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I have a harmonic vibration that comes and goes like every 3 seconds and you can fill it from 55 and faster. I replace all 4 wheel bearing and it still does it. I also put new wheels and tires and rebalanced then a few times and still have this issue. Ive got the car up to 75 to 80 put in neutral and still have vibration and even turn car off so shaft in tunnel tube would stop and still have vibration.
Could this problem be in the rear end. Ive serviced rear end two times less than 2000 mile apart just to make sure.
2001 auto 315 gears
My car does the exact same thing. I think it's the tie rods in my case because I've noticed that inducing even the slightest steering load (slowly changing lanes for example) makes this "shudder" go away.
Check your rear tie rod ends. My 2000 auto did the same thing and both rear outer tie rod ends were badly worn (67,000 miles) along with one of the front outers. Just don't buy replacements for the front from Ecklers. They won't fit and don't allow enough adjustment to set the toe properly. The rear outers from Ecklers worked fine. Rock Auto seem to have the best price on Moogs for the front.
After replacement and alignment it smoothed out quite a bit.
I would think in the automatic with the torque converter in the rear, the torque tube will always be rotating so long as the engine is. But he said that at speed with the engine off it still does it. I would also consider the rear axle joints also since they will be rotating so long as the car is moving. The faster you go the more a problem here would be noticed. I have also heard of issues with the nut that secures the axle at the outside (wheel locations) to be loose and to cause similar issues. You sure don't want that be be loose.
The drive shaft rotates, the torque tube does not. Drive shaft runs on bearings inside the torque tube. Those bearings can also fail as well as the couplers.