I used to work for the Cumberland Pencil company and have seen a few of these in my time.
I have to admit I have not sharpened any. However the Boston sharpener you have the silver disc with the holes in "should " be spring loaded, The grippers at the top edge are pinched open and the pencil fed in to JUST touch the cutter let go of the grips and then crank the handle.
I am not accusing you of doing this but a lot of people are too impatient and push the pencil in hard by hand which overloads the cutter making it hard to crank.
The cutter should be making a fine planing cut as it rotates / slides past the stationary pencil.
Has the sharpener seen it lot of use, particularly on graphite ? If so then it is probably blunt. graphite leads are all fired in a furnace so you are in effect cutting rock. its just that 9B is a soft rock and 9H a very hard rock.
We always used to tell people to buy cheap hand sharpeners frequently and as soon as you start getting splinters, instead of a nice apple peel ribbon, throw it out its blunt.
Quality Pencils are far more expensive than a hand sharpener. After all you don't cut steak with a butter knife.
I hope you get it fixed. it should sharpen though as the carrier it sits in is just that, a carrier to hold the pencil in place. It does not form any part of the cutting action.
sorry if I have tought you to suck eggs.
Good Luck Clive