Can You Power a Hex Axle Conveyor Roller Without a Chain and Sprocket?

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I am trying to power my conveyor roller but have a 7/16" hex axle. I have been trying to find a sprocket that has a hex bore and is able to handle a
ANSI Standard Size 40 Roller Chain. Is there any other efficient way to power this other than chain and sprocket? Also, this sounds dumb, but I was wondering if I was able to use a round sprocket with set screws on the hex axle if they were the same diameter?
 
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There must be a block with a hexagonal same-size hole somewhere. One that could be machined to fit into the centre of a sprocket. Can you find one?

Six set screws will contact the faces, but that will not be tight, (due to cosine rule), and will work free. Likewise the corners of the hex will dent the inside of a circle.

Maybe two blocks that are clamped together to lock onto the hexagonal shaft. File half the hex hole into each block.
Then bolt the sprocket to that assembled and clamped block.
 
What is that 7/16" hex axle attached to?
Could you post a picture or diagram of your machine and power train?
 
Every hex shaft conveyor roller I have ever seen, or even heard of, has bearings. The shaft drops into slots in the conveyor frame, and the roller spins on the bearings. The rollers can be driven by a belt from a reducer that is wrapped around the roller:
Roller Conveyor Drive 1.jpg

They can be driven by an adjacent roller:
Roller Conveyor Drive 2.jpg

There is a third way to drive the rollers, but I did not find a good drawing of it. You can search roller conveyor drive for more information.
 
As @jrmichler suggests, the hex shafts are probably idler rollers that contain free running bearings.
Those internal bearings, pressed into the ends of each idler, may be “hex bore” conveyor bearings.
https://www.minibearings.com.au/store/partslist/bearingsconveyorhexborestainlesssteeldoublerow/?v=8148

If you still need a hex bore drive sprocket ...
1. There may be a “taper lock” centre bush for the sprocket you require. You could machine the round bush to have an internal hexagon, it would then lock to the hex shaft.
2. You might buy a 6-point impact socket, cut off the square drive, then split it to fit inside a round taper lock bush.
3. You might bolt your sprocket to the side of a hex shaft, two part collar.
https://www.bearingshop.com.au/store/categories/collars+shaft+hex+bore+two+piece+steel+categories/

Although it does not directly solve the roller drive problem, there are also agricultural bearings for square or hexagonal shafts used on tillage equipment. The sacrificial points are clamped onto, and rotate with that shaft. I wonder how that shaft is driven?
https://universalbearings.com.au/products/plough-bearings-hexagonal-bore-ubc