Disconnect the battery and clean the output stud and wire terminal on the alternator and cable. Also clean the connector for the other wire to the alternator and battery posts and terminals using contact cleaner.
Reconnect the battery positive first then negative last.
Start engine and read charging voltage.
Let engine warm up some then place a load on the electrical system by turning on ac with blower motor on high and the high beams. Rev engine to at least 1500 rpms and read charging voltage again.
If not within spec of 13.5 to 14.5 volts, using a volt meter or multimeter read voltage from alternator output stud (+) to negative battery post.
Be careful to avoid shorting the output stud to alternator case with the probe.
Let us know what the voltages are.
I just cleaned off the battery terminals until I exposed the copper and sanded the battery posts,
The starting voltage is 13.6 after engine start
Underload voltage 13.8 v
Reving the engine didn't make any noticable difference
I also checked the voltage from the alternator, I didn't notice any voltage drop from to the battery.
Does it mean any thing, is it smart charge as "theoldwizard1" said ?