What is a non chemical way to clean the grates on top of your stove?

I love bar keepers friend for heavier stains and just regular vinegar

make a paste of white vinegar and baking soda

is your stove gas or electric or smooth surface glass, or induction?

I put mine in the dishwasher - been doing that for 20+ years.

Steel wool, and elbow grease.

I would try to steam them clean and use tin foil to rub the hard to clean spots and that should work.

As you said NON chemical, The brass grill brushes sold for bar b q grills should work

vinegar & baking soda

Make bottle of lemon juice, and white vinegar. Put the peels in too. Let sit for a week or two, and get strong if you can.

Spray that onto the grates and even the stainless, and then add baking soda to the surfaces. Let sit.

After a bit clean off with a Mr. Clean sponge for the stainless, and a plastic scrubby for the grates. (For stainless, always go in the direction of the grain.)