You should first understand some fundamental principals about push-pull
controls so that you can visualize what might be happening inside.
You should consider the outer sheath as merely a guide (or pipe) for
the inner core. The sheath is flexable (for most applications) as a convenience
for ease of installation only.
This means that, for most applications,
the sheath is not something that moves during normal operations.
The inner core is almost always a flexable wire core. When the core
is inside the sheath, its movement is constrained to just slide backward
and forward inside the sheath.
There is, also, a small amount of sideways movement possible as the
core is somewhat smaller than the ID of the sheath. This will be lost motion.
The first consideration for specification is the load that the control must overcome. The load level will
dictate the size of the movable core and it's containing sheath.
Most engine controls in single engine aircraft use a .200 diameter sheath. Connection to a turbo-charger
will usually be a .250 sheath. Twins will frequently use a .250 sheath, because of the increased length of the control.
Seat controls will probably be a 3/32 diameter sheath.
The next consideration will be sheath terminations - a simple proportionally sized stud is best here,
but we frequently see terminations with a depressed ring cut into it, to be pushed into a slot in a metal bracket.
Next consideration is the termination of the movable inner core. Usually a proportionately sized stud.
the moving stud is usually supported by a dust tube. If the core moves straight in and out, then a non-movable dust tube is used.
If the movable core (and stud) has to swing thru an arc, then a swiveling dust tube is required.
The core may have to swing thru an arc because it is attached to an arm that forms an arc as it moves back and forth (attached to a shaft).
The purpose of the dust (or support) tube is to limit the motion of the stud to moving in and out from the sheath, while also swinging thru
a small arc. In other words, it keeps the stud in line with the work it has to do.
When the stud is fully pushed outward, it is mostly outside if the
dust tube, and, since it is attached to the core, a certain amount of the
core is now outside of the sheath and is no longer supported by the sheath.
Since the ID of the dust tube is much greater than the OD of the core,
the core now has the freedom to go out of column, and, given enough compression,
even assume a cork screw shape, or, open up and become a bird cage like
structure.
This is a key to some common failure modes: the core is overloaded,
in compression, and becomes permanently deformed, and therefore, unable
to be pulled back into the sheath.
Another common failure is that the swivel joint of the dust tube fails,
the tube is now free of the sheath and no longer constrains the movement
of the stud. The stud now flops around and the core permanently bends.
Of course, there is also the failure from physical damage: the dust
tube gets bent, or crushed, and now the stud cannot slide freely inside
it. This damage you can readily see.
These same principals also apply to the other end of the control.
Lubrication: The lubrication is determined by the operating temperature and is applied to the core as it is slid into the sheath during assembly. You should not attempt to pump a grease into an assembled control: it will go into hydraulic lock. You can pump in a thin oil. Simply applying lubricant to the outside of the sheath is a very poor practice. Don't.