last fall I replaced the rear ax bearings on my 62 Fairlane.
The procedure is a bit simple. You will need to borrow from Autozone four tools. Two of those tools you will need a few parts of the tool to make one to install the seals. Also remove the gear oil before starting. I used a turkey baster with a rubber hose. You need to get all of the gear oil out. Bet it's black as night too. The other two tools are a ax puller, and a wheel puller. These two go together to pull out the ax's. With the wheel puller. (The thing thats on the wheel studs, you might need to file the sides that go on to the wheel studs. Todays wheel pullers, don't have the little extra wideness.
you will also need to go to NAPA for the seals. NAPA is the OLNY store that has them. Autozones are wrong, they are too small. They won't work. NAPA part number: 13875. Get the tools first before you start the job. These seals are for 8 inch or 9 inch rears I am told. Double check with your local NAPA store.
You will also need to locate a shop that can press the old bearings out and press in the new bearings. I also suggest you use TIMKIN bearings. These are the best ones and they last. You only need to do this job once, and not twice. Your store can look up the bearing numbers for you.
First, Remove drum. There are 4 bolts inside on the drum dust cover. Remove the nuts and leave the bolts in. They are special bolts with almost square heads. If you do take them out, you will see there and how they go. Not a problem. The hole in the part where the wheel nuts are, is for removal of the plate bolts. No need to remove the brake shoes or brake parts.
Second, Pull the axels, label them right-left, so you know. Then, take to your presser remove old, press new in. Then, use the autozone tools to tap in the new seals. Get the old ones out anyway you can without scuffing up the ax's edges. I used water pump pliers, and started to nibble it out until I could get a good grab. Then, tap in the new ones.
Make sure they seated correctly, all the way inside of the bearing ax hole. The bearings are close to the seal wall, but not touching the bearing. Place your finger and feel the seal against the inner loop wall. No apace inbetween, correct. Put the ax's back in, plate back, nuts back, and refill the pumpkin.
Here's two videos. These are on you tube along with the total restoration of my 62 fairlane. You can also check my car's web site. This is the page with the two bearings videos. The 1962 Antique Ford Fairlane- LogBook Page 72
This is the two videos up on you tube.
That should be enough to get you going. If it really is the bearings. But, sounds like it is. Usually you would hear whirring sound, constant. Also you can hear on the part 2 video. Before and after drives. But anyway, here's the rear ax replacement information. Hope this helps.