First, indeed the DSNGRR museum has paper wheels. When I first began working at the museum, I could not understand how the paper inside the wheel could make for a softer ride. After all, everything is bolted together, so all the vibration is still transmitted to the axle. But, that turns out not to have been the idea. Not softer, but quieter, was the goal.
Richard Allen, a former railroad engineer, invented the paper railroad wheel and founded a company with his brother in 1867 which made these wheels, as well as other laminated paper products. George Pullman was a strong supporter of the paper wheels and used them to "bring quiet elegance to Pullman's dining and sleeping cars. According the an article from the University of Houston, "Allen's wheels did not fail."It was other composite wheels which failed. If you'd like more information, go to
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www.uh.edu]
On that site you'll also find an audio of the show (which was on NPR)
To find out more about the technical information on paper wheels, use Google, with the query " illegal paper railroad wheels " and you'll find a Feb 15, 1891 article from the NY Times. However, in the article itself there is no mention of illegal wheels. Instead the "illegal" part of the page comes from a different story, but in the same column of the paper.
I cannot find anything about the wheels being illegal, so if you have a source for that, please let me know.