single point broaching a lathe is a quick and dirty way of getting ones ass out of a hole and also very effective.
you can do the same in a mill with a rotary table with less hassles ( powering the table up and down is cheating )
HSS is fine, just take you time with the tool grinder ( or if you have a water pump drown the bugger )
otherwise couple of passes and leave, don't get color run though in your application whats a couple of rockwells..
generally we have worked out number of splines then ground a three point ( triangular broach end on ) to provide
full support or equal stress to stop the little buggers from wandering off... genrally we also stick a lead on them
and provide a decent releif area for swarf to curl up in ( and a cutting edge )
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