Final answer:
The welding method that involves a solid-state process, uses no filler, suitable for both aluminum and titanium, and can be performed on CNC machines for smaller welds is Friction Stir Welding (FSW).
Step-by-step explanation:
The welding method being described is Friction Stir Welding (FSW). This innovative welding process was primarily developed for welding aluminum, including long continuous welds in aluminum extrusion, and is also commonly used for welding titanium. In Friction Stir Welding, a non-consumable tool is rotated and slowly plunged into the joint, which heats the metal by friction and plastic deformation, rather than by melting. This solid-state process creates a weld between the pieces of metal without the need for a filler material. Friction Stir Welding is capable of creating small detailed welds with CNC machinery, yet larger welds require dedicated, specialized equipment.