Eddy Currents in Disks: Driving and Damping Forces and Torques

When two a-c fluxes, in quadrature, pass through a disk, driving forces and torques are produced. Theory is developed herein, and formulas and procedures are presented whereby the force or torque can be solved for, even when the fluxes are irregular as to area and distribution. As an example, the driving torque of a watthour meter is solved for. A chart for greatly facilitating the work is described. When a constant flux (or fluxes) passes through a rotating disk, a damping or braking torque is produced. With the aid of what may be a new concept, theory, formulas, and procedures are presented whereby the torque may be found, even though the flux (or fluxes) has an irregular area. To illustrate, the damping torque of a watthour meter is computed. The method can deal also with fluxes of non-uniform density. A chart is described which greatly reduces the work. When a disk with constant flux through it is moved translationally, damping forces occur. Curves covering a wide range are presented, by which those designing the damping for accelerometers and other instruments may design easily in direct fashion rather than by trial-and-error. For their benefit, this part of the paper is written so that it is complete in itself. For both driving and damping torques, reciprocity laws are proved; when needed, these laws greatly reduce the time required for a solution.