I have 2001 cherokee 4.0 , charging problems had battery and alternator checked both checked good ,

 

What kind of problems? Just some general advice: try cleaning all of your battery cable terminals, and any other ground points you can find.

 

Provide details of your charging problems. Belvedere had some good advice.

*Freshen engine grounds

*Freshen battery and alternator connections

*Know that bench testing of alternators at parts stores is not always conclusive

 

Yea cleaned batt posts and cables, it sure does act like alternator is problem did have it bench tested and just not sure if it isn't the alternator

 

Reinstalled alternator after tested ran voltage check , voltage was holding good after running for about 20 mins then voltage dropped slowly, batt was at 12 volts when running was at 13.8 to 14 then started dropping

 

When you said the battery was 12. Were you meaning while not running it was showing 12 volts and then while running the voltage increased? Sounds like alternator is charging. That battery should show more than twelve volts right after you turn the engine off. It may be the post or cables or maybe just a week battery. Take one of the cables off and let it sit for a little while and see if the voltage keeps dropping. That may help eliminate some problem.

 

How far does the voltage drop? A 2001 has that battery temp sensor that lowers the charge rate as the battery gets warmer for whatever reason. As long as the charge is not dropping below like 13v you should be fine. If your battery is not good it could be getting hot and the sensor will shut down charging to avoid an exploding battery. That said, when my 2000 was having charge issues I replaced the alternator and all was fine. Also, make sure your belt is really tight. I thought mine was good until the voltage started to drop off when all the lights and heater and stuff were on. It was slipping. Tightened it some more and its been good so far.

 

Definitely could be the belt.

Is the alternator original? If so, I would replace it anyway just to be safe if you cant narrow down why the voltage is not staying constant.
A healthy charging system should show around 14-14.4v with all electrical stuff on. 13v is not exactly a strong charge.

What happens when you turn everything on (all lights, AC, Blower on high, stereo, power windows, etc)? The voltage will obviously drop but should not drop past 13v.

 

Ask me how I know if you wish but I would highly recommend replacing the cheapest parts first. Start with good heavy gauge battery cables ( you could prob weld with the cables I used LOL ) and GOOD battery connectors. Personally I build out my own and use mil spec type connectors like these:
http://www.ebay.com/itm/1-Positive-1-Negative-Military-Heavy-Duty-Truck-Battery-Terminals-/271343780258?pt=Motors_Car_Truck_Parts_Accessories&hash=item3f2d5981a2&vxp=mtr( I am NOT promoting this seller or his parts just showing the style I use)