A 12 volt battery needs an input voltage above 14 volts to keep it charged properly. Battery charging is like two football linemen shoving on each other. Unless one pushes harder than the other, they just stay put at the line of scrimmage. The generator must develop enough higher voltage than the battery to force charging current into it. Since a fully-charged lead-acid battery cell produces about 2.1 volts, six of them connected in series will have an open-circuit voltage of about 12.6 volts. The generator or alternator needs to make 13.5-14.5 volts to assure that the battery stays fully charged.

You'll need a 12 volt generator and the corresponding regulator for your conversion. Simply installing a 12V regulator will not make the 6V generator produce the higher voltage. I'd strongly recommend installing an original-equipment Delco regulator, even if it's a good-condition used item rather than using a Chinese-made aftermarket item. They've got a huge failure rate right off the shelf and/or a very short useful lifespan. Ebay has plenty of OEM regulators available, and the cost isn't bad if you do some careful shopping.
Jerry


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