How to modify a rotary pencil sharpener to sharpen off-center leads?

[Stephen Tashi]

TL;DR Summary

Suggest ways to modify a rotary electric pencil sharpener so it sharpens pencils whose leads are off center without leaving a sliver of wood along the lead.

When inexpensive pencils are sharpened in rotary pencil sharpeners, the result is often a pencil point that has a long sliver of wood running along one side of it. I think this is due to the pencil lead being off center in the pencil. Turning the pencil while sharpening it usually doesn't fix the problem. (I don't understand why.)

How could I modify an electric pencil sharpener so it would not leave the sliver of wood along the point? I wouldn't mind having to turn the pencil as I sharpened it, if that was required.

 

[Torbert]

Once the cone is established by the initial sharpening the subsequent sharpening is self centering. Turning the pencil during the first time in may help. The pencil lead/wood assembly is done by machine and is centered pretty well.
The sharpener is usually set for multiple sizes of pencil and has a large bore with a smaller hole matching the pencil covering the front. This can act as a lever transferring any side load into misalignment with the cutters.
A guide sleeve keeping the pencil centered and parallel should eliminate the problem. This also limits how short the pencils can get.

 

[DaveC426913]

I think this is due to the pencil lead being off center in the pencil.

Before a solution can be found, I think you'd have to determine if this is indeed the cause.

If it is, and the lead is actually off-centre, I suggest trying this:

Take a knife and cut a sliver or two off the side where the lead is farthest from the outside.
When you insert the pencil, it should slip into the cone off-centre, so the rotation axis of the cutters will (ideally) line up with the off-centre lead:

This will only help initially. As Torbert points out, the next time you sharpen it, the body of the pencil will self-centre, and you'll be back to the same problem. Unless, I suppose, you repeat the sliver shaving each time.