DIAGNOSIS That's almost certainly the carriage assembly (the part that holds the ink cartridges) hitting an obstruction or struggling to move on its rail. The cause is usually dried ink gunk on the silver rod (the rail) it slides on, or a foreign object like a paperclip or torn piece of paper in its path.
FIX Unplug the printer. Open the cartridge access door. You'll see the carriage on the right and a long, shiny metal rod it rides on. Move the carriage by hand from side to side—it should glide smoothly. If it's sticky or crunchy, you've found it. Put a couple drops of distilled water on a lint-free cloth and thoroughly wipe the entire length of that silver rod. Then use a dry part of the cloth to wipe it again. Manually move the carriage back and forth a few times to spread the lubrication.
IF THAT DIDN'T WORK While you have the door open, check the white plastic strip that runs along the back of the carriage path. This is the encoder strip. If it's smudged with ink or dust, the carriage can lose its position. Gently wipe it clean with a dry cloth. Never use alcohol or cleaner on it.
HEADS UP Never use oil, WD-40, or household cleaners on the metal rod. They'll attract more dust and gum things up worse. A tiny bit of moisture from water is all you need to dissolve ink residue. If the noise persists after cleaning, a mechanical part in the carriage motor might be failing.