Howling sound from rear end while accelerating increases

It sounds like the axle bearing that was on the used axle is out. This will need to be replaced to fix the problem and you will need press to do it, here is a guide that will show you what to do after the axle is out.

https://www.2carpros.com/articles/bearing-press-how-to-use

There could also be a noisy bearing in the differential. The noise will change with the load on it meaning coasting and cruising vs. accelerating.

The other possibility is a problem with the exhaust system. The tail pipe likely got pushed around if the entire axle assembly was replaced and a pipe could be rubbing or a hanger could be making contact. Either of those will transmit that noise into the body. Exhaust hangers are always two pieces of metal separated with a piece of hard rubber. If the two metal brackets touch, you'll get a horrendous noise. That can change too when accelerating because engines rock from the increased torque, and that causes the exhaust system to shift position.

To complicate diagnosis, there won't be any load on the drive train if you run it in gear on a hoist so it might not make the noise. A tool that will help in this case is called the "Chassis Ear". You might be able to borrow or rent one from an auto parts store that borrows them. It is a set of six microphones, a switch box, and headphones. You clip the microphones to suspect points, then drive around while listening with the headphones. You can move the microphones around to zero in on the source of the noise. Be aware that many mechanics have never seen or even heard of this tool. Suspension and alignment mechanics use it to find rattles, squeaks, and other noises.

He's referring to the contact pattern. The teeth wear a pattern that matches between them. When anything happens to move a gear a little, or if the contact pattern never was adjusted perfectly, the teeth will make a slight noise when they mesh. As the gears turn, the teeth slide across each other's points of contact and that leads to the noise you can hear.

The two really large "carrier" bearings can become noisy too. Most noise occurs on acceleration. That's when the load on the gears makes it harder for the teeth to slide across each other, and it's when there's the most pressure on the carrier bearings. In some cases the noise gets worse during coasting. That's when the tires are pulling the engine instead of the other way around, and the other sides of each gear tooth makes contact.

In either case, a special yellow ink is used to observe the tooth contact area. It is applied to the sides of some of the teeth on one gear, then the drive shaft is turned while trying to hold back on the wheels. The ink will rub off where the teeth from the other gear made contact. To adjust the contact pattern the large ring gear can be adjusted left or right, or the pinion gear can be adjusted forward and rearward with shims. Changing the pinion gear is a pretty involved job, but typically if that adjustment is not right, either something is coming apart or it wasn't set up correctly before. It doesn't just change on its own without there being some other underlying problem.

If the contact pattern looks good there are other possible causes of gear noise. The most logical one is the gear lube was contaminated with water from driving through deep water. Under normal conditions the gear lube doesn't need to be changed periodically because there are no detergents or other additives that wear out like in engine oil.

Probably the most common cause of a differential failure is getting stuck, then abusing it by trying to get unstuck. If only one wheel is turning the small axle and spider gears will be turning real fast. Normally they only turn a very little when you go around a corner and one wheel turns faster than the other one. Those four little gears don't ride on bearings, just gear lube, because they don't turn much. With one wheel spinning when you're stuck, those gears can overheat and destroy the lubricating properties of the lubricant. That is something you do not want to smell! I had to work next to a fellow one time who had to rebuild an overheated differential. That smell is 100 times worse than a skunk and will clear the entire shop!

I think I'd start over with checking the previous repair. Do I understand correctly that just one axle shaft was replaced? If so, was it a used one with the bearing already on it? That might be all that's wrong is that axle bearing. Consider my suggestion about the Chassis Ear. Put one microphone right by the outer end of the housing near the wheel and listen to that bearing.

Do a search for it on Amazon. Com. I followed that suggestion a few weeks ago and found it for one third the cost of what they charge for 'em on the tool trucks. It was around 70 bucks for the version with six wired microphones. There's a newer version that has two wired microphones and four that are wireless.

I haven't worked on that many differentials but my understanding is if it was quiet at one time and the noise developed gradually, it is gear noise or noisy bearings, but not a problem with the initial setup and adjustments. Checking the tooth contact pattern with a special ink will tell if the area of contact is correct. If it's the cause of the noise, the howl is normally constant and steady, and will change with load. Bearing noise usually has more of a pulsing howl that gets louder once per wheel revolution.

If the pinion bearings are bad, (pinion gear is the one hooked to the drive shaft), there will often be leaking gear lube right behind the rear universal joint. Sometimes you can move it up and down a little too.

Replacing the gears is pretty involved. It can require the use of a case spreader tool and a shim kit. The contact pattern has to be checked, then everything is disassembled to try a different thickness shim, then it's all reassembled again, ... Many times, until it's right. Because sometimes the cause of the noise is hard to diagnose, some mechanics automatically replace the gears and all of the bearings. That gets to be very labor-intensive and costly so it's much more common to just get a used axle assembly from a salvage yard. Differential noise is not a common problem so your chances of getting a bad one from the salvage yard are small.