Apparatus and associated systems or methods include a linear machine with an elongate, axially-slidable core member (i.e., shaft). In one embodiment, the shaft includes at least one radial aperture to provide fluid (e.g., air) communication from an interior volume of a winding tube that contains one or more stationary windings, to either end of the shaft through a lumen that extends axially through the length of the shaft. The stationary windings are spaced apart to permit fluid to flow through a plurality of radial apertures in the winding tube. In particular, fluid circulation across the windings may provide sufficient cooling to increase the machine's maximum current rating. The fluid circulation may also provide pneumatic processing capabilities (e.g., vacuum hold, blow-off). In one exemplary embodiment, the apparatus may be used to insert tube-and-square paper separators into battery casings at high rates.