Interaction of multiple brushes on a slip ring

When uniform contact on a slip ring is broken into a periodic sequence of rectangular footprints, there is an increase in contact resistance, termed segmentation resistance. This approximates the condition of liquid-metal wetted brushes where uniform contact may occur over the rectangular brush footprint. It is shown that for a footprint length of 2c in the direction of sliding and center-to-center space of 2L, a Fourier series expansion shows that for c /L<0.5 the resistance increment is equivalent to an increase, δ of slip ring thickness by δ≈0.15L in the direction of current inflow. For c/L>0.5 the thickness increment drops almost linearly to δ=0 at c=L