For the reasons noted below; a new o-ring should make the hub cap feel tight again. And also stop any more of your grease from being spun out.
See this diagram for parts reference:
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Note that the 6 screws that go through the hub body only thread into the "hub clutch gear". The splines on the OD of the HCG are designed to be a fairly loose fit with the splines on the ID of the wheel hub.
Also, by necessity (so that the "clutch ring" can easily move in/out), the splines on the ID of the HCG are designed to have an even greater degree of clearance with the splines on the OD of the CR.
And finally, since the inner splines of the CR have to move freely in/out on the "hub shaft" splines, there is additional clearance there too.
So what you basically have is 3 nested gears loosely fitted to each other - with the hub body fastened to the outer most component. The end result is that - without the presence of the o-ring - you could wiggle the **** out of that group of gears.
The outer surface of the o-ring should be slightly raised above the OD of the hub body - where the hub body fits into the wheel hub. It is sized to fit tightly against the hub's ID. This creates a water tight seal and also reduces any play in the hub body:
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Here are some images I took when I last went through my hubs. They show a 30 spline locking hub - used with the D60 but you get the idea.
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The rest of this is mostly just my thoughts on lubricating the locking hubs. It is important to keep in mind that the only time that there is any relative motion between the 3 gears (that make up the locking hub assembly) is when the hubs are being engaged/disengaged. And that motion is limited to the distance that the clutch ring slides in/out - maybe 1/2".
The only reason for filling the hub cavity with grease is to prevent ingress of water. But for that to happen requires two things;
Loose or missing hub seals and submergence of the axles in water.
It is a good idea to stuff them pretty full if you have plans to do any serious off-roading (that involves water deeper than your axles) or if the seals are shot - up to a point.
It is not uncommon for some hubs (Warn for example) to have binding problems. This is especially true with dis-engagement. If there is excessive grease, the dis-engage spring on the inboard side of the clutch ring isn't strong enough to shift the clutch back out. This condition is made worse in the winter - when the viscosity of the grease increases due to cold temperatures.
If you do not intend to drive through streams and ponds a light coat of paste lubricant is all that is required.
Excerpted from Warn's maintenance manual:
Service Instructions
Service Kits are available. Hubs should be serviced at the same interval as the wheel bearings. Remove in reverse order of Installation Procedure(III). Then clean and lightly grease internal working surfaces. Do not pack the hubs with grease, the hubs will not function properly.
Maintenance
When new: Warn Hubs are assembled at the factory with the proper amount of grease so an additional amount is not required. When servicing:A "light coat" of molylube #1 will suffice.
(Note) Hubs should be serviced at the same manufacturers suggested intervals as the wheel bearings. I just brush on a thin coat of Permatex Nickel Anti-seize and wet that down with a good amount of WD-40. Never have a problem, the clutch ring and operating group slide smoothly - even in NH winters.