A double helical gear comprises two gears of opposite hand, fixed relative to each other, and sometimes generated from the same blank, as in the referenced photograph. Torque transmitted by the paired gears produces thrust loads that try to drive the gears axially, i.e. together or apart, but the forces are in opposing directions and the gears are fastened together or integral, so there is theoretically no net thrust load generated external to the gear itself, so the gearsets need relatively small thrust bearings. Double gears are commonly found in very high power drives where the added cost of the second gear pair is less than the cost of thrust bearings and housings strong enough to deal with the reaction forces from a single helical gear pass.
A split gear comprises two adjacent coaxial gears, both meshing with the same single (wider) mating gear. One of the split gears is free to rotate relative to the other over a limited range. Relative rotation between the gears is resisted by springs nested circumferentially within the gear pair, rather like the damping springs within a disc clutch hub. At assembly time, the gears are rotated relative to each other, compressing the springs, so that the restoring torque provided by the springs causes adjacent teeth of the split gear to close, scissor- like, on the teeth of the mating gear. Thus, imperfect gears on imperfect bearings can run at zero lash. They are typically found in mechanical computers, i.e., in instrument sizes, and with straight spur teeth, not helical. There's no reason why you couldn't make split helical gears (two of the same hand), or in really large sizes, but I've never seen a big one.
I.e., the gear is split in a plane perpendicular to the axis of rotation.
Mike Halloran
NOT speaking for
DeAngelo Marine Exhaust Inc.
Ft. Lauderdale, FL, USA