[JustinLiang]

What would happen if the bore hole of a pulley in a conveyor was significantly larger than the shaft like in the figure below:


I would imagine if the RPM was high, the whole system would shake violently. However, what if the RPM was around 30 RPM. Would the conveyor still function properly? At such low speeds I feel like it would still work, however, I have never seen something like this in the industrial world which is why I am curious.

The shaft diameter is approximately 1 inch and the bore is approximately 2 inches.

[dmalicky]

It depends on the belt length and elasticity.
A "short stiff" belt would go from tight to loose. Tight could easily be so tight it stalls the motor. Loose would be loose enough to stop travel. If the setup is just right, it would give intermittent motion, mostly stopped but moving for maybe 30 deg of rotation when the belt tension is reasonable.
If the belt is very long and stretchy enough (no cords), it would cycle between fast and slow velocity.

EDIT: I assume the pulley would be locked to the shaft somehow... eccentric bushing and/or lots of set screws. If not, the shaft would just spin like Andy says.

[andypugh]

What would happen if the bore hole of a pulley in a conveyor was significantly larger than the shaft

If the shaft is a motor shaft and meant to be driving the pulley, then it probably won't give any drive.
If the belt tension is very high then there night be sufficient friction between the shaft and the pulley to provide some drive in a 2:1 ratio.

What are you hoping to achieve with this arrangement?

In any scenario I can see both the shaft and the pulley bore would wear more rapidly than normal.