Check for mechanical problems (loose screws in camera lens mount, lens, etc.).
If you have loose lens mount screws on the lens or camera (so that the camera screw drive and slot for it to mesh with in the lens are not engaging properly), that can cause problems with the screw drive mechanism for focusing and may be what's causing the grinding you're hearing.
If the problem occurs on more than one camera, it's probably a lens issue. If the problem isn't obvious (tighten the mount screws on the lens and/or camera and all works fine), then I'd just get another lens. Just look at the camera mount with the lens removed and you'll see screws in the round mount you can tighten. Ditto if you're looking at the lens with it removed. Sometimes those screws come loose and prevent a solid connection between the camera and lens.
It the problem is internal to the lens (internal gears, etc.), versus a mechanical problem with how the camera's focus screw drive and lens mesh together, then I'd just get another lens (as the 18-70mm kit lens isn't worth a lot anyway, and a replacement shouldn't cost you much).