I have a 2005 4.0 4WD. In 4WD low, and only in low, if I am climbing a hill, either on pavement [I tested it there] or off road, every 30 seconds or so there is a popping or clunking noise like I have driven over a rock that the tire has dislodged. It does not happen in 2WD or in 4WD high. The 4WD continues to work. There are no indicator lights at all. Not sure, but it appears to be coming from somewhere in the rear. Any suggestions? Many thanks from the Big Island of Hawaii.

 

Assuming all tires and wheels are the same, and there is not 1 or 2 tires that are "almost the same size"

If on high traction surfaces then there will be a bit of binding and releasing in 4WD, more noticeable in 4low because of the torque, on low traction surfaces you shouldn't notice it, because tires can/do slip.

If it occurs more when turning then a front CV joint could be going out.

Rear axle on 4wd rangers is often limited slip, this type of axle needs a friction modifier added to allow it to slip when it needs to and lock at other times.
If you change the oil in the rear axle then you need to add this or use an oil that has it added already.
But if this were the problem you would notice it in 2WD on dry roads when going around a corner.

 

I tested it on a slight hill on blacktop, going 10mph. It made the pop or clunk every 15 seconds or so in 4WD low, but not in 4WD high or in 2WD. It made no noise going downhill. I had the actuator replaced a month ago because the 4WD would disengage every 30 seconds or so but then reengage. That took care of that but now I have this noise that sounds like I have driven over a small rock that the tire dislodges. It happens when I'm going straight. Again, it is only in 4WD low. Any more ideas?

 

Check out the fluid in your transfercase. You'll find it along the main driveshaft with another smaller driveshaft connecting to it, which goes to the front of the vehicle. This box is the transfer case.

There will be two 3/8ths box-end plugs, which utilize the ratchet's drive to be moved. There's an upper fill plug and a lower drain plug. Undo the upper fill plug and insert a wire, like a coat hanger, 1/4 to 1/2 an inch like a dipstick. Pull it out and blot the wire on a white paper towel. Assuming you got any fluid, it ideally should be a bright pink to a dark red, but not black or brown and certainly not smelling burnt. If metallic flakes are present you've pretty much just found your problem right there.

If you're feeling apt to changing the fluid, two quarts of Mercon V ATF will suffice. There's no filter, so no filter to change.

 

This sounds very familiar. When my Ranger was fairly new a similar thing happened. I am pretty sure it happened only in 4WD low. I could test it by accelerating hard on pavement in a straight line or like you said or climbing a hill.

It was still under warranty so I took it to the dealer. They decided to replace some things in the transfer case per Ford instructions. When I got it back, I immediately tested it by accelerating on pavement in 4WD low. I got the same clunk and slight jerk.

I took it right back to the dealer and told them to save us both a lot of time and just put a new transfer case in it. They contacted Ford and got authorization to order and install a new transfer case. Once installed, the problem was gone.

Unfortunately, I don't know exactly what was wrong with the transfer case because the dealer didn't know. I was given a an explanation of probable cause by someone that knows the internal workings of that transfer case but I got lost in the details since I am not familiar with the internal working of the transfer case. So, I am not able to repeat what was said.

My guess is, you have the same problem but it is possible it could be something else.

 

over time the internal drive chain that runs from the main rear main output shaft

it powers the front axle output shaft , over time , the teeth on the driven gear wear down , causing the drive chain to slip on the teeth , this may be the popping you are hearing

the new process 231 chain driven transfer cases on the jeeps were notorius for chain popping inside the transfer case .

with rear parking brake fully engaged , transmission in 1st gear ( assuming engine is off )

try to turn the front output shaft yoke with your hand , anymore than a 1/2 inch of play is bad
( remember that the chain will have slack in it , but the chain tensioner should be working .