The best way to remove rust from steel or cast iron is by electrolysis, period!
See the links below, but a few points need to be emphasized first:
DO wear rubber, latex or other waterproof gloves
DO wear old clothes, cuz the solution will stain just about anything!
DON'T put the solution where it can be kicked or spilled, it will leave a killer stain!
DON'T hook up what you are removing the rust off to the positive (+) terminal!
And most critically important DON'T USE STAINLESS STEEL AS THE ANODE (+ electrode)!!!
Ok, now to the links that explain the method:
A few suggestions. Use no more than 6 volts, particularly if you don't want to remove paint. Use washing soda (sodium carbonate, aka NaCO3) as the ingredient, not salt or lye. Small quantities of NaCO3 can be made by heating baking soda spread on a cookie sheet for 300 degrees F (150C) for about 1 hr.
Don't pour the old liquid on your lawn or garden, the sodium could damage the soil. The solution is safe to pour down a laundry or basement drain, but be sure to wash out the drain afterwards.
At most only 1 tbsp per gallon NaCO3 is needed - using more is just a waste.
If you use an old wall-wart, the negative is usually the wire bearing a white line or bead on it and is usually hooked to the outside ring on the outlet plug.