I have a 1987 GMC customized van with a 350 v8 and a 700r4 transmission. It has a driveline vibration between the speed of 40 and 55 with about 47 being the worst. I have changed torque converter, the differential and had a new drive shaft built. The vibration is still there. I had the new shaft balanced which helped but did not solve the problem. I took the shaft to a different shop and they cut the ends of the shaft off and trued the shaft to within 11 thousands of an inch they took all the weights off the shaft and did not rebalance it. I still have the problem only it is worse. It is a 2 piece shaft with single joints. Do you think a double cardan joint would help? any ideas? There has beeen no changes to the drive line angels.

which engine is there or decode your VIN or read the RPO code for the engine 4.2 or 5.3L
Got 4wd? and 4L60-E transmission
I can not guess drivelines.

transmission mount?
UJoints all, /CV joints bad.

inspect all joints or loose and bad.

Over Voltage?

https://www.google.com/search?q=1987+gmc+2500+voltage+regulator

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Have your motor mounts and transmission mounts checked. Common problem. Or are you talking about the bump you feel while coming to a stop? Another common problem, grease the slip yoke on the driveline to fix this particular problem.

Have the u joints checked on the drive shaft that goes from the front diff to the transfer case one or more my be seized or loose .

If you have spark but extra fuel, then you probably have a carburetor problem

The pinion bearing has escessive preload. When this happens there excessive vibration.On 4x4 the front and the rear drive shaft has to rotate at the same speed. you are mainly locking up, the pinion is not moving freely

VIBRATION - DRIVELINE RESONANCE/VIBRATIONBETWEEN 1400 AND 2000 RPM WITH CONVERTER
Clutch ENGAGED DURING MEDIUM TO HEAVY
THROTTLE CONDITIONS - VEHICLES WITH 7.3L DI
TURBO ENGINE AND TRANSMISSION BUILT PRIOR
TO 11/13/95 (5L13)
^ TRANSMISSION - E40D - DRIVELINERESONANCE/VIBRATION BETWEEN 1400 AND 2000
RPM WITH CONVERTER
Clutch ENGAGED
DURING MEDIUM TO HEAVY THROTTLE
CONDITIONS - VEHICLES WITH 7.3L DI TURBO
ENGINE AND TRANSMISSION BUILT PRIOR TO
11/13/95 (5L13)

FORD:
1995-1996 E-350, F-250 CREW CAB, F-350 CREW CAB
Article 96-26-21 is being republished in its entirety as part of a consolidated 7.3L diagnostic aid booklet.
ISSUE
Some vehicles with transmissions built prior to 11/13/95 (5L13) may exhibit a driveline resonance/vibration between 1400 and 2000 RPM with the torque convertor engaged. This may be caused by the torque converter.
ACTION
Prior to torque converter replacement, refer to the following Service Procedure for details to verify conditions.
SERVICE PROCEDURE
1. Verify the resonance/vibration does not occur in neutral and is most noticeable between 1400 and 2000 RPM with the converter clutch engaged during medium to heavy throttle conditions. Also watch for the vibration to diminish at engine speeds lower than 1400 and higher than 2000 RPM. If the concern meets all of these conditions and the transmission has a built date prior to 11/13/95 (5L13), replace the torque converter. Refer to the appropriate Service Manual for removal and installation procedures.
2. If the vibration concerns do not meet the conditions, check for non-factory installed items that could affect driveline and verify proper installation. Also refer to the appropriate Service Manual, Section 05-00 for diagnosis and testing.

possibly a bad u-joint. Sometimes a u joint will feel ok but if it is too tight it can cause a vibration. you will need to remove the shaft to feel if a joint is too tight and binding. Or you have a tire out of balance. Usually a driveline vibration is more of a buzzing high frequency type of vibration the kind that puts your foot to sleep and a tire is more of a wheel speed vibration which is a lower frequency vibration.

The tailshaft housing is removable from the transmission, inside it there is a large bushing that the yoke rides on. That bushing is probably worn out, if so, check the yoke real well too, it is probably worn out as well. The bushing must be pressed in, have a machine shop do it for you. Good luck!

Lets take this piece by piece.
The 4x4 switch is defective.
A driveline vibration regardless of engine speed is usually a shaft or cv joint. To verify a visual inspection is necessary.
The poor acceleration in any gear is the begining of torque converter problems( stator or pump).As long as ATF level is correct.
I recommend having a transmission repair shop look this over and preform a pressure test of the main line of the transmission.(it may not be necessary if the condition of ATF is burnt). Good luck