First of all, a bad battery can lead to alternator damage and a bad alternator can lead to battery damage. So it's important to address such issues when they occur and not delay any longer than necessary.
Second, while the electrical system of older cars is pretty simple, some modern cars are a bit more complex due to the needs of the computer systems on the vehicles. A battery may, for example, seem OK in that it cranks the engine fairly strongly, but it may not be able to support the proper voltage requirements for the onboard computer systems at the same time. And the charging systems may be "smarter" than simply an alternator from the days of old.
Third, while alternator output voltage is a pretty good indicator, that alone doesn't mean it's capable of charging the battery properly. A faulty diode can still result in a measured DC output voltage that's "good" (typically 13.5 to 14.5 Volts), but that alone doesn't mean it's capable of providing the required current to charge the battery.
Fourth, 12.2 Volts DC on the battery is a bit low for a fully charged car battery. 12.6 Volts would be normal.
Fifth, sometimes new components don't last, and this includes the battery. My wife had her battery replace and in less than a year it was bad. Not a problem, except for the annoyance, because it was fully covered by the warranty. The same for the alternator. Sometimes the new one will require replacing again. So maintenance history is important.
Sooo....questions:
What year is your Explorer? (Probably not that important...I don't think even the newer Explorers have what I would call a "smart" charging system, but you never know. )
How old is the battery?
What work have you done on this in the past?
Things to do:
- Clean the battery terminals, whether they look like they need it or not.
- Ensure all cable connections are tight...that includes the battery terminals, the ground connection, and the alternator connections. The cables/wiring, clamps, and lugs should all be in good condition, too.
- Check the age of the battery. Battery life is typically 3 to 5 years. If you're in this range, then any suspected battery problem that aren't directly attributable to something else (like a loose connection) is an indicator that the battery should be replaced. If you're beyond 5 years, then you've definitely gotten your money's worth and you're living on borrowed time at this point anyway.
- If your battery seems "weak" at this point when you start the vehicle, then jump it and see what happens. If it starts right up, then the battery is weak, which is either the result of the battery going bad, the alternator being bad, or both.
- At this point, take the vehicle to Auto Zone, Advance, etc. and have them check the battery and alternator with their tester. They should test the battery with the vehicle off, then have you start the vehicle and they'll perform a series of tests to check the alternator. Replace what needs to be replaced accordingly.
LAST WEEKEND:
My wife wanted me to take a look at her sister's car, a 1999 Cherokee, which wouldn't start. Bit of a conversation revealed it was weak when turning over. She didn't know when her battery had last been replaced.
I popped the hood and the positive terminal was crusty with corrosion and the battery clamp covered the installation year on the sticker. I cleaned the terminals, made sure everything was tight, checked battery voltage (12.2 Volts) and got a weak crank. Jumped her battery and it started up fine. Let it run a while during my clean-up, then went out and (because I'm a nice guy) put $20 worth of gas in it (while still running....because I'm not that trusting yet), then did some interstate driving for another 20-30 minutes.
Came back home, shut the vehicle off, and then restarted it with no problems. Shut it off for about 5 minutes, then got a weak crank, but it still started. Battery voltage was back down to 12.2 Volts.
Replaced the battery, problem solved.
Age of the old battery, if you're curious, was 16 years. It had been in her Jeep since 2006! Previously, the most number of years I've ever seen on a car battery was between 7 and 8 years. I was amazed, quite frankly.