For small details like that, scale the model up by a factor of 100 or 1000. This will help prevent the missing faces.
Another approach to putting the bevels on would be to draw a cone at the sharpening angle and intersect it with the drill.
[image: IXqq_drill.png]
For something like this model, I find it helpful to think in terms of how the bevel would be put on the real object. For a drill you would do that with a grinder and rotate the drill rod. The surface of the cone represents the contact line between the wheel and the drill.
