The output from your generator is an alternating current like the mains electricity. However your battery and bike need a direct current DC charge - thats what the regulator rectifier does. The regulator sets a top limit to the voltage that goes from the generator to the battery (i.e. fixed at no more than 14volt for a 12 volt battery) and the rectifier converts the alternating current of the generator into the fixed DC voltage the battery needs.
A failing rectifier will prevent you battery charging as it will no longer produce the required DC current.
A failing regulator can cause damage to your battery & electrical system as it is not supplying the correct voltage. The battery may be damaged beyond repair as it gets too hot and you may find that bulbs are brighter than normal & have a shorter lifespan.
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