Disc brakes make a grinding sound
From your description there are two different areas this could fall under: problems with adjustment that are causing the rotor to hit the disc caliper or adaptor, or problems with bed-in. 

They shouldn't be loud under normal braking. You should get some slightly "textured" feedback as the pad bites down on the rotor as you use the brake, but it shouldn't shudder. That you mention shudder is the clue something is wrong here.

The first thing you should do is double check very carefully that the brake(s) in question are not adjusted such that the rotor can ever get contact the caliper body or the caliper adapter (if present). It should only ever be able to touch brake pad. If it's contacting anything else, hopefully it's just a case of re-adjustment, but too much riding like that can destroy things.

If that's not the problem, i.e. everything is adjusted properly but it's giving these symptoms anyway, the first thing I would do is remove, lightly sand, and re-install the pads, then lightly sand the rotor(s) and clean thoroughly with alcohol or brake cleaner. Then do a thorough bedding procedure after reading some good long thing that explains the theory and practice of bed-in. If they still do it, replace the pads. If they still do it after that, replace the rotor too. Some of the brakes out there now have this tendency to just start making a rapid-fire shudder when you brake, as the pad goes over the cut-outs of the rotor, and I don't know that it's even something that has to do with bed-in. Maybe.