The dust cover with a grease fitting in it, also known as a Bearing Buddy, where made for boat trailers to help purge the cavity between the bearings with grease to help keep the water out.
They should not be used on a TT. They have newer axles called EZ Lube where there is a grease fitting in the end of the axle and a long hole drilled down the center of the axle where the grease comes up behind the inner bearing and then works its way back toward the end of the axle to vent out. Those setups where made to be able to grease this way.
With the bearing buddy or they dust cap you are referring to there is no internal grease relief. When you pump the grease in it forces it way towards the inner bearing. As you keep pumping the grease pressure has to escape. It does this by blowing past the inner seal and up onto the electric brakes. Then you have a mess and the brakes do not do much. After enough grease gets embedded in the linings there is no cleaning it out and new shoes will be needed.
If your axles are not made with the EZ lube feature, odds are high they are not, then the your only option is to hand pack.
Hope this helps
Current Sunlines: 2004 T310SR, 2004 T1950, 2004 T2475, 2007 T2499, 2004 T317SR
Prior Sunlines: 2004 T2499 - Fern Blue
2005 Ford F350 Lariat, 6.8L V10 W/ 4.10 rear axle, CC, Short Bed, SRW. Reese HP trunnion bar hitch W/ HP DC
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