet for watt or joule balance

Abstract

A permanent magnet with soft magnetic yokes has been widely adopted in the watt or joule balance for precisely measuring the Planck constant. A circularly symmetric structure is conducive to the alignment of the coil but is also an enormous challenge for machining and assembly. In this paper, we mathematically prove that one of the mechanical requirements—the misalignment of the inner and outer yoke centers—can be compensated by horizontally moving the coil in a 2D magnetic plane and the compensating displacement is analytically calculated. There is a strong linear relationship between the compensating displacement and misalignment of yoke centers. The scaling factor is obtained by reasonable simplification. Then, the method for designing the tolerance for the misalignment of yoke centers is proposed. Although a new equilibrium position can be found when the inner and outer yokes are not concentrically aligned, torque is generated when the coil radially expands with heat and the torque is proportional to the increment of the radius of the coil and the misalignment of the yoke centers.