Something wrong here I have both a 1940 Unisaw purchased well used by me & a 1957 Craftsman contractors saw which was purchased new by my Dad & use in a commercial cabinet shop. Both just fine after all these years.
You usually only need to just snug the arbor nut reasonably tight & not crank it down forcefully, it will tighten down further by the very virtue of being against the blade.
I'm sure you already know all this.
What brand of saw & how old is it?
"Forget the flat stuff slap something on the spinny thing and lets go, we're burning daylight" Bart Leetch
"If it ain't round you may be a knuckle dragger""Turners drag their nuckles too, they just do it at a higher RPM"Bart