I have been all over the Internet looking at reamers, cone grinders, cone sanders, tapered wheel polishers and more, and I never seem to find a solution. Everything is too small, too large or the angle is too far off. I have a need to drill tapered holes in 1/2" acrylic sheet for #10 rubber stoppers, which are 50mm in diameter at their largest and 42mm at the narrowest. I need the hole to exactly match the slope of the stopper, which I calculated to be 9.09 degrees, or, more simply, if the smaller diameter is 43mm and the larger diameter is 47mm, that's almost perfectly the slope of the stopper. I can drill the 43mm hole with an adjustable bit I have. What I need help with is a method to taper the hole out from there. Maybe this means spinning something inside the 43mm hole and bringing the top out to 47mm. Any ideas (without spending too much money) on achieving this? Thanks so much in advance!
Your comment presents the use of a drill press. This may turn your project into something that can be completed.
It's important to note that you MUST clamp your work piece securely. Acrylic plastic is prone to "catching" and cracking, so use recommended practices to drill a pilot hole. The diameter of the hole will depend on the next step.
Attach a piece of tool steel to an arbor/shaft, at the angle you have determined to provide your desired hole.
This portion may be best accomplished by using the services of a qualified shop. A good welding operation may be able to get the tool made in short order:
image created by OP (me) using OpenSCAD
I knocked this out to better present the concept. The angle shows is 9.09 degrees from vertical. The dimensions are arbitrary, but it should be clear that if the pilot hole is smaller than the base of the reamer, you'll be in trouble. I suppose I could have extended the triangle to a more narrow point, but this should give you a starting point. I did not scale this cutter to match your 43/47 mm dimensions.
Note also that the cutting edges of the reamer are at an angle to the radius of the tool. This prevents the trailing edge from becoming a cutting edge.
This is experimental, but it's what I would do, considering acrylic isn't very hard. The goal is to make a rotary sanding block with the right taper.
First drill to the small diameter. Then take a rubber bung of the right size and taper, ready-bored.
Run a bolt through the bore, making sure to use one that's a tight fit, and 4-5cm (a couple of inches) longer than the bung. The bolt head should be at the narrow end, with a large (mudguard/repair/penny) washer under it. At the wide end, another washer and two nuts, so everything is locked together solidly.
Cover the bung smoothly and as thoroughly as you can with a single piece of coarse wet & dry sandpaper (silicon carbide paper). A gap is better than an overlap. Secure the workpiece and put the home-made tool in the drill press. Spin it up gently, wet the workpiece and sand.
You're likely to have to change the sandpaper a couple of times, and finish with a finer grade.
The biggest potential issue I can see is if the hole on a pre-bored bung isn't central. With a slightly smaller bolt it may be possible to centre it up. Alternatively make sure th drill is held square to the workpiece but allow them to move relative to each other.