When the turbofan is spinning inside the housing, what holds the axis? All I know is that the axis holds the fan blades.
The longest shaft (N1, low pressure spool) is supported at each end by a frame with struts linking all engine elements (mount, core envelope and shaft).
The shaft rotates at the center of the frames, by the mean of bearings to prevent significant friction, heat and wear. Frames are known as fan frame and low pressure turbine rear frame, due to their positions.
Location of the two frames supporting the LP shaft and the associated bearings for LP and HP shafts. Source: CFM56-7B Familiarization Manual (modified)
The important point is that these two frames hook up the LP shaft to the engine mounts. The LP shaft which is usually depicted floating, as you correctly pointed out, is actually supported nearly directly by the pylon, and the rest of the engine is, for a large part, supported by the LP shaft.
CFM56 with the two frames visible (source)
Additional bearings are used between the two frames to maintain the shorter HP shaft in place around the LP shaft (as visible in the drawing above). See details in the full answer below.
As the shafts are finally attached to the mounts, where the engine is linked to the pylon, let's start with the mounts.
1. The pylon supports the engine
In a turbofan, most of the thrust being provided by the fan (bypass air), the main attachment is on the forward section of the engine. One or more additional attachment locations complete the fixing. E.g. for a CFM56:
Systems of Commercial Turbofan Engines, page 188 (source)
2. Engine core design
One of the most common engine types for airliners is composed of rotating elements spinning at two different speeds (N1 and N2). The innermost discs, spinning at the highest speed (N2), are bearing the highest pressure:
This requires two coaxial shafts. The shorter (HP) shaft makes the inner compressor and turbine discs interdependent and spins at N2, while the LP shaft links the outer compressor (including the fan) and turbine discs, and spins at N1. Let's look inside an actual two-spool engine.
3. CFM56-7B engine
- Stators vanes are inserted between rotors blades.
- Vanes and blades are mounted on discs.
- Vanes outer circumference forms a continuous envelope enclosing the volume of the core (a similar envelope is formed by the feet of the blades and vanes; air circulates between the two envelopes)
- N1 shaft is located at the center of this volume.
- N2 shaft rotates freely around N1 shaft, and is maintained concentric by bearings.
- Rotor discs are fixed to either of the shafts, according to their role.
4. Bearing locations on the CFM56-7B
Bearing 3 (dual) and 4 support the shorter and wider HP shaft. Bearing 4 supports the radial load of the HP shaft on the LP shaft (source).
The type of bearing elements is indicated. Roller bearings will only receive and counter axial efforts, while ball bearings can also counter longitudinal forces.
Struts. Lots of them, and with an aerodynamic shape so they don't cause too much drag. Some of those struts double as stator vanes and reduce the swirl of the internal flow. By doing this they add a little thrust. Others house the driveshafts by which rotational energy is taken from the shaft to spin pumps and generators.
Maybe it helps to watch this YouTube video. I pasted a screen shot from it below:
Jet engine cutaway. The bright orange shows where the structure has been cut. In the grey gaps you see plenty of vanes and struts: They hold the shaft bearings in place.
On multi-spool engines the outer spool is held in place by the struts and has internal bearings to keep the inner spool in place. Since the outer, high-pressure spool is shorter, the inner, low-pressure spool emerges from the outer spool at both ends.
This drawing from a patent shows moveable stator vanes. They are arranged like spokes on a wheel. Each disk of stators is placed between two rotor disks.
Stator vanes (26 and 28) held moveably in place by bolts (32 and 44) and interspersed with rotor vanes (24). A lever (38) on each vane is moved by an actuator ring (36) and adjusts the incidence of the stator vanes.
I'm assuming you're asking about the shaft support. In that case, the engine shaft is supported on the engine casing using bearings (the type of which may vary).
I Believe the 1st picture don't show the turbine frame, but the fan frame (By the way, i'm not sure if Turbine Frame can have use of the VBV System), after some research I believe that CF6 and CFM56 have the exact same model of Fan Frame, probably they shares some other parts too... And maybe some others GE motors get shared others same parts